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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 


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 



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 



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 


Errata in Report of Observations of Luminous Meteors, 1861-62 .... 527 






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 


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 



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 


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 



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 


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 


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 


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 



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 



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 


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 


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 


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 



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 


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 


Mr. Thomas Wright on the Human Remains found in the course of the Ex- 
cavations at Wroxeter 149 


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 


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 


Mr. R. W. Woollcombe on Oblate Projectiles with Cycloidal Rotation, con- 
trasted with Cylindro-ogival Projectiles having Helical or Rifle Rotation. . 187 


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 





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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- 

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. 


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. 


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. 


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. 


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. 


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- 


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. 


A President, two or more Vice-Presidents, one or more Secretaries, and a 
Treasurer, shall be annually appointed by the General Committee. 


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 


_ The Author of any paper or communication shall be at liberty to reserve 
his right of property therein. 


The Accounts of the Association shall be audited annually, by Auditors 
appointed by the Meeting. 




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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., 

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 

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 

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. 

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. 

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. 

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 

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., 

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- 

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. 


REPORT 1862. 

Goodwin, The Very Eev. EL, D.D., Dean of 

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., 

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 

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). 
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. 


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 

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., 

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 

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. 



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., 

Oxford, Samuel Wilberforce, D.D., Lord 

Bishop of, F.E.S., F.G.S. 
Palmerston, Viscount, KG, G.C.B., M.P., 

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. 

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., 

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., 


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. 

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 ). 



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. 


THE REV. ROBERT WILLIS, M.A., F.R.S., Jacksonian Professor of Natural and Experimental 
Philosophy in the University of Cambridge. 


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 

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. 



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. 


A. Noble, Esq. 
Augustus H. Hunt, Esq. 
R. C. Clapham, Esq. 


Thomas Hodgkin, Esq. 


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. 
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. 

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. 


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. 


GEORGE GRIFFITH, Esq., M.A., Deputy Professor of Experimental Philosophy in the University of 



William Spottiswoode, Esq., M.A., F.R.S., F.G.S., 19 Chester Street, 
Belgrave Square, London, S.W. 


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. 

J. P. Gassiot, Esq. Robert Hutton, Esq. Dr. Norton Shaw. 




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. 



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. 


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. 


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. 


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. 


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. 

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. 


REPORT 1862. 


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. 


Professor Agassiz, Cambridge, Massa- 
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. 


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 

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, 

Professor Wartmann, Geneva. 


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 

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, 


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- 

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- 

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- 


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 

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 

A Differential Declinometer for the Government Observatory at Mauritius 
has been verified and forwarded to Prof. Meldrum, who has received it in 

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- 

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 

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 : — 


" 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. 


" 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 

" I have the honour to be, 
" 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 : — 


" 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 

" 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. 


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. 


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 

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 


REPORT 186.2. 








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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 

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 

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 

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. 


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 

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- 

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 

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 

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 

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. 


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 


Matthiessen, Dr. — Alloys 20 

Dupre, M. — Carbon under pressure 10 

Gages, Mr. — Chemistry of Rocks 8 


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 


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 of Sums which have been paid on Account of Grants 

for Scientific Purposes. 



.. 20 




.. 62 

British Fossil Ichthyology 



.. 163 






British Fossil Ichthyology 105 

Thermometric Observations, &c. 50 
Experiments on long-continued 
Heat 17 


.. 15 

.. 60 


.. 15 




.. 284 






.. 24 


.. 70 

.. 100 

.. 150 

Meteorology and Subterranean 


.. 150 



.. 30 

... 11 


£9 IS 



.. 29 





. 100 


Meteorological Observations and 
Anemometer (construction) ... 100 

Cast Iron (Strength of) 60 

Animal and Vegetable Substances 

Railway Constants r — 41 



Bristol Tides 

.. 50 




... 50 



Subterranean Temperature ... 

... 100 



Meteorological Committee ... 

, 31 
.. 16 




Meteorological Observations 






... 144 



£ 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 

















£1505 11 


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 9 

£1546 16 4 


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 








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 



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 



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 






1 6 

18 8 

1 10 
6 3 

10 11 





14 7 

17 6 



8 6 

1 11 


17 8 


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 
























10 2 


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 




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 


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 














12 8 

14 6 

18 11 

16 8 
11 9 

17 8 



14 8 

1) 9 

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 






















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~ 

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 


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 

Maintaining the Establishment at 

Kew Observatory 255 18 

Transit of Earthquake Waves ... 50 


report — 1862. 

£ s. d. 

Periodical Phenomena 15 

Meteorological Instrument, 

Azores 25 

£345 IS (i 


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 

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 


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 



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 

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 

Maintaining the Establishment at 
Kew Observatory: — 

1854 £ 75 01 

1855 £500 0] 

Strickland's Ornithological Syno- 

Dredging and Dredging Forms... 

Chemical Action of Light 

Strength of Iron Plates 

Registration of Periodical Pheno- 

Propagation of Salmon 

_ £ 










7 34 13 9 


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 



7 8 

7 4 

£507 15 4 

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 

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 






£684 11 1 



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 


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- 











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 



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 






5 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. 




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 


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 

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. 



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 

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 

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 


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 

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 

£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 


Statistics, Geography, and Ethnology, to which small sums have been as- 

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 

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 


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. 







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. 



Position, or 



Place of 

Apparent Size. 



Altitude and 


h m 

July 16 

9 30 p.m. Weston - super - 

Large as Venus at 

Duller than:3or 4 seconds; 

Exploded when W, 

Mare. (Also 


Venus at 


altitude 45°. 

seen in Dor- 

max. bril- 





9 58 p.m. 

Whitehall, Lon- 

Very large ball, but 

Very brilliant.. 

Slower than 

Began almost E 


not quite full. 

move ; 
" leisurely." 

and disappears 
behind the 
houses on th 
west side c 


Exactly 10 Gainford, 

Like Jupiter, seen 

Motion not From 10° below 


ington, York- 

in a good tele- 
scope, but not 
exactly spherical. 


Aquilse, throug' 
the E. to N.E.j 
from altitude 30 
to about altitud 


Greenwich and 

Kensington. Alrca 

dy inserted, 

p. 10 of Report 
Endured very 

/orl861 J 


Soon after 

10 p.m. 

long, about 
15 seconds. 


10 p.m., or 
] 5m,. after 




A companion 

From S.E. to 1 

of the ob- Came from ov< 

10 p.m. 


server walk-' a 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. 


Between 10 
p.m. and 

Whitburn, near 

Like ball of quick- 
silver, or an 





enormous star. 


About 10 40 

Furness Abbey, 

Threw a strong 


Moved ven From behind a hi 

slowly ; 

south of tri 


Abbey ; NortH 
ward through El 
lost behind tree! 



Conway, N. 


Very slow in 
its motion, 
" quiet and 

Over the hills 1 
and S. of Peij 
maen-Vach ; di 
appeared behini 




Appearance; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




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 


)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 

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. 


oman candle-ball. Phos- 
phorescent train, closely 
adhering and sharply 
terminated, without 

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- 


tional Gallery, near 
the top of Parliament 

Horizontal, or very 
slightly declining at 

Came over from the 
right of the house, 
descending as a rocket 
in the form of an 

Mrs. E. Addison 

[of Argyll. 
./. Hoire ; Dule 
John Borough. 

Openbav-window faced Mrs. Davies. 

Quite horizontal j from 
left to right. 

Horizontal, or very 
slightly inclined to- 
wards the earth. 

Slightly declining ; per- 
haps curved down- 

Point of observation 
upon the sands mid- 
way between Pen- 
maen-Mawr and Pen- 

M. M. 

G. II. Chambers. 

H. II. Bemrose. 


REPORT 1862. 



Place of 

Apparent Size. 



Position, or 

Altitude and 


July 16 


h in 

11 p.m 

11} p.m. .., 

Bristol , 



114 p.m. 


Much > than any 

Threw a brilliant 
light when high 
in the heavens, 
expanding and 
increasing in 
brightness a3 it 
neared the ho 

Like a toy balloon.. 


11 30 p.m 






11 -j p.m. 

1H P-m 
or soon 

11 32 p.m 




Flimwell, Hurst 
Green, Sussex. 

1611 33 p.m. 


11 33 p.m. 

Samlown, Isle of 

Euston Road, 

Large as a full 


and more 

Clear bluish. 

As it neared 
the horizon 
it assumed 
a beautiful 
blue colour. 

Bright clear 
blue and 

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 

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 

Disappeared a few; 
degrees abovei 
the horizon. 

Appeared near the. 
meridian ; disap- 
peared behind 


at 45°. 


Large signal-rocket 

A sudden lumino- 
sity overhead. 


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 

From the zenith, 
near a. Lyra, to 
a few degrees 
from the S.W. 

First seen 15°sout' 
of zenith ; passe 
downwards di- 
rect through 
Scorpio, and dis- 
appeared near! 
the horizon. 


Appearance ; Train, if any, 
and its Duration. 

Length of 

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 


rrack very bright, endured ' 
3 minutes ; like a half 
circular mark of phos- 
phorus upon a wall. 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 



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 

First emitted sparks ; after- 
wards a bright train 
which endured some 

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. 



Course from N. to S. 

Passed over from E. 


Took a south-westerly 

From the S.E. to S.W. 

Nearly vertical to S.W, 
by W. or S.W. 

Nearly vertically down, 

Vertically, S.W. 


By letter to W. H. 
Wood, Weston-super- 

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 

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 

Probably originated in 

J. Ellis. 

F. R. Cooper. 

John Griffin, 

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 
Euston Road). 


REPORT 1862. 



Place of 

Apparent Size. 

1881. | h m 

July 16,11 34 p.m.jBetween St. 
Albans and 

16 11 38 p.m. 

16 11 40 p.m. 


About j to 
12 p.m. 

Seacombe, Birk- 
enhead, Che- 

Bristol , 

Brading Downs, 
Isle of Wight. 

Much brighter than 
1st mag.* 

Very large 

About 10 | Bristol , 

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. 



Lat. 53- 29'-5, 
Long.2° 15'W. 

Trafalgar Square, 


Greenwich Ob 



A ball of fire, in- 
tensely brilliant. 

Very brilliant 

Like Pleiades, but 
three times as 


1st mag.*. 

Considerably ex- 
ceeding % in 

Equalled in size the 
great meteor, 
11.33 p.m., July 

2nd mag.* 
2nd mag.* 
Very small 
2nd mag.* 



Position, or 

Altitude and 


Brilliantbluish'lO to 13 sees, 


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 
than it attained 
before explosion, 


Moved slowlv 

Vivid bluish- 

Estimated not 
to have ex- 
ceeded 2 


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 
10:From about a Co- 
in ronae to x Ursae 
Majoris; near the 



Fast motion... 
1 to 2 seconds 
1 second 

From yDraconis... 
Through Cassiopeia 
/t Cygni to Sagitta. 

Very rapid;* Cygni to Del- 
2 seconds. phinus. 


Appearance ; Train, if any, 
and its Duration. 

Length of 

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 


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 

Lppeared to burst 

eft a bright track, cigar- 

loursc bent up rather 
suddenly in the middle 
with two maxima of 

'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°. 


,eft a small track 

.eft no track 

ieft a small track 

Only about 
3° or 4°. 




About fi. to W. ; 



At its centre the path 
was inclined 18° to 
the horizon. 

E. to W. 

Passed directly over 

E. to W. 

A complete view from 
first to last. 

One or two smaller 
meteors during the 
night in same direc- 

Towards the left; 15° 
from horizontal ; 

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- 


William Taylor ; 

Miss J. 


Presented a sweep of David Walker, 
magnificent splendour M.D. 
through the sky. 

by W. H. 

John A. James. 

Bristol News- 

Six shooting-stars re- Rev. F. Howlett. 
corded from 11.15 to 
12.15 p.m. 


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., 
T. Crumplen and 
J. Townsend 

Herbert M c Leod. 

W. C. Nash. 


W. C. Nash and 
J. Howe. 


REPORT 1862. 



Place of 

Apparent Size. Colour. 

1861. h m s 
Aug. 810 32 5 Cambridge Ob- 2nd mag.* 
p.m. servatory. 

10 34 


10 35 p.m 

10 35 p.m 

10 40 

10 45 

10 49 

10 50 

8 10 50 





810 51 p.m 

910 11 


9,10 14 p.m 





10 27 45 

10 45 

10 47 

10 47 

10 52 

10 57 






Aylesbury (Hart- 
well Observa- 

Birkenhead (Sea- 

Aylesbury (Hart- 
well Observa- 

Cambridge Ob- 

Birkenhead (Sea- 

Trafalgar Square, 

Greenwich Ob- 

Cambridge Ob- 

Birkenhead (Sea- 

A bright star, 1st 

Much brighter than 
any star. 

A flame of light 

A fine shooting-star 

1st mag.# 

1st mag.*. 
1st mag.*. 

A splendid meteor. 


Greenwich Oh 

Birkenhead (Sea- 


1st mag.* . 

1st mag.* . 

1st mag.* . 
1st mag.* . 
Very bright 
1st mag.*.... 

1st mag.* 

1st mag.* 


colours seen, 

Fine blue light 


Position, or 

Altitude and 




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 


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 
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 

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 


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 

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- 

luminous track, 20° bril 

'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 

Tail endured 1 second ... 

Tail endured 1£ second ... 

or 7 shooting-stars in 
succession ; fell 10° or 
12° and burst. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 



No path dis- 





About 15 c 




10° or 12 c 

To right, 30° from hori 
zontal; down. 


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 

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 



Arthur Bovvden. 

Wilfred Airy. 

At Greenwich, two ob- 
servers recorded G 
shooting-stars ; very 

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. 

D. Walker, M.D. 

T. Crumplen and 
J. Townsend. 

J. Howe. 

Arthur Bowden. 

D. Walker, M.D 


Herbert M c Leod 
W. C. Nash. 
D. Walker, M.D, 



REPORT' — 1862. 





h in 

9 53 p.m. 

10 10 8 p.m. 

1010 18 p.m 


10 21 p.m. 

10,10 23 p.m. 
W10 23ip.m. 

lo'lO 24 p.m. 

Place of 
Observation. ! 

Apparent Size. 


Cranford Ob- 






5th mag.* 

3rd mag.* 

Brilliant meteor ; 
1st mag.* 

1st mag.*; as bright 
as Venus. 

6th mag.* 

3rd mag.* 

Greenwich Ob- Small 

3rd mag.* 

Cranford Ob- 
10 21 p.m. Greenwich Ob- Si 

10 10 25 p.m. 

10 10 26 p.m. 

10 10 27 p.m. 

Cranford Ob- 

2 brilliant meteors. 



5th mag.* 

1st mag.* 

10 10 27 p.m. Greenwich Ob- 2nd mag.* 


10 28 p.m. Cranford Ob- 

10 10 29 p.m. 


5th mag.* 


1st mag.*; brilliant ? 
as Venus. 


Position, or 

Altitude and 


Rapid ; 1 se- 

Rapid ; 1 se- 

2 seconds. 

Centre B.; altitude 

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- 

Near Cygnus . . . 

Centre E.S.E. , near 

Centre E.S.E., i 

Passed from a few 
degrees above * 
Andromedae tojl] 
between * and /S.i 

Centre E.N.E. ; al-1 
titude 15°. 

From 30° to 15° I 
altitude ; centre ■ 



.ppearance ; Train, if any, 
and its Duration. 

fo track left 

eft no track 

Length of 

•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° 



eft no track ' ? 

bright track marked its 15° 
course throughout (15°) J 

Direction ; noting also 

■whether Horizontal, 

Perpendicular, or 


To right ; 6° from verti- 
cal ; down. 

To right j 6° from verti- 
cal ; down. 

To right } 25° from ver- 
tical ; down. 



To right; nearly hori- 




W. De la Rue. 


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. 


W. C. Nash. 

W. De la Rue. 


REPORT 1862. 



Place of 

Apparent Size. 



Position, or 

Altitude and 


1861. h m s 
Aug.1010 323 p.m. 

Greenwich Ob- ; 2nd mag.* 

10 32 32 

1010 39 p.m, 

Cambridge Ob- 

10 32 47 




10 40 p.m. 

10 42 p.m. 

1010 50£p.m. 

lo'lO 51 p.m. 

1010 51 1 

Cranford Ob- 

Trafalgar Square, 

Cranford Ob- 

Greenwich Ob- 

3rd mag.* 
1st mag.* 
6th mag.* 

Very luminous 

4th mag.* 


10 56 p.m. 

Cambridge Ob- 

Trafalgar Square, 



10 10 57 20 
10 57 30 

10 57 30 ^Trafalgar Square, 



3rd mag.* 


3rd mag.* 

2nd mag.* 

1st mag.* 
1st mag.* 

Very brilliant 

10 10 58 p.m. Greenwich Ob- 







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- 

Weston - super • 

Hawkhurst, Kent 

Trafalgar Square, 

Very bright.... 
1st mag.* .... 

Blue light 



1 second 

Slow motion.. 

From y Ursa? Ma- 
joris to the N.W 

Centre 13° S. front 
W. ; altitude 20° 

Centre same as th< 

Centre E.S.E. ; al 
titude 4°. 

^° below % Ursa 

Centre S.E.; alti- 
tude 9°. 

1 second 
1 second 
Rapid ... 

From a Cygni to t 

From a. Cygni to 

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 

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 


Like the elec- 
tric light. 


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° 



.ppearance ; Train, if any 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




•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 


eft a track 

eft a track 

eft a track 20° long 


eautiful track; 30° in 

rack endured 1 second.., 



lis star curved consider- 
ably in its path before it 

■ack of 3° 15' broad; 
lasted 4 seconds. 

3 train or sparks 


Vertical ; down 

To left; 45° from verti- 
cal ; down. 

To right; 30° from 

vertical ; down. 
Vertical ; down 

To left; 30° from verti- 
cal; down. 


ight enduring track. 


To right ; horizontal 

To left; 37° from hori- 
zontal ; down. 

W. C. Nash. 



, W. De la Rue. 

T. Crumplen and 
J. Townsend 

W. De la Rue. 

\V. C. Nash. 
J. Howe. 


T. Crumplen and 
J. Townsend. 

Herbert M c Leod 


T. Crumplen and 
J. Townsend. 

J. Howe. 

D. Walker, M.D 

Mostly divergent from Two observersdelineated W. W. Boreham 

Diverging from Cassio- 

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. 


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. 




Aug. 11 



Place of 

Apparent Size. 


h m s 

9 27 p.m. Flimwell, Hurst Jupiter. 
Green, Sussex. 

9 27 p.m. Ibid 

11 9 30 p.m. Hawkhurst, Kent 


10 p.m 

11 10 15 p.m 




10 17 4 


10 20^p.m 

10 22 p.m 

Flimwell, Hurst 
Green, Sussex. 



Hawkhurst, Kent 


4th mag.* 


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.* 

1110 37 p.m. Ibid 

1st mag.* 

lljlO 37 p.m.'lbid 2nd mag.* 

11 10 47 59 Hawkhurst, Kent 2nd mag.* 

11 10 11 p.m. Haverhill . 


3rd mag.* 



Position, or 

Altitude and 


Very slow 


2 seconds ; 
slow motion. 

Moved very 
slowly ; 2j 

l^or 14, sec, 

Centre 30 Q S, 

from E. ; altitud 

From near i Cygn 

to *i Pegasi. 
Centre 30° 

from E. ; altitud 

From | (y Equuli 

and y Delphin! 

to Equilat. wii 

(9 and c Del 

Down ; W. margi: 

of E. branch 

Milky Wav. 
From \ (c X 

Aquilae to <p Sa 

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 
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* ? 




Slow motion.. 

Very slow 

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 

Centre 3' S. fro 
W. ; altitude 26' 
Centre 3° S. froi 
W.j altitude 26 
Very fast Centre in zenith . 





Appearance ; Train, if any, 
and its Duration. 

jeft a track. 


traight track left in 1st 
two-thirds (the rest 
barren) ; remained 4 

t was a large pear-shaped 

Length of 

20 ; 

20° .. 


28 c 


10 : 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 


Tc right ; 45° from ho- 
rizontal ; down. 

To right ; 45° from ho 
rizontal ; down. 

To right ; horizontal ... 


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 


;ft a track. 
:ft a track. 


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. 


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 

Rev. F. Howlett 


A. S. Herschel. 

Rev. F. Howlett. 


A. S. Herschel. 

Three meteors fell 

Two observers counted 
46 meteors in one 
hour ; clear sky. 

Two meteors pursued 
the same apparent 

From \ {a *•) Andro 
medae to i (/3, 7) Ce- 

W. Airy. 

A. S. Herschel. 

W. Airy. 

Rev. F. Howlett 

W. H. Wood. 



A. S. Herschel. 

W. \V. Boreham 
and J. Hobler. 

W. H. Wood. 


A. S. Herschel. 

Rev. F. Howlett. 



REPORT 1862. 



1861. h m s 
Aug. 11 11 23 p.m 

11 11 23 10 

11 11 23 20 

11 11 38 p.m 

11 11 41 10 


Place of 


Apparent Size. 






Weston - super 

Hawkhurst, Kent 

1 20 


31 20 

12 52 5 

12 1 9 50 

12 1 18 20 




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. 



Sept. 6 

2 6 2 

2 14 30 

2 14 40 














Momentary . . 

2nd mag.* .... 

2nd mag.* j Brilliant white 1 

Brilliant white Slow motion. 

1st mag.* 
3rd mag.* 
1st mag.*.. 

Very slow 

3rd mag.* 

4th mag.* 
4th mag.* 

2nd mag.* 
2nd mag.* 
1st mag.*.. 

4th mag.* 
2nd mag.* 

8 p.m. Blackheath 

26 10 p.m. Greenwich 




? Moderate 


? ;Moderate 


? Fast motion . 

Twice the width of White 
the moon ; ir- 
regular circle. 


= 2nd mag.* Bluish white .. 1 to 2 sees 

3rd mag. 

Position, or 

Altitude and 


Centre 30° N. fron* 
E. ; altitude 33°| 
Good observaJ 

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 

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 

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« 

Appeared ^ (t I 

£) Ursae Major 



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 



lo track or sparks; 
straight course. 

to track or sparks 

Slight track throughout, 

15' broad; enduring 2 

■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. 



15° or 16°.. 



ood observation of track, 15° 
which brightened up 
after meteor was flown. 

2ft a tracl^. 

;ft no track 

:bulous ; left no track. 


ight train 5° 


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. 


A. S. Herschel. 

Remarkable for direc-Id 
tion, length, andi 

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. 

10 6 


30° from horizontal 

60° from horizontal 
30° from horizontal 

Three meteors to left ; 
downwards ; appeared 

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). 


] 862. 


W. II. Wood. 

A. S. Herschel. 







W. C. Nash. 

3., S. following Cloudy night 'J. MacDonald 


REPORT — 1862. 





Oct. 2 



Place of 

Apparent Size. 

h m 


8 40 p.m. Ibid. 
8 52 p.m. Ibid. 


8 40 

9 30 

p.m. Greenwich Park 
p.m. Greenwich 

9 48 
4 10 29 
4 10 36 



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 



= lst mag.*. 



= 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 

10 10 7 

p.m. Ibid 

p.m. Harrogate 

p.m. Ibid 

p.m. Ibid 

Small faint meteor 

= 3rd mag.* 

=2nd mag.* 

= 3rd mag.* 

= 2nd mag.* 
= 3rd mag.* 
— 2nd mag.* 





Bluish white., 



2 seconds. 

1 second ... 
1 to 2 seconds 

3 seconds... 

1 second ... 
1 second ... 
1 to 2 seconds 

Position, or 

Altitude and 



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| 

From Delphini| 
across * Aquila 
to 3 Aquila:. 

Moved in a south-, 
erly direction t 
few degrees 
below the 

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 

From the Pleiades 
to y Tauri. 

Across Capella ; 
about 20° in a 
northerly direc-| 

From y Pegasi, 
halfway to « 

Passed rapidly froi 
i Persei to 

From y Andro- 
meda; to k 

From fi Andro- 
meda; to d Cas- 

From j3 Cygni t 
£ Aquila;. 

30° from zenith U 

Fell from zenitl 
towards the S 

From y to /S Ce 

Across Cassiop 
to y Cephei. 


Appearance; Train, if any, 
and its Duration. 

Slight train , 


imall train 


irilliant train . 





any shooting'Stars 

»ne ,,.., 

Dne ,.. 

nail train ,, ,, 

Length of 

Direction; noting also 

whether Horizontal, 

Perpendicular, or 


22 c 


one Ahout 10 

10° to 15° 

About 45° 



Rather cloudy 

J. MacDonald. 




A very brilliant meteor.. 

Almost perpendicular . . 
S. to N. ; horizontally. 






W. C. Nash. 


Perpendicular , 







J. Coupland. 

J. MacDonald. 

W. C. Nash. 


C 2 


REPORT — 18G2. 



Place of 

1861.! h in 

Oct. 10 



10 16 p.m. 

10 20 p.m 
9 25 p.m, 






9 30 p.m. 
9 30 p.m 
9 42 p.m. 

8 20 p.m. 
10 26 p.m. 






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. 







Apparent Size. 



= 2nd mag.* 


2nd mag.* j White 

=2nd mas'.* White 

= 1st mag.* ... 

Small Bluish white. 


Position, or 

Altitude and 


1 second 

=2nd mag.* 


= lst mag.* Bluish white. 

= lst mag.*.... 
2nd mag.* . 


1 second Across a Lyri 

towards N.W.' 

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 «,| 
Shot up from thql 
southern ho- i| 

1 second Passing from E. ttl 

W. a few de- 
grees above thili 

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 

From Equuleus to, 
wards the W 

= 2ndmag.» Bluish white 

= 3rd mag.* 

Very bright , 

= lst mag.*.. 
= 2ud mag.* 


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 

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 

From the neigh, 
bourhood of Ca 
pella, in the da 
rection of Alda 
baran for aboul 

— L 


Appearance ; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




W. C. Nash. 


J. MacDonald. 

W. C. Nash. 
J. MacDonald. 

W. C. Nash. 


D. Walker. 

J. MacDonald. 










Moon shining brightly.. 



S. toN 

The next meteor fol- 
lowed this one at an 
interval of a few 
seconds, springing 
from nearly the same 

Cloudy after this time 
for the remainder of 
the evening. 



Left a luminous tail for 
about 3 seconds and 
burst, leaving the frag- 
ments luminous for a 
short period. 


Inclined upwards 



REPORT 1862. 

Position, or 



Place of 

Apparent Size. 



Altitude and 


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 


lft O OO t. n\ fimoYiwinK 

Momentary ... 

From the direction 


.» £.£. I'.lll. 

of Camelopardus, 

passed midway 

between Polaris 

and a Draconis. 

10 'fi iJ ""1 


From i Tauri to 
a poiut a little 

*" ""• I"-"" 

above » Gemi- 



10 38 p.m. 



From between £ 

Tauri and » Ge- 

minorum to 8 



11 1 p.m. 



Passed from y Ge- 
minorum in a 

westerly direc- 

tion, across the 

upper part of 



9 p.m. 



Fell from a few 
degrees W. of 

Ursa Major to 

about 10° from 



10 36 p.m. 



1 to 2 seconds 

From the Lynx 
constellation ; 

disappeared a 

few degrees below] 



10 52 p.m. 


Bluish white... 

From i Eridani to- 
wards the S. ho- 



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 


of Galaxy, be- 
tween Altasi and 
Ophiuchus, to 
10° above the 
horizon, W.S.W. 


5 45 p.m. 

Weston - super - 

Nearly the size of 
the moon. 


From 3° above « 
Herculis to near I 

the S.W. by S. 



5 45 p.m. 

Southern Hay, 

Larger than any 
Roman candle- 


From the tail of the 1 
Great Bear. 



5 48 p.m. 

Barlaston, Stone 

Elongated as long 


Fell slower 

From 20° W. of j 

as the moon's 


than a 

S. altitude 40° ; ! 


shooting - 

to 40° W. of S. 1 
altitude 8° or | 


ippearance ; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




iurst into a bright light 
when first seen ; left 
here a transitory track ; 
dropped to objects on 
the horizon fading away; 

mall train 

Fell vertical 



rain 10° to 15 



15 c 

25 c 

Another light was seen 
in the W. an hour 

Horizontally, E. to W. 


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 

G. A. Lance. 

W. C. Nash. 




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. 


Longitudinally west- 

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. 


Rev. T. AV.Webb. 


A. J. dimming. 

G. Wedgwood. 


REPORT— 1862. 


Nov. 12 



Place of 


p.m. Manchester (12 
miles S.E.). 

Apparent Size. 


5 50 p.m. 
5 50 p.m. 

Bristol . 

Stone, near 

> 6 3 p.m. Oxwich, 
Local time. 'Wales. 

ab — 60' ; bd= 13' ; Nucleus yel 


3« seconds 


lowish flame, 
conical part 

Brighter than theVivid blue 

Oval shape, nearly Pale brilliant 

= to the moon. blue. 

Position, or 

Altitude and 


From S.S.E. 
tude 35° ; 
nearly S. 
tude 8°. 


South As large as a 


10 14 p.m. Greenwich 

15 10 15 p.m 

= Venus 

About 6 sees. 




Very nearly overjB 

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 

Shooter's Hill, 

15 About 


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 | 

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, 


Last 3° = 

Mars, and 

faded away. 

Oval nucleus 8' long Bluish 3seconds , 

19 5 30 p.m. Sherwood, 7miles 

Much larger than 
any of the fixed 

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 (?). 



ppearance ; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




gure sharply defined ; 
very few sparks or 
breaks ; no permanent 
tail left ; no disruption 
at disappearance. 


To right ; from 43° to 
61° to the horizontal; 

R. P. Greg. 


\ c ' 

eft a track of golden 

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 


Figure of the meteor 
compared with the 

Rev. W. M. 

William Penn. 

S. G. L. 


(130° to 

Very foggy. Flashed 
an intense light, as 
if it broke out from 
behind a cloud before 
it was seen ; loose 

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 


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. 


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. 



REPORT 1862. 

Position, or 



Place of 

Apparent Size. 



Altitude and 



h m s 


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 



like a spent 
rocket ; like 
a Roman 

ing into 3 piece 
when almost 


Between 9 
&10 p.m. 

A bright body as 
large as the 



Burst into 3 part) 
nearly overhead 



9 35 p.m. 

A splendid meteor.. 



The grand exph> 
sion took plaoi 
close underneatt 
the Great Bear. 


9 35 p.m. 

Guestling Hill... 

Half diameter of 
the moon. 



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°. 



Greenwich Ob- 

One-half the dia- 


Nearly 10 sees. 

Appeared betweenii 

9 38 23 


meter of the 

y Orionis and 




Aldebaran (from 
behind great | 
dome of equato- 
real). Passed I 
or 8° below 
Pollux, and dis-i 
appeared 15° 
further N. 


9 40 p.m. 

At first stationary ; 

Pale green 

At least 10 

At first stationary! 

=Venus. When 

when under- 


for 2 seconds 

under the moon 

neath the 

at a point in 

=i of moon's 

moon, then 

Cetus. Ad- t 



vanced north-: 
ward under the! 
moon at half its 
altitude, and < 
finally disap- ! 
peared without! 


pearance ; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




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 


S.E. towards the N. 



About 80 or 90 seconds 
after the explosion, 
three distinct reports 
like heavy ordnance 
or distant thunder 
were audible. 


From S. by W. towards 

S.S.W. to N.N.E., hori- 
zontally across the 

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 

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. 


Mr. Felgate; G. 
Webb ; G. 
Pulham ; Ro- 
bert Bixby ; 
Frank May- 
hew ; John 
Steel ; Charles 
cated by G. 

Rev. G. Gilbert. 

James Pearce. 

Messrs. James 
Rock and 
C. Savery, 

Inclined downwards 15° 
or 20° from hori 


W. T. Lynn. 

John Hill. 


REPORT — 1862. 

Altitude and I 



Nov. 19 





h m 

9 40 p.m. 

9 40 p.m 

9 45 p.m 

9 45 p.m 



Place of 

Godstone, Surrey 


One-third the size 
of full moon. 


North Foreland 


Wroth am 


Apparent Size. 

Light very bright 
and steady ; oc- 
in some parts 
than others ; 
like an unusually 
large star. 

body nearly 
equalling the 
moon, but far 

Much larger and 
brighter than 
Roman candle 

Threw a great light 
on the opposite 
side from the 


White with a 
bluish shade. 


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\ 


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, 
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° 

At the Tan Ya 
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 


pearanee; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




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 

appearance was that 
of a light running along 
an outstretched line 
like the light of a rocket 

N'early due S. 
horizontal ; 

to N. 

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 
( = 60°). 

Full 70° .. 

Direction from S.W. 
N.E. ; horizontal. 


Appeared to drop some- 
thing as it went along. 

W. Mitchell; 
John Harruer 

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. 


REPORT — 1862. 



Place of 

Apparent Size. 



Position, or 

Altitude and 



h m 



7 40 p.m. 

8 10 p.m. 

2410 2 p.m 



5 42 p.m, 

9 32 p.m 

Wrotham Hill, Four times the size 
Kent. of one of the 

planets ; threw 
shadows on the 

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 



27 10 6 p.m 

2710 16 p.m, 


8 54 


3011 11 p.m, 

Greenwich Ob- 



i Sirius 

Brilliant blue.. 

1^ second 

2 seconds 

Appeared 5° W.i 
/3 Cygni ; disaji 
peared 4° E. ( 
a Aquilrc on tt 

Appeared in Pleii 
des ; disappeare 
near « Ceti. 

= 2nd mag.* Bluish white 

1 second 


= 2nd mag.* 

= 2nd mag.* 

ie hi 

1 di 

Bluish white . 

1 second 



1 second 

Dec. 1 



1 50 p.m, 

8 26|p.m, 



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 

Passed through tl 
Pleiades iu tl 
direction of A 

From y Geminonr 
to a point b 
twecn a. and 
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 

Appeared near 

From X Lvrse 
within 10" J off 
W. horizon. 



07 second 

a LyrK Moderate 

Blue 2 seconds. 



ipearauce ; Train, if any, Length of 
and its Duration. Path. 

)od-red ; tail like a ? 
Roman sword. 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




.in about 9° in length... ? 

Horizontal when under- Clear sky ; no smell of James Douse, 
neath the moon. sulphur. 







Many came from this 
locality far several 
evenings. This was 
the largest and 

train ; disappeared 

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 

a short tail 20° 



Inclined towards N. .. 

Towards the W., at an 
angle of 45° to the 

A fine bright night , 


It was very small and H. C. Criswick. 


i of some length 


Rapid motion 

Nearly vertical 

The sun shining at the 

Directly from Polaris... Remainder of flight in 
tercepted by houses. 

W. C. Nash. 

Herbert M c Leod. 
W. C. Nash. 




Dec. 1 


h ra 

8 50 p.m. 

9 8 p.m 


Place of 

Apparent Size. 


= 2nd mag.* 

Blackheath Hill, Size of Sirius . 

9 14 p.m. Walthamstow ... 

9 15 p.m. Weston - super 


1 second 

Position, or 

Altitude and 


The colour of 1*5 second 
the un- 

Somewhat smaller Pale yellow . 
than Polaris. 

Diameter 2'. 

Very slow ; 
5 seconds ; 
speed slack- 
ening stead 
ily, until 
almost sta 

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 

From between tl 
Pleiades and 
Algol ; neare) 
the latter. 

. From | (Aldebar* 
and a. Orionii 
to 8° W. 
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. 


Stone, Salop. 

Birkenhead (Sea. 


but not so bright. 

= 1st maa;.* 

Bright meteor , 

Large meteor 

the greenest 
rays of stars, 


Less than 
1 second. 

From altitude 4<| 
due E. 

From direction 
Cassiopeia to 

? 5 seconds From centre 

quadrate stars 
Ursa Major 
within 10° oft! 

Lancaster Almost as large as ' 

the moon. 

8 15 p.m. St. Bees, 1 { r mile 
exactly. inland. 

8 About Si 

Ball of fire 5 inches 
in diameter. 

? Burst; altitudc2 

or 30° a little ' 

3 seconds in 
state ; 6 
seconds in 

Bridlington As large as the 

Quay. moon. 



ppearance ; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




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 

ght unsteady, brighten' 
ing, and then diminish 

I'ew brighter and pear- 
shaped in falling ; train 
10° ; half disap- 
peared in the flight ; 
fragments proceeded 
as streamers after 
bursting; 5°, diverg 

ew to size of Venus; 
dear drop of green 
light disappearing 
suddenly at maxi. 
mum, with a red 

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 



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 

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 

J. MacDonald. 

H. C. Criswick. 

H. S. Eaton. 

W. H. Wood. 

W. C. Nash. 

D. Walker, M.D 

by R. P. Greg. 


' Lancaster 


Isaac Sparks. 

S., Correspond 
ent,' Manchester 


REPORT 1862. 


Dec. 8 


Place of 

Apparent Size. 



Position, or 

Altitude and 


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 


Size varied; light 
exceeded that of 
the moon. 

White, then 

2 seconds. 

From 10° to 15' 
above the moon 
whence move 
in a curved lin 
towards the 
earth westward 
to 20° above th 

8 15 p.m 

8 15 p.m. 

York (Holgate)... 


8 15 p.m. 

Manchester , 

Half the size of a 

Almost as large as 
the moon ; bright 
as noon-day. 

Longest diameter 
equal that of the 

Blue light ; 
colour pale 

Pale blue . 

From about the 
Pole-star to alti 
tude 25° or 30' 
a little "W. o 

From a point neal 
the Pole-star t 
the horizon, • 


Like the moon as 
seen at the time, 

Rapid flight 
3 seconds. 



Prestwich, Man 


land ; 3 miles 

One-third diameter 
of the moon. 

Brilliant meteor or 
shooting, star. 

Bright white, 
like molten 

10 or 15 sees. 

Castletown, Isle 
of Man. 

Considerable fire- 
ball; lighted up 
the scene in a 
very remarkable 

Several sees 

About the altitnii 
of Sirius or 
Orionis ; abo 
the horizon 
the time. 

From altitude 
due S. dov 

S.W. towar 




Appearance ; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




'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 

Baker Edwards, 

tail ending in green ; 
very even and somewhat 
'arted into 7 or 8 frag- 
ments, like red - hot 

)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 

Moved N.E. to S.W. . 

Correspondent to 
' Liverpool 

R. P. Greg. 

' Scotus,' Corre- 
spondent to 
' Manchester 

John Jenkins. 

Correspondent to 
' Mona Herald.' 

closed shutters as it it 

k. spearhead-like crescent 
moon five days old, 
with a short shaft 
was followed by rec 
star-like balls clustered 

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 

he fireball was suddenly 
arrested in its progress, 
remained stationary for 
several seconds, and 
burst without noise. 



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. 


No sound could be 

Moon clouded at the 





REPORT — 1862. 



Place of 

1861. h ro 
Dec. 8 8 20 p.m. Liverpool 

Apparent Size. 


Bluish - 

8 23 p.m. Birkenhead (Sea- 

8 8 25 p.m. 

8 25 p.m. 

8 8 30 p.m. 

8: 8 30 p.m. 

8 About 8 30 


Silloth, Cumber 

Dungannon, Ire- 

Double of Venus; 
£ of a minute of 

Nearly size 



Position, or 

Altitude and 


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 
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 

of full Palish blue ... 5 or 6 seconds, 


Strong glare in 

8 8 30 p.m. Wakefield 

As large as a man's 

8| 8 30 p.m. Coatbridge, La- B 

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 


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' 


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. 


\ppearance; Train, if any, Length of 
and its Duration. Path, 

Direction; noting also 

whether Horizontal, 

Perpendicular, or 




? 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 
blazing track followed 
it, and immediately 
following were many 
smaller globes or bulbs 
I of fire ; several bright 

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 

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 

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 

Cloudy night, moon con- 
cealed ; attention 
caught by crimson 
flush like lurid light- 

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- 
Fell vertical 

by Albert Greg 

W. R. Milner. 

Arthur Neild. 


REPORT — 1862. 


Dec. 8 


Place of 

h m 


Bowdon, Man- 



Settle, Yorkshire 

Newcastle - on 

In the even- 

Apparent Size. 



Position, or 

Altitude and 


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 

Very brilliant 

Light blue .. 

Cartmel, Lan- 

Douglas, Isle of 

Langdale , 

Holcombe Hill, 

Islington, Lon 


8 10 24 p.m. 

8 10 45 p.m. 

11 5 p.m. 

9 5 15 p.m. 
9 5 30 p.m. 

9 9 35 p.m. 


3 seconds 'From a little N.W.I 

of the zenith ; I 
described an arc 
towards the W. I 
At the altitude of al 

Many coloured 2 or 3 seconds 

Like full moon let 
loose in the sky 

Start liugly 
pale colour. 

Larger and brighter 
than the largest 

Most brilliant 
meteor; eclipsed 
the light of the 

= 3rd mag.* 

5 or 6 seconds. 

Visible 10 
before it 


It appeared to cornel 
out of the moon.! 

Glasgow Fine meteor 

Birkenhead(Sea- Meteors and shoot- 




Hawkhurst, Kent Brighter than 1st ? 
mag.*; large and| 
bright meteor. 



Disappeared behind 

woods N.W. 
? Disappeared behind 

a cloud near th 

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- 

1 second Appeared from 

behind a cloud 
moving parallel 
to the horizon. 



Appearance; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




jeft a long broad train 

Carried a luminous train, 
and burst at disappear, 

Outline very irregular, 
oval shaped ; tail formed 
of consecutive bulbs of 

i ball of fire 

Jurst in sparks like a 

./ike six or seven falling 

changeable in colour, 
pursued by a vari- 
coloured tail several 
degrees in length ; no 
explosion, no sparks. 

Humiliated the whole 




Hsappeared without ex- 

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 

Report very loud 
alarmed the inhabit- 

People greatly alarmed; 
no noise heard. 

They fell vertically . 

By memory, at same 
spot following day. 

Took a north-westerly 

More fell here at this 
time than at the 
highest time of last 
August or November. 

As if from Cassiopeia 

Correspondent to 
' Liverpool 

T. S. G., Corre- 
spondent to 
' Manchester 

W.H. Cockshott 

to ' Northern 
Advertiser,' R. 

by Albert Greg. 

Samuel Simpsou. 

John Richardson 
J. W. Wraith. 

James Foote. 

E. G. P., Corre 
spondent to 
' Manchester 

W. C. Nash. 

D. Walker, M.D 


by R. P. Greg. 

10° Parallel to the horizon... Rather cloudy 

J. MacDonald. 


REPORT 1862. 


Dec. 9 


Tlace of 

h m s 

9 40 p.m. Greenwich 

9 10 50 p.m. Ibid 

10! 9 45 p.m. Weston - super 





10 30 p.m.? Ibid 

9 12 p.m. Royal Observa- 
tory, Green- 

11 11 p.m. 1 Ibid 

11 23 p.m. Ibid 

11 28 p.mJlbid. 

13 10 p.m 



11 37 p.m, 
7 p.m 

7 p.m, 
to 4 a.m, 

24 9 p.m 

110 to 11 


11 38 34 

25 9 p.m, 

2511 45 46 

Weston - super • 

Birkenhead (Sea- 

Royal Observa- 
tory, Green- 

London . 

Hitchen ., 

Royal Observa- 
tory, Green- 


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. 


Small stars 

= a Andromeda? . . . 

= 2nd mag.* 




Dull or smoky 

Bright blue ... 


Bluish white... 


Smoky blue ... 



White and 
yellow ; 


Between a and 1 Blue 


Position, or 

Altitude and 


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- 

Fell from the I 
neighbourhood | 
of Orion towards < 
the W., moving 
over 20° of 

Across a. Ursa? 

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 

From a point a fei 
degrees above *'> 
Ononis to y On- 

[Fell perpendicu-^ 
larly from (3 Ge 
minorum towards 

From Z Tauri to 
wards a Tauri. 

Appeared by Ca 

Centre immediately 
below (3 Persei. 

From the direction 
of Cassiopeia to 
a Ursa; Ma- 

Chiefly near the! 
radiant before) 
midnight, after- 
wards in all 

In the S I 

2 seconds. 

I to 2 seconds 

In Orion 

1 second 

From near o to! 
below a Andro-I 

Shot in a northerly J 
direction be- 
tween a. and j8j 

Between a Cygni! 
and y Draconis,] 
below k Cygni. 



>pearance ; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 





20° Inclined 


5° N. to S., inclined 

Hess; light alternated 
en times a second. 





Slightly inclined N. of 

E. to W. 

As if a rapidly revolving 


The only two meteors 
seen ; night fair. 

A fine meteor 

less ; decreased 

ipidly until lost to 


v small train 

E. to W., inclined ...... Generally cloudy Id 

J. MacDonald. 

W. C. Nash. 
W. H. Wood. 


W. C. Nash. 

5° Perpendicular 


16° to 18° 

E. to W., horizontally. 
W. to E., due 

Horizontal from E.toW. 

Very cloudy. 

Very cloudy 

Ni;rht unfavourable. 



W. H. Wood. 

e left trains; courses 3° to 40°, 
raight. very va- 


ral small shooting- 
lrs without tails. 

)f a track lasting about 

About 2° ... 

General direction from 
Bellatrix to k On- 

25 to 30 per hour at 
10 p.m.; fewer after- 

Several shooting-stars 
within a short 

Almost horizontally, S, 

No other visible for 30 D. Walker, M.D 

W. C. Nash. 

A. S. Herschel. 

John Hill. 
W. Penn. 
Herbert M c Leod 
W. C. Nash. 

Straight down Herbert M c Leod 


REPORT — 1862. 


Dec. 26 



Place of 

Apparent Size. 

h m s 
11 27 23 


7 55 p.m. Belfast Lough. 

8 57 p.m. Ibid 

= 1st mag.* 

Twice size of Venus 

2710 34 p.m. Weston - super - 



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 



7 5 p.m 

About 7 p.m 




= y Draconis 

White . 



= Sirius 

\ Ursae Majoris 

Larger than Sirius 
and less than 

= Venus 

= Procyon 


1 second 

Bright blue . 

Bright blue . 
Very dark . 

Very bright 

2 seconds , 

6^ seconds ... 

Near 2 seconds 


Appeared betwefl 
£ and X Draconil 
disappeared bi 
tween y and 

18° above the hi 
rizon, near 

Centre at (i Dn 

2 seconds. 

Less than 
1 second. 

Nearly 3 sees. 

Bluish . 

Euston Square, 

Edgware Road 

= lst mag.*. 

Position, or 

Altitude and 


At appearance 
tween j8 and 

Near \ Leonis 


Between /3 andi 

Near Z, Cygni ....I 

3£ seconds 
If second 

Bluish \i second 

Brighter than Venus More yellow Slow move- 
than Venus, ment, 
in strong 

Considerably larger Similar to 
than Venus. Venus. 


Centre 2° belli 

Centre at luilfv* 

{y Oriouis a 

Centre almost hi|ki 

way (a Oriol 


Appeared below m 

moon; disali 

peared 3 : abo» 




pearance; Train, if any, 
and its Duration. 

•y slight train, scarcely 


Length of 

ck ending the whole 

ime of flight ; some' 

trhat radiated in ap 




ite tail 16° long ; dis- 
ppeared nearly simul- 
ineously with meteor. 



U train 
U train 

11 train , 

1 globular, surrounded 
sparks ; short evan- 

bent tail of flame 

ce character or ap 


>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° ... 


Direction ; noting also 

whether Horizontal, 

Perpendicular, or 



Almost horizontal 


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 

Inclined north side 

Inclined (most) westiNear 61 Cygni 

side of perpendicular,! 

let fall from its ap 

Path parallel to 3 and y 

Cygni, from the 

former towards the 


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. 


W. H. Wood. 



Vertical; down 

D. Walker, M.D, 

The latter half of thejObserving Venus and 
path appeared curved, the moon ; clear 

An inclined direction 
from beneath the 


W. R. Birt. 

C. Herb. Bright. 


REPORT — 1862. 


Jan. 11 











h m 
9 43 p.m 

Place of 

Apparent Size. 

Weston - super -| = Sirius 

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. 



= Jupiter 

--K (foot) of Ursa 

Ibid =Capella. 



= Capella. 

Islington, Lon- 


Weston - super 



= 3rd mag.* 
= 3rd mag.* 

= lst mag.*.. 
= 3rd mag.* 

= 3rd mag.* 
= 3rd mag.* 

= 2nd mag.* 

Birkenhead (Sea- = Rcgulus 

Islington, Lon- =3 - 5 mag.* 


11 25 p.m. Ibid 

= 1st mag.*. 

25 11 47 p.m. Weston - super -= 3rd mag.* 


Vivid blue 

Bright yellow 

A very dark 



Position, or 

Altitude and 


3 seconds, 
slow motion, 

Less than 
1 second. 


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 

Appeared at i Dr; 
conis ; disap. 
peared at y Dn 

Appeared very nei 

Rigel ; disappeart 

near y Eridani. 

Appeared very nei 

Appeared near Pnjj 

Slow ; 1 sec. 
§ second 

Appeared near 3 

From a star fll 
following w Drl 
conis to i Dr 

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 

Same track 

Smoky blue... 
Smoky blue . . 

Bright blue.., 

Fast ; i sec... 
Fast; -J sec... 

Bluish . 

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' 

From £ (r, v) A 
dromeda; towar 
(i Andromedse. 

From /3 Andr 
medse towar 
v Andromedse.. 

Appeared near 
Bootis ;disappe» 
ed near /3 Bootis 


I learance ; Train, if any, Length of 
and its Duration. Path. 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 


- Path nearly perpendicu- 
lar to the horizon. 



jack left 

t tail 3° long followed 
e meteor. 

tail ; intermittent 
;ht ; two alterna- 
jns; almost disap- 

rack left ; no sparks., 

Serpentine path ; very 

10° Inclined 50° southward 

Auroral glare ; N.W. by 


Rapid lightning from 
N.W. by N. 


W. H. Wood. 






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. 


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. 


W. H. Wood. 



D. Walker, M.D 
A. S. Herschel. 

A. S. Herschel. 

\V. II. Wood. 


REPORT — 1862. 


Jan. 25 


h m 
11 49 p.m 

2511 55 p.m 
2511 56-£p.m, 

Place of 

Islington, Lon- 

Weston - super ■ 

Islington, Lon- 




2511 57i p.m. Ibid 


2512 p.m. Birkenhead (Sea- 

24 a.m. 
30 a.m. 

Weston - super 


35 a.m. Ibid 

6 10 p.m. 

Birkenhead (Sea 

2611 44£ p.m. Islington, Lon 






Feb. 2 

Apparent Size. 

2-5 mag.*.. 
= 3rd mag.* 
= 0-4 mag.* 

= 3rd mag.* 


Faint yellow... 
Dull blue 

White, bril 
liant, then 


9> Leonis jBluish 

= 2nd mag.* Blue 

= 4th mag.* 

= 2nd mag.* 
= Capella 

Very dark 

= 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. 


Stone, near 

Islington, Lon- 

Birkenhead (Sea- 
Kilburn, London 

= 4th mag.* 
= lst mag.*.. 


0'9 second .. 

j second 

1-7 second .. 

Position, or 

Altitude and 


From 1° N. 

S to X Cassiji 

Disappeared neaw 


From a star 2V J 
of a> Draconfl 
2° beyond o Djj 

- 7 second ...;From y to ? Cij 

\ second Disappeared 2i 

below a li 
joining n audi 

Slow ;f second 


^ second 

f second 


Tolerably large ; 
=3rd mag.* 

Orange colour 


White light,,, 



= 0-8 mag.*. 

= 1st mag.*. 

= Venus at maxi 

Large blue light . . 

= Rigel 


White .. 
Blue .. 

Appeared at wl 

foot of U| 

From § Ursae 
joris to a. Drac 
£ second Centre 2° 

and 8° E. 


5 S. of i I 
conis to 1° S 
Draconis, i 
two-thirds as 

From £ (k, y) ( 

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 

From i (i 
Ursre Majoris* 

From beneath & 

0-8 second .... 

0'5 second ... 
0-5 second ... 
2£ seconds ... 

1-3 second ... 


J second 

Very slow mo- 

slowly ; \ 

2 J- seconds ... 

From 2° above I 
belt of OriOiil 
about 15° all 


i pearance ; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




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 


18° or 20 3 


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, 


7 ... 

11 ; 


To left; 7° or 8° from 
vertical ; down. 

W. to E., horizontal 

To left ; horizontal. 

Parallel to y, a. Cassio- 
Directed from i Persei... 

To left ; 20° from hori- 
zontal ; down. 

To left ; horizontal. 

Inclined downwards to 

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. 


D. Walker, M.D. 

W. H. Wood. 



D. Walker, M.D 

A. S. Herschel. 

W. Penn. 

A. S. Herschel. 

D. Walker, M.D 

C. H. Bright. 

Correspondent to 
' Manchester 

D. Walker, M.D 


REPORT — 1862. 

1862. h m 
Feb. 2; 8 20 p.m. Tarporley, Che- 



Place of 

Apparent Size. 

2 8 20 p.m. Liverpool 

Lighted sky and 
landscape like a 
flash of light- 



White ; after 6 seconds, 
purple wrap- 
ped in white, 
then red. 

2 8 21 p.m. Observatory, 

2 8 30 p.m 

Manchester , 




Mold, Flintshire 

= lst mag.*, then a The globe was 
large globe. of a bluish 


Not as large as Unchanged 
moon, but ap-! blue 

Position, or 

Altitude and 


proaching to it 
much brighter. 

In size it looked to 
a star as a billiard 
ball does to a 

About as big as the 
moon, light as 
brilliant light- 


to Visible 3secs. ; 
and; slow motion, 

? 6seconds;mo- 

derate speed. 

10 or 11 inches 




Whitish colour 

2 seconds 

From nearly S. 
a little E. o 
Pleiades to net 

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»; 

From altitude 30 
E.S.E. ; disa; 
peared 20 D aba 

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 

= one-fourth of the ? 


Bright amber.. 6 seconds 

Moving slowly 

= half size of full 

Colour of 
moon, pale 

but ■ 

Not more than 
2 or 3 sees. 

E.S.E. ; altitud 



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 

From 3° N. oft 

Centre I (Cor (• 

roli and n Ur 



jpearance ; Train, if any, Length of 
and its Duration. Path. 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 


irst white, then bursting 
[like a rocket ; it took 
a purple hue with 
white light ; then red ; 
iu which state it disap- 
No luminous track 

ft many stars and sparks 
in its track of various 

ad with a tolerably 
defined edge ; circular ; 
long white track ; visible 
20 to 25 seconds. 

rfectly round ; very 
'.ittle train ; vanished 

•cular ; luminous track ; 
asted half a minute. 

30 c 

peared to explode twice 

fectly round; burst 

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. 

i track left 

Nearly horizontal 

S.W. to N.E., obliquely 
towards the earth. 



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. 


Thin strata of fleecy 

Moved along among A. H. Allcock. 
belts of clouds. 


In an oblique direction 
towards the north 

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. 



byll. C. Sorby, 
Messrs. Roberts, 

Mappin, and 

W. P. W. Bux 

ton ; Mr. 


to Carnarvon 

R. Owen. 

C. H. B. Kambly 
John Hall, jun. 

D. Walker, M.D. 



REPORT 1862. 



1862. h ra 
Feb. 2 10 54 p.m 

211 11 p.m 

Place of 

Apparent Size. 


Ibid , 

2 11 30 p.m. Ibid 

9 p.m. Kilmarnock, 

4 11 46 p.m. 

Weston - super 

9 11 41 p.m. Birkenhead(Sea- = Jupiter 

= Castor 

= Cor Caroli 

= Cor Caroli 




Quarter diameter of White 
moon, or 3 times 
Venus at maxi- 


Position, or 

Altitude and 



Bright blue...|H second 
Blue 2 second . 

1011 32 p.m, 


18 8 37 p.m. Greenwich 

= Arcturus 

i second IFrom % to i Uri 


3 seconds Centre i (Cor Ca|s 

rob: and Arc- 
turus), 2° higher 
Centre £ (j3 Leonif « 
and a Coif 
More than half [Appeared close 
a minute. Pollux ; disapi 1 

peared close ti 
Appeared near 

Centre 2° below / ;, 
Ursae Majoris 



9 12 p.m. Ibid 
11 12 p.m. 

23 a.m. 

1911 32 p.m. 
1911 50 p.m 

Islington, Lon- 

Birkenhead (Sea- 

Islington, Lon- 

= 3rd mag.* 

= 3rdmag.* 

= y Cassiopeiae .. 



\ second 

1 second 

Twice diameter of Yellow 


19 12 10 p.m. Ibid. 


8 45 p.m. 

9 30 p.m. 
2011 p.m. to 
12 p.m. 



Weston - super - 


= 4th mag.* 

= Sirius 

Aquilae , 

= 2nd and 3rd mag, 

11 Z2\ p.m. Islington, Lon- 
10 57 p.m. Greenwich 

11 5 p.m. Islington, Lon- 

= 3rd mag. shoot- 

■ t Cassiopeiae 
= 2nd mag.* .. 

= a. Persei 




Nearly 1 sec. 
0*6 second .. 

| second 

0*2 second 

L3 second 



Centre betweei 

Arcturus and 

From direction c 

Capella ; disap 

peared near 

From ? Tauri acros, 

a. Ononis, 
t Cassiopeiae,! 

A Cameloparda! 

to I (X. «1 
From H c to righ 
of ti Draconis. 

Centre i (y Cephi 
and ;> Cassio- 

From i (Polaris , 
fi Aurigae) to 
§ (9 to «) A* 

Appeared near 

0-25 second . 

White About 2secs., 


06 second 

Centre ^ (y Cf 
phei, /3 Cassic •, 



1^° following 1 
Aurigae to H 
following /3 Ai 



ppearance; Train, if any,! Length of 
and its Duration. Path. 

!o track left 

< small track left 

o track remained , 


;eadylight, very brilliant, 
like the electric light, 
or a fine ball ; no train 

noky appearance ; semi- 
o track remained 

3 track left 


Direction ; noting also 

whether Horizontal, 

Perpendicular, or 



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. 


11° or 12° 

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° 

To left ; 30° from hori. 

zontal ; down. 



Vertical ; down 

Almost N. to S. 

Vertical ; down 

Direct from Polaris. 


track left; nosparks...'3°.., 
ne 120° 

Nearly from Polaris 

From Polaris 

D. Walker, M.D. 


Robert Ctaig, 

W. II. Wood. 
D. Walker, M.D. 


W. C. Nash. 


A. S. Herschel. 

One meteor in an hour.. D - Walker, M.D 

Radiant in Perseus 
N. P. D. 33° ; A. R 

Radiant Polaris , 

From Polaris 

track left ; no sparks... 

Fell from zenith to- 
wards the western 

From Polaris , 

Radiant Polaris 

Tailed star; 1st mag- 
nitude ; blue ; 10° in 
3 seconds; tail as- 
cended and dissipated 
like steam. 

A. S. Herschel. 


W. H. Wood. 


J. MacDonald. 
A. S. Herschel. 



REPORT — 1862. 



1862. | h m 
Feb. 21 U 15 p.m. 

21 11 15 p.m, 


9 25 p.m, 



23 9 25 p.m, 





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 

Islington, Lon- 

■y Cassiopeiae .. 

As bright as Ju- 

Magnificent meteor 

Weston - super 

Liverpool, Wal- 
lisby, Cheshire 

Bramboro, Ches- 

Cross Nouses, 


Weston - super 



Islington, Lon 

Weston - super 

Apparent Size. 




1 second 

About 2 sees. 

y Cephei to | 
Cephei ; ^° fol 

=half diameter of Vivid red light 

Bright light filled A cold light, 

the streets. 

A bright light 
thrown from the 

Exceedingly bril- ? 

not flame- 

= 2nd mag.* 
= 2nd mag.* 

= one-eighth of 

= 4th mag.*. 


= lst mag.* 

= lst mag.*. 


Pale red 




H- second 

Leisurely , 

Position, or 

Altitude and 



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- 

Origin near Jupiter, 

Flashes 2 sees., 
then ran 
across the 

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 

From Cassiopeia 

Appeared close | 


Centre 1° S. 
p q Camelopar 

From Sinus 



ippearance ; Train, if any, 
and its Duration. 

to track left ; no sparks.. 

Length of 

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 

explosion ; long di- 
stinct train of light, 
disappearing slowly like 
smouldering twine. 



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 

to flashes like lightning, 
then ran along the ho 
rizon in one long broad 
line, which endured 
five minutes, not chang- 

track left 

netary, or better, a 

'•mentary train. 

overcast with haze 


Direction ; noting also 

whether Horizontal, 

Perpendicular, or 



f covered with thick 


From Polaris 

In the N., fell from the 
zenith, disappearing 
behind the houses. 

E. to W., at an angle of 
about 80° with the 

E. to W., nearly hori- 
zontal ; west end de- 
pressed 2° or 3°. 

From E. to W. by S. 


A. S. Herschel. 

J. MacDonald. 

The tail faded graduallyjcorrespondentto 
no change. ' Liverpool 


Slightly inclined to the 

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 

Directed from o Ursa? 

The stars seemed to go 
out on that side of 
the hemisphere, and 
did not recover their 
brightness for half an 

Studley Martin. 

T Juman. 

Sky obscured at 10 p.m. 

James Caswell 
and Son. 

Perpendicular to ho- Fell one per hour 

One star in an hour; 
N.W. ; cloudless. 

Perpendicular to ho- 

W. H. Wood. 


A. S. Herscliel. 

W. H. Wood, 


REPORT 1862. 



Place of 

Apparent Size. 



Position, or 

Altitude and 


Apr. 14 

h m 

7 42 p.m 









10 10 p.m. 


8 30 p.m. Greenwich Hill. 

8 56 p.m. 

9 50 p.m, 

Weston - super 


10 35 p.m. St. John's Wood, 

10 26 p.m. 

to 10 times as 
bright as Jupiter. 


Fine meteor. 

Larger than Jupiter 

Larger than 1st 

3 seconds. 

From 10° or 12 1 
over Jupiter H 
altitude 32 % S 
by W. 

3 seconds. 



Nearly as large as Deep yellow. . . 

Brilliant body of j Bluish colour- 
light, ed, 

2 seconds .. 
Slow ; 1| sec. 

Slow ; 2 sees. .. 

Weston - super - =lst mag.*. 

Brilliant blue. 

11 33i p.m. Islington, Lon- 

10 30 p.m. 

Weston - super - 

= Pollux 


25 10 30ip.m. 

26 10 52 p.m. Ibid. 



10 52|p.m 

8 42 p.m 

: Spica Virginis . 

= Spica Virginis . . 

Birkenhead (Sea- = Jupiter 


=2nd mag.* 


Spica Virginis 

Spica Virginis 

7 seconds. 

I second 

0-4 second 

joris and Polaris 
to centre of Ck 
rona Borealis. 

Between p and 

16 Draconis tc 
y Draconis, 
close and parall 
to a. and y Dr. 

From Arcturus 1 
18/i Bootis. 

Between N. and 1 
altitude 45°. 

At appearance ne 
41 and 42 C 

From 1° S. < 

| second At appearance ne 

66 Virginis. 



J second 
1 second 

66 Virginis .... 

From «■ 1 Cyg 
passing betwe 
the head stars | 

2\ seconds ... Close to /i Hi 

1 to 2 seconds 

From the direct!) 
of Ursa? Majo 
towards the' 
horizon past 



Direction; noting also 
Lppcarance ; Train, if any, Length of whether Horizontal, 

and its Duration. 


Perpendicular, or 



'ear-shaped ; no track 
visible through clouds ; 
faded gradually, and 
disappeared quietly ; 
very slight train. 

.eft a train like a sky- 

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. 



io track; no sparks;. 7° 
brightest in the middle. 



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.. 

by W. Penn. 

W. Airy. 
W. H. Wood. 




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 ; 

To left; 30° from verti- 
cal ; down. 

W. H. Wood. 


Appeared first as aid. 
second magnitude 
star, and gradually 
increased until equal 
Venus, when it be- 
came suddenly ex- 

; D. Walker, M.D, 

W. C. Nash. 


REPORT — 1862. 



Place of 

Apparent Size. 



Position, or 

Altitude and 


1862. h m 
\pr. 27 8 51 p.m. Greenwich 

27 10 10 p.m. Birkenhead (Sea- 

= 2ndmag.» Yellow [1 second 

= Venus 

. Blue i second 

27,10 50 p.m. Ibid 

2711 25 p.m. 


28 10 46 p.m. Weston - super 

29! 9 53 p.m. ! Ibid 

29 11 6 p.m. Islington, Lon- 
29 11 33 p.m. Ibid 


May 21 


10 27 p.m 

10 10 p.m. Ibid 


11 37J p.m. Ibid. 
11 55 p.m. Ibid. 

Weston - super 

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 : 

Half as bright as White, then 

ollrsae Majoris 


0'2 second ... 

4 - 5 seconds; 

= 2nd mag.* Blue 

= 1st mag.* 

= 1st mag.* 
= lst mag.* 

the month of June 

Yellow . 


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 

Centre 2° below ) 

From £ (Crateris)j 

to y (Corvis). ; 
From Ursa Major..! 

to U° S. ol 
6 Cassiopeia?. 

From $ {q, p) t<l 
L Camelopar- 


From /* Cephei it 
within 4£° of 

1-j second 

2 seconds. 

1-J second 

From a Cephei to 
wards /3 Cassio 

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. 


= Venus 

Yellow 4 seconds. 

From stars 4, 5, an> 
6 Camelopardal 
to 14 and 15 Le 


Ipearance ; Train, if any, 
and its Duration. 

Length of 

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 



18 : 

To right; 45° from ho- 
I rizontal; down. 


8° Vertical; down 

t a slight track 10 c 

le '.... 

le „ 

t no track 

track ; no sparks . 

To left ; horizontal , 

track ; no sparks 




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. 




Directed from (3 Ursae 

Course straight, but as 

if wrinkled in the last 

half, a Cephei to » 


Brilliance in first half of 
flight uniform ; com 
mencement not seen 
diameter of dull disc 


faint tail 


W. C. Nash. 

D. Walker, M.D. 



W. H. Wood. 


A. S. Herschel. 



A remarkable object 
resembling in shape 
an elongated spindle, 
gradually increased 
and decreased in 
size ; the magnitude 
given refers to its 

The data not accurate... 

W. H. Wood. 




10 : 

e tail 15° long Inclined 

W. H. Wood, 

Burst with sparks ; tail Id. 
not durable. 


REPORT 1862. 



Place of 

Apparent Size. 




Position, or 

Altitude and 


July 19 




h m 
11 30 p.m. 

11 7 p.m. 

11 7 p.m. 
11 10 p.m. 

Weston - super - 


= Jupiter (plane- 


From /3 Cassiope 
From Polaris ..» 
Head of Cepheus 





From a Draconia 

stars H 30 and 
Ursae Majoris. 




9 50 p.m. 

10 22 p.m. 

11 1 p.m. 

11 8 p.m. 
11 12 p.m. 
11 17 n.m. 




About 2 or 3 

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 

From H 30 and 4 

Weston - super - 



Ursae Majorii 
passed bet we | 
a and £ Url 
From 6 Draconis; 


Head of Cepheui i 
y Andromedse.,,! 




28jll 43 p.m. 

28 11 48 p.m. 
28 Midnight... 



5° below a Pegu! 

From H 30 and 
Ursae Major 
passed bfitwe 
a and /3 Ur, 

From p to Ur 

From s Cassic 



1 to 2 seconds 




10 a.m. 

32 a.m. 

10 18 p.m. 





Bluish white .. 

Shot from «|] 
Aquarii towai 
the zenith a 
short distan 
from a, Cygni. 



pearance ; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also ; 

whether Horizontal, 

Perpendicular, or 




i throughout 












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. 



Very fine; cloudless .. 


J. MacDonald. 

A very fine meteor , 

W. H. Wood. 


W. C. Nash. 


REPORT 1862. 



Tlace of 

Apparent Size. 



Position, or j 

Altitude and! 

Azimuth. I 

July 31 


Aug. 1 

h in 
10 34 p.m. 

10 53 p.m. 

10 10 p.m, 




10 48 p.m. Ibid. 

10 57 p.m. Ibid. 

11 18 p.m. Ibid 
10 39 p.m 

Weston - super 

10 42 p.m. Ibid. 

11 45 p.m. Ibid. 

11 50 p.m. Ibid. 

11 54 p.m. 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 


1 44 a.m. 

3 10 15 p.m. 
310 47 p.m. 



Weston - super 

= 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 , 


1 second 

1 second 
1 second 

1 to 2 seconds 


5 second 

Yellow ,., 

% second 
% secoud 


^ second 
I second 



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 £ 

From the directi 
of a Persei 1 
wards north I 
rizon, passing 
few degrees I 
low Capella. 

From the directi 
of Cassiopei 
disappeared n« 

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] 


£ 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* 

(36) Ursa; Majoi* 

to horizon. 
From « Pegasi '* 

■x Aquarii. 
a. Pegasi ^ 


learance; Train, if any, 
and its Duration. 

Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




15° to 20° 

27 c 

11 train 10 



15° to 20° 







\V. C. Nash. 






Towards S. 

A red thick tail curled W. H. Wood, 
off from nucleus andi 
disappeared within 
the latter. 


Great numbers left un- Id. 

recorded between 10 h 

42 m and 11" 45 m . 

Horizontal, westward... Tail endured 2 \ seconds 

Horizontal, S 


Horizontal, S Tail endured 2 seconds. 

Near -J- 

Horizontal, southwards. 
Horizontal, southwards. 

tail; 2£ seconds .. 

5° Northwards 

8° U- 



15° i 


13 : 

10° Inclined E. 

Tail brightest in centre, 
fading at ends. 







W. C. Nash. 

W. H. Wood. 


REPORT — 1862. 


Aug. 3 


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 

Weston - super 


Weston - super 


11 p.m. 

9 5 p.m. 

9 5 p.m 

10 32 p.m, 

9 55 p.m 

Weston - super 




Weston - super 


Weston - super 

Apparent Size. 

= 2nd mag.* 
: 2nd mag.* 

= 3rd mag.* 
; 1st mag.* 

= Capella. 

= lst mag.* 


= 2nd mag.* 


Weston - super 


10 45 p.m.] 

10 54 p.m. Ibid. 

10 54 p.m. Ibid. 

11 8 p.m. Ibid. 

= Sinus 

= 2nd mag.* 

= 2nd mag. 


= 3rd mag.* 

Nearly = Venus .. 



i second 
1 second 


Deep yellow. 



White | second .. 

Bluish white... 1 1 second 


Position, or 

Altitude and 


•§ second ... 
1 to 2 seconds 

\ second .. 
1J second 

£ second 

1 second 

From (12) (13) ( 

From « Peg! 
two-thirds of 4 
distance to 

From (12) (1 3) ( 

Moved from a po 
midway betwe 
j3 and a Peg 
towards horizc 
near/3 Piscium 

From (12) (13) ( 

From c Cassiopt 
to R. A. 50 ill 
nutes, Dec. ] 

From Z Cassiope 
to y Andromed 

Vivid blue .. 



= Sirius White 

A little less than Bright yellow 

= 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 

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. 



H 24 Camel 

dali to /} 

t Cassiopeia '! 

II 5 Cameloparch 
| to head of Lyi J 
j3 Cassiopeia? ..ft 

From Polaris " 
between /3 an 
Ursae Minoris 



Ipearance ; Train, if any, 
and its Duration. 


all train 



Length of 

5 Q 

11 : 



tail ; length 12° ; du 
ation half a second. 

rt streak 

15° ToN.W 

25 c 



tail, 15° ; endured 

Direction ; noting also 

■whether Horizontal, 

Perpendicular, or 


Nearly horizontal, east 

To N.W. 



Serpentine; made two 

E. to W. 

Increased from a yellow 
2nd mag.*; tail curled 
off thickly till all 

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. 




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 

August 8th overcast andjW. H. Wood. 

wet at Weston-super-j 

Bright moonlight night. Id. 

Suddenly blotted outjld. 
when most brilliant. | 




REPORT — 1862. 



Place of 

1862. h m 
Aug. 911 11 p.m 



11 17 


10 28 


12 10 49 
1210 50 



Apparent Size. 



Weston - super 



= Capella Bright blue ... 1 second 

Trafalgar Square, 


1211 9 p.m 

18 9 17 
18 9 55 


=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 


Star-cluster, head 
of Auriga to N. 

Not more than 

2 or 3 sees. 

1-5 second ... 


10 7 

18 10 31 




1810 42 p.m 





= 1st mag.*. 


= 2nd mag.* 

= 2nd mag.* 

Very small 

White, then 5 seconds 
red, then 


Bright blue.. 

1 second 

2 seconds. 

2 seconds. 

3 seconds. 

I second 

a. Draconis to body* 
of Ursa Minor. 

Head of Lynx to N. 

)3 Ursaj Majoris 
to x Ursse Ma- 

D Aurigae to £ Au-,| 

From 85 to 62 Her- 

From ^ (? Uro^l 
Majoris and « 
Bootis) to m 

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 

From a Lyrae to 
wards the S.W: 

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°. 


Appearance ; Train, if any, 
and its Duration. 


Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 





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 


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 , 


To left ; slightly down, 

To right ; slightly down 

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. 




T. Crumplen and 

J. Townseud. 
A. S. Herschel. 


J. MacDonald. 

tht train , 

Fine night , , Id. 





REPORT — 1862. 

Position, or 



Place of 

Apparent Size. 



Altitude and 


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. 


9 44 p.m. 


Bluish white. . 

Fell from the zenith 
towards the N. 

for a distance of 



10 32 p.m. 



From a point near 
Capella to # Au- 



10 46 p.m. 


About 0-5 sec. 

Started near a. An- 
dromeda?, and 

passed across /3 



30 a.m. 

Weston - super - 


From j8 Ursa? Ma- 



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. 


9 47 p.m. 




From the zenith 
towards the W. 

for 5°. 


10 p.m. 

From the neigh- 
bourhood of « 

Cygni towards 

the W. for 17°. 


10 7 p.m. 

Weston - super - 

Bright blue . . . 

From the mouth of 
Ursa Major to 
the fore-foot. 


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 


10 36 p.m 



From a Lyras to- 
wards the S. for 

a few degrees. 


10 43 p.m 

Weston - super • 


lg second ... 

From the mouth of 

Ursa Major to 

the fore-foot. 


10 45 p.m 


Appeared in the 

N. about 10° to 

the W. of Ursa 

Major, passed 

through that con- 

stellation, disap- 

pearing about 15° 

to the E. 




Appearance ; Train, if any 
and its Duration. 

, Length of 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




A. train of brilliant rer 
sparks, remaining nearh 
one second after the 
meteor had disappeared 


J. MacDonald. 


W. C. Nash. 

W. H. Wood. 






15° to 20 D 

E. to W. .. 

Light train of red sparks, 
which lingered for half 
a second or more after 
the body of the meteor 
had disappeared. 



W. H. Wood. 

Brilliant train of red sparks 
Faint streak 


Slight train 



W. H. Wood. 

J. MacDonald. 





REPORT— 1862. 




h m 
11 30 p.m 

Place of 

Apparent Size. 

Weston - super - = Jupiter. 

22 11 32 p.m.ilbid. 

23 2 am. Ibid. 
23 10 43 p.m. Ibid. 








11 30 p.m. 
11 35 p.m. 

11 49 p.m 



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.* 



Position, or 

Altitude and 


Very bright 2£ seconds ... (4, 2, 6) Lyncis 



Bright blue . . 

Istmag.* 'White \ second 

Venus +globular... Orange 2 or 3 seconds 


9 58 p.m. 
27|10 19 p.m 
2711 17 p.m 



Greenwich Park 



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 


9 18 p.m. Ibid. 

= 2nd mag.* 

= lst mag.* 


= Jupiter.... 


= 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 

From the zenith, 
towards the W. 
for a distance of 

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- 



Appearance; Train, if any, 
and its Duration. 

Length of 

An adhering short white 

20° + 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 






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. 



Long yellowish tail, 4 sees, 


20° N. 

25° N. 
20° ... 



Light train of blue sparks. 



Path horizontal 
S.S.W. to W. 



Illuminated the heavens 
termination not seen ; 
threw off red sparks 
in its course like a 

About 15°. 


ight train 

Hidden for a short period 
behind clouds. 



J. MacDonald. 


W. C. Nash. 



J. MacDonald. 






REPORT 1862. 




h m 

10 47 p.m. 

2911 29 p.m. 





About 5 40 

5 45 p.m. 

6 5 p.m 

9 45 p.m 


9 45 p.m. 

Place of 





Apparent Size. 

= 2nd mag.* 

Very small 

Saw a most brilliant 

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 

Worcester Sudden bright 

light ; brilliant 
ball of light. 



Bright white... 



1 second 

1 second 

For about £ of 
a minute. 

Position, or 

Altitude and 


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 

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 


Gedling, near Exceedingly bright; Colour bright 

(3^ miles E. of| 

10 13 p.m 

Beeston, near 

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 

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 

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 


From S.E. by S. to 
S. by E. When 
first seen, the 
meteor was pass- 
ing near y Pegasij 
it ended near S 

From 40° above 
S.E. by S. bo 
rizon to about 
20° to 25° above 
S. by E. horizon; 
the same meteor 
as above. 


Appearance; Train, if any, 
and its Duration. 


Length of 

Direction; noting also 

whether Horizontal, 

Perpendicular, or 




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 

A track of sparks pursued 
the head but did not 

Seemed to burst, and 
left a trail of sparks 
which gradually dis- 
appeared in about a 

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. 


It proceeded in a north- 
erly direction [?]. 

N.E.toS.W. ; consider- 
ably inclined down- 

The sun, though nearly 
setting, was shining 
brightly ; not a cloud. 

W. S. Tomlin; 
' Evening 
Sept. 23rd. 

In clear blue sky ; before FrederickReeves, 

Proceeded in a south- Cloudless sky 
westerly direction. 

In the S.W., from E. to 

Fell rapidly towards the Wind E. or N.E. ; clear 
earth. ' sky, not a cloud. 

A cloudless night 

by A. S. Her- 

Correspondent to 
the ' Standard.' 

The Rev. S. K. 
Swann, M.A., 

S. Watson. 


BEPORT 1862. 



1862. h m 
Sept.19 10 13 p.m 

19 10 13 p.m 

19 10 15 p.m 




10 15 p.m. 

19 10 

Place of 

Apparent Size. 

Euston Square, Amazing meteor 
London. head = full moon; 

light = noonday 



Gave more light 
than the bright 
est lightning. 

i Completely lighted 
up the road. 

Dullmgham Hill, A brilliant meteor 
near Hulling-: in the atmo , 


Hay (S. Wales). 

Bristol, Glouces- 

1 5 p.m. Weston - 


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 

Meteor of unusual 
size and bril- 
liance ; shed 
much light. 

As large as the 
moon, but much 
brighter; noticed 
by candle-light 
with closed 



Head ruddy 
the other 
and the dif- 
fused light 


20 seconds 

Position, or 

Altitude and 


The extremity 
decided blue. 

Bright light of 
a bluish 

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 

Nearly S.E. 

Slanting down- 
wards from E. to 

2 or 3 seconds 
duration of 

Bodyrich blue 
at explosion 
showed red 
and blue 

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 

In the north-east 
era sky it ex- 
ploded a few 
degrees above 
the horizon. 

From due E. altl 
altitude 20°. 

Would have met the 
horizon 15° fur 
ther on its path, 



>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- 

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 

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 


Iried in its track a line 

i f ruby-coloured fire ; 

: exploded. 

Length of 

nerous prismatic . 

larks and a yellow 
lil accompanied the 
ieteor; the latter re- 
mined visible two 
stream of fire moving63 c 
•rward ; no explosion ; 
isappeared gradually. 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 



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 

First seen directly over- 


It appeared one hundred 

T. Slater; T 
Crumplen ; J 

S. Richards, Jun 


high when it 


Writer in the 
' Cambridge 

Rev. T. W.Webb. 

Inclined 70° to the ho- 
rizon; downwards to 

Paragraph in the 
' Bristol Mer- 
cury.' P. S 

by W.H.Wood, 

Path appeared 

recti- Communicated 
by A. S. Her- 


REPORT — 1862. 




h m 

10 15 p.m. 

19 About 10 20 


10 30 p.m. 

Place of 

Wellington, So- 


.9 About 10 30 Thetford 







London Wall, 

Apparent Size. 



= 4 times 11, or 10| Body and train 
times Sirius. blue 

Illuminated eve 

Yellow , 

Lighted up the: Most brilliant 
town like the, colours, 
noonday sun. 

Entirely lighted up 
the road. 

West End, Lon- Diffused light; Diffused light, 


Torquay (the 



Enfield Highway 

brighter than 
full moon. 

a line blue. 

Diffusedlight, equal Diffused light 
to noonday. 

Lasted several 

in a few 
leaving all 
as dark as 

Flash 1 sec. ; 
seen in mo- 
tion 1 sec. 

Position, or 

Altitude and 


From 'C Persei to 


From S. 
the W. 


Rectilinear in 
rection ; mo? 


A few degrees I 
of the zeuith. 


of a 



From 9° N. ofl 
altitude 23° ; t 
27° N. of ' 
altitude 20°. 

Streak remaine . 
parallel to tt 
Ecliptic, from 
Aquarii to r Pi 

In a line, butvei 

few degrees 

of the zenitl, 

An explosic 

must ha' 

taken plac 

but slightly r 

moved from tl 



pearance ; Train, if any, Length of 
and its Duration. Path. 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 




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 

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 

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- 

ak remained . 


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 

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 


Writer in 
' Norwich 


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.' 


Dr. E. Burder. 

James Edmunds. 

Ellis Hall. 


KEPOKT 1862. 










h ra 

8 15 p.m. 

Place of 


6 15 p.m. Weston 

6 15 p.m 

6 15 p.m 

6 30 p.m 

6 30 p.m. 

6 35 p.m, 


Ticehurst, Sussex 

Apparent Size. 



Position, or 

Altitude and 


Venus at its bright- Blue 
est, or somewhat 

: 2 seconds. 

Much larger than Red 
Venus ; very 
splendid meteor. 

5 to 8 seconds 

As large as 

Lamberhurst, Large and bright. 

Weston - super 



Larger than Venus 

= Sirius 

Green nucleus 
within a red 

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 

Appeared 60° 
from S., 
tude 40 ; disap i 
peared due W. , 
altitude 20°. 

From 15° N.E'I 
of the zenitl 
to altitude 40' 

Inclined at ai, 
angle of 50° t< ( 
the horizon 
disappeared at . 
height of 10° o 
11° above th< 




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, 



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 


7° or 8° 

Direction ; noting also 

whether Horizontal, 

Perpendicular, or 


■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. 



The sun had not quite 
gone down at the 
appearance of this 

a. Lyras appeared 30° 
from its point of 


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. 

by W.H.Wood, 

Rev. F. Howlett. 

H. Moreland. 

by W. H. Wood, 

J. Moore. 

H. S. C, Corre- 
spondent to 
the ' Stand- 

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. 


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, 





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. 



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. 


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. 





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 


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 
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 
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. 




(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 



July 16. 


Aug. 6. 

Nov. 12. 

Nov. 19. 

Dec. 8. 

Feb. 2. 

Feb. 23. 

Diameters "| 
of burning \ 
globes. J 

ft. in. 
21 8 



ft. in. 
39 6 

ft. in. 
35 9 

ft. in. 
49 5 


ft. in. 
14 3 








Diameters of"| 
incandescent > 
globes. J 









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. 


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, 


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 ; 




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 ; 


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 ; 


(6#— 12r 



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 

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 




REPORT — 1862. 











O "^3 


° '3 4 
o s 

is s 

Ci_i "^w 

o © 
08 .3 











? f 
n a) 
+ I 



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, -, 


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. 


would give ajwsitive value of A, and no other term in the deviation. 


A soft iron rod, such as that in. figure 2, 


Kg. 2. 


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. 



Fig. 3. 



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, 



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 

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- 

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 

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. 


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 


.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 


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 

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 

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. 


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 


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 

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 


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 


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 

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- 

. 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 

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. 


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. 


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, 


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. 





Penetration into Armour- 

Armstrong 110-pounder, 


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. 





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 

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 


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- 

[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 

" 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- 


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 

" 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 


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 

"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," 


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 


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- 

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 


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 


Tunicata 11 


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 

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 

" 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- 

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 


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 

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 


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 


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 

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 

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., 

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 


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 


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 

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 



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 

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 


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 



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 

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. 


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 


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 

130 REPORT— 1862. 


7- should be ascertained with increased accuracy, in order that the 


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 

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 

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 


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 

dynamical calculations. In favour of the = it was argued that, when 


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 


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 


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- 

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 


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. 


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. 


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. 


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 


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, 

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- 

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 

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. 


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. 


("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. 


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. 


T. Found. 

12-0 4-506 

56-0 4-384 

100-0 4-271 

Length 381-5 mm. 

; diameter 0-451 mm. 

Conducting power. 









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. 

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. 

(7) Silver G6-6 

Platinum 33-4 

Commercial alloy. 

\=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. 









)13960« + 0-00001183« 2 . 

Length 169 mm. ; 

diameter 0-408 mm 

Conducting power. 












Pure iron 

Other pure metals in a solid state 
Alloy 3 






1 .... 

German silvert 

Conducting power 










Percentage variation in 
conducting power be- 
tween 0° and 100°. 









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. 


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 : — 












Silver : 
Silver : 
Silver : 
Silver : 

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- 


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. 


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. 


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 : — 


No. 1. 

No. 3. 


















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 

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 : — 








Experiment. . 

. 1016-52 






Calculated . . . 

. 1025-54 






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 


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 

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°. 









3-42 at 18-9 











14-4 at 20-4 


10-5 at 20-7 



If now mercury be taken as unit, we find the following values : — 









100 at 18'7 












8-72 at 20-4 

636 at 20-7 




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. 


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. 


1 100-0 


2 95-8 


3 102-9 


4 100-8 


5 98-1 


6 89-9 


7 80-6 


* 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. 


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- 


Hard- drawn. 












* • * * 














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. 


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- 

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 


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 


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 

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 


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 

Mercury is, of all metals, that which is best suited to supply a reproducible 

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 

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- 


ducting power of all solid bodies is too dependent on their molecular struc- 

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- 

A. Matthiessen, Ph.D., F.R.S. (Lon- 

Fleeming Jen kin, Esq. (London). 

Professor A. W. Williamson, F.R.S. 

(University College, London). 
Professor Charles Wheatstone, F.R.S. 

Professor William Thomson, F.R.S. 


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. 



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- 

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 

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. 


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 


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 ,'. 


Fza. 9. 

Common fir 


■ ■ 



ntl V III A D.AXI'E . 





.. Q| IV IM 


. in, I .1 

i. , , ,.•;■. 


■' ■■' ■ /■■■■-■■ ■ ,. . 

Utm ./,„,,. ; : ;., / ,/ ...„n„-,..l witJ, . . 

■..,,■ imulami I 

■ ■ .1 rtmntited * i th ftil n rtfi ■ 


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. 


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- 


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. 


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 

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 

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. 


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 


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 


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 
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 


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 

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 

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- 

"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. 


" 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- 


" 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 

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- 


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- 

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 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, loop, of on. and two m.tah 

HT) ''!!•■- ltl"'ll 

nearly proiiortiuuitt to the strengths of currents 

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 


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. 


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 n *— 

Heateil at right title. 
Loose contact *. mm 110 
Tight contact mm it-weak 

Heated in middle. 

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 


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. 


Heated at rigid side. 

Loose contact -* mm- 5 

Tight contact ■ — 10 

Heated in middle. 


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. 

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 ■■ 

» 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. 


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 

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 

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 

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- 


ance of plates of different thicknesses to missiles of various weights and velo- 

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 : — 

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. 



REPORT — 1862. 

No. of 



weight in 




in inches. 


per square inch 

in lbs. 


per square inch 

in tons. 








55-13 } B <>th ends flat. 



54-82 Ureas -5674 and -7088. 






n i mm \ iOne end rounded. 
2a- 1 1 J 



26-86 Ureas -7088 and -7088. 






„, ,., 1 Both ends rounded. 
23'67 J 





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 


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 


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. 



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 


weight in 




in inches. 

per square 
inch in lbs. 


per square 

inch in tons. 








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 

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 ; 


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. 


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- 


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 


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- 

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. 


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- 

2. Equal to that acquired in falling from infi- 


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 


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 


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. 


dt = T ± , 


{-^ + r"-(C-2/?dr)} i 
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 

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 


— \ 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 


B P 

upon that of a force P, so that the motions for the forces Ar-\-— and — +— 

r 3 r* r 3 


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- 

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, 

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^ 



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" 

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 


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 


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- 

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. 


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 

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 ' 


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 


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 

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 


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 

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. 


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 > 



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 „ 

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. 


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 


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. 

provided only X, XU, — are of the forms 


where the functional symbols <j>, <P, &c. denote any arbitrary functions what- 

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 

a* y 2 

.2 ¥ 



(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 


equations of motion, viz., the problem is reduced to a plane one by means of 
the addition of a force OC— (ante, No. 56). 


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 

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 

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 

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. 


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 

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 = 

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 


(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 

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 


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- 

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 ' -. 


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 


of integration to vanish), he obtains between s and u the equation of the first 

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 

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). 


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)+ ^' 

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 

\=(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 

( ^ = 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 


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- 

103. In particular, if 

Fy=gv-g'p+Jc(r i -b 2 t > 2 ), 

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 


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. 


x 2 y 2 z 2 



or, what is the same thing, 


Vp 2 - 

-b 2 s/p 2 - 

-b°Wb 2 - 


&Vc 2 - 
-<rVc 2 - 

-b 2 


- 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* 


)(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 


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 


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. 


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. 


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, 


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, 


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 





cos t cos 9 — sin r sin 9 cos 

— sin r cos 0— cos r sin 9 cos 

sin sin <f> 


cos t sin 0+sin r cos 9 cos <p 

— sin t sin 0+ cos r cos $ cos 

—cos sin <p 


sin r sin <p 

cos r sin 


The foregoing very convenient algorithm, viz., the employment of 















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 



a?X, yX, zX=90°-C, 90°-£', 90°— £", 
/.'YXx,YXy,YXz=T,, v ', „", 

then the formulae of transformation are 






cos £ sin r\ 

COS £ COS j; 



cos £' sin -q 

COS f ' COS Jj' 



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), 

— A ± __ ,, —A , „, —A 

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' 



> 7 

"— 1 


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- 


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 






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) 


l-X 2 -^^^ 


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. 


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, 


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, 

* 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 


REPORT 1862. 


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 

+G' u, 

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 







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, 


And the equations (1), p. 49, taking therein the original axes as rect- 
angular, are 

hi — g\ cos a+ W cos/? 4- & 

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 


&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 


(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, 


(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 


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, 


(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 


* + ? 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 

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 


, / 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 

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, 

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 

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" 


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 

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- 


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 *, 

dt= ~ Bd g , 


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) 


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- 


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 

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 

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 

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 


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 


/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 


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 

\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 


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" 



+p|tan ' 


p^v-^-fll 2 




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 » 

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 


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 , 

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 

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 


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- 


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 

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, 


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 

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 

. 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 

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 

. 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. 


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). 


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. 


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). 
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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 


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 : — 





Direction of vibra- , 














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). 


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 , 

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). 


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 


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 


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 


Direction of vibra- 



L + G 












* "Sur la Polarisation rectUigne, et la double Refraction," Mem. de l'Acadeniie, torn, 
xviii. p. 153. 


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). 


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. 


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 : — 





P Q R 




P Q R 

P Q R 



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 


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 



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 

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 

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 

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. 



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 : — 



Direction of vibra- 



N + B 

M + C 




L + 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 

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. 


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 

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 

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. 


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. 


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). 


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 

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. 


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. 


Denoting for shortness the partial differential coefficients of — <p with 
respecttog,, £ fa ^/(||)/(|) &C we have 

.,/du\ dhi „,/du\ dlu „ 


=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- 

The equating of the double integrals gives 

* These agree with Professor Haughton's equations (5). 


> • • • (20)* 


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 


the sign II, so that 

*=</(£Mg) + ./(J> 



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. = 



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. 


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 


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. 


REPORT 1862. 

independent variables. Should the three equations (27) be satisfied, the 
expression (31) will be simplified, becoming 

fdu . dw\ 

+ T d(—+' 


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 


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\ 


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 



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 




z dx dy 

T'^=D-C^-E ( 


T =E-A^-F 

zx dx 




T =F-B— -D 

*» rh. dz 


y dx dy 

dy dz 

T' yx =F-E^_A^ 

* dz dx 



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' 


p . p< rp . mi rn .HP' "I . till | »t> 


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 


p ,=»( 1 +$)+»S+*: 

\ dz) dx dy 


T„=e('i + *) +d r<^ + g*« 

\ dz) dy dx 


\ dx) dy dz 

T " =jr ( 1+ l) +e £+*£ T -=< i+ £)+ ffl S+* i 


REPORT 1862. 

Substituting now these expressions in (31) and integrating, we have 



+ C 

+ 233 

+ 2<£ 

2 du /du\? / dv 
dec \dx) \dx 


2— + 
dy \dy 


du\ 2 


™ + ( du 


Vffo/ \dzj 



dv dw du du 

dz dy dy dz 

dw du du du dv dv 

dx dz dz dx dz dx 


dv dv dw dw ] 
dy dz dy dz J 

dw dw \ 
dz dx J 

dv dv 



o jf. J cZtt <&/ cZw cZw 

dx dy dx dy 


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. 


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. 


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. 


[" 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 

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 

The publication of the three Admiralty Tables will also render it un- 


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. 

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 

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. 


"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 

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, indicated power at time of experiment, direction and force of wind. 

A lithographed sheet has been added to the Appendix, containing nine 
indicator diagrams and a scale of displacements, as your Committee considered 
those elements to be necessaiy for the proper consideration of the returns and 
particulars furnished to them. 

The other indicator diagrams, which have been received by your Committee 
too late to be embodied in the present Eeport, may be seen by any one inter- 
ested therein on application at the Offices of the Committee. 

The thanks of the Association are due to Colonel Paradis, the Technical 
Director of the Austrian Lloyds' Company, who, at the request of the Com- 
mittee, caused the information in the Appendix relating to the vessels of 
this Company to be compiled expressly for insertion in the present Report. 

The thanks of the Committee are also due to — 

The Lords Commissioners of the Admiralty, the Secretary of the Admiralty, 
the Comptroller of the Navy, and the Engineer-in-Chief of the Admiralty, 
for such information as they have furnished, or permitted to be supplied 
to your Committee, relating to the trials and sea performances of vessels 
in Her Majesty's service. 

To the heads of the various Departments of the Service, and to the officers 
under them, for the facilities afforded to your Committee in obtaining 
such information as the rules of the Service allow, or which have been 
specially permitted to your Committee. 

To the Officers of Her Majesty's Navy, by whom returns have been fur- 



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