1 THE PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON, FROM THEIR COMMENCEMENT, IN 1665, TO THE YEAR 1800; gfttttrgeti^ WITH NOTES AND BIOGRAPHIC ILLUSTRATIONS, BY CHARLES BUTTON, LL.D. F.R.S. GEORGE SHAW, M.D. F.R.S. F.L.S. RICHARD PEARSON, M.D. F.S.A. VOL. XVI. FROM 1785 TO 1790. LONDON: PRINTED BY AND FOR C. AND R. BALDWIN, NEW BRIDGE-STREET, BLACKFRIARS. 1809. /i^kSz. LOAN STACK CONTENTS OF VOLUME SIXTEENTH. HPage OME, of a New Marine Animal .... 1 Hunter, John, on the same 4 Wollaston, Fr. New Set of Wires in a Teles. 7 Barker, R. a Stag's Head and Horns 9 Bruce, R. Sensitive Quality of a Tree .... 10 Fordyce, Loss of Weight by Heat 13 Peacock, Instrum. for drawing in Perspect. 15 Cavendish, Experiments on Air ib. Roy, Measure of a Base on Hounslow-heath 22 Baker, T. Meteorolo. Reg. 30, 95, 206, 507, 563 Smeaton, Graduation of Astron, Instruments 30 Hindley's method to Divide Circles 40 Goodricke, Variation of the Star ^ Cephei. . o6 Cavallo, Magnetical Experiments 57 Waring, on Infinite Series 6l Kirwan, Experiments on Hepatic Air .... 68 Elliot, Affinities of Subst. in Spirits of W. 79 Lightfoot, on Minute British Shells 80 Watson, Bp. Sulphur Wells at Harrogate. . 83 Pigott, Edw. on tlie Changeable Stars .... ib. Lyon, Subsidence of Ground at Folkstone. . 91 M'Causland, Customs of the Americans , . 93 Cavendish, Freezing Mixtures at Hudson's B. 96 Thompson, New Experiments on Heat ... 108 Letsom, on an Extraord. Introsusception . . 1 19 Darwin, R. W. Ocular Spectra of Light, &c. 121 Clarke, Mortality of Males and Females . . 122 Hamilton, State of Mount Vesuvius 131 Paterson, on a New Electrical Fish 1 34 Pigott, Nath. on the Transit of Mercury . . 135 Pigott, Edw. on the same .... ib. Wedgwood, Thermom. for High Degrees 136 Pigott, Edw. Lat. and Long, of York .... 145 Maskelyne, on the Comet of 1532 and l66l 147 Vince, New Method of Finding Fluents . . 150 Camper, Petrifactions at Maestricht 151 Herschel, Cat. of 1000 New Nebul« 158 , on an Indistinctness of Vision .. l65 Miss Herschel, on a New Comet 169 Herschel, Wm. Remarks on the same .... 170 Cavallo, Magnetical Experiments ib. Bennet, Abr. on a New Electrometer .... 173 , Appendix to the same 176 More, Sam. Account of an Earthquake . . ib. Bugge, Longitude and Node of Saturn .... 177 Baxter, Halos and Parhelia in America .... 181 Kohler, Transit of Mercury in 1786 182 Rumovski, on the same subject 183 Limbird, Strata of a Well at Boston ib. Fr. Wollaston, Obs. on M iss Herschel'sComet 186 Brydone, Thunder Storm in Scotland .... ib. Waring, Values of Algebraic Quantities . . 19I Thompson, Dephlogisticated Air from Water 198 VOL. XVI. Page Herschel, 2 Satellites to his New Planet . . 214 Earl Stanhope, on Brydone's Thund. Storm 2l6 Maskelyne, Lat. and Long, of Greenwich . . 218 Roy, Measures for the same 240 Herschel, Volcanos in the Moon 255 Hunter, J. on Extirpating one Ovarium . . . 256 Thompson, Moisture absorbed by Substances 26O Nicholson, Log. Lines on Instruments .... 262 Hunter, J. on the Wolf, Jackal, and Dog 264, 562 Keir, Congelation of Vitriolic Acid 27 1 Beddoes, Production of Artificial Cold .... 279 Bennet, A. on a Doubler of Electricity . . . 282 Blane, on the Production of Borax ibid Rovato, on the same subject 284 Hassenfratz, on Hepatic Airs or Gases .... 286 Dryander, on the Benjamin Tree 287 Fordyce, Experiments on Heat 288 Smeaton, Astron, Obs, and Micrometer . . . 292 Garthshore, on Numerous Births 294 Swartz, a New Genus of Plants 302 Vince, Precession of the Equinoxes 303 Hunter, J. Struct, and Economy of Whales 306 Blagden, on Ancient Inks and Writings . . 351 Cavallo, on different Electrometers 354 Fordyce, on Muscular Motion 36 1 De Cells, on a Mass of Native Iron 369 Darwin, E. Mechan. Expansion of Air .... 372 Hunter, Dr. J. on Subterranean Heat .... 377 Heberden, Mean Heat for every Month . . 384 Waring, on Centripetal Forces 384 Six, Experiments on Local Heat 404 Gray, Manner of Electrifying Glass 407 Biogr, Notice of Edw. Wh. Gray, M.D. . . 407 Blagden, Cooling Water below Freez. Point 409 Priestley, on Acidity, corap. of Water,&c,41Q, 473 Smith, on the Irritability of Vegetables .... 42 1 Cavendish, on the Freezing of Acids 425 R, S. Meteorological Observations 431, 556, 652 Jenner, Natural History of the Cuckoo .... 432 Cavallo, Temperament of Musical Instrum. 442 — — — , a New Electrometer 449 Cavendish, Airs changed into Nitrous Acid 451 Blagden, on Lowering the Point of Congela. 459 Morgan, Survivorships and Reversions 475, 529 Baillie, a Transposition of the Viscera .... 483 Herschel, the Georgian and its satellites . . 489 Austin, Formation of Volatile Alkali, &c. 493 Waring, on the Sum of Divisors 4^7 Walker, Production of Artificial Cold .... 501 Nicholson, a New Electrical Machine .... 505 Barker, on the Growth of Trees 507 Marsden, on the Mahometan Era Hejera . . 509 Smeaton, Improv. of Celestial Globes .... 517 17 CONTENTS. Page Priestley, Compos, of Water and Phlogiston 518 Gray, on Linnaeus's Amphibia and Serpents 521 Hutchinson, Dryness of the Year 17 US 528 Piazzi, on an Eclipse of the Sun ,. . 529 Anderson, a Bituminous Lake in Trinidad.* 531 Baillie, Change of Structure in the Ovarium 535 Saunders, on the Vegetable and Mineral Pro- ductions of Boutan and Thibet 539 Priestley, Phlogis. of Spirit of Nitre 557 Herschel, Observations of a Comet 560 Marsham, Indications of Spring 56' 1 Anderson, on a Human Monster ibid Waring, Method of Correspondent Values 563 , Resolution of Attractive Powers . . 572 Walker, on Congealing Quicksilver 579 Herschel, a 2d 1000 New Nebulae 586 Maskelyne, on the Theory of Vision 595 Nicholson, Experiments on Electricity 599 Priestley, Vapour of Acids thro' Hot Tubes 602 Milner, on Nitrous Acid and Air 6o6 Herschel, on Saturn's Ring and Satellites 6l3, 730 Bugge, Observations on Venus and Mars . . 621 Hey, account of Luminous Arches 627 Page WoUaston, F. J. H. on Luminous Arches , . 630 Hutchinson, B. on the same ibid Franklin, J. on the same 631 Pigott, Edward, on the same ibid Austin, on Heavy Inflammable Air 632 Mills, on the Strata and Volcanic Appear- ances in Ireland and the Western Isles 639 Cavendish, Height of a Luminous Arch .. 6^5 Priestley, Observations on Respiration .... 6^7 Roy, Trigonometrical Survey 649 Russell, P. account of the Tabasheer .... 65$ Blane, on the Nardus Indica, or Spikenard 658 Withering, Extraor. Effects of Lightning . . 662 Home, of a Child with a Double Head .... 663 Wedgwood, a Mineral fi'om N. South Wales 667 Blagden, on the Excise of Spirituous Liquors 675 Castles, on the Sugar Ants in Grenada .... 688 Keir, Dissolution of Metals in Acids 694> Pigott, Edw. Lat. and Longitudes of Places 709 Crawford, on the Matter of Cancer 710 Wildbore, on Spherical Motion 740 Biogr. Notice of the Rev. Cha. Wildbore . . ibid MarsdeUj on the Hindoo Chronology 742 THE CONTENTS CLASSED UNDER GENERAL HEADS. Class I. Mathematics. 1. Arithmetic, Annuities, Political Arithmetic, Mortality of Males and Females, Clarke.. 122 Survivorships and Reversions,.. . .Morgan. . 475 Log. Lines on Instruments, Nicholson 262 The same subject, Morgan. . 529 2. Algebra, Analysis, Fluxions, Series. On Infinite Series, Waring. . 61 On the Sum of Divisors, Waring. , 497 New Method of finding Fluents, Vince .. 150 Method of Correspondent Values, Waring. . 563 Values of Algebraic Quantities,. . Waring. . 191 3. Geometry, Trigonometry, Land-surveying. Measure of a Base on Hounslow-heath, Roy 22 Trigonometrical Survey, Roy 64 Class II. Mechanical Philosophy. 1. Dynamics. Precession of the Equinoxes, .... Vince . . 303 Resolution of Attractive Powers,. . Waring 572 On Centripetal Forces, Waring 384 On Spherical Motion, Wildbore 740 2. Astronomy, Chronology, Navigation. Variation of the Star (J'Cephei, . . Goodricke 56 On the Comet of 1532 and 1661, Maskelyne 147 On Changeable Stars E. Pigott 83 Catalogue of 1000 New Nebulae, Herschel 158 On the Transit of Mercury, .... N. Pigott 135 On a New Comet, Miss Herschel 169 On the same, E. Pigott ibid Remarks on the same, .... W. Herschel 170 Latit. and Longitude of York ., E. Pigott 145 Longitude and Node of Saturn, Bugge .. 177 COJfTENTS. m Transit of Merciiry in 1786^ . . On the sanae, Obs. on Miss Herschel's Comet, Two Satellites to the New Planet Latit. andliOngit. of Greenwich, Measures for the same, Volcanos in the Moon, Astron. Obs. and M icrometer, . Precession of the Equinoxes, . . . The Georgian and its Satellites, , Page PaRc Kohler .. 182 The Mahometan Era Hejera, .... Marsden 509 Rumovski 183 Improv. of Celestial Globes, ... . Smeaton 517 Wollaston 186 On a Solar Eclipse, Piazzi . . 529 ,Herschel 214 Observations of a Comet, Herschel 560 Maskelyne 218 A 2d 1000 New Nebulae, Herschel 586 Roy 240 On Saturn's Ring and Satel., Herschel 6 13, 730 Herschel 255 Observations on Venus and Mars, Bugge . . 621 Smeaton 292 Latit. and Longitudes of Places, E. Pigott 709 Vince . . 303 On the Hindoo Chronology, .... Marsden 742 Herschel 489 3. Pneumatics, Experiments on Air, Cavendish 15 On Hepatic Airs or Gases, .... Hassenfratz 286 Experiments on Hepatic Air . . . Kirwan. . 68 Mechanical Expansion of Air, . . Darwin.. 372 Dephlogisticated Air from Water, Thompson ip? 4. Acoustics, Music. Temperament of Musical Instrum., Cavallo 442 5. Optics. New Set of Wires in a Telescope, Wollaston 7 An Indistinctness of Vision, ... . Herschel l65 Ocular Spectra of Light, &c. R.W.Darwin 121 On the Theory of Vision, Maskelyne 595 6. Electricity, Magnetism, Thermometry. Loss of Weight by Heat, .... Fordyce . . 13 On different Electrometers, Magnetical Experiments, Cavallo 57, 170 New Experiments on Heat, .... Thompson 108 On a New Electrical Fish, .... Paterson . . 134 Thermometer for High Degrees, Wedgwood 1 36 On a New Electrometer, . . Ab. Beniiet 173, 176 On a Thunder Storm, Stanhope. . 2 ! 6 A Doubler of Electricity Ab. Bennet 282 Experiment on Heat, Fordyce . . 288 On Subterranean Heat, Mean Heat for every Month, Experiments on Local Heat,. Way of Electrifying Glass, . A New Electrometer, A New Electrical Machine, . Experiments on Electricity, . . . Cavallo . . 354 Dr. J. Hunter 377 . . Heberden 384 , . . Six 404 . . . Gray. . . . 407 . . Cavallo . . 449 ■ . . Nicholson 505 . . . Nicholson 599 Class III. Natural History. 1. Zoology. A New Marine Anin^l, Home . . 1 Natural History of the Cuckoo, , , Jenner . . 432 On the same, J. Hunter 4 On Linnaeus's Amphibia and Serpents, Gray 521 Minute British Shells, Lightfoot 80 On the Sugar Ants in Grenada, .. Castles . . 688 On the Wolf, Jackal, and Dog, J. Hunter 264, 562 2. Botany, Dryander . . 287 On the Growth of Trees Barker . . 507 Swartz .... 302 The Nardus Indica or Spikenard, Blane . . . 658 3. Mineralogy, Fossilogy, &c. . R, Barker 9 On a Mass of Native Iron, .... De Cells . . S69 Bituminous Lake in Trinidad,. . Anderson. . 531 Mineral Productions of Thibet, &c. Saunders b^g Strata and Volcanic Productions, &c. . . Mills 639 A Mineral from N. South Wales, Wedgwood 667 On the Benjamin Tree, . A New Grenus of Plants, A Stag's Head and Horns, . , Petrifactions at Maeslricht, . Strata of a Well at Boston, . , On the Production of Borax, On the same subject, Camper . , Linibird . Blane . . . . Rovato . . 183 282 284 4. Geography and Topography. Subsid. of Ground at Folkstone, Lyon 91 Account of an Earthquake, . . S. More . , 176 Customs of the Americans, . . M'Causland 93 Meas. for Lat. and Long, of Greenwich, Roy 240 State of Mount Vesuvius, . . . Hamilton . . 131 Productions of Boutan and Thibet, Saunders 539 Latit. and Longitude of York, E. Pigott . . 145 IV CONTENTS. Class IV. Chemical Philosophy. — 1. Chemistry. Page Page Experiments on Hepatic Air,. . . . Kirwan. . 6's Lowering the Point of Congelat., Blagden, . 459 Affinities of Subst. in Spirits of W. . . Elliot 79 Formation of Volatile Alkali, &c. Austin . . 493 On the Sulphur Wells at Harrogate, Watson 83 Production of Artificial Cold, ..Walker.. 301 Freezing Mixt. at Hudson's Bay, Cavendish 96 Compos.of Water and Phlogiston, Priestley 518 Dephlogisticated Air from Water, 1 hompson 198 Phlogiston of Spirit of Nitre, Priestley 557 Moisture absorbed by Substances, Thompson 260 On Congealing Quicksilver, , . . Walker. . 579 Congelation of Vitriolic Acid, . . Keir .... 271 Vapour of Acids thro' Hot Tubes, Priestley 602 Production of Artificial Cold, . . Beddoes. . 279 On Nitrous Acid and Air Milner . . 6o6 On Ancient Inks and Writings, Blagden.. 351 On Heavy Inflammable Air,. .. . Austin.. 632 Cool. Water below Freez. Point, Blagden. . 409 On the Excise of Spirituous Liq., Blagden 675 Acidity, Compos, of Water,&:c. Priestley 419> 473 Dissolut. of Metals in Acids, Keir .... 694 On the Freezing of Acids, .... Cavendish 425 On the Matter of Cancer, Crawford 710 Airs changed into Nitrous Acid, Cavendish 45 1 2. Meteorology. Meteorol. Reg., T. Barker 30, 95, 306, 507, 563 Of Luminous Arches, Hey .... 627 Account of an Earthquake, More .... 176 On the same, F. J. H. WoUaston 630 Halos and Parhelia in America, Baxter . . 181 On the same, B. Hutchinson ibid Thunder Storm in Scotland, Brydone. . 186 On the same, J. Franklin 631 Observations on the same, Stanhope 2l6 On the same, E. Pigott ibid Meteorol. Journal R. S. 431,556,652 Height of a Luminous Arch, .. Cavendish 645 Drynessof the year 1738, .... Hutchinson 528 Extraord. Effects of Lightning, Withering 662 Indications of Spring, Marsham 56 1 3. Geology. On Subterranean Heat, Dr. J. Hunter 377 Class V. Physiology. — 1. Anatomy. Struct, and Economy of Whales, J. Hunter 306 1. Physiology of Animals, An Extraordinary Introsusception, Letsom 119 On Muscular Motion, Fordyce 36l Mortality of Males and Females,. . Clarke 122 A Transposition of the Viscera,. . Baillie . . 483 On a New Electrical Fish, Paterson 13+ Change of Struct, in the Ovarium, Baillie . . 535 On Extirpating one Ovarium, J. Hunter 256 On a Human Monster, Anderson 56l On Numerous Births, Garthshore 294 Observations on Respiration, .... Priestley 647 StructuEe and Econ. of Whales,. . J. Hunter 306 Of a Child with a Double Head,. . Home. . 663 3. Physiology of Plants. Sensitive Quality of a Tree, .. R.Bruce.. 10 Account of the Tabasheer, ... , P.Russell 653 On the Irritability of Plants, .. Smith 421 Class W. The Arts. — 1. Mechanical. GraduationofAstron. Instruments, Smeaton 30 Hindley's Method to Divide Circles, Smeaton 40 2. Fine Arts. Instrum. for Drawing Perspective, Peacock 15 Class VII. Biography ; or. Account of Authors. Dr. Edw. Whitaker Gray, 407 Rev. Charles Wildbore 740 ERRATUM. Page 746, hi the table, for 1846 read 1847 i and/or 56 read 57 before Christ. THE PHILOSOPHICAL TRANSACTIONS OP THE ^ ROYAL SOCIETY OF LONDON; ABRIDGED. XVII. /description of a New * Marine Animal. In a Letter from Mr. Everard Home, to John Hunter, Esq., F. R. S. With a Postscript by Mr. Hunter, containing Anatomical Remarks on the same. Dated Sept. 20, 1784. p. 333. About 3 years before Mr. H. sent this sea animal from Barbadoes, which was unlike any one he had ever seen. And even after his arrival in England, his in- quiries concerning it had been without success. The specimen sent was found on a part of the coast which had undergone very remarkable changes, in conse- quence of a violent hurricane. These changes were indeed the means of its being discovered, and present a probable reason why it was not discovered before. The animal was found on the south-east coast of Barbadoes, close to Charles Fort, about a mile from Bridge Town, in some shoal water, separated from the sea by the stones and sand thrown up by the dreadful hurricane, which hap- pened in the year 1780, and did so much mischief to the island. The wind, in the beginning of the storm, which was in the afternoon, blew very furiously from the north-west, making a prodigious swell in the sea ; and in the middle of the night changing suddenly to the south-east, it blew from that quarter on the sea, already agitated, forcing it on the shore with so much violence, that it threw down the rampart of Fort Charles, which was opposed to it, though 30 feet broad, by the bursting of one sea. It forced up, at the same time, im- mense quantities of large coral rocks from the bottom of the bay, making a reef along this part of the coast for the extent of several miles, at only a few yards distance from the shore. The soundings of the harbour were found afterwards to be entirely changed, by the quantity of materials removed from the bottom in different places. In * This animal seems greatiy allied to the Serpula gigantea of Linneus and PalJas, and which has sometimes been found on our own coasts^ and is described, in the 7th vol. of the Linnean Transac- tions, by Col. Montagu, under the name of Amphitrite volutacornis. VOL. XVI. B 4 PHILOSOPHICAL TRANSACTIONS. [anNO 1785. the reef of coral was found ^n infinite number of large pieces of brain-stone, containing the shell of this animal ; but the animals had either been long dead, or more probably destroyed by the motion of the rocks in the storm : some few of the brain-stones, however, that had been thrown beyond the reef, and lodged in the shoal water, receiving less injury, the animals were preserved unhurt. The animal, with the shell, was almost entirely inclosed in the brain-stone, so that at the depth in which they generally lie, they are hardly discernible, through the water, from the common surface of the brain-stone ; but when in search of food they throw out two cones, with membranes twisted round them in a spiral manner, which have a loose fringed edge, looking at the bottom of the sea like two flowers ; and in this state they were discovered. The animal, when taken out of the shell, including the two cones and their membranes, is 5 inches in length ; of which the body is 3-| inches, and the apparatus for catching its prey, which may be considered as its tentacula, about an inch and a quarter. The body of the animal is attached to its shell, for about 4 of an inch in length, at the anterior part where the two cones arise, by means of two cartilagi- nous substances, with one side adapted to the body of the animal, the other to the internal surface of the shell : the rest of the body is unattached, of a darkish white colour, about half an inch broad, a little flattened, and rather narrower towards the tail. The muscular fibres on its back are transverse; those on the belly longitudinal, making a band the whole length of the body, on the edge of which the transverse fibres running across the back terminate. The two cartilaginous substances by which the animal adheres to its shell, are placed one on each side of the body, and are joined together on the back of the animal at their posterior edges : they are about -f of an inch long, are very narrow at their anterior end, becoming broader as they go backwards ; and at their posterior end they are the whole breadth of the body of the animal. On their external surface there are 6 transverse ridges, or narrow folds ; and along iheir external edges, at the end or termination of each ridge, is a little eminence resembling the point of a hair pencil, so that on each side of the animal there are 6 of these little projecting studs, for the purpose of adhering to the sides of the shell in which the animal is inclosed. The internal surfaces of these carti- lages are firmly attached to the body of the animal, in their middle part, by a kind of band or ligament ; but the upper and lower ends are lying loose. From the end of the body, between the two upper ends of these cartilages, arise what he supposes to be the tentacula, consisting of 2 cones, each having a spiral membrane, twining round it : they are close to each other at their bases, and diverge as they rise up, being about an inch and a quarter in length, and nearly -^ of an inch in thickness at their base, and gradually diminishing till they terminate in points. The membranes which twine round these cones also take yOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. 3 their origin from the body of the animal, and make 5^ spiral turns round each, being lost in the points of the cones ; they are loose from the cone at the lowest spiral turn which they make, and are nearly half an inch in breadth ; they are exceedingly delicate, and have at small distances fibres running across them from their attachment at the stem to the loose edge, which gives them a ribbed ap- pearance. These fibres are continued about -^ of an inch beyond the mem- brane, having their edges finely serrated, like the tentacula of the Actiniae found in Barbadoes : these tentacula shorten as the spiral turns become smaller, and are entirely lost in that part of the membrane which terminates in the point of the cone. Behind the origin of these cones arises a small shell, which, for -^ of an inch from its attachment to the animal, is very slender : it is about -f- of an inch in length, becoming considerably broader at the other end, which is flat, and about 4- of an inch broad ; the flattened extremity is covered with a kind of hair, and has rising out of it 2 small claws, about -^ of an inch in length. If the hair, and mucus entangled in it, be taken away, this extremity of the shell becomes concave, is of a pink colour, and the 2 claws rising out from its middle part have each 3 short branches, not unlike the horns of a deer. The body of this shell has a soft cartilaginous covering, with an irregular but polished surface : on this the cones rest in their collapsed state, in which state the whole of the shell is drawn into the cavity of the brain-stone, excepting the flattened end with the 2 claws. Before the cones there is a thin membrane, which appears to be of the same length with the shell just described. In the collapsed state it lies between the cones and the shell in which the animal is inclosed ; but, when the tentacula are thrown out, it is also protruded. The shell of this animal is a very thin tube, adapted to its body : the internal surface is smooth, and of a pinkish white colour ; its outer surface is covered by the brain-stone in which it is inclosed, and the turnings and windings which it makes are very numerous. The end of the shell, which opens externally, rises above the surface of the stone on one side half an inch in height, for about half the circumference of the aperture, bending a little forwards over it, and becom- ing narrower and narrower as it goes up, terminating at last in a point just over the centre of the opening of the shell ; on the other side it forms a round margin to the surface of the brain-stone. This part of the shell is much thicker and stronger than that part which is inclosed in the brain-stone : its outer surface is of a darkish brown colour; its inner of a pinkish white» The animal, when at rest, is wholly concealed in its shell ; but when it seeks for food, the moveable shell is pushed slowly out with the cones and their mem- branes in a collapsed state ; and when the whole is exposed, the moveable shell falls a little back, and the membrane round each of the cones is expanded, the B 2 4 PHILOSOPHICAL TIIANSACTIONS. [aNNO 1785. tentacula at the bases of the cones having just room enough to move without touching each other. The thin membrane which lay between the cones and the inclosing shell is protruded in the form of a fold, and lies over the external shell which projects from the brain-stone. The membranes have a slow spiral motion, which continues during the whole time of their being expanded; and the tentacula on their edges are in constant action. The motion of the membrane of the one cone seems to be a little dif- ferent from that of the other, and they change from the one kind of motion to the other alternately, a variation in the colour of the membrane at the same time taking place, either becoming a shade lighter or darker ; and ihis change in the colour, while the whole is in motion, produces a pleasing effect, and is most striking when the sun is very bright. The membranes however at some particular times appear to be of the same colour. While the membranes are in motion, a little mucus is often separated from the tentacula at the point of the cone. On the least motion being given to the water, the cones are immediately, and very suddenly, drawn in. This apparatus for catching food is the most deli- cate and complicated that he had seen. He annexed 2 drawings of the animal in its two different states, one in search of food, and one while lying at rest. Mr. Hunter s Postscript. — Animals which come from foreign countries, and which cannot be brought to England alive, must be kept in spirits to preserve them from putrefaction, which makes them less fitted for anatomical examina- tion ; for the spirits, which preserve them, produce a change in many of their properties, and alter the natural colours, and texture of the parts, so that often the structure alone of the animal can be ascertained ; and where this is not naturally distinct, it becomes often quite obscured, and the texture of the finer parts is wholly destroyed, requiring a very extensive knowledge of such parts in animals at large, to assist us in bringing them to light : this happens to be the case with the animal whose dissection is the subject of this postscript. The animal may be said to consist of a fleshy covering, a stomach and intes- tinal canal, and the two cones with their tentacula and moveable shell, which last may be considered as appendages. The body of the animal is flattened, and terminates in two edges, which are intersected by rugae, the fasciculi of trans- verse muscular fibres which run across the back being continued over them. On each of these edges is placed a row of fine hairs, which project to some dis- tance from the skin. The fleshy covering consists principally of muscular fibres: those on the back are placed transversely, to contract the body laterally ; those on the belly longitudinally, to shorten the animal when stretched out, and to draw it into the shell. The stomach and intestine make one straight canal : the anterior end of this forms the mouth, which opens into the grooves made by the spiral turns of the tentacula round the stem of each of the cones; and the in- ^^Wip VOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. $. testine at the posterior end opens externally, forming the anus. From the con- tracted state of the animal, the intestine is thrown into a number of folds. On examining the cones and the tentacula, Mr. H. at first believed that the spiral form arose from their being in a contracted state ; and that when the. tentacula were erected, the cone untwisted, forming a longer cone with the ten- tacula arising from its sides, like the plume from the stem of a feather ; and that this stem was drawn in or shortened by means of a muscle passing along the centre, which threw the tentacula into a spiral line, similar to the penis of many birds ; but how far this is really the case, he was not able to ascertain. The internal structure of this animal, like most of those which have tentacula, is very simple ; it differs however materially from many, in having an anus, most animals of this tribe, as the Polypi, having only one opening, by which the food is received, and the excrementitious part of it also afterwards thrown out ; this we must have supposed, from analogy, to take place in the animal which is here described, more particularly since it is inclosed in a hard shell, at the bottom of which there appears to be no outlet ; but as there is an anus this cannot be the case. It is very singular, that in the leach, polypi, &c. where no apparent inconve- nience can arise from having an anus, there is not one, while in this animal, where it would seem to be attended with many, we find one ; but there being no anus in the leach, polypi, &c. may depend on some circumstance in the animal economy which we are at present not fully acquainted with. Tiie uni- valves, whose bodies are under similar circumstances respecting the shell with this animal, have the intestine reflected back, and the anus, by that means, brought near to the external opening of the shell, the more readily to discharge the excrement ; and though this structure, in these animals, appears to be solely intended to answer that purpose, yet when we find the same structure in the black snail, which has no shell, this reasoning will not wholly apply, and we must refer it to some other intention in the animal economy. In this animal we must therefore rest satisfied that the disadvantageous situation of the anus, with respect to the excrement's being discharged from the shell, answers some purpose in the economy of the animal, which more than counter-balances the inconveniences produced by it. It would appear, from considering all the cir- cumstances, that the excrement thrown out at the anus must pass from the tail along the inside of the tube, between it and the body of the animal, till it comes to the external opening of the shell, as there is no other evident mode of dis- charging it. How the tube or shell is formed in stone or coral is not easily ascertained. It may be asked, whether this animal has the power of boring backwards as the Teredo Navalis probably does, or whether the stone or coral is formed at the 6 PHILOSOPHICAL TRANSACTIONS. [aNNO 1785. same time \vith the animal, and grows and increases with it : and if we consider all tiie circumstances, this last would appear to be most probable, and agree best with the different phenomena ; for the coral is lined with a shell, which could not be the case if the animal was continually increasing this hole, both in length and breadth, in proportion to its growth ; but if the coral and the animal in- crease together, it is then similar to the growth of all shells, whether bivalve or univalve. The animal does not appear to have the power of increasing its canal, being only composed of soft parts. This however is no argument against its doing it, for every shell fish has the power of removing a part of its shell, so as to adapt the new and the old together ; which is not done by any mechanical power, but by absorption. The tribe of animals which have tentacula consists of an almost infinite variety, and many of the species have been described. Of that kind however which has the double cones, he believes hitherto no ac- count has been given. It is most probably to be found in the seas surrounding the different islands in the West Indies ; for he once received an animal from St. Vincent's ; which, on examination, proved to be the same animal with that above described, only that the moveable shell was wanting. After writing this postscript, Mr. H. found a description of a double-coned Terebella, published by the Rev. Mr. Cordiner, at Bamf in Scotland, which was found on that coast ; in which the cones have their tentacula passing out from the end, and when erected they spread from the cone as from a centre. . This proves that the double-coned tentacula also have different species. Explanation of the Figures. — Fig. 1 , pi. 1 , is a drawing of the animal after death, as it appeared in spirits, a, the under side of tlie body ; bb, the cartilages which attach the animal to the sides of the cavity in which it lies ; c, one of the cones covered by its membrane in a collapsed state ; t>, the lowest spiral turn of the membrane and its tentacula spread out ; ee, tlie cut edges of the divided membrane, which are turned on each side to show the cone ; f, the cone as it appears in the intervals between the spiral turns of the membrane ; o, the moveable shell, with the smooth cartilaginous covering, in an outside view ; h, the flattened end of the moveable shell, with hair on it J II, the two claws tliat arise from the surface of the flattened end of the moveable shell } k, the anus, into which a hog's bristle is introduced. Fig. 2 is a drawing of the animal, with its tentacula expanded in search of food, as it appears in the sea ; taken from a sketch made in Barbadoes, where no draughtsman could be procured while the animal was alive : a, the sort of brain-stone in which the animal was discovered ; h, the exter- nal prominent shell ; cc, the membrane which is protruded with the cones and moveable shell, and makes a fold over the edges of the prominent shell ; dd, the membranes and tentacula in a state of expansion ; e, the inner side of the moveable shell, as it appears when protruded ; f, the hole in the brain-stone as it appears when the prominent shell is broken off, and which may be seen in many- specimens of brain-stone. TOL. LXXV.] PHILOSOFHICAL TRANSACTIONS.' 7- XVI II. A Description of a New System of Wires in the Focus of a Telescope, for Observing the comparative Right Ascensions and Declinations of Celestial Objects, &c. By the Rev. Francis fVollaston, LL. B., F. R. S. p. 346. The rhombus (for a rhombus, and not a rhomboid, it ought most properly to be called) is very good in theory ; but very difficult to get executed with pre- cision, and liable to some inaccuracy in the observation. The truth of it de- pends on the longer diagonal being exactly twice the length of the shorter one ; which requires an awkward angle (53° 7' 48 ) at the vertex, not easily to be hit by the workmen, and therefore seldom sufficiently true. Beside this, as the sides of the rhombus, on which depends the calculation for differences of decli- nation, are but 26° 33' 54'' declining from the perpendicular or horary wire, a very small error in observing the passage of a star makes a very material differ- ence in the result. This determined Mr. W. to make trial of a square placed angularly, an addi- tion to M. Cassini's wires at 45°, which seems to answer better. The whole extent of the field is employed as it is in the rhombus (the want of which was said to be Dr. Bradley's objection to M. Cassini's wires) ; but being formed of right angles or half-right angles, to which workmen are most accustomed, they will alvv;4ys be apt to execute their part better ; and the obliques, from the differ- ences being just double to what they are in the rhombus, give the comparative de- clinations with twice the certainty. To this the number of corresponding observa- tions in the passage of every star add considerably ; since we may calculate its dis- tance from the centre, or from the angles, or from one of the intermediate angles, as occasion may require, with double the precision of the rhombus. In each of them, the parallel wires will tell whether the placing of the instrument be true or faulty ; because, if truly made and truly set, th6 same star must take the same time in passing from one wire to its corresponding parallel ; which will differ considerably, and in every star the same way, if the position be faulty. It may be proper to add, what indeed is nothing new, that if the position of the instrument be found erroneous, the formula given by M. De Lalande in his Astronomy will serve to rectify the observation. Calling the larger interval between the passage of any oblique and the horary wire m, and the smaller one n, then — ^ — ~!^ will give the difference of declination (in time to be converted into degrees, and multiplied by the cosine of declination) from the angle where that oblique meets the horary ; and — -— the difference in rierht ascension from the same angle. It is almost needless to mention, that where the position is true, half the interval of time between a star's passing any two corresponding obliques, converted into degrees, and multiplied by the cosine of declination. 8 PHILOSOPHICAL TRANSACTIONS. [aNNO 1785. will give the difference in declination of that star from the angle where those obliques meet, as the whole interval does in the rhombus. But it may perhaps be of service to astronomy, or at least not unacceptable to those gentlemen who use the rhombus, says Mr. W., that I should subjoin another formula (contrived for me the last summer by my son, now Mathema- tical Lecturer at Sidney College, Cambridge), for investigating the comparative right ascensions and declinations of stars observed by it, when the instrument is not placed truly in the plane of the equator. I was led to wish for some such formula, in consequence of an ingenious paper, kindly communicated to me by Sir H. C. Englefield, Bart., p. r s., giving an account of his method of doing it by a scale and figure ; which, though very easy when one is provided with such a scale, appeared to be of less general use than by calculation ; and I do not know that any thing of the kind is to be met with in any publication. Let the angle dll, fig. 3, pi. 1, which by construction is 63° 26', be called a ; the diagonal ll be called b \ The larger interval observed between the passage of a star by an oblique and the horary wire, as hc^ be called m ; The smaller ditto of the same star, as cd, be n ; The large ditto of another star, as (Sy, be ^ ; The smaller ditto, as y^, be y : Then— ^"^^^ = tangent of the angle which ll makes with a parallel of decli- nation : call this a : the angle q being thus found, then ^^" "^' ^ sin.(a+g) ^ ^ 030 ^ j^^ sm, a q. = difference in declination between the two points on the vertical wire where those stars pass it. Which, being in time, must be converted into degrees, and multiplied by cosine of declination as usual, to give the true difference in decli- nation between the stars. A J ^u • • 2 (•» co») X sin. (a + q) ^^ • ., i-ar And the same expression, viz. — ^ : — -^^ ^^ X sin. o = the difference ^ R X sin. a ^ in a. r. between those two points ; to be applied as a correction to the observed times. The same may be done by the larger intervals m and [/., only by substituting a — a instead of a 4- q, thus: '^ '^ xsm.^a—q ^^^ __ ^^ff^^^^^^ -^^ jg_ ^ ' ' ' R X sin. a ^ clination as above; or X sin. q = ascensional difference. If the stars differ too much in declination to come within the expression above (as N** 1 and 3) then the differences of the angles d and e in declination and right ascension may be found thus : — : — ^ ^"^' ^ = diff. in declin. between d and e ; ' — ^1_!!!L? = their ascen. diff., and R R ' the difference of each star from its respectively nearest angle of the rhombus. VOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. g may be deduced by the former expression, leaving out the consideration of tiie Other star, thus: ^ '" ^ ^'"J.!"^ ^^ ^ ^°^* ^ ~ ^^^' ^^ ^^^ ^^^^ ^" declin. from its nearest angle, and ... x sin. g = its difference in right ascension. The application of these formulae is very easy : for having found q, if you set down its cosine in one column for declination, and its sine in another column for right ascension, and under each the constant sin. (a + 9), and the arithmetical compl. of sin. a ; these being added together will make two sums, for the com- parative observations of every star which may pass the field ; and, unless the field be very large, and the declination of the stars very great, if to the column for declination be added the cosine of declination of the centre of the field, it will adapt itself to all the products. J[IX. Account of a Stag's Head and Horns, found at Alport j Derbyshire. By the Rev. Robert Barker , B. D. p. 353. About the year 178O, some men working in a quarry of that kind of stone which in Derbyshire is called tuft,* at about 5 or 6 feet below the surface, in a very solid part of the rock, met with several fragments of the horns and bones of animals. Among the rest, out of a large piece of the rock, which they got entire, there appeared the tips of 3 or 4 horns, projecting a few inches from it, and the scapula of some animal adhering to the outside of it. A. friend sent the piece of the rock to Mr. B. in the state they got it, in which he let it remain for ' some time. But suspecting that they might be tips of the horns of some head inclosed in the lump, he determined to gratify his curiosity by clearing away the stone from the horns. On doing which he found that the lump contained a very large stag's head, with two antlers on each horn, in a very perfect preservation, inclosed in it. Though the horns are so much larger than those of any stag he ever saw, yet, from the sutures in the skull appearing very distinct in it, one would suppose that it was not the head of a very old animal. He had one of the horns nearly entire, and the greatest part of the other, but so broken in the getting out of the rock, that one part will not join to the other, as the parts of the other horn do. The horns are of that species which park-keepers in this part of the coun- try call throstle-nest horns, from the peculiar formation of the upper part of them, which is branched out into a number of short antlers, which form a hollow about large enough to contain a thrush's nest. Below are the dimensions of the different parts of them, compared with the horns of the same species of a large stag, which have probably hung in the place whence he pro- ♦ Tuft is a stone formed by the deposit left by water passing through beds of sticks, roots, vegeta- bles, &c. of which there is a large stratum at Matlock, Bath, in this county.— Orig. VOL. XVI. C 10 PHILOSOPHICAL TRANSACTIONS. [aNNO 1785. cured them 2 or 3 or perhaps more centuries ; and with another pair of horns of a different kind, which are terminated by one single pointed antler, and which were the horns of a seven-year-old stag. The river Larkell runs down the valley, and part of it falls into the quarry where these horns were found, the water of which has not the property of in- crusting any bodies it passes through. It is therefore probable that the animal to which these horns belonged was washed into the place where they were found, at the time of some of those convulsions which contributed to raise this part of the island out of the sea. Besides this complete head, Mr. B. had several pieces of horns, bones, and several vertebrae of the back, found in the same quarry ; some, if not all, of them probably belonging to the same animal. Dimensions of the three kinds of horns above-mentioned, Found at Throstle-nest Seven years Alport. horns. stag's. Ft. In. Ft. In. Ft. In. Circumference at their base ,....0 9^ 07 05| Length of the lowest antler 12 10 0 9 Length of second ditto 0 11^ 0 10| 0 10 Length of third ditto 1 l| 0 ll| 0 10 Length of the horn 3 sf 2 7h 2 8| XX. On the Sensitive Quality of the Tree ^verrhoa Caramhola. By Robert Bruce, M.D. p. 356. The averrhoa carambola of Linneus, a tree called in Bengal the camruc or camrunga, is possessed of a power somewhat similar to those species of mimosa termed sensitive plants ; its leaves, on being touched, move very perceptibly. In the mimosa the moving faculty extends to the branches ; but, from the hard- ness of the wood, this cannot be expected in the camrunga. The leaves are alternately pinnated, with an odd one ; and in their most common position in the day-time are horizontal, or on the same plane with the branch from which they come out. On being touched, they move themselves downwards, frequently in so great a degree that the two opposite almost touch each other by their under sides, and the young ones sometimes either come into contact or even pass each other. The whole of the leaves of one pinna move by striking the branch with the nail of the finger, or other hard substance ; or each leaf can be moved singly, by making an impression that shall not extend beyond that leaf. In this way, the leaves of one side of the pinna may be made to move, one after an- other, while the opposite continue as they were ; or you may make them move alternately, or in short in any order you please, by touching in a proper manner the leaf you wish to put in motion. But if the impression, though made on a single leaf, be strong, all the leaves on that pinna, and sometimes on the neigh- bouring ones, will be affected by it. What at first seemed surprizing was, that notwithstanding this apparent VOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. 1 1 sensibility of the leaf, I could with a pair of sharp scissars make large incisions in it, without occasioning the smallest motion ; nay, even cut it almost entirely off, and the remaining part still continue unmoved ; and that then, by touching the wounded leaf with the finger or point of the scissars, motion would take place as if no injury had been offered. But, on further examination I found, that though the leaf was the ostensible part which moved, it was in fact entirely passive, and that the petiolus was the seat both of sense and action : for though the leaf might be cut in pieces, or squeezed with great force, provided its direc- tion was not changed, without any motion being occasioned ; yet if the impres- sion on the leaf was made in such a way as to affect the petiolus, the motion took place. When therefore I wanted to confine the motion to a single leaf, I either touched it so as only to affect its own petiolus, or, without meddling with the leaf, touched the petiolus with any small-pointed body, as a pin or knife. By compressing the universal petiolus near the place where a partial one comes out, the leaf moves in a few seconds, in the same manner as if you had touched the partial petiolus. Whether the impression be made by puncture, percussion, or compression, the motion does not instantly follow ; generally several seconds intervene, and then it is not by a jerk, but regular and gradual. Afterwards, when the leaves return to their former situation, which is commonly in a quarter of an hour or less, it is in so slow a manner as to be almost imperceptible. On sticking a pin into the universal petiolus at its origin, the leaf next it, which is always on the outer side, moves first ; then the first leaf on the opposite side, next the 2d leaf on the outer, and so on. But this regular progression seldom continues through- out ; for the leaves on the outer side of the pinna seem to be affected both more quickly, and with more energy, than those of the inner, so that the 4th leaf on the outer side frequently moves as soon as the 3d on the inner ; and sometimes a leaf, especially on the inner side, does not move at all, while those above and below it are affected in their proper time. Sometimes the leaves at the extre- mity of the petiolus move sooner than several others which were nearer the place where the pin was put in. On making a compression with a pair of pincers on the universal petiolus, between any two pair of leaves, those above the com- pressed part, or nearer the extremity of the petiolus, move sooner than those under it, or nearer the origin ; and frequently the motion will extend upwards to the extreme leaf, while below it perhaps does not go farther than the nearest pair. If the leaves happen to be blown by the wind against each other, or against tlie branches, they are frequently put in motion ; but when a branch is moved gently, either by the hand or the wind, without striking against any thing, no motion of the leaves takes place. When left to themselves in the day-time, c 2 12 PHILOSOPHICAL TRANSACTIONS. [anNO 1785. shaded from the sun, wind, rain, or any disturbing cause, the appearance of the leaves is different from that of other pinnated plants. In the last a great uni- formity subsists in the respective position of the leaves on the pinna ; but here some will be seen on the horizontal plane, some raised above it, and others fallen under it ; and in about an hour, without any order or regularity, which I could observe, all these will have changed their respective positions. I have seen a leaf, which was high up, fall down ; this it did as quickly as if a strong impression had been made on it, but there was no cause to be perceived. Cutting the bark of the branch down to the wood, and even separating it about the space of half an inch all round, so as to stop all communication by the vessels of the bark, does not for the first day affect the leaves, either in their position or their apti- tude for motion. In a branch, which I cut through in such a manner as to leave it suspended only by a little of the bark no thicker than a thread, the leaves next day did not rise so high as the others ; but they were green and fresh, and, on being touched, moved, but in a much less degree than formerly. After sun-set the leaves go to sleep, first moving down so as to touch each other by their under sides ; they therefore perform rather more extensive motion at night of themselves than they can be made to do in the day-time by external impressions. With a convex lens I have collected the rays of the sun on a leaf, so as to burn a hole in it, without occasioning any motion. But when the expe- riment is tried on the petiolus, the motion is as quick as if from strong percus- sion, though the rays were not so much concentrated as to cause pain when applied in the same degree on the back of the hand ; nor had the texture of the petiolus been any ways changed by this ; for next day it could not be distinguished, either by its appearance or moving power, from those on which no experiment had been made. The leaves move very fast from the electrical shock, even though a very gentle one ; but the state of the atmosphere was so unfavourable for experiments of this kind, that I could not pursue them so far as I wished. There are 2 other plants mentioned as species of this genus by Linneus. The first, the averrhoa bilimbi, I have not had an opportunity of seeing. The other, or averrhoa acida, does not seem to belong to the same class ; nor do its leaves possess any of the moving properties of the carambola. Linneus's generic de- scription of the averrhoa, as of many other plants in this country which he had not an opportunity of seeing fresh, is not altogether accurate. The petals are connected by the lower part of the lamina, and in this way they fall off while the ungues are quite distinct. The stamina are in 5 pairs, placed in the angles of the germen. Of each pair only one stamen is fertile, or furnished with an anthera. The filaments are curved, adapted to the shape of the germen. They may be pressed down gently, so as to remain ; and then, when moved a little upwards, rise with a spring. The fertile are twice the length of those destitute of antherae. — Calcutta, Nov. 23, 1783. VOL. LXXV.] PHILOSOPHICAL TRAXS ACTIONS. 13 XXI. Experiments on the Loss of IVeighl in Bodies on being Melted or Heated. By George Fordyce, M.D. F.R.S. p. 36l. Though I have made many experiments on the subject of the loss of weight in bodies on being melted, or heated, I do not think, it worth while to lay them all before the Society, as there has not appeared any circumstance of contradiction in them. I shall content myself with relating the following one, which appears conclusive in determining the loss of weight in ice when thawed into water, and subject to the least fallacy of any I have hitherto made, in showing the loss of weight in ice on being heated. The beam I made use of was so adjusted as that, with a weight between 4 and 5 ounces in each scale, -rrW P^^^ of a grain made a difference of 1 division on the index. It was placed in a room the heat of which was 37 degrees of Fahrenheit's thermometer, between 1 and 2 in the afternoon, and left till the whole apparatus and the brass weights acquired the same tem- perature. A glass globe, of 3 inches diameter nearly, with an indentation at the J\ bottom, and a tube at the top, weighing about 451 grains, had about /^ ^ 1700 grains of New River water poured into it, and was hermetically \„^^ sealed, so that the whole, when perfectly clean, weighed 2150^ of a grain exactly ; the heat being brought to 32 degrees, by placing it in a cooling mixture of salt and ice till it just began to freeze, and shaking the whole together. After it was weighed it was again put into the freezing mixture, and let stand for about 20 minutes ; it was then taken out of the mixture ; part of the water was found to be frozen ; and it was carefully wiped, first with a dry linen cloth, and after- wards with dry washed leather ; and on putting it into the scale it was found to have gained about the -^ part of a grain. This was repeated 5 times : at each time more of the water was frozen, and more weight gained. In the mean time the heat of the room and apparatus had sunk to the freezing point. When the whole was frozen, it was carefully wiped and weighed, and found to have gained ^ of a grain and 4 divisions of the index. Standing in the scale for about a minute, I found it began to lose weight, on which I immediately took it out, and placed it at a distance from the beam. I also immediately plunged a thermometer in the freezing mixture, and found the temperature ]0 degrees; and on putting the ball of the thermometer in the hollow at the bottom of the glass vessel, it showed 1 2 degrees. I left the whole for half an hour, and found the thermometer, applied to the hollow of the glass, at 32°. Every thing now beir-g at the same temperature, I weighed the glass containing the ice, after wiping it carefully, and found it had lost -i- and 5 divisions; so that it weighed -J^, all but 1 division, more than when the water was fluid. I now melted the ice, except- ing a very small quantity, and left the glass vessel exposed to the air in the tern- M PHILOSOPHICAL TRANSACTIONS. [aNNO 1785, perature of 32 degrees for a quarter of an hour ; the little bit of ice continued nearly the same. I now weighed it, after carefully wiping the glass, and found it heavier than the water was at first 1 division of the beam. Lastly, I took out the weights, and found the beam exactly balanced as before the experiment. The acquisition of weight found by water being converted into ice, may arise from an increase of the attraction of gravitation of the matter of the water ; or from some substance imbibed through the glass, which is necessary to render the water solid. Which of these positions is true, may be determined by forming a pendulum of water, and another of ice, of the same length, and in every other respect similar, and making them swing equal arcs. If they mark equal times, then certainly there is some matter added to the water. If the pendulum of ice is quicker in its vibrations, then the attraction of gravitation is increased. For there is no position more certain, than that a single particle of inanimate matter is perfectly incapable of putting itself in motion, or bringing itself to rest ; and therefore, that a certain force applied to any mass of matter, so as to give it a certain velocity, will give half the quantity of matter double the velocity, and twice the quantity, half the velocity ; and, generally, a velocity exactly in the inverse proportion to the quantity of matter. Now if there be the same quantity of matter in water as there is in ice, and if the force of gravity in water be -s-tt-s-t part less than in ice, and the pendulum of ice swing seconds,, the pendulum of water will lose ^-g-^-o of a second in each vibration, or 1 second in 'ZSOOO, which is almost 3 seconds a day, a quantity easily measured. I shall just take notice of an opinion which has been adopted by some, that there is matter absolutely light, or which repels instead of attracting other matter, I confess this appears absurd to me ; but the following experiment would prove or disprove it. Supposing, for instance, that heat was a body, and absolutely light, and that ice gained weight by losing heat ; then a pendulum of ice would swing through the same arc in -rr-ro-ff ^^ss time than a similar pendulum of water ; for the same power would not only act on a less quantity of matter, but a counter- acting force would also be taken away. I shall only observe, that heat certainly diminishes the attractions of cohesion, chemistry, magnetism, and electricity ; and if it should also turn out, that it diminishes the attraction of gravitation, I should not hesitate to consider heat as th6 quality of diminution of attraction, which would in that case account for all its effects. ' We come, in the next place, to take notice of the 2d part of the experiment, viz. that the ice gained an 8th part of a grain on being cooled to 12 degrees of Fahrenheit's thermometer. In this case, a variation may arise from the contrac- tion of the glass vessel, and consequent increase of specific gravity in proportion to the air. But it is unnecessary to observe, that this would be so very small a quantity as not to be observable on a beam adjusted only to the degree of sensi- VOL. LXXV.] PHILOSOPHICAL TRANSACTIONS, 1*J bility with which this experiment was tried. In the 2d place, the air cooled by the ice above the scale becoming heavier than the surrounding atmosphere, would press on the scale downward with the whole force of the difference. If a little more than half a pint of air was cooled over the scale to the heat of the ice and glass containing it, that is, 20° below the freezing point, the difference, accord- ing to General Roy's table, would have been the 8th part of a grain, which was the weight acquired; but the air within half an inch of the glass vessel being only 1° below the freezing point, I cannot conceive, that even an 8th part of a pint of air could be cooled over the scale to 20° below the freezing point ; nor that the whole difference of the weight of the air over the scale could ever amount to the 32dofagrain. I have however contrived an apparatus which is executing, in which this cause of fallacy will be totally removed. I shall therefore rest at pre- sent the state of this part of the subject ; and leave it only proved, that water gains weight on being frozen. XXII. Sketches and Descriptions of Three Simple Instruments for Drawing Architecture ctnd Machinery in Perspective. By Mr. Jas. Peacock, p. 366. These machines, and descriptions of their use, appear to be too complex and operose to be employed in such practical cases of drawing. XXIII, Experiments on Air. By H. Cavendish^ Esq. F. R. S. and A, S^ p. 372. In a paper, printed in the last volume of the Philosophical Transactions, in which I gave my reasons for thinking that the diminution produced in atmospheric air by phlogistication, is not owing to the generation of fixed air, I said it seemed most likely, that the phlogistication of air by the electric spark was owing to the burning of some inflammable matter in the apparatus ; apd that the fixed air supposed to be produced in that process, was only separated from that inflam- mable matter by the burning. At that time, having made no experiments on the subject myself, I was obliged to form my opinion from those already pub- lished ; but I now find, that though I was right in supposing the phlogistication of the air does not proceed from phlogiston communicated to it by the electric spark, and that no part of the air is converted into fixed air ; yet that the real cause of the diminution is very different from what I suspected, and depends on the conversion of phlogisticated air into nitrous acid. The apparatus used in making the experiments was as follows : The air through which the spark was intended to be passed, was confined in a glass tube m, bent to an angle, as in fig. 4, pi. 1, which, after being filled with quicksilver, was in- verted into two glasses of the same fluid, as in the figure. The air to be tried was then introduced by means of a small tube, such as is used for thermo- l6 PHILOSOPHICAL TRANSACTIONS. [aNNO 1785. meters, bent in the manner represented by abc, fig. 5, the bent end of which, after being previously filled with quicksilver, was introduced, as in the figure, under the glass def, inverted into water, and filled with the proper kind of air, the end c of the tube being kept stopped by the finger ; then, on removing the linger from c, the quicksilver in the tube descended in the leg bc, and its place was supplied with air from the glass def. Having thus got the proper quantity of air into the tube abc, it was held with the end c uppermost, and stopped with the finger ; and the end a, made smaller for that purpose, being introduced into one end of the bent tube m, fig. 4, the air, on removing the finger from c, was forced into that tube by the pressure of the quicksilver in the leg bc. By these means I was enabled to introduce the exact quantity I pleased of any kind of air into the tube m ; and, by the same means, I could let up any quantity of soap- lees, or any other liquor which I wanted to be in contact with the air. In one case however, in which I wanted to introduce air into the tube many times in the same experiment, I used the apparatus represented in fig. 6, con- sisting of a tube ab of a small bore, a ball c, and a tube de of a larger bore. This apparatus was first filled with quicksilver ; and then the ball c and the tube ab were filled with air, by introducing the end a under a glass inverted into water, which contained the proper kind of air, and drawing out the quicksilver from the leg ed by a syphon. After being thus furnished with air, the apparatus was weighed, and the end a introduced into one end of the tube m, and kept there during the experiment; the way of forcing air out of this apparatus into the tube being by thrusting down the tube ed a wooden cylinder of such a size as almost to fill up the whole bore, and by occasionally pouring quicksilver into the same tube, to supply the place of that pushed into the ball c. After the experi- ment was finished, the apparatus was weighed again, which showed exactly how much air had been forced into the tube m during the whole experiment ; it being equal in bulk to a qpantity of quicksilver, whose weight was equal to the increase of weight of the apparatus. The bore of the tube m used in most of the following experiments, was about -fLj. of an inch ; and the length of the column of air, occupying the upper part of the tube, was in general from l-i- to 4 of an inch. It is scarcely necessary to in- form any one used to electrical experiments, that in order to force an electrical spark through the tube, it was necessary, not to make a communication between the tube and the conductor, but to place an insulated ball at such a distance from the conductor as to receive a spark from it, and to make a communication be- tween that ball and the quicksilver in one of the glasses, while the quicksilver in the other glass communicated with the ground. I now proceed to the experi- ments. When the electric spark was made to pass through common air, included be- VOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. If tween short columns of a solution of litmus, the solution acquired a red colour, and the air was diminished, conformably to what was observed by Dr. Priestley. When lime-water was used, instead of the solution of litmus, and the spark was continued till the air could be no further diminished, not the least cloud could be perceived in the lime-water ; but the air was reduced to -§■ of its original bulk; which is a greater diminution than it could have suffered by mere phlogistication, as that is very little more than 4- of the whole. The experiment was next re- peated with some impure dephlogisticated air. The air was very much diminished, but without the least cloud being produced in the lime-water. Neither was any cloud produced when fixed air was let up to it ; but on the further addition of a little caustic volatile alkali, a brown sediment was immediately perceived. Hence we may conclude, that the lime-water was saturated by some acid formed during the operation ; as in this case it is evident that no earth could be preci- pitated by the fixed air alone, but that caustic volatile alkali, on being added, would absorb the fixed air, and thus becoming mild, would immediately precipi- tate the earth ; whereas, if the earth in the lime-water had not been saturated with an acid, it would have been precipitated by the fixed air. As to the brown co- lour of the sediment, it most likely proceeded from some of the quicksilver having been dissolved. It must be observed, that if any fixed air, as well as acid, had been generated in these two experiments with the lime-water, a cloud must have been at first perceived in it, though that cloud would afterwards disappear by the earth being re-dissolved by the acid ; for till the acid produced was sufficient to dissolve the whole of the earth, some of the remainder would be precipitated by the fixed air ; so that we may safely conclude, that no fixed air was generated in the operation. When the air is confined by soap-lees, the diminution proceeds rather faster than when it is confined by lime-water ; for which reason, as well as on account of their containing so much more alkaline matter in proportion to their bulk, soap-lees seemed better adapted for experiments designed to investigate the na- ture of this acid, than lime-water. I accordingly made some experiments to de- termine what degree of purity the air should be of, in order to be diminished most readily, and to the greatest degree; and I found that when good dephlogisti- cated air was used, the diminution was but small ; when perfectly phlogisticated air was used, no sensible diminution took place ; but when 5 parts of pure de- phlogisticated air were mixed with 3 parts of common air, almost the whole of the air was made to disappear. It must be considered, that common air consists of 1 part of dephlogisticated air, mixed with 4 of phlogisticated ; so that a mix- ture of 5 parts of pure dephlogisticated air, and 3 of common air, is the same thing as a mixture of 7 parts of dephlogisticated air with 3 of phlogisticated. VOL. XVI, D Ifif PHILOSOPHICAL TRANSACTIONS. [annO 1/85. Having made these previous trials, I introduced into the tube a little soap-lees, and then let up some dephlogisticated and common air, mixed in the above-men- tioned proportions, which rising to the top of the tube m, divided the soap-lees into its two legs. As fast as the air was diminished by the electric spark, I con- tinued adding more of the same kind, till no further diminution took place : after which a little pure dephlogisticated air, and after that a little common air, were added, in order to see whether the cessation of diminution was not owing to some imperfection in the proportion of the two kinds of air to each other ; but without effect.* The soap-lees being then poured out of the tube, and separated from the quicksilver, seemed to be perfectly neutralized, as they did not at all dis- colour paper tinged with the juice of blue flowers. Being evaporated to dryness, they left a small quantity of salt, which was evidently nitre, as appeared by the manner in which paper, impregnated with a solution of it, burned. For more satisfaction, I tried this experiment over again on a larger scale. About 5 times the former quantity of soap-lees were now let up into a tube of a larger bore; and a mixture of dephlogisticated and common air, in the same pro- portions as before, being introduced by the apparatus represented in fig. 6, the spark was continued till no more air could be made to disappear. The liquoi*, when poured out of the tube, smelled evidently of phlogisticated nitrous acid, and being evaporated to dryness, yielded 1^ gr. of salt, which is pretty exactly equal in weight to the nitre which that quantity of soap-lees would have afforded if saturated with nitrous acid. This salt was found, by the manner in which paper dipped into a solution of it burned, to be true nitre. It appeared, by the test of terra ponderosa salita, to contain not more vitriolic acid than the soap-lees them- selves contained, which was excessively little ; and there is no reason to think that any other acid entered into it, except the nitrous. A circumstance however occurred, which at first seemed to show that this salt contained some marine acid ; namely, an evident precipitation took place when a solution of silver was added to some of it dissolved in water ; though the soap-lees used in its formation were perfectly free from marine acid, and though, to pre- vent all danger of any precipitate being formed by an excess of alkali in it, some purified nitrous acid had been added to it, previous to the addition of the solution of silver. On consideration however I suspected that this precipitation might • From what follows it appears, that the reason why the air ceased to diminish was, that as the soap-lees were then become neutralized, no alkali remained to absorb the acid formed by the opera- tion, and in consequence scarce any air was turned into acid. The spark however was not continued long enough after the apparent cessation of diminution, to determine with certainty, whether it was only that the diminution went on remarkably slower than before, or that it was almost come to a stand, and could not have been carried much fiirther, though I had persisted in passing the sparks.— • Orig. VOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. IQ arise from the nitrous acid in it being phlogisticated ; and therefore I tried whether nitre, much phlogisticated, would precipitate silver from its solution. For this purpose I exposed some nitre to the fire, in an earthen retort, till it had yielded a good deal of dephlogisticated air ; and then, having dissolved it in water, and added to it some well purified spirit of nitre till it was sensibly acid, in order to be certain that the alkali did not predominate, I dropped into it some solution of silver, which immediately made a very copious precipitate. This solution how- ever being deprived of some of its phlogiston by evaporation to dryness, and ex- posure for a few weeks to the air. lost the property of precipitating silver from its solution ; a proof that this property depended only on its phlogistication, and not on its having absorbed sea-salt from the retort, or by any other means. Hence it is certain that nitre, when much phlogisticated, is capable of making a pre- cipitate with a solution of silver ; and therefore there is no reason to think that the precipitate, which our salt occasioned with a solution of silver, proceeded from any other cause than that of its being phlogisticated ; especially as it ap- peared by the smell, both on first taking it out of the tube, and on the addition of the spirit of nitre, previous to dropping in the solution of silver, that the acid in it was much phlogisticated. This property of phlogisticated nitre is worth the attention of chemists ; as otherwise they may sometimes be led into mistakes, in investigating the presence of marine acid by a solution of silver. In the above-mentioned paper I said, that when nitre is detonated with char- coal, the acid is converted into phlogisticated air; that is, into a substance which, as far as I could perceive, possesses all the properties of the phlogisticated air of our atmosphere ; from which I concluded, that phlogisticated air is nothing else than nitrous acid united to phlogiston. According to this conclusion, phlogisticated air ought to be reduced to nitrous acid by being deprived of its phlogiston. But as dephlogisticated air is only water deprived of phlogiston, it is plain, that adding dephlogisticated air to a body, is equivalent to depriving it of phlogiston, and adding water to it ; and therefore phlogisticated air ought also to be reduced to nitrous acid, by being made to unite to, or form a chemical combination with de- phlogisticated air ; only the acid formed this way will be more dilute, than if the phlogisticated air was simply deprived of phlogiston. This being premised, we rnay safely conclude, that in the present experiments the phlogisticated air was enabled, by means of the electrical spark, to unite to, or form a chemical combination with the dephlogisticated air, and was thus reduced to nitrous acid, which united to the soap-lees, and formed a solution of nitre; for in these experiments those two airs actually disappeared, and nitrous acid was actually formed in their stead; and as moreover it has also been just shown, from other circumstances, that phlogisticated air must form nitrous acid, D 2 20 PHILOSOPHICAL TKANSACTIONS. [aNNO 1785. when combined with dephlogisticated air, the above-mentioned opinion seems to be sufficiently established. A further confirmation of it is that, as far as I can perceive, no diminution of air is produced when the electric spark is passed either through pure dephlogisticated air, or through perfectly phlogisticated air; which indicates the necessity of a combination of these two airs to produce the acid. It was also found in the last experiment, that the quantity of nitre procured was the same that the soap-lees would have produced if saturated with nitrous acid; which shows that the production of the nitre was not owing to any decomposition of the soap-lees. It may be worth remarking, that whereas in the detonation of nitre with inflammable substances, the acid unites to phlogiston, and forms phlogisticated air, in these experiments the reverse of this process was carried on; namely, the phlogisticated air united to the dephlogisticated, which is equivalent to being deprived of its phlogiston, and was reduced to nitrous acid. In the above-mentioned paper I also gave my reasons for thinking that the small quantity of nitrous acid, produced by the explosion of dephlogisticated and inflammable air, proceeded from a portion of phlogisticated air mixed with the dephlogisticated, which I supposed was deprived of its phlogiston, and turned into nitrous acid, by the action of the dephlogisticated air on it, assisted by the heat of the explosion. This opinion, as must appear to every one, is confirmed in a remarkable manner by the foregoing experiments; as from them it is evident that dephlogisticated air is able to deprive phlogisticated air of its phlogiston, and reduce it into acid, when assisted by the electric spark; and therefore it is not extraordinary that it should do so when assisted by the heat of the explosion. The soap-lees used in the foregoing experiments were made from salt of tartar prepared without nitre; and were of such a strength as to yield -pL of their weight of nitre when saturated with nitrous acid. The dephlogisticated air also was prepared without nitre, that used in the first experiment with the soap-lees being procured from the black powder formed by the agitation of quicksilver mixed with lead,* and that used in the latter from turbith mineral. In the first experiment, the quantity of soap-lees used was 33 measures, each of which was equal in bulk to 1 grain of quicksilver; and that of the air absorbed was 4l6 such measures of phlogisticated air, and 9 14 of dephlogisticated. In the 2d experiment, 178 measures of soap-lees were used, and they absorbed 1920 of phlogisticated air, and 486o of dephlogisticated. It must be observed however, that in both experiments some air remained in the tube uncondensed, whose degree of purity I had no way of trying; so that the proportion of each species of air absorbed is not known with much exactness. As far as the experiments hitherto published extend, we scarcely know more of * This air was as pure as any that can be procured by most processes. I propose giving an account of the experiment, in which it was prepared, in a future paper.— Orig. VOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. 21 the nature of the phlogisticated part of onr atmosphere, than that it is not dimi- nished by lime-water, caustic alkalis, or nitrous air; that it is unfit to support fire, or maintain life in animals; and that its specific gravity is not much less than that of common air; so that, though the nitrous acid, by being united to phlogiston, is converted into air possessed of these properties, and consequently, though it was reasonable to suppose that part at least of the phlogisticated air of the atmosphere consists of this acid united to phlogiston, yet it might fairly be doubted whether the whole is of this kind, or whether there are not in reality many different substances confounded together by us under the name of phlo- gisticated air. I therefore made an experiment to determine, whether the whole of a given portion of the phlogisticated air of the atmosphere could be reduced to nitrous acid, or whether there was not a part of a different nature from the rest, which would refuse to undergo that change. The foregoing experiments indeed in some measure decided this point, as much the greatest part of the air let up into the tube lost its elasticity; yet, as some remained unabsorbed, it did not appear for certain whether that was of the same nature as the rest or not. For this purpose I diminished a similar mixture of dephlogisticated and common air, in the same manner as before, till it was reduced to a small part of its ori- ginal bulk. I then, in order to decompound as much as I could of the phlo- gisticated air which remained in the tube, added some dephlogisticated air to it, and continued the spark till no further diminution took place. Having by these means condensed as much as I could of the phlogisticated air, I let up some solu- tion of liver of sulphur to absorb the dephlogisticated air; after which only a small bubbl of air remained unabsorbed, which certainly was not more than T-l-5- of the bulk of the phlogisticated air let up into the tube; so that if there is any part of the phlogisticated air of our atmosphere which differs from the rest, and cannot be reduced to nitrous acid, we may safely conclude, that it is not more than -^-1-^- part of the whole. The foregoing experiments show that the chief cause of the diminution which common air, or a mixture of common and dephlogisticated air, suffers by the electric spark, is the conversion of the air into nitrous acid; but yet it seemed not unlikely, that when any liquor, containing inflammable matter, was in con- tact with the air in the tube, some of this matter might be burnt by the spark, and thereby diminish the air, as I supposed in the above-mentioned paper to be the case. The best way which occurred to me of discovering whether this hap- pened or not, was to pass the spark through dephlogisticated air, included be- tween different liquors; for then, if the diminution proceeded solely from the conversion of air into nitrous acid, it is plain that, when the dephlogisticated air was perfectly pure, no diminution would take place; but when it contained any phlogisticated air, all this phlogisticated air, joined to as much of the deplilogis- 22 PHILOSOPHICAL TRANSACTIONS. [aNNO 1785. ticated air as must unite to it in order to reduce it into acid, that is, 2 or 3 times its bulk, would disappear, and no more; so that the whole diminution could not exceed 3 or 4 times the bulk, of the phlogisticated air: whereas, if the diminu- tion proceeded from the burning of the inflammable matter, the purer the de- phlogisticated air was, the greater and quicker would be the diminution. The result of the experiments was, that when dephlogisticated air, containing only ^V o( its bulk of phlogisticated air, that being the purest air I then had, was confined between short columns of soap-lees, and the spark passed through it till no further diminution could be perceived, the air lost -5V0 of its bulk; which is not a greater diminution than might very likely proceed from the first-men-» tioned cause; as the dephlogisticated air might easily be mixed with a little com- mon air while introducing into the tube. When the same dephlogisticated air was confined between columns of distilled water, the diminution was rather greater than before, and a white powder was formed on the surface of the quicksilver beneath ; the reason of which probably was, that the acid produced in the operation corroded the quicksilver, and formed the white powder; and that the nitrous air, produced by that corrosion, united to the dephlogisticated air, and caused a greater diminution than would other- wise have taken place. When a solution of litmus was used, instead of distilled water, the solution soon acquired a red colour, which became paler and paler as the spark was continued, till at last it was quite colourless and transparent. The air was diminished by almost half, and I believe might have been still further diminished had the spark been continued. When lime-water was let up into the tube, a cloud was formed, and the air was further diminished by about -f. The remaining air was good dephlogisticated air. In this experiment therefore the litmus was, if not burnt, at least decompounded, so as to lose entirely its purple colour, and to yield fixed air; so that, though soap-lees cannot be decompounded by this process, yet the solution of litmus can, and so very likely might the so- lutions of many other combustible substances. But there is nothing, in any of these experiments, which favours the opinion of the air being at all diminished by means of phlogiston communicated to it by the electric spark. XXIV. Account of the Measurement of a Base on Hounslow-heath. By Major General William Roy^ F. R. S., and A. S. p. 385. The rise and progress of the rebellion which broke out in the Highlands of Scotland in 1745, gave occasion to commence government surveys in that part of the island. These were conducted by Lieut. Gen. Watson, a military engi- neer, and chiefly under him executed by our author, then a subaltern officer in the same corps. Though this work, which is still in manuscript, says Gen. R., and in an unfinished state, possesses considerable merit, and perfectly answered VOL. LXXV.] * PHILOSOPHICAL TKANSACTIONS. 23 r the purpose for which it was originally intended; yet having been carried on with instruments of the common, or even inferior kind, and the sum annually allowed for it being inadequate to the execution of so great a design in the best manner, it is rather to be considered as a magnificent military sketch, than a very accu- rate map of a country. It would however have been completed, and doubtless many of its imperfections remedied; but the breaking out of the war of 1755 prevented both, by furnishing service of other kinds for those who had been employed on it. On the conclusion of the peaee of 1763, it came for the first time under the consideration of government, to make a general survey of the whole island at the public cost. Towards the execution of this work, the direc- tion of which was to have been committed to our author, the map of Scotland was to have been made subservient, by extending the great triangles quite to the northern extremity of the island, and filling them in from the original map. Thus that imperfect work would have been effectually completed, and the nation would have reaped the benefit of what had been already done, at a very mode- rate extra-expence. Certain causes however prevented any progress being made in the work for 12 years longer, previous to the nation's being unfortunately involved in the Ame- rican war;' it was therefore obvious that peace must be once more restored before any new effort could be made for that purpose. The peace of 1783 being con- cluded, and official business having detained Gen. R. in or near town during the whole of that summer, he embraced the opportunity, for his own private amuse- ment, to measure a base of 7744.3 feet, across the fields between the Jew's Harp, near Marybone, and Black-lane, near Pancras; as a foundation for a series of triangles, carried on at the same time, for determining the relative situations of the most remarkable steeples, and other places, in and about the capital, with regard to each other, and the Royal Observatory at Greenwich. The principal object he had here in view (besides that it might possibly serve as a hint to the public, for the revival of the now almost forgotten scheme of 17^3) was, to faci- litate the comparison of the observations, made by the lovers of astronomy, within the limits of the projected survey; namely, Richmond and Harrow on the west; and Shooter's-hill and Wansted on the east; when very unexpectedly he found that an operation of the same nature, but much more important in its object, was really in agitation. In the beginning of October, 1783, Comte D'Adhemar, the French ambas- sador, transmitted to Mr. Fox, then one of his Majesty's principal secretaries of state, a memoir of M. Cassini de Thury, in which he set forth the great advan- tage that would accrue to astronomy, by carrying a series of triangles from the neighbourhood of London to Dover, there to be connected with those already executed in France, by which combined operations the relative situations of the 24 PHILOSOPHICAL TRANSACTIONS. * [aNNO 1785. two most fiimous observatories in Europe, Greenwicli and Paris, would be more accurately ascertained than they are at present. The execution of this business was confided to the care and diligence of Gen. R., which naturally divides into 2 parts. First, the choice and measurement of the base, with every possible care and attention, as the foundation of the work; 2dly, the disposition of the triangles, by which the base is to be connected with such parts of the coast of this island as are nearest to the coast of France, and the determination of their angles, by means of the best instrument that can be obtained for the purpose, from which the result or conclusion will be drawn. With regard to the first of these, the choice of the base, it is observed, that Hounslow-heath having always appeared to be one of the most eligible situations for any general purpose of the sort now under consideration, because of its vici- nity to the capital and Royal Observatory at Greenwich, its great extent, and the extraordinary levelness of its surface, without any local obstructions whatever to render the measurement difficult; being likewise commodiously situated for any future operations of a similar nature; accordingly a particular inspection of the heath was made, to assign and trace out a proper position for the purpose. Gen. R. then minutely describes the clearing of the ground, and the construc- tion of the steel chain and other instruments employed in the measurement of the base, which must be performed with the utmost care. After the description of the chain, which consisted of 100 links of 1 foot each, the measuring rods are next described. The bases which had hitherto been measured in different countries, with the greatest appearance of care and exact- ness, had all, or for the most part, been done with deal rods of one kind or other, whose lengths being originally ascertained by means of some metal standard, were, in the subsequent applications of them, corrected by the same standard. Having thus had so many precedents, serving as examples to guide them in their choice, it was natural enough that they should pursue the same method in the measurement to be executed on Hounslow-heath; taking however all imaginable care, that the rods should be made of the very best materials that could be pro- cured; with this further precaution, that by trussing them, they should be ren- dered perfectly inflexible, a circumstance not before attended to. Three mea- suring rods were accordingly ordered to be made, and also a standard rod, with which the former were from time to time to be compared. Their stems were each 20 feet 3 inches in length, reckoning from the extremities of the bell-metal tippings; very near 2 inches deep; and about ]-l inch broad. Being trussed laterally and vertically, they were thus rendered perfectly, or at least as to sense, inflexible. Next follows a description of the brass standard scales employed in setting oflf the length of the deal rods. At the sale of the instruments of the late inge- VOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. 25 nioLis optician Mr. James Short, Gen. R. purchased a finely divided brass scale, of the length of 42 inches, with a Vernier's division of 1 00 at one end, and one of 50 at the other, by which the 1000th part of an inch is very perceptible. It was originally the property of the late Mr. Graham, the celebrated watch-maker; has 'the name of Jonathan Sisson engraved on it; but is known to have been divided by the late Mr. Bird, who then worked with Sisson. The brass standard scale of the r. s. about 42 inches long, which contains on it the length of the standard yard from the Tower, that from the Exchequer, and also the French half-toise, together with the duplicate of the said scale, sent to Paris for the use of the Royal Academy of Sciences, were both made by Mr. Jonathan Sisson, under Mr. Graham's immediate direction. Now, though there seemed to be every reason to suppose that the scale above-mentioned, originally Mr, Graham's property, would correspond with those above-mentioned, which he had been directed by the r. s., with so much care and pains, to provide; yet, that nothing of this sort might remain doubtful, it was judged right, that the two scales should be actually compared. Accordingly the extent of 3 feet, being carefully taken from the Society's standard, and applied to Gen. R.'s scale, it was found to reach exactly to 36 inches, the temperature being 65°. In like manner, the beam compasses being applied to the length of the Exchequer yard, the extent was now found by the micrometer to over-reach that yard by t^Vo-o-j or nearly j^7__ parts of an inch. Having thus shown that his scale was accurately of the same length with the Society's standard, he next points out the use that was made of it, for ascertaining the lengths of the deal rods intended for the opera- tion on Hounslow-heath; which was, by the assistance of Mr. Ramsden, to measure and set off the true length of those rods. Other preparatory matters are then described, such as, the stands for the measuring rods, the boning tele- scope and rods, the cup and tripod for preserving the point measured to during each night, marks for terminating in a permanent manner the extremities of the base, clearing the ground, &c. Next, about the middle of June 1784, we enter on the sought measurement of the base with the chain, and determination of the relative heights of the sta- tions by means of the telescopic spirit level, a business which was completed the 22d of the same month, extending from the south-east extremity near Hampton Poor-house, to the north-west extremity near the Magpye public-house at King's Arbour. This measurement gave IQ hypothenusal distances of 6oo feet each, and one of 404.55, making in the whole 11804.55 feet, the mean temperature being 62^°. Now, when the length of the chain, in its original state, was ascertained by the dots on the brass pins in the New-England plank, it was found, in the then temperature of 74°, to exceed the 100 feet by near -j- of an inch, or 0.245 inch. Therefore in the temperature of 63°, being that in which the lengths of VOL. XVI. E 26 PHILOSOPHICAL TKANSACTIONS. [aNNO 1785. the deal rods were laid off, and differing very little from what was likewise the mean heat of the air, when applied on the heath, the chain, according to the experiments on the expansion of the very same steel, would exceed the 100 feet by 0.161 inch, or 0.0134 foot. Hence the sum of the 3 sections of the base, 274 chains, being multiplied by 0.0134 foot, we shall have 3.67 feet for the equation of the chain, +4.55 feet, to be added to its length, which will then become 27408.22 feet from the centre of one pipe to the centre of the other: and this would have been the true length of the base, as given by the rough measurement with the chain, if the surface had been one uniform inclined plane throughout its whole extent. But though the ascent of Houn slow-heath is so small, and so gradual, as to occasion little more than half an inch of reduction, from the 46 hypothenusal to the 46 base distances, into which it is divided; yet each of these hypothenuses containing again many other small irregularities, all of which affect the measurement by the chain, in proportion to their number and height, in every space of 60O feet, their united effects, including the lateral deviations from the true line in measuring, do somewhat more than compensate for the extra-length of the chain, as will be seen hereafter in comparing the length of the base just now obtained with that given by the rods. Next succeeds the measurement of the base with the deal rods, which amounts to 27404.31 feet, being the total length as given by these rods, without regard to expansion and reduction of the hypothenusal lines, the former of which was found to be very frequent and considerable, from the various degrees of moisture, contrary to what had heretofore been thought to be the case. By examining tlie numerous observations on this head, it appears that the total expansion on the 1370 deal rods, including the small equation for the lengthening of the standard, amounts to 24.223 inches, or 2.02 feet; which being added to the apparent length of the base 27404.31 feet formerly obtained, we have, for the hypothe- nusal length, 27406.33 feet: and from this deducting O.07 foot, the excess of the hypothenusal above the base line, there remains 27406.26 for the distance given, by the deal rods, between the centres of the pipes terminating the base, reduced to the level of the lowest, or that at Hampton Poor-house, in the tem- perature of 63°, being that of the brass scale when the lengths of the deal rods were laid off. All this however supposes 3 things to be absolutely certain: 1st, that the expansion of the rods has been accurately estimated ; 2dly, that no error has arisen from the butting of the rods against each other, in order to bring them into contact; and, 3dly, that no mistake of any kind has been committed in the execution. When we come to give the true length of the base, as ulti- mately ascertained by means of the glass rods, it will appear, that one or more of these 3 have actually taken place; though it is most probable, that only the first 2 sources of error have contributed their share to the total difference between VOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. 27 the two results. It is further remarked, that the last week of July was so wet as to occasion a total suspension of the operations on Hounslow-heath. On the 26th of that month, at 8^ a. m. the temperature being then 63°, the rods were compared with the standard, and found to exceed it, at a medium, -^V part of an inch. Now, if we suppose the whole base to have been measured with the rods in that state, the difference would have amounted to more than 7-|- feet, exclusive of what the standard itself might have altered from its original length. Another comparison was made at Spring-grove, in the beginning of September, by which it was found that the dew imbibed only in one night, or a space of time not exceeding 14 hours, occasioned such an expansion in the deal rods, as in the whole base would have amounted to 45.484 inches. It is sufficiently ob- vious, that this last mentioned experiment was more accurate, in the proportion of about 1 5 to 1 , than any comparison we could at that time have made with the standard. But since immediately after it was finished, the sun shone out very bright, it is by no means certain how soon the rods would again have contracted to their former length, or near it, had they been exposed to his rays. Repeated comparisons for ascertaining facts of this sort, at very short interims, are abso- lutely incompatible with the nature of such tedious and troublesome operations as the measurement of long bases; and here indeed lies the great objection to the use of deal rods, that at no time can we be certain how soon, after a compa- rison has been made, they may alter their length in a proportion, and sometimes too even in a sense, different from what was expected. We then arrive at the description of the glass rods, or rather tubes, ultimately- used to determine the length of the base. These were finally resorted to, as less heavy and variable in their length, than metal rods, and not at all varying by humour like the deal rods. Notwithstanding their great length, above 20 feet, and weighing about 6l lbs. each, they were found to be so straight that, when laid on a table, the eye, placed at one end looking through them, could see any small object in the axis of the bore at the other end. After a minute description of the manner of preparing and fitting up these rods, we next arrive at their application in the actual measurement of the base line. This was com- menced on the 18th of August, both with the steel chain and the glass rods, for a mutual comparison and check on each other. In this manner they pro- ceeded, and in the course of the day were only able to measure the length of 10 chains, or 1000 feet. Being arrived at this point it was found, that the fine line on the brass slide, marking the extremity of the 10th chain, fell short of another fine line on the same slide, denoting the end of the 50th glass rod, just -^ of an inch. Now it appears by the experiments with the pyrometer, what the real contractions of the chain and glass rods were, for the degrees of difference of b2 28 PHILOSOPHICAL TRANSACTIONS. [aNNO 1785. temperature ♦ below that in which their respective lengths were laid off, that this small apparent difference of -V of an inch, between the two modes of mea- suring the 1000 feet, should have been 0.17938 inches, to have made the two results exactly agree, which is a real difference of only O.O2062 of an inch. Supposing then every 1 000 feet of the base to have been measured by the chain with the same attention, and consequently with the same, or nearly the same success, we shall have 27.404 X O.02062 in. = 0.565 in. or a defect of some- thing more than half an inch only on the whole length of the base. So nice an agreement between two results, with instruments so very dif- ferent, could not fail to be considered as astonishing; and as it rarely happens, that the graduation of thermometers will so nearly correspond with each other, as not to occasion a much greater error, all were very desirous that it could have been further confirmed by continuing the operation in the same way through a more considerable proportion of the whole length. But besides the tedious na- ture of the double measurement, owing to the multiplicity of stands, platforms, coffers, and other articles, that were now successively to be moved forward ; the operation had already trained out to a much more considerable length than had been expected; the summer was now far advanced, and the continuance of good weather uncertain ; in short, all these reasons contributed to induce them to give up, for the present, any further experiment with the chain, and to proceed with the glass rods alone in the completion of the measurement. Accordingly, on Aug. 19, the operation with the glass rods was continued for the other hypo- thenuses, and thus continued from day to day till the 30th of the same month, when the measurement was finally completed; when the extremity of the 1370th rod over-shot the centre of the pipe terminating the base towards the south-east by 17.875 inches, or I.49 foot. Hence, when the several equations for expan- sions are respectively taken into the account, we find, that the alteration of the * When the length of the chain was laid off, the heat was 66^°, and that of the glass rods 68°. They will therefore only agree with each other accurately in these respective temperatures. The mean of 20 thermometers for the 4 chain lengths of the 46'th hypothenuse gave a heat of 6l°.6; and for the 6 chain lengths of the 45th, the mean of 30 thermometers gave 59°.75. The temperature ■ of the 400 feet of glass by the mean of 40 thermometers was 6"5°.3 ; and of the 60O feet, by the mean of 60 thermo meter s, it was 6o°.8. Now, from these data, and the expansions of steel and glass, as determined by the pyrometer, the computation will stand as follows : ° ° ° In. In. In. o, , f 400 66.5 - 61.6 = 4.9 X 0.03052 = 0.14955 1 _ ^ ..^.fy f contract, of bteei I 600 ... . 66.5 — 59-75 = 6.75 x 0.04578 = O.30901 J — ^-^^^^^ \ looo feet. , f 400 68.0 - 65.3 = 2.7 X 0.02068 = 0.05.584 \ _ ^ n^ois / contract, of Uiass -^ gQQ gg Q _ gQ g _ ^2 X 0.03102 = 0.22334 J ~ ".^/yi» "[ j^qq f^^^ The 1000 feet of steel should have contiatced more than the 1000 feet 1 _ ^ , -^qq of glass / - ^-^7938 But tlie difference was found to be = 0.20000 Therefore the error of the chain in defect was 0.02062 X 27.404 =s 0.565 in. or little more than half an inch on the whole base. — Orig. rOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. ^Q deal rods from the humidity of the air, which, by comparison with the standard," was apparently most considerable in the 1st and 2d sections of the base, has now wholly vanished; that is to say, the total amount of it has been over-rated by 20.964 inches. After this follows a description of the microscopic pyrometer, invented by Mr. Kamsden, and employed for determining by experiment the expansion of the chief instruments concerned in the measurement of the base, viz. the standard scale, the steel chain, and the glass rods, with experiments on the same. After which the ultimate determination of the length of the base^ by bringing to ac- count the several particulars, is given as follows: feet. The hypothenusal length of the base, as measured by 1 369 .925521 glass rods of 20 feet each + 4.31 feet, being the distance between the last rod and the centre of the north-west pipe, was 27402.8204 The reduction of the hypothenuses to the horizontals O.0714 Hence the apparent length of the base, reduced to the level of the south-east extremity, becomes 27402. 749O The apparent length is to be augmented by the excess of the ex- pansion above the contraction of the glass rods, = 4.1 867 inches, reduced to the heat of 62°, as has been usually done in former ope- rations of this nature 0.3489 The apparent length is further to be augmented by the equation for 6° difference of temperature of the standard brass scale * between 62" and 68", this last being the heat in which the lengths of the glass rods were laid off = 20.3352 inches, as deduced from the expe- riments with the pyrometer *1.6946 Hence we have the correct length of the base in the temperature of 62^ reduced to the level of the lowermost extremity near Hamp- ton Poor-house 27404.7925 This last length requires yet a small reduction for the height of this lowermost end above the mean level of the sea, supposed to be 54 feet, or 9 fathoms O.0706 • There occurs a small oversight in this article, as was remarked in the Philos. Trans, of 1795, be- ing an account of another measurement of the same base by Col. Williams, Capt. Mudge, and Mr. Dalby. By which it appears that the equation for 6° difference of temperature above-mentioned, should consist of the difference between the numbers for brass and glass, and not of that for brass alone j that is, it should be 6° x (3.38938 — 1.41058) = 11.8368 inches = .9864 feet, instead of 1.6946 above employed, which made the base come out too much by 0.7082. This being deducted from 27404.7219 the ultimate number above found, leaves 27404.0843, for what should be Gen. Roy's length of the base as measured with the glass rodsj being only about 2| inches less than it waa made by the other measures. so PHILOSOPHICAL TRANSACTIONS. [anno 1766, Hence the true or ultimate length of the base, reduced to the level of the sea, and making a portion of the mean circumference of the earth, becomes 27404.7219 XXF. Abstract of a Register of the Barometer, Thermometer, and Rain, at Lyndon, in Rutland, 1784. By Thomas Barker, Esq. Also of the Rain at South Lambeth, Surrey; and at Selbourn and Fyfeld, Hampshire, p. 481. Barometer • Thermometer. Rain. In the House. Abroad. Lyndon, S. Lamb.lSelbourn Highest Lowest. Mean. Hig. Low iMean Hig. Low Mean Surry, Hamp. Fyfield. Inches. laches. I aches. 0 0 0 0 0 0 Inch. Inih. Inch. Incb, Jan. Mom. Aftern. 29.96 28.49 29.34 40^ 42I 28 29 33h 34 40 48^ 15^ 24| 27 32| 1.877 2.54 3.18 2.44 Feb. Mom. : Aftern. 30.00 28.50 29.23 47 47* 30 31 36 37 45 52h 9 23 29 36 1.225 1.49 0.77 1. 7 Mar. Morn. Aftern. 29.63 28.59 29.23 471 48i 36 36 39h 40i 45 52 21 38^ 32i 40i 1.096 2.63 3.82 2.24 Apr. Mom. Aftern. 29.74 28.44 29.26 50| 53 35| 36 43| 45 51 60* 29 35 38| 48 1.741 2.56 3.92 2.10 May Morn. Aftern. 29.92 29.17 29.62 661 69^ 47 48 57h 59^ 63 78 41 48^ 52 65- 2,890 1.36 1.52 i.5r June Morn. Aftern. 29.92 ' 28,98 29.43 62 63^ 55^ 56^ 58 6H 71 48 53 54 63^ 3.810 3.45 3.65 2.45 July Mom. Aftern. 29.85 28.74 29.48 69 72 56 57 61 63 66 79k 51 57^ 56 67 5.080 2.26 2.40 2.80 Aug. Morn. Aftern. 29.92 29.04 29.56 65 67 54 55 59 60 60i 7H 42| 51 52 63 2,814 2.84 3.88 2.79 Sept. Morn. Aftem. 29.90 29.01 29.55 66^ 7n 53 54 61 63 57 73i 39 51* 54 64 1,740 1.65 2.51 2. 7 Oct. Mom. Aftern. 30.00 28.98 29.62 521 53 1 42 43 48| 49* 45 55h 27i 40 39h 49 0.223 0.83 0.39 0.17 Nov. Mom. Aftem. 29.85 28.75 29.38 51 51 39k 41 45 45J 5ih 23^ 53 33| 38 44 2,376 1 5.60 4.70 3.14 Dec. Morn. Aftem. 29.75 28.15 29.26 43^ 43 3\h 32| 36i 371 41 13| 46i 19 29 32i 2.335 3.06 1.72 Mean of « dl 29.41 49 46 27.207 27.21 33.80 24.56 END OP VOL. SEVENTY-FIVE OP THE ORIGINAL. /. Observations on the Graduation of Astronomical Instruments; with an Expla- nation of the Method invented by the late Mr. Henry Hindley, of York, Clock- maker, to divide Circles into any given Number of Parts. By Mr. John Smeaton, F.R,S. Anno 1786, FoL LXXFL p. 1. Perhaps no part of the science of mechanics has been cultivated by the inge- nious with more assiduity, or more deservedly so, than the art of dividing circles for the purpose of astronomy and navigation. It is said, that Tycho Brahe and Hevelius laboured this part of their instruments with their own hands. Dr. VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 31 Hook, in his animadversions on the Machina Coelestis of Hevelius, published in the year 1 674, has given an elaborate description of a quadrant, whose divisions were formed, and afterwards read off, by means of an endless screw, working on the outermost border of the limb of a quadrant ; which, he says, " does not at all depend on the care and diligence of the instrument-maker, in dividing, graving, or numbering the divisions, for the same screw makes it from end to end ;" yet he has given us no account of any particular care or caution that he used, in preventing the same screw from making larger or smaller paces, in consequence of unequal resistance, from a different hardness of the metal in different parts of the limb ; nor any method of correcting or check- ing the same ; nor of making a screw, the angle of whose threads with the axis shall be equal in every part of the circumference ; therefore the whole of this business (in which accurate mechanists well know consists the whole of the dif- * ficulty) he refers to the ingenious workman ; and in particular to the then cele- brated Mr. Tompion, who he says was employed by him to make his instru- ment, and who had thereby " seen and experienced the difficulties that do occur therein :" but was any ingenious workman now to pursue the directions of Dr. Hook, so far as his communication extends, we may conclude that he would make a very inaccurate piece of work, far inferior in performance to what the doctor seems to expect from it. But yet I believe it was the first attempt to apply the endless screw and wheel, or arch, to the purpose of forming divisions for astronomical instruments ; for the doctor says himself that the perfection of this instrument is the way of making the divisions ; that it " excels ail the common ways of division :" and in the table of contents it is entitled, " An Explication of the new Way of dividing." This method however, of Dr. Hook's, was not laid aside without a very full and sufficient trial : for Mr. Flamsteed, in the Prolegomena of the 3d volume of Historia Coelestis, informs us, that he contrived the sextant, with which his observations were chiefly made, from his entrance into the Royal Observatory in the year 1676, to the year 1689. This sextant was first made of wood, and afterwards of iron, with a brass limb of 2 inches broad, by Mr. Tompion, at the expense of Sir Jonas Moore ; its radius was 6 feet QJ- inches ; it was fu,r- nished with an endless screw on its limb of 17 threads in an inch, and with telescopic sights. Of this instrument Mr. Flamsteed gives the figure at the latter end of his Prolegomena before-mentioned, sufficiently large to see the general design ; the whole being mounted on a strong polar axis of iron, of 3 inches diameter. Though, in the full description of this instrument, Mr. Flamsteed men- tioned the limb's being furnished with diagonal divisions, distinguishing the arch to 10 seconds ; yet it is pretty clear, that it had not these originally on it; but 32 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. that the dependance was wholly on the screw divisions, when it came out of Mr. Tompion's hands. This one may reasonably infer from the observations them- selves ; for the first observation, set down as taken with this instrument, being on the 29th of October, 1676, it was not till the llth of September, 1677, that the column which contained the check angle by diagonal lines was filled up ; and there was also a space of time, antecedent to that last-mentioned, wherein no observations are recorded as taken with this instrument, in which time the diagonal divisions might be put on ; and this will be put beyond a doubt, as he says expressly, that finding, in the year \677i that the threads of the screw had worn the border of the limb, he divided the limb into degrees himself, and drew a set of diagonal divisions ; and then comparing the two sets of divisions toge- ther, he sometimes found them to differ a whole minute ; therefore, for correc- * tion thereof, he constructed a new table for converting the revolutions and parts of the screw into degrees, minutes, and seconds ; and which he applied in the observations taken in 1678. However, notwithstanding this correction, in looking over the observations noted down as deduced each way, I often find a difference of half a minute ; not unfrequently AO" ; but in an observation of the moon, of the Qth June, 1687, I find a difference of 55^'', which on a radius of 6 feet 9 inches amounts to more than -^V part of an inch. In the year 1689, Mr. Flamsteed completed his mural arc at Greenwich ; and ■ in the Prolegomena before mentioned, he makes an ample acknowledgement of the particular assistance, care, and industry of Mr. Abraham Sharp ; whom, in the month of August, 1688, he brought into the observatory, as his amanuensis; and being, as Mr. Flamsteed tells us, not only a very skilful mathematician, but exceedingly expert in mechanical operations, he was principally employed in the construction of the mural arc ; which in the compass of 14 months he finished, so greatly to the satisfaction of Mr. Flamsteed, that he speaks of him in the highest terms of praise. This celebrated instrument, of which he also gives the figure at the end of the Prolegomena, was of the radius of 6 feet 74- inches ; and, in like manner as the sextant was furnished both with screw and diagonal divisions, all performed by the accurate hand of Mr. Sharp. But yet, whoever • compares the different parts of the table for conversion of the revolutions and parts of the screw belonging to the mural arc into degrees, minutes, and seconds, with each other, at the same distance from the zenith on different sides ; and with their halves, quarters, &c. will find as notable a disagreement of the screw- work from the hand-divisions, as had appeared before in the work of Mr. Tom- pion : and hence we may conclude, that the method of Dr. Hook, being exe- cuted by two such masterly hands as Tompion and Sharp, and found defective, is in reality not to be depended on in nice matters. From the account of Mr. Flamsteed it appears also, that Mr. Sharp obtained the zenith point of the in- VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 33 strument, or line of collimation, by observation of the zenith stars, with the face of the instrument on the east and on the west side of the wall : and that having made the index stronger (to prevent flexure) than that of the sextant, and thereby heavier, he contrived, by means of pullies and balancing weights, to re- lieve the hand that was to move it from a great part of its gravity. I have been the more particular relating to Mr. Sharp, in the business of nstructing this mural arc ; not only because we may suppose it the first good and valid instrument of the kind, but because I consider Mr. Sharp as the first person who cut accurate and delicate divisions on astronomical instruments ; of which, independent of Mr. Flamsteed's testimony, there still remain considerable proofs : for, after leaving Mr. Flamsteed, and quitting the department above- mentioned ; * he retired into Yorkshire, to the village of Little Horton, near Bradford, where he ended his days about the year 1743 ; and where I have seen not only a large and very fine collection of mechanical tools (the principal ones being made with his own hands,) but also a great variety of scales and in- struments made with them, both in wood and brass, the divisions of which were so exquisite, as would not discredit the first artists of the present times : and I believe there is now remaining a quadrant, of 4 or 5 feet radius, framed of wood, but the limb covered with a brass plate ; the subdivisions being done by diagonals, the lines of which are as finely cut as those on the quadrants at Greenwich. The delicacy of Mr. Sharp's hand will indeed permanently appear from the copper-plates in a quarto book, published in the year 17 18, intitled, " Greometry improved by A. Sharp, Philomath," of which not only the geo- metrical lines on the plates, but the whole of the engraving of letters and figures, were done by himself, as I was told by a person in the mathematical line, who very frequently attended Mr. Sharp in the latter part of his life. I therefore consider Mr. Sharp as the first person that brought the affair of hand division to any degree of perfection. Some time about the establishment of the mural arc at Greenwich, the cele- brated Danish astronomer Olaus Roemer began his domestic Observatory, which he finished in the year 1715, as we are informed by his historian Peter Horre- bow, in the 3d volume of his works, in the tract, intitled, Basis Astronomige, published in the year 1741. In this tract is the description of an instrument which not only answered the purpose of the meridian arc ; but, its telescope being mounted on a long axis, became also in reality what we now call a Tran- sit Instrument ; and which furnished, so far as I have been able to learn, the first idea of it. One end of the axis of this instrument being the centre of the * Mr. Sharp continued in strict correspondence with Mr. Flamsteed so long as he lived, as ap- peared by letters of Mr. Flarasteed's found after Mr. Sharp's death ; many of which I have seen. — Orig. VOL. X.VI. F 34 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. meridian arc, and carrying its index, M. Roemer thus avoided the errors arising from the plane of the mural arc not being accurately a vertical plane ; and which Mr. Flamsteed endeavoured to check, by observing the passage of known stars nearly in the same parallel of declination ; that is, passing nearly over the same part of the plane of the arc ; by which he was enabled to correct or check the errors of the arc in right ascension. But it is the peculiar method in which Roemer divided his instruments, that occasions him here to be introduced. Though it is a very simple problem by which geometricians teach how to divide a given right line into any number of parts required ; yet it is still a much more simple thing to set off on a given right line, from a point given, any number of equal parts required, where the total length is not exactly limited ; for this amounts to nothing more than assuming a convenient opening of the com- passes, and beginning at the point given, to set off the opening of the com- passes as many times in succession, as there are equal parts required ; which process is as applicable to the arch of a circle as it is to a right line. Of this simple principle Roemer endeavoured to avail himself. For this purpose he took 2 stiff, but very fine-pointed pieces of steel, and fixed them together, so as to avoid, as much as possible, every degree of spring that would necessarily attend long-legged compasses, or even those of the shortest and stifFest kind when the points are brought near together. The distance of the points that he chose was about the ^ or -fV of an inch. This, on a radius of 2i- or 3 feet, would be about 10 minutes. With this opening, beginning at the point given, he set off equal spaces in succession to the end of his arch, which was about 75*^. Those were distinguished on the limb of the instrument by very fine points, which were referred to by a grosser division, the whole being properly numbered. The sub- division of those arches of 10 minutes each was performed by a double micros- cope, carried on the arm or radius of the instrument, the common focus being furnished with parallel threads of single silk, of which ] I being disposed at 10 equal intervals, comprehending together one lO' division, the distance of the nearest threads became a very visible space, answerable to 1 ' each, and therefore capable of a much further subdivision by estimation. The divisions of this instrument were therefore, properly speaking, not degrees and minutes ; but yet, if exactly equal, would serve the purpose as well, when their true value was found, which was done by comparison with larger instruments. Now, if it be considered, that in going step by step of lO' each, through a space of 75° there will be a succession of 450 divisions, dependant on each other ; if it be also considered, that the least degree of extuberance in the sur- face of the metal, where each new point is set down, or the least hard particle (with which all the base metals seem to abound) will cause a deviation in the first impression of a taper point, and so produce an inequality in the division ; it VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 35 is evident that though this inequality may be very small, and even imperceptible between neighbouring divisions, yet among distant ones, it may and will arise to something considerable , which, in the mensuration of angles, will have the same ill tendency as near ones. Now, as M. Roemer has given no means of checking the distant divisions, in respect of each other, it is very probable that no one has followed his steps, in cases where great accuracy was required, in a considerable number of divisions. For in reality this method is likely to fall far short of Dr. Hook's ; as Dr. Hook's divisions being cut in a similar successive manner, by the rotation of the sharp edge of the threads of a screw against the exterior edge of the limb of the instrument, a very slight degree of pressure will bring a fine screw of 30 threads in an inch, which he prescribes, to touch against an arch whose radius is 4 or 5 feet in more than 1, 2, 3, or 4 threads at once ; so that the threads supporting each other, a small extuberance, or even a small hard particle in the metal, will be cut through or removed by the grinding or rather sawing motion of the screw ; and which, in regard to its contact, being in reality an edge, will be much more effectual, that is, more firm, in its reten- tion, than a mere simple point : and a repetition of the operation, from the support of the threads to each other, will tend to mend the first traces ; whereas, in Roemer's way, a repetition will make them worse ; for whatever drove forward or backward the point on first entering, will, from the sloping of the point, be confirmed and increased in driving it deeper. When Dr. Halley was chosen Astronomer Royal, Mr. Flamsteed's instru- ments being taken away by his executors, Mr. Graham undertook to make a new mural quadrant, about the year 1725; who, uniting all that appeared valuable in the different methods of his predecessors, executed it with a degree of contrivance, accuracy, and precision, before unknown : and he performed the division with his own hand. The model of this quadrant, for strength, easy management, and convenience, has been ever since pursued as the most perfect. What I apprehend to be peculiar in it, was the application of the arch of qQ° ; not only as a check on the arc of degrees and minutes, but as superior to it, being derived from the more simple principle of continual bisection. To make room for this, he has entirely rejected the subdivision by diagonals, and has adopted the method of the vernier ; but the subdivision of the vernier divi- sions he, as I apprehend for the first time, measured by the turns of the detached adjusting screw, making it in fact a micrometer, by which the distance of the set of the instrument was to be measured from the perfect coincidence of one of the actual divisions of the limb with the next stroke of the vernier ; by which means the observation could not only be read oflf with all the precision that the division of the instrument was capable of, but the two sets of divisions could be checked and compared with each other. Another thing that I apprehend to be p 2 36 PHILOSOPHICAL TRANSACTIONS. [aNNO IJSO, peculiar in this instrument, was the more certain method of transferring and cutting the divisions, from the original divided points, by means of the beam- compass, than could possibly be done from a fiducial edge, as had doubtless been constantly the practice in cutting diagonals ; for, placing the steady point of the beam-compass in the tangent line to that part of the arc where each division was to be cut, the opening of the compass being nearly the length of the tangent, the other point would cut the division in the direction of the radius nearly ; and though in reality an arch of a circle, yet the small part of it in use would be so nearly a right line, as perfectly to answer the same end ; all which advantages put together, it is probable, induced Mr. Graham to reject the diagonals. Soon after the completion of this quadrant, Mr. Graham undertook to exe- cute a zenith sector for the Rev, Dr. Bradley, which was fixed up at Wanstead, in Essex, in the year 1727. The very simple construction that he adopted for this instrument, the plumb-line itself being the index, did not admit of the use of a vernier : he therefore contented himself with dividing the arch of the limb of this instrument by primary points, as close as he thought necessary, that is, by divisions of 5' each, and measuring the distance from the set of the instru- ment to the next point of division by a micrometer screw, in the construction of which screw he used uncommon care and delicacy. I have mentioned this in- strument to introduce this observation ; that I think it highly probable, had Mr. Graham constructed the great quadrant after the zenith sector had been fully tried, he would have rejected not only the diagonals but the verniers also as containing a source of error within themselves which may be avoided by a well-made screw. It seems also, that Mr. Graham, at the time he constructed both these in- struments, was not aware how much error could arise from the unequal expan- sions of different metals by heat or cold : for in both, the radius, or frame of the instrument, was iron, while the limbs were of brass. They however remain n the Royal Observatory, perfect models, in all other respects, of every thing that is likely to be attained in their respective destinations, and monuments of the superlative abilities of that great mechanician Mr. Graham.* Mr. Graham lived till the year 1751 ; and during his time there were few in- struments of consequence constructed without his advice and opinion. They were for many years done by Mr. Sisson, to whom doubtless Mr. Graham would fully communicate his method of division ; and from this school arose that very eminent and accurate artist Mr. Bird, whose delicate hand, joined with great care and assiduity, enabled him still further to promote this branch of division ; * I have been informed, that Dr. Maskelyne has caused this objection to the sector to be rectified, since its removal to the Royal Observatory, by substituting an iron limb instead of that of brass, the points being made upon studs of gold, — Orig, VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 3/ and which being carried by him to a great pitch of perfection, the Commis- sioners of Longitude did themselves the credit, by a handsome reward, to induce him to publish to the world his particular method of dividing astronomical instruments; which being drawn up by himself, in the year 1767, this matter is fully set forth to the public : I shall therefore only take this oppor- tunity of observing, that there seems to be one article in which Mr. Bird's me- thod may be still improved. I apprehend that no quadrant, which has ever undergone a severe examina- tion, has been found to form a perfect arch of QO" ; nor is it at all necessary it should : the perfect equality of the divisions throughout the whole is the first and primary consideration ; as the proportion of error, when ascertained by proper observations, can be as easily and readily applied, when the whole error of the rectangle is 15", as when it is but 5. In this view, from the radius taken, I would compute the chord of l6° only. If I had an excellent plain scale, I would use it ; because I should expect the deviation from the right angle to be less than if taken from a scale of more moderate accuracy ; but if not, the equality of the divisions would not be affected, though taken from any common diagonal scale. This chord, so prepared, I would lay off 5 times in succession, from the primary point of O given, which would complete 80°. I would then bisect each of those arches of 16°, as prescribed by Mr. Bird, and laying off 1 of them beyond the 80th, vv^ould give the S8th degree : proceeding then by bi- section, till I came to an arch of 2°, laying that off from the 88th degree, would give the point of 90°. Proceeding still by bisection, till I had reduced the degrees into quarters =15' each, I would there stop ; as from experience I know, that when divisions are too close, their accuracy, even by bisection, , cannot be so well attained, as where they are moderately large. If a space of tV of an inch, which is a quarter of a degree, on an 8 feet radius, be thought too large an interval to draw the index over by the micrometer screw, this may be shortened, by placing another line at the distance of -^ of a division on each side of the index line ; in which case the screw will never have to move the index plate more than 4 of a division, or 5'; and the perfect equality of these side lines, from the index line, may be obtained, and adjusted to 5' precisely, by putting each of the side lines on a little plate, capable of adjustment to its true distance from the middle one, by an adjusting screw. The above hint is not confined to the chord of 16*^, which prohibits the subdivisions going lower than 15': for if it be required to have divisions equivalent to 5' on the limb itself; then I would compute the chord of 2\^ 2V only ; and laying it off 4 times from the primary point, the last would mark out the division 85° 20', pointed out by Mr. Bird ; supplying the remainder to a quadrant, from the bisected divisions as they arise, and not by the application of other computed chords. 38 PHILOSOPHICAL TRANSACTIONS. [aNNO 1780. In my introduction to M. Roemer's method of division, I have shown, that divisions laid off in succession, by the same opening of the compasses, either in a right line, or in the arch of a circle, being in its idea geometrically true, and in itself the most simple of all processes, it has the fairest chance of being mechanically and practically exact, when cleared of the disturbing causes. The objection therefore to his method is, the great number of repetitions, which de- pending on each other in succession (requiring no less than 540 to a quadrant, when subdivided to lO' each,) the smallest error in each, repeated 540 times, without any thing to check it by the way, may arise to a very sensible and large amount : but in the method I have hinted, this objection will not lie ; for, in the first case, the assumed opening is laid off but 5 times ; and in the latter case but 4 times ; nor does this repetition arise out of the nature of the thing ; for, if you like it better, you may, in the former case, at once compute the chord of Oa° ; and in the latter that of 85° 20', and then proceed wholly by bisection ; supplying what is wanted to make up the quadrant, from the bisected divisions, as they arise. Mr. Bird prescribes this method himself, for the division of Hadley's sextants and octants. I suppose he was the first who conceived the idea of laying off chords of arches, whose subdivisions should be come at by continual bisection ; but why he mixed with it divisions that were derived from a different origin, as prescribed in his method of dividing, I do not well conceive. He says, that after he had proceeded by the bisections, from the arc of 85° 20', the several points of 30^ 6o°, 75°, and 90°, all of which were laid down from the principle of the chord of 60° being equal to radius, fell in without sensible inequality ; and so indeed they might ; but yet it does not follow that they were equally true in their places as if they had been, like the rest, laid down from the bisection from 85° 20', and therefore being the first made, whatever error was in them, would be communicated to all connected with them, or taking their departure from them. Every heterogeneous mixture should be avoided where equal divisions are required. It is not the same thing, as every good artist will see, whether you twice take a measure from a scale as nearly the same as you can, and lay them off separately ; or lay off 2 openings of the compasses, in succession, unaltered ; for though the same opening, carefully taken off from the same scale a 2d time, will doubtless fall into the points made by the first, without sensible error ; yet as the sloping sides of the conical cavities made by the first point will conduct the points themselves to the centre, there may be an error which, though insensible to the sight, would have been avoided by the more simple process of laying off the opening twice, without ever altering the compasses. The 96 arc was, I have no doubt, invented by Mr. Graham, from having TOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. SQ perceived, in common with all preceding artists, how very much more qasy a given line was to bisect, than to trisect, or quinquisect : and therefore the g6 arc which proceeded by bisections only, or by laying off the same identical openings, which, as already shown, is still more simple and unexceptionable, was wholly intended by him by way of checking the division of the arc of QO, which required trisections and quinquisections. But experience soon showed the superior advantage of it so strongly, that the use of the QO arc is now wholly set aside, where accuracy is required ; whereas th^ ingenuity of Mr. Bird having shown a way to produce the 90 arc by bisection, when this is really pursued quite through the piece, by rejecting all divisions derived from any other origin, the 90 arc will have nothing in it to prevent its being equally unexceptionable with the 96 arc ; and consequently if, instead of the 96 arc, another arc of 90 was laid down, which being on a different radius, its divisions will stand totally unconnected with the former, then these two arcs would in reality be a check on each other ; for being of equal validity, the mean might be taken : and if, in- stead of vernier divisions, strokes at the distance of any odd number, as 7, 9, 11, or 13, are marked on, and carried along with the index plate; these will produce a check on neighbouring divisions ; and the angle may then be deduced irom the medium of no less than 4 readings. The last works that have been made known to the public in the line of graduation, so far as have come to my knowledge, are those of the very ingenious Mr. Ramsden, which were published, by order of the Board of Longitude, in the year 1777. From his own information I learn, that in the year 1760 he turned his thoughts towards making an engine for dividing mathematical instru- ments ; and this he did in consequence of a reward offered by the Board of Longitude to Mr. Bird, for publishing his method of graduating quadrants ; for as several years previous to that period, he had taken great pains to accomplish himself in the art of hand-dividing, in which line Mr. Bird had acquired his eminence, he conceived by this publication of Mr. Bird's he should be reduced to the same standard of performance with the rest of the trade. He therefore, partly to save time, and that kind of weariness to an ingenious mind that ever must attend the endless repetition of the same thing from morning to night ; partly still to preserve the pre-eminence he had then gained ; and partly to pro- cure dispatch in the great increase of demand for Hadley's sextants and octants, in consequence of the successful application of the moon's motion to the purpose of ascertaining the longitude at sea, which instruments for this purpose required a degree of accuracy and certainty in the division, by no means necessary when applied to the simple purpose of observing latitudes ; I say,, for these considera- tions, Mr. Ramsden determined to set about something in the instrumental way, that should be sufficient effectually to answer these purposes. 40 PHILOSOPHICAL TRANSACTIONS. [aNNO 1780. Accordingly, considering the nature of the endless screw, he set about an engine whose divided wheel or plate was of 30 inches diameter ; and though the performance of this first essay was inferior to his expectations and wishes, yet with it he was able to divide theodolites with a degree of precision far superior to any thing of the kind that had been exhibited to the public. This engine I saw in the spring of the year 1768 ; and it appeared to me not only a very laudable attempt towards instrumental divisions, but a very good model for the construc- tion of an engine of the most accurate kind for that purpose. And at the same time he showed me the model or pattern for casting a wheel of a much larger size, which he proposed to make on the same plan, and with considerable im- provements. This being effected some time in or about the year 1774, its accuracy was proved by making a sextant, afterwards subjected to the examina- tion of Mr. Bird ; who in consequence approved the method, not only as fully sufficient for the division of Hadley's sextants and octants for any purpose what- ever, but in fact for dividing any instrument whose radius did not exceed that of the dividing wheel, which was 45 inches in diameter : on which the Board of Longitude very properly and usefully resolved to confer a handsome reward on Mr. Ramsden, for delivering a full explanation of his method of making the said engine ; which, in consequence, was published by order of the Board of Longitude in the year 1777, above-mentioned ; the designs of which are so full and explicit, that whoever could not understand that description, so as to enable him to make it, would be unfit to undertake it on other accounts. From what I have said on the works of the different artists above-mentioned, it would seem that the art of graduation was brought to such a degree of excel- lence that nothing material can now be added to it : and I should have been apt to have thought so myself, if I had not happened, in the course of my life, to have had a communication made to me, under the seal of secrecy, which seems to promise yet further light and assistance in perfecting that important art ; and every impediment to the discovery of it being now removed, I shall in the re- mainder of this essay give the clearest description of it that I am able_, with such elucidations and improvements as seem to be naturally pointed out by the me- thod itself. In the autum of the year 1741, I was first introduced to the acquaintance of that then eminent artist, Mr. Henry Hindley, of York, clock-maker. He imme- diately entered with me into the greatest freedom of communication, which founded a friendship that lasted till his death, which did not happen till the year 1771, at the age of 70. On the first interview, he showed me, not only his general set of tools, but his engine, at that time furnished with a dividing plate, with a great variety of numbers for cutting the teeth of clock wheels, and also, for more nice and curious purposes, furnished with a wheel of about 1 3 inches ▼OL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 41 diameter, very stout and strong, and cut into 36o teeth ; to which was applied an endless screw, adapted to it. The threads of this screw were not formed on a cylindric surface, but on a solid whose sides were terminated by arches of circles. The whole length contained 1 5 threads ; and as every thread, on the side next the wheel, pointed towards the centre, the whole 15 were in contact together ; and had been so ground with the wheel, that, to my great astonish- ment, I found the screw would turn round with the utmost freedom, inter- locked with the teeth of the wheel, and would draw the wheel round without any shake or sticking, or the least sensation of inequality. How long this en- gine might have been made before this first interview, I cannot now exactly as- certain : I believe not more than about a couple of years ; but this I well re- member, that he then showed me an instrument intended for astronomical pur- poses, which must have been produced from the engine, and which of itself must have taken some time in making.* I in reality thought myself much indebted to Mr. Hindley for this communi- cation ; but though he showed me his engine, and told me that the screw was cut by the rotation of the point of a tool, carried round on a strong arm, at the distance of the radius of the wheel from the centre of motion, which arm was carried forward by the wheel itself, and the wheel was put forward by an endless screw, formed on a cylinder to a proper size of thread, cut by his chock lathe ; though he showed me also this chock lathe, and the method employed to make the threads of the screw equiangular with the axis^ that is, to free the screw * This instrament was of the equatorial kind ; the wheel parallel to the equator, the quadrant of latitude, and semi-circle of declination, being all furnished with screws containing 15 threads each framed and moved in the same manner as that of the engine j the whole of which instrument was already framed, and the telescope tube in its place, which was intended to be of the inverting re- fracting kind, and to be furnished with a micrometer. This however was not completed tiU some years after ; but in the year 1 748 I received it in London for sale. It was with me 2 years, in which time I showed it to all my mechanical and philosophical friends, among whom was Mr. Short, who afterwards published in the Philos. Trans, vol. 46, an account of a portable observatory, but without claiming any particular merit from the contrivance. However, the model of it differs from Hind- ley's equatorial only in the following articles. He added an azimuth circle and compass at the bottom. He omitted the endless screws, placing verniers in their stead ; and at the top, a reflecting telescope instead of a refractor. This insfrument of Hindley's being afterwards returned to him un- sold, I pointed out the principal deficiencies that I found in it ; viz. that, in putting the instrument into different positions, the springing of the materials was such as in some positions to amount to con- siderable errors. This remained with him in the same state till the year of the first transit of Venus, viz. 1761 } when it was sold to Constable, Esq. of Burton Constable, in Holdemess. Mr. Hindley, to remedy the evil above-mentioned, applied balances to the different movements. He soon afterwards completed one, de novo, on this improved plan, for his Grace the late Duke of Norfolk. A method of balancing in much the same way, without the knowledge that it had been done before, has been fiilly explained, and laid before the Society, by our ingenious and worthy brother Mr. Nairne. Phil. Trans, vol. 59, p. 108, — Orig. VOL. XVI. G 42 PHILOSOPHICAL TRANSACTIONS. . [anNO 1786. from what workmen term drunkenness ; and also showed me how, by the single screw of his lathe, he could cut, by means of wheel-work, screws of every ne- cessary degree of fineness,* and by taking out a wheel, could cut a left-handed screw of the very same degree of fineness ; by which means he was enabled not only to adapt his plain screw to the size of the teeth of his wheel, but also to prevent any drunkenness that otherwise the curved screw would be subject to in consequence of being produced from the plain one ; also, that the screw and wheel, being ground together as an optic glass to its tool, produced that degree of smoothness in its motion that I observed ; and lastly, that the wheel was cut from the dividing plate : yet, how the dividing plate was produced, he for par- ticular reasons reserved to himself. Nor can he be blamed for the reservation of this one secret ; as he had, even at the time of my early acquaintance with him, a kind of foresight that from the superior merit of Hadley's quadrant, a demand for that, and other instruments for the purpose of navigation, was likely to increase ; and that he might live to see a public reward offered for a method of dividing them with greater accuracy and dispatch than had at that time appeared. Indeed he had himself an idea, from the satisfactory success that had attended his operations in dividing, that a screw and wheel, produced from his engines of 1 foot diameter, would have as much truth as the 8-feet quadrant at Greenwich : and though he doubtless greatly over-rated the accuracy of these miniature performances, yet it does not follow, as his methods were not confined to so narrow a compass, but that, his, scale of operation being proportionably enlarged, a degree of accuracy in the graduation of astronomical instruments may be attained in proportion. I must here beg leave to observe, that there appears to me to be a natural limitation to the accuracy of instruments, consisting of considerable portions of a circle, such as quadrants, Scc.-f- I do not find that the finest stroke on the limb of a quadrant, made by Bird's own hand, if removed from its coincidence with its index, can be replaced with any degree of certainty nearer than the 4000th part of an inch, though aided by a magnifying glass. J A 4000th part of an inch being then determined to be the minimum visibile by the strokes of an instrument, this will be less than 1''' of a degree on a radius of 4 feet; and * A machine for cutting the endless screw of Mr. Ramsden's engine, on principles exactly similar, is fully and accurately set forth in his description of his dividing engine above-mentioned. — Grig. "t The zenith sector consists but of few degrees, with little variation of its position in using it.— Orig. + It will be to little purpose to attempt it with a greater power. Double microscopes can doubt- less be formed to magnify objects, far less than a 4(;00th part of an inch, to distinct surfaces ; but then the advantage of such degrees of magnifying power is chiefly on the organized bodies of nature. Let a dot, or the finest point that can be made by human art, be so viewed, and it will appear not round, but a very ragged irregulai" figure. — Orig. VOL. LXXVI.J PHILOSOPHICAL TRANSACTIONS. ' 43 therefore, if the whole set of divisions on the limb could be preserved true to this aliquot part of an inch, the 8-feet quadrants of Greenwich might be ex- pected to be true to half a second. How far they are from this, I do not exactly know ; but I have reason to think they vary from it some seconds : nay I believe it is generally allowed that our largest quadrants, even when executed by the accurate hand of Mr. Bird, do not exceed those of a less size, by the same hand, in proportion to their increase of radius : nor can it well be ex- pected that they should ; since, as the weight necessarily increases in a triplicate ratio of the radius, the great weight of the Greenwich quadrants in moving and fixing them, as they could not be divided in their place, may easily derange the framing ; or even the internal elasticity of the materials may give way, by a change of position, to so minute a quantity as a 4000th part of an inch. It therefore appears to me, that since the divisions of a quadrant of 4 feet radius are more than sufficient, and even those of 3 feet admit of all the distinctness that in other respects is wanted, a 3 -feet quadrant, in point of size, is capable of all attainable exactness ; and would be as much to be depended on as any of those now in being of 8 feet. By adopting quadrants of this smaller size, we shall of course get rid of -ff of the present weight ; and consequently of much cumber, unhandiness, and derangement, that must arise from that weight, as well as the fear of totally discomposing them, if ever moved out of their place. It is now time to open a principle on which there is a prospect of effecting such an improvement. I have shown that a 4000th part of an inch is the ulti- matum that we are to expect from sight, though aided by glasses, when ob- serving the divisions of an instrument. But in the 48th volume of the Philos. Trans, for the year 1754, I have shown the mechanism of anew pyrometer, and experiments made with it, by which it appears that, on the principle of contact, a '24,000th part of an inch is a very definite quantity. I remembered very well that I did not then go to the extent of what I might have asserted, being wil- ling to keep within the bounds of credibility : but on occasion of the present subject, I have re-examined this instrument, and find myself very well autho- rized to say, that a 6o,OOOth part of an inch, with such an instrument, is a more definite and certain quantity, than a 4000th part of an inch is to the sight, conditioned as above specified. The certainty of contact is therefore 15 times greater than that of vision, when applied to the divisions of an instrument : and if this principle of certainty in contact did not take place even much beyond the limit I have now assigned, we never should have seen those exquisite mirrors for reflecting telescopes, that have already been produced. These reflections apply immediately to my present subject, as Hindley*s method of division proceeds wholly by contact, and that of the firmest kind ; there being scarcely need of magnifying glasses in any part of the operation. G 2 44 PHILOSOPHICAL TRANSACTIONS. [anNO 1786. In the year 1748 I came to settle in London; and the first employment I met with was that of making philosophical instruments and apparatus. In this situa- tion, my friend Hindley, from a principle the reverse of jealousy, fully com- municated to me, by letter, his method of division ; and though I was enjoined secrecy respecting others, for the reasons already mentioned, yet the communi- cation was expressly made with an intention that I might apply it to my own purposes. The following are extracts from 2 letters, which contain the whole of what related to this subject ; and since I have many things to observe on them, so that the paraphrase would be much greater than the text, I think it best not to interrupt the description with any commentary, as perhaps his own mode of expression will more briefly and happily convey the general idea of the work, than any I can use instead of it. MY dear FRIEND, York, 14 Nov. 1748. As to what you was mentioning about my brother's knowing how I divided my engine plate, I will describe it as well as I can myself ; but you will want a good many things to go through with it. The manner is this : first chuse the largest number you want, and then chuse a long plate of thin brass ; mine was about 1 inch in breadth, and 8 feet in length, which I bent like a hoop for a hogshead, and soldered the ends together ; and turned it of equal thickness, on a block of smooth-grained wood, on my great lathe in the air, (that is, on the end of the mandrel :) one side of the hoop must be rather wider than the other, that it may fit the better to the block, which will be a short piece of a cone of a large dia- meter : when the hoop was turned, I took it off, cut, and opened it straight again. The next step was to have a piece of steel bended into the form as per margin ; * which had 2 small holes bored in it, of equal size, one to receive a small pin, and the other a drill of equal size. I ground the holes, after they were hardened, to make them round and smooth. The chaps formed by this steel plate were as near to- gether as just to let the long plate through. Being open at one end, the chaps so formed would spring a little, and would press the long plate close, by setting in the vise. Then I put the long plate to a right angle to the length of the steel chaps, and bored one hole through the long plate, into which I put the small pin ; then bored through the other hole ; and by moving the steel chaps a hole J forward, and putting in the pin in the last hole, I proceeded till I had divided the whole length of the plate. The next thing was to make this into a circle again. After the plate was cut * The figure is considerably less than the real tool should be. — Orig. VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 45 off at the end of the intended number, I then proceeded to join the ends, which I did thus: I bored 2 narrow short brass plates* as I did the long one, and put one on the inside, and the other on the outside of the hoop, whose ends were brought together; and put 2 or 3 turned screw pins, with flat heads and nuts to them, into each end, which held them together till I rivetted 2 little plates, one on each side of the narrow plate, on the -outside of the hoop. Then I took out the screws, and turned my block down, till the hoop would fit close on; and by that means my right line was made into an equal divided circle of what number I pleased. The engine plate was fixed on the face of the block, with a steel hole fixed before it to bore through ; and I had a point that would fall into the holes of the divided hoop; so by cutting shorter, and turning the block less, I got all the numbers on my plate. I need not tell you, that you get as many prime numbers as you please; nor that the distance of the holes in the steel chaps must be proportioned to the length of the hoop. You may ask my brother what he knows about my method of dividing; but need not tell him what I have said about it; for I think neither he nor John Smith know so much as I have told you, though I believe they got some knowledge of it in general terms.-^ 1 desire you to keep the method of dividing to yourself, and conclude with my best wishes, &c. Henry Hindley. Though the above letter was in itself very clear and explicit, as to the general traces of the method, yet some doubts occurring to me, a further explanation became necessary. A copy of my letter not being preserved, the purport of it may be inferred from the answer, which was as follows : DEAR FRIEND, Yovk, March 13, 1748-9. I think in your last you seem to be apprehensive of some difficulties in drilling the hoop for dividing: First, that the centre of the hole in the hoop might not be precisely in the centre of the hole of the steel chaps, it was drilled in ; but if I described fully to you the method I used, I can see no danger of error there : for my chaps were very thick, and the two corresponding holes were a little conical, and ground with a steel pin; first one pair, and then the other, alter- nately, till the pin would go the same depth into each. Then for drilling the hoop, I took any common drill that would pass through, and bore the hole. After that I took a five-sided broach, which opened the hole in the brass between the steel chaps, but would not touch the steel; so consequently the centre of * These I shall hereafter distinguish by the name of saddle-plates. — Orig. f The persons here referred to were both bred with him. His brother, JMr. Roger Hindley, who has many years followed the ingenious profession of a watch-cap-maker in London, was so much younger as to be an apprentice to him. Mr. John Smith, now dead, had some years past the honour to work in the instrument way, under the direction of the late Dr. Demainbray, for his present Majesty. — Orig. 46 PHILOSOPHICAL TRANSACTIONS. [aNNO I786. the holes in the brass must be concentric with the holes in the chaps: and for alterations by air, heat, cold, &c. I was not above 2 or 3 hours in drilling a row of holes, as far as I remember. 2dly^ For drilling in a right line, I had a thin brass plate, fastened between the steel chaps, for the edge of the hoop to bear against, while I thrust it for- ward from hole to hole. What you propose of an iron frame with a lead out- side, will be better than my wooden block ; but considering the little time that past, between transferring the divisions of the hoop to the divisions of my dividing plate, I did not suffer much that way. It was when I drilled the holes in my dividing plate that I used a frame for drilling, which had one part of it that had a steel hole, that in lying on the plane of the dividing plate was fixed fast in its place for the point of the drill to pass through: then, at the length of the drill, there was another piece of steel, with a hole in it, to receive the other end of the drill to keep it at right angles to the plane of the plate. This piece was a spring, which bended at the end, where it was fastened to the frame of the lathe, at about 18 inches from the end of the drill ; so it pushed the drill through with any given force the drill would bear: and though that end of the drill moved in the arch of a circle, it was a very small part of it, being no more than equal to the thickness of the dividing plate. Henry Hindley. Whoever attentively considers the communication contained in the above letters will see, that more happy expedients could not have been devised to pro- cure a set of divisions, where there should be the most exact equality among neighbours ; and which, for the purposes of clock-making, is the principal thing to be wished for. But herein, as in M. Roemer's method, there were no means of checking the distant divisions, which run on to 360: now such a check, when the expansion of metals is considered, and particularly the difference of expan- sion between brass and steel, seems absolutely necessary for the purpose of divi- sions on instruments, where the accurate mensuration of large angles is required, as much as the equality of neighbouring divisions.* With this view the inven- tion of this ingenious person suggested to him the thought of making his curved screw to lay hold of 1 5 teeth or degrees together : this, in effect, becomes a pair of compasses, 24 removes of which complete the whole circle, and produce 24 checks in the circumference: and whoever considers the very exquisite de- gree of truth that results from the grinding of surfaces in contact, as already * The ingenious Mr. StanclifFe, some years a workmen of Hindley's, has suggested, that the difference of expansion between the steel chaps and the brass hoop may be avoided by makino^ the diaps of brass also, with hard steel holes set separately in them, somewhat similar to the jewelled holes of watches. — Orig. VOL. LXXVl.] PHILOSOPHICAL TRANSACTIONS. A^ noticed, must expect a very great degree of rectification of whatever errors might subsist in the wheel after its first cutting. What degree of truth it might in reality be capable of, on its first production and adjustment, is not now to be ascertained, he never having used it for the graduation of any capital instrument. Those that he made with a view to an accurate measure of angles, he always made with a screw and wheel, or parts of circles cut by his engine into teeth, and ground together as before-mentioned; but I have reason to think that its performance, if put to a strict test, was never capable of the accuracy that he himself supposed it to have. The method itself however, from its simplicity and ease of execution, seems to be a founda- tion for every thing that can be expected in truth of graduation; and in con- sequence for reducing instruments to the least size that is capable of bringing out all that can be expected from the largest; when it shall, like manual divi- sion, have received those advantages that the joint labours of the most ingenious men can bestow on it. That I may not appear to be without grounds for my expectations, I beg leave to propose, what near 40 years occasional contempla- tion has suggested to me on the subject ; and as I can describe the process I would pursue, where different from Hindley's, in fewer words than I could make out a regular criticism on his letters, I will immediately proceed to the descrip tion of it. Proposed Improvements of H'mdleys method. — I would recommend the num- ber of parts into which the circle is to be reduced, to be 1440, that is 4 times 360 ; which divisions will therefore be quarters of a degree; the distances of the holes in the chaps will therefore, to a 3-feet radius, be -'iroV o^ ^n inch nearly; that is, between the -^ and 4^ of an inch distance centre and centre. Having provided myself with a stout mandrel, or arbor, for a chock Lathe, properly framed, that would turn a circle of 6 feet diameter, I would prepare a chock, or platform, for the end of it, of that diameter, or a little more, composed of clean-grained mahogany plank, all cut out of the same log; which, when finished, to be about 1-|- inch thick, and formed in sectors of circles, suppose 16 to make the circle; the middle line of each sector lying in the direction of the grain of the wood, this will consequently every where point outward: the me- thod of framing this kind of work is well known. The way of getting a slip of brass to answer the circumference of this plat- form is suggested in Mr. Bird's Account of constructing Mural Quadrants. Let a parallelogram of brass, of about 3 feet long, and of a competent sub- stance, suppose half an inch, to make it when finished about -^l of an inch in thickness, be cast of the finest brass; and this to be rolled down till it be- comes of sufficient length for the hoop, and about a 5th part more. I would 4$ PHILOSOPHICAL TRANSACTIONS. [aNNO 1780. then cut off, from the whole length, somewhat better than a 6th part, the whole being sufficiently reduced to a thickness by the rollers. Perhaps no way will be more ready and convenient to get such a long strip of brass reduced to an equal breadth, than the method prescribed by Hindley; viz. by turning it on the chock prepared; but I would not make it wider on one side than the other, like the hoop of a cask, as he describes, but exactly to fit the chock, when truly cylin- dric; for the internal elasticity of the brass, in so great a length, will be very sufficient for fitting it on tight enough, without any tapering. This I will now suppose done; and a pair of steel chaps, as described by Hindley, to be also prepared, and ready for grinding; which, by such a careful admeasurement as can easily be made, will give the length of the hoop sufficiently near, on its first preparation. Ale t hod of forming a pair of straps as a check to the divisions. — ^The part first cut off must be again cut into 2 equal parts in length; which, for distinction sake, I will call the straps; and which are to serve as checks to every 6oth and every 1 20th division of the circle. A steel plate, of about half an inch in breadth, the same thickness as the straps, and in length equal to the breadth of the hoop plate, must be soldered with silver solder to one end of each of the straps, by which means their length will be increased half an inch by the steel. A hole must then be made through each steel plate, of the same size as those through the chaps, and answerable to the middle of the straps; but so near the border of the steel, that when the chaps are put on, and adapted to the steel hole, the next hole will fall through the brass. The steel plates must then be hardened; and a pin being put through the two holes and the two plates, these must be wrought to a right line in contiguity to each other; by this means the straight edge of each of the straps will be reduced to the same distance from the steel hole: the hard steel edges may be rectified by the grindstone, if necessary. This being done, not only the holes in the chaps, but the holes in the two steel plates, applied to each other, like the two sides of the chaps, must be respectively ground together; not with a taper pin, as prescribed by Hindley; but so as not only to be cylindrical, but that the same cylindrical pin shall equally fit them all, and leave them smooth and polished; which is a process no ways diffi- cult to a curious artist, and of which therefore a minute description is unneces- sary. The chaps being then put on one of the straps, with its straight edge uppermost, and a pin put through the holes on the left-hand, and through the steel hole in the strap under operation, the chaps must be set upright, so that the line joining the centres of the holes shall be parallel to the upper edge of the strap ; the brass plate, mentioned by Hindley, between the chaps, as a guide VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. '4Q for directing them always to that upright position, may be then adjusted and fixed to the inside of the chap next the operator.* The performance of the ensuing part of this work should be at a season when the temper of the air is not very variable; rather above the mean temper, sup- pose at 60°, than below it; but above all things the artist should be himself cool; that is, not in a state of sensible perspiration; and there should be a free circulation in the room. Things being thus conditioned in respect to tempera- ture, he may begin to drill the holes in one of the straps; the pin being first put through the chaps and through the steel hole of the strap; and the next hole, being drilled through the brass with a common drill, that and every hole as it goes is to be finished with a taper broach, as prescribed by Hindley; and he may then prove or finish every hole by the application of a thorough broach, made so full as to require a degree of pressure to force it through ; and this broach being a little tempered, and the holes quite hard, there will be no fear of injuring the steel holes. Calling the hole in the steel plates o, and observing the time of beginning, you may proceed to drill 60 holes as prescribed by Hindley; and noting how long you have been about it, you may lay the work aside a length of time, equal to the time you took in drilling; that any addition of warmth it may have acquired in handling or working may be again lost in a great degree. After this pause you may begin again, and go on to finish 60 holes more; that is, to the length of 120 holes from the beginning; you then proceed in the same manner with the other strap. Method of Drilling the hoop. — You are now prepared to commence the work on the long or hoop-plate; and you proceed with it, in forming the first hole with the chaps, as before directed by Hindley, and this first hole you call o. You then place the straps one on each side the hoop, with their gaged edges upward, and put the pin through the holes denominated 60 on the straps, and through the first hole already made, and denominated O on the hoop; then, bringing the gaged edges of the steel plates to be even with the upper or work- ing side of the hoop, you pinch them together in the vise, and drill and broach the hole through the st + A Wp ' )r(jr — p) ' p(p — w^)' ^ Tp • »»■. C'" — P) f . (p — »»■)' = 0: for write O, tt, and p, respectively for ar in the equation, and there will result the quantities a, b, and c. He then gives some general approximating equated values of the roots of equations, which he says will nearly be the same as found, where a near approximate is given, from the method given by Vieta, Harriot, Oughtred, Newton, De Lagny, Halley, &c. Sir Isaac Newton found the sum a, of the 2n*^ power of each of the roots of a given equation, and then extracted the 2n}^ root of a, viz. "^^a, for an approxi- mate value of the greatest root of the equation ; and further added some similar rules on the same principle. In the Miscell. Analyt. and Meditationes the same principle is applied in different rules for finding approximates to the greatest and other roots of the given equation; and also limits of the ratios of the approxi- mate values of the roots found by these rules to the roots themselves are given. It is observed in the Meditationes, that from these rules in general to find the greatest root, it is often necessary that the greatest possible root be greater than the sum of the quantities contained in the possible and impossible part of any impossible root of the given equation: for example, \f a -\- b\/ — 1 be an im- possible root of the given equation, then it is necessary that the greatest pos- sible root be greater than a -\- b. It may further be observed, that in equations of high dimensions, unless purposely made, it is probable that the number of impossible will greatly exceed the number of possible roots; and consequently these rules most commonly fail. M. Bernoulli assumed a fraction whose numerator is a rational function of the unknown quantity, and denominator the quantity which constitutes the equation; and reduced the fraction into a series, whose terms proceed according to the di- mensions of the unknown quantity ; and thence found an approximate value of the greatest or least root of the given equation or its reciprocal, by dividing the co-efficient of any term of the series resulting by the co-efficient of the preceding or subsequent term. The rule of false has been found very useful in finding approximates to the two unknown quantities contained in two given equations, and has been applied to n equations having n different unknown quantities : for example, it has been observed, that if 2 or more m values of an unknown quantity x are nearly equal to each other, and to its given approximate value x^, the unknown quantity v = X — >r' will ascend to 2 or more m dimensions in one of the resulting equations; or in more equations than one will be contained such powers of the quantity v, that if the more equations were reduced to one whose unknown quantity is v, the resulting equation will contain m dimensions of the quantity v. Hence it appears, that in this case alsc^ the con vergency of the approximate values found will depend ©n the given approximate being much more near to one root than to any other. VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 63 In the 3d part Dr. W. remarks that the first algebraists divided quantities, and extracted their roots, no further than the quantities themselves: they did not per- ceive the utility of proceeding any further, otherwise the operation would have been the same continued. Mr. Gregory St. Vincent, and Mr. Mercator divided, and Sir Isaac Newton divided and extracted the roots of quantities, in which only one unknown quantity x is contained, by the operations then used by arithme- ticians, into series ascending or descending, according to the dimensions of x in infinitum. They clearly saw the utility of it in finding the fluents of fluxions, as Dr. Wallis and others some little time before had found the fluent of the ^ m fluxion ax^'x; or, which is the same, the area of a curve whose ordinate is ax~ and abscissa is x. M. Leibnitz asked from Mr. Newton the cases in which the above-mentioned serieses would converge; for it would be altogether useless when they diverge, and of little use when they converge slowly. To this question an answer, Dr. W. believes, was first given in the Medita- tiones, viz. reduce the function to its lowest terms; and also in such a manner that the quantities contained in the numerator and denominator may have no denominator: make the denominator a = O, and every distinct irrational quan- tity contained in it = O; and also every distinct irrational quantity h contained in the numerator = O; then, let a be the least root, affirmative or negative, (but not = O) of the above-mentioned resulting equations, the ascending series will always converge, if the value of x is contained between a. and — a; but if ^ be greater than a or — «, the above-mentioned series will not converge. If the above-mentioned series, s, be multiplied into x, and its fluent found; then will the series denoting the fluent contained between two values a and ^, of the quan- tity X, converge, when a and b are both contained between a and — a : the fluent always converges faster than the series s, the unknown quantity x having the same values in both. The infinite series a^ + mdJ^^x -|- m . ^-^ a'"~V -j- &c. = (a -f- a?) will always converge when a is greater than x, and diverge when less; and consequently its convergency does not depend on the index m, unless when a; = + a: and in the Meditationes Analyticae are given the cases in which it converges or diverges when ip a = ar; and also if the series af -f- maoif^'^ -f- &c. =z {x •{- aY descends according to the dimensions of x, when it converges or diverges. Sir Isaac Newton, in the binomial theorem, reduced the power or root of a binomial into a series proceeding according to the dimensions of the terms con- tained in the binomial. M. de Moivre reduced the power or root of a multino- mial into a like series; but in all cases, except the most simple, we must still recur to the common division, extraction of roots, &c. Messrs. Euler, Mac- laurin, and other mathematicians, finding tha the serieses before-mentioned (54 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. often converged slowly, or, if the truth may he confessed, commonly not at all, to deduce the area of a curve contained hetween two values a and b of the ab- sciss, or fluent of a fluxion between two values a and /; of the variable quantity a:, interpolated the series or area between a and b\ that is, found the area or fluent contained between the abscissae a and a -\- a, then between the abscissae a -}- a and a -\- 2a, and then between the abscissae a + 2a and a -j- 3a, and so on, till they came to the area between b — a and b. M. Euler observed, that when the ordinate became O or infinite, the series expressing the area converges slowly; and therefore, in order to investigate the area near the points of the absciss where the ordinates become O or infinite, he transforms the equation, and finds serieses expressing the area near those points, in which serieses the abscissae or unknown quantities begin from those points. In the Meditationes it is asserted, that in a series proceeding according to the dimensions of x^ if any root f the above-mentioned equations be situated be- tween the beginning of the absciss O and its end x, the series will not converge; it is therefore necessary to transform the absciss so that it may begin or end at each of the roots of the above-mentioned equations, and consequently where the ordinates become O or infinite, &c.; those cases excepted where the ordinate be- comes O, and its correspondent abscissa is a root of a rational function w of a;- without a denominator, and /wp.r is equal to the given series ; and in general the abscissae ought to begin from the above-mentioned points ; for if they end there, the series will converge very slow, if at all. It is further asserted, that if a and /;, the values of the abscissse between which the area is required, be both more near to one root of the above-mentioned equations than to any other, and rz, serieses are to be found, whose sum expresses the area contained between a and b\ then that the sum of the n serieses may converge the swiftest, the distances of the beginnings of each of the n abscissae from the adjacent root will form a geometrical progression. Mr. Craig found the fluent of any fluxion of the formula (a -}- bx^ -\- cx^" -j- &c.)".r'^~^r by a series of the following kind (a -f bx"" -\- cx^" -f &c.)'"+^ X x^ X (a 4- pa;" -f yx^" -\- &c. in infinitum). Sir Isaac Newton, by serieses of the same kind, found the fluents of fluxions of this formula {a -f bx^ -j- cx'^" -\- &c.y X (e+/i" + g^'"-" -\- &C.)'" X hc.x^-\v; the same principle is extended somewhat more general in the Meditationes. Mr. John Bernoulli found the fluent of any fluxion fnz = nz — 77^ + o T-l — ^^' f^^m the principles which Mr. Craig published for finding the fluents effluxions involving fluents. In the Meditationes something is added of the convergency of these series; and also, in them a new method is given of finding approximations. Let some terms in the given quantity be much less or greater than the rest; then reduce the quan- tity into terms proceeding according to the dimensions of the small quantities, or VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 65 according to the reciprocals of the great quantities, and it is done. If the fluent of the quantity resulting be required, find it from the common methods, if pos- sible; but if not, reduce the terms not to be found into an infinite series, and then find approximate values to each of the terms, &c. M. Euler, and others, reduced the series koc'' + bx'^-^* -\- ca:'+*' -|- &c. into a series a' sin. ra. -\- -& sin. (?• + *) a + &c. &c. where a denotes the arc of a circle, whose sine is ax, &c. It may be easily reduced into infinite other serieses proceeding according to the dimensions of quantities, which are functions of x ; but it is most commonly preferable to reduce it into serieses proceeding according to the sines, cosines, tangents, or secants of the arcs of circle, which sines, &c. can immediately be procured from the common tables. It has been observed in the first part, that to find the root of an equation, an approximate value much more near to one root of the equation than to any other must be given. In this part it is further observed, that serieses deduced from expanding given quantities, so as to proceed according to the dimensions of the unknown or variable quantities, will not converge if the unknown quanti- ties be greater than the least roots of the above-mentioned equations ; and that they will not converge much, unless the unknown quantities have a small pro- portion to the least roots: and if the given quantities be expanded into serieses descending according to the dimensions of the unknown quantities, then the se- rieses resulting will not converge if the greatest roots of the equations before- mentioned be greater than the unknown quantities ; and unless the unknown quantities have a great ratio to the greatest roots the serieses will converge slowly : for example, the serieses -|- ^y^ -\- &c. will never converge if x, z, or y, be greater than 1 ; but will always converge when less than + 1 or + 1 -/ — 1 the least or only roots of the equations 1 -f a; = 0, 1 — 3/* = 0, and 1 -f z^ = O. The series y -\- ^y^ -|- &c. will always converge wheny is situated between -f 1 and •— ], in which case alone it is possible. The same is true also of a series arising from expanding the r(ax'" ■\- bx"'~^ -f- cx'"-^ -{• &c.)*'".f into a series proceeding according to the dimensions of x, if the equation ax^ ■\- bx"' -\- cx'""'^ -f- &c. = O have only 2 possible roots a and — a, which are less in the manner before-mentioned than any impossible root contained in it. If in either of the above-mentioned serieses the unknown quantity x, z, or y, has a great proportion to 1, the series will converge very slow ; for example, if a; = 1, ten thousand numbers at least are to be calculated, to procure the sum of the series true to 4 figures ; therefore, in these and most other serieses, it is necessary first to find a near value, viz. when x either = z, when e is very small ; VOL. XVI. K 66 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. or = e, when z is very small ; and then write z + ^ fo** -^ »" the quantit) , and reduce it in the former case into a series proceeding according to the dimensions of e, in the latter case according to the dimensions of z, and there will arise '2 serieses, of which the fluents properly corrected, viz. by adding the fluent con- tained between the values a and e to the latter, and that between a and z to the former, will give the same fluent. The first term of the series, in which e is supposed very small, will be the fluent of the given fluxion, when x = z. If a fluxion p.r, where p is a function of x, be transformed into another ai, where q is a function of z, and they be reduced into serieses a and b, proceed- ing according to the dimensions of x and z respectively ; find a. and tt, corres- pondent values of the quantities x and z ; then in ascending serieses, if a has a less ratio to the least root of the equation p = O, than tt has to the least root of the equation a = O, the series a (exceptis excipiendis) will converge swifter than the series b. Dr. Barrow, in some equations, expressing the relation between the absciss x and ordinate 2/, found 7/ in the first 2 terms of x, viz. 3/ = a + ^^) which is an equation to the asymptotes of the curves. Sir Isaac Newton, from an algebrai- cal equation given, expressing the relation between t/ and x, found a series pro- ceeding according to the dimensions of x, expressing 1/ in terms of x. M. Leibnitz performed the same problem by assuming a series ax" -j- bx" + '' -f- ca;"+*'' -|- &c. with general co-efficients, and substituting this series for 3/ in the given equation, &c. from equating the correspondent terms he deduced the indexes and co-efficients. M. De Moivre, Mr. Maclaurin, &c. observed, that when the highest terms of the given equations have 2 or more {m) divisors equal; for example, (y — ax")'" ; to which we must add, and when a value of 1/ in this r case is required nearly equal to ax", a series ax" -\- bx "* -f- &c. is to be as- sumed, whose indexes differ only by -, &c. if otherwise they would differ by r. This reduction seldom answers any other purpose than finding the fluents of fluxions, as / z/.r, &c. ; or the asymptotes, &c. of curves, which depend on some of the first terms of the series ; but will very seldom be used for finding the roots of an equation. The rule of false, or method given by Vieta, will ever be substituted in its stead. The values of x may be required between which the above-mentioned series Aoif + Bx"+'' -|- ca?"+^'' -j- &c. will converge, as the infinite series answers no pur- pose when it diverges. First, if an ascending be required, write for y in the given algebraical equation an infinite quantity, and find the roots of x in the equation thence resulting p = 0 ; which for y write in the same equation, and find the roots of x in the resulting equation which contain irrational quantities, VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 67 viz. if one root he x =z a; then let it contain {x — a)", where m is not a whole number ; find the roots of the equations resulting from making every irrational function of x contained in the given equation = O, there being no irrational function of ^ contained in it ; then, if a:* be greater than the least root not = O of the above-mentioned equations, the series will not converge ; but if it be a series descending according to the dimensions of x, and x be less than the g eatest root of the above-mentioned equations, the series will not converge. In interpolating seriesee to investigate the fluent contained between two values a and b of the fluxion (a^t* -j- bx''+'' -{- &c.) Lv, it is preferable to make the ab- scissa? begin from every one of the above-mentioned roots contained between a and b. Most commonly these serieses will not converge unless x be less, &c. than other quantities not investigated by this rule. Sir Isaac Newton gave an elegant example of this rule in the reversion of the series, y = ax -[• bx'^ -{- cx^ -\- &c. from which the investigation of the law of the series has never been attempted. In the year 1757 1 sent the first edition of my Meditationes Algebraic'ae to the r. s., and published it in 1760, and after- wards in 1762, with another part added, on the properties of curves, under the title of Miscellanea Analytica, in all which was given the law of a series for finding the sum of the powers of the roots of an equation from its co-efficients. That great mathematician M. Le Grange and myself printed about the same time an observation known to me at the time that I printed the above-men- tioned book, that the law of its powers and roots, if it proceeds in infinitum, is the same ; from which series of mine, with great sagacity, M. Le Grange found the law which Sir Isaac Newton's reversion of series observes. In the Medita- tiones the law is given, and the series is made to proceed according to the dimensions of x, &c. It is asserted in the Meditationes, that in most equations of high dimensions, unless purposedly constituted, the sum of the terms which, from the given by pothesis, become the greatest, being supposed = O, only an approximate to the value ax" of y in the resulting equation can by the common algebra be deduced. In this case the approximate to the quantity a is to be found so near as the ap- proximate value of the quantity sought requires ; or perhaps it is preferable to correct in every operation the approximate values of the quantities a, b, c, &c» in the series required aV -f- b'x''+'' -\- cx''+^'' -\- &c. In the equation the quantity z + e may be substituted for Xj and from the equation resulting a series express- ing the value of 7/ may be found, proceeding either according to the dimensions of the quantity z, or its reciprocals, according to the conditions of the problem. If there be more than one (rz) equations having n -J- 1 unknown quantities, X, y, z, &c., in each of the equations, for y, z, &c. write respectively at", Pl'ocT, &c. ; and suppose the terms of each of the equations, which result the K 2 68 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. greatest from the given or assumed hypothesis = O, and from the resulting equa- tions may be found the first approximates ax", A'a?", &c. either accurately or nearly ; then, in the given equations for y, 2, &c. write ?/' -f (a -|- a) x" -{- ^x"-^"' -f- &c. z 4- (a' + a) x"" 4- Bx'"+"'', where a, a', &c. are very small quan- tities; and suppose the terms of each of the equations which become greatest from the above-mentioned hypothesis respectively = 0, and from the equations resulting deduce the quantities a, a, &c. ; w', rn, &c. ; b, b', &c. ; and so on : or assume 2/ = (a + la + al + &c.) x" -\- (b -\- lb + bl -{■ &cc.)x''+"' -f &c. ; z = (a' -f la -\- a I -f- &c.) X'" -|- (b' -f 1^' + b'l + &c.) x'"+''' + &c. &c. ; substitute these quantities for their values in the given equations, and from equating the correspondent terms of the resulting equations may be deduced the quantities required. The differences of the indexes n, &c. m\ &c. may be deduced by writing X", x^y &c, for 7/f 2, &c. in the given equations, from the differences of the in- dexes of the quantities resulting. The same principles may be applied in finding the above-mentioned differences, when two or more values are ax", &c. which were applied in a like case to one equation having two unknown quantitieSi The same principles which discover the cases in which a series deduced from an equation having two unknown quantities will converge, may be applied for the same purpose to these series. In finding the series which expresses the value of y in terms of x, there will always occur as many invariable quantities to be assumed at will, as is the order of the fluxional equation, provided the series begins from its first terms ; and to find them there will result equations easily reducible to homogeneous fluxional equations, of which the orders do not exceed m. V^. Experiments on Hepatic Air.* By Rich. Kirwany Esq. F.R.S. p. 118. Hepatic air is that species of permanently elastic fluid which is obtained from combinations of sulphur with various substances, as alkalis, earths, metals, &c. It possesses many peculiar and distinct properties ; among which the most ob- vious are, a disagreeable characteristic smell emitted by no other known sub- stance ; inflammability, when mixed with a certain proportion of respirable or nitrous air; miscibility with water, to a certain degree; and a power of dis- colouring metals, particularly silver and mercury. These properties were first discovered by that incomparable analyst Mr. Scheele. This air acts an important part in the economy of nature. It is frequently found in coal-pits ; and the truly excellent and ever to be regretted M. Bergman has shown it to be the prin- ciple on which the sulphureous properties of many mineral waters depend, and thus happily terminated the numerous disputes which the obscurity of that * Termed sulph'aretted hydrogen gas, in the new chemical nomenclature. VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 6Q subject had occasioned. There is also great reason to think that it is the peculiar product of the putrefaction of many, if not all, animal substances. Rotten eggs and corrupt water are known to emit the smell peculiar to this species of air, and also to discolour metallic substances in the same manner. M. Viellard has lately discovered several other indications of this air in putrefied blood. Yet, deserving as this substance appears to be of a thorough investigation, it has as yet been very little attended to. The experiments of M. Bergman have not been sufficiently numerous, and thence he has been led into some mistakes. Dr. Priestley has entirely overlooked it. The researches of the ingenious Mr. Sennebier, of Geneva, have indeed been very extensive ; but as, for particular reasons, he operated on this air over water, by which it is in great measure ab- sorbed, instead of quicksilver, his conclusions appear in many respects objec- tionable. The experiments now laid before the Society were all made over quicksilver, and several times repeated. Of the Substances that yield hepatic air, and the means of obtaining it. — It is well known, that saline liver of sulphur is formed, in the dry way, of a mixture of equal parts of vegetable or mineral alkali and flowers of sulphur, melted together by a moderate heat, in a covered crucible. When this mixture vi^as slightly heated, it emitted a bluish smoke, which gradually became whiter as the heat was increased, and at last, when the mixture was perfectly melted, and the bottom of the crucible slightly red, became perfectly white and inflammable. To examine the nature of this smoke, Mr. K. made a pretty pure fixed alkali, by deflagrating equal parts of cream of tartar and nitre in a red-hot crucible in the usual way; and mixing this salt perfectly dry with flowers of sulphur in much smaller quantity, he gradually heated the mixture in a small coated glass retort, and received the air proceeding from it over quicksilver. The first por- tion of air that passed with a very gentle heat, was that of the retort itself, slightly phlogisticated. It amounted to 1 .5 cubic inches, and with Dr. Priest- ley's nitrous test, (that is, an equal measure of nitrous air) its goodness was 1.29. It contained no fixed air. The 2d portion of air obtained by increasing the heat amounted to about 18 cubic inches. It was of a reddish colour, and seemed a mixture of nitrous and common air. It slightly acted on the mercury. The 3d portion consisted of 20 cubic inches, and appeared to be of the same kind, but mixed with a little fixed air. This was succeeded by 64 cubic inches of almost perfectly pure fixed air; and the bottom of the retort being now red, some sulphur sublimed in its neck. When all was cold, liver of sul- phur was found in the bulb of the retort. Hence we see that the blue smoke consists chiefly of fixed air, and the white or yellow smoke of sulphur sublimed; and that no hepatic air is thus formed; nor vitriolic air, unless the retort be so large as to contain a sufficiency of com- 70 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. moil air to admit the combustion of part of the sulphur. 2dly, That the aerial, or any other acid, combined with the alkali, must be expelled, before the alkali will combine with the sulphur. Liver of sulphur exercises a strong solving power on the earth of crucibles, and readily pierces t. rough them. The best liver of sulphur is made of equal parts of salt of tartar and sulphur; but as about -f of the salt of tartar consists of air which escapes during the operation, it seems that the proportion of sulphur predominates in the result- ing compound; yet as some of the sulphur also sublimes and burns, it is not easy to fix the exact proportion. lOOgrs. of the best, that is, the reddest liver of sulphur, afford, with dilute marine acid, about 40 cubic inches of hepatic air, in the temperature of 6o°: a quantity equivalent to about 13 grs. of sulphur. The marine acid is the best adapted to the production of hepatic air. If the concentrated nitrous acid be used, it will afford nitrous air; but having diluted some nitrous acid, whose specific gravity was 1.347, with 20 times its bulk of water, he obtained, with the assistance of heat, as pure hepatic air as with any other acid. The concentrated vitriolic acid, poured on liver of sulphur, afford but little hepatic air without the assistance of heat, though it instantly decomposes the liver of sulphur; and it is partly for this reason that the proportion of air is so small; for it is during the gradual decomposition of sulphureous compounds that hepatic air is produced. Distilled vinegar extricates this air in the temperature of the atmosphere; but it is not pure, its peculiar smell being mixed with that of vinegar. The acid of sugar also produced some quantity of this air in the temperature of 59°. Having made some liver of sulphur, in which the propor- tion of sulphur much exceeded that of the alkali, Mr. K. poured on part of it some oil of vitriol, whose specific gravity was 1 .863 : by this means he obtained hepatic air, so loaded with sulphur, that it deposited some in the tube through which it was transmitted, and on the upper part of the glass receiver. This air he transferred to another receiver; but though it was then perfectly clear and transparent, and amounted to 6 cubic inches, yet the next morning the inside of the glass was thickly lined with sulphur, and the air reduced to 1 cubic inch, which was pure vitriolic air. He also procured this airYrom a mixture of 3 parts filings of iron and one of sulphur, melted together, and treated with marine acid. It is remarkable, that this sulphurated iron, dissolved in marine acid, affords scarce any inflammable, but mostly hepatic air. A mixture of equal parts filings of iron and sulphur, made into a paste with water, after heating and becoming black, afforded hepatic air when an acid was poured on it; but this hepatic air was mixed with inflammable air, which probably proceeded from the uncombined iron. After a few days, this paste lost its power of producing hepatic air. Mr. Bergman has remarked, that combinations of sulphur with some other metals yield hepatic air. VOL. LXXVlJ PHILOSOPHICAL TRANSACTIONS. 7I Mr. K. attempted to extract air from a mixture of oil of olives with caustic vegetable alkali. It immediately whitenedj and on applying heat effervesced so violently as to pass over into the receiver: nor had he better success on adding an acid. The event was different when on a few grains of sulphur he poured some of the oil, and heated them in a phial with a bent tube; for as soon as the sulphur melted, the oil began to act on it, got red, and emitted hepatic air, similar to that produced by other processes. He also obtained this air in great plenty from a mixture of equal parts sulphur and pulverized charcoal, out of which its adventitious air had been as much as possible expelled by keeping it a long time heated to redness, in a crucible on which a cover was luted, with a small perforation to permit the air to escape. This air was inflammable, as ap- peared by holding a lighted candle before it during its emission; yet it is hardly possible to free charcoal wholly from foreign air, for it soon re-attracts it when exposed to the atmosphere. This last mixture, when distilled, affording a large quantity of hepatic and some inflammable air. Six grs. of pyrophorus, made of alum and sugar, effervesced with marine acid, and afforded 2.5 cubic inches of hepatic air. This pyrophorus had been made 6 years before, and was kept in a tube hermetically sealed, and for many summers exposed to the strongest light of the sun. It was so combustible, that some grains of it took fire while it was introduced into the phial out of which the hepatic air was expelled. A mixture of 2 parts white sugar (previously melted in order to free it from water) with I part sulphur, when heated to about 6oo or 700 degrees, gave out hepatic air very rapidly. This air had a smell much re- sembling that of onions; it contained no fixed air, nor saccharine, or other acid. But sugar and sulphur, melted together, gave out no hepatic air when treated with acids. Water, spirit of wine, and marine acid, decompose this mixture, dissolving the sugar^ and leaving the sulphur. A mixture of sulphur and plumbago afforded no hepatic air. On the General Characters of Hepatic Air. — Mr. K. found the absolute weight of this air by weighing it in a glass bottle, previously exhausted by Mr. Hurter's new improved air-pump, whose effect is so considerable as to leave in general only -g-i-g- and frequently but -rVo-r part of unexhausted air. This bottle contained nearly ll6 cubic inches; and this quantity of hepatic air weighed 38.58 grains, the thermometer being then ^7^.5, the barometer 29.94, andM. Saussure's hygrometer 84°, the weight of 1 16 cubic inches of atmospheric air being at the same time 34.87 grs; hence a cubic foot of hepatic air weighs, in these circumstances, 574.7O89 grains, and 100 cubic inches of it weigh about 33 grains: and its weight, relatively to that of common air, is as lOOOO to 9038.* This hepatic air was extracted from artificial pyrites by marine acid. • Hence the weight, says Mr. K., which I have assigned to common air in my first paper, after 72 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. The inflammability of this air has been already mentioned. It never detonates with common air; nor can it be fired in a narrow-mouthed vessel, unless mixed with a considerable proportion of this air. M. Scheele found it to inflame when mixed with -f- of this air. According to M. Sennebier it cannot be fired by the electric spark, even when mixed with any proportion of respirable air. Mr. K. found a mixture of one part of hepatic air and 1.5 of common air to burn blue, without flashing or detonating. During the combustion sulphur is constantly deposited, and a smell of vitriolic air is perceived. A mixture of half hepatic and half nitrous air burns with a bluish, green, and yellow lambent flame; sul- phur is also deposited, and in proportion as this is formed, a candle dipped in this air burns more weakly, and is at last extinguished. A mixture of 2 parts nitrous and 1 of hepatic air partially burns, with a green flame, and a candle is extinguished in the residuum, which then reddens on coming in contact with atmospheric air. He made a mixture of 1 part nitrous and one part hepatic air, and to this admitted 1. part also of common air; the instant the common air was introduced, sulphur was precipitated, and the 3 measures occupied the space of 2.4 measures; this burned on the surface with a wide greenish flame, but the candle was extinguished when sunk deeper. A mixture of 4 parts common air and 1 part hepatic burned blue and rapidly; but a mixture of ] part dephlogis- ticated and 1 part hepatic, which had stood 8 days, went oflT with a report as ioud as that of a pistol, and so instantaneously that the colour of the flame could scarcely be discerned. With respect to solubility in water, hepatic airs extracted from different mate- rials difl^er considerably. In the temperature of 66°, water dissolves, by slight agitation, -§- of its bulk of alkaline or calcareous hepatic air, extracted by marine acid; 4- of its bulk of martial hepatic air, extracted by the same acid; -V of that extracted by means of the concentrated vitriolic acid, or the dilute nitrous or saccharine acids in the temperature of 6o°; -^ of sedative hepatic air; -j\ of acetous hepatic air, and of that afibrded by oil of olives; and of its own bulk of that produced from a mixture of sugar and sulphur. In general, I imagined that which required most heat for its production to be most soluble; though in some instances, particularly that of acetous hepatic air, that circumstance does not take place. But the most remarkable phenomenon attending the union of hepatic air with water is, that it is not permanent. Even water, out of which its own air had been boiled, in a few days after saturation with hepatic air grows M. Fontana, is evidently erroneous ; and indeed, by that determination, common air would not be even 7C0 times lighter than vi^ater, in the temperature of 55°, and the barometer 29.5, which con- tradicts all barometrical and aerostatic experiments : and I cannot omit mentioning the very near agreement of the weight of common air here found with that resulting from the calculation of Sir George Shuckburgh, it is so great as to differ only by 2 grains in a cubic foot. — Orig. VOL. LXXVI.j PHILOSOPHICAL TRANSACTIONS. 73 turbid, and in a few weeks deposits most of it in the form of sulphur, though the bottle be ever so well stopped, or stand inverted in water or mercuryo Yet water no way decomposes hepatic air by absorbing it; for the part left unab- sorbed by a quantity of water is absorbable by a larger quantity of water, and burns like other hepatic air. Heat does not expel this air from water, till car- ried to the degree of ebullition. Of all the tests of hepatic air, the most delicate and sensible is the solution of silver in the nitrous acid. This, according as the nitrous acid is more or less saturated with silver, becomes black, brown, or reddish brown, by contact with hepatic air however mixed with any other air or substance. When the acid is not saturated, or is in large proportion, the brown or black precipitate, which IS nothing but sulphurated silver, is re-dissolved. Of the Action of Hepatic and other Aerial Fluids oneach other. — Six cubic inches of common and 6 of hepatic air being mixed with each other, and standing over mercury for 8 days, were not in the least altered in their dimensions or otherwise; though a diminution of a -p^-g- part might be perceived. The mercury was slightly blackened. The event was the same when 3 measures of common and 1 of hepatic air were used. Water took up the hepatic air. No fixed air was found. Five mea- sures of hepatic and 5 of dephlogisticated air, so pure that one measure of it and 1 of nitrous air made only -rV of a measure, remained unaltered for 8 days, the mer- cury only being blackened. No fixed air was produced, nor the dephlogisticated air phlogisticated. When the mixture was fired, it went off all at once with a loud report. Four measures of phlogisticated and 4 of hepatic air remained unaltered for l6 days: water then took up the hepatic, and left the phlogisticated air. Four measures of inflammable and 4 of hepatic air remained unaltered for 6 days. Two measures of hepatic and 2 of marine acid air suffered no diminu- tion in 3 days. The mercury on which they stood was not blackened. Water took up both, and precipitated the solution of silver black. The same quan- tity of hepatic and fixed air remained 4 days without any sensible diminution. Four measures of water absorbed the greater part of both, had an hepatic smell, precipitated lime from its solution, and also silver, as usual. The residuum extinguished a candle. But vitriolic, nitrous, and alkaline airs had very remarkable effects on he- patic air. Two measures of hepatic being introduced to 2 of vitriolic air, a whitish yellow deposition immediately covered both the tops and sides of the jar, and both airs were, without any agitation, reduced to little more than 1 measure; but the opacity of the incrusted glass prevented the ascertaining the diminution with precision. Hence he repeated this experiment more at large, in the follow- ing manner. To 5 measures of vitriolic air (each measure containing a cubic inch) he added 1 of hepatic air. In less than a minute, without any agitation, VOL. XVI. L 74 PHILOSOPHICAL TRANSACTIONS. [aNNO 1780. the sides of the glass were covered with a whitish scum, which seemed moist, and a diminution took place of more than 1 measure, in 4 hours after, he introduced a second measure of hepatic air, which was followed by a similar diminution and deposit. The next day he added 3 more measures of this last, at the interval of about 4 hours between each ; and still finding a considerable diminution after each, the following day he added another measure; the diminu- tion produced by this last appeared not to exceed 1 measure. He then poured off the residuary air into another jar, and found it not to exceed 3 measures, namely, 5 of vitriolic and 6 of hepatic air, were reduced to 3. kito one mea- sure of this residuary air he introduced a lighted candle: it was immediately quenched. To the 2 remaining measures he added 1 measure of water: by agitation it took up -jV of its bulk. To part the remainder he added nitrous air, which had no effect on it. Another part of it extinguished a candle. It had not a vitriolic smell. With nitrous air Mr. K. made the following experiments. First, he found that 2 measures or cubic inches of nitrous and 2 of hepatic air were little altered when first mixed, even by agitation; but after 36 hours both were reduced to rather more than -^ of the whole. Yellow particles of sulphur were deposited both on the mercury, and on the sides of the jar, but the mercury was not blackened. The residuary air had still an hepatic smell, and was somewhat further diminished by water; and in the unabsorbed part a candle burned natu- rally. The water had all the properties of hepatic water. On the Action of Hepatic Air, and Acid, Alkaline, and Inflammable Liquids, on each other. — One measure of oil of vitriol, whose specific gravity was 1 .s63, absorbed ^ measures of hepatic air except -^. The acid was whitened by a copious deposition of sulphur. On introducing, over mercury, a measure of red nitrous acid, whose specific gravity was 1.430, to an equal measure of hepatic air; red vapours instantly arose, and only -^ or ^-V of a measure remained in an aerial form ; but as the acid acted on the mercury, he was obliged to carry the jar into the water tub, by which means the whole was absorbed: no sulphur was here precipitated. Finding it so difficult to subject hepatic air to the direct action of the con- centrated nitrous acid, he diluted it to that precise degree at which it could not act on mercury without the assistance of heat, and then passed through it an equal bulk of the same hepatic air; the acid was whitened, and -^ of the air absorbed, and the residuum detonated. Repeating the same experiment, with hepatic air from liver of sulphur, he found still more of it absorbed by the acid: but the residuum no longer detonated, but burned with a blue and greenish flame, and sulphur was deposited on the sides of the jar. Distilled vinegar absorbs nearly its own bulk of air, and becomes slightly VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 75 whitened; but by agitation it may be made to take up about its bulk, and then becomes very turbid. One measure of caustic vegetable alkali, whose specific gravity was 1.C43, absorbed nearly 4 measures of alkaline hepatic air. It was at first rendered brown by it; but after some time it got clear, sulphur was deposited, and the surface of the mercury blackened. This shows that alkalis are not dephlogisticated by silver or other metals, as Mr. Baume imagined, but only cleared of part of the sulphur, which they commonly contain, it being formed by the tartar vitriolate contained in the plant, and coal, during com- bustion. One measure of caustic volatile alkali, whose specific gravity was 0.9387, absorbed 18 of hepatic air. If the caustic liquor contained more alkali, it would absorb more hepatic air, as 6 measures of hepatic unite to 7 of alkaline air; and thus the strength of alkaline liquors, and their real contents, may be determined better than by any other method. Also the smoking liquor of Boyle, which is difficultly prepared in the usual way, may easily be formed by placing the volatile alkali in the middle glass of Dr. Nooth's apparatus for making artificial mineral waters, and decomposing artificial pyrites-, or liver of sulphur, in the lower glass, by marine acid. Oil of olives absorbs nearly its own bulk of this air, and obtains a greenish tinge from it. But new milk scarcely absorbs -^ of its bulk of this air, which is very remarkable, and is not in the least coagu- lated. Oil of turpentine also absorbs its own bulk of this air, and even more; but then becomes turbid. Water seems also to precipitate this air from it, for when shaken with it a white cloud appears. Spirit of wine, whose specific gra vity was 0.835, absorbed nearly 3 times its bulk of this air, and became brown. By this means sulphur may be combined with spirit of wine much more easily than by Count Lauragais's method, the only hitherto known. Water precipi- tates the sulphur in part. Of the Properties of Water saturated with Hepatic air. — This water turns tincture of litmus red. It does not affect lime-water. It does not form a cloud in the solution of marine, though it does in that of acetous baro-selenite. The solutions of other earths in the mineral acids are not altered in it. When dropped into a solution of vitriol of iron or marine salt of iron, it produces a white precipitate. In nitrous salt of copper it causes a brown precipitate, and the liquor is changed from blue to green: The precipitate re-dissolves by agita- tion : in vitriolic of copper it forms a black precipitate. The solution of tin in aqua regia is precipitated by it of a yellowish white colour; that of gold, black; that of regulus of antimony, red and yellow ; that of platina, red mixed with white. The solution of silver in the nitrous acid, and also that of lead, whether in acetous or nitrous acid, are precipitated black. If the solutions are not perfectly saturated with metal, the precipitates will be brown or reddish brown, and may be re-dissolved by agitation. The nitrous, solution of mercury is precipitated of L 2 ^6 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. a yellowish brown ; th?t of sublimate corrosive, yellow mixed with black; but by agitation it becomes white. The nitrous solution of bismuth becomes, by mixture with this water, reddish brown, and even assumes a metallic appear- ance; that of cobalt becomes dark; that of zinc, of a dirty white, that of arsenic, in the same acid, yellow mixed with red and white, orpiment and realgar being formed. If oil of vitriol, whose specific gravity is 1 .863, be dropped into hepatised water, it renders it slightly turbid; but if the volatile vitriolic acid be dropped into it, a bluish white and much denser cloud is formed in the water. Strong nitrous acid, whether phlogisticated or not, causes a copious white precipitation; but dilute nitrous acid produces no change. Green nitrous acid, whose specific gravity was 1.328 immediately precipitated sulphur from it. Strong marine acid produced a light cloud; but neither distilled vinegar nor acid of sugar had any effect. Of the Properties of Alkaline Liquors, impregnated with Hepatic Air. — Colourless fixed alkaline liquors receive a brownish tinge from this air. The residuum they leave is of the same nature as the part they absorb. A caustic fixed alkaline liquor, saturated with this air, precipitates barytes from the acetous acid, of a yellowish white colour. It also decomposes other earthy solutions, and the colour of the precipitates varies according to their purity, and perhaps this test might be so far improved as to supply the place of the Prussian alkali. It precipitates the solution of vitriol of iron, and also marine salt of iron, black; but this latter generally whitens by agitation. The solutions of silver and lead are also precipitated black with some mixture of white; that of gold is also blackened; but that of platina becomes brown. Solutions of copper let fall a reddish black or brown precipitate. Sublimate corrosive by this test discovers a precipitate partly white and black, and partly orange and greenish. In the nitrous solution of arsenic it forms a yellow and orange; and in that of regulus of antimony, in aqua regia, an orange precipitate mixed with black. Nitrous solution of zinc, thus treated, shows a dirty white; that of bismuth a brown mixed with white; and that of cobalt a brown and black precipitate. As Prussian alkali always contains some iron, it gives a purple precipitate with this test, which precipitate is easily dissolved. It turns tincture of radishes, which is my test for alkalis, green. Water saturated with the condensed residuum of alkaline hepatic air, that is, with the purest volatile liver of sulphur, does not precipitate marine selenite, though it forms a slight brown and white cloud in that of marine baro-selenite. It produces a black precipitate in the solution of vitriol of iron, and a black and white in that of marine salt of iron; but by agitation this last becomes wholly white. It precipitates both vitriol of copper, and the nitrous salt of copper, red. VOL. LXXVI,] PHILOSOPHICAL TRANSACTIONS. 77 and brown. Tin in aqua regia gives a yellowish precipitate; gold a dilute yellow and reddish brown; platina a flesh-coloured precipitate; and regulus of antimony a yellowish red. Silver is precipitated black; and so is lead, both from the nitrous and acetous acids. Sublimate corrosive appeared for an instant red; but soon after its precipitate appeared partly black and partly white. The nitrous solution of bismuth affords also a precipitate, partly black, partly white, and partly reddish brown, and of a metallic appearance ; that of cobalt is also black or deep brown. Arsenical solutions give yellow precipitates more or less red; but those of zinc only a dirty white. Of the Constitution of Hepatic Air. — From an attentive consideration of the above experiments, it is difficult to conclude that hepatic air consists of any thing else than sulphur itself, kept in an aerial state by the matter of heat. Every attempt to extract inflammable air from hepatic air, when drawn from materials that previously contained nothing inflammable, namely, from alkaline or calcareous hepars, proved abortive: on the contrary, when the materials could previously supply inflammable air, as when martial carbonaceous and saccharine compounds were employed, inflammable air, in ever so small a proportion, was detected: nor could hepatic air be procured from the direct union of inflam- mable air and sulphur, as we have seen. Of Phosphoric Hepatic Air. — As phosphorus, in respect to its constituent partSp bears a strong resemblance to sulphur, Mr. K. was naturally led to examine its phenomena when placed in the same circumstances : he therefore gently heated about 10 or 12 grains of phosphorus, mixed with about half an ounce of caustic fixed alkaline solution, in a very small phial, furnished with a bent tube, and received the air over mercury. On the first application of heat two small explosions took place, attended with a yellow flame and white smoke, which penetrated through the mercury into the receiver ; these were followed by an equable production of air. At last the phosphorus began to swell and froth, and fearing the rupture of the phial, he stopped the tube to prevent the access of atmospheric air, and removed the phial to a water tub, intending to throw it in ; but in the mean while the phial burst with a loud explosion, by reason of an obstruction in the tube, and a fierce flame immediately issued from it. However he obtained about 8 cubic inches of air. This air was diminished very slightly, by agitation with an equal bulk of water, and then became cloudy like white smoke, but soon after recovered its transparency. On turning up the mouth of the tube to examine the water, the unabsorbed air instantly took fire, and burned with a yellow flame without ex- ploding, leaving a reddish deposit on the sides of the tube. Water impregnated with phosphoric air, and over which this air had burned, slightly reddened tine- 78 PHILOSOPHICAL TKANSACTIONS. [aNNO 1786. tiire of litmus. Did not affect Prussian alkali. Had no effect on the nitrous solutions of copper or lead, zinc or cobalt, nor on marine solution of iron or tin, or of tin in aqua regia, nor on the vitriolic solutions of iron, copper, tin, lead, zinc, regulus of antimony, arsenic, or manganese ; nor on the marine solutions of iron, copper, lead, zinc, cobalt, arsenic, or manganese. But it precipitated the nitrous solution of silver black, and vitriol of silver brown ; also nitrous solution of mercury made without heat brown and black ; but vitriol of mercury first became reddish, and afterwards white ; and sublimate corrosive yellow and red mixed with white. Gold dissolved in aqua regia is precipitated purplish black, and from the vitriolic acid brownish red and black ; but reguius of antimony in aqua regia is precipitated white by this phosphorated water. The nitrous solution of bismuth showed first a white, and presently after a brown precipitate. Vitriol of bismuth and marine salt of bismuth were also precipitated brown ; this latter re-dissolved by agitation. The nitrous solution of arsenic also became brown, but re dis solved by agitation. Phosphoric air was scarce at all diminished by the addition of an equal mea- sure of alkaline air ; and water being put to these, took up in appearance little else than alkaline air ; yet on turning up the mouth of the jar, the residuary air smoked without flaming. The water, thus impregnated, had exactly the smell of onions. It turned tincture of radishes green. It precipitated solution of silver black ; and that of copper in the nitrous acid brown ; but this precipitate was re-dissolved by agitation, and the liquor became green. Sublimate corrosive was precipitated yellow mixed with black. Iron was precipitated white, both from the vitriolic and marine acids ; but a pale yellow solution of it in the nitrous acid was not affected ; and a red solution of it in the same acid was only congrumated. Regulus of antimony in aqua regia gave a white, cobalt in nitrous acid a very slight reddish, and bismuth in the same acid a brown pre- cipitate. But neither the nitrous solution of lead or zinc, nor that of tin in marine acid or aqua regia, nor that of regulus of antimony in aqua regia, were any way affected. Fixed air, mixed with an equal proportion of phosphoric air, produced a white smoke, some diminution, and a yellow deposit. On agitating the mixture in water, the fixed air was all taken up except -tV- The residuum smoked, but did not inflame spontaneously. From these few experiments, Mr. K. thinks it may be concluded, that phos- phoric air is nothing else but phosphorus itself in an aerial state, and differs from sulphur in this, among other points, that it requires much less latent heat to throw it into an aerial form, and hence may be disengaged from fixed alkalis, without the assistance of an acid. YOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. * 7^ VI. Observations on the j^ffinities of Substances in Spirit of Wine. By John Elliot, M.D. p. 155. In Mr. Kirwan's papers on the attractive powers of the mineral acids, it is shown that metallic calces have stronger attractions to those acids, than alkalis and earths. The following experiments not only confirm this doctrine, but also a position that I have lately ventured to advance,* " that certain decompositions will take place in spirit of wine, which will not at all in water, nor in the dry way.** I have shown, that if expressed oil be mixed with slaked lime into a paste, * so as to form calcareous soap, and mild alkali be added, the latter will not de- compose the former, either in water or by fusion. But that if spirit of wine be substituted for water, an alkaline soap and mild calcareous earth will be formed. As sea salt contains the fossil alkali, and as by the table of affinities acids have stronger attraction to metallic calces than to alkalis, I concluded, that if sea salt were added to a metallic soap, a similar double decomposition would take place. To try this, I took some diachylum, which had been bought at Apothecaries- Hall, and added to it sea salt ; then covered them to a sufficient height with spirit of wine, and set the bottle over the fire. Soon after they had boiled, the decomposition of the diachylum began to be apparent. When the boiling had continued some time, I removed the vessel from the fire, and after it had stood a few minutes, decanted the clear liquor while hot ; then evaporating it, obtained a true alkaline soap. The residuum of course contained a quantity of calx of lead, combined with marine acid. But much of the diachylum remained either wholly or partly undecomposed : I therefore added more sea salt and spirit of wine, and obtained a further yield of soap. But though much sea salt remained behind, diachylum was still found in the residuum. I found indeed, that if the ingredients were previously freed from their water, the process succeeded to somewhat better advantage. From 5 oz. of diachylum I did not get quite 3 oz. of soap. This soap was likewise soft, and contained a portion of oil not combined with a sufficient quan- tity of alkali. The oil I suppose had existed in a similar state in the diachylum : and I remarked, that as the spirit evaporated, it gave out the true soap first, the unsaturated oil not till afterwards; so that the latter might easily be obtained separate from the formefr. If too much salt was employed, much of it was taken up by the liquid, and communicated to the soap, at least if the ingre- dients had not been previously deprived of their water. To separate this salt I * In an Appendix to the 2d edit. •£ the " Elements of the Branches of Nat. Philos. connected with Medicine." — Orig. 80 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. dissolved the soap in hot water. When the liquor was cold, the soap floated at top, the salt remaining in the water underneath. If too little salt was used, this inconvenience did not happen, or not in so great a degree, though then less soap was of course obtained. As diachylum, though with a greater proportion of litharge, and boiled longer than that I had from the Hall, still contained oil not sufficiently saturated, I made the metallic soap in another way. To a solution of sugar of lead in water I added a solution of alkaline soap in the same liquid. A double decomposition took place, the oil uniting with the calx of lead, the alkali with the acid of salt. Using this metallic soap instead of the other, I obtained an alkaline soap harder and more perfect than in the preceding process ; but still found that parts of the oil remained with the calx of lead in the residuum, and adhered so firmly, that repeated quantities of sea salt and spirit of wine did not wholly separate it. p. s. Since writing the above I have found, that if mild fixed alkali be added to diachylum in hot water, they unite into a gelatinous mass, which is miscible with the water. This may be considered as a kind of hepar. If this substance be put into hot spirit of wine, the decomposition already described takes place. If chalk be substituted for alkali, there is a similar result. I have found that nitre is decomposed by diachylum in spirit of wine. I have also found, that if the compound of diachylum and common salt be put into hot spirit of turpen- tine, the diachylum is dissolved, but the salt remains at the bottom of the vessel. Vll. An Account of some Minute British Shells, either not duly observed^ or totally unnoticed by Authors. By the Rev. John Lightfoot, M. A., F. R. S. p. 160. The shells which form the subject of this paper were discovered in the neigh- bourhood of Bullstrode, in Buckinghamshire, by Mr. Agnew, gardiner to the Duchess Dowager of Portland. The drawings of the shells were also made by Mr. Agnew. The first-mentioned shell, a, pi. 2, named by Mr. Lightfoot Nautilus lacustris, is of a flatted spiral figure, umbilicated on one side, convex on the other, but slightly depressed in the centre, and measures about a quarter of an inch in dia- meter: its volutes or spires are 4 in number: the mouth of the shell is obliquely semioval, the upper edge projecting further than the lower: the substance of the shell is very brittle and pellucid, and when recent is of a reddish brown or ches- nut-colour, except 3 or 4 whitish curving streaks, from the centre to the circum- ference, at nearly equal distances from each other. The internal structure of this shell is extremely curious, the whole cavity being divided, according to the VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 81 age of the shell, into 3, 4, or 5 chambers, by so many transverse, white, brittle, semipellucid septa, each of which has a triradiated aperture, through which the animal protrudes itself when in motion. As to the real nature of these septa, Mr. Lightfoot does not pretend to guess at the intention of Nature in their for- mation. If it should be said, that they only point out the different periods of the shell's growth, and are nothing else but the limits or terminations of the animal's periodical increase, Mr. Lightfoot will not dispute the opinion, but, supposing it to be so, he asks whether it is not equally probable that the trans- verse septa in all the nautili are nothing else? The inhabitant of this curious shell is of the slug kind, but of the aquatic tribe, and has filiform tentacula, the eyes being placed on the head of the animal, near their bases, and not at the tip, as in the land kinds: the colour of the animal is a grey brown. Mr. Light- foot gives the following specific character of this species, viz. Nautilus lacmtris. N. testa spirali compressa umbilicata carinata, anfractibus tribus supra convexis contiguis, apertura semiovata, septis triradiato-perforatis. Fresh-water nautilus. Nautilus with spiral, compressed, umbilicated, carinated shell, with 3 wreaths convex above and contiguous, semiovate aperture, and triradiate-perforated septa. In Mr. Walker's publication on minute shells it is described under the name of Helix lineaia; but the chambered internal structure was unknown to Mr. Walker. Fig. 1, shell A, pi. 2, shows the shell of its natural size, with the umbilicated side uppermost. Fig. 2, the same with the depressed side uppermost. Fig. 3, the shell magnified, with the depressed side uppermost, and showing the living animal. Fig. 5, the same magnified, with the umbilicated side uppermost. Fig. 4, the same in front, but cut away to the first septum. Fig. 8, the animal's excrement. Fig. 6, 7, horizontal sections of the shell, in order to show the in- ternal structure. The 2d shell, b, Mr. Lightfoot names Helix fontana or Fountain Helix, and thus gives its character, viz. Helix testa compressa obtuse carinata, hinc umbili- cata, anfractibus tribus utrinque convexis, apertura semiovata. Helix with com- pressed, obtusely carinated shell, umbilicated on one side, with 3 wreaths convex on both sides, and semiovate aperture. Fig. 1 shows the shell of the natural size, with the most convex side upper- most. Fig. 2, the same with the umbilicated side uppermost. Fig. 3, the shell magnified, with the most convex side uppermost. Fig. 4, the same with the umbilicated side uppermost. This species vyas found in a spring of clear water among rotten leaves, its co- lour is reddish brown or chesnut. VOL. XVI. M 82 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. The 3d shell c, is a very minute, but curious, species of Helix, of a snbco- nical form, consisting of about 5 convex wreaths, gradually diminishing towards . the apex. The colour of the whole shell is brown. Mr. Lightfoot names it Helix spinulusa or tender prickly Helix, and characterises it in the following manner, viz. Helix testa subconica umbilicata, anfractibus quinque convexis, annulis membranaceis acutis cinctis, dorso spinuloso-carinatis, apertura suborbi- culari. The shell is umbilicated at the base, and the wreaths are transversely sur- rounded with numerous sharp-edged rings, which are produced in the middle or back of each wreath into a kind of spur, formed of compressed and ver)^- tender spines. It was found at the foot of pales on old bricks and stones, &c, after rainy weather in June and July. Fig. 1 , 2, the shell of the natural size, in different positions. Fig. 3, 4, 5, the same magnified. The 4th species d, is a Turbo. It strongly resembles the depressed helices, but its circular mouth forbids its being ranked in that Linnean genus. It is of a brown colour, and consists of 4 cylindric or rounded volutions, which are sur- rounded transversely with numerous sharp-edged membranaceous rings, which are very fragile and deciduous; the mouth, when perfect, is bordered with a com- pressed erect margin. Mr. Lightfoot gives the specific character thus, viz. Turbo helicinus. T. testa depresso-plana, hinc umbilicata, anfractibus quatuor torosis, annulis numerosis acutis membranaceis cinctis. Fine ringed turbo. Turbo with depressed-flat shell, umbilicated on one side, with 4 torose wreaths, surrounded by numerous acute membranaceous rings. Fig. 1, 2, the shell on both sides, of its natural size. Fig. 3, 4, the same magnified. It was found in spring, near Bullstrode, on base stones, &c. The 5 th and last shell, e, is a species of Patella, and is about a quarter of an inch in length, and a tenth of an inch in diameter, having a pointed vertex nearest to the lower end, turned downwards, and leaning to one side. Mr. Lightfoot names it patella oblonga or oblong fresh-water patella, and thus gives its specific character, viz. Patella testa integerrima oblonga compressa membra- nacea, vertice mucronato reflexo obliquo. Patella with perfectly entire, oblong, compressed, membranaceous shell, with reflex, oblique, mucronated vertex. It was found in waters near Beaconsfield, adhering to the leaves of the iris pseudacorus. Fig. 1 , 2, 3, show it in its natural size, in different positions. Fig. 5, mag- nified, with the vertex upward. Fig. 6, a view of the patella lacustris of Lin- neus, in order to show the plan of the two different species. VOL. LXXVI.] PHILOSOPHICAL THANSACTIONS. 83 VIII. Observations on the Sulphur IVells at Harrogate, made in July and Aug. 1785. By the Right Rev. Rich. Lord Bishop of Landaff, F. R.S. p. 17 I . Reprinted in the 5th vol. of the Bishop of LandafTs (Dr. Watson's) Chemical Essays. IX. Observations and Remarks on those Stars which the Astronomers of the last Century suspected to be Changeable. By Edw. Pigott, Esq. p. ISQ. It is about a century since Hevelius, Montanari, Flamsteed, Maraldi, and Cassini, noticed a certain number of stars which they supposed had either dis- appeared, changed in brightness, or were new ones; and yet to this day we have acquired no further knowledge of them. This may be attributed to the difficulty of finding out what star is meant, and the not having exact observations of their relative brightness. I therefore have drawn up the following catalogue, and made the necessary observations; so that in future we can examine them without much trouble, and be certain of any change that may take place. To accom-. plish this, it was requisite to compare with attention many authors and most of the catalogues of stars; in doing which, I have perceived several undoubted errors, and others highly probable. In order to separate certainty from doubt, I have classed these stars in 2 divi- sions; the first are undoubtedly changeable; the others remain yet to be better authenticated. Though some of them bear all the appearance of being variable, still no certainty of their being so has come to my knowledge. To those of the first class are subjoined observations made on them within these last 4 years, from which the period and progressive changes of some are deduced, though never settled before; and if already known, are more exactly determined by com- paring my observations with former ones. Also, as the position of several are determined only by ancient astronomers, and therefore inaccurately, I have ob- served them with great exactness, the declinations being taken with a Bird's 18- inch quadrant, and the right ascensions with a 3-feet transit instrument; these last may serve in future to discover their proper motions in right ascension, for which reason I shall specify the stars to which they were compared. The stars of the 2d class have either their relative brightness exactly settled, or their non- existence ascertained. I have also pointed out the probability of a mistake in several, and in general given an account of the appearance they have had within these few years. M 2 84 PHILOSOPHICAL TRANSACTIONS. [anno 1786. Catalogue of variable Stars^ reduced to the beginning of 1786. Class the first. Names. Nova 1 572, in Cassiopeia. . • Ceti Algol Mayer's 420th in Leo . . . . In Hydra Nova l604 in Serpentarius y8 Lyrae Near the Swan's head . . . . « Antinoi In the Swan's neck In the Swan's breast ^ Cephei R. A. in time. Declination. 2 8 33 2 54 19 9 36 5 13 18 4 17 18 0 18 42 11 19 38 58 19 41 34 19 42 21 20 9 54 22 21 0 + 62° 58' 3 57 40 6 12 25 22 21 33 26 48 0 28 32 22 37 22 bl 20 + "N 25 s, bS N, 0 N. 38 s is 46 N, 14 N. 58 N. 37 N. 0 N. Hevelius's 6 Cassiopeae 46 or I Andromedae 50 or t- Andromedae Hevelius's 41 Andromedae . Tycho's 20th Ceti 5b or Neb. Andromedae . . . Ptol. and Ul. Beigh