? I QS/ U '0 REPORT OF THE THIRTY-SECOND MEETING OF THE BRITISH ASSOCIATION FOE THE ADVANCEMENT OE SCIENCE; HELD AT CAMBRIDGE IN OCTOBER 18G2. 32. LONDON: JOHN MURRAY, ALBEMARLE STREET. 1863. PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET. ALEHK J FLAMMAM. CONTENTS. Page Objects and Rules of the Association xvii Places of Meeting and Officers from commencement xx Treasurer's Account xxiv Members of Council from commencement xxv Officers and Council, 1861-62 xxviii Officers of Sectional Committees xxix Corresponding Members xxx Report of the Council to the General Committee xxxi Report of the Kew Committee, 1861-62 xxxii Report of the Parliamentary Committee xxxix Recommendations of the General Committee for Additional Reports and Researches in Science xxxix Synopsis of Money Grants xliii General Statement of Sums paid on account of Grants for Scientific Purposes xlv Extracts from Resolutions of the General Committee xh'y Arrangement of the General Meetings 1 Address of the President, the Rev. R. Willis, M.A., F.R.S., &c li REPORTS OF RESEARCHES IN SCIENCE. Report on Observations of Luminous Meteors, 1861-62. By a Com- mittee, consisting of James Glaisher, F.R.S., F.R.A.S., Secretary to the British Meteorological Society, &c. ; R. P. Greg, F.G.S., &c. ; E. W. Brayley, F.R.S., &c. ; and A. Herschel 1 On the Strains in the Interior of Beams. By George Biddell Airy, F.R.S., Astronomer Royal 82 VI CONTENTS. Page Keport on the three Reports of the Liverpool Compass Committee and other recent Publications on the same subject. By Archibald Smith, M.A., F.R.S., and Frederick John Evaws, R.N., FJLS 87 Report on Tidal Observations on the Huniber. Presented by James Oldham, C.E. ; John Scott Russell, C.E., F.R.S. ; J. F. Bateman, C.E., F.R.S. ; and Thomas Thompson 101 On Rifled Guns and Projectiles adapted for Attacking Armour-plate Defences. By T. Aston, M.A., Barrister-at-Law 103 Extracts, relating to the Observatory at Kew, from a Report presented to the Portuguese Government by Dr. Jacintho Antonio de SorzA, Professor of the Faculty of Philosophy in the University of Coimbra. (Communicated by J. P. Gassiot, F.R.S.) 109 Report on the Dredging of the Northumberland Coast and Dogger Bank. Drawn up by Henry T. Mennell, on behalf of the Natural History Society of Northumberland, Durham, and Newcastle-on-Tyne, and of the"Tyneside Naturalists' Field Club 116 Report of the Committee appointed at Manchester to consider and report upon the best means of advancing Science through the agency of the Mercantile Marine. By Cuthbert Collingwood, M.B., F.L.S 122 Provisional Report of the Committee, consisting of Professor A. Wil- liamson, Professor C. Wheaxstone, Professor W. Thomson, Professor \V. H. Miller, Dr. A. Matthiessen, and Mr. Fleeming Jenkin, on Standards of Electrical Resistance 125 Preliminary Report of the Committee for Investigating the Chemical and Mineralogical Composition of the Granites of Donegal, and the Mine- rals associated with them 163 On the Vertical Movements of the Atmosphere considered in connexion with Storms and Changes of Weather. By Henrt Hennesst, F.R.S., M.R.I. A., &c, Professor of Natural Philosophy in the Catholic Uni- versity of Ireland 165 Report of a Committee, consisting of the Rev. Dr. Lloyd, General Sabine, Mr. A. Smith, Mr. G. Johnstone Stoney, Mr. G. B. Airy, Professor Donkin, Professor Wm. Thomson, Mr. Cayley, and the Rev. Professor Price, appointed to inqvrire into the adequacy of existing data for carrying into effect the suggestion of Gauss, to apply his General Theory of Terrestrial Magnetism to the Magnetic Variations 170 On Thermo-electric Currents in Circuits of one Metal. By Fleeming Jenkin. (Plate I.) 173 On the Mechanical Properties of Iron Projectiles at High Velocities. By W. Fairbairn, F.R.S 178 Report on the Progress of the Solution of certain Special Problems of Dynamics. By A. Cayley, F.R.S., Correspondent of the Institute. . 184 Report on Double Refraction. By G. G. Stokes, M.A., D.C.L., Sec. U.S., Lucasian Professor of Mathematics in the University of Cambridge . . 253 CONTENTS. Vll Page Fourth Report of the Committee on Steamship Performance. (Plate III.) 282 On the Fall of Rain in the British Isles during the Years 1860 and 1801. By G. J. Symons, M.B.M.S. (Plate II.) 293 On Thermometric Observations in the Alps. By J. Ball, M.R.I.A.., F.L.S., &c 363 Report of the Committee for Dredging on the North and East Coasts of Scotland. By J. Gwyn Jeffreys, F.R.S 371 Report of the Committee, consisting of the Rev. W. Vernon Harcottrt, Right Hon. Joseph Napier, Mr. Tite, M.P., Professor Christison, Mr. J. Heywood, Mr. J. F. Bateman, and Mr. T. Webster, on Tech- nical and Scientific Evidence in Courts of Law . 373 An Account of Meteorological and Physical Observations in Eight Bal- loon Ascents, made, under the Auspices of the Committee of the British Association for the Advancement of Science at Manchester, by James Glaisher, F.R.S., at the request of the Committee, consisting of Colonel Stkes, Mr. G B. Airy, Lord Wrottesley, Sir D. Brewster, Sir J. Herschel, Dr. Lloyd, Admiral FitzRoy, Dr. Lee, Dr. Robinson, Mr. Gassiot, Mr. Glaisher, Dr. Tyndall, Mr. Fairbairn, and Dr. W. A. Miller 376 Report on the Theory of Numbers. — Part IV. By H. J. Stephen Smith, M.A., F.R.S., Savilian Professor of Geometry in the University of Oxford 503 APPENDIX I. Errata in Report of Observations of Luminous Meteors, 1861-62 .... 527 Vlll CONTENTS. NOTICES AND ABSTRACTS OF MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. MATHEMATICS and PHYSICS. Mathematics. Page Address by G. G. Stokes, M.A., F.R.S., Lucasian Professor of Mathematics in the University of Cambridge, President of the Section 1 Rev. F. Bashforth on Capillary Attraction 2 Professor Boole on the Differential Equations of Dynamics 3 Rev. Dr. Booth on an Instrument for describing Geometrical Curves ; invented by H. Johnston 3 Professor A. Cayley on a certain Curve of the Fourth Order 3 on the Representation of a Curve in Space by means of a Cone and Monoid Surface 3 Mr. W. Esson on the Curvature of the Margins of Leaves with reference to their Growth 3 Sir William Rowan Hamilton, Quaternion Proof of a Theorem of Reci- procitj' of Curves in Space 4 Rev. Robert Harley on a certain Class of Linear Differential Equations . . 4 Mr. T. A. Hirst on tbe Volumes of Pedal Surfaces 5 Professor William John Macquorn Ranktne on the Exact Form and Mo- tion of Waves at and near the Surface of Deep Water 5 Mr. W. H. L. Russell on Recent Discoveries made in the Calculus of Symbols 7 Mr. C. M. Willich on some Models of Sections of Cubes 8 Astronomy. Mr. Isaac Ashe's Cosmogonical Speculations 8 Mr. W. R. Birt on a Group of Lunar Craters imperfectly represented in Lunar Maps 9 Rev. Professor Challis on the Augmentation of the Apparent Diameter of a Body by its Atmospheric Refraction 12 on the Zodiacal Light, and on Shooting-Stars 12 Professor Hennessy on some of the Characteristic Differences between the Configuration of the Surfaces of the Earth and Moon 14 Mr. William Lassell on a Brilliant Elliptic Ring in the Planetary Nebula, M 20° 56', N.P.D. 101° 56' 14 CONTENTS. IX Page Rev. R. Main, Observed R.A. and N.P.D. of Comet II. 1862 15 on the Dimensions and Ellipticity of Mars 15 Mr. J. Nasmyth on some Peculiar Features in the Structure of the Sim's Sur- face 1G Mr. Norman Pogson's Observations on Three of the Minor Planets in 1860. (Communicated by Dr. Lee.) 16 Mr. W. Ogilby on the Excentricitv of the Earth, and the Method of finding the Coordinates of its Centre of Gravity * 17 M. J. Schvarcz on the probable Origin of the Heliocentric Theory 17 Rev. Professor Selwyn on Autographs of the Sun 17 Mr. W. Spottiswoode on the Hindu Method of Calculating Eclipses 18 M. C. J. Villa on some Improved Celestial Planispheres 18 Light and Heat. Mr. A. Claudet on the Means of following the Small Divisions of the Scale regulating the Distances and Enlargement in the Solar Camera 18 M. A. Des Cloizeaux sur la Relation entre les Phenomenes de la Polarisation Rotatoire, et les Formes Hemiedres ou Hemimorphes des Cristaux a un ou a deux Axes Optiques 19 Mr. James Croll on the Cohesion of Gases, and its relations to Carnot's Function and to recent Experiments on the Thermal effects of Elastic Fluids in Motion 21 Rev. .T. Dingle on the Supernumerary Bows in the Rainbow 22 Dr. Esselbach on the Duration of Fluorescence 22 Mr. J. M. Menzies on an Optical Instrument which indicates the Relative Change of Position of Two Objects (such as Ships at Sea during Night) which are maintaining Independent Courses 22 Rev. J. B. Reade's Experiments on Photography with Colour 22 Mr. J. Smith on the Complementary Spectrum 23 Mr. Charles Tomlinson on the Motion of Camphor, &c. towards the Light 23 Electricity, Magnetism. Mr. James Croll on the Mechanical Power of Electro-Magnetism, with spe- cial reference to the Theory of Dr. Joule and Dr. Scoresby 24 Dr. Esselbach on Electric Cables, with reference to Observations on the Malta- Alexandria Telegraph 26 on an Experimental Determination of the Absolute Quantity of Electric Charge on Condensers 27 Mr. G. M. Guy on an Electromotive Engine 27 Meteorology. Mr. Isaac Ashe on Balloon Navigation 27 on some Improvements in the Barometer 28 Mr. John Ball on the Determination of Heights by means of the Barometer 28 Rev. Professor Ciiallis on the Extent of the Earth's Atmosphere 29 X CONTENTS. Page Mr. F. Galton on tlie "Boussole Burnier," a new French Pocket Instrument for measuring Vertical and Horizontal Angles 30 on European Weather-Charts for December 1861 30 Dr. Gladstone on the Distribution of Fog round the Coasts of the British Islands 31 Mr. J. Glaisher on a New Barometer used in the last Balloon Ascents .... 31 Mr. J. Pake Harrison on the Additional Evidence of the Indirect Influence of the Moon over the Temperature of the Air, resulting from the Tabulation of Observations taken at Greenwich in 1861-02 31 Professor Hennessy on the Relative Amount of Sunshine falling on the Torrid Zone of the Earth 31 Mr. E. J. Lowe on the Hurricane near Newark of May 7th, 1862, showing the force of the Hailstones and the violence of the Gale 32 Mr. Robert Mallet's Proposed Measurement of the Temperatures of Active Volcanic Foci to the greatest attainable Depth, and of the Temperature, state of Saturation, and Velocity of Issue of the Steam and Vapours evolved 33 Mr. T. L. Plant on Meteorology, with a Description of Meteorological Instru- ments 34 Rev. T. Rankin's Meteorological Observations registered at Huggate, York- shire 34 Mr. S. A. Ro well's Objections to the Cyclone Theory of Storms 34 Mr. G. J. Symons on the Performance, under trying circumstances, of a very small Aneroid Barometer 35 Professor James Thomson on the Disintegration of Stones exposed in Build- ings and otherwise to Atmospheric Influence 35 CHEMISTRY. Address by Professor W. H. Miller, M.A., F.R.S., President of the Section 35 Mr. George Bowdler Buckton on the Formation of Organo-Metallic Ra- dicals by Substitution 36 Mr. Dugald Campbell on the Action of Nitric Acid upon Pyrophosphate of Magnesia 37 M. A. Des Cloizeaux sur les modifications temporaires et permanentes que la Chaleur apporte a quelques proprietes optiques de certains, corps cristallise's 38 Mr. J. P. Gassiot on the Mode of preparing Carbonic Acid Vacua in large Glass Vessels 42 Dr. J. H. Gladstone on the Essential Oil of Bay, and other Aromatic Oils. . 43 on the Means of observing the Lines of the Solar Spec- trum due to the Terrestrial Atmosphere 43 Mr. A. Vernon Harcourt on a particular Case of induced Chemical Action 43 Dr. G. Harley on Schonbein's Antozone 44 Mi - . "W. H. Harris on the Adulteration of Linseed Cake with Nut-cake .... 45 Mr. Charles Heisch on a Simple Method of taking Stereomicro-photographs 46 Mr. E. J. Lowe on his Ozone Box 46 Observations on Ozone 46 Dr. Moffat on the Luminosity of Phosphorus 47 Dr. W. Odling on Ferrous Acid 48 CONTENTS. XI Page Dr. ling on the Synthesis of some Hydrocarbons 48 on the Nomenclature of Organic Compounds 48 Mr. J. W. Osborne on the Essential Oils and Resins from the Indigenous Vegetation of Victoria 48 Details of a Photolithographic Process, as adopted by the Government of Victoria, for the publication of Maps 49 Dr. B. H. Paul on the Manufacture of Hydrocarbon Oils, Paraffin, &c, from Peat 50 on the Decay and Preservation of Stone employed in Build- ing 50 Dr. T. L. Phipson on the Artificial Formation of Populine, and on a new Class of Organic Compounds 50 on the Existence of Aniline in certain Fungi which be- come Blue in contact with the Air, &c 51 Analysis of the Diluvial Soil of Brabant, &c, known as the Limon de la Hesbaj - e 53 Professor H. E. Roscoe on Hypobromous Acid 54 Mr. T. Sutton's Description of a rapid Dry-Collodion Process 54 GEOLOGY. Address by J. Beete Jukes, M.A., F.R.S., President of the Section 54 Professor Allman on an Early Stage in the Development of Comatula, and its Palseontological Relations 65 Professor Ansted on Bituminous Schists and their Relation to Coal 65 on a Tertiary Bituminous Coal in Transylvania, with some remarks on the Brown Coals of the Danube 66 Captain Godwin-Austen on the Glacier Phenomena of the Valley of the tipper Indus , 67 Dr. A. Carte and Mr. W. H. Baily on a New Species of Plesiosaurus from the Lias near Whitby, Yorkshire 68 Mr. W. T. Blanford on an Extinct Volcano in Upper Burmah 69 Rev. T. G. Bonney on some Flint Implements from Amiens 70 Rev. J. Cromptox on Deep or Artesian Wells at Norwich 70 Dr. Daubeny on Flint Implements from Abbeville and Amiens 71 on the last Eruption of Vesuvius 71 Mr. W. Boyd Dawkins on the Wokey Hole Hysena-den 71 Rev. J. Dingle on Specimens of Flint Instruments from North Devon 72 Mr. Doughty on Flint Instruments from Hoxne 72 Mr. F. J. Foot on the Geology of Burren, co. Clare 72 Dr. Fhitsch on some Models of Foraminifera 72 Professor Darkness on the Skiddaw Slate Series 72 Mr. J. Gwyx Jeffreys on an Ancient Sea-bed and Beach near Fort William, Inverness-shire 73 Dr. W. Lauder Lindsay on the Geology of the Gold-fields of Otago, New Zealand 77 Xll CONTENTS. Page Dr. W. Lauder Lindsay on the Geology of the Gold-fields of Auckland, New Zealand 80 Mr. Charles Moore on the Palaeontology of Mineral Veins; and on the Secondary Age of some Mineral Veins in the Carboniferous Limestone .... 82 , Contributions to Australian Geology and Palaeontology 83 Mr. C. W. Peach on the Fossils of the Boulder-clay in Caithness 83 on Fossil Fishes from the Old Eed Sandstone of Caithness 85 Mr. W. Pengelly on the Correlation of the Slates and Limestones of Devon and Cornwall with the Old Red Sandstones of Scotland, &c 85 Mr. T. A. Read win on the Gold-bearing Strata of Merionethshire 87 Mr. C. B. Rose on some Mammalian Remains from the Bed of the German Ocean 91 Mr. J. W. Salter on the Identity of the Upper Old Red Sandstone with the Uppermost Devonian (the Marwood Beds of Murchison and Sedgwick), and of the Middle and Lower Old Red with the Middle and Lower Devonian. . 92 Mr. S. P. Saville on a Skidl of the Rhinoceros tichorhinus 94 Mr. H. Seeley on a Whittled Bone from the Barnwell Gravel 94 Rev. Gilbert N. Smith on a Successful Search for Flint Implements in a Cave called " The Oyle," near Tenby, South Wales 95 Mr. H. C. Sorby on the Cause of the Difference in the State of Preservation of different kinds of Fossil Shells 95 on the Comparative Structure of Artificial and Natural Igneous Rocks 96 Rev. W. S. Symonds on Scutes of the Labyrinthodon, from the Keuper Bone- Breccia of Pendock, Worcestershire 96 Mr. A. B. Wynne on the Geology of a Part of Sligo 96 ZOOLOGY and BOTANY, including PHYSIOLOGY. Botany. Mr. James Buckman on the Ennobling of Roots, with particular reference to the Parsnip 97 , Experiments with Seed of Malformed Roots 97 Dr. Daubeny's Reply to the Remarks of M. F. Marcet on the Power of Selec- tion ascribed to the Roots of Plants 98 Mr. F. J. Foot on a Botanical Chart of the Barony of Burren, co. Clare. ... 98 Mr. John Gibbs on the Inflorescence of Plants 98 Dr. W. Lauder Lindsay on the Toot-poison of New Zealand 98 Rev. W. S. Symonds on the Occurrence of Asplenium viride on an Isolated Travertine Rock among the Black Mountains of Monmouthshire 100 Zoology. Professor Allman on the Generative Zooid of Clavatella 100 — on an Early Stage in the Development of Comatula 101 on the Structure of Corymorpha nutans 101 on some new British Tubularidce 101 CONTENTS. XU1 Page Mr. A. D. Bartlett on the Habits of the Aye-aye living in the Gardens of the Zoological Society, Regent's Park, London 103 Dr. Gilbert W. Child on Marriages of Consanguinity 104 Dr. Cleland on Ribs and Transverse Processes, with special relation to the Theory of the Vertebrate Skeleton 105 Dr. Collingwood on Geoft'roy St.-Hilaire's Distinction between Catarrhine and Platyrrhine Quadrumana 106 Dr. J. E. Gray on the Change of Form of the Head of Crocodiles ; and on the Crocodiles of India and Africa 106 Rev. T. Hincks on the Production of similar Medusoids by certain Hydroid Polypes belonging to different Genera 107 Mr. J. Gwtn Jeffreys on a Species of Limopsis, now living in the British Seas ; with Remarks on the Genus 108 on a Specimen of Astarte compressa having its Hinge- teeth reversed 108 Professor W. King on some Objects of Natural History lately obtained from the Bottom of the Atlantic 108 Mr. John Lubbock on Sphcerularia Bombi 109 on two Aquatic Hymenoptera 110 Rev. W. N. Molesworth on the Influence of Changes in the Conditions of Existence in Modifying Species and Varieties Ill Professor R. Owen on the Characters of the Aye-aye, as a test of the Lamarckian and Darwinian Hypothesis of the Transmutation and Origin of Species 114 on the Zoological Significance of the Cerebral and Pedial Characters of Man 116 on the Homologies of the Bones of the Head of the Poly- pter^us niloticus 118 Sir J. Richardson on Zoological Provinces 118 Professor Rolleston on certain Modifications in the Structures of Diving Animals 118 Mr. James Samuelson's recent Experiments on Heterogenesis, or Spontaneous Generation 119 Physiology. Mr. Isaac Ashe on the Function of the Auricular Appendix of the Heart . . 120 on the Function of the Oblique Muscles of the Eye 120 Mr. Thomas Ashworth on the Scientific Cultivation of Salmon Fisheries . . 121 Professor Beale, an Attempt to show that every living Structure consists of Matter which is the Seat of Vital Actions, and Matter in which Physical and Chemical Changes alone take place 122 Dr. John Davy on the Coloured Fluid or Blood of the Common Earthworm (JLumbricus terrestris) t J24 — ■ — — — on the Vitality of Fishes, as tested by Increase of Tem- perature 125 — on the Question whether the Oxide of Arsenic, taken in very minute quantities for a long period, is Injurious to Man 125 — — — on the Coagulation of the Blood in relation to its Cause 125 xiv CONTENTS. Page Mr. James Dowie on the Loss of Muscular Power arising from the ordi- nary Foot-clothing now worn, and on the Means required to obviate this Loss 125 Mr. Robert Garner on Pearls ; their Parasitic Origin 120 , on an Albino Variety of Crab ; with some Observations on Crustaceans, and on the Effect of Light 126 on the Skull-sutures in connexion with the Superficies of the Brain 126 Dr. George D. Gibb on the Physiological Effects of the Bromide of Ammo- nium 1*° on the Normal Position of the Epiglottis as determined by the Laryngoscope 128 Dr. George Harley on Secret Poisoning 129 Mr. James Hinton's Suggestions towards a Physiological Classification of Animals 130 Dr. Charles Kidd on Simple Syncope as a Coincident in Chloroform Acci- dents 130 Mr. J. W. Osborne's Observations made at Sea on the Motion of the Vessel with reference to Sea-Sickness 133 Mr. T. Reynolds on Tobacco in relation to Physiology 134 Dr. George Robinson on the Study of the Circulation of the Blood 134 Professor Rolleston on the Difference of Behaviour exhibited by Inuline and ordinary Starch when treated with Salivary Diastase and other converting Agents 135 Dr. Edward Smith on Tobacco-Smoking : its effects upon Pulsation 135 GEOGRAPHY and ETHNOLOGY. Sir R. Alcock on the Civilization of Japan 136 Professor Ansted on the Climate of the Channel Islands 138 Dr. Charles T. Beke's Journey to Harran in Padan-Aram, and thence over Mount Gilead into the Promised Land 141 Rev. T. G. Bonney on the Geography of Mont Pelvoux, in Dauphine 143 Mr. J. Crawfurd on Colour as a Test of the Races of Man 143 on Language as a Test of the Races of Man 144 Mr. Robert Dunn on the Psychological Differences which exist among the Typical Races of Man 144 M. Jules Gerard's Exploration dans l'Afrique eentrale, de Serre-Leone a, Alger, par Timbuctu 14< i Dr. Livingstone, a Letter from, communicated by Sir Roderick Murehison . 146 Mr. W. Mathews, jun., on Serious Inaccuracies in the Great Survey of the Alps, south of Mont Blanc, as issued by the Government of Sardinia 147 Rev. Dr. Mill's Decipherment of the Phoenician Inscription on the Newton Stone, Aberdeenshire 147 Signor Pierotti on Recent Notices of the Rechabites 147 Chevalier Ignazio Villa on Terrestrial Planispheres 148 Mr. Alfred R. Wallace on the Trade of the Eastern Archipelago with New Guinea and its Islands 148 CONTENTS. XV Page Mr. Thomas Wright on the Human Remains found in the course of the Ex- cavations at Wroxeter 149 STATISTICAL SCIENCE. Mr. J. C. Buckmaster on the Progress of Instruction in Elementary Science among the Industrial Classes under the Science Minutes of the Department of Science and Art 150 Mr. David Chadwick on the Cotton Famine, and the Substitutes for Cotton 150 Rev. G. Fisher on the Numerical Mode of estimating Educational Qualifica- tions, as pursued at the Greenwich Hospital School 153 Mr. James Heywood on Endowed Education and Oxford and Cambridge Fel- lowships 153 Mr. Edwin Hill on the Prevention of Crime 154 Mr. W. S. Jkvons on the Study of Periodic Commercial Fluctuations 157 , Notice of a General Mathematical Theory of Political Eco- nomy 158 Mr. Henry Dunning Macleod on the Definition and Nature of the Science of Political Economy 159 Mr. Herman Meriyale on the Utility of Colonization 161 Rev. W. N. Molesworth on the Training and Instruction of the Unemployed in the Manufacturing Districts during the present Crisis 162 Mr. Frederick Purdy on Local Taxation and Real Property 162 on the Pauperism and Mortality of Lancashire .... 165 Mr. Henry Roberts, Statistics showing the Increased Circulation of a Pure and Instructive Literature adapted to the Capacities and the Means of the Labouring Population 172 Di'. Edward Smith, Statistical Inquiry into the Prevalence of numerous Conditions affecting the Constitution in 1000 Consumptive Persons 174 Mr. W. T. Thornton on the Income Tax 175 Mr. Charles M. Willich on Expectation of Life 178 MECHANICAL SCIENCE. Address of William Fairbairn, Esq., LL.D., F.R.S., President of the Section 178 Mr. E. E. Allen on the Importance of Economizing Fuel in Iron-plated Ships 182 Professor D. T. Ansted on Artificial Stones 183 Mr. Charles Atherton on Unsinkable Ships 183 Mr. John Coryton on Vertical-Wave-Line Ships, Self-Reefing Sails, and Guide-Propeller 184 Dr. F. Grimaldi on a New Marine Boiler for generating Steam of High Pres- sure 186 Mr. J. Sewell on the Prevention of Railway Accidents 186 Mr. W. Thorold on the Failure of the Sluice in Fens, and on the Means of securing such Sluices against a similar Contingencj r 186 Mr. L. Williamson on the Merits of Wooden and Iron Ships, with regard to cost of repairs and security for life 187 XVI CONTENTS. Page Mr. R. W. Woollcombe on Oblate Projectiles with Cycloidal Rotation, con- trasted with Cylindro-ogival Projectiles having Helical or Rifle Rotation. . 187 APPENDIX II. Professor Sylvester on the Solution of the Linear Equation of Finite Dif- ferences in its most General Form 188 Professor N. S. Maskelyne on Aerolites 188 Messrs. J. B. Lawes and J. H. Gilbert on the Effects of different Manures on the Mixed Herbage of Grass Land 191 Rev. W. Emery on the Past and Present Expenses and Social Condition of University Education 193 List of Papers of which the Abstracts were not received 195 OBJECTS AND RULES OP THE ASSOCIATION. OBJECTS. The Association contemplates no interference with the ground occupied by other institutions. Its objects are, — To give a stronger impulse and a more systematic direction to scientific inquiry, — to promote the intercourse of those who cultivate Science in different parts of the British Empire, with one an- other, and with foreign philosophers, — to obtain a more general attention to the objects of Science, and a removal of any disadvantages of a public kind which impede its progress. RULES. ADMISSION OP MEMBERS AND ASSOCIATES. All persons who have attended the first Meeting shall be entitled to be- come Members of the Association, upon subscribing an obligation to con- form to its Rules. The Eellows and Members of Chartered Literary and Philosophical So- cieties publishing Transactions, in the British Empire, shall be entitled, in like manner, to become Members of the Association. The Officers and Members of the Councils, or Managing Committees, of Philosophical Institutions, shall be entitled, in like manner, to become Mem- bers of the Association. All Members of a Philosophical Institution recommended by its Council or Managing Committee, shall be entitled, in like manner, to become Mem- bers of the Association. Persons not belonging to such Institutions shall be elected by the General Committee or Council, to become Life Members of the Association, Annual Subscribers, or Associates for the year, subject to the approval of a General Meeting. COMPOSITIONS, SUBSCRIPTIONS, AND PRIVILEGES. Life Members shall pay, on admission, the sum of Ten Pounds. They shall receive gratuitously the Reports of the Association which may be pub- lished after the date of such payment. They are eligible to all the offices of the Association. Annual Subscribers shall pay, on admission, the sum of Two Pounds, and in each following year the sum of One Pound. They shall receive gratuitously the Reports of the Association for the year of their admission and for the years in which they continue to pay without intermission their Annual Subscription. By omitting to pay this Subscription in any particu- lar year, Members of this class (Annual Subscribers) lose for that and all future years the privilege of receiving the volumes of the Association gratis : but they may resume their Membership and other privileges at any sub- sequent Meeting of the Association, paying on each such occasion the sum of One Pound. They are eligible to all the Offices of the Association. Associates for the year shall pay on admission the sum of One Pound. They shall not receive gratuitously the Reports of the Association, nor be eligible to serve on Committees, or to hold any office. 1862. b XV111 RULES OP THE ASSOCIATION. The Association consists of the following classes : — 1. Life Members admitted from 1831 to 1845 inclusive, who have paid on admission Five Pounds as a composition. 2. Life Members who in 1846, or in subsequent years, have paid on ad- mission Ten Pounds as a composition. 3. Annual Members admitted from 1831 to 1839 inclusive, subject to the payment of One Pound annually. [May resume their Membership after in- termission of Annual Payment.] 4. Annual Members admitted in any year since 1839, subject to the pay- ment of Two Pounds for the first year, and One Pound in each following year. [May resume their Membership after intermission of Annual Pay- ment.] 5. Associates for the year, subject to the payment of One Pound. 6. Corresponding Members nominated by the Council. And the Members and Associates will be entitled to receive the annual volume of Reports, gratis, or to purchase, it at reduced (or Members') price, according to the following specification, viz. : — 1. Gratis. — Old Life Members who have paid Five Pounds as a compo- sition for Annual Payments, and previous to 1845 a further sum of Two Pounds as a Book Subscription, or, since 1845, a further sum of Five Pounds. New Life Members who have paid Ten Pounds as a compo- sition. Annual Members who have not intermitted their Annual Sub- scription. 2. At reduced or Members' Prices, viz. two-thirds of the Publication Price. — Old Life Members who have paid Five Pounds as a composition for Annual Payments, but no further sum as a Book Subscription. Annual Members who have intermitted their Annual Subscrip- tion. Associates for the year. [Privilege confined to the volume for that year only.] 3. Members may purchase (for the purpose of completing their sets) any of the first seventeen volumes of Transactions of the Associa- tion, and of which more than 100 copies remain, at one-third of the Publication Price. Application to be made (by letter) to Messrs. Taylor & Francis, Red Lion Court, Fleet St., London. Subscriptions shall be received by the Treasurer or Secretaries. MEETINGS. The Association shall meet annually, for one week, or longer. The place of each Meeting shall be appointed by the General Committee at the pre- vious Meeting ; and the Arrangements for it shall be entrusted to the Officers of the Association. GENEEAI COMMITTEE. The General Committee shall sit during the week of the Meeting, or longer, to transact the business of the Association. It shall consist of the following persons : — 1. Presidents and Officers for the present and preceding years, with authors of Reports in the Transactions of the Association. 2. Members who have communicated any Paper to a Philosophical Society, which has been printed in its Transactions, and which relates to such subjects as are taken into consideration at the Sectional Meetings of the Association. RULES OF THE ASSOCIATION. XIX 3. Office-bearers for the time being, or Delegates, altogether not exceed- ing three in number, from any Philosophical Society publishing Transactions. 4. Office-bearers for the time being, or Delegates, not exceeding three, from Philosophical Institutions established in the place of Meeting, or in any place where the Association has formerly met. 5. Foreigners and other individuals whose assistance is desired, and who are specially nominated in writing for the Meeting of the year by the Presi- dent and General Secretaries. 6. The Presidents, Yice-Presidents, and Secretaries of the Sections are ex-officio members of the General Committee for the time being. SECTIONAL COMMITTEES. The General Committee shall appoint, at each Meeting, Committees, con- sisting severally of the Members most conversant with the several branches of Science, to advise together for the advancement thereof. The Committees shall report what subjects of investigation they would particularly recommend to be prosecuted during the ensuing year, and brought under consideration at the next Meeting. The Committees shall recommend Reports on the state and progress of particular Sciences, to be drawn up from time to time by competent persons, for the information of the Annual Meetings. COMMITTEE OP RECOMMENDATIONS. The General Committee shall appoint at each Meeting a Committee, which shall receive and consider the Recommendations of the Sectional Committees, and report to the General Committee the measures which they would advise to be adopted for the advancement of Science. All Recommendations of Grants of Money, Requests for Special Re- searches, and Reports on Scientific Subjects, shall be submitted to the Com- mittee of Recommendations, and not taken into consideration by the General Committee, unless previously recommended by the Committee of Recom- mendations. LOCAL COMMITTEES. Local Committees shall be formed by the Officers of the Association to assist in making arrangements for the Meetings. Local Committees shall have the power of adding to their numbers those Members of the Association whose assistance they may desire. OFFICEES. A President, two or more Vice-Presidents, one or more Secretaries, and a Treasurer, shall be annually appointed by the General Committee. COUNCIL. In the intervals of the Meetings, the affairs of the Association shall be managed by a Council appointed by the General Committee. The Council may also assemble for the despatch of business during the week of the Meeting. 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EM c H 13 <D bE Tt r: "in ■- -= U "Z T! yj g^-s £ Is; C3 — ■a tu v CCft! o T3 S 3 T3 B t: £ ft. -iPJS MEMBERS OF THE COUNCIL. XXV II. Table showing the Names of Members of the British Association who have served on the Council in former years. Aberdeen, Earl of, LL.D, E.G., E.T, F.E.S. (deceased). Acland, Sir Thomas D, Bart., M.A., D.C.L., F.E.S. Acland, Professor H. W., M.D.. F.E.S. Adams, Prof. J. Couch, M.A., D.C.L., P.E.S. Adamson, John, Esq., F.L.S. Ainslie, Eev. Gilbert, D.D., Master of Pem- broke Hall, Cambridge. Airy,G.B,M.A, D.C.L, F.E.S, Astronomer Boyal. Alison, ProfessorW. P,M.D,F.E.S.E. (dec d ). Allen, W. J. C, Esq. Anderson, Prof. Thomas, M.D. Ansted, Professor D. T, M.A., F.E.S. Argyll, George Douglas, Duke of, F.E.S. L. &E. Arnott, Neil, M.D., F.E.S. Ashburton, William Bingham, Lord, D.C.L. Atkinson, Et. Hon. E,Lord Mayor of Dublin. Babbage, Charles, Esq, M.A, F.E.S. Babington, Professor C. C, M.A, F.E.S. Baily, Francis, Esq, F.E.S. (deceased). Baines, Et. Hon. M. T, M.A, M.P. (dec"). Baker, Thomas Barwick Lloyd, Esq. Balfour, Professor John H.'M.D, F.E.S. Barker, George, Esq, F.E.S. (deceased). Beamish. Eichard, Esq, F.E.S. Beechey, Eear-Admiral, F.E.S. (deceased). Bell, Professor Thomas, V.P.L.S, F.E.S. Bengough, George, Esq. Bentham, George, Esq, Pres.L.S. Biddell, George Arthur, Esq. Bigge, Charles, Esq. Blakiston, Peyton, M.D, F.E.S. Boileau, Sir John P, Bart, F.E.S. Boyle, Eight Hon. D, Lord Justice-General (deceased). Brady.The Et. Hon. Maziere, M.E.I.A, Lord Chancellor of Ireland. Brand, William, Esq. Breadalbane, John, Marquis of, K.T., F.E.S. (deceased). Brewster, Sir David, E.H, D.C.L, LL.D, F.E.S. L. & E, Principal of the Uni- versity of Edinburgh. Brisbane, General Sir Thomas M, Bart, E.C.B, G.C.H, D.C.L, F.E.S. (dec"). Brodie, Sir B. C, Bart, D.C.L, V.P.E.S. (deceased). Brooke, Charles, B.A.. F.E.S. Brown, Eobert, D.C.L, F.E.S. (deceased). Brunei, Sir M. I, F.E.S. (deceased). Buckland, Very Eev. William, D.D, F.E.S, Dean of Westminster (deceased). Bute, John, Marquis of, E.T. (deceased). Carlisle, George Will. Fred, Earl of, F.E.S. Carson, Eev. Joseph, F.T.C.D. Cathcart,Lt.-Gen,Earlof, K.C.B, F.E.S.E. (deceased). Challis, Eev. J, M.A, F.E.S. Chalmers, Eev. T, D.D. (deceased). Chance, James, Esq. Chester, John Graham, D.D, Lord Bishop of Christie, Professor S. H, M.A, F.E.S. Clare, Peter. Esq.. F.E.A.S. (deceased). Clark, Eev. Prof, M.D, F.E.S. (Cambridge.) Clark, Henry. M.D. Clark, G. T.^ Esq. Clear, William, Esq. (deceased). Clerke, Major S, E.H, E.E, F.E.S. (dec"). Clift, William, Esq, F.E.S. (deceased). Close, Very Eev. F, M.A, Dean of Carlisle. Cobbold, John Chevalier, Esq, M.P. Colquhoun, J. C, Esq, M.P. (deceased). Conybeare, Very Eev. W. D, Dean of Llan- daff (deceased). Cooper, Sir Henry, M.D. Corrie, John, Esq, F.E.S. (deceased) Crum, Walter, Esq, F.E.S. Currie, William Wallace, Esq. ("deceased). Dalton, John, D.C.L, F.E.S. (deceased). Daniell, Professor J. F, F.E.S. (deceased). Darbishire, E. D, B.A, F.G.S. Dartmouth, William, Earl of, D.C.L, F.E.S. Darwin, Charles, Esq, M.A, F.E.S. Daubenv, Prof. C. G. B, M.D..LL.D, F.E S DelaBeche,SirH. T.. C.B., F.E.S, Director- Gen. Geol. Surv. United Eingdom (dec d ). De la Eue, Warren, Ph.D., F.E.S. Derby, Earl of, D.C.L, Chancellor of the University of Oxford. Devonshire, William, Duke of, M.A, D.C L F.E.S. Dickinson, Joseph, M.D, F.E.S. Dillwyn, Lewis W, Esq, F.E.S. (deceased). Donkin, Professor W. F„ M.A, F.E.S. Drinkwater, J. E, Esq. (deceased). Ducie, The Earl of, F.E.S. Dunraven, The Earl of, F.E.S. Egerton, Sir P. de M. Grey, Bart, M.P., F.E.S. Eliot, Lord. M.P. Ellesmere, Francis, Earl of, F.G.S. (dec d ). Enniskillen, William. Earl of, D.C.L, FES Estcourt, T. G. B, D.C.L. (deceased). Fairbaim. WiUiam, LL.D, C.E, F.E.S. Faraday, Professor, D.C.L, F.E.S. Ferrers, Eev. N. M, M.A. FitzEov, Eear-Admiral, F.E.S. Fitzwiliiam, The Earl, D.C.L, F.E.S. (dec d ). Fleming, W, M.D. Fletcher, Bell, M.D. Foote, Lundy E, Esq. Forbes, Charles, Esq. (deceased). Forbes, Prof. Edward, F.E.S. (deceased). ForbesProf. J. D, LL.D, F.E.S„Sec E.S.E., Principal of the University of St. An- drews. Fox, Eobert Were, Esq, F.E.S. Frost, Charles, F.S.A. Fuller, Professor, M.A. Galton, Francis, F.E.S, F.G.S. Gassiot, John P, Esq, F.E.S. Gilbert, Davies, D.C.L, F.E.S. (deceased). Gladstone, J. H, Ph.D., F.E.S. XXVI REPORT 1862. Goodwin, The Very Eev. EL, D.D., Dean of Ely. Gourlie, William, Esq. (deceased). Graham, T., M.A., D.C.L., F.R.S., Master of the Mint. Gray, John E., Esq., Ph.D., F.R.S. Gray, Jonathan, Esq. (deceased). Gray, William, Esq., F.G.S. Green, Prof. Joseph Henry, D.C.L., F.R.S. Greenough, G. B., Esq., F.R.S. (deceased). Griffith, George, M.A., F.C.S. Griffith, Sir R. Griffith, Bt., LL.D., M.R.I.A. Grove, W. R, Esq., M.A., F.R.S. Hallam, Henry, Esq., M.A., F.R.S. (dec d ). Hamilton, W. J., Esq., F.R.S., Sec. G.S. Hamilton, Sir Win. R., LL.D., Astronomer Royal of Ireland, M.R.I.A, ERAS. Hancock, W. Neilson, LL.D. Harcourt, Rev. Wm. Vernon, M.A., F.R.S. Hardwicke, Charles Philip, Earl of, F.R.S. Harford, J. S., D.C.L., F.R.S. Han-is, Sir W. Snow, F.R.S. Harrowby, The Earl of, F.R.S. Hatfeild, William, Esq., F.G.S. (deceased). Henry, W. C, M.D., F.R.S. Henry, Rev. P. S., D.D., President of Queen's College, Belfast. Henslow, Rev. Professor, M.A., F.L.S. (dec d ). Herbert, Hon. and Very Rev. Wm., LL.D., F.L.S., Dean of Manchester (dec d ). Herschel, Sir John F.W., Bart., M. A., D.C.L., F.R.S. Heywood, Sir Benjamin, Bart., F.R.S. Heywood, James, Esq., F.R.S. Hill, Rev. Edward, M.A., F.G.S. Hincks, Rev. Edward, D.D., M.R.I.A. Hincks, Rev. Thomas, B.A. Hinds, S., D.D., late Lord Bishop of Norwich (deceased). Hodgkin, Thomas, M.D. Hodgkinson, Professor Eaton, F.R.S. (dec d ). Hodgson, Joseph, Esq., F.R.S. Hooker, Sir William J., LL.D., F.R.S. Hope, Rev. F. W., M.A, F.R.S. Hopkins, William, Esq., M.A., LL.D.. F.R.S. Horner, Leonard, Esq., F.R.S., Pres.G.S. Hovenden, V. F., Esq., M.A. Hugall, J. W., Esq. Hutton, Robert, Esq., F.G.S. Hutton, William, Esq., F.G.S. (deceased). Ibbetson,Capt.L.L.Boscawen,KR.E.,F.G.S. Inglis, Sir R. H, Bart., D.C.L., M.P. (dec d ). Imnan, Thomas, M.D. Jacobs, Bethel, Esq. Jameson, Professor R., F.R.S. (deceased). Jardine, Sir William, Bart., F.R.S.E. Jeffreys, John Gwyn, Esq., F.R.S. Jellett, Rev. Professor. Jenyns, Rev. Leonard, F.L.S. Jerrard, H. B., Esq. Jeune, Rev. F., D.C.L., Master of Pembroke College, Oxford. Johnston, Right Hon. William, late Lord Provost of Edinburgh. Johnston, Prof. J. F. W., M.A., F.R.S. (deceased). Keleher, William, Esq. (deceased). Kelland, Rev. Prof. P., M.A., F.R.S. L. & E. Kildare, The Marquis of. Lankester, Edwin, M.D., F.R.S. Lansdowne, Hen., Marquisof, D.C.L.,F.R.S. Larcom, Major, R.E., LL.D., F.R.S. Lardner, Rev. Dr. (deceased). Lassell, William, Esq., F.R.S. L. & E. Latham, R. G, M.D., F.R.S. Lee, Very Rev. John, D.D., F.R.S.E., Prin- cipal of the University of Edinburgh (deceased). Lee, Robert, M.D., F.R.S. Lefevre, Right Hon. Charles Shaw, late Speaker of the House of Commons. Lemon, Sir Charles, Bart., F.R.S. Liddell, Andrew, Esq. (deceased). Liddell, Very Rev. H. G, D.D., Dean of Christ Church, Oxford. Lindley, Professor John, Ph.D., F.R.S. Listowel, The Earl of. Liveing, Prof. G. D., M.A., F.C.S. Lloyd, Rev. B., D.D., Provost of Trin. Coll., Dublin (deceased). Lloyd, Rev. H., D.D., D.C.L., F.R.S. L.&E., M.R.IA. Londesborough, Lord, F.R.S. (deceased). Lubbock, Sir John W., Bart., M.A., F.R.S. Luby, Rev. Thomas. Lycll, Sir Charles, M.A, LL.D., D.C.L., MacCullagii, Prof., D.C.L., M.R.I.A. (dec d ). MacDonneU, Rev. R., D.D., M.R.I.A, Pro- vost of Trinity College, Dublin. Macfarlane, The Very Rev. Principal. (dec d ). MacGee, William, M.D. MacLeay, William Sharp, Esq., F.L.S. MacNeiil, Professor Sir John, F.R.S. Malahide, The Lord Talbot de. Malcolm,Vice-Ad. Sir Charles, K.C.B. (dec d ). Maltby, Edward, D.D., F.R.S., late Lord Bishop of Durham (deceased). Manchester, J. P. Lee, D.D., Lord Bishop of. Marlborough, Duke of, D.C.L. Marshall, J. G, Esq., M.A, F.G.S. May, Charles, Esq., F.R.A.S. (deceased). Meynell, Thomas, Esq., F.L.S. Middleton, Sir William F. F, Bart. Miller, Professor W. A., M.D., Treas. and V.P.R.S. Miller, Professor- W. H, M.A., For. Sec.R.S. Milnes, R. Monckton, Esq., D.C.L., M.P. Moggridge, Matthew, Esq. Moillet, J. D., Esq. (deceased). Monteagle, Lord, F.R.S. Moody, J. Sadleir, Esq. Moody, T. H. C, Esq. Moody, T. F., Esq. Morley, The Earl of. Moseley, Rev. Henry, M.A, F.R.S. Mount-Edgecumbe, Ernest Augustus, Earl of. Murchison, Sir Roderick I..G.C. St.S., D.C.L., LL.D., F.R.S. Neild, Alfred, Esq. Neill, Patrick, M.D., F.R.S.E. Nicol, D., M.D. MEMBERS OF THE COUNCIL. XXY11 Nicol, Professor J., F.E.S.E., F.G.S. Nicol, Eev. J. P., LL.D. Northampton, Spencer Joshua Alwyne, Mar- quis of, V.P.B.S. (deceased). Northumberland, Hugh, Duke of, KG..M.A., F.E.S. (deceased). Ormerod, G. W., Esq., M.A., F.G.S. Orpen, Thomas Herbert, M.D. (deceased). Orpen, John H., LL.D. Osier, Follett, Esq., F.R.S. Owen, Professor Eichd.,M.D.,D.C.L.,LL.D., F.E.S. Oxford, Samuel Wilberforce, D.D., Lord Bishop of, F.E.S., F.G.S. Palmerston, Viscount, KG, G.C.B., M.P., F.E.S. Peacock, Very Eev. G., D.D., Dean of Ely, F.E.S. (deceased). Peel,Et.Hon.SirE,Bart.,M.P.,D.C.L.(dec d ). Pendarves, E. W., Esq., F.E.S. (deceased). Phillips, Professor John, M.A.,LL.D.,F.E.S. Phillips, Eev. G., B.D., President of Queen's College, Cambridge. Pigott,The Et. Hon. D. E, M.E.I. A., Lord Chief Baron of the Exchequer in Leland. Porter, G. E., Esq. (deceased). Portlock, Major-General,E.E.,LL.D., F.E.S. Powell, Eev. Professor, M.A., F.E.S. (dec d ). Price, Eev. Professor, M.A., F.E.S. Prichard, J. C, M.D., F.E.S. (deceased). Eamsay, Professor William, M.A. Kansome, George, Esq., F.L.S. Eeid, Maj.-Gen. Sir W., K.C.B., E.E., F.E.S. (deceased). Eendlesham, Et. Hon. Lord, M.P. Eeonie, George, Esq., F.E.S. Eennie, Sir John, F.E.S. Eichardson, Sir John, C.B., M.D., LL.D., F.E.S. Eichmond, Duke of, E.G., F.E.S. (dec d ). Eipon, Earl of, F.E.G.S. Eitehie, Eev. Prof., LL.D., F.E.S. (dec"). Eobinson, Capt, E.A. Eobinson, Eev. J., D.D. Eobinson, Rev. T. E, D.D., F.E.S., F.E.A.S. Eobison, Sir John, Sec.E.S.Edin. (deceased). Eoche, James, Esq. Eoget, Peter Mark, M.D., F.E.S. Eolleston, Professor, M.D., F.L.S. Eonalds, Francis, F.E.S. Eoscoe, Professor H. E., B.A., F.E.S. Eosebery, The Earl of, K.T., D.C.L., F.E.S. Eoss, Eear-Adniiral Sir J. C, E.N., D.C.L., F.E.S. (deceased). Eosse, Wm., Earl of, M.A, F.E.S., M.E.I. A. Eoyle, Prof. John F, M.D., F.E.S. (dec d ). Eussell, James, Esq. (deceased). Eussell, J. Scott, Esq., F.E.S. Sabine, Major-GeneralEdward,E.A., D.C.L., LL.D., President of the Eoyal Society. Sanders, William, Esq., F.G.S. Scoresby, Eev. W., D.D., F.E.S. (deceased). Sedgwick, Eev. Prof. Adam, M.A., D.C.L., F.E.S. Selby, Prideaux John, Esq., F.E.S.E. Sharpey, Professor, M.D., Sec.E.S. Sims, Dillwyn, Esq. Smith, Lieut-Colonel C. Hamilton, F.E.S. (deceased). Smith, Prof. H. J. S., M.A., F.E.S. Smith, James, F.E.S. L. & E. Spence, William, Esq., F.E.S. (deceased). Spottiswoode, W., M.A., F.E.S. Stanley, Edward, D.D., F.E.S., late Lord Bishop of Norwich (deceased). Staunton, Sir G. T., Bt., M.P., D.C.L, F.E.S. St. David's, C.Thirlwall,D.D.,LordBishop of. Stevelly, Professor John, LL.D. Stokes, Professor GG.,M.A.,D.C.L.,Sec.E.S. Strang, John, Esq., LL.D. Strickland, Hugh E., Esq., F.E.S. (deceased). Sykes, Colonel W. H., M.P., F.E.S. Symonds, B. P., D.D., Warden of Wadham College. Oxford. Talbot, W. H. Fox, Esq., M.A., F.E.S. Tayler, Eev. John James, B.A. Taylor, John, Esq., F.E.S. (deceased). Taylor, Eichard, Esq., F.G.S. Thompson, William, Esq., F.L.S.(deceased). Thomson, A., Esq. Thomson, Professor William, M.A., F.E.S. Tindal. Captain, E.N. (deceased). Tite, William, Esq., M.P., F.E.S. Tod, James, Esq., F.E.S.E. Tooke, Thomas, F.E.S. (deceased). Traill, J. S., M.D. (deceased). Turner, Edward, M.D., F.E.S. (deceased). Turner, Samuel, Esq., F.E.S., F.G.S. (dec d ). Turner, Eev. W. Tyndall, Professor John, F.E.S. Vigors, N. A., D.C.L, F.L.S. (deceased). Vivian, J. H, M.P., F.E.S. (deceased). Walker, James, Esq., F.E.S. Walker, Joseph N., Esq., F.G.S. Walker, Eev. Professor Eobert, M.A., F.E.S. Warburton, Henry, Esq.,MA., F.E.S.(dec d ). Ward, W. Sykes, Esq., F.C.S. Washington, Captain, E.N., F.E.S. Webster, Thomas, M.A., F.E.S. West, Williain, Esq., F.E.S. (deceased). Western, Thomas Burch, Esq. Wharncliffe, John Stuart,Lord,F.E.S.(dec d ). Wheatstone, Professor Charles, F.E.S. Whewell, Eev. William, D.D., F.E.S., Master of Trinity College, Cambridge. White, John F, Esq. Williams, Prof. Charles J. B., M.D., F.E.S. Willis, Eev. Professor Eobert, M.A., F.E.S. Wills, William, Esq., F.G.S. (deceased). Wilson, Thomas, Esq., M.A. Wilson, Prof. W. P. Winchester, John, Marquis of. Woollcombe, Henry, Esq., F.S.A. (deceased). Wrottesley, John, Lord, M. A., D.C.L., F.E.S. Tarborough, The Earl of, D.C.L. Yarrell, William, Esq., F.L.S. (deceased). Yates, James, Esq., M.A., F.E.S. Yates, J. B., Esq., F.S.A., F.E.G.S. (de« d ). OFFICERS AND COUNCIL, 1862-63. TRUSTEES (PERMANENT). Sir Roderick I. Murchison, K.C.B., G.C.St.S., D.C.L., F.R.S. Major-General Edwaed Sabine, R.A., D.C.L., Pres. R.S. Sir Philip de M. Grey Egerton, Bart., M.P., F.R.S. PRESIDENT. THE REV. ROBERT WILLIS, M.A., F.R.S., Jacksonian Professor of Natural and Experimental Philosophy in the University of Cambridge. VICE-PRESIDENTS. The Rev. the Vice-Chaxcellor of the University or Cambridge. The Very Rev. the Dean of Ely, D.D. The Rev. W. Whewell, D.D., F.R.S., Master of Trinity College, Cambridge. The Rev. A. Sedgwick, M.A., F.R.S., Woodwardian " Profossor of Geology in the University of Cambridge. The Rev. J. Challis, M.A., F.R.S., Plumian Professor of Astronomy in the University of Cambridge. G. B. Airy", Esq., M.A., F.R.S., Astronomer Royal. G. G. STOKES, Esq., M.A., F.R.S., Lueasian Professor of Mathematics in the University of Cambridge. J. C. Adams, Esq., M. A., F.R.S., Lowndesian Professor of Astronomy and Geometry in the University of Cambridge, and President of the Cambridge Philosophical Society. PRESIDENT ELECT. Sir WILLIAM G. ARMSTRONG, F.R.S. VICE-PRESIDENTS ELECT. Sir Walter C. Trevelyan, Bart., M.A. Sir Charles Lyell, LL.D., D.C.L., F.R.S., F.G.S. High Taylor, Esq. Isaac Lowthian Bell, Esq. Nicholas Wood, Esq. Rev. Temple Chevallier, B.D., F.R.A.S. William Fairbairn, Esq., LL.D., F.R.S. LOCAL SECRETARIES FOR THE MEETING AT NEWCASTLE-ON-TYNE. A. Noble, Esq. Augustus H. Hunt, Esq. R. C. Clapham, Esq. LOCAL TREASURER FOR THE MEETING AT NEWCASTLE-ON-TYNE. Thomas Hodgkin, Esq. ORDINARY MEMBERS OF THE COUNCIL. De laRue,Warren, Esq., F.R.S. FitzRoy, Admiral, F.R.S. Galton, Francis, Esq., F.R.S. Gassiot, J. P., Esq., F.R.S. Gladstone, Dr., F.R.S. Grove, W. H., Esq., F.R.S. Heyvtood, James, Esq., F.R.S. Hutton, Robert, Esq., F.G.S. Hogg, John, Esq., M.A., F.L.S. Lyell, Sir Charles, F.R.S. Lankester, Dr. E., F.R.S. Miller, Prof. W. A., M.D., F.R.S. PRICE,Rev.Professor,M.A.,F.R.S. Sharpey, Professor, See.R.S. Sykes, Colonel, M.P., F.R.S. Tite, William, Esq.,M.P.,F.R.S. Wheatstone, Professor, F.R.S. Webster, Thomas, Esq., F.R.S. Williamson, Prof. A.W., F.R.S. EX-OFFICIO MEMBERS OF THE COUNCIL. The President and President Elect, the Vice-Presidents and Vice-Presidents Elect, the General and Assistant-General Secretaries, the General Treasurer, the Trustees, and the Presidents of former years, viz. — Rev. Professor Sedgwick. The Duke of Devonshire. Rev. W. V. Harcourt. Rev. W. Whewell, D.D. The Earl of Rosse. Sir John F. W. Herschel, Bart. Sir Roderick I. Murchison, K.C.B. The Rev. T. R. Robinson, D.D. Sir David Brewster. G. B. Airy, Esq., the Astronomer Roval. General Sabine, D.C.L. William Hopkins, Esq., LL.D. The Earl of Harrowby. The Duke of Argvll. Professor Dau- beny, M.D. The Rev. H. Lloyd, D.D. Richard Owen, M.D., D.C.L. The Lord Wrottesley. William Fairbairn, Esq., LL.D. GENERAL SECRETARIES. William Hopkins, Esq., M.A., F.R.S., St. Peter's College, Cambridge. John Phillips, Esq., M.A., LL.D., F.R.S., Professor of Geology in the University of Oxford. Museum House, Oxford. ASSISTANT-GENERAL SECRETARY. GEORGE GRIFFITH, Esq., M.A., Deputy Professor of Experimental Philosophy in the University of Oxford. GENERAL TREASURER. William Spottiswoode, Esq., M.A., F.R.S., F.G.S., 19 Chester Street, Belgrave Square, London, S.W. LOCAL TREASURERS. William Gray, Esq., F.G.S., York. Prof. C. C. Babington, M.A., F.R.S., Cambridge. William Brand, Esq., Edinburgh. John H. Orpen, LL.D., Dublin. William Sanders, Esq., F.G.S., Bristol. Robert MAndrew, Esq., F.R.S., Liverpool. W. R. Wills, Esq., Birmingham. Robert P. Greg, Esq., F.G.S.. Manchester. John Gwvn Jetl'revs, Esq., F.R.S., Swansea. Robert Patterson, 'Esq., M.R.I.A., Belfast. Edmund Smith, Esq., Hull. Richard Beamish, Esq., F.R.S., Cheltenham. John Metcalfe Smith, Esq., Leeds. John Forbes White, Esq., Aberdeen. Professor Ramsay, M.A., Glasgow. Rev. John Griffiths, M.A., Oxford. AUDITORS. J. P. Gassiot, Esq. Robert Hutton, Esq. Dr. Norton Shaw. OFFICERS OF SECTIONAL COMMITTEES. XXIX OFFICERS OF SECTIONAL COMMITTEES PRESENT AT THE CAMBRIDGE MEETING. SECTIOX A. MATHEMATICS AND PHYSICS. President. — G. G. Stokes, M.A., F.R.S., Lucasiau Professor of Mathematics. Vice-Presidents. — Professor Adams, F.R.S. ; Rev. Professor Challis, F.R.S. ; Rev. Dr. Lloyd, F.R.S. ; Rev. Professor Price, F.R.S. ; General Sabine, President R.S. ; Rev. Dr. Whewell, F.R.S. ; Lord Wrottesley, D.C.L., F.R.S. Secretaries. — Professor Stevelly, LL.D., Professor H. J. S. Smith, F.R.S., and Pro- fessor R. B. Clifton, F.R.A.'S. SECTION B. CHEMISTRY AND MINERALOGY, INCLUDING THEIR APPLICATIONS TO AGRICULTURE AND THE ARTS. President. — W. H. Miller, M.A., F.R.S., Professor of Mineralogy in the University of Cambridge. Vice-Presidents.— C. G. B. Daubenv, M.D., F.R.S. ; J. P. Gassiot, F.R.S. ; J. H. Gladstone, Ph.D., F.R.S. ; Rev. W. Vernon Harcourt, F.R.S. ; Dr. Joule, F.R.S. Secretaries.— W. Odling, M.B., F.R.S.; Professor H. E. Roscoe, Ph.D., B.A. : H. W. Elphinstone, M.A., F.L.S. SECTION C. GEOLOGY. President.— J. B. Jukes, M.A., F.R.S. Vice-Presidents. — Rev. Professor Sedgwick, F.R.S. ; Sir Charles Bunburv, F.R.S. : R. A. C. God win- Austen, F.R.S. ; Professor Ansted, F.R.S. Secretaries. — Professor T. Rupert Jones: Lucas Barrett, F.L.S., F.G.S. ; H. C. Sorby, F.R.S. SECTION D. ZOOLOGY AND BOTANY, INCLUDING PHYSIOLOGY. President. — Professor Huxley, F.R.S. Vice-Presidents. — Professor Balfour, F.R.S.; Rev. Dr. Cookson, Master of St. Peter's College ; J. Gwyn Jeffreys, F.R.S. ; Rev. Leonard Jenyns, M.A., F.L.S. ; Edwin Lankester, M.D., F.R.S. Secretaries.— Alfred Newton, M.A., F.L.S. ; E. Perceval Wright, M.D., F.R.C.S.I. SUB -SECTION D. PHYSIOLOGICAL SCIENCE. President— G. E. Paget, M.D. Vice-Presidents.— John Davy, M.D., F.R.S. ; G. M. Humphry, M.D., F.R.S. ; Pro- fessor Owen, LL.D., F.R.S. ; Professor Rolleston, M.D., F.R.S. Secretaries.— Edward Smith, M.D., F.R.S. ; G. F. Helm. SECTION E. GEOGRAPHY AND ETHNOLOGY. President. — Francis Galton, M.A., F.R.S. Vice-Presidents.— Rev. J. W. Blakesley, M.A. ; J. Crawfurd, F.R.S. ; William Spottiswoode, M.A., F.R.S., General Treasurer of the British Association ; Rev. George Williams, B.D. Secretaries.— Dr. Norton Shaw ; Thomas Wright, M.A. ; Dr. Hunt ; Rev. J. Glover, M.A. ; and J. W. Clarke, M.A. SECTION F. — ECONOMIC SCIENCE AND STATISTICS. President. — Edwin Chadwick, C.B. Vice-Presidents.— Colonel Svkes, M.P., F.R.S.; William Tite, M.P., F.R.S.; Thomas AYebster, F.R.S. ; James Heywood, F.R.S. Secretaries.— Edmund Macrory, M.A. ; H. D. Macleod, B.A. XXX REPORT 1862. SECTION G. MECHANICAL SCIENCE. President— W. Fairbaim, LL.D., F.R.S. Vice-Presidents.— James Nasruyth, F.R.A.S. ; Professor J. M. Rankine ; Dr. Ro- binson, F.R.S. ; John Scott Russell, F.R.S. ; Professor James Thomson, M.A. ; Charles Vignoles, F.R.S. Secretaries. — P. Le Neve Foster, M.A. ; William M. Fawcett, M.A. CORRESPONDING MEMBERS. Professor Agassiz, Cambridge, Massa- chusetts. M. Babinet, Parts. Dr. A. D. Backe, Washington. Dr. D. Bierens de Haan, Amsterdam. Professor Bolzani, Kasan. Dr. Barth. Dr. Bergsnia, Utrecht. Mr. P. O. Bond, Cambridge, U.S. M. Boutigny (d'Evreux). Professor Braschmann, Moscow. Dr. Cams, Leipzig. Dr. Ferdinand Colin, Breslau. M. Antoine d'Abbadie. M. De la Rive, Geneva. Professor Wilhelni Delffs, Heidelberg. Professor Dove, Berlin. Professor Dumas, Paris. Dr. J. Milne-Edwards, Paris. Professor Ehrenberg, Berlin. Dr. Eisenlohr, Carlsruhe. Professor Encke, Berlin. Dr. A. Erman, Berlin. Professor A. Escher von der Linth, Zurich, Switzerland. Professor Esrnark, Cliristiania. Professor A. Favre, Geneva. Professor G. Forchhanimer, Copenhagen. M. Leon Foucault, Paris. Professor E. Freiny, Paris. M. Frisiani, Milan. Dr. Geinitz, Dresden. Professor Asa Gray, Cambridge, U.S. Professor Henry, Washington, U.S. Dr. Hoehstetter, Vienna. M. Jacobi, St. Petersburg. Prof. Jessen, Med. et Phil. Dr., Griess- wald, Prussia. Professor Aug. Kekule, Ghent, Belgium. M. Kkanikoff, St. Petersburg. Prof, A. Kolliker, Wurzburg. Professor De Koninck, LUge. Professor Kreil, Vienna. Dr. A. Kupffer, St. Petersburg. Dr. Lamont, Munich. Prof. F. Lanza. M. Le Vender, Paris. Baron von Liebig, Munich. Professor Loomis, New York. Professor Gustav Magnus, Berlin. Professor Matteucci, Pisa. Professor P. Merian, Bale, Switzerland. ProfessorvonMiddendorfl',iS<.Pe<ers6i<r</. M. l'Abb6 Moigno, Paris. Professor Nilsson, Sweden. Dr. N. Nordenskiold, Finland. M. E. Peligot, Paris. Prof. B. Pierce, Cambridge, U.S. Viscenza Pisani, Florence. Gustav Plaar, Strasburg. Chevalier Plana, Turin. Professor Pliicker, Bonn. M. Constant PreYost, Paris. M. Quetelet, Brussels. Prof. Retzius, Stockholm. Professor W. B. Rogers, Boston, U.S. Professor H. Rose, Berlin. Herman Schlagintweit, Berlin. Robert Schlagintweit, Berlin. M. Werner Siemens, Vienna. Dr. Siljestrom, Stockholm. Professor J. A. de Souza, University of Coimbra. M. Struve, Pidkoiva. Dr. Svanberg, Stockholm. M. Pierre Tchihatchef. Dr. Van der Hoeven, Leyden. Professor E. Verdet, Paris. M. de Verneuil, Paris. Baron Sartorius von Waltershausen, Gbttingen. Professor Wartmann, Geneva. REPORT OF THE COUNCIL. XXXI Report of the Council of the British Association, presented to the General Committee, Wednesday , October 1, 1862. 1. The Council were directed by the General Committee at Manchester to maintain the Establishment of the_ Kew Observatory, and a grant of ,£500 was placed at their disposal for the purpose. They have received at each of their Meetings regular accounts of the proceedings of the Committee of the Observatory, and they now lay before the General Committee a General Report of these proceedings during the year 1861-62. (See Report of Kew Committee for 1861-62.) 2. A sum of £40 was placed at the disposal of the Kew Committee for the employment of the Photoheliometer ; and a further sum of £150 for the pur- pose of obtaining a series of photographic pictures of the Solar surface, with the cooperation of the Royal Society. The Report of the Kew Committee will make known the results of these recommendations. 3. The Report of the Parliamentary Committee has been received by the Council for presentation to the General Committee today, and is printed for the information of the Members. (See Report of Parliamentary Committee.) 4. The Council have to regret the absence from this Meeting of the General Secretary, Mr. Hopkins, through indisposition, which they sincerely hope will soon be removed. 5. The ' Classified Index ' to the Transactions of the Association, which was authorized to be prepared under the direction of Professor Phillips, is completed in one of the main divisions ; the remainder will be printed with- out delay, and will be delivered to the Members who have subscribed for it before the end of the present year. 6. At that date it is the request of Professor Phillips to be allowed to withdraw from the office of Assistant General Secretary to which he has been appointed, by Annual Election in the General Committee, for nearly thirty- two years. Having for two years received the useful aid of Mr. G. Griffith, M.A., of Jesus College, Oxford, he has expressed to the Council his conviction of the fitness of that gentleman to undertake the duties which have been so long entrusted to himself. 7. The Council having considered the subject, and having ascertained from Professor Phillips that he would be happy to cooperate 'with Mr. Hopkins as Junior General Secretaiy in the next year, recommend that the arrangement here suggested be carried out by the General Committee. 8. The Council received in April, 1862, a communication from Mr. John Taylor, Jim., and Mr. Richard Taylor, requesting that, on account of his great age, their father, Mr. Taylor, might be relieved of all further duties as General Treasurer and Co-Trustee of the Association. The warmest thanks of the Council were given to Mr. Taylor for his kind attention and most valuable services rendered to the Association in two im- portant offices, as one of the Trustees and sole Genei'al Ti'easurer, and their regret that any cause should render it necessary for him to desire to be re- lieved from the duties which he has so efficiently performed for the great advantage of the Association, almost from its foundation. 9. Sir Philip de Grey Egerton, Bart., was then requested to accept the office of Trustee of the British Association ; and Mr. W. Spottiswoode to undertake the duty of General Treasurer to the Association. These Gentlemen have kindly consented to act, and have entered on their duties. 10. The Council have been informed that Invitations will be presented to xxxii report — 1862. the General Cuinmittee at its Meeting on Monday, October 6, from Newcastle- on-Tyne, Birmingham, Bath, Nottingham, and Dundee. 11. That the Vice-Chancellor of the University of Cambridge and the Rev. Professor Challis be elected Vice-Presidents for the next year. October 1, 1862. William Eairbairx, President. Report of the Kexo Committee of the British Association for the Advancement of Science for 1861-1862. The Committee of the Kew Observatory submit to the Association the following Report of their proceedings during the past year. Deeinin°- it desirable that the instrumental arrangements and scientific processes at use in the Observatory should be represented at the International Exhibition, application was made to the Commissioners for space. This was granted in the nave of the building, where the following instru- ments are at present exhibited : — 1. A set of Self-recording Magnetographs. 2. An instrument for tabulating from the traces furnished by the Mag- netographs. 3. A Unifilar. 4. A Dip Circle. 5. A Self-recording Anemometer. G. Barometers. 7. An instrument for testing Thermometers, also a Kew Standard Ther- mometer. 8. Sun Pictures, taken by the Kew Heliograph. The Committee have the pleasure to inform the Association that a Medal has been awarded to the Kew Observatory for excellence and accuracy of construction of instruments for observing terrestrial magnetism ; and that two Medals have likewise been awarded to Mr. R. Beckley, Mechanical Assistant at Kew, for his Registering Anemometer, and for his Photographs of the Sun. It is proposed that application be made to the Government Grant Com- mittee of the Royal Society for the expenses incurred through this exhibition. At the time when the last Report was made to the Association, the Staff" at Kew were occupied with the verification of a set of magnetic instruments belonging to Prof. De Souza, of the University of Coimbra, a gentleman who ■was present at the Meeting at Manchester. The examination of these was shortly after completed, and the instruments, consisting of a set of Self- recording Magnetographs, a tabulating instrument, a Dip Circle, and a Unifilar, have since been safely received at Coimbra. The following letter was addressed to the Chairman by Prof. De Souza shortly before his departure : — " London, 26th October, 1861. " Mr dear Sir, — I cannot leave England, where I have been exceedingly favoured by the Committee of the Kew Observatory of the British Associa- tion, without expressing to you my hearty thanks for the help I have expe- rienced from the Committee in the construction and verification of the Magnetic and Meteorologic instruments for the University of Coimbra, as well as for the valuable instruction which I have received, guided by the Director of the Kew Observatorv, and the kindness which the British Asso- REPORT OF THE KEW COMMITTEE. XXxiii ciation has shown me in their magnificent Meeting. I shall never forget the help afforded to me in so many different "ways, and I desire earnestly to put it in immediate contribution towards the advancement of science. " The Observatory of Coimbra inust have in its library, as a memorial, the valuable collection of Transactions of the British Association, and I hope that you may be so land as to put me in the way of obtaining these volumes. " I remain, dear Sir, " Sincerely yours, "J. P. Gassiot, Esq." " Jacixtho A. de Souza." The request of this letter has been complied with by the Council of the Association, and a complete set of the Transactions has been dispatched to Coimbra. The Director of the Lisbon Observatory has since requested the Committee to superintend the construction of a set of self-recording Magnetographs. The Committee, in complying with his request, have made arrangements for the instruments at present exhibited in the International Exhibition, and these will afterwards be mounted at the Kew Observatory for inspection and verification. A Differential Declinometer for the Government Observatory at Mauritius has been verified and forwarded to Prof. Meldrum, who has received it in safety. Lieut. Rokeby, of the Royal Marines, already favourably known by a me- teorological register very carefully kept at Canton during its occupation by the British troops, has received instruction at Kew in the use of magnetical in- struments, and has been furnished with a Dip Circle, a Unifilar, a Bifilar, and a Differential Declinometer, of which the constants have been deter- mined at the Observatory. Lieut. Rokeby proposes to employ these instru- ments at the Island of Ascension during his term of service at that station. He has also been furnished by Admiral FitzRoy with a complete equipment of the meteorological instruments supplied by the Board of Trade. The importance of Ascension as a magnetical station has long been recognized. Situated very nearly on the line of no magnetic dip, the determination of the periodical variations and of the secular changes of the three mag- netic elements cannot fail to possess a high value ; and as a meteorological station, a rock in the mid-ocean, within 6° of the Equator, presents an almost unrivalled locality for an exact measure of the amount of the lunar atmo- spheric tide, and of the variations in direction and force of the trade-wind. The Admiralty, apprised of Lieut. Rokeby's meritorious purposes, have sanc- tioned the appropriation of the officers' quarter at the summit of the Green Mountain, known as the " Mountain House," as an observatory ; and the department of the Board of Trade, under Admiral FitzRoy's superintendence, has authorized the expenditure of .£50 in providing the additional accommo- dation required for the instruments. Lieut. Rokeby has arrived at Ascension with the instruments uninjured, and writes in strong terms of the support he receives from Captain Barnard, the commander of the troops on the island. On June 19th the Chairman received a letter from the Astronomer Royal, in which he stated that he was very desirous of comparing the Greenwich records of the vertical-force magnet with those at Kew ; and that, if agree- able to the Committee, he would request Mr. Glaisher to endeavour to arrange a meeting with Mr. Stewart for that purpose. The Chairman immediately replied, offering every facility, and Mr. Glaisher has since visited the Observatorv, where the comparison has been made. 1862. c xxxiv REPORT — 1862. The usual monthly absolute determinations of the magnetic elements con- tinue to be made, and the self-recording magnetographs are in constant operation under the zealous superintendence of Mr. Chambers, the Mag- netical Assistant. Major-General Sabine, Pres. R.S., has laid before the Royal Society a paper entitled " Notice of some conclusions derived from the Photographic Records of the Kew Declinometer in the years 1858, 1859, 1860, and 1861." The exceedingly good definition which the labours of the late Mr. "Welsh procured for the magnetic curves, has also enabled the Superintendent, Mr. Stewart, to discuss the disturbance-curves by a peculiar method, depend- ing on such definition ; and he has presented a paper to the Royal Society " On the forces which are concerned in producing the larger magnetic dis- turbances." The Committee are at present engaged in investigating the best means of multiplying copies of these curves, and exhibit to the Association two prints from such — one kindly taken by Sir Henry James by his process, and the other taken by that of Mi*. Paul Pretsch. The expense incurred by Mr. Pretsch has been defrayed by <£25 obtained from the Government Grant through the Royal Society. The Chairman of the Balloon Committee having applied to the Super- intendent for the instruments used by the late Mr. Welsh in his ascents, these were delivered over to Mr. Criswick on the 12th of March last, having been previously verified at the Observatory. The Meteorological work of the Observatory continues to be performed in a satisfactory manner by Mr. George Whipple, and each Member of the Staff of the Observatory seems much interested in the duties he is called upon to discharge. During the past year 184 Barometers and 282 Thermometers have been verified ; and, to give an idea of the amount of this kind of work which has been accomplished since first the subject was commenced in the year 1854, it may be stated that no fewer than 1185 Barometers and 6429 Thermometers have been verified up to this date. Rear- Admiral FitzRoy having been informed of the existence at the Ob- servatory of a Barograph invented and used by Mr. Ronalds, the following letter was addressed by him to the Chairman : — {Copy.) " Board of Trade (and Admiralty) Meteorological Department, 2 Parliament Street, London, S.W., 7th April, 1862. " Sir, — I have the honour to address you as Chairman of the Kew Com- mittee of the British Association for the Advancement of Science, on behalf of this branch department of the Board of Trade and the Admiralty. "I am authorized to request that you will allow us to endeavour to benefit by your regidar photographic self- registration of the Barometer at the Kew Meteorological and Magnetical Observatory during at least one com- plete year of continuous record, by causing this office to be furnished with copies of photographic tracings, or their results, in full detail. " The objects specially in view here, are : — "Such accurate and indisputable continuous delineation of atmospheric pressure, or (rather) tension, as can only be obtained by perfectly reliable means ; and " Such details of occasional oscillations, or pulsations (so to speak), as can best be obtained photographically. REPORT OF THE KEW COMMITTEE. XXXV " For practical daily purposes, a self-registering Barometer, on the Milne principle, may be sufficient ; but for elaborate analysis of atmospherical con- ditions and changes, in connexion with the numerous influences operating, some occasionally, some frequently, others always, in the air and its ever- restless currents, such an apparatus as that now available at Kew would appear to be indispensable. " Besides ordinaiy meteorological peculiarities, the direction of magnetic earth-currents, the occurrence of magnetic storms, the differing electrical conditions of various currents of air, the phenomena of earthquakes, and their ' lightnings ' *, seem to be more or less in certain relations to atmo- spheric tension, and therefore to require a close and unbroken barometrical registration. Towards some additional expense incurred by the Kew Ob- servatory in complying with this request, I am authorized to say that this department will contribute, on principle similar to that of verification of instruments. " I have the honour to be, "Sir, " Your obedient Servant, (Signed) " Bobert FitzBoy, B. Adm." " P.S. Probably two scales of tracing, analogous to ' Sailing Charts ' and ' Particular Plans,' would be convenient." " John Peter Gassiot, Esq., F.B.S., Chairman of the Kew Committee of the British Association." To which the Chairman shortly afterwards replied in the following terms : — {Copy.) " Kew Observatory, 23rd April, 1862. " Sm, — I have the honour to acknowledge receipt of your letter of 7th inst., addressed to me as Chairman of the Kew Committee of the British Association. " On behalf of this Committee, I may state in reply that it will afford us much satisfaction to furnish your department with Photographic Self- registrations of the state of the Barometer at Kew Observatory. " I am informed by Mr. Stewart, our Superintendent, that we have in our possession an instrument well calculated, with some slight alterations, to produce the results you desire. " It possesses a compensation for temperature ; ■besides which, it will be placed, when finally in action, in a room where the daily range of tempera- ture is not more than half a degree Fahrenheit. " This instrument is not yet, however, in working order, and two months may perhaps elapse before it is quite ready. As you seem to think it de- sirable to obtain occasionally curves on an enlarged scale, it will be matter for our consideration whether this can be managed, and how. Tou will be duly informed of our resolution ; but, in the mean time, I may state that it would be somewhat more than two months before such additional curves could be ready. In conclusion, without binding ourselves to any specified time (which, indeed, would not be desirable in a matter of this nature), I beg- to assure you that we shall do all in our power to hasten the desired residt ; and, as we hope to have things ready in the course of two or three months, * Secchi and Palmieri, 1862. c2 xjcxvi REPORT— 1862. we shall then also be prepared to reply to yon with respect to remuneration for the additional work which the Observatory would thus undertake. " I have the honour to be, " Sir, " Your obedient Servant, (Signed) " J. P. Gassiot." " Rear- Admiral FitzRoy, F.R.S., $c." The Mechanical Assistant being engaged at the Exhibition, it was found impossible to complete the alterations alluded to quite so soon as anticipated ; but a curve was procured about the middle of August, which was sent to Admiral FitzRoy, and approved of by him. The Barograph has since received some further alterations, with a view to increase its stability and general efficiency. These are now completed, and the instrument will be henceforth kept in constant operation. One of the curves from this instrument is presented to the Association. Arrangements were made for recording photographically, by means of the Heliograph, the transit of Mercury which took place on the 12th of Novem- ber lost, but the weather proved unfavourable. This instrument was also in readiness for the partial eclipse of the sun which took place on the 31st of December last ; but, owing to the unfavourable state of the sky, only two imperfect pictures were obtained. A very good series of sun-pictures was obtained by Mr. Beckley during the months of November and December. The Heliograph was sent from Kew at the beginning of January to Mr. De la Rue's Observatory, and Mr. Reckley attended at Cranford to assist in erecting and adjusting it to focus ; but the weather was so unfavourable during the remainder of that montli that no pictures of the sun could be obtained. It had somewhat improved about the 7th of February, when the first photograph was taken, and since then others have been obtained by Mr. Reynolds (Mr. De la Rue's assistant) on every day on which this has been possible. Altogether, up to the 12th of September inclusive, 177 pho- tographs have been taken on 124 days, namely : — Number of Number of pho- In the Month of working clays. tographs procured. February 7 13 March 10 17 April 17 31 May 17 26 June 23 28 July 20 27 August 21 26 Up to September 12 . 9 9 124 177 From February 7th to September 12th inclusive there are 218 days ; so that on the average one photograph was procured for 1-77 day. Nearly half of the pictures have been obtained by taking advantage of breaks in the clouds, and many have been taken through haze. In several of the photographs, owing to the unpropitious state of the atmosphere, there is a want of that beauty and perfection which the Heliograph is capable of affording ; but all the pictures are sufficiently perfect for measurement by means of Mr. De la Rue's Micrometer. Many of these are extremely perfect, and all would have been so had the state of the atmosphere permitted. REPORT OF THE KEW COMMITTEE. XXXVU During the month of August Dr. Sahler, Director of the Observatory of Wilna in Russia, resided at Cranford, and received instruction in Astrono- mical Photography. A Photohcliograph is being constructed for him under Mr. De la Rue's superintendence by Mr. Dallmeyer, and a Micrometer by the Messrs. Simms. This Heliograph will embody all the optical and mechanical improvements suggested by the experiments with the Kew instrument ; and it is expected that the Wilna apparatus will be in operation in the spring of 1863. In the event of the Kew Heliograph being worked continuously, Sir John Herschel's suggestion that daily records of the sun should be taken by means of photography will therefore be carried out both in England and Russia ; if this were done in one or two other localities, a considerable amount of information would be obtained respecting physical changes con- tinually occurring on the sun's surface. The experience obtained during the past year has been such as to lead Mr. De la Rue to recommend that photographic records should be continued for a series of years at some public Observatory. The Committee have had in consideration whether this could be done at Kew without interfering with the other work, and have come to the conclusion that the Heliograph might be worked at an annual expense of £200, which sum would cover the cost of an additional Assistant, who might at the same time do the other photogra- phic work of the Observatory. The old dome formerly used for the Heliograph is so inconveniently situ- ated as to be quite unfit for such work, and it will be necessary to niako some addition to one of the present out-buildings in order to contain the in- strument. The cost of this structure is estimated at £100. The Committee strongly recommend that the General Committee of the Association take such steps as they may consider advisable for carrying this desirable object into practical effect. The self-recording Electrometer of Prof. W. Thomson continues in con- stant operation. Mr. Francis Galton having made arrangements in the Observatory Park for testing sextants, the Observatory is now prepared to receive such instruments for examination, and to issue certificates to such as may fulfil the conditions of any of the following classes : — A. Sextants of the highest order of workmanship for lunar observations and general service, on shore as well as at sea. B. Sextants for naval surveys and for the determination of altitudes with as much precision as is available at sea. C. Quadrants or sextants to be used without telescopes, for the determina- tion of altitudes with an exactness equal to the requirements of general navigation. The charges for examination under classes A and B will be 5s., under class C, Is. ; and the minute constant errors of instruments under class A will be determined, when desired, at an additional charge of 5s. Eight sextants have been verified at Kew since the last Meeting of the British Association. The Observatory has been honoured with a visit from the following distin- guished men of science, who had visited this country in consequence of the International Exhibition : — Professors Dove, Magnus, and Quincke, of Berlin ; Professor Forchbammer, of Copenhagen ; Professors Bunsen, Kirchhoff, and Eisenlohr, of Heidelberg; Professors Kraft and Pisko, of Vienna ; Professor Govi, of Turin ; Professor Donati, of Florence ; Professor Bolzani, of Kasan; Professor Lapschine, of XXXVU1 REPORT 186.2. CO co co Is SQ S 3S © -^« © © © »-< >— ' © I— I <-* »n •* oo © cm r» o — i © -^ CO "*1* i— i cn *-* «rt H S P-, pq to 1— 1 <N oo eo CM 00 CM OS o t^ «t? C3 • 3 o CD o *-• **" C<2 - cd •• S o g J2SH 5 n <=■ -3 3^ eo O . 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X B o 13 B CD — CD CO co CS c cS — ~cs — ' s a *o CD CO CD U •2Q CD h« -** f^ to i-H s RECOMMENDATIONS OF THE GENERAL COMMITTEE. XXXIX Kharkof ; Professors Clausius and Wartinann, of Geneva ; Captain Belavenetz, Russian Navy ; and Captain Skariatine, Russian Marines. A reference to the annexed financial statement will show that, although the expenditure has exceeded the income, the Observatory has been conducted with the utmost regard to economy.; and the Committee recommend that for the ensuing year a sum of £600 should be granted, which, with other amounts to be received, will, it is expected, meet the necessary requirements. John P. Gassiot, Kew Observatory, Chairman. Sept. 29th, 1862. Report of the Parliamentary Committee to the Meeting of the British Association at Cambridge, October 1862. The Parliamentary Committee have the honour to report as follows : — The Bishop of Oxford, in furtherance of the resolution adopted at Liverpool in 1854, must be deemed to have vacated his seat in this Committee, but we recommend that he should be re-elected. * Your Committee have also to report that Mr. James Heywood has not found it necessaiy to call upon them to interfere in the matter referred to them at Manchester by the General Committee. Wrottesley, Chairman. Sept. 14, 1862. Recommendations adopted by the General Committee at the Cambridge Meeting in October 1862. [When Committees are appointed, the Member first named is regarded as the Secretary of the Committee, except there be a specific nomination.] Involving Grants of Money. That the sum of £600 be placed at the disposal of the Council, for main- taining the Establishment of Kew Observatory. That the sum of £100 be placed at the disposal of the Council, for the pur- pose of making an addition to the out-buildings at Kew Observatory, to receive the Photoheliograph, now in the hands of Mr. De la Rue. That the cooperation of the Royal Society be requested for the purpose of completing and proving the instruments devised for obtaining Photographic registration of the physical aspect of the Sun. That the Committee, consisting of Professor Williamson, Professor Wheat- stone, Professor W. Thomson, Professor W. H. Miller, Dr. A. Matthiessen, and Mr. Fleeming Jenkin, appointed at the Manchester Meeting, be requested to continue their Report on Standards of Electrical Resistance, and to extend it to other Electrical Standards ; and that Dr. Esselbach, Sir C. Bright, Pro- fessor Maxwell, Mr. C. W. Siemens, and Mr. Balfour Stewart be added to the Committee; and that the sum of £100 be placed at their disposal for the purpose. That the Committee to report upon Standards of Electrical Resistance, be Xl REPORT 1862. authorized to distribute gratuitously provisional Standards of Electrical Re- sistance, should it appear to them advantageous to do so; and that the sum of £50 be placed at their disposal for the purpose. That as all the Balloon Observations hitherto made under the authority of the British Association (owing to unavoidable circumstances) have been con- fined to the autumnal period of the year, these operations should be repeated at other periods of the year, especially during the east winds of spring, with u view to test the normal character of the observations already made ; That Colonel Sykes, Professor Airy, Lord Wrottesley, Sir D. Brewster, Sir J. Hersckel, Dr. Lloyd, Admiral FitzRoy, Dr. Lee, Dr. Bobinson, Mr. Gassiot, Mr. Glaisher, Dr. Tyndall, Mr. Fairbairn, and Dr. W. A. Miller be a Balloon Committee ; and that the sum of =£200 be placed at their disposal for the purpose. That the sum of £70 be placed at the disposal of the Balloon Committee, to meet the deficiency in the Grant of £200 made at Manchester. That a sum not exceeding £25, the amount of expenses necessarily in- curred by Mr. Glaisher in the prosecution of the Balloon experiments, be repaid to him. That the Committee on Luminous Meteors and Aerolites, consisting of Mr. Glaisher, Mr. R. P. Greg, Mr. E. W. Brayley, and Mr. Alexander Her- schel, be reappointed ; and that the sum of <£20 be placed at their disposal for the purpose. That Mr. Fleeming Jenkin be requested to continue his Report on Thermo- Electrical Experiments ; and that the sum of £15 (being the balance of the Grant made to him last year) be placed at his disposal for the purpose. That the Committee, consisting of Professor Hennessy, Admiral FitzEoy, and Mr. Glaisher, be requested to continue their inquiries relative to the con- nexion of Vertical Movements of. the Atmosphere with Storms ; and that the sum of £20 be placed at their disposal for the purpose. That Dr. Matthiessen be requested to continue his Experiments on Alloys ; and that the sum of £20 be placed at his disposal for the purpose. That Dr. A. Dupre be requested to continue his Experiments upon the action of Beagents on Carbon under Pressure ; and that the sum of £10 be placed at his disposal for the purpose. That the Balance of Grant of £8 made at the Manchester Meeting to Mr. Alphonse Gages, of Dublin, be placed at the disposal of that gentleman. That the Committee, consisting of Mr. R. H. Scott, Sir Richard Griffith, and the Bev. Prof. Haughton, be requested to complete their Report on the Chemical and Mineralogical Composition of the Granites of Douegal and the associated Rocks ; and that the sum of £5 be placed at their disposal for the purpose. That Mr. DZ. C. Sorby and Mr. C. II. B. Hambly be a Committee to make Experiments on the Fusion and Slow Cooling of various Igneous Rocks ; and that the sum of £30 be placed at their disposal for the purpose. That Professor Huxley and Sir Philip de 'Grey Egerton be a Committee to aid Mr. Molyneux in his Researches into the Characters and Distribution of the Organic Remains of the North Staffordshire Coal-field; and that the sum of £20 be placed at their disposal for the purpose. That Mr. Mallet be requested to conduct Experiments to ascertain the Temperatures of the Volcanic Craters of Vesuvius and of the Temperature and Issuing Velocity of the Steam evolved at the Mouths, — the Experiments, if possible, to be extended to other Volcanic Vents in the Mediterranean Basin ; and that the sum of £100 be placed at his disposal for the purpose. RECOMMENDATIONS OF THE GENERAL COMMITTEE. xli That a Committee, consisting of Dr. Cobbold and Mr. J. Lubbock, be re- quested to prosecute their Investigations respecting the Reproduction, Development, and Migration of the Entozoa ; and that the sum of £25 be placed at their disposal for the purpose. That Professor Huxley and the Rev. Mr. Macbride be a Committee to con- duct Experiments on the Artificial Eecundation of the Herring ; and that the sum of .£20 be placed at their disposal for the purpose. That Mr. J. Gwyn Jeffreys, Mr. Joshua Alder, the Rev. A. M. Norman, and Mr. H. T. Mennell be a Committee for exploring the Doggerbank and other portions of the Sea-coast of Durham and Northumberland by means of the Dredge ; and that the sum of £25 be placed at their disposal for the purpose. That Mr. J. Gwyn Jeffreys, Professor Allman, Mr. John Leckenby, Pro- fessor Wyville Thomson, and the Rev. Thomas Hincks be a Committee for exploring the Coasts of Shetland by means of the Dredge ; and that the sum of £50 be placed at their disposal for the puqjose. That Mr. J. Gwyn Jeffreys, Professor Allman, Professor Dickie, the Rev. Dr. Gordon, and Mr. Robert Dawson be a Committee for exploring the North-east Coast of Scotland by means of the Dredge ; and that the sum of £25 be placed at their disposal for the purpose. That Mr. J. Gwyn Jeffreys, Mr. Robert M' Andrew, Mr. G. C. Hyndman, Professor Allman, Dr. Jvinahan, Dr. Collingwood, Dr. Edwards, Professor Greene, Rev. Thomas Hincks, Mr. R. D. Darbishire, and Dr. E. Perceval Wright be a Committee to superintend all the Dredging Committees of the Association ; and that the sum of £10 be placed at their disposal for the pur- pose. That the Committee, consisting of Dr. Edward Smith and Mr. Milner, be requested to continue their inquiries on the Influence of Prison Punishment and Dietary upon the Bodily Functions of Prisoners ; and that the sum of £20 be placed at their disposal for the purpose. That Dr. Gibb be requested to inquire into the Physiological Effects of Bromide of Ammonium ; and that the sum of £S be placed at his disposal for the purpose. That Dr. Carpenter, Professor Huxley, and Mr. Rupert Jones, assisted by Mr. Parker, be a Committee to aid in the Construction of a Series of Models showing the External and Internal Structure of the Eoraminifera ; and that the sum of £25 be placed at their disposal for the purpose. That Professor Allman and Dr. E. P. Wright be a Committee to complete a Report on the Reproductive System of the Hydroida ; and that the sum of £10 be placed at their disposal for the purpose. That Mr. Thomas Webster, the Right Honourable Joseph Napier, Sir W. G. Armstrong, Mr. W. Fairbairn, Mr. W. R. Grove, Mr. James Heywood, and General Sabine be reappointed, for the purpose of taking such steps as may appear expedient for rendering the Patent Law more efficient for the reward of the meritorious inventor and the advancement of practical science ; and that the sum of £30 be placed at their disposal for the purpose. That the Committee on Steamship Performance be reappointed, consisting of the Duke of Sutherland, The Earl of Gifford, M.P., The Earl of Caith- ness, Lord Dufferin, Mr. W. Fairbairn, Mr. J. Scott Russell, Admiral Paris, The Hon. Captain Egerton, R.N., The Hon. L. A. Ellis, M.P., Mr. J. E. M c Conncll, Mr. W. Smith, Professor J. Macquorn Rankine, Mr. James R. Napier, Mr. Richard Roberts ; Mr. Henry Wright to be Honorary Se- cretary ; and that the sum of £100 be placed at their disposal. xlii report — 1862. That a Committee, consisting of Messrs. W. Fairbairn, Joseph Whitworth, James Nasmyth, J. Scott Russell, John Anderson, and Sir W. G. Armstrong, be requested to cooperate with a Committee appointed by Section B, viz. Dr. Gladstone, Professor W. A. Miller, and Dr. Frankland, for the purpose of investigating the application of Gun Cotton to warlike piu-poses ; and that the sum of =£50 be placed at their disposal for the purpose. That the Committee for Tidal Observations in the Humber, consisting of Mr. J. Oldham, Mr. J. F. Bateman, Mr. J. Scott Russell, and Mr. T. Thomp- son, be reappointed, to extend their observations to the Trent and the York- shire Ouse; and that the sum of =£50 be placed at their disposal for the purpose. That Sir John Rennie, Mr. John Scott Russell, and Mr. C. Vignoles (with power to add to their number), Mr. G. P. Bidder, Jun., as Secretary, be a Committee to inquire and report as to the effect upon the Tides in the Nene and the Ouse by the opening of the Outfalls below Wisbeach and Lynn to the Wash; and that the sum of £25 be placed at their disposal for the purpose. That the Committee for investigating the causes of Railway Accidents, consisting of Mr. W. Fairbairn, Mr. J. E. M c Connell, and Mr. W. Smith, be reappointed ; and that the sum of =£25 be placed at their disposal for the purpose. Applications for Reports and Researches not involving Grants of Money. That Mr. Johnstone Stoney be requested to continue his Report on Molecu- lar Physics. That Mr. James Cockle be requested to prepare a Report on the History of the Theory of Equations. That a Committee be appointed for the purpose of carrying into effect the objects of the Report on Scientific Evidence in Courts of Law. That Dr. Gray, Dr. Sclater, Mr. Alfred Newton, and Mr. Wallace be a Committee to report on the Acclimatization of Domestic Quadrupeds and Birds, and how they are affected by migration. That Dr. Gray, Professor Babington, and Mr. Newbold be a Committee to report on the Plants of Ray's ' Synopsis Stirpium,' for the examination of the original Herbaria of Ray, Richardson, Buddie, Plukenet, and others. That Dr. Collingwood, Mr. J. A. Turner, M.P., Mr. James Heywood, Mr. John Lubbock, Mr. J. Gwyn Jeffreys, Mr. R. Patterson, Mr. P. P. Carpenter, and the Rev. H. H. Higgins be a Committee to inquire into the best mode of pro- moting the advancement of Science by means of the Mercantile Marine. That Mr. Consul Swinhoe and Dr. Sclater be a Committee to report on the Zoology of the Island of Formosa. That Dr. Edward Smith be requested to prepare for the next Meeting of the British Association a Report on the present state of our knowledge upon Nutrition, and especially its relation to Urea. That the Rev. W. Vernon Harcourt, Right Hon. Joseph Napier, Mr. Tite, M.P., Professor Christisou, Mr. J. Heywood, Mr. J. F. Bateman, Mr. T. Web- ster (with power to add to their number) be a Committee for the purpose of giving effect to the Report of the Committee on Technical and Scientific Evidence in Courts of Law. RECOMMENDATIONS OF THE GENERAL COMMITTEE. xliii Involving Applications to Government or Public Institutions. That a Deputation, consisting of Mr. E. Chadwick, C.B., Mr. J. Heywood, Mr. Marsh, M.P., Dr. Farr, Mr. Tite, M.P., Mr. S. Gregson, M.P., and Col. Sykes, M.P., be requested to wait upon the Secretary of State for the Home Department and the Registrar-General, and represent to them the import- ance of having prepared Mortuary Statistics in respect to Classes and Occupa- tions, in such forms as were recommended by the International Statistical Congress, or in such other form as will distinguish the Occupations or the Classes of those who die. That the Committee, consisting of Dr. Eobinson, Professor Wheatstone, Dr. Gladstone, and Professor Hennessy, which was appointed at Manchester to confer as to Experiments on Fog Signals, and to act as a Deputation to the Board of Trade, be requested to impress upon the Board the importance of inquiries on the subject. Communications to be printed entire among the Reports. That the Extract of Professor De Souza's Report to the Portuguese Government, regarding the Instruments used at Kew Observatory, be printed entire in the Reports. That Mr. Symons's Papers on Rainfall be printed entire among the Reports. That the Paper by the Astronomer Royal, on the Strains in the interior of Beams and Tubular Bridges, be printed entire among the Reports. That Mr. Aston's Paper on Projectiles, with reference to their Penetration, be printed entire among the Reports. That Mr. "W. Fairbairn's Paper on the Results of some Experiments on the Mechanical Properties of Projectiles be printed entire among the Reports. Synopsis of Grants of Money appropriated to Scientific Purposes by the General Committee at the Cambridge Meeting in October 1862, with the name of the Member who alone, or as the First of a Com- mittee, is entitled to draw the Money. Kew Observatory. £ s. d. Maintaining the Establishment of Kew Observatory 600 House for the Photoheliograph at Kew 100 Mathematics and Physics. "Williamson, Prof. — Electrical Standards 100 Williamson, Prof. — For constructing and distributing ditto. ... 50 Sykes, Col. — Balloon Ascents 200 Sykes, Col. — Balloon Committee (deficiency) 70 Sykes, Col.— Other expenses of Balloon Ascents 25 Glaisher, Mr. — Meteors 20 Jenkin, Mr. — Thermo-Electricity 15 Carried forward .£1180 xliv REPORT — 1862. £ s. d. Brought forward 1180 Hennessy, Prof. — Vertical Atmospheric Movements 20 Chemistry. Matthiessen, Dr. — Alloys 20 Dupre, M. — Carbon under pressure 10 Gages, Mr. — Chemistry of Rocks 8 Geology. Scott, Mr. — Granites, &c 5 Sorby, Mr. — Fusion of Eocks 30 Huxley, Prof.— Coal Fossils 20 Mallet, Mr. — Volcanic Temperature 100 Zoology and Botany. Cobbold, Mr. — Entozoa 25 Huxley, Prof. — Herrings 20 Jeffreys, Mr. — Dredging (Doggerbank) 25 Jeffreys, Mr. — Dredging (Shetland) 50 Jeffreys, Mr.— Dredging (KE. coast of Scotland) 25 Jeffreys, Mr. — Committee for Dredging 10 Smith, Dr. E. — Prison Discipline 20 Gibb, Dr. — Bromide of Ammonium 8 Carpenter, Dr. — Foraminifera 25 Allman, Prof. — Hydroids 10 Mechanics. Webster, Mr. — Patent Laws 30 Sutherland, Duke of. — Steamships 100 Gladstone, Dr. — Gun Cotton 50 Oldham, Mr. — Tidal Observations 50 Rennie, Mr. — Action of Tides below Wisbeach to the Wash . . 25 Fairbairn, Mr. — Railway Accidents 25 Total 1891 GENERAL STATEMENT. xlv General Statement of Sums which have been paid on Account of Grants for Scientific Purposes. 1S34. £ .. 20 d. n 1835. .. 62 British Fossil Ichthyology £167 1836. .. 163 1 13 6 14 n British Fossil Ichthyology 105 Thermometric Observations, &c. 50 Experiments on long-continued Heat 17 9 .. 15 .. 60 n .. 15 n £434 1837. .. 284 1 13 12 5 4 18 14 .. 24 6 .. 70 .. 100 .. 150 Meteorology and Subterranean n .. 150 8 6 .. 30 ... 11 fi £9 IS C 1838. .. 29 1 12 6 3 8 6 9 4 12 . 100 n Meteorological Observations and Anemometer (construction) ... 100 Cast Iron (Strength of) 60 Animal and Vegetable Substances Railway Constants r — 41 10 10 Bristol Tides .. 50 75 3 6 ... 50 5 n Subterranean Temperature ... 8 ... 100 7 o Meteorological Committee ... , 31 .. 16 5 £956 2 1839. Meteorological Observations at 63 10 2 18 ... 144 () G £ s. d. Meteorology and Subterranean Temperature 21 Vitrification Experiments 9 Cast Iron Experiments 100 Railway Constants 28 Land and Sea Level 274 Steam-vessels' Engines 100 Stars in Histoire Celeste 331 Stars in Lacaille 11 Stars in It.A.S. Catalogue 6 Animal Secretions 10 Steam-engines in Cornwall 50 Atmospheric Air 16 Cast and Wrought Iron 40 Heat on Organic Bodies 3 Gases on Solar Spectrum 22 Hourly Meteorological Observa- tions, Inverness and Kingussie 49 Fossil Reptiles 118 Mining Statistics 50 11 4 7 7 2 1 4 18 16 6 10 1 7 s 2 9 £1505 11 1840. Bristol Tides 100 Subterranean Temperature 13 Heart Experiments 18 Lungs Experiments 8 Tide Discussions 50 Land and Sea Level 6 Stars (Histoire Celeste) 242 Stars (Lacaille) 4 Stars (Catalogue) 264 Atmospheric Air 15 Water on Iron 10 Heat on Organic Bodies 7 Meteorological Observations 52 Foreign Scientific Memoirs 112 Working Population 100 School Statistics 50 Forms of Vessels 184 Chemical and Electrical Pheno- mena 40 Meteorological Observations at Plymouth 80 Magnetical Observations 185 13 6 19 13 11 1 10 15 15 17 6 1 6 7 13 9 £1546 16 4 1841. Observations on Waves 30 Meteorology and Subterranean Temperature 8 Actinometers 10 Earthquake Shocks 17 Acrid Poisons 6 Veins and Absorbents 3 Mud in Rivers 5 Marine Zoology 15 Skeleton Maps 20 Mountain Barometers 6 Stars (Histoire Celeste) 185 8 7 12 8 18 6 xlvi REPORT 1862. £ Stars (Lacaille) 79 Stars (Nomenclature of) 17 Stars (Catalogue of) 40 Water on Iron 50 Meteorological Observations at Inverness 20 Meteorological Observations (re- duction of) 25 Fossil Reptiles 50 Foreign Memoirs 62 Railway Sections 38 Forms of Vessels 193 Meteorological Observations at Plymouth 55 Magnetical Observations 61 Fishes of the Old Red Sandstone 100 Tides at Leith 50 Anemometer at Edinburgh 69 Tabulating Observations 9 Races of Men 5 Radiate Animals , 2 ~£l235 1842. Dynamometric Instruments 113 Anoplura Britannia; 52 Tides at Bristol 59 Gases on Light 30 Chronometers 26 Marine Zoology 1 British Fossil Mammalia 100 Statistics of Education 20 Marine Steam-vessels' Engines... 28 Stars (Histoire Celeste) 59 Stars (Brit. Assoc. Cat. of ) 110 Railway Sections 161 British Belemnites 50 Fossil Reptiles (publication of Report) 210 Forms of Vessels 180 Galvanic Experiments on Rocks 5 Meteorological Experiments at Plymouth 68 Constant Indicator and Dynamo- metric Instruments 90 Force of Wind 10 Light on Growth of Seeds 8 Vital Statistics 50 Vegetative Power of Seeds 8 Questions on Human Race 7 £1449 1843. Revision of the Nomenclature of Stars 2 Reduction of Stars, British Asso- ciation Catalogue 25 Anomalous Tides, Frith of Forth 120 Hourly Meteorological Observa- tions at Kingussie and Inverness 77 Meteorological Observations at Plymouth 55 Whewell's Meteorological Ane- mometer at Plymouth 10 8, d. 5 19 6 1 6 12 18 8 1 10 6 3 10 11 11 12 2 8 14 7 17 6 5 10 8 6 1 11 9 17 8 2 12 8 £ Meteorological Observations, Os- ier's Anemometer at Plymouth 20 Reduction of Meteorological Ob- servations 30 Meteorological Instruments and Gratuities 39 Construction of Anemometer at Inverness 56 Magnetic Cooperation 10 Meteorological Recorder for Kew Observatory 50 Action of Gases on Light 18 Establishment at Kew Observa- tory, Wages, Repairs, Furni- ture and Sundries 133 Experiments by Captive Balloons 81 Oxidation of the Rails of Railways 20 Publication of Report on Fossil Reptiles 40 Coloured Drawings of Railway Sections 147 Registration of Earthquake Shocks 30 Report on Zoological Nomencla- ture 10 Uncovering Lower Red Sand- stone near Manchester 4 Vegetative Power of Seeds 5 Marine Testacea (Habits of) ... 10 Marine Zoology ]0 Marine Zoology 2 Preparation of Report on British Fossil Mammalia 100 Physiological Operations of Me- dicinal Agents 20 Vital Statistics 36 Additional Experiments on the Forms of Vessels 70 Additional Experiments on the Forms of Vessels 100 Reduction of Experiments on the Forms of Vessels 100 Morin's Instrument and Constant Indicator 69 Experiments on the Strength of Materials 60 £1565 5. A 6 12 8 2 10 16 1 4 8 7 18 3 4 3 14 6 8 11 II 5 8 4 10 (1 10 2 1844. Meteorological Observations at Kingussie and Inverness 12 Completing Observations at Ply- mouth 35 o Magnetic and Meteorological Co- operation 25 S Publication of the British Asso- ciation Catalogue of Stars 35 Observations on Tides on the East coast of Scotland 100 Revision of the Nomenclature of Stars 1842 2 9 Maintaining the Establishment in Kew Observatory 117 17 Instruments for Kew Observatory 56 7 GENERAL STATEMENT. xlvii £ Influence of Light on Plants 10 Subterraneous Temperature in Ireland 5 Coloured Drawings of Railway Sections 15 Investigation of Fossil Fishes of the Lower Tertiary Strata ... 100 Registering the Shocks of Earth- quakes 1S42 23 Structure of Fossil Shells 20 Radiata and Mollusca of the JEgean and Red Seas 1842 100 Geographical Distributions of Marine Zoology 1S42 Marine Zoology of Devon and Cornwall 10 Marine Zoology of Corfu 10 Experiments on the Vitality of Seeds 9 Experiments on the Vitality of Seeds 1842 8 Exotic Anoplura 15 Strength of Materials 100 Completing Experiments on the Forms of Ships 100 Inquiries into Asphyxia 10 Investigations on the Internal Constitution of Metals 50 Constant Indicator and Morin's Instrument, 1842 10 £981 1845. Publication of the British Associa- tion Catalogue of Stars 351 Meteorological Observations at Inverness 30 Magnetic and Meteorological Co- operation 16 Meteorological Instruments at Edinburgh 18 Reduction of Anemometrical Ob- servations at Plymouth 25 Electrical Experiments at Kew Observatory 43 Maintaining the Establishment in Kew Observatory 149 For Kreil's Barometrograph 25 Gases from Iron Furnaces 50 The Actinograph 15 Microscopic Structure of Shells... 20 Exotic Anoplura 1843 10 Vitality of Seeds 1S43 2 Vitality of Seeds 1844 7 Marine Zoology of Cornwall 10 Physiological Action of Medicines 20 Statistics of Sickness and Mor- tality in York 20 Earthquake Shocks 1843 15 £830 s. d. 17 6 11 10 10 3 7 3 3 6 12 8 14 6 18 11 16 8 11 9 17 8 15 7 14 8 1) 9 1846. British Association Catalogue of Stars 1S44 211 15 £ Fossil Fishes of the London Clay 100 Computation of the Gaussian Constants for 1S39 50 Maintaining the Establishment at Kew Observatory 146 Strength of Materials 60 Researches in Asphyxia 6 Examination of Fossil Shells 10 Vitality of Seeds 1844 2 Vitality of Seeds 1845 7 Marine Zoology of Cornwall 10 Marine Zoology of Britain 10 Exotic Anoplura 1844 25 Expenses attending Anemometers 1 1 Anemometers' Repairs 2 Atmospheric Waves 3 Captive Balloons 1844 8 Varieties of the Human Race 1844 7 Statistics of Sickness and Mor- tality in York 12 £685 s. d. 16 7 16 2 15 10 12 3 7 3 6 3 3 19 3 6 3 16 1847. Computation of the Gaussian Constants for 1839 50 Habits of Marine Animals 10 Physiological Action of Medicines 20 Marine Zoology of Cornwall ... 10 Atmospheric Waves 6 9 3 Vitality of Seeds 4 7 7 Maintaining the Establishment at Kew Observatory 107 8 6 £208 5 4~ 184S. Maintaining the Establishment at Kew Observatory 171 15 11 Atmospheric Waves 3 10 9 Vitality of Seeds 9 15 Completion of Catalogues of Stars 70 On Colouring Matters 5 On Growth of Plants 15 £275 i 8 1849. Electrical Observations at Kew Observatory 50 Maintaining Establishment at ditto 76 2 5 Vitality of Seeds 5 8 1 On Growth of Plants 5 Registration of Periodical Phe- nomena 10 Bill on account of Anemometrical Observations 13 9 £159 19 6 1850. Maintaining the Establishment at Kew Observatory 255 18 Transit of Earthquake Waves ... 50 xlviii report — 1862. £ s. d. Periodical Phenomena 15 Meteorological Instrument, Azores 25 £345 IS (i 1851. Maintaining the Establishment at Kew Observatory (includes part of grant in 1849) 309 2 2 I Theory of Heat 20 1 1 Periodical Phenomena of Animals and Plants 5 Vitality of Seeds 5 6 4 Influence of Solar Radiation 30 Ethnological Inquiries 12 Researches on Annelida 10 £391 9 1 1S52. Maintaining the Establishment at Kew Observatory (including balance of grant for 1S50) ... 233 17 S Experiments on the Conduction ofHeat 5 2 9 Influence of Solar Radiations ... 20 Geological Map of Ireland 15 Researches on the British Anne- lida 10 Vitality of Seeds 10 6 2 Strength of Boiler Plates 10 £304" C 7 1853. Maintaining the Establishment at Kew Observatory 165 Experiments on the Influence of Solar Radiation 15 Researches on the British Anne- lida 10 Dredging on the East Coast of Scotland 10 Ethnological Queries 5 £205 1854. Maintaining the Establishment at Kew Observatory (including balance of former grant) 330 15 4 Investigations on Flax 11 Effects of Temperature on Wrought Iron 10 Registration of Periodical Phe- nomena 10 British Annelida 10 Vitality of Seeds 5 2 Conduction of Heat 4 2 " £380 19 1855. Maintaining the Establishment at Kew Observatory 425 Earthquake Movements 10 Physical Aspect of the Moon 11 8 5 Vitality of Seeds 10 7 11 Map of the World 15 Ethnological Queries 5 Dredging near Belfast 4 £480 16 4 1856. Maintaining the Establishment at Kew Observatory: — 1854 £ 75 01 1855 £500 0] Strickland's Ornithological Syno- nyms Dredging and Dredging Forms... Chemical Action of Light Strength of Iron Plates Registration of Periodical Pheno- mena Propagation of Salmon _ £ 575 100 9 13 y 20 10 10 10 7 34 13 9 1857. Maintaining the Establishment at Kew Observatory 350 Earthquake Wave Experiments. . 40 Dredging near Belfast 10 Dredging on the West Coast of Scotland 10 Investigations into the Mollusca of California 10 Experiments on Flax 5 Natural History of Madagascar. . 20 Researches on British Annelida 25 Report on Natural Products im- ported into Liverpool 10 Artificial Propagation of Salmon 10 Temperature of Mines Thermometers for Subterranean Observations Life-Boats 7 8 7 4 £507 15 4 1858. Maintaining the Establishment at Kew Observatory 500 Earthquake Wave Experiments.. 25 Dredging on the West Coast of Scotland 10 Dredging near Dublin 5 Vitality of Seeds 5 Dredging near Belfast 18 Report on the British Annelida... 25 Experiments on the production of Heat by Motion in Fluids ... 20 Report on the Natural Products imported into Scotland 10 £618 If 1859. Maintaining the Establishment at Kew Observatory 500 Dredging near Dublin 15 Osteology of Birds 50 Irish Tunicata 5 Manure Experiments 20 British Medusidse 5 Dredging Committee 5 Steam-vessels' Performance 5 Marine Fauna of South and West oflreland 10 Photographic Chemistry 10 Lanarkshire Fossils 20 Balloon Ascents 39 5 13 2 1 1 £684 11 1 GENERAL STATEMENT. xlix I860. £ i. d. Maintaining the Establishment of Kew Observatory 500 Dredging near Belfast 16 6 Dredging in Dublin Bay 15 Inquiry into the Performance of Steam-vessels 124 Explorations in the Yellow Sand- stone of Dura Den 20 Chemico-mechanical Analysis of Rocks and Minerals 25 Researches on the Growth of Plants 10 Researches on the Solubility of Salts 30 Researches on the Constituents ofManures 25 Balance of Captive Balloon Ac- counts 1 13 6 £1241 7 1861. Maintaining the Establishment of Kew Observatory Earthquake Experiments Dredging North and East Coasts of Scotland Dredging Committee : — 1860 .£50 0\ 1861 £22 OJ Excavations at Dura Den Solubility of Salts Steam-vessel Performance Fossils of Lesmahago Explorations at Uriconium Chemical Alloys Classified Index to the Transac- tions 500 25 23 72 20 20 150 15 20 20 £ Dredging in the Mersey and Dee 5 Dip Circle 30 Photoheliographic Observations 50 Prison Diet 20 Gauging of Water 10 Alpine Ascents 6 Constituents of Manures 25 £1111 100 1862. Maintaining the Establishment of Kew Observatory 500 Patent Laws 21 Mollusca of N.-W. America 10 Natural History by Mercantile Marine 5 Tidal Observations 25 Photoheliometer at Kew 40 Photographic Pictures of the Sun 150 Rocks of Donegal 25 Dredging Durham and North- umberland 25 Connexion of Storms 20 Dredging North-East Coast of Scotland 6 Ravages of Teredo 3 Standards of Electrical Resistance 50 Railway Accidents 10 Balloon Committee 200 Dredging Dublin Bay 10 Dredging the Mersey 5 Prison Diet 20 Gauging of Water 12 Steamships' Performance 150 Thermo-Electric Currents 5 £1293 J. d s 1 5 10 6 9 6 11 10 16 6 Extracts from Resolutions of the General Committee. Committees and individuals, to "whom grants of money for scientific pur- poses have been entrusted, are required to present to each following meeting of the Association a Eeport of the progress which has been made ; with a statement of the sums which have been expended, and the balance which re- mains disposable on each grant. Grants of pecuniary aid for scientific purposes from the funds of the Asso- ciation expire at the ensuing meeting, unless it shall appear by a Eeport that the Eecommendations have been acted on, or a continuation of them be ordered by the General Committee. In each Committee, the Member first named is the person entitled to call on the Treasurer, William Spottiswoode, Esq., 19 Chester Street, Belgrave Square, London, S.W., for such portion of the sum granted as may from time to time be required. In grants of money to Committees, the Association does not contemplate the payment of personal expenses to the members. In all cases where additional grants of money are made for the continua- tion of Eesearches at the cost of the Association, the sum named shall be deemed to include, as a part of the amount, the specified balance which may remain unpaid on the former grant for the same object. 1862. d 1 REPORT 1862. General Meetings. On "Wednesday Evening, October 1, at 8 p.m., in the New Assembly Boom, Guildhall, "William Fairbairn, Esq., F.R.S., resigned the office of President to the Eev. R. Willis, M.A., F.R.S., who too 1 ! the Chair, and delivered an Address, for which see page li. On Thursday Evening, October 2, at 8 p.m., in the New Assembly Room, Guildhall, Professor Tyndall, E.R.S., delivered a Discourse on the Forms and Action of "Water. On Friday Evening, October 3, at 8 p.m., a Soiree, with Experiments, took place in the New Assembly Rooms. On Monday Evening, October 5, at 8 p.m., Dr. Odling, F.R.S., delivered a Discourse on Organic Chemistry. On Tuesday Evening, October 6, at 8 p.m., a Soiree, with Microscopes, took place in the New Assembly Rooms. On "Wednesday, October 7, at 3 p.m., the concluding General Meeting took place, when the Proceedings of the General Committee, and the Grants of Money for Scientific purposes, were explained to the Members. The Meeting was then adjourned to Newcastle-on-Tyne*. * The Meeting is appointed to take place on Wednesday, August 26, 1863. ADDRESS BY THE REV. R. WILLIS, M.A., E.R.S., Jacksonian Professor, &c. Gentlemen of the British Association, — I have the honour to announce to you that we are now opening the Thirty-second Meeting of the British Asso- ciation, and are for the third time assembled in this University. At its first coming hither in 1833 its organization was scarce completed, its first Meeting having been devoted to explanations, discussions, and allotment of work to willing labourers ; its second Meeting, to the reception of the first instalment of those admirable preliminary Keports which served as the founda- tion of its future labours, and to the division of scientific communications to the Sectional Committees. But it was at Cambridge that the original plan of the Association bore fruit, by the receipt of the first paper which contained the results of experiments instituted expressly at the request of the Association. The success of the Association was now confirmed by the number of compositions and annual subscriptions paid in, and by the help of these funds a most important measure was introduced, namely, the practice of granting, in aid of philosophical researches to be undertaken by individuals or committees at the request of the Association, sums of money to meet the outlay required for apparatus or other expenses, which could not be asked from persons who were otherwise willing to devote their time to the advancement of science. It was at Cam- bridge that the importance and authority of the Association had become so manifest, that the first of its applications for Government assistance towards scientific objects was immediately complied with by a grant of £500 to reduce the Greenwich Observations of Bradley and Maskelyne. At the third Meeting improvements were made in the distribution of the Sciences to the Sections, and a Section of Statistics added. The only change in this respect that was subsequently found necessary was the establishment of a separate Section for Mechanical Science applied to the Arts, in 1837. The employment of alpha- betical letters to distinguish the Sections had been introduced in 1835. I have said enough to claim for the Cambridge Meeting the honour of com- pleting the development of the Association ; and I may be permitted to quote from our fourth Report the gratifying assurance, that so obvious was the utility of the proposed undertaking, that, in its very infancy, there were found several distinguished individuals, chiefly from the University of Cambridge, who volunteered to undertake some of the most valuable of those Reports which appeared in the first volume of the Proceedings. With a mixture of regret and shame I confess, that although my name is enrolled in the honourable list of those who undertook Reports, it will be d2 Hi KEroRT — 1862. sought in vain amongst those who promptly performed their promises. Yet I may he permitted to say that I still hope to be enabled at some future time to complete the Eeport on Acoustics, of which I delivered merely an oral sketch at the second Meeting of the Association, in 1832. The Association quitted Cambridge to pursue, with its matured organization, and with continually increasing stability and influence, the career of brilliant and useful labours in every branch of Science that it has never ceased to run during the two-and-thirty years that have elapsed since its foundation. It revisited Cambridge after an interval of twelve years, in 1845 ; and now, after a lapse of seventeen years, we have the high gratification of welcoming once more the Association to this scene of its early meetings. This appears a fitting occasion for a concise review of the leading principles and prominent labours of the body. Scientific Societies, as usually constituted, receive and publish papers which are offered to them by individuals, but do not profess to suggest subjects for them, or to direct modes of investigation, except in some cases by offering prizes for the best Essay in some given branch. This Association, on the contrary, is not intended to receive and record individual originality. Its motto is, suggestion and cooperation, and its purpose is thus to advance science by cooperation, in determinate lines of direction laid down by suggestion. To give form and authority to this principle, the admirable conception of suggestive Eeports was in the first place developed ; a collection that should constitute a general survey of the Sciences as they stood at the foundation of the Association, each branch reported by some member who had already shown his devotion to the cultivation of it by his own contribution to its advance- ment, and each Eeport passing in review its appointed subject, not for the purpose of teaching it, but of drawing forth the obscure and weak places of our knowledge of it, and thus to lay down the determinate lines of direction for new experimental or mathematical researches, which it was the object of the Association to obtain. The requests for these Eeports were zealously responded to, and so rapidly that at the second Meeting ten were received, and at the third eight others. In this manner in five or six years the cycle of the Sciences was well nigh exhausted ; but the series of such Eeports has been maintained in succeeding years, even to the present time, by the necessity of supplemental Eeports, to point out not merely the advances of each science already treated, but the new lines of direction for inquiry that develope themselves at every step in advance. The Eeports thus described were entitled " On the progress and desiderata of the respective branch of Science," or " On the state of our knowledge re- specting such Science," and must be considered as merely preparations for the great work for which the Association was formed. They constitute the suggestive part of the scheme : the cooperative mechanism by which each new line of research recommended in the Eeports was to be explored, was energetically set in motion by the annual appointment of Committees or indi- viduals to whom these especial investigations were respectively assigned, with adequate sums at their disposal. These Committees were requested to report their labours from year to year, and thus a second set of documents have been produced, entitled " Eeports of Eesearches undertaken at the request of the Association," which are entirely distinct from the " suggestive Eeports," but immediately derived from them, and complementary to them. ADDRESS. liii Such is a concise view of the system at first laid down by the wisdom of our founders, and which, with some modifications, has produced the inestimable contents of our printed volumes. In practice the " suggestive Report " is often a paper contributed by some able investigator to some meeting of the Association, which produces a request from the body that he will pursue his researches with their sanction and assistance, and write a Report comple- mentary to his own suggestions. Again, although we did not profess to receive and publish individual re- searches, the number of these received at each meeting is very great ; the merit of some of them so eminent, that they are authorized to be printed entire amongst the Reports ; and the Notices and Abstracts of the remainder, which at first occupied a small proportional part of each volume, now occupy nearly half of it. I will now direct your attention to the principal objects to which our funds have been directed. To appreciate the value of an investigation by the money it costs, may ap- pear at first sight a most unworthy test, although it be a thoroughly British view of the subject. But there are undoubtedly a great number of most important inquiries in science that are arrested, not for want of men of zeal and ability to carry them out, but because from their nature they require an outlay of money beyond the reach of the labourers who ardently desire to give their time and thoughts to them, and because the necessity and value of the proposed investigation are wholly unappreciable by that portion of society who hold the purse-strings. But it is in the cases above alluded to of expensive investigation that the direct use and service of our body has been made the most manifest. The British Association holds its own purse-strings, and can also perfectly under- stand when they should be relaxed. Nay, more, by its influence and cha- racter, established by the disinterested labours and successful exertions of more than thirty years, it may be said to command the national funds ; for the objects in aid of which Government assistance has been requested, have been so judiciously chosen, that such applications have very rarely been un- successful, but have been, on the contrary, most cordially acceded to. Indeed it may be observed, that from the period of the foundation of the Association the Government of this country has been extending its patronage of Science and the Arts. "We may agree with the assertion of our founder, Sir David Brewster, in supposing that this change was mainly effected by the interference of this Association and by the writings and personal exertions of its members. For the above reasons it appears to me that by a concise review of the principal objects to which the funds of our body have been applied, and of those which its influence with the Government has forwarded, we obtain a measure of the most important services of the British Association. But in considering the investigations carried out by committees or indi- vidual members by the help of the funds of the Association, it must always be remembered that their labours, their time and thoughts, are all given gratuitously. One of the most valuable gifts to Science that has proceeded from our Association is the series ofits printed Reports, now extended to thirty volumes. Yet these must not be supposed to contain the complete record even of the labours undertaken at the request and at the expense of the body. Many of these have been printed in the volumes of other societies, or in a separate form. Several, unhappily, remain in manuscript, excluded from the public by the great expense of publication. liv REPORT- — 1862. I am the more induced to direct attention to this'great work at present because I hold in my hand the first printed sheets of a general Index to the series from 1831 to 1860, by which the titles and authors of the innumerable Memoirs upon every possible scientific subject, which are so profusely but promiscuously scattered through its eighteen thousand pages, are reduced to order, and reference to them rendered easy. This assistance is the more necessary because so many investigations have been continued with inter- missions through many years, and the labour of tracing any given one of them from its origin to its termination through the series of volumes is extremely perplexing. For this invaluable key to the recorded labours of the Association we are indebted to Professor Phillips, and the prospect of its speedy publication may be hailed as a great subject of congratulation to every member of our body. In every annual volume there is a table of the sums which have been paid from the beginning on account of grants for scientific purposes. The amount of these sums has now reached .£20,000 ; and an analysis of the objects to which this expenditure is directed will show that if we divide this into eighteen parts, it will appear, speaking roughly, that the Section of Mathematics and Physics has received twelve of these parts, namely two-thirds of the whole sum, the Sections of Geology and Mechanical Science two parts each, while one part has been given to the Section of Botany and Zoology, and one divided among the Sections of Chemistry, Geography, and Statistics. The greater share assigned to the first Section is sufficiently accounted for by the number and nature of the subjects included in it, which require innu- merable and expensive instruments of research, observatories, and expeditions to all parts of the globe. If we examine the principal subjects of expenditure, we find, in the first place, that more than £1800 was expended upon the three Catalogues of Stars, namely, the noble Star Catalogue, which bears the name of the British Asso- ciation, commenced in 1837, and completed in eight years, and the Star Catalogues from the observations of Lalande and Lacaille, commenced in 1835 and 1838, and reduced at the expense of the British Association, but printed at the expense of Her Majesty's Government. £150 was applied principally to the detennination of the Constant of Lunar Nutation, under the direction of Dr. Robinson, in 1857, and to several other minor Astronomical objects. At the very first Meeting at York, the perfection of Tide Tables, Hourly Meteorological Observations, the Temperature of the atmosphere at increasing heights, of Springs at different depths, and observations on the Intensity of Terrestrial Magnetism, were suggested as objects to which the nascent organi- zation of the Association might be directed. Its steady perseverance, increasing power and influence as successive years rolled on, is marked by the gradual carrying out of these observations, so as to embrace nearly the whole surface of the globe. Thus, under the direction of Dr. Whewell, a laborious system of observations, obtained by the influence and reduced at the expense of the Association, who aided this work with a sum of about £1300, has determined the course of the Tide-wave in regard to the coasts of Europe, of the Atlantic coast of the United States, of New Zealand, and of the east coast of Australia. Much additional information has been since collected by the Admiralty through various surveying expeditions ; but it appears that much is still wanting to complete our knowledge of the subject, which can only be obtained by a vessel specially employed for the purpose. More than £2000 have been allotted to Meteorology and Magnetism, for the construction of instruments, and the carrying out of series of observations ADDRESS. IV and surveys in connexion with them. To this must be added a sum of between .£5000 and £6000 for the maintenance of Kew Observatory, of which more anon. The advance made in these important sciences, through the labours of the Committees of the British Association, may be counted among the principal benefits it has conferred. To the British Association is due, and to the suggestion of General Sabine, the first survey ever made for the express purpose of determining the positions and values of the three Isomagnetic Lines corresponding to a particular epoch over the whole face of a country or state. This was the Magnetic Survey of the British Islands, executed from 1834 to 1838, by a Committee of its members, General Sabine, Prof. Phillips, Sir J. Boss, Mr. Fox, and Mr. Lloyd, acting upon a suggestion brought before the Cambridge Meeting in 1833. It was published partly in the volume for 1838, and partly in the Philosophical Transactions for 1849. This was followed by a recommendation from the Association to Her Majesty's Govern- ment, for the equipment of a naval expedition to make a magnetic survey in the southern portions of the Atlantic and Pacific Oceans. This recom- mendation, concurred in by the Boyal Society, gave rise to the voyage of Sir James Clark Boss in the years 1839 to 1843. In a similar manner was sug- gested and promoted the magnetic survey of the British possessions in North America, authorized by the Treasury in 1841 ; the completion of the magnetic survey of Sir James Boss, by Lieutenant Moore and Lieutenant Clark in 1845, in a vessel hired by the Admiralty ; the magnetic survey of the Indian Seas, by Captain Elliot, in 1849, at the expense of the Directors of the East India Company ; and the magnetic survey of British India, commenced by Captain Elliot in 1852, and completed between 1855 and 1858 by Messrs. Schlagint- weit. Finally, in 1857 the British Association requested the same gentlemen who had made the survey of the British Islands in 1837, to repeat it, with a view to the investigation of the secular changes of the magnetic lines. This has been accomplished, and its results are printed in the new volume for 1861 *. The Association also, aided by the Boyal Society, effected the organization in 1840 of the system of simultaneous Magnetical and Meteorological Obser- vatories, established as well by our own Government as by the principal foreign Governments at different points of the earth's surface, which have proved so eminently successful, and have produced results fully equalling in importance and value, as real accessions to our knowledge, any anticipations that could have been formed at the commencement of the inquiry f. General Sabine, whose labours have so largely contributed to these inves- tigations, has given to the University an admirable exposition of the results during the present year, in the capacity of Sir Bobert Bede's Lecturer. In 1854, in consequence of representations originating with the British Association, our Government created a special department, in connexion with the Board of Trade, under Admiral FitzBoy, for obtaining Hydrographical and Meteorological observations at sea, after the manner of those which had been for some years before collected by the American Government at the instance and under the direction of Lieut. Maury. Observations on the wind have been carried on by means of the various self-registering Anemometers of Dr. "Whewell, Mr. Osier, Dr. Bobinson, and Mr. Beckley, which instruments have been improved, tested, and thoroughly brought into practice by the fostering care of our body ; and by the aid of its funds, experiments have been made on the subterranean temperature of deep mines ; and on the temperature and other properties of the Atmosphere * Vide volume for 1859, p. xxxvii. t Report, 1858, p. 298. lvi REPORT — 1862. at great heights hy means of Balloon Ascents. Four of these were made in 1852, in which heights between nineteen and twenty thousand feet were reached. But in the present year Mr. Glaisher has attained an altitude of nearly thirty thousand feet. We may hope that some account of this daring achievement, and its results to science, may be laid before the Association at its present Meeting. Earthquake shocks were registered in Scotland by a Committee of the Association, from 1841 to 1844 ; and Mr. Mallet commenced, in 1847, a most valuable series of Reports on the Pacts and Theory of Earthquake Phenomena from the earliest records to our own time, which have graced our volumes even to the one last published. One of the most remarkable and fruitful events in our history, in relation to Physical observations, is the grant by Her Majesty, in 1842, of the Obser- vatory erected at Kew by King George the Third, which had been long standing useless. It gave to the Society a fixed position, a depository for instruments, papers, and other property, when not employed in scientific inquiry, and a place where Members of the Association might prosecute various researches. This establishment has been, during the twenty years of its existence, gradually moulded into its present condition of a most valuable and unique establishment for the advancement of the Physical Sciences. After the first few years its existence was seriously perilled, for in 1845 the expediency of discontinuing this Observatory began to be entertained ; but upon examination, it then appeared that the services to science already rendered by this establishment, and the facilities it afforded to Members of the Association for their inquiries, were so great as to make it most desirable to maintain it. Again, in 1848, the burthen of continuing this Observatory in a creditable state of efficiency pressed so heavily upon the funds of the Asso- ciation, then in a declining state, that the Council actually recommended its discontinuance from the earliest practical period. This resolution was hap- pily arrested. In 1850 the Kew Committee reported that the Observatory had given to science self-recording instruments for electrical, magnetical, and meteorolo- gical phenomena, already of great value, and certainly capable of great further improvement ; and that if merely maintained as an Experimental Observatory, devoted to open out new physical inquiries and to make trial of new modes of research, but only in a few selected cases to preserve continuous records of passing phenomena, a moderate annual grant from the funds of the Associa- tion would be sufficient for this most valuable establishment for the advance- ment of the Physical Sciences. In this year it fortunately happened that Lord J. Russell granted to the Royal Society the annual sum of .£1000 for promoting scientific objects, out of which the Society allotted £100 for new instruments to be tried at Kew, — the first of a series of liberal grants which have not only very greatly con- tributed to the increasing efficiency of the establishment, but have ensured its continuance. It now contains a workshop fitted with complete tools, and a lathe and planing machine, &c. by which apparatus can be constructed and repaired, and a dividing engine for graduating standard thermometers, all presented by the Royal Society. The work done, besides the maintenance of a complete set of self-recording magnetographs, established in 1857, at the expense of £250, by the Royal Society, consists in the construction and verification of new apparatus and in the verification of magnetic, meteorolo- gical and other instruments, sent for that purpose by the makers. For ex- ample, all the barometers, thermometers, and hydrometers required by the ADDRESS. lvii Board of Trade and Admiralty are tested, standard thermometers are gra- duated, magnetic instruments are constructed, and their constants determined for foreign and colonial observatories, and sextants are also verified. An example of its peculiar functions is given in the very last Report (1861), where it appears that an instrument contrived by Professor William Thom- son, of Glasgow, for the photographic registration of the electric state of the atmosphere, has been constructed by Mr. Beckley in the workshop of this Observatory, with mechanical arrangements devised by himself, and that it has been in constant and successful operation for some time. Those who have experienced the difficulty of procuring the actual construction of appa- ratus of this kind devised by themselves, and the still greater difficulty of conveniently carrying out the improvements and alterations required to per- fect it when brought into use, will agree that the scientific importance and utility of an establishment cannot be overrated, in which under one roof are assembled highly skilled persons not only capable of making and setting to work all kinds of instruments for philosophical research, but also of gradually altering and improving them, as experience may dictate. The creation of this peculiar Observatory must be regarded as one of the triumphs of the British Association. As far as the Association is concerned, its maintenance has absorbed be- tween five and six thousand pounds, the annual sum allotted to it from oiir funds having for each of the last six years reached the amount of .£500. The construction of the Photohellograph may be also quoted as an ex- ample of the facilities given by this establishment for the developing and perfecting of new instruments of observation. A suggestion of Sir John Herschel in 1854, that daily photographs of the sun should be made, has given birth to this remarkable instrument, which at first bore the name of the Solar Photographic Telescope, but is now known as the Kew Photoheliograph. It was first constructed under the direction of Mr. De la Eue by Mr. Ross. The British Association aided in carrying out this work by assigning the dome of the Kew Observatory to the instrument, and by its completion in 1857 in their workshops by Mr. Beckley the as- sistant ; but the expense of its construction was supplied by Mr. Oliveira, amounting to .£180. This instrument was conveyed to Spain under the care of Mr. De la Rue on occasion of the eclipse in 1860, who most successfully accomplished the proposed object by its means, and it was replaced at Kew on his return. But to carry on the daily observations for which it was con- structed requires the maintenance of an assistant, for which the funds of the Association are inadequate, although it has already supplied more than £200 for that purpose. Mr. De la Rue, in consequence of the presence of the Heliograph at Kew being found to interfere with the ordinary work of the establishment, has kindly and generously consented to take charge for the present of the instrument [and of the observations, at his own Observatory, where celestial photography is carried on. But it is obvious that the continuation of these observations for a series of years, which is neces- sary for obtaining the desired results, cannot be hoped for unless funds are provided. I cannot conclude this sketch of the objects in the Physical Section to which the funds of the Association have been principally devoted, without alluding to Mr. Scott Russell's valuable experimental investigations on the motion and nature of waves, aided by £274. If we now turn to Geology we find £2600 expended, of which £1500 were employed in the completion of the Fossil Ichthyology of Agassiz, and upon lviii report — 1862. Owen's Reports on Fossil Mammalia and Reptiles, with some other researches on Fossils. The remainder was principally devoted to the surveys and measurement, in 1838, of a level line for the purpose of determining the permanence of the relative level of sea and land, and the mean level of the Ocean ; and to the procuring of drawings of the geological sections exposed in railroad operations before they are covered up — a work which was carried on from 1840 to 1844, when the drawings were deposited in the Museum of Practical Geology, and the further continuance of it handed over to the geological surveyors of that establishment. £2300 have been devoted to the carrying out of various important experi- mental investigations in relation to the Section of Mechanical Science. Of this sum £900 were paid between 1840 and 1844, in aid of a most important and valuable series of experiments on the Forms of Yessels, prin- cipally conducted by Mr. Scott Russell, in connexion with the experiments on "Waves. This investigation was ready for press in 1844, but it is greatly to be regretted that the great expense of printing and engraving it has hitherto prevented its publication. Nearly the same sum has given to us various interesting and instructive experiments and facts relating to steam-engines and steam-vessels, carried on by different Committees from 1838 to the present time : amongst which may be especially noted the application of the Dynamometric instruments of Morin, Poncelet, and Moseley, to ascertain the Duty of Steam-engines, from 1841 to 1844. Experiments on the Strength of Materials, the relative strength of Hot and Cold Blast Iron, the effect of Temperature on their tensile strength, and on the effect of Concussion and Vibration on their internal constitution, carried on principally by our late President and by the late Mr. Eaton Hodgkinson, at different intervals from 1838 to 1856, have been aided by grants amounting to £400. The remainder of the sum above mentioned was principally devoted to the experimental determination of the value of Railway Constants, by Dr. Lardner and a Committee in 1838 and 1841. The Section of Botany, Zoology, and Physiology has absorbed about £1400, of which nearly £900 have been applied to Zoology, partly for the expense of Dredging Committees for obtaining specimens of Marine Zoology on our own coasts and in the Mediterranean and other localities — whose useful labours have been regularly reported from 1840 to 1861 — but principally for zoolo- gical researches in different districts and countries. In Botany may be remarked the labours of a Committee, consisting of Professors Daubeny and Henslow and others, formed in 1840, to make expe- riments on the preservation of Vegetative Powers in Seeds ; who continued their work for sixteen successive years, reporting annually, and assisted by a sum of £100. The greatest age at which the seeds experimented upon was found to vegetate was about forty years. Another Committee, with Mr. Hunt, was engaged during seven years, from 1841, in investigating the influence of coloured light on the germination of seeds and growth of plants. These are specimens of the admirable effect of the organization of our Asso- ciation in stimulating and assisting with the funds the labours of investi- gators in new branches of experimental inquiry. It would occupy too much time to particularize a variety of interesting researches in the remaining sections of Chemistry and in the sections of ADDRESS. Hx Statistics, Geography, and Ethnology, to which small sums have been as- signed. The newly issued Report of our Manchester Meeting is admirably calcu- lated to maintain the reputation of the Association. Besides a number of excellent Reports which are the continuation of researches already published in our volumes, it contains elaborate and important Reports by Mr. Stewart on the Theoiy of Exchanges in Heat ; by Dr. Smith and Mr. Milner on Prison Diet and Discipline ; by Drs. Schunck, Angus Smith, and Roscoe on the progress of Manufacturing Chemistry in South Lancashire ; Mr. Hunt on the Acclimatization of Man ; Dr. Sclater and M. Hochstetter on the Apteryx of New Zealand ; Professor Phillips and Mr. Birt on the Physical Aspect of the Moon. Professor Owen contributes a most interesting paper on the Natives of the Andaman Islands. The President of the Royal Society re- ports the Repetition Magnetic Survey of England ; and Mr. Fairbairn, our late President, reports on the Resistance of Iron-Plate Pressure and Impact. The Transactions of the Sections occupy nearly as much space as the Reports, and are replete with valuable and original matter, which it would be impossible to particularize. Many of my predecessors in their Addresses have alluded to the most striking advances that have been made in the various sciences since the last Meeting ; I will mention a few of these in Astronomy, Chemistry, and Mechanics. In Astronomy, M. Delaunay has communicated to the Academy of Sciences of Paris the results of his long series of calculations in the Lunar Theory, destined to fill two volumes of the Memoirs of the Academy. The first volume was published in 1861 ; the printing of the other is not yet begun. This theoiy gives the expressions for the three coordinates of the moon under an analytic form, and carries those for longitude and latitude to terms of the seventh order inclusive, that of Plana extending generally only to terms of the fifth order. The addition of two orders has required the calculation of 1259 new terms for the longitude, and 1086 new terms for the latitude. It was by having recourse to a new process of calculation, by which the work was broken up into parts, that M. Delaunay has been able to advance the calcu- lation of the lunar inequalities far beyond the limits previously reached. The Earl of Rosse has given to the Royal Society (in a paper read June 20, 1861) some further account of researches in Sidereal Astronomy carried on with a Newtonian telescope of six-feet clear aperture. These researches are prefaced by an account of the process by which the six-feet specula were made, a description of the mounting of the instrument, and some considera- tions relative to the optical power it is capable of. A selection from the observations of nebulae is given in detail, illustrated by drawings, which con- vey an exact idea of the bizarrerie and astonishing variety of form exhibited by this class of cosmical bodies. Argelander, the eminent director of the Observatory at Bonn, is carrying on with great vigour the publication of his Atlas of the Stars of the Northern •Heavens within 92° of Polar Distance. A large portion of this enormous work is completed, and two volumes, containing the data from observation for the construction of the Charts, were recently published. These volumes contain the approximate places of 216,000 stars situated between the parallels of 2° south declination and 41° north declination. Simultaneously with the construction of Star-charts, among which those of M. Chacornac of the Paris Observatory deserve particular mention, addi- tions have been made to the number of the remarkable group of small planets lx REPORT 1862. between the orbits of Mars and Jupiter, their discovery being facilitated by the use of charts. The last announced, which is No. 74 of the Series, was discovered on the morning of Sept. 1 of this year, by M. Luther of Bilk, near Diisseldorf, whose diligence has been rewarded by the discovery of a large number of others of the same group. The present year has been signalized by the unexpected appearance of a comet of unusual brightness, which, although its tail was far from being as conspicuous as those of the comets of 1858 and 1861, exhibited about its nucleus phenomena of a distinct and remarkable character, the records of which may possibly at some future time aid in the discovery of the nature of that mysterious action by which the gaseous portion of these erratic bodies is so strangely affected. On an application made by the Council of the Eoyal Astronomical Society, Government has granted £1000 for the establishment, during a limited period, under the superintendence of Captain Jacob, of an Observatory at a consi- derable altitude above the level of the sea, in the neighbourhood of Bombay. The interesting results of the ascent by Professor Piazzi Smyth a few years since of the Peak of Teneriffe, for the purpose of making astronomical and physical observations, suggested to the President and Council of the Society the desirableness of taking this step. In Chemistry, the greatest advance which has been made during the past year is probably the formation of compounds of Carbon and Hydrogen by the direct union of those elements. M. Berthelot has succeeded in producing some of the simpler compounds of carbon and hydrogen by the action of carbon intensely heated by electricity or hydrogen gas ; and from the simpler com- pounds thus formed he is able to produce, by a succession of steps, compounds more and more complex, until he bids fair to produce from inorganic sources all the compounds of carbon and hydrogen which have hitherto been only known as products of organic origin. Mr. Maxwell Simpson has also added to his former researches a step in the same direction, producing some organic products by a synthetical process. But these important researches will be fully laid before you in the lecture on Organic Chemistry which Dr. Odling has kindly promised for Monday evening next. Dr. Hofmann has continued his indefatigable researches on Poly-ammo- nias, as well as on the colouring matters produced from coal-tar. M. Schlae- sing proposes a mode of preparing chlorine by a continuous process, which may perhaps become important in a manufacturing point of view. In this process nitric acid is made to play the same kind of part that it does in the manufacture of sulphuric acid, the oxides of nitrogen acting together with oxides of manganese as carriers of oxygen from the atmosphere to the hydro- chloric acid. The methods of dialysis announced last year by the Master of the Mint, and of spectrum analysis are now in everybody's hands, and have already pro- duced many interesting results. In Civil or Mechanical Engineering there is nothing very new. The remarkable series of experiments carried on at Shoeburyness and else- where have developed many most interesting facts and laws in relation to the properties of iron, and its resistance to projectiles at high velocities, which will doubtless be fully laid before you at some future period ; but in the present imperfect state of the investigation, and in consideration of the purpose of that investigation, prudential reasons forbid the complete publi- cation of the facts. My able predecessor in this Chair, who has taken so pro- minent a part in these experiments, has given an account of some of the ADDRESS. lxi results in a communication to the Royal Institution in May last, and also in the new volume for 1861 ; and is, as he informs me, engaged with a long series of experiments on this subject, which, with his experience and ability, cannot fail to develope new facts, and will, in all probability, ultimately de- termine the law of penetration. In London we may direct attention to the commencement of the Thames Embankment and to the various works in progress for the concentration of the Metropolitan Railways ; especially to the proximate completion of the Underground Railway. The lamentable disaster in the Pens of last summer has been most ably subdued, but the remedial measures adopted are not fully completed, and the interests involved are of so great a magnitude and com- plexity, that it is scarcely possible for this event to be discussed on the pre- sent occasion with due impartiality. The magnificent collection of machinery in the Great Exhibition shows a great advance in construction ; but this is not the proper occasion to enter in detail into the various contrivances and processes which it displays. Before I conclude I have the painful duty of reminding you that since our last meeting we have had to deplore the loss of that most illustrious patron of science and art, His Royal Highness the Prince Consort, the President of our Association at Aberdeen and the Chancellor of this University. In the latter capacity he afforded us many opportunities of observing his scientific attainments and genuine zeal and love for all branches of knowledge : his gracious kindness and respect to men of science and literature have left an impression upon us that can never be effaced. I must also ask a tribute to the memory of our late Professors of Chemistry and Botany, both of whom have done in their lifetime excellent good service to science, and especially to the British Association ; Professor Cumming by contributing one of the invaluable primary Reports upon which our proceedings were based, as well as other communications ; Professor Henslow by various Reports, some of which I have already alluded to. "We have had also to lament the loss of that able scientific navigator, Sir J. Clark Ross. It remains for me to express my sense of the high and undeserved honour conferred upon me by the position in which you have placed me, and in the name of the University to welcome you hither, and wish you a prosperous and fruitful meeting, alike conducive to the progress of science and impulsive to its cultivation in the place of your reception. EEPOETS ON THE STATE OF SCIENCE. REPORTS ON THE STATE OF SCIENCE. Report on Observations of Luminous Meteors, 1861-62. By a Committee, consisting of James Glaisher, F.R.S., F.R.A.S., Secretary to the British Meteorological Society, fyc. ; R. P. Greg, F.G.S. tyc. ; E. W. Brayley, F.R.S. fyc. ; and A. Herschel. The Committee are indebted to Members of tbe Association and to other observers for a larger number of observations bearing upon individual meteors than has fallen to their lot to assemble during previous years. They may be counted as follows : — (A) Meteor 1, July 16th, eight accounts ; (B) meteor 2, July 16th, thirteen accounts ; (C) meteor, August 6th, three ac- counts ; (D) meteor, November 12th, eight accounts ; (E) meteor, November 19th, eleven accounts; (F) meteor, December 8th, twenty-eight accounts; (G) meteor, February 2nd, 1862, eleven accounts ; (H) meteor, February 23rd, 1862, five accounts. Of the small shooting-stars, double observations only are found. The discussion of these observations follow the Catalogue in Appendix I. Eight accounts of one and thirteen of the second of the meteors visible on the evening of July 16th, 1861, show those of the Duke of Argyll and Mr. Frost to have been distinct meteors, succeeding each other with an interval of more than an hour. The accouuts are embodied in the present Catalogue, and the results discussed in Appendix I. Of the meteor August 6th, a further account from excellent observers in London, has afforded a good determination ; the accounts and their interpre- tation are presented in the Catalogue and Appendix I. Numerous accurate observations of shooting-stars of the 10th August, period 1861, too voluminous for separate insertion in the Catalogue, have been col- lected and examined for accordances, and the accordant observations only entered in the Catalogue, together with individual observations which ap- peared of particular interest from among the entire number ; the results of the accordant observations are tabulated in Appendix I. 1862. * B REPORT — 18G2. A CATALOGUE OF OBSERVATIONS 1 Position, or Date. Hour. Place of Observation. Apparent Size. Colour. Duration. Altitude and Azimuth. 1861. h m July 16 9 30 p.m. Weston - super - Large as Venus at Duller than:3or 4 seconds; Exploded when W, Mare. (Also max. Venus at moving altitude 45°. seen in Dor- max. bril- slowly. setshire.) liancy. 16 9 58 p.m. Whitehall, Lon- Very large ball, but Very brilliant.. Slower than Began almost E don. not quite full. meteors usually move ; " leisurely." and disappears behind the houses on th west side c Whitehall. 16 Exactly 10 Gainford, Like Jupiter, seen Motion not From 10° below p.m. ington, York- shire. in a good tele- scope, but not exactly spherical. rapid. Aquilse, throug' the E. to N.E.j from altitude 30 to about altitud 20°. 16 Greenwich and Kensington. Alrca dy inserted, p. 10 of Report Endured very /orl861 J 16 Soon after 10 p.m. long, about 15 seconds. 16 10 p.m., or ] 5m,. after Southborough, Tunbridge- a > A companion From S.E. to 1 of the ob- Came from ov< 10 p.m. wells. server walk-' a v.ing of tl ing (at call) house; disaj 13 or 14 yds.' pearedsomelitt from another distance abovl room, saw the horizon. the spark which was cast off at the close. 16 Between 10 p.m. and Whitburn, near Sunderland, Like ball of quick- silver, or an 5 ■> half-past. Durham. enormous star. 16 About 10 40 p.m. Furness Abbey, Lancashire. Threw a strong light. > Moved ven From behind a hi slowly ; south of tri "gracefully" Abbey ; NortH ward through El lost behind tree! 16 a Penmaen-Mawr, Conway, N. Wales. J Very slow in its motion, " quiet and deliberate." Over the hills 1 and S. of Peij maen-Vach ; di appeared behini Penmaen-Vachi - A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 3 OF LUMINOUS METEORS. Appearance; Train, if any, and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. White train 8° in length attended the nucleus Burst into sparks which continued 3 seconds, advancing 10° before i they disappeared. Carried a blunted or spread 1 tail 1 o or 20 times longer than the head. Shortly before disappear- About 90°. i jng threw off a part of its substance, which ; followed it closely like a 1 lesser luminary till both were suddenly extin- guished in a sudden and peculiar manner in clear sky. A track of light endured for some se- conds at this part of the path. )isappeared in mid-air, like a Roman candle ball ; but the train which pursued it did not look exactly like sparks. Majestic." Left a track of light behind it, but no sparks till just before it disappeared, when one spark was cast off from it. eaving no train. Sailing without change until it disappeared in a cloud, ollowed by a bright train • threw off no sparks. Appeared in the N.W. 60° oman candle-ball. Phos- phorescent train, closely adhering and sharply terminated, without sparks. Downwards at an angle of 25° to the horizon. First horizontal, then declining slightly. Personal ac- counts to W. II. Wood. of observation Charles Reed, facing the Na- Point was tional Gallery, near the top of Parliament Street. Horizontal, or very slightly declining at last. Came over from the right of the house, descending as a rocket in the form of an arch. Mrs. E. Addison [of Argyll. ./. Hoire ; Dule John Borough. Openbav-window faced Mrs. Davies. N.N.E. Quite horizontal j from left to right. Horizontal, or very slightly inclined to- wards the earth. Slightly declining ; per- haps curved down- wards. Point of observation upon the sands mid- way between Pen- maen-Mawr and Pen- maen-Vach. M. M. G. II. Chambers. H. II. Bemrose. b2 REPORT 1862. Date. Hour. Place of Observation. Apparent Size. Colour. Duration. Position, or Altitude and Azimuth. 1861 July 16 16 h in 11 p.m 11} p.m. .., Bristol , Sittingbourne, Kent. 16 114 p.m. Banburv Much > than any planet. Threw a brilliant light when high in the heavens, expanding and increasing in brightness a3 it neared the ho rizon. Like a toy balloon.. 16 11 30 p.m Frome 16 16 16 16 lUp.ni. 11 -j p.m. 1H P-m or soon after. 11 32 p.m EastlsleyDowns, Newbury, Berks. Brentwood Cheltenham. Flimwell, Hurst Green, Sussex. 1611 33 p.m. 16 11 33 p.m. Samlown, Isle of Wight. TavistockSquare, Euston Road, London. Large as a full moon, light. and more Clear bluish. As it neared the horizon it assumed a beautiful blue colour. Bright clear blue and white. About H sec. Like Capella in theiWhite zenith. Lit up; zenith the clouds like 1 upon Probably burst in view in the zenith. First seen high in the heavens, goings S.W. Lost il haze of the horizon. 3° above e Pegasi j| 3° above G Aqui-I lae; 2° above o Serpentis. Here! houses inter-i vened. Beve-t loped the tailj in the last 30° of the visible track. Disappeared a few; degrees abovei the horizon. Appeared near the. meridian ; disap- peared behind cloud. and the crescent at 45°. moon Large signal-rocket A sudden lumino- sity overhead. clouds. Half a minute ;'From about 45° steady and altitude to about equable. 30° altitude. 3 seconds from Passed in zenith zenith to ex-! between /3 y Dra- plosion. conis ; burst about >)Ophiuchi. 4 seconds from zenith to disappear- ance. From the zenith, near a. Lyra, to a few degrees from the S.W. horizon. First seen 15°sout' of zenith ; passe downwards di- rect through Scorpio, and dis- appeared near! the horizon. A CATALOGUE OF OBSERVATIONS OP LUMINOUS METEORS. Appearance ; Train, if any, and its Duration. Length of Path. No sparks or train. Left 15° to 20 a long clear white streak high. for some little time. Disappeared in haze of the] ? horizon. At the point of disappearance the stream of light was visible for 5 minutes after. rrack very bright, endured ' 3 minutes ; like a half circular mark of phos- phorus upon a wall. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. rrack of luminous matter lasted 4 or 5 minutes ; curiously contorted by degrees, as if by currents of air. Large body of sparks thrown off at disappearance. First emitted sparks ; after- wards a bright train which endured some minutes. 3urst with few sparks. Track at the last visible some minutes. Duly momentary; sparks seen in the zenith ; white, and extending half J 's diameter to either side of the nucleus ; not in front or behind. No track seen to remain. Most brilliant track ; visi- ble for 5 minutes. Bright train visible several minutes. The lower portion took a crescent form, the horns drifting 15° or 20° S. into the Milky Way in 5 minutes before disappearance. 90° 90° Course from N. to S. Vertical Passed over from E. S.W. to Took a south-westerly course. From the S.E. to S.W. Nearly vertical to S.W, by W. or S.W. Nearly vertically down, wards. Vertically, S.W. Observer. By letter to W. H. Wood, Weston-super- Mare. The curved tail was clearly seen by a com- panion called out of a house by the observer. Brightest in the Milky Way. Saw at least 4 meteors, of more or less bril liancy, from 10£ to 12 p.m. The time distinguishes this meteor from that of 10 p.m. Overcast W. and S.W., exceptnear the zenith, where the meteor was lost at altitude 70°. The track at first straight ; soon curved opposite to the rising wind. Portions drifted fading into the Milkv Way. Probably originated in Andromeda. J. Ellis. F. R. Cooper. John Griffin, M.D. William Dunn. L. Lousley. J. L. P. James Philps. F. Howlett and A. S. Herschel. W. M. Frost. '. Cmmplen and J. Townsend (Assistants to Mr. Slater's Observatory, Euston Road). 6 REPORT 1862. Date. Hour. Place of Observation. Apparent Size. 1881. | h m July 16,11 34 p.m.jBetween St. Albans and Barnet. 16 11 38 p.m. 16 11 40 p.m. 10 About j to 12 p.m. Seacombe, Birk- enhead, Che- shire. Bristol , Brading Downs, Isle of Wight. Much brighter than 1st mag.* Very large About 10 | Bristol , p.m. Aug. 4 11 37 p.m. Flimwell, Hurst Green, Sussex Midnight ... 10 10 p.m. 11 21 p.m. 11 22 p.m 8 10 11 p.m. 10 21 p.m. 810 3Hp.m. 8 10 31| p.m. Ibid. WestEnd.Hamp stead. Manchester, Lat. 53- 29'-5, Long.2° 15'W. Trafalgar Square, London. Deal Greenwich Ob servatory. Ibid Ibid A ball of fire, in- tensely brilliant. Very brilliant Like Pleiades, but three times as bright. Jupiter 1st mag.*. Considerably ex- ceeding % in brilliancy. Equalled in size the great meteor, 11.33 p.m., July 16. 2nd mag.* 2nd mag.* Very small 2nd mag.* Colour. Duration. Position, or Altitude and Azimuth. Brilliantbluish'lO to 13 sees, tint. Blue. Deep blue Originated undei the Milky Way below Cassiopeia, and exploded about the same height near the opposite horizon. From altitude 40° S.E. by E. to S. by W. Altitude 70° 5 or 6 seconds Originated some- what nearer td thehorizon,N.E., than it attained before explosion, S.W. Quick Moved slowlv Vivid bluish- white. Estimated not to have ex- ceeded 2 seconds. Occupied seconds passage. From a direction nearly dueN. ; it shot in a westerly direction towards the horizon. Near 30 Aquarii Centre 30° E. frort S. ; altitude 4 7 6 From 8° E. of S. j altitude 22° to 10° W. of S.j altitude 10°. Disappeared about 2° west of thd star i Capri corni. 10:From about a Co- in ronae to x Ursae Majoris; near the horizon. Blue. 5 Fast motion... 1 to 2 seconds 1 second From yDraconis... Through Cassiopeia /t Cygni to Sagitta. Very rapid;* Cygni to Del- 2 seconds. phinus. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. Appearance ; Train, if any, and its Duration. Length of Path. ipanned the heavens like About 140' rainbow-arch ; prismatic momentary sparks were first emitted, but be5'ond the zenith a tail like that of a falling star was left, and continued visible 5 minutes, jke a brilliant blue light. 60° to 70°.. Very luminous tail visl ble 8 or 10 seconds burst into fragments luminous for 3 seconds after explosion. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. l luminous track became visible several degrees before reaching the zenith. Devoid of train before this point. Broad phosphorescent wake ; endured 3 minutes. h-ight track of silvery light. Lppeared to burst eft a bright track, cigar- shaped. loursc bent up rather suddenly in the middle with two maxima of brightness. 'he meteor in its course appeared to be extin- guished, and then sud- denly rekindled. Left a train of about20°, which lasted a few seconds. [o train or sparks About 20°. 20° ,eft a small track .eft no track ieft a small track Only about 3° or 4°. 48° 10° 30° 30° About fi. to W. ; overhead. almost Remarks. At its centre the path was inclined 18° to the horizon. E. to W. Passed directly over head. E. to W. A complete view from first to last. One or two smaller meteors during the night in same direc- tion. Towards the left; 15° from horizontal ; down. To right ; 50° from ver- tical ; down. To left; 30° from hori- zontal ; up. S. preceding Shot upwards To right; 15° from hori- zontal ; down. To right, 10° from ver- tical ; down. The sparks in the first half of the course did not pass away imme- diately. Observer. William Taylor ; Miss J. Taylor. W. Presented a sweep of David Walker, magnificent splendour M.D. through the sky. Communicated by W. H. Wood. John A. James. Bristol News- paper. Six shooting-stars re- Rev. F. Howlett. corded from 11.15 to 12.15 p.m. Id. T. Potter. Gave the impression of Joseph Baxen- a path of considerable length, nearly in the line of sight The same gentlemen observed the meteor July 16th, 11.33 p.m. Six meteors recorded, 10.11p.m. No trains At Greenwich, two ob- servers recorded 14 shooting-stars fromlO to 11 p.m. dell, Observa- tory,Stock St., Manchester. T. Crumplen and J. Townsend Herbert M c Leod. W. C. Nash. Id. W. C. Nash and J. Howe. 8 REPORT 1862. Date. Hour. Place of Observation. Apparent Size. Colour. 1861. h m s Aug. 810 32 5 Cambridge Ob- 2nd mag.* p.m. servatory. 10 34 p.m. 18 10 35 p.m 10 35 p.m 10 40 10 45 10 49 p.m. 10 50 8 10 50 p.m, p.m p.m 34 p.m, 25 810 51 p.m 910 11 p.m 26 9,10 14 p.m 9 9 9 9 9 9 10 10 27 45 p.m p.m p.m p.m. 10 45 10 47 10 47 10 52 p.m. 10 57 p.m. 25 45 45 a.m, Ibid.. Ipswich Aylesbury (Hart- well Observa- tory). Birkenhead (Sea- combe). Aylesbury (Hart- well Observa- tory). Cambridge Ob- servatory. Birkenhead (Sea- combe). Trafalgar Square, London. Greenwich Ob- servatory. Cambridge Ob- servatory. Birkenhead (Sea- combe). A bright star, 1st mag. Much brighter than any star. A flame of light A fine shooting-star 1st mag.# 1st mag.*. 1st mag.*. A splendid meteor. Ibid. Deal Greenwich Oh servatory. Birkenhead (Sea- combe). Ibid. Ibid. Ibid. 1st mag.* . 1st mag.* . 1st mag.* . 1st mag.* . Very bright 1st mag.*.... 1st mag.* 1st mag.* Shooting-stars. Prismatic colours seen, Fine blue light Duration. Position, or Altitude and Azimuth. Rapid Brief Centre 11° E.from S. ; altitude 40 17° S. from E. altitude 61°. ? Exactly N., half- way between the Pole star and horizon. (The place may be relied on.) Only for a In the head or moment. sword of Perseus. ? Due E.; altitude 17°. 4 seconds ;Near Polaris ? Centre 67° W. from S. ; altitude 55°. 1 second Centre 30° E. from S.; altitude 13°. Rather slow... From 3° N. of Mizar to 1|° below x Bootis. 2 to 3 seconds Appeared near /3 Draconis, and passed to Arc turus. Centre 3° N. from E. ; altitude 39°. Nearly 2 sees, Centre 45° E. from S. ; altitude 6 C 1 second Centre due S. ; alti- tude 37°. ? Between » and J Ophiuchi. Near Polaris ... Momentary ... 2 seconds ... Nearly 1 sec. 2£ seconds ... Centre due N.E.; altitude 20°. Centre 5° E. from S. ; altitude 7°. Centre 55° E. from S.; altitude 21°. In W. ; altitude 40°. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. Appearance ; Train, if any, and its Duration. Left no track Flashed out and was ira. mediately extinguished. A flash Like a gaslight suddenly lighted and then put out. Fell ahout 2° and seemed to hurst. Luminous track 30° to 35° Luminous track of inter- mediate length, and broken up. rail endured 1 second .. rhe brilliant train of 10' remained luminous several seconds after the nucleus had disap- peared. luminous track, 20° bril liant. 'rain 20° long fail endured 1 second ... rail endured If second ... .■uminous track, remained 15 seconds at least, ^o track left Tail endured 4 seconds nearly. Tail endured 1 second ... Tail endured 1£ second ... or 7 shooting-stars in succession ; fell 10° or 12° and burst. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. No path dis- cernible 25° 50° 25- 25° About 15 c 20° 10° 55° 10° or 12 c To right, 30° from hori zontal; down. Stationary Vertical ; down E. to W. Vertical ; down To right, 45° from hori. zontal ; down. Vertical; down To right ; horizontal To left; 10° from verti- cal ; down. To right ; 38° from ver- tical ; down. As if from Polaris Shot out from the clouds. To right; 15° from ver- tical ; down. To left ; 15° from verti- cal; down. To right; 45° from ver- tical ; down. Almost vertical At Cambridge, three observers recorded 15 shooting - stars from 10 to 11 p.m. At Ipswich, one ob- server recorded 2 shooting- stars from 10 to 11 p.m. At Aylesbury, several observers recorded 32 shooting-stars from 10 to 11 p.m. At Birkenhead, one observer recorded 7 shooting-stars. Observer. Itev.J.L.Challis Arthur Bovvden. Wilfred Airy. At Greenwich, two ob- servers recorded G shooting-stars ; very cloudy. At Cambridge, three observers recorded 6 shooting-stars ; cloudy At Birkenhead, one observer recorded 32 shooting-stars (quite clear) ; 8 of these left tracks of light. At Deal, one observer re- corded 5shooting-stars (cloudy) ; 3 of these left tracks of light. Samuel Horton. D. Walker, M.D Samuel Horton. Rev.J.L.Challis. D. Walker, M.D. T. Crumplen and J. Townsend. J. Howe. Arthur Bowden. D. Walker, M.D Id. Herbert M c Leod W. C. Nash. D. Walker, M.D, Id. Id. Id. 10 REPORT' — 1862. Date. 1861. Aug.10 10 Hour. h in 9 53 p.m. 10 10 8 p.m. 1010 18 p.m 10 10 21 p.m. 10,10 23 p.m. W10 23ip.m. lo'lO 24 p.m. Place of Observation. ! Apparent Size. Colour. Cranford Ob- servatory. Ibid. Ibid. Ibid. Ibid. Ibid. 5th mag.* 3rd mag.* Brilliant meteor ; 1st mag.* 1st mag.*; as bright as Venus. 6th mag.* 3rd mag.* Greenwich Ob- Small servatory. 3rd mag.* Cranford Ob- servatory. 10 21 p.m. Greenwich Ob- Si servatory. 10 10 25 p.m. 10 10 26 p.m. 10 10 27 p.m. Cranford Ob- servatory. 2 brilliant meteors. Ibid. Ibid. 5th mag.* 1st mag.* 10 10 27 p.m. Greenwich Ob- 2nd mag.* servatory. 10 28 p.m. Cranford Ob- servatory. 10 10 29 p.m. Ibid. 5th mag.* Bluish 1st mag.*; brilliant ? as Venus. Duration. Position, or Altitude and Azimuth. Rapid ; 1 se- cond. Rapid ; 1 se- cond. 2 seconds. Centre B.; altitude 10°. Centre S.S.E. ; altU tude 10°. Between Aquili and Capricornus. Under Aquila i.:t<J Centre E.S.E. ; al- titude 3°. Centre S.W. ; 3° below a, Lyrae. Passed from * Her- culis towards the! S.W. horizon. Same track as 10.23 p.m. Passed from Cygni to * ller- culis. Near Cygnus . . . Centre E.S.E. , near horizon. Centre E.S.E., i Pegasus. Passed from a few degrees above * Andromedae tojl] between * and /S.i Pegasi. Centre E.N.E. ; al-1 titude 15°. From 30° to 15° I altitude ; centre ■ S.S.E. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 11 .ppearance ; Train, if any, and its Duration. fo track left eft no track Length of Path. •eft a bright track 35° eft a track eft no track eft no track eft no track eft no track eft no track eft tracks eft no track eft a track eft a track 5° in length... 15° 20° 40° eft no track ' ? bright track marked its 15° course throughout (15°) J Direction ; noting also ■whether Horizontal, Perpendicular, or Inclined. To right ; 6° from verti- cal ; down. To right j 6° from verti- cal ; down. To right } 25° from ver- tical ; down. * f To right; nearly hori- zontal. Remarks. \ Observer. W. De la Rue. Id. At Greenwich, two ob- Id. servers recorded 33 shooting-stars from 10 to 11 p.m. At Cambridge, three observers recorded 30 shooting-stars from 10 to 11 p.m. |ld. At Cranford, one ob- server recorded 29 shooting-stars from 10 toll p.m. At Birkenhead, one ob- server recorded 16 Id. shooting-stars froml 10 to 11 p.m. At Deal, one obserrerild. recorded 9 shooting- stars from 10.20 to W. C. Nash. 11 p.m. At Trafalgar Square, London, two observ- W. De la Rue. ers recorded 12 shoot- ing-stars from 10 to W. C. Nash. 11 p.m. W. De la Rue. Id. Id. W. C. Nash. W. De la Rue. Id. 12 REPORT 1862. Date. Hour. Place of Observation. Apparent Size. Colour. Duration. Position, or Altitude and Azimuth. 1861. h m s Aug.1010 323 p.m. Greenwich Ob- ; 2nd mag.* servatorv. 10 32 32 p.m. 10 10 1010 39 p.m, Cambridge Ob- servatory. 10 32 47 p.m. Ibid. 10 10 10 40 p.m. 10 42 p.m. 1010 50£p.m. lo'lO 51 p.m. 1010 51 1 p.m. Cranford Ob- servatory. Trafalgar Square, London. Cranford Ob- servatory. Greenwich Ob- servatory. Ibid 3rd mag.* 1st mag.* 6th mag.* Very luminous meteor. 4th mag.* 10 10 56 p.m. Cambridge Ob- servatory. Trafalgar Square, London. 10 10 Deal 10 10 57 20 p.m. 10 57 30 p.m. 10 57 30 ^Trafalgar Square, p.m. London. 3rd mag.* Small 3rd mag.* 2nd mag.* 1st mag.* 1st mag.* Very brilliant meteor. 10 10 58 p.m. Greenwich Ob- servatory. 10 10 10 10 11 11 11 11 10 59 p.m From 10 to 11 p.m. From 11 to 11$ p.m. 11 45 p.m. 1 3 a.m. 8 40 p.m. 8 45 p.m. 8 53 p.m Birkenhead(Sea- combe). Haverhill Ibid., Birkenhead (Sea- combe). Weston - super • Mare. Hawkhurst, Kent Trafalgar Square, London. Very bright.... 1st mag.* .... Shooting-stars. Shooting-stars. Blue light Hawkhurst Mars 1 second Slow motion.. From y Ursa? Ma- joris to the N.W horizon. Centre 13° S. front W. ; altitude 20° Centre same as th< last. Centre E.S.E. ; al titude 4°. ^° below % Ursa Majoris. Centre S.E.; alti- tude 9°. 1 second 1 second Rapid ... From a Cygni to t Lyrae. From a. Cygni to Delphini. Centre 26° W.froni S.; altitude 46°, 1° E. of a Herculis /3 to a Bootis Blue light ... Fast motion.., 2 seconds Moved lsec. « to y Ursx Ma joris. 2° ahove Benel nasch to 2 C above ArCturus. From a Pegasi. Passed Delphi nus to a Aquila?. Centre 26° E.fron S. ; altitude 30° In all quarters... In all quarters the sky. 1st mag.* Grand and lumi- nous, even in strong twilight Jupiter Like the elec- tric light. Rapid Rather slow.. Slow motion. Centre 40° W. front N. j altitude 18° Centre 22° W.fron S. ; altitude 39° 15° below Merak., Centre 22° W.froni S.; altitude 37° A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 13 .ppearance ; Train, if any and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. •eft a small track .eft no track .eft a track eft no track larked track 8° in length eft no track eft no track eft no track eft no track eft no track (25°) (30°) eft a track eft a track eft a track 20° long 20° 15° eautiful track; 30° in length. rack endured 1 second.., (45°) 20° lis star curved consider- ably in its path before it burst. ■ack of 3° 15' broad; lasted 4 seconds. 3 train or sparks 10° 10° Vertical ; down To left; 45° from verti- cal ; down. To right; 30° from vertical ; down. Vertical ; down To left; 30° from verti- cal; down. Stationary ight enduring track. 20° To right ; horizontal To left; 37° from hori- zontal ; down. W. C. Nash. Rev.J.L.Challis Id. , W. De la Rue. T. Crumplen and J. Townsend W. De la Rue. \V. C. Nash. J. Howe. Rev.J.L.Challis T. Crumplen and J. Townsend. Herbert M c Leod Id. T. Crumplen and J. Townsend. J. Howe. D. Walker, M.D Mostly divergent from Two observersdelineated W. W. Boreham Cassiopeia. Diverging from Cassio- peia. Inclined westward 30° to the vertical. To right; 30° from vertical ; down. To left ; 30° from verti- cal ; down. the courses of 70 meteors in the hour. Two observersdelineated 45 meteors. and J. Hobler. Id. D. Walker, M.D, From 1.25 a.m. to 1.40iW. H. Wood. a.m., meteors fell too fast to be registered. Strong twilight A. S. Herschel. Too cloudy for betterJT. Crumplen and observation. J. Townsend. A. S. Herschel. 14 bepqiit-^1862. Date. 1861. Aug. 11 11 Hour. Place of Observation. Apparent Size. Colour. h m s 9 27 p.m. Flimwell, Hurst Jupiter. Green, Sussex. 9 27 p.m. Ibid 11 9 30 p.m. Hawkhurst, Kent 11 10 p.m 11 10 15 p.m 11 11 11 10 17 4 p.m. 10 20^p.m 10 22 p.m Flimwell, Hurst Green, Sussex. Ibid. Jupiter. Jupiter. Hawkhurst, Kent Ipswich 4th mag.* Jupiter. Venus, or some- what larger in first two-thirds of course. Vivid meteor ...... 11,10 27 p.m, Hawkhurst, Kent Brighter than Venus. It cast a shadow. Ipswich 'Very bright Bright bluish in first two- thirds, then dull red. It was a palish meteor, not A brilliant white one Pure white 11:10 28 p.m. Flimwell, Hurst Jupiter. |. Green, Sussex. 11 10 37 p.m. Weston - super - 2nd mag.* Mare. 1110 37 p.m. Ibid 1st mag.* lljlO 37 p.m.'lbid 2nd mag.* 11 10 47 59 Hawkhurst, Kent 2nd mag.* p.m. 11 10 11 p.m. Haverhill . 11 11 Shooting-stars. 3rd mag.* White Duration. Position, or Altitude and Azimuth. Very slow Moderate speed. 2 seconds ; slow motion. Moved very slowly ; 2j seconds. l^or 14, sec, Centre 30 Q S, from E. ; altitud 31°. From near i Cygn to *i Pegasi. Centre 30° from E. ; altitud 31°. From | (y Equuli and y Delphin! to Equilat. wii (9 and c Del phini). Down ; W. margi: of E. branch Milky Wav. From \ (c X Aquilae to <p Sa gittarii. Down the Mil Way from Aqui to Sagittarius In a line throu| S Ursae Major just above Ursae Majoris. Centre 33° N. fror E.; altitude 16' Ceased at y Pega 11 11 p.m. Weston - super Mare. 11 2 p.m. Ibid 4th mag.* I? 11 8 p.m. Hawkhurst.Keut 1st mag.* 1111 20 p.m. Flimwell, Hurst 3rd mag.* , Green, Sussex. 11 11 20 p.m. Ibid 3rd mag.* ? 11 11 20£ p.m. Ibid 2nd mag* ? Rapid Rapid Rapid Slow motion.. Very slow motion. Centre 72° E. frofl N. ; altitude 19' Centre 29° W. froi N.j altitude 10' Centre 43° E. froi N. ; altitude 24' Centre 15 ; S. froi E. ; altitude 35' In all parts of th sky. Centre 3' S. fro W. ; altitude 26' Centre 3° S. froi W.j altitude 26 Very fast Centre in zenith . Rapid Rapid Rapid A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 15 Appearance ; Train, if any, and its Duration. jeft a track. >,. traight track left in 1st two-thirds (the rest barren) ; remained 4 Seconds. t was a large pear-shaped meteor. Length of Path. 20 ; (30°) 20° .. 5°. 28 c 25° 10 : Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Tc right ; 45° from ho- rizontal ; down. To right ; 45° from ho rizontal ; down. To right ; horizontal ... Remarks. Vertical; down eft a white bright track Not more throughout, lasting 7] than 7° seconds in the middle. or 8°. eft a good tail, which. A short run i lasted 5 or 6 seconds. rilliant white track . . . o train or sparks o train or sparks o train or sparks j ower and redder at last ; I turning to left, and tail ceasing. ;ft a track. :ft a track. 5°.., 5°.., 15° 5°... To right; 15° from ver- tical ; down. To right ; 15° from ver- tical ; down. To right ; 40° from ho- rizontal; down. Path was arched convex to Delphi uus. Observer. To right; 30° from ver- tical ; down. 5° or 6° 5° or 6° Vertical; down To right ; 30° from ver- tical ; down. From Cassiopeia , ft a long track visible 20 a o seconds. To left ; 30° from hori- zontal ; down. To left ; 30° from hori- zontal ; down. Vertical ; towards 45° W. from S. From 6 Cassiopeiae to 16 Cap. Medusae. Brightest seen this night. Rev. F. Howlett Id. A. S. Herschel. Rev. F. Howlett. Id. A. S. Herschel. Three meteors fell simultaneously. Two observers counted 46 meteors in one hour ; clear sky. Two meteors pursued the same apparent path. From \ {a *•) Andro medae to i (/3, 7) Ce- phei. W. Airy. A. S. Herschel. W. Airy. Rev. F. Howlett W. H. Wood. Id. Id. A. S. Herschel. W. \V. Boreham and J. Hobler. W. H. Wood. Id. A. S. Herschel. Rev. F. Howlett. Id. Id. 16 REPORT 1862. Date. Hour. 1861. h m s Aug. 11 11 23 p.m 11 11 23 10 p.m. 11 11 23 20 p.m. 11 11 38 p.m 11 11 41 10 p.m. Place of Observation. Hawkhurst,Kent Apparent Size. Colour. Ibid. Ibid. 12 12 Weston - super Mare. Hawkhurst, Kent 1 20 a.m. 31 20 a.m. 12 52 5 a.m. 12 1 9 50 a.m. 12 1 18 20 a.m. 12 12 12 1 31£a.m 1 31-Ja.m 2nd mag.* 4th mag.* 2nd mag.* 1st mag.* 1 31 J a.m. 121 1 31ia.m. 12 2 6 a.m. 12 12 12 Sept. 6 2 6 2 a.m. 2 14 30 a.m. 2 14 40 a.m. Ibid. Ibid. Ibid. Ibid. Ibid. Ibid. Ibid. Ibid. Ibid. Ibid. Ibid. Ibid. Ibid. Duration. Slow. White Exceedingly swift. Momentary . . 2nd mag.* .... 2nd mag.* j Brilliant white 1 Brilliant white Slow motion. 1st mag.* 3rd mag.* 1st mag.*.. Very slow motion. 3rd mag.* 4th mag.* 4th mag.* 2nd mag.* 2nd mag.* 1st mag.*.. 4th mag.* 2nd mag.* 8 p.m. Blackheath (approxi- mate time). 26 10 p.m. Greenwich Rapid Moderate speed. Moderate speed. ? Moderate speed. ? ;Moderate speed. ? Fast motion . Twice the width of White the moon ; ir- regular circle. Rapid Rapid = 2nd mag.* Bluish white .. 1 to 2 sees 3rd mag. Position, or Altitude and Azimuth. Centre 30° N. fron* E. ; altitude 33°| Good observaJ tion. Centre due E. ; alF titude 40°. Centre 23° S. froJl E. ; altitude 30°l Centre 29° S. frodP E.; altitude 26°l From ? to } (/3 -A Lyrse. Centre 40° W. fron S.; altitude 36°ij Centre 7° E. frou* N. ; altitude 45°i| Centre 23° E. froni N.; altitude 57°ll Near /J Cephei.li Centre 27° W from N. ; alti tude 73°. y Cygni to £ Cygn!| Centre 40° Sil from W. ; alt tude 65A; . E. from S. 38°l altitude 80°. E. from S. 117°| altitude 52°. E. from S. 45° I altitude 44°. Out of y Pegasjl Centre due S. ! altitude 56°. ' Just below the las} Centre 8° E. froil S. ; altitude 27 I Centre 3° or 4JJ below the last. From a point bf, tween Polar! and a DraconJ to o Urs« joris. Appeared ^ (t I £) Ursae Major A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 17 Appearance ; Train, if any, Length of and its Duration. Path. -eft a bright track visible 8 some seconds. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. lo track or sparks; straight course. to track or sparks Slight track throughout, 15' broad; enduring 2 seconds, ■right white track throughout ; endured 3 seconds. O sparks ; no track"... right track ; endured 3 seconds at centre, o track ; the light ap peared to sparkle, rack brightened up when nucleus had vanished ; visible 3 seconds. 25° 10° 15° or 16°.. 10- 10 ood observation of track, 15° which brightened up after meteor was flown. 2ft a tracl^. ;ft no track :bulous ; left no track. .me ight train 5° 15° 15° To right ; 20° to 25°|A slow meteor with en- from vertical ; down. during track. To left; 38° from hori- zontal; up. To right; 30° from ver- tical ; down. To right ; 15° from ver- tical ; down. Observer. A. S. Herschel. Remarkable for direc-Id tion, length, andi smallness. Ordinary appearance ... To left ; 35° from ver- tical; down. Curved to left at last. To left ; 35° from ver- tical ; down. To left ; horizontal . To right ; 35° from ver- tical ; down. 3°.. 10 6 15° 15° 30° from horizontal 60° from horizontal 30° from horizontal Three meteors to left ; downwards ; appeared together. To right ; 15° from ho- rizontal ; down. Parallel to last 12° jToright; 35°fromver- tical ; down. Parallel to the last J A singular brush. Flew crooked, 10 seconds after the last, and like its ghost (cloudless sky, calm air). 25- ] 862. Id. W. II. Wood. A. S. Herschel. Id. Id. Id. Id. Id. Id. Id. Id. Id. Id. Id. Id. Id. W. C. Nash. 3., S. following Cloudy night 'J. MacDonald 18 REPORT — 1862. Date. 1861. Sept.26 29 29 Oct. 2 4 Hour. Place of Observation. Apparent Size. h m 10 p.m. 8 40 p.m. Ibid. 8 52 p.m. Ibid. Blackheath 8 40 9 30 p.m. Greenwich Park p.m. Greenwich 9 48 4 10 29 4 10 36 p.ra, p.m. p.m Ibid. Ibid. Ibid. 4 10 40 p.m. Ibid. 4 10 46 p.m. Ibid. 9 8 50 p.m.'lbid. 9 9 20 p.ra. Ibid. ■■ 1st mag.* = 3rd mag.* Blue Colour. White = lst mag.*. Faint Blue = twice the size of Pale green a 1st mag.* ■■ 2nd mag.* = 3rd mag.* = 1st mag.*.. = 2nd mag.* 9 9 31 9 9 50 10 8 42 10 8 43 I 10 10 7 p.m. Ibid p.m. Harrogate p.m.jGreenwich p.m. Ibid p.m. Ibid Small faint meteor = 3rd mag.* =2nd mag.* = 3rd mag.* = 2nd mag.* = 3rd mag.* — 2nd mag.* Blue Blue Blue Duration. Bluish white., White Blue 2 seconds. 1 second ... 1 to 2 seconds Momentary... 3 seconds... 1 second ... 1 second ... 1 to 2 seconds Position, or Altitude and Azimuth. Blue White 1 second 1 second 1 second 1 second 1 second Bluish white., 1 second 1 second Appeared a feM degrees above Ursa Major, passing between the stars a and] /J, disappearing] behind a cloud at about 10° oi 15° from thii| constellation. From Delphini| across * Aquila to 3 Aquila:. Moved in a south-, erly direction t few degrees below the Pleiades. From i Persei tc £ Auriga?. From about th«j centre of Came-i lopardus ; passec diagonally across Ursa Major frott a to y, and dis- appeared a few degrees below the latter star, j From «i across 9 Draconis. From the Pleiades to y Tauri. Across Capella ; about 20° in a northerly direc-| tion. From y Pegasi, halfway to « Pegasi. Passed rapidly froi i Persei to Arietis. From y Andro- meda; to k Persei. From fi Andro- meda; to d Cas- siopeia;. From j3 Cygni t £ Aquila;. 30° from zenith U N.W. Fell from zenitl towards the S From y to /S Ce phei. Across Cassiop to y Cephei. A CATALOGUE OP OBSERVATIONS OF LUMINOUS METEORS. 19 Appearance; Train, if any, and its Duration. Slight train , ■lone imall train lone irilliant train . one one rain one one any shooting'Stars »ne ,,.., Dne ,.. nail train ,, ,, Length of Path. Direction; noting also whether Horizontal, Perpendicular, or Inclined. 22 c 10° one Ahout 10 10° to 15° About 45° Remarks. Observer. Rather cloudy J. MacDonald. 7°... 11° 20° A very brilliant meteor.. Almost perpendicular . . S. to N. ; horizontally. 29° 17° 22° 15° ? 8°... 12° 20° W. C. Nash. Id. Id. Id. Perpendicular , Id. Id. Id. Id. Id. Id. Id. Id. J. Coupland. J. MacDonald. W. C. Nash. Id. C 2 20 REPORT — 18G2. Date. Hour. Place of Observation. 1861.! h in Oct. 10 10 11 10 16 p.m. 10 20 p.m 9 25 p.m, Greenwich 11 11 11 14 14 22 23 23 9 30 p.m. 9 30 p.m 9 42 p.m. 8 20 p.m. 10 26 p.m. Ibid Blacklieath Greenwich Blacklieath Ibid Greenwich Ibid. 10 21 p.m. Ibid. 7 28 p.m. Ibid. 7 28 p.m 24 8 59 p.m, Nov. 2 10 47 p.m 7 p.m. 7 8 45 p.m. 8 49 p.m. Ibid. Ibid. Birkenhead Greenwich Blacklieath Ibid. Apparent Size. Colour. Duration. = 2nd mag.* Blue 2nd mag.* j White =2nd mas'.* White = 1st mag.* ... Small Bluish white. Small Position, or Altitude and Azimuth. 1 second =2nd mag.* Blue = lst mag.* Bluish white. = lst mag.*.... 2nd mag.* . Blue 1 second Across a Lyri towards N.W.' horizon 1 to 2 seconds From \ to 8 Cygni Fell from a fe degrees abovel" the Pleiades, I passing through! them ; disap- I pearing about I 15 D below. Passed rapidly frorojl , i Auriga: to «,| Ceti. Shot up from thql southern ho- i| rizon. 1 second Passing from E. ttl W. a few de- grees above thili Pleiades. 1 second Passed from nea t Hcrculis acros: fi Draconis. 1 to 2 seconds From 8 Arietis t< y Trianguli. 2 to 3 seconds Across a Geminoi rum. From Equuleus to, wards the W horizon. = 2ndmag.» Bluish white = 3rd mag.* Very bright , = lst mag.*.. = 2ud mag.* White 1 second 1 second From a. Equuleitfl. /3 Aquikc. 1 second 8 or 9 seconds 2 seconds. Small 2 seconds Passed rapidly froE S Cygui to il Lyrse. From centre o Pleiades to lefj of Aldebaran. Fell from the zenitl towards the 9 for about \2 J . I From the neignl bourhood of Ca jiella, and passei to y Ursa: Ma joris. From the neigh, bourhood of Ca pella, in the da rection of Alda baran for aboul 5°. — L A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. Appearance ; Train, if any, and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. W. C. Nash. Id. J. MacDonald. W. C. Nash. J. MacDonald. Id. W. C. Nash. Id. Id. Id. Id. Id. D. Walker. J. MacDonald. Id. Id. 15° 20° 40° 8° 7° Horizontal 20° i5° Moon shining brightly.. 30° 15° S. toN The next meteor fol- lowed this one at an interval of a few seconds, springing from nearly the same place. Cloudy after this time for the remainder of the evening. 20° 15° Left a luminous tail for about 3 seconds and burst, leaving the frag- ments luminous for a short period. 12° Inclined upwards 5° 22 REPORT 1862. Position, or Date. Hour. Place of Observation. Apparent Size. Colour. Duration. Altitude and Azimuth. 1861. h m Nov. 8 R S n.m. Larger than a Ro- man candle-ball. ....»..••......•»• S.S.E., over Torbay or mouth of the Exe. From alti- tude 30° or 40° to very near the earth. lft O OO t. n\ fimoYiwinK Momentary ... From the direction XV .» £.£. I'.lll. of Camelopardus, passed midway between Polaris and a Draconis. 10 'fi iJ ""1 Ibid From i Tauri to a poiut a little *" ""• I"-"" above » Gemi- norum. 10 10 38 p.m. Ibid Blue From between £ Tauri and » Ge- minorum to 8 Aurigae. 10 11 1 p.m. Ibid Blue Passed from y Ge- minorum in a westerly direc- tion, across the upper part of Orion. 11 9 p.m. Ibid Blue Fell from a few degrees W. of Ursa Major to about 10° from Aldebaran. 11 10 36 p.m. Ibid. Blue 1 to 2 seconds From the Lynx constellation ; disappeared a few degrees below] Polaris. 11 10 52 p.m. Ibid Bluish white... From i Eridani to- wards the S. ho- rizon. 12 5 45 p.m. Hay, S. Wales... Pear-shaped ; 30' by 15' at first, but 20' by 10' at middle of its A fine blue . . . About 5 sees... From near the body of Cygnus. Alti- tude 60° or 70°, ! down W. branch course. of Galaxy, be- tween Altasi and Ophiuchus, to 10° above the horizon, W.S.W. 12 5 45 p.m. Weston - super - Mare. Nearly the size of the moon. > From 3° above « Herculis to near I the S.W. by S. horizon. 12 5 45 p.m. Southern Hay, Exeter. Larger than any Roman candle- > From the tail of the 1 Great Bear. ball. 12 5 48 p.m. Barlaston, Stone Elongated as long Greenish Fell slower From 20° W. of j as the moon's white. than a S. altitude 40° ; ! diameter. shooting - star. to 40° W. of S. 1 altitude 8° or | 9°. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 23 ippearance ; Train, if any, and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. iurst into a bright light when first seen ; left here a transitory track ; dropped to objects on the horizon fading away; skittle-shaped. mall train Fell vertical ram rain rain 10° to 15 10 17° 15 c 25 c Another light was seen in the W. an hour later. Horizontally, E. to W. 20° iddy sparks emitted be hind. Pursued by a long pale streak of light. (60° to 65°) rew strong moving50° shadows. Left a bright track 50°, which lasted |10 seconds, peared to burst ; , rgest and brightest at ithe head, tapering to a reddish tail. A. short course. G. A. Lance. W. C. Nash. Id. Id. Id. Almost perpendicular. J. MacDonald. W. C. Nash. To right ; from 20° to Flashed overhead like 8° or 10° from verti-| sudden moonlight, cal ; at last down. Inclined Longitudinally west- ward. Inclined downwards in a slightly curved line, not straight. but did not continue so bright as it ad- vanced. Moon ten days old. Probably started from W. H. Wood, the head of Draco. Id. Rev. T. AV.Webb. Cloudy A. J. dimming. G. Wedgwood. 24 REPORT— 1862. Date. 1861. Nov. 12 Hour. m 40 Place of Observation. 12 12 p.m. Manchester (12 miles S.E.). Apparent Size. Colour. 5 50 p.m. 5 50 p.m. Bristol . Stone, near Aylesbury. > 6 3 p.m. Oxwich, Local time. 'Wales. ab — 60' ; bd= 13' ; Nucleus yel Duration. 3« seconds :10'. lowish flame, conical part brilliant blue. Brighter than theVivid blue moon. Oval shape, nearly Pale brilliant = to the moon. blue. Position, or Altitude and Azimuth. From S.S.E. tude 35° ; nearly S. tude 8°. 15 South As large as a cricket-ball. Steel-blue 10 14 p.m. Greenwich 15 10 15 p.m = Venus About 6 sees. alti- toT alti- Very nearly overjB head. First seen a little N. of Pole-star (y Cephei), to 15° above hori-' zon, W.S.W. A greenish tint 4 or 5 seconds predominated. Shooter's Hill, Woolwich. 15 About p.m [5Styall,nearMan Chester. Aldebarau or Mars for half its course, then flaming ; diameter 5' ; last 3° = Mars. : From 6° or 7 and W. of Plei; des to same height at theli opposite side ol the heavens. Started 3° S. of Pennard Castle, from Oxwich | Rectory. From the zenith ini a northerly di- rection. Owing! to the dense hazel the path of thd meteor among! the stars coulrii not be traced. Mars for half 3^ seconds byFrom its course, 1 chronometer dull : then steel - blue, brilliant. Last 3° = Mars, and faded away. Oval nucleus 8' long Bluish 3seconds , 19 5 30 p.m. Sherwood, 7miles N.W.ofExeter. Much larger than any of the fixed stars. 1 Hev. CaJ melcopardi t( /3 Ursse Minorisj Began to flamrt at the Pole-star.. I Blue, bursting 7 or 10 seconds like a Ro- man candle. From S.E. by Bfl altitude 42° ; t< S.E. by S. alti tude 18° : burs | ■with sparks (?). A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. OK ppearance ; Train, if any, and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. gure sharply defined ; very few sparks or breaks ; no permanent tail left ; no disruption at disappearance. 25° To right ; from 43° to 61° to the horizontal; down. R. P. Greg. \Q) \ c ' eft a track of golden light. o sparks or tail ; burst into large fragments ; much scattered ; no noise heard. oman candle-ball, with red sparks and fire ; tail 8° or 10°, tapering into detached sparks. ■> As nearly as possible S.S.W. it Figure of the meteor compared with the moon. Rev. W. M. Burch. William Penn. S. G. L. (90°) (130° to 140°.) Very foggy. Flashed an intense light, as if it broke out from behind a cloud before it was seen ; loose clouds. Appeared level with the eye, and stationary at first ; very bright. Mounted as it approach- ed, moving apparently level with the sea. rilliant train throughout the whole of its course. About 1 second before the meteor disappeared, it threw off a small luminous fragment ap- parently ith the size of the whole body, which suddenly disappeared after travelling 1° cr 2°. No noise was heard. o track left ; when nu- cleus flamed blue, red sparks were emitted all round = £ diameter of moon. 50° S. toN An exceedingly hazy night. Moon and one or two principal stars seen. Afinelunarhalc. The flaming nucleus ir- regular in figure, but not elongated ; hazy sky ; full moon ; halo. (No other meteor was visible in the heavens from 9^ to 11 p.m.) The position carefully taken from memory. W. C. Nash. A. S. Herschel. R. P. Greg. 40° Almost vertical ; down.. To right; 35° from vertical; down. From y Ursac Majoris... The meteor appeared to drop between us and the opposite bill ; we felt certain it dropped in the valley. ArthuiCumming. 26 REPORT 1862. Position, or Date. Hour. Place of Observation. Apparent Size. Colour. Duration. Altitude and Azimuth. .i 1861. h m s Nov.19 9 15 to 9 35 p.m. Large as the moon, but very much A bright stream of It did not move very fast, but Approached froi| the S.E., burst brighter. fire. like a spent rocket ; like a Roman candle-ball. ing into 3 piece when almost overhead. 19 Between 9 &10 p.m. A bright body as large as the 5 > Burst into 3 part) nearly overhead moon. 19 9 35 p.m. A splendid meteor.. 5 > The grand exph> sion took plaoi close underneatt the Great Bear. 19 9 35 p.m. Guestling Hill... Half diameter of the moon. White ? Rose from a bank of clouds 30° E, from S. ; disap- peared a littk left of Witter^ ham, 20° E from N. Passed} 4° or 5° undeil the moon, which had altitude about 40°. 19 Disappeared Greenwich Ob- One-half the dia- > Nearly 10 sees. Appeared betweenii 9 38 23 servatory. meter of the y Orionis and p.m. • moon. Aldebaran (from behind great | dome of equato- real). Passed I or 8° below Pollux, and dis-i appeared 15° further N. 19 9 40 p.m. At first stationary ; Pale green At least 10 At first stationary! =Venus. When when under- seconds. for 2 seconds under the moon neath the at a point in =i of moon's moon, then Cetus. Ad- t diameter. blue. vanced north-: ward under the! moon at half its altitude, and < finally disap- ! peared without! noise. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 27 pearance ; Train, if any, and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. rew strong moving shadows. Broke into J pieces or streams of ire, which soon disap leared ; as large as a nan's fist. rst into 3 parts ; one or wo appeared to fall, ind the other seemed o rise. oloded with an appear. ince of 6 to 8 balls of ire. S.E. towards the N. o^* ■^w-iV. About 80 or 90 seconds after the explosion, three distinct reports like heavy ordnance or distant thunder were audible. 120° From S. by W. towards N.E. S.S.W. to N.N.E., hori- zontally across the sky. A full minute afterwards heard a loud report. train of prismatic olours ; . fragments uddy brown. Threw ut fragments, and arted into two before caching and in passing nder the moon. When isappearing, three lddy brown fragments ere the last things sen. rnificent meteor ; car- ed a splendid coloured ain with sparks, and I last broke into 3 or 4 id vanished. ed forth suddenly near e moon like oxyhydro- n lime - light ; then veloped a fiery tail, icleus becoming blue, •oke into 3 or 4, like ads on a string, just fore disappearance. Horizontal Mr. Felgate; G. Webb ; G. Pulham ; Ro- bert Bixby ; Frank May- hew ; John Steel ; Charles Lawrence (communi- cated by G. Biddell). Rev. G. Gilbert. James Pearce. Messrs. James Rock and C. Savery, M.R.C.S. Inclined downwards 15° or 20° from hori zontal. Horizontal W. T. Lynn. John Hill. 28 REPORT — 1862. Altitude and I Azimuth. Date. 1861. Nov. 19 19 19 19 Hour. h m 9 40 p.m. 9 40 p.m 9 45 p.m 9 45 p.m 19 19 Place of Observation. Godstone, Surrey Tunbridge One-third the size of full moon. Hcavitree,Exeter North Foreland Dover Wroth am Kent. Hill, Apparent Size. Light very bright and steady ; oc- casionallythicker in some parts than others ; like an unusually large star. body nearly equalling the moon, but far brighter. Much larger and brighter than Roman candle hall. Threw a great light on the opposite side from the moon. Colour. White with a bluish shade. Duration. First seen S. of some distan before it came the moon. I ploded plain, J Bright white- Ball of yellow fire, pure and pale. From 10 to 15 First seen as o\ seconds. Moving by no means quick- ly in a straight line. Langley Poh Pevensea Hj bour. Passed n more than below the moo . Came out from sky, and disa peared withe noise; miifoi altitude of 1 to 20°. Moved slowly, continuing in sight 10 to 12 sees. From 60° altituc S.E. ; passed 1 E. of the zeni towards true J burst N. byV altitude 12° 15°. At the Tan Ya Stembrcok, Dover, the meteor disi peared behin the Castle Hil From the S.S part of the In vens ; travel! many miles \ fore it came the moon. Passed under t moon and vi lost to vi behind chalj hills. A CATALOGUE OF OBSERVATIONS OP LUMINOUS METEORS. 29 pearanee; Train, if any, and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. Companion of observer thought that his coat was on fire. Observer thought it lightened. W. Blackstone. ly the top of the moon was visible, the lower part being outshone by the meteor. When the explosion took place balls of fire about the size of an orange formed themselves into a sort of tail. rew shadows half as deep as those of the moon ; rocket-like tail 8 or 10 feet long. Di- vided into two parts on passing the moon ; burst into 10 or 12 fragments, which were red. appearance was that of a light running along an outstretched line like the light of a rocket N'early due S. horizontal ; 30°. to N. altitude Brightness did not vary A hissing noise was heard as it passed. lon 6 , head ; rried a tail 3 : violet at the apering to a flickering point ; flame coloured I or 3 seconds before bursting a globular body separated from the head ;o halfway along the ;ail, and there con ;inued. Exploded into nany fragments, which 'ell some distance, idows in the street noved rapidly. er passing the moon, legan to vomit fire of he most brilliant hues. About £th of the circle of the ho rizon ( = 60°). Full 70° .. Direction from S.W. N.E. ; horizontal. to Appeared to drop some- thing as it went along. W. Mitchell; John Harruer (communicated byC.V.Walker). R. T. Abraham. Curving towards the About two minutes after earth. extinction, a short dull but loud report was heard ; distinctly but closely double. James Chapman The meteor was ob- served to explode near Maldon, in Essex. The air smelt of sulphur Edmund Brown. James Douse. 30 REPORT — 1862. Date, Hour. Place of Observation. Apparent Size. Colour. Duration. Position, or Altitude and Azimuth. 1861. Nov.19 h m 24 24 7 40 p.m. 8 10 p.m. 2410 2 p.m 20 27 5 42 p.m, 9 32 p.m Wrotham Hill, Four times the size Kent. of one of the planets ; threw shadows on the fields. Brilliant white Appeared S.S.E. passed 4i widtl underneath tn moon. Burst wit bright coloui near the N. Broxbourne ...Somewhat larger White with than Sirius. bluish tinge Weston - super Mare. Greenwich Ibid. 27 10 6 p.m I 2710 16 p.m, 30 8 54 p.m, 3011 11 p.m, Greenwich Ob- servatory. Ibid. Ibid. Ibid. i Sirius Brilliant blue.. 1^ second 2 seconds Appeared 5° W.i /3 Cygni ; disaji peared 4° E. ( a Aquilrc on tt equator. Appeared in Pleii des ; disappeare near « Ceti. = 2nd mag.* Bluish white 1 second Small = 2nd mag.* = 2nd mag.* passe ie hi High 1 di Bluish white . 1 second White Blue 1 second Dec. 1 1 1 1 50 p.m, 8 26|p.m, Greenwich Wakefield London 8 37 p.m. Greenwich = 1st mag.* Bluish white = 5 th mag.# Small but bright... Very brilliant = a Lyrse = 2nd mag.* Started near Orionis ; pi towards the rizon throug] Orion, and appeared a litt to the left of Orionis. Passed through tl Pleiades iu tl direction of A debaran From y Geminonr to a point b twecn a. and Orionis. 1 to 2 seconds Shot between a. ai /3 Geminorum.' Moved below Ui Major towan N. horizon Nearly iu the plai of the meridia and about 2( from the horizo About half &«. Orionis to i Oi second. onis. Bluish white.. 1 From overhead eastward ; di peared behind railway emban ment. Appeared near Draconis. From X Lvrse within 10" J off W. horizon. Blue Blue 07 second a LyrK Moderate speed. Blue 2 seconds. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 31 ipearauce ; Train, if any, Length of and its Duration. Path. )od-red ; tail like a ? Roman sword. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. .in about 9° in length... ? Horizontal when under- Clear sky ; no smell of James Douse, neath the moon. sulphur. tail. in ie n Inclined 15° Many came from this locality far several evenings. This was the largest and brightest. train ; disappeared iddenly. 18° A fine bright night Rather cloudy . 5° to 7°. .. Inclined path, S. to N... A fine bright night H. S. Eaton. W. H. Wood. W. C. Nash. J. MacDonald. W. C. Nash. a long train behind ; no explosion was en. a short tail 20° 1° 10° Inclined towards N. .. Towards the W., at an angle of 45° to the horizon. A fine bright night , Id. It was very small and H. C. Criswick. rapid. Id. i of some length 20° Rapid motion Nearly vertical The sun shining at the time. Directly from Polaris... Remainder of flight in tercepted by houses. W. C. Nash. Herbert M c Leod. W. C. Nash. 3.2 REPORT 18G2. Date. 1861. Dec. 1 Hour. h ra 8 50 p.m. 9 8 p.m Greenwich Place of Observation. Apparent Size. Colour. = 2nd mag.* Blackheath Hill, Size of Sirius . Greenwich. 9 14 p.m. Walthamstow ... 9 15 p.m. Weston - super Mare. Duration. 1 second about. Position, or Altitude and Azimuth. The colour of 1*5 second the un- clouded moon. Somewhat smaller Pale yellow . than Polaris. Diameter 2'. Very slow ; 5 seconds ; speed slack- ening stead ily, until almost sta tionarv. 9 45 p.m. Barlaston, near Larger than Venus, Greener than Rapid motion.. 3 seconds Fell perpendica larly from point a littli above and to t\ AV. of Ursa Major. From between tl Pleiades and Algol ; neare) the latter. . From | (Aldebar* and a. Orionii to 8° W. Castor. Appeared betwet y Ononis ar, a Orionis, burst 4° ah k Orionis. 5 20 p.m. 2 5 a.m. At night ... 8 15 p.m. Blackheath Stone, Salop. Birkenhead (Sea. combe). Preston but not so bright. = 1st maa;.* Bright meteor , Large meteor the greenest rays of stars, Blue Less than 1 second. From altitude 4<| due E. From direction Cassiopeia to Pegasi. ? 5 seconds From centre quadrate stars Ursa Major within 10° oft! horizon. I Lancaster Almost as large as ' the moon. 8 15 p.m. St. Bees, 1 { r mile exactly. inland. 8 About Si p.m. Ball of fire 5 inches in diameter. ? Burst; altitudc2 or 30° a little ' ofN.W. 3 seconds in perfect state ; 6 seconds in all. Bridlington As large as the Quay. moon. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 33 ppearance ; Train, if any, and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. aere was no train ; but 7° after having travelled about 3° or 4°, it broke into five portions, three of the portions being as large and bright as the meteor when first seen. ght unsteady, brighten' ing, and then diminish ing. I'ew brighter and pear- shaped in falling ; train 10° ; half disap- peared in the flight ; fragments proceeded as streamers after bursting; 5°, diverg ing. ew to size of Venus; dear drop of green light disappearing suddenly at maxi. mum, with a red fragment. 1 gently ilar to that of the ,iight following. the last half of its x>urse shot out a housand most bril- iant stars ; diminished i size, and vanished at st, leaving a cloud .bout it. "t a blaze of light )ehind. LS02. 20" rt took a course due S. the path, which was short, appeared to be a horizontal line. A serpentine course This meteor, although not very large, was exceedingly bright ; after breaking up, it was visible for about - 5sec. ; no noise was heard. Fell vertical Perpendicular , From the Pole - star downwards to due W. From overhead down- wards, N.W. Appeared to descend into the Irish Chan- nel, between St. Bees and the Isle of Man. Hissing sound like quenching iron during the passage of the meteor ; two minutes later, a sound like the discharge of a heavy gun. J. MacDonald. H. C. Criswick. H. S. Eaton. W. H. Wood. W. C. Nash. D. Walker, M.D Communicated by R. P. Greg. Correspondent, ' Lancaster Guardian.' Isaac Sparks. S., Correspond ent,' Manchester Guardian.' 34 REPORT 1862. Date. 1861. Dec. 8 Hour. Place of Observation. Apparent Size. Colour. Duration. Position, or Altitude and Azimuth. h m 8 15 p.m. 8 15 p.m 8 8 15 p.m 8 8 16 p.m 8 18 p.m 8 20 p.m 8 20 p.m Hull. Size varied; light exceeded that of the moon. White, then blue. 2 seconds. From 10° to 15' above the moon whence move perpendicularly in a curved lin towards the earth westward to 20° above th horizon. 8 15 p.m 8 15 p.m. York (Holgate)... Southport 8 15 p.m. Manchester , Half the size of a cricket-ball. Almost as large as the moon ; bright as noon-day. Longest diameter equal that of the Blue light ; colour pale blue. Pale blue . From about the Pole-star to alti tude 25° or 30' a little "W. o N.W. From a point neal the Pole-star t the horizon, • westerly. Liverpool. Like the moon as seen at the time, Rapid flight 3 seconds. Ibid. Blue light.like lightning. Prestwich, Man Chester. Dundee St.Bees.Cumber- land ; 3 miles inland. One-third diameter of the moon. Brilliant meteor or shooting, star. Bright white, like molten metal. 10 or 15 sees. Castletown, Isle of Man. Considerable fire- ball; lighted up the scene in a very remarkable manner. Several sees remained stationary. About the altitnii of Sirius or Orionis ; abo the horizon the time. From altitude due S. dov wards. Horizontally S.W. towar N.E. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 35 Appearance ; Train, if any, and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. 'irst a bright light of large size, then faded with a few sparks as if going out, immediately enlarged, elongated, brilliant blue, leaving red sparks behind shading into the blue. lluwing red envelope ; ? > Moon bright in a cloud- less sky. Cast shadows in the moonlight ; moon six days old. Hissing noise like quenching iron ac- companied the ap- pearance. Two mi- nutes later, a sound was heard like the discharge of a heavy gun. Baker Edwards, Ph.D. tail ending in green ; very even and somewhat permanent, 'arted into 7 or 8 frag- ments, like red - hot cinders. )val shape followed by long broad train ; the flame repeated itself three or four times. It gave three distinct flashes of light upon the ground and sky. .long tail showing all the prismatic colours. ? L., Correspond- ent to 'Manches- ter Guardian.' J. T. Slugg. ? Ran rather low and horizontally. Moved N.E. to S.W. . Correspondent to ' Liverpool Mercury.' R. P. Greg. ' Scotus,' Corre- spondent to ' Manchester Guardian.' John Jenkins. Correspondent to ' Mona Herald.' closed shutters as it it lightened. k. spearhead-like crescent moon five days old, with a short shaft was followed by rec star-like balls clustered behind. l reddish bolt issued from behind filmy clouds like a flash. The bolt or meteor afterwards sepa- rated into a number of small and brilliant particles. he fireball was suddenly arrested in its progress, remained stationary for several seconds, and burst without noise. 10° > Sailed slowly from E. to W., with a little dip towards the horizon. Downwards at 45° to the horizon. Moved horizontally till it stopped and burst. 5 No sound could be heard. Moon clouded at the moment. ? I 2 36 REPORT — 1862. Date. Hour. Place of Observation. 1861. h ro Dec. 8 8 20 p.m. Liverpool Apparent Size. Colour. Bluish - light. 8 23 p.m. Birkenhead (Sea- combe). 8 8 25 p.m. 8 25 p.m. 8 8 30 p.m. 8: 8 30 p.m. 8 About 8 30 p.m. Stone.neaiAyles- bury. Silloth, Cumber land. Dungannon, Ire- Double of Venus; £ of a minute of arc. Nearly size moon. green Duration. Position, or Altitude and Azimuth. The spark sprang from a little below Capella, proceeded with scintillations to the Pole, then inflamed, crossed the head of; Draco and be- 1 came suddenly extinguished. Darted down-!Appeared 8° or !q wards ; not E. of Cassiopeia 4 seconds. Red flush, then 5 second a purple | flush, and then a blue flush of light. of full Palish blue ... 5 or 6 seconds, rapid. land. Ulverston. Liverpool. Strong glare in moonlight. 8 8 30 p.m. Wakefield As large as a man's head. 8| 8 30 p.m. Coatbridge, La- B narkshire. 8 8 40 p.m. Lancaster 8 45 p.m. Wakefield ? ... Large as the moon Red Lasted a few From altitude 30° Light great enough Purplish to render distant objects visible. ? Manchester Large as \ of the moon. burst 35° to 40° above the ho4 rizon, some- where about N.N.W. by W. From /3 Cephei to a. Cygni (the stars doubtful). From altitude 50°' i in the S. ; dis-j appeared a little to the N. bv W.j' seconds. due E. Several sees. Quite overhead, down the wes em sky. Seeme to burst 50yar< off, 10 feet fro the ground. In the S.W. sky .. Descended fron altitude 50°N. to altitude 10 N.W. by W. On turning, sa\< the meteor falljl ing perpeudicu larly N.N.W. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 37 \ppearance; Train, if any, Length of and its Duration. Path, Direction; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. ? irst a reddish spark ; in combustion at the meri dian ; increased in in- tensity to apparently i large sheet of flame extinguished suddenly. <ight slackened at burst iug, but explosion the most brilliant ; frag' ments violet. tar-like, and very bril- liant for two seconds, then burst, and con- tinued like a rocket, followed by coloured fragments, blazing track followed it, and immediately following were many smaller globes or bulbs I of fire ; several bright red. arge ball of fire with coloured sparks and long train. il riant ave out like a stream of crimson fire, expand- ing like a trumpet, and then bursting without uoise. tail 18 inches long issued above, then ceased, and issued at the side, till bursting with sparks. nail red balls left behind 1 tail followed, and stars'... about the latter portions! fell from it. ie light seemed uniform' ? and ceased suddenly. Several shooting-stars J.BakerEdwards, and meteors this Ph.D night. Inclined 22° towards Sky hazy ; small halo the horizon. about the moon. Inclined at a great angle to the horizon. Descended slightly , Fell down towards the earth. Cloudy night, moon con- cealed ; attention caught by crimson flush like lurid light- ning. Seen in clear sky. E. to W. Fell from near the Light clouds ; moon and zenith straight down sta rs more or less in the northern sky. visible. D. Walker, M.D, W. Penn. Rev. F. Redford. S.E. to N.W. ., .. After walking 200 yards a loud noise was heard like a gun. Appeared to move in a No noise or explosion, straight line, but the movement was irre- gular. Fell vertical Communicated by Albert Greg W. R. Milner. Arthur Neild. 38 REPORT — 1862. Date. 1861 Dec. 8 Hour. Place of Observation. h m 8 Bowdon, Man- chester. Liverpool. Llandudno Settle, Yorkshire Newcastle - on Tyne. In the even- ing. Apparent Size. Colour. Duration. Position, or Altitude and Azimuth. Nearly as large as the moon ; brighter than the sun. Very brilliant, giving out con siderable glare. Light exceeded that of the moon more like that of the sun. At the flash, ob server turned to examine the moon. Very brilliant meteor. Light blue .. Cartmel, Lan- caster. Douglas, Isle of Man. Langdale , Holcombe Hill, Bury. Islington, Lon don. Twickenham 8 10 24 p.m. 8 10 45 p.m. to 11 5 p.m. 9 5 15 p.m. 9 5 30 p.m. 9 9 35 p.m. Greenwich 3 seconds 'From a little N.W.I of the zenith ; I described an arc towards the W. I At the altitude of al rocket. Many coloured 2 or 3 seconds Like full moon let loose in the sky Start liugly pale colour. Larger and brighter than the largest star. Most brilliant meteor; eclipsed the light of the moon. = 3rd mag.* 5 or 6 seconds. Visible 10 seconds before it burst. It appeared to cornel out of the moon.! Glasgow Fine meteor Birkenhead(Sea- Meteors and shoot- combe). ing-stars. Blue Hawkhurst, Kent Brighter than 1st ? mag.*; large and| bright meteor. Greenwich Small Disappeared behind woods N.W. ? Disappeared behind a cloud near th horizon. From altitude 50 c or 45° \Y. ? From the Pole-sta Haifa second.. Across y Aurigac i the direction i the Pleiades. BetweenUrsa Majo and Orion, S.E. 9 seconds In the S.W. sky 2\ or 3 sees. ; Across /3 Ursse slow motion. Minoris ; extincl halfway betweer. £ Ursae Minoris and X, Ursaj Ma- joris. 1 second Appeared from behind a cloud moving parallel to the horizon. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 39 Appearance; Train, if any, and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. jeft a long broad train behind. Carried a luminous train, and burst at disappear, ance. Outline very irregular, oval shaped ; tail formed of consecutive bulbs of fire. i ball of fire Jurst in sparks like a rocket. ./ike six or seven falling stars. changeable in colour, pursued by a vari- coloured tail several degrees in length ; no explosion, no sparks. Humiliated the whole country. 40° rain 7°. Hsappeared without ex- plosion. A rushing sound heard during the passage. Moved S.E. to N.W. Clear night Sky free from clouds .. Many shooting-stars seen this evening at Newcastle. Report very loud alarmed the inhabit- ants. People greatly alarmed; no noise heard. They fell vertically . By memory, at same spot following day. Took a north-westerly direction. More fell here at this time than at the highest time of last August or November. As if from Cassiopeia Correspondent to ' Liverpool Mercury.' T. S. G., Corre- spondent to ' Manchester Guardian.' W.H. Cockshott Correspondent to ' Northern Advertiser,' R. Hawthorn. Communicated by Albert Greg. Samuel Simpsou. John Richardson J. W. Wraith. James Foote. E. G. P., Corre spondent to ' Manchester Guardian.' W. C. Nash. D. Walker, M.D Communicated by R. P. Greg. J.F.W.Herschel 10° Parallel to the horizon... Rather cloudy J. MacDonald. 40 REPORT 1862. Date. 1861. Dec. 9 Hour. Tlace of Observation. h m s 9 40 p.m. Greenwich 9 10 50 p.m. Ibid 10! 9 45 p.m. Weston - super Mare. 10 11 11 11 11 10 30 p.m.? Ibid 9 12 p.m. Royal Observa- tory, Green- wich. 11 11 p.m. 1 Ibid 11 23 p.m. Ibid 11 28 p.mJlbid. 13 10 p.m 18 23 24 11 37 p.m, 7 p.m 7 p.m, to 4 a.m, 24 9 p.m 110 to 11 p.m. 24 11 38 34 p.m. 25 9 p.m, 2511 45 46 p.m. Weston - super • Mare. Birkenhead (Sea- combe). Royal Observa- tory, Green- wich. London . Woodford Hitchen ., Deal Royal Observa- tory, Green- wich. Deal Apparent Size. = 2nd mag.* .. = 2nd mag.* .. =2nd mag.*, Ursa? Majoris = Capella = lst mag.* = 2nd mag.* .. = 2nd mag.* .. = 3rd mag.* .. --P Auriga? = 1st mag.* ,. = 2nd mag.* .. Mostly 2nd and 3rd mag. None so large as Venus. Shooting-stars. Small stars = a Andromeda? . . . = 2nd mag.* Colour. Blue Blue Dull or smoky blue. Bright blue ... Blue Blue Bluish white... White Smoky blue ... Bluish White White and yellow ; steady lights. White Between a and 1 Blue Cygni. Duration. Position, or Altitude and Azimuth. 2 seconds .. 1 second Less than 1 second. Nearly 2 sees. 1 to 2 seconds 1 second 1 second 1 second Less than 1 second. 3 j seconds . . 1 second More swift after mid- night than before; mo- derate. Fell from the I neighbourhood | of Orion towards < the W., moving over 20° of space. Across a. Ursa? Majoris. Appeared near Ursa? Minoris j disappeared nea « Draconis. Appeared azimuth 40°, altitude 20°| N. of W. From i Auriga? to point a few de grees below th moon. From a point a fei degrees above *'> Ononis to y On- onis. [Fell perpendicu-^ larly from (3 Ge minorum towards horizon. From Z Tauri to wards a Tauri. Appeared by Ca pella. Centre immediately below (3 Persei. From the direction of Cassiopeia to a Ursa; Ma- joris. Chiefly near the! radiant before) midnight, after- wards in all quarters. In the S I 2 seconds. I to 2 seconds In Orion 1 second From near o to! below a Andro-I meda?. Shot in a northerly J direction be- tween a. and j8j Geminorum. Between a Cygni! and y Draconis,] below k Cygni. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 41 >pearance ; Train, if any, and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. ne 20° Inclined tin 5° N. to S., inclined Hess; light alternated en times a second. Hess m in 8°.., 40° Slightly inclined N. of W. E. to W. As if a rapidly revolving light. The only two meteors seen ; night fair. A fine meteor less ; decreased ipidly until lost to ght. v small train E. to W., inclined ...... Generally cloudy Id J. MacDonald. W. C. Nash. W. H. Wood. Id. W. C. Nash. 5° Perpendicular 8°. 16° to 18° 20° E. to W., horizontally. W. to E., due Horizontal from E.toW. Very cloudy. Very cloudy Ni;rht unfavourable. Id. Id. W. H. Wood. e left trains; courses 3° to 40°, raight. very va- rious. ral small shooting- lrs without tails. )f a track lasting about econd. About 2° ... General direction from Bellatrix to k On- onis. 25 to 30 per hour at 10 p.m.; fewer after- wards. Several shooting-stars within a short period. Almost horizontally, S, toN. No other visible for 30 D. Walker, M.D minutes. W. C. Nash. A. S. Herschel. John Hill. W. Penn. Herbert M c Leod W. C. Nash. Straight down Herbert M c Leod 42 REPORT — 1862. Date. 1861 Dec. 26 21 27 Hour. Place of Observation. Apparent Size. h m s 11 27 23 p.m. 7 55 p.m. Belfast Lough. 8 57 p.m. Ibid = 1st mag.* Twice size of Venus 2710 34 p.m. Weston - super - Mare. 27 27 31 1862, Jan. 2 10 34 p.m. Ibid. 11 8 p.m. Ibid. 7 37 p.m. Ibid 12 43 a.m. 11 48 p.m, 311 49 p.m 11 11 7 5 p.m About 7 p.m Birkenhead(Sea- combe). Ibid Ibid. = y Draconis White . Yellow Yellow =Rigel = Sirius \ Ursae Majoris (foot). Larger than Sirius and less than Venus. = Venus = Procyon Colour. 1 second Bright blue . Bright blue . Very dark . Very bright blue. 2 seconds , 6^ seconds ... Near 2 seconds Duration. Appeared betwefl £ and X Draconil disappeared bi tween y and Draconis. 18° above the hi rizon, near Auriga?. Centre at (i Dn conis. 2 seconds. Less than 1 second. Nearly 3 sees. Yellow Bluish . Euston Square, London. Edgware Road Kilburn. = lst mag.*. Position, or Altitude and Azimuth. At appearance tween j8 and Draconis. Near \ Leonis " Between /3 andi Draconis. Near Z, Cygni ....I 3£ seconds If second Bluish \i second Brighter than Venus More yellow Slow move- than Venus, ment, in strong contrast. Considerably larger Similar to than Venus. Venus. Slow. Centre 2° belli Aldebaran. Centre at luilfv* {y Oriouis a Aldebaran). Centre almost hi|ki way (a Oriol andyGeminorurj Appeared below m moon; disali peared 3 : abo» Procyon. ■ A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 43 pearance; Train, if any, and its Duration. •y slight train, scarcely isible. Hess Length of Path. ck ending the whole ime of flight ; some' trhat radiated in ap earance. Hess Hess Hess ite tail 16° long ; dis- ppeared nearly simul- ineously with meteor. 12° 15° U train U train 11 train , 1 globular, surrounded sparks ; short evan- bent tail of flame ce character or ap arar.ce. >ks of a golden hue nanated laterally from fa head of the me- l>r, also leaving a <nsiderable train of nilar sparks behind In its descent, which * s particularly slow. 13° ... 10° ... 18" Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Almost horizontal Observer. Position at disappear ance near the two stars 80 Herculis. Near y Leonis To left ; 52° from hori- zontal; down. A little inclined west of perpendicular to horizon. Inclined north side perpendicular. Inclined (most) westiNear 61 Cygni side of perpendicular,! let fall from its ap pearance. Path parallel to 3 and y Cygni, from the former towards the latter. To right ; 45° from ho- rizontal ; down. To right; 30° from ver- tical ; down. Over ? Cygni. There was an interval of three seconds of time between this and another meteor. They merged from the head of Draco. This meteor in its transit passed exactly midway between i and y Cygni ; de creased before dis appearance; the sky became overcast for the night ; such was the case on the 28th, 29th, and 30th. Herbert M'Leod, D. Walker, M.D. Id. W. H. Wood. Id. Id. Id. Vertical; down D. Walker, M.D, Id. The latter half of thejObserving Venus and path appeared curved, the moon ; clear evening. An inclined direction from beneath the moon. Id. W. R. Birt. C. Herb. Bright. 44 REPORT — 1862. Date. 1862. Jan. 11 11 12 23 23 23 23 23 23 24 24 24 25 25 25 25 Hour. h m 9 43 p.m Place of Observation. Apparent Size. Weston - super -| = Sirius Mare. 11 48 p.m. 1 a.m. 9 p.m. 9 p.m. 9 14 p.m. 9 21 p.m. 11 14 p.m. 11 29 p.m. 8 20 p.m. 9 28 p.m. 9 28 p.m. 12 15 a.m. 11 22 p.m. 11 22.^ p.m. Ibid. Ibid. = Jupiter --K (foot) of Ursa Major. Ibid =Capella. Ibid. Ibid. Ibid. = Capella. Islington, Lon- don. Ibid. Weston - super Mare. Ibid. Ibid. Ibid. = 3rd mag.* = 3rd mag.* = lst mag.*.. = 3rd mag.* = 3rd mag.* = 3rd mag.* = 2nd mag.* Birkenhead (Sea- = Rcgulus combe). Islington, Lon- =3 - 5 mag.* don. 11 25 p.m. Ibid = 1st mag.*. 25 11 47 p.m. Weston - super -= 3rd mag.* Mare. Colour. Vivid blue Bright yellow A very dark colour. Rigel Duration. Position, or Altitude and Azimuth. 3 seconds, slow motion, Less than 1 second. Reddishyellow 2 seconds. = 3rd mag.* Smoky blue.. Smoky blue . Yellow .... l\ second Rapid ; \ sec. Appeared near . Bootis ; disap peared 4° ab<n a Pegasi. Appeared near Bootis ; disap peared near y Bootis. Appeared at i Dr; conis ; disap. peared at y Dn conis. Appeared very nei Rigel ; disappeart near y Eridani. Appeared very nei Rigel. Appeared near Pnjj cyon. Slow ; 1 sec. § second Appeared near 3 Cassiopeia. From a star fll following w Drl conis to i Dr conis. e i second From £ (/3, y) Til anguli towanj ■r Piscium. Smoky blue... Fast; £ sec.... Appeared midwil k and a. Dr conis ; disap- ) peared near ij Draconis. Same track last. Smoky blue... Smoky blue . . Bright blue.., Fast ; i sec... Fast; -J sec... Bluish . Yellow Moderate ; ^ second. j second 5 second White 06 second Dull blue I second Appeared near J Draconis; pa over /3 Ursa; M noris as far j the feet. Centre 10° belo' Regulus. From £ (r, v) A dromeda; towar (i Andromedse. From /3 Andr medse towar v Andromedse.. Appeared near Bootis ;disappe» ed near /3 Bootis A CATALOGUE OP OBSERVATIONS OF LUMINOUS METEORS. 45 I learance ; Train, if any, Length of and its Duration. Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. - Path nearly perpendicu- lar to the horizon. Remarks. less jack left t tail 3° long followed e meteor. tail ; intermittent ;ht ; two alterna- jns; almost disap- aring. rack left ; no sparks., Serpentine path ; very surprising. 10° Inclined 50° southward Auroral glare ; N.W. by N. Rapid lightning from N.W. by N. 8°. Observer. W. H. Wood. Id. Id. Id. Id. Id. 11° rack left; no sparks... 7 Along the Via lactea, Thunder and lightning Id. northwards. at 3 a.m., Jan. 24th. rack left ; no sparks. ack left ; no sparks., •ack ; no sparks rack left; sparks or julous radiations from terior hemisphere, ! a semi-corona. 12° Radiant between k and a Draconis. Parallel to horizon, E to W. ack left ack left ; some sparks 5° lack left ; no sparks., ack left To right; 35° from ver- tical; down. A. S. Herschel. Id. W. H. Wood. Id. Id. Id. D. Walker, M.D A. S. Herschel. A. S. Herschel. \V. II. Wood. 46 REPORT — 1862. Date. 1862. Jan. 25 Hour. h m 11 49 p.m 2511 55 p.m 2511 56-£p.m, Place of Observation. Islington, Lon- don. Weston - super ■ Mare. Islington, Lon- don. 2G 26 26 26 2511 57i p.m. Ibid I 2512 p.m. Birkenhead (Sea- combe). 24 a.m. 30 a.m. Weston - super Mare. Ibid. 35 a.m. Ibid 6 10 p.m. Birkenhead (Sea combe). 2611 44£ p.m. Islington, Lon don. 27 27 28 28 29 j Feb. 2 Apparent Size. 2-5 mag.*.. = 3rd mag.* = 0-4 mag.* = 3rd mag.* Colour. Faint yellow... Dull blue White, bril liant, then red. Colourless 9> Leonis jBluish = 2nd mag.* Blue = 4th mag.* = 2nd mag.* = Capella Very dark blue. = 0-8 mag*. 11 24 p.m 11 25ip.m. 11 3 p.m. 11 4 J p.m 7 22 p.m 7 p.m 8 15 p.m 8 20 p.m. Ibid. Ibid. Stone, near Aylesbury. Islington, Lon- don. Birkenhead (Sea- combe). Kilburn, London = 4th mag.* = lst mag.*.. Duration. 0'9 second .. j second 1-7 second .. Position, or Altitude and Azimuth. From 1° N. S to X Cassiji peias. Disappeared neaw Bootis. From a star 2V J of a> Draconfl 2° beyond o Djj conis. - 7 second ...;From y to ? Cij siopeia?. \ second Disappeared 2i below a li joining n audi Virginia. Slow ;f second Blue Bluish ^ second f second Yellowish. Tolerably large ; =3rd mag.* Orange colour Yellow White light,,, Burslem Birkenhead(Sea^ combe). = 0-8 mag.*. = 1st mag.*. = Venus at maxi mum. Large blue light . . = Rigel Yellowish. Whitish White .. Blue .. Appeared at wl foot of U| Major. From § Ursae joris to a. Drac £ second Centre 2° and 8° E. Persei. 5 S. of i I conis to 1° S Draconis, i two-thirds as again. From £ (k, y) ( siopeiae. Centre 1° pre< ing <r Persei From 2° pre< ing (u Cepha i (e, «) Cl peiae ; 1° na to the latter. From 1° bel 4 (0. *) O peiae to 1°' ceding -x Cai peiae. From i (i Ursre Majoris* From beneath & moon. 0-8 second .... 0'5 second ... 0-5 second ... 2£ seconds ... 1-3 second ... Blue J second Very slow mo- tion. Travelling slowly ; \ minute. 2 J- seconds ... From 2° above I belt of OriOiil about 15° all Sirius. A CATALOGUE OP OBSERVATIONS OF LUMINOUS METEORS. 47 i pearance ; Train, if any, and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. track left ; appeared 10° o give out sparks. I track left (Lyra? in motion 10°; laded to dull red in U°, and disappeared gradually. No track left; no sparks. I track left ; sparkled . . track left tht or "off" side of Circumference; hazy. I track left ; no sparks. . . I track left ; no sparks. I track left 15° 18° or 20 3 12" I track left ; sparkled ... 9 track left ; no sparks... rkled; no track left . . track left; sparkled; ent downwards, and ower at last. track left Tain of golden sparks ursued the nucleus, ill balls like stars kept illing from it in a track ike fire. pdl train and sparks I :companied the head, 8°. 7 ... 20° 11 ; 6°. To left; 7° or 8° from vertical ; down. W. to E., horizontal To left ; horizontal. Parallel to y, a. Cassio- peia?. Directed from i Persei... To left ; 20° from hori- zontal ; down. To left ; horizontal. Inclined downwards to left. S. toN To left; 30° from hori- zontal; down. Clear night , Only two shooting-stars from 10 to 11 p.m. Fine passing clouds. A. S. Herschel. W. H. Wood. A. S. Herschel. Id. D. Walker, M.D. W. H. Wood. Id. Id. D. Walker, M.D A. S. Herschel. Id. Id. W. Penn. A. S. Herschel. D. Walker, M.D C. H. Bright. Correspondent to ' Manchester Guardian.' D. Walker, M.D 48 REPORT — 1862. 1862. h m Feb. 2; 8 20 p.m. Tarporley, Che- shire. Date. Hour. Place of Observation. Apparent Size. 2 8 20 p.m. Liverpool Lighted sky and landscape like a flash of light- ning. Colour. Duration. White ; after 6 seconds, bursting purple wrap- ped in white, then red. 2 8 21 p.m. Observatory, Beeston. 2 8 30 p.m Manchester , Newark Sheffield Ibid. Mold, Flintshire = lst mag.*, then a The globe was large globe. of a bluish colour. Not as large as Unchanged moon, but ap-! blue Position, or Altitude and Azimuth. proaching to it much brighter. In size it looked to a star as a billiard ball does to a pea. About as big as the moon, light as brilliant light- ning. pink green. to Visible 3secs. ; and; slow motion, aud ? 6seconds;mo- derate speed. 10 or 11 inches diameter. Newtown Worlow Eastbourne Whitish colour 2 seconds From nearly S. a little E. o Pleiades to net Gemini. First appeared a first magnitw star in the regie of Orion. From W.S.W., ju above Venus then burst b hind a cloud ai quickly dis»; peared. From altitude 30 E.S.E. ; disa; peared 20 D aba horizon. Directly towa the moon ; bu in a cloud ten twelve diametel off the moon. I Exploded S.W., altitude 32° ;1 altitude 30°. I It looked to a star ... as a football to a marble. = one-fourth of the ? moon. Bright amber.. 6 seconds Moving slowly = half size of full moon. Colour of moon, pale yellow. var but ■ en Not more than 2 or 3 sees. E.S.E. ; altitud 50°. ndl 1 9 154 p.m. Birkenhead(Sea- Twice a3 bright as White combe). Venus. 2 10 23 p.mJlbid jjupiter Blue 2 10 25 p.m. Ibid. Capella j Pale blue . 2 seconds.. 1$ second | second Probably kin due E. ; seen N.E. ; tude 45° ; came extinci N.E. by N. " Probabl'v S.S. to n.n.w." ; (H. C. S.) Halfway betwej the Pole-star a the horjzon. i From « to « Dir conis. From 3° N. oft Virginis. Centre I (Cor (• roli and n Ur Majoris). A CATALOGUE OP OBSERVATIONS OF LUMINOUS METEORS. 49 jpearance ; Train, if any, Length of and its Duration. Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. irst white, then bursting [like a rocket ; it took a purple hue with white light ; then red ; iu which state it disap- peared. No luminous track seen. ft many stars and sparks in its track of various colours. ad with a tolerably defined edge ; circular ; long white track ; visible 20 to 25 seconds. rfectly round ; very '.ittle train ; vanished quietly. •cular ; luminous track ; asted half a minute. 30 c peared to explode twice fectly round; burst uddenly. itted stars, and left a arge track of sparks. »d pear-shaped, en- ircled by red fiery lare. Comet-like tail ne yard in length, ringed with blue; no rack left. ;r shooting across the ky and disappearing, urst forth again and xploded like a rocket. >nge-red train with i parks ; one second. Itrackleft i track left Nearly horizontal S.W. to N.E., obliquely towards the earth. Remarks. Observer. An uninterrupted view.. W. Vicars Downward, at 45 c the horizon. to Illuminated the ground W. Brown ; P so as to see quite! Parr, small objects, Fell almost vertically , At 45 ° downward S.E. to N.W. ; E. to W. From altitude 40° E.; moved 40° N.W. quite! Thin strata of fleecy clouds. Moved along among A. H. Allcock. belts of clouds. Horizontal In an oblique direction towards the north horizon. From S. to N., or a little W. of N. N. to N.W., downwards To left ; 45° from hori- Slight curve in the d zontal ; down 6° [Vertical ; down 12° |To left; 45° from hori- zontal ; down. rection. Communicated byll. C. Sorby, Messrs. Roberts, Mappin, and Watson. W. P. W. Bux ton ; Mr. Furniss. Correspondent to Carnarvon Paper. R. Owen. C. H. B. Kambly John Hall, jun. D. Walker, M.D. Id. Id. 50 REPORT 1862. Date. Hour. 1862. h ra Feb. 2 10 54 p.m 211 11 p.m Place of Observation. Apparent Size. Birkenhead(Sea- combe). Ibid , 2 11 30 p.m. Ibid 9 p.m. Kilmarnock, Glasgow. 4 11 46 p.m. Weston - super Mare. 9 11 41 p.m. Birkenhead(Sea- = Jupiter combe). = Castor = Cor Caroli = Cor Caroli Colour. White White White Quarter diameter of White moon, or 3 times Venus at maxi- mum. Capella Duration. Position, or Altitude and Azimuth. second Bright blue...|H second Blue 2 second . 1011 32 p.m, Ibid. 18 8 37 p.m. Greenwich = Arcturus i second IFrom % to i Uri Majoris. 3 seconds Centre i (Cor Ca|s rob: and Arc- turus), 2° higher Centre £ (j3 Leonif « and a Coif Berenicis). More than half [Appeared close a minute. Pollux ; disapi 1 peared close ti Aldebaran. Appeared near Cassiopeia?. Centre 2° below / ;, Ursae Majoris IS 18 19 9 12 p.m. Ibid 11 12 p.m. 23 a.m. 1911 32 p.m. 1911 50 p.m Islington, Lon- don. Birkenhead (Sea- combe). Islington, Lon- don. = 3rd mag.* = 3rdmag.* = y Cassiopeiae .. White Blue Blue White \ second 1 second Twice diameter of Yellow Jupiter. Ibid. 19 12 10 p.m. Ibid. 20 8 45 p.m. to 9 30 p.m. 2011 p.m. to 12 p.m. 20 21 21 Weston - super - Mare. Ibid = 4th mag.* = Sirius Aquilae , = 2nd and 3rd mag, shooting-stars. 11 Z2\ p.m. Islington, Lon- don. 10 57 p.m. Greenwich 11 5 p.m. Islington, Lon- don. = 3rd mag. shoot- ing-stars. ■ t Cassiopeiae = 2nd mag.* .. = a. Persei Yellow White White Nearly 1 sec. 0*6 second .. | second 0*2 second L3 second Yellow second Centre betweei Arcturus and Mirae. From direction c Capella ; disap peared near Arietis. From ? Tauri acros, a. Ononis, t Cassiopeiae,! A Cameloparda! to I (X. «1 Persei. From H c to righ of ti Draconis. Centre i (y Cephi and ;> Cassio- peiae). From i (Polaris , fi Aurigae) to § (9 to «) A* rigae. Appeared near Draconi3. 0-25 second . White About 2secs., Yellow 06 second Centre ^ (y Cf phei, /3 Cassic •, peiae). ii .... 1^° following 1 Aurigae to H following /3 Ai rieae. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 51 ppearance; Train, if any,! Length of and its Duration. Path. !o track left < small track left o track remained , 10° ;eadylight, very brilliant, like the electric light, or a fine ball ; no train noky appearance ; semi- corona, o track remained 3 track left )ne Direction ; noting also whether Horizontal, Perpendicular, or Inclined. 15° 6°... 5 rj ) track left ; no sparks brightest at middle. Illest and brightest at centre of its flight. rpentine flight ; three undulations ^° wide. track ; no sparks track left considerable display .. considerable display ; all ;ailless save one. 10° 11° or 12° 3° To left; 30° from hori zontal ; down. To right; 30° from hori- zontal ; down. To left; 30° from verti- cal ; down. Parallel to y Orionis and * Orionis. E. to W., inclined 10° W. To left ; 30° from hori. zontal ; down. Remarks. Observer. Vertical ; down Almost N. to S. Vertical ; down Direct from Polaris. 10° track left; nosparks...'3°.., ne 120° Nearly from Polaris From Polaris D. Walker, M.D. Id. Id. Robert Ctaig, jun. W. II. Wood. D. Walker, M.D. Id. W. C. Nash. Id. A. S. Herschel. One meteor in an hour.. D - Walker, M.D Radiant in Perseus N. P. D. 33° ; A. R 29°. Radiant Polaris , From Polaris track left ; no sparks... Fell from zenith to- wards the western horizon. From Polaris , Radiant Polaris Tailed star; 1st mag- nitude ; blue ; 10° in 3 seconds; tail as- cended and dissipated like steam. A. S. Herschel. Id. Id. W. H. Wood. Id. J. MacDonald. A. S. Herschel. e2 52 REPORT — 1862. Date. Hour. 1862. | h m Feb. 21 U 15 p.m. 21 11 15 p.m, 23 9 25 p.m, Greenwich Liverpool 23 9 25 p.m, 23 23 23 23 23 Mar. 3 Apr. 3 9 30 p.m 9 8 p.rn 9 29 p.m. 11 25 p.m 8 10 p.m 9 5 p.m Place of Observation. Islington, Lon- don. ■y Cassiopeiae .. As bright as Ju- piter. Magnificent meteor Weston - super Mare. Liverpool, Wal- lisby, Cheshire Bramboro, Ches- ter. Cross Nouses, Salop. Salop Weston - super Mare. Ibid Ibid. Islington, Lon don. Weston - super Mare. Apparent Size. Colour. Duration. Yellow Blue 1 second About 2 sees. y Cephei to | Cephei ; ^° fol lowing. =half diameter of Vivid red light Bright light filled A cold light, the streets. A bright light thrown from the sky. Exceedingly bril- ? liant. not flame- coloured. = 2nd mag.* = 2nd mag.* = one-eighth of moon. = 4th mag.*. Ibid. = lst mag.* = lst mag.*. Blue Blue Pale red White Blue Blue H- second Leisurely , Position, or Altitude and Azimuth. I From N.N.E. half - E. altitude 20° J to N. altitude 18J . Moved as if from over Manchester into Wales, Great Bear to Orion, horizont- ally. Origin near Jupiter, Flashes 2 sees., then ran across the sky. li second. 2j sees., slow. 0'7 second .. \ second ^ second From Jupiter From S.W. by S, along the ho- rizon at a great altitude; pro- bably 40° or 50 r between Junitei and Ursa Major. From a great height, nearly to thi ground. From Cassiopeia Appeared close | Sinus. Centre 1° S. p q Camelopar dali. From Sinus I A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 53 ippearance ; Train, if any, and its Duration. to track left ; no sparks.. Length of Path. light train . tar of light remained about 20 seconds after the first appearance of the meteor. tarlike meteor ; became suddenly extinct, leav- ing a bar of red light 25° in length, fluctuating between red and orange, and lasting 8 seconds until disappearance. explosion ; long di- stinct train of light, disappearing slowly like smouldering twine. 15° 25- turning round, two bars of white light were seen, which en- dured fifteen seconds. Their length together was 26° ; the south bar faded sooner than the north. to flashes like lightning, then ran along the ho rizon in one long broad line, which endured five minutes, not chang- ing. track left netary, or better, a ;lohe. '•mentary train. overcast with haze 8°. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. f covered with thick laze. 10° From Polaris In the N., fell from the zenith, disappearing behind the houses. E. to W., at an angle of about 80° with the horizon. E. to W., nearly hori- zontal ; west end de- pressed 2° or 3°. From E. to W. by S. Observer. A. S. Herschel. J. MacDonald. The tail faded graduallyjcorrespondentto no change. ' Liverpool Mercury.' Slightly inclined to the horizon. W. H. Wood. Jupiter appeared to shine brighter when the bars disappeared than he did before. Parallel to the horizon, yet in a descending position, inclining especially to the S. Vertical; down A little inclined To left; 30° from verti- cal; down. Perpendicular to the horizon. Directed from o Ursa? Majoris. The stars seemed to go out on that side of the hemisphere, and did not recover their brightness for half an hour. Studley Martin. T Juman. Sky obscured at 10 p.m. James Caswell and Son. Perpendicular to ho- Fell one per hour rizon. One star in an hour; N.W. ; cloudless. Perpendicular to ho- rizon. W. H. Wood. Id. Id. A. S. Herscliel. W. H. Wood, td. 54 REPORT 1862. Date. Hour. Place of Observation. Apparent Size. Colour. Duration. Position, or Altitude and Azimuth. 1862. Apr. 14 h m 7 42 p.m 17 20 2a 23 23 24 24 25 Clerkenwell, London. 10 10 p.m. Hitchen 8 30 p.m. Greenwich Hill. 8 56 p.m. 9 50 p.m, Weston - super Mare. Ibid. 10 35 p.m. St. John's Wood, London. 10 26 p.m. to 10 times as bright as Jupiter. White Fine meteor. Larger than Jupiter Larger than 1st niag.* 3 seconds. From 10° or 12 1 over Jupiter H altitude 32 % S by W. 3 seconds. > White Nearly as large as Deep yellow. . . Jupiter. Brilliant body of j Bluish colour- light, ed, 2 seconds .. Slow ; 1| sec. Slow ; 2 sees. .. Weston - super - =lst mag.*. Mare. Brilliant blue. 11 33i p.m. Islington, Lon- don. 10 30 p.m. Weston - super - Mare. = Pollux Ibid. 25 10 30ip.m. 26 10 52 p.m. Ibid. 26 27 10 52|p.m 8 42 p.m : Spica Virginis . = Spica Virginis . . =Venus Birkenhead (Sea- = Jupiter combe). Greenwich =2nd mag.* Pollux Spica Virginis Spica Virginis Venus 7 seconds. I second 0-4 second Fromi(*UrsaeMi joris and Polaris to centre of Ck rona Borealis. Between p and Camelopardali. 16 Draconis tc y Draconis, close and parall to a. and y Dr. conis. From Arcturus 1 18/i Bootis. Between N. and 1 altitude 45°. At appearance ne 41 and 42 C melopardali. From 1° S. < Camelopardus. | second At appearance ne 66 Virginis. Blue Reddish J second 1 second 66 Virginis .... From «■ 1 Cyg passing betwe the head stars | Lacerta. 2\ seconds ... Close to /i Hi culis. 1 to 2 seconds From the direct!) of Ursa? Majo towards the' horizon past Arcturus. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 55 Direction; noting also Lppcarance ; Train, if any, Length of whether Horizontal, and its Duration. Path. Perpendicular, or Inclined. Remarks. Observer. 'ear-shaped ; no track visible through clouds ; faded gradually, and disappeared quietly ; very slight train. .eft a train like a sky- rocket. tationary ; varied little in brightness. ursued by faint phospho- rescent train. <o track ; disappeared and reappeared three or four times. locket - like, but kite - shaped ; left a few sparks for half a second on dying out. [one 40° io track; no sparks;. 7° brightest in the middle. one one one irain visible three seconds; 15 c i burst at last with strong light; pink, and bright as Venus. To right ; 20° from ho. rizontal ; down. 2° or 3° ... 15° to 20° Horizontal, W. to E., inclining downwards at last. T. Crumplen ; A. S. Herschel Strong twilight ; quite overcast; rain falling, ' Inclined west of Increased in brilliancy.. Communicated by W. Penn. W. Airy. W. H. Wood. Id. Id. Id. To left; 35° to 40° from Only one other star in'A. S. Herschel, vertical ; down. Ditto, west side of vertical, at an angle of 75°. Inclined 65° west of • Inclined , the hour ; very faint ; cloudless To left; 30° from verti- cal ; down. W. H. Wood. H. Appeared first as aid. second magnitude star, and gradually increased until equal Venus, when it be- came suddenly ex- tinguished. ; D. Walker, M.D, W. C. Nash. 56 REPORT — 1862. Date. Hour. Place of Observation. Apparent Size. Colour. Duration. Position, or Altitude and Azimuth. 1862. h m \pr. 27 8 51 p.m. Greenwich 27 10 10 p.m. Birkenhead (Sea- combe). = 2ndmag.» Yellow [1 second = Venus . Blue i second 27,10 50 p.m. Ibid 2711 25 p.m. Ibid. 28 10 46 p.m. Weston - super Mare. 29! 9 53 p.m. ! Ibid 29 11 6 p.m. Islington, Lon- don. 29 11 33 p.m. Ibid 29 29 May 21 24 10 27 p.m 10 10 p.m. Ibid 23 25 11 37J p.m. Ibid. 11 55 p.m. Ibid. Weston - super Mare. 10 40 p.m. Ibid. 10 55 p.m.jlbid. or 11 p.m.' No meteors seen throughout = Jupiter 'Whitish = a Lyrae Bluish = 2ndmag.* Blue J second ., i second ., 1-J second = lstmag.# White 1 second, fast. = Capella. = Ursae Majoris.. Capella ,0 - 9 second .., ollrsae Majoris - l second ... = Ursae Majoris.. ilf as : Jupiter Half as bright as White, then ollrsae Majoris hite, red. 0'2 second ... 4 - 5 seconds; exceedingly slow. = 2nd mag.* Blue = 1st mag.* = 1st mag.* = lst mag.* the month of June Yellow . Blue Blue Dropped from near Polaris ir. a N. l.y E. du| rection toward! the horizon. 5° beneath i(/3an« y llerculis). Centre i {y Sew pentis aud I llerculis). Centre 2° below ) Serpentis. From £ (Crateris)j to y (Corvis). ; From Ursa Major..! to U° S. ol 6 Cassiopeia?. From $ {q, p) t<l L Camelopar- dali. From/Lyncis From /* Cephei it within 4£° of Pegasi. 1-j second 2 seconds. 1-J second From a Cephei to wards /3 Cassio peiae. From Right Ascenl sion 1°, Decimal tion 51° N. til Kight Asceusioi, 13°, Declinatioil N. 48°. From y Sagittac t a. Delphini. S.W. ; altitude 30 July 12 10 41 p.m. Weston - super - 1 = Sirius .White ^second From y Cassiopeii Mare. to X Persei. 1610 45 p.m. Ibid ; = 2ndmag.* Blue (Fast) i sec. .. Head of Cepheus.. 19 11 17 p.m. Ibid. = Venus Yellow 4 seconds. From stars 4, 5, an> 6 Camelopardal to 14 and 15 Le Minor. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 57 Ipearance ; Train, if any, and its Duration. Length of Path. nt train 25° -st with a very bright lash ; track remained talf a second, t a small track Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. 18 : To right; 45° from ho- I rizontal; down. Observer. 8° Vertical; down t a slight track 10 c le '.... le „ t no track track ; no sparks . To left ; horizontal , track ; no sparks r Horizontal 4°. t no track. Brilliance>22° anished suddenly at! Lacertae, remaining 5 ; light red (Mars I maximum robbed of lis rays) ; very inter- iittent or vacillating ; l"3 seconds ; died out. train 10° 10" Directed from (3 Ursae Majoris. Course straight, but as if wrinkled in the last half, a Cephei to » Pegasi. Brilliance in first half of flight uniform ; com mencement not seen diameter of dull disc 1'. Inclined Inclined faint tail Inclined Inclined W. C. Nash. D. Walker, M.D. Id. Id. W. H. Wood. Id. A. S. Herschel. Id. Id. Id. A remarkable object resembling in shape an elongated spindle, gradually increased and decreased in size ; the magnitude given refers to its centre. The data not accurate... W. H. Wood. Id. Id. (Communicated toW.H.Wood.) 10 : e tail 15° long Inclined W. H. Wood, 'id. Burst with sparks ; tail Id. not durable. 58 REPORT 1862. Date. Hour. Place of Observation. Apparent Size. Colour. Duration. — Position, or Altitude and Azimuth. 1862. July 19 21 21 21 h m 11 30 p.m. 11 7 p.m. 11 7 p.m. 11 10 p.m. Weston - super - Mare. Ibid. = Jupiter (plane- tary). Blue From /3 Cassiope From Polaris ..» Head of Cepheus Ibid Blue Ibid Ruddy From a Draconia stars H 30 and Ursae Majoris. 27 27 28 28 28 9 50 p.m. 10 22 p.m. 11 1 p.m. 11 8 p.m. 11 12 p.m. 11 17 n.m. Ibid Yellowish white. Blue About 2 or 3 seconds. From y Bootis. .J From a few degre to the east Ursa Minor, passing throu that constel tion, and a)j through Ui Major, disi pearing abc 10° above t horizon. From H 30 and 4 Weston - super - Mare. Ibid Blue Ursae Majorii passed bet we | a and £ Url Majoris. From 6 Draconis; Ibid Head of Cepheui i y Andromedse.,,! 28 Ibid Blue 28jll 43 p.m. 28 11 48 p.m. 28 Midnight... Ibid. Blue 5° below a Pegu! From H 30 and Ursae Major passed bfitwe a and /3 Ur, Majoris. From p to Ur Majoris. From s Cassic Ibid Blue 1 to 2 seconds Ibid Blue 29 29 31 10 a.m. 32 a.m. 10 18 p.m. Ibid Blue Ibid Blue Bluish white .. peiae. Shot from «|] Aquarii towai the zenith a disappeared short distan from a, Cygni. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 59 pearance ; Train, if any, and its Duration. Length of Path. Direction ; noting also ; whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. i throughout 15° 10° 12" 15° 10° 10° 2°... 10° 10° 15° 12° 12° 50° Inclined N. Inclined N. Towards the W. Towards N. ... Towards N. ... Towards N. . . . Towards N. ... Towards N.E. Towards N. Like a gas-light sud denly lit and put out. ] These meteors were V within one second J of each other. A beautiful meteor, like a fiery comet, slowly wending its way ; tail very thick and bright came from the nucleus in curls like steam, until the nucleus was wholly diffused into the tail, which remained one second after. W. H. Wood. Id. Id. Id. Very fine; cloudless .. Id. J. MacDonald. A very fine meteor , W. H. Wood. Id. Id. Id. Id. Id. Id. Id. Id. W. C. Nash. 60 REPORT 1862. Date. Hour. Tlace of Observation. Apparent Size. Colour. Duration. Position, or j Altitude and! Azimuth. I 18G2. July 31 31 Aug. 1 h in 10 34 p.m. 10 53 p.m. 10 10 p.m, Greenwich Ibid. Ibid. 10 48 p.m. Ibid. 10 57 p.m. Ibid. 11 18 p.m. Ibid 10 39 p.m Weston - super Mare. 10 42 p.m. Ibid. 11 45 p.m. Ibid. 11 50 p.m. Ibid. 11 54 p.m. Ibid. Ibid. Ibid. Ibid. Ibid. -- 2nd mag*. = 3rd mag.* = 2nd mag.* = 2nd mag.* = 2nd mag.* = 2nd mag.* = Mars 211 55 p.m 211 58 p.m 3 55 a.m. 3 59 a.m. a u d» a.m. iina 3 13 a.m.ibid 115 a.m. Ibid. 1 19 a.m. 1 22 a.m. 1 24 a.m. Ibid 1 35 a.m.llbid Ibid. Ibid. 1 44 a.m. 3 10 15 p.m. 310 47 p.m. Ibid. Greenwich Weston - super Mare. = 1st mag.* = lst mag.* = lst mag.* = 2nd mag.* = 2nd mag.* = 1st mag.* = lst mag.* = 2nd mag.* = Mars = 3rd mag.* = 1st mag.* = 2nd mag.* = 2nd mag * = Capella = 2nd mag.* = 3rd mag.* : 2nd mag*. Bluish white- Blue Blue Blue Blue Blue Greenish Blue . Yellow Blue Blue , Blue , Blue Blue , Blue Ruddy Blue 1 second 1 second 1 second 1 to 2 seconds Blue 5 second Yellow ,., Blue % second % secoud Blue ^ second I second Blue Blue f second 1 to 2 seconds 1 second 3 seconds. 1 second 1 second 1 second ... I second ... second ... -j second ... 5 second ... J second ... 2^ seconds 1 second Blue £ second From a point I tween « and- Pegasi towai horizon across . Aquarii. From a. Andi medae to £ gasi. From the directi of a Persei 1 wards north I rizon, passing few degrees I low Capella. From the directi of Cassiopei disappeared n« Delphinus. Crossed a Dracoi and disappear in the centre Ursa Major. Started between and « Pega! disappeared ne a. Andromeda?. From y Serpen' to Arcturus. From ? Pegasi.. .J From y Serpentis 1 From 9 Pegasi. Head of Cap] cornus. £ Pegasi I y Serpentis * y Aquarii \ 19 Aquarii t R. A. 20 minutd D.S. 3° toR. 23 hours 20 n mites, D. S. q Pegasi .... Markab .... Markab ...I a. Andromedse ov* Scheat. (36) Ursa; Majoi* to horizon. From « Pegasi '* ■x Aquarii. a. Pegasi ^ A CATALOGUE OP OBSERVATIONS OF LUMINOUS METEORS. 61 learance; Train, if any, and its Duration. Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. 15° to 20° 27 c 11 train 10 25" 20° 15° to 20° 10° 10° 15° 10° 10° 5° 10° \V. C. Nash. Id. Id. Id. Id. Id. Horizontal Towards S. A red thick tail curled W. H. Wood, off from nucleus andi disappeared within the latter. Id. Great numbers left un- Id. recorded between 10 h 42 m and 11" 45 m . Horizontal, westward... Tail endured 2 \ seconds Horizontal, S I Horizontal, S Tail endured 2 seconds. Near -J- Horizontal, southwards. Horizontal, southwards. tail; 2£ seconds .. 5° Northwards 8° U- S In 15° i Perpendicular 13 : 10° Inclined E. Tail brightest in centre, fading at ends. Hazy Id. Id. Id. Id. Id. Id. Id. Id. Id. Id. Id. Id. Id. W. C. Nash. W. H. Wood. 62 REPORT — 1862. Date. 1862 Aug. 3 Hour. h m 10 52 p.m. 10 56 p.m. 10 57 p.m. 11 p.m. 11 11 p.m. 9 43 p.m. 9 54 p.m. 10 37 p.m. Place of Observation. Weston - super Mare. Greenwich Weston - super Mare. Greenwich 11 p.m. 9 5 p.m. 9 5 p.m 10 32 p.m, 9 55 p.m Weston - super Mare. Ibid Ibid. Greenwich Weston - super Mare. Greenwich Weston - super Mare. Apparent Size. = 2nd mag.* : 2nd mag.* = 3rd mag.* ; 1st mag.* = Capella. = lst mag.* :Sirius = 2nd mag.* Greenwich Weston - super Mare. Ibid. 10 45 p.m.] 10 54 p.m. Ibid. 10 54 p.m. Ibid. 11 8 p.m. Ibid. = Sinus = 2nd mag.* = 2nd mag. Colour. = 3rd mag.* Nearly = Venus .. Blue Blue Blue Blue i second 1 second Blue Deep yellow. Capella Blue White | second .. I Bluish white... 1 1 second Duration. Position, or Altitude and Azimuth. •§ second ... 1 to 2 seconds \ second .. 1J second £ second 1 second From (12) (13) ( melopardali. From « Peg! two-thirds of 4 distance to Pegasi. From (12) (1 3) ( melopardali. Moved from a po midway betwe j3 and a Peg towards horizc disappearing near/3 Piscium From (12) (13) ( melopardali. From c Cassiopt to R. A. 50 ill nutes, Dec. ] 83°. From Z Cassiope to y Andromed Vivid blue .. Blue Blue = Sirius White A little less than Bright yellow Mars. = Capella 1.J second 1 second $ second =/3 Ursae Majoris.. 1 second J second White |i second Blue \ second ass ; Shot rapidly front of clouds from rection of Cai peia, across D conis, passin above Ursa Minor. From J Aurigae 66 Aurigae Fell from a po situated near I centre of U Major to a po about 12° hel< From mouth Ursa Major tJ Ursae Majori From a point /3 Andromeda y Pegasi. ris. tn * H 24 Camel dali to /} Majoris. t Cassiopeia '! Polaris. II 5 Cameloparch | to head of Lyi J j3 Cassiopeia? ..ft From Polaris " between /3 an Ursae Minoris A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 63 Ipearance ; Train, if any, and its Duration. me all train le in le Length of Path. 5 Q 11 : 20° 20° tail ; length 12° ; du ation half a second. rt streak 15° ToN.W 25 c 12° 25° tail, 15° ; endured econds. Direction ; noting also ■whether Horizontal, Perpendicular, or Inclined. Nearly horizontal, east ■ward. To N.W. Remarks. Observer. Serpentine; made two deflections. E. to W. Increased from a yellow 2nd mag.*; tail curled off thickly till all consumed. A very stormy night ; observations between clouds; lightning. Clouds in all directions. W. H. Wood. W. C. Nash. W. H. Wood. W. C. Nash. W. H. Wood. Perpendicular Id. Id. W. C. Nash. W. H.Wood. Fine clear night ; moon J. MacDonald. very bright. Bright moonlight W. H. Wood. 3° to zenith Moon very bright. W. C. Nash. August 8th to 13th were cloudy nights at Greenwich. August 8th overcast andjW. H. Wood. wet at Weston-super-j Mare. Bright moonlight night. Id. Suddenly blotted outjld. when most brilliant. | Id. Id. 64 REPORT — 1862. Date. Hour. Place of Observation. 1862. h m Aug. 911 11 p.m 9 10 10 11 17 15 25 10 28 i 12 10 49 1210 50 p.m. a.m. a.m. a.m. p.m. p.m. Apparent Size. Colour. Duration. Weston - super Mare. Ibid. Ibid. Ibid. Ibid. = Capella Bright blue ... 1 second Trafalgar Square, London. Hawkhurst,Kent 1211 9 p.m 18 9 17 18 9 55 Ibid. =S Ursae Majoris. — 3rd mag.* — a Lyrae = Sirius = lst mag.* = « Ursae Majoris. First a, Lyrae, then Capella, then disc = Jupiter. Blue . Blue . « Lyrae. White . White . White . \ second •} second 1 second | second Position, or Altitude and Azimuth. Star-cluster, head of Auriga to N. horizon. Not more than 2 or 3 sees. 1-5 second ... 18 10 7 18 10 31 p.m p.m, p.m p.m Greenwich 1810 42 p.m Ibid. Ibid. Ibid. Ibid. = 1st mag.*. Small = 2nd mag.* = 2nd mag.* Very small White, then 5 seconds red, then dull. Yellowish white. Bright blue.. 1 second 2 seconds. 2 seconds. 3 seconds. I second a. Draconis to body* of Ursa Minor. Head of Lynx to N. horizon. )3 Ursaj Majoris to x Ursse Ma- joris. D Aurigae to £ Au-,| rig*. From 85 to 62 Her- cutis. From ^ (? Uro^l Majoris and « Bootis) to m Bootis. On a line from (3 Bootis to V Ursa; Majoris Began 2° fron the first star | vanished at distance fr< second star=tc y Ursaj Majoris, I short of thi second. From a Lyrae to wards the S.W: horizon. From a Cygni to| wards the W. ii nearly a hori zontal direction. From Corona Boi j realis towards the Great Bear. From the neigh' I bourhood of La I certa, disappear ing about twelv degrees below. From the neigt bourhood of Pi laris towards th northern borizo for about 5°. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 65 Appearance ; Train, if any, and its Duration. None Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. None Observer. A remarkable display W. H. Wood. of Aurora Borealis ; commenced at ll h 10 m ; I therefore I omitted several me- teors of 2nd and 3rd magnitude, from « and » Draconis and (5 and y Ursae Minoris, be- tween ll h 10 m and 11 h 45m w hilst taking notes. ? jeft a slight track Iparkled in appearance rew to = « Lyraej then left red sparks in a ball, which moved less quickly, and expired 4° in the rear; nucleus then became dull with visible disc. ight train , >ne To left ; slightly down, ward. To right ; slightly down ward. Cloudy at h 45 m a.m... Cloudy and conjectural Clear sky Began to give off sparks between Cor. Caroli and 1 Ursae Majoris ; disc travelled in barren state 5° to extinction. Id. Id. Id. Id. T. Crumplen and J. Townseud. A. S. Herschel. Id. J. MacDonald. tht train , Fine night , , Id. Id. Id. Id. 66 REPORT — 1862. Position, or Date. Hour. Place of Observation. Apparent Size. Colour. Duration. Altitude and Azimuth. 1862. Aug.18 h m 11 17 p.m. Bright green... Appeared at a point about 20° above the horizon due S.; passed to a point situated about 10° above the horizon, nearly due E. 19 9 44 p.m. Ibid Bluish white. . Fell from the zenith towards the N. for a distance of 10°. 19 10 32 p.m. Ibid. Blue From a point near Capella to # Au- riga?. 19 10 46 p.m. Ibid. About 0-5 sec. Started near a. An- dromeda?, and passed across /3 Pegasi. 22 30 a.m. Weston - super - Mare. White From j8 Ursa? Ma- joris. 22 9 15 p.m. 2 J- seconds ... From Polaris to- wards the N. ; after moving over a space of 12°, it disappeared behind a range of houses. 22 9 47 p.m. Ibid. Small White From the zenith towards the W. for 5°. 22 10 p.m. From the neigh- bourhood of « Cygni towards the W. for 17°. 22 10 7 p.m. Weston - super - Mare. Bright blue . . . From the mouth of Ursa Major to the fore-foot. 22 10 22 p.m. Bright blue . . . Appeared in the S. at an eleva- tion of 50°, dis- appearing in the S.W. at an ele- vatiou of about 30°. 22 10 36 p.m Ibid. White From a Lyras to- wards the S. for a few degrees. 22 10 43 p.m Weston - super • Mare. White lg second ... From the mouth of Ursa Major to the fore-foot. 22 10 45 p.m Small Appeared in the N. about 10° to the W. of Ursa Major, passed through that con- stellation, disap- pearing about 15° to the E. 4 - A CATALOGUE OF OBSERVATIONS OP LUMINOUS METEORS. 6f Appearance ; Train, if any and its Duration. , Length of Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. j Observer. A. train of brilliant rer sparks, remaining nearh one second after the meteor had disappeared 1 J. MacDonald. Id. W. C. Nash. Id. W. H. Wood. r 10° Train 8° Train 15° to 20 D 3°S.W E. to W. .. Light train of red sparks, which lingered for half a second or more after the body of the meteor had disappeared. 5° Id. W. H. Wood. Brilliant train of red sparks Faint streak 17° Slight train 20° Id. W. H. Wood. J. MacDonald. |> ■ s2 68 REPORT— 1862. Date. Hour. 1862. Aug.22 h m 11 30 p.m Place of Observation. Apparent Size. Weston - super - = Jupiter. Mare. 22 11 32 p.m.ilbid. 23 2 am. Ibid. 23 10 43 p.m. Ibid. 23 23 23 2-1 24 24 25 27 27 11 30 p.m. 11 35 p.m. 11 49 p.m 55 a.ni Ibid. Ibid. Ibid. Ibid. 9 17 p.m 9 45 p.m. 9 23 p.m 9 11 p.m. = Sirius = 2nd mag.* = 1st mag.* = 2nd mag.* = 1st mag.* Colour. Duration. Position, or Altitude and Azimuth. Very bright 2£ seconds ... (4, 2, 6) Lyncis blue. White Blue Bright blue . . Istmag.* 'White \ second Venus +globular... Orange 2 or 3 seconds Greenwich 9 58 p.m. 27|10 19 p.m 2711 17 p.m Ibid. Ibid. Greenwich Park Greenwich Ibid Blue White 1£ second ... P to « Bootis . | second t Ursse Majoris 1 second . 1 second .. 1£ second Small 'Bluish white.. 1 second 3 seconds. = 2nd mag.* ... = 1st mag.* Blue 1 to 2 seconds 28 Ibid. 9 18 p.m. Ibid. = 2nd mag.* = lst mag.* Small = Jupiter.... Blue = 2ndmag.# 1 second 1 second ... 1 second ... ;5| seconds 1 second Halfway between X Draconis and « Ursa? Majoris x Draconis 76 Ursae Majoris, passing over Ursae Majoris. 5 to A Cephei From 35° to 40 altitude; azimuth S.S.W. From the zenith, towards the W. for a distance of 15°. From Polaris to- wards Ursa Ma- jor for about half the distance. Started near i An dromedae, and disappeared I little to the right of y Arietis. From the direction of «■ Coromel Borealis, passedl to the left of Arcturus towards tha horizon. From Polaris to- wards the W. From the zenith towards the E. From the zenith towards the E. for 17°. From * Lyra: to- wards the S. ho- rizon. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 69 Appearance; Train, if any, and its Duration. Length of Path. An adhering short white tail. 20° + Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. Nearly None A beautiful meteor il- luminated the ele- ments ; finished its course behind a piece of detached cumulus cloud. A detonation was heard similar to the explosion of a sky-rocket in mid-air, but strange to say, before its disappear- ance; a detonation was also heard by J. H. Smyth Pigott, Esq., Lord of the Manor. W. H. Wood. None None Long yellowish tail, 4 sees, 3°N... 20° N. 25° N. 20° ... None 15° Light train of blue sparks. Train ram Path horizontal S.S.W. to W. from 20° Illuminated the heavens termination not seen ; threw off red sparks in its course like a rocket. About 15°. fone ight train Hidden for a short period behind clouds. Id. Id. Id. [rl. id. J. MacDonald. Id. W. C. Nash. 17° Id. J. MacDonald. Id. Id. one Id. 70 REPORT 1862. Date. 1862. Auqr.28 Hour. h m 10 47 p.m. 2911 29 p.m. Sept.19 19 19 1!) About 5 40 p.m. 5 45 p.m. 6 5 p.m 9 45 p.m 1!) 9 45 p.m. Place of Observation. Greenwich Ibid. Dorking Delmonden, Hawkhurst. Apparent Size. = 2nd mag.* Very small Saw a most brilliant light. Like a cricket-ball. Worting, Basing- A wonderful light, stoke, Hants. I of the size and form of an egg. Hawkhurst, Kent A large and bright head. Worcester Sudden bright light ; brilliant ball of light. Colour. Blue Bright white... Ked Duration. 1 second 1 second For about £ of a minute. Position, or Altitude and Azimuth. From the neigh bourhood of c Lyrae towards the W. From the neigh- bourhood of Ursa Major towards the N., dis- appearing be- hind a row of houses. The meteor appear- ed to be about 50° from the ho rizon, and nearly W. or S. of W. 2J to 3 seconds From altitude 36°, 5|° S. of W., to altitude 6£°, 37 S. of W. 19 About 10 13 p.m. 19 Gedling, near Exceedingly bright; Colour bright Nottingham (3^ miles E. of| Nottingham). 10 13 p.m Beeston, near Nottingham. so bright as to I obliterate all the stars and Mars (which was very: near to it) ; it gave as much light as the brightest flashes of lightning. Not above half the size of the moon. blue, purple, and crim- son, the train being of the same colours Exceedingly bright ; as light as day ; colour vivid blue and reddish 2 or 3 seconds From 10° W. of! S., altitude 28°, to 50° W. of S altitude 18 c where the meteor disap- peared behind obstacles. Rapid 'In the S.E ,. Slow in move- ment ; du- ration about or under two seconds, and the middle of the train lasting two sees, more after the meteor it- self had vanished. Slow From S.E. by S. to S. by E. When first seen, the meteor was pass- ing near y Pegasij it ended near S Aquarii. From 40° above S.E. by S. bo rizon to about 20° to 25° above S. by E. horizon; the same meteor as above. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 71 Appearance; Train, if any, and its Duration. None Length of Path. Direction; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. Somewhat the appearance of a rocket ; it ap peared to explode, leaving a train of sparks behind it for some seconds. Left no tail ; burst into several pieces. Left a luminous train of blended colours like the rainbow, orange and blue. A track of sparks pursued the head but did not endure. Seemed to burst, and left a trail of sparks which gradually dis- appeared in about a minute. No definition of shape ; a train left in its track the meteor itself sepa rated into balls, but close together. Train in track ; burst into separate balls. J. MacDonald. Id. It proceeded in a north- erly direction [?]. N.E.toS.W. ; consider- ably inclined down- wards. The sun, though nearly setting, was shining brightly ; not a cloud. W. S. Tomlin; ' Evening Standard,' Sept. 23rd. In clear blue sky ; before FrederickReeves, sunset. Proceeded in a south- Cloudless sky westerly direction. In the S.W., from E. to W. Fell rapidly towards the Wind E. or N.E. ; clear earth. ' sky, not a cloud. A cloudless night Communicated by A. S. Her- schel. Correspondent to the ' Standard.' The Rev. S. K. Swann, M.A., F.R.A.S. S. Watson. 72 BEPORT 1862. Date. Hour. 1862. h m Sept.19 10 13 p.m 19 10 13 p.m 19 10 15 p.m 19 19 19 10 15 p.m. 19 10 Place of Observation. Apparent Size. | Euston Square, Amazing meteor London. head = full moon; light = noonday Brentford. Edinburgh (Greenlaw Barracks). Gave more light than the bright est lightning. i Completely lighted up the road. Dullmgham Hill, A brilliant meteor near Hulling-: in the atmo , sphere. Hay (S. Wales). Bristol, Glouces- tershire. 1 5 p.m. Weston - Mare. super 1910 15 p.m. Hawkhurst.Kent Diffused light ; su perior to full moon ; subsided gradually. (Head like the moon, but much bright er j second ob server.) Meteor of unusual size and bril- liance ; shed much light. As large as the moon, but much brighter; noticed by candle-light with closed blinds. Colour. Head ruddy the other extremity and the dif- fused light blue. Duration. 20 seconds Position, or Altitude and Azimuth. The extremity decided blue. Bright light of a bluish cast. Diffused light, had a yel- lowish cast. Formed an endur- ing cloud of sparks overhead; If. A. 22 h 30 ra . The streak passed d, e, % Ct- phei to R. A. 17 h 50 m . Both at declination 48° 20' N. ; main head proceeded N.W. by N. fragment S.E. Traversed a direc- tion slightly S.W. 20 sees, from first flash to explosion. Nearly S.E. Slanting down- wards from E. to \V. 2 or 3 seconds duration of brightness, Bodyrich blue at explosion showed red and blue colour. 3 seconds. 2 to 3 seconds (Appeared to a scend, turn over to the right under « and /3 Arietis, and de. scend almost vertically ; second ob- server.) Streak passed at brightest part between a. and y Ceti. In the north-east era sky it ex- ploded a few degrees above the horizon. From due E. altl tude28°;toN.E altitude 20°. Would have met the horizon 15° fur ther on its path, at66°W.fromN A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 73 >pearance ; Train, if any, and its Duration. Ircular ; appeared to I separate overhead ; the (northern head red, I emitting prismatic (sparks, and leaving a (streak of 45° visible i'sleven minutes at place of bursting. Other ex- I'.remity, or fragment, blue; disappeared gra- dually. I >bular, then rapidly pgg-shaped ; then elon- gating itself and gradu illy disappearing from Liew. Track ribbon- like, yellow overhead, I he rest blue ; endured iome minutes, seedingly beautiful neteor, presenting a uddeu and bright ight. endid meteor, rushing trough the air, and it last bursting verti- ally downwards into nany pieces the size I >f two-shilling pieces. Ibright streak seen on jurning round; glowing Intensely at the lowest jiart ; fading quickly ; a ! mall cloud of sparks (emained at last, near ICeti. Iried in its track a line i f ruby-coloured fire ; : exploded. Length of Path. nerous prismatic . larks and a yellow lil accompanied the ieteor; the latter re- mined visible two linutes. stream of fire moving63 c •rward ; no explosion ; isappeared gradually. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Vertical from overhead. A little inclined to ver tical ; downwards to- wards the right. Tail broken at intervals, zigzag. Patch over head circular ; 1° dia- meter ; visible 1 1 minutes ; not resolved by power 120 with an aperture of 10in., 20 ft focal length refractor, which resolves the cluster of Hercules freely. First seen directly over- head. Observer. It appeared one hundred T. Slater; T Crumplen ; J Townsend. S. Richards, Jun yards burst. high when it W.L.B.Coulson Writer in the ' Cambridge Chronicle.' Rev. T. W.Webb. Inclined 70° to the ho- rizon; downwards to left. Paragraph in the ' Bristol Mer- cury.' P. S Hamlyn. Communicated by W.H.Wood, Path appeared linear. recti- Communicated by A. S. Her- schel. 74 REPORT — 1862. Date. 1862. Sept.19 Hour. h m 10 15 p.m. 19 About 10 20 p.m. 19 10 30 p.m. Place of Observation. Wellington, So- merset. Ipswich Norwich .9 About 10 30 Thetford p.m. 19 19 19 1!) 19 19 London Wall, London. Apparent Size. Colour. Duration. = 4 times 11, or 10| Body and train times Sirius. blue Illuminated eve object. Yellow , Lighted up the: Most brilliant town like the, colours, noonday sun. Entirely lighted up the road. West End, Lon- Diffused light; Diffused light, dou. Torquay (the Pier). Nottingham. London Enfield Highway London. brighter than full moon. a line blue. Diffusedlight, equal Diffused light to noonday. Lasted several seconds. Disappeared in a few seconds, leaving all as dark as before. Flash 1 sec. ; seen in mo- tion 1 sec. Position, or Altitude and Azimuth. From 'C Persei to Auritrae. 0' From S. the W. towarc Rectilinear in rection ; mo? N. A few degrees I of the zeuith. 1 of a violet lour. pale co- From 9° N. ofl altitude 23° ; t 27° N. of ' altitude 20°. Streak remaine . parallel to tt Ecliptic, from Aquarii to r Pi cium. In a line, butvei few degrees of the zenitl, An explosic must ha' taken plac but slightly r moved from tl zenith. „ A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 75 pearance ; Train, if any, Length of and its Duration. Path. Direction ; noting also whether Horizontal, Perpendicular, or Inclined. Remarks. Observer. e a sudden discharge f fireworks. The ame burst suddenly, I hrowing out brilliant (parks like a rocket; he long tail of white light endured two or jhree seconds and then I radually faded away. } trail was like a locket's ; its light a i right yellow, and •.hen it burst, a mul | tude of sparks ap i eared to fall from the lody. I meteor presented an xtraordinary blaze of ght, likened to a long ibe of fireworks ghted at both ends, ich of which in turn roke into smaller Darks. liant stream of fire fce rocket-tail ; left a niinous track visible iany seconds, jk of fire remained like ail of a rocket, show- g that a meteor had issed overhead. Descended towards N.W. or N.E. No report heard W. A. Sanford. Paragraph in the ' Ipswich Ex- press.' ak remained . (25°) n preserved an illumi- iting power for nearly minute, and then faded adually away. tiense streak appeared the sky. Bright ' tie violet at west end, J it changing through I d to vermilion and ' rniine in the rest of i e path, until lost in . e sky. Flight longer than the Northern stars. Mean direction from N to S. W. to E. ; perfectly ho- rizontal from Milky Way to the planet Mars. An explosion was heard Correspondent to at Norwich like that! the ' Norwich of a rocket in the air No such meteor seen in London for ten years before. Mercury.' Writer in ' Norwich Mercury.' the An observer considered it to be an unusual flash of lightning, as bricks could be counted on a wall sixty yards distant. Correspondent to the ' Times.' Writer in ' Times.' the Dr. E. Burder. James Edmunds. Ellis Hall. 76 KEPOKT 1862. Date. 1862. Sept.24 25 25 25 25 25 25 Hour. h ra 8 15 p.m. Place of Observation. Broadstairs,Kent 6 15 p.m. Weston Mare. 6 15 p.m 6 15 p.m 6 30 p.m 6 30 p.m. 6 35 p.m, super Ticehurst, Sussex Apparent Size. Colour. Duration. Position, or Altitude and Azimuth. Venus at its bright- Blue est, or somewhat brighter. : 2 seconds. Much larger than Red Venus ; very splendid meteor. 5 to 8 seconds As large as cricket-ball. Lamberhurst, Large and bright. Sussex. Weston - super Mare. Stonyhurst Oxford Larger than Venus = Sirius Green nucleus within a red envelope. White, with blue tint. 2 or 3 seconds 3 seconds. Nearly 10 sees Entered the Milk] Way from thl left, and disap peared a littl below a. Aquilaj. Appeared due E.l altitude 26° disappeared S.] altitude 18°. From altitude 45' to altitude 15° a little S. the point sunset. Appeared 60° from S., tude 40 ; disap i peared due W. , altitude 20°. From 15° N.E'I of the zenitl to altitude 40' S.W. Inclined at ai, angle of 50° t< ( the horizon disappeared at . height of 10° o 11° above th< horizon. o o W altil I. Meteor, 1861, July 16th, 10 h 15 ra p.m. G.M.T. By Mrs. E. Addison, of Gainsford, Durham, this meteor was first seen 2'.)° from the horizon, in the direction of the towns Dunkirk or Ostend, upon the Greenwich latitude. Mr. J. Howe, of Greenwich, observed the meteor to pass within 8° or 9° of his zenith, as may be inferred from the position of a Lyrae at the time of the meteor's appearance ; but this is at variance with the ac- counts of Mr. Charles Beed at Westminster, and Mrs. Davies at South- borough, who describe the meteor in the E. as far from vertical. If we assume the meteor to have passed over Duukirk at an altitude of 30°, as seen from Gainsford, its height was here 172 miles above the French coast, The obstruction of houses on the west side of Whitehall in Mr. Charles Eeed's account, shows the meteor to have disappeared nearly due N. from London, at an altitude of 10°, pointed out by Mr. Howe at Greeny ich. At Gainsford, A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 77 pearance ; Train, if any, and its Duration. slight tail of red sparks pursued the head. magnificent meteor nucleus surrounded by a halo, and attended by a short train of sparks ; disappeared without sparks, sappeared in the open sky ; globular ; no sparks ; enveloped in a faint light. tail or sparks. sappeared gradually without sparks. illiant, although the twilight was sufficient o read by. first part of its lescent the tail length med, but just before ts disappearance, col- apsed and gathered tself into the nucleus, endering that much arger and brighter. Length of Path. 20° 7° or 8° Direction ; noting also whether Horizontal, Perpendicular, or Inclined. ■Vt right angles to the Milky Way. Vertically down Inclined downwards from left to right. E. to W. N.N.E. to S.S.W. downwards. fell Remarks. The sun had not quite gone down at the appearance of this meteor. a. Lyras appeared 30° from its point of commencement. Observer. I was prevented from observing the be- ginning of its path by a projecting building near the window at which 1 was sitting. K. E. Rufenacht. Communicated by W.H.Wood, Rev. F. Howlett. H. Moreland. Communicated by W. H. Wood, J. Moore. H. S. C, Corre- spondent to the ' Stand- ard.' the same point of the path had altitude 20° in due ISCE. The latter lines of sight approach within eleven miles of each other, eighty-eight miles due E. of Newcastle, and forty-four miles above the sea. It is probable, from the account of Mrs. Davies, that the meteor first appeared somewhat S. of the latitude of Dunkirk, and that the entire path of 395 or 400 miles was per- formed in not less than ten to twelve seconds of time. II. Meteor, 1861, July 16th, IP 32 m p.m. G.M.T. A similar comparison of the catalogued accounts of this meteor assigns its path with somewhat greater certainty at 300 miles of length, from 195 miles over North Foreland to sixty-five miles above the sea, sixty miles S. of Ply- mouth. The meteor passed the Isle of Wight at a height of 150 miles ; and here a durable tail first began to be developed from the nucleus. The dura- tion of the flight was five to six seconds, at the largest estimation. 78 REPORT 1862. Meteor, 1861, August 6th, ll h 21 m p.m. G.M.T. The accounts of Mr. Joseph Baxendell at Manchester, and Messrs. T. Crumplen and J. Townsend at London, determine the centre of this meteor at eighty miles above a point halfway between Leicester and Birmingham ; and, assuming its course to have been direct upon Manchester, a path of 176 miles in five seconds is inferred, from 126 miles above Winchester to twenty- one miles above the northern point of Staffordshire. ±i, JULU, Time. Appearance. A. B. C. D. E. h m 1861. Aug. 8, 10 31| p.m. G.M.T. „ „ 8, 10 34 „ „ „ 10, 10 27 „ „ 10, 10 50| „ „ 11, 10 20 „ A second-magnitude star. A flash ; first-magnitude. Fine tailed shooting-star ; first-magni- tude star. Third-magnitude star. Bright white-tailed shooting-star, and equal to Venus. Place of Centre. Direction of Flight. A. B. C. D. E. 67 miles over Sandhurst (Kent). 50 miles over Bury St. Edmunds. 20 miles E. of N. Foreland; 47 miles over the sea. 70 miles over Leatherhead. 70 miles E. of Ipswich ; 32 miles above the sea. From alt. 46°, 3° N. of E. Nearly vertical ; down. From alt. 38°, 48° N. ofE. From alt. 54°, 20° N. of E. From alt. 42°, 70° N. of E. Length of Flight. Velocity of Flight. A. B. C. D. E. 20 miles (approx.). 6 miles. 35 miles (approx.). 20 miles (approx.). 36 miles. 30 miles a second (approx.). 30 miles a second (approx.). 30 miles a second (approx.). 27 miles a second. Brilliance. A. B. C. D. E. At 352 yards would have shown like full moon. At 398 yards „ „ „ At 692 yards At 274 yards „ „ „ At 1484 yards Meteor, 1861, November 12th, 5 h 49 m p.m. The accounts of Mr. L. and Mr. W. Penn at Oxwich and the earliest appearance of this meteor at 90 to 100 miles borough_ or Cambridge. Its approach to the zenith, both at - Bristol, indicates a passage between the latter stations ; and the remaining accounts will be found to be satisfied with considerable accuracy by a eom-se of sixty miles above Lundy island, terminated with a slight dip towards the sea, Stone, place over Peter- Hay and at A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 79 and explosion twenty miles above it, upon the meridian of Land's End. The flight of 360 miles appears to have occupied seven or eight seconds of time. Meteor, 1861, November 15th, 10 h 14 m p.m. The meteor described by Mr. Nash at Greenwich, and Mr. Herschel at Shooter's Hill, although identical, do not admit of useful comparison with one another, nor with that observed by Mr. Greg at Styall, near Manchester, — the base-line in the former case being too small for such a purpose, and the third meteor being apparently distinct from the former two. Meteor, 1861, November 19th, 9 h 38 ffl 30 s p.m. The Ipswich and Norwich accounts place the audible explosion of this bril- liant meteor at no great height between the two towns ; thirty miles of height must be allowed to it for the altitude as seen from Exeter, although such a height is at variance with the view obtained from Greenwich and North Fore- Iand. It is not impossible that explosion, audible at Norwich and Ipswich, and perhaps also at North Foreland, may have depressed the last portion of the flight, for this was hidden from view at Exeter. The near verticality at North Foreland, the passage over the moon (whose altitude was 3S° E. by S.) in the eastern parts of Kent, and the low southern position of the nucleus as first perceived by Messrs. Hill at Woodford, Mitchell and Harmer at Tun- bridge, and James Rock, jim. at Guestling, show this meteor to have taken a nearly meridian and nearly horizontal course. A flight of 260 miles in 10 or 12 seconds, from fifty-five miles above Paris to thirty miles above Beceles (between Suffolk and Norfolk), is found to satisfy the whole of the accounts with considerable accuracy. Meteors, 1861, November 24th, 8 h m p.m. The resemblance of these meteors is casual, — the lines of sight of com- mencement lying widely upon opposite sides of the base-line between the stations, while those of termination approach no nearer than twenty-six miles upon the southern side of the base-line. Meteors, 1861, December 1st, 9 h 15 m p.m. The resemblance of these meteors is not borne out by the uranographical positions assigned to them at the two distant stations, — the point of com- mencement having little or no parallax with considerable deviation of the lines of sight, while the lines of sight of termination lie upon opposite sides of the base-line. Meteor, 1861, December 8th, 8 h 16 m p.m. At Dungannon in Ireland this meteor appeared to fall vertically, while at Wakefield (Yorkshire) it passed overhead. The observation of Dr. Walker at Birkenhead (Seacombe), assigns Strangford, on the Irish coast, as the spot between these two towns where the body would have struck the earth. By Mr. Bedford's account, from Silloth near Carlisle, the height at disappearance is found to be fifty miles above the sea, halfway from Lancaster to the Isle of Man ; the height above Wakefield eighty-five miles, and at Hull 110 to 115 miles. Modified by the remaining accounts, a course of 160 miles from 110 miles above Hull to forty-five miles above the Irish Sea, twenty miles E. of Douglas Town, performed in six or eight seconds of time, appears to be a near approximation to the truth. It is possible that an explosion loudly heard at Lancaster and Southport, but not heard at Douglas, may have caused the deflection by which the meteor in the latter portion of its flight appeared sta- 80 REPORT— 1862. tionary at Castletown some seconds. On the 3rd of the same month, a similar detonating meteor appeared in Germany, bursting sixty miles over Dessan, and directed almost from the Pole (see the Calculation of Professor Heis). Mr. Greg at this time observed the radiant point of shootiug-stars to lie between Gemini and Auriga. On the 24th of December it was in Taurus. Meteors, 1861, December 9th, 5 h 30 m p.ar. The resemblance is casual. The uranographical position at Hawkhurst places this meteor at a great height towards Edinburgh, upon the latitude of Glasgow. Shooting-star (F), 1862, January 28th, ll b 4 m p.m. The base-line of forty miles between the stations of London and Stone affords a good determination of this shooting-star. The lines of sight for the commencement are only three miles apart at their nearest approach, namely, at 44| miles above Melton Mowbray in Leicestershire, while those of termi- nation are only 2\ miles asunder at 47| miles above Macclesfield in Cheshire. The horizontal flight of sixty miles was performed in 11 to li second, by careful estimation at the time of the observation. Direction from 32° S. of E. At 880 yards it would have equalled the full moon. Meteor, 1862, February 2nd, 8 h 20 m p.m. The astronomical accounts of Mr. E. J. Lowe and Mr. Alcock at Beeston Observatory and Newark, together with similar details from Tarporley in Cheshire, appear to fix the disappearance of this meteor with precision at fourteen or fifteen miles above Cheadle, on the borders of Derbyshire, where the meteor arrived after a flight in the air of 236 miles from 190 miles above Lyme Regis, occupying six seconds of time and directed to earth in the valley of the Dove, or at the foot of the Peak of Derbyshire. The point of first ap- pearance in Orion or the Pleiades, as seen at Liverpool and Tarporley, places this meteor among the few whose true courses are observed to lie from "W". to E. of the meridian. Meteor, 1802, February 23rd, 9 h 25 ra p.ir. This meteor, which passed nearly over Liverpool towards S.W., appeared to Mr. W. H. Wood, at Weston-super-Mare, to move 30° horizontally in the N. at 20° from the horizon. It appears to have sought the earth at Pembroke, and had its flight from forty miles above Stockport, near Manchester, to twenty miles above Aberystwith, in Wales. The following comparison of the brightness of these meteors is offered as leading to an estimation of their probable dimensions. The photometric tables of the light of certain stars compared with that of the full moon, published by Sir John Herschel, enable us to compare the light of ordinary shooting-stars with a standard generally familiar ; and the same may be done when fireballs are compared in their illuminating power to dif- ferent phases of the moon ; but the class of meteors intermediate between these in the scale of brilliancy are usually compared with the planets of whose light at different phases no tables arc prepared. Among the preceding known meteors, one only of the latter class (shooting-star e) is found. The follow- ing deductions aim at no greater accuracy than is commensurate to the cha- racter of the observations themselves. (A) I. Meteor, 1861, July 16th, 10 h 15 ra p.m. : shone apparently as half of a moon two days old, at Furness, 150 miles from the meteor's termination. At 25^ miles it ivould have equalled the full moon. i A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 81 (B) II. Meteor, 1861, July 16th : shone as one-fourth of moon two days old, at Flimwell, distant 220 miles from bursting. At 37^ miles it would have equalled full moon. (C) Meteor, 1861, August 6th, ll h 21 m p.m. : shone one-tenth of moon two days old, at London, 150 miles from brightest point. At eight miles it would have equalled full moon. Shooting-stars, August 8th, 10th, 11th, would have equalled full moon at distance of 352, 398, 692, 274, 1484 yards. (D) Meteor, 1861, November 12th, 5 U 49 m p.m. : lighted the turnpike-road at Hay fully as much as the moon itself shining upon it, and ten days old. Meteor overhead, seventy-five miles from Hay. At sixty-three miles it would have equalled full moon. (E) Meteor, 1861, November 19th, 9 h 38 m p.m. : threw shadows half as deep as the moon, then full, at Tunbridge, seventy-seven miles from the first burst of light. At fifty -four miles it woidd have equalled full moon. (F) Meteor, 1861, December 8th, 8 h 16 m p.m. : exceeded the light of the moon then shining clear and six days old, at Hull, 130 miles from the flash over Walney Isle. At eighty-eight miles it would have equalled full moon. (G) Meteor, 1862, February 2nd, 8 h 20 m p.m. : shone as brightly as the moon unclouded and ten days old, at Beeston, forty miles from the explosion. At thirty miles it would have equalled full moon. (H) Meteor, 1862, February 23rd, 9 h 25 m p.m. : threw a bright light from the sky which filled the streets at Liverpool and Bromborough, distance forty miles ; perhaps equal to a moon four days old. At 16£ miles it would have eqiudled fidl moon. Assuming an ordinary flame of street gas to measure a cubic inch of in- candescent matter, and at 15 yards to throw a light equal to the direct light of full moon, we have 13,690 gas flames at a mile equivalent to full moon ; and the following are the globes of burning coal-gas which would shed the light produced by the separate meteors and shooting-stars of the foregoing list. Meteors. I. July 16. II. Julyl6. Aug. 6. Nov. 12. Nov. 19. Dec. 8. Feb. 2. Feb. 23. Diameters "| of burning \ globes. J ft. in. 21 8 ft. 28 ft. 10 ft. in. 39 6 ft. in. 35 9 ft. in. 49 5 ft. 24 ft. in. 14 3 Shooting-stars. A. B. C. D. E. F. Diameters of"| incandescent > globes. J in. 10-2 in. Ill in. 16-1 in. 87 in. 267 in. 14-0 It is possible that these results afford a juster idea of the real sizes of the luminous bodies than those derived from angular measurements of their ap- parent discs. [For Errata of the Catalogue, &c, see Appendix I. at the end of the Reports in this volume.] 1862, e 82 report— 1862. On the Strains in the Interior of Beams. By George Biddell Airy, F.R.S., Astronomer Royal. [A communication ordered to be printed among the Eeports.] The author states that he had long desired to possess a theory which should enable hira to compute numerically the strains on every point in the interior of a beam or girder, but that no memoir or treatises had given him the least assistance*. He had therefore constructed a theory which solved completely the problems for which he wanted it, and which appears to admit of applica- tion at least to all ordinary cases. The theory contemplates forees acting in one plane. A beam therefore is considered as a lamina in a vertical plane, the same considerations applying to every vertical lamina of which a beam may be conceived to be composed. The author remarks that it is unnecessary to recognize every possible strain in a beam. Metallic masses are usually in a state of strain, from circum- stances occurring in their formation ; but such strains are not the subject of the present investigation, which is intended to ascertain only those strains which are created by the weight of the beam and its loads. The algebraical interpretation of this remark is, that it is not necessary to retain general solutions of the equations which will result from the investigation, but only such solutions as will satisfy the equations. After defining the unit of force as the weight of a square unit of the lamina, and the measure of compression-thrust or extension-pull as the length of the ribbon of lamina, whose breadth is the length of the line which is subject to the transverse action of the compression or tension, and whose weight is equal to that compression or tension, the author considers the effect of tension, &c. estimated in a direction inclined to the real direction of the tension, and shows that it is proportional to the square of the cosine of inclination. He then considers the effect of compounding any number of strains of compression or tension which may act simultaneously on the same part of a lamina, and shows that their compound effect may in every case be replaced by the com- pound effect of two forces at right angles to each other, the two forces being both compressions or both tensions, or one compression and one tension. Succeeding investigations are therefore limited to two such forces. Proceeding then to the general theory of beams, it is remarked that if a curve be imagined, dividing a beam into any two parts, the further part of the beam (as estimated from the origin of coordinates) may be considered to be sustained by the forces which act i:i various directions across that curve, taken in combination with the weight of the further part of the beam, tho load upon that part, the reaction of supports, &c. Expressing the forces in conformity with the principles already explained, and supposing that there is one compression-force B making an angle /3 with y (in the direction of y diminishing for increase of x), and another compression-force C making an angle 90° -f fl with y, it is easily seen that the element Ss of the curve, sup- posed to make the angle with y, sustains the forces In.r, B.&sx sin(/3 + 0)x sin/3 + C.Ssx sin(/3 + 9O° + 0)x sin(/3 + 90°). Iny, -B.hx sin 03 + 0) x cos/3-C. tsx sin (/3 + 9O°+0)x cos(/3+90°). The weight of lamina bounded by y and y + Sy, and estimated as acting * Subsequently to the communication of this Report, the author learned that one in- stance (the second) of those given here had been treated by Professor Eankine, by methods peculiar to that instance. ON THE STRAINS IN THE INTERIOR OF BEAMS. 83 upwards, is —yfa\ And the reaction K of a support may act upwards at distance h. Expanding the sines and cosines, putting Sx for sin d . $s, and Sy for cos . Is ; putting also L=B.sin 2 /34-C.cos 2 /3, M=(B— C) . sin /3 . cos j3, Q=— B.cos 2 /3-C.sin 2 /3, 0=3,-0, dx and forming the equations of equilibrium in the usual way, they will be found to be— Equation for forces in x, fclx . (Lp + M)=0. Equation for forces in y, JclxQilLp+Q)— B,=0. Equation of momenta, fdx(Lyp + M.y + M.xp + Ox) — RA = 0. Now these equations, applying to any curve, will apply to any two curves very close together ; and therefore their variation, taken by the rules of the Calculus of Variations, will be 0. The proper equation (in the usual nota- tion) is N— *■ ^ =0. Applying this, the results are dM ^_r\ dy dx rfO_^M =Q dy dx From this it follows that (omitting some arbitrary functions which represent original strains in the formation of the beam) L, M, 0, are partial differential coefficients of the same function of x and y, which we may call F : so that T d*F , r d 2 F n d 2 F L=_ , M=— -, 0=—. dy z dxdy dx Substituting these, the equations become Considerations, of a somewhat detailed character, depending partly on the relation assumed to exist between tension-force and material extension, are necessary to show the form which must be assumed for F in the various cases to be examined. The conditions to be secured are— that the horizontal part of the thrust, &c. shall be the same as that given by ordinary theories, on the relation just mentioned ; and that the equations above shall be satisfied. After due application of these in the following five cases, these forms are found for F. Case 1. A beam of length r and depth s projecting from a wall ; Case 2. A beam of length 2r and depth s supported at both ends ; *4-«-*->-(¥Hf)- g2 84 REPORT 1862. Case 3. A beam like the last, carrying a weight W at the distance a from one end. In this case the function is discontinuous ; its forms are — Fr» m *-«. to ,=2,-, *=« . { ?5? + (*-Wi)*-*> } . (t-^) . (Of this case, two instances are given in the curves below.) Case 4. A beam like that in Case 2, with a straining momentum applied at each end, as in the middle tubes of the Britannia Bridge ; F= 6x 2 — I2rx + 3r 2 Case 5. A beam like that in Case 2, with a straining momentum applied at one end only, as in the exterior tubes of the Britannia Bridge ; F=- (6#— 12r >H) (H)- By forming the differential coefficients of F symbolically, L, M, and Q, (=2/ — 0) are obtained in a form which admits of numerical calculation for every value of x and y. And from these, B, C, and /3 are computed without difficulty. In this way the values of B, C, and /3 have been found for every combi- nation of the values x=r x 0*1, x=rxO-2, x=rx0-'3, &c, with the values y=sxO'l, y=sx 0-2, y=sx0-3, &c. In Case 1, 121 points were thus treated : in each of the other cases the computations were made for 231 points. In the following diagrams are given the curves representing the directions of pressure and tension through the beam, together with a few numerical values at the most critical points, for each of the cases to which allusion has been made. Curves representing the strains in beams, under different circumstances. The continuous curves indicate the direction of thrust or compression ; the interrupted curves or chain hues indicate the direction of pull or tension. The figures denote the measure of the strain ; the sign + meaning compres- sion, and — meaning tension. The unit of strain is the weight of ma- terial lamina whose length = depth of beam. No. 1. Beam projecting from a wall ON THE STRAINS IN THE INTERIOR OF BEAMS. 85 8G REPORT — 1862. (3 o o o a p* id o o H O (5 + c5 O "^3 pa ° '3 4 o s is s Ci_i "^w o © 08 .3 a o o ,0 ^3 o o 2 o CD d ? f n a) + I I ON THE THREE REPORTS OF THE LIVERPOOL COMPASS COMMITTEE. 87 Report on the three Reports of the Liverpool Compass Committee and other recent Publications on the same subject. By Archibald Smith, M.A., F.R.S., and Frederick John Evans, R.N., F.R.S. The task which, we have undertaken, at the request of the British Asso- ciation, is in some degree lightened by the publication, since the last meeting, of the ' Admiralty Manual for ascertaining and applying the De- viations of the Compass,' a work which has been compiled under our joint editorship, and published by the direction of the Lords Commissioners of the Admiralty. The publication of this work allows us to treat as known, various methods and formulae which had not previously been published, and to which it will be necessary to refer in the sequel. It, however, makes it necessary that we should give some account of our own work, and this we think it will be most convenient that we should do at the outset. The ' Manual ' is divided into four parts. Part I. contains the well- known " Practical Bules " published by the Admiralty, drawn up originally, in 1842, by a committee consisting of the late Admirals Sir F. Beaufort and Sir J. C. Boss, Captain Johnson, B.N., Mr. Christie, and General Sabine. These rules were, and still are, purely practical, — the object being to enable the seaman, by the process of swinging his ship, to obtain a table of the deviations of his compass on each point, and then to apply the tabular corrections to the courses steered. Part II. is a description of the valuable graphic method known as " Napier's method," in which the deviations of the compass are represented by the ordinates of a curve, of which the " courses " or azimuths of the ship's head which correspond to the deviations are the abscissae. These azimuths may be measured either from the " correct magnetic north," in which case they are called the " correct magnetic courses," or from the direction of the disturbed needle, in which case they are called " compass courses ;" and we should in general obtain one curve if the abscissae represent one set of courses, and a different curve if the abscissae represent the other set. It was, we bebleve, first observed by Mr. J. B. Napier that, by drawing the two sets of ordinates in proper directions, each may be made to give the same identical curve, and, conversely, that the same curve may be made to give the devi- ations as well on the correct magnetic courses as on the compass courses, with the additional advantage that the one set of courses may be at once derived from the other by going from the axis of abscissae to the curve, in a direction parallel to one of the sets of ordinates, and returning to the axis of abscissae in a direction parallel to the other. The original direction of each set of ordinates is arbitrary, the scale, however, depending on those directions. By drawing the ordinates at angles of 60° and 120° from the axis of abscissae, we have the advantage that the scale along each axis of ordinates and also along the axis of abscissae is the same ; and these directions are in general the most convenient, although in particular cases, as when the deviations are very small, it is convenient to take a larger scale for the ordi- nates than for the abscissae. The practical advantages of the method are very great. It enables the navigator, from observations of deviations made on any number of courses, whether equidistant or not, to construct a curve in which the errors of observation are, as far as possible, mutually compen- sated, and which gives him the deviation as well on the compass courses as on the correct magnetic courses. Various modifications of this method have been proposed, of which one by Capt. A. P. Byder, B.N., deserves particular mention from the facility with which it may be used by those to whom the 88 report — 1862. method is unfamiliar ; but for general use there seems to be no form supe- rior to the usual form of Napier's diagram. Part III. contains the practical application to this subject of mathematical fornmla? derived from the fundamental equations deduced by Poisson from Coulomb's theory of magnetism. This part was published separately in the year 1851, and afterwards as a Supplement to the " Practical Rules " in 1855. At that time it was considered sufficient to use approximate formulae, going as far only as terms involving the first powers of the coefficients of deviation. The very large deviations found in iron-plated ships of war rendering it desirable to use in certain cases the exact instead of the approximate formulae, this part has been re-written. It may be desirable to give here some account of these formulae. Poisson's equations are derived from the hypothesis that the magnetism of the ship, except so far as it is permanent, is transient induced magnetism, the intensity of which is proportional to the intensity of the inducing force, and that the length of the compass-needle is infinitesimal compared to the distance of the nearest iron. On this hypothesis the deviation of the compass is represented exactly by one or other of the following formulae : — sin S=a cos 3+J3 sin ? + £ cos f + B sin (2£' + 3) + G cos (2p+8) . . (1) g+33 sin Z+£ cos f+B sin 2 f +<£ cos 2£ , g > tan S- 1 + 33 CQS £_ c gin £ + jg cos 2 £_<£ gin 2 £ in which <5 represents the deviation, £ the " correct magnetic course," £' the " compass course ;" &, 20, <£ are coefficients depending solely on the soft iron of the ship ; $} and C coefficients each consisting of two parts, one part a co- efficient depending on the soft iron and multiplied by the tangent of the dip, the other part a coefficient depending on the hard iron and multiplied by the reciprocal of the earth's horizontal force at the place, and by a factor, -, A generally a little greater than unity, and depending on the soft iron. In these equations the sign + indicates an easterly, —a westerly deviation of the north point of the compass. If the coefficients are so small that their squares and products may be neglected, the first equation may be put under the form 3=A+B sin t' + C cos £' + D sin 2£'+E cos 2£' (3) in which it will be observed that the coefficients are now expressed in arc, the Eoman letters being nearly the arcs of which the German letters are the sines. When the deviations do not exceed 20°, this equation is sufficiently exact. As the subject with which we are now dealing cannot be understood or followed without distinctly apprehending the meaning of the several parts of this expression, we do not apologise for pausing to explain them. The term A is what is called the " constant part of the deviation." A real value of A can only be caused by soft iron unsymmetrically arranged with reference to the compass. It will easily be seen that such an arrangement of horizontal soft iron rods, such as that in figure 1, Fig. 1. O would give ajwsitive value of A, and no other term in the deviation. ON THE THREE REPORTS OF THE LIVERPOOL COMPASS COMMITTEE. 89 A soft iron rod, such as that in. figure 2, O Kg. 2. O would give + A to the starboard compass, combined, however, with +E ; and — A, combined with — E, to the port compass. The last arrangement is one sometimes found in the relative positions of the horizontal iron spindle of the wheel and the binnacle compasses placed near it. In compasses placed in the midship bine of the ship, such unsymmetrical arrangements of soft iron can seldom have any sensible operation. In such cases A is always small ; and when it has a sensible value, it seems more likely to arise from index error of the compass, or from error of observation, and may probably be best dealt with as such, and disregarded in the table of deviations. Tbe terms B sin £' + C cos £' make up together what is called the " semi- circular deviation." This is the part of the deviation which it is most difficult to deal with, as well from each coefficient being made up of the two parts which we have described, which cannot be distinguished by observa- tions made in one latitude, as from that part of the ship's magnetism, which we have treated as permanent, being in fact only subpermanent. To this we shall have occasion to revert in the sequel. At present we will only point out that + B indicates an attraction of the north point of the compass to the ship's head, — B to the stem, +'C an attraction of the north point to the star- board side, — C to the port side. The terms D sin 2£' + E cos 2£' make up what is called the "quadrantal" deviation. This can only be caused by horizontal induction in soft iron. E can only be caused by horizontal induction in soft iron unsymrnetrically distributed, and is therefore, except in such cases as those represented in fig. 2, very small. +D may be caused by the following arrangements of sym- metrically arranged soft iron, in which the ship's head is supposed to be directed towards the top or bottom of the page. — D may be caused by the same arrangements, the ship's head being now supposed to be directed to the right or left of the page. n:i. N°2. Fig. 3. N°3. N54, n:5. Between these various arrangements there is this most important dif- ference, that in No. 1 and No. 4 the directive force of the needle would be increased, while in No. 2 and No. 5 it would be diminished. 90 REPORT— 1862. might be either increased, or diminished, or left unaltered, according as the effect of the longitudinal and the transverse iron preponderated. "We may, therefore, by observing the effect on the directive force, as well as on the quadrantal deviation, ascertain how much of the latter is caused by fore-and- aft iron, how much by transverse iron. This explanation of the coefficients will probably be sufficient for the purposes of this Report, and we now revert to Part III. of the ' Manual.' The principal object of this part is to find the means of computing A, B, C, D, E, from the deviations observed or derived by Napier's curve for a certain number (8, 16, or 32) equidistant points. This is easily done by formulae founded on the method of least squares ; and the method is made of ready application by tabular forms and tables given in this part. The direct computation of the exact coefficients &, 33, C, 13, <B by the method of least squares would be a matter of very great labour ; but they are easily derived to terms of the 3rd order inclusive from the approximate coefficients A, B, C, D, E by formulae which are given for the first time in this part. There are two other coefficients, the knowledge of which is of great importance, but which can only be derived from observations of force, viz. X, or the ratio of the mean force to north at the place of the compass to the earth's horizontal force, and fi, the ratio of the mean vertical force at the same place to the earth's vertical force. One of the most important errors in the modern iron-built and iron- plated vessels is the heeling error. The deviations obtained by the usual pro- cess of swinging are for a vessel on an even keel. It is found by experience that as the vessel heels to one or other side, the north point of the compass is drawn either to the weather or lee side, generally the former ; and the deviation so produced, when the ship's course is near north or south, often exceeds the angle of heel. This not only produces a deviation which may cause a serious error in the ship's course, but if the ship is rolling, and par- ticularly if the period of each roll approximates to the period of oscillation of the compass, produces a swinging of the compass-needle, which may amount to many times the angle of heel, and make the compass for the time useless for steering. This is a part of the deviation which has been involved in some obscurity. Mr. Airy, in a paper in the • Transactions of the Institution of Naval Architects,' vol. i. p. 107 (1860), says that the disturbance produced by heeling has not been well observed, and its correction has not yet been reduced to easy laws ; and that the effect of heeling is the only part of the magnetic disturbance in regard to which the practical correction of the com- pass is really at fault ; and the Reports of the Liverpool Compass Committee refer to it as one of the most perplexing parts of the subject. It therefore appeared to us desirable to deduce from Poisson's formulae, expressions for the alteration of the coefficients introduced by tbe inclination of the ship. This has been done in the 'Manual,' and the result is, we think, to remove entirely the obscurity which rested on the subject. The effect of the heeling error is, as might have been anticipated, to leave unaltered the coefficients wbich depend on fore-and-aft action, viz. B and D, to alter C, and to give a value to A and E. The latter appear to be, except when the compass is near either extremity of the vessel, of small amount. The alteration of C is the only one which is important. The formulas show that it consists of two parts, which are caused^by arrangements of iron, such as that in the follow- ing figure, in which the vertical line represents iron permanently magnetized, ON THE THREE REPORTS OF THE LIVERPOOL COMPASS COMMITTEE. 91 or vertical iron magnetized by induction, drawing the north end of the needle downwards in the northern hemisphere ; the horizontal line a rod, such as that in fig. 3, No. 2, which would give + D, and which, when the ship's head is Fig. 4. north or south, will have no effect till the ship heels, when its upper (weather) end will attract the north point of the compass. Each rod in the figure will therefore cause a deviation of the north point of the needle to the weather side. In order to correct this, the vertical magnetism must either act upwards, or the transverse magnetism must be such as would be caused by a horizontal transverse rod on each side of the compass, the formula indi- cating the relation which must exist between the vertical and the transverse horizontal magnetism in order that the heeling error may be zero. The 4th Part of the 'Manual' contains charts of the bines of equal variation, equal dip, and equal horizontal force over the globe ; the first for the purpose of enabling the navigator at sea to determine the deviation by astronomical observations ; the two latter to throw light on the changes which the deviations undergo on a lengthened voyage, and to enable the navigator to anticipate the changes which will take place on a change of geographical position. Of the Appendices, one (No. 2) contains a short account of the method proposed by Mr. Airy for the mechanical correction of the semicircular and quadrantal deviation, and a notice of a method lately proposed by Mr. Evans for the correction of the quadrantal deviation when excessive. No. 3 is on the mathematical theory of the deviations of the compass, being the deduction from Poisson's equations of such formulae as may be most conveniently ap- plied to the analysis of the tables of deviations derived from actual obser- vation. There is a graphical method of representing the magnetic state of a ship as regards deviation, described in pp. 106 and 107, which we may shortly describe. If from the centre of a compass, in any part of the ship, we draw a horizontal line, representing in amount and direction the ship's disturbing force on the north end of the needle of that compass, the ends of all the lines so drawn will, as is shown in this appendix, trace out an ellipse. If the soft iron of the ship be symmetrically distributed, so that <&, and <B are zero, the construction of this ellipse is simplified, as its axes are then parallel and perpendicular to the fore-and-aft lines of the ship. The position of the centre of the ellipse gives the amount of the force to head, and force to side, which cause the semicircular deviation. The fore-and-aft and transverse 92 report — 1862. axes of the ellipse give the amount of the fore-and-aft transverse inductive forces which give rise to the quadrantal deviation. An ellipse so drawn, therefore, gives to the eye, at a glance, the whole magnetic character of the ship as regards deviation on an even keel. If the mean directive force of the needle is not altered, the ellipse be- comes a circle, the coordinates of the centre of which are 33 and C, and the radius J3, on the scale in which the mean force to north represents unity. If we have no observations of horizontal force, the circle is all we can draw ; it gives all the information to be derived from the ellipse, except the diminu- tion of the directive force. For the complete representation of the deviation and force, it is convenient to have both the circle and the ellipse drawn. In the diagrams the direction and force of the earth's magnetism as the ship is on different azimuths are represented by the radius of a circle, of which the compass is centre, and which is divided in the reverse order of the compass-card. A line drawn from a point in the circle to the correspond- ing point in the ellipse or small circle represents, on the common principle of the parallelogram of forces, the direction and amount of the force on the needle*. A modification of this diagram is described at p. 96 of the ' Manual' under the name of " dygogram " (dynamo-gonio-gram), applied to it from its showing the force as well as the angle of deviation of the needle. The principle of its construction is the following. If we draw a vertical line representing the magnetic meridian, and from a given point in it draw lines representing in length and direction the directive force and direction of the needle for each azimuth of the ship's head, the extremities of such bines will trace out an epicycloid which is very easily constructed by points when the coefficients &, 33, C, 29, <£ are determined. The method is applied in plate 2 to the deviations of the standard compass of the 'Warrior,' and has been applied by us to many other ships, and has been found a most efficient aid in discussing the observed deviations"!". We now come to what we consider the proper subject of this Eeport, viz., the practical results as to the deviations of the compass which have been deduced from actual observation on board ship ; and the works to which we shall principally confine our attention are the following : — " Account of Experiments on Iron-built Ships, instituted for the purpose of * A practical application of the diagram to the correction of the compass was suggested by its being accidentally held to the light and looked at from behind. When this is done, it will be seen that the large circle is divided in the same way as the compass-card. If, then, the radius of the large circle represent the direction of the disturbed compass-needle, the line joining the corresponding points in the large circle and on the ellipse or small circle will represent the direction of the magnetic meridian. By therefore drawing on an ordinary compass-card a circle of which the coordinates of the centre are —38 and +C, and the additional coordinates of the north point —IB, and dividing the small circle in the reverse order, we get the following rule for the correction of the compass : — " Take the given course on the card, and also on the small circle, and suppose a straight line drawn through these. Then keep the ship's head in the direction of the line, disre- garding, of course, the lubber-line." t If X be the force to north in terms of the mean force to north, T the force to east, then X and Y representing rectangular coordinates, X=l+38 cos ?-C sin S+S3 cos 2 %-<& sin 2 ?, Y=8+33 sin ?+<£ cos Z+m sin 2 ?+(£ cos 2 ?, which is the equation to an epicycloid traced out by a point VIP+<!P from the centre ot a circle whose radius is V23'-'+C 2 an ^ which rolls on a circle of equal size, and the co- ordinates of the centre of which are X=l, Y=9. ON THE THREE REPORTS OF THE LIVERPOOL COMPASS COMMITTEE. 93 discovering a Correction for the Deviation of the Compass produced by the Iron of the Ship, by G. B. Airy, Esq., Astronomer Royal " (Phil. Trans. 1839, p. 167). " Discussion of the Observed Deviations of the Compass in several Ships, wood- built and iron-built, by G. B. Airy, Esq." (Phil. Trans. 1856, p. 53). " Practical Illustrations of the Necessity for Ascertaining the Deviations of the Compass, &c, by Capt. Edward J. Johnson, R.N., F.R.S., Superintendent of the Compass Department of the Royal Navy." 1st edition, 1848 ; 2nd edition, 1852. " Magnetical Investigations by the Rev.W. Scoresby, D.D." 2 vols. 1844-1852. " Journal of a Voyage to Australia and round the World, for Magnetical Re- search, by the Rev. W. Scoresby, D.D." Lond. 1859. " First and Second Reports of the Liverpool Compass Committee to the Board of Trade, 1857." " Third do., 1861." " Reduction and Discussion of the Deviation of the Compass observed on board of all the Iron-built Ships, and a Selection of the Wood-built Steam-ships in Her Majesty's Navy, and the Iron Steam-ship ' Great Eastern,' by F. J. Evans, Master R.N., Superintendent of the Compass Department of H. M. Navy" (Phil. Trans. 1860, p. 337). The first and most important general result which is derived from all the observations recorded in these works, and from many more which have not been published, is, that the observed deviations are represented by the formula? derived from Poisson's theory with a correctness which is within the limits of error of observation. In saying this, we are in some degree differing from a conclusion which the Reports of the Liverpool Compass Committee draw from observed deviations, viz. that there is a difference in the amount of the quadrantal deviation in different quadrants, depending either on some quality of the iron as regards its capacity for induction in different directions, or on the greater or less time occupied in moving the ship's head over one or other of the quadrants. That some difference may, under certain circumstances, be caused by the latter cause we do not dispute, but we are not satisfied that it is appreciable in the ordinary process of swinging. On the contrary, we believe that, within very small limits of error, Poisson's theory may be considered as exact for the ordinary process of swinging a ship. As regards more lengthened periods, particularly when the ship has been exposed to mechanical violence, the hypothesis no doubt ceases to be exact ; but even then the most convenient mode of treating the subject is analogous to that which is familiar in physical astronomy and other mixed sciences, viz. to consider the theory as exact, but the coefficients derived from that theory as being themselves subject to changes to be derived from observations, and reduced or not, as the case may be, to law. Mr. Airy, in the first paper to which we have referred, describes very careful observations made by him on board of two iron ships, the ' Rainbow ' iron-built steamer, and the ' Ironsides ' iron-built sailing-ship. In the first, observations were made at four stations: station 1, near the binnacle' 13 feet 2 in. from the stern ; station 2, at a part in which a standard compass woidd probably be placed, being 31 feet 9 in. from the stern ; station 3, 48 feet 3 in. from the stern ; station 4, 47 feet from the knight-heads, or 151 § feet from the stern. Each compass was raised 4 feet from the deck. In the <■ Ironsides ' the compass was placed in the position of the binnacle compass. 94 .REPORT 1862. From Mr. Airy's observations we derive the following values for the coefficients : — The most remarkable features in the deviations of these ships are the very- small amount of the quadrantal deviation, and also in the ' Rainbow ' the small diminution of the horizontal force. These features led Mr. Airy to the conclusion that the amount of in- duced magnetism was small, and that nearly the whole of the semicircular deviation was caused by permanent magnetism. That this was the case as regards the coefficient C there can be no doubt ; but as regards the coefficient B the case is different, as any part of it may have arisen from the induction in vertical masses of iron before or abaft the compass. These results, and the conclusions which Mr. Airy drew as to the amount of permanent magnetism, were the foundation of his well-known method of correcting the deviations by means of magnets and soft iron, which has been so extensively practised in the mercantile marine. Another remark may be made on the results. One of the most import- ant conclusions which have been drawn from the numerous observations which have been made on the deviation of iron-built vessels is, that, in a well-selected place for the standard compass, the semicircular devi- ation depends on the position of the ship in building, the magnetism which would be assumed if the iron were soft being then, by the process of hammering, fixed in the vessel, and a character then impressed which the ship never afterwards loses, — the general result being that the north point of the compass is attracted to that part of the ship which was south in building, so that +B indicates a ship built head south, — B a ship built head north of the (magnetic) east and west line, -f C a ship built head east, and — C a ship built head west of the magnetic meridian. With our present knowledge, we should have little hesitation in drawing the conclusion from Mr. Airy's observations, that the ' Rainbow ' was built with her head not far from N.W., and the 'Ironsides' with her head not far from N.E. At that time, however, the connexion between the direction of building and the semicircular deviation was unsuspected*, and the direction in which those ships * To this there is one exception, which deserves to be recorded. In the year 1835, Captain Johnson made elaborate experiments on the magnetism of the iron steam-vessel ■ Garry Owen,' the results of which are contained in a paper in the Phil. Trans, for 1836, p. 267. Captain Johnson ascertained, from observations made on a needle on shore, that the ' Garry Owen ' acted as a permanent magnet, her head repelling, and her stern attracting, the north end of the needle ; and he says, p. 285 : — " As, in the construction of iron vessels, hammering the numerous rivets might elicit magnetic influences, it would be well to note, by compass, the direction of their heads and sterns when building, with a view of ascertaining whether (in combination with the former circumstances) any distinct magnetic properties indicated by those parts are due to the line of direction of the vessel with respect to the magnetic meridian." " The head of the ' Garry Owen,' when building, was W.N.W." It may seem singular that Captain Johnson did not observe how nearly this direction ON THE THREE REPORTS OP THE LIVERPOOL COMPASS COMMITTEE. 95 were built was probably unknown to Mr. Airy. He suggested that the particular character of the semicircular deviation in these vessels might be due to the direction of rolling of the plates of which the ship was composed. Subsequent experiments, made by the same eminent philosopher, on iron rolled in different directions, lately communicated to the Eoyal Society, but not yet published, show, as we understand, that the effect of direction in rolling, though appreciable in each separate plate, is not great, and probably has little, if any, appreciable effect in a ship. In concluding our observations on the paper, we must not omit to say that one of the most valuable parts of Mr. Airy's paper, viz. the mechanical correction of the deviation, does not, as we consider, come within the scope of this Report, and that, in passing it over, we must not be considered as underrating its importance. Mi\ Airy's second paper has not that value which is given to the first by careful observations made by himself on selected ships. It contains a dis- cussion equivalent to the determination of 33, C, and j9 of the magnetism of various wood-built and iron-built ships from observations made in various latitudes, and an endeavour to deduce from such observations the two parts of which 33 is composed ; but Mr. Airy had the disadvantage which is still met with by those who attempt the discussion, viz. the want of sufficient determinations of the deviations of the same iron vessel in different magnetic latitudes, and he was consequently unable to obtain any very precise evidence of the amount of the subpermanent magnetism in iron ships, or its change on a change of latitude. The work of Captain Johnson, to which we have referred, is a great store- house of the results of observations of deviation made on board ships of war. There are, however, several reasons why it does not require very detailed mention here. The deviations are chiefly those of wood-built ships. They are, therefore, generally small and regular. They are not compared with theory, and do not in all cases furnish sufficient data for the comparison. Such comparison as can be made will, as regards iron-built vessels, be found in Mr. Evans's paper in the Phil. Trans, of 1860, referred to above. It is to Dr. Scoresby that we are indebted for the observation that the semicircular deviation of iron ships is chiefly due to their position when building. In considering this subject, there are one or two points which must be borne in mind. Supposing, as we may no doubt do, that the iron is, as regards position and quality, symmetrically placed on each side of the midship line, we may consider separately the permanent or subpermanent magnetism caused by fixing, first, the magnetism induced by the horizontal force, and secondly, that induced by the vertical force. As regards C, the same reasoning which shows that it cannot arise from transient induced magnetism also shows that it cannot be caused by the fixing any vertically induced magnetism, but must arise either from independent permanent magnetism in the iron, or from fixing the horizontally induced magnetism. On the other hand, as regards 33 the case is different. It may be caused not only by the subpermanent magnetism originally induced by the horizontal force, and fixed in building, but by transient vertically induced magnetism, and also by the subpermanent magnetism arising from fixing, in the process of building, the transient vertically induced magnetism. Between approximated to that of the line of no deviation in the ' Garry Owen,' which was about N.W. by W. i W., and that in his subsequent works he did not revert to the subject ; and that the hint here given was not pursued by subsequent investigators. 96 report— 1862. these there is the great difference that the force which gives rise to C and to the first part of 33 ceases to operate, or at least ceases to operate in the same direction, the moment the ship has been launched, and has her head directed to different points of the compass, while the force causing the other part of 33 continues to act in its original direction as long as the ship remains in and near its original geographical position. C, whatever its magnitude, may therefore be expected to diminish rapidly after launching, and until the originally impressed magnetism reaches (as it appears ultimately, and in fact after no long period, to do) the limit beyond which sensible change does not proceed, and on a change of latitude it will vary inversely as the horizontal force. 38, on the other hand, although it may change considerably after launching, if the ship has been built north or south, will, if the ship has been built east and west, remain unchanged. On the other hand, on a change of magnetic latitude, while the effect of the subpermanent magnetism induced by the horizontal force will vary inversely as the horizontal force, that part which has been caused by the original ver- tical magnetism may change more rapidly from the change in the inducing cause, and the remaining part, or the transient vertically induced magnetism, will in its effect vary as the tangent of the dip. The combination of these several causes renders the discovery of the true source of the 33 a matter of great difficulty, even when observations have been made in several different latitudes. That the distribution of the permanent magnetism of iron ships is principally owing to tbeir position in building appears to have been first strongly insisted on by Dr. Scoresby in the 4th Part of his magnetical investigations published in 1852. The great importance of the service thus rendered by Dr. Scoresby cannot be over-estimated. Dr. Scoresby also en- deavoured to investigate the changes which the subpermanent magnetism of a ship undergoes on a change of magnetic latitude. He did so, however, with very insufficient materials, and it appears to us (as one of us has endeavoured to point out with greater detail in the introduction to the 'Journal of a Voyage of Magnetic Eesearch'), without having sufficient regard to the amount of transient vertically induced magnetism which acts or may act as a cause of semicircular deviation. At the meeting of the British Association at Liverpool in 1854, Dr. Scoresby brought the subject of the change of a ship's magnetism promi- nently before the Association, in a paper on the loss of the ship 'Tayleur' and the changes of the compasses of iron ships. The discussion so occa- sioned gave rise to the formation of the Liverpool Compass Committee, whose valuable Eeports are one of the special subjects on which we are commis- sioned to report, and also to Dr. Scoresby's voyage in the ' Eoyal Charter ' for the purpose of observing the changes which take place in the magnetism of an iron ship on a change of magnetic latitude. To these we now address ourselves. The Liverpool Compass Committee have had the assistance throughout of a most able Secretary, Mr. W. W. Eundell, who has brought to the subject an amount of practical and scientific knowledge, combined with industry and zeal, which have given to the three Eeports which have been published the highest possible value. The first Eeport bears date the 5th of February, 1856, shortly before Dr. Scoresby sailed in the ' Eoyal Charter.' The second Eeport bears date February, 1857, and embodies the principal results of the observations in the * Eoyal Charter.' The third Eeport bears date the 13th of February, 1861. ON THE THREE REPORTS OF THE LIVERPOOL COMPASS COMMITTEE. 97 The first Report was merely preliminary, and stated the steps which the Committee were taking to obtain information. One of the few points on which the Committee had made observations, the details of which they give, was the direction of the neutral lines, or of those lines in the iron structure of the ship which separate the parts in which the iron attracts the north end of the compass-needle from those in which it attracts the south end. These observations, we may observe, though to a certain extent useful as enabling us to see generally the nature of the action of the body of the ship on the com- pass, do not give any very definite results, from the transient induced mag- netism being even more mixed up with the permanent or subpermanent magnetism than in the case of ships "swung." The Committee, in the first Report, draw the following inference from these observations, viz. that " the diverse direction of the magnetic lines appears to countenance Dr. Scoresby's supposition that they depend on the position of the ship when building." _ The second Report contains the results of much more extended observa- tions and matured views. On the point of most marked importance — the connexion of the magnetism of an iron ship with her position when building — the Committee had now arrived at a definite opinion. They say: — "The records of the Committee no longer allow a doubt as to the connexion which exists between the direction of a ship's original magnetism and her position when upon the building-slip. In all the ships which have been examined, the north end of the compass-needle invariably deviated towards that part of the ship which was furthest from the north when she was build- ing) if the compass was placed in a central position ami free from the influence of individual masses of iron." * The attention of the Committee was also directed to the changes which the deviations undergo shortly after an iron ship has been launched, and they came to the conclusion that the subpermanent magnetism undergoes consider- able changes at and immediately after launching, and during the first voyage ; but that after this early reduction of a ship's magnetism has taken place, the remaining portion appears to be comparatively permanent. This, however, is subject to the qualification mentioned in the Report, and which may be stated as follows : — that when a ship has been for a considerable time in one position or on one course, the induced magnetic state acquires a certain degree of permanence which modifies the previous subpermanent magnetism. The general effect of this, it will be easily seen, is upon a change of course to cause the vessel to deviate from her course, by dead reckoning, in the direction of her previous course. ■ In this Report attention is called to the very important subject of the variation of the directive force in iron ships on different points of the com- pass. With reference to this, it may be observed, that we think it is a result of the observations generally, that the degree of correctness of observations of force is much inferior to that of observations of deviation. The observations of deviation give, by theory, the proportions of the directive forces on the * We have distinguished by italics the last part of this sentence in order to draw atten- tion to one circumstance which continually forces itself into notice in the perusal of the Reports, viz. the very little attention which is paid in the mercantile marine to the selec- tion of a place for the compass. In these ships the compass is constantly placed so near iron Bternposts, spindles of capstans, bulkheads, roundhouses, spindles of wheel, &c, that the effect produced on the compass is not only extravagantly large, and the rapidity of variation of the force in the field very great, but the effect produced is in truth not so much that caused by the ship considered aa a whole, a.3 that caused by the particular masses of iron in the vicinity of the compass. 1862. „ 98 report — 1862. different courses. Each, observation of force, therefore, when compared with the proportionate force derived from the deviations, gives a value of the factor (X,) by which the forces derived from the deviation ought to be multiplied. ■• The second Report of the Liverpool Compass Committee also mentions the interesting fact, which has been completely verified in the ships of the Royal Xavy, that the quadrantal deviation of all ships is, with very rare and special exceptions, positive, or such as to cause a deviation of the north end of the compass to the north end of the ship and from the north side of the ship. Such a deviation might be caused by an attraction to the north end or a repidsion from the north side. We may distinguish between the two causes by observing that the former would increase, and the latter diminish, the mean directive force of the needle. Observations of the directive force, therefore, show from which cause this deviation arises, and indicate that in general in iron-built ships the quadrantal deviation is principally caused by the repulsion of the north side of the ship, the north end of some ships attract- ing the north point of the needle, of others repelling it, but in almost all such ships with a force inferior to that of the repulsion of the north side. In wood-built ships the case is different : there is no transverse horizontal iron to cause repulsion from the sides ; and the positive quadrantal deviation is caused by the attraction of the masses of iron before and abaft the compass. The exceptions are generally in the case of wooden screw-streamers, when the screw-shaft, passing through the place of the compass, causes a repulsion from the north end, or in the case of elevated compasses, in which the original + D has depended on an excess of repulsion of the sides over the repulsion of the ends. As the compass is elevated, the direction of the former force, be- coming more oblique, loses its effect much more rapidly than the latter, and the D consequently changes its sign. The Committee also observed on the heeling error, and on the general tendency being to draw the north end to the weather side, but stated that the evidence which they had obtained did not enable them to draw any definite conclusions on this subject. The third Report embodies the results of very extended and varied obser- vations, leading to very definite conclusions, which may nearly to the full extent be accepted as being now established. As we have already observed, the present state of the mathematical theory is such, and the mathematical results coincide so exactly with observations, that the details of observation lose much of their interest, and the results involved in the coefficients extracted by rule from the observations are suf- ficient for all practical as well as theoretical purposes. The Report commences with a summary of the points which the Committee consider as established ; they are — 1. That the magneasm of iron ships is distributed according to precise and well-determined laws. 2. That a definite magnetic character is impressed on every iron ship while on the building-slip, which is never afterwards entirely lost. 3. That a considerable reduction takes place in the magnetism of an iron ship on first changing her position after launching, but afterwards that any permanent change in its direction or amount is a slow and gradual process. 4. That the original magnetism of an iron ship is constantly subject to small fluctuations from change of position arising from new magnetic inductions. ON THE THREE REPORTS OF THE LIVERPOOL COMPASS COMMITTEE. 99 5. That the compass-errors occasioned hy the more permanent part of a ship's magnetism may be successfully compensated, and that this compensation equalizes the directive po-wer of the compass-needle on the several courses on which a ship may be placed. The first two points we have already adverted to, and we fully agree with the Committee in considering that they may now be accepted as well established. The third point is one of the most important of the results to which the making, registering, and discussing the observations of deviation in iron ships is at present leading us. It is clear that when an iron ship is first launched, her magnetic cha- racter depends almost entirely on her position in building, but that this magnetic state is extremely unstable ; that very great changes take place within a few days, or even hours, after launching ; but that, after no long time (the length of time depending no doubt, to a great extent, on the ser j vice in which the vessel has been employed), what may be called the tem- porary magnetism gets " shaken out " of her, and the magnetism of the ship acquires an extremely stable character. This is a matter on which exact and varied observations are much wanted; but we think it may be taken at present as the most probable result, that after about twelve months there is very little change in the magnetism of a ship which has made some voyages in the interval. In some ships the stability is most striking. It must, how- ever, be remembered that it does not folio iv from this that the whole of the magnetism which remains, and which affects the compass, is the permanent magnetism of hard iron. There is in all iron ships, as shown by the amount of the quadrantal deviation, a large quantity of soft iron, and consequently a large quantity of magnetism developed instantaneously (or nearly so) by induction ; and the magnetism developed in the soft iron by vertical induc- tion is not, in any given geographical position, distinguishable from the per- manent magnetism of hard iron. The test of the kind of permanence which is acquired by the magnetism of an iron ship after the lapse of the period we had referred to is, that her table of deviation shall always be the same when swung at the same geographical position. If, in addition to this, her semi- circular deviation in different parts of the globe is inversely proportional to the horizontal force of magnetism at the place, we infer that the vertically induced magnetism is so distributed as to produce a compensation of effects, and that the only cause which operates is the permanent magnetism of the hard iron. In some ships this appears to be the case. In H. M. S. ' Trident,' which has been particularly discussed by Mr. Airy, the magnetism is not only extremely stable, but nearly the whole of the semicircular deviation appears, from observations made in various latitudes, to be due to hard iron. The same is the case with H. M. S. 'Adventure ' and with many other iron ships. The practical conclusion which, it appears to us, may be drawn from these facts, is the importance in all iron ships of having their magnetic history carefully recorded, and the observations discussed. We need hardly say that, to give any value to such a record, observations should be made with the compass in a fixed position in the ship, and not corrected in any way by magnets or soft iron. On the fourth point we have, in fact, already expressed our opinion. "We are not satisfied that the effects here referred to are in general of appreciable amount in so short a space of time as that occupied by the process of swinging a ship. There seems, however, no doubt that the cause operates sensibly in h2 100 REPORT 1862. many cases when a ship has been long sailing in one direction ; and this re- mark might be taken as a qualification of what we have remarked as to the permanence of the magnetism of a ship. On the fifth point we quite agree with the Liverpool Compass Com- mittee, subject, however, to the qualification that this correction cannot be depended on in the case of a newly-built ship, and that when the correction is applied to compasses having large deviations, and placed near large vertical masses of iron, as a stern-post, there must always be great uncertainty as to the correction on a change of magnetic latitude. It is also right that we should not pass over this remark without protesting against the application of such correction to the standard compass (properly placed) of a ship which may be called on to make a voyage during which there is any great change in the dip or horizontal force. The Committee notice as the principal points left for further discussion and inquiry, the effect of heeling on the compasses of iron ships, and the changes which occur on a change of magnetic latitude ; and to these the Eeport is chiefly directed. On the effect of heeling a considerable body of evidence is collected, but with the disadvantage that at that time the mathematical theory of the heeling error, and the formula? which express it, had not been fully investi- gated, and that consequently the comparison of theory with observation could not be precisely made ; nor do the observations in all cases furnish sufficient data for the comparison. We think, however, that it may be said, with confidence, that the results of observations agree with theory as to the connexion between the amount and direction of the heeling error and the coefficients of quadrantal deviation and of horizontal and vertical force j and that we may therefore feel assured that the heeling error may be predicted with sufficient accuracy from obser- vations made on an even keel. The most important practical results as to the amount of the heeling error, are the very great amount to which it reaches in certain ships, and in eertain positions in the ship. This heeling error is conveniently measured by the fraction of a degree or the number of degrees of error produced by every degree of heel when the ship's head is North or South. Estimating it in this way, it will be seen that the error may have serious effects if it exceed •5 or -6, when an inclination of 10° may produce half a point of error. Among the examples given we have — Coefficients of Iron S. S. City of Baltimore (built head North). heeling error. Compass placed above the aft end of iron round-house . . +6-70 Port steering-compass compensated — '30 Starboard steering-compass compensated — "50 Standard compass 4-2-20 Azimuth compass + 2* Dipping-needle compass +2 - Fore compass compensated + "80 Compass over fore hatch + '85 Aphrodite (built head East). Compass under companion + 2- Compass near companion +2-85 Admiralty standard compass + 1"20 Dipping-needle compass , +1-15 ON TIDAL OBSERVATIONS ON THE HUMBEB. 101 Simla (built head West). heebngTrror. Steering- compass +2-06 Compass over companion + 1-65 Dipping-needle compass _)_ -go Standard compass _|. .73 Forward compass _j_ .70 Slieve Donard (built head S.E. to E.). Aftermost steering-compass compensated . . . .• _|_ -4Q Second steering-compass compensated 4- -12 Skylight-compass compensated _|_ -33 Mast-compass ^_ -23 Port skylight compass -f -26 In other compasses of the ' Slieve Donard ' the heeling error was almost imperceptible. In the case of the ' City of Baltimore,' the large heeling error is evidently due to the vertical force downwards near the stern, arising from the ship having been built head north. In the ' Slieve Donard,' the small heeling error is evidently due to the ship having been built with her head to the southward. Before leaving the subject of the third Beport, we must beg leave to mention one point which has made the duty of reviewing the Beport more difficult than it would otherwise have been, and which we fear will detract from its general utility, viz. that the mathematical formulae made use of in reducing the observations are nowhere given, and that we have been unable, in some cases, to verify or use them. We hope that the Admiralty Manual may be of some use to future investigators, as providing a uniform notation and mode of reduction, which will make the results derived by one investi- gator intelligible to all. In concluding this notice, we think we may say that the principal deside- rata at present are — 1. That in the construction of iron vessels, regard should be had to the providing a proper place for the compass. It is not difficult for any one who has studied the question to point out arrangements which would greatly mitigate the injurious effects of the iron of the ship ; the difficulty is to recon- cile them with the requirements of construction and of working the vessel. 2. That for throwing light on the points which are still obscure, what is chiefly required is, that the complete magnetic history of some iron vessels in various latitudes should be known. This, we think, might easily be accom- plished by observations of deviations and horizontal and vertical force made at various fixed positions in an iron vessel in an extended voyage in both hemispheres. We need hardly add, that this should be a vessel of war of moderate size, and in which the magnetical observations would be made an object of importance. Report on Tidal Observations on the Humber. Presented by James Old- ham, C.E. ; John Scott Russell, C.E., F.R.S. ; J. F. Bateman, C.E., F.R.S. ; and Thomas Thompson. At the Meeting of the British Association held at Manchester last year a paper was read in Section G, on the Port of Hull, in which occurred the .102 report— 1862. following remark, referring to the tides of the Humber : " I would notice here a -singular tidal phenomenon which exists at the Port of Hull ; I refer to the fact, that whenever the tide reaches the 16-feet mark " (over the dock-sill), " it is then three hours to high water, whether they be spring tides or neap tides. I am not aware that the same thing occurs at any other port ; but such is the fact at Hull, that three hours after the tide has attained to the 16-feet mark, there is no more rise." These remarks gave rise to an animated discussion on the alleged pheno- menon, and resulted in the appointment of the following members of the Association as a Committee to conduct a series of tidal observations on the Humber, and report on the same to the next Meeting to be holden at Cam- bridge, viz. Mr. James Oldham, C.E., Mr. John Scott Eussell, C.E., F.R.S., Mr. J. F. Bateman, C.E., F.R.S., and Mr. Thomas Thompson, with £25 at their disposal. In commencing the arrangements for carrying out the wishes of the Asso- ciation, application was made to the directors of the Manchester, Sheffield, and Lincolnshire Railway Company for a month's observations to be taken at their self-acting tide-gauge at the Great Grimsby Docks, but it was not con- venient to the directors to grant the request; they, however, permitted a gauge-pole to be fixed at their landing-pier at New Holland, oh the Lincoln- shire coast of the Humber, a little above Hull, and gave every facility in the progress of the operation of observing the tides. The Hull Dock Company, through their secretary, Mr. W. H. Huffam, have complied with a request to have a month's observations from their self- acting gauge of the Victoria Docks ; and the resident engineer of the com- pany, Mr. R. A. Marrillier, has furnished the month's valuable tidal obser- vations. . Mr. Thomas "Wilson, of Leeds, an active member of the British Associa- tion, kindly offered a month's observations from the self-acting tide-gauge of the docks of the Air and Calder Works, at the Port of Goole, on the river Ouse, which have also been furnished by Mr. W. H. Bartholomew, the resident engineer. Those on the Humber were commenced at or about 11 a.m., July 9th, and terminated at 3 p.m., August 6th ; but those at Goole, which were begun at 11 a.m. on the 9th July, were continued until twelve o'clock at noon on the 10th of August. The gauge at New Holland is so fixed as to correspond with, and is on the same level as, the Victoria Dock gauge at Hull, i. e. the zeros are made to coincide. The observations were taken every five minutes at New Holland, but every fifteen minutes at the Hull Dock gauge ; the observations at Goole were taken at intervals of five minutes. .. As a result of these tidal investigations it was seen, by the series of obser- vations at both the stations on the Humber, how accurately the statement is borne out as to rise of tides for three hours after attaining the 16-feet mark, and also that the time which the tide is falling from the period of high water to the same level again of 16 feet is also found to average about three hours. The observations are also important and valuable, as showing the general fate of the rising and falling of the tides at the various periods and places reported on. Although little or no light may have been thrown on the phenomenon in question, yet the various tidal observations obtained on the Humber and the river Ouse will no doubt prove valuable records on the question of tides. ON RIFLED GUNS FOR ATTACKING ARMOUR-PLATE DEFENCES. 103 From the various observations the following are the results : — The obser- vations made on the Humber comprised 55 tides : the greatest variation at spring tides was 22 feet 3 inches flow ; and the least variation at neap tides a rise only of 10 feet 7 inches. The lowest level of low water at spring tides was 3 feet 8 inches, and the highest rise 27 feet 11 inches; the highest at low water of neap tides 11 feet 2 inches. The mean rise of the 55 tides above low water was found to be 16' 95 feet. The average time of rising tide is about 5^ hours, and the falling tide about 6| hours. At the season of the year when the observations were taken it is generally calm, and there is no undue influence exerted on the rise and fall of the tides on the Humber ; but at the time of the equinox, and in stormy winter seasons, particularly during north-westerly gales, there is a much greater rise and fall during spring tides than would otherwise occur. The observations made at Goole (which port is about 30 miles above Hull) show on the 63 tides a mean rise of 11-67 feet, — the greatest rise above low water being 15 feet 4 inches, and the least rise from low- water line 7 feet 7 inches. The tides at Goole average about 3 hours in rising, and a little over 9 hours in falling. The mean rate of the tidal wave on the Humber is from 2| to 3 miles at neap tides, and 4 to 5 miles per hour at spring tides. On Rifled Guns and Projectiles adapted for Attacking Armour-plate Defences. By T. Aston, M.A., Barrister at Law. [A communication ordered to be printed among the Reports.] As it is now an admitted fact that naval warfare will be carried on by iron- clad navies, it has become an imperative necessity that the navy of England shall henceforth be armed with artillery adapted for attacking the new armour-plate defences which all nations are hastening to adopt. The supe- riority which defence so suddenly acquired over attack, by simply putting on a coat of armour, threatened to upset not only the theoretical but the practical tactics of modem warfare. The necessity of improving the means of attack so as to restore, as far as possible, the disturbed equilibrium was obvious to every one ; and the contest which has been carried on in this country for the last two or three years between the attack of improved artil- lery and the defence of improved armour-plates has been watched by all of us with the greatest interest. From a scientific point of view, with which we are on this occasion more immediately concerned, the subject was one Which engaged the attention of some of the keenest and most experienced intellects of the country, — these, on the one hand, giving practical aid on the side of defence, those, on the other, devoting their best energies to restore attack to what must be considered its normal position of superiority. For a long time — for too long a time — the defence-people had much the best of it. Under the energetic superintendence of the Plate Committee (who in this matter de repu blica bene meriti sunt), armour-plate targets were erected by our able engineers which at fighting-ranges laughed to scorn the utmost efforts of the artillery attack brought against them. Some of the targets combined the resistance of iron with wood ; others, constructed with far-seeing KM kepokt — 1862. ingenuity, depended upon iron alone. The Ordnance Select Committee were challenged to bring forward the best gun their artillery science, aided by all the resources of the Koyal arsenals and the public purse, was able to provide. The science brought to bear by the Ordnance Select Committee, after exhausting itself in repeated efforts to cover its repeated defeats (efforts that were fruit- less for reasons that will be explained), was at length compelled to confess itself vanquished. But Ordnance had other resources which it hoped to have dispensed with, and upon which in its disappointment it was glad to fall back : it said to the Committee of Defence, " If yoa will obligingly set up your armour-targets within a shortened range (say, for instance, a Robin Hood bowshot of 200 yards), you shall see what the brute force of the old smooth- bore will do. True it is that cast iron will be brought to attack wrought iron — that a rounded missile will have to punch its way through a flat and possibly at times inclined armour-plate — science, which proved but a broken reed iu our hands, must be abandoned ; but with a gun big enough, a shot heavy enough, a charge of powder large enough, and a range short enough, the smooth-bore shall smash your target." Of course it would ; and so would a battering-ram like those Titus used to break the gates of Jerusalem. If therefore the old smooth-bore had failed the Ordnance Committee, like the service rifled gun, they might have fallen back on the older battering-ram. Looking at it from a scientific point of view, this retrogression was very humiliating, and it caused the country serious anxiety to hear Her Majesty's Ministers state in Parliament, as they did in the last session, on the authority, of course, of their official scientific advisers, that the Navy of England, after all the vast expenditure that had been lavished upon it, was at last obliged to be armed with the old smooth-bores to meet the iron-clad navies of her pos- sible enemies. This was indeed proclaiming England's weakness to other nations who were more scientifically informed and better anred than she. In further explanation of what was the actual condition in which this all- important question stood no later than May last, I will quote the statement of Sir William Armstrong, who, at a meeting of the United Service Institu- tion, May 20, 1862, expressed himself in these words: — '• It certainly may be said that shells are of no avail against iron-plated ships ; but, on the cher hand, I may say that neither 68-pounders nor 110-pounder guns with solid round shot are effective against such iron vessels. The fact is, what we want is a gun, in addition to our 110-pounder rifled gun, especially adapted for breaking through iron plates. That is what we are in want of now." This statement made in 1862 was very startling to all of us, who knew that long ago Prance armed her 'Gloires' and ' Kormandies' with rifled 90-pounders said to be efficient against iron plates. Such being the state of the question a few months back, we may proceed to consider, first, the reason why the artillery hitherto employed in the service, including rifled guns and smooth-bores, has always failed to make any impression on the plated defences at ordinary fighting-range ; and secondly, by what means artillery sciei ce has lately re- conquered its lost ground. Sir William Armstrong put the case very plainly when he said that shells were in fact of no avail again c t plated ships, and that the solid shot of the 110-pounder rifled gun was not effective against srch iron vessels. But late experiments at Shoebiuyness, in which the 'Warrior' target was pierced and shattered at 600 yards, have proved that the case as put by Sir William Armstrong was based on his experience of shells that were not made of the proper form, nor of the proper material, and on his ex- perience of rifled guns that were unable to propel their projectiles with the requisite velocity. ON RIFLED GUNS FOR ATTACKING ARMOUR-PLATE DEFENCES. 105 Three conditions may be laid down as necessary to enable artillery to attack successfully armour-plate defences : 1st, the projectile must be of the proper form ; 2nd, of the proper material ; and 3rd, be propelled from a gun able to give it the necessary velocity. The artillery of the Ordnance Select Committee failed because they utterly neglected the first two conditions, and had recourse to the brute force of the smooth-bore for the third. The ex- pression accepted as representing the penetrating power of shot was " velo- city squared, multiplied by weight;" but the form of the shot and the mate- rial were conditions altogether omitted from the expression ; and the import- ance of the omission will be obvious at once if we take an analogous case, say that of a punching-machine employed to perforate wrought-iron plates. What would be the result if the punch itself, which is made of suitable shape and material, were removed, and a round-headed poker, of brittle cast iron or soft wrought iron, were substituted in its place ? The great importance of suf- ficient velocity is conceded — it is a sine-qud-non condition; but has there not been great misconception in supposing that the old smooth-bore gives a greater initial velocity than the rifled gun? The results obtained will show how this is. The average initial velocity of the 68-pounder is, in round num- bers, 1600 feet per second with a charge of powder one-fourth the weight of the shot, the length of the shot being of course one calibre. Sir William Armstrong stated that with a charge of powder one-fourth the weight of the shot, he obtained with his rifled gun an initial velocity of 1740 feet per second: he did not state the length of his projectile. Mr. Whitworth, with a projec- tile one and a half calibre long, obtains an initial velocity of 1900 feet per second ; and with a projectile one calibre long, like that of the smooth-bore, an initial velocity of 2200 feet per second, being greater than that of the smooth- bore in the proportion of 22 to 10. The reason why, under nearly similar con- ditions as to charge and length of projectile, the rifled gun had an initial velocity 60 greatly superior to that of the smooth must be ascribed to the action of the first condition I ventured to lay down as necessary. The rifled projectile, as compared with the spherical, has a form which is better adapted for flight, and fits more accurately the bore of the gun, so that the gases of explosion exert a greater pressure upon it while propelling it through the barrel. In practice the initial velocity of the rifled projectile is lower than that of the smooth-bore, because with the rifled gun the charge of powder used is much less, while the projectile is much longer and heavier, and has a greater vis inertias to be overcome at starting than that of the smooth-bore. If very large charges be used with the rifled guns, and long projectiles, with the view of obtaining increased velocity, the strain becomes too great for the guns to bear ; but if rifled guns arc fired with charges so low that they are not made to perform half the work they ought to do, then, though the defects of weak construction may not be made patent by the gun being destroyed, they are very plainly manifested by the weak results of their projectiles fired against armour-plates. It is proved by well-known results that the con- structors of the 110-pounder rifled gun, now adopted in the service, do not dare to make the gun perform its full work ; but, on the contrary, they find themselves forced gradually to reduce their charges, until they are well beaten by the old smooth-bore they undertook to supersede. The only conclusion that can be drawn from this fact is, that the gun is weak in construction, and the projectile used with it is defective in principle. The power of the smooth-bore, with its large windage, to fire large charges, and thereby obtain great velocities, has procured it many advocates ; but Mr. Whitworth 's experiments have shown that if length of projectile be given up, 106 REPORT 1862. which may be looked upon as the price to be paid for increased velocity, he can get an initial velocity much greater than that of the smooth-bore. But is the result worth the price paid ? Not if a more efficient compromise can be obtained. I use the word " compromise " advisedly, because I think that every one who has had experience in artillery practice will agree with me that the best results are only to be obtained by means of the best com- promise. You cannot have long projectiles and very high velocities without burning too much powder and taking too much out of your gun, or else making it an unwieldy monster. The problem we have placed before us now is, How can artillery be best adapted for attacking armour-defences ? The advocates of the smooth-bore are satisfied with one condition — high velocity. Mr. Whitworth objects, and says, " If velocity were all that is needed, I can get more than you do in the pro- portion of 22 to 16 ; but to sacrifice all to velocity is a bad compromise to effect a solution of the penetration-problem. You set down velocity as c/reatest possible, form of projectile of no account, material of no account, and after all can do nothing at an ordinary fighting-range while you wrongly take it as proved that 'shells are of no avail' against iron-plated ships. It would be a far better compromise to be satisfied with a lower velocity, getting however all you can at a fair price, and combining therewith conditions one and two — proper form and proper material for the projectile." Let us now compare the actual results obtained in the way of penetration by the Armstrong 110- pounder (the proposed naval gun), the old 68-pounder smooth-bore, and the two naval "Whitworth guns lately fired at Shoeburyness. Gun. Range. Projectile. Powder- charge. Penetration into Armour- plate. Armstrong 110-pounder, |200 J200 {■200 J600 110 lb. solid. 68 lb. solid. /701b. shot! \ and shell. J 130 lb. shell. 14 lbs. 16 lbs. 12 lbs. 25 lbs. 1£ to 2 inches. 2 1 to 3 inches. Through plate and backing. Through plate and backing. Old 68-pounder, smooth- Whitworth 70-pounder, ■Whitworth 120-pounder, The first two results* will lead every one to the same conclusion that it is to be presumed they led the Ordnance Committee, viz. that the Armstrong rifled gun is a worse compromise than the old gun it was intended to super- sede. The reason may be inferred from the facts to be, that besides neglect- ing conditions one and two, form and material of projectile, it is very much behind in respect of condition three, velocity ; this is to be attributed to the weak construction of the gun, which cannot fire with safety efficient charges of powder, and to the use of the lead-coated projectiles. Taking all the results, they show themselves to be indisputably in favour of the Whitworth, — the old 68-pounder coming second, and the Armstrong last. Let us next examine how they stand in regard to velocity, as shown in the following Table, which, like the one given above, is compiled from official sources. * These results were subsequently much surpassed. The Whitworth 70-pounder pene- trated 4£-inch plate and backing with shell at 600 yards range, and the Whitworth 120- pounder fired its shot and shell through 5-inch plate and 18 inches of teak-backing and |rinch iron-plate skin at 800 yards' range. ON RIFLED GUNS FOR ATTACKING ARMOUR-PLATE DEFENCES. 107 Gun. Charge. Velocity. 16 lbs. 12 lbs. 25 lbs. 14 lbs. Initial, 1600 feet per second. Initial, 1350 feet per second. Terminal at 600 yards, 1260 feet per second. Initial, 1210 feet per second. With regard to initial velocity, therefore, the order of the guns may be taken to be, with the charges used — 1st, 68-pounder ; 2nd, Whitworth ; 3rd, Arm- strong. It is worthy of notice, however, that the velocity of the Whitworth 120-pounder after traversing 600 yards (a good fighting-range) was found actually to be 1260 feet, whereas the initial velocity of the Armstrong is only 1210 feet. The total results in respect of penetration proving themselves to be so decidedly in favour of Whitworth, who combines with condition three, viz. sufficient velocity, conditions one and two, proper form and material of pro- jectile, it follows that his must be the best compromise. The slight inferiority in initial velocity of his rifled gun, as compared with the smooth-bore, is more than compensated for by employing a projectile of proper form and material, as is shown by the penetration being through-and-through both 5-inch plate and backing in the case of the Whitworth, while it is barely half-through the armour-plate in the case of the smooth-bore, and not half- through in the case of the Armstrong gun. The form of projectile employed by Mr. Whitworth for penetrating armour- plates is like the one now before the Section. It has a flattened front, the centre being slightly rounded; the middle part of the projectile is rifled hexagonally, like the bore of the gun ; the front and rear of the projectile are made of the requisite taper to allow the air displaced in front to close in readily behind — a form which gives a great increase of velocity as compared with the form parallel throughout, as I endeavoured to explain to this Section in a paper I had the honour of reading at its meeting last year. The material of which the projectile is composed is what is termed homo- geneous metal, combining the toughness of copper with the hardness of steel : it is made hard enough to penetrate the wrought-iron plate, but not so hard as to be brittle and break up when the projectile strikes against its sur- face. The advantage of the flat front as compared with a pointed front is apparent, when it is considered that when the flat front strikes a plate, the whole resistance it meets with is that offered by the area of the plate covered by the flat front in a direction in line with the axis of the impinging projectile : it consequently piinches out a clean hole, with a sudden impact. In the case of a pointed shot, as soon as the point begins to penetrate, the inclined sides begin to push aside the particles of the plate in a lateral direc- tion, and an accumulating lateral resistance is offered by every part of the plate whose particles are disturbed ; the passage of the shot is thereby gra- dually retarded, if not altogether arrested. It has been thought that the flat-fronted projectile will glance from the surface of an inclined plate like a round projectile : this is not found to be the case, as is proved by the plate now shown to the Section, which was completely penetrated by a flat-fronted projectile when inclined at an angle of 37° to the perpendicular. The Whitworth penetration-shell, whose destructive power was shown by its penetrating and shattering the ' Warrior ' target at Shoeburyness, has the same form outwardly, and is made of the same material (homogeneous metal) as the flat-fronted solid projectile which has already been described. A 108 REPORT — 1862. cavity is formed in the projectile of the size required to contain the hursting charge of ordinary powder. The rear is closed entirely by a screwed plate or cap. The uncertain complications of percussion-fuses, and also the sim- pler time-fuses, are wholly dispensed with. No fuse or detonating substance of any kind is used. On firing his shell through iron plates, Mr. "Whitworth found that by the force of impact and friction sufficient heat was generated to fire the bursting charge without any fuse at all. In practice the action upon the powder was found to be even too rapid. To retard its action for the time necessary to enable the shell to effect a complete penetration and then to burst, Mr. Whitworth interposes between the metal of his shell and his bursting powder-charge a substance that is a non-conductor of heat: by preference he encloses the powder in a flannel case, and finds that by simply diminishing or increasing the thickness of his flannel he can burst his shell in the armour-plate or in the timber-backing, or after it has passed through both. The fragments of the shell now before the Section are those of one which was fired through this armour-plate, and which burst and shattered this backing of timber, 9 inches thick, placed behind the plate. There is one point in connexion with the Shoeburyness trials which should be specially noticed, and it is this, that all the previous experiments against the ' "Warrior ' target had been confined to the short range of 200 yards ; at longer distances the smashing, monster smooth-bores cannot be made to hit the mark ; whereas Mr. "Whitworth has proved that at a good fighting-range of GOO yards he can hit his mark to a few inches, and can at that distance — and there is good reason to believe at twice that distance — send his shells through the ' Warrior's ' sides. That 600 yards may be fairly called a good fighting-range will be admitted when we remember that the 'Agamemnon,' at Sebastopol, fought all the guns of Fort Constantine at a range of 500 yards ; and the ' Albion ' signalled, " Well done, Agamemnon! — where you lead, we will follow." With respect to the 120-pounder gun itself, it should be explained that it was made at Woolwich, under the able superintendence of Mr. Anderson, at Mr. "Whit- worth's own request, and according to drawings originally supplied by him. It has the same bore as the Armstrong 110-pounder, stated by Sir "William not to be effective against iron-plated ships. It is a built-up gun, and its hoops are made of coiled iron, welded ; but that method of manufacture was adopted by Mr. Whitworth in the first built-up gun that he made, and was well known in this country many years before rifled guns were introduced into the service. Mr. Whitworth has himself employed by preference the homogeneous metal, which he has found to answer perfectly for small arms and field guns, as well as for the penetration-shells which have been described. Practical improvements have been made in the process of forging and annealing the metal, which now enable it to be worked in masses of any required size, whose quality may be henceforth depended upon with certainty. "Whitworth heavy guns are now being made with both interior tubes and outer of homogeneous metal of the improved manufacture, so that the guns will be constructed throughout of one uniform metal without any welding at all. Experience justifies the expectation that they will be free from the objections which it is well known are inherent in all welded guns, and be fully able to resist the severe and searching strain which is sure, sooner or later, to disable a gun built up of forged coiled tubes, if it be called upon to do its full work by discharging heavy rifled projectiles at the most efficient velocities. ON THE OBSERVATORY AT KEW. 109 Extracts, relating to the Observatory at Kew, from a Report presented to the Portuguese Government by Dr. Jacintho Antonio de Souza, Professor of the Faculty of Philosophy in the University of Coimbra. Communicated by J. P. Gassiot, F.R.S. [Ordered to be printed among the Beports.] Dr. Jacintho Antonio be Souza has published an account of a visit in 1860 to the Scientific Establishments of Madrid, Paris, Brussels, Greenwich, and Kew, and of a second visit in 1861 to the Observatory of Kew, both visits having been made by the desire of his Government, and having for their principal object to obtain information preparatory to the establishment of a Magnetical and Meteorological Observatory at the University of Coimbra. His first visit was to Madrid, where he states that he found nothing doing in magnetism ; and that in meteorology the only instrument presenting any novelty was the ingenious and comprehensive meteorograph of Padre Secchi, intended to register atmospheric pressure, the amount of rain, and the direc- tion and velocity of the wind. Prof, de Souza commends this instrument for the small space which it occupies, but adds that some of its indications, particularly those of temperature, appeared to him to be subject to much uncertainty. He was disposed to attribute the absence of any magnetical investigations at Madrid rather to the indifference of the Government than to any want of zeal on the part of the distinguished Director, Don Antonio Aguilar, of whose kind reception he also speaks gratefully. He next proceeded to Paris, where he arrived on the 15th of August, " the birthday of the first Napoleon," and was dazzled with the splendour of all that met his eyes in the general aspect of that brilliant capital. He had looked forward to finding in "the Imperial Observatory directed by Le Yerrier," besides a " typical Astronomical Observatory," one of the best in " magnetism and meteorology, where there would be much to see and to study ; " but after obtaining access to that fine establishment, " not without difficulty and loss of precious time," he derived, as he states, " little interest and profit from the hasty view which M. Le Yerrier afforded him of the Astronomical Ob- servatory (which is indeed excellent)," whilst, in regard to the special objects of his journey, though MM. Desains and Charault courteously showed him whatever could be said to ajraertain to magnetism or meteorology, he states that he " came away disappointed." At Brussels he refers gratefully to the frank and delicate kindness with which, on presenting himself at the Observatory, he was received by M. Quetelet, and expresses his admiration of what that philosopher had accom- plished with means from which very few others could have educed similar results, and of the impulse imparted by him to the advancement of the "physique du globe," saying at the same time that, without this knowledge, the inspection of the magnetical and meteorological portion of the Observatory- would lead a visitor to regard it as not being at the present time in a state of prosperity. Approaching London by the Thames, and entering " the vast cupola of smoke which covers that great capital," he seems to have been powerfully impressed by the dissimilarity to what he had previously seen in France and Belgium; and by the grandeur as well as the sombre character of the spectacle presented to his view. On arriving at Greenwich he was courteously received at the Royal Obser- vatory, admired the general arrangements of that great establishment, and inspected minutely the magnetical and meteorological portion, with the 110 REPORT— 1862. " advantage of verbal explanations by the Eev. Robert Main, who was there at the moment, besides the written explanations kindly given to him by Mr. Airy." He thus became well acquainted with the localities, arrange- ments, and instruments, of which he gives a detailed description ; but as he ultimately preferred ordering for his own Observatory instruments on the pattern of those employed at Kew, we may pass at once to his account of that establishment, which will be given nearly in his own words : — " The Observatory at Kew, besides occupying itself with meteorological and magnetical phenomena, and the photographic registry of the spots of the sun, verifies meteorological and magnetical instruments, compares them with the excellent patterns which it possesses, determines their constants, and improves the methods of observation. The Director (Mr. Balfour Stewart) was absent ; but Mr. Chambers, assistant observer, and Mr. Beckley, mechanical engineer of the Observatory, attended me so obligingly, and with such sincere desire to satisfy all my importunate inquiries, that I derived great profit from the visit. " The self -registering magnetic instruments at Kew were constructed in 1857, about ten years after the registering apparatus at Greenwich was adapted to the previously existing instruments at that Observatory. Based on the same general principles, they differ in size, and in certain happy innovations introduced by Mr. Welsh and executed by Adie (a skilful artist in London). They have been in action since 185S, and give results which leave nothing to be desired. " The locality in which the self-registering magnetic instruments are placed at Kew is in the basement-story of the building, which was formerly an astronomical observatory : the choice was determined by a condition which should never be lost sight of, viz. the greatest attainable constancy of tem- perature." [Having already described the magnetographs at Greenwich, Prof, de Souza, whilst giving a very elaborate description of the Kew instruments, dwells at length principally on the points in which they differ from those at Greenwich ; but the description is here omitted, as the Kew instruments have been care- fully and well described by Mr. Balfour Stewart in the volume of Reports of the Aberdeen Meeting of the British Association, p. 200-228. Prof, de Souza proceeds as follows : — ] " A short time before my visit to the Observatory Dr. Bergsma had been there, sent by the Dutch Government to examine the magnetographs destined for an observatory in Java, and constructed on the Kew pattern. I may say in passing that this examination consists in receiving practical instruction on the mode of manipulating with the instruments, in assisting in their collocation in the verification-house, and in the determination of constants. Some modifications were introduced in Dr. Bergsma's magneto- graphs which I will now notice, and which constitute their last state of improvement. " The great bell-glasses which rest on the marble disks were replaced by cylinders of gun-metal surmounted by smaller glass cylinders. Each has an aperture to which is adapted a plate of glass with parallel faces, taking the place which in the great bell-glasses was occupied by the openings of the glass plate and of the achromatic lens ; by this new arrangement the achro- matic lens is independent of the cylinder, and can be brought near to, or removed further from, the mirror according to convenience. In this manner any disarrangement of the cylindrical glasses, or the taking of them away, does not alter the position of the lens, or interrupt the march of the magneto- ON THE OBSERVATORY AT KEW. Ill graphs. These different pieces fit so as to enclose the magnet hermetically, and thus the air can be rarefied or withdrawn by means of an air-pump in communication with a tube which passes through the marble disk and opens into the enclosure. This exhaustion of the air prevents the influence upon the magnets of currents of air. "Three telescopes, directed to the mirrors of the magnetographs, are established on two stone pillars, and have each an ivory scale the divisions of which are reflected, by the moveable and by the fixed mirror, into the interior of the telescope, offering in the field of view two very distinct images of the scale, one of which moves with the mirror of the magnet, so that at different times different divisions of this scale will appear to coincide with the vertical wire of the telescope. By the comparison of these divisions with that of the image which is fixed, the position of the magnet at any moment may be known ; so that, besides the continuous photographic record going on out of sight, and only taken account of every other day, there may be obtained, on any occasion, direct observations, which is a consideration of great importance. For example, if there is a magnetic disturbance, not only can it be observed at the instant of its occurrence, but also direct observations may be obtained of oscillations which by their amplitude exceed the limits of the photographic paper. " In describing the magnetographs at Greenwich two scales were mentioned, one elastic, the other of paper, with which the times corresponding to the different points of the base-line were obtained, and the values of the ordinates of the curves calculated. These scales at Kew are metallic, and make part of an apparatus very simple and ingenious, which, being subject to a graduated movement, is both easy and exact in operation. It is, however, not easily described without the assistance of a figure. "For absolute determinations and secular changes there is a detached building of wood (copper-fastened) at a distance from the Observatoiy, where there are three wooden pillars solidly fixed in the ground, one for the instru- ments with which the coefficients of temperature and of induction of the magnetic bars are determined, and two for the inclinometer of Barrow and the unifilar of Gibson. These two instruments and a good chronometer constitute the necessary furniture of this building." After a very careful and detailed description of the inclinometer and unifilar, Prof, de Souza proceeds, in his account of his first visit to Kew, as follows : — " In the verification-house, sixty yards from the observatory, Mr. Beckley was setting up for trial for the first time the registering electrometer of Pro- fessor Thomson of Glasgow. This new invention, which seems destined to supply a great desideratum in meteorology, would have been one of the objects of the greatest interest to me, if I could have seen it in action and have appreciated some of its results. Dispersed as were its different parts, I could not well make to myself a clear idea of the who 1 ^. The following is what I gathered from the explanations of Mr. Beckley. "Professor Thomson's electrometer has for its object the photographic registration, by the system of Brooke, of variations in the difference between the electric tension of the atmosphere and of the earth. A semicircle of brass communicates with the earth; another semicircle of the same metal is insulated from the earth, and is in communication with the external air by means of the water of a reservoir, which is thrown into the air in a constant jet. From the top of the discontinuous circle formed by these semicircles, and in the direction of the space which they leave 112 REPORT— 1832. between them, there is suspended a metallic needle insulated from the whole of the apparatus, but in communication with a Leyden jar, to which is given a constant charge measured by the angle of torsion made by another needle suspended to the thread of another apparatus. With the first needle there moves a small mirror, on which falls the light of a lamp reflecting upon the registering cylinder where the electric curve is produced upon sensitive paper. Another fascicle of light which comes from the fixed mirror gives the base- line. One of the semicircles being in the state of the earth's, and the other in that of the atmosphere's electric tension, and the needle which moves at the top of the space which separates them having a known and constant electricity, it is clear that the slightest alteration in the difference between the tensions, or in the quality of the electricity by which they are produced, will be directly indicated by the movement of the needle which impresses itself immediately on the photographic paper. If this instrument receives at Kew the attention of which inventions conducing to the advancement of science are there thought worthy, and if any imperfections which may be discovered in it in practice are successfully removed, Professor Thomson will have the honour of having discovered the most sensitive and instantaneous electrometer in existence, which will doubtless smooth the great difficulties which impede the advance of the science of atmospheric electricity. In the presence of this electrometer the electric apparatus employed at Greenwich will fall into disuse, as it has already done at Kew, where it is dismantled. Of the other meteorological instruments in the Kew Observatory, I will only mention the great standard barometer, or rather the process by means of which its large tube is filled. The barometer and a cathetometer, with which are observed the differences of level of the indices of the mercury in the cistern and in the column, are fixed to a wall which formerly supported the mural gradient of the Astronomical Observatory. It is essentially the barometer of Eegnault ; but it can turn around its axis, which is adjusted in the vertical position by means of screws of pressure : the indices move until they touch the surface of the mercury of the cistern ; one terminates in an edge, the other in a cone : the diameter of the tube is 1*1 inch." Prof, de Sauza here describes in considerable detail the process of making and filling such a barometer-tube. [For this process the English reader is referred to Mr. Welsh's original paper in the Philosophical Transactions for 1856, Art. XXIII. ] Before returning to London, Prof, de Souza visited the Gardens at Kew, and takes occasion to express his very great admiration of the gardens, the palm-house, and especially of the museum. He then proceeds as follows : — " In London I addressed myself to Major-General Sabine. I have great satisfaction in declaring thus publicly, that the relations acquired with this courteous gentleman so long engaged in magnetical science, constitute one of the most valuable acquisitions which I made in England. It is known that General Sabine has devoted himself for almost half a century, with an ardour and activity never interrupted, to the study of terrestrial magnetism. From 1818 to 1822 he made four successive long scientific voyages ; in 1837 he published the first general map of the isodynamic lines of the globe ; after- wards he brought about the establishment of four observatories very differ- ently circumstanced in regard to the intensity of the terrestrial magnetic force, and in opposite positions in regard to the magnetical and geographical poles and equators — ?'. e. the observatories of Toronto, Hobarton, Cape of Good Hope, and St. Helena. He has also superintended these establishments, and reduced and analysed their observations, from whence have resulted ON THE OBSERVATORY AT KEW. 113 numerous and important publications. He continues himself to observe during a portion of the year, and has almost completed a map of the different magnetic elements over England. " As was to be hoped, General Sabine heard with lively interest that tbe establishment of a magnetical and meteorological observatory at Coimbra was in contemplation, and readily offered to help forward the realization of this good idea by directing the construction of the magnetic and other instruments required, and also undertook that they should be verified and their constants obtained at the Kew Observatory, where I should be enabled to make practical studies, and receive suitable instruction for their establishment and manipulation, "General Sabine, speaking of the University of Coimbra in terms very agreeable to a Portuguese auditor, expressed satisfaction at so good an oppor- tunity of sending to this respectable Academy eleven large volumes of obser- vations analysed by him and published, under his superintendence, by the English Government. Besides the observations of the four observatories above mentioned, there are also contained in these volumes observations from Lake Athabasca, Fort Simpson, Fort Carlton, Fort Confidence, the Falkland Islands, and Pekin. " I informed the Faculty at their first meeting after my arrival at Coimbra of the courtesies received from this savant, and I presented to your Excellency at the proper time the books of which I was the bearer." Prof. deSouza then proceeds toconsiderthe results of his journey, and its bear- ing on the establishment of his own hoped-for observatory. Having obtained permission to employ the funds available in the current year in the purchase of magnetic instruments, he wrote to General Sabine, asking him to bespeak for him both the self-registering instruments, and those for absolute deter- minations (as will be specified in the sequel), with any further improvements that he mightdeem desirable. He had previously consulted General Sabine on an important question, that of the choice between the different dimensions of the magnets in use at Greenwich and at Kew, and says that " the instructive reflections so obtained " had left him " completely satisfied in determining for the Kew dimensions." In regard to the locality, it appears that the University of Coimbra does not possess any building suitable and available for the purpose ; but the Kector pointed out a site which appeared to M. de Souza highly suitable, if he could assure himself that the ferruginous particles contained in the new red sandstone rock would not be objectionable. He sent specimens of the rock (a well- known one in England) through the Portuguese Ambassador to London, and experiments made with them discovered no sensible magnetic action. But although this doubt was thus satisfactorily removed, unfortunately the site in question is private property, and means are wanting both for its purchase and for the building. He presses on the authorities the urgency of this provision being made without further delay, and states that the plan proposed, after full consultations, and for which Mr. Beckley has offered to make the drawings, combines the greatest economy with all that can be desired scientifically. Finally, he discusses the question of meteorological instru- ments, and concludes for obtaining them also from England, proposing to devote to this purpose the means at his disposal up to the termination of the University year in 1862. Second Visit to the Kew Observatory. Hearing on the 5th of July (1861) from General Sabine that the magnetic 1862, i 114 REPORT 1862. instruments were nearly ready for trial and verification, lie proposed to devote his approaching holidays to profit by the opportunity of gaining practical instruction and experience in their use ; proposing at the same time to study Professor Thomson's electrometer — the only apparatus, he says, which holds out the hope of satisfying the present exigences of science, which require continuous registration— and to obtain the other meteorological instruments and compare them with the Kew standards. The first part of the report is dated July 25, 1861; the second part November 16, 1861, and gives an account of his second visit to the Kew Observatory. It is prefaced by acknowledgements of the kindness and help he received from Messrs. Stewart and Chambers at the Observatory, from General Sabine, Mr. Gassiot, and the whole of the " directing Committee," from the British Association, and from the Royal Society. He arrived in London on the 24th of August, and finding General Sabine absent in Wales, proceeded at once to the artists, Adie, Barrow, and Gibson, who informed him that his instruments were at Kew, whither he lost no time in repairing, and where the Director arranged that the work should begin at once. Prof, de Souza took up his abode at Richmond, and went daily to the Observatory, remaining there from 9.30 a.m. to 5.30 p.m. He speaks of the great kindness, instruction, and constant assistance which he received from the Director and the whole personal staff of the Observatory, in their different degrees and functions, in the practical study of the instruments. This study consists, he says, in setting them up in the trial house precisely as they are to be set up at Coimbra, in determining their constants, in repeatedly observing the magnetic elements with them and comparing the results with those of the Observatory, and in reducing these observations. In the course of the observations some little faults, which would otherwise have escaped notice, were discovered in the instruments ; to correct these the artists were repeatedly called to Kew, or the Director conferred with them in London. The collection of magnetic instruments consists, firstly, of the magneto- graphs which register continuously the horizontal force, the vertical force, and the declination ; and, secondly, of the portable instruments, viz. Barrow's circle for the absolute determination of the inclination, with the apparatus for determining the total force by Dr. Lloyd's method ; and the unifilar, by Gibson, with its apparatus for the absolute determinations of the declination, and of the horizontal force by the method of vibrations and deflections. The magnetographs are accompanied by three telescopes, for the direct observation of the magnetic elements when requisite, and by all things necessary for beginning work as soon as they are established — utensils for photographic manipulation, a year's supply of chemical ingredients, waxed paper, spare bell-glasses, chimneys and mirrors, coloured glasses for the photographic house, <fcc. The portable instruments, which are indispen- sable in an observatory, being also proper for the observations of a magnetic survey, are conveniently packed in portable boxes, and accompanied by a tripod stand. The existence of the Astronomical Observatory at Coimbra makes it possible to dispense with a transit-instrument and clocks, but a good chronometer is essential ; and by the kind aid of the Hydrographer, Admiral Washington, to whom General Sabine wrote on the subject, Prof, de Souza received permission to purchase one of those examined at Greenwich, and guaranteed by the Astronomer Royal, at the price which would be paid for the same by the British Admiralty. "Besides the barometer required for the ordinary direct observations," ON THE OBSERVATORY AT KEW. 115 Prof, de Souza desired an absolute standard such as is at Kew. So large a tube could neither be filled by the ordinary method, nor, of course, transported full. The course taken was therefore to learn at Kew how to perform the filling process by Mr. ."Welsh's method, so as to put it in practice at Coimbra. The experiment was made with two glass tubes of ordinary size, of which Prof, de Souza filled and closed one in the proposed manner, and Mr. Casella the other, with equal success. Prof, de Souza then ordered from Mr. Casella two tubes of large dimension, very clean and the air exhausted, with the cistern and all the appurtenances of the barometer to be made with one of them. If he succeeds, according to his hopes, as he did at Kew, Coimbra, he 6ays, will possess an absolute standard, which will be the standard for Portugal as that of Kew is for England. But he proposes not to order the cathetometer until the tube is actually filled and raised into its proper position. He then gives the list of the other meteoro- logical instruments, all verified at Kew. "A standard thermometer graduated in divisions of 0-2 Centigrade. It was one of the best old tubes in the possession of the Observatory, only wanting the graduation, which was skilfully performed under my sight by the young George "Whipple, assistant at the Observatory. " Two psychrometers with divisions of 0-5 Centigrade. " A maximum registering thermometer on Professor Phillips's principle. " A minimum registering spirit thermometer. " A minimum registering mercurial thermometer ; a recent invention of Mr. Casella, which was tried at Kew with a good result, and may be advan- tageously substituted for the spirit thermometer, of which the defects have long been recognized by meteorologists. " A Herschel'6 actinometer. " A spirit thermometer for registering terrestrial radiation, with a suitable parabolic mirror. " Two rain-gauges. " A vaporimeter with the corresponding pluviometer." With the above, and a pluviometer and hygrometer of Eegnault, and an anemograph by Salleron belonging to the Cabinet de Physique at Coimbra (which requires to receive some modifications), Prof, de Souza considers that an equipment is provided for immediate work, contemplating eventually the addition of " apparatus for the continuous registry of barometric and thermometric variations, the cost of which will be under £120." The continuous registry of atmospheric electricity by the photographic process must be given up for the present : Professor Thomson's electrometer, excellent in principle, leaves, however, somewhat to be desired in practice. Prof, de Souza examined the one at Kew with great attention, watching its march carefully, and afterwards having it taken to pieces ; and he is of opinion, as is also Mr. Stewart, that slight modifications would obviate some of the defects to which it is liable. Mr. Beckley has drawn a plan and elevation for the Observatory at Coimbra, which is submitted to the Council of the University : it provides both for the instruments which have been ordered, and for such as may, it is hoped, be subsequently acquired, these being a barograph and thermograph ; and possibly hereafter a photo-heliograph for obtaining images of the solar spots, especially with a view to their supposed relations to magnetic pheno- mena. The cost of a photo-heliograph would now be about £80. In a few years many improvements will probably be made in it, and meantime what is wanted for this particular object may be supplied by observations of the i2 116 REPORT— 1862. solar spots with an ordinary telescope, or by data obtained by the Astrono- mical Observatory as part of its own work. Besides the excellent collection of magnetic instruments (one of the finest and most complete in existence, with scrupulously determined constants) which is thus placed in the possession of the University of Coimbra, Prof, de Souza has blank forms for the record of all the observations, and the formirioe for their reduction, collected both from the instruction given to him at Kew, and from his own careful examination of the manuscript books of the Ob- servatory. The magnetic instruments have arrived safely at Coimbra, and measures have been taken for the similar conveyance of the meteorological instruments. Mr. Beckley's drawings furnish all the data for the construction of the building, which will be simple and of small cost. An estimate, M. de Souza says, is appended ; but it does not appear in the printed report. M. de Souza further alludes to his having reported, both to the University and to the Government, his attendance at the Meeting of the British Associa- tion at Manchester, as a member of its Committee of Mathematics and Physics, where he was enabled to enter into relations with the distinguished men assembled there from all pai'ts, some of whom were Directors of Observatories, who promised the accounts of their results, and would doubtless expect his. The British Association has granted a complete copy of their annual Reports from the commencement, and with these and the works previously received, the Coimbra establishment would find itself at once in possession of a good library of tbe best writings on the subjects of its investigations. He once more recalls all the kindness and assistance he received in England, adding that the Eoyal Society granted ^30 from their " Donation-fund " for the expenses of the verification of the magnetic instruments prepared for the Coimbra Observatory, and concludes by urging the completion of the arrange- ments for an establishment which he trusts will prove alike honourable to his University and to his country. Report on the Dredging of the Northumberland Coast and Dogger Bank, drawn up by Henry T. Mennell, on behalf of the Natural History Society of Northumberland, Durham, and Newcastle-on-Tyne, and of the Tyneside Naturalists' Field Club. The Committee to whom the grant of the Association for " Dredging on the Dogger Bank and tbe coasts of Northumberland and Durham " was entrusted having, at the request of the Natural History Society of Northumberland, Durham, and Newcastle-on-Tyne, and of the Tyneside Naturalists' Field Club, courteously committed the practical carrying out of the proposed inves- tigations to these bodies, their members contributed the large sum required in addition to the Association grant, and I have now to report the result of our labours. , Tlie dredging took place at the end of August ; hence the time which has since elapsed has been too limited to do full justice to the specimens obtained in many departments. It was confined to the following localities: 1st, on a line due east of Tynemouth, extending to the Dogger Bank, a distance of about 100 miles. The dredging commenced about twenty miles from land, was resumed at ON THE DREDGING OF THE NORTHUMBERLAND COAST. 117 about fifty miles from land, and continued at intervals of about five miles for the remainder of the distance. The depth of water never exceeded 40 fathoms, and ranged chiefly from 25 to 35 fathoms, the bottom being mainly composed of fine sand and ooze. On the second cruise, the coast twenty miles off Coquet Island, and twenty to thirty miles off Berwick, was thoroughly dredged ; in the latter locality the water attained a depth of 55 fathoms, being the deepest we possess off the Northumberland coast. The bottom consisted of coarse sand and gravel. The vessel employed was a steamer. The following gentlemen have, at the request of the two Societies, prepared lists of the specimens obtained, and are responsible for the determination of the species, viz. : — Mollusca (except Tunicata), Mr. H. T. Mennell. Mollusca Tunicata, Mr. Joshua Alder. Crustacea, Rev. Alfred Merle Norman. Pycnogonoidea, Mr. George Hodge. Echinodermata, Mr. George S. Brady. Polyzoa, 1 Hydrozoa, [■ Mr. Joshua Alder. Actinozoa, | Foraminifera, Mr. Henry B. Brady, F.L.S. The results, as arrived at by these gentlemen, are summarized below. Of Mollusca 136 species were obtained, viz. : Cephalopoda 1 Proso- Opistho- Nudi-brancbiata. Gasteropoda 64 = 51 + 7 + 6 Lamellibranchiata , 60 Brachiopoda] Tunicata 11 136 No species new to science was obtained, and but one previously unrecorded as British. This is the Cynthia glacialis of Sars, two specimens of which had been previously obtained by Mr. John Stanger on the Northumberland coast, and noticed in the Tyneside Club Transactions under the provisional name of Cynthia vestita (Alder). It has since been ascertained, however, that Professor Sars had taken the species on the Norwegian coast, and published it in 1858 under the name we now adopt. Pour other species were added to those recorded in Mr. Alder's excellent " Catalogue of the Mollusca of Northumberland and Durham," published in the ' Tyneside Club Transactions,' viz. Rissoa sculpta (Forbes and Hanley), new to the east coast of Britain, Eulima nitida (Lamarck), Eulima gracilis (Alder, MS.), and Syndosmya intermedia. Several species hitherto considered to be of great rarity on our coast were obtained in some plenty, e.g. Trophon Barvicensis, Mangelia Trevelyana, Chemnitzia fidvocincta, Scalaria Trevelyana, Trochus millegnmus, Puncturella Noachina, and Lucina flexuosa. Of the rarer species previously recorded, there were found, but not abundantly, Mangelia teres, Natica Grcenlandica, Philine quadrata, Cylichna strigella, Crenella decussata, and Neaira cuspidata. Of the special varieties of the Dogger Bank which have hitherto only been taken on the fishing-lines, the only trace obtained was a single capsule of Fusus Turtoni. Further efforts are therefore required to ascertain the exact habitat on our coast of the rare larger Fusi, of Buccinum (?) Dalei and Pano- 118 REPORT— 1862. pcsa Norvegiea. "When this is discovered we may expect to find associated with them many interesting Boreal species, perhaps too small to have attracted the attention of the fishermen. Some interest attaches to the subfossil or upper tertiary shells which were dredged in very deep water twenty to thirty miles east of Berwick. Amongst these were Astarte ellipticd and Mya truncata, var. Uddevallensis, neither of which have been found living on our coast, and Margarita cinerea, an extinct species, which has been recently dredged under similar conditions in other localities. The whole of the Crustacea which were obtained have not as yet been examined ; but among those already determined are many of great interest. In all about 90 species were dredged. Among the Podophthahnia, mention may be made oilnaclius Dorsettensis as new to the N.E. coast of England, and of Crangon spinosus, bispinosus, and Altmanni. The last of these, a recently distinguished species, was abundant both off the Durham and Northumberland coasts. From several specimens of Hippolyte securifrons which were obtained, Mr. Norman is enabled to correct an error in the specific character which he gave at the last meeting of the Association, from the Shetland type specimen. He finds that there are four instead of three pairs of spines on the front margin of the carapace, two spines being placed together over each orbit. Both sexes of Mysis spiritus (Norman), only previously known from three or four females taken near Hartlepool, were dredged in considerable numbers ; and also an undescribed species of the same genus, which Mr. Norman thus describes : — "Mysis didelphys (Norman, n. sp.). " Antennal scale lanceolate, twice as long as the eye, two-jointed, ciliated all round ; the second joint very short, with a rounded apex terminating in five cilia. Telson entire, not more than two-thirds the length of the in- termediate, and half the length of the external laminaj of the tail; lateral mar- gins of telson armed with ten spines, some of which are situated quite at the base ; apex with a large spine at each corner, but no central intermediate spines. " This is a much stouter species than Mysis vidgaris, to which it is nearly allied. The antennal scale is less produced ; and the second joint is much shorter, and terminates in five cilia instead of in an acutely pointed spine. The telson is likewise shorter, with fewer lateral spines, and without the two intermediate apical spines which are present in Mi vulgaris. Mysis didelphys was dredged in deep water, forty miles off the coast, while the habitat of M. vulgaris appears to be invariably the brackish waters of estuaries and salt- marshes." The curious and abnormal family of the Diastylidae was well represented by Diastylis Raihkii, Eudora truncatula, Vaunthomsonia cristata, and three undescribed species. These are thus named and described by Mr. Norman : — " Cuma rosea (Norman, n. sp.). " Last five segments of the thorax uncovered by the carapace. No abdominal legs. Carapace unarmed above and below, rounded in front. Telson well developed, as long as the basal portion of the caudal appendages, furnished with two spines on each side, and having the rounded apex closely surrounded by seven subequal spines. Colour white, mottled with rosy spots. Dredged 50-60 miles east of Tynemouth. " Cyrianassa elegans (Norman, n. sp.). " Only three pairs of abdominal legs, which are the appendages of the first three segments. Telson produced, as long as the basal joints of the caudal ON THE DREDGING OF THE NORTHUMBERLAND COAST. 119 appendages, armed with a spine on each 8ide and eight spines around the extremity. Deep water off Tynemouth. " Cyrianassa cilidta (Norman, n. sp.). " Carapace hispid, truncate in front, and furnished with a toothed process on the antero-lateral margin. Lower antennae longer than the body. Five seg- ments of the thorax uncovered by the carapace. Abdominal legs, two pairs, attached to the first two segments. Telson short, one-third the length of the basal joint of the lateral appendages, with a rounded unarmed extremity. Caudal appendages furnished with plumose cilia, which are remarkably long on the outer branch. Deep water off Tynemouth." Among the more interesting Amphipoda obtained were Montagua Alderii and pollexiana, Callisoma crenata, Anonyx dentieidatus, Ampelisca Gaimardi and Belliana, Phoxus plumosus, Ipjhimedia obesa, Acanthonotus testudo, Atylus bisphiosus, Microdeutopus anomalus, Caprella lobata, Dexamine Vedlomensis, Kroyera altamarina, and Melita proximo,. Of the last three species only the type specimens were previously known. Two Entomostraca were dredged which are new to the British fauna, Cypridina globosa (Liljeborg) and Ichthyophorba hamata (Liljeborg), and a third, new to science, thus described by Mr. Norman : — " Cythere limicola (Norman, n. sp.). " Carapace-valves slightly quadrilateral, front margins oblique, greatest height at the anterior third. Sculptured with two elevated, lougitudinal, slightly curved parallel lines on the lower half of the valves, from the anterior extremity of which a transverse elevated line passes to the hinge-margin, where it terminates in a large tubercle. Two similar tubercles close together near the hinder extremity of the hinge-margin." Among the other Entomostraca were Nebalia bipes, Cythere quadridentata and acuta, and what is perhaps a variety of flavkla, Cythereis jimbriata, Evadne Nordmanni, and Anomalocera Patersonii. Of Pycnogonoidea (which we only separate from the Crustacea because they have been on this occasion examined by different gentlemen, and not as expressing an opinion that they should be so separated) ten species were obtained, belonging to four genera, Pycnogonum, Phoxichilidium, Pallene, and Nymplwn. Of these, two are new to Britain and two are new to science ; the latter are thus described by Mr. George Hodge : — " Pallene attenuata, n. sp., Hodge. "Rostrum thick, constricted at the base, swollen near the middle, and rounded at the apex. Legs long, sparingly hispid ; first, second, and third joints short, the second the longer ; fourth rather stout, and as long as the second and third united ; fifth and sixth slender, and about the length of the fourth ; seventh very short ; eighth convex on the outer margin, straight on the inner, with a few short hairs scattered along both margins. A single claw at the extremity, which, when pressed against the limb, reaches to the junction of the seventh joint. Eoot-jaws long and slender, projecting con- siderably beyond the end of the rostrum. Anterior portion of thorax attenuated, and advanced nearly in a line with the tip of the rostrum, where it slightly bulges and gives origin to foot-jaws, immediately behind which is seated the oculiferous tubercle, which is long and narrow. Abdomen long, rounded at apex, slightly tapering to base. At the origin of each leg on the dorsal aspect is a large wart-like protuberance. " Nymphon brevirostris, n. sp., Hodge. " Rostrum short and stout ; foot-jaws thick, divergent, second joint or hand nearly as long as the first; palpi five-jointed, brush-like, first and second 120 REPORT — 1862. joints long and nearly of the same length, either of them equal to the three terminal joints, the last of which is the shortest. Thorax robust. Abdomen stout and conical. Oculiferous tubercle midway between the first pair of legs. Legs stout, sparingly furnished with stout spine-like hairs ; first and third joints short ; second slender at its origin, swelling upwards ; fourth and fifth joints each as long as the first three ; sixth much longer, and slender ; seventh short; eighth long, slightly bent, furnished along its inner margin with a few short spines, and terminating in one moderately large and two small claws." Two species of Nymplwn new to Britain were also taken, viz. Nymphon hirtum, 0. Fabr., and N. brevitarse, Kroyer. The rarity of male Nymphons is singular ; none were obtained during the expedition, although the number of females was considerable : on the contrary, the males of Pycnoyonum were abundant, and the females rarely seen. This seems to be the usual experience of collectors. The researches of Mr. Hodge into the development and structure of the Pycnogonidse have led him to place them with the Entomostraca, as an order of that subclass, Araehnopoda or Pycnoyonoidea. A great number of Annelids were dredged, but these have not yet been catalogued ; we trust, however, next year to present a satisfactory list of these animals. Sipunaihis Bernhardus was one of the most abundant species, occu- pying every dead Dentalium which was brought up. It may be remarked also that in the deepest water dredged, that is, off Berwick, the dredge showed the bottom to consist almost entirely of fragments of the deserted tubes of these creatures. Few opportunities existed of obtaining Entozoa ; those that did occur were not neglected, but the number was so meagre that no list has been attempted. Of Echinodermata wo dredged twenty-seven species ; amongst these is one species of Opliiura hitherto undescribed, of which Mr. G. Hodge, who had a short time before taken it on the Durham coast, gives the following description : — " Ophiura Normani (n. sp., George Hodge). "Disk either pentangular or round, the former pertaining to well-grown, the latter to young specimens. Upper surface of disk rotulatcd, under surface corresponding with that of the other members of the genus. Two clasping scales at the origin of each ray, each bearing about ten short spines. A crescent of eight or ten short blunt spines on the upper surface of the rays, close to the disk. Lateral ray-plates bearing five moderately long spines. Upper ray-scales nearly square, slightly tapering towards the disk. Bays about four times as long as the diameter of the disk, which in well-grown individuals measures about ^ of an inch. Colour reddish yellow, occasionally of a pale sandy tint." The Rev. A. M. Norman has also taken a single specimen of this species in the Clyde, and three or four in the Shetlands. Bryssus lyrifer, a species previously considered to be of much rarity on the coast, was met with in great plenty and of unusual size ; still more abundant were Spatangus purpureas and Amphidotus roseus. All the species of Ophiuroidea, Asteroidea, and Echinoidea were much more plentiful on the muddy ground which lies immediately within the Dogger Bank than elsewhere. Uraster rosea, a fine species not before met with on the east coast, was added to the local fauna. Among the Holothuridse, several specimens of a small Thyonidium were ON THE DREDGING OF THE NORTHUMBERLAND COAST. 121 dredged in Berwick Bay, which appear to be the Holothuria pellucida of Midler, and not the Cuciimaria hyalina of Forbes, the latter of which appears to belong to the genus Thyone. Should a further examination confirm this view, the species is new to Britain. Thyonidium commune was also added to our loeal fauna. No Zoophytes were obtained previously unrecorded in Mr. Joshua Alder's " Catalogue of the Zoophytes of Northumberland and Durham," published in the ' Transactions of the T}-nesidc Club ;' nevertheless the list is a good one, containing as it does 77 species, viz. — Polyzoa 27 Hydrozoa 40 Actinozoa 10 77 Among the Polyzoa, Menipea ternata and CeJhdaria Peacldi, two northern deep-water species rare on other parts of the English coast, were procured in considerable abundance. Of Biujula Murrayana and B. fastiyiata, also northern forms, only two or three specimens were obtained. Among the Hydrozoa the most noteworthy is Sertularia fusca, a species peculiar to the north-eastern coasts of England and to Scotland. Sertularia 'pinaster was also met with, and S. tamarisca with female capsules. The Medusida? are not included in Mr. Alder's Catalogue just referred to, and of these very few species were identified. A very fine and strikingly beautiful Medusa was, however, taken some seventy or eighty miles from the coast, [which appears not to have been hitherto met with in our seas ; nor, indeed, have we seen the description of any genus to which it woxdd seem to be assignable. The Rev. A. M. Norman describes it as follows : — " The hydrosoma is inverted cup-shaped, moderately convex, about 41 inches in diameter, tinged with deeper and paler shades of indigo-blue. " The margin is divided into eight major lobes, each of which is subdivided into four minor lobes, making thirty-two lobes in all. The disk of the hydro- soma is elevated into sixteen radiating ridges, alternating with as many intermediate furrows. A radiating canal, of an intenser blue than the rest of the hydrosoma, passes down each of the ridges ; and these radiating canals terminate in the deeper sinuses of the margin and in the central sinuses of the major lobes, while each furrow is traversed by a white vessel whose distal extremity is situated at one of the intermediate sinuses of the major lobes. Numerous transverse branches proceed from the blue and elevated canals, and pass down the slopes of the ridges to the base of the furrows. These transverse vessels are recognized by the deeper tint of blue which marks their course. " There are no tentacles on the margin of the disk ; but, situated a short distance within the margin, opposite each of the greater sinuses, there is seen a semicircle of about forty pale-yellow simple tentacles, which are so short that they scarcely hang below the margin of the disk. The horns of the semicircle of tentacles point outwards. " There are eight eyes, which are placed at the centre of the major lobes, on the blue canal, at a short distance from the margin. ** The oral appendages are greatly developed in the form of four (?) large, many-folded, ochreous-yellow curtains, exquisitely margined with a short, finely-cut fringe. The length of the curtains, as they hang suspended in the hydrosoma, is somewhat greater than their united breadth. 122 report— 1862. " The ovaries. — I take it that the brownish-pink masses which were seen suspended just outside the curtains in the living animal were the ovaries, but, not having had the opportunity of examining these bodies, I hesitate to state that they actually are the reproductive organs." The specimen described has been well preserved in a mixture of diluted spirit and creosote In Actinozoa our list is not rich ; Stomphia ChurcMce (Gosse), and a Phellia not yet ascertained, but probably the Phellia gausipata of Gosse (a species hitherto only taken at Wick), are among the rarer species obtained. The list of Foraminifera is a very rich one, considering the short timo and the limited area over which the dredging extended. Of the 101 species and varieties enumerated in Prof. Williamson's mono- graph, our list contains 55 ; and besides these, several are reserved for further examination. Fully twenty of those had not previously been found on our coast by Mr. Joshua Alder or Mr. H. B. Brady, the only observers. The most noticeable facts respecting the Foraminifera obtained are, first, the extraordinary prevalence of the various forms of Dentalina in the Berwick Bay dredgings, occurring as they do in every gradation from the extreme form of Dentalina subarcuata to the extreme of D. legumen. No line of demarcation can be drawn between tho hyaline shell constricted at the septa (the septal lines being oblique) and the more robust, much-curved form of D. legumen. On the same ground PolymorpJiina frequently assumes the more luxuriant form known as variety Jtstulosa. And secondly, the number and beauty of the Lagenw, of which every British variety was taken, most of them abundantly. Of the Sponges no list has been attempted, the very few species obtained waiting further examination. Altogether, the results are, I trust, such as to justify further efforts on the same coast ; and they are, at any rate, most interesting to our local natu- ralists, who are, through the medium of the Tyneside Naturalists' Field Club, working out the fauna of the district with a completeness which few districts can equal. Report of the Committee appointed at Manchester to consider and report upon the best means of advancing Science through the agency of the Mercantile Marine. By Cuthbert Collingwood, M.B., F.L.S. The Committee appointed at the Manchester Meeting of the British Asso- ciation consisted of the folio win": gentlemen : — . J o o v Dr. Collingwood, Liverpool. E. Patterson, F.E.S., Belfast. John Lubbock, F.R.S., London. J. Aspinall Turner, M.P., Manchester. P. P. Carpenter, Ph.D., Warrington. Rev. H. H. Higgins, M.A., Liverpool. Since that time much has been done in promoting the scheme suggested in the paper then read before Section D. That paper has been printed in the ' Proceedings of the Literary and Philosophical Society of Liverpool,' and copies of it have been struck off, and very largely circulated among ship- owners, merchants, and all the large and influential list of correspondents to whom the documents of the Mercantile Marine Association of Liverpool are ON THE MERCANTILE MARINE. 123 usually forwarded. I have also forwarded copies to all whom I know to he interested in the subject, and, in the volume of Proceedings, it has passed to all the scientific societies in correspondence with the Liverpool Literary and Philosophical Society. Mr. Robert Patterson, of Belfast, has brought the subject under the notice of the shipping interest and the Natural History Society of that town ; and many copies have been circulated in America through Captain Anderson (of the R.M.S.S. ' China'), Professor Agassiz, and Mr. "Wm. Stimpson of the Smithsonian Institution. Among those to whom I forwarded copies of the paper was Mr. E. Newman, who reprinted it in the ' Zoologist ' for July and August 1862. The subject has thus been brought fairly before the mercantile and scientific public, and the attention of a large number of persons has been directed towards it — the general opinion being decidedly in its favour, on the score of advantages to be derived at once by science and by philanthropy. In the autumn of 1861, in conversation with Earl Granville, Lord Pre- sident of the Committee of Council on Education, I had an opportunity of bringing the subject under his Lordship's notice, and of explaining to him the advantages which we proposed to ourselves from this scheme, well know- ing the important assistance which his Lordship might afford in case of its meeting with his approval. He expressed an interest in the matter, and desired to be further informed upon it. On the publication of the paper, therefore, at his Lordship's request, I sent him a copy, and shortly after received the following communication : — " Science and Art Department of the Committee of Council on Education, South Kensington, London, W., Jan. 30, 1862. " Sir, — I am directed by the Lords of the Committee of Council on Educa- tion to request that you will be good enough to furnish me with twenty copies of your pamphlet ' On the Opportunities of Advancing Science enjoyed by the Mercantile Marine,' to send to all the Navigation Schools under this department. " I am, Sir, " Your obedient Servant, " Normal M'Leod, " Dr. Collingwood, " Assistant Secretary. 15 Oxford Street, Liverpool." The next important advance was as follows : — It being considered of the last importance that the sanction and cooperation of shipowners should be obtained, a meeting was convened in the mayor's parlour, Town-hall, Liverpool, at which some of the most influential shipowners of that port, as well as the chairman and secretary of the Mercantile Marine Association, were present ; Mr. T. M. Mackay (a gentleman ever ready to cooperate in every scheme for the good of seamen) occupying the chair. The meeting having been informed of the nature and progress of the movement, and the subject having been discussed, the gentlemen present promised their support, both nominal, and pecuniary if it were required. Believing that much might be effected by associating merchant-officers with existing scientific societies, in an honorary manner, the reporter, as Secretary to the Liverpool Literary and Philosophical Society, brought the matter before the council and members. This Society, established in 1812, has just celebrated its fiftieth anniversary, and is the oldest scientific society in Liverpool. An addition to the laws was duly passed and confirmed, to the effect that the Society " be empowered to elect as Associates masters of vessels or 124 report— 1862. others engaged in marine pursuits, who may have peculiar facilities for adding to the scientific interest of the Society's proceedings ; such Associates to be in every case recommended by the council, and to have the same privileges as honoraiy members — their number to be limited to twenty-five." This plan, there is little doubt, may be productive of much good, and it is hoped will bo adopted by some other societies. It offers a stimulus to the intelligent ship- master, and tends to increase his self-respect, by showing that he is held in respect by those who appreciate his efforts to advance science and his own mental culture. Although it is hoped that in the course of time some tangible results may be obtained in several branches of science, the writer, being chiefly interested in the science of zoology, determined to make a beginning by causing to be prepared plain directions for the study and preservation of animals in all parts of the world. It being evident that, if we are to expect anything from the mercantile marine, its members should be definitely in- formed as to what we wish them to do, a committee of the Literary and Phi- losophical Society was appointed, at the writer's suggestion, to draw up such plain directions as should not fail to be sufficient for the end in view. The preparation of such a paper was entrusted to Mr. T. J. Moore, curator of the Liverpool Free Public Museum, a gentleman well qualified for the task ; and having received the sanction of the Committee, the paper was published as an Appendix to the ' Proceedings of the Literary and Philoso- phical Society ' for 1861-62. It is entitled, " Suggestions offered on the part of the Literary and Philosophical Society of Liverpool to Members of the Mercantile Marine who may be desirous of using the advantages they enjoy for the promotion of Science, in furtherance of Zoology," pp. 51. This pamphlet, containing full directions for the preparation of all kinds of animals, methods of study, and lists of text-books and useful apparatus, has been separately published by the Society, for distribution in quarters where it is likely to prove useful. It is desirable that such manuals for other sciences should be also carefully compiled, in order that every intelligent seaman may have scope to exercise his talents in whatever direction his own tastes may conduct him ; and thus, there can be no doubt that a useful and valuable body of scientific information would be collected to aid the researches of men of science at home. It is much to be regretted that a united body of members of the mercan- tile marine, such as the Mercantile Marine Service Association of Liverpool, should not enter cordially into a scheme which they have themselves acknow- ledged to be one fraught with usefulness. Had the executive council of this Association shown an ordinary interest in its progress, still greater advances would already have to be recorded ; but the writer is sorry to have to report that he has not met with that assistance and cooperation from that body which he felt entitled to look for. Although from the first invited to coope- rate in the plans proposed, no steps have been taken by them, beyond the tardy publication of some valuable suggestions urged upon them by one member of the council (since resigned) and one of the most intelligent mem- bers of the service. This lukewarmness of a body of men who, by their example, might be of the most material assistance is likely to retard, although not to destroy, the prospects of the scheme ; and could the services of a small and active committee of influential gentlemen be secured, success must ultimately crown their efforts. There can be no doubt whatever that it is to the rising generation of seamen that we must chiefly look for the fruits of any scheme of improved ON STANDARDS OF ELECTRICAL RESISTANCE. 125 education which may be adopted in the present day, and such establish- ments as the ' Conway ' training-frigate in the Mersey are powerfully useful to that end ; still, in order to collect together the elements of scientific in- dustry and laudable ambition, which doubtless exist, scattered among the present body of merchant-seamen, it is desirable, as a beginning, to offer a certificate of merit to such commanders and other oificers as hold the extra certificate of the Marine Board, or who keep the meteorological log-book supplied by the Observatory, or who show in various other ways a desire to improve their minds and to encourage industry in those under their charge. It must strictly be borne in mind, however, that the sea is the only place where the sailor's mind can be properly influenced. Churches, schools, and sailors' homes on shore are only attended by those whom better influences at sea have inclined for good. Masters of vessels, therefore, who encourage their apprentices to continue their studies at sea, and who open schools for the purpose of teaching those who have had no benefits of education on shore, are in the first place well deserving of some reward, such as a certificate of merit, which should be so constructed and signed as to carry some weight. The nature, therefore, of this certificate, and by whom it should be signed, are questions of great importance to the success of the movement, and woidd require mature consideration. If the Committee of Council on Education or the Board of Trade, or both, could be induced to take an active and official interest in the matter, the difficulty would be at once solved. It should be mentioned, as a practical encouragement of some value, that the Colonial and Continental Church Society (9 Serjeants' Inn, Fleet Street) has, through Captain Anderson, offered to grant libraries for sailors afloat, on the following conditions : — 1. The Council of the Mercantile Marine Service Association are to recommend to them four captains each year, to each of whom the above Society will grant a library, value £5. 2. It will be understood that it is desirable to select such captains as have communi- cation with our colonial possessions. Enough has now been said and done to prove that there is a current at work, setting in the right direction ; and we can only now leave the matter to time, feeling fully assured that it will go on, and bear ultimate fruit, both in the advancement of science and in the elevation of the character of the merchant-seaman. Provisional Report of the Committee appointed by the British Association on Standards of Electrical Resistance. Members of the Committee :— Professor A. Williamson, F.E.S. ; Professor C. Wheatstone, E.R.S.; Professor W. Thomson, F.R.S.; Professor W. H. Miller, F.R.S. ; Dr. A. Matthiesson, F.R.S. ; Mr. P. Jenkin. The Committee regret that they are unable this year to submit a final Ecport to the Association, but they hope that the inherent difficulty and importance of the subject they have to deal with will sufficiently account for the delay. The Committee considered that two distinct questions were before them, admitting of entirely independent solutions. They had first to determine what would be the most convenient unit of resistance ; and secondly, what would be the best form and material for the standard representing that unit. The meaning of this distinction will be apparent when it is observed that, if 126 report — 1862. first point were decided by a resolution in favour of a unit based on fessor Weber's or Sir Cbarles Bright and Mr. Latimer Clark's system, tbis tbe Professor decision would not affect tbe question of construction ; while, on the other hand, if the second question were decided in favour of any particular arrange- ment of mercury or gold wire as the best form of standard, tbis choice would not affect the question of what the absolute magnitude of the unit was to be. The Committee have arrived at a provisional conclusion as to the first question ; and tbe arguments by which they have been guided in coming to this decision will form the chief subject of tbe present Report. • They have formed no opinion as to the second question, or the best form and material for the standard. In determining what would be the most convenient unit for all purposes, both practical and purely scientific, the Committee were of opinion that tbe unit chosen should combine, as far as was possible, tbe five following quabties. 1. The magnitude of the unit should be such as would lend itself to the more usual electrical measurements, without requiring the use of extravagantly high numbers of ciphers or of long series of decimals. 2. The unit should bear a definite relation to units which may be adopted for the measurement of electrical quantity, currents, and electromotive force ; or, in other words, it should form part of a complete system for electrical measurements. 3. The unit of resistance, in common with the other units of the system, should, so far as is possible, bear a definite relation to the unit of work, the great connecting link between all physical measurements. 4. The unit should be perfectly definite, and should not be Hable to require coi'rection or alteration from time to time. 5. The unit should be reproducible -with exactitude, in order that, if the original standard were injured, it might be replaced, and also in order that observers who may be unable to obtain copies of the standard may be able to manufacture one for themselves without serious error. The Committee were also of opinion that the unit should be based on tbe French metrical system, rather than on that now used in this country. Fortunately no very long use can be pleaded in favour of any of the units of electrical resistance hitherto proposed, and the Committee were therefore at Hberty to judge of each proposal by its inherent merits only ; and they bebeve that, by tbe plan which they propose for adoption, a unit will be obtained combining to a great extent the five quabties enumerated as desi- rable, although they cannot yet say with certainty how far the fourth quabty, of absolute permanency, can be ensured. The question of the most convenient magnitude was decided by reference to those units which have already found some acceptance. These, omitting for the moment Weber's -, were found to range between one foot of seconds copper wire weighing one hundred grains (a unit proposed by Professor Wheatstone in 1843) and one mile of copper wire of -j^th in. in diameter, and weighing consequently about 841 grains per foot. The smaller units had generally been used by purely scientific observers, and the larger by engineers or practical electricians. Intermediate between the two lay Dr. Werner Siemens's mercury unit, and the unit adopted by Professor W. Thomson as approximately equal to one hundred millions of absolute — . ' The former is approximately equal to seconds ON STANDARDS OF ELECTRICAL RESISTANCE. 127 371 feet, and the latter to 1217 feet, of pure copper wire T Lth in. in diameter at 15° C. Both of these units have heen adopted in scientific experiments and in practical tests ; and it was thought that the absolute magnitude of the unit to be adopted should not differ widely from these resistances. The importance of the second quality required in the unit, that of forming part of a coherent system of electrical measurements, is felt not only by purely scientific investigators, but also by practical electricians, and was indeed ably pointed out in a paper read before this Association in Manchester by Sir Charles Bright and Mr. Latimer Clark. The Committee has thus found itself in the position of determining not only the unit of resistance, but also the units of current, quantity, and electro- motive force. The natural relations between these units are, clearly, that a unit electromotive force maintained between two points of a conductor separated by the unit of resistance shall produce the unit current, and that this current shall in the unit of time convey the unit quantity of electricity. The first relation is a direct consequence of Ohm's law ; and the second was independently chosen by Weber and by the two electricians above named. Two only of the above units can be arbitrarily chosen ; when these are fixed, the others follow from the relations just stated. Sir Charles Bright and Mr. Latimer Clark propose the electromotive force of a Daniell's cell as one unit, and choose a unit of quantity depending on this electromotive force. Their resistance-unit, although possessing what we have called the second requisite quality, and superior consequently to many that have been proposed, does not in any way possess the third quality of bearing with its co-units a definite relation to the unit of work, and has therefore been considered inferior to the equally coherent system proposed by Weber many years since, but until lately comparatively little known in this country. Professor Weber chose arbitrarily the unit of current and the unit of electromotive force, each depending solely on the units of mass, time, and length, and consequently independent of the physical properties of any arbi- trary material. Professor W. Thomson has subsequently pointed out that this system possesses what we have called the third necessary quality, since, when defined in this measure, the unit current of electricity, in passing through a conductor of unit resistance, does a unit of work or its equivalent in a unit of time*. The entire connexion between the various units of measurement in this system may be summed up as follows. A battery or rheomotor of unit electromotive force will generate a current of unit strength in a circuit of unit resistance, and in the unit of time will convey a unit quantity of electricity through this circuit, and do a unit of work or its equivalent. An infinite number of systems might fulfil the above conditions, which leave the absolute magnitude of the units undetermined. Weber has proposed to fix the scries in various ways, of which two only need be mentioned here — first by reference to the force exerted by the current on the pole of a magnet, and secondly by the attraction which equal quantities of electricities exert on one another when placed at the unit distance. In the first or electro -magnetic system, the unit current is that of which the unit length at a unit distance exerts a unit of force on the unit magnetic pole, the definition of which is dependent on the units of mass, time, and * Vide " Application of Electrical Effect to the Measurement of Electromotive Force," Phil. Mag. 1851. 128 report— 1862. length alone. In the second or electro-static system, the series of units is fixed by the unit of quantity, which Weber defines as that quantity which attracts another equal quantity at the unit distance with the unit force. Starting from these two distinct definitions, "Weber, by the relations defined above, has framed two distinct systems of electrical measurement, and has determined the ratio between the units of the two systems — a matter of great importance in many researches ; but the electro-magnetic system is more convenient than the other for dynamic measurements, in which currents, resistances, &c, are chiefly determined from observations conducted with the aid of magnets. As an illustration of this convenience, we may mention that the common tangent galvanometer affords a ready means of determining the value in electro-magnetic units of any current y in function of the horizontal com- ponent of the earth's magnetism H, the radius of the coil R, its length L, and the deflexion S, y=tang. 2 -j- . In this Report, wherever Professor Weber's, or Thomson's, or the absolute system is spoken of, the electro-magnetic system only is to be understood as referred to. The immense value of a coherent system, such as is here described, can only be appreciated by those who seek after quantitative as distinguished from merely qualitative results. The following elementary examples will illustrate the practical application of the system. It is well known that the passage of a current through a metal conductor heats that conductor ; and if we wish to know how much a given conductor will be heated by a given current in a given time, we have only to multiply the time into the resistance and the square of the current, and divide the product by the mechanical eqiuvalent of the thermal unit. The quotient will express the quantity of heat developed, from which the rise of tempera- ture can be determined with a knowledge of the mass and specific heat of the conductor. Again, let it be required to find how much zinc must necessarily be con- sumed in a Daniell's cell or battery to maintain a given current through a given resistance. The heat developed by the consumption of a unit of zinc in a Daniell's battery has been determined by Dr. Joule, as also the mechanical equivalent of that heat ; and we have only to multiply the square of the current into the resistance, and divide by the mechanical equivalent of that heat, to obtain the quantity of zinc consumed per unit of time. Again, do we wish to calculate the power which must necessarily be used to generate by a magneto-electric machine a given current of (say) the strength known to be required for a given electric light. Let the resistance of the circuit be determined, and the power required will be simply obtained by multiplying the resistance into the square of the current. Again, the formula for deducing the quantity of electricity contained in the charge of a Ley den jar or submarine cable from the throw of a galvanometer needle depends on the relation between the unit expressing the strength of current, the unit of force, and the unit magnet-pole. When these are expressed in the above system, the quantity in electro -magnetic measure is immediately obtained from the ballistic fornmla. In estimating the value of the various insulators proposed for submarine cables, this measure is of at least equal importance with the measure of the resistance of the conductor and of the insulating sheath ; and the unit in which it is to be expressed would be at onco settled by the adoption of the general system described. ON STANDARDS- OF ELECTRICAL RESISTANCE. 129 These four very simple examples of the use of Weber's and Thomson's system might be multiplied without end, but it is hoped that they will suffice to give some idea of the range and importance of the relations on which it depends to those who may hitherto not have had then' attention directed to the dynamical theory. No doubt, if every unit were arbitrarily chosen, the relations would still exist hi nature, and, by a liberal use of coefficients experimentally determined, the answer to all the problems depending on these relations might still be calculated; but the number of these coefficients and the complication re- sulting from their use would render such an arbitrary choice inexcusable. A large number of units of resistance have from time to time been proposed, founded simply on some arbitrary length and section or weight of some given material more or less suited for the purpose ; but none of these units in any way possessed what we have called the second and third requisite qualities, and could only have been accepted if the unit of resistance had been entirely isolated from all other measurements. We have already shown how far this is from being the case ; and the Committee consider that, however suitable mercury or any other material may be for the construction or reproduction of a standard, this furnishes no reason for adopting a foot or a metre length of some arbitrary section or weight of that material. Nevertheless it was apparent that, although a foot of copper or a metre of mercury might not be very scientific standards, they produced a perfectly definite idea in the minds of even ignorant men, and might possibly, with certain precautions, be both permanent and reproducible, whereas Weber's unit has no material existence, but is rather an abstraction than an entity. In other words, a metre of mercury or some other arbitrary material might possess what we have called the first, fourth, and fifth requisite qualities, to a higli degree, although entirely wanting in the second and third. Weber's system, on the contrary, is found to fulfil the second and third conditions, but is defective in the fourth and fifth ; for if the absolute or Weber's unit were adopted without qualification, the material standard by which a decimal multiple of convenient magnitude might be practically represented would require continual correction as successive determinations made with more and more skill determined the real value of the absolute unit with greater and greater accuracy. Few defects could be more prejudicial than this continual shifting of the standard. This objection would not be avoided even by a determination made with greater accuracy than is expected at present, and was considered fatal to the unqualified adoption of the absolute unit as the standard of resistance. It then became matter for consideration whether the advantages of the arbitrary material standard and those of the absolute system could not be combined, and the following proposal was made and adopted as the most likely to meet every requirement. It was proposed that a material standard should be prepared in such form and materials as should ensure the most absolute permanency; that this standard should approximate as nearly as possible in the present state of science to ten millions of - re , but seconds that, instead of being called by that name, it should be known simply as the unit of 1862, or should receive some other simpler name, such as that proposed by Sir Charles Bright and Mr. Latimer Clark in the paper above referred to ; that from time to time, as the advance of science renders this possible, the difference between this unit of 1862 and the true ten millions of 1862. 130 REPORT— 1862. m^tre 7- should be ascertained with increased accuracy, in order that the seconds error resulting from the use of the 1862 unit in dynamical calculations instead of the true absolute unit may be corrected by those who require these correc- tions, but that the material standard itself shall under no circumstances be altered in substance or definition. By this plan the first condition is fulfilled ; for the absolute magnitude of this standard will differ by only 2 or 3 per cent, from Dr. Siemens's mercury standard. The second and third conditions will be fulfilled with such accuracy as science at any time will allow. The fourth condition, of permanency, will be ensured so far as our know- ledge of the electrical qualities of matter will permit; and even the fifth condition, referring to the reproduction, is rendered comparatively easy of accomplishment. There are two reasons for desiring that a standard should be reproducible : first, in order that if the original be lost or destroyed it may be replaced ; secondly, in order that men unable to obtain copies of the true standard may approximately produce standards of their own. It is indeed hoped that accurate copies of the proposed material standard will soon be everywhere obtainable, and that a man will no more think of producing his own standard than of deducing his foot rule from a pendulum, or his metre from an arc of the meridian ; and it wi 11 . be one of the duties of the Committee to facilitate the obtaining of such copies, which can be made with a thousandfold greater accuracy than could be ensured by any of the methods of reproduction hitherto proposed. It is also hoped that no reproduction of the original standard may ever be necessary. Nevertheless great stress has been lately laid upon this quality, and two methods of reproduction have been described by Dr. "Werner Siemens and Dr. Matthiessen respectively ; the former uses mercury, and the latter an alloy of gold and silver, for the purpose. Both methods seem susceptible of considerable accuracy. The Committee have not yet decided which of the two is preferable ; but their merits have been discussed from a chemical point of view in the appended Report C, by Prof. Williamson and Dr. Matthiessen. An interesting letter from Dr. Siemens on the same point will also be found in the Appendix E. This gentleman there advocates the use of a metre of mercury of one square millimetre section at 0° C. as the resistance unit ; but his arguments seem really to bear only on the use of mercury in constructing and reproducing the standard, and would apply as well to any length and section as to those which he has chosen. When the material 1862 standard has once been made, whether of platinum, gold and alloy, or mercury, or otherwise, the exact dimensions of a column of mercury, or of a wire of gold- silver alloy, corresponding to that standard can be ascertained, published, and used where absolutely necessary for the pur- pose of reproduction. It should at the same time be well understood that, whether this reproduc- tion does or does not agree with the original standard, the unit is to be that one original material permanent standard, and no other whatever, and also that a certified copy will always be infinitely preferable to any reproduction. The reproduction by means of a fresh determination of the absolute unit would never be attempted, inasmuch as it would be costly, difficult, and uncertain ; but, as already mentioned, the difference between new absolute ON STANDARDS OF ELECTRICAL RESISTANCE. 131 determinations and the material standard should from time to time be ob- served and published. The question, whether the material standard should aim at an approxima- tion to the or , was much debated. In favour of the latter it second second was argued that, so long as in England feet and grains were in general use, the re woidd be anomalous, and would entail complicated reductions in second dynamical calculations. In favour of the = it was argued that, when second new standards were to be established, those should be chosen which might be generally adopted, and that the metre is gaining universal acceptance. Moreover the close accordance between Dr. Siemens's unit and the decimal TH PJ"T*P * multiple of the — weighed in favour of this unit ; so that the question second was decided in favour of the metrical system. In order to carry out the above views, two points of essential importance had to be determined. First, the degree of accuracy with which the material standard could at present be made to correspond with the = ; and second secondly, the degree of permanency which could be ensured in the material standard when made. The Committee are, unfortunately, not able yet to form any definite opinion upon either of these points. Eesistance-coils, prepared by Professor W. Thomson, have been sent to Professor Weber; and ho has, with great kindness, determined their resistance in electro-magnetic units as accurately as he could. It is probable that his determinations are very accurate ; nevertheless the Committee did not feel that they would bo justified in issuing standards based on these determina- tions alone. In a matter of this importance, the results of no one man could be accepted without a check. Professor Weber had made some similar deter- minations with less care some years since, but, unfortunately, he has not pub- lished the difference, if any, between the results of the two determinations. Indirect comparisons between the two determinations show a great discre- pancy, amounting perhaps to 7 per cent. ; but it is only fair to say that this error may have been due to some error in other steps of the comparison, and not to Professor Weber's determination. Meanwhile, it was hoped that a cheek on Weber's last result would by this time have been obtained by an independent method due to Professor Thomson. Unfortunately, that gentle- man and Mr. Fleeming Jenkin, who was requested to assist him, have hitherto been unable to complete their experiments, owing chiefly to their occupation as jurors at the International Exhibition. The apparatus is, however, now nearly complete, and it is hoped will before Christmas give the required deter- minations. If Professor Weber's results accord within one per cent, with these new determinations, it is proposed that provisional standards shall be made of German- silver wire in the usual way, and that they should be at once issued to all interested in the subject, without waiting for the construction of the final material standard. The construction of this standard may possibly be delayed for some con- siderable time by the laborious experiments which remain to be made on the absolute' permanency of various forms and materials. An opinion is very x2 132 report— 1862. prevalent that the electrical resistances of wires of some, if not all, metals are far from permanent ; and since these resistances are 'well known to vary as the wires are more or less annealed, it is quite conceivable that even the ordinary changes of temperature, or the passage of the electric cm-rent, may cause such alterations in the molecular condition of the wire as would alter its resistance. This point is treated at some length in the two Reports; E and G, appended, by Professor Williamson and Dr. Matthiossen. The ex- periments hitherto made have not extended over a sufficient time to establish any very positive results ; but, so far as can be judged at present, some, though not all, wires do appear to vary in conducting power. Mercury would be free from the objection that its molecular condition might change ; but, on the other hand, it appears from Report C that the mercury itself would require to be continually changed, and that consequently, even if the tube containing it remained unaltered (a condition which could not be absolutely ensured), the standards measured at various times would not really be the same standard. A possibility at least of error would thus occur at each determination, and certainly no two successive determinations would absolutely agree. If, therefore, wires can be found which are permanent, they would be preferred to mercury, although, as already said, no conclusion has been come to on this point. Some further explanation will now be given of the resolutions passed from time to time by the Committee, and appended to this Report. Dr. Matthicssen was requested to make experiments with the view of determining an alloy with a minimum variation of resistance due to change of temperature. Tbe object of this research was to find an alloy of which resistance- coils could be made requiring little or no correction for tempera- ture during a series of observations. A preliminary Report on this subject is appended (A), in which the curious results of Dr. Matthiessen's experiments on alloys are alluded to, and, in particular, the following fact connected with the resistance of alloys of two metals is pointed out. Let us conceive two wires of the two pure metals of equal length, and containing respectively the relative weights of those two metals to be used in the alloy. Let us further conceive these two wires connected side by side, or, as we might say, in multiple arc. Then let the difference be observed in the resistance of this multiple arc when at zero and 100° Cent. This difference will be found almost exactly equal in all cases to the difference which will be observed in the resistance of a wire drawn from the alloy formed of those two metal wires at zero and 100°, although the actual resist- ance at both temperatures will in most cases be very much greater than that of the hypothetical multiple arc. In order to obtain a minimum percentage of variation with a change of temperature, it was consequently only necessary to make experiments on those alloys which offer a veiy high resistance as compared with the mean resistance of their components. The results of a few experiments are given in the Report, but these are only the first of a long series to be undertaken. Hitherto an alloy of platinum and silver is the only one of which the conduct- ing power and variation with temperature are less than that of German silver. Professor W. Thomson and Dr. Matthiessen were requested to examine the electrical permanency of metals and alloys. A preliminary Report on the subject by Dr. Matthiessen is appended (B), in which he shows that, after four months, one copper and two silver hard-drawn wires have altered, becoming more like annealed wires, but that no decided change has yet been detected in the great majority of the wires. ON STANDARDS OF ELECTRICAL RESISTANCE. 133 Several eminent practical electricians were requested to advise the Com- mittee as to the form of coil they considered most suitable for a material standard, and also to furnish a sample coil such as they could recommend. Sir Charles Bright informed the Committee that he was ready to comply with the request. The point is one of considerable importance, respecting which it was thought that practical men might give much valuable information. Coils of wire may be injured by damp, acids, oxidation, stretching and other mechanical alterations. They may be defective from imperfect or uncertain insulation ; and they may be inconveniently arranged, so that they do not readily take the temperature of the surrounding medium, or cannot be safely immersed in water- or oil-baths, as is frequently desirable. No definite con- clusion as to the form of coil to be recommended, even for copies, has been arrived at. It was resolved " That the following gentlemen should be informed of the appointment of the present Committee, and should be requested to furnish suggestions in furtherance of its object : — Professor Ecllund (TJpsala) Professor T. Fechner (Leipsic). Dr. Henry (Washington). Professor Jacobi (St. Petersburg). Professor G. Kirchhoff (Heidelberg). Professor C. Matteucci (Turin). Professor Neumann (Konigsberg). Professor J. C. PoggendorfT (Berlin). M. Pouillet (Paris). Werner Siemens, Ph.D. (Berlin). Professor W. E. Weber (Gbttingen)." A letter, appended to this Report, was consequently addressed to each of these gentlemen. Answers have been received from Professor Kirchhoff and Dr. Siemens, which will be found in the Appendix. The resolution arrived at by the Committee to construct a material standard will entirely meet Professor Kirchhoffs views. The Committee have been unable entirely to adopt Dr. Siemens's suggestions ; but his statements as to the accuracy with which a standard can be reproduced and preserved by mercury will form the subject of further special investigation, and the Committee will be most happy to take advantage of his kind offers of assistance. A letter was also received from Sir Charles Bright, containing an ingenious method of maintaining a constant tension or difference of potentials. This point will probably come before the Committee at a later period, when Sir Charles Blight's suggestion will not be lost sight of. The Committee also received on the 29th of Sept., after the present Report had been drawn up, a letter from Dr. Essclbach, a well-known electrician, who had charge of the electrical tests of the Malta and Alexandria Cable during its submergence. In this letter Dr. Esselbach arrives at substantially the same conclusions as those recommended by the Committee. Thus, his first conclusion is "to adopt Weber's absolute unit substantially, and to derive from it, by the multiple 10 10 , the practical unit." This practical unit is precisely that recommended by your Committee. Dr. Esselbach uses the multiple 10 10 , starting from the II L r !^ where your Committee recommend second > the multiple 10 7 , starting from the mc ie : the residt is the same. second Dr. Esselbach's next conclusion is also of great practical value. He points out that the electro-magnetic unit of electromotive force, also multiplied by 10 10 , differs extremely little from the common DanielFs cell, and that, without doubt, by proper care such a cell could be constructed as would form a practical unit of electromotive force. This suggestion has the approval of 134 ■ report — 1862. the Committee. Dr. Esselbach next points out that the unit of resistance which he proposes differs very little from Dr. Siemens's mercury unit, which he, like your Committee, considers a great advantage ; and the difference is, indeed, less than he supposes. He also proposes to use "Weber's absolute unit for the unit of current — a suggestion entirely in accordance with the fore- going Report ; and he further points out that this current will be of con- venient magnitude for practical purposes. He next approves of the sugges- tions of Sir Charles Bright and Mr. Latimer Clark with reference to nomen- clature and terminology. In the body of his letter he gives some valuable data with reference to the unit of quantity, which he defines in the same manner as your Committee. This result will be analysed in the Report which Professor W. Thomson and Mr. Heeming Jenkin will make on the fresh de- termination of the absolute unit of resistance. The Committee attach high importance to this communication, showing as it does that a practical electrician had arrived at many of the very same conclusions as the Committee, quite independently and without consultation with any of the members. Dr. Esselbach has omitted to point out, what he no doubt was well aware of, that, if, as he suggests, two equal multiples of the absolute units of resistance and electromotive force are adopted, the practical unit of electromotive force, or Daniell's cell, will, in a circuit of the practical unit of resistance, produce the unit current. Mr. Fleeming Jenkin was requested to furnish an historical summary of the various standards of resistance, but he has been unable to complete his Report in time for the present meeting. Professor Williamson and Dr. Matthiessen were requested to put together the facts regarding the composition of the various materials hitherto used for standards of resistance, and the physical changes they were likely to undergo. "Wires of pure solid metals, columns of mercury, and wires of alloys have been used for the purpose. The Report of the above gentlemen is appended (C). In it they arrive at the following conclusions : — First, with reference to pure metals in a solid state, they consider that the preparation of those metals in a state of sufficient purity to ensure a constant specific resistance is exceedingly difficult, as is proved by the great discre- pancy in the relative conducting powers obtained by different observers. Electrotype copper is excepted from this remark. They also point out that the influence of annealing on the conducting powers of pure solid metals is very great, and would render their use for the purpose of reproducing a stand- ard very objectionable, inasmuch as it is impossible to ensure that any two wires shall be equally hard or soft. They observe that errors of the same kind might be caused by unseen cavities in the wires, and give examples of the actual occurrence of these cavities. They point out another objection to the use of pure solid metals as standards, in the fact that their resistance varies rapidly with a change of temperature, so that slight errors in a ther- mometer or its reading would materially affect the results of an experiment. Secondly, with reference to mercury, they show that it is comparatively easily purified, varies little in resistance with a change of temperature, and can undergo no change analogous to that caused by annealing ; but that, on the other hand, measurements of its conducting power by different observers vary much, that the tube used cannot be kept full of mercury for any length of time, as it would become impure by partial amalgamation with the ter- minals, and that consequently each time a mercury standard is used it has, practically, to be remade. The accuracy with which different observers can reproduce mercury standards has not been determined. ON STANDARDS OF ELECTRICAL RESISTANCE. 135 Thirdly, with reference to alloys, they say that there is better evidence of the independent and accurate reproduction of a standard by a gold-silver alloy of certain proportions than by a pure solid metal or by mercury. They point out that annealing and changes of temperature have far less effect on alloys than on pure metals, and that consequently any want of homogeneity or any error in observing the temperature dimng an experiment is, with alloys, of little consequence, but that, on the other hand, the existence of cavities must be admitted as possible in all solid wires. They are of opinion that the permanence of jewellery affords strong ground for believing that a gold-silver alloy will be quite as permanent as any solid pure metal ; and in the course of the Report they point out some curious facts showing that a great change in the molecular condition of some pure metals and alloys may occur without any proportional change in their conducting powers. Finally, they recommend that practical experiments should be made inde- pendently by several gentlemen to determine whether mercury or the gold- silver alloy be really the better means of reproducing a standard. The main resolution arrived at by the Committee, viz. that a material standard shall be adopted which at the temperature of 17° Cent, shall approxi- TV) f*T T"f* mate to 10 7 , as far as present data allow, has been already fully seconds explained. It was not arrived at until after several meetings had been held and the merits of the various proposals fully discussed. This resolution was passed (unanimously) at a meeting when five out of the six members of the Committee were present. It was at the same time resolved that provisional copies should be distri- buted at the present Meeting; but the circumstances have been already explained which have prevented this resolution from being carriedjnto effect. It was thought desirable that an apparatus should be designed which could be recommended by the Committee for use in copying and multiplying the units to be issued, since it is certain that some of the glaring discrepancies in coils intended to agree must have been due to defective modes of adjust- ment. Mr. Fleeming Jenkin has consequently designed an apparatus for the purpose, of which a description is appended. Messrs. Elliott Brothers have kindly constructed a couple of these instruments, which were seen in action, at the Meeting of the Association, by members interested in this subject. The present Report was drawn up by Mr. Jenkin, and adopted at a meeting of the Committee on the 30th of September. Appendix to Report on Standards of Electrical Resistance. A. On the variation of the electrical resistance of alloys due to change of temperature, by Dr. Matthiessen, F.R.S. B. On the electrical permanency of metals and alloys, by Dr. Matthiessen, F.R.S. C. On the reproduction of electrical standards by chemical means, by Professor Williamson, F.R.S., and Dr. Matthiessen, F.R.S. D. Professor Kirchhoff's letter. E. Dr. Siemens's letter. F. Dr. Esselbach's letter. G. Circular addressed to foreign men of science. H. Description of apparatus for copying and multiplying the units of re- sistance. 135 report— 1862. ArrENDix A. — On the Variation of the Electrical Resistance of Alloys clue to Change of Temperature. By Dr. Matthiessex, F.R.S. It has been shown* that the influence of temperature on the electric conduct- ing power of the metals amounts to 29-3 per cent, on their conducting power between 0° and 100° C. : an exception to this law has been found in ironf, the conducting power of which decreases between those limits 38-2 per cent. It was, therefore, useless to try any of the other pure metals, as they would, in all probability, have decreased by the same amount, as well as from the fact that the metals which would have suited the purpose had already been tried. I therefore turned my attention to the alloys, and, in conjunction with Dr. C. V~ogt, have made a long series of experiments respecting the influence of temperature on their electric conducting power. After having determined the conducting power of a few of them at different temperatures, together with the help of the few experiments which have already been made by different observers, it became obvious that the percentage decrement in their conducting power stands in some relation to the fact that, when a solid metal is alloyed with another (with the exception of lead, tin, zinc, and cadmium amongst each other), a lower conducting power is observed than the mean of that of the components %. The law which we found to regulate this property was with most alloys the following, viz. : — " The percentage decrement between 0° and 100° in the conducting power of an alloy in a solid state stands in the same ratio to the mean percentage decrement of the components between 0° and 100° as the conducting power of the alloy at 100° does to the mean conducting power of the components at 100° ;" or, in other words, " the absolute difference in the observed, resistance between 0° and 100° of an alloy is equal to the absolute difference between the means of the resistance of the component metals between 0° and 100°." For example, the conducting power of the hard-drawn gold-silver alloy was found equal to 15-03 at 0° (taking silver equal 100° at 0°), and de- creases 6-49 per cent, between 0° and 100°. The mean decrement of the components between 0° and 100° being 29-3 per cent., the conducting power of the alloy is 14-05 at 100°, and that of the mean of the components is 62-58 at 100°. If we now calculate the percentage decrement in the conducting power of the alloy between 0° and 100° from the above data, we find it equal to 0-58 per cent., and by experiments it was found equal to 6-49 per cent. Or, taking the resistance of silver at 0° = 100, and that of gold at 0°= 128-3, we find the resistance of the alloy at 0°=6G5-3, and at 100°=711-7, and that calculated from a mean of the volumes of its components at 0°= 113-2, and at 100°=159-8 ; therefore the absolute difference between the observed resistance at 0° and 100° is 46-4, and that between the calculated at 0° and 100°=46-8. Knowing already, from my experiments on the electric conducting power of alloys§, that when two metals are alloyed together in any proportion, if the alloy is merely a solution of the two metals in one another, its conducting power may be approximatively foretold, and that, from the above law, it is necessary that if the conducting power of an alloy should vary between the limits of 0° and 100° to a minimum extent, the alloy itself must have a minimum conducting power as compared with that calculated from its * Phil. Trans. 1862, pt. 1. t Matthiessen and Vogt, unpublished researches. % Assuming that the conducting-power or resistance of an alloy is equal to that of parallel wires of the components forming it. § Phil. Trans. I860, p. 161. ON STANDARDS OF ELECTRICAL RESISTANCE. 137 components, — I at once foresaw that it would be useless, as was afterwards proved by the research made in conjunction with Dr. Yogt, to make any experiments with the two metal-alloys, which may be looked upon as a solution of one metal in the other, as no j>ractical alloy would be found which woidd vary in its conducting power between 0° and 100° to a small extent. It must also be borne in mind that the alloy sought for must be a ductile one, capable of being drawn into wire, not too soft, as would easily be damaged by covering and winding, easily produced, and cheap in price. Bearing this in mind, wo turned our attention to some three metal- alloys, thinking that we had some chance there of obtaining a good result ; for it is well known that the conducting power of German-silver wire varies in such a slight extent between 0° and 100°. It also appeared worth while to experiment with some of those alloys which may perhaps be considered chemical combinations, or to contain such, as, for instance, platinum and silver ; and, on account of their other physical properties, the platinum-iridium alloys were also experimented with. In the following Table I give the results obtained in conjunction with Dr. Vogt. The unit here taken for comparison is that of a hard-drawn silver wire at 0°. The normal wires were made of German silver, and in order to obtain their values in terms of hard-drawn silver, they were compared with the gold-silver alloy. In these experiments it was thought better first to use those pure metals which are easily obtained, so as to learn some- thing regarding the manner in which the three metal- alloys behave, and then try some alloys made of the cheaper commercial metals. As will be seen by the Table, only the first part has been as yet carried out. Table. ("With each series, the formula deduced from the observations for the correc- tion of the conducting power of the alloy for temperature is given, when \ is equal to the conducting power at the temperature t C.) Composition of alloy. Weight. (1) Gold 58-3 Copper 26-5 Silver 15-2 Made from pure metals. Hard- drawn. Length 532 mm. ; diameter 0-625 mm. Conducting power. T. Found. 9-0 11-956 53-5 11-674 100- 11-438 X = 12-017-0-0069033*+0-0000im 2 . This alloy was taken as Karmarsch states it is the hardest and most elastic of all the gold-silver-copper alloys. Length 341-5 mm. ; diameter 0-618 mm. Conducting power. T. Found. 10-95 10-5637 33-52 10-4341 55-15 10-3130 78-35 10-1846 97-52 10-0852 X = 10-0220 - 0-0056248i + 0-0000009863f. This alloy was tried as it corresponded to equal volumes of gold-copper and gold-silver, and these again correspond to an alloy possessing the lowest conducting power of any of those made of gold-copper or gold-silver. (2) Gold 66-5 Silver 18-1 Copper .... 15-4 Made of pure metals. Hard- drawn. 138 REPORT 1862. Composition of olloy. Weight. Length 764 mm. ; diameter 0-553 mm. (3) Copper 78-3 n , .. Silver 14-3 Conduct** power. Gold 7-4 T - :Found - Made from pure metals. 11-0 45-591 Hard-drawn. 55-5 40-333 100- 37-560 X=44-472-0-081525< + 0-0003240< 2 . This alloy was taken to see the effect such a combination would have. Length 244 mm. ; diameter 0-682 mm. Conducting power. (±) Platinum . Iridium . . . Commercial alloy. Hard-drawn. 66-6 33-4 T. Found. 12-0 4-506 56-0 4-384 100-0 4-271 X=4-541-0-0029307*+0-000002724f. Length 381-5 mm. ; diameter 0-451 mm. Conducting power. T. Pound. 12-0 31-173 56-0 29-550 100-0 28-068 This alloy was tried as it possesses very great elasticity and does not become softer on annealing. On account of these properties, as well as its permanency in air (not oxidizing on its surface), it would serve exceedingly well for making springs and contacts for electric and telegraphic apparatus. (5) Silver 95-0 Platinum 5-0 Made from pure silver and commercially pure platinum. Hard-drawn. X=31-640-0-039363*+0-00003642« 3 . This and the following two alloys were taken as they probably contain chemical combinations. (6) Silver 90-2 Platinum 9-8 The metals employed were the same as in No. 5. Hard-drawn. (7) Silver G6-6 Platinum 33-4 Commercial alloy. Hard-drawn. \=6-7032-0-0022167<+0-000001394i 2 . In the following Table I have given the results in such a manner that they may be easily compared. Length 708 mm ; diameter 0-26 mm Conducting power. T. Found. 9-0 17-920 54-5 17-319 100-0 16-767 )13960« + 0-00001183« 2 . Length 169 mm. ; diameter 0-408 mm Conducting power. T. Found. 8-270 6-6850 54-00 6-5826 99-90 6-4987 ON STANDARDS OF ELECTRICAL RESISTANCE. 139 Table. Pure iron Other pure metals in a solid state Alloy 3 5 6 Gold-silver* 4 2 1 .... German silvert Conducting power atO°. 44-5 31-6 18-0 15-0 4-5 10-6 12-0 7-8 6-7 Percentage variation in conducting power be- tween 0° and 100°. 38-2 29-3 15-5 11-3 7-1 6-5 5-9 5-2 4-8 4-4 3-1 The method and apparatus employed for the above determinations, together with the precautions taken to ensure correct residts, have already been described^. We have made only three observations between 0° and 100°, for it was found that they gave almost exactly the same formulae for the correction of the conducting power for temperature as if we had taken seven or more observations between 0° and 100°. Each of the above values for the conducting power, at those temperatures, is the mean of three or more observations. It was easy to obtain the desired temperatures as a mean of several observations, after veiy little practice. I have no doubt that, in the course of our experiments, we shall be able to find an alloy, the conducting power of which will decrease between 0° and 100° even less than that of silver- platinum. The experiments are being continued, and I hope, before the next meeting of the Association, to be able to lay before you results which will throw more light on the subject, as well as to propose an alloy with a minimum variation in its conducting power due to change of temperature, which may be made commercially in a cheap manner of the common com- mercial metals, and possessing those properties which are essential that it should have. Appendix B. — On the Electrical Permanency of Metals and Alloys. By Dr. Matthxessen, F.B.S. Having, in conjunction with Prof. Thomson, been requested by your Com- mittee to make some experiments on this subject, we thought it advisable for one of us to undertake some preliminary experiments in which all possible disturbing causes were isolated. The chief of these are, oxidation by the oxygen of the air, as well as by acids produced by the oxidation of the oil or grease with which a wire is almost always covered when drawn, as the holes in the draw-plates are generally oiled or greased ; stretching during the process of covering and winding ; and after being wound on the bobbin, elon- gation by expansion or contraction, owing to variations of temperature, &c. These, I think, have been obviated in the following manner : — The wires were carefully wound round a glass tube in order to bring them into a smaller compass, and after taking them off, they were placed inside wide glass tubes, and soldered to two thick copper wires, these having been previously passed through corks which fitted into the ends of the glass tube ; through each of the corks a small glass tube passed, drawn out in the middle to enable it to be * Phil. Mag. Feb. 1861. t Pbil. Trans. 1862, pt. 1. J Ibid. 140 REPORT 1862. drawn off easily, and sealed hermetically by a lamp. The wire being soldered to the thick copper connectors, and the corks fitted into the tube, dry carbonic- acid gas was led through it for the space of about six hours, for the purpose of drying it perfectly, as well as of displacing the air contained in it ; after which the small glass tubes were melted off at the points, when they hare been previously drawn out. Tin caps, filled with melted marine glue, were then fitted over the corks and the ends of the tube, to prevent diffusion of the carbonic acid and air through the corks. The whole of the tin caps outside, as well as those parts of the copper- wire connectors which dipped in water of the bath in which they were placed whilst being tested, were covered with a thick coating of marine glue. The wires experimented with were as follows : — 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. Silver : Silver : Silver : Silver : Copper hard- drawn annealed hard-drawn annealed hard-drawn Copper : annealed Copper : hard-drawn Copper : annealed Gold : hard-drawn Gold : annealed Gold : hard-drawn Gold : annealed Platinum : hard-drawn .... Platinum : hard-drawn .... Gold-silver alloy : hard-drawn Gold- silver alloy : hard- drawn German silver : annealed .... German silver : annealed .... German silver : annealed .... Cut from the same piece ; pure. Cut from the same piece, but different from 1 and 2 ; pure. Cut from the same piece ; pure. Cut from the same piece, but different from 5 and 6 ; pure. Cut from the same piece ; pure. Cut from the same piece, but different from 9 and 10 ; pure. Cut from the same piece ; commercial. Cut from same piece. Made by Messrs. Johnson and Matthews. Cut from the same piece. No. 19 ar- ranged with longer connectors, and used as normal wire with which the rest were compared. The reason why duplicates were made in each case was that, in case any of them should by any cause get damaged, the experiments might be continued with the duplicate. When being tested, they were placed in a large bath containing from 40 to 50 litres of water. By testing the wires at 20° it was found easy to keep that temperature in tho bath, diuing the experiments, to 0-1° or 0-2°. Up to the present time, that is to say, four months since they were first tested, the conducting power of the wires 1, 3, and 5 has altered, owing to becoming, in all probability, partially annealed. "Wire 8 has also altered mate- rially, having decreased in conducting power 3-5 per cent. : this decrement may be possibly due to bad soldering. The differences found with the other wires are so very small, that it is impossible to say whether they have altered or not ; for 04° or 0-2° will account for them. It was, therefore, thought better to wait for another two or four months before giving an opinion as to whether they alter or not ; for as the wires are in tubes and only surrounded by carbonic acid, we can never be absolutely sure that the wire has exactly the same temperature as the bath, more especially when it is considered that each time the con- nexion with the battery is made the wire becomes somewhat heated. If, two or four months hence, they still show no difference in their con- ducting powers, it is proposed to expose the one set to variations of tempera- ON STANDARDS OF ELECTRICAL RESISTANCE. 141 ture such as may occur (for instance, from 0° to 40°), and then, should no change occur in then- conducting powers, to lead a weak current through them, say, for a month ; for it has been asserted that a cm-rent passing through wire causes a permanent change in its conducting power. If after these experiments the conducting power of the wires remains un- altered, the different forms of resistance-coils, made from those wires, which have shown themselves permanent will then be tested in order to prove which is the best form of coil for the British Association unit. Appendix C— On the Beproduetion of Electrical Standards ly Chemical Means. By Professor "Williamson, F.R.S., and Dr. Matthtessen, F.B.S. In the following Report we have discussed, more especially from a chemical point of view, the relative merits of the different propositions which have been made to reproduce standards of electric resistance, and have treated them under three heads : — I. Those reproduced ly a given length and section or weight, at a given temperature, of a pure metal in a solid state. II. Those reproduced hy a given length and section or weight, at a given temperature, of a pare metal in a liquid state. III. Those reproduced hy a given length and section or weight, at a given tenipercrfure, of an cdloy. The points on which we shall speak will be — 1. On their p>reparation in a state of purity. 2. On their homogeneity and their molecular condition. 3. On the effect of annealing on their conducting power. 4. On the influence of temperature on their conducting power. I. Those reproduced ly a given length and section or weight, at a given temperature, of a pure metal in a solid state. _ As type of this class we have chosen copper, for it has been more exten- sively used as unit of electric resistance, both by scientific as well as by practical men, than any other metal or alloy ; but what we are about to say regarding copper will hold good in almost every case for all pure metals in a solid state. 1. On its preparation in a state of purity.— As traces of foreign metals materially affect the conducting power of most pure metals, it is of the utmost importance that those used for the reproduction of units of electric resistance should be absolutely chemically pure. The difficulty in obtaining absolutely pure metals even by chemists is very great. Thus, for instance, Becquerel* found the conducting power of pure gold at 0° equal to 68-9, compared with that of pure silver at 0° equal to 100 ; whereas, under the same circumstance, Matthiessen and von Bosef found it equal to 77-9,— showing a difference of about 12 per cent, in the values observed for the conducting power of gold, prepared pure by different chemists. This difference may be due to the silver not being pure, or to all of them being more or less pure. Now when we consider that these standards are required by electricians and other physicists who have little or no acquaintance with chemical manipulation, and that the cost of the preparation of absolutely pure metals by scientific chemists would be very expensive on account of the time and trouble they require, we think that this fact alone constitutes a very serious drawback to their use * Ann. de CMm. et de Phys. (1846) t. xyii. p. 242. + Phil. Trans. 1862, pt. 1. 142 report— 1862. as a means for the reproduction of standards of electric resistance. From the experience which one of us has had on this subject, it is more than pro- bable that if pure metals be prepared by different chemists in the ordinary way of business, variations in their conducting power would be found equal to several per cent. Thus, copper supplied as pure by a well-known assayer had a conducting power equal to 92, whereas pure copper conducts at the same temperature 100*. Again, the pure gold of the assayer conducts oidy 65-5, whereas pure gold at the same temperature would have a conducting power equal to 73 f. In order to show that the conducting power of com- mercial metals varies to a great extent, we give in the following Table (X.) the values found for that of the different coppers of commerce ; and it will be evident from it,. that to take a given length and weight or section of a com- mercial metal as unit, as has often been done, is very wrong, and can only lead to great discrepancies between the results of different observers. Table X.+ (All the wires were annealed.) Conducting power. Pure copper 100-0 at 15-5 Lake Superior native, not fused 98-8 at 15"5 Ditto, fused, as it comes in commerce. . . . 92 - 6 at 15-0 Burra Burra 88-7 at 14-0 Best selected 81-3 at 14-2 Bright copper wire 72-2 at 15-7 Tough copper 71-0 at 17-3 Demidoff 59-3 at 127 Rio Tinto 14-2 at 14-8 Similar variations will be found with most other metals, and we shall give examples of these further on. 2. On its homogeneity and ite molecular condition. — It is well known that the wires of some metais require much more care in drawing than in others : thus, copper and silver, if not annealed often enough during the process of drawing, will often become quite brittle, and break off short when bent. Now, if the fracture be closely observed, it will be seen that the wire is hol- low ; in fact, wherever it is broken, cavities will be found, and sometimes of a miDimetre or two in length ; so that such a wire may almost be regarded as a tube with a veiy fine bore. The reason of this is simply that in not an- nealing the wire often enough, the internal part of it becomes hard and brit- tle, whilst the outside remains annealed, from the heat evolved by its passage through the holes of the draw-plates ; after a time, however, the inside, being very brittle, will give way, whilst the outside is still strong enough to bear the force used in drawing it through the draw-plates. These places in the wires are easily discovered on drawing the wire finer ; for then at these points the wire slightly collapses, owing to the quicker elongation of the weak points by the force used in drawing. Silver and cojmer are the only metals which have been experimented with in this manner ; we are therefore unable to say whether it may occur with the other metals. However, although no such wires could be used for experiments, yet what has been shown possible to occur to such a marked extent when purposely trying to obtain such results, may occur * Proceedings of the Eoyal Society, vol. xi. p. 126. t Phil. Trans. 1860, p. i76. % Report of the Government Submarine Cable Committee, p. 335. ON STANDARDS OF ELECTRICAL RESISTANCE. 143 to some slight extent, especially when great care is not used, and when the wires are drawn by different persons. This may explain why, with some metals and alloys of the same preparation, conducting powers are often obtained which vary several per cent. For instance, W. Thomson* found the conduct- ing power of several alloys of copper which he had had made and tested to alter considerably on being drawn finer ; some of them were faulty from the cause we have just mentioned, and, on their being drawn finer, these places showed themselves, and were then cut away. It has also been shownf that when copper wire is heated to 100° for seve- ral days, a permanent alteration takes place in its conducting power : thus, with the first wire experimented on, it increased almost to the same extent as if it had been annealed. With the second wire the increment was not nearly so large as with the first, and with the third it hardly altered at all. That this is not due to one or the other of the wires being faulty in the just- mentioned manner is proved, 1st, By the close agreement in the conducting powers. 2nd, By the close agreement between the differences in the values found for the conducting powers of the hard-drawn and annealed wires. They were — 1st wire 2nd wire 3rd wire at 0°. at 0°. at 0°. Hard-drawn 99-5 100-0 100-3 Annealed 101-8 102-1 102-2 The values given for the hard-drawn wires are those which were observed before the wire was heated at all. 3rd, That the same occurs with pressed wires : thus, with bismuth it was found that the pieces of the same wire behaved differently ; wire 1 showing, after 1 day's heating to 100°, an increment in the conducting power of 16 per cent., whereas wire 2 increased, although a piece from the same length of wire, 9 per cent. Again, take the case of tellurium, and taking the conducting power of each bar at first equal to 100, we find that the conducting power of bar 1 had decreased after 13 days' heating to 4, where it then remained constant, that of bar 2 after 32 days became constant at 19, and that of bar 3 after 33 days at 6. The cause of these marked changes in the conducting power must therefore be looked for in the molecular arrangement of the wires or bars employed. In the case of copper, they may be, and probably are, due to the partial annealing of the wires ; for we find that wire 1, although the conducting power increased after having been kept at 100° for several days almost to the same extent as if it had been annealed, yet, on annealing it, it only gained as follows (the results obtained with wires 2 and 3 are added) : — 1st wire 2nd wire 3rd wire at 0°. at 0°. at 0°. Hard-drawn 99-5 100-0 100-3 After annealing 101-8 102-1 102-2 The above shows tbat, in all probability, the annealing plays here a part, but not the whole, in the change ; for otherwise why do the wires behave dif- * Proceedings of the Eoyal Society, vol. xi. p. 126. t Phil- Trans. 1862, jat. 1. 144 . report — 1862. ferently ? This point will be fully discussed in another Report which will be laid before your Committee, and in which it will be shown where the hard- drawn wires become partially annealed, and annealed wires partially hard- drawn, by age. It is a curious fact that a change in the molecular arrangement of the particles of wire of some metals which may be considered homogeneous has very little effect on its electric conducting power. Thus pure cadmium*, which when cold is exceedingly ductile, becomes quite brittle and crystal- line at about 80°, and returns again to its ductile condition on cooling, shows no marked change in its conducting power at that temperature ; in fact, it behaves as if no such change had taken place. Again, when iron wire is heated in a current of ammonia it becomes perfectly brittle and crystalline, without altering its conducting power to any marked extent. That a wire which changes its molecular condition in becoming crystalline does not necessarily materially alter in its conducting power, is an important as well as a veiy interesting point, and has also been proved in the case of German silver. 3. On the effect of annealing on the conducting power. — When hard-drawn wires of silver, copper, gold, &c, are heated to redness and cooled slowly, they become much softer, and on testing their conducting powers they will be found to have increased thus : — Silver. Copper. Gold. According to Taking the hard-drawn wire 100-0 100-0 100-0 The annealed will be . . 107*0 102-6 101-6 Becquerelf. Ditto 109-0 102-3 102-0 { M ^thiessen and [ von BoseJ. Ditto 110-0 106-0 — Siemens§. Now there is a certain difficulty in drawing a wire which is hard-drawn ; and if annealed wires be used for the reproduction of standards, the molecular condition, or perhaps the process of annealing, has an influence on the incre- ment of the conducting power. Thus, according to Siemens [, the difference in the conducting power between hard-drawn and annealed silver varies be- tween 12-6 and 8 per cent., and that of copper between 6 and — 0-5 per cent. ; according to Matthiessen and von Bose^f, that of silver varies between 10 and 6 per cent., and that of copper between 2-6 and 2 per cent. Again, the annealed wires of pure metals arc so soft that they would easily get damaged in covering them with silk or winding them on the bobbins, so that in using them the utmost care would have to be employed in order to prevent their getting injured. 4. On the influence of temperature on the electric conducting power. — It has been shown that the conducting power of most pure metals decreases, between 0° and 100°, 29-3 per cent. : pure iron has been found to form an exception to this law, its conducting power decreasing between those tempera- tures 38-2 per cent. If pure metals be therefore used as standards, very accurate thermometers are necessary, as an error of 0-1° in comparing two standards would cause an error in the resistance of about 0-04 per cent. Now there is great difficulty in obtaining normal thermometers ; and we must * Phil. Trans. 18G2, pt. 1. t Ann. de Chim. et de Phys. 1846, t. xvii. p. 242. % Phil. Trans. 1862, pt. 1. § Phil. Mag. Jan. 1861. || Phil. Mag. Jan. 1861. •ft Matthiessen and Vogt's unpublished researches. ON STANDARDS OF ELECTRICAL RESISTANCE. 145 bear in mind that supposing the zero-point of the thermometer is correct to- day, we are not at all justified in assuming that it will be so in six months time ; so that we ought to redetermine the zero-point of the thermometer be- fore using it for the above purpose. Again, it has been proved that the in- fluence of temperature on the conducting power of wires of the same metal is not always the same*. Thus, for the conducting power of annealed copper wires the following values were found : — o No. 1. No. 3. 100-0 100-0 20 92-8 92-4 40 86-3 85-6 60 80-4 79-6 80 75-1 74-4 100 70-5 70-0 showing therefore that if standards of pure metals be used, the influence of temperature on the conducting power of each would have to be ascertained. It must also be borne in mind that it is not at all easy to maintain a stand- ard, even in a bath of oil or water at a given temperature, for any length of time. II. Those reproduced by a given length and section or weight of a pure metal in a liquid state. The only metal which has been proposed to be used in a liquid state for the reproduction of units of resistance is mercury. We shall only have to speak of its preparation in a state of purity, and on the influence of tempe- rature on its conducting power. For a tube, carefully filled with mercury, will certainly form a homogeneous column, and its molecular condition will always be the same at ordinary temperatures. On its preparation in a pure state. — Although this metal is one of the most easily purified, yet the use of it as a standard is open to the same objec- tions, although in a less degree, as have been advanced against the use of pure metals in a solid state when speaking of their preparation. We there stated that metals prepared by different chemists conducted differently. Now although the same manipulator may obtain concordant results in purifying metals from different sources, yet that by no means proves that the results of different observers purifying the same metal would show the same concor- dance. Thus we find that the values obtained by one experimenterf for the resistance of mercury, determined in six different tubes, varied 1-6 per cent. This difference, he says, is not greater than was to be expected. The resist- ances found were as follows : — Tubes. I. II. III. IV. V. VI. Experiment. . . 1016-52 427-28 555-38 217-73 194-70 1142-3 Calculated . . . . 1025-54 427-28 555-87 216-01 193-56 1148-9 Again, the values found for the conducting power of different preparations of pure hard- drawn gold, by the same observer %, were found equal to * Phil. Trans. 1862, part 1. t Phil. Mag. Jan. 1861. The same experimenter (Dr. Siemens) states, however, in a later paper (Pogg. Ann. cxiii. p. 95), that he is able to reproduce standards of resistance by means of mercury with an accuracy equal to 0'05 per cent., but does not indicate what other precautions he takes (see remarks on the above, Phil. Mag. Sept. 1861). X Phil. Trans. 1862. p. 12. 1862. i 146 REPORT 1862. 78-0 at 0° 78-2 at 0° 76-8 at 0° 79-5 at 0° 78-3 at 0° 76-7 at 0° 77-0 at 0° 78-0 at 0° 77-3 at 0° These values agree together as well as might be expected, considering that 0-01 per cent, impurity would cause these differences. Now the values- obtained by different observers vary between the numbers 59 and 78. If we now take the case of copper, the values found by the same experi- menters* for different preparations of the pure hard- drawn metal were — 99-9 at 0° 99-4 at 0° 99-8 at 0° 101-0 at 0° 99-4 at 0° 100-3 at 0° 99-8 at 0° 99-9 at 0° 100-0 at 0° 99-9 at 0° They were drawn by themselves, and all, with one exception, electrotype copper. It is well known how differently the so-called pure copper conducts when prepared by different experimenters. In the following Table, in order to show these facts more clearly, we have given the conducting powers of the metals, taking that of silver equal 100 at 0°. Silver, copper, gold, and pla- tinum were hard-drawn. All values given, except where the contrary is mentioned, have been reduced to 0°. Siemens. Lenz. Becquerel. Matthiessen. Silverf 100 96-9 14-2 1-72 100 73-4 58-5 22-6 13-0 107 10-4 3-42 at 18-9 100 95-3 669 263 257 150 131 8-8 86 1-86 100 99-9 78-0 23-7 29-0 12'3 14-4 at 20-4 Q.O 10-5 at 20-7 1-65 Gold Tin If now mercury be taken as unit, we find the following values : — Siemens. Lenz. Becquerel. Matthiessen. Silver 58-20 5640 8-25 1-00 29-24 21-46 1710 6-59 3-80 312 304 100 at 18'7 53-76 51-23 3704 14-14 13-82 8-10 7-04 4-73 4-62 1-00 6060 60-55 47-27 14-42 1770 7-45 8-72 at 20-4 503 636 at 20-7 100 Gold Tin A glance at the foregoing Tables will suffice to show how badly Lenz's series agrees with the rest when mercury is taken as unit ; and, in fact, we obtain more concordant results if, in the above series, we take any other metal * Phil. Trans. 1862, p. 9. t This and the following Table have been copied from a paper published in the Phil. Mag. for Sept. 1861. ON STANDARDS OF ELECTRICAL RESISTANCE. 147 as unit. These facts therefore seem to indicate that mercury is not yet proved to be a safe means of reproducing standards of electric resistance. The influence of temperature on the conducting power of mercury, between 0° and 100°, is, comparatively speaking, small, being only 8-3 per cent., whereas that of the metals in a solid state decreases between those limits 29-3 per cent. This property would, of course, render the use of very accurate thermometers unnecessary ; for 1° would only cause a difference in the con- ducting power of about 0-08 per cent., and therefore 0-1 only 0-008 per cent., so that an error of 1 or 2 tenths of a degree might almost be overlooked. A fact has just come to our knowledge through Mr. Jenkin. He informs us that, having to make a report on the electric apparatus in the International Exhibition, he tested, amongst other things, several resistance-coils. Now he found two sets of coils made by the same firm, the one exhibited in the Prus- sian, the other in the English department. Both were said to be multiples of the mercury unit proposed by Siemens*, and their resistances determined by comparing a coil in each set with that of a tube filled with mercury. Taking each set by itself and comparing the coils in it with one another in the proper combination, they were found to be perfect ; in fact, the adjust- ment of them was perfectly accurate. When, however, Mr. Jenkin compared coils of the two sets with each other, instead of being equal, they were found to show a difference of 1-2 per eent.t III. On those reproduced by a given length and section or weight, at a given temperature, of an alloy. The alloy on which we have to speak is that composed of two parts by weight of gold and one of silver. The reason why this alloy was proposed is that the use of (say) 1 per cent, more or less gold does not materially alter its conducting power. 1. On its preparation. — It has been shown that the alloy may be made of commercially pure metals and have the same conducting power as that made from chemically pure ones ; for the maximum differences in the conducting power between those made in different parts of the world are not greater than those of a pure metal, either in a solid or liquid state, prepared by the same experimenter. But it may be urged that part of the differences obtained by different observers is due to the different methods employed in determining their conducting powers, and therefore had the conducting power of these alloys being determined by different persons, much greater differences would have been found. In answer to this, we give, in the fol- lowing Table, the determination of the conducting power of several alloys by Thomson and Matthiessen J, independently of one another. The alloys were made by Messrs. Johnson and Matthey. Alloy. Thomson. Matthiessen. 1 100-0 100-05 2 95-8 95-0 3 102-9 102-7 4 100-8 991 5 98-1 97-7 6 89-9 92-7 7 80-6 80-06 * PHI. Mag. Feb. 1861. t This discrepancy may perhaps be attributed to some inaccuracy in the reproduction of the mercury standard. J Proceedings of the Eoyal Society, Feb. 1861. l2 148 report — 1862. Pure copper. Thomson. Matthiessen. 1 107-0 107-2 2 107-5 105-9 3 108-7 106-9 4 107-7 108-1 The differences here, with the exception of alloy 6 and copper 2, may be due to the temperature at which the observations were made not being in both cases the same ; for 2 or 3 degrees' difference will account for them. The Table, however, shows that different observers do obtain the same values for the conducting power of the same wires. The values obtained for the conducting power of the gold-silver alloy, made by different persons, of different gold and silver, are given in the fol- lowing Table- Alloy. Hard- drawn. Annealed. 1 100-3 100-6 2 100-2 100-7 3 98-8 99-2 4 * • * * 100-2 5 100-4 100-7 & 99-7 99-8 7 100-3 100-8 8 100-1 100-4 which shows, therefore, that the alloy may be prepared in a commercial way, and still have a conducting power which varies less than that of a pure metal prepared at different times by the same experimenter. If we look at the hard-drawn series, we find five out of the seven wires tested agree toge- ther exceedingly well, the greatest difference being only 0-3 per cent. These five alloys were made, three in London, by scientific chemists, one in Frank- fort-on-the-Maine, and one in Brussels. Those which agree least with the others were made in New York (No. 3) and by a well-known assayer in Lon- don (No. 6). 2. On its homogeneity and its molecular condition. — If the wires of the alloy made and drawn by different persons were not homogeneous, the values obtained for the conducting power could not have agreed so well together. It has been already mentioned that some of the alloys determined by Thom- son, when redrawn, were found to have a different conducting power*. Conducting power of wire Conducting power Alloy. as received from the wire- after being re- drawer, drawn. 1 100-0 100-0 2 100-7 95-8 3 103-9 102-9 4 94-6 100-8 5 96-0 98-1 6 92-0 89-9 7 74-7 86-0 Pure copper. 100-0 98-6 Of conrse, here again, some of these differences are due to the temperature in each case not being the same ; but the differences found with the alloys 2, 4, and 6 were undoubtedly due to faulty wires. It was for this reason * Proceedings of the Eoyal Society, Feb. 1861. ON STANDARDS OF ELECTRICAL RESISTANCE. 149 that care was taken to have the alloy drawn by different persons, in order to see if this would influence the results obtained with them, as well as to ascer- tain whether the wires would show the same faults as silver and copper does when not carefully drawn. It has been argued that the molecular condition of all alloys is liable to undergo a change by age, and that, therefore, alloys are not fit to be used as standards. Thus, it is well known that brass and German silver become brittle and crystalline by age, and that the same may occur with the gold-silver alloy ; but on looking at the composition of the alloy, it will be found to have nearly the same as that of the gold chains of commerce. Now, we do not know of a single instance where such a chain, even after years of use, becomes brittle or crystalline ; so that we think it more than possible that the alloy will not change its molecular condition by age. It must also be remembered that even when German sil- ver becomes brittle, it does not materially alter in its conducting power. The same has already been proved, and mentioned in this Report, to be the case with iron and cadmium. 3. On the effect of annealing on the conducting power of the alloy. — When the alloy is heated to redness and cooled slowly, its conducting power was found to have increased only 0-3 per cent. — this value being the mean of eight wires annealed in different ways, — proving, therefore, that if the wires may be only partially hard-drawn, it will make but little difference in the conducting power. 4. On the influence of temperature on the conducting power of the alloy. — When wires of this alloy are heated from 0° to 100°, a decrement in the con- ducting power, amounting to 6-5 per cent., will be found. The same argu- ments may, therefore, be put forward in favour of the use of the alloy as a standard, as were done in the case of mercury when speaking of this pro- perty. To sum up, therefore, the arguments in favour of and against the use of the three propositions made to reproduce standards of electric resistance, we find in favour of a pure metal in a solid state : — 1. That it appears that all descriptions of electrotype copper, when carefully drawn, have the same conducting power. Against it : — 1. That their preparation, with the exception of the electrotype copper in a state of purity, is exceedingly difficult ; so that independent persons pre- paring the same metal find, on comparing the conducting powers obtained for them, that they vary several per cent. 2. That the influence of annealing on their conducting powers is so great that differences may occur simply because the wires are partially hard-drawn. 3. That the influence of temperature on their conducting power is very great ; so that slight errors in thermometers, or in the reading of them off, would materially affect the result. In favour of using mercury as a means of reproducing standards the fol- lowing may be said : — 1. That no molecular change can take place in the metal, nor can any alteration occur in its conducting power, on account of annealing ; for its tem- per is always the same. 2. That the influence of temperature has only a small effect upon its con- ducting power. And against it : — 1. That there is a difficulty in obtaining absolutely pure mercury; bo that the results obtained by different observers show great variations. 150 REPORT— 1862. 2. That the standard tube cannot be kept full of mercury for any length of time, owing to the diffusion of impure metal, arising from the amalgamated terminals into the narrow tube ; so that each time the standard has to be used, it must practically be remade. 3. If the tube be broken during the process of cleaning or otherwise, it is not yet certain with what exactitude the standard could be reproduced. 4. It is doubtful whether the resistance of a tube filled with mercury today will have the same resistance if filled a year hence ; for we have no proof if the dimensions of the tube will not alter by being kept. It is well known that the bulbs of thermometers are liable to change, and are conti- nually changing, in capacity. In favour of the gold-silver alloy may be said : — 1. That this material, when prepared and drawn by different persons, was found not to vary in its conducting power more than 1-6 per cent. ; whereas the variations found with the metals in a solid state, prepared and drawn by different persons, amounts to several per cent., and those found for mercury by different observers amount also in all cases to several per cent. 2. That the homogeneity and molecular corfdition of this alloy are always the same. 3. That the effect of annealing on the conducting power is very small, being only 0-3 per cent. ; so that if a wire be partially hard-drawn, its con- ducting power will not suffer to any appreciable extent. 4. That the influence of temperature on its conducting power between 0° and 100°, viz. a reduction of 6-5 per cent., is smaller than either that of the metals in a solid state, viz. 29-3 per cent., or that of mercury, vk. 8-3 per cent. And against it : — That the conducting power may alter by age, as the physical properties of alloys are more likely to change than those of metals. From the foregoing statements, based on facts at present known, it would appear that the best method of reproducing standards, for those who are un- able to procure copies of the British Association unit of electrical resistance, is that they should make, or have made, a certain amount of the gold-silver alloy (as described in the Phil. Mag., Feb. 1861), by two or three different persons, in order to ensure a correct result, and take a given length and sec- tion or weight of it, at a given temperature, which has been found equal in resistance to the British Association unit. We would recommend, in order further to test what we have stated in the foregoing Report, that three or more scientific men and electricians be requested to compare the resistances of pure mercury, obtained by them from the best sources they are able, and of the gold-silver alloy (made in the manner described in the Phil. Mag.) with a German-silver standard supplied to them by your Committee. If this be done, results would be obtained which would put an end to many disputes on the subject, as well as decide which of the above means is practically the best for reproducing standards of electrical resistance where no copies of the British Association unit can be obtained. Appendix D. — Professor Kirchhoff's Letter. To Fheming Jenkin, Esq. Heidelberg, June 8, 1862. Dear Sir, — I have the honour to acknowledge the receipt of your letter of the 31st of May, in which you inform me of the labours of the Committee appointed by the British Association, to try and bring about the general ON STANDARDS OF ELECTRICAL RESISTANCE. 151 introduction of one unit of electrical resistance. I gladly respond to the invitation to express my view on the manner in which the desired object might be best attained. To define the unit of resistance by the resistance of a wire of given dimensions of a pure metal appears to me impossible, for the reasons which have been urged by the Committee ; hence, of the three proposals discussed by the Committee, there only remain two for our consideration. 1. To adopt the unit proposed by "Weber ; or, 2. To establish, as unit of resistance, the resistance of a column of pure mercury of given dimensions and at a given temperature. I do not think that to these a third of equal value can be added ; for to define the unit of resistance by the thermal action of an electrical current would certainly never answer the purpose, because this thermal action cannot be measured with the necessary accuracy, and the resistance of any wire which is to be permanently kept cannot be fixed as unit ; for the resistance of any wire for a given temperature certainly undergoes changes if electrical currents are transmitted through it, and it is exposed to fluctuations of temperature. Of the above two units, the first recommends itself by coming up more satisfactorily to the demands of science ; the second, as I think, by being capable for the present of being practically carried out with greater accuracy. But is it really necessary to decide for one and against the other of these two units ? I think not. If the ratio between them is established with the accu- racy which is now attainable, there can, I think, arise no more confusion from their simultaneous use, than from the practice of expressing lengths sometimes in metres and sometimes in millimetres. You say, " It is proposed that the unit adopted shall be represented by one particular standard, constructed of very permanent materials, laid up in a national repository;" and further, " The Committee will probably endeavour to devise some plan by which copies of the actual material standard adopted may be easily procured at a reasonable cost." This plan, the execution of which I consider highly desirable, might evidently be realized in all its essential points without its being necessary to give the preference to one of these units over the other : it would only be necessary to measure the resistance of the normal standard in both units, and to add to each copy its resistance expressed in both units. In choosing the metal or the alloy of which the normal standard and the copies are to be made, care must undoubtedly Jirst be taken that the resistance is as unalterable as possible for one temperature. It is undoubtedly desirable that the resistance shall not vary rapidly with the temperature. This is, however, not very important, provided that the temperature of the wire can be accurately observed at any moment. To satisfy this condition, the wires must not be coiled upon cylinders, but fastened so that, for the greater part of their extent, they He clear, and hence rapidly assume the temperature of the surrounding air or of the non-conducting liquid in which they may have been immersed. You request me to point out to you any researches of mine which refer to a unit of electrical resistance. I have to mention a short treatise only, which appeared in vol. lxxvi. of PoggendorfPs ' Annalen,' under the title " Deter- mination of the Constants on which the Intensity of Induced Electrical Currents depends," and which formed the answer to an academical prize-question which Professor Neumann, in Konigsberg, had proposed in the year 1846. In thig treatise a unit of electrical resistance has not been suggested ; but in it the resistance of a wire has been measured by the unit (or rather by double the 152 report — 1862. unit), which was afterwards proposed by Weber in his " Electrodynamic Measurements." Professor Weber has subsequently had the kindness to compare the copper wire whose resistance I measured, with those whose resistances he himself had determined (Pogg. Ann. vol. lxxxii. p. 360) ; he thereby found the resistance of my wire about one-seventh greater than I had found it. The reason of this want of agreement consists partly in the im- perfection of the instruments which I had used, and partly in the fact that in my experiments the temperature was little above 0° R., while in Weber's experiments it was about 20° R. Allow me, my dear Sir, to record the very great respect with which I have the honour to be, Yours very truly, Gr. Ktbchhoff. Appendix E. — Dr. Slemens's Letter. — Suggestions for the adoption of a Common Unit in measurement of Electrical Resistance. To the Committee appointed by the British Association to report on Standards of Electrical Resistance. Gentlemen, — I beg to acknowledge, with thanks, the honour you have done me, in requesting me to furnish you with suggestions in furtherance of your endeavours to procure the adoption of a common unit of electrical resistance. I proposed in Poggendorffs Annalen (vol. ex. p. 1) to supply this want by the adoption of the conducting power of mercury as unit, and of the resist- ance which a prism of that metal a metre long, and a square millimetre section, at 0° C, opposes to the passage of a current, as unit of resistance. The method by which I constructed standards in this unit was as follows : From the ordinary glass tubes of commerce, pieces were selected whose calibre was found to vary most regularly. After the selected tubes had been ground to the length of a metre, they were carefully cleaned and filled with pure mercury — the temperature being measured. The contents were then weighed, and the values reduced to 0° C. for expansion of glass and metal. The resistances of the tubes were calculated by the formula _1 W=JjL 1 + Va+ Va, g' 3 which represents the resistance to a current in the longer axis of a prismatic conductor either in the above unit or in 0-001 unit, according as I is ex- pressed in metres and g in grammes, or I in millimetres and g in milligrammes respectively. o= 13-557, the specific gravity of mercury, at 0°C. 1+ */a+ hj a 3 is the coefficient for conicalness, which in good tubes equals 1, very nearly. a is the ratio of the greatest to the least transverse section of the tube. All the data therefore necessary for the value of W are exact measures of length and weight. Measurements of the same tube, at different times, gave results corresponding within 0-01 per cent, with each other. The first objection which is raised against the adoption of mercury as unit, " that the tubes cannot be made of uniform or similar wires, and that the ON STANDARDS OF ELECTRICAL RESISTANCE. 153 standard once broken is lost for ever," is clearly untenable, since the tubes are not required to be uniform, and the breakage of the standard involves only the necessity of anew tube, and the determinations of length and weight anew, to put the operator in possession of a new standard, whose agreement with the broken one will depend solely on his own handiness in manipulating. Every standard, of whatever material, is liable to injury ; but the breakage of a glass is infinitely to be preferred to the treacherous results of a bruised wire. Mercury is, of all metals, that which is best suited to supply a reproducible standard. In the first place, it is procurable pure in sufficient quantities. I heated for some hours samples of commercial mercury under sulphuric acid con- taining a few drops of nitric acid, and found their conducting powers after- wards to be precisely the same as that of a quantity of chemically pure mer- cury reduced from the oxide. Secondly, mercury has always the same molecular structure, and has there- fore, at the same temperature, always the same resistance. From these two grounds it is possible to couple with this unit a geome- trical conception which is indispensable in practice. Thirdly, of all metals capable of being used for resistances, mercury has the lowest conducting power ; and of all pure metals capable of the same applica- tion, its resistance varies least with variations of temperature. Having formed such original standards, it only remained to copy them in a convenient form for employment in practice. This I have done, — 1 . In raercury contained in glass spirals, and 2. In German-silver wire. The resistance-bridge which I made use of in these measurements, with a reflecting galvanometer in its circuit, enabled me to attain a precision of within 0-01 per cent. The mercury spirals, as may be seen by the accompanying drawing*, are provided with cups at their ends, for convenience of filling and for receiving the contacts of the measuring apparatus. They are either of known resist- ances, approximating only to a multiple of the unit, or may be adjusted to an exact multiple by boring out one of the ends of the tube, which, in this case, must stand up half an inch inside the cup. The resistances of the bridge must then be arranged so that no current passes through the instrument only when the desired resistance in the fourth side is reached. When the spiral is filled, a vulcanized india-rubber ring is put round the cups, and the spiral is suspended in a vessel of ice-water or water kept in circulation by passing a current of air through it, and the temperature measured by a delicate thermometer. The electrical value of each spiral which I have made has been determined by comparing it with at least two of the straight normal tubes, both being kept during the measurement in ice-water. The greatest differences which I have found between such determinations do not exceed 05 per cent., to which limit the copies may be trusted. In answer to the objection that an admixture takes place between the mercury and the solid metal used for the terminals, I must remark that I have found this occasion really less inconvenience than is generally believed. I kept the copper connexions immersed in the mercury a whole week, but could not perceive the slightest decrease in its resistance. Platinum elec- * The drawings have been omitted, the descriptions being intelligible without them. 154 report — 1862. trodes of considerable surface might be employed ; but I believe that the removal of the copper connexions after each test, and the removal of the old mercury from their surfaces before using them again, are a sufficient safeguard against error arising from this source. Besides, it is easy to fill the spiral with fresh mercury whenever it is suspected to have dissolved any quantity of copper, or even on every occasion when a measurement with it is to be made. Nor -does mercury change its resistance in the least by standing in the air. This I have proved by keeping a spiral six months filled without changing the mercury, and found its resistance to be constant. The material which I have extensively employed in copying this measure, viz. German silver, may be classed under the same head as the expensive gold- silver alloy of Dr. A. Matthiessen, over which it has, however, the con- siderable advantages of a greater specific resistance, and that its resistance varies less with temperature variations. As a preventive against alteration of resistance by the influence of the air, I have usually had the resistances made of this metal covered with a coating of silk and lac. Intermediate between the resistances to be measured and the measure itself, I have introduced resistance-scales. These contain each a series of resistances (multiples of the unit), and are so arranged that each resistance is exact when it stands stopped alone in the circuit. When carefully made, these scales may be depended on to 0-1 per cent. Being convinced of the sufficiency of the method I have described of repro- ducing a standard of electrical resistance, I have the honour to suggest to you, 1st. To recommend the universal adoption of the conducting power of mercury as unit, and of the resistance which a prism of that metal, a metre long, and square milhmetre section, at 0° C, opposes to a current of electri- city as common unit of resistance. 2nd. To have the value of this measure ascertained, with the greatest pos- sible exactness, in absolute units. 3rd. To have copies of this unit constructed in mercury contained in glass spirals for preservation in scientific repositories. In the event of my suggestions being adopted, the mercury unit should be determined again with the greatest possible care, and with all the help which pure and applied science offers, and copies of it made with equal exactness. According to a late determination by Weber, the mercury unit is only about 2| per cent, greater than 10 10 absolute units, or one mercury unit at— 26° C. would equal 10,000,000,000 absolute units. Since those cases in which the expression of resistances in absolute measure is of advantage in facilitating calculations occur only very seldom, and only in purely scientific exercises, a single determination of the relation of the two measures would be amply sufficient. Should the absolute unit or any mul- tiple of it be adopted as common unit of resistance, there would still be wanted a unit for expressing the conducting powers of bodies ; and mercury is indisputably the best calculated for this purpose. And for practical pur- poses, which in adopting a universal unit should be principally taken into consideration, it is indispensable to define the resistance -measure as a geo- metrical body of that material which is selected as unit of conducting power. Every other definition would not only burden unnecessarily the calculations which occur in common life, but also confuse our conception of the measure. The reason why the arbitrary unit proposed by Jacobi (a length of copper only approximately defined) found no admittance into general use is to be sought in the fact that it failed to fulfil this condition, and because the con- ON STANDARDS OP ELECTRICAL RESISTANCE. 155 ducting power of all solid bodies is too dependent on their molecular struc- ture. The same objection renders the adoption of the gold-silver alloy proposed by Dr. A. Matthiessen equally incapable. Another disadvantage in the way of a solid metal unit is the impossibility to solder thick connexions into the ends of a denned length of any wire without altering its resistance. Should the adoption of the mercury unit be deemed advisable, I would place at the service of the British Association any further information or assist- ance in my power. I have the honour to be, Gentlemen, Tour most obedient Servant, "W. Siemens. Appendix F. — Extracts from a Letter addressed to Professor "Williamson by Dr. Esselbach. The two objections against the practical applications of "Weber's absolute unit bave been sufficiently pointed out as being — 1. Its minuteness ; and 2. Tbat the electromotive force of galvanic elements does not allow of vari- ation (as strength of current, tension, and resistance do), but that we have to accept certain constants as nature has fixed them. I take it for granted that the standard of absolute unit would not lose in authority if a plain multiple of it were adopted. I need not point out that the French metre itself is only a submultiple, 100( ^ 000 th of a natural unit — the earth's quadrant. The multiple of the natural electro-magnetic unit I am about to suggest for practical use is 10 10 , therefore very simple (which is of no little importance) ; and it is a multiple which leads us to those standards wbieh are practically used. M. Bosscha gives the electromotive force of his Daniell's cells in absolute measure as 1025-80 . 10 s , and calculates the one used by Mr. Joule to be 1045-1 . 10 8 . It will therefore be practicable to determine such concentration of sulphuric acid as to make the electromotive force equal to 10 . 10 10 ; and I believe the concentration required would be very near what is actually used in telegraphy. Resistance. — Tbe different copies of Jacobi's etalons are well known to differ as much between each other as Daniell's cells ; and if Siemens had done nothing else for galvanometry than to give us copies which agree among themselves within a quarter per cent., the progress is obvious. "Weber's copy of Jacobi's etalon is 598 . 10 7 ; and that of M. Bosscha was 607 . 10 7 in absolute measure. Other statements (of Kirchhoff and others) give a much smaller value. In comparing Mr. Siemens's mercury standard with three copies of Jacobi's etalon in his possession, I found two of them agreeing tolerably well with 156 report— 1862. each, other, and with a third one copied by my friend Dr. Teddersen, at Leipzig, from the original of M. Leyser, which I took therefore to be the more correct ones. I found the absolute value of Siemens's unit to be ^- 3 10" 660 * ' or 1-1 Siemens's unit=10 10 . We should therefore only have to multiply all observations expressed in 10 10 Siemens's units by — -. to reduce them to absolute measure, and the suggested multiple for the future standard would not be far from 1-1 of Siemens's units, which every one admits to be for metallic conductors a practical unit. For the resistance of insulating materials the figures become impracticably high ; but it would be a matter of professional telegraphy to adopt, in con- formity with the system, the '. resistance ' 10 10 and, besides, another ' great resistance ' containing 10 10 ' resistances.' While the resistance of a mile of copper in an ordinary cable would be (say) 4 R. (four resistances), the insulation-resistance of a mile of cable would be about 0-04 G. R. (great or gutta-percha resistances). My suggestion would therefore be — 1. To adopt Weber's absolute unit, and to derive from it, by the multiple 10 10 (or 10,000,000,000), the practical unit. 2. To adopt 10 10 of Weber's electro-magnetic units as the 'practical abso- lute unit ' for electromotive force and resistance. (10 of these units would be exactly 1 Daniell's cell.) 3. 1 of these units would be 1-1 of Siemens's units. 4. To allow, besides, a ' practical great unit,' viz. 10 10 of the ' practical units,' for resistances in order to express the insulation-resistance of cables in convenient figures. 5. To allow also a ' practical small unit ' of tkt absolute units to express insulation-currents and charge-quantities of cables in convenient figures. 6. To adopt, in order to avoid confusion, for such ' practical units ' a terminology as proposed by Messrs. Bright and Clark. London, September 18, 1862. Appendix G. — Circular addressed to Foreign Men of Science. Sra, — I am requested to inform you that a Committee was appointed by the British Association, which met last year at Manchester, to report on Electrical Standards of Resistance. The Committee consists of the following gentlemen : — Professor W. H. Miller, F.R.S. (Cam- bridge). A. Matthiessen, Ph.D., F.R.S. (Lon- don). Fleeming Jen kin, Esq. (London). Professor A. W. Williamson, F.R.S. (University College, London). Professor Charles Wheatstone, F.R.S. (London). Professor William Thomson, F.R.S. (Glasgow). The Committee met on December 6th, 1861, and on April 3rd, 1862. On the latter occasion the following Resolution was passed : — " Resolved, — That the following gentlemen be informed of the appoint- ment of the present Committee, and be requested to furnish suggestions in furtherance of its object. ON STANDARDS OF ELECTRICAL RESISTANCE. 157 Professor Edhind (Upsala). Professor Th. Fechner (Leipzig). Dr. Henry (Washington). Professor Jacobi (St. Petersburg). Professor G. Kirchhoff (Heidelberg). Professor C. Matteucci (Turin). Professor Neumann (Konigsberg). Professor J. C. Poggendorff (Berlin). M. Pouillet (Paris). "Werner Siemens, Ph.D. (Berlin). Professor W. G. Weber (Gottingen)." I have, in consequence, the honour of addressing you the present letter. The Resolutions passed at the two meetings are enclosed, and from them you will gather the general scope of the Committee's inquiry. I add some further explanation as to the object and intentions of the Committee. Great inconvenience has been felt from the absence of any generally adopted unit for the measurement of electrical resistance, and it was thought that the influence of the British Association might be successfully exerted to procure the adoption of a common standard. The present time was thought especially favourable, since, although the methods of observation have been brought to great perfection, no local units have as yet taken very deep root. The units which up to the present time have been considered by the Committee may be classed under three heads : — 1st. A given length and weight or section of wire made of some pure metal, and observed at a given temperature, as originally proposed by Professors Wheatstone, Jacobi, and others. 2nd. Units based on Weber's and Gauss's system of absolute measure- ment. 3rd. A given length and section of pure mercury at a given temperature. Whatever basis is adopted for the unit, it is proposed that the unit adopted shall be represented by one particular standard, constructed of very permanent materials, laid up in a national repository ; and it has been proposed to use Dr. A. Matthiessen's gold-and-silver alloy for this purpose. The arguments which have been used for and against these systems are as follows : — In favour of the use of a wire of some pure metal it is said — That the plan is the simplest possible, and admits of independent observers forming their own standard. Against the plan it is said — 1st. That even when pure, two apparently similar wires do not resist equally unless their temper or molecular condition be the same — a condition which cannot practically be ensured. 2nd. That there is reason to believe that the resistance of a given wire is not constant even at a constant temperature. 3rd. That the resistance of all pure metals varies very rapidly with the temperature. 4th. That great difficulty is found in obtaining any metal pure, and that the attempt of most persons to reproduce the unit for their own use would be attended with incorrect results. This is evidenced by the different relative results as to the resistance of pure metals published by different observers. In favour of Weber's units it is urged — 1st. That their use will ensure the adoption of a complete system of corre- sponding standards for electrical currents, quantities, and tension or difference of potential. 2nd. That their use is essential in the dynamic treatment of any problem connected with electricity ; for instance, in determining the heat generated, the force exerted, the work done, and the chemical action required or pro- duced under any given circumstances. 158 report— 1862. 3rd. That their use would he a simple extension of the system already universally adopted in magnetic measurements. 4th. That the unit is independent of the physical properties of any material. Against the system it is urged that the unit cannot he determined with sufficient accuracy, and that even its approximate reproduction, where copies cannot he obtained, is difficult and expensive. In favour of the mercury standard the following arguments are used : — 1st. No change can occur in the molecular structure or temper of the material, and therefore the same tuhe filled with pure mercury will certainly always conduct alike. 2nd. Change of temperature causes only a slight difference in resistance. Against this plan it is said — 1st. That tubes cannot be made of uniform or similar wires, and that, therefore, the standard once broken is lost for ever. 2nd. That the standard tube cannot be kept full of pure mercury, owing to the admixture which would take place of the solid metal used for the terminals, so that each time the standard has to be used it has practically to be remade. 3rd. That the attempt, by most observers, to reproduce the unit for their own use would be attended with incorrect results, as is shown by the different results obtained by different observers. In favour of Dr. Matthiessen's alloy, as compared with wires of pure metal, or with mercury, as a material for the standard, it is said — 1st. That the variations of resistance, corresponding with variations of temperature or temper, are small. 2nd. That a unit expressed in this material can be more readily and certainly reproduced than one expressed by a pure metal, because the presence of slight impurities in the component metals, or a slight change in their proportion, does not sensibly affect the result. Against this plan it is said that the physical properties of an alloy are more likely to change than those of a pure metal. Against all the plans for standards, based on an arbitrary length and section of an arbitrary material, the supporters of the absolute units state that the adoption of such an arbitrary standard would lead to great con- fusion and complication in the measurement of all other electrical properties, and in the expression of the relation of such measurements to those of force, work, heat, ifcc. This objection does not, of course, apply to the expression of the absolute unit by means of a wire of pure metal, of an alloy, or by mercury : but it is urged that no observer should ever attempt the reproduction of a 'standard when a copy of the proposed universal standard can possibly be obtained ; and the Committee will probably endeavour to devise some plan by which such copies of the actual material standard adopted may be easily procured at a reasonable cost. It will be seen from the resolutions passed, that the Committee are now engaged in investigating the degree of accuracy with which Weber's units can be obtained, and the degree of permanency which may be expected from the use of the metal or alloy forming the material standard expressing these or other units. The Committee will feel greatly indebted to you if you will afford them the benefit of your valuable advice and experience on the above points, and on any others which may occur to you. They also venture to hope that such a standard may be selected as will give very general satisfaction ; and, if approved by you, that you will kindly take an interest in procuring its general adoption. ON STANDARDS OF ELECTRICAL RESISTANCE. 159 Personally being charged with the duty of preparing an historical summary of the various units proposed, I shall be grateful if you will favour me with any remarks as to your own labours in this field, or if you could oblige me with references to any papers or works in which the subject is treated. I am, Sir, Your obedient Servant, Fleejung Jenkik. Appendix H. — Description of the Electrical Apparatus arranged by Mr. Flee- ming Jenkin for the production of exact copies of the Standard of Resistance. This apparatus is a simple modification of that generally known as "Wheat- stone's bridge." It contains, however, some special arrangements, in virtue of which various practical difficulties are avoided, so that very great accuracy can be ensured with comparative ease. The usual bridge-arrangement is shown in Plate I. fig. 9, where the irregular scrolls, A, C, R, S, represent the four conductors of which the resistance is to be compared ; the thick black lines show those portions of the circuit which join the coils with the four corners, TJ, V, Z, Y, and are supposed to have no sensible resistance in comparison with the coils ; finally, the thin lines show connexions, the resistance of which in no way affects the accuracy of the comparison between the four coils. By this arrangement the four conductors, A, C, R, S, are so connected with the galvanometer, G, and the battery, B, that no current passes through the galvanometer when the conductors bear such a relation to one another that A S the equation q=t5 holds good; whereas a current in one or other direction A S passes so soon as ^ is greater or less than ^*. Thus the direction and strength of the current observed serve as guides by which the resistance of any one of the conductors may be gradually adjusted by shortening or lengthening the wire, until on the completion of the circuit no deflection whatever can be observed on the galvanometer, however delicate it may be, or however powerful the battery used. When this has been done, we may be sure that the above relation exists between the four conductors. In practice, it is seldom desirable to use powerful batteries ; the test is made delicate by the use of an extremely sensitive astatic galvanometer. In speaking of the four conductors, A, C, E, S, which are generally all coils of wire of similar construction, although each fulfilling a distinct function, some difficulty often occurs in explaining readily which coil or conductor is referred to. They can of course be distinguished by letters, but this requires reference to a diagram on every occasion, and the writer has therefore been in the habit of distinguishing the four coils by names drawn from a very obvious analogy existing between this electrical arrangement and the common balance in which one weight is compared with another. The equality between the two weights on either side of a balance, when the index is at zero, depends on the equality of the arms of the balance ; and if the arms are unequal, the weights required to bring the index to zero are proportional to the arms (inversely). Let A and C be called the arms of the electrical balance, while S and R are looked on as analogous to the standard weight and mass to be weighed respectively, and let the galvanometer needle * This statement holds good also if the battery and galvanometer wires, as shown in diagram, are interchanged. 160 REPORT— 1862. stand for the index of the balance. Then all the above statements, with respect to the weights and arms, hold good for the electrical arrangement (except that the proportion between the electrical arms and weights is direct instead of inverse). The writer therefore calls this arrangement an electric balance — A and C the arms, S the standard, and R the resistance measured*. In the adjustments of resistance-coils or copies of a standard, the object is to produce a second coil, R, exactly equal to the first or standard, S; and 'the arms, A, C, must therefore be absolutely equal before, by this arrangement, an exact copy can be made. Hitherto it has often been the practice to use for the arms, A, C, two coils made as equal as possible, and placed so close as to remain at sensibly equal temperatures ; so that the equality between R and S is dependent on the equality between A and C, and cannot be deter- mined with greater accuracy than that between these coils. This limit to the accuracy is a defect for our present purpose, and the writer has moreover found it undesirable to depend on the permanent equality of two coils. It is by no means certain that, without very extraordinary precautions, the two arms will remain unaltered in their original equality. A slight molecular change, or a slight chemical action on the surface of the wires, disturbs this equality permanently ; and even if the coils are so constructed as to remain really equal at equal temperatures, the accidental passage of a current through one arm, and not through the other, for a very short time, will disturb their accuracy very sensibly for a considerable time. There are various devices by which the equality to be established between It and S may be rendered independent of the absolute equality between A and C, and the writer has adopted a plan, now to be explained with the aid of the diagrams (figs. 7, 8). This plan allows the approximation to equality between II and S to be almost indefinitely increased. It will be seen that fig. 7 does not differ from fig. 9, except by the addition of a wire, WX, of sensible resistance, between the two coils A and C. The point U is no longer fixed, but can be moved along WX. The arms of the balance are therefore no longer A and C, but A + XU and C + WU. Thus the moveable point U affords the means of slightly altering or adjusting the ratio of the two arms. A and C are made as equal as possible, independently of "WX, which is a very short wire. The test is made as follows : — When the standard and coil to be measured have been put in their places as in fig. 7, the point U is moved along the wire WX until the galvanometer-index is not deflected when the circuit is closed. The position of the point TJ is noted by a scale. R and S are then reversed, so as to occupy the position relatively to A, C shown in fig. 8. The point TJ is again moved until the galvanometer-needle remains undeflected on the circuit's being closed. The new position of U is again observed by a scale. If the point U does not require to be moved at all, we may be quite sure that R is exactly equal to S, and that A + XU=C + WU, since it would A-t-XTT R S be quite impossible that the ratio should be equal to both — and -, unless this ratio were equal to 1. Moreover, if WX be made of the same * The name of parallelogram, sometimes given to the arrangement, is objectionable, inasmuch as the relation obtaining between the four conductors is not that which exists between the four sides of any parallelogram, except in the one case of equality between all four conductors. The connexions are, however, most easily followed in a drawing when arranged as the four sides of a quadrilateral figure. Professor Wheatstone's original name of Differential Kesistance Measurer does not, as it seems to the writer, sufficiently distin- guish this arrangement from other differential methods. Report B Ka . Z O.ih J.W Low) | ., ,,/ Plate J. Tiq.l. Diawam of cormeatona when commutator is in position ctraavn I'i^.I d connected vrith ,1,\ ftrith f , "Diagram of- conne/cicms with commutator D / across board •! connected with f& </ with ,'. J Fza. 9. Common fir ■ ■ ■ ■ ' ntl V III A D.AXI'E . ■ ■ i D .. Q| IV IM ■ . in, I .1 i. , , ,.•;■. L ■' ■■' ■ /■■■■-■■ ■ ,. . Utm ./,„,,. ; : ;., / ,/ ...„n„-,..l witJ, . . ■..,,■ imulami I ■ ■ .1 rtmntited * i th ftil n rtfi ■ ON STANDARDS OP ELECTRICAL RESISTANCE. 161 wire as the coils A and C, and if those coils are formed of about 100 inches of wire, and if the observed positions of TJ differ by a given distance, cc, this length, x, measured in inches, will express very nearly the difference between R and S in a percentage of the whole length of R. Thus, if a; be one inch, the standards S and R differ by about one per cent. If the point IT, when adjusted in each case, be found nearer R than S, then R is the smaller of the two, and vice versa. The percentage of error in R, thus measured, is not of course strictly accurate, inasmuch as the ratio between the two arms is not exactly 101 . jqq ; but if WX be not more than three or four inches long, the percentage of error measured in this way is quite sufficiently accurate to allow the new coil to be so exactly adjusted after very few trials, that no greater movement of U than (say) J^th of an inch is required to prevent any deflection on the galvanometer when R and S are reversed. We may then be sure that no greater error than (say) about 0-1 per cent, exists in the equality between the new coil and the standard. Two fresh coils, A„ C v are then taken, containing each about 1000 inches of wire similar to WX, or an equivalent resistance. It will then be found that, to maintain the index at zero when R and S are reversed, U must be moved about ten times as much as before, or (say) one inch. R can then be still further adjusted till U is not moved more than jLth of an inch, when a new degree of approximation to equality, with an error of not more than 0-01 per cent., will have been reached. Then the coils Aj, C, are changed for a fresh pair, A 2 , C 2 , with a resistance equal to about 1 0,000 inches of the wire WX : one-tenth of an inch on WX will then represent an error of only 0-001 per cent. By a repetition of this process, quite independently of any absolute equality between the pairs A, C, ■A-i> ®i> -A-2> Qj> &c -> a gradual approximation to any required extent may be ensured. The delicacy of the galvanometer used, and the nicety of the means available for increasing or diminishing the resistance of R, form the only limits to the approximation. A slight want of equality between any pair of arms will simply bring the point U a little to one side or the other of the centre of WX, as the final adjustment with that pair is made, but will not affect the truth of the comparison between R and S. Each pair must, however, be so nearly equal that the addition of part of the short wire, WX, to one side will be sufficient to correct the other ; otherwise the adjustible point U would not bring the index to zero, even when at one end of the wire. This arrangement, besides rendering us independent of the accuracy of any two arms, has some incidental advantages of considerable practical importance. At each test it gives a measure of the amount by which the new coil to be adjusted must be lengthened or shortened. The test is at first comparatively rough, or adapted to errors of one or two per cent., and only gradually increases in delicacy as the desired equality is more and more nearly approached. It is not necessary that the resistance of WX should remain absolutely constant, since it is only used (numerically) to give a rough approximation to the percentage of error. It is desirable that the battery should remain in circuit as short a time as possible ; the circuit is therefore broken between 1 and 2, figs. 7 and 8, by a key, K, with which contact should be only momentarily made, when all the other connexions are complete. The direction of the jerk of the galvanometer-needle to one side or the other need alone be observed; no permanent deflection is required with this arrangement as a guide to the amount of error. This is a considerable advantage, inasmuch as it avoids heating the wires, and saves time. The induction of the coils on themselves might lead to some false indications. 1862. M ' 162 report— 1862. unless special precaution -were taken against it, as pointed out by Professor "W. Thomson*. To avoid this source of error, the galvanometer circuit is broken between 3 and 4, figs. 7 and 8, at K v and should only be closed after the battery circuit has been completed at K and equilibrium established throughout all the conductors. Before passing to a detailed description of the apparatus as actually con- structed, some remarks are required as to the means of making temporary connexions. All connexions "which require to be altered may be the means of introducing errors, inasmuch as the points of contact are very apt to offer a sensible but uncertain resistance. In measuring small resistances, the resistance at the common binding-screws is found to create very considerable errors. Binding-screws have therefore to be avoided at all points where an uncertain resistance could cause error. Mercury-cups, made as follows, have been found in practice very suitable for temporary connexions, and have been adopted in the apparatus. The bottom of each cup is a stout copper plate, with its surface well amalgamated, forming one of the two terminals to be joined. A stout copper wire, 1 inch in diameter, with a flat end well amal- gamated, forms the other terminal. When the amalgamation is good, and care is taken that the wire shall rest on the plate, this form of connexion offers no sensible resistance. The amalgamated wire is easily kept bright aud clean by being dipped from time to time in a solution of chloride of mercury and wiped. The copper plate should also be removed from the cup, cleaned, and re-amalgamated occasionally. All permanent connexions should be soldered. The apparatus itself, as actually constructed, will now be described (figs. 1 to 6). It consists of a wooden board, about 12 in. x 7 in., containing the mercury-cups, the adjusting wire, "WX, the key, K, and the terminals to which the battery and galvanometer are connected. The letters in the figures 1 to 6 correspond exactly to those used in the diagrams 7 and 8 ; and the apparent complexity of the connexions can thus be easily disentangled. cc v aa x are two pairs of mercury-cups, into which the terminal wires on the bobbin, C, A, dip. This bobbin contains the two coils, C and A, forming the arms of the balance. rr x and ss 1 are mercury-cups, into which the terminals of the standard and coil to be adjusted are placed. These mercury- cups are so connected with the four cups, d,d v f,f v that when d is con- nected with d v and / with f v by a couple of wires in a small square of wood, D, then A, C, S, and K are connected as in fig. 7 ; but when D is turned round, so as to connect d with/, and d 1 with f v A, C, B, and S are connected as in fig. 8. D is called the commutator. The same end might be effected without a commutator by simply interchanging B and S ; but it is frequently incon- venient to do this. All these connexions are made by short stout copper bars, dotted in fig. 2. The wire "WX, the sliding brass piece H, carrying a spring for the contact at II (fig. 4), and the scale E, by which the position of H is observed, wiH be readily understood from the drawing. The sliding piece, H, is connected with the proper points by the helix of copper wire, h, and the screw, I. G G x and B B t are common binding-screws, to which the wires from the galvanometer and battery are attached. K is the key, by depress- ing which, first, the battery is thrown into circuit, and then the galvano- meter. It consists of three brass springs, 1, 2, 3 (fig. 5), each insulated one from the other, and connected by three screws, 1, 2, 3 (fig. 2), with the necessary points of the arrangement. A fourth terminal, 4 (figs. 2 and 6), * Vide Phil. Mag. August 1862. ON TEE GRANITES OF DONEGAL. 163 is immediately under the free end of the springs, and is armed with a small platinum knob or contact-piece. The three springs are also all armed with platinum contact-pieces, all in a line one above the other (fig. 6). When the finger-piece, T, is pressed down, 1 and 2 are first joined, and then 3 and 4 ; 3 is insulated from 2 by the vulcanite, (J. AH the connexions per- manently made, under the board, are shown in fig. 2. Those which have no sensible resistance are stout copper bars, and form the bottoms of the mer- cury-cups : those of which the resistance is immaterial are made of wire, insulated by giitta percha, and are simply shown as dotted irregular lines in fig. 2 ; they will be found, on comparison, to corresj>ond with the thin lines on fig. 7. It will also be found that all those parts shown by thick lines in the diagram are made by thick bars or rods and mercury-cups. Three sets of arms, C A, C l A v C„ A 2 , are provided ; the shortest pair is first used, and U adjusted by the slide, H, till the galvanometer does not de- flect when T is pressed down. The commutator, D, is then turned round, and U adjusted afresh. The coil, E, is then altered according to the two positions of U, and this process repeated, using the second and third pair of arms as required, until the desired approximation between E and S has been obtained. An astatic galvanometer, with a very long coil, will, for most purposes, give the best results ; and one or two elements will be found a sufficient battery. The construction of E and S recommended, and the pre- cautions to ensure perfect equality of temperature, will form part of next year's Eeport. The apparatus, although specially designed for the production of equal coils, is applicable to ordinary measurements of resistances by comparison with a set of resistance-coils ; for this purpose the terminals of the resist- ance-coils should be put in the place of the standard S, and any conductor of which the resistance is to be measured in the place of E. If a comparison by equality is to be made, the wire WX can be used as already described ; it is, however, frequently desirable to make a comparison with one arm ten- fold or a hundredfold greater than the other, by which means measurements of resistances can be made ten or a hundred times greater or smaller than could be done if equality alone between E and S were measured ; for this pur- pose the three pairs, A C, A l C T , A 2 C 2 , are made exactly decimal multiples one of the other, and then, by taking A and G 1} or A and C„, &c, in the cups aa t and e c l5 the required decimal ratio is obtained. The resistance of the wire WX would, however, falsify this ratio, and it is eliminated by a simple copper rod, which is placed for the purpose between the two cups e e v and maintains the whole wire WX at sensibly one potential. The commutator also is useless in measurements of this kind, and should be left untouched in the position shown in fig. 1. The apparatus exhibited was manufactured for the Committee by Messrs. Elliott Brothers, of London, and gives excellent results. Preliminary Report of the Committee for Investigating the Chemical and Miner alogical Composition of the Granites of Donegal, and the Minerals associated with them. In accordance with the resolution of the General Committee at the Man- chester Meeting, the Committee, consisting of Sir E. Griffith, the Eev. Prof. Haughton, and Mr. Scott, proceeded to investigate " the chemical and mine- m2 164 report— 1862. ralogical composition of the granites of Donegal, and the minerals associated ■ with them." In furtherance of this object, Mr. Haughton and Mr. Scott re- paired, last Easter, to the northern part of the county, as they had visited the S.W. portion of the district in the summer of 1861. They were accompanied on their tour by Mr. Jukes, Local Director of the Geological Survey of Ireland, who gave them the valuable benefit of his experience and assistance throughout the tour. The exploration commenced at Moville, on the E. shore of Innis- howen, whence a section was earned along the N. coast of that peninsula pearly as far as Malin Head. This section exhibited a great thickness of "primary rocks, consisting of quartzite and mica-slate, accompanied by several beds of limestone, and a number of beds of igneous rocks, which appeared to be contemporaneous with the sedimentary rocks. These are best exhibited at a place called the Mintiaghs or Bar of Inch, where there are several alternations of quartz-rock and syenite exhibited in an escarpment of several hundred feet in height. This locality is situated about five miles N". of Buncrana. From Bimcrana. the granite of Urrismcnagh, near DunafF Head, was visited. Erom Milford an excursion was made to the extremity of the promontory of Fanad, lying between Lough Swilly and Sheep Haven, in order to visit the granite of this district. This patch of granite is not a continuation of that which traverses the country in a N.E. and S.W. direction, as it lies to the K". of that axis and exhibits a slight difference in composition from the granite of the central axis. From Milford the route lay to Divnfanaghy ; and a section was made across the northern end of the granitic axis of the county at Glen, in which its gneissose character was very strongly exhibited. This was marked in a most decisive manner between Lackagh Bridge and Creeshlagh, where the rock might be observed changing from gneiss, by almost insensible gradations, on the one hand into granite, and on the other into hornblende slate and crystalline syenite. The latter is most highly crystalline at Horn Head, where it contains large quantities of titanic iron. On the return-journey from Dunfanaghy to Letterkenny, it was determined to make two sections across the granite ; so that Mr. Haughton and Mr. Scott took the road from Creesh- lagh through the Gap of Barnesbeg, while Mr. Jukes took that by Owencarrow Bridge, about four miles higher up the valley. It having now been found necessaiy to compare the facts observed with those which were to be observed in other countries, Sir B. Griffith repaired to Scotland in the month of July. Mr. Haughton traversed the centre of Scotland, and paid a visit to Sweden, Finland, and Bussia. Both these gen- tlemen discovered facts strongly confirming the views propounded at the Manchester Meeting, of the similarity of the geological structure of Donegal to that of the Scandinavian peninsula and of Scotland. For this latter fact the Committee had been prepared by the examination of a series of specimens of Scotch granites which had been furnished to them by Sir B. I. Murchison, in accordance with his kind promise made at the last Meeting. While these tours were in progress, Mr. Scott repaired, for the third time, to Donegal, and spent the month of July in the re-examination of several points connected with the geology of the southern district. He visited the granite of Barnesmore, near the town of Donegal, which is essentially non- gneissose, and is penetrated by numerous pitchstone dykes, some of which are amygdaloidal. Numerous minerals were discovered here, which were in some cases new to the district. In the neighbourhood of Glenties, a consi- derable quantity of andalusite was found in the mica-slate — a mineral which is replaced near Barnesmore by kyanite, and in the Bosses, near Dungloe, by a white variety of kyanite. ON THE VERTICAL MOVEMENTS OF THE ATMOSPHERE. 165 From Dungloe, as head-quarters, the structure of Crohy Head was carefully examined, and also the island of Arranniore, which differs materially in its structure from the mainland of Ireland, from which it is only distant three miles. The southern portion of this island is nearly entirely composed of white granite, penetrated by numerous dykes of syenite and of felspathic porphyry. The strike of these rocks is neaily E. and W., while that of the flaggy quartz-rocks on the northern shore of the island approaches N. and S. During the course of this tour, two more sections were made across the granite of the main axis, exhibiting the same facts which had been observed before, viz. numerous beds of limestone and of altered slate lying in the granite, stratified nearly conformably with it. These were observed in the centre of Glenveagh, close to Ballaghgeeha Gap, on the pass through the Poisoned Glen from Dunlewy. At Glenleheen, where the same occurrence of non-granitic rocks had been observed in the previous year, four beds of limestone and several beds of slate were discovered. Almost all these beds of limestone contained garnet, idocrase, and epidote in quantity ; and at Glen- leheen itself, scapolite, a mineral whose occurrence in the British Islands has escaped the notice of modern English mineralogists, was discovered. Inas- much as the specimens brought home by the members of the Committee from their several tours are very numerous, it is not possible for them to present their complete report at this Meeting. They hope to embody in it some valuable information relating to the granitic rocks of Canada, which Dr. T. Sterry Hunt has kindly offered to supply to them. They have to express their thanks to him and to Mr. Harte, C.E., county surveyor of the western district of the county, who, with the Rev. Frederick Corfield, has afforded them most efficient assistance. They have succeeded in procuring some of the granite of Eockall, through the kindness of the officers of H.M.S. Porcupine, who furnished it to Mr. Harte, and will include its analysis in their paper. On the Vertical Movements of the Atmosphere considered in connexion with Storms and Changes of Weather. By Henry Hennessy, F.R.S., M.R.I. A., fyc, Professor of Natural Philosophy in the Catholic University of Ireland. The labours of the Committee, consisting of Admiral FitzEoy, Mr. Glaisher, and myself, who were appointed, at Manchester, for the purpose of studying the vertical disturbances of the atmosphere with the aid of instruments, have, for the present, been restricted to the work of a single observer. This has arisen from the circumstance that the money-grant appropriated to the Committee has sufficed only to defray the cost of erecting a single instrument. As this instrument is likely to afford opportunities for observing the vertical motions of the atmosphere more completely than has been hitherto possible, it is to be hoped that similar apparatus will before long be in the hands of the other members of the Committee. The fact that all the preliminary work has thus necessarily devolved on the writer of the present Eeport will suffi- ciently account also for its provisional nature. Hitherto the only kind of atmospherical currents which have formed the subjects of definite observation by instruments are those whose existence is manifested by the movements of ordinary wind-vanes and anemometers. But as these instruments indicate horizontal movements exclusively, ordinary 166 report— 1862. winds as well as storms are almost always conceived as currents flowing in perfect parallelism to the earth's surface. It is true that no physical theory of the motions of the atmosphere can be attempted without some considera- tions which involve the necessity of vertical and oblique motions among the masses of air, as well as horizontal motions ; but while direct comparisons of the latter among themselves have continued for many years to be made in different parts of the world, we possess scarcely any such data relative to non-horizontal movements as would enable us to make the.m subjects of exact inquiry. The only writer who, as far as I am aware, has hitherto endeavoured to deduce any well-defined results from observation relative to the vertical movements of the atmosphere is M. Foumet, and his studies were almost ex- clusively directed to the elucidation of the phenomena of some remarkable local winds that frequently prevail among the Alps and in the valley of the Rhone*. A local phenomenon in Ireland + induced me to study the vertical motions of the air in a more general way than was necessary for the explana- tion of this phenomenon itself ; and my first step was an attempt at devising a vane capable of showing the existence and direction of non-horizontal currents. This was a non-registering instrument, and the results obtained were therefore somewhat unconnected ; but they seemed to establish some important relations between vertical currents and other atmospherical dis- turbances J. Among these, I may be permitted to notice the phenomena which preceded the disastrous gale of February 9, 1861. For many days, at the close of January and beginning of February, the weather was remarkably fine, and no vertical currents were observed ; but on the 7th very distinct evidences of vertical disturbance came under my notice, while the air had as yet no remarkable horizontal motion. On the 8th, at 2 p.m., my attention was called to the vane by its shifting round through N". towards N\E., with decided and frequent downward plunges of the disk exposed to the vertical action of the air. It appeared as if showers of cold air were descending ; for the thermometer showed at the same time a rapidly falling temperature. While vertical convection had become already highly developed, the horizontal motion of the air was not as yet greater than that of an ordinary brisk breeze. Next day, during the storm, although the disk of the vane was in constant oscillation from the undulatory motion which my observations had already shown to be a necessary accompaniment of all high winds passing over terrestrial obstacles, no marked prevalence of upward or downward motious could be observed corresponding to the plunges of the disk noticed on the preceding day. The mercury in the barometer had been falling with great regularity during four days before that on which I had noticed the first decided indications of vertical disturbance. On that and the next day, as well as on the very day of the storm, the barometric column was rising, while the temperature was steadily falling. Here the rise in the barometer was accompanied by north-easterly winds, and the air at the earth's surface was thus rapidly mingled with cooler masses descending from above, as shown by the vane ; so that the increased pressure was due to the increased density of the entire aerial column above the barometer. * See Annales de Chimie et de Physique, tome lxxiv. p. 337 ; and a resume of his results in a note to M- Martin's translation of Kaeintz's Meteorologie, p. 35. t Proceedings of the Royal Irish Academy, vol. iv. p. 279. % Atlantis, vol. iii.' p. 166 ; Phil. Mag. for May 1860 ; and Proceedings R. I. A. for May 1861, p, 232. ON THE VERTICAL MOVEMENTS OF THE ATMOSPHERE. 167 Among the phenomena attending the more tranquil conditions of the air, 1 had noticed in my earlier observations, during the summer of 1857, that upward currents generally prevailed by day, while downward currents became more prominent at night. This alternation was manifestly connected, as shown by the horizontal vane, with the action of land and sea breezes ; for at this time the observations were made at a point situated about two miles from the sea-shore. By day, the convection due to the heating of the lower stratum of air in contact with the ground could not take place by equal upward and downward exchanges of masses of air, because the place of the ascending warm air was partly supplied by the lateral influx of colder sea air, which, in its turn, would become sufficiently heated to ascend and give place to a fresh lateral influx. By night, the colder air from the land flowed towards the sea, and its place was filled by descending currents from above. At the same time the warmer ah- from the sea probably tended to occupy the place of these currents, and thus to equalize the temperature of the upper and lower strata of air so as to lessen the energy of the convective movement over the land. Before the termination of the Meeting of the Association at Manchester, I had resolved, with the concurrence of Mr. Glaisher, the only other member of the Committee then present, to cause a registering instrument to be con- structed which would record the existence of non-horizontal atmospheric motions. The following is a description of the anemoscope which I ultimately decided upon as most suitable in its construction for the purposes we have in view. Fig. 1 is a vertical section of the portion of the apparatus which is exposed to the wind, and fig. 3 an elevation of the same portion. A is a cast-iron pillar which supports a cup, h, containing friction-balls made of gun- metal ; on these a disk, g, rests, and this is firmly attached to a box from which an arm projects at one side, and is terminated by the cone, P, which acts as a counterpoise for the opposite and working arm of the anemoscope. A short arm, n, shown in fig. 3, supports a wheel, d, in one side of which teeth are cut ; the other side is firmly attached to a hollow light copper box, B, which forms the tail. This box is a truncated pyramid, and while its vertical sides are exposed to the horizontal action of the wind, its upper and lower surfaces are exposed to its vertical action. This tail is balanced by a coun- terpoise, i, which is connected by a bent arm with the axle of the wheel, d. The teeth of this wheel catch those of the pinion, e (fig. 1), and this catches in the rack, /. The rack is attached to a shaft, c, which descends through the hollow supporting pillar and communicates with the registering apparatus. In fig. 2 the most essential part of the arrangements for registering the indications of the upper part of the instrument are shown. The shaft, c, passes through brass guides, and carries a small circular projecting piece, s, which catches in a notch made in the bit, v, attached to the pencil-carrier, p. This pencil-carrier is capable of upward and downward motions only, and the rod to which it is attached passes through guides. The carrier is, more- over, supported by an ivory friction-wheel, t, which turns when the piece, s, revolves beneath it. From this brief description, it is apparent that the cone, P, will always indi- cate the direction of the wind in azimuth, like ordinary vanes. At the same time the vertical component (if any) of the wind will raise or depress the tail, B. In the former case it is manifest that the wheel, d, will cause e to turn, so as to raise the rack, /, and in the latter case the effect will be to lower the rack. It follows, therefore, that the shaft, c, and consequently the pencil- carrier which it moves, must rise or fall according as the vertical motion of 168 REPORT 1862. the air is upward or downward. A spring within the pencil-carrier con- stantly presses tho pencil against a sheet of paper placed in front of it. This paper is for the present carried on a flat board, which is moved by a clock. The registering sheets are ruled with vertical hour lines and with horizontal lines which assist in estimating the angle of inclination to the horizon made by the disk during the action of an upward or downward impulse from the air. This follows because the tail and the wheel, d, revolve on the same centre, and each tooth in d describes an arc similar to that described by the axis of the tail. An equal number of teeth in e are raised or lowered, and thus the rack and the shaft, c, move through spaces proportional to arcs de- scribed by the teeth of the wheel, d, and the axis of the tail, B. The board ON THE VERTICAL MOVEMENTS OF THE ATMOSPHERE. 169 which, carries the registering paper can be detached by loosening a clamping- scre-w which fastens it to the support turned by the clock, so that the sheets can be removed and replaced with speed and facility. The entire apparatus was constructed by Mr. Spencer, of Aungier Street, Dublin ; and he has executed the portion connected with the indication of horizontal movement in such a way, that the addition of a registering apparatus for this part of the instrument will not only be easy, but will render the entire combination a complete indicator of the absolute direction of the wind. The results of the instrument in its present state are exhibited on the regis- tering sheets as nearly vertical pencil lines, some above and some below the neutral line, to which each sheet is carefully adjusted. The anemoscope is at present so placed as not to be overtopped by any building ; for it stands on the roof of one of the highest houses in Dublin, in a quarter remarkably open, and close to the south suburbs. Owing to a variety of delays and obstacles in finishing the apparatus, it was not brought into action until the 31st of August, and thus I am able to report only on the residts furnished by little more than the records of a single month. These records appear to indicate that vertical oscillations prevail more during the mid-day hours than at other periods ; for although ten sheets show no definite predominance at any specific period of the day, and two predominance of vertical movements towards midnight, twenty-one show that these move- ments are most frequent at the hours about noon. From a journal of the weather which was kept at the same time, it appeared that on bright days, when the air had little horizontal motion, gentle upward movements pre- vailed at mid-day. Such phenomena are distinctly manifested by the sheets for September the 5th, 6th, 7th, 8th, and 9th, and all of these were bright sunny days. Before the 5th, the weather had been changeable and unsettled : but on comparing the two sheets comprehending from noon of the 3rd to noon of the 5th, I noticed that the amplitude of the osculations of the anemoscope progressively and regularly diminished; and it occurred to me that this might indicate a tendency towards convective equilibrium of the atmosphere, and more settled weather. The weather continued fine until the 13th, -when there was both high wind and rain, accompanied and preceded by energetic oscillations of the anemoscope. If the general circulation of the atmosphere takes place, as seems to be now completely established, by a twofold motion, one of translation, whether cyclonic or lineal, and the other undulatory, it follows that the pulsations of the latter movement may be influenced by aerial disturbances. The frequency, regularity, intensity, prevalent direction, and more or less intermittent character of these pulsations must depend on varia- tions of pressure, density, moisture, and temperature, as well as on the rippling motion of the air. It is natural, therefore, to expect, what our limited number of observations seem already to indicate, namely, that the sudden and abrupt commencement of such pulsations is usually a precursor of other disturbances, while their gradual and regular diminution in energy woidd show a tendency in the air to approach a state of convective equili- brium, and might, therefore, be safely relied upon as a forerunner of fine weather. This point is illustrated by the remarks of the late Professor Daniell relative to the rapid oscillations of the water-barometer during high winds, and their gradual diminution preceding a return to a tabner state of the air*. Although the atmospheric pulse is undoubtedly compounded of the undulatory movements resulting from the flow of an elastic fluid over the * Phil. Trans. 1832, p. 573. 170 REPORT — 1862. irregularities of the earth's surface, with the effects of convection, in such a way as would render the separation of these effects extremely difficult, yet the careful study of this pulse in connexion with other phenomena may he reasonably expected to add to our power of forming correct conclusions regarding the coming changes of the weather. Report of a Committee, consisting of the Rev. Dr. Lloyd, General Sa- bine, Mr. A. Smith, Mr. G. Johnstone Stoney, Mr. G. B. Airy, Professor Donkin, Professor Wm. Thomson, Mr. Cayley, and the Rev. Professor Price, appointed to inquire into the adequacy of existing data for carrying into effect the suggestion of Gauss, to apply his General Theory of Terrestrial Magnetism to the Magnetic Variations. In order to explain the views of the Committee upon the question submitted to them, it is necessary to refer briefly to the leading points of Gauss's theory. If dp denote the quantity of free magnetism in any element of the earth's mass, and p the distance of that element from the point (x, y, z), and if we make the partial differential coefficients of V with respect to the three coordinates, x, y, z, respectively, are equal to the components of the earth's magnetic force in the direction of the axes of coordinates. Y is a function of oc, y, and z, or of their equivalents u, X, and r, — r being the distance of the point from the centre of the earth, and u and X the angles corresponding to the north polar distance, and the longitude, on the sphere whose radius = r. This quantity may be expanded in a series proceeding according to the inverse powers of r, whose coefficients, P,, P 2 , P 3 , &c, are functions of u and X alone ; and it is readily seen that, at the surface of the earth, the three com- ponents of the magnetic force are V, du du du J sin u V «X d\ <xX / Z = 2P 1 + 3P 2 +4P 3 + &c, and are therefore given when P x , P„ P 3 , &c. are known. The form of these functions is deduced from the well-known partial dif- ferential equation »(.+l)g.+ffi+«ltlig*B + .. 1 h ffi -0, du 2 du sin u «X n being the number indicating the order of the function. It is found that the first, P,, contains three unknown coefficients ; the second, P 2 , five ; the third, P 3 , seven, &c. Hence, if the approximation be extended so as to in- clude terms of the fourth order, there will be 24 coefficients to be determined. Each given value of X, Y, or Z, on the earth's surface, furnishes an equation on gauss's theory and terrestrial magnetism. 171 among these unknown coefficients ; and for each place at which the three elements are known we have three such equations. Hence to obtain the general expressions of X, Y, Z, to the fourth order inclusive, it is theoretically sufficient to know the three elements at eight points on the earth's surface. But, owing to the errors of observation, and to the influence of the terms neglected in the approximation, the number of determinations must, in prac- tice, be much greater than the number of unknown coefficients. The foregoing conclusions are hased upon the hypotheses that magnetic attraction and repulsion vaiy according to the inverse square of the distance, and that the magnetic action of the globe is the resultant of the actions of all its parts. It is likewise assumed that there are two magnetic fluids in every magnetizable element, and that magnetization consists in their separation. ' But for these hypotheses we may substitute that of Ampere, which supposes the magnetic force to be due to electric currents circulating round the mole- cules of bodies. This theory may be applied to the changes of terrestrial magnetism, whe- ther regular or irregular, provided only that the causes of these changes act in the same manner as galvanic currents, or as separated magnetic fluids. We have only to consider whether the data which we possess are sufficient for such an application. It has been already stated that, for the general determination of X, Y, and Z, we must know their values at eight points (at least) on the earth's sur- face, these points being as widely distributed as possible. The same thing holds with respect to the changes oX, hY, IZ ; and to apply the formula? so determined, and to compare them with observation, corresponding values must be known for (at least) one more point. In the case of the irregular changes these observations must, of course, be simultaneous. The regular changes must be inferred from observations extending over considerable periods ; and there is reason to believe that these periods must be identical, or nearly so, for all the stations, since the changes are known to vary from month to month and from year to year, The regular variations of the three elements X, Y, Z, or their theoretical equivalents, have been obtained by observation, for nearly the same period, at Greenwich, Dublin, and Makerstoun, in the British Islands ; at Brussels and Munich, on the Continent of Europe ; at Toronto and Philadelphia, in North America ; at Simla, Madras, and Singapore, in India ; and at St. Helena, the Cape of Good Hope, and Hobarton, in the southern hemisphere. Of these thirteen stations, however, the three British must be regarded, for the pre- sent purpose, as equivalent to one only, on account of their proximity ; and the same thing may be said of the two North American stations and of the two stations in Hindostan. This reduces the number of available stations to nine, the minimum number required for the theoretical solution of the pro- blem in the degree of approximation already referred to, and considered by Gauss to be necessary. It is true that we may add to these the stations at which two only of the three elements have been observed, viz. Prague and St. Petersburg, the three Russian stations in Siberia, and Bombay. But even with this addition, the number is probably insufficient for the satisfactory determination of the unknown coefficients ; for it is to be remembered that the places, few as they are, are not distributed with any approach to uni- formity, and that very large portions of the globe are wholly unrepresented by observations. For the reason already stated, this defect in the existing data cannot be now repaired by supplemental observations at new stations, unless the series 172 report — 1862. at all were so far extended as to embrace the whole period of the cyclical changes. The simultaneous observation of the irregular changes is limited nearly to the same stations. In their case, too, there is the further imperfection, as respects the present problem, that the changes observed on "term-days" are for the most part inconsiderable, while those on days of great magnetic disturbance have seldom been observed continuously for any considerable time at all the stations. For the foregoing reasons the Committee are of opinion that the data which we at present possess respecting the changes of terrestrial magnetism, whether regular or irregular, are not sufficient for the application of Gauss's theory, if, as above assumed, the approximation is to be extended so as to include terms of the fourth order (P x to P 4 inclusive). It is deserving of considera- tion, however, whether an inferior degree of approximation may not afford some valuable information. The affirmative side of this question has been so earnestly advocated by one of the members of the Committee, that it has been thought advisable to append his letter on the subject to this Report. (Signed by order of the Committee) H. Lloyd. Letter from Professor "W. Thomson to Eev. Dr. Lloyd. " Eosbven, Strontian, Sept. 24, 1862. " My dear Sir, — I am sorry to have been so long prevented from writing to you on the subject of the Committee's Report on the expression of the Variations of the Terrestrial Magnetic elements in series of Laplace's functions. " I perfectly agree with the conclusions stated in the draft report of which you sent me a proof, so far as they relate to a complete expression of any class of variations of the elements, or of any individual variation, by means of which its amount in other localities than those of observation could be de- termined with any considerable approach to accuracy. But, on the other hand, the amount of knowledge from observation, shown in the report to be available, would, I believe, be sufficient to allow us to estimate, possibly with considerable accuracy, and certainly with a sufficient approach to accuracy for highly important application, the first terms in the harmonic (Laplace's) series. I would therefore advise that some such method as the following should be adopted. " Choosing any particular variation, for instance the diurnal or the secular, for which the data from observation are most abundant, find either by trial and error, or any other proper algebraic method, an expression by terms of the first order (three coefficients for each) for the three elements which most nearly represent it. (The method of least squares would give a precise de- finition of what would be the most near representation, on this principle ; but ruder and quicker methods might suffice in first trials.) Then, judging by the results, tiy similarly for expressions in series of two terms (3 + 5, or eight coefficients in all, in each expression). After trials of this kind it would be easy to judge within what limits may be the probable errors of the estimated first terms from the true first terms, and possibly even to arrive at some probable knowledge regarding the true second terms of the harmonic ex- pressions. "Avery moderate degree of success in such operations as these would allow us to decide whether the origin (magnetic or electrodynamic) of the variation is within the earth's surface or outside. ON THERMO-ELECTRIC CURRENTS IN CIRCUITS OF ONE METAL. 173 " I hope, then, a result of the Committee's action may be to carry out an attempt of this kind for every class of variations for which the data give even the narrowest foundation. It might be applied, I believe, with success, as regards the main conclusion, to every case in which each of the three compo- nents has been well determined for even only xhbee stations widely apart from one another. " It seems probable that an individual deflection of a magnetic storm cannot be identified in localities at very great distances from one another. This must certainly be the case if an individual deflection, and individual flash or flicker of aurora, are simply related to one another, because the individual auroras are certainly local in the sense of being only seen at once over a very limited area of the earth, being in fact actually situated at some distance of not more than 150 miles (which I believe is the highest estimate) from the surface. Heuce it is probable that it will be found whether the seat of the disturbing action, producing an individual deflection in a magnetic storm, is above or below the surface, by comparing observations made at stations within a few hundred miles of one another, and endeavouring to identify a single disturb- ance in the three components at all the localities. If the three components could thus be determined at three localities so wide apart as to show con- siderable differences in the amounts, but yet not so wide as to render the identification of the disturbance difficult, the question whether the seat of the disturbance is in the earth or the air woidd be answered with high proba- bility. " I remain, yours very truly, (Signed) " William Thomson." On Thermo-electric Currents in Circuits of one Metal. By Fleeming Jenkin, Esq. Last year I had the honour of directing the attention of the Association to the fact, that an electric current of considerable intensity may be obtained in a circuit of one metal by the application of heat to one or the other side of an interruption in the wire composing the circuit. The experiment is most simply performed by looping together the two ends of two perfectly similar wires connected to the terminals of a galvanometer, and heating one of the loops to a white or red heat in a spirit-lamp, or Bunsen's burner. If the one loop rests very lightly on the other a current will be obtained, which in the copper wires will flow from the hot to the cold loop across the joint with sufficient intensity to deflect a moderately sensitive galvanometer, even with a resistance in circuit equal to 1000 miles of No. 16 copper wire. The electromotive force of the combination is about one-tenth that of a Daniell's cell. "With two iron loops a permanent current in the opposite direction is obtained, flowing from cold to hot across the joint, but the elec- tromotive force in this case is very much smaller. "When the loops are drawn tightly together the current ceases, but reappears as soon as the strain is slackened. I was at the time unable to show the connexion between these singular currents and other electrical phenomena, but I am now, in consequence of further experiments undertaken for the Association, able to point out that connexion. 174 report— 1862. The currents were clearly not due to chemical action on the wires ; for, in the first place, currents of considerable strength were obtained from two per- fectly homogeneous platinum wires, flowing from hot to cold across the loose contact ; and in the second place, the direction of the current was different in copper and iron, whereas the chemical action undergone by the wire was alike in tbe two cases. The researches of Becquerel, Pouillet, Buff, Hankel, and Grove were ex- amined, to see whether the electricity produced during combustion, or the properties of flame, would account for the currents, but it was found that all the electrical effects produced by flame could be divided into two classes : first, phenomena depending on the relative position of the two wires in the flame ; and secondly, phenomena depending on the voltaic couple formed by the metals used, and the hot vapour acting as an electrolyte between them. My results were independent of the position of the wires in the flame, and could not be accounted for by supposing these wires to form a voltaic couple, inas- much as though in some cases, where wires of two metals were looped together as described, the current flowed from the metal most attacked across the imaginary electrolyte to the other wire, in other cases it flowed in the oppo- site direction. It remained to be seen whether the currents might not have a thermo- electric origin. Last year I imagined that the effect observed might be di- rectly due to discontinuity, but that idea was dispelled by some experiments with loose contacts between wires of different metals, which have thrown great light on the question. Loops of iron, silver, platinum, gold, and copper wires were combined two by two in all the possible arrangements, and the currents measured which were obtained when one or the other or both loops were heated with loose and tight contacts between them. A Table was thus formed, which is appended to the present paper. The resistance of the circuit was so large (2050 x 10% Weber's absolute t-~) that the inherent resistance of the joint and of the different short seconds' ° wires used in each experiment could be neglected, and the deflections ob- tained on a reflecting galvanometer could be taken as approximatively pro- portional to the electromotive force of each combination. The common thermo-electric currents produced by the metallic contact between dissimilar wires almost vanish in comparison with those produced by the loose contacts. I need not present a complete analysis of the Table, but will speak only of the combination of iron and copper with which the most remarkable results were obtained. When the usual tight metallic contact was made between these two wires and the two loops equally heated, the current first flowed from copper to iron across the joint, and then as the temperature rose ceased altogether, and finally, at a red or white heat, flowed from iron to copper. The maximum deflection obtained in either direction was three divisions. These deflections showed the celebrated inversion discovered by Cumming. If the pressure between the loops was relaxed, the current ceased alto- gether ; but when the loops were moved, so that the copper became red-hot while the iron was cool, a current flowed from the copper to the iron, or from hot to cold across the joint, giving a deflection of 100 divisions ; whereas if the iron was heated red-hot and the copper cooled, a current giving 90 divi- sions flowed in the opposite direction, or from iron to copper, but from hot to cold as before. Thus in these two cases the loose-contact currents given when one or the other loop was heated, flowed in the opposite direction be- ON THERMO-ELECTRIC CURRENTS IN CIRCUITS OF ONE METAL. 175 tween the metals, but in both cases from hot to cold across the joint, and were in each case about thirty times as great as the currents given by the thermo-electric difference between the metals. It was found on examining the Table, that wherever copper appeared in con- junction with any other of the metals named, the direction of the loose-con- tact current could invariably be determined by the following rule : — "When the copper was the hot wire, the current flowed from the copper to the other metal across the joint ; but when copper was the cold metal, the current flowed from the other metal to the copper, or in both cases from hot to cold. Exactly the contrary was found wherever iron appeared in conjunction with any of the five metals but copper ; the current then always flowed from cold to hot. Two copper wires alone gave the largest deflection, of about 220 divisions ; and two iron wires alone gave the next largest of those obtained where single metals only were used, but of course in the opposite direction to the deflection from copper. It was then perceived that all these results would be explained if the thin coating of oxide on the copper wire might be regarded as a conductor with a hot and cold junction, and endowed with thermo-electric properties far more positive than the iron, while at the same time the coating of oxide on the iron wire would have to be regarded as far more negative than the copper. It was, however, difficult to suppose that two bodies so similar in some re- spects as the oxides of copper and iron should be at opposite extremities of the thermo-electric scale, but the following direct experiment left no doubt on my mind. A little spiral was made of platinum wire, and a small quantity of oxide of copper laid upon it, and held in a flame till white-hot ; another platinum wire was then dipped in the melted mass, when a strong current was at once ob- served from the hot to the cold wire, as if a loose contact had been made between two copper wires. When either of the oxides of iron was tested in a similar manner, a strong current was obtained from the cold to the hot platinum wire, as if a loose contact had been made between two iron wires. I do not yet know positively what the substances are which, interposed between silver and platinum and gold wires, give rise to the loose-contact currents, but I feel no doubt that these are as much thermo-electric currents as those given by the oxides of copper and iron, and are produced in a circuit composed of the metal and a veiy thin hot film, of which the two surfaces are unequally heated. There are, however, some good reasons for doubting whether electrolytes can be included in a true thermo-electric series, and I consulted many autho- rities with reference to this point. Seebeck himself includes many electrolytes in his thermo-electric scale, and places acids below bismuth, a result con- firmed lately by Gore (in 1857) ; he also places certain salts above antimony, a result subsequently confirmed by Andrews of Belfast in 1837. This gentleman observed that the tension produced by the salts between the wires was about equal to that between a platinum and silver plate in dilute sulphuric acid, and that the metals used as electrodes did not influence the deflection. He considered the current certainly due to a thermo-electric action. Faraday in 1833 discovered what Becquerel subsequently called pyro-elec- tric currents ; the currents were in different directions with different substances used, and some, if not all, were of the same nature as those I have described. Leroux and Buff obtained currents where glass acted as the electrolyte. Leroux considered them thermo-electric, and Buff chemical effects. Buff also attributes some of the electrical phenomena connected with flame to a 176 report — 1862. thermo-electric action in which unequally heated air or gas forms part of the circuit. The currents obtained when a hot and cold platinum wire are dipped into dilute sulphuric acid and other liquids are well known ; and finally (in 1858), Mr. Wild published a laborious research, in which he seems to prove the development of thermo-electric currents not only at the junction between metals and various solutions, but also between two different solutions. Thus, although none of the above observers seem to have tested the oxides, there seems little reason to doubt that they may be classed with other elec- trolytes, and may give rise to currents in the same manner. On the other hand, I cannot yet consider it definitively proved that any of the currents obtained from electrolytes are due to a true thermo-electric action— that is to Bay, to an absorption of heat only, especially as Mr. Wild could find no trace of the Peltier heating and cooling effect at the junctions of his solutions. Further research, showing the source of the power developed, is most de- sirable. While .consulting the literature connected with this subject, I found that Gaugain had to some extent preceded me in the discovery of the loose-con- tact currents, in a paper published in the ' Comptes Eendus ' in 1S53. He comes to the same conclusion as I had done independently, that they were due to the unequally heated film of foreign matter, and places oxide of iron below platinum, and oxide of copper above gold and zinc, but below iron, instead of very much above it as I find. He does not appear to have ob- served the exceedingly high electromotive force to be obtained from these bodies, no doubt owing to the use of a short galvanometer coil of thick wires, such as is commonly used for thermo-electric researches. He introduces a carburet of iron, of which I find no trace, with more positive properties than oxide of copper, to explain some of his results. He gives very few data on which to found his theory, but simply mentions his conclusions, and appears to have made no direct experiment whatever with the oxides. Owing to these circumstances his experiments seem to have attracted little attention. I have endeavoured to contrive a convenient apparatus by which to study the properties of the oxides, but have not hitherto met with much success, owing to the great difficulty in maintaining a constant difference of temperature between the surfaces of the veiy thin film, which can alone be used with success. Xext year I hope to obtain further residts in elucidation of these quasi thermo-electric currents from electrolytes. I now wish to add a few remarks on the currents which occur when true metallic contact is made between a hot and cold end of a wire of one metal. The existence of these currents was placed beyond all doubt by Magnus's careful experiments, but their connexion with other thermo-electric phenomena has hitherto remained entirely without explanation. Wild has suggested that they might be due to a thermo-electric couple formed with hot air or gas at the moment of junction ; but experiments which I have made show this explanation to be founded on a mistaken conception of the duration of the current, which is by no means instantaneous, but lasts at least five minutes with copper or with iron wires, very gradually decreasing in intensity from a maximum to zero. Another explanation, viz. that the deflection is due to a sort of discharge of a statical effect produced by the unequal distribution of heat, is also nega- tived by the same consideration, as well as by the fact that a tension of suffi- cient magnitude to produce such a charge could not possibly have escaped observation by direct measurement. Professor W. Thomson has shown conclusively, in his ' Dynamic Theory of ' [Tofaapag, 177 T.,1,,1 mkbDN .fmm.it in »tmj cu. about 2048x10- »b,oIutoJ;^ dH =l«27. Sieman.'. mercury unit.. The nnmb.r. .ntered ale deviation, ob.crved on « reflecting galvanometer, „„ m VBy TaUM .Lowing the comparative thermo-electric oftVotl obtained with loo.e nnd tight contact, botw.cn loop, of on. and two m.tah HT) ''!!•■- ltl"'ll nearly proiiortiuuitt to the strengths of currents seconds TTOT MCTALS ON RIGHT (i-xrept when words "in middle" fire used). Heated at right ride. Loose contact i Tight contact ; Heated at right ride, Loose contact mm * 8 Tight contact mm *-w Heated in middle. 1st maximum ;•» *-2 2nd do.(hotter) -* «■» 5 Sii.vr.u. Heated nt right side. Loose contact ^ *-12 Tight contact *■ » 1 UtaUd in middle. 1st maximum -* «*9 2nd do. ( hotter , ^ » 6 Heated at right tide. Loose contact mm i 10 or 15 Tight contact t m m 10 Heated at right side. I»ose contact *»» ^-weak Tight contact mm* *-weak Seated i« middle. Maximum Heated at right tide. Loose contact — ' 12 Tight contact m m » 10 Heated in middle. Maximum mm t 10 Heated al right ride. Loose contact mm i 15 light contact m m i 15 //, aled in miSfle. Maximum »» ■ 12 Heated at right tide. Loose contact mm *- 15 to 20 Tight contact mm * woa Heated in middl, 1'nd do.i h..tt. n *— Heateil at right title. Loose contact *. mm 110 Tight contact mm it-weak Heated in middle. let 2nd 4o. (hotter)-* Heated at right ride. Loose contact ^>» »- 10 Tight contact *m- » - weak Heated m middle. Maximum mm *-2 Heated at right tide. Loose contact i — "10 Tight contact *■* *-weak Heated in middle. Maximum -mm *-2 Heated ii addle. Heated at right side. Loose contact s» »-15 Tight contact mm i 2 Heated I! 1st maximum -*- 2nd do. (hotter)* Heated at right side. Ixiosn contact -* «■« 100 to 150 Tight contact -* — t- 10 Heated in middle. Maximum — « ^k 12 Heated at right tide. I ■••■ contact * tmmi 5 Tight contact Healed in middle. Maximum Heated at rigid side. Loose contact -* mm- 5 Tight contact ■ — 10 Heated in middle. ■add!,: Heated at right ride. Loose contact -* mm 100 Tight contact mm ,- weak Heated in middle. 1st maximum -* *■ .; 2nd do.(hotter) mm *-:j Healed at right ride. Loose contact i » 10 Tight contact * — in nlr Heated in middle. Maximum -* mm 1 Heated at right ride. Loose contact -mm *- 10 Tight contact — > 10 Heated in middle. Maximum mm *-10 Heated at right ride. Loose contnet ••* *■ 250 Tight contact i .m uncertain Heated in middle. Maximum i — 15 Heated at right ride. Loose contact c — weak Tight contact mm »-weak Heated in middle. Maximum Heated at right side. Loose contact -* ■*■:- 100 Tight contact i ii Heateil in middle Maximum ~* •>• 2 Heateil at right ride. Loose contact * i TO Tight contact m m * -10 ZiVuiYrf I Maximum ■■ middle. » i-lfi Heated at right ride. Loose contact -*- Tight contact -*- Heated ii Maximum -*- Heated at right ride, Loose contact ■ — 17 Tight contact -* «wv Heated in middle. Maximum mm *~w Heated at right side. Loose contact «* mm '220 Tight contact -* mm weak Heated in middle. Maximum ON THERMO-ELECTRIC CURRENTS IN CIRCUITS OF ONE METAL. 177 Heat,' that if the condition, of metal at a certain temperature depended ex- clusively on that temperature, no distribution or movement of heat could possibly give rise to a current of electricity in a circuit of one metal ; never- theless I find, as above stated, that in a circuit of one metal wire a current is maintained for five minutes at a time, gradually vanishing to nothing when the two ends of the homogeneous wire have been for some time in contact, but rocommeucing if one wire is cooled for a minute and then again applied to the hot one. One explanation of this might be that the condition of the wires does not solely depend on their temperature, but is influenced to a con- siderable extent by the time during which they have remained at that tem- perature. Nor is this a gratuitous assumption : Dr. Matthiessen has proved that wires of several metals do not attain a constant conducting power until they have been kept for some time at a constant temperature ; he finds that the conducting power of bismuth increases, while that of tellurium decreases when kept for a time at 100°. Quite similarly, some metals may rise and some may fall in the thermo-electric scale after being heated for some time, a supposition which is necessary to account for the metallic contact currents by the theory I suggest. Another possible explanation of the metallic contact currents may be found in a partial hardening on the one. side and annealing on the other, caused by the sudden contact of the hot and cold metal. If this be so, the current between annealed and unannealed wires of the same metal would correspond with the contact current between two homogeneous wires, in a way which it does not seem to do. I am, however, now engaged in investigating this subject, and hope before next year to be able to give facts which may decide whether either of these theories is tenable. There is great difficulty in forming any conclusion from experiments hitherto made, inasmuch as none of the observers, except Dr. Matthiessen, have used chemically pure metal, and it is found that the electrical properties of a metal are affected to an extraordinary degree by the presence of impurities in very small quantities. Explanation of tlie Tahle. The names of the metals of which the loops were made are entered at the side and top of the Table. The experiments made with each combination are entered in the subdivision at the intersection of the horizontal and vertical columns corresponding to the two metals. The nietals named at the top formed the right-hand loop, those at the side the left-hand loop. The arrows show the direction of the current across the joint. The first entiy in each subdivision shows the deflection observed when the right-hand metal was heated and the wires held loosely together. The second entry shows the deflection when the same metal was heated but the wires drawn tightly together. The third entry gives the maximum deflection, and the direction of the current, when the middle of the joint is gradually heated and the two wires held tightly together. The fourth entry (where given) shows the maximum deflection from a current in the opposite direction when greater heat was applied. The two last entries show the common well-known metallic thermo-electric effects. The first entry shows the new loose-contact effect. The second entry shows an uncertain combined effect of metallic and imperfect contact effects. An example will perhaps make this clearer. When copper and iron were 1862. N 178 report— 1862. used and copper loop heated, a loose contact produced a current from copper to iron across the joint, giving a deflection of 100 divisions. A tight contact gave nothing decided. When the iron loop was heated (the copper cold) the loose contact produced a current from iron to copper across the joint, giving a deflection of 90 divisions. A tight contact in this case gave a weak current in the opposite direction. "When the joint was heated in the middle, as the temperature gradually rose, a maximum deflection of 3 divisions was first reached, showing a current from copper to iron across the joint ; and as the heat increased still further this current was reversed, and finally, at a white heat, gave a maximum deflection of 3 divisions with a current from iron to copper. On the Mechanical Properties of Iron Projectiles at High Velocities. By W. Fairbairn, F.R.S. A valuable series of experiments were made at Manchester upon portions of plates fired at by the Iron Plate Committee at Shoeburyness. These expert ments comprised the determination of the resistance to punching, to a tensile strain, to impact, and to pressure. They show that the tenacity varied from 11 to 29 tons per square inch in the iron plates, and from 26 to 33| tons in the homogeneous iron plates. The average strength of the iron plates between lg and 3 inches thick varied from 23| to 24^ tons per square inch, and this, or about 21 tons, may proba- bly be insisted upon as a measure of strength in future contracts for iron plates. The elongation of the plates under a tensile strain may be taken as a mea- sure of the ductility of the material ; it varied in the thicker iron plates from 0-91 to 0-27 per unit of length, and averaged 0-27 inch in the homogeneous metal plates. The maximum observed was 0-35. The most important results in connexion with the question of the resist- ance are, however, those obtained by combining the tensile breaking weight with the ultimate elongation, as first indicated by Mr. Mallet in a paper read before the Institution of Civil Engineers. By finding in this manner the product of the tenacity and ductility, numbers are obtained which, though not identical with those expressing the resistance of the plates in the experiments with guns at Shoeburyness, are yet in close correspondence with them. The average value for Mr. Mallet's coefficient in the thicker iron plates was about 6500 lbs., and in the steel or homogeneous plates 8300 lbs. But the resist- ance of the iron plates increases with the thickness, whilst that of the homo- geneous metal diminishes. The correspondence of these numbers is indicated in the Eeport addressed to the War Office and the Admiralty ; but a more extended series of experiments are yet wanting to determine the true value of the coefficient as a guide to be insisted upon iu the manufacture of iron plates. 9000 foot-pounds is the maximum for iron given by the 'results already obtained ; but an extended series of experiments might develope new features of resistance and new improvements in the manufacture. The experiments on punching afford an explanation of the greatly increased perforating power of the flat-headed shot over- that of the round-headed projectiles. They also lead to a formula for the ordinary cast-iron service shot, which appears to give with approximate accuracy the law of the resist- ON THE MECHANICAL PROPERTIES OF IRON PROJECTILES. 179 ance of plates of different thicknesses to missiles of various weights and velo- cities. These investigations led to inquiries into the state of the manufacture of plates calculated to resist heavy and powerful projectiles directed against the sides of an iron-plated ship, and, moreover, to determine the exact thickness of plates that a vessel was able to carry. Again, they had reference to the quality of the plates and their powers of resistance to impact. There were three conditions necessary to be observed in the manufacture : 1st, that the material should be soft and ductile ; 2nd, that it shoidd be of great tenacity ; and, lastly, that it should be fibrous and tough. All these conditions apply to the manufacture of plates, and they also apply, with equal force, to the projectiles in their resistance to pressure and impact. In the experiments at Shoebiiryness, it was found that the ordinary cast- iron service shot were not adapted for penetration, as they invariably broke into fragments when discharged against a sufficiently thick armour-plate. In most cases when delivered at high velocities, they had the power of damaging and breaking the plates ; but owing to their crystalline character and defective tenacity, a considerable portion of the power was expended in their own destruction. To some extent the same law was applicable to wrought-iron shot, as part of the force, from its greater ductility, was employed in distorting its form, and depriving it of its powers to penetrate the plate. Cast and wrought iron are therefore inferior as a material for projectiles intended to be employed against iron-plated ships and forts. With steel hardened at the end the case is widely different, as its tenacity is not only much greater than that of cast and wrought iron, but the process of hardening the head prevents compression and its breaking up by the blow when the whole of its force is delivered upon the plate. Steel, although much superior to cast or wrought iron in its power of resistance in the shape of shot, is, nevertheless, suscep- tible of distortion and compression, and in every instance when employed against powerful resisting targets the compression, and consequently the dis- tortion, was distinctly visible. There is another consideration besides the material which enters largely into the question of the resisting powers of shot, and that is form. It will be recollected that, some years since, the late Professor Hodgkiiison instituted a series of experiments to determine the strength of iron pillars, and the results obtained were in the following ratios : — lbs. 1st. That pillars of about 20 to 30 diameters in length, with ) on nn two flat ends, broke with J ^ UUU 2nd. Pillars with one end rounded and one flat broke with 2000 And 3rd. Pillars with both ends rounded broke with 1000 being in the ratio of 1, 2, 3. Now in order to ascertain the effects of form on cylindrical shot, a series of experiments were instituted to determine the force of impact and statical pressure produced upon shot of different shapes, and from these experiments the following results were obtained. The description of shot experimented upon was cast-iron of the cylindrical form, with flat and round ends ; and it is interesting to observe that the re- sults correspond with those where both ends are rounded and one end only rounded, as obtained by Mr. Hodgkiiison on long columns ; but in the short specimens with both ends rounded the results are widely different, as may be seen by the following Table. n2 180 REPORT — 1862. No. of Experi- ments. Crushing weight in lbs. Ultimate compression in inches. Pressure per square inch in lbs. Pressure per square inch in tons. Remarks. I. 2. 73,428 68,062 •120 •092 122,115 125,787 55-13 } B <>th ends flat. Mean 123,951 54-82 Ureas -5674 and -7088. 3. 4. 35,540 40,916 •22 •24 62,636 57,725 n i mm \ iOne end rounded. 2a- 1 1 J Mean 60,180 26-86 Ureas -7088 and -7088. 5. 6. 38.2G0 37,580 •25 •25 53,978 53,030 „, ,., 1 Both ends rounded. 23'67 J Mean 37,920 •25 53,504 2388 Areas -7088 and -7088. From the above experiments, it is evident that the round-ended shot loses more than one-half its power of resistance to pressure in the direction of its length ; and this may be accounted for by the hemispherical end concentrating the force on a single point, which, acting through the axis of the cylinder, splits off the sides by a given law of cleavage in every direction. On the other hand, the flat-ended specimens have the support of the whole base in a vertical direction ; and from these we derive the following comparative resxdts : — Taking the resistance of the flat-ended shot at 54-82 tons per scmare inch, and that with hemispherical ends at 26-86, we have a reduction from tho mean of the flat-ended columns of 27'96 tons, being in the ratio of 100 : 49 ; or, in other words, a flat-ended shot will require more than double the force to crush it than one with one of its ends rounded. Now, as the same results were obtained at Shoeburyness, in the appearance of the fractured ends, when similar shot was fired from a gun, we arrive at the conclusion that the same law is in operation whether rupture is produced by impact or statical pressure. In the experiments on cast-iron shot, the mean compression per unit of length of the flat-ended specimen was -0665, and of the round-ended *1305. The ratio of the compression of the round- to the flat-ended was therefore as 1-96 : 1, or nearly in the inverse ratio of the statical crushing pressure. It has been correctly stated that it requires a considerable amount of force to break up shot when delivered with great velocity against an unyielding object, such as the side of an iron-cased ship, or a target representing a por- tion of that structure ; and it may be thence inferred that the force expended in thus breaking up the shot must be deducted from that employed in doing work on the plate. This is confirmed by experiment, which shows that though the whole of the force contained in the ball, when discharged from a gun at a given velocity, must be delivered upon the target, the amount of work done, or damage done to the plate, will depend on the weight and the tenacity of the material of which the shot is composed. If, for example, we take two balls of the same weight, one of cast iron and the other of wrought iron, and deliver each of them with the same velocity upon the target, it is obvious that both balls carry with them the same pro- jectile force as if they were composed of identically the same material. The dynamic effect or work done is, however, widely different in the two cases, the one being brittle and the other tough : the result will be, that the cast iron is broken to pieces by the blow, whilst the other either penetrates the plate or, what is more probable, flattens its surface into a greatly increased area, and ON THE MECHANICAL PROPERTIES OF IRON PROJECTILES. 181 inflicts greatly increased punishment upon it. In this instance the amount of -work done is in favour of the wrought iron : but this does not alter the condition in which tho force was first delivered upon the target ; on the con- trary, it is entirely due to the superior tenacity of wrought iron to that of cast iron, which yields to the blow, and is broken to pieces in consequence of its inferior powers of resistance. The same may be said of steel in a much higher degree, which delivers nearly the whole of its vis viva upon the plate. In the foregoing experiments it will be observed that the resistance of cast- iron flat-ended shot to a crushing force is about 55 tons per square inch, whilst in the two following we find that the round-ended specimens, of the same material, gave way and were crushed with a pressure of only 26| tons — rather less than one-half the force required to crush the flat-ended ones. It is a curious but interesting fact (provided the same law governs the force of impact as dead pressure) that the round-ended projectile which strikes tho target should lose, from shape alone, one-half its powers of resistance. This may be accounted for as under. Take, for example, a cylinder of cast iron, «, with a rounded end forcibly pressed against the steel plate A, -until it is crushed by a fixed law of fracture ob- servable in every description of crystalline structure; that is, the rounded end or part s forms itself into a cone, which, acting as a wedge, splits off the sides c c in every direction at the angle of least resistance, and these, sliding along the sides of the cone, are broken to pieces on the surface of the plate. At Shoeburyness the same results were observable in all the experiments with spherical and round-ended shot, each of them following precisely the same law. In every case where the shot was broken to pieces, the fractured parts took the same direction, forming a cone or central core similar to that shown at s, as exhibited in my own experi- ments on statical pressure with the round-ended cylindrical shot. The law of fracture of cast iron has been carefully investigated by the lato Professor Hodgkinson in his paper on the strength of pillars, to which we have referred. It is there clearly shown that the resistance of columns when broken by compression is in the ratio of 1, 2, and 3 ; the middle one, with only one end rounded, being an arithmetical mean between the other two. Now these important facts, according to all appearance, bear directly upon the forms necessary to be observed in the manufacture of projectiles, as we find cylindrical shot with round ends loses one-half its powers of resist- ance to a pressure or a blow which tends to rupture or to break it in pieces. My own experiments given above do not exactly agree with those of Pro- fessor Hodgkinson — the ratio of resistance in a column with one end rounded, and that of a column with both ends flat, being as 3 : 1*5, instead of as 3 : 2 as in his experiments, — a discovery probably explained by considering that he employed cast-iron pillars from 20 to 30 diameters in length, whereas my own were only two diameters long. Professor Hodgkinson has, indeed, ex- pressed an opinion that the difference of the strengths of the three forms of pillars becomes less according as the number of times the length of the pillar exceeds the diameter decreases, which is the reverse of the results obtained in the foregoing experiments. JBut on this I may observe, that the conclusion 182 KEPOET 1862. is founded on a very limited number of experiments on wrought-iron columns of 15 to 30 diameters long as compared with others of 60 diameters, which, in my opinion, has been prematurely assumed as a general law. With wrought iron especially, the crushing-up of the rounded ends would soon bring pillars of that form into the condition of flat-ended pillars when the breaking weight approached the ultimate strength of the material — a conclusion confirmed by observing that the experiments in question are exactly those in Mr. Hodg- kinson's table in which the breaking weights of the pillars are greatest. However this may be, the experiments I have given show that short cylinders with flat ends have twice the strength of similar cylinders with one end rounded. From this it would appear that the law for short cylinders is not the same, but altogether different from that obtained by Mr. Hodgkinson for long cylinders. The discrepancies which appeared to exist between my own experiments and those of Professor Hodgkinson induced me still further to inquire into the law which seems to govern short bolts of columns of two diameters in length. To account for those discrepancies, the experiments were extended to columns with both ends rounded ; and what renders them interesting is, that in short columns with both ends rounded the powers of resistance are nearly the same as those with one end flat and one end rounded, and moreover they appear to follow a different law from that of Professor Hodgkinson's long columns, which, in most cases, broke by flexure. The difference in strength between short columns with both ends rounded and those with one end flat and one end rounded is almost inappreciable, as will be seen by comparing their values as under : — Tons per square inch. Columns of two diameters long with flat ends crushed with 54-82 Columns with one end rounded and one flat „ „ 26-86 Columns with both ends rounded „ „ 23-88 So that the difference between them may be taken as the numbers 55, 27, and 24, or, in other words, in the ratio of 1 : -49 with one end rounded and one end flat — that with both ends flat representing unity — and as 1 : -44 with both ends rounded ; a comparatively slight difference between those with one end flat and the others with both ends rounded. With regard to the dynamic effect, or work done, by round-ended shot as compared with flat-ended ones, it has already been shown that with dead pres- sure the indentations produced on wrought-iron plates by a round-ended shot are nearly 3| times greater than by those with the flat ends, and that the work done is twice as great in the case of the round ends as compared with that by the flat ends. This may be accounted for by rounded shot striking the plate with itsj pointed end, and the force of the blow being given by a comparatively small area ; the vis viva or the whole force is thus concentrated and driven into the target to a depth consider- ably greater than if spread over the whole area of the projectile. The flat-ended cylindrical shot, which indicates such powerful resistance to pressure, is gene- rally fractured by one or more of its sides being forced downwards in the direction of the line a, and hence its superior resist- ance when the whole area of the cylinder forms the base as the means of support. ON THE MECHANICAL PROPERTIES OP IRON PROJECTILES. 183 The difference of form does not, however, lessen the quantity of mechanical force (the weights being the same), as each ball has the same work stored in it when delivered from the gun at the same velocity, and the blow upon the target ought to be the same in effect but for the difference of shape in the case of the round ends, which break to pieces with one-half the pressure. It is difficult to estimate the difference of force or work done upon the target by the two balls ; it is certainly not in the ratio of their relative tenacities (the metal being the same), but arising from form, as the one would strike the target with its whole sectional area in the shape of a punch adapted for perforation, whilst the other, although much easier fractured, would effect a deeper indentation upon the plate. The same law of defective resistance is observable in wrought iron and steel as is indicated in cast iron, but not to the same extent. On com- paring the mean of twenty-six experiments on wrought iron with those on cast iron, it is evident that the difference between the two is considerable in their respective powers of resistance to compression. In the experiments on cast iron the specimens were invariably broken into fragments, and those of wrought iron, although severely crushed, were not destroyed. The same law, however, appears to be in operation in regard to the flat- and the round- ended specimens, although less in that of wrought iron, as both forms were squeezed so as to be no longer useful, the ratios being as 75 : 50 nearly, or 100 : 07-4. The round-ended shot, as might be expected, supported con- siderably more than one-half the pressure applied to the flat-ended one before it was finally distorted, whilst the cast iron was broken with less than one- half the pressure required to crush the flat-ended specimens. From these and the experiments on impact, there cannot exist a doubt as to the damaging effects of wrought-iron projectiles. The experiments on steel indicate similar results to those on cast and wrought iron, as may be seen from the mean of nineteen experiments given in the following summary of results : — No. of Experiments. Breaking weight in lbs. Ultimate compression in inches. Pressure per square inch in lbs. Pressure per square inch in tons. Remarks. 9 10 145,756 114,980 •04 •21 269,419 202,643 120-27 90-46 Flat-ended. Round-ended. Here the same law of defective resistance is present in the round- ended cylinders as in those of east iron, and doubtless the same ratio woidd have been obtained, provided the apparatus had been sufficiently powerful to have fractured the flat-ended specimens ; we may therefore conclude that, instead of the above ratio of 100 -. 75, it would have been 100 : 50 or thereabouts. From these facts, and those on wrought iron, we are led to the conclusion that the power of resistance to fracture of a cylindrical shot with both ends flat is to that with its front end rounded as 2 : 1 nearly. The experiments of which the above is an abstract were extended to lead, as well as cast and wrought iron, and steel ; but those on lead were of little value, as the compression was the same whether the ends were rounded or flat. This is accounted for by the extreme ductility of the metal and the facility with which it is compressed. As regards the wrought-iron specimens it may be observed that no definite results were arrived at, excepting the enormous statical pressure they sustained, equivalent to 78 tons per square inch of 184 report — 1862. sectional area, and the large permanent set which they exhibit. These com- parative values are as follows : — Statical resistance in Dynamical resistance in tons per square inch, foot-pounds per square inch. Cast iron, flat ends =55-32 776-8 Cast iron, round ends =26-87 821-9 Steel, round ends =90-46 2515-0 From the experiments on the wrought iron, the flat-ended steel specimens, and the lead, no definite conclusion was arrived at, the material being more or less compressed without the appearance of fracture. The mean resistance of the cast iron is 800 foot-pounds per square inch, whilst that of steel is 2515 foot-pounds, or more than three times as much. The conditions which appear to be derivable from these facts, in order that the greatest amount of force may be expended oa the iron plate, are therefore : — Yery high statical resistance to rupture by compression. In this respect wrought iron and steel are both superior to cast iron ; in fact, the statical resistance of steel is more than three times that of cast iron, and more than two and a half times that of wrought iron. Lead is inferior to all the other materials experimented upon in this respect. Again, resistance to change of form under severe pressure and impact is an important element in the material of shot. In this respect hardened steel is infinitely superior to wrought iron. Cast iron is inferior to both. In fact, the shot which would produce the greatest damage on armour-plates would be one of adamant, incapable of change of form, and perfect in its powers of resistance to impact. Such a shot "would yield up the -whole of its vis viva on the plate struck, and, so far as experiment yet proves, those projectiles which approach nearest to that condition are the most effective. Report on the Progress of the Solution of certain Special Problems of Dynamics. By A. Cayley, F.R.S., Correspondent of the Institute. My "Report on the Recent Progress of Theoretical Dynamics" was pub- lished in the Report of the British Association for the year 1857. The present Report (-which is in some measure supplemental thereto) relates to the Special Problems of Dynamics : to give a general idea of the contents, I wiU at once mention the heads under which these problems are considered ; viz., relating to the motion of a particle or system of particles, wc have Rectilinear Motion ; Central Forces, and in particular Elliptic Motion ; The Problem of two Centres ; The Spherical Pendulum ; Motion as affected by the Rotation of the Earth, and Relative Motion in general ; Miscellaneous Problems : The Problem of three bodies. And relating to the motion of a solid body, we have The Transformation of Coordinates ; Principal Axes, and Moments of Inertia ; ON THE SPECIAL PROBLEMS OP DYNAMICS. 185 Rotation of a Solid Body ; Kinematics of a Solid Body ; Miscellaneous Problems. As regards the first division of the subject, I remark that the lunar and planetary theories, as usually treated, do not (properly speaking) relate to the problem of three bodies, but to that of disturbed elliptic motion — a problem which is not considered in the present Report. The problem of the spherical pendulum is that of a particle moving on a spherical surface ; but, with this exception, I do not much consider the motion of a particle on a given curve or surface, nor the motion in a resisting medium ; what is said on these subjects is included under the head Miscellaneous Problems. The first six heads relate exclusively, and the head Miscellaneous Problems relates princi- pally to the motion of a single particle. As regards the second division of the subject, I will only remark that, from its intimate connexion with the theory of the motion of a solid body, I have been induced to make a separate head of the geometrical subject, " Transformation of Coordinates," and to treat of it in considerable detail. I have inserted at the end of the present Report a list of the memoirs and works referred to, arranged (not, as in the former Report, in chronological order, but) alphabetically according to the authors' names : those referred to in the former Report formed for the purpose thereof a single series, which is not here the case. The dates specified are for the most part those on the title- page of the volume, being intended to show approximately the date of the researches to which they refer, but in some instances a moi»e particular speci- fication is made. ^ I take the opportunity of noticing a serious omission in my former Report, viz., I have not made mention of the elaborate memoir, Ostrogradsky, " Memoire sur les equations clifferentielles relatives au probleme des Isope'ri- metres," Me'm. de St. Pet. t. iv. (6 se'r.) pp. 385-517, 1850, which among other researches contains, and that in the most general form, the transformation of the equations of motion from the Lagrangian to the Hamiltonian form, and indeed the _ transformation of the general isoperimetric system (that is, the system arising from any problem in the calculus of variations) to" the Hamil- tonian form. I remark also, as regards the memoir of Cauchy referred to in the note p. 12 as an unpublished memoir of 1831, there is an " Extrait du Memoire presente a l'Academie de Turin le 11 Oct. 1831," published in lithograph under the date Turin, 1832, with an addition dated 6 Mar. 1833. The Extract begins thus : — " § I. Variation des Constantes Arbitraires. Soient donne'es entre la variable t, . . . n fonctions de t designees par x, y, z . . et n autres fonctions de * designees par u, v, w, . . 2n equations differentielles du premier ordre et de la forme <te = dQ dy_ dQ dz_ dQ dt du' dt~ dv' di~ dw' — = - c 19i d i- _^ *?_ d ® & » dt~ dx' dt~ dy dt dz' °' without explanation as to the origin of these equations ; and the formulas are then given for the variations of the constants in the integrals of the foregoing system ; this seems sufficient to establish that Cauchy in the year 1831 was familiar with the Hamiltonian form of the equations of motion. Bour's " Memoire sur Fintegration des equations differentielles de la Me'- canique," as published, Me'm. pre's. de l'lnst. t. xiv. pp. 792-821, is substan- 186 report— 1862. tially the same as the extract thereof in * Liouville's Journal,' referred to in my former Report ; but since the date of that Report there have been published in the ' Comptes Rendus,' 1861 and 1862, several short papers by the same author ; also Jacobi's great memoir, see list, Jacobi, Nova Methodus &c. 1862, edited after his decease by Clebsch ; some valuable memoirs by Natani and Clebsch (Crelle, 1861 and 1862) relating to the Pfaffian system of equations (which includes those of Dynamics), and Boole " On Simultaneous Differential Equations of the First Order, in which the number of the Variables exceeds by more than one the number of the Equations," Phil. Trans, t. clii. (1862) pp. 437-454. Rectilinear Motion, Article Nos. 1 to 5. 1. The determination of the motion of a falling body, which is the case of a constant force, is due to Galileo. 2. A variable force, assumed to be a force depending only on the position of the particle, may be considered as a function of the distance from any point in the line, selected at pleasure as a centre of force ; but if, as usual, the force is given as a function of the distance from a certain point, it is natural to take that point for the centre of force. Tbe problem thus becomes a particular case of that of central forces ; and it is so treated in the ' Principia,' Book I. § 7; the method has the advantage of explaining the paradoxical result which presents itself in the case Force OC (Dist.) -2 , and in some other cases where the force becomes infinite. According to theory, the velocity becomes infinite at the centre, but the direction of the motion is there abruptly reversed ; so that the body in its motion does not pass through the centre, but on arriving there, forthwith returns towards its original position ; of course such a motion cannot occur in nature, where neither a force nor a velocity ever is actually infinite. 3. Analytically the problem may be treated separately by means of the d?x /clx\* /* equation -^=X, which is at once integrablein the form y-r f \ =C+2/Xefa\ 4. The following cases may be mentioned : — Force OC Dist. The law of motion is well known, being in fact the same as for the cycloidal pendulum. Force OC (Dist.) -2 , =-^, which is the case above alluded to. X' Assuming that the body falls from rest at a distance a, we have A'r=«(l— cos<£), where, if n=—^=, <p is given in terms of the time by means of the equation V fi nt=<j> — sin (p. If the body had initially a small transverse velocity, the motion woiild be in a very excentric ellipse, and the formulae are in fact the limiting form of those for elliptic motion. 5. There are various laws of force for which the motion may be determined. In particular it can be determined by means of Elliptic Integrals, in the case of a body attracted to two centres, force OC (dist.) -2 : see Legendre, Exercices de Cal. Integ. t. ii. pp. 502-512, and Theorie des Fonct. Ellip. t. i. pp. 531- 538. ON THE SPECIAL PROBLEMS OF DYNAMICS. 187 Central Forces, Article Nos. 6 to 26. 6. The theory of the motion of a body under the action of a given central' force was first established in the ' Principia,' Book I. §§ 2 & 3 : viz. Prop. I. the areas are proportional to the times, that is (using the ordinary analytical so notation), r-dd=Mt, and Prop. VI. Cor. 3, Poc^yr- py>=^ 2 M 2 \'T& + U )> that - cPu J> 7. 1\ is to be noticed that, given the orbit, the law of force is at once determined ; and § 2 contains several instances of such determination ; thus, Prop. VII. If a body revolve in a circle, the law of force to a point S is force oc g p 2 f y 3 (P the body, PV the chord through S). Prop. IX. If a body move in a logarithmic spiral, force oc (dist.)- 3 . Prop. X. If a body move in an ellipse, force to centre OC dist., and as a parti- cular case, if the body move in a parabola under the action of a force parallel to the axis, the force is constant. The particular case of motion in a parabola had been obtained by Galileo. And § 3. Props. XL XII. XIII. If a body move in an ellipse, hyperbola, or parabola under the action of a force tending to the focus, force OC (dist.) -2 . 8. But Newton had no direct method of solving the inverse problem (which depends on the solution of the differential equation), "Given the force to find the orbit." Thus force OC (dist.)- 2 , after it has been shown that an ellipse, a hyperbola, and a parabola may each of them be described under the action of such a force. The remainder of the solution consists in showing that, given the initial circumstances of the motion, a conic section (ellipse, parabola, or hyperbola, as the case may be) can be constructed, passing through the point of projection, having its tangent in the direction of the initial motion, and such that the velocity of the body describing the conic section under the action of the given central force is equal to the velocity of pro- jection ; which being so, the orbit will be the conic section so constructed. This is what is done, Prop. XVII. ; it may be observed that the latus rectum is constructed not very elegantly by means of the latus rectum of an auxiliary orbit. 9. A more elegant construction was obtained by Cotes (see the ' Harmonia Mensurarum,' pp. 103-105, and demonstration from the author's papers in the Notes by R. Smith, pp. 124, 125), depending on the position of a point C, such that the velocity acquired in falling under the action of the central force from C directly or through infinity* to P the point of projection, is equal to the given velocity of projection. 10. But Newton's original construction is now usually replaced by a con- struction which employs the space due to the velocity of projection considered as produced by a constant force equal to the central force at the point of pro- jection. 11. Section 9 of Book I. relates to revolving orbits, viz., it is shown that a body may be made to move in an orbit revolving round the centre of force, * In the second case C lies on the radius vector produced beyond the centre, and the body is supposed to fall from rest at C (under the action of the central force considered as repulsive) to infinity, and then from the opposite infinity (with an initial velocity equal to the velocity so acquired) to P. 188 REPORT 1862. by adding to the central force required to make the body move in the same orbit at rest, a force a (clist.) -3 - This appears very readily by means of the differential equation (ante, No. 6), viz. -writing therein P+cw 3 for P, and then 0', U in the place of 6\/l— Jj, Ivl-,-, respectively, the equation retains its original form, with 6', V, in the place of 6. h respectively. 12. It may bo remarked that when the original central forco vanishes, the fixed orbit is a right line (not passing through the centre of force). It thus appears by § 9 that the curve ii=A cos (n6 + B) may be described under the action of a force OC (dist.) -3 . A proposition in § 2, already referred to, shows that a logarithmic spiral may be described under the action of such a force. 13. But the case of a force OC (dist.)- 3 was first completely discussed by Cotes in the ' Harmonia Mensurarum,' pp. 31-35, 98-104, and Notes, pp. 117 -173. There are in all five cases, according as the velocity of projection is 1. Less than that acquired in falling from infi- nity, or say equal to that acquired in fall- ing from a point C to P, the point of pro- jection. 2. Equal to that acquired in falling from infi- nity. 3. 4, 5. Greater than that acquired in falling from infinity, or say equal to that acquired in falling from a point C, through infinity, to P ; viz. P Q being the direction of pro- jection,and SQ, C'T perpendiculars thereon from S and C respectively, 3. SQ<TQ 4. SQ=TQ 5. SQ>TQ the equations of the orbits being 1. u=Ae m9 +'Be~ m9 , A and B same sign, so that rad. vector is never infinite. 2. *<=Ae m9 orBe -m8 j logarithmic spiral. 3. u=A.e me +~Be~ me , A and B opposite signs, so that rad. ector becomes infinite. 4. m=A0+B, m=0, reciprocal spiral. 5. ?{=Acos(n0 + B), m=J^V — 1. 1 4. The before-mentioned equation, #u J> 3-f-W— 7 o , — 0, dd 2 ftV is in effect given (but the equation is encumbered with a tangential force) in Clairaut's " The'orie de la Lune," 1765. It is given in its actual form, and ex- tensively used (in particular for obtaining the above-mentioned equations for Cotes's spirals) in "Whewell's ' Dynamics,' 1823. The equation appears to be but little known to continental writers, and (under the form u" + u — aVK=0) it is given as neiv by Schellbach as late as 1853. The formula) used in place of it are those which give t and each of them in terms of r ; viz. ON THE SPECIAL PROBLEMS OF DYNAMICS. 189 dt = T ± , dB- {-^ + r"-(C-2/?dr)} i hdr r {_7 t 2 +r 2 (C-2/Pc?r)} i which, however, assume that P is a function of r only. 15. Force OC (dist.)- 2 . The law of motion in the conic sections is implicitly given by Newton's theorem for the equable description of the areas. For the parabola, if a denote the pericentric distance, and /the angle from pericentre or true anomaly, we have <= o§V2/ tan|/+itan 3 |/ \ Vm \ ' For the ellipse we have an angle g, the mean anomaly varying directly as the time (g=nt if n=-^\ ■ an auxiliary angle «, the excentric anomaly, connected with g by the eqiiation g=u — esmw, and then the radius vector r and the true anomaly / are given in terms of v, by the eqiiations r=a (1 — e cos u), and j. cos it — e . r Vl — r sin « t . i. u? <v/l + e i i cos/= , sin/= , and /. tan |/= V __L_tanitt. 1— ecosw 1— ecosw 1— e 16. It is very convenient to have a notation for - and / considered as func- a " tions of e, g, and I have elsewhere proposed to write r=a elqr. (e, g), /=elta (e, g), read elqr elliptic quotient radius, and elta elliptic true anomaly. 17. The formula for the hyperbola correspond to those for the ellipse, but they contain exponential in the place of circular functions (see post, Elliptic Motion). 18. Euler, in the memoir " Determinatio Orbitae Cometaa Anni 1742," (1743), p. 16 et seq., obtained an expression for the time of describing a para- bolic arc in terms of the radius vectors and the chord ; viz. these being /, g, and h, the expression is Time =- 6 V> (f+9+A % - (f+ff-^, which, however, as remarked by Lagrange, ' Mec. Anal.' t. xi. (3rd edit. p. 28), is deducible from Lemma X. of the third book of the < Principia.' But the theorem in its actual form is due to Euler. 19. Lambert, in the « Proprietates Insigniores, &c.' (1761), Theorem VII. Cor. 2, obtained the same theorem, and in section 4 he obtained the corre- sponding theorem for elliptic motion ; viz. the expression for the time is J V — \ p— <(,'— (sin 6— sin^') L 190 REPORT — 1862. if -i.i /f+Q—k ■ i v i Yf+9—k Bmif = l^/-LZA , sin i<p =i^/ J y a • The form of the formula is, it will be observed, similar to that for motion in a straight line (antt, No. 4), and in fact the motion in the ellipse is, by an ingenious geometrical transformation, made to depend upon that in the straight line. The geometrical theorems upon which the transformation depends are stated, Cayley " On Lambert's Theorem &c." (1861). 20. The theorem was also obtained by Lagrange in the memoir " Be- cherches &c." (1767) as a corollary to his solution of the problem of two centres ; viz. upon making the attractive force of one of the centres equal to zero, and assuming that such centre is situate on the curve, the expression for the time presents itself in the form given by Lambert's theorem. 21. Two other demonstrations of the theorem are given by Lagrange in the memoir " Sur une maniere particuliere d'exprimer le temps &c." (1778), reproduced in Note V. of the second volume of the last edition (Bertrand's) of the ' Mecanique Analytique.' As M. Bertrand remarks, these demonstrations are very complete, very elegant, and very natural, assuming that the theorem is known beforehand. Demonstrations were also given by Gauss, " Theoria Motus " (1809), p. 119 etseq.; Pagani, "Demonstration d'un theoreme ifcc." (1834); and (in con- nexion with Hamilton's principal function) by Sir W. E. Hamilton, " On a General Method &c." (1834), p. 282; Jacobi, "Zur Tbeorie &c." (1837),. p. 122 ; Cayley, « Note on the Theory of Elliptic Motion " (1856). 22. Connected with the problem of central forces, we have Sir W. B. Hamilton's ' Hodograph,' which in the paper (Proc. E. Irish Acad. 1847) is defined, and the fundamental properties stated ; viz. if in an orbit round a eentre of force there be taken on the perpendicular from the centre on the tangent at each point, a length equal to the velocity at that point of the orbit, the extremities of these lengths will trace out a curve which is the hodograph. As the product of the velocity into the perpendicular on the tangent is equal to twice the area swept out in a unit of time (i^=7i), the hodograph is the reciprocal polar of the orbit with respect to a circle described about the centre of force, radius = \/h. "Whence also the tangent at any point of the hodo- graph is perpendicular to the radius vector through the corresponding point of the orbit, and the product of the perpendicular on the tangent into the corresponding radius vector is =h. If force oc (dist.) -2 , the hodograph, qua reciprocal polar of a conic section with respect to a circle described about the focus, is a circle. 23. The following theorem is also given without demonstration ; viz. if two circular hodographs, which have a common chord passing or tending through a common centre of force, be both cut at right angles by a third circle, the times of hodographically describing the intercepted arcs (that is, the times of describing the corresponding elliptic arcs) will be equal. 24. Droop, " On the Isoehronism &c." (1856), shows geometrically that the last-mentioned property is equivalent to Lambert's theorom ; and an analytical demonstration is also given, Cayley, " A demonstration of Sir W. B. Hamilton's Theorem &c." (1857). See also Sir W. B. Hamilton's < Lec- tures on Quaternions ' (1853), p. 614. 25. The laws of central force which have been thus far referred to, are force 11. C OLr, CX—nf OC — , ; and it has been seen that the case of a force P-f-^ depends ON THE SPECIAL PROBLEMS OF DYNAMICS. 191 B P upon that of a force P, so that the motions for the forces Ar-\-— and — +— r 3 r* r 3 T> are deducible from those for the forces Ar and — respectively. Some other A A B C D laws of force, e. g. -±Br, _ + _+ + are considered by Legendre, " Theorie des Fonctions EUiptiques " (1825), being such as lead to results expressible by elliptic integrals, and also the law — , for which the result in- r volves a peculiar logarithmic integral. But the most elaborate examination of the different cases in which the solution can be worked out by elliptic integrals or otherwise is given in Stader's memoir " De Orbitis &c." (1852)> where the investigation is conducted by means of the formulas which give t and 6* in terms of r (ante, No. 14). 26. In speaking of a central force, it is for the most part implied that the force is a function of the distance : for some problems in which this is not the case, see pos£, Miscellaneous Problems, Nos. 86 and 87. It is to be noticed that, although the problem of central forces may be (as it has so far been) considered as a problem in piano (viz. the plane of the motion has been made the plane of reference), yet that it is also interesting to consider it as a problem in space ; in fact, in this case the integrals, though of course involved in those which belong to the plane problem, present them- selves under veiy distinct forms, and afford interesting applications of the theory of canonical integrals, the derivation of the successive integrals by Poisson's method, and of other general dynamical theories. Moreover, in the lunar and planetary theories, the problem must of necessity be so treated. Without going into any details on this point, I will refer to Bertrand's memoir " Sur les equations differentielles de la Mecanique " (1852), Donkin's memoir "On a Class of Differential Equations &e." (1855), and Jacobi's pos- thumous memoir, " Nova Methodus &c." (1862). Elliptic Motion, Article Nos. 27-40. 27. The question of the development of the true anomaly in terms of the mean anomaly (Kepler's problem), and of the other developments which pre- sent themselves in the theory of elliptic motion, is one that has very much occupied the attention of geometers. The formulas on which it depends are mentioned ante, No. 15 ; they involve as an auxiliary quantity the excentric anomaly u. 28. Consider first the equation <7=w — c sin u, which connects the mean anomaly g with the excentric anomaly u. Any function of u, and in particular u itself, and the functions c ? s nu mav sin J be expanded in terms of g by means of Lagrange's theorem (Lagrange, * Me'm de Berlin,' 1768-1769, " Theorie des Fonctions," c. 16, and " Traite de la Eesolution des equations Numeriques," Note 11). 29. Considering next the equation tan|/=^/l±ftan| M , which gives the true anomaly in terms of the excentric anomaly, then, by replacing the circular functions by their exponential values (a process em- 192 report — 1862. ployed by Lagrange, <Me'm. de Berlin,' 1776), /can be expressed in terms of u ; viz. tbe result is /= u + 2\ sin u + 2X 2 . £ sin 2u + 2X 3 . ^ sin Bu + &c., where \— ^~ v ^ 1 ~ e ( — e — }. Hence if u, sin «, sin 2«, &c. are 6 \ l+Vl-e 2 / expressed in terms of tbe mean anomaly, / will be obtained in tbe form f=g+a, series of multiple sines of g, tbe coefficients of the different terms being given in tbe first instance as functions of e and X ; and to complete tbo development X and its powers bave to be developed in powers of e. Tbe solu- tion is carried tbus far in tbe 'Mecanique Analytique' (1788), and in tbe ' Mecanique Celeste ' (1799). 30. We have next Bessel's investigations in the Berlin Memoirs for 181 G, 18X8, and 1824, and which are carried on mainly by means of the integral h f 2ir 2k1 = 1 cos Qui— I- shin) du, Jo and various properties are there obtained and applications made of this im- portant transcendant. 31. Relating to this integral we have Jacobi's memoir, "Eormulce trans- formationis &c." (1836), Liouville, « Sur l'integrale I "cos i (u—x sin u) du" (1841), and Hansen's "Ermittelung der absoluton Storungen" (1843); the researches of Poisson in the ' Connaissance des Temps ' for 1825 and 1836 arc closely connected with those of Bessel. 32. A very elegant formula, giving the actual expression of the coefficients considered as functions of e and X, is given by Grcatheed in the paper " Inves- tigation of the General Term &c." (1838) ; viz. this is f=rj + 2^{e^ + ^ + X- r e-^ + ^y^ V 3 where, after developing in powers of X, the negative powers of X must be rejected, and the term independent of X divided by 2. This result is ex- tended to other functions of/, Cayley "On certain Expansions &c." (1842). 33. An expression for the coefficient of the general term as a function of e only is obtained, Lcfort, " Expression Numerique &c." (1846). The expres- sion, which, from the nature of the case, is a very complicated one, is obtained by means of Bessel's integral. This is an indirect process which really comes to the combination of the developments of / in terms of u, and « in terms of g; and an equivalent result is obtained directly in this manner, Greedy, " General and Practical Solution &c." (1855). 34. We have also on the subject of these developments the very valuable and interesting researches of Hansen, contained in his « Fundamenta Nova, &c.' (1838), in the memoir "Ermittelung der absoluten Storungen &c/' (1845), and in particular in the memoir " Entwickelung des Products &c" (1853). COS • 35. But the expression for the coefficient of the general term gin rg m any of these expansions is so complicated that it was desirable to have for the coefficients corresponding to the values r=0, 1, 2, 3, . . . the finally redueed expressions in which the coefficient of each power of e is given as a numerical ON THE SPECIAL PROBLEMS OF DYNAMICS. 193 fraction. Such formulae for the development of (- — l\ m c ? 3 jf, where,/ is a general symbol, the expansion being carried as far as e 7 , were given, Lever- rier, ' Annales de l'Observatoire de Paris,' t. i. (1855). 36. And starting from these I deduced the results given in my " Tables of the Developments, &c." (1861); viz. these tables give fx=Z— 1\, all carried to e' '. 37. The true anomaly / has been repeatedly calculated to a much greater extent, in particular by Schubert (Ast. Theorique, St. Pe't. 1822), as far as e 20 . The expression for - as far as e u is given in the same work, and that for log - as far as e 9 was calculated by Oriani, see Introd. to Delambre's • Tables du Soled,' Paris (1806). 38. It may be remarked that when the motion of a body is referred to a plane which is not the plane of the elliptic orbit, then we have questions of development similar in some measure to those which regard the motion in the orbit ; if, for instance, z be the distance from node, cj> the inclination, and x the reduced distance from node, then cosz=cos<pcos.r, from which we may derive z=x-\- series of multiple sines of as. And there are, moreover, the questions connected with the development of the reciprocal distance of two particles — say (a 2 -\-a' 2 —2aa' cosd)~* — which present themselves in the pla- netary theory ; but this last is a wide subject, which I do not here enter upon. I will, however, just refer to Hansen's memoir, " Ueber die Entwicke- lung der negativen und uugeraden Potenzen &c." (1854). 39. The question of the convergence of the series is treated in Laplace's memoir of 1823, where he shows that in the series which express r and /in multiple cosines or sines of g, the coefficient of a term . os ig, where i is very great, is at most equal in absolute value to a quantity of the form *— r:( -), A and \ being finite quantities independent of i, whence he concludes that, in order to the convergency of the series, the limiting value of the excentricity is e=X, the numerical value being €=0-66195. 40. The following important theorem was established by Cauchy, as part of a theoiy of the convergence of series in general ; viz. so long as e is less than 0-6627432, which is the least modulus of e for which the equations 7T 2 = it— e sinw, l=fcosu can be satisfied, the development of the true anomaly and other developments in the theory of elliptic motion will be convergent. This was first given in 1862. o 194 report-— 1862. the " Me'moire sur la Me*canique Celeste," read at Turin in 1831, but it is reproduced in the memoir " Considerations nouvelles sur les suites &c.," Mem. d'Anal. et de Phys. Math. t. i. (1840) ; and see also the memoirs in ' Iiou* ville's Journal ' by Puiseux, and his Note i. to vol. ii. of the 3rd ed. of the ' Mecanique Analytique ' (1855). There are on this subject, and on subjects connected with it, several papers by Cauchy in the • Comptes Rendus,' 1840 et seq., which need not be particularly referred to. The Problem of tiuo Centres, Article Nos. 41 to 64. 41. The original problem is that of the motion of a body acted upon by forces tending to two centres, and varying inversely as the squares of the distances ; but, as will be noticed, the solutions apply with but little variation to more general laws of force. 42. It may be convenient to notice that the coordinates made use of (in the several solutions) for determining the position of the body, are either the sum and difference of the two radius vectors, or else quantities which are respectively functions of the sum and the difference of these radius vectors*. If the plane of the motion is not given, then there is a third coordinate, which is the inclination of the plane through the body and the two centres to a fixed plane through the two centres, or say the azimuth of the axial plane, or simply the azimuth. 43. Calling the first-mentioned two coordinates r and s, and the azimuth \p, the solution of the problem leads ultimately to equations of the form dr els _ \dr ^ds pdr ads where R and S are rational and integral functions (of the third or fourth degree, in the case of forces varying as (dist.) -2 ) of r, s respectively (but they are not in general the same functions of r, s respectively) ; \ and p are simple rational functions of r, and fi and a simple rational functions of s ; so that the equations give by quadratures, the first of them the curve described in the axial plane, the second the position of the body in this curve at a given time, and the third of them the position of the axial plane. In the ordinary case, where R and S are each of them of the third or the fourth order, the quadratures depend on elliptic integrals t ; but on account of the presence in the formulae of the two distinct radicals VR> \Zs> it would appear that the solutionis not susceptible of an ulterior development by means of elliptic and Jacobian functions f similar to those obtained in the problems of Rotation and the Spherical Pendulum. 44. It has just been noticed that when R, S are each of them of the fourth order, the quadratures depend on elliptic integrals ; in the particular cases • • 071 (ll % 'iXClS m which the relation between r, s is of the form — t=.=-t=, R and S being VR Vs * If v, u are the distances of the body P from the centres A and B, a the distance AB, K, i) the angles at A and B respectively, and^=tan £ I tan \ r), j=tan \ S^-tan \ jj, then, as may he shown without difficulty, v+u=a = — -. «—«=«—— -, so that p and q are •" ' 1—p' 1+2 functions of »+•« and v —u respectively ; these quantities p and q are Euler's original coordi- nates. t The elliptic integrals are Legendre's functions F, E, IT ; the elliptic and Jacobian functions are sinain., cosam., Aam., and the higher transcenclants 0, H. ON THE SPECIAL PROBLEMS OF DYNAMICS. 195 the same functions of r, s respectively, and m and n being integers (or more generally for other relations between the forms of R, S given by the theory of elliptic integrals), the equation admits of algebraical integration ; but as the relations in question do not in general hold good, the theory of the algebraical integration of the equations plays only a secondary part in the solution of the problem. It is, however, proper td remark that Euler, when he wrote his first two memoirs " On the Problem of the two Centres " (post, Nos. 45 and 46), had already discovered and was acquainted with the theory of the algebraic integration of the equation -7g=-T= ( R > s > m , n , «* supra), although his memoir, " Integratio oaquationis dx dy ^ "Vl+l^+C^+D^+l^' - " V A + By + (y + By 3 + Ey 4 '" N. Coram. Petrop. t. xii. 1766-1767?, bears in fact a somewhat later date. 45. Having made these preliminary remarks, I come to the history of the problem. It is I think clear that Eider's earliest memoir is the one " De Motu Corporis etc." in the Petersburg Memoirs for 1764 (printed 1766). In this memoir the forces vary as (disk)-*, and the body moves in a given plane. The equations of motion are taken to be which, if £, ,, are the inclinations of the distances v, u to the axis respectively (sec foot-note to No. 42), lead to dv* + vhW=±gd? A + B ( D + E \ v V d£ dtj = 2gadf (A cos £ + B cos >? + D), where D, E are constants of integration. Substituting for v, u their values in terms of rj, £ and eliminating dt, Euler obtains . casing P+VP 2 — Q 2 dr) sin £~ Q ' where A cos t) + B cos £ -f D cos £ cos v + E sin £ sin rj = P, Acos£+Bcosj;+D = Q. And he then enters into a very interesting discussion of the particular case r 7 v ° r *° ^ nz ' the Case where one of the attracting masses vanishes, which was of course known to be integrable); and after arriving at some paradoxical conclusions which he does not completely explain, although he remarks that the explanation depends on the circumstance that the integral lound is a singular solution of a derivative equation, and as such does not satisty the original equations of motion,— he proceeds to notice that an inquiry into the cause of the difficulty led him to a substitution by which the variables were separated. ft, *%S^ k J he memoir « Probleme, un Corps &c." in the Berlin Memoirs ior uw (printed 1767), after obtaining the last-mentioned formula;, he gives o2 196 report— 1862. at once, without explaining how he was led to it, the analytical investigation of the substitution in question, viz. in each of the two memoirs he in fast writes d? sin i) •+• dq sin L-\ /P+Q d^ sin tj—dr) sin tan|£=/, tan| 7 =<7, fg—p, J -=q, that is p = tan K tan ir, ; ? = tan \? 4- tan 1 n ; and in terms of these quantities p, q, the equation becomes dp dq where P=( A + B + D) i > + 2Ep 8 + (-A-B + D)y, Q=(-A + B-D)r / + 2Er/ + ( A-B-D) 2 \ so that P and Q are cubic functions (not the same functions) of p and q respectively ; and the equation for the time is found to be dts/2<i_ pdp qdq which are the formulae for the solution of the problem, as obtained in Euler's first and second memoirs. 47. In his third memoir, viz. that " De Motu Corporis &c." in the Petersburg Memoirs for 1765 (printed 1707), Euler considers the body as moving in space, the forces being as before as (dist.) -2 . Assuming that the coordinates y, z are in the plane perpendicular to the axis, there is in this case dz d\i . . , . the equation of areas y j;~ z -^r=const. ; and writing y =y sin \p, z=y cos >//, that is, y'=*/y 2 + z 2 , and \p the azimuth, the integral equations for the motion in the variable plane (coordinates x, y') are not materially different in form from those which belong to the motion in a fixed plane, coordinates x, y (see post, No. 56, Jacobi) ; and the last-mentioned equation, which reduces dd> itself to the form y' 2 -rr=const., gives at once d\p in a form such as that above alluded to (ante, No. 43), and therefore \p by quadratures. The variables employed by Euler in the memoir in question are v + u, v— u (say r, s) and \p, v, u being, as above, the distances from the two centres, and \js the azimuth of the axial plane. The functions of r, s under the radical signs are of the fourth order ; this is so, with these variables, even if the motion is in a fixed plane ; but this is no disadvantage, since, as is well known, the case of a quartic radical is not really more complicated than that of a cubic radical, the two forms being immediately convertible the one into the other. 48. Lagrange's first memoir (Turin Memoirs, 1766-1769) refers to Euler's three memoirs, but the author mentions that it was composed in 1767 with- out the knowledge of Euler's third memoir. The coordinates ultimately made use of are v + u, v — u (say r, s) and \p, the same as in Euler's third memoir, and the results consequently present themselves in the like form. ON THE SPECIAL PKOBLEMS OP DYNAMICS. 197 49. If the attractive force of one of the centres is taken equal to zero, then the position of such centre is arbitrary, and it may be assumed that the centre lies on the curve, which is in this case an ellipse (conic section) ; the expression of the time presents itself as a function of the focal radius vectors and the chord of the arc described; which, as remarked, ante, No. 20, leads to Lambert's theorem for elliptic motion. 50. The case presents itself of an ellipse or hyperbola described under the action of the two forces, viz. the equation —==-^ will be satisfied vE VS byr— a = 0, if r— a be a double factor of E, or by s— /?=0,"if s—fi be a double factor of S, a case which is also considered in the ' Me'canique Ana- lytique ; ' and see in regard to the analytical theory, t. ii. 3rd ed. Note III. by M. Serret, and "These," Liouv. 1848. It is remarked by M. Bonnet, Note IV. and Liouv. t. ix. p. 113, 1844, that the result is a mere corollary of a general theorem, which is in. effect as follows, viz. if a particle under the separate actions of the forces P, F, . . . starting in each case from the same point in the same direction but with the initial velocities v, v', &c. respectively, describe the same curve, then such curve will also be described under the conjoint action of all the forces, provided the body start from the same point in the same direction, with the initial velocity V= a/'v- + v" 2 + . . 51. Lagrange's second memoir (same volume of the Turin Memoirs) contains an exceedingly interesting discussion as to the laws of force for which the problem can be solved. Writing U, V, u, v in the place of Lagrange's P, Q, p, q, the equations of motion are d\v , Q-rQU , (.r-a)V_ A d?~ t u + v ' *y , (y-*)U , (y-/S)V _ ft •7/2 "T" „. T 7. U > where dt dt u v ^(z-c)U , O-y)V_ 0j U V «= V {x-ay + (y-bf + (z-c)\ v= *J(.v- a y+(y-py + (z -yf, and putting also/(= V(«— a) 2 + (6-/3) 2 + (c— y) 2 ) the distance of the centres, U V and then u 2 =f.v, v 2 =f 2 y, -=X, - =Y {x,y are of course not to be con- founded with the coordinates originally so represented), Lagrange obtains the equations , d\v _ (x+y~ 1)Y ,. i -^+Xx+ y - ^— *- +f(Xdx+Ydy)=0, \ 1 jk+Yy + K - ^-J-+f { & dx+Y dy)=0, which he represents by , d 2 cc „ i^+M=0, 198 beport— 1862. and he then inquires as to the conditions of integrability of these equations, for which purpose he assumes that the equations multiplied by mdx-\-ndy and ficlv + vdy respectively and added, give an integrable equation. 52. A case satisfying the required conditions is found to be X=2a+-^,Y=2 a - xsjx ys/y or, what is the same thing, TJ=2au+C, Y=2av + *£ ; vr v Bf 3 vf 3 that is, besides the forces "L., £L. ( w hich vary as (dist.)- 2 , there are the forces 2au, 2av, varying directly as the distance, and of the same amount at equal distances ; or, what is the same thing, there is, besides the forces varying as (dist.)- 3 , a force varying directly as the distance, tending to a third centre midway between the other two, a case which is specially considered in the memoir ; it is found that the functions in r, s under the radicals (instead of rising only to the order 4) rise in this case to the order 6. 53. Among other cases are found the following, viz. :— TT 7 ^ ■ 5 *- . 1°. u = a,u+-pii +-pU, 7\ , 5\ , 2°. V=au+j 2 u 3 , where B=e, or else ae=/33=2/3e. In regard to the subject of tbis second memoir of Lagrange, see post, Mis- cellaneous Problems, Liouville's Memoirs, Nos. 100 to 105. 54. In the ' Mecanique Analytique ' (1st ed. 1788, and 2nd cd. t. ii. 1813), Lagrange in effect reproduces his solution for the above-mentioned law of a B force (say U= -^ + 2yu, Y=—i + 2yv)*. There are even in the third edition a few trifling errors of work to be corrected. The remarks above referred to, as made by Lagrange in his first memoir, are also reproduced (see anU, Nos. 49 and 50). 55. Legendre, "Exercices de Calcullntegral," t. ii.(1817), and "Thcorie des Fonctions EUiptiques," t. i. (1825), uses p 2 and q 2 in the place of Euler's p, q ; the forces are assumed to vary as (dist.) -2 , and in consequence of the change Euler's cubic radicals are replaced by quartic radicals involving only even powers of p and q respectively ; that is, the radicals are in a form adapted for the transformation to elliptic integrals ; in certain cases, however, it becomes necessary to attribute to Legendre's variables p and q imaginary values. The various cases of the motion are elaborately discussed by means of the elliptic integrals ; in particular Legendre notices certain cases in which the * In the ' Mecanique Analytique,' Lagrange's letters are k, q for the distances r-\-q=s, r—q=u: the change in the present Eeport was occasioned by the retention of p, q or Euler's variables. ON THE SPECIAL PROBLEMS OF DYNAMICS. 199 motion is oscillatory, and which, as he remarks, seem to furnish the first instance of the description by a free particle of only a finite portion of the curve which is analytically the orbit of the particle ; there is, however, nothing surprising in this kind of motion, although its existence might easily not have been anticipated. 56. § 26 of Jacobi's memoir " Theoria Novi Multiplicatoris &c." (1845) is entitled " Motus puncti versus duo centra secundum legem Neutonianum attracti." The equations for the motion in space are by a general theorem given in the memoir " De Motu puncti singidaris " (1842), reduced to the case of motion in a plane : viz. if x, y are the coordinates, the centre point of the axis being the origin, and y being at right angles to the axis, and if the distance 72 of the centres is 2a ; then the only difference is that to the expression for — ^ there is added a term — , which arises from the rotation about the axis. Two integrals are obtained, one the integral of Vis Viva, and the other of them an integral similar to one of those of Euler's or Lagrange's. And then x', y' being the differential coefficients of x, y with regard to the time, the remain- ing equation may be taken to be y'dx — x'dy—0, where x', y' are to be expressed as functions of x, y by means of the two given integrals. This being so, the principle of the Ultimate Multiplier * furnishes a multiplier of this differential equation, and the integral is found to' be y'dx — x'dy xy (x't-y^ + ^-af+y^x'y' = € > the quantity under the integral sign being a complete differential. To verify a, posteriori that this is so, Jacobi introduces the auxiliary quantities X', X" defined as the roots of the equation X 2 + X(x 2 +y 2 — a 2 )— « 2 ?/ 2 =0, which in fact, if as before u, v are the distances from the centres, leads to u+v=2»Ja 2 — X', u— i/=2Va 2 - \", so that X', \" are functions of u+v, u— v respectively; and the formulae, as ultimately expressed in terms of X', X", are substantially of the same form with those of Euler and Lagrange. 57. The investigations contained in Liouville's three memoirs " Sur quel- ques cas particuliers &c." (1846), find their chief application in the problem of two centres, and by leading in the most direct and natural manner to the general law of force for which the integration is possible, they not only give some important extension of the problem, but they in fact exhibit the pro- blem itself and the preceding solutions of it in their true light. But as they do not relate to this problem exclusively, it will be convenient to consider them separately under the head Miscellaneous Problems. 58. In Serret's ' These sur le Mouvement &c.' (1848), the problem is very elegantly worked out according to the principles of Liouville's memoirs as follows : viz. assuming that the expression of the distance between two con- secutive positions of the body is «V = X(mdfi 2 + ndv 2 ) + X"dy 2 , where m, n are functions of /z, v respectively, and if the forces can be repre- sented by means of a force-function U, then the motion can be determined, * Explained in Jacobi's memoir "Theoria Novi Multiplicatoris &c," Crelle, tt. xxvii. xxviii. xxix. 1844-45. £ 200 report — 1862. X" provided only X, XU, — are of the forms X \=<p/ji—<bi', where the functional symbols <j>, <P, &c. denote any arbitrary functions what- ever. 59. It is then assumed that //, v are the parameters of the confocal ellipses and hyperbolas situate in the moveable plane through the axis, viz. that wo have a* y 2 .2 ¥ i=l| V (the origin is midway between the two centres, 26 being their distance ; |yu, \v are in fact equal to the sum and difference u+v, u—v of the two centres respectively) ; and that the position of the moveable plane is deter- mined by means of y, the inclination to a fixed plane through the axis, or say, as before, its azimuth. In fact, with these values of the coordinates, tho expression of ds 2 is v* * '{fS—b^b*— v 2 r v r which is of the required form. And moreover if the forces to the two centres vary as (dist.)- 2 , and there is besides a force to the middle point varying a3 the distance, then V=JL-+jL+K(,c + S-b% whence (observing that X=/i 2 — r 2 ) XU is of the required form. The equa- tions obtained by substituting for U the above value give the ordinary solution of the problem. 60. Liouville's note to the last-mentioned memoir (1848) contains the demonstration of a theorem obtained by a different process in his second memoir, but which is in the present note, starting from Serret's formulae, demonstrated by the more simple method of the first memoir, viz., it is shown that the motion can be obtained if the two centres, instead of being fixed, revolve about the point midway between them in a circle in such manner that the diameter through the two centres always passes through the projection of the body on the plane of the circle. It will be observed that the circular motion of the two centres is neither a uniform nor a given motion, but that they are, as it were, carried along with the moving body. 61. In Desboves's memoir " Sur le Mouvement d'un point materiel &c." (1848), the author developes the solution of the foregoing problem of moving centres, chiefly by the aid of the method employed in Liouville's second memoir. And he shows also that the methods of Euler and Lagrange for the case of two fixed centres apply with modification to the more complicated problem of the moving centres. 62. The problem of two centres is considered in Bertrand's " Memoire 6ur les equations differentielles &c." (1852), by means of Jacobi's form of the ON THE SPECIAL PROBLEMS OF DYNAMICS. 201 equations of motion, viz., the problem is reduced to a plane one by means of the addition of a force OC— (ante, No. 56). y 63. Cayley's " Note on Lagrange's Solution &c." (1857) is merely a repro- duction of the investigation in the ' Mecanique Analytique ;' the object was partly to correct some slight errors of work, and partly to show what were the combinations of the differential equations, which give at once the integrals of the problem. 64. In § II. of Bertrand's " Memoire sur quelques unes des formes &c." (1857), the following question is considered, viz., assuming that the dynamical equations d 2 x_dJJ d 2 y (W W~dx' de = dy~' have an integral of the form a = P.v' 2 + Qx'y' + By' 2 + St/' + IV + K (where a is the arbitrary constant, and P, Q . . . K are functions of x and y), it is required to find the form of the force-function t T . It is found that U must satisfy a certain partial differential equation of the second order, the general solution of which is not known ; but taking U to be a function of the distance from any fixed point (or rather the sum of any number of such functions), it is shown that the only case in which the differential equations for the motion of a point attracted to a fixed centre of forces have an inte- gral of the form in question is the above-mentioned one of two centres, each attracting according to the inverse square of the distance, and a third centre midway between them, attracting as the distance. The Spherical Pendulum, Article Nos. 65 to 73. 65. The problem is obviously the same as that of a heavy particle on the surface of a sphere. I have not ascertained whether the problem was considered by Euler. Lagrange refers to a solution by Clairaut, Mem. de l'Acad. 1735. The question was considered by Lagrange, Mec. Anal. 1st edit. p. 283. The angles which determine the position are i// the inclination of the string to the horizon, <f> the inclination of the vertical plane through the string to a fixed vertical plane, or say the azimuth. And then forming the equations of motion, two integrals are at once obtained ; these are the integrals of Vis Viva, and an integral of areas. And these give equations of the form <?r=funct. (\P) dxp, cty=funet. (\l)d\j, ; so that t, <p are each of them given by a quadrature in terms of \p, which is the point to which the solution is carried. It is noticed that ^ may have a constant value, which is the case of the conical pendulum. 66. In the second edition, t. xi. p. 197 (1815), the solution is reproduced; only, what is obviously more convenient, the angles are taken to be \p, the inclination to the vertical, <p, the azimuth. It is remarked that ^ will always lie between a greatest value a and a least value ft, and the integrals are transformed by introducing therein instead of i/> the angle a, which is such that cos \L = cos a, sin 2 a + cos ft cos 2 <r, 202 report— 1862. by which substitution they assume a more elegant form, involving only the radical V 1+Jc'- (cos ft— cos a) cos 2a, where Jc is a constant depending on cos a, cos ft ; and the integration is effected approximately in the case where cos/3 — cos a is small. M. Bravais has noticed, however, that by reason of some errors in the working out, Lagrange has arrived at an incorrect value for the angle <i>, which is the apsidal angle, or difference of the azimuths for the inclinations a and ft : see the 3rd edition (1855), Note VII., where M. Bravais resumes the calculation, and he arrives at the value <l>=^(l + §a/3), a and ft being small. Lagrange considers also the case where the motion takes place in a resist- ing medium, the resistance varying as velocity squared. 67. A similar solution to Lagrange's, not carried quite so far, is given in Poisson's ' Mecanique,' t. i. pp. 385 et seq. (2nd ed. 1833). A short paper by Puiseux, " Note sur le Mouvement d'un point materiel sur une sphere " (1842), shows merely that the angle <J> is > ^. 68. The idterior development of the solution consists in the effectuation of the integrations by the elliptic and Jacobian functions. It is proper to re- mark that the dynamical problem the solution whereof by such functions was first fairly worked out, is the more difficult one of the rotation of a solid body, as solved by Jacobi (1839), in completion of Rueb's solution (1834), 2>ost, Nos. 186 and 197. 69. In relation to the present problem we have Gudermann's memoir " De pendulis sphajricis &c." (1849), who, however, does not arrive at the actual expressions of the coordinates in terms of the time ; and the perusal of the memoir is rendered difficult by the author's peculiar notations for the elliptic functions*. 70. It would appear that a solution involving the Jacobian functions was obtained by Durege, in a memoir completed in 1849, but which is still un- published ; see § XX. of his ' Theorie der elliptischen Functionen' (1861), where the memoir is in part reproduced. It is referred to by Bichclot in the Note presently mentioned. 71. We have next Tissot's ' These de Mecanique,' 1852, where the ex- pressions for the variables in terms of the time are completely obtained by means of the Jacobian functions H, G, and which appears to be the earliest published one containing a complete solution and discussion of the problem. 72. Richelot, in the Note " Bemerkungen zur Theorie des Raumpendels " (1853), gives also, but without demonstration, the final expressions for the coordinates in terms of the time. Donkin's memoir " On a Class of Differential Equations &c." (1855) con- tains (No. 59) an application to the case of the spherical pendulum. 73. The first part of the memoir by Dumas, " Leber die Bewegung des Baumpendels," &c. (1855), comprises a very elegant solution of the problem of the spherical pendulum based upon Jacobi's theorem of the Principal Func- tion (1837), and which is completely developed by the elliptic and Jacobian functions. The latter part of the memoir relates to the effect of the rotation of the Earth ; and we thus arrive at the next division of the general subject. * The mere use of sn., en., da. as an abbreviation of the somewhat cumbrous sinam., cosam., Aani. of the ' Fundaments Nova ' is decidedly convenient. ON THE SPECIAL PROBLEMS OF DYNAMICS. 203 Motion as affected by the Eolation of the Earth, and Relative Motion hi general. Article Nos. 74 to 85. 74. Laplace (Me'c. Celeste, Book X. c. 5) investigates the equations for the motion of a terrestrial body, taking account of the rotation of the Earth (and also of the resistance of the air), and he applies them to the determination of the deviations of falling bodies, &c. He does not, however, apply them to the case of the pendulum. 75. We have also the memoir of Gauss, " Fundamental-gleichungen, tfcc." (1804) : the equations ultimately obtained are similar to those of Poisson. I have not had the opportunity of consulting this memoir. 76. Poisson, in the "Hemoire sur le mouvement des Projectiles &c." (1838), also obtains the general equations of motion, viz. (omitting terms involving n 2 ), these may be taken to be d*® «r r> Afy • n dz \ w= x +H^ sm/3+ ^ C0S/ 7' d 2 V „ ~ dx . _ -£= Y + 2n dt^e, d~z „ „ dee n de=v+ z + 2n dt coa(i (see p. 20), where the axes of x, y, z are fixed on the Earth and moveable with it : viz., z is in the direction of gravity ; x, y in the directions perpendicular to gravity, viz., y in the piano of the meridian northwards, x westwards ; g is the actual force of gravity as affected by the resolved part of the centrifugal force ; ft is the latitude. There are some niceties of definition which are carefully given by Poisson, but which need not be noticed here. 77. Poisson applies his formulas incidentally to the motion of a pendulum, which he considers as vibrating in a plane ; and after showing that the time of oscillation is not sensibly affected, he remarks that upon calculating the force perpendicular to the plane of oscillation, arising from the rotation of the Earth, it is found to be too small sensibly to displace the plane of oscillation or to have any appreciable influence on the motion — a conclusion which, as is well known, is erroneous. He considers also the motion of falling bodies, but the memoir relates principally to the theory of projectiles. 78. That the motion of the spherical pendulum is sensibly affected by the rotation of the Earth is the well-known discovery of Foucault ; it appears by his paper, " Demonstration Physique &c," Comptes Rendus, t. xxxii. 1851, that he was led to it by considering the case of a pendulum oscillating at the pole ; the plane of oscillation, if actually fixed in space, will by the rotation of the Earth appear to rotate with the same velocity in the contrary direction • and he remarks that although the case of a different latitude is more compli- cated, yet the result of an apparent rotation of the plane of oscillation, dimi- nishing to zero at the equator, may be obtained either from analytical or from mechanical and geometrical considerations. Some other Notes by Eoucault on the subject are given, ' Comptes Rendus,' t. xxxv. (1853). 79. An analytical demonstration of the theorem was given by Binet 'Comptes Rendus,' t. xxxii. (1851), and by Baehr (1853). Various short papers on the subject will be found in the ' Philosophical Magazine,' and elsewhere. 80. In regard to the above-mentioned problem of falling bodies, we have a Noto by W. S., Camb. and Dub. M. Journ. t. iii. (1848), containing some errors 204 report— 1862. ■which are rectified in a subsequent paper, " Remarks on the Deviation of Palling Bodies," &c. t. iv. (1849), by Dr. Hart and Professor W. Thomson. 81. The theory of relative motion is considered in a very general manner in M. Quet's memoir, " Des Mouvements relatifs en general &c." (1853). Sup- pose that x, y, z are the coordinates of a particle in relation to a set of move- able axes ; let £' , rj , £' be the coordinates of the moveable origin in reference to a fixed set of axes, and treating the accelerations — £-, — '-, — ~ as if they at' at at- were coordinates, let these, when resolved along the moveable axes, give u', v, w : suppose, moreover, that p, q, r denote the angular velocities of the system of the moveable axes (or axes of x, y, z) round the axes of x, y, and z respectively ; u, v', w'. p, q, r are considered as given functions of the time, and then, if _^ +2 (,.|-_ i ^ + .*_,<| +1 . (4 .-_,. i/) _ J>(i); ,_ s , )+ „., v = cli d 2 . ^ 2 (^-^) + ^fS+^< ra? -^>-2^-^)+ w '' it is shown that the equations of motion are to be obtained from the equation Sm[(«— X)&r+(«— Y)2y+(w— Z)&]=0, where las, hj, h are the virtual velocities of the particle m in the directions of the moveable axes. This equation is in fact obtained as a transformation of the equation K(*- x ) s+ @- T ) 8 ' + (£- z )">°- which belongs to a set of fixed axes of £ , >/, £. 82. The equations for the motion of a free particle are of course «=X, v=Y, w=Z. In the case where the moveable axes are fixed on the Earth, and moveable with it (the diurnal motion being alone attended to), these lead to equations for the motion of a particle in reference to the Earth, similar to those obtained by Gauss and Poisson. The formulae are applied to the case of the spherical pendulum, which is developed with some care ; and Foucault's theorem of the rotation of the plane of oscillation very readily presents itself. The general formulae are applied to the relative motion of a solid body, and in particular to the question of the gyroscope ; the memoir contains other in- teresting results. 83. The principal memoirs on the motion of the spherical pendulum, as affected by the rotation of the Earth, are those of Hansen, " Theorie der Pen- delbewegung &c." (1853), which contains an elaborate investigation of all the physical circumstances (resistance of the air, torsion of the string, &c.) which can affect the actual morion, and the before-mentioned memoir by Dumas, " Ueber der Bewegung des Eamnpendels &c." (1855). The investigation is conducted by means of the variation of the constants ; the integrals for the undisturbed problem were, as already noticed, obtained by means of Jacobi's Principal Function, that is, in a form which leads at once to the expressions for the variation of the constants ; and the investigation appears to be carried out in a most elaborate and complete manner. 84. In concluding this part of the subject I refer to Mr. "Worms's work, 'The Botation of the Earth' (1862), where the last-mentioned questions ON THE SPECIAL PROBLEMS OF DYNAMICS. 205 (falling bodies, the pendulum, and the gyroscope) are, in reference to the proofs they afford of the rotation of the Earth, considered as well in an experi- mental as in a mathematical point of view. The second part of the volume contains the theory (after Laplace and Gauss) of falling bodies, that of the pendulum (after Hansen), and that of the gyroscope (after Yvon Villarceau) ; and the whole appears to be a complete and satisfactory resume of the experi- mental and mathematical theories to which it relates. 85. We have also Cohen " On the Differential Coefficients and Determinants of Lines &c." (1S62), where the equations for relative motion are obtained in a very elegant manner. The fundamental notion of the memoir may be con- sidered to be the dealing directly with lines, velocities, &c, which are variable in direction as well as in magnitude, instead of referring them, as in the ordi- nary analytical method, to axes fixed in space. The memoir is a highly in- teresting and valuable one, and the results are brought out with great facility ; but I cannot but think that the great care required to apply the method cor- rectly is an objection to it, if used otherwise than by way of interpretation of previously obtained results, and that the ordinary method is preferable. I may remark that the theory of relative motion connects itself with the lunar and planetary theories as regards the reference of the plane of the orbit to the variable ecliptic, and as regards the variations of the position of the orbit; but this is a subject which I have abstained from entering upon. Miscellaneous Problems. Article Nos. 86 to 111 (several subheadings). Motion of a single particle. 86. Jacobi, in the memoir "De Motu puncti singularis " (1842), notices (§ 5) the case of a body acted on by a central force which is any homogeneous function of the degree — 2 of the coordinates ; or representing these by r cos <p, r sin 0, then the force is =— , where is any function of the angle <j>. In fact, after integrating by a process different from the ordinary one the case of a central force CX—., he remarks that the method in fact applies to the more r general law of force just mentioned. 87. Jacobi, in the memoir " Theoria Novi Multiplicatoris &c." (1845), con- siders (§ 25) the case of a body acted on by a central force P a function of the distance, and besides by forces X and Y, which are homogeneous functions of the degree — 3 of the coordinates (x, y) ; viz. the equations of motion are in this case d 2 x ¥x W~~T +Xf d?~~T + ' and there is an integral Uxy'-x'yf— fv\xY-~yX)d^=const. >y x (the function under the integral sign is obviously a function of the degree in (x, y), that is, it is a function of V. ). If X, Y are the derived functions of a force-function TJ of the degree —2 in (x, y), then there is, besides, the in- tegral of Vis Viva, and thence a third integral is obtained by means of the 206 report — 1862. theorem of the Ultimate Multiplier. It may be noticed that in the last-men- tioned case the force-function is of the form -, so that if we represent also r the central force by means of a force-function R (= function of r), then the entire force-function is B+*. The case is a very interesting one; it in- r eludes that considered § iv. of Bertrand's " Memoire sur les equations differen- tielles de la Mecanique" (1852), where the force-function is of the form =-. Motion of three mutually attracting bodies in a right line. 88. The problem is considered by Euler in the memoir "De Motu rcctilineo &c." (1765), the forces being as the inverse square of the distance ; and a solution is obtained for an interesting particular case. Let A, B, C be the masses, and suppose that at the commencement of the motion the distances CB, BA are in the ratio a : 1, and that the velocities (assumed to be in the same sense) are proportional to the distances from a fixed point. Then, if a. be the real root (there is only one) of the equation of the fifth order C(l + 3a + 3a 2 )=Aa 3 (a 2 + 3a-|-3)+B(« + l 2 )-(a 3 -l), the distances CB, BA will always continue in the ratio a : 1. It may be added that the distances CB, BA each of them vary as r 2 — a-, where a is a constant, and r is, according to the initial circumstances, a function of t de- fined by one or the other of the two equations t=n 3 r t/r^tf-n'cf log r+«'-' J -«\ t=n 3 r*^a 2 — r 2 -|-n 3 « 2 sin ' -. a 89. The bodies are considered as restricted to move in a given line ; but it is clear that if the bodies, considered as free points in space, are initially in a line, and the initial velocities are also in this line, then the bodies will always continue in this lino, which will be a fixed line in space. But if the distances and velocities are as above, except only that the velocities, instead of being along the line, are parallel to each other in any direction whatever, then the bodies will always continue in a line, which is in this case a moveable line in space (see post, No. 93). 90. Euler resumes the problem in the memoir of 177G in the ' Nova Acta Petrop.' The distances AB, BC being p and q, then d 2 p_ A+B C C_ dt 2 ~ f + q 2 (p + qf ( El-—- A B + C . df~p 2 (p+q) 2 q 2 and in particular he considers the before-mentioned case of a solution of the form p=nq; and also the partievdar problem where one of the masses vanishes, C = ; in this case, introducing (instead of p, q) the new variables u, s, where q=up, dq=sdp (a transformation suggested by the homogeneity of the equations), and making, moreover, the particular supposition that the integral of the first equation is /^ ) =_ L_+_J (viz. making the constant ON THE SPECIAL PROBLEMS OP DYNAMICS. 207 of integration to vanish), he obtains between s and u the equation of the first order 2(A + B)*( S -,.)=(A + B) S+ A- (T A ? _|„ which, however, he is not able to integrate. 91. Jacobi has given in the memoir " Theoria Novi Multiplicatoris " (1845) (§28, entitled "De Problemate trium corporum in eadem recta motorum. Sub- stitute Euleriana. Theoremata de viribus homogeneis ") a very symmetrical and elegant investigation of the same problem. The centre of gravity being assumed to be at rest, the coordinates x, x v x 2 of the three bodies are in the first instance expressed as linear functions of the two variables u, v (being, as Jacobi remarks, the transformation employed in his memoir " Sur 1' elimination des Nceuds" (1843), post, No. 114), J and ^ come out respectively equal to homogeneous functions of the degree —2 of these variables u and v, and the integral of Vis Viva exists. The subsequent transformation consists in the introduction of the variables r, <p, s, rj, where u=r cos <p, v=r sin <j>, s= Vr — , »;= Vr 3 -^ ; this gives a system of equations independent of r ; viz., df : ds : dt}=T) : §s 2 +j/ 2 — $ : —i S t} + <b', where $ is a given function of <f>, and $' is the derived function. If these equations were integrated, the equation of Vis Viva gives at once r=. j (*— K^ + j? 2 )); and finally the time t would be given by a quadrature. The system of three equations has the multiplier M— ,bflncn if one integral were known the other would be at once furnished by the general theory. There is a simplification in the form of the solution if h (the constant of Vis Viva) = 0. It is remarked that the method is equally appli- cable when the force varies as any power of the distance ; and moreover that when the force varies as (dist.) -3 , then the solution. depends upon one qua- drature only. 92. The concluding part of the section relates to the very general problem of a system of n particles acted on by any forces homogeneous functions of the coordinates (this includes the case of n particles mutually attracting each other according to a power of the distance), and this more general investiga- tion illustrates the method employed in regard to the three bodies in a line. It may be remarked that in the general theorem for the n particles " sint vires &c.," the constant of Vis Viva is supposed to vanish. Particular cases of the motion of three bodies. 93. In the case of three bodies attracting each other according to the in- verse square of the distance, the bodies may move in such manner as to be constantly in a line (a moveable line in space) ; this appears by the memoir Euler, " Considerations generales, &c." (1764), in which memoir, however (which it will be observed precedes the memoir " De Motu rectilineo &c " (1765), referred to No. 88), Euler assumes that the mass of one of the bodies is so small as not to affect the relative motion of the other two. Calling the bodies the Sun, Earth, and Moon, and taking the masses to be 1, m, 0, then a result obtained is, that in order that the Moon may bo perpetually 208 report— 1862. in conjunction, its distance must be to that of the Sun as a : 1, where m(l— a) 2 =3a 3 — 3a 4 + a% or a= 3 /I^ nearly. It appears, however {antt, No. 88), that the foregoing restriction as to the masses is unnecessary, and, as will be mentioned, the jjroblem has since been treated without such restriction. Euler investigates the motion in the case where the initial circumstances are nearly but not exactly as originally supposed ; this assumes, however, that the motion is stable — i. e. that the bodies will continue to move nearly, but not exactly as originally supposed, which is at variance with the conclusions of Liouville's memoir, post, No. 95. I have not examined the cause of this discrepancy. 94. In the 'Mecanique Celeste' (1799), Book x. c. 6, Laplace considers two cases where the motion can be exactly determined. 1°. Force varies as any function of the distance. It is shown that the motion may be such that the bodies form always an equilateral triangle of variable magnitude — the motion of each body about the centre of gravity being the same as if that point were a centre of force attracting the body according to a similar law. 2°. Force oc(dist.) n . The motion may be such that the three bodies are always in a right line (moveable in space), the relative distances being in fixed ratios to each other. In particular, if force OC (dist.)~ 2 , then m, m! , m" being the masses, the quantity z which determines the ratio of the distances m"m' , trim is given by 0=m: 2 [(l+r) 3 -l]-Ht'(l + ~) 2 (l-~ 3 )-m"[(l + r) r, -^]=0, which is, in fact, the formula in Euler's memoir " De Motu rectilineo &c." 95. Liouville's memoir " Sur un cas particulier &c." (1842) has for its object to show that if the initial circumstances are not precisely as supposed in the second of the two cases considered by Laplace, or, what is the same thing, in Euler's memoir " Considerations gencrales &c," then the motion is unstable ; the instability manifests itself in the usual manner, viz. the expres- sions for the deviations from the normal positions are found to contain real exponentials which increase indefinitely with the time. 9G. It may be proper to refer here to Jacobi's theorem, ' Comptes Rendus,' t. iii. p. 61 (1836), quoted in the foot-note p. 15 of my Report of 1857, which relates to the motion of a point without mass revolving round the Sun, and disturbed by a planet moving in a circular orbit, and properly belongs (as I have there remarked) to the problem of two centres, one of them moveable and the other revolving round it in a circle with uniform velocity. The theorem (given without demonstration by Jacobi) is proved by Lioiiville in his last-mentioned memoir, and he remarks that the theorem follows very simply as a corollary of the theorem by Coriolis, " On the Principle of Vis Viva in Relative Motions," Journ. de l'Ecole Polyt. t. xiii. p. 268 (1832). There is, however, no difficulty in proving the theorem ; another proof is given, Cayley, " Note on a Theorem of Jacobi's &c." (1862). Motion in a resisting medium. 97. I do not consider the various integrable cases of the motion of a par- ticle in a resisting medium, the resistance varying with the velocity according to some assumed law, the particle being either not acted on by any force, or acted upon by gravity only. Some interesting cases are considered in Jacobi's memoir "DeMotu puncti singularis" (1842), §§ 6 and 7 (see post, No. 108). ON THE SPECIAL PROBLEMS OF DYNAMICS. 209 98. In the case of a central force varying as (disk) -2 , the effect of a resist- ing medium (E QC v 2 ) is considered in reference to the lunar theory, in the ' Mecanique Celeste,' Book VII. c. 6. Formula? for the variations of the elliptic elements are given in the ' Mecanique Analytique,' t. ii. (2nd edition). Biit the variations of the elliptic elements are fully worked out by means of elliptic and Jacobian functions in Sohncke's valuable memoir " Motus Corporum &c." (1833). 99. The effect of the resistance of the air on a pendulum has been elaborately considered by Poisson, Bessel, Stokes, and others ; as the dimensions of the ball are attended to, the problem is in fact a hydrodynamical one. The effect on the spherical pendulum is considered in Hansen's memoir " Theorie der Pendelbewegung &c." (1853). The effect on the motion of a projectile is considered in Poisson's memoirs " Sur le Mouvement des Projectiles &c." (1838). Liouville's memoirs " Sur quelques Cas particidiers ou les equations du mouvement d'un point materiel peuvent s'integrer" (1846-49). 100. In the first memoir (§ 1) the author considers a point moving in a plane or on a given surface, where the principle of Vis Viva holds good (or say where there is a force-function U). The coordinates of the point, and the function U, may be expressed in terms of two variables a, /3, and it is assumed that these are such that ds*=\(da 2 +dl3 2 ), where X is a function of a and /3. That is, we have T=|X(a' 2 +/3' 2 ) ; and the equations of motion are d.Xa' _ld\^ l2 , om , dTJ ~dr~2^ a +ii ) + d*' d.Xfl'ldk , 2 dJJ ~dr~2dfi ia +l * )+ dp- One integral of these is X(a' 2 + / 3' 2 )=2U + C ; and by means of it the equations take the form d.\a,'_ 1 dX, 9TT p . dTJ ~dt — 2Xc7^ (2U+C)+ ^' -dJ—^djs^+V+dp- These equations, it is easy to show, may be integrated if (2U + C)X=/a-F/3, and they then in fact give XV 2 =/a— A, X 2 /3 /2 =A-F/3, where A is an arbitrary constant. And we then have da. dfi >/fa— A"~VA-F/3' which gives the path, and the expression for the time is easily obtained by means of a quadrature. It is not more general, but it is frequently convenient to employ instead of a, (3, two variables p and v, such that ds 2 =\(mdfi 2 +ndv 2 ), 1862. p 210 REPORT — 1862. where mis a function of ji only and n of v only, while \ contains fi and v. The geometrical signification of the equation ds 2 =k(da 2 +dfi 2 ), or of the last- mentioned equivalent form, is that the curves a or \= const., /3 or fx = const., intersect at right angles. The foregoing differential equation of the path, writing //i, Fv in the place of fa, F/3 respectively, may be expressed in the form f/j. cos 2 i + Fv sin 2 i = A, where i, 90°— i are the inclinations of the path at the point (A, p) to the two orthotomic curves through this point. 101. The before-mentioned equation (2U + C)\=/a-F/3 may be satisfied independently of C, or else only for a particular value of C. In the former case the law of force is much more restricted, but on the other hand there is no restriction as regards the initial circumstances of the motion; it is the more important one, and is alone attended to in the sequel of the memoir. In the case in question (changing the functional symbols) we must have \=(j>cc— B7/3, \U=/a— F/3; so that the functions denoted above by fa, F/3 now are 2fa + C<pa, 2F/3 + Cnr/3 ; the equation of the trajectory is da d(3 */2fa+C<j>a-A~ VA-2F/3+CV/3' and for the time the formula is , <j>ada ct/3 d(i ~ ^2fa + C<pa^A~ VA— 2F/3 + C^/3' It is noticed also that taking B, e to denote two new arbitrary constants, and writing ■ 9 =pa V 2fa + Cfa- A+jd/3 V A-2F/3 + Cw/3, the equation of the trajectory and the expression for the time assume the forms ( ^ = B, t = 2 ( l° + e, . dA. «C as is known & priori by a theorem of Jacobi's. If the forces vanish, the path is a geodesic line ; and denoting by a the ratio of the constants A, C, we have da dfi . V^a — a V a—wft and moreover ds=da^(pa—a+dj3 , i/a—<pl3, which are geometrical properties relating to the geodesic line. 102. Passing to the applications : in the first place, if a, (3 are rectangular coordinates of a point in piano, then writing instead of them x, y, we have ds 2 =dar + dy 2 , which is of the required form ; but the result obtained is the self-evident one, that the equations may be integrated by quadratures when TJ is of the form funct. x — funct. y. But taking instead the elliptic coordinates ft, v of a point in piano, — viz., as ON THE SPECIAL PROBLEMS OF DYNAMICS. 211 employed by the author, these are the semiaxes of the confocal ellipse and hyperbola represented by the equations — very interesting results are obtained. The equations give b 2 x 2 = H . 2 v 2 , by=(f-b 2 )(b 2 -v 2 ), and thence which is of the proper form, and the corresponding expression of U is so that the force -function having this value (//u, Fv being arbitrary functions of n and v respectively), the equations of motion may be integrated by qua- dratures. 103. In particular, if Fy=gv-g'p+Jc(r i -b 2 t > 2 ), then V=-9—+^-+]c( f M 2 +v 2 -b 2 ). H+v fi—v But fi + y, /u — v are the distances of the point from the two foci, and fS+v 2 — b\=x 2 +y 2 ) is the square of the distance from the centre, so that the expression for U is U^+^ + ZcR 2 ; r r and the case is that of forces to the foci varying inversely as the squares of the distances, and a force to the centre varying directly as the distance— the case considered by Lagrange in the problem of two centres. But this is merely one particular case of those given by the general formula. The cases g=0, g'=0, k=0 (no forces), and g=0, g' = (a force to the centre) lead to some interesting results ; it is noticed also that the expression for the force-function may be written TJ= — — -. — -> and that it may be thereby ascertained (without transforming to elliptic coordi- nates) whether a given value of the force-function is of the form considered in the theory. In § 3 the author considers the expression dx*-\- dy 2 =\(da 2 +dj3 2 ), \ being in the first instance any function whatever of a and /3 ; and he shows that the expressions of x, y are given by the equation 4* being any real function. If, however, it is besides assumed that X is of the required form=/a — F/3, then he shows that the system of elliptic coordi- nates is the only one for which the conditions are satisfied. §§ 4, 5, 6, and 7 relate to the motion of a point on a sphere, an ellipsoid, a surface of revolu- tion, and the skew helicoid respectively ; and the concluding § 8 contains only a brief reference to the author's second memoir. 104. Liouville's second and third memoirs may be more briefly noticed. In the second memoir the author starts from Jacobi's theorem of the V p2 212 report— 1862. function, viz., assuming that there is a force-function U independent of the time, then in order to integrate the equations of motion ( —= — iJlz= C - — , ° * \df dx' d? dy' — =_ V all that is required is to find a function 8 of x, y, z containing three €lt ClZ / arbitrary constants A, B, C (distinct from the constant attached to by mere addition) satisfying the differential equation eiMiK*)*= 2(u+ °" for then the required integrals of the equations of motion are dA- A 'dB- B >dC- t+t ' A', B', C being new arbitrary constants. Liouvifle introduces in place of x, y, z, the elhptic coordinates p, p, v, which are such that p>^ p>-b 2 p 2 -c 2 ' ^■l_ ?/" _ g2 _i .a ' ..a _i2 ^2 2 » fl fi — o c — p. =1, x 2 y 2 z 2 2 X^^l or, what is the same thing, y Vp 2 - -b 2 s/p 2 - -b°Wb 2 - -V' &Vc 2 - -<rVc 2 - -b 2 *V- - A r\/(r- -v 2 and he then finds that the resulting partial differential equation in p, p, y may be integrated provided that U is of the form n- fr'- y8 )/P+(P a -^)FM+(p a -">'' (p 2 -p 2 )(p>- v * ){ p>S) > f, F, tzr being any functional symbols whatever: viz., the expression for G is 2fp+A+B P 2 + 2Cp* -jV^ )(p 2 -c 2 ) . f 7 /2^ + A+B^ 2 +2C/ TV . y-^y-y) " In the case where TJ=0 we have a particle not acted on by any forces, and the path is of course a straight fine. The peculiar form in which these equa- tions are obtained leads to very interesting results in regard to the theory of Abelian integrals, and to that of the geodesic lines of an ellipsoid. The formulae require to be modified in certain cases, such as c=b or 6=0. The case 6=0 leads to the theory developed in the first memoir in relation to ON THE SPECIAL PROBLEMS OF DYNAMICS. 213 the problem of two centres. The case is indicated where 6=0, c=0, the ratio b : c remaining finite. The case is briefly considered of a particle moving on a given surface. 105. The third memoir purports to relate to a system of particles, but the Formulae are exhibited under a purely analytical point of view ; so much so, that the coordinates of the points (3 for each point) are considered as forming a single system of variables x } , x 2 , . . . x x . The partial differential equation is which is transformed by introducing therein the new variables p v p 2 . . . p t analogous to the elliptic coordinates of the second memoir. The memoir really belongs rather to the theory of the Abelian integrals (in regard to which it appears to be a very valuable one) than to dynamics. Memoirs by Jacobi, Bertrand, and Dentin, relating to various Special Problems. 106. I have inserted this heading for the sake of showing at a single view what are the special problems incidentally considered in the under-mentioned memoirs which are referred to in several places in the present Report. 107. Jacobi, " De Motu puncti singularis " (1842). — I call to mind that the memoir chiefly depends on the theorem of the Ultimate Multiplier (the theory in its generality being developed in the later memoir " Theoria Novi Multiplicatoris &c," 1844-45). § 4 is entitled " The motion of a point on the surface of revolution," which, the principle of the conservation of areas holding good, is reduced to the problem of the motion on the meridian curve, and thus depends upon quadratures only. § 5 is entitled " On the motion of a point about a fixed centre attracted according to a certain law more general than the Newtonian one" (ante, No. 85). § 6. " On the motion of a point on a given curve and in a resisting medium" (resistance =a+be e " 2 , or=a+6i/ 2 ); and§ 7. "On the Ballistic Curve," viz., the forces are gravity and a resistance = a + &v™. 108. In Jacobi's memoir " Theoria Novi Multiplicatoris &c." (1845), § 25 is entitled " On the motion of a point attracted towards a fixed centre " (see ante, No. 87) ; § 26. " On the motion of a point attracted towards two fixed centres according to the Newtonian law " (ante, No. 56) ; § 27. " On the rota- tion of a solid body about a fixed point" (post, No. 193); § 28. " On the problem of three bodies moving in a right line ; the Eulerian substitution ; theorems on homogeneous forces" (ante, No. 91)]; and§ 29, "The principle of the ultimate multiplier applied to a free system of material points moving in a resisting medium ; on the motion of a comet in a resisting medium about the sun." 109. And in Jacobi's memoir " Nova Methodus &c." (1862), besides § 64 and § 65, which are applications of the method to general dynamical theorems, we have § 66, containing a simultaneous solution of the problem of the motion of a point attracted to a fixed centre and of that of the rotation of a solid body (post, No. 206), and § 67, relating to the motion of a point attracted to a fixed centre according to the Newtonian law. 110. Bertrand's " Memoire sur les integrales differentielles de la Mecanique" (1852). — § III. relates to the motion of a point attracted to a fixed centre by a force varying as a function of the distance ; § IV. to the case where the forces arise from a force-function TJ = jbl - ) (or, what is the same thing, 214 report— 1862. =^\ (ante,T$o. 87); § V. to the problem of two centres (antt, No. 62), and § VI. r V to the problem of three bodies {post, No. 117). 111. Donkin's memoir " On a Class of Differential Equations &c." (1855). Part I. Nos. 27 to 30 relate to the problem of central forces (in space), No. 31 to the rotation of a solid body, and §111. to the same subject, viz. Nos. 40 and 41 to the general case, Nos. 42 to 44 to the particular case A=B; and Nos. 45 to 48 to the reduction thereto of the general case by treating the forces -which arise from the inequality of A and B as disturbing forces. Part II. Nos. 59 and 60 relate to the spherical pendulum ; Nos. 72 and 73 to " Transformation from fixed to moving axes of coordinates," say to Relative Motion ; and Nos. 84 to 96 to the problem of three bodies (post, No. 120). The Problem of Three Bodies, Article Nos. 112 to 123. 112. A system of differential equations, such as (n equations between «+l variables), may be termed a system of the nth order, or more simply a system of n equations. Let (u v u 2 . . . . u n+1 ) be any functions of the original variables (x\, x 2 , . . . . # n+1 ), the system may be transformed into the similar system du r du 2 du , j and if it happens that we have e. g. JJ l identically equal to zero, then the system becomes so that we have an integral t* x =c, and then in the remaining equations substituting this value, or treating u x as constant, the system is reduced to one of (m — 1) equations. Or again, if it happen that we have in the trans- formed system m equations (m<w), say du 1 _du 2 _du m+ , which are such that \J 1 , TJ 2 . . . TJ m+1 are functions of only the m-\-l variables Mj, u 2 . . .u m+v then the integration of the proposed system of n equations depends on the integration in the first instance of a system of m equations. It is to be observed that if the system of m equations can be integrated, then the completion of the integration of the original system depends on the integration of a system of n — m equations, and in this sense the original system of n equations may be said to be broken up into two systems of m equations and n — m equations respectively : but non constat that the system of m equations admits of integration ; and it is therefore more correct to say that, from the original system of the n equations, there has been separated off a system of m equations. 113. The bearing of the foregoing remarks on the problem of three bodies will presently appear. It will be seen that whereas the problem as it stood before Jacobi depends on a system of seven equations, it has been shown by him that there may be separated off from this a system of six equations. ON THE SPECIAL PROBLEMS OF DYNAMICS. 215 114. Jacobi's memoir "Sur l'elimination des Noeuds &c." (1843). — The problem of the motion of three mutually attracting bodies is in the first instance reduced to that of the motion of two fictitious bodies (which may be considered as mutually attracting bodies, attracted by a fixed centre of force)*. In fact, in the original problem the centre of gravity of the three bodies moves uniformly in a right line, and it may without any real loss of generality be taken to be at rest ; that is, if the ^-coordinates of the three bodies are £ lS £ 2 , £ 3 , then m,£ 1 -|-m.,£ 2 - r -m 3 £ 3 =0, or £ l? | 2 , £ 3 maybe taken to be linear functions of two quantities a?, and x 2 . And similarly for the ^-coordinates and the z-coordinates respectively. And (.r^ y v zj, (x 2 , y 2 , z 2 ) may be regarded as the coordinates of two bodies revolving about a fixed centre of force. Hence representing the differential coefficients in regard to the time by # x ', &c, and treating these as new variables, the equations of motion will assume the form do^^dy^ ^efe, = dx 2= dy ? ^dz^ < HI K *.' vl < _dx r ' _dy l ' _dz l ' _dx 2 ' _dy 2 ' _dz'_, . ~ X, ~ Y l ~ Z, _ X 2 - Y 2 ~ V where X 1? Y,, Z lt X 2 , Y 2 , Z 2 are forces capable of representation by means of a force-function U. This is a system of twelve equations ; but since X x , Y v Z v X 2 , Y„ Z 2 are independent of the time, we may omit the equation (=dt), and treat "the system as. one of eleven equations between the variables x v y v z x , x 2 , y 2 , z 2 , fljj', y t ', z/, x 2 , y.', z 2 ' : if this system were integrated, the deter- mination of the time would then depend on a quadrature only. But for the system of eleven equations we have four integrals, viz., the integral of Vis Viva and the three integrals of areas, and the system is thus reducible to one of (11 — 4=) seven equations. This preliminary transformation in Jacobi's memoir explains the remark that the problem, as it stood before him, depended on a system of seven equations. 115. Jacobi remarks that in the transformed problem the three integrals of areas show (1) that the intersection of the planes of the orbits of the two bodies lie in a fixed plane, the invariable plane of the system ; (2) that the inclinations of the planes of the two orbits to this fixed plane, and the para- meters of the two orbits considered as variable ellipses, are four elements any two of which rigorously determine the two others. And then choosing for variables the inclinations of the two orbits to the invariable plane, the two radius vectors, the angles which they form with the intersection of the planes of the two orbits, and lastly the angle between this intersection (being as already mentioned a hne in the invariable plane) with a fixed hne in the invariable plane, he finds that the last-mentioned angle entirely disappears from the system of differential equations, and is determined after their integration by a quadrature. In this new form of the differential equations there is no trace of the nodes. The differential equations which determine the relative motion of the three bodies are reduced to five equations of the first order and one of the second order. The equations in question are the equations I. to VI. given at the end of the memoir. It is to be remarked that the differential dt is not eliminated from these equations ; the last of . d 2 them is — (nr 2 + pj'*) =2U— 27t ; and if to reduce them to a system of equa- * This is the effect of Jacobi's reduction ; but the explicit statement of the theorem, and actual replacement of the problem of the three bodies by that of the two bodies attracted to a fixed centre, is due to Bertrand {post, No. 117). 216 report— 1862. tions of the first order we write —(^ir 2 +/x 1 r 1 2 )= 0, and therefore i--= 2 IT— 2h, Ctv (It the system may he presented in the form du du x di di 1 dr __ dr 1 dd,-,^ v = u; = t = i7 _ e""e;~0 c "~ ; ' which if we do, and then omit the equation (=cfr), we have a system of six equations between the seven quantities u, u v i, i 1} r, r v 6 ; when this is integrated, the equation (=dt) gives the time by a quadrature ; and finally, Jacobi's equation VII. / <to=tan u ——, ) gives by a quadrature the angle before \ sin i/ referred to as disappearing from the system of equations I. to VI. 116. But when Jacobi says, " Par suite on a fait cinq integrations. Les integrates connues n'etant qu'au nombre de quatre, on pourra done dire que Ton a fait une integration de plus dans le systeme du monde. Je dis dans le systeme du monde puisque la meme methode s'applique a, un nombre quelconque de corps," the language used is not, I think, quite accurate. It, in fact, appears from the memoir that it is only on the assumption of the integration of the system of six equations that, besides the integral of Vis Viva and the integrals of areas, the remaining two integrals are known ; in fact, after, but not before the system of the order six has been integrated, the time t and the angle CI are each of them given by a quadrature. • 117. Bertrand's " Memoire sur l'integration des equations differentielles de la Mecanique " (1852). — I have spoken of this memoir in No. 56 of my former Keport. The course of investigation is the inquiry as to the integrals, which, combined according to Poisson's theorem with the integral of Vis Viva or any other given integral, give rise to an illusory result. But as regards the appli- cation made to the problem of three bodies, it will be more convenient to state from a different point of view the conclusions arrived at : and I may mention that when the author says " Je parviens . . a reduire la question a l'integration de six equations tout du premier ordre, e'est-a-dire que j'effectue une integra- tion de plus que ne l'avait fait Jacobi," he seems to have overlooked that Jacobi's system of five equations of the first order and one of the second order really is, as above noticed, a system of the six equations with another equation which then gives the time by a quadrature, and that, at least as appears to me, he has not advanced the solution beyond the point to which it had been carried by Jacobi*. 118. Presenting Bertrand's results in the slightly different notation in which they are reproduced in Bour's memoir ( post, No. 122), then if (x, y, z), (x v y v z x ) are the coordinates of the two bodies (the problem actually con- sidered being, as by Jacobi, that of the motion of two bodies about a fixed centre of force), and representing the functions x 2 -\-y~-\-z 2 , x 2 +y 2 -\-z x 2 , m* {x 12 + y' 2 + z' 2 ), m? (gf + y^+ Zl "), m (xx + yy + zz'), m, (x^ 1 + yjjj + z^'), rn(x 1 x' + y lV ' + z x z"), m^xx^ + yy{ + zz^), (xx x + yy r + assj mrn^dte/ + y'y,' + z'z\) by m, u x , v, v v iv, w v r, r lf q, s respectively, then the last-mentioned quanti- ties are connected by a single geometrical relation, so that any one of them, say s, may be considered as a given function of the remaining nine. And the author in effect shows that the equations of motion give a system * These remarks were communicated by me to M. Bertram! — see my letter "Sur l'integration des equations differentielles de la Mecanique," Comptes Rendus (1863) — and, in the answer he kindly sent me, he agrees that they are correct. ON THE SPECIAL PROBLEMS OF DYNAMICS. 217 du du dv dv x div div l dr dr x dq , u = u" 1 l= v ~~v7 = w = w7 = r = r; ~ -Q = ( dt >> where IT, JJ V &c. axe functions of the quantities u, u v v, &c. Omitting from the system the equation (—dt), there are eight equations between nine quan- tities ; but there are two known integrals, viz., the integral of Vis Viva and the integral of principal moment (or sum of the squares of the integrals of areas) ; that is to say, the system is really a system of siv equations. 119. Painvin, "Recherche du dernier Multiplicateur &c." (1854). — The author investigates the ultimate multiplier for two systems of differential equations : — 1°. The system of the equations I. to VI. in Jacobi's memoir " Sur l'elimination des Nceuds &c." (antt, No. 114). "Writing in the equations C?v* fly* -j ==r', -j- } =r 1 ', and treating r , i\ as new variables, the system may be written in the form du du x di di x dr di\ dr' dr' u = D7 - r _ i7 _ R = r; = R = ^( =dt )> which, omitting the equation ( = dt), is a system of seven equations be- tween eight variables ; and it is for this form of the system that the value of M is determined, the result obtained being the simple and elegant one, ,, sin i sin i. m . „ ' M= =— ^= — *. lhe system of seven equations has an integral which is in fact the equation V. of the system in Jacobi's form, so that it is really a system of six equations (antt, No. 115). 2°. The system secondly discussed is Bertrand's system of nine equations (antt, No. 118). The multiplier M is obtained under four different forms, ^— /-r>2 *n = — r-^ = Ti7-r^b = — (I ^o not stop to explain the notation), VB — AC v a.a. l AZ + B mn r r " the last of them being referred to as a result announced by M. Bertrand in his course. But it is shown by M. Bour in the memoir next referred to (post, No. 122), that the multiplier for the system in question can be obtained in a very much more simple manner, almost without calculation. 120. In connexion with Jacobi's theory of the elimination of the Nodes, I may refer to the investigations " Application to the Problem of three Bodies " Nos. 84 to 96 of Donkin's memoir " On a Class of Differential Equations &c." Part II. The author remarks that his differential equations No. 93 an°ord an example of the so-called elimination of the Nodes, quite different however (in that they are merely transformations of the original differential equations of the problem without any integrations) from that effected by Jacobi. 121. It may be right to refer again in this place to the concluding part of § 28 of Jacobi's memoir " Nova Theoria Multiplicatoris " (ante, No. 92), as bearing on the problem of three bodies. 122. Bour's " Memoire sur le Probleme des Trois Corps " (1856). — The author remarks that Bertrand's system of equations have lost the remarkable form and the properties which characterize the ordinary equations for the solution of a dynamical problem. But by selecting eight new variables functions of Bertrand's variables, the system may be brought back to the standard Hamiltonian form dq i _dR d Pi _ dR dt dp- dt dqS or to the form adopted by M. Bour, of a partial differential equation 218 report— ] 862. and guiding himself by a theorem in relation to canonical integrals obtained in his memoir of 1855 (see No. 66 of my former Report), he finds by a somewhat intricate analysis the expressions of the eight new variables Pd Z>2> J?a> Pi> 1\> Iv ?3' If ^-^ e resu lts ultimately obtained are of a very remarkable and interesting form, viz. H=funct. {p v p 2 ,p 3 , p 4 , q x , q 2 , q 3 , ? 4 ) is equal to the value it would have for motion in a plane, plus a term admitting of a simple geometrical interpretation, and he thus arrives at the following theorem as a resume of the whole memoir, viz., " In order to integrate in the general case the problem of three bodies, it is sufficient to solve the case of motion iu a plane, and tben to take account of a disturbing function equal to the product of a constant depending on the areas by the sum of the moments of inertia of the bodies round a certain axis, divided by the square of the triangle formed by the three bodies." 123. It may be remarked that the only given integral of the system of eight equations is the integral of Vis Viva, H = const., and that using this equation to eliminate one of the variables, and omitting the equation (=dt), we have, as in the solutions of Jacobi and Bertrand, a system of six equations between seven variables. As the equations are in the standard dynamical form, no investigation is needed of the multiplier M, which is given by Jacobi's general theory, and consequently when any five integrals of the six equations are given, the remaining integral can be obtained by a quadrature. In the case of three bodies moving in a plane, the solution takes a very simple form, which is given in the concluding paragraph of the memoir. Transformation of Coordinates, Articles Nos. 124 to 141. 124. It may be convenient to remark at once that two sets of rectangular coordinates maybe related to each other properly or improperly, viz., the axes to which they belong (considered as drawn from the origin in the positive directions) may be either capable or else incapable of being brought into coincidence. The latter relation, although of equal generality with the former one, may for the most part be disregarded ; for by merely reversing the direc- tions of the one set of axes, the improper is converted into the proper relation. 125. In the memoir " Problema Algebraicum <fec." (1770) Euler proposes to himself the question " Invenire novem numeros ita in quadratum disponendos A, B, C D, E, F G, H,I ut satisfiat duodecem sequentibus conditionibus," &c, viz., substituting for A, B, C, &c. the ordinary letters a/3 + a'/3' + a"/3"=0, /3y+/3y+/3V=0, y a + y a = U, ax +/3/3' + yy' =0, a a |>/3 +yy =0, aa" +/3"/3+y"y=0. a, \i, «!, /3', «", /3", the twelve conditions are y ■ a 2 +a' 2 +a" 2 = l, /3 2 +/3' 2 +/3" 2 =1, y 2 +y' 2 +y" 2 = l, a? +py +y 2 =1, a' 2 +/3' 2 +y' 2 =l, a" 2 + /3" 2 + y" 2 =l, ON THE SPECIAL PROBLEMS OF DYNAMICS. 219 And he remarks that this is in fact the problem of the transformation of coor- dinates, viz., if we have X=ax +ftij + y z, Y=a!x + ft'y + y 'z, Z=x"x+ft"y + y"z, then the first equations are such as to give identically X 2 + Y 2 +Z 2 =.v 2 +f + z\ 126. Assuming the first six equations, he shows by a direct analytical process that a 2 =(ft'y"— ft"y') 2 , or a= ±(fi'y"~ /3"y') 5 or taking the positive sign (for, as the numbers may be taken as well positively as negatively, there is nothing lost by doing so) a.=ft' y " —ft" y ' , which gives the system a =ft' y"-l3"y' , ft = y' a" - yV , y =a' ft"-a"ft' , a' =ft"y -ft y", ft' =y" a -y a ", y' =a!'ft -a ft", a "=/3 y' -ft' y , i 8" =ya '_ y ' aj y"=a/3'— a'/?', and from these he deduces the second system of six equations. The inverse system of equations X = ax -\-a'y + oc"z, Y=ftx + ft'y + ft"z, Z =yx + y'y + y"z is not explicitly referred to. 127. He then satisfies the equations by means of trigonometrical substitu- tions, viz., assuming a=cos£, then a' 2 + a" 2 = sin 2 £, which is satisfied by a'=sin£ cosr;, a"=sin£ sin/j, &c, and he thus obtains for the coefficients a set of values involving the angles £, rj, 6, which are the same as those men- tioned post, No. 130. And he shows how these formulae maybe obtained geo- metrically by three successive transformations of two coordinates only. The remainder of the memoir relates to the analogous problem of the transforma- tion of four or more coordinates. 128. I have analysed so much of Euler's memoir in order to show that it contains nearly the whole of the ordinary theory of the transformation of coordinates ; the only addition required is the equation a , ft , y «', ft', 7 a", ft", y" = ±1, where the sign + gives a=ft' y "— ft" y ', &c. (ut supra), but the sign — would give a = -(ft'y"-ft"y'), &c. 129. The distinction of the ambiguous sign is in fact the above-mentioned one of the proper and improper transformations ; viz., for the sign + the two sets of axes can, for the sign — they cannot, be brought into coincidence : this very important remark was, I believe, first made by Jacobi in one of his early memoirs in Crelle's Journal, but I have lost the reference. As already mentioned, it is allowable to attend only to the proper transformation, and to consider the value of the determinant as being = + 1 ; and this is in fact almost always done. 130. Euler's formulae involving the three angles are those which are ordi- narily made use of in the problem of rotation and the problems of physical astronomy generally. It is convenient to take them as in the figure, viz., 6, the longitude of node, 220 report — 1862. 0, the inclination, r, the angular distance of X from node, and the formulae of transformation then are X Y Z X cos t cos 9 — sin r sin 9 cos — sin r cos 0— cos r sin 9 cos sin sin <f> y cos t sin 0+sin r cos 9 cos <p — sin t sin 0+ cos r cos $ cos —cos sin <p e sin r sin <p cos r sin COS The foregoing very convenient algorithm, viz., the employment of X Y z X a ft 7 y a' ft' r 7 z a ft" | v" to denote the system of equations a;=aX +/3Y + y Z, y=a'X +/3T +y'Z, z=a"X+/TY+ y "Z, is due to M. Lame. 131. But previously to the foregoing investigations, viz., in the memoir " Du Mouvement de Rotation &c," Mem. de Berlin for 1758 (pr. 1765), Euler had obtained incidentally a very elegant solution of the problem of the transforma- tion of coordinates ; tbis is in fact identical with the next mentioned one, the letters I, on, n ; X, ft, v being used in the place of £, £', £" ; »/, r,' , r>". 132. In the memoir "Formulae generates pro translatione &c." (1775), Euler °ives the following formulae for the transformation of coordinates, viz., if the position of the set of axes XYZ in reference to the set .ryz is determined by ON THE SPECIAL PROBLEMS OF DYNAMICS. 221 a?X, yX, zX=90°-C, 90°-£', 90°— £", /.'YXx,YXy,YXz=T,, v ', „", then the formulae of transformation are X Y Z X sin£ cos £ sin r\ COS £ COS j; y sin£' cos £' sin -q COS f ' COS Jj' z sinf" cos J" sin 7j" COS £" COS i/' with the following equations connecting the six angles, viz., if — A a =cos(i/— ij") cos(jj"— ij) cos(i,-V), then — A ± __ ,, —A , „, —A tan £=- tan£'=- -, tan £"=- cos (l,'— ,") COS(lj"— ,,)' ' cos (,—,')" 133. It is right to notice that these values of £, f , f" give the twelve equations a 2 +/3 2 + y 2 =l, &c, but they do not give definitely cc=ft'y"— /3"y', &c, but only a= ±(/3'y"— /3"y') ! that is, in the formulae in question the two sets of axes are not of necessity displacements the one of the other. In the same memoir Euler considers two sets of rectangular axes, and assuming that they are displacements the one of the other (this assumption is not made as explicitly as it should have been), he remarks that the one set may be made to coincide with the other set by means of a finite rotation about a certain axis (which may conveniently be termed the Eesultant Axis). This considera- tion leads him to an equation which ought to be satisfied by the coefficients of transformation, but which he is not able to verify by means of the fore- going expressions in terms of £, £', £", v , »/, v ". 134. I remark that Euler's equation in fact is a ~ 1» ft ,7 a' , ft'-l, y' a ,P" > 7 "— 1 =0, or, as it may be written, -* i > 7 -(0'y"-/3"y')-(7"«-y a ")-(a/3'-a'/3) + a +/3' + y"-l=O, a , ft' , y' ,," (ill II a > ft , 7 in which form it is an immediate consequence of the equations a , ft , y =1, a =/3'y"_ /3"y', &c, a!, ft', y' —it nil it <*■ > ft , 7 which are true for the proper, but not for the improper transformation. 135. In the undated addition to the memoir, Euler states the theorem of the resultant axis as follows : — " Theorema. Quomodocunque sphsera circa centrum suum convertatur, semper assignari potest diameter cujus directio in situ translate conveniat cum situ originali ;" and he again endeavours to ob- tain a verification of the foregoing analytical theorem. 136. The theory of the Eesultant Axis was further developed by Euler in the memoir « Nova Methodus Motum &c." (1775), and by Lexell in the me- 222 REPORT 1862. moir "Nonnulla theoremata generalia &c." (1775): the geometrical investi- gations are given more completely and in greater detail in Lexell's memoir. The result is contained in the following system of formulae for the transfor- mation of coordinates, viz., if a, fl, y are the inclinations of the resultant axis to the original set, and if is the rotation about the resultant axis, or say the resultant rotation, then we have y 7 X Y Z cos 2 * 4- sin- «cos tj> cos«cos/3(l — cos0) -fcosysin^ cosocosy ( 1 — cosip) — cosfisiiHp cos/3cos«(l — cos^) — cosysinip cos 2 /3 + sin 2 /3cos0 cos/3eosy(l — cos<p) 4-cosasm0 cosycos«(l — cos0)-|-cos/3siii0 cosycos/3(l — cosip) — cosasin^ cos 2 y -f- sin 2 y cos(j> Euler attempts, but not very successfully, to apply the formulae to the dvnamical problem of the rotation of a solid body : he does not introduce them into the differential equations, but only into the integral ones, and his results are complicated and inelegant. The further simplification effected by Rodrigues was in fact required. 137. Jacobi's paper, " Euleri formulae &c." (1827), merely cites the last- mentioned result. 138. I find it stated in Lacroix's ' Differential Calculus,' t. i. p. 533, that the following system for the transformation of coordinates was obtained by Monge (no reference is given in Lacroix), viz., the system being as above, a , /3 , y , I /v t a ,p » y i I a , (i , y , and the quantities a, 0', y" being arbitrary, then putting l+ a + /3' + y"=M, n-«-j8'- y "=isr, l-a + /3'-y" = P, l-a.-j3' + y" = Q, so that M + N+P + Q=4, we have 2/3 = VNP+ VMQ, 2y' = VPQ+ VMN, 2a." = VQN+ VMP, 2a'=VNP-VMQ, 2/3"== VPQ— VOT, 2y =v / QN-VMP. These are formulae very closely connected with those of Rodrigues. 139. The theory was perfected by Rodrigues in the valuable memoir "Des lois geometriques &c." (1840). Using for greater convenience X, /x, v in the place of his jpn, \n, %p, he in effect writes tan^ cosa=X, tan|<p cos (3=fi, tan l;<p cos y=>', and this being so, the coefficients of transformation are l + X'-fS-S, 2(X M + „) , 2(\*-p) 2(/iX-r) , l-X 9 +/i a -K" } 2(jiy + \) 2{v\ + n) 2vn—\ l-X 2 -^^^ ON THE SPECIAL PROBLEMS OF DYNAMICS. 223 all divided by the common denominator l + \ 2 +p 2 + v 2 . Conversely, if the coefficients of transformation are as usual represented by r /51 r a > P , y > n riii it a , p , y , then \ 2 , fi 2 , v 2 , X, fi, v are respectively equal to l + a -/3'-y", l-a+p-y", l- a -/3' + y ", y '-/3" , a"-/3 , /3-a' each of them divided by l + a+fi' + y". The memoir contains very elegant formulae for the composition of finite rotations, and it will be again referred to in speaking of the kinematics of a solid body. 140. Sir "W. E. Hamilton's first papers on the theory of quaternions were published in the years 1843 and 1844 : the fundamental idea consists in the employment of the imaginaries i, j, k, which are such that i 2 =f=k 2 = — l,jk=—kj=i, ki=—ik=j, ij=—ji=k, whence also O + ix +jy + kz) (w/ + ix' +jy' + kz') = ww' — xx' — yy' — zz' + i(wx' + iv 'x + yz' — y'z) +j(ivy' + w'y + zx' — z'x) + k(wz' + w'z+xy'—xy) ; so that representing the right-hand side by W+iX+jY + kZ, we have identically W-+X 2 +Y 2 +Z 2 =(iv 2 +x 2 +y 2 +z 2 )(iv' 2 + x ,2 +y' 2 + z' 2 ). It is hardly necessary to remark that Sir W. E. Hamilton in his various publications on the subject, and in the ' Lectures on Quaternions,' Dublin, 1853, has developed the theory in detail, and has made the most interesting applications of it to geometrical and dynamical questions ; and although the first explicit application of it to the present question may have been made in my own paper next referred to, it seems clear that the whole theory was in its original conception intimately connected with the notion of rotation. 141. Cayley, " On certain Eesults relating to Quaternions" (1845). — It is shown that Eodrigues' transformation formula may be expressed in a very simple manner by means of quaternions ; viz., we have ix+jy+kz=(l+i\+jv + kv)-i(iX+jY+kZ)(l+i\+jfx + kv), where developing the function on the right-hand side, and equating the coeffi- cients of i, j, k, we obtain the formulas in question. A subsequent paper, Cayley, "On the application of Quaternions to the Theory of Eotation" (1848), relates to the composition of rotations. Principal Axes, ami Moments of Inertia. Article Nos. 142-163. 142. The theorem of principal axes consists herein, that at any point of a solid body there exists a system of axes Ox, Oy, Oz, such that fyzdm=0, Jzxdm=0, jxydm=0. 224 report — 1862. But this, the original form of the theorem, is a mere deduction from a general theory of the representation of the integrals fx 2 dm, fy 2 dm, fz\lm, fyzdm, fzxdm, fxydm for any axes through the given origin hy means of an ellipsoid depending on the values of these integrals corresponding to a given set of rectangular axes through the same origin. 143. If, for convenience, we write as follows, ~K=fdm the mass of the body, and A.'=fx*dm, B'=/fdm, C'=fz 2 dm, F=fyzdm, G' = fzxdm, W=fxydm, and moreover A= J-(y* +z *)dm, B=f(z 2 +x 2 )d?n, C=f(x 2 +y 2 )dm, F=— fyzdm, Q=— fzxdm, B.=— fxydm*, so that A=B' + C, B = C' + A', C=A' + B', F=-F, G=-G, H=-H', then the ellipsoid which in the first instance presents itself for this purpose, and which Prof. Price has termed the Ellipsoid of Principal Axes, but which I would rather term the " Comomental Ellipsoid," is the ellipsoid (A, B', C, F, G', H'X*, y, z) 2 =Wc\ where k is arbitrary, so that the absolute magnitude is not determined. But it is more usual, and in some respects better to consider in place thereof the " Momental Ellipsoid" (Cauchy, " Sur les Moments d'Inertie," Exercices de Mathematique, t. ii. pp. 93-103, 1827), (A, B, C, F, G, Kjx, y, zf=Wc\ or as it may also be written, (A + B' + C')(^ + 2/ 2 + Z 2 )-(A', B', C, F, G, Wjx, y, z) 2 =Wc\ which shows that the two ellipsoids have their axes, and also their circular sections coincident in direction. 144. And there is besides this a third ellipsoid, the " Ellipsoid of Gyra- tion," which is the reciprocal of the momental ellipsoid in regard to the con- centric sphere, radius h. The last-mentioned ellipsoid is given in magnitude, viz., if the body is referred to its principal axes, then putting A=Ma 2 , B=Mo 2 , C=Mc 2 , the equation of the ellipsoid of gyration is a2 -|- 6 2-t- c2 The axes of any one of the foregoing ellipsoids coincide in direction with the principal axes of the body, and the magnitudes of the axes lead very simply to the values of the principal moments A, B, C. 145. The origin has so far been left arbitrary : in the dynamical applica- tions, this origin is in the case of a solid body rotating about a fixed point, the fixed point ; and in the case of a free body, the centre of gravity. But the values of the coefficients (A, B, C, F, G, H), or (A, B', C, F, G, H'), corresponding to any given origin whatever, are very easily expressed m * I have ventured to make this change instead of writing as usual ~$=fyzdM, &c. ; as in most cases F=G=H=0, the formulae affected by the alteration are not numerous. ON THE SPECIAL PROBLEMS OP DYNAMICS. 225 terms of the coordinates of this origin, and the values of the corresponding coefficients for the centre of gravity as origin ; or, what is the same thing, any one of the ellipsoids for the given origin may be geometrically constructed by means of the ellipsoid for the centre of gravity. The geometrical theory, as regards the magnitudes of the axes, does not appear to have been any- where explicitly enunciated ; as regards their direction, it is comprised in the theorem that the directions at any point are the three rectangular directions at that point in regard to the ellipsoid of gyration for fhe centre of gravity*, post, No. 159. The notion of the ellipsoids, and of the relation between the ellipsoids at a given point and those at the centre of gravity, once established, the theory of principal axes and moments of inertia becomes a purely geo- metrical one. 146. The existence of principal axes was first established by Segner in the work 'Specimen Theorise Turbinum,' Halle (1755), where, however, it is remarked that Euler had said something on the subject in the [Berlin] Me- moirs for 1749 and 1750 {post, No. 167), and had constructed a new mecha- nical principle, but without pursuing the question. Segner's course of inves- tigation is in principle the same as that now made use of, viz. a principal axis is defined to be an axis, such that when a body revolves round it the forces arising from the rotation have no tendency to alter the position of the axes. It is first shown that there are systems of axes at, y, z such that fyzdm=0, and then, in reference to such a set of axes, the position of a principal axis, say the axis of X, is determined by the conditions fXYd?n=0, fXZdm=0 ) viz. the unknown quantities being taken to be / = — . — T = L (a, 3, y, COS y COS y being the inclinations of the principal axis to those of x, y, z), and then putting A=fx 2 dm, &c. (F=0 by hypothesis), Segner's equations for the de- termination of t, t are G'< 2 4-(C'-A')i-G'-H'r=0, (C'-B')r-G'fr-+H'*=0, the second of which gives _ S!t T ~B'-C' + G't' and by means of it the first gives G' 2 i 3 -G'(A'-B')< 2 + {(B'-C')(C'-A')-G' 2 -H' 2 }<+G'(B'-C') = 0, which being a cubic equation shows that there are three principal axes ; and it is afterwards proved that these are at right angles to each other. 147. To show the equivalence of Segner's solution to the modern one, I remark that if u=f~Ssdm, we have (A.'—tt)*+ H' r+G' =0, B' « + (B'— u)r+F =0, G' t+ F r+C'-u=0, whence * The rectangular directions at a point in regard to an ellipsoid are the directions of the axe3 of the circumscribed cone, or, what is the same thing, they are the directions of the normals to the three quadric surfaces confocal with the given ellipsoid, which pass through the given point. The theory of confocal surfaces appears to have been first given by Chasles, Note XXXI. of the ' Apercu Historique ' (1837). 1862. • a 226 REPORT 1862. t: tr= B'C'-F 2 - (B' + C>+tt 2 , C'A'-G' 8 — (C'4-A>4-w 2 ,. A'B'-H' 2 - (A'4-B>+u 2 , G'H'— A'F H'F-B'G' FG'-C'H' +G' u, 4-H'tt, or putting therein F'=0, i 2 : r 2 : 1 : r: t : t T = -(B' + C>+« a -G' 2 -(C' + A')m+m 2 -H' 2 -(A'+B>+m 2 B'C C'A- AB'- G'H' -B'Q'+G'u -C'H'+H'tt by means of which Segner's equations may he verified. I have given this analysis, as the first solution of such a problem is a matter of interest. 148. There is little if anything added to Segner's results by the memoir, Euler, "Becherches sur la Connaissance Hecanique des Corps" (1758), which is introductory to the immediately following one on Rotation. 149. Relating to the theory of principal axes we have Binet's "Memoire sur les Axes Conjugues," &c. (1813). The author proposes to make known the new systems of axes which he calls conjugate axes, which, when they are at right angles to each other, coincide with the principal axes ; viz. consider- ing the sum of the molecules each into its distance from a plane, such distance being measured in the direction of a line, then (the direction of the line being given) of all the planes which pass through a given point, there is one for which the sum in question is a minimum, and this plane is said to be con- jugate to the given line, and from the notion of a line and conjugate plane he passes to that of a system of conjugate axes. The investigation (which is throughout an elegant one) is conducted analytically; the coordinates made use of are oblique ones, and the formulae are thus rendered more com- plicated than they would otherwise have been ; in referring to them it will be convenient to make the axes rectangular. 150. One of the results is the well-known equation (A'-e)(B'-e)(C'-e)-F 2 (A , -e)-G 2 (B'-e)-H' 2 (c'-e)4-2FG'H'=o ; which, if x v y v z x are the principal axes, has for its roots fxfdm, J'y^dm, fzfclm. And the equations (1), p. 49, taking therein the original axes as rect- angular, are hi — g\ cos a+ W cos/? 4- & COSy = 0, COSy=0, +fc'- cosa + M8'-|^cos/3+ df + ©' cos«4- df cosj8+(C— Qr)cosy=0, where % US', <£', df , ©', &' denote the reciprocal coefficients S'= B'C'-F 2 ON THE SPECIAL PROBLEMS OF DYNAMICS. 227 &c, and K' is the discriminant =A'B'C— AT' 2 — B'G' 2 — C'H' 2 +2F'G'H' : this is a symmetrical system of equations for finding cos a : cos (5 : cos y, less simple however than the modern form (post, No. 154), the identity of which with Binet's may be shown without difficulty. 151. Another result (p. 57) is ttat if the original axes are principal axes, and if Ox, Oy, Oz are the principal axes through a point the coordinates whereof are/, g, h, and if 9/= (say) fx^clm, then we have f + 9 2 , ^ _1 9/-A' ' 9/-B' ' e/— c~m (in which I have restored the mass M, which is put equal to unity) , so that if 9/ have a given constant value, the locus of the point is a quadric surface, the nature whereof will depend on the value of 1# The surfaces in question are con- --2 2 2 ~\ focal with each other [and with the imaginary surface — - — l — ^ 1 — - — =— . 6 J — A^ — B'^ — C M' 2 2 2 "I which is similar to the ellipsoid _.jJl_|__ = which is the reciprocal of .A. 1) (_., 3.1. the comomental ellipsoid A'f +B'y 2 + C'z 2 =HF in regard to a concentric 2 2 2 1 sphere, radius &]. The author mentions the ellipsoid — -f- V- _j_ ?L = _ (see p. 64) ? ■A. Jj C Ju. and he remarks that his conjugate axes are in fact conjugate axes in respect to this ellipsoid, and consequently that the principal axes are in direction the principal axes of this ellipsoid : it is noticeable that the ellipsoid thus inci- dentally considered is not the comomental ellipsoid itself, but, as just re- marked, its reciprocal in regard to a concentric sphere. 152. Poisson, 'Mecanique' (1st ed. 1811, and indeed 2nd ed. 1833), gives the theory of principal axes in a less complete form than in Binet's memoir ; for the directions of the principal axes are obtained in anything but an elegant form. 153. Ampere's Memoir (1823). — The expression permanent axis is used in the place of principal axis, which is employed to designate a principal axis through the centre of gravity. The memoir- contains a variety of very interesting geometrical theorems, which however, as no ellipsoid is made use of, can hardly be considered as exhibited in their proper connexion. The author arrives incidentally at certain conies, which are in fact the focal conies of (a? 2 v 2 z 2 1 \ _.f :Z__I_:_ = 1 for the centre of gravity. A Jj C M/ 154. Cauchy, in the memoir « Sur les Momens d'Inertie " (1827), considers the momental ellipsoid (A, B, C, F, G, HJ#, y, z) 2 =l, and employs it as well to prove the existence of the principal axes as to determine their di- rection, and also the magnitudes of the principal moments; the results are obtained in the simplest and best forms ; viz. the direction cosines are given by (A— 9)cosa+H cos/3 + G cosy=0, H cosa+(B— 9)cos/3 + F cosy=0, G cosa+F cos/3 + (C— 9)cosy=0, where (A-9)(B-9)(C-0)-(A-9)F 2 -(B-9)G 2 -(C-9)H 2 +2FGH=O, 9 being one of the principal moments. 155. Poinsot, « Memoire sur la Rotation " (1834), defines the « Central a2 228 report— 1862. Ellipsoid " as an ellipsoid having for its axes the principal axes through the centre of gravity, the squares of the lengths being reciprocally proportional to the principal moments ; and he remarks in passing that the moment about any diameter of the ellipsoid is inversely proportional to the square of this dia- meter. It is to be noticed that Poinsot speaks only of the ellipsoid having its centre at the centre of gravity, but that such ellipsoid may be constructed about any point whatever as centre, so generalized, it is in fact the mo- mental ellipsoid Ax 2 +By 2 -t-Cz 2 =~Mk i ; and moreover that Poinsot defines his ellipsoid by reference to the principal axes. 156. Pine, " On the Principal Axes, &c." (1837), obtained analytically in a very elegant manner equations for determining the positions of the prin- cipal axes ; viz. these are (A'— e')cosa+H' cos/3 + G' cosy=0, H' cosa + (B'— 9')cos/3+F cosy=0, G' cosa + F cos/3 + (C— 6')cos 7 =0, where (A'-e')(B'-e')(C'-e , )-(A'-e')F 2 -(B'-e')G' 2 -(C'-e')F' 2 -|-2FG'H'=0; viz. these are similar to those of Cauchy, only they belong to the comomental instead of the momental ellipsoid. 157. Maccullagh, in his Lectures of 1844 (see Haughton), considers the momental ellipsoid (A,B, C,F,G,HX.r,2/,^=MP (A, B, C, P, G, H ut Supra,'), which is such that the moment of inertia of the body with respect to any axis passing through the origin is proportional to the square of the radius vector of the ellipsoid ; and from the geometrical theorem of the ellipsoid having principal axes he obtained the mechanical theorem of the existence of principal axes of the body ; at least I infer that he did so, although the conclusion is not explicitly stated in Haughton's account ; but in all this he had been anticipated by Cauchy. And after- wards, referring the ellipsoid to its principal axes, so that the equation is Ax 2 + ~By 2 + Cz 2 =~ZA.k i , he writes A=Ma' 2 , B=M6 2 , C=Mc 2 , which reduces the equation to a 2 v 2 -\-b 2 y 2 + c 2 z 2 =k i , and he considers the reciprocal ellipsoid x 2 y 2 z 2 a? v 2 z 2 1 '-^-(-•f; 4-^ = 1, or, what is the same thing, l - r +~ + -?;=Trj which is theellip- ar 6- c 2 A B C M soid of gyration. 158. Thomson, " On the Principal Axes of a Solid Body " (1846), shows analytically that the principal axes coincide in direction with the axes of the momental ellipsoid (A, B, C, P, G, HJ.t, y, g) a =Mfc*; but the geometrical theorem might have been assumed : the investigation is really an investigation of the axes of this ellipsoid. And he remarks that the ellipsoid (A, B', C, F', G', H.'~£x, y, z) 2 =Wc x (the comomental ellipsoid) might equally well have been used for the purpose. 159. He obtains the before-mentioned theorem that the directions of the principal axes at any point are the rectangular directions in regard to the / v 2 v 2 ~ 2 1 \ ellipsoid of gyration ( '+^+1.= \ for the centre of gravity. And for determining the moments of inertia at the given point (say its coordinates are £, n , £) he obtains the equation ON THE SPECIAL PROBLEMS OF DYNAMICS. 229 * + ? i i- -, A— P B— P ' P p =1 > ?+v*+?+-^ p-ty+r+^r «"+^+r+^ where the three roots of the cubic in P are the required moments. Analyti- cally nothing can be more elegant, but, as already remarked, a geometrical construction for the magnitudes of these moments appears to be required. 160. Some very interesting geometrical results are obtained by consider- ing the " equimomental surface " the locus of the points, for which one of the moments of inertia is equal to a given quantity n ; the equation is of course and which includes Fresnel's wave-surface. In particular it is shown that the equimomental surface cuts any surface •r 2 . ?/ 2 , z 2 1 A+0 ' B+0^C+0 - M confocal with the ellipsoid of gyration in a spherical conic and a curve of curvature ; a theorem which is also demonstrated, Cayley, " Note on a Geo- metrical Theorem, &c." (1846). 161. Townsend, "On Principal Axes, &c." (1846).— This elaborate paper is contemporaneous, or nearly so, with Thomson's, and several of the conclusions are common to the two. From the character of the paper, I find it difficult to give an account of it ; and I remark that, the theory of principal axes once brought into connexion with that of confocal surfaces, all ulterior deve- lopments belong more properly to the latter theory. 162. Haton de la Goupilliere's two memoirs, " Sur la Theorie Nouvelle de la Geometrie des Masses " (1858), relate in a great measure to the theory of the integraiy*. vydm, and its variations according to the different positions of the two planes x=0 and y=0 ; the geometrical interpretations of the several results appear to be given with much care and completeness, but I have not examined them in detail. The author refers to the researches of Thomson and Townsend. 163. I had intended to show (but the paper has not been completed for publication) how the momental ellipsoid for any point of the body may be obtained from that for the centre of gravity by a construction depending on the " square potency " of a point in regard to the last-mentioned ellipsoid. The Rotation of a solid body. Article Nos. 164-207. 164. It will be recollected that the problem is the same for a body rotating about a fixed point, and for the rotation of a free body about the centre of gravity; the case considered is that of a body not acted on by any forces. According to the ordinary analytical mode of treatment, the problem depends upon Euler's equations Adp+(G— B)g«fc=0, Bdq+(A-C)r I )dt=0 ) Cdr+(B—A) M dt=0, for the determination of p, q, r, the angular velocities about the principal 230 report— 1862. axes ; considering jp, q, r as known, we obtain by merely geometrical consi- derations a system of three differential equations of the first order for the determination of the position in space of the principal axes. 165. The solution of these, which constitutes the chief difficulty of the problem, is usually effected by referring tbe body to a set of axes fixed in space, the position whereof is not arbitrary, but depends on the initial circum- stances of the motion ; viz. the axis of z is taken to be perpendicular to the so-called invariable plane. The solution is obtained ivithout this assumption both by Euler and Lagrange, although, as remarked by them, the formulas are greatly simplified by making it ; it is, on the other hand, made in the solution (which may be considered as the received one) by Poisson ; and the results depending on it are the starting-point of the ulterior analytical deve- lopments of Rueb and Jacobi ; the method of Poinsot is also based upon the consideration of the invariable plane. 166. D'Alembert's principle, which affords a direct and general method for obtaining the equations of motion in any dynamical problem whatever, was given in bis " Traite de Dynamique " (1743) ; and in his memoir of 1749 he applied it to the physical problem of the Precession of the Equinoxes, which is a special case of the problem of Rotation, the motion of rotation about the centre of gravity being in fact similar to that about a fixed point. But, as might be expected in the first attempt at the analytical treatment of so difficult a problem, the equations of motion are obtained in a cumbrous and unmanageable form. 167. They are obtained by Euler in the memoir " Decouverte d'un Nou- veau Principe de Mecanique," Berlin Memoirs for 1750 (1752) (written before the establishment of the theory of principal axes), in a perfectly elegant form, including the ordinary one already mentioned, and, in fact, reducible to it by merely putting the quantities F, G-, H (which denote the integrals fyzdm, &c.) equal to zero. But Euler does not in this memoir enter into the question of the integration of the equations. 168. The notion of principal axes having been suggested by Euler, and their existence demonstrated by Segner, we come to Euler's investigations contained in the memoirs " Du Mouvement de Potation &c," Berlin Me- moirs for 1758 (printed 1765) and for 1760 (printed 1767), and the " Theoria Motus Corporum Solidorum &c." (1765). In the memoir of 1760, and in the "Theoria Motus," Euler employs b, the angular velocity round the in- stantaneous axis, but not the resolved velocities 8 cos a, 8 cos /3, 8 cos y ( = _P> 2» r ) '• these quantities (there called x, y, z) are however employed in the memoir, Berlin Memoirs (1758), which must, I apprehend, have been written after the other, and in which at any rate the solution is developed with much greater completeness. It is in fact carried further than the ordinary solutions, and after the angular velocities p, q, r have been found, the remaining investigation for the position in space of the principal axes, conducted, as above remarked, without the aid of the invariable plane, is one of great elegance. 169. In the last-mentioned memoir Euler starts from the equations given by d'Alembert's principle ; viz. the impressed forces being put equal to zero, these are *K y S-4fO=°- & - or, what is the same thing, using a, v, iv to denote the velocities of an element in the directions of the axes fixed in space, these are ON THE SPECIAL PROBLEMS OF DYNAMICS. 231 , / clw dv\ - 7 / du dw\ „ 2dm(x^-yf) = 0. It is assumed that at any moment the body revolves round an instantaneous axis, inclinations a, (3, y, with an angular velocity 8 ; this gives u= 8 (z cos /3 — y cos y) = qz — ry, v=v (x cos y — z cos a) = rx —pz, w=v(y cos a — x cos/3) =px—qy, if 8 cos a, e cos /3, 8 cos y are denoted by p, q, r. The values of du, dv, dw are obtained by diiferentiating these formulas, treating p, q, r, x, y, z as variable, and replacing dx, dy, dz by udt, vdt, wdt respectively; ya. the resulting formulae for ydw—zdv, &c, x, y, z are considered as denoting the coordinates of the element in regard to axes fixed in the body and moveable with it, but which at the moment under consideration coincide in position with the axes fixed in space. The expressions for 2 {ydw—zdv) dm involve the integrals A=~f(y 2 +z 2 )dm, &c, where the coordinates refer to axes fixed in the body ; and if these are taken to be principal axes, the expression for 2 (ydw—zdv) dm is =Adp + (C— B)qrdt, which gives the three equations Adp+ (C— B) qrdt=0, Bdq + (A—C)rpdt=0, Cdr + (B—A)pqdt=0, already referred to as Euler's equations. 170. Next, as regards the determination of the position in space of the principal axes : if about the fixed point we describe a sphere meeting the principal axes in x x , y v z x , and if P be an arbitrary point on the sphere and PQ an arbitrary direction through P, the quantities used to determine the positions of x x , y v z x are the distances x x P, y L P, z 2 P ( = 1, m, n) and the incli- nations a-jPQ, yJ^Q,, ZjPQ, ( = X, /t, r) of these arcs to the fixed direction PQ (it is to be observed that the sines and cosines of the differences of X, p., v are given functions of the sines and cosines of I, m, n, and, moreover, that cos 2 Z-t-cos 2 m + cos 2 n=l, so that the number of independent parameters is three). The above is Euler's definition ; but if we consider a set of axes fixed in space meeting the sphere in the points X, Y, Z, then if the point X be taken for P, and the arc XT for PQ, it is at once seen that the angles used for determining the relative positions of the two sets of axes are the same as in Euler's memoir "Eormulae Generales, &c," 1775 (ante, No. 132), where the formulae for this transformation of coordinates are considered apart from the dynamical theory. Euler expresses the quantities p, q, r in terms of an auxiliary variable u, which is such that du=pqrdt ; p, q, r are at once obtained in terms of w, and then t is given in terms of u by a quadrature. Euler employs also an auxiliary angle TJ, given in terms of u by a quadrature. And he obtains finite algebraical expressions in u, cos U, sin U for the cosines or sines of l,m,n; s (the angular distance IP, if I denote the point in which the instan- taneous axis meets the sphere), <p (the angle IPQ,) and A — <p, fi — <j>, v — <p. 232 report — 1862. The formula}, although complicated, are extremely elegant, and they appear to have been altogether overlooked by subsequent writers. 171. Euler remarks, however, that the complexity of his solution is owing to the circumstance that the fixed point P is left arbitrary, and that they may be simplified by taking this point so as that a certain relation G— W=0 may be satisfied between the constants of the solution ; and he gives the far more simple formula? corresponding to this assumption. This amounts to taking the point P in the normal of the invariable plane, and the resulting formulae are in fact identical with the ordinary formulas for the solution of the problem. The expression invariable plane is not used by Euler, and seems to have been first employed in Lagrange's memoir " Essai sur le Pro- blems de Trois Corps," Prix de l'Acad. de Berlin, t. ix. (1772) : the theory in reference to the solar system has been studied by Laplace, Poinsot, and others. 172. Lagrange's solution in the memoir of 1773 is substantially the same with that in the ' Mecanique Analytique.' Only he starts from the integral equations of areas and of Vis Viva, but in the last-mentioned work from the equations of motion as expressed in the Lagrangian form by means of the Vis Viva function T (=^(x' 2 +y' 2 +z' 2 )clm). The distinctive feature is that he does not refer the body to the principal axes but to any rectangular axes whatever fixed in the body: the expression for T consequently is T=! (A, B, C, F, G, HY», q, rf, instead of the more simple form T=i(Ap 2 + Bq 2 + Cr 2 ), which it assumes when the body is referred to its principal axes. And Lagrange effects the integration as well with this more general form of T, as without the simplification afforded by the invariable plane ; the employment, however, of the more general form of T seems an unnecessary complication of the problem, and the formulae are not worked out nearly so completely as in Euler's memoir. It may be observed that p, q, r are expressed as functions of the instantaneous velocity w(= Vp 2 +2 2 + r 2 ), and thence t obtained by a quadrature as a function of w. 173. Poisson's Memoir of 1809. — The problem is only treated incidentally for the sake of obtaining the expressions for the variations of the arbitrary constants ; the results (depending, as already remarked, on the consideration of the invariable plane) are obtained and exhibited in a very compact form, and they have served as a basis for further developments ; it will be proper to refer to them somewhat particularly. The Eulerian equations give, in the first place, the integrals Ap 2 +Bq 2 + 2 =h, Ay+BY+CV=P; and then by means of these, p, q being expressed in terms of r, we have t in terms of r by a quadrature. 174. The position in space of the principal axes is determined by referring them, by means of the angles 0, 0, c, to axes Ox, Oy, Oz fixed in space ; if, to fix the ideas, we call the plane of xy the ecliptic (Ox being the origin of longitudes), and the plane of the two principal axes x x y 1 the equator, then we have 6, the longitude of node, <p, the inclination, C, the hour-angle, or angular distance of Ox 1 from the node, and a, /3, y the cosine inclinations of Ox v a, /3', y those of Oy v and a", /3", y" ON THE SPECIAL PROBLEMS OF DYNAMICS. 233 those of 0-z, to Ox, Oy, Oz respectively are given functions of 6, 0, t (the values of a", fi", y" depending upon 6, <j> only), we have pdt= sin t sin <p d0-\- cos t d<p, qdt =cos c sin <j> dd — sin t d<f>, rdt=dz + cos f dd. 175. A set of integrals is Apa + ~Rqfi +Cry =Tc cos X, Apa' + Bqfi' +Cry =h cos //, Apa"+Bqfi"+Cry"=Ie cos v, equivalent to two independent equations, the values of \, fi, v being such that cos 2 A+cos 2 /i + cos 2 j' = l ; but the position of the axis of z may be chosen so that the values on the right-hand sides become 0, 0, Tc ; the axis of z is then perpendicular to the invariable plane, the condition in qiiestion serving as a definition. And the three equations then give Ap=Tca", Bq=hfi", Cr=l y ", where the values of a", fi", y" in fact are a"=sin c sin <p, fi"=cos t sin $, y"=cos0; we have thus t, <p in terms of r. And the equation rdt = dt + cos <pdd then leads to the value of dd, or is determined as a function of r by a quadrature. 176. The constants of integration are h, Tc, I (the constant attached to i), g (the constant attached to 0) ; and two constants, say a the longitude of the node, and y the inclination of the invariable plane in reference to an arbitrary plane of xy and origin x of longitudes therein. I remark in passing that Poisson obtains an elegant set of formulae for the variations of the constants h, Tc, g, I, a, y, not actually in the canonical form, but which may by a slight change be reduced to it. 177. Legendre considers the problem of Eotation in the 'Exerciees de Calcul Integral,' t. ii. (1817), and the " Theorie des Fonctions Elliptiques," t. i. pp. 366-410 (1826). He does not employ the quantities p, q, r, but obtains de novo a set of differential equations of the second order involving the angles which determine the position of the principal axes with regard to the axes fixed in space : these angles are in fact (calling the plane of the fixed axes x, y the ecliptic) the longitude and latitude of one of the principal axes, and the azimuth from the meridian through such principal axis of an arbitrary axis fixed in the body and moveable with it. The solution is developed by means of the elliptic integrals. Erom the peculiar choice of variables there would, it would seem, be considerable labour in comparing the results with those of other writers, and there would be but little use in doing so. 178. Poinsot's "The'orieNouvelle de la Eotation des Corps." — The 'Extrait ' of the memoir was published in 1834, but the memoir itself was not published in extenso until the year 1851 . The ' Extrait ' contains, however, not only the fundamental theorem of the representation of the motion of a body about a fixed point by means of the momental ellipsoid rolling on a fixed tangent plane, but also the geometrical and mechanical reasonings by which this theorem is demonstrated ; it establishes also the notions of the Poloid and Serpoloid curves ; and it contains incidentally, and without any developments, a very important remark as to the representation of the motion by means of the rolling and sliding motion of an elliptic cone. The whole theory (includ- ing that of the last-mentioned representation of the motion) is in the memoir 234 report— 1862. itself also analytically developed, but without the introduction of the elliptic and Jacobian functions : to form a complete theory, it would be necessary to incorporate the memoir with that of Jacobi. 179. The following is an outline of the ' Extrait ' : — The instantaneous motion of a body about a fixed point is a motion of rotation about an axis (the instantaneous axis) ; and hence the finite motion is as if there were a cone fixed in the body which rolls (without sliding) upon another cone fixed in space. The instantaneous motion of a body in space is a motion of rotation about an axis combined with a translation in the direction of this axis : this remark is hardly required for Poinsot's purpose, and he does not further develope the theory of the motion of a body in space. The effect of a couple in a plane perpendicular to a principal axis is to turn the body about this axis with an angvdar velocity proportional to the moment of the couple divided by the moment of inertia about the axis. And hence by resolving any couple into couples perpendicular to the prin- cipal axes, the effect of such couple may be calculated ; but more simply by means of the central ellipsoid (momental ellipsoid a 2 x 2 + b 2 y a + c 2 z 2 =k i , if A, B, C=Ma 2 , M6 2 , He 2 ), viz., if the body is acted on by a couple in a tangent plane of the ellipsoid, the instantaneous axis passes through the point of con- tact ; and reciprocally given the instantaneous axis, the couple must act in the tangent plane. 180. Considering now a body rotating about a fixed point, and taking as the plane of the couple of impulsion a tangent plane of the ellipsoid, the instantaneous axis is initially the diameter through the point of contact ; the centrifugal forces arising from the rotation produce however an accelerating couple, the effect whereof is continually to impress on the body a rotation which is compounded with that about the instantaneous axis, and thus to cause a variation in the position of this axis and in the angular velocity round it. The axis of the accelerating couple is always situate in the plane of the couple of impulsion. 181. Hence also 1°. Throughout the motion the angular velocity is proportional to the length of the instantaneous axis considered as a radius vector of the ellipsoid. 2°. The distance of the tangent plane from the centre is constant ; that is, the tangent plane to the ellipsoid at the extremity of the instantaneous axis is a fixed plane in space. Or, what is the same thing, the motion is such that the ellipsoid remains always in contact with a fixed plane, viz., the body revolves round the radius vector through the point of contact, the angular velocity being always pro- portional to the length of this radius vector. It is right to remark that in Poinsot's theory the distance of this plane from the centre depends on the arbitrarily assumed magnitude of the central ellipsoid ; the parallel plane through the centre is the invariable plane of the motion. 182. The motion is best understood by the consideration that it is implied in the theorem that the pole of the instantaneous axis describes on the ellip- soid a certain curve, " the Poloid," which is the locus of all the points for which the perpendicular on the tangent plane has a given constant value (the curve in question is easily seen to be the intersection of the ellipsoid by a concentric cone of the second order) ; and that the instantaneous axis describes on the fixed tangent plane a curve called the Serpoloid, which is the locus of the points with which the several points of the poloid come successively in con- ON THE SPECIAL PROBLEMS OF DYNAMICS. 235 tact with the tangent plane, and is a species of undulating curve, viz., the radius vector as it moves through the angles 6 to 0J + 2II, ^ + 211 to 6^ + 411, &c. as- sumes continually the same series of values. This is in fact evident from the mode of generation ; and it is moreover.clear that the serpoloid is an algebraical or else a transcendental curve according as II is or is not commensurable with jf, [Treating the poloid and serpoloid as cones instead of curves, the motion of the body is the rolling motion of the former upon the latter cone, which agrees with a previous remark.] There is a very interesting special case where the perpendicular distance from the tangent plane is equal to the mean axis of the ellipse. 183. Poinsot remarks that the motion is such that [considering the plane of the couple of impulsion as drawn through the centre of the ellipsoid] the section of the ellipsoid is an ellipse variable in form but of constant magni- tude, and that this leads to a new representation of the motion, viz., that it may be regarded as the motion of an elliptic cone which rolls on the plane of the couple [the invariable plane] with a variable velocity, and which slides on this plane ivith a uniform velocity. 184. The theory of the last-mentioned cone, say the " rolling and sliding cone," is developed in the memoir, Liouville, t. xvi. p. 303, in the chapter entitled " Nbuvelle Image de la Rotation des Corps." If a, b, c signify as before (viz., A, B, C=H« 2 , H6 2 , He 2 ), and if h be the distance of the centre from Poinsot's fixed tangent plane (7t<«>c), then the invariable axis describes in the body a cone the equation whereof is (rt 2 - h 2 ) x 2 +(b 2 -h 2 ) y 2 + (c 2 -7r) z 2 =0 ; the cone reciprocal to this, viz. the cone the equation whereof is • ** ■ 2/ 2 _,_ z 2 , = a 2 -h 2 ' b 2 —h 2 ' c 2 — h 2 is the " rolling and sliding cone." The generating line OT of this cone is perpendicular to the plane of the instantaneous axis 01, and of the invariable axis OG ; and the analytical expressions for the rolling and sliding velocities follow from the geometrical consideration that the motion at any instant is a rotation round the instantaneous axis 01 : that for the sliding velocity is the instantaneous angular velocity into the cosine of the angle IOG, which is in fact constant ; that for the rolling velocity is given, but a further explanation of the geometrical signification is perhaps desirable. 185. I may in this place again refer to Cohen's memoir " On the Differential Coefficients and Determinants of Lines &c." (1862), the latter part of which contains an application of the method to finding Eider's equations for the motion of a rotating body. 186. Rueb in his memoir (1834) first applied the elliptic and Jacobian func- tions to the present problem. Starting from the equations Ap 2 -r-B 2 2 +Cr 2 =7t, A 2 p 2 + B 2 q 2 + C 2 r 2 =l 2 *, and dt= ~ Bd g , (A-C)rp' it is easy to perceive that by assuming q = a proper multiple of sin £, the ex- * I is Poisson's k, the constant of the principal area ; it is the letter afterwards used by Jacobi ; Eueb's letter is g. In quoting (infra) the expressions for p, q, r, I have given them with Eueb's signs, but it would be too long to explain how the signs of the radicals are determined. 936 report — 1862. nression for dt takes the form ndt=—— J * , so that writing £=ani u, r Vl— Psin 2 £ the integral equation is nt—e=u, or u is an angle varying directly as the time (and corresponding to the mean longitude, or, if we please, to the mean anomaly in the problem of elliptic motion). And then p, q, r are expressed as elliptic functions of u. The value of the modulus I; and that of n (nt—e=u ut supra) are / (B-CX-P+iA) n ~ V ABC ' (A-B)(Z 2 -C7i) ABC and then , / l-—Qh P=± VA7^C C0SamV ' / P—Ch . ri = "VBTB3c Smam "' V C.A-C am m. 187. Substituting forp, q, r their values in terms of u, we have dd, and thence d (the longitude of the node of the equator on the invariable plane) in the form I , e=-^«+*n(«,io) (t=v-i), which by Jacobi's formute for the transformation of the elliptic integral of the third class becomes \ An / 6(«+«i) which Bueb reduces to the real f<_ 0= — -zi'u + tan-'W, W being given in the form of a fraction, the numerator and denominator whereof are series in multiple sines and multiple cosines respectively of 188. Bueb investigates also the values in terms of u of the cosine inclina- tions of the instantaneous axis to the axes fixed in space ; and he obtains a very elegant expression for the angle £, which is the angular distance from x of the projection on the plane of any (the invariable plane) of the instantaneous axis ; viz., this is . / ABji A am u \ Q Z^tan-'l — — — =—> -. 1 — 0, \ (A — B)f sin am u cos am u) and there is throughout a careful discussion of the geometrical signification of the results. 189. The advance made was enormous ; the result is that we have in terms of the time sin c sin f, cos c sin <p, cos <p (the cosine inclinations of the inva- riable axis to the principal axes), and also d, the longitude of the node. The cosine inclinations of the axes of as and y to the principal axes could of course be obtained from these, but they would be of a very complicated and un- ON THE SPECIAL PROBLEMS OF DYNAMICS. 237 manageable form ; the reason of this is the presence in the expression for 6 of the non-periodic term — n'u. It will presently be seen bow tbis difficulty was got over by Jacobi. 190. Briot's paper of 1842 contains an analytical demonstration of some of the theorems given in the 'Extrait' of Poinsot's memoir of 1834. 191. In Maccullagh's Lectures of 1844 (see Haughton, 1849 ; Maccullagh, 1847) the problem of the rotation of a solid body is treated in a mode some- l x 2 v 2 z 2 what similar to that of Poinsot's; only the ellipsoid of gyration 1 1^_|-^-| — 5 =1, if A, B, C=Ha 2 , M6 2 , He 2 ) is used instead of the momenta! ellipsoid. Thus, reciprocal to the poloid curye on the momental ellipsoid we have on the ellipsoid of gyration a curve all the points whereof are equidistant from the centre ; such curve is of course the intersection of the ellipsoid by a concen- tric sphere, that is, it is a spherical conic ; and the points of this spherical conic come successively to coincide with a fixed point on the invariable axis. This is a theorem stated in Art. YI. of Haughton's memoir : it may be added that the several tangent planes of the ellipsoid of gyration at the points of the spherical conic as they come to coincide with the fixed point, form a cone reciprocal to Poinsot's serpoloid cone. It is clear that every theorem in the one theory has its reciprocal in the other theory ; I have not particularly examined as to how far the reciprocal theorems have been stated in the two theories. 192. Cayley, " On the Motion of Rotation of a Solid Body " (1843).— The object was to apply to the solution of the problem Rodrigues' formulae for the resultant rotation ; viz., if the principal axes, considered as originally coin- ciding with the axes of x, y, z, can be brought into their actual position at the end of the time t by a rotation 6 round an axis, inclined at angles /, g, h to the axes of x, y, z, and if \ = tan ±d cos/, yu=tan \Q cos g, »>=tan *0 cos h, then the principal axes are referred to the axes fixed in space by means of the quantities X, jj, v. And these are to be obtained from the equations icpdt = 2( dk + vdjj. —jidv), k qdt=2( — vd\ + d/j, + \dy), k rdt=2( nd\—\dn+ dv), where k=1 + \ 2 4-/* 2 + »' 2 , and^, q, r are to be considered as given functions of t, or of other the variable selected as the independent one. But for effecting the integration it was found necessary to take the axes of z as the invariable axes. 193. The solution by Jacobi, § 27 of the memoir " Theoria Novi Multi- plicatoris" (1845), is given as an application of the general theory, the author remarking that, as well in this question as in the problem of the two fixed centres, he purposely employed a somewhat inartificial analysis, in order to show that the principle (of the Ultimate Multiplier) would lead to the result without any special artifices. The principal axes are referred to the axes fixed in space by the ordinary three angles (here called q v q 2 , q 3 ), and the solution is carried so far as to give the integral equations, without any reduc- tion of the integrals contained in them to elliptic integrals. The solution is, howeve*, in so far remarkable that the integrations are effected without the aid of the invariable plane. 194. Cayley, " On the Rotation of a Solid Body &c." (184G). — It appeared desirable to obtain the solution by means of the quantities X, p, v, without the assistance of the invariable plane, and Jacobi's discovery of the theorem of the 238 report — 1862. Ultimate Multiplier induced me to resume the problem, and at least attempt to bring it so far as to obtain a differential equation of the first order between two variables only, the multiplier of which could be obtained theoretically by Jacobi's discovery. The choice of two new variables to which the equa- tions of the problem led me, enabled me to effect this in a simple manner ; and the differential equation which I finally obtained turned out to be inte- grable per se, so that the laborious process of finding the multiplier became unnecessary. 195. The new variables £2, v have the following geometrical significations : £2=Ztan|0 cosT, where I is the principal moment (A 2 p 2 + B 2 ^ 2 -l-CV=Z 2 ) J (as before) the angle of resultant rotation, and I is the inclination of the resultant axis to the invariable axis ; and v=l~ cos 2 |J, where if we imagine a line AQ, having the same position relatively to the axes fixed in space that the invariable axis has to the principal axes of the body, then J is the incli- nation of this line to the invariable axis. It is found that p, q, r are func- tions of v only, whereas X, p, v contain besides the variable £2. In obtaining these relations, there occurs a singular relation £2 2 =«/— Z 2 , which may also be written 1 + tan 2 10 cos 2 I=sec 2 id cos 2 |J, where the geometrical significa- tions of the quantities I, J have just been explained. The final results are that the time t, and the arc tan - : — are each of them expressible as the integrals of certain algebraical functions of v. There might be some interest in comparing the results with those of Euler's memoir of 175S, where the principal axes are also referred to an arbitrary system of axes fixed in space ; but I was not then acquainted with Euler's memoir. The concluding part of the paper relates to the determination of the varia- tions of the constants in the disturbed problem. 196. Cayley, " Note on the Rotation of a Solid of Revolution " (1849), shows the simplification produced in the formulae of the last- mentioned memoir in the case where two of the moments of inertia are equal, say A=B. 197. Jacobi's final solution of the problem of Rotation was given without demonstration in the letter to the Academy of Sciences at Paris ; the demon- stration is added in the memoir, Crelle, t. xxxix. (1849). The fundamental idea consists in taking in the invariable plane, instead of the fixed axes xy, a set of axes xy revolving with uniform velocity, such that the angular distance of the axis of as from its initial position is precisely = — n'u ; and consequently if 6' be the longitude of the node of the equator on the invariable plane, mea- sured from the moveable axis of x as the origin of longitude, we have i and in consequence of this form of the expression for d' (=«-. into a loga- rithmic function) in passing to the trigonometrical functions sin 6', cos 0' the logarithm disappears altogether ; and we have in a simple form the expres- sions for the actual functions sin &, cos 6', through which 6' enters into the formulae, and thus, Jacobi remarks, the barrier is cleared which stands in the way when the expression of an angle is reduced to an elliptic integral of the third class. 198. For the better expression of the results, Jacobi joins to the functions H, e, considered in the " Fundamenta Nova," the functions 0^ = 6 (K— u), H 1 («)=H(K-«); so that ON THE SPECIAL PROBLEMS OF DYNAMICS. 239 /T . TIu /h H> 1 G,m V &sinamu= — -, a / ,-cos amit=— ^-, -:= Aamit= 77-, and then considering the cosine inclinations of the principal axes to the invariable axis and the revolving axes in the invariable plane, these are all fractions which, neglecting constant factors, have the common deno- minator Qu ; a", /3", y" (as shown by Eueb's formulae) have the numerators H^, Hm, and Q^t, respectively; and a, a,' have the numerators ~K(u-\-ia) +H (u—ia), /3, ft the numerators H 1 (u— ia)+H 1 (u+ia), y, y the nume- rators Q(u+ia) + Q (u—ia) 'respectively : there are also expressions of a similar form for the angular velocities about the axes of x and y ; that about the axis of z (the invariable axis) having, as was known, the constant value -. The memoir is also very valuable analytically, as completing the systems u of formulae given in the " Fundamenta Nova" in reference to elliptic integrals of the third class. 199. It is worth noticing how the residts connect themselves with Poinsot's theorem of the rolling and sliding cone, the velocity of the rolling motion depends only upon the position, on the cone, of the line of contact, so that the same series of velocities recur after any number of complete revolutions of the cone ; that is, the total angle desci'ibed by the line of contact in conse- quence of the rolling motion, consists of a part varying directly with the time (or say varying as u) and a periodic part ; the former part combines with the similar term arising from the sliding motion, and the two together give Jacobi's term n'u. 200. Somoff's memoir (1851), written after Jacobi's Note in the * Comptes Rendus,' but before the appearance of the memoir in Crelle, gives the de- monstration of the greater part of Jacobi's residts. 201. Booth's " Theory of Elliptic Integrals &c." (1851) (contemporaneous with the publication of Poinsot's memoir of 1834) contains various interest- ing analytical developments, and, as an interpretation of them, the author obtains (p. 93) the theorem of the rolling and sliding cone. The investiga- tions involve the elliptic integrals, but not the elliptic or Jacobian functions. 202. Bichelot's two Notes (Crelle, tt. xlii. & xliv.) relate to the solution of the problem of rotation given in his memoir " Eine neue Losung &c." (1851). This is an application of Jacobi's theorem for the integration of a" system of dynamical equations by means of the principal function S (see my " Report " of 1857, art. 34). Retaining Bichelot's letters <p, \p, 0, which signify \p, the longitude of the node, 6, the inclination, <p, the hour-angle, the question is to find a complete solution of the partial differential equation ^^{fe^^+^jsini-^ 00 ^ . 1 [ (dY a , d\\ cos a , dV . + 2B{U CO80+ ^)sin0 + ^ Sin ^ ^2C Vty/ ^dt' that is, a solution involving (besides the constant attached to V by a mere 240 REPORT 1862. addition) three arbitrary constants ; these are t x , \p iy p. Writing in the first place Y=W+tt 1 + \p\l/ 1 , the resulting equation for "W may be satisfied by taking W, a function of <p and 6, without \p or t ; and it is sufficient to have a solution involving only a single arbitrary constant. This leads to a solu- tion which is as follows, — Y=tt l + ] p x p i — ^ 1 tan" 0, \V-^-0/ +p|tan ' M p^v-^-fll 2 tan" 0A ■K where ^ and d x arc certain given functions of t L , \p v p, and of and 0. The solution of the dynamical problem is then obtained by putting the differential dV dY dY coefficients — -, — — , — - equal to arbitrary constants L, cc, G l'espectively ; CMj a^/j dp the results are somewhat more simple than might be expected from the very complicated form of the function V. The foregoing results (although not by themselves very intelligible) will give an idea of the form in which the ana- lytical solution in the first instance presents itself. 203. Richelot proceeds to remark that the solution iu question, and the resulting integral equations of the problem, may be simphfied in a peculiar manner by the method which he calls " the integration by the spherical tri- angle." Eor this purpose he introduces a spherical triangle, the sides and angles whereof are and then assuming 2/ j 2 » v, X, fi ; N, A, M, N constant, M=7r — (c _ a) siu2 y +v ) sin2A + (c~b) cos2 ^ + "- ) sin2A== c + where p and t x are constant, the solution is Y=t l t— p(4> — \)cosN— pM+pfcos Ad(<p-\-v) ; and that this expression leads to all the results almost without calculation. 204. I have quoted the foregoing results from the Note (Crelle, t. xlii.), having seen, but without having studied, the Memoir itself : the results appear very interesting and valuable ones ; but they seem to require a more com- plete geometrical development than they have received in the Memoir ; and I am not able to bring them into connexion with the other researches on the subject. 205. The solution, § 3 of Donkin's memoir " On a Class of Differential Equations &c." (part i. 1854), is given as an illustration of the general theory to which the memoir relates ; it contains, however, some interesting geometrical developments in regard to the case (A=B) of two equal moments of inertia. I have not compared the results with those in my Note of 1849. i 206. The solution of the rotation problem, § 66 of Jacobi's memoir " Nova Methodus &c." (1862), has for its object to show the complete analogy which exists between this problem and the problem of a body attracted to a ON THE SPECIAL PROBLEMS OF DYNAMICS. 241 fixed centre. The section is in fact headed " Solutio simultanea problematis de motu puncti versus centrum attracti atque problematis de rotatione &c"; and Jacobi, after noticing that Poisson, in his memoir of 1816 (Mem. de lTnst. t. i.), had shown that the expressions for the variations of the elements in the two problems coidd be investigated by a common analysis, remarks, " Sed ipsa problemata duo imperturbata hie primum, quantum credo, amplexus sum." The solution is in fact as follows: — Suppose that in the one problem the position of the point in space, and in the other problem the position of the body in regard to the fixed axes is determined in any manner by the quantities q x , q 2 , q 3 . Let dt »' dt~ q *' dt~ q *' and expressing the Vis Viva function T in terms of q v q 2 , q 3 , o:,', q 2 , q 3 , let dT __ dT__ cTI _ Wi~ Pl ' fy*~ p * i hi~ P3 ' and let H be the value of T expressed in terms of q v q 2 , q 3 , p v p 2 , p 3 , so that K = a is the integral of Vis Viva (this is merely the transformation to the Hamiltonian form). And let H,=a 1 , <t>=a l ', \p=a 1 " be the three integrals of areas (H, Hj, (f>, \p are functions of the variables only, not containing the arbitrary constants a, a v «/, a"). Then, expressing H,H 1 ,H 2 (=VH 1 2 + f + «p 2 ) in terms of p v p 2 , p 3 , q v q 2 , q 3 , and by means of the equations H=a, H 1 =a 1 , H 2 =« 2 (where a 2 = Vre^ + a^+a," 2 ) expressing }\,p 2 , p 3 in terms of q v q 2 , q 3 , we have p l dq l +p 2 dq 2 +p 3 dq 3 a complete differential ; and putting J \l\ d( I 1 +P2 d ^+2 ) 3 c h 3 )= Y ' then (a, a v a 2 , h, b v h 2 being arbitrary constants) we have H=«, H^ssay H 2 =a 2 , dY da n as the complete integrals of either problem, the last three of them being the final integrals. And it is added that if in either problem we have H. + CI instead of H, the expressions for the variations of the elements assume the canonical forms da_ dQ, db _d£l ~dt~~~db' dt~~da' The solution is not further developed as regards the rotation problem, but it is so (§ 67) as regards the other problem. 207. It must, I think, be considered that a comprehensive memoir on the 1862. * 242 keport— 1862. Problem of Rotation, embracing and incorporating all tbat has been done on the subject, is greatly needed. Kinematics of a solid body. Article Nos. 208 to 215. 208. The general theorem in regard to the infinitesimal motions (rotations and translations) of a solid body is that these are compounded and resolved in the same way as if they were single forces and couples respectively. Thus any infinitesimal rotations and translations are resolvible into a rotation and a translation ; the rotation is given as to its magnitude and as to the direction of its axis, but not as to the position of the axis (which may be any line in the given direction) : the magnitude and direction of the translation depend on the assumed position of the axis of rotation ; in particular this may be taken so that the translation shall be in the direction of the axis of rotation ; and the magnitude of the rotation is then a minimum. I remark that the theorem as above stated presupposes the establishment of the theory of couples (of forces) which was first accomplished by Poinsot in his 'Siemens de Statique,' 1st edit. 1804 ; it must have been, the whole or nearly the whole of it, familiar to Chasles at the date of his paper of 1830 next referred to (see also Note XXXIV of the Apertju Historique, 1837) ; and it is nearly the whole of it stated in the ' Extrait ' of Poinsot's memoir on Rotation, 1834. 209. Chasles' paper in the ' Bulletin Univ. des Sciences ' for 1830. — The corresponding theorem is here given for the finite motions (rotations and translations) of a solid body as follows, viz. if any finite displacement be given to a free solid body in space, there exists always in the body a certain inde- finite hue which after the displacement remains in its original situation. The theorem is deduced from a more general one relating to two similar bodies. It may be otherwise stated thus : viz., any motions may be represented by a translation and a rotation (the order of the two being indifferent) ; the rotation is given as regards its magnitude and the direction of its axis, but not as to the position of the axis (which may be any line in the given direction) ; the magnitude and direction of the translation depend on the assumed position of the axis of rotation ; in particular this may be taken so that the translation shall be in the direction of the axis of rotation ; the magnitude of the trans- lation is then a minimum. It may be noticed that a translation may be represented as a couple of rotations ; that is, two equal and opposite rotations about parallel axes. 210. It is part of the general theorem that any number of rotations about axes passing through one and the same point may be compounded into a single rotation about an axis through that point ; this is, in fact, the theory of the " Resultant Axis " developed in Euler's and Lexell's memoirs of 1775. 211. The following properties are also given, viz., considering two similar solid bodies (or in particular any two positions of a solid body) and joining the corresponding points, the lines which pass through one and the same point form a cone of the second order ; and the points of either body form on this cone a curve of the third order (skew cubic). And, reciprocally, the lines, intersections of corresponding planes, which lie in one and the same plane envelope a conic, and such planes of either body envelope a developable surface, which is such that any one of these planes meets it in a conic [or, what is the same thing, the planes envelope a developable surface of the fourth order]. And also, given in space two equal bodies situate in any manner in respect to each other, then joining the points of the first body to the homologous points of the second body, the middle points of these lines form a body capable ON THE SPECIAL PROBLEMS OF DYNAMICS. 243 of an infinitesimal motion, each point of it along the line on which the same is situate. 212. The entire theory, as well of the infinitesimal as of the finite motions of a solid body, is carefully and successfully treated in Rodrigues' memoir " Des lois geornetriques &c." (1840). It may be remarked that for the purpose of compounding together any rotations and translations, each rotation may be resolved into a rotation about a parallel axis and a couple of rotations, that is, a translation ; the rotations are thus converted into rotations about axes through one and the same point, and these give rise to a single resultant rotation given as to its magnitude and the direction of the axis, but not as to the position of the axis (which is an arbitrary line in the given direction) ; the translations are then compounded together into a single translation, and finally the position of the axis of rotation is so determined that the translation shall be in the direction of this axis ; the entire system is thus compounded (in accordance with Chasles' theorem) into a rotation and a translation in the direction of the axis of the rotation. The problem of the composition depends therefore on the composition of rotations about axes through one and the same point ; that is, upon Euler's and Lexell's theory of the resultant axis. But, as already noticed, the analytical theory of the resultant axis was per- fected by Rodrigues in the present memoir (see ante, ' Transformation of Co- ordinates,' Nos. 139-141, as to this memoir and the quaternion representation of the formulae contained in it). 213. It was remarked in Poinsot's memoir of 1834 that every continuous motion of a solid body about a fixed point is the motion of a cone fixed in the body rolling upon another cone fixed in space. The corresponding theorem for the motion of a solid body in space is given Cayley, "On the Geometrical Representation &c. "(1846), viz. premising that a skew surface is said to be " deformed " if, considering the elements between consecutive generating lines as rigid, these elements be made in any manner to turn round and slide along the successive generating lines : — and that two skew surfaces can be made to roll and slide one upon the other, only if the one is a deformation of the other — and that then the rolling and sliding motions are perfectly determined — and that such a motion may be said to be a " gliding " motion : the theorem is that any motion whatever of a solid body in space may be represented as the gliding motion of one skew surface upon another skew surface of which it is the deformation. 214. The same paper contains the enunciation and analytical proof of the following theorem supplementary to that of Poinsot just referred to, viz. that when the motion of a solid body round a fixed point is represented as the rolling motion of one cone on another, then " the angular velocity round the line of contact (the instantaneous axis) is to the angular velocity of this line as the difference of the curvatures of the two cones at any point in this line is to the reciprocal of the distance of the point from the vertex." 215. There are a great number of theorems relating to the composition of forces and force-couples, which consequently relate also to infinitesimal rota- tions and translations. See, for instance, Chasles, " Theoremes generaux &c." (1847), Mobius, " Lehrbuch der Statik " (1837), Steichen's Memoirs of 1853 and 1854, &c. Arising out of some theorems of Mobius in the " Statik," we have Sylvester's theoiy of the involution of six lines : viz. six lines (given in position) may be such that properly selected forces along them (or if we please, properly selected infinitesimal rotations round them) will counter- balance each other ; or, what is the same thing, the six lines may be such that a system of forces, although satisfying for each of the six lines the con- e2 244 report— 1862. dition moraent=0, will not of necessity be in equilibrium ; such six lines are said to be in involution, and the geometrical theory is a very extensive and interesting one. Miscellaneous Problems. Article j^os. 21G to 223. 216. As under the foregoing head, " Rotation round a fixed point," I have considered only the case of a body not acted upon by any forces, the case where the body is acted upon by any forces comes under the present head. The forces, whatever they are, may be considered as disturbing forces, and the problem be treated by the method of the variation of the elements ; this is at any rate a separate part of the theory of rotation round a fixed point, and I have found it convenient to include it under the present head ; the only case in which the forces have been treated as principal ones, seems to be that of a heavy body (a solid of revolution) rotating about a point not its centre of gravity. The case of a body suspended by a thread or resting on a plane comes under the present head, as also would (in some at least of the questions connected with it) the gyroscope. But none of these questions are here considered in any detail. Rotation round a fixed point — Variation of the elements. 217. The forces acting on the body are treated as disturbing forces. Formulas for the variations of the elements were first obtained by Poisson in the memoir '• Sur la Variation des Constantes Arbitraires &c." (1809). The variations are expressed in terms of the differential coefficients of the disturb- ing function in regard to the elements, and, as the author remarks, they are very similar in their form to, and can be rendered identical with, those for the variations of the elements in the theory of elliptic motion. 218. Cayley, " On the Rotation &c." (1846).— The latter part of the paper relates to the variations of the elements therein made use of, which are different from the ordinary ones. 219. Richelot, " Eine neue Ldsung &c." (1851).— The form in which the integrals are obtained by means of a function V, satisfying a partial differen- tial equation, leads at once to a canonical system for the variations of the elements ; these formulas are referred to in the introduction to the memoir, but they are not afterwards considered. 220. Cayley, « On the Rotation of a Solid Body" (I860).— The elements are those ordinarily made use of, with only a slight variation occasioned by the employment of the " departure " of the node. The course of the investigation consists in obtaining the variations in terms of the differential coefficients of the disturbing function in regard to the coordinates (formulas which were thought interesting for their own sake), and in deducing therefrom those in terms of the differential coefficients in terms of the elements. Other cases of the motion of a solid body. 221. In regard to a heavy solid of revolution rotating about a fixed point not its centre of gravity, we have Poisson, " Memoire sur un cas particulier &c." (1831), and the elaborate memoir Lottner, "Reduction der Bewegung <fcc." (1855), where the solution is worked out by means of the Elliptic and Jacobian functions. 222. As regards a heavy solid suspended by a string, Pagani, " Memoire sur l'equilibre &c." (1839). 223. As regards the motion of a body resting on a fixed plane, ON THE SPECIAL PROBLEMS OF DYNAMICS. 245 Cournot, " Memoire sur le Mouvement &c." (1830 and 1832). Puiseux, "Du Mouvement &c." (1848). To -which several others might doubtless be added ; but the problems are so difficult, that the solutions cannot, it is probable, be obtained in any very complete form. In conclusion, I can only regret that, notwithstanding the time which has elapsed since the present Peport was undertaken, it is still — both as regards the omission of memoirs and works which should have been noticed, and the merely cursory examination of some of those which are mentioned — far from being as complete as I shoidd have wished to make it. To have reproduced, to any much greater extent than has been done, the various mathematical investigations, would not have been proper, nor indeed practicable ; at the same time, more especially as regards the subjects treated of in the second part of this Report, or say the kinematics and dynamics of a solid body, sxich a reproduction, incorporating and to some extent harmonizing the original researches, but without ignoring the points of view and methods of investi- gation of the several authors, would be a work which would well repay the labour of its accomplishment. List of Memoirs and Works. Ampere. Memoire sur quelques proprietes nouvelles des axes permanens de rotation des corps, et des plans directeurs de ces axes. 4to. Paris, 1823. . Memoire sur la Potation. Mem. de l'lnstitut, t. v. 1834. . Memoire sur les equations gene'rales du mouvement. Liouv. t. i. pp. 211-228 (1836). (Written 1826.) Anon. Note on the problem of falling bodies as affected by the earth's rota- tion. C. & D. M. J. t. hi. pp. 206-208 (1848). — . Pemarks on the deviation of falling bodies to the east and south of the perpendicular, and corrections of a previously published paper on the same subject. C. & D. M. J. t. iv. pp. 96-105 (1849). Baehr. Notice sur le mouvement du pendide ayant egard a la rotation de la terre. 4to. Middelbourg, 1853. Bertrand. Memoire sur l'inte'gration des equations diffe'rentielles de la Mecanique. Liouv. t. xvii. pp. 393-436 (1852). . Note sur le Gyroscope de M. Foucault. Liouv. t. i. 2 ser. (1856) pp. 379-382. Memoire sur quelques unes des formes les plus simples que puis- sent presenter les equations diffe'rentielles du mouvement d'un point materiel. Liouv. t. ii. 2 ser. (1857) pp. 113-140. Bessel. Analytische Auflosung der Keplerschen Aufgabe. Berl. Abh. 1816-17, pp. 49-55. (Pead July 1818.) i . Ueber die Entwickelung der Functionen zweier Winkeln u und u' in Peihen welche nach der Cosinussen und Sinussen der Vielfachen von u und v! fortgehen. Berl. Abh. 1820-21, pp. 56-60. (Pead June 1821.) Untersuchung des Theils der planetarischen Stbrungen welche aus der Bewegung der Sonne entsteht. Berl. Abh. 1824, pp. 1-52. Binet. Memoire sur la theorie des axes conjugues et des momens d'inertie des corps. Journ. Polyt. t. ix. (cah. 16) pp. 41-67 (1813). (Pead May . Note sur le mouvement du pendule simple en ayant e'gard a Tin- 246 report — 1862. fluence de la rotation diurne de la terre. Comptes Rendus, t. xxxii. (1851) pp. 157-160 & 197-205. Bonnet. Note sur tin the'oreme de Me'canique. Liouv. t. ix. p. 113 (1844), and Note iv. of t. ii. of the last edition of the Mec. Anal. pp. 329-331 (1855). Booth. Theory of Elliptic Integrals. 8vo. Lond. 1851. Bour. Memoire sur le probleme des trois corps. Journ. Polyt. t. xxi. (cah. 36) pp. 35-58 (1856). Bravais. Me'moire sur l'influence qu'exerce la rotation de la terre sur le mouvemeut d'un pendule a, oscillations coniques. Liouv. t. xix. pp. 1-50 (1854). . Note sur une formule de Lagrange relative au mouvemeut peudu- laire. Note vii. of t. ii. of the last edition of the Me'c. Anal. pp. 352-355 (1855). Briot. These sur le mouvement d'un corps solide autour d'un point fixe. Liouv. t. vii. pp. 70-84 (1842). Cauchy. Sur les momens d'inertie. Ex. de Math. t. i. pp. 93-103 (1827). . Resume d'un memoire sur la Mecanique Celeste et sur un nouveau calcul appele des limites. (Read at Turin Oct. 1831.) Exer. d'Anal. &c. t. ii. pp. 41-109 (1841). Cayley. On certain expansions in multiple sines and cosines. Camb. M. J. t. iii. pp. 162-167 (1842). . On the motion of rotation of a solid body. Camb. M. J. t. iii. pp. 224-232 (1842). On certain results relating to quaternions. Phil. Mag. t. xxvi. (1845) p. 141. On the geometrical representation of the motion of a solid body. C. <fc D. M. J. t. i. pp. 164-167 (1846). On the rotation of a solid body round a fixed point. C. & D. M. J. t. i. pp. 167-173 & 264-274 (1846). Note on a geometrical theorem in Prof. Thomson's memoir on the principal axes of a solid body. C. & D. M. J. t. i. pp. 207-208 (1846). On the application of quaternions to the theory of Rotation. Phil. Mag. t. xxxiii. (1848) p. 196. . Note on the motion of rotation of a solid of revolution. C.& D.M.J. t. iv. pp. 268-271 (1849). Sur les determinants gauches. Crelle, t. xxxviii. (1849) pp. 93-96. Note on the theory of Elliptic Motion. Phil. Mag. t. xi. (1856) pp. 425-428. A demonstration of Sir W. R. Hamilton's theorem of the Iso- chrouism of the Circular Hodograph. Phil. Mag. t. xiii. (1857) p. 427. Report on the recent progress of Theoretical Dynamics. Rep. Brit. Assoc, for 1857, pp. 1-42. On Lagrange's solution of the problem of two fixed Centres. Quart. Journ. M. J. t. ii. pp. 76-82 (1858). Note on the expansion of the true anomaly. Quart. M. J. t. ii. pp. 229-232 (1858). ON THE SPECIAL PROBLEMS OP DYNAMICS. 247 Cayley. Tables in the theory of Elliptic Motion. Mem. B. Astr. Soc. t. xxix. (1860) pp. 191-306. . A Memoir on the problem of the rotation of a solid body. Mem. B. Astr. Soc. t. xxix. (1860) pp. 307-342. On Lambert's theorem for Elliptic Motion. Monthly Not. R. Astr. Soc. t. xxii. pp. 238-242 (1861). Note on a theorem of Jacobi's in relation to the problem of three bodies. Monthly Not. E. Astr. Soc. t. xi. pp. 76-79 (1861). Chasles. Note sur les proprietes generales du systeme de deux corps sem- blables entr'eux et places d'une maniere quelconque dans l'espace, et sur le deplacement fini ou infim'ment petit d'un corps solide libre. (Eead Feb. 1831.) Bull. Univ. des Sciences (Eerussac), t. xiv. pp. 321-326. . Theoremes gene'raux sur les systemes de forces et leurs moments. Liouv. t. xii. pp. 213-224 (1847). Clairaut. Theorie de la Lune deduite du seul principe de l'attraction reci- proquement proportionnelle aux carres des distances. 4to. St. Pet. 1752, . and Paris, 1765. Cohen. On tbe Differential Coefficients and Determinants of Lines, and their Application to Theoretical Mechanics. Phil. Trans, t. 152 (1862), pp. 469-510. Cotes. Harmonia inensurarum sive analysis et synthesis per rationum et angulorum mensuras promotse ; accedunt alia opuscula mathematica. 4to. . Camb. 1722. Cournot. Memoire sur le mouvement d'un corps rigide soutenu par un plan fixe. Crelle, t. v. pp. 133-162 & 223-249 (1830) ; Suite, t. viii. pp. 1-12 (1832). Creedy. General and practical solution of Kepler's Problem. Quart. M. J. t. i. pp. 259-271 (1855). D'Alembert. Traite de Dynamique. Paris, 1743. . Eecherches sur la precession des equinoxes et sur la nutation de l'axe de la terre. Mem. de Berl. (1749). Desboves. These sur le mouvement d'un point materiel attire en raison inverse du carre des distances vers deux centres fixes. Liouv. t. xiii. pp. 369-396 (1848). Donkin. On an application of the calculus of operations to the transforma- tion of trigonometric series. Quart. M. J. t. ii. pp. 1-15 (1858). . On a class of Differential Equations, including those which occur in Dynamical Problems. Part I. Phil. Trans, t. cxliv. (1854) pp. 71-113 ; Part II. t. cxlv. (1855) pp. 299-358. Droop. On the Isochronism of the Circular Hodograph. Q. M. J. t. i. (1856) pp. 374-378. Dumas. Ueber die Bewegung des Eaumpendels mit Eucksicht auf die Eotation der Erde. CreUe, t. 1. pp. 52-78 & 126-185 (1855). Durege. Theorie der elliptischen Functionen. 8vo. Leipzig, 1861. (§ xx. reproduces some results on the spherical pendulum obtained in an unpub- lished memoir of 1849.) Euler. Determinatio Orbitae Cometee anni 1742. Misc. Berl. t. vii. (1743) p. 1. . Theoria motuum planetarum et cometarum. 4to. Berl. 1744. 248 report— 1862. Euler. De motu corporis ad duo virium centra attracti. Nov. Comm. Petrop. t, x. for 1764, pub. 1766, pp. 207-242. . Probleme : un corps etant attire en raison re'ciproque carree des dis- tances vers deux points fixes donnes, trouver les cas ou la courbe decrite par ce corps sera algebrique. Mem. de Berl. for 1760, pub. 1767, pp. 228-249. De motu corporis ad duo centra virium fixa attracti. Nov. Comm. Petrop. t. xi. for 1765, pub. 1767, pp. 152-184. Considerationes de motu corpomm coelestium. Nov. Comm. Petrop. t. x. for 1764, pub. 1766, pp. 544-558. De motu rectilineo trium corporum se mutuo attrahentium. Nov. Comm. Petrop. t. xi. for 1765, pub. 1767, pp. 144-151. De motu trium corporum se mutuo attrabentium super eadem linea recta. Nov. Acta Petrop. t. iii. (1776) p. 126-141. Problema algebraicum ob affectiones prorsus singulares memora- bile. Nov. Comm. Petrop. t. xv. (1770) p. 75; Comm. Aritb. Coll. t. i. pp. 427-443. Formulae generales pro translation© quacunque corporum rigi- dorum. Nov. Comm. Petrop. t. xx. 1775, pp. 189-207. Nova metbodus motum corporum rigidorum determinandi. Nov. Comm. Petrop. t. xx. (1775) pp. 208. Rechercbes sur la precession des equinoxes et sur la nutation de l'axe de la terre. Mem. de Berl. t. v. for 1749, pub. 1751, pp. 326-338. (Euler mentions, t. vi., tbat tbis was written after he had seen D'Alem- bert's memoir.) Decouverte d'un nouveau principe de Mecanique. Mem. de Berl. t. vi. for 1750, pub. 1752, pp. 185-217. Eecherches sur la connaissance mecanique des corps. Me'm. de Berl. for 1758, pub. 1767, pp. 132-153. Du mouvement de rotation des corps solides autour d'une axe variable. Mem. de Berl. for 1758, pub. 1765, pp. 154-193. Du mouvement d'un corps solide lorsqu'il tourne autour d'une axe mobile. Mem. de Berl. for 1760, pub. 1767, pp. 176-227. Tbeoria motus corporum solidorum. 4to. Rostock, 1765. Foucault. Demonstration physique du mouvement de rotation de la terre an moyen du pendule. Comptes Rendus, t. xxxii. (1851) pp. 135-138. Gauss. Fundamental-Gleichungen fur die Bewegung schwerer Korper auf der rotirenden Erde, 1804. • . Theoria motus corporum coelestium. 4to. Hamb. 1809. Greatheed. Investigation of the general term of the expansion of the true anomaly in terms of the mean. Camb. M. J. t. i. pp. 228-232 (1838). Gudermann. De pendulis sphsericis et de curvis quae ab ipsis describuntur sphaericis. Crelle, t. xxxviii. pp. 185-215 (1849). Hamilton, Sir W. R. A theorem of anthodographic isochronism. Proc. R. Irish Acad. 1847, t. iii. pp. 465-466. . Lectures on Quaternions. 8vo. Dublin, &c. (1853). Hansen. Fundamenta Nova investigationis orbitae verae quam Luna per- lustrat. 4to. Gothte, 1838. . Ermittelung der absoluten Storungen in Ellipsen von beliebigen Excentricitat und Neigung. Gotha, 1843, pp. 1-167. ON THE SPECIAL TROBLEMS OF DYNAMICS. 249 Hansen. Entwickclung des Products einer Potenz des Eadius-Yectors mit dem Sinus odcr Cosinu seines Vielfachen der wahren Anomalie in Reihen die nach den Sinussen oder Cosinussen der Vielfachen der wahren excen- trischen oder mittleren Anomalie fortschreiten. Abh. d. K. Sachs. Ges. zu Leipzig, t. ii. pp. 183-281 (1853). . Entwickclung der negativen und ungeraden Potenzen der Qua- dratwurzel der Function r 2 +r' a — 2rr' (cos U cos TJ' + sin U sin U' cos J). Abh. d. K. Sachs. Ges. zu Leipzig, pp. 286-376 (1854). . Theorie der Pendelbewegung- 4to. Dantzig. 1856. Haton de la Goupilliere. Meinoire sur une the'orie nouvelle de la ge'ometrie des masses. Journ. Polyt. t. xxi. (cah. 37) 1858, l r Memoire, pp. 35- 72 ; 2d Memoire, pp. 73-96. Haughton. On the rotation of a solid body round a fixed point, being an account of the late Professor Maccullagh's lectures on that subject, Hilary Term, 1S44, in Trinity College, Dublin ; compiled by the Rev. S. Haugh- ton. Trans. E. Irish Acad. t. xxii. (1849) pp. 1-18. Jacobi. Euleri formulas de transformatione coordinataruni. Crelle, t. ii. pp. 188-189 (1827). . Zur Theorie der Variations-Rechnung und der Differentiel- Gleichungen. Crelle, t. xvii. (1837) pp. 68-82. Formulae transformationis intcgralium definitorum. Crelle, t. xv. pp. 1-26 (1836). . De motu puncti singularis. Crelle, t. xxiv. pp. 5-27 (1842). Elimination des nceuds dans le probleme des trois corps. Crelle, t. xxvi. (1843) pp. 115-131. Theoria novi multiplicatoris systemati aequationum diiferentialium vulgariuin applicandi (§26, two centres). Crelle, t.xxix. pp. 333-337 (1845). Sur la rotation d'un corps. Extrait d'une lettre adressee a l'Aca- demie des Sciences. Comptes Rendus, t. xxix. p. 97 ; and Liouv. t. xiv. pp. 337-344 (1849). (With addition containing the demonstration of the formulae.) Crelle, t. xxxix. pp. 293-350 (1850). Nora methodus cequationes differentiales partiales primi ordinis inter numerum variabilium quenicunque propositas integrandi (posthumous, edited by A. Clebsch). Crelle, t. lx. pp. 1-181 (1862). Lagrange. Mecanique Analytique. 1st ed. 1788 ; 2nd ed. t. i. 1811 ; t. ii. 1815 ; 3rd ed. 1855. . Sur une maniere particuliere d'exprimer le temps dans les sections coniques decrites par des forces tendantes au foyer et reciproquement proportionnelles aux carres des distances. Mem. de Berlin for 1778; and Note Y. of t. ii. of the 3rd edition of the Mec. Anal. pp. 332-349. Recherches sur le mouvement d'un corps qui est attire vers deux centres fixes. Premier Memoire, ou l'on suppose que 1' attraction est en raison inverse des carres des distances. Anc. Mem. de Turin, t. iv. (1766- 1769) pp. 118-215. Second Memoire, ou l'on applique la methode pre'cedente a differentes hypotheses d' attraction. Anc. Mem. de Turin, t. iv. (1766- 1769) pp. 215-243. Lagrange. Nouvelle solution du probleme du mouvement de rotation d'un corps. Mem. de Berl. for 1773. 250 report— 1862. Lambert. Insigniores Orbite Cometarum Proprietates. 8vo. Aug. 1765. Laplace. Mecanique Celeste, t. i. 1799 ; t. ii. 1799 ; t. iii. 1802 ; t. iv. 1805 ; t. v. 1823. . Memoire sur le developpement de l'anomalie vraie et du rayon vecteur elliptique en series ordonnees suivant les puissances de l'excen- tricite. Mem. de l'Inst. t. vi. (1823) pp. 63-80. Lefort. Expressions numeriques des integrates definies qui se presentent quand on cberche les termes generaux des developpements des coordonnes d'un planete dans son mouvement elliptique. Liouv. t. xi. pp. 142-152 (1846). Legendre. Exercices de Calcul Integrate, t. ii. (containing tbe dynamical applications) 1817. . Traite des Eonctions Elliptiques, t. i. (1825) (but tbe dynamical applications are for the most part reproduced from tbe Exercices). Leverrier. Annales de l'Observatoire de Paris, t. i. (1855). Lexell. Theoremata nonnulla generalia de translatione corporum rigidorum. Nov. Comm. Petrop. t. xx. (1775) pp. 239-270. Liouville. Sur Vmtegv&le J cos i (u— x sin.u) du. Liouv. t. vi. pp. 36-37 • (1841). ° . Extrait d'un memoire sur un cas particulier du probleme de trois corps. Liouv. t. vii. pp. 110-113 (1842). Sur quelques cas particuliers ou les equations du mouvement d'un point materiel peuvent l'integrer. 3 Memoirs. Liouv. t. xi. pp. 345-379 (1846), t. xii. pp. 410-44 (1847), and t. xiv. pp. 257-300 (1849). Memoire sur un cas particulier du probleme de trois corps. Conn. des Temps for 1845, and Liouv. t. i. (2 ser.) pp. 248-256 (1842). Note ajoutee au memoire de M. Serret (two revolving centres). Liouv. t. xiii. pp. 34-37 (1848). Lottner. Eeduction der Bewegung eines scbweren um einen festen Punct rotirenden Kevolutions-Kbrpers auf die elliptiscben Transcendenten. Crelle, t. 1. pp. 111-125 (1855). . Zur Tbeorie des Foucaultscben Pendelversuchs. Crelle, t. Iii. pp. 52-58 (1856). Maccullagh, see Haughton. Mobius. Leber die Zusammensetzung unendlicb kleiner Drehungen. Crelle, t. xviii. pp. 189-212 (1838). Der barycentrische Calcul. Svo. Leipzig, 1827. . Lehrbuch der Statik. Svo. Leipzig, 1837. •. Die Elemente der Mechanik des Himmels. 8vo. Leipzig, 1843. Newton (Sir Isaac). Philosophise Naturalis Principia Mathematica. 4to. London, 1687. Pagani. Demonstration d'un theort-me de Lambert. Crelle, t. xv. pp. 350- 352 (1834). . Memoire sur l'equilibre d'un corps solide suspendu a un cordon flexible. Crelle, t. xxix. pp. 185-204 (1839). Painvin. Eecherches du dernier multiplicateur pour deux formes speciales et remarquables des equations differentielles du probleme de trois corps. Liouv. t. xix. pp. 88-111 (1854). Poinsot. Memoire sur la rotation. Extrait, 8vo. Paris, 1834. ON THE SPECIAL PROBLEMS OF DYNAMICS. 251 Poinsot. Theorie nouvelle de la rotation des corps. Liouv. t. xvi. pp. 9- 130 & 289-236 (1851). . Theorie des cones circulaires roulants. Liouv. t. xviii. pp. 41-70 (1853). Questions dynamiques sur la percussion des corps. Liouv. t. ii. (2 ser.) pp. 281-329 (1859). Poisson. Traite de Mecanique. 1 ed. Paris, 1811 ; 2 ed. Paris, 1833. . Me'moire sur un cas particulier du moxivement de rotation des corps graves. Journ. Polyt. t. ix. (cah. 16) pp. 247-262 (1813). Sur une nouvelle maniere d'exprimer les coordonnes des planetes dans le mouvement elliptique. Conn, des Temps for 1825, pp. 379-386. Sur la developpement des coordonnes d'une planete dans son mouvement elliptique et de la fonction perturbative de ce mouvement. Conn, des Temps for 1836, pp. 3-31. Me'moire sur le mouvement d'un corps solide (read 1834). Mem. de Tlnst. t. xiv. pp. 275-432 (1838). Sur le mouvement des projectiles en ayant egard a, la rotation de la terre. Journ. Polyt. t. xvi. pp. 1-68 (1838). Memoire sur le mouvement des projectiles dans Pair, en ayant egard a leur rotation. Journ. Polyt. pp. 69-176 (1838). Prony. Analyse detaillee des differentes questions qui se rapportent au mouvement d'un corps sollicite par des puissances quelconques. Journ. Polyt. t. iv. (cah. 11) pp. 87-143 (1802). Puiseux. Note sur le mouvement d'un point materiel pesant sur une sphere. Liouv. t. vii. pp. 517-520 (1842). . Du mouvement d'un solide de revolution pose sur un plan hori- zontal. Liouv. t. xiii. pp. 249-256 (1848). Sur la convergence des series qvri se presentent dans la theorie du mouvement elliptique des planetes. Liouv. t. xiv. pp. 33-39 (1849). Seconde Note sur la convergence des series du mouvement ellip- tique. Liouv. t. xiv. pp. 247-248 (1849). Solution de quelques questions relatives au mouvement d'un corps solide pesant pose sur un plan horizontal. Liouv. t. xvii. pp. 1-30 (1852). Sur la convergence des series ordonnees suivant les puissances de l'excentricite qui se presentent dans la theorie du mouvement elliptique. Mec. Anal. 3 ed. t. ii. (Note I.) pp. 313-317 (1855). duet. Des mouvements relatifs en general, et specialement des mouvements relatifs sur la terre. Liouv. t. xviii. pp. 213-298 (1853). Richelot. Bemerkung iiber einen Fall der Bewegung eines systems von materiellen Puncten. Crelle, t. xl. pp. 178-182 (1850). . Auszug eines Schreibens am Herrn Prof. Jacobi. Crelle, t. xlii. pp. 32-34 (1851). Bemerkungen zur Theorie des Raumpendels. Crelle, t. xlii. pp. 233-238 (1853). Eine neue Losung des Problems der Rotation eines festen Korpers um einen Punct. (Auszug einer zu Berlin, 1851, erschienenen Schrift.) Crelle, t. xliv. pp. 60-65. Rodrigues. Des lois geom etriques qui regissent les deplacements d'un systeme solide dans l'espace, et de la variation des coordonnes provenants de ces 252 report — 1862. de'placements considerees inde'pendamment des causes qui peuvent les pro- duire. Liouv. t. iii. pp. 380-440 (1840). Rueb. Specimen inaugurale de motu gyratorio corporis rigidi nulla vi acceleratrice sollicitati. Utrecht, 1834. Schellbach. Mathematische Miszellen. No. I.-IV. Ueber die Bewegung eines Puncts der von einem festen Puncte angezogen wird. Crelle, t. xlv. pp. 255-266 (1853). Schubert. Astronomic The'orique. 4to. St. Pet. (1822). Segner. Specimen theorioe turbinum. 4to. Halse, 1755. Serret. These sur le mouvement d'un point attire par deux centres fixes en raison inverse du earre des distances. Liouv. t. xiii. pp. 17-33 (1848). . Sur la solution particutiere que peut admettre le probleme du mouvement d'un corps attire vers deux centres fixes par des forces reci- proquement proportionnelles aux carres des = distances. Note iii. to t. ii. of the 3rd ed. of tbe Mec. Anal. pp. 327-331 (1855). Sohncke. Motus corporum ccelestium in medio resistente. Crelle, t. x. pp. 23-40 (1833). Somoff. Demonstration des formules de M. Jacobi relatives a la theorie de la rotation d'un corps solide. Crelle, t. xlii. pp. 95-116 (1851). Stader. De orbitis et motibus puncti cujusdam corporei circa centrum at- tractivum aliisquani Neutoniana attractionis legibus sollicitati. Crelle, t. xlvi. pp. 262-327 (1852). Steichen. De la propriete fondamentale du mouvement cycloidal, et de sa liaison avec le principe de la composition des mouvements de rotation autour des axes paralleles et des axes qui se coupent. Crelle, t. xlvi. pp. 24-42 (1853). . . Memoire sur la question re'ciproque du centre de percussion. Crelle, t. xlviii. pp. 1-68 (1854). Memoire de Mecanique relatif au mouvement de rotation et au mouvement naissant des corps solides. Crelle, t. xliii. pp. 161-244 (1852), and Addition do. t. xliv. pp. 43-46 (1853). Sylvester. Sur l'involution des lignes droites daus l'espace conside'rces comme des axes de rotation. Comptes Rendus, t. Iii. (1861) p. 741. . Note sur l'involution de six lignes dans l'espace. Comptes Rendus, t. hi. (1861) p. 815. Thomson. On the principal axes of a solid body. C, & D. M. J. t. i. pp. 127-133 & 195-206 (1846). Tissot. These de Mecanique. Liouv. t. xvii. pp. 88-116 (1852). Townsend. On the principal axes of a solid body, their moments of inertia and distribution in space. C. & D. M. J. t. i. pp. 209-227, and t. ii. pp. 19-42, 140-171 & 241-251 (1846-47). Walton. Instantaneous lines and planes in a body revolving round a fixed point. C. & D. M. J. t. vii. pp. 111-113 (1852). Whewell. A Treatise on Dynamics. 1 ed. Cambridge, 1823. Worms. The Earth and its Mechanism — being an account of the various proofs of the rotation of the Earth, with a description of the instruments used in the experimental demonstrations : to which is added the theoiy of Eoucault's Pendulum and Gyroscope. 8vo. London, 1862. ON DOUBLE REFRACTION. 253 Report on Double Refraction. By Gr.G. Stokes, M.A.,D.C.L.,Sec.R.S., Lucasian Professor of Mathematics in the University of Cambridge. I regret to say that in consequence of other occupations the materials for a complete report on Physical Optics, which the British Association have re- quested me to prepare, are not yet collected and digested. Meanwhile, instead of requesting longer time for preparation, I have thought it would be well to take up a single branch of the subject, and offer a report on that alone. I have accordingly taken the subject of double refraction, having mainly in view a consideration of the various dynamical theories which have been advanced to account for the phenomenon on the principle of transversal vibra- tions, and an indication of the experimental measurements which seem to me most needed to advance this branch of optical science. As the greater part of what has been done towards placing the theory of double refraction on a rigorous dynamical basis is subsequent to the date of Dr. Lloyd's admirable report on " Physical Optics," I have thought it best to take a review of the whole subject, though at the risk of repeating a little of what is already con- tained in that report. The celebrated theory of Presnel was defective in rigour in two respects, as Presnel himself clearly perceived. The first is that the expression for the force of restitution is obtained on the supposition of the absolute displacement of a molecule, whereas in undulations of all kinds the forces of restitution with which we are concerned are those due to relative displacements. Presnel endeavoured to show, by reasoning professedly only probable, that while the magnitude of the force of restitution is altered in passing from absolute to rela- tive displacements, the law of the force as to its dependence on the direction of vibration remains the same. The other point relates to the neglect of the com- ponent of the force in a direction perpendicular to the front of a wave. In the state of things supposed in the calculation of the forces of restitution called into play by absolute displacements, there is no immediate recognition of a wave at all, and a molecule is supposed to be as free to move in one direction as in another. But a displacement in a direction perpendicular to the front of a wave would call into play new forces of restitution having a resultant not in general in the direction of displacement ; so that even the component of the force of restitution in a direction parallel to the front of a wave would have an expression altogether different from that determined by the theory of Fresnel. But the absolute displacements are only considered for the sake of obtaining results to be afterwards applied to relative displacements ; and Fresnel distinctly makes the supposition that the ether is incompressible, or at least is sensibly so under the action of forces comparable with those with which we are concerned in the propagation of light. This supposition re- moves the difficulty ; and though it increases the number of hypotheses as to the existing state of things, it cannot be objected to in point of rigour, unless it be that a demonstration might be required that incompressibility is not in- consistent with the assumed constitution of the ether, according to which it is regarded as consisting of distinct material points, symmetrically arranged, and acting on one another with forces depending, for a given pair, only on the distance. Hence the neglect of the force perpendicular to the fronts of the waves is not so much a new defect of rigour, as the former defect appear- ing under a new aspect. I have mentioned these points because sometimes they are slurred over, and Fresnel's theory spoken of as if it had been rigorous throughout, to the injury of students and the retardation of the real progress of science ; and 254 HEPORT 1862. sometimes, on the other hand, the grand advance made by Fresnel is depre- ciated on account of his theory not being everywhere perfectly rigorous. If we reflect on the state of the subject as Fresnel found it, and as he left it, the wonder is, not that he failed to give a rigorous dynamical theory, but that a single mind was capable of effecting so much. The first deduction of the laws of double refraction, or at least of an ap- proximation to the true laws, from a rigorous theory is due to Cauchy*, though Neumann t independently, and almost simultaneously, arrived at the same results. In the theory of Cauchy and Neumann the ether is supposed to consist of distinct particles, regarded as material points, acting on one another by forces in the line joining them which vary as some function of the distances, and the arrangement of these particles is supposed to be dif- ferent in different directions. The medium is further supposed to possess three rectangular planes of symmetry, the double refraction of crystals, so far as has been observed, being symmetrical with respect to three such planes. The equations of motion of the medium are deduced by a method similar to that employed by Navier in the case of an isotropic medium. The equations arrived at by Cauchy, the medium being referred to planes of symmetry, contain nine arbitrary constants, three of which express the pressures in the principal directions in the state of equilibrium. Those employed by Neumann contain only six such constants, the medium in its natural state being sup- posed free from pressure. In the theory of double refraction, whatever be the particular dynamical conditions assumed, everything is reduced to the determination of the velocity of propagation of a plane wave propagated in an)' given direction, and the mode of vibration of the particles in such a wave which must exist in order that the wave may be propagated with a unique velocity. In the theory of Cauchy now under consideration, the direction of vibration and the reciprocal of the velocity of propagation are given in direction and magnitude respec- tively by the principal axes of a certain ellipsoid, the equation of which con- tains the nine arbitrary constants, and likewise the direction-cosines of the wave-normal. Cauchy adduces reasons for supposing that the three constants G, H, I, which express the pressures in the state of equilibrium, vanish, which leaves only six constants. For waves perpendicular to the principal axes, the squared velocities of propagation and the corresponding directions of vibration are given by the following Table : — Wave-normal X y a Direction of vibra- , r cc L E Q y E M P % Q P N For waves in these directions, then, the vibrations are either wholly normal or wholly transversal. The latter are those with which we have to deal in the theory of light. Now, according to observation, in any one of the prin- cipal planes of a doubly refracting crystal, that ray which is polarized in the principal plane obeys the ordinary law of refraction. In order therefore that the conclusions of this theory should at all agree with observation, we must * Memoires de l'Aeademie, torn. x. p. 293- t PoggendorlFs Aumlen, vol. xxv. p. 418 (1832). ON DOUBLE REFRACTION. 255 suppose that in polarized light the vibrations are parallel, not perpendicular, to the plane of polarization. Let I, m, n be the direction-cosines of the wave-normal. In the theory of Cauchy and Neumann, the square v 2 of the velocity of propagation is given by a cubic of the form v' + ay + a^ + a^O, where a 2 , a 4 , a 6 are homogeneous functions of the 1st order as regards L, M, N, P, Q, E, and homogeneous functions of the orders 2, 4, 6 as regards I, m, n, involving even powers only of these quantities. For a wave perpen- dicular to one of the principal planes, that of y z suppose, the cubic splits into two rational factors, of which that which is of the first degree in v 2 , namely, v 2 -m 2 ~R— n 2 Q, corresponds to vibrations perpendicular to the principal plane. This is the same expression as results from Fresnel's theory, and accordingly the section, by the principal plane, of one sheet of the wave-surface, which in this theory is a surface of three sheets, is an ellipse, and the law of refraction of that ray which is polarized perpendicularly to the principal plane agrees exactly with that given by the theory of Fresnel. _ For the two remaining waves, the squared velocities of propagation are given by the quadratic (v 2 -m 2 M-ii 2 P) (i; 2 -m J P-,i ! N)-4»)i 2 « 2 P 2 =0 ; (1) but according to observation the ray polarized in the principal plane obeys the ordinary law of refraction. Hence (1) ougbt to be satisfied by v 2 — (m 2 + OP=0, which requires that (M-P) (N-P)=4P 2 , on which supposition the remaining factor must evidently be linear as regards m 2 , n 2 , and therefore must be v 2 -m 2 ~K—n 2 ~N, since it gives when equated to zero v 2 = M, or v 2 = N for m = 1, or n = 1 . And since the same must hold good for each of the principal planes, we must have the three following relations between the six constants, (H-P)(N-P) = 4P 2 ; (N-Q)(L- Q) = 4Q 2 ; (L-E)(M-E) = 4E 2 . . . (2) The existence of six constants, of which only three are wanted to satisfy the numerical values of the principal velocities of propagation in a biaxal crystal, permits of satisfying these equations ; so that the law that the ray polarized in the plane of incidence, when that is a principal plane, obeys the ordinary law of refraction is not inconsistent with Cauchy's theory. This simple law is, however, not in the slightest degree predicted by the theory, nor even rendered probable, nor have any physical conditions been pointed out which would lead to the relations (2) ; and, indeed, from the form of these equations, it seems hard to conceive what physical relations they could express. Hence an important desideratum would be left,' even if the theory were satisfactory in all other respects. The equation for determining v 2 virtually contains the theoretical laws of double refraction, which are embodied in the form of the wave-surface. The Avave-surface of Cauchy and Neumann does not agree with that of Fresnel, except as the sections of two of its sheets by the principal planes, the third sheet being that which relates to nearly normal vibrations. Nevertheless the first two sheets, being forced to agree in their principal sections with Fres- nel's surface, differ from it elsewhere extremely little. In Arragonite, for instance, in a direction equally inclined to the principal axes, assuming Eud- 256 report — 1862. berg's indices* for the line D, I find that the velocities of propagation of the two polarized wares, according to the theory of Cauchy and Neumann, differ from those resulting from the theory of Fresnel only in the tenth place of decimals, the velocity in air being taken as unity. Such a difference as this would of course be utterly insensible in experiment. In like manner the directions of the planes of polarization according to the two theories, though not rigorously, are extremely nearly the same, the plane of polarization of a wave in which the vibrations are nearly transversal being defined as that containing the direction of propagation and the direction of vibration, in har- mony with the previously established definition for the case of strictly trans- versal vibrations. Hence as far as regards the laws of double refraction of the two waves which alone are supposed to relate to the visible phenomenon, and of the accompanying polarization, this theory, by the aid of the forced relations (2), is very successful. I am not now discussing the generality, or, on the con- trary, the artificially restricted nature, of the fundamental suppositions as to the state of things, but only the degree to which the results are in accordance with observed facts. But as regards the third wave the case is very different. That theory should point to the necessary existence of such a wave consisting of strictly normal vibrations, and yet to which no known phenomenon can be referred, is bad enough ; but in the present theory the vibrations are not even strictly normal, except for waves in a direction perpendicular to any one of the principal axes. In Iceland spar, for instance, for waves propagated in a direction inclined 45° to the axis, it follows from the numerical values of the refractive indices for the fixed line D given by Rudberg that the two vibrations in the principal plane which can be propagated independently of each other are inclined at angles of 9° 50' and 80° 10', or say 10° and 80°, to the wave-normal. We can hardly suppose that a mere change of inclination in the direction of vibration of from 10° to 80° with the wave front makes all the difference whether the wave belongs to a long-known and evident pheno- menon, no other than the ordinary refraction in Iceland spar, or not to any visible phenomenon at all. It is true that before there can be any question of the third wave's being perceived it must be supposed excited, and the means of exciting it consist in the incident vibrations in air, which by hypothesis are strictly transversal. Hence we have to inquire whether the intensity of the third wave is such as to lead us to expect a sensible phenomenon answering to it. This leads us to the still more uncertain subject of the intensity of light reflected or refracted at the surface of a crystal — more uncertain because it not only depends on the laws of internal propagation, and involves all the hypotheses on which these laws are theoretically deduced, but requires fresh hypotheses as to the state of things at the confines of two media, introducing thereby fresh elements of uncertainty. But for our present purpose no exact calculation of intensities is required ; a rough estimate of the intensity of the nearly normal vibrations is quite sufficient. In order to introduce as little as possible relating to the theory of the in- tensity of reflected and refracted fight, suppose the incident light to fall per- pendicularly on the surface of a crystal, and let this be a surface of Iceland spar cut at an inclination of 45° to the axis. For a cleavage plane the result would be nearly the same. Let the incident fight be polarized, and the vibrations be in the principal plane, which therefore, according to the theory * Annales de Chimie, toin. xlviii. p. 254 (1831). ON DOUBLE REFRACTION. 257 now under consideration, must be the plane of polarization. The incident vibrations are parallel to the surface, and accordingly inclined at angles of 9° 50' and 80° 10' to the directions of the nearly transversal and nearly nor- mal vibrations, respectively, within the crystal. Hence it seems evident that the amplitude of the latter must be of the order of magnitude of sin 9° 50', or about i the amplitude of vibration in the incident light being taken as unity. The velocity of propagation of the nearly normal vibrations being to that of the nearly transversal roughly as \^3 to 1, as will immediately be shown, it follows that the vis viva of the nearly normal would be to that of the nearly transversal vibrations in a ratio comparable with that of \Z3xsin 2 9° 50' to 1, or about ^ to 1. Hence the intensity of the nearly normal vibrations is by no means insignificant, and therefore it is a very serious objection to the theory that no corresponding phenomenon should have been discovered. It has been suggested by some of the advocates of this theory that the normal vibrations may correspond to heat. But the fact of the polarization of heat at once negatives such a supposition, even without insisting on the accumulation of evidence in favour of the identity of radiant heat and light of the same refrangibility. But the objections to the theory on the ground of the absence of some un- known phenomenon corresponding with the third ray, to which the theory necessarily conducts, are not the only ones which may be urged against it in connexion with that ray. The existence of normal or nearly normal vibra- tions entails consequences respecting the transversal which could hardly fail to have been detected by observation. In the first place, the vis viva belong- ing to the normal vibrations is so much abstracted from the transversal, which alone by hypothesis constitute light, so that there is a loss of light inherent in the very act of passage from air into the crystal, or conversely, from the crystal into air. About -^th of the whole might thus be expected to be lost at a single surface of Iceland spar, the surface being inclined 45° to the axis, and the light being incident perpendicularly, and being polarized in the prin- cipal plane ; and the loss would amount to somewhere about ^th in passage across a plate bounded by parallel surfaces, by which amount the sum of the reflected and transmitted light ought to fall short of the incident. And it is evident that something of the same kind must take place at other inch- nations to the axis and at other incidences. The loss thus occasioned in mul- tiplied reflexions could hardly have escaped observation, though it is not quite so great as might at first sight appear, as the transversal vibrations produced back again by the normal would presently become sensible. But the most fatal objection of all is that urged by Green* against the supposition that normal vibrations could be propagated with a velocity com- parable with those of transversal. As transversal vibrations are capable (according to the suppositions here combated) of giving rise at incidence on a medium to normal or nearly normal vibrations within it, so conversely the latter on arriving at the second surface are capable of giving rise to emergent transversal vibrations ; so that not only would normal vibrations entail a loss of light in the quarter in which light is looked for, but would give rise to light (of small intensity it is true, but by no means imperceptible) iu a quar- ter in which otherwise there would have been none at all. Thus in the case supposed above, the intensity of the light produced by nearly normal vibra- tions giving rise on emergence to transversal vibrations would be somewhere about the (- a l 8 ) 2 or the -^^ of .the incident light. In the case of light trans- * Cambridge Philosophical Transactions, vol. vii. p. 2. 1862. s 258 REPORT 1862. mitted through a plate, the rays thus produced would be parallel to the inci- dent, or to the emergent rays of the kind usually considered ; but if the plate were wedge-shaped the two would come out in different directions, and with sunlight the former could not fail to be perceived. The only way apparently of getting over this difficulty, is by making the perfectly gratuitous assumption that the medium, though perfectly transparent for the more nearly transversal vibrations, is intensely opaque for those more nearly normal. Lastly, Green's argument respecting the necessity of supposing the velocity of propagation of normal vibrations very great has here full force as an objection against this theory. The constants P, Q, R are the squared reci- procals of the three principal indices of refraction, which are given by obser- vation, and L, M, N are determined in terms of P, Q, R by the equations (2), by the solution of a quadratic equation. In the case of a uniaxal crystal everything is symmetrical about one of the axes, suppose that of z, which requires, as Cauchy has shown, that L=M=3R, and P=Q; and of the equations (2) one is now satisfied identically, and the two others are identical with each other, and give 4P 2 ^3R-P For an isotropic medium we must have L=M=N=3P=3Q=3R, and the three equations (2) are satisfied identically. The velocity of propagation of normal must be to that of transversal vibrations as \/3 to 1, and cannot therefore be assumed to be what may be convenient for explaining the law of intensity of reflected light. The theory which has just been discussed is essentially bound up with the supposition that in polarized light the vibrations are parallel, not perpendicu- lar, to the plane of polarization. In prosecuting the study of light, Cauchy saw reason to change his views in this respect, and was induced to examine whether his theory could not be modified so as to be in accordance with the latter alternative. The result, constituting what may be called Cauchy's second theory, is contained in a memoir read' before the Academy, May 20, 1839*. In this he refers to his memoir on dispersion, in which the funda- mental equations are obtained in a manner somewhat different from that given in his ' Exercices,' but based on the same suppositions as to the constitution of the ether. In the new theory Cauchy retains the three constants G, H, I, expressing the pressures in equilibrium, which formerly he made vanish, the medium being supposed as before to be symmetrical with respect to three rectangular planes. The squares of the velocities of propagation, and the corresponding directions of vibration for the three waves which can be pro- pagated in the direction of each of the principal axes, are given by the fol- lowing Table. ,v y c Direction of vibra- 1 so L + G R+H Q+I y R+G M+H P+I L JV Q+G P+H W+I * "Sur la Polarisation rectUigne, et la double Refraction," Mem. de l'Acadeniie, torn, xviii. p. 153. ON DOUBLE REFRACTION. 259 According to observation, in each of the principal planes the ray polarized in that plane obeys the ordinary law of refraction, and therefore if we suppose that in polarized light the vibrations, at least when strictly transversal, are perpendicular to the plane of polarization, we must assume that R-f-H=(J4-I, P + I=R+G, Q+G=P + H, which are equivalent to only two distinct rela- tions, namely P_G=Q-H=R-I (3) For a wave parallel to one of the principal axes, as that of x, the direction of that axis is one of the three rectangular directions of vibration of the waves which are propagated independently. For such vibrations the velocity (v) of propagation is given by the formula v 2 = m 2 (R + H) + n 2 (Q + 1), which by (3) is reduced to i> 2 =R+H=Q+I, so that on the assumption that the velocity of propagation is the same for a wave perpendicular to the axis of y as for one perpendicular to the axis of z when the vibrations are parallel to the axis of x, the law of ordinary re- fraction in the plane of yz follows from theory. For the two remaining waves which can be propagated independently in a given direction perpendicular to the axis of x, the vibrations are only approxi- mately normal and transversal respectively. In fact, for the three waves which can travel independently in any given direction, the directions of vibra- tion are not affected by the introduction of the constants expressing equili- brium-pressures, but only the velocities of propagation. The squares of the velocities of propagation of the two waves above mentioned are given as be- fore by a quadratic ; and in order that the velocity of propagation of the nearly transversal vibrations may be expressed by the formula v 2 =c 2 m 2 + b 2 n 2 (4), in conformity with the ellipsoidal form of the extraordinary wave surface in a uniaxal crystal, and the assumed elliptic form of the section of one sheet of the wave-surface in a biaxal crystal by a principal plane, the quadratic in question must split into two rational factors, which leads to precisely the same condition as before, namely that expressed by the first of equations (2) ; and by equating to zero the corresponding factor, we get ^ 2 =(P + H)m 2 + (P + I)»i 2 , which is in fact of the form (4). Applying the same to each of the other principal axes, we find again the three relations (2). Hence Cauchy's second theory, in which it is supposed that in polarized light the vibrations (in air or in an isotropic medium) are perpendicular to the plane of polarization, leads like the first to laws of double refraction, and of the accompanying polarization, differing from those of Fresnel only by quantities which may be deemed insensible. This result is, however, in the present case only attained by the aid of two sets of forced relations, namely (2) and (3), that is, relations which there is nothing a priori to indicate, and which are not the expression of any simple physical idea, but are obtained by forcing the theory, which in its original state is of a highly plastic nature from the number of arbitrary constants which it contains, to agree with observation in some particulars, which being done, theory by itself makes known the rest. As regards the third ray by which this theory like its pre- decessor is hampered, there is nearly as much to be urged against the present theory as the former. There is, however, this difference, that, as there are only five relations, (2) and (3), between nine arbitrary constants, there remains s 2 260 report — 1862. one arbitrary constant in the expressions for the velocities of propagation after satisfying the numerical values of the three principal indices of refrac- tion, by a proper disposal of which the objections which have been mentioned may to a certain extent be lessened, but by no means wholly overcome. I come now to Green's theory, contained in a very remarkable memoir " On the Propagation of Light in Crystallized Media," read before the Cambridge Philosophical Society, May 20, 1839*, and accordingly, by a curious coinci- dence, the very day that Cauchy's second theory was presented to the French Academy. Besides the great interest of the memoir in relation to the theory of light, Green has in it, as I conceive, given for the first time the true equations of equilibrium and motion of a homogeneous elastic solid slightly disturbed from its position of equilibrium, which is one of constraint under a uniform pressure different in different directions. In a former memoirf he had given the equations for the case in which the undisturbed state is one free from pressure J. When I speak of the true equations, I mean the equations which belong to the problem when not restricted in generality by arbitrarily assumed hypotheses, and yet not containing constants which are incompatible with any well- ascertained physical principle. It is right to mention, however, that on this point mathematicians are not agreed ; M. de Saint- Venant, for instance, maintains the justice of the more restricted equations given by Cauchy§, though even he would not conceive the latter equations applicable to such solids as caoutchouc or jelly. In these papers Green introduced into the treatment of the subject, with the greatest advantage, the method of Lagrange, in which the partial differ- ential equations of motion are obtained from the variation of a single force- function, on the discovery of the proper form of which everything turns. Green's principle is thus enunciated by him : — " In whatever manner the elements of any material system may act on each other, if all the internal forces be multiplied by the elements of their respective directions, the total sum for any assigned portion of the mass will always be the exact differential of some function." In accordance with this principle, the general equation may be put under the form ^*'**(»»^S fc +ar , ")-JH***»» • < 5 >> where x, y, z are the equilibrium coordinates of any particle, p the density in equilibrium, u, v, w the displacements parallel to x, y, z, and <p the function in question. <p is in fact the function the variation of which in passing from one state of the medium to another, when multiplied by dx cly dz, expresses the work given out by the portion of the medium occupying in equilibrium the elementary parallelepiped dx dy dz, in passing from the first state to the second. The portion of the medium which in the state of equili- brium occupied the elementary parallelepiped becomes in the changed state an oblique-angled parallelepiped, whose edges maybe represented by dx(l-\-s^), dy (l+s 2 ), dz (l+s 3 ), and the cosines of the angles between the second and third, third and first, and first and second of these edges by a, j3, y, which in case the disturbance be small will be small quantities only. It is manifest that the function <j> must be independent of any linear or angular displacement of the element dx dy dz, and depend only on the change of form of the element, * Cambridge Philosophical Transactions, vol. vii. p. 120. f " On the Reflexion and Refraction of Light," Cambr. Phil. Trans, vol. vii. p. 1. Read Dec. 11, 1837. X They are virtually given, though not actually written down at length. § Coinptes Rendus, torn. liii. p. 1105 (1861). ON DOUBLE REFRACTION. 261 and therefore on the six quantities s v s 2 , s a , a, (3, y, -which may he expressed hy means of the nine differential coefficients of u, v, iu with respect to x, y, z, of which therefore <j> is a function, hut not any function, since it involves not nine, but only six independent variables. If the disturbance be small, the six quantities s v s 2 , s 3 , a, /3, y will be small likewise, and <j> may be expressed in a convergent series of the form 1>=fo + <t>i + <t>2+1> 3 + -- ■> where <j> , <p v <p 2 , 3 , &c. are homogeneous functions of the six quantities, of the orders 0, 1, 2, 3, &c. ; and if the motion be regarded as indefinitely small, the functions 3 , tp 4 . . . will be insensible, the left-hand member of equation (5) being of the second order as regards u, v, w. <p , being a constant, will not appear in equation (5), and 1 will be equal to zero in case the medium in its undisturbed state be free from internal pressure, but not otherwise. The function <p 2 , being a homogeneous function of six independent variables of the second order, contains in its most general shape twenty-one arbitrary con- stants, and <p l which is of the first order introduces six more, so that the most general expression for <p contains no less than twenty-seven arbitrary constants, all which appear in the expressions for the internal pressures and in the partial differential equations of motion*. The general expressions for the internal tensions in an elastic medium and the general equations of equilibrium or motion which were given by Cauchy, and which are written at length in the 4th volume of the ' Exercices de Mathe'- matiques,' contain twenty-one arbitrary constantswhen the undisturbed state of the medium is one of uniform constraint, and fifteen when it is one of freedom from pressure. In the latter case, Green's twenty-one constants are reduced to two, and Cauchy 's fifteen to only one, when the medium is isotropic. Green's equations comprise Cauchy's as a particular case, as will be shown more at length further on. It becomes an important question to inquire whether Cauchy's equations involve some restrictive hypothesis as to the constitution of the medium, so as to be in fact of insufficient generality, or whether, on the other hand, Green's equations are reducible to Cauchy's by the introduction of some well-ascertained physical principle, and therefore contain redundant constants. In the formation of Cauchy's equations, not only is the medium supposed to consist of material points acting on one another by forces which depend on the distance only (a supposition which, at least when coupled with the next, excludes the idea of molecular polarity), but it is assumed that the displace- ments of the individual molecules vary from molecule to molecide according to the variation of some continuous function of the coordinates ; and accordingly the displacements u', v', w' of the molecule whose coordinates in equilibrium are x+Ax, y+Ay, z + Az are expanded by Taylor's theorem in powers of. Ax, Ay, Az, and the differential coefficients -?-, <kc. are put ouis'.de the sign of summation. The motion, varying from point to point, of the medium taken as * The twenty-seven arbitrary constants enter the equations of motion in such a manner as to be there equivalent to only twenty-sis distinct constants, the physical interpretation of which analytical result will be found to be that a uniform pressure alike in all directions, in the undisturbed state of the medium, produces the same effect on the internal move- ments when the medium is disturbed as a certain internal elasticity, alike in all directions, and of a very simple kind, which is possible in a medium unconstrained in its natural state. The twenty-one arbitrary constants belonging to a medium unconstrained in its natural state are not reducible in the equations of motion, any more than in the expressions for the internal tensions, to a smaller number. 262 report — 1862. a whole, or in other words the mean motion, in any direction, of the molecules in the neighbourhood of a given point, must not be confounded with the motion of the molecules taken individually. The medium being continuous, so far as anything relating' to observation is concerned, the former will vary Continuously from point to point. But it by no means follows that the motion of the molecules considered individually should vary from one to another according to some function of the coordinates. The motion of the individual molecules is only considered for the sake of deducing results from hypotheses as to the molecular constitution and molecular forces of the medium, and in it we are concerned only with the relative motion of molecules situated so close as to act sensibly on each other. It would seem to be veiy probable, a priori, that a portion by no means negligible of the relative displacement of a pair of neighbouring molecules shoidd vary in an irregular manner from pair to pair ; and indeed if the medium tends to relieve itself from a state of constrained distortion, this must necessarily be the case ; and such a re- arrangement must assuredly take place in fluids. The insufficient generality of Cauchy's equations is further shown by their being absolutely incompatible ■with the idea of incompressibility. "We may evidently conceive a solid which resists compression of volume by a force incomparably greater than that by which it resists distortion of figure, and such a conception is actually realized in such a solid as caoutchouc or jelly. I have not mentioned the hypothesis of what may be called, from the analogy of surfaces of the second order, a central arrangement of the molecules, that is, an arrangement such that each molecule is a centre with respect to which the others are arranged in pairs at equal distances in opposite directions, because the hypothesis was merely casually introduced as one mode of making certain terms vanish which are of a form that clearly ought not to appear in the expressions relating to the mean motion, with which alone we are ulti- mately concerned. The arguments in favour of the existence of ultimate molecules in the case of ponderable matter appear to rest chiefly on the chemical law of definite proportions, and on the laws of crystallography, neither of which of course can be assumed to apply to the mysterious ether, of the very existence of which we have no direct evidence. If, for aught we know to the contrary, the very supposition of the existence of xdtimate molecules as applied to the ether may entail consequences at variance with its real constitution, much more must the accessory hypotheses be deemed precarious which Cauchy found necessary in order to be able to deduce any results at all in proceeding by his method. There appears, therefore, no sufficient reason a priori for preferring the more limited equations of Cauchy to the more general equations of Green. Green, on the other hand, takes his stand on the impossibility of perpetual motion, or in other words, on the principle of the conservation of work, which we have the strongest reasons for believing to be a general physical princi- ple*. The number of arbitrary constants thus furnished in the case in which the undisturbed state of the medium is one of freedom from pressure is, as has been stated, twenty- one. Professor Thomson has recently put this result in a form which indicates more clearly the signification of the con- stants t, and at the end of his memoir promises to show how an elastic solid, * Whether vital phenomena are subject to this law is a question which we are not here called upon to discuss. t " Elements of a Mathematical Theory of Elasticity," Phil. Trans, for 1856, p. 481. Read April 24, 1856. ON DOUBLE REFRACTION. 263 which as a whole should possess this number of arbitrary constants, could be built up of isotropic matter. Green supposes, in the first instance, that the medium is symmetrical with respect to planes in three rectangular directions, which simplifies the investi- gation and reduces the twenty-seven or twenty-one arbitrary constants to twelve (entering the partial differential equations of motion in such a manner as to be there equivalent to only eleven) or nine. It may be useful to give a Table of the constants employed by Green, with their equivalents in the theo- ries of Cauchy and Neumann, the density of the medium at rest being taken equal to unity for the sake of simplicity. The Table is as follows : — Green ABC GHI LMN P Q R Cauchy Gil LMN P Q R P Q R Neumann DCB A, A A , A A A, so that Green's equations are reduced to Cauchy's by making , L=P, M=Q, N=E (6) Por a plane wave propagated in any given direction there are three velocities of propagation, and three corresponding directions of vibration, which are determined by the directions of the principal axes of a certain ellipsoid U=l, which he proposes to call the ellipsoid of elasticity, the semiaxes at the same time representing in magnitude the squared reciprocals of the corresponding velocities of propagation; and Green has shown that U may be at once obtained from the function — 2p by taking that part only which is of the second order in u, v, w, and replacing u, v, w by x, y, z, and the symbols of 111 differentiation -j-, y-, -r, by the cosines of the angles which the wave-normal makes with the axes. This applies whether the medium be symmetrical or not with respect to the coordinate planes. Green then examines the conse- quences of supposing that for two of the three waves the vibrations are strictly in the front of the wave, as was supposed by Fresnel, and consequently that the vibrations belonging to the third wave are strictly normal. This hypothesis leads to five relations between the twelve constants, namely G=H=I= M suppose, P= M -2L, Q= F -2M, E =/ i-2N; . (7) and gives for the form of the fundamental function -2d>=2A— + 2~B c ^+2C d ^ dx ay dz /du\* /dv\* /dw\ 2 ) *,f/<2»V /dv\- /du>\* w +u) + u) } + E iy + y + \w n f /<M 2 /<&Y {dw\ 2 1 , (du dv dwV C |U) +(«) + {Tz) ) + '(dx + d-y + dz-) T J /dv div\* dv dm) f /dw dtty dw du \\dz~T~ dy) ~ dy dz J + [\dx "*" dz) ~ dz dx , >T f {du dv\ 2 du dv) /a . + *\{dy- + ^)-±dxdy\> < 8 > from which the equations of motion, the expressions for the internal pressures, and the equation of the ellipsoid of elasticity may be at once written down. The simpler case in which the medium in its natural state is supposed free +A « 264 report — 1862. from pressure is first considered*. Green shows that the ellipse which is the section of the ellipsoid of elasticity by a diametral plane, parallel to the wave's front, if turned 90° in its own plane, belongs to a fixed ellipsoid, which gives at once Fresnel's elegant construction for the velocity of propagation and direction of the plane of polarization ; but it is necessary to suppose that in polarized light the vibrations are parallel, not perpendicular, to the plane of polarization. The general case in which the medium is not assumed to be symmetrical with respect to three rectangular planes, and in which therefore $ contains twenty- one arbitrary constants, is afterwards considered ; and it is shown that the hypothesis of strict transversality leads to fourteen relations between them, leaving only seven constants arbitrary. But the function obtained on the assumption of planes of symmetry contains no fewer, for the four constants relating to these planes would be increased by three when the medium was referred to general axes. Hence therefore the existence of planes of symmetry is not an independent assumption, as in Cauchy's theory, but follows as a result. In this beautiful theory, therefore, we are presented with no forced rela- tions like Cauchy's equations; the result follows from the hypothesis of strictly transversal vibrations, to which Fresnel was led by physical considera- tions. The constant /x remains arbitrary, and it is easy to see that this constant expresses the square of the velocity of propagation of normal vibra- tions. Were this velocity comparable with the velocity of propagation of transversal vibrations, theory would lead us still to expect normal vibrations to be produced by light incident obliquely, though not by light incident perpendicidarly, on the surface of a crystal, and the theory would still be exposed to many of the objections which have been already brought forward. But nothing hinders us from supposing, in accordance with the argument contained in Green's former paper, that p. is very great or sensibly infinite, which removes all the difficulty, since the motion corresponding to this term in the expression for — 2 ty woidd not be sensible except at a distance from the surface comparable with the length of a wave of light. Hence, although it might be said, so long as p was supposed arbitrary, that the supposition of rigorous transversality had still something in it of the nature of a forced relation between constants, we see that the single supposition of incompressi- bility (under the action of forces at least comparable with those acting in the propagation of light) — the original supposition of Fresnel — introduced into the general equations, suffices to lead to the complete laws of double refrac- tion as given by Fresnel. "Were it not that other phenomena of light lead us rather to the conclusion that the vibrations are perpendicular, than that they are parallel to the plane of polarization, this theory would seem to leave us nothing to desire, except to prove that we had a right to neglect the direct action of the ponderable molecules, and to treat the ether within a crystal as a single elastic medium, of which the elasticity was different in different directions. In his paper on Reflexion, Green had adopted the supposition of Fresnel, that the vibrations are perpendicular to the plane of polarization. He was naturally led to examine whether the laws of double refraction could be explained on this hypothesis. When the medium in its undisturbed state is exposed to pressure differing in different directions, six additional constants are introduced into the function <jt, or three in case of the existence of planes * The results obtained for this case remain the same if we suppose the medium in its undisturbed state to be subject to a pressure alike in all directions. ON DOUBLE REFRACTION. 265 of symmetry to which the medium is referred. For waves perpendicular to the principal axes, the directions of vibration and squared velocities of propagation are as follows : — Wave-normal iV Direction of vibra- X G+A N + B M + C y N+A H+B L + C z M+A L+B i+c Green assumes, in accordance with Fresnel's theory, and with observation if the vibrations in polarized light are supposed perpendicular to the plane of polarization, that for waves perpendicular to any two of the principal axes, and propagated by vibrations in the direction of the third axis, the velocity of pro- pagation is the same. This gives three, equivalent to two, relations among the constants, namely, A— L=B— M=C— N=»< suppose, (9) which are equivalent to Cauchy's equations (3). The conditions that the vibrations are strictly transversal and normal respectively do not involve the six constants expressing the pressures in equilibrium, and therefore remain the same as before, namely (7). Adopting the relations (7) and (9), Green proves that for the two transversal waves the velocities of propagation and the azimuths of the planes of polarization are precisely those given by the theory of Fresnel, the vibrations in polarized light being now supposed perpendicular to the plane of polarization. As to the wave propagated by normal vibrations, the square of its velocity of propagation is easily shown to be equal to F + Al 2 + ~Bm 2 + Cn 2 ; and as the constant fi does not enter into the expression for the velocity of pro- pagation of transversal vibrations, the same supposition as before, namely that the medium is rigorously or sensibly incompressible, removes all difficulty arising from the absence of any observed phenomenon answering to this wave. The existence of planes of symmetry is here in part assumed. I say in part, because Green shows that the six constants, expressing the pressures in equilibrium, enter the equation of the ellipsoid of elasticity under the form K (# 2 +i/ 2 -r-z 2 ),_where K is a homogeneous function of the six constants of the first order, and involves likewise the cosines I, m, n. Hence the directions of vibration are the same as when the six constants vanish ; the velocities of propagation alone are changed ; and as the existence of planes of symmetry for the case in which the six constants vanish was demonstrated, it is only requisite to make the very natural supposition that the planes of symmetry which must exist as regards the directions of vibration, are also planes of symmetry as regards the pressure in equilibrium. We see then that this theory, which may be called Green's second theory, is in most respects as satisfactory (assuming for the present that Fresnel's construction does represent the laws of double refraction) as the former. I say in most respects, because, although the theory is perfectly rigorous, like the former, the equations (9) are of the nature of forced relations between the constants, not expressing anything which could have been foreseen, or 266 report— 1862. even conveying when pointed out the expression of any simple physical relation. The year .1839 was fertile in theories of doiible refraction, and on the 9th of December Prof. MacCullagh presented his theory to the Royal Irish Academy. It is contained in " An Essay towards a Dynamical Theory of Crystalline Reflexion and Refraction"*. As indicated by the title, the determination of the intensities of the light reflected and refracted at the surface of a crystal is what the author had chiefly in view, but his previous researches had led him to observe that this determination was intimately connected with the laws of double refraction, and to seek to link together these laws as parts of the same system. He was led to apply to the problem the general equation of dynamics under the form (5), to seek to determine the form of the function <p (V in his notation), and then to form the partial differential equations of motion, and the conditions to be satisfied at the boundaries of the medium, by the method of Lagrange. He does not appear to have been aware at the time that this method had previously been adopted by Green. Like his predecessors, he treats the ether within a crystallized body as a single medium unequally elastic in dif- ferent directions, thus ignoring any direct influence of the ponderable mole- cules in the vibrations. He assumes that the density of the ether is a constant quantity, that is, both unchanged during vibration, and the same within all bodies as in free space. We are not concerned with the latter of these suppositions in deducing the laws of internal vibrations, but only in investi- gating those which regulate the intensity of reflected and refracted light. He assumes further that the vibrations in plane waves, propagated within a crystal, are rectilinear, and that while the plane of the wave moves parallel to itself the vibrations continue parallel to a fixed right hue, the direction of this, right line and the direction of a normal to the wave being functions of each other, — a supposition which doubtless applies to all crystals except quartz, and those which possess a similar property. In this method everything depends on the correct determination of the form of the function V. From the assumption that the density of the ether is unchanged by vibration, it is readily shown that the vibrations are entirely transversal. Imagine a system of plane waves, in which the vibrations are parallel to a fixed line in the plane of a wave, to be propagated in the crystal, and refer the crystal for a moment to the rectangular axes of x', y', z', the plane of x'y being parallel to the planes of the waves, and the axis of y' to the direction of vibration ; and let c be the angle whose tangent is -jy With respect to the form of Y, MacCullagh reasons thus : — " The function V can only depend upon the directions of the axes of x', y', z' with respect to fixed lines in the crystal, and upon the angle which measures the change of form produced in the parallelepiped by vibration. This is the most general supposition which can be made concerning it. Since, however, by our second supposition, any one of these directions, suppose that of x', determines the other two, we may regard V as depending on the angle k and the direction of the axis of x' alone," from whence he shows that V must be a function of the quantities X, Y, Z, denned by the equations dz dy dx dz dy dx This reasoning, which is somewhat obscure, seems to me to involve a fallacy. * Memoirs of the Eoyal Irish Academy, vol. xii. p. 17. ON DOUBLE REFRACTION. 267 If the form of V were known, the rectilinearity of vibration and the constancy in the direction of vibration for a system of plane waves travelling in any given direction would follow as a result of the solution of the problem. But in using equation (5) we are not at liberty to substitute for Y (or <j>) an expression which represents that function only on the condition that the motion be luhat it actually is, for we have occasion to take the variation cV of V, and this varia- tion must be the most general that is geometrically possible though it be dynamically impossible. That the form of V, arrived at by MacCullagh, is inadmissible, is, I conceive, proved by its incompatibility with the form deduced by Green from the very same supposition of the perfect transversality of the transversal vibrations ; for Green's reasoning is perfectly straightforward and irreproachable. Besides, MacCullagh's form leads to consequences abso- lutely at variance with dynamical principles*. But waiving for the present the objection to the conclusion that V is a function of the quantities X, Y, Z, let us follow the consequences of the theory. The disturbance being supposed small, the quantities X, Y, Z will also be small, and Y may be expanded in a series according to powers of these quantities ; and, as before, we need only proceed to the second order if we regard the disturbance as indefinitely small. The first term, being merely a constant, may be omitted. The terms of the first order MacCullagh concludes must vanish. This, however, it must be observed, is only true on the supposition that the medium in its undisturbed state is free from pressure. The terms of the second order are six in number, involving squares and products of X, Y, Z. The terms involving YZ, ZX, XY may be got rid of by a transformation of coordinates, when Y will be reduced to the form Y=-|(« 2 X 2 + & 2 Y 2 +c 2 Z 2 ), (10) the constant term being omitted, and the arbitrary constants being denoted by — |a 2 , — \b % , -±c 2 . Thus on this theory the existence of principal axes is proved, not assumed. If MacCullagh's expression for Y (10) be compared with Green's expression for </> (8) for the case of no pressure in equilibrium, so that A=0, B = 0, C = 0, it will be seen that the two will become identical, provided first we omit the term pi- — |-i_-)-^j i n Green's expression, and secondly, we treat the symbols of differentiation as literal coefficients, so as to confound, for instance, -j- 77 an( i -5- -7-. The term involving /j. does not appear in the expressions for transversal vibrations, since for these ^+ — + — =0, and doc ay dz therefore does not affect the laws of the propagation of such vibrations, although it would appear in the problem of calculating the intensity of reflected and refracted light ; and be that as it may, it follows from Green's rule for forming the equation of the ellipsoid of elasticity, that the laws of the propagation of transversal vibrations will be precisely the same whether we adopt his form of f or Y (for the case of no pressure in equilibrium) or MacCullagh's. Indeed, if we omit the term u [ C -^+ C ^- + ~\ , the partial differential equations of \dx dy dz) motion, on which alone depend the laws of internal propagation, would be just the same as the two theories f. Accordingly MacCullagh obtained, though * See Appendix. ♦_ t See Appendix. MacCullagh's reasoning appears to be so far correct as to have led to correct equations, although tli. ough a form of V which may, I conceive, be shown to be inadmissible. 268 Heport — 1862. independently of, and in a different manner from Green, precisely Fresnel's laws of double refraction and the accompanying polarization, on the condition, however, that in polarized light the vibrations are parallel to the plane of polarization. It is remarkable that in the previous year MacCullagh, in a letter to Sir David Brewster*, published expressions for the internal pressures identical with those which result from Green's first theory, provided that in the latter the terms be omitted which arise from that term in which contains p, a term which vanishes in the case of transversal vibrations propagated within a crystal. It does not appear how these expressions were obtained by MacCullagh ; it was probably by a tentative process. The various theories which have just been reviewed have this one feature in common, that in all, the direct action of the ponderable molecules ia neglected, and the ether treated as a single vibrating medium. It was, doubtless, the extreme difficulty of determining the motion of one of two mutually penetrating media that led mathematicians to adopt this, at first sight, unnatural supposition ; but the conviction seems by some to have been entertained from the first, and to have forced itself upon the minds of others, that the ponderable molecules must be taken into account in a far more direct manner. Some investigations were made in this direction by Dr. Lloyd as long- as twenty-five years agof. Cauchy's later papers show that he was dissatisfied with the method, adopted in his earlier ones, of treating the ether within a ponderable body as a single vibrating medium^ ; but he does not seem to have advanced beyond a few barren generalities, towards a theory of double refraction founded on a calculation of the vibrations of one of two mutually penetrating media. In the theory of double refraction advanced by Professor Challis§, the ether is assimilated to an ordinary elastic fluid, the vibrations of which are modified by resisting masses ; and his theory leads him at once to Fresnel's elegant construction of the wave surface by points. The theory, however, rests upon principles which have not received the general assent of mathematicians. In a work entitled " Light explained on the Hypothesis of the Ethereal Medium being a Viscous Fluid "||, Mr. Moon has put in a clear form some of the more serious objections which may be raised against Fresnel's theory ; but that which he has substituted is itself open to formidable objec- tions, some of which the author himself seems to have perceived. In concluding this part of the subject, I may perhaps be permitted to express my own belief that the true dynamical theory of double refraction has yet to be found. In the present state of the theory of double refraction, it appears to be of especial importance to attend to a rigorous comparison of its laws with actual observation. I have not now in view the two great laws giving the planes of polarization, and the difference of the squared velocities of propagation, of the two waves which can be propagated independently of each other in any given direction within a crystal. These laws, or at least laws differing from them only by quantities which may be deemed negligible in observation, had previously been discovered by experiment ; and the deduction of these laws by Fresnel from his theory, combined with the verification of the law, which his theory, correcting in this respect previous notions, first pointed out, that * Philosophical Magazine for 1836, vol. viii. p. 103. t Proceedings of the Eoyal Irish Academy, vol. i. p. 10. X See his optical memoirs published in the 22nd volume of the 'Memoires de 1'Academie.' § Cambridge Philosophical Transactions, vol. viii. p. 524. || Macmillan & Co., Cambridge, 1853. ON DOUBLE REFRACTION. 269 in each principal plane of a biaxal crystal the ray polarized in that plane obeys the ordinary law of refraction, leaves no reasonable doubt that Fresnel's construction contains the true laws of double refraction, at least in their broad features. But regarding this point as established, I have rather in view a verification of those laws which admit of being put to the test of experiment with extreme precision ; for such verifications might often enable the mathe- matician, in groping after the true theory, to discard at once, as not agreeing with observation, theories which might present themselves to his mind, and on which otherwise he might have spent much fruitless labour. To make my meaning clearer, I will refer to Fresnel's construction, in which the laws of polarization and wave-velocity are determined by the sections, by a diametral plane parallel to the wave-front, of the ellipsoid * aV+&V+fiV=l (11), where a, b, c denote the principal wave-velocities. The principal semiaxes of the section determine by their direction the normals to the two planes of polarization, and by their magnitude the reciprocals of the corresponding wave-velocities. Now a certain other physical theory which might be pro- posed leads to a construction differing from Fresnel's only in this, that the planes of polarization and wave-velocities are determined by the section, by a diametral plane parallel to the wave-front, of the ellipsoid 2 2 2 ^2 + ^2+^ = 1 (12), the principal semiaxes of the section determining by their direction the normals to- the two planes of polarization, and by their magnitudes the corresponding wave-velocities. The law that the planes of polarization of the two waves propagated in a given direction bisect respectively the two supplemental dihedral angles made by planes passing through the wave- normal and the two optic axes, remains tbe same as before, but the posi- tions of the optic axes themselves, as determined by the principal indices of refraction, are somewhat different ; the difference, however, is but small if the differences between a 2 , b 2 , c 2 are a good deal smaller than the quantities themselves. Each principal section of the wave surface, instead of being a circle and an ellipse, is a circle and an oval, to which an ellipse is a near approximation f. The difference between the inclinations of the optic axes, and between the amounts of extraordinary refraction in the principal planes, on the two theories, though small, are quite sensible in observation, but only on condition that the observations are made with great precision. We see from this example of what great advantage for the advancement of theory observations of this character may be. One law which admits of receiving, and which has received, this searching comparison with observation, is that according to which, in each principal plane of a biaxal crystal, the ray which is polarized in that plane obeys the ordinaiy law of refraction, and accordingly in a uniaxal crystal, in which every plane parallel to the axis is a principal plane, the so-called ordinary ray follows rigorously the law of ordinary refraction. This law was carefully verified by Fresnel himself in the case of topaz, by the method of cutting plates parallel to the same principal axis, or axis of elasticity, carefully * It would seem to be just as well to omit the surface of elasticity altogether, and refer the construction directly to the ellipsoid (11). t The equation of the surface of wave-slowness in this and similar cases may be readily obtained by the method given by Professor Haughton in a paper " On the Equilibrium and Motion of Solid and Fluid Bodies." Transactions of the Eoyal Irish Academy, vol. xxi. p. 172. 270 report— 1862. ■working them to the same thickness, and then interposing them in the paths of two streams of light proceeding to interfere, as well as by the method of prismatic refraction ; and he states as the result of his observations that he can affirm the law to be, at least in the case of topaz, mathematically exact. The same result follows from the observations by which Rudberg so accu- rately determined tbe principal indices of Arragonite and topaz *, for the principal fixed lines of the spectrum. Professor MacCullagh having been led by theoretical considerations to doubt whether, in Iceland spar for instance,' the so-called ordinary ray rigorously obeyed the ordinary law of refraction, whether the refractive indices in the axial and equatorial directions were strictly the same, Sir David Brewster was induced to put the question to the test of a crucial experiment, by forming a compound prism consisting of two pieces of spar cemented together in the direction of the length of the prism, and so cut from the crystal that at a minimum deviation one piece was tra- versed axially and the other equatoriallyt. Tbe prism having been polished after cementing, so as to ensure the perfect equality of angle of the two parts, on viewing a slit through it the bright line D was seen unbroken in passing from one half to the other. More recently Professor Swan has made a very precise examination of the ordinary refraction in various directions in Iceland spar by the method of prismatic refraction J, from whence it results that for homogeneous light of any refrangibility the ordinary ray follows strictly the ordinary law of refraction. It is remarkable that this simple law, which ought, one woidd expect, to lie on the very surface as it were of the true theo.y of double refraction, is not indicated a priori by most of the rigorous theories which have been ad- vanced to account for the phenomenon. Neither of the two theories of Cauchy, nor the second theory of Green, lead us to expect such a result, though they furnish arbitrary constants which may be so determined as to bring it about. The curious and unexpected phenomenon of conical refraction has justly been regarded as one of the most striking proofs of the general correctness of the conclusions residting from the theory of Fresnel. But I wish to point out that the phenomenon is not competent to decide between several theories leading to Fresnel's construction as a near approximation. Let us take first internal conical refraction. The existence of this phenomenon depends upon the existence of a tangent plane touching the wave surface along a plane curve. At first sight this might seem to be a speciality of the wave-surface of Fresnel ; but a little consideration will show that it must be a property of the wave surface resulting from any reasonable theory. For, if possible, let the nearest approach to a plane curve of contact be a curve of double curva- ture. Let a plane be drawn touching the rim (as it may be called) of the surface, that is, the part where the surface turns over, in two points, on opposite sides of the rim ; and then, after having been slightly tilted by turning about one of the points of contact, let it move parallel to itself towards the centre. The successive sections of the wave-surface by this plane will evidently be of the general character represented in the annexed figures, 12 3 4 5 6 * Annates de Cliimie, torn, xlviii. p. 225 (1831). t Report of the British Association for 1843, Trans, of Sect. p. 7. X Transactions of the Koyal Society of Edinburgh, vol. xvi. p. 375. ON DOUBLE REFRACTION. 271 and in four positions the plane will touch the surface in one point, as repre- sented in figs. 1, 2, 4, 5. Should the contacts represented in figs. 4 & 5 take place simultaneously, they may be rendered successive by slightly altering the inclination of the plane. Hence in certain directions there would be four possible wave-velocities. Now the general principle of the superposition of small motions makes the laws of double refraction depend on those of the propagation of plane waves. But all theories respecting the propagation of a "series of plane waves having a given direction, and in which the disturbance of the particles is arbitrary, but the same all over the front of a wave, agree in this, that they lead us to decompose the disturbance into three disturbances in three particular directions, to each of which corresponds a series of plare waves which are propagated with a determinate velocity. If the medium be incompressible, one of the wave-velocities becomes infinite, and one sheet of the wave surface moves off to infinity. The most general disturbance, subject to the condition of incompressibility, which requires that there be no displacements perpendicular to the fronts of the waves, may now be expressed as the resultant of two disturbances, corresponding to displacements in parti- cular directions lying in planes parallel to that of the waves, to each of which corresponds a determinate velocity of propagation. We see, therefore, that the limitation of the number of tangent planes to the wave-surface, which can be drawn in a given direction on one side of the centre, to two, or at the most three, is intimately bound up with the number of dimensions of space ; so that the existence of the phenomenon of internal conical refraction is no proof of the truth of the particular form of wave-surface assigned by Fresnel rather than that to which some other theory would conduct. Were the law of wave-velocity expressed, for example, by the construction already mentioned having reference to the elhpsoid (12), the wave-surface (in this case a surface of the 16th degree) woidd still have plane cuiTes of contact with the tangent plane, which in this case also, as in the wave-surface of Fresnel, are, as I find, circles, though that they should be circles could not have been foreseen. The existence of external conical refraction depends upon the existence of a conical point in the wave-siu-face, by which the interior sheet passes to the exterior. The existence of a conical point is not, like that of a plane curve of contact, a necessary property of a wave-surface. Still it will readily be con- ceived that if Fresnel's wave-surface be, as it undoubtedly is, at least a near approximation to the true wave-surface, and if the latter have, moreover, plane curves of contact with the tangent plane, the mode by which the exterior sheet passes within one of these plane curves into the interior will be very approximately by a conical point ; so that in the impossibility of operating experimentally on mere rays the phenomena will not be sensibly different from what they woidd have been had the transition been made rigorously by a conical point. There is one direction within a biaxal crystal marked by a visible phenomenon of such a nature as to permit of observing the direction with precision, while it can also be calculated, on any particidar theory of double refraction, in terms of the principal indices of refraction ; I refer to the direction of either optic axis. Eudberg himself measured the inclination of the optic axes of Arragonite, probably with a piece of the same crystal from which his prisms were cut, and found it a little more than 32° as observed in air, but he speaks of the difficulty of measuring the angle with precision. The inclination within the crystal thence deduced is really a little greater than that given by Fresnel's theory ; but in making the comparison 272 report— 1862. Rudberg used the formula for the ray-axes instead of that for the wave-axes, which made the theoretical inclination in air appear about 2° greater than the observed*. A very exact measure of the angle between the optic axes of Arragonite for homogeneous light corresponding to the principal fixed hues of the spectrum has recently been executed by Professor Kirchhoff f, by a method which has the advantage of not making any supposition as to the direction in which the crystal is cut. The angle observed in air was reduced by calculation to the angle within the crystal, by means of Rudberg's indices for the principal axis of mean elasticity ; and the result was compared with the angle calculated from the formula of Fresnel, on substituting for the con- stants therein contained the numerical values determined by Rudberg for all the three principal axes. The angle reduced from that observed in air proved to be from 13' to 20' greater than that calculated from Presnel's formula. This small difference seems to be fairly attributable to errors in the indices, arising from errors in the direction of cutting of the prisms employed by Rudberg. The angle measured by Kirchhoff would seem to have been trust- worthy to within a minute or less. It is doubtful, however, how far we may trust to the identity of the principal refractive indices in different specimens of the mineral. Chemical analysis shows that Arragonite is not pure carbonate of lime, but contains a variable though small proportion of other ingredients. To these variations doubtless correspond variations in the refractive indices ; and De Senarmont has shown how the inclination of the optic axes of minerals is liable to be changed by the substitution one for another of isomorphous elements J. More- over, M. Des Cloizeaux has recently shown that in felspar and some other minerals, which bear a high temperature without apparent change, the inclination of the optic axes is changed in a permanent manner by heat§ ; so that even perfect identity of chemical composition is not an absolute guarantee of optical identity in two specimens of a mineral of a given kind. The exactness of the spheroidal form assigned by Huygens to the sheet of the wave-surface within Iceland spar corresponding to the extraordinary ray, does not seem to have been tested to the same degree of rigour as the ordinary refraction of the ordinary ray; for the methods employed by Wollaston|| and Halus If for observing the extraordinary refraction can hardly bear comparison for exactness with the method of prismatic refraction which has been applied to the ordinary ray ; and observations on the absolute velocities of propagation in different directions within biaxal crystals are still almost wholly wanting. This has long been recognized as a desideratum, and it has been suggested to employ for the purpose the displacement of fringes of interference. It seems to me that a slight modification of the ordinary method of prismatic refraction would be more convenient and exact. Let the crystal to be examined be cut, unless natural faces or cleavage planes answer the purpose, so as to have two planes inclined at an angle suitable for the measure of refractions ; there being at least two natural faces or cleavage-planes left undestroyed, so as to permit of an exact measure of the directions of any artificial faces. The prism thus formed having been mounted as usual, and placed in any azimuth, let the angle of incidence or * Annates de Chimie, tome xlviii. p. 258 (1831). t Poggendorff s Annalen, vol. cviii. p. 567 (1859). % Annates de Chimie, tome xxxiii. p. 391 (1851). § Annates des Mines, tome ii. p. 327 (1862). 11 On the Oblique Eefraction of Iceland Spar, Plul. Trans, for 1802, p. 381. *IT Memoires de l'lnstitut ; Say. Etrangers, tome ii. p. 303 (1811). ON DOUBLE REFRACTION. 273 emergence (according as the prism remains fixed or turns round with the tele- scope) be measured, by observing the light reflected from the surface, and like- wise the deviation for several standard fixed lines in the spectrum of each refracted pencil. Let the prism be now turned into a different azimuth, and the deviations again observed, and so on. Each observation furnishes accurately an angle of incidence and the corresponding angle of emergence ; for if a be the angle of incidence, i the angle of the prism, D the deviation, and $ the angle of emergence, D = + ^— i. But without making any supposition as to the law of double refraction, or assuming amjthing beyond the truth of Huycjens's principle, which, following directly from the general principle of the superposition of small motions, lies at the very foundation of the whole theory of undulations, we may at once deduce from the angles of incidence and emergence the direction and velocity of propagation of the wave within the prism. For if a plane wave be incident on a plane surface bounding a medium of any kind, either ordinary or doubly refracting, it follows directly froni^Huygens's principle that the refracted wave or waves will be plane, and that if A be the angle of incidence, a' the inclination of a refracted wave to the surface, V the velocity of propagation in air, v the wave-velocity within the medium, sin 0_sin a' Hence if a\ ,/,' be the inclinations of the refracted wave to the faces of our prism, we shall have the equations v sin 0=V sin 0', (13) v sin t//=V sin i//, (14) <t>' + ^'=i (15) The equations (13) and (14) give, on taking account of (15), v sin t^t cos ^^=V sin I cos ^~, .... (16) VC os^±^siniZ^=Vcos|sinl=i.; . . . (17) whence by division tan^=tanjtan^cot£+i (18) The equations (15) and (18) determine a' and $, and then (16) gives v. Hence we know accurately the velocity of propagation of a wave, the normal to which lies in a plane perpendicular to the faces of the prism, and makes known angles with the faces, and is therefore known in direction with reference to the crystallographic axes. A single prism would enable the observer to explore the crystal in a series of directions lying in a plane perpendicular to its edge; but as these directions are practically confined to limits making no very great angles with a normal to the plane bisecting the dihedral angle of the prism, more than one prism would be required to enable him to explore the crystal in the most important directions ; and it would be necessary for him to assure himself that the specimens of crystal, of which the different prisms are made, were strictly comparable with each other. It would be best, as far as practicable, to cut them from the same block. The existence of principal planes, or planes of optical symmetry, for light 1862. x 274 report— 1862. of any given refrangibility, in those cases in which they are not determined by being at the same time planes of crystallographic symmetry, is a matter needing experimental verification. However, as no anomaly, so far as I am aware, has been discovered in the systems of rings seen with homogeneous light around the optic axes of crystals of the oblique or anorthic system, there is no reason for supposing that such planes do not exist. Appendix. Further Comparison of the Theories of Green, MacCullagh, and Cauchy. In a paper "Ona Classification of Elastic Media and the Laws of Plane "Waves propagated through them," read before the Royal Irish Academy on the 8th of January, 1849*, Professor Haughton has made a comparative examina- tion of different theories which have been advanced for determining the motion of elastic media, more especially those which have been applied to the expla- nation of the phenomena of light. Some of the results contained in this Appendix have already been given by Professor Haughton ; in other instances I have arrived at different conclusions. In such cases I have been careful to give my reasons in detail. Consider a homogeneous elastic medium, the parts of which act on one another only with forces which are insensible at sensible distances, and which in its undisturbed state is either free from pressure, or else subject to a pressure or tension which is the same at all points, though varying with the direction of the plane surface with reference to which it is estimated^ Let x, y, z be the coordinates of any particle in the undisturbed state, x+u, y+v, z-\-w the coordinates in the disturbed state, and for simplicity take the density in the undisturbed state as the unit of density. Then, according to the method followed both by Green and MacCullagh, the motion of the medium will be determined by the equation (d 2 u . d 2 v , d 2 w df Z u +dF Sv+ d? lw \dxdy dz= 111 %<$> dx dy dz, . (19) where <j> is the function due to the elastic forces. To this equation must be added, in case the medium be not unlimited, the terms relative to its boundaries. The function <f> multiplied by dx dy dz expresses the work given out by the element dx dy dz in passing from the initial to the actual state if we assume, as we may, the initial state for that in which 0=0. According to the sup- position with which we started, that the internal forces are insensible at sensible distances, the value of at any point must depend on the relative displacements in the immediate neighbourhood of that point, as expressed by the differential coefficients of u, v, iv with respect to x, y, z. For the present let us make no other supposition concerning <p than this, that it is some function ( — /) of those nine differential coefficients; and let us apply the equation (19) to a limited portion of the medium bounded initially by the closed surface S. We must previously add the terms due to the action of the surrounding portion of the medium, which will evidently be of the form of a double integral having reference to the surface S, an element of which we may denote by c?S. Hence we must add to the right-hand side of equa- tion (19) the expression for E having yet to be found. * Transactions of the Eoyal Irish Academy, vol. xxii. p. 97. ON DOUBLE REFRACTION. 275 Denoting for shortness the partial differential coefficients of — <p with respecttog,, £ fa ^/(||)/(|) &C we have .,/du\ dhi „,/du\ dlu „ whence =jp"(») a " * y * + JJ- f (I) fa " s * + JJ / (s) iu "* dy + itc. i-cta (7?/ cfe. We must now equate to zero separately the terms in our equation involving triple and those involving double integrals. The result obtained from the former further requires that the coefficient of each of the independent quan- tities lu, Sf, $iv under the sign j j j shall vanish separately, whence (Pu_d L Jdu\ d Jdu\ d Jdu\ df ~dx J \dx) + dy J \dyj + dz J \dz)' d?v_d L Jdv\ d JJri\ d. f(—\ df ~dx J \dx) + dy ? \dy) + dz J \dzf d~w_d_ (dw\ d Jdw\ d Jdw\ df ~dx J \dx) + dy J \dy) + dz J \dz )\ equations which may be written in an abbreviated form as follows : — d*u rdcj)l d 2 v_ [d<f\ d 2 w_ PcZ 0~j ,„... df \jhtj' If \jfo]' df ~~ [f&J* " ' { ' where the expressions within crotchets denote differential coefficients taken in a conventional sense, namely by treating in the differentiation the symbols j-, j -, -5- as if they were mere literal coefficients, and prefixing to the whole term, and now regarding as a real symbol of differentiation, whichever of these three symbols was attached to the u, v, or w that disappeared by differ- entiation. The equating of the double integrals gives * These agree with Professor Haughton's equations (5). t2 > • • • (20)* 276 REPORT 186.2. ■where I, m, n are the direction-cosines of the element dS of the surface which bounded the portion of the medium under consideration -when it was in its undisturbed state. This expression leads us to contemplate the action of the surrounding medium as a tension having a certain value referred to a unit of surface in the undisturbed state. If P, Q, R be the components of this tension parallel to the axes of x, y, z, they must be the coefficients of %u, Zv, ho under ff the sign II, so that *=</(£Mg) + ./(J> > (22) These formula; give, in terms of the function f, the components of the tension on a small plane which in its original position had any arbitrary direction. If we wish for the expressions for the components of the tensions on planes originally perpendicular to the axes of as, y, z, we have only to put in succession 1=1, m=l, »=1, the other two cosines each time being equal to zero. If then P x , T x , T zx denote the components in the direction of the axis of x of the tension on planes originally perpendicular to the axes of x, y, z, with similar notation in the other cases, we shall have T. = w(t) (23)* The formulas hitherto employed are just the same whether we suppose the disturbance small or not ; and we might express in terms of P^., T , &c. (and therefore in terms of f), and of the differential coefficients of u, v, w with respect to x, y, and z, the components of the tension referred to a surface given in the actual instead of the undisturbed state of the medium, without supposing the disturbance small. As, however, the investigation is meant to be applied only to small disturbances, it would only complicate the formulae to no purpose to treat the disturbance as of arbitrary magnitude, and I shall therefore regard it henceforth as indefinitely small. On this supposition we may expand according to powers of the small quantities y-_, <Src, proceeding as far as the second order, the left-hand member of (19) being of the second order as regards u, v, w. The formulae (22) or (23) show that $ will or will not contain terms of the first order according as the undisturbed state of the medium is one of uniform constraint, or of freedom from pressure. In Green's first theory, and in the theory of MacCullagh, <p is supposed not to contain terms of the fii-st order. Accordingly in considering the point with respect to which these two theories are at issue, I shall suppose the * These agree with Professor Haughton's equations at p. 100, but are obtained in a different manner. ON DOUBLE REFRACTION. 277 medium in its undisturbed state to be free from pressure. The tensions P, Q, R, F x , &c. will now be small quantities of the first order, so that in the fornruhe (22) and (23) we may suppose the tensions referred to a unit of surface in the actual or the undisturbed state of the medium indifferently, and may moreover in these formula?, and in the expression for <f>, take x, y, z for the actual or the original coordinates of a particle. Green assumes as self-evident that the value of <j> for any element, suppose that which originally occupied the rectangular parallelepiped dx chj dz, must depend only on the change of form of the element, and not on any mere change of position in space. Any displacement which varies continuously from point to point must change an elementary rectangular parallelepiped into one which is oblique-angled, and the change of form is expressed by the ratios of the lengths of the edges to the original lengths, and by the angles which the edges make with one another or by their cosines. If the medium were originally in a state of constraint, <p would contain terms of the first order, and the expressions for the extensions of the edges and the cosines of the angles would be wanted to the second order, but when is wholly of the second order, those quantities need only be found to the first order. It is easy to see that to this order the extensions are expressed by du du dw dx> dtf Tz' ( 24 ) and the cosines of the inclinations of the edges two and two by dv dw dw du du dv Tz + dJ' d7v + dz~' dlydx' ( 25 ) and <p being a function of these six quantities, we have from (23) T,,=1V T,,=T«, T^=T yx (26) These are the relations pointed out by Cauchy between the nine components of the three tensions in three rectangular directions, whereby they are reduced to six. The necessity of these relations is admitted by most mathematicians. Conversely, if we start with Cauchy's three relations (26), we have from (23) . CMS) /(£)=/(£> /(SHI) <m The integration of the first of these partial differential equations gives /=a function of -y- +-j- and of the seven other differential coefficients. J ay dz Substituting in the second of equations (27) and integrating, and substituting the result in the third and integrating again, we readily find /=a function of the six quantities (24) and (25). We see then that Green's axiom that the function q, depends only on the change of form of the element, and Cauchy's relations (26), are but different ways of expressing the same condition ; so that either follows if the truth of the other be admitted. Cauchy's equations were proved by applying the statical equations of moments of a rigid body to an elementary parallelepiped of the medium, and taking the limit when the dimensions of the element vanish. The demonstra- tion is just the same whether the medium be at rest or in motion, since in the latter case we have merely to apply d'Alembert's principle. It need hardly be remarked that the employment of equations of equilibrium of a rigid body in the demonstration by no means limits the truth of the theorem to rigid bodies ; for the equations of equilibrium of a rigid body are 278 report — 1862. true of any material system. In the latter case they are not sufficient for the equilibrium, but all that we are concerned with in the demonstration of equations (26) is that they should be true. On the other hand, the form of Y or to which MacCullagh was led is that of a homogeneous function, of the second order, of the three quantities dw dv du dw dv du fi dy dz dz da? dx dy' ^ ' which, as is well known, are linear functions of the similarly expressed quantities referring to any other system of rectangular axes. On substituting in (23), we see that the normal tensions on planes parallel to the coordinate planes, and therefore on any plane since the axes are arbitrary, vanish, while the tangential tensions satisfy the three relations T y2 =-T sy , T«=-T„, T.,-- -V • • • (29) so that the equations of moments of an element are violated. The relative motion in the neighbourhood of a given point may be resolved, as is known, into three extensions (positive or negative) in three rectangular directions and three rotations. The directions of the axes of extension, and the magnitudes of the extensions, are determined by the six quantities (24) and (2o), while the rotations or angular displacements are expressed by tbe halves of the three quantities (28). In this theory, then, the work stored up in an element of the medium would depend, not upon the change of form of the element, but upon its angular displacement in space. It may be shown without difficulty that, according to the form of cp assumed by MacCullagh, the equations of moments are violated for a finite portion of the mass, and not merely for an element. Supposing for simplicity that the medium in its undisturbed state is free from pressure or tension, let us leave the form of <p open for the present, except that it is supposed to be a function of the differential coefficients of the first order of u, v, w with respect to x, y, z, and let us form the equation of moments roimd one of the axes, as that of x, for the portion of the medium comprised within the closed surface S. This equation is \\\{ ~Wy + W z } dxd V dz +\ ((%-Qz)cZS=0, the double integrals belonging to the surface. Since all the terms in this equation are small, we may take x, y, z for the actual or the equilibrium coordinates indifferently. Substituting from equations (20), and integrating by parts, we find The double integrals in this equation destroy each other by virtue of (22), bo that there remains JBKIMs)}***- - • • • • < 30) But this equation cannot be satisfied, since the surface S within which the ON DOUBLE REFRACTION. 279 integration is to be performed is perfectly arbitrary, unless / 1 y- 1 =/ \-r) at all points. "We are thus led back to the equations (27), which are violated in the theory of MacCullagh. The form of the equations such as (30) is instructive, as pointing out the mode in which, the condition of moments is violated. It is not that the resultant of the forces acting on an element of the medium does not produce its proper momentum in changing the motion of translation of the element ; that is secured by the equations (20) ; but that a couple is supposed to act on each element to which there is no corresponding reacting couple. The only way of escaping from these conclusions is by denying that the mutual action of two adjacent portions of the medium separated by a small ideal surface is capable of being represented by a pressure or tension, and saying that we must also take into account a couple ; not, it is to be observed, a couple depending on variations of the tension (for that would be of a higher order and would vanish in the limit), but a couple ultimately proportional to the element of surface. But it would require a function $ of a totally different form to take into account the work of such couples ; and indeed the method by which the expressions for the components of the tension have been here deduced seems to show that in the case of a function <j> which depends only on the differential coefficients of the first order of u, v, w with respect to x, y, z, the mutual action of two contiguous portions of a medium is fully repre- sented by a tension or pressure. Indeed MacCullagh himself expressly disclaimed having given a mechanical theory of double refraction*. His methods have been characterized as a sort of mathematical induction, and led him to the discovery of the mathematical laws of certain highly important optical phenomena. The discovery of such laws can hardly fail to be a great assistance towards the future establishment of a complete mechanical theory. I proceed now to form the function <f> for Caucby's most general equations. 72 72 ,72 If we have given the expressions for i— , —?, C —^. in terms of the differential at dv air coefficients of u, v, w with respect to x, y, z, they do not suffice for the com- plete determination of the function <p, as appears from the equations (20) or (21) ; but if we have given the expressions for the tensions P x , T z , &c., <h is completely determinate, as appears from equations (23). In using these equations, it must be remembered that the tensions are measured with reference to surfaces in the undisturbed state of the medium ; and therefore, should the expressions be given with reference to surfaces in the actual state, they must undergo a preh'minary transformation to make them refer to surfaces in the undisturbed state. Supposing then the tensions expressed as required, in order to find 6 we have only to integrate the total differential the nine differential coefficients, of which <p is a function, being regarded as * Transactions of the Koyal Irish Academy, vol. xxi. p. 50. It would seem, however, that he rather felt the want of a mechanical theory from which to deduce his form of the function <p or Y, than doubted the correctness of that form itself. 280 REPORT 1862. independent variables. Should the three equations (27) be satisfied, the expression (31) will be simplified, becoming fdu . dw\ V + T d(—+' (32) where T x denotes T or T '■ , and similarly for T y , T g . The general expressions for the tensions resulting from Cauchy's method are written at length in the equations numbered 17 and 18, pp. 133, 134 of the 4th volume of his ' Exercices de Mathematiqucs,' where the normal and tangential tensions, referred to surfaces in the actual state of the medium, are denoted by A, B, C, D, E, E. These expressions contain 21 arbitraiy constants, of which six, <3, 33, C, 23, <£, ff, denote the tensions in the state of equilibrium. If these be for the present omitted, the remaining terms will be wholly small quantities of the first order, and therefore the tensions may be supposed to be referred to a unit of surface in the actual, or in the undisturbed state of the medium indifferently. On substituting now for P x , P , P z , T x , T y , T z in (32) the remaining parts of A, B, C, D, E, E (observing that the I, rj, £ in Cauchy's notation are the same as it, v, w), it will be seen that the right-hand member of the equation is a perfect differential, integrable at once by inspection, and giving , -d f /du , (Zt'Y , dn dv -2<p=Lh div\ 2 , p f /dv dw\ 2 - dv div \ UF \\d Z + Ty) + -Tydji "> \d,vj ' \dyj ' *" \dz J ,-. f /dw , du\ 3 , „ dw du ) , -n f /du dv\ i ott f du /dv dw\ (dw du\ (du dv\ ) + 2 dx dy . ov J dv (dw du\ /du dv\ (dv dw\ ) + 2V \d-^v + Tz) + \Ty + (Lv)\dz + d^)\ l ow / dw /du dv\ /dv dw\ /dw du\ ) +2W 1 Tz \dj + T-) + \dz + dy) (dTv + dz) i i ( \ + 2W — (—+ —\+ 2V '*/ dy\dy dx) > (33) 9V du /dw du dx\d.v d, , dw (dv dw\ Tyjz+dj,) 9 -ry du /du dv\ ivjTtdv /dv dw\ gy„ dw (dw du\ + " di\dl / + dI-) ± ~ dJ / \dz + T l/ ) + " dz~\Tx + Tz)' the arbitrary constant being omitted as unnecessary. "We see that this is a homogeneous function of the second degree of the six quantities (24) and (25), but not the most general function of that nature, containing only 15 instead of 21 arbitrary constants. Let us now form the part of the expression for <p involving the constants which express the pressures in the state of equilibrium. It will be convenient to effect the requisite transformation in the expressions for the tensions by two steps, first referring them to surfaces of the actual extent, but in the original position, and then to surfaces in the original state altogether. Let Fj, T' , &c. denote the tensions estimated with reference to the actual extent but original direction of a surface, so that P' x cZS, for instance, denotes the component, in a direction parallel to the axis of x, of the tension on an ON DOUBLE REFRACTION. 281 elementary plane passing through the point (ar, y, z) in such a direction that in the undisturbed state of the medium the same plane of particles was perpendicular to the axis of x, (7S denoting the actual area of the element. Consider the equilibrium of an elementary tetrahedron of the medium, the sides of which are perpendicular to the axes of x, y, z, and the base in the direction of a plane which was perpendicular to the axis of x; and let I, m, n be the direction- cosines of the base ; then P' x =?A + mF+«E, T^-lF+mB+nD, T'„=ZE + »iD + nC; (34) but to the first order of small quantities 7 , da du l=\, m=— -=-, »== — _-; dy dz substituting in (34), and writing down the other corresponding equations, we have F =A-F— — E — dy dz p-^b-d^-f^ dz dx z dx dy T'^=D-C^-E ( dz T =E-A^-F zx dx dx dw dy du T =F-B— -D *» rh. dz dy y dx dy dy dz T' yx =F-E^_A^ * dz dx 1 ►(35) Lastly, since an elementary area rfS originally perpendicular to the axis of x becomes by extension ( 1 + -T-+-77 ) dS, and similarly with regard to y and z, we have P : F =T " " ^dy^dz' *y p . p< rp . mi rn .HP' "I . till | »t> (36) Expressing P x , T^, &c. in terms of P' x , T' Jy , &c. by (36), then Y x , T' , &c. in terms of A, B, C, D, E, F by (35), and lastly substituting for A, B . . . F the expressions given by Cauchy, we find \ dx) dy dz ,dv dx p ,=»( 1 +$)+»S+*: \ dz) dx dy <u-»(i+J)+*£+«$|v»(i+S)+«£+c* T„=e('i + *) +d r<^ + g*« \ dz) dy dx W37) \ dx) dy dz T " =jr ( 1+ l) +e £+*£ T -=< i+ £)+ ffl S+* i 282 REPORT 1862. Substituting now these expressions in (31) and integrating, we have -20=& +115 + C + 233 + 2<£ 2 du /du\? / dv dec \dx) \dx ;) 2— + dy \dy I du\ 2 dw dx ™ + ( du Hi) Vffo/ \dzj /duA ~\ dv dw du du dz dy dy dz dw du du du dv dv dx dz dz dx dz dx m dv dv dw dw ] dy dz dy dz J dw dw \ dz dx J + dv dv >■ (38) o jf. J cZtt <&/ cZw cZw dx dy dx dy J which is exactly Green's expression*, Green's constants A, B . . . F answer- ing to Cauchy's &, 93 . . . Jf. The sum of the right-haud members of equa- tions (33) and (38) gives the complete expression for — 2<£ which belongs to Cauchy's formulse. It contains, as we see, 21 arbitrary constants, and is a particular case of the general form used by Green, which latter contains 27 arbitrary constants. I have been thus particular in deducing the form of Green's function which belongs to Cauchy's expressions, partly because it has been erroneously asserted that Green's function does not apply to a system of attracting and repelling molecules, partly because, when once the function f is formed, the short and elegant methods of Green may be applied to obtain the results of Cauchy's theory, and a comparison of the different theories of Green and Cauchy is greatly facilitated. * Cambridge Philosophical Transactions, vol. vii. p. 127. Fourth Report of the Committee on Steamship Performance. _ , C STENTS. Report. Sheet of indicator diagrams of H.M.S. ' Colossus,' ' Arrogant,' and ' Hansa,' and scale of displacement of the ' McGregor Laird.' Appendix, Table 1. — Form of Engineers' Pocket Log, issued by the Committee. Table 2. — Return of the particulars of the dimensions of 20 vessels in H.M. Navy, with the results of their trials upon completion for service. Table 3. — Table showing the results of the performances at sea, and when on trial, of H.M.S. ' Arrogant,' £ Colossus,' and ' St. George.' Tables 4, 5, and 6. — Results of trials of H.M. screwships, officially tabulated by the Admiralty, in 1850, 1856, and 1861. Steam Transport Service.— TMes Nos. 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16 (the last 5 tables being summaries of the Tables 7 to 11) show the results obtained from vessels employed in transport service during the latter part of the Russian War, showing the respective values of the several steamships, classified according to the nature of the employment, or the special character of the duties required to be performed ; and giving, in addition, the cost of moving each ship 1000 miles, &c. Table 17. — Table showing performances of the Royal West India Mail Company's Steamers from June 1861 to July 1862. Table 18. — Summations of the indicator diagrams taken on all the voyages included in Table 17. ON STEAMSHIP PERFORMANCE. 283 Table 18 A. — Table showing the manner in which the summaries in preceding table are obtained. Table 19. — Return of the particulars of the dimensions of the Peninsular and Orien- tal Steam Navigation Company's steamship ' Mooltan,' with tabulated statement showing the results of her performance as compared with six other vessels in the same service. Table 20. — Table of the results of the performances of 68 vessels of the Austrian Lloyds' Steamship Company. Table 21. — Return of experiments with H.M.S. ' Stork,' ' Shannon,' and ' Psyche,' with different kinds of screw propellers. Table 22. — Seven logs of voyages of the ' Great Eastern ' for 1861-62. Table 23. — Statement showing the summary of the performances of the Pacific Steam Navigation Cort^auy's new vessels ' Peru ' and ' Talca.' Table 24. — Abstract log of, and notes upon, the performance of the African Royal Mail Company's steamship ' McGregor Laird.' Table 25. — Notes on the performance of the North German Lloyds' Company's steamship ' Hansa.' Table 26. — Log of the Earl of Durham's sailing-yacht ' Beatrix,' on her recent Medi- terranean voyage. Report. [" The object of the Committee is to make pubhc such recorded facts through the medium of the Association, and being accessible to the pubhc hi that manner, to bring the greatest amount of science to the solution of the difficulties now existing to the scien- tific improvement of the forms of vessels and the qualities of marine engines. They will especially endeavour to guard against information so furnished to them being used in any other way, and they~trust they may look for the cooperation of members of Yacht Clubs having steam-yachts, of sliipowners, as well as of steamship-builders and engineers." — Third Beport, 1861, p. 16.] At the meeting of the British Association held at Manchester in September 1861, the Committee were reappointed in the following terms : — " That the Committee on Steamship Performance be reappointed. " That the attention of the Committee be also directed to the obtaining of information regarding the performance of vessels under sail, with a view to comparing the result of the two powers of wind and steam, in order to their more effectual and economical combination ; with £150 at their disposal." The following noblemen and gentlemen were nominated to serve on the Committee : — The Duke of Sutherland. The Earl of Gifford, M.P. The Earl of Caithness. The Lord Dufferin. W. Fairbairn,Esq.,LL.D.,F.R.S. J. Scott Bussell, Esq., F.E.S. Admiral E. Paris, C.B. (Imperial French Navy). The Hon. Capt. Egerton, R.N. The Hon. Leopold AgarEllis,M.P. J. E. McConnell, Esq., C.E. Wm. Smith, Esq., C.E. Prof. J. M. Rankine, LL.D. J. R. Napier, Esq. R. Roberts, Esq., C.E. Henry Wright, Esq., Secretary. "With power to add to their number. The following noblemen and gentlemen, having consented to assist your Committee, were, during the present year, elected as corresponding members: — Lord C. Paget, M.P., C.B. The Earl of Durham. The Marquis of Hartington, M.P. Viscount Hill. Lord John Hay. Admiral Elliott. Captain Hope, R.N. Captain Ryder, R.N. Robert Dalglish, Esq., M.P. Captain Robertson, R.N. Captain Sulivan, R.N., C.B. Captain Mangles. T. R. Tufnell, Esq. Wm. Froude, Esq. W. Just, Esq. John Elder, Esq. David Rowan, Esq. J. Mc F. Gray, Esq. 284 report — 1862. Your Committee have the pleasure of stating that, at the unanimous request of the members of the Committee, his Grace the Duke of Sutherland undertook the office of Chairman. The Committee have, since February last, held monthly meetings, and intermediate meetings of a sub-Committee. Your Committee have pleasure in reporting very satisfactory progress, and that they have had an increasing amount of useful information placed at their disposal. Much greater interest is now taken in the objects of the inquiry, and a still increasing number of observers have adopted the forms of the Committee, for recording the performances of vessels. The importance of the information collected by your Committee is attracting the attention of steamship-owners, as veil as scientific investigators ; and it is hoped the result of greater efficiency and economy in the application of steam as well as improvements in the construction of steam- vessels, will be the result of these Reports ; and your Committee have reason to believe that considerable advantages have already been derived from their labours by steamship-owners. The Royal Navy. — Your Committee, in their Third Annual Report, stated the results of their communications with the Admiralty, and have now to report that the objects of your Committee continue to meet with the approval of the Lords Commissioners of the Admiralty, and of the intelligent scientific officers in that branch of Her Majesty's service ; that your Committee have been furnished from time to time with accurate returns of the performances of the more important steamships in Her Majesty's service which have been tried at the measured mile during the last twelve months, and also some similar returns, received too late for insertion in the Report of last year. In the Appendix will be found a selection from these returns, preference having been given to the returns of vessels of which the future steam performances at sea have been promised. Your Committee have received several returns of performances of Her Majesty's ships at sea, the publication of which, owing to their being incom- plete in some important particidars, and to the lateness of the time at which they were received, is necessarily postponed. Your Committee call attention to the selection they have made, which will be found in the Appendix. As numerous inquiries have, from time to time, been made of your Com- mittee as to the particulars of certain of Her Majesty's steamships, the per- formances of which were noticed in previous Reports, your Committee, with a view to avoid unnecessary correspondence, and to give the required infor- mation more fully than can be done by written communications, determined to include in the present Report three sets of tables of trials of H.M.'s ships, which were officially tabulated by the Admiralty, but not issued by them to the public. The reprinting of those tables, and the textual information accompanying them, in the Appendix to the present Report will now supply those who possess the previous Reports of your Committee with the means of comparing the results obtained upon the trials of nearly the entire of the steamships of war composing the British Navy, and will also enable them to compare with the results of such trials the performances whilst at sea of very many of the vessels included in the complete and extensive lists to be found in the three Reports previously published, and in the present Report of your Committee, without the necessity, which before existed, of searching elsewhere for the information. The publication of the three Admiralty Tables will also render it un- ON STEAMSHIP PERFORMANCE. 285 necessary hereafter to repeat many particulars as to the dimensions, &c, of the ships, and the power and other details of the engines of such of H.M.'s ships of which your Committee may, from time to time, receive returns of performances at sea. In the previous Reports, the records of special trials with propellers of various kinds, in the steamships ' Plying Fish,' ' Bullfinch,' ' Doris,' &c, were given ; and the Committee are now enahled to furnish another series of experiments with Her Majesty's gunboat ' Stork,' which are very interest- ing, and to which is added a short abstract of the trials of the • Shannon ' and ' Psyche.' The Steam Transport Service. — A series of tables, prepared by Mr. G. Murdoch, Superintending Engineer at Constantinople during the Crimean War, and now Inspecting Engineer of Her Majesty's Steam Reserve at Ports- mouth, having been carefully calculated for the purpose of showing the respective values of the several steamships, classified according to the nature of the employment or the special character of the duties required to be per- formed, have been placed at the disposal of your Committee. These tables, besides giving the expense of moving each ship 1000 miles, and the cost of conveying sick and wounded officers and troops, cavalry, cattle, and cargo, over the same distance, give the daily coal-consumption and the distance run for each ton of coal consumed. They have also the additional value arising from contrasting the different results obtained, and costs incurred, when propelling the same vessels at different speeds. Royal Mail Service. — Your Committee have been favoured with a copy of the Engine Register kept by the West India Royal Mail Steam Packet Company, showing the exact performances of some of their largest steamships. The tabulated statement, which will be found appended to this Report, is for the twelve months ending June last, and has reference only to the steamers em- ployed on the West India Transatlantic route between Southampton and St. Thomas. To this Porm of Return your Committee would invite special attention, as they are not aware that such is kept by any of the other large Steam Packet Companies or steamship-owners ; and the great value of the informa- tion it affords, as also the very complete form in which that information is rendered, will, it is thought, be admitted by every one who is conversant with such matters. The importance of such a record to a corporation like the Royal Mail Company can hardly be over-estimated, when it is considered that they have no less than nine distinct routes of steamers in the West Indies and the Brazils, and that exactly the same system is adopted in regard to all these ; so that the performance of every vessel engaged on these lines is, on the completion of each succeeding voyage, thus carefully analysed and brought under the immediate notice of the managers. In addition to the above, indicator diagrams are taken from the engines on every voyage, and sent home for inspection ; the particulars of these are further entered in a register kept for that purpose. The Royal Mail Company have kindly furnished your Committee with a copy of their register of the diagrams taken on all the voyages comprised in the first-mentioned table, thus affording a complete synopsis of the working both of their ships and engines on the West India Transatlantic route, during the twelve months referred to. Your Committee have included also the dimensions and other particulars 286 report — 1862. of the ' Mooltan,' a new vessel belonging to the Peninsular and Oriental Steam Navigation Company, with returns of a voyage from Southampton to Alex- andria and back, showing the results of the performance of this vessel, as compared with some other vessels in the same service. It is to be regretted that the Peninsular and Oriental Company found they were unable to give a continuance of the reports of the performances of the vessels composing their fleet of ships this year in time for the publication of this Eeport. The Com- mittee have reason to believe that next year full reports of the performances of these vessels for this and next year will be forthcoming. The Pacific Koyal Mail Company have furnished your Committee with the dimensions and abstract of the performances of their last additions to their fleet (see Appendix). The particulars of the other vessels have been given in previous Reports. It is worthy of remark that the vessels belonging to this Company fitted with double-cylinder expansion engines, specially noticed by your Committee in previous Reports as remarkable for their economy, have continued to per- form in the same economical manner ; and, under the circumstances, it has not been considered necessary to furnish a continuation of the logs previously given. The City of Dublin Company's Returns for the past year are omitted ; and your Committee regret that the log of the ' Munster,' and the results attained by working out her performances, — although the calculations have involved considerable trouble to the Committee in their preparation, — have also to be omitted. Tour Committee have received from the Royal African Mail Company an abstract of the log of the screw steamship ' McGregor Laird ' on her first voyage from Liverpool to Madeira, and the particulars of the vessel and her machinery. To the performances of this ship your Committee call especial attention, on account of the great economy exhibited in the con- sumption of fuel. Foreign Mail Service. — Your Committee would call attention to the returns supplied of the performances of the steamships belonging to the Austrian Lloyds' Steamship Company ; and although they are to some extent incom- plete (which arises from no systematic recording having previously been adopted), this, it is promised, will be remedied in future by the adoption of the forms supplied by your Committee. The Mercantile Marine Service. — Your Committee have been occupied prin- cipally in effecting arrangements by which a more thorough and extended organization of the means of obtaining returns of the performances of mer- cantile steamships employed in ocean navigation can be secured, and also in making personal application to many of the largest steamship-owners at the principal ports of Great Britain. They have succeeded in enlisting the active cooperation of many proprietors of steamships. In some cases the owners of mercantile marine ships, upon being called on by members of this Com- mittee, at once requested their superintending engineers to adopt the " forms of returns " prepared by this Committee, and in other cases the result of such personal communication has been the suggestions of modifications in the " forms ; " but, in all instances, or nearly so, the engineers have undertaken that, in future, a more perfect and systematic recording of the performance at sea shall be adopted, and that the results shall be regularly placed at the disposal of your Committee. ON STEAMSHIP PERFORMANCE. 287 "With a view of obtaining, with greater facility than heretofore, returns of performances, as well as the dimensions and particulars, of ships, engines, and machinery, your Committee have adopted a form of pocket-book, or " En- gineers' Pocket Log," which contains a greater number of details than were included in their previous " forms of returns." This log is so arranged that the returns can be removed from the case when filled up, and the blank form inserted. Each book is furnished with a pocket to receive and preserve the indicator diagrams or " cards." Although these books have only recently been issued, considerable numbers of them are in course of being filled up by the engineers of ocean-going steam- ships ; and arrangements have been made for the regular transmission of these returns from each ship during the next twelve months. Since the issuing of these Pocket Logs, your Committee have received particulars of between 30 and 40 first-class ocean-going screw steamships, which were, however, received too late to be properly tabulated so as to accompany the present Eeport. These returns are being examined and arrauged for pub- lication. The Engineers' Pocket Logs have been freely circulated and well received, and they promise to yield a large amount of valuable information to the Association. A list of the particulars asked for will be found in the Appendix. The particulars of the ' Great Eastern ' having been already published, the logs of her performances on her Transatlantic voyages have been regularly supplied to your Committee since she has been refitted and placed upon the North American service. These logs have been collected, and are given in the Appendix to the present Eeport. Performances of Vessels under Sail. — In compliance with the recommenda- tion of the Council of the Association, your Committee have succeeded in obtaining promises of copies of the logs or returns of the performances of several of thelargestsailing-ships belonging to the Australian, India, and China Packet Services, and to this end special observations are being made; and it is hoped that the results of the labours of those who have undertaken the duty of supplying your Committee with these returns may be included in the next Eeport in such a form as will render them available for comparison with the performances of full-powered and auxiliary steamships performing similar voyages. Your Committee have received from the Earl of Durham the logs of the sailing schooner-yacht ' Beatrix,' on her Mediterranean voyages. The dimen- sions and particulars of this vessel, together with scale of displacement, have also been received, but not in time to be included in the Eeport. Your Committee have been promised the particidars of some auxiliary- powered ocean steamships. The Committee purpose to act upon a suggestion made to them, of forming a list of the Engineers of the several classes employed in the mercantile steam service, who have, with the sanction of the owners, supplied your Committee with returns of the performances of ships under their charge, to which re- ference may be had by such members of your Association as are interested in the subject, and with a view to afford opportunities for the advancement of such Engineers as have shown the greatest amount of scientific ability in connexion with their calling. Your Committee have determined to act upon a suggestion by which the 288 report — 1862. performances of some steamships, which, are at present withheld, may in future be supplied for the use of the Committee, viz., that such returns shall be published under a distinguishing number, instead of publishing the name of the vessel, her builders, and the constructors of her machinery, and that the latter particidars shall only be disclosed with the consent of the owners. Your Committee continue to receive from steamship-owners and engineers invitations to be present at the trials of steamships. The sum of ,£150, voted by the Council of the Association to defray the expenses of your Committee, has been expended and slightly exceeded. Your Committee have thought it desirable to add the following particulars of items to be included in a form of return to be printed, and circulated with the logs and forms of returns issued by the Committee. Position of centre of gravity of vessel. Position of centre of buoyancy. Position of metacentre for rolling. Position of metacentre for pitching. Wedges of immersion and emersion at an angle of 1\, or 15, or any other number of degrees. Approximate radius of gyration of vessel about longitudinal axis. Approximate radius of gyration of vessel about transverse axis. Number of rolling oscillations per minute. Number of pitch oscillations in a minute. ( Under given circumstances, those an- Angles through which vessel rolls. gles to be measured not by a pen- Angles through which vessel^ dulum, plummet, or spirit-level, but pitches. either by observing the horizon or 1^ the stars, or by a gyroscope. Length, height, period and direction of waves at time of experiment, sail carried, ind