Full text of "Report of the British Association for the Advancement of Science"

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REPORT

TWENTY-SEVENTH MEETING

BRITISH ASSOCIATION

ADVANCEMENT OP SCIENCE:

HELD AT DUBLIN IN AUGUST AND SEPTEMBER 1857.

LONDON:

JOHN MURRAY, ALBEMARLE STREET.

1858.

PRINTED BY

BICHAHD TAYLOR AND WILLIAM FRANCIS,

RED LION COURT, FLEET STREET.

CONTENTS.

Page

Objects and Rules of the Association xvii

Places of Meeting and Officers from commencement xx

Treasurer's Account , xxm

Table of Council from commencement xxiv

Officers and Council y.x\i

Officers of Sectional Committees xxvii

Corresponding Members xxviii

Report of the Council to the General Committee xxviii

Report of the Kew Committee xxxi

Report of the Parliamentary Committee •• xxxviii

Recommendations for Additional Reports and Researches in Science xxxix

Synopsis of Money Grants xli

General Statement of Sums paid for Scientific Purposes xlii

Extracts from Resolutions of the General Committee xlv

Arrangement of the General Meetings xlvi

Address of the President xlvii

REPORTS OF RESEARCHES IN SCIENCE.

Report on the Recent Progress of Theoretical Dynamics. By A.
Caylky ••• 1

Sixteenth and final Report of a Committee, consisting of Professor
Daubeny, Professor Henslow, and Professor Lindley, appointed
to continue their Experiments on the Growth and Vitality of Seeds . 43

IV CONTENTS,

Page

Continuation of Report on Steam Navigation at Hull. By James
Oldham, C.E. Hull, M.I.C.E 57

Report of a Committee, consisting of The Rt. Hon. Earl of HARnwiCKE,
Chairman ; Mr. Andrew Henderson, Mr. John Scott Russell,
Mr. James Robt. Napier, Mr. Charles Atherton, Mr. Arthur
Anderson, Rev. Dr. Woolley, Admiral Moorsom (vice Mr. W.
Mann), Mr. John Macgregor (vice Mr. G. F. Young), Captain
J. O. Owen, Professor Bennett Woodcroft, James Perry, and
Mr. James Yates, Secretary, appointed to inquire into the Defects
of the present methods of Measuring and Registering the Tonnage of
Shipping, as also of Marine Engine-Power, and to frame more perfect
rules, in order that a correct and uniform principle may be adopted
to estimate the Actual Carrying Capabilities and Working-Power of
Steamships 62

Report on the Temperature of some Deep Mines in Cornwall. By
Robert Were Fox, F.R.S., F.G.S 96

-«a<i+ifl'i+'g<l+»
De quelques Transformations de la Somme 2^ ^i + i t\ + i 1,+^ , a

lye

Itant entier negatif, et de quelques cas dans lesquels cette somme est
exprimable par une combinaison de factorielles, la notation a'l+i desig-
nant le produit des t facteurs a(a + l)(a + 2) &c. . . .(^a + t — 1).
Par G. Plarr, Docteur es Sciences de Strasbourg 101

Report on the Marine Zoology of Strangford Lough, County Down,
and corresponding part of the Irish Channel. By G. Dickie, M.D.,
Professor of Natural History, Queen's College, Belfast 104-

Suggestions for Statistical Inquiry into the extent to which Mercantile
Steam Transport Economy is affected by the Constructive Type of
Shipping, as respects the Proportions of Length, Breadth, and Depth.
By Charles Atherton, Chief Engineer of Her Majesty's Dock-
yard, Woolwich 112

Further Report on the Vitality of the Spongiadas. By J. S. Bower-
bank, LL.D., F.R.S., &c. (With a Plate) 121

On Flax. By John P. Hodges, M.D., F.C.S., Professor of Agriculture,
Queen's College, Belfast, and Chemist to the Chemico-Agricultural
Society of Ulster 126

Report of the Committee on the Magnetic Survey of Great Britain. By
Major-General Sabine 130

CONTENTS. V

Page

Keport on Observations of Luminous Meteors, 1856-57. By the Rev.
Baden Powell, M.A., F.R.S., F.R.A.S., F.G.S., Savilian Professor
of Geometry in the University of Oxford 131

On the Adaptation of Suspension Bridges (o sustain the passage of
Railway Trains. By C. Vignoles, C.E., F.R.S 154

On Electro-Chemistry. By Professor W. A. Miller, M.D., F.R.S... . 158

Results of Thermometrical Observations made at the ' Plover's' Winter-
ing-place, Point Barrow, latitude 71° 21' N., long. 156° 17' W., in
1852-54. By John Simpson, Esq., R.N., F.R.C.S., F.R.G.S., Sur-
geon o{ HM"s. ' Flover' (With a Plate) 159

On the Algebraic Couple ; and on the Equivalents of Indeterminate
Expressions. By Charles James Hargreave, LL.D., F.R.S. ... 184

Report on the Improvement of Telescope and Equatorial Mountings. By
Thomas Grubb, M.R.I.A. &c 195

Report on the Experimental Plots in the Botanical Garden of the Royal
Agricultural College at Cirencester. By James Buckman, F.L.S.,
F.A.S., F.G.S. &c., Professor of Geology and Botany, Lecturer on
Geology, &c. at the Cheltenham Proprietary College 200

On the Resistance of Tubes to Collapse. By William Fairbairn,
F.R.S 215

Report of the Proceedings of the Belfast Dredging Committee. By
George C. Hyndman 220

On the Mechanical Effect of combining Girders and Suspension Chains,
and a Comparison of the Weight of Metal in Ordinary and Suspension
Girders, to produce equal deflections with a given load. By Peter
W. Barlow, F.R.S 238

Evidences of Lunar Influence on Temperature. By J. Park Harrison,
M.A 248

Report on the Animal and Vegetable Products imported into Liverpool
from the year 1851 to 1855 (inclusive) 254

Report on the Statistics of Life-boats and Fishing-boats on the Coasts of
the United Kingdom. By Andrew HendebsoNj F.S.A. and A.I.C.E. 308

vi contBnts.

NOTICES AND ABSTRACTS

MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS.

MATHEMATICS AND PHYSICS.

Mathematics.

Page
Rev. T. R. Robinson's Opening Address 1

Professor Boole on the Theory of Astronomical Observatiods, afld oa some
related Questions ^.........i.^ 2

on certain Additions to the Integral Calculus 2

Professor Curtis on a System of Geodetics and the Conjugate System, traced
on the two Sheets of a Surface of Centres, with special reference to the Case
in which the Surface of Centres consists of an Ellipsoid and a Confocal
Hyperboloid 2

Rev. Charles Graves on the Interpretation of certain Symbolic Formulae and
Extensions of Taylor's Theorem 3

Sir W. R. Hamilton on some Application of Quaternions to Cones of the
Third Degree 3

on the Icosian Calculus 3

Mr. Commissioner Hargrave on Infinite Angles and on the Principle of Mean
Values 3

Mr. John Pope Hennessy on the Origin and Elimination of Euclid's " Re-
ductio ad absurdum" 3

Rev. Professor Jellett on some General Propositions connected with the
Theory of Attractions 3

Mr. T. Martin on certain Properties of the Radii of Curvature of Curves and
Surfaces, and their Application to the Method of Polar Reciprocation 4

Mr. B. A. Murray's Demonstration that the Three Angles of evtry Triangle
are equal to Two Right Angles 4

Rev. G. Salmon on the Surface of Centres of an Ellipsoid 4

Light, Optical Instruments.

Sir David Brewster on the Centring of the Lenses of the Compound Object-
Glasses of Microscopes < ».......;... 4

M. Leon Foucault on a new Polarizer, resulting from a Modification of the

Prism of Nicol 5

■ on a Telescope Speculum of Silvered Glass 6

Dr. J. H. Gladstone on the Colour of Salts in Solution, each Constituent of
which is coloured 8

on the Effects of Heat on the Colour of Dissolved Salts 8

CONTENTS. Vll

Page
Mf. Thomas Grubb on Improvements in the Optical Details of Reflecting
Telescopes and Equatoreal Instruments 8

M. l'Abbe Moigno on a Method of determining whether the Luminiferous
Vibrations are Parallel or Perpendicular to the Plane of Polarization 9

Electricity, Magnetism.

Captain Blakely's Mathematical Investigation of the Proportion between the
Length required for an Electric Telegraph Cable and its Specific Gravity ... 11

Rev. Professor Callan on the Electro-dynamic Induction Machine 11

Mr. John Hartnup on Controlling the Movements of ordinary Clocks by
Galvanic Currents .; ^ 13

Major-General Sabine on the Amount and Frequency of the Magnetic Dis-
turbances and of the Aurora at Point Barrow, on the Shores of the Polar Sea 14

Professor W. B. Rogers's Brief Account of the Construction and EflFects of a
very powerful Induction Apparatus, devised by Mr. E. S, Ritchie, of Boston,
United States 15

M. Louis Soret's Researches on the Correlation of Dynamic Electricity and
the other Physical Forces 16

Mr. G. Johnstone Stoney's Description of an Arrangement of Grove's
Battery ;..... .......; ;..;...... .i. 20

Professor W. Thomson on Mr. Whilehouse's Relay and Induction Coils in

action on Short Cii-CUit...; ;; ;;..;...... ;.....;iu... 21

• on the Effects of Induction in long Submarine Lines of

Telegraph i.; ;. a.... 21

Mr. J. Dhummond's Outline of a Theory of the Structure and Magnetic Phe-
nomena of the Globe ;. 22

Mr. W. Rundell's Magnetic Experimehts made on board the ' Great Eastern*
Steamer. (Communicated by Admiral FitzRoy.) 22

Sound.

Mr. M. Donovan on a singular Acoustic Phenomenon 22

Professor G. G. Stokes on the Effect of Wind on the Intensity of Sound 22

Astronomy.
Cavaliere 0. F. Mosotti on the Distribution of the Orbits of the Comets in

Space ;:;:.;.;.;.;;;. ; i....; ;..;...... 23

Mr. M. Donovan on a Moveable Horizontal Sun-dial, which shows correct
Solar Time within a Fraction of a Minute i 24

Mr. C. Thomson's Tables to simplify and render more general the Method of
finding the Time, by observing Circumpolar Stars in the same Vertical. (Com-
municated by Sir W. R. Hamilton.) w t..,. 24

Professor Hennessy on the Direction of Gravity at the Earth's Surface....*.... 24
— ■- — — on the Solidification of Fluids by Pressure i...4i...... 25

Professor Lookis oh the relative Accuracy of the different Methods of deter-
mining Geographical Longitude ..^ ....; ;.; 25

Mr. J. J. Murphy oti a Proposal for the Establishment of a Uniforin Refckoli-
ing of Time in connexion with the Telegraph * ..; 26

Mr. Ji Nasmyth on some Phenomena in connexion with Molten Substances... 26

VUl CONTENTS.

Page
Rev. W. G. Penny on certain Planetary Perturbations ,., 27

Rev. T. R. Robinson on Transit Observations of the Moon " 27

Professor P. Smyth on Lunar Physics 28

Meteorology.

Notice of Meteorological Observations made at Sea. (Communicated by Rear-
Admiral FitzRoy.) 28

Mr. C. FuLBROOK on the Variation in the Quantity of Rain due to the Moon's
Position in reference to the Plane of the Earth's Orbit 29

Professor Hennessy on Simultaneous Isothermal Lines 29

on the Distribution of Heat over the Surface of the British

Isles 30

on the Vertical Currents of the Atmosphere 30

Dr. Lee on the Discovery of the Asteroid, No. 46, on the 1 7th of August, 1857,
by Mr. Pogson, at Oxford 31

Rear-Admiral Smyth on the Results of Measurements of y Virginis for the
' Epoch 1857. (Communicated by Dr. Lee.) 32

Professor Loomis on certain Electrical Phenomena in the United States 32

Mr. J. J. Murphy's Account of an instance of Converging Rays seen at Green-
island, on the Antrim Shore of Belfast Lough, August 13, 1857 35

M. 1,'ABBi; Raillard's Examination of some Problems of Meteorology. New

and complete Explanation of the Rainbow 35

Rev. T. Rankin on Meteorological Phenomena at Huggate, Yorkshire 37

Mr. John Simpson on the Temperature of the Air registered at the ' Plover's'
Winter-quarters at Point Barrow, in the years 1852, 1853, 1854 37

Mr. James Thomson on the Grand Currents of Atmospheric Circulation 38

on the Plasticity of Ice 39

Mr. D. Vaughan on Secular Variations in Lunar and Terrestrial Motion from

the influence of Tidal Action 40

on the Light of Suns, Meteors, and temporary Stars 42

CHEMISTRY.

ProfessorT. Andrews on Ozone 44

on the Heat of Combination of Acids and Bases 44

Professor James Apjohn on the Amount of Nitrogen in the Algse 44

on some Compounds of Cyanogen 44

Mr. P. Buchan on the Composition of the Iron Ores of the Leitrim Coal Field,
■with some Remarks on the Advantages of that District for the Manufacture

of Iron 44

Mr. R. Barnes and Mr. W. Odling on the Condition of Thames Water, as
aflFected by London Sewage 44

Dr. Charles A. Cameron on Urea as a Direct Source of Nitrogen to Vege-
tation 44

Professor Daubeny on a Method of Refining Sugar 45

on the Conversion of Paper into Parchment 45

Mr. M. Donovan on Hygrometers and Hygrometry, with a description of a

New Modification of the Condenser Hygrometer and Hygroscope 45

CONTENTS. IX

Page
Mr. G. C. Foster's Suggestions towards a more Systematic Nomenclature for
Organic Bodies 45

M. Alphonse Gages on some Arseniates of Ammonia 47

— on the Specific Gravity of Chloride of Nitrogen, with

some Remarks upon its Action on Alcohol 47

Dr. J. H. Gladstone's Chemical Notes 47

on the Decomposition by Heat of certain Ammoniacal

Salts 48

on the Use of the Prism in detecting Impurities 48

Mr. Archibald H. Hamilton on Electrical Currents in the Earth's Surface . 48

Dr. A. A. Hayes on some Modified Results attending the Decomposition of

Bituminous Coals by Heat 50

M. le Baron Heurteloup on a New Method of administering Chloroform.

(Communicated by M. l'Abbe Moigno.) 51

Mr. R. L. Johnson on Illuminating Peat Gas 51

Messrs. Lawbs, Gilbert, and Pugh's Notice of Researches on the Assimila-
tion of Nitrogen by Plants 51

Mr. John J. J. Kyle on the Chemical Composition of an ancient Iron Slag
found at Lochgoilhead, Argyleshire. (Communicated by Dr. Stevenson

Macadam.) 52

Dr. Lloyd on the Purification of Large Towns by means of Dry Cloacae 53

Professor J. W. Mallet on the Atomic Weight of Aluminium 53

Dr. Miall on the Melting-points of Bodies 53

M. l'Abbe Moigno's Notices of Photography 53

on Three New Electrotype Processes 54

Sir James Murray on the Choice of Perennial rather than Annual Fertilizers 54

Dr. M'Namara on Coloured Confectionary 55

Mr. W. Odling on the EiFects of Alum in Panification 55

Mr. W. Odling and Dr. A. Dupre on the Presence of Copper in the Tissues of

Plants and Animals 55

Rev. J. B. Reade on a New Method of forming Ammonio-Iodides of Metals... 55
Mr. E. Riley on Fused Wrought Iron. (Communicated by Dr. Odling.) ... 57
Mr. Jasper W. Rogers on the Nutritive Properties of the Potato, when pro-
perly manipulated, as compared with Wheat, &c 57

on some of the Medicinal and Chemical Properties of

Carbonized Peat Moss 58

Professor W. B. Rogers' Ozone Observations 58

Professor W. K. Sullivan on a Process for the Determination of the Nitrates

in Plants 58

on the Presence of several Acids of the Series

C H" O* among the Products of the Distillation of Peat 58

Remarks on the Solubility of Salts at high tempe-

ratures, and on the action of Saline Solutions on Silicates under the influence

of Heat and Pressure 59

Professor Voelcker on the Composition of Norwegian Apatite 59

on the Methods of Analysing the Superphosphates 60

on the Proportion of Organic Phosphorus in Legumine... 60

Mr. W. Sykbs Ward on the Preservation of Albuminized Collodion Plates ... 61

X CONTENTS.

Page
Professor G. Wilson on the Processes for the Detection of Fluorine 61

Dr. T. Woods on the Time required by Compounds for Decomposition 61

GEOLOGY.

Mr. Robert Godwin-Austen's Notice of the occurrence of a Boulder of Gra-
nite in the White Chalk of the South-east of England 62

Mr. W. H. Baily on Carboniferous Limestone Fossils from the County of
Limerick, collected by the Geological Survey 62

on a New Fossil Fern from the Coal-Measures near Glin,

County Limerick 63

Mr. J. Birmingham on the Drift of West Galway and the Eastern parts of
Mayo 64

Dr. Clarke on certain Alterations of Level on the Sea-coast of part of the
County of Waterford, and the cause thereof 65

Mr. F. J. Foot on the Geology of the Neighbourhood of Tralee 65

Sir Richard Griffith on the Relations of the Rocks at or below the base of
the Carboniferous Series of Ireland 66

Mr. G. F. Habershon's Notes from the Barbary Coast, with Fossils. (Com-
municated by Dr. Gladstone.) 67

Professor Harkness on the Geology of Caldbeck Fells, and the Lower Sedi-
mentary Rocks of Cumberland 67

on the Jointing and Doloraitization of the Lower Carbon-
iferous Limestone in the Neighbourhood of Cork 68

—^ on the Records of a Triassic Shore 68

Rev. Professor Haughton on a Model illustrative of Slaty Cleavage 69

— — . on Fossil Stems allied to Stigmaria, recently obtained

from the Upper Beds of the Old Red Sandstone of Hook Point, County of
Wexford .'.... 69

Professor Hennesst on the Existence of Forces capable of changing the Sea-
level during different Geological Epochs 69

Mr. William Hopkins on the Conductivity of various Substances for Heat . 70

Mr. J. Beete Jukes and Mr. G. V. Du Noyer on the Geological Structure of
the Dingle Promontory, Co. Kerry 70

. Notes on the Old Red Sandstone of South Wales 73

Messrs. Jukes and Du Noyer on the Geology of Lambay Island 75

Mi-. G. H. Kinahan on the Valentia Trap-District i. 75

Professor J. R. Kinahan on the Zoological Relations of the Cambrian Rocks

of Bray Head and Howth 75

Professor King on the Relation between the Cleavage of Minerals and the

Cleavage of Rocks 76

Mr. J. O. Kelly on a Section across Slieve-na-Muck, Co. Tipperary 76

Professor L. de Koninck and Mr. Edward Wood on the genus Woodocrinm 76

Professor Car. G. Meneghini's Notice of the recent Advances of Paleeontolo-
gical Discovery in Tuscany 79

Sir Roderick I; Murchison on the Quartz Rocks, Crystalline Limestones,
and Micaceous Schists of the North-western Highlands of Scotland, proved
to be of Lower Silurian Age, through the recent Fossil discoveries of
Mr. C. Peach? 82

CONTENTS. XI

Page

Mr. ^. W. Salter's Note on the Fossils from Durness ;.* 83

Mr. George V. Du Noyer on the Junction of the Mica-slates and Granite,

Killiney Hill, Dublin 84

Mr. Thomas Oldham's General Sketch of the Districts already visited by the

Geological Survey of India ; 85

Professor John Phillips on the Ironstones in the Oolitic District of Yorkshire 89

Professor W* B, Rogers on the Discovery of Paradoxides in New England.... 89

Professor H; D. Rogers on the Geological Survey of Pennsylvania 89

Mr. J. W. Salter on the Fossils of the Dingle District 89

Messrs. Hermann and Robert Schlagintweit on Erosion of Rivers in India 90

Mr. H. C. SoRBY on some Facts connected with Slaty Cleavage 92

Rev. W. S. Symonds on a Fossil of the Severn Drift 93

— --^ on a New Species of Eurypterits from the Old Red Sand-
stone of Herefordshire 93

Mr. A. B. Wynne on the Geology of the Galty Mountains, &c ; 93

on the Tertiary Clay and Lignite of Ballyraacadam, near Caher,

in the County of Tipperary 94

BOTANY AND ZOOLOGY, including PHYSIOLOGY.

Botany.

Professor J. Buckman on the finding of Cnicus tuberosus at Avebury Hills 95

Dr. BuisT on the Lotus or Sacred Bean of India. (Communicated by Dr.
Norton Shaw.) ; ; ...<..;.;...;... .^ gQ

Mr. John Hogg on some Variations of British Plants 96

Mr. T. Maxwell Masters' Contributions to Vegetable Teratology gf

Rev. E. O'Meara on the Forms of Diatomaceae found in Chalk ...; 97^

Mr. D. Moore's Observations on the Plants which, by their Growth and De-
composition, form the principal part of the Irish Turf-Bogs ......: ,...-..;., gj'

Mr. N. NivEN on the Importance of a thorough understanding of the Root
Principle in the Cultivation of Trees n *., 98

-■ — - — — — '— on the Remarkable Result of an Experiment upon a Fruit-
bearing Tree ;.....;. ;.ii..ji.ii.j;,.; 100

Mr. J. Ralfs' Remarks on the Siliceous Cells formed in the Friistules of Dia-
tomaceee.. i..i < ;....;..; .;..... ..^ 101

Zoology.

Mr. William Andrews on tlie Sea Fisheries of ti^eland, with reference tci their

investigation practically and scientifically *i. <..... i....u 101

Mf. E. BiRCHALL on a List of additions to Irish Lepidoptera 101

Mr. Philip P. Carpenter's Note on Peculiarities of Growth in Caecidae 102

Mr. R. Q. Couch on the Embryo State of Palinurus vulgaris 102

Mr. Joseph R. Greene on British Naked-eyed Medusae, with notices of seven

tindeSCribed forms...,. -..........;..... ...'........ .;....;;........;..;......;.-.•...;.-. lo3

XU CONTENTS.

Page
Mr. G. C. Hyndman's Notice of a curious Monstrosity of Form in the Fusus

antiqutis 104

Professor J. R. Kinahan's Remarks on certain Genera of Terrestrial Isopoda... 104
on a New Species of Galathea 104

Professor Macdonald on the Cranium of Osseous Fishes and its Vertebrate
and Articulate Homologies.... 104

Rev. F. O. Morris on the Specific Distinctions of Uria troile and Uria lacrymans 105

Mr. W. Ogilby on the Dispersion of Domestic Animals in connexion with the
Primary Ethnological Divisions of the Human Race 105

Professor Redfern on a Method of applying the Compound Microscope to the
sides or top of Aquaria less than two feet in height 106

on Flustrella hispida 106

Messrs. Hermann and Robert Schlagintweit's Notes on some of the Ani-
mals of Tibet and India 106

Professor Wyville Thompson on the Reproductive Zooids of Comafula rosacea 108

Mr. W. Thompson on Dredging in Weymouth Bay 108

Dr. E. Percival Wright's Notes of a Visit to Mitchelstown Caves 108

Physiology.

Professor Alison on certain a priori Principles of Biology 109

Mr. R. Dowden's Brief Suggestion, recommending a more complete Compila-
tion of the Facts illustrating the Physiology of Vegetable and Animal Secre-
tions 110

M. FayJ; on the Action of some Animal Poisons 110

Dr. Gairdner on the Action of the Auriculo-Ventricular Valves of the Heart 110

. — on the Mortality from certain Diseases 110

Dr. Edward Haughton on the Oriental Bath 110

Professor Hayden on the Physiological Relations of Albumen 110

Mr. J. P. Hennessy on certain Pathological Characters of the Blood Corpus-
cles 113

Dr. E. Lankester on the Alternation of Generations and Parthenogenesis in

Plants and Animals 113

Mr. Joseph Lister on the Flow of the Lacteal Fluid in the Mesentery of the

Mouse 114

Professor Lyons on the Importance of introducing a New and Uniform Stand-
ard of Micrometric Measurement 115

Dr. Robert M'Donnell on the Valvular Apparatus connected with the Vas-
cular System of certain Abdominal Viscera 115

Dr. PozNANSKi on the Connexion between Atmospheric Vicissitudes and Epi-
demic Diseases 115

Sir J. Richardson's Note on Electric Fishes 115

Professor G. Wilson on the Employment of the Living Electric Fishes as
Medical Shock-Machines 115

Miscellaneous.
Professor H. Cablile on the Functions of the Human Ear 116

CONTENTS. XIU

GEOGRAPHY AND ETHNOLOGY.

Page
M. Antoine d'Abbadie on the Ethnological and Physical Characters of the
Negro variety of mankind 117

Dr. Henry Baeth on the Anomalous Period of the Rising of the Niger 118

Mr. Richard Beamish on the Human Hand, an Index of Mental Development. 118

Dr. John Beddoe on the Physical Characters of the Ancient and Modern Ger-
mans 118

Mr. W. Bollaert's Ethnological and Antiquarian Researches in New Gra-
nada, Quito and Peru, with Observations on the Pre-Incareal, Incareal, and
the Monuments of neighbouring Nations in Peru 121

Major-General Chesney on the Routes of Communication between England

and India 123

Professor J. H. Corbett on Australian Crania 126

Mr. Richard Cull on the Character, Extent, and Ethnological Value of the
Indo-European Element in the Language of Finland 127

Sir John F, Davis on China, in more immediate reference to pending Opera-
tions in that Quarter 129

Dr. John O'Donovan on the Physical Characteristics of the Ancient Irish ... 129

on the Intellectual Characteristics of the Ancient Irish 130

on the Surnames of the Irish People, their Meanings,

and the various changes which they have undergone since the English In-
vasion of Ireland 130

Rear-Adrairal FitzRoy on the Probable Migrations and Variations of the
Earlier Families of the Human Race 130

Mr. John Grattan on some Skulls discovered in an ancient Sepulchral Mound
near Mount Wilson in King's County, Ireland 131

Rev. Professor Graves on the Progress already made in the Transcription and
Translation of the Ancient Laws of Ireland, called the Brehon Laws 131

Professor Hennessy on the Influence of the Gulf-stream on the Climate of
Ireland , 132

Mr. Gordon M. Hills on the Round Towers of Ireland 133

Rev. E. Hincks on the Relation between the newly-discovered Accadian Lan-
guage and the Indo-European, Semitic, and Egyptian Languages; with
remarks on the original values of certain Semitic Letters, and on the state of
the Greek Alphabet at different periods 134

Mr. John Hogg on the supposed Biblical Names of Baalbec, and on the
position of Baalgad 143

Mr. T. Hopkins on the Cause of the Mild Winter Temperature of the British
Islands 144

Mr. W. Hughes on the application of a Decimal Scale to the construction
of Maps 145

Mr. Santiago Jackson on Routes from Lima to the Navigable Branches of the

Amazon, with Notes on Eastern Peru as a field for Colonization 145

Rev. Dr. Livingstone's short Statement of Discoveries in Southern Africa... 146
Dr. W. Macdonald on the Sources and Origins of Human Races and their

Languages, more especially the Celtic 146

Mr. Clements R. Markham on the Final Arctic Searching Expedition 146

Dr. Minchin on the Macrocephali of Hippocrates 146

XIV CONTENTS.

Page
Mr. George V. Du Noyer on the Remains of EarlyStone-built Fortresses and
Habitations in the County of Kerry 148

Captain S. Osborn on the Sea of Azof, and the Sivash or Putrid Sea 148

Sir JouN Richardson's Abstract of the Report of James Anderson, Esq., Chief
Factor of the Hudson's Bay Companj', commanding a Searching Party that
descended the Great Fish River in quest of the Remains of the Crews of the
'Erebus' and 'Terror ' in 1855 148

Rev. Charles Russell on the Inhabitants and Dialect of the Barony of Forth
in the County of Wexford 149

Mr. Robert Schlagintweit on the Routes pursued by Herren Hermann,
Adolphe, and Robert Schlagintweit in India, the Himalayas, Tibet, and
Turkistan 149

M. Hermann Schlagintweit on some Human Races in India and Upper
Asia ,. 151

Professor W. K. Sullivan on the Influence which Physical Characteristics
exert upon the Language and Mythology of a People, as a means of tracing
the affinities of races 153

Mr. Kenneth Leith Sutherland's Observations on Vancouver Island 153

Dr. R. Siegeried on an Inscription in the Language of Ancient Gaul, and on
the recent researches of Zeuss and others into that Language 154

Rev. J. Threlkeld on the present Condition of the Natives of Australia, in 4

Letter to R. Cull 154

Dr. D. Wilson on the supposed Unity of the American Race 154

STATISTICS.

Introductory Address by the Archbishop of Dublin, President of the Section 154
Mr. C. BiANCONi on the Car Establishment of Mr. Bianconi in Ireland........ 155

Mr. S. Browne on the Proportion of Marriages at different Ages of the Sexes. 156
Professor Cairnes on some of the Principal Effects of the New Gold, as an

Instrument of Purchase, on the Production and Distribution of Real Wealth 1 56
Mr. E. Chadwick on the Dependence of Moral and Criminal on Physical Con-
ditions of Populations , , 158

. on the Economical, Educational, and Social Importance of

open and public Competitive Examinations 158

Mr. H. Clay on the Effect of Good and Bad Times on Committals to Prison.. 158
Mr. J. T. Danson on the Ages of the Population in Liverpool and Manchester 158

Mr. J. Chawfuhd on the Effects of the Gold of Australia and California 160

Mr. Richard Dowden on a Cash Land-Trade for Ireland, Retail and Whole-
sale ••... IGO

Mr. James Haughton on the Necessity of Prompt Measures for the Suppres-
sion of Intemperance and Drunkenness ,,. I6l

Mr. John Pope Hennessy on Agricultural and Manufacturing Industry , 162

Mr. William H. Jemison on the Prevention of Crime 162

M. Jottrand on the Progress of Free Trade on the Continent 163

Mr. J. W. Kavanagh's Sketch of the Rise, Progress, and Present Prospects
of Popular Education in Ireland , .,,...,, ,, 163

Professor LeslIe on Competition at the Ear .., 163

on Professional Incomes 163

CONTENTS. XY

age
Mr. John Lockk on the Land- Revolution in Ireland 163

M. CoRR Vander Maeren on the Progress of Free Trade on the Continent.. 164

Dr. H. M'Cormac on the Influence of inadequate or perverted Development in

the production of Insanity, Disease, Want and Crime ,. 164

Mr. Arthur Moore on the Registration of Births, Deaths and Marriages in

Ireland 164

Mr. Joseph J. Murphy's Reasons for extending Limited Liability to Joint-Stock

Banks 165

Mr. Robert Napier on the Apprenticeship System in reference to the Freedom

of Labour 166

M. NiVERE on Cottage Gardening and Labourers' Holdings 166

Mr. W. Newmarch on some of the Economical Questions connected with the
Effect of the New Gold in diminishing the Difficulties of the last few years . 166

^ on the Recent Legislation relative to Joint- Stock Com-^

panies and Joint-Stock Banks 166

Mr. Henry John Porter on the Census of the Province of Canterbury, New

Zealand iQf

on the Census of Sydney, New South Wales , 167

Professor Phillips on the Money Grants of the British Association 167

Dr. J. Strang on the Rise, Progress, and Value of the Embroidered Muslin
Manufacture of Scotland and Ireland 167

on the Advantages arising from the Improvement of Tidal Rivers

as exemplified by the State of the Clyde ,,,...,,, I6f

Mr. J. C. Symons on Criminal Statistics ,,,. 168

Mr. W. M. Tartt on the Criminal Statistics of this and certain Foreign
Countries , ,.,...,...,. 168

Mr. Richard H. Walsh on Equitable Villages in America 170

Mr. James Moncrieff Wilson on Statistics of Crime in Ireland, 1842 to 1856 171

Mr. Cadogan Williams on Deferred Annuities ,.,, 172

Mr. Charles M. Willich on Annuities on Lives 17?

— on aFormula for ascertaining the Expectation ofLife 172

Mr. James Yates on the Application of the Decimal Scale in the Construction
of Maps 172

— on the Use of Prime Numbers in English Measures,

Weights, and Coinage 174

MECHANICAL SCIENCE.

Address by the Earl Rosse, President of the Section ....,..., 175

Mr. James Barton on a detailed Model oftheBoyne Viaduct which carries the
Belfast Junction Railway over the River Boyne at Drogheda, with a descrip-
tion of it, and the Principles of its Construction 178

Mr. J. S. Beattie on Coal-burning Engines 178

on Electro-Magnetic Engines 178

Captain Blakeley on Improvements in Ordnance 179

Mr. John Brakenridge on the Working and Ventilation of Coal Mines 180

Mr. C. Brooke on a Plan for diminishing the Strain on the Atlantic Cable by
an Elastic Regulator 180

XVI CONTENTS.

Page
Mr. J. W. DoDDS on Improvements in Iron and Steel, and their Application to

Railway and other purposes 180

Mr. G. H. Frith on Macadamized Roads 180

Mr. A. S. Hart on the Effect of the Resistance of Water to an Extended Cable 180

Mr. John Hartnup on Controlling the Movements of ordinary Clocks by Gal-
vanic Currents 180

Mr. J. J. Hayes on the Mode of rendering Peat economically available as a

Fuel, and as a Source of Illuminating Gas 181

Captain Leach on the Use of Percussion Lights for preventing Collisions at

Sea and on Railways 181

Mr. John Macguegor on Early Methods of Propelling Ships 182

Dr. Gray on a new Railway Signal 185

Mr. R. Mallet on the Construction of the 36-inch Mortars made by order of

Her Majesty's Government ' 186

Mr. Guildford L. Molesworth on Tangent-Wheels 186

Admiral Moorsom on the want of Facts respecting the Performance of Vessels

at Sea 187

Mr. T. Moy's Improvements in the mode of Working Steara-Engines 187

' on the Philosophy of the Wave-Line System of Ship-building... 188

Sir J. Murray on the Laying of Submarine Telegraph Cables 188

Mr. J. Neville on the Flow of Water through Circular Pipes 189

Mr. A. Balestrini on the Submarine Electric Telegraph Cable 189

Mr. W. J. Macquorn Rankine on the Principle of the Transformation of

Structures 189

Mr. George Rennie's continuation of Experiments to determine the Resistances
of Screw-Propellers when revolving in Water at different Depths and Velo-
cities 189

on the Quantity of Heat developed by Water when rapidly

agitated 190

Mr. J. Scott Russell on the Mechanical Structure of the 'Great Eastern' Steam

Ship 195

Mr. T. Silver on the Importance of Regulating the Speed of Marine Engines. 1 98

Mr. BiNDON B. Stoney on the Formation of the Entrances to Tidal Basins... 198

Professor W. Thomson on Machinery for laying Submarine Telegraph Cables 199

Mr. J. Wetherhead on Superheated Steam 199

APPENDIX.

Dr. HoDGKiN on the proposed Ship Canal through the Isthmus of Suez 199

Index 201

OBJECTS AND RULES

THE ASSOCIATION.

OBJECTS.

The Association contemplates no interference with the ground occupied by
other Institutions. Its objects are, — To give a stronger impulse and a more
systematic direction to scientific inquiry, — to promote the intercourse of those
who cultivate Science in different parts of the British Empire, with one an-
other, and with foreign philosophers, — to obtain a more general attention to
the objects of Science, and a removal of any disadvantages of a public kind
which impede its progress.

RULES.

ADMISSION OF MEMBERS AND ASSOCIATES.

All Persons who have attended the first Meeting shall be entitled to be-
come Members of the Association, upon subscribing an obligation to con-
form to its Rules.

The Fellows and Members of Chartered Literary and Philosophical So-
cieties publishing Transactions, in the British Empire, shall be entitled, in
like manner, to become Members of the Association,

The Officers and Members of the Councils, or Managing Committees, of
Philosophical Institutions, shall be entitled, in like manner, to become Mem-
bers of the Association.

All Members of a Philosophical Institution recommended by its Council
or Managing Committee, shall be entitled, in like manner, to become Mem-
bers of the Association.

Persons not belonging to such Institutions shall be elected by the General
Committee or Council, to become Life Members of the Association, Annual
Subscribers, or Associates for the year, subject to the approval of a General
Meeting.

COMPOSITIONS, SUBSCRIPTIONS, AND PRIVILEGES.

Life Members shall pay, on admission, the sum of Ten Pounds. They
shall receive gratuitously the Reports of the Association which may be pub-
lished after the date of such payment. Tliey are eligible to all the offices
of the Association.

Annual Subscribers shall pay, on admission, the sum of Two Pounds,
and in each following year the sum of One Pound. They shall receive
gratuitously the Reports of the Association for the year of their admission
and for the years in which they continue to pay without intermission their
Annual Subscription. By omitting to pay this Subscription in any particu-
lar year. Members of this class (Annual Subscribers) lose for that and all
future years the privilege of receiving the volumes of the Association gratis :
but they may resume their Membership and other privileges at any sub-
sequent Meeting of the Association, paying on each such occasion the sum of
One Pound. They are eligible to all the Offices of the Association.

Associates for the year shall pay on admission the sum of One Pound.
They shall not receive gratuitously the Reports of the Association, nor be
eligible to serve on Committees, or to hold any office.

1857. b

XVIU RULES OF THE ASSOCIATION.

The Association consists of the following classes : —

1. Life Members admitted from 1831 to 184:5 inclusive, who have paid
on admission Five Pounds as a composition.

2. Life Members who in 1846, or in subsequent years, have paid on ad-
mission Ten Pounds as a composition.

3. Annual Members admitted from 1831 to 1839 inclusive, subject to the
payment of One Pound annually. [May resume their Membership after in-
termission of Annual Payment.]

4. Annual Members admitted in any year since 18S9, subject to the pay-
ment of Two Pounds for the first year, and One Pound in each following
year. [May resume their Membership after intermission of Annual Pay-
ment.]

5. Associates for the year, subject to the payment of One Pound.

6. Corresponding Members nominated by the Council.

And the Members and Associates will be entitled to receive the annual
volume of Reports, gratis, or to purchase it at reduced (or Members') price,
according to the following specification, viz. : —

1. Gratis. — Old Life Members who have paid Five Pounds as a compo-

sition for Annual Payments, and previous to 1845 a further
sum of Two Pounds as a Book Subscription, or, since 1 845, a
further sum of Five Pounds.

New Life Members who have paid Ten Pounds as a com-
position.

Annual Members who have not intermitted their Annual Sub-
scription.

2. /4t reduced or Members' Prices, viz. two-thirds of the Publication

Price. — Old Life Members who have paid Five Pounds as a
composition for Annual Payments, but no further sum as a
Book Subscription.

Annual Members, who have intermitted their Annual Subscrip-
tion.

Associates for the year. [Privilege confined to the volume for
that year only.]

3. Members may purchase (for the purpose of completing their sets) any

of the first seventeen volumes of Transactions of the Associa-
tion, and of which more than 100 copies remain, at one-third of
the Publication Price. Application to be made (by letter) to
Messrs. Taylor & Francis, Red Lion Court, Fleet St., London.
Subscriptions shall be received by the Treasurer or Secretaries.

MEETINGS.

The Association shall meet annually, for one week, or longer. The place
of each Meeting shall be appointed by the General Committee at the pre-
vious Meeting ; and the Arrangements for it shall be entrusted to the Offi-
cers of the Association.

GENERAL COMMITTEE.

The General Committee shall sit during the week of the Meeting, or
longer, to transact the business of the Association. It shall consist of the
following persons : —

1. Presidents and Officers for the present and preceding years, with
authors of Reports in the Transactions of the Association.

2. Members who have communicated any Paper to a Philosophical Society,
which has been printed in its Transactions, and which relates to such subjects
as are taken into consideration at the Sectional Meetings of the Association.

RULES OP THE ASSOCIATION. XIX

3. Office-bearers for the time being, or Delegates, altogether, not exceed-
ing three in number, from any Philosophical Society publishing Transactions.

4. Office-bearers for the time being, or Delegates, not exceeding three,
from Philosophical Institutions established in the place of Meeting, or in any
place where the Association has formerly met.

5. Foreigners and other individuals whose assistance is desired, and who
are specially nominated in writing for the Meeting of the year by the Presi-
dent and General Secretaries.

6. The Presidents, Vice-Presidents, and Secretaries of the Sections are
ex-officio members of the General Committee for the time being.

SECTIONAL COMMITTEES.

The General Committee shall appoint, at each Meeting, Committees, con-
sisting severally of the Members most conversant with the several branches
of Science, to advise together for the advancement thereof.

The Committees shall report what subjects of investigation they would
particularly recommend to be prosecuted during the ensuing year, and
brought under consideration at the next Meeting.

The Committees shall recommend Reports on the state and progress of
particular Sciences, to be drawn up from time to time by competent persons,
for the information of the Annual Meetings.

COMMITTEE OF RECOMMENDATIONS.

The General Committee shall appoint at each Meeting a Committee, which
shall receive and consider the Recommendations of the Sectional Committees,
and report to the General Committee the measures which they would advise
to be adopted for the advancement of Science.

All Recommendations of Grants of Money, Requests for Special Re-
searches, and Reports on Scientific Subjects, shall be submitted to the Com-
mittee of Recommendations, and not taken into consideration by the General
Committee, unless previously recommended by the Committee of Recom-
mendations.

LOCAL COMMITTEES.

Local Committees shall be formed by the Officers of the Association to
assist in making arrangements for the Meetings.

Local Committees shall have the power of adding to their numbers those
Members of the Association whose assistance they may desire.

OFFICERS.

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

COUNCIL.

In the intervals of the Meetings, the affiiirs of the Association shall be
managed by a Council appointed by the General Committee. The Council
may also assemble for the despatch of business during the week of the
Meeting.

PAPERS AND COMMUNICATIONS.

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

ACCOUNTS.

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

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II. Table Blowing the Names of Members of tbe British Association who
have served on the Coimcil iii former years.

Acland, Sir Thomas D., Bart., F.E.S.
Acland, Professor H. W., M.D, F.K.S.
Adams, J. Couch, M.A., F.E.S.
Adamson, Jolm, Esq., F.L.S.
Ainslie, Eev. Gilbert, D.D., Master of Pem-
broke Hall, Cambridge.
Airy,G.B.,D.C.L..F.E.S.,A8tronomerEoyal.

Alison, Professor W. P., M.D., F.E.S.E.

Ansted, Professor D. T., M.A., F.E.S.

Argyll, George Douglas. Duke of, F.E.S.

Arnott, Neil, M.D., F.E.S.

Ashbiu-ton, William Bingham, Lord, D.C.L.

Atkinson, Et. Hon. E.,LordMayor of Dublin.

Babbage, Cliarles, Esq., M.A., F.E.S.

Babington, C. C, Esq., M.A., F.E.S.

Baily, Francis, Esq., F.E.S. (deceased).

Baker, Thomas Barwick Llovd, Esq.

Balfour, Professor John H.,'M.D., F.E.S.

Barker, George, Esq., F.E.S. (deceased).

Bell, Professor Thomas, Pres. L.S., F.E.S.

Beechey, Eear-Admu-al, F.E.S. (deceased).

Bengough, George, Esq.

Bentham, George, Esq., F.L.S.

Bigge, Charles, Esq.

Blakiston, Peyton, M.D., F.E.S.

Boileau, Su- Jolm P., Bart., F.E.S.

Boyle, Et.Hon. D., Lord Justice-Gen'. (deCi).

Brady,The Et. Hon. Maziere, M.E.I.A., Lord
Chancellor of Ireland.

Brand, William, Esq.

Breadalbane, Jolm, Marquis of, K.T., F.E.S.

Brewster, Sii- David, K.H., D.C.L., LL.D.,
F.E.S., Principal of the United College of
St.Salvator and St.Leonard, St. Andrews

Brisbane, General Sir Thomas M., Bart.,
K.C.B., G.C.H., D.C.L., F.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. WiUiam, D.D., F.E.S.,
Dean of Westminster (deceased).

Bute, John, Marquis of, K.T. (deceased).

CarUsle, George Will. Fred., Earl of, F.E.S.

Carson, Eev. Joseph, F.T.C.D.

Cathcart, Lt.-Geu., Earl of, K.C.B., F.E.S.E.

Chalmers, Eev. T., D.D. (deceased).

Chance, James, Esq.

Chester, Jolm 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, Henrv, M.D.

Clark, G. T.* Esq.

Clear, William, Esq. (deceased).

Gierke, Major S., K.H., E.E., F.E.S. (deC^).

Chft, WOli'am, Esq., F.E.S. (deceased).

Close, Very Eev. F., M.A., Dean of Carlisle.

Cobbold, John Cheyalier, Esq., M.P.

Colqulioun, J. C, Esq., M.P. (deceased).

Conybeare, Very Eev. W. D., Dean of Llan-
daff (deceased).

Corrie, John, Esq., F.E.S. (deceased).

Crum, Walter, Esq., F.E.S.

Currie, William Wallace, Esq. (deceased).

Dalton, Jolin, D.C.L., F.E.S. (deceased).

DanieU, Professor J. F., F.E.S. (deceased).

Dartmouth, WilUam, Earl of, D.C.L., F.E.S.

Dai-win, Charles, Esq., M.A., F.E.S.

Daubeny, Prof Charles G. B., M.D., F.E.S.

DelaBeche,Su-H. T., C.B., F.E.S., Director-
Gen.Geol. Sm*v.UnitedKingdom(dec'').

Devonshire, William, Duke of, M.A., F.E.S.

Dillwyn, Lewis W., Esq., F.E.S. (deceased).

Drinkwater, J. E., Esq. (deceased).

Ducie, The Earl, F.E.S.

Dmiraven, The Earl of, F.E.S.

Egertou.Sir P. de M. Grey, Bart.,M.P.,F.E.S.

EHot, Lord, M.P.

EUesmcre, Francis, Earl of, F.G.S. (dec"').

EnniskiUcn, William, Earl of D.C.L., F.E.S.

Estcom-t, T. G. B., D.C.L. (deceased).

Faraday, Professor, D.C.L.. F.E.S.

Fitzwilliam, The Earl, D.C.L., F.E.S. (dec<').

Fleming, W., M.D.

Fletcher, Bell, M.D.

Forbes, Charles, Esq. (deceased).

Forbes, Prof Edward, F.E.S. (deceased).

Forbes, Prof J. D., F.E.S., Sec. E.S.E.

Fox, Eobert Were, Esq., F.E.S.

Frost, Charles, F.S.A.

Gassiot, John P., Esq., F.E.S.

Gilbert, Davies, D.C.L., F.E.S. (deceased).

Graham, T., M.A., F.E.S., Master of the Mint.

Gray, Jolm E., Esq., Ph.D., F.E.S.

Gray, Jonathan, Esq. (deceased).

Gray, WiUiam, Esq., F.G.S.

Green, Prof Joseph Henry, D.C.L., F.E.S.

Greenough, G. B., Esq., F.E.S. (deceased).

GrifEth, SirE. Griffith, Bt., LL.D., M.E.I.A.

Grove, W. E., Esq., M.A., F.E.S.

Hallam, Henry, Esq., M.A., F.E.S.

Hamilton, W. J., Esq., F.E.S., For. Sec. G.S.

Hamilton, Sir \Vm. E.. LL.D., Astronomer

Eoyal of Ireland, M.E.I.A., F.E.A.S.
Harcom-t, Eev. Wm. Vernon, M.A., F.E.S.
Hardwicke, Charles PliiUp, Earl of, F.E.S.
Harford, J. S., D.C.L., F.E.S.
Harris, Sir W. Snow, F.E.S.
Harrowby, The Earl of, F.E.S.
Hatfeild,' WiUiam, Esq., F.G.S. (deceased).
Henry, W. C, M.D., F.E.S. [Col., Belfast.
Henry, Eev. P. S., D.D., President of Queen's
Henslow, Eev. Professor, M.A., F.L.S.
Herbert, Hon. and Very Eev. \A'm., LL.D.,

F.L.S., Dean of Manchester (dec'').
Herschel.Sii- John F.W., Bart.,D.C.L., F.E.S.
Heywood, Sir Benjamin, Bart., F.E.S.
Heyvvood, James, Esq., F.E.S.
HiU, Eev Edward, M.A.. F.G.S.
Hincks, Eev Edward, D.D., M.E.I.A.
Hinds, S., D.D., late Lord Bishop of Norwich.
Hodgkin, Thomas, M.D.
Hodgkinson, Professor Eaton, F.E.S.
Hodgson, Joseph, Esq., F.E.S.
Hooker, Sir William J., LL.D.. F.E.S.
Hope, Eev F. W., M.A., F.E.S.
Hopkins, WiUiam. Esq., M.A., F.E.S.
Horner, Leonard, Esq., F.E.S., F.G.S.
Hovenden, V. F., Esq., M.A.
Hutton, Eobert, Esq., F.G.S.
Hutton, WUliam, Esq., F.G.S.
Ibbet80n,Capt.L.L.Boscawen,K.E.E.,F.G.S.
IngHs, Su- E. H., Bart., D.C.L., M.P., (deC").
Jameson, Professor E., F.E.S. (deceased).
Jardine, Sir WUUam, Bart., F.E.S.E.
Jeffreys, John Gwyn, Esq., F.E.S.
Jenyns, Eev. Leonard, F.L.S.
Jerrard, H. B., Esq.
Jolmston, Eight Hon. William, late Lord

Provost of Edinburgh.
Johnston, Prof J. F. W., M.A., F.E.S. (deC").
Keleher, William, Esq. (deceased).
KeUand, Eev. Professor P., M.A.
Eildai'e, The Marquis of.

Lankester, Edwin, M.D., F.R.S.

Lansdowiie, Hen., Marquisof, D.C.L.,F.R.S.

Larconi, Lt.-Colonel, E.E., LL.D., E.E.S.

Lardner, Eev. Dr.

Lassell, WiUiam, Esq., F.E.S. L. & E.

Latham, E. G., M.D., F.E.S.

Leo, Very Eev. John, D.D., F.E.S.E., Prin-
cipal of the University of Edinburgh.

Lee, Eobert, M.D., F.E.S.

Lefevre, Eight Hon. Charles Shaw, late
Speaker of the House of Commons.

Lemon, Su- Charles, Bart., F.E.S.

Liddell, Andrew, Esq. (deceased).

Lindley, Professor John, Ph.D., F.E.S.

Listowel, The Earl of. [DubUn (dee-').

Lloyd, Eev. B., D.D., Provost of Trin. Coll.

Lloyd, Eev. H., D.D., D.C.L., F.E.S. L. &E.,

Londesborough, Lord, F.E.S.

Lubbock, Sir John W., Bart., M.A., F.E.S.

Lubv, Eev. Thomas.

Lyeil, Sii- Charles, M.A., F.E.S.

MacCidlagh. Prof., D.C.L., M.E.I.A. (dec'').

MacDonnell, Eev. E, D.D., M.E.I.A., Pro-
vost of Trmity College, Dublin.

Macfarlane, The Very Eev. Principal, (dec'').

MacLeay, William Sharp, Esq., F.L.S.

MacNeiil, Professor Su- Jolui, F.E.S.

Malaliide, The Lord Talbot de.

Maleokn,Vice-Ad. Su- Charles, K.C.B. (dec*!).

Maltby, Edward, D.D., F.E.S., late Lord
Bishop of Diu-ham.

Manchester, J. P. Lee, D.D.. Lord Bishop of.

MeyneU, Thomas, Esq., F.L.S.

Middleton, Su- WilUam F. F., Bart.

MiUer, Professor W. A., M.D., F.E.S.

Miller, Professor W. H., M.A., F E.S.

MoUlet, J. D., Esq. (deceased).

Milnes, E. Monektou, Esq., D.C.L., M.P.

Moggridge, Matthew, Esq.

Moody, J. Sadleir, Esq.

Moody, T. H. C, Esq.

Moody, T. F., Esq.

Morley, The Earl of.

Moseley, Eev. Henry, M.A., F.E.S.

Mount-Edgeeumbe, ErnestAugustus,Earl of.

Murehison, Sir Eoderick L.G.C. St.S., F.E.S.

Neill, Patrick, M.D., F.E.S.E.

Nicol, D., M.D.

Nicol, Eev. J. P., LL.D.

Northampton, Spencer Joshua AI wyne, Mar-
quis of, V.P.E.S. (deceased).

Northumberland, Hugh, Duke of, K.Gr.,M.A.,
F.E.S. (deceased).

Ormerod, G. W., Esq., M.A., F.G.S.

Orpen, Thomas Herbert, M.D. (deceased).

Orpen, Jolm H., LL.D.

Osier, FoUett, Esq., F.E.S.

Owen, Professor Eichd.,M.D., D.C.L.,F.E.S.

Oxford, Samuel Wilberforce, D.D., Lord
Bishop of, F.E.S., F.G.S.

Pabnerston, Viscount, G.C.B., M.P.

Peacock, VeryEev.G.,D.D.,DeanofEly,F.E.S.

Peel,Et.Hon.Su-E.,Bart.,M.P.,D.C.L.(dec'').

Pendarves, E., Esq., F.E.S.

Phillips, Professor John, M.A.,LL.D.,F.E.S.

Pigott, The Et. Hon. D. E., M.E.I.A., Lord
Chief Baron of the Exchequer in Ireland.

Porter, G. E., Esq. (deceased).

Powell, Eev. Professor, M.A., F.E.S.

Priehard, J. C, M.D., F.E.S. (deceased).

Eamsay, Professor WilUam, M.A.

Eeid, Maj.-Gen. Sh- W., K.C.B., E.E., F.E.S.

E«ndlesham, Et. Hon. Lord, M.P.

Eennie, George, Esq., F.E.S.

Eennie, Sir John, F.E.S.

Eichardson, Sir John, M.D., C.B., F.E.S.

Eitchie, Eev. Prof., LL.D., F.E.S. (dec").

Eobinson, Eev. J., D.D.

Eobinson, Eev. T. E, D.D., F.E.A.S.

Eobison, Sir John, Sec.E.S.Edin. (deceased).

Eoche, James, Esq.

Eoget, Peter Mark, M.D., F.E.S.

Eonalds, Francis, F.E.S.

Eosebery, The Earl of, K.T., D.C.L., F.E.S.

Eoss, Eear-Ad. Sir J. C, E.N., D.C.L., F.E.S.

Eosse, Wm., Earl of, M.A., F.E.S., M.E.I.A.

Eoyle, Professor John F., M.D., F.E.S.

Eussell, James, Esq. (deceased).

Eussell, J. Scott, Esq., F.E.S. [V.P.E.S.

Sabine, Maj.-Gen., E.A., D.C.L., Treas. &

Sanders, W'iUiam, Esq., F.G.S.

Scoresby, Eev. W., D.D., F.E.S. (deceased).

Sedgwick, Eev. Prof. Adam, M.A., F.E.S.

Selby, Prideaus John, Esq., F.E.S.E.

Sharpey, Professor, M.D., Sec.E.S.

Smith, Lieut.-Colonel C. Hamilton, F.E.S.

Smith, James, F.E.S. L. & E.

Spence, William, Esq., F.E.S.

Stanley, Edward, D.D., F.E.S., late Lord

Bishop of Norwich (deceased).
Stawiton, Sir G. T., Bt., M.P., D.C.L., F.E.S.
St. David's, C.Thii-lwaU,D.D.,LordBishop of.
Stevelly, Professor Jolm, LL.D.
Stokes, Professor G. G., 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., Vice-Chancellor of

the University of Oxford.
Talbot, W. H. Fox, Esq., M.A., F.E.S.
Tayler, Eev. John James, B.A.
Taylor, Jolm, Esq., F.E.S.
Taylor, Eichard, Esq., F.G.S.
Thompson, William, Esq., F.L.S. (deceased).
Thomson, Professor William, M.A., F.E.S.
Tindal, Captain, E.N.
Tite, WiUiam, 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).
Tiu-ner, Edward, M.D., F.E.S. (deceased).
Tm-ner, Samuel, Esq., F.E.S., F.G.S. (deC").
Turner, Eev. W.
TyndaU, Professor, 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.
Warbiu-ton, Henry, Esq.. M.A., F.E.S.
Wasliington, Captain, E.N., F.E.S.
Webster, Thomas, M.A., F.E.S.
West, WUUam, Esq., F.E.S. (deceased).
Western, Thomas Burch, Esq.
WharncUffe, John Stuart, Lord, F.E.S.
Wheatstone, Professor Charles, F.E.S.
WheweU, Eev. WUUam, D.D., F.E.S., Master

of Trinity College, Cambridge.
WUUams, Prof. Charles J. B., M.D., F.E.S.
WilUs, Eev. Professor Eobert, M.A., F.E.S.
WUls, WilUam, Esq., F.G.S.
Winchester, John, Marquis of.
WooUcombe, Henry, Esq., F.S.A. (deceased).
Wrottesley, John, Lord, M.A., Pres.E.S.
Yarborough, The Earl of, D.C.L.
YarreU, WiUiam, Esq., F.L.S. (deceased).
Yates, James, Esq., M.A., F.E.S.
Yates, J. B., Esq., F.S.A., F.E.G.S. (dec"*).

OFFICERS AND COUNCIL, 1857-58.

TRUSTEES (PERMANENT).
Sir Roderick I. MuRCHisoN,G.C.S'.S.,F.R.S. The Very Rev. George Pjbacock,D.D., Dean
John Taylor, Esq., F.R.S. of Ely, F.R.S.

PRESIDENT.
The REV. HUMPHREY LLOYD, D.D., D.C.L., F.R.S. L. & E., V.P.R.LA.,
Trinity College, Dublin.

VICE-PRESIDENTS.
The Rt. Hon. the Loau Mayor of Dublin. Sir William R. Hamilton, LL.D.,F.R.A.S.,
The Pkovost of Trinity College, Dublin. Astronomer Royal of Ireland.

The MARauis of Ktldare. Lt.-Colonel Larcom, R.E., LL.D., F.R.S.

The Lord Talbot de Malahide. Sir Richard J. Grifkith, Bart., LL.D.,

The Lord Chancellor of Ireland. M.R.I.A., F.R.S.E., f .G.S.

The Lord Chief Baron, Dublin.

PRESIDENT ELECT.

RICHARD OWEN, M.D., D.C.L., V.P.R.S., F.L.S., F.G.S.,

Superintendent of the Natural History Departments of the British Museum.

VICE-PRESIDENTS ELECT.
The Lord Monteagle, F.R.S. The Rev. William Whewell, D.D., F.R.S.,

The Lord Viscount Goderich, M.P., Hon. M.R.I.A., F.G.S., F.R.A.S., Master of

F.R.G.S. Trinity College, Cambridge.

The Rt. Hon. M. T. Baines, M.A., M.P. James Garth Marshall, Esq., M.A.,

Sir Phihi" de M. Grey Egerton, Bart., F.G.S.
M.P., F.R.S., F.G.S. R. Monckton Milnes, Esq., D.C.L., M.P.

LOCAL SECRETARIES FOR THE MEETING AT LEEDS.
The Rev. Thomas Hincks, B.A., 6 Woodsley Terrace, Leeds.
William Sykes Ward, Esq., F.C.S., Claypit House, Leeds.
Thomas Wilson, Esq., M.A., Crimbles House, Leeds.
LOCAL TREASURERS FOR THE MEETING AT LEEDS.
Arthur Lupton, Esq., Leeds. John Metcalfe Smith, Esq., Leeds.

ORDINARY MEMBERS OF THE COUNCIL.
Adams, J. C, D.C.L., F.R.S. Lyell, Sir C, D.C.L., F.R.S. Rennie, George, F.R.S.
Bell, Prof., Pres.L.S., F.R.S. Miller, Prof. W. A., M.D., Russell, J. S., F.R.S.
Darwin, Charles, F.R.S. F.R.S. SHARPEY,Professor,Sec. R.S.

FiTzRoY,RearAdmiral,F.R.S. Portlock, Lt. -Colonel, R.E., Stokes, Professor, Sec.R.S.
GasSiot, John P., F.R.S. F.R.S. Walker, Rev. Prof., F.R.S.

Grove, William R., F.R.S. Price, Rev. Prof., F.R.S. Webster, Thomas, F.R.S.

Horner, Leonard, F.R.S. RAWLiNSON,ColonelSirH.C., WRoTTESLEY,Lord,Pres.R.S.
Hutton, Robert, F.G.S. K.C.B., F.R.S. Yates, James, M.A., F.R.S.

Latham, R. G., M.D., F.R.S.

EX-OFFICIO MEMBERS OF THE COUNCIL.
The President and President Elect, the Vice-Presidents and Vice-Presidents Elect, the Ge-
neral and Assistant-General Secretaries, the General Treasurer, the Trustees, and the Presi-
dents of former years, viz. Rev. Professor Sedgveick. Sir Thomas M. Brisbane. The Marquis
of Lausdowne. The Duke of Devonshire. Rev. W. V. Harcourt. The Marquis of Bread-
albaue. Rev. Dr. Whewell. The Earl of Rosse. The Dean of Ely. Sir John F. W. Her-
schel, Bart. Sir Roderick I. Murchison. The Rev. Dr. Robinson. Sir David Brewster.
G. B. Airy, Esq., the Astronomer Royal. General Sabine. WUliam Hopkins, Esq., F.R.S.
The Eai-1 of Harrowby. The Duke of Argyll. Professor Daubeny, M.D.
GENERAL SECRETARY.
Major-General Edward Sabine, R.A., Treas. & V.P.R.S., F.R.A.S.,
13 Ashley Place, Westminster.
ASSISTANT GENERAL SECRETARY.
John Phillips, Esq., M.A., LL.D., F.R.S., Pres.G.S., Reader in Geology in the University
of Oxford ; Magdalen Bridge, Oxford.
GENERAL TREASURER.
John Taylor, Esq., F.R.S., 6 Queen Street Place, Upper Thames Street, London.
LOCAL TREASURERS.
William Gray, Esq., F.G.S., Yuri. Professor Ramsay, M.A., Glasgow.

C.C.Babington,Esq.,M.A.,F.R.S.,CamAr%e. Robert P. Greg, Esq., F.G.S., Manchester.
William Brand, Esq., Edinburgh. John Gwyn Jeffreys, Esq., F.R.S., Swansea.

John H. Orpen, LL.D., Dublin. J. B. Alexander, Esq., Ipswich.

William Sanders, Esq., F.G.S., Bristol. Robert Patterson, Esq., M.R.I.A., Belfast.

Robert M' Andrew, Esq., F.R.S., Liverpool. Edmund Smith, Esq., Hull.
W. R. Wills, Esq., Birmingham. Richard Beamish, Esq., F.R.S., Cheltenham.

AUDITORS.
Edwin Lankester, M.D. James Yates, Esq. Dr. Norton Shaw.

OFFICERS OF SECTIONAL COMMITTEES. XXVU

OFFICERS OF SECTIONAL COMMITTEES PRESENT AT THE
DUBLIN MEETING.

SECTION A. MATHEMATICS AND PHYSICS.

President.— Rev. T. R. Robinson, D.D., F.R.S., M.R.I.A.

Vice-Presidents.— J. C. Adams, F.R.S. ; Rev. Professor Graves, Sec. R.I.A. ;
Sir W. R. Hamilton, LL.D., M.R.I.A. ; Rev. George Salmon, D.D., M.R.I.A. ; Rev.
W. Whewell, D.D., F.R.S. ; Lord Wrottesley, President of the Royal Society.

Secretaries. — Professor Curtis, A.M ; Professor Hennessy, M.R.I.A.; P. A.
Ninnis, B.A. ; W. J. Macquorn Rankine, F.R.S. ; Professor Stevelly, LL.D.

SECTION B. CHEMISTRY AND MINERALOGY, INCLUDING THEIR AVPLICATIONS

TO AGRICULTURE AND THE ARTS.

PresWen^.— Professor Apjohn, M.D., F.R.S., M.R.I.A.

Fiice-Presjrfe»<s.— Professor T. Andrews, M.D., F.R.S., M.R.I.A. ; Professor E.
Davy, F.R.S., M.R.I.A. ; Rev. Wm. Vernon Harcourt, F.R.S. ; Professor W. A.
Miller, M.D., F.R.S. ; Professor G. Wilson, M.D., F.R.S.E.

Secretaries.— Dr. Gladstone, F.R.S. ; Professor W. K. Sullivan, M.R.I.A. ; Dr.
E. W. Davy, M.R.I.A.

SECTION C. GEOLOGY.

President. — ^The Lord Talbot de Malahide, President of the Geological Society of
Dublin.

Vice-Presidents. — Richard Griffith, LL.D. ; Profesi?or Haughton, M.R.I.A.,
F.G.S. ; J. Beete Jukes. F.R.S., M.R.I.A.; Thomas Oldham, F.R.S., M.R.I.A.;
Colonel Portlock, R.E., F.R.S., M.R.I.A.

Secretaries. — Professor Harkness, F.R.S. ; Gilbert Sanders, M.R.I.A. ; Robert
H. Scott, Esq.

SECTION D. ZOOLOGY AND BOTANY, INCLUDING PHYSIOLOGY.

President. — Professor William Henry Harvey, M.D., M.R.I.A.

Vice-Presidents.— Professor G.J.AUman, M.D., F.R.S.,M.R.LA, ; Professor C.G.
Daubenv, M.D., F.R.S. ; A. H. Halliday, M.R.I.A., F.L.S, ; Professor Robert Har-
rison, M. D., M.R.I.A. ; W. Ogilby, F.L.S., M.R.I.A. ; Sir John Richardson,
F.R.S.

Secretaries. — Professor John R. Kinahan, M.B., M.R.LA. ; Edwin Lankester,
M.D., F.R.S. ; Robert Patterson, M.R.I.A.; William Edward Steele, M.D.

SUB-SECTION D. PHYSIOLOGICAL SCIENCE.

President. — Robert Harrison, M.D., M.R.I.A., Professor of Anatomy and Phy-
siology, T.C.D.

Vice-Presidents. — SirH.Marsh,Bart.,M.R.I.A.; Professor Hugh Carlile, M.R.LA.;
Professor F. C. Faye, Christiania ; Dr. Jacob ; Dr. Laycock, Professor of Practice of
Medicine, University of Edinburgh ; Sir Philip Crampton, Bart., F.R.S., M.R.I.A.

Secretaries. — Robert D. Lyons, M.B., M.R.I.A. ; Professor Redfern.

SECTION E. GEOGRAPHY AND ETHNOLOGY.

President. — Rev. James Henthorn Todd, D.D., Pres. R.I.A.

Vice-Presidents. — Major-General Chesney, R.A., D.C'.L., F.R.S.; John Crawford
F.R.G.S. ; Rear-Admiral R. FitzRoy, F.R.S. ; Rev. Edward Hincks, D.D. • Rev'
Charles Wm. Wall, D.D., Vice Provost T.C.D., M.R.I.A. ; Wm. R. Wilde, M.R.La!

Secretaries. — Richard Cull, F.S.A. ; Samuel Ferguson, M.R.LA.; Richard R
Madden, M.D., F.R.C.S, Eng. ; Dr. Norton Shaw, Sec. R.G.S.

SECTION F. ECONOMIC SCIENCE AND STATISTICS.

President. — The Archbishop of Dublin, M.R.I.A.

Vice-Presidents. — Lord Monteagle, F.R.S. ; Edwin Chadwick,C.B. ; The Recorder
of Birmingham ; JamesA.Lawson, Q.C., LL.D., M.R.I.A.; Edward Baines,Esq.; John
Strang, LL.D. ; Wm. Donnelly, LL.D.; F. G. P. Nelson, F.S.S. ; James R. Napier.

Secretaries. — William Newmarch, F.S.S. ; Professor Cairnes, M.R.LA. ; Henry
Dix Hutton, LL.B.

SECTION G. MECHANICAL SCIENCE.

President.— The Earl of Rosse, F.R.S., M.R.I.A.

Vice-Presidents.-George Rennie, F.R.S. ; Robert Mallet, M. Inst. C.E., F.R.S.,
M.R.I.A.; Sir John Macneill, F.R.S., M.R.LA.; John Scott Russell, F.R.S.;
William Dargan, M.R.I.A.

Secretaries. — James Thompson, C.E. ; William T. Doyne, M. Inst. C.E. ; Henry
Wright; ProfessorDowning, LL.D., M.R.I.A.; AlexanderTate, Secretary Inst. C.E.I.

REPORT — 1857.

CORRESPONDING MEMBERS.

Professor Agassiz, Cambridge, Massa-

chusetts.
M. Babinet, Paris.
Dr. A. D. Baclie, Washington.
Professor Balzani, Kazan.
Barth, Dr.

Mr. P. G. Bond, Cambridge, U.S.
M. Boutigny (d'Evreux).
Professor Braschmann, Moscow.
Chevalier Bunsen, Heidelberg.
Dr. Ferdinand Cohn, Breslaii.
M. Antoine d'Abbadie.
M. De la Rive, Geneva.
Professor Dove, Berlin.
Professor Dumas, Paris.
Dr. J. Milne-Edwards, Paris.
Professor Ehrenberg, Berlin.
Dr. Eisenlohr, Carlsruhe.
Professor Encke, Berlin.
Dr. A. Erraan, Berlin.
Professor Esmark, Cliristiania.
Professor G. Forchhammer, Copenhagen.
M. Leon Foucault, Paris.
Prof. E. Fremy, Paris.
M. Frisian!, Milan.
Professor Asa Gray, Cambridge, U.S.
Professor Henry, JFashington, U.S.
Baron Alexander von Humboldt, Berlin.
M. Jacobi, St. Petersburg.
Prof. A. Kblliker, Wurzburg.
Prof. De Koninck, Liege.
Professor Kreil, Vienna.
Dr. A. Kupffer, St. Petersburg.
Dr. Lamont, Munich.
Prof. F. Lanza, Spoleto.

M. Le Verrier, Paris.

Baron von Liebig, Munich.

Baron de Selys-Longchamps, Li^ge.

Professor Loomis, New York.

Professor Gustav Magnus, Berlin.

Professor Matteucci, Pisa.

Professor von Middendorff, St. Petersburg.

M. I'Abbe Moigno, Paris.

Professor M. Morren, Liege.

Professor Nilsson, Swedeii.

Dr. N. Nordengsciold, Finland.

M. E. Peligot, Paris.

Viscenza Pisani, Florence.

Gustave Plaar, Strasburg.

Chevalier Plana, Turin.

Professor PI ticker, Bonn.

M. Constant Prevost, Paris.

M. Quetelet, Brussels.

Prof. Retzius, Stockholm.

Professor C. Ritter, Berlin.

Professor H. D. Rogers, Boston, U.S.

Professor W. B. Rogers, Boston, U.S.

Professor H. Rose, Berlin.

Herman Schlagintvveit, Berlin.

Robert Schlagintvveit, Berlin.

Baron Senftenberg, Bohemia.

Dr. Siljestrom, Stockholm.

M. Struve, Pulkowa.

Dr. Svanberg, Stockholm.

M. Pierre Tchihatchef.

Dr. Van der Hoeven, Leyden.

Baron Sartorius von Waltershausen,

Gottingen.
Professor Wartmann, Geneva.

Report of the Council of the British Association as presented
TO THE General Committee at Dublin, August 26th, 1857.

I. With reference to the subjects referred to the Council by the General
Committee at Cheltenham, the Council have to report as follows : —

a. The General Committee directed that copies of the two last Reports
of the Parliamentary Committee should be transmitted to each Member
of the General Committee, with a request that opinions might be expressed
on the important subject, "Whether any measures could be adopted
by the Government or Parliament that would improve the position of
Science and its cultivators ;" and that such opinions should be forwarded
for the consideration of the Council before the 20th of September, 1856.
This direction having been complied with, and a considerable number of
letters expressing the opinions of individual Members of the General Com-
mittee having been received, the Council requested the Assistant-General
Secretary to prepare a digest, and to make such an arrangement of the
communications themselves as might best facilitate their full consideration
at a Special Meeting of the Council in January, 1857. At this meeting,
Lord Wrottesley, President of the Royal Society, being one of the Members

REPORT OP THE COUNCIL. XXIX

of the Council of the Association, communicated for the information of
the Council, certain resolutions which had been adopted by the President
and Council of the Royal Society, bearing on the same question ; and
after a full consideration of these resolutions, and of the opinions expressed
in the letters of the individual Members of the General Committee of the
Association, the Council adopted the following Minute, viz. — " That the
Council concur generally in the course of proceeding which has been
talcen on this subject by the Royal Society, as now explained to them by
the President of that Society." This Minute was communicated by order
to the Royal Society, and the Resolutions have been since transmitted by
Lord Wrottesley to Lord Palmerston, as having been adopted by the Pre-
sident and Council of the Royal Society and concurred in by the Council
of the British Association.

b. The recommendation, that " the application to Government for an
Expedition to complete our knowledge of the Tides be renewed," was
referred by the Council to the Committee of 1851, by whom the previous
application had been made. The Committee consisted of the Rev. Dr.
Whewell, the Earl of Rosse, Sir John Herschel, and the Astronomer
Royal. No report has yet been received by the Council of the Com-
mittee's consequent proceedings.

c. The recommendation, that " the Application made to Government in
September 1852, concerning the great Southern Telescope, be renewed,"
was communicated by the Council to the President and Council of the
Royal Society, by whom the steps were taken in 1852 to promote this
important object, and a hope was expressed on the part of the Association
that the President and Council of the Royal Society would renew their
efforts to carry out an object of so much interest to astronomy. The
Council have not been informed of any subsequent proceedings.

d. The General Committee having directed that " a Memorial should
be presented to the Admiralty praying for the publication in a simple,
uniform, and complete shape, tabular and descriptive, of the results of the
trials of steam-ships employed in the public service," the Council referred
to the President of the Section of Mechanical Science, with whom the
request for this publication had originated, for the information required to
enable the Council to proceed in drawing up the desired Memorial. The
information was supplied, and a document, drawn up in more limited terms
than the recommendation, and stating fully the data required and the
purpose to which it was proposed to apply them, was transmitted to the
Secretary of the Admiralty, who replied that the Lords Commissioners
did not think it would be proper for them to give information in regard to
vessels belonging to private companies. This reply was communicated to
the President of the Mechanical Section and a Committee acting with him
on the registration of ships' tonnage, by whom the subject will be again
brought under the consideration of the Association at this Meeting.

e. The deputation appointed to wait on Her Majesty's Secretary for
Foreign Affairs to " urge the desirableness of sending out an annual expe-
dition to the Niger, as proposed by Dr. Baikie," have informed the Council
that they have had an interview with Lord Clarendon, and have presented a
Memorial which was very favourably received, and that the expedition has
since been appointed, and has proceeded to the Niger under Dr. Baikie's
direction.

IL At the Glasgow Meeting of the British Association, a Committee was
appointed by the General Committee to consider a proposition which had
been submitted to them for making a catalogue of the Philosophical Papers

XXX REPORT — 1857.

contained in the various Scientific Transactions andjournals of all countries.
The Report of this Committee was made at the Cheltenham Meeting, and
was communicated by direction of the Council to the President and Council
of the Royal Society, whose cooperation in this important undertaking was
requested. The original Committee appointed by the Association, with the
addition of two Members named by the Council of the Royal Society, were
requested to give the subject a second and more full consideration. Their
Report was presented to the Council of the Royal Society in June last, and
was ordered to be printed and 250 copies to be sent to the British Association,
for distribution amongst the Members of the General Committee at the Dublin
Meeting, with a view to obtain the thorough concurrence and cooperation of
the two Societies in the plan which shall be ultimately adopted for carrying
out a work which promises to be of very considerable advantage to the cul-
tivators of science in all countries.

III. The Council congratulate the General Committee on the publication
which has taken place in the current year of the Meteorological Observations
made by the Officers of the Irish Trigonometrical Survey at Mountjoy
Barracks, near Dublin. It will be remembered that at the Southampton
Meeting of the Association in the year 1846, a Committee was appointed
to communicate with the Master- General of the Ordnance relative to the
publication of these valuable observations, and that in January 1847, the
Marquis of Anglesey, then holding the office of Master-General of the
Ordnance, expressed to the Committee his readiness to meet the wishes of
the British Association if the Treasury could be induced to grant the neces-
sary funds, for which the Ordnance had not and could not make any pro-
vision. In consequence of this communication, the Council appointed a
deputation to solicit from the Treasury that a grant for the purpose should
be placed at the disposal of the Master-General, and were informed in
reply, through the Secretary of the Ordnance, under date May 31, IS't?,
that the Treasury would be prepared to include the expense of the publica-
tion in the estimate to be laid before Parliament in 1848. The Council were
also favoured with a letter from the Marquis of Anglesey, dated July 10,
1848, stating that " he had directed the publication of the Mountjoy Ob-
servations to be carried into effect with as little delay as possible." The
publication having now taken place, it has appeared to the Council de-
sirable that the part taken by the British Association in recommending and
in procuring the funds for this valuable contribution to the Meteorology
of the British Islands should be thus fully stated ; because it has happened
(no doubt accidentally) that no notice of any of these circumstances appears
in the Preface or in the Introduction of the publication itself.

IV. The Council have been informed that circumstances will deprive the
Dublin Meeting of the attendance of Edward J. Cooper, Esq., who was
named as one of the Vice-Presidents for the Meeting ; and with the con-
currence of the Local Committee in Dublin, they recommend to the General
Committee that the name of the Lord Chancellor of Ireland should be sub-
stituted for that of Mr. Cooper.

V. The Council have received letters of invitation to the Association to
hold its Meeting in 1858 in Manchester, from —

The General Purposes' Committee of the City Council.

The Board of Directors of the Athenaeum.

The Literary and Philosophical Society of Manchester.

The Botanical and Horticultural Society.

The Natural History Society.

The Photographic Society.

REPORT OF THE KEW COMMITTEE. XXXI

The Principal and Professors of Owens College.

VI. The Council has this day received letters of invitation to the Asso-
ciation to hold its Meeting in 1858 in Leeds, from —

The Mechanics' Institution and Literary Society.
The School of Practical Art.

VII. The Council have also this day been informed of an invitation to be
presented from the Literary and Philosophical Society of Newcastle-on-Tyne
and the Fine Arts Society "of the North of England, to hold an early meeting
at Newcastle.

VII. The General Committee will receive full information, in the sub-
joined Report from the Kew Committee, of the proceedings of that establish-
ment during the past year ; and the Council are persuaded that the General
Committee will see with pleasure the evidences of the still increasing public
utility of that institution, and of the credit thereby accruing to the British
Association.

Report of the Kew Committee of the British Association for the
Advancement of Science, for 1856-57.

Since the last Meeting of the British Association, the works necessary for
lighting the Observatory with gas have been executed at a cost of S250,
which has been defrayed by a Grant from the WoUaston Fund by the Pre-
sident and Council of the Royal Society.

Soon after the last Meeting of the Association, the Board of Works com-
menced the external repairs of the Observatory. These were completed in
November last. The Chairman having represented to the Chief Commis-
sioner of Works the necessity for considerable repairs to the interior of the
Building, the Board of Works agreed to execute such repairs as soon as the
necessary funds should be voted by Parliament. The Committee understand
that the requisite vote has been passed, and that the works will be proceeded
with in the course of the present summer.

The following memorandum relative to the re-establishment of self-re-
cording magnetic instruments at the Kew Observatory was submitted to the
Committee by General Sabine on July 22, 1 856 : —

" 1. The decennial period in the solar magnetic variations, and its coinci-
dence with a similar period in the frequency and amount of the solar spots,
appear to be highly deserving of attention in an observatory established, as
Kew is, for physical researches.

" 2. There is reason to suppose that the permanency and regularity in the
occurrence of the decennial period in the magnetic variations, and its coinci-
dence with the periodic variation of the solar spots, might be eiFectually and
satisfactorily tested by observations of both classes of phenomena at the
alternate periods of maximum and minimum, say for example, in 1857 and
1858 as the anticipated period of maximum, and in 1863 and 1864' as the
anticipated period of minimum, and so forth.*

" 3. The apparatus constructing under the superintendence of Mr. De la
Rue will, it is hoped, fully meet the requirements of the research in respect
to the solar spots.

"4. Since the time when the magnetic self-recording instruments belong-
ing to the Kew Observatory were constructed under the direction of Mr.
Ronalds, very considerable improvements have been made in the art of Pho-
tography, and the six months' trial which was made by Mr. Welsh of Mr.
Ronalds' instruments, has led in several other respects to suggestions for im-
provements which could not but be expected to be required in instruments

XXxii REPORT — 1857.

of so novel a kind, while at the same time the six months' trial referred to has
placed bej'ond doubt the sufficiency of a properly conducted research by
means of self-recording instruments for the examination of the solar magnetic
variations,"

The Committee authorized Mr. Welsh to proceed with the construction of
the instruments, which have now been completed at an expense not exceeding
£250, this sum being defrayed from the funds supplied by the Government
Grant through the Council of the Royal Society, the instruments remaining
at Kew at the disposition of the Council of the Royal Society.

With the assistance of apparatus lent from General Sabine's department,
the observatory is now possessed of the means of determining with great ac-
curacy the various constants required in magnetic observation. Some alter-
ations in the method of manipulation have, it is believed, added considerably
to the accuracy of observation of the absolute value of the Magnetic
Force.

At the request of the Foreign Office, Magnetical and Meteorological In-
struments have been prepared at the Observatory for Mr. Lyons M'Leod,
Consul at Mozambique. Mr. M'Leod attended on several occasions in
order to make himself acquainted with their manipulation.

The following correspondence has taken place relative to an application
from the Austrian Government to be supplied with Magnetical Instruments,
to be employed in the scientific voyage undertaken by His Imperial Majesty's
Frigate " Novara."

(Copy.)

" Admiralty, 31st December, 185(5.
" Dear General Sabine, — The Austrian Consul, Baron Rothschild, has
written a pressing note to the Admiralty to ask where the enclosed list of
instruments can be procured, and for any assistance we can give in ensuring
their being the best. Will you be so good as to say what answer shall be
sent? would it be too much to ask you to see that they are properly sent,
and as nearly as you can, will you name the time the instruments could be
ready ?

" Yours faithfully,
(Signed) "John Washington."

" Memorandum of Instruments required by His Imperial Majesty's
Frigate ' Novara.'

"a. The Azimuth Compass.

" b. The Unifilar Magnetometer.

" c. Mr. Fox' s]apparatus for observing the magnetic force and inclination.

" d. Mr. Barrow's Circle for observing the magnetic inclination.

" To the apparatus b belongs also a peculiar apparatus for its erection and
use on board ship.

" For the further use of these instruments and for taking the observations
made thereby, it is desired that they may be delivered with the indication
of their respective constants, as the moment of inertia, the temperature,
coefficients, &c. &c.

" The Consulate-General will apply to the British Admiralty, who will, no
doubt, kindly give the names of the makers who supply the British Admiralty,
as it is desired that they be the same instruments as those on board Her
Majesty's ships of war."

" London, 29th December, 1856."

REPORT OF THE KEW COMMITTEE. XXXIU

(Copy.)

" 13, Ashley Place, London,
January 7th, 1857.

" Sir, — I have received from Mr. James Yates a copy of the letter which
you addressed to him on the ii6th of last month, describing the scheme of the
scientific voyage of circumnavigation about to be undertaken by His Impe-
rial and Royal Majesty's Frigate ' Novara,' and requesting to be furnished with
any suggestions which may assist you in carrying out the objects for which
this voyage has been undertaken. I have deemed, therefore, that it may be
agreeable to you to be informed, that in consequence of an application from
Baron Rothschild to the British Admiralty, I have been requested to under-
take, and have undertaken, to prepare the following instruments named in
Baron Rothschild's letter for the magnetical observations to be made during
the voyage, viz. —

" 1. A Standard Azimuth Compass for the Declination.

" 2. A Barrow's Inclinometer for the Inclination.

" 3. A Fox's apparatus with Gimbal Stand for Inclination and Magnetic
Force at sea.

" 4. A Unifilar Magnetometer for observations of the Absolute Horizontal
Magnetic Force on land.

" These instruments will be examined and their constants determined at the
Kew Observatory of the British Association for the Advancement of Science,
and will be ready by the end of February or beginning of March, together
with instructions for the use of each of the instruments, and blank forms for
the convenient record of the observations to be made with them. It is most
desirable, however, that the physicist who is to be charged with the observa-
tions should have some previous practice with the instruments, and I would
therefore beg leave to suggest that the gentleman who may be appointed to
that duty should be directed to proceed in the first instance to London, so
as to arrive there about the third week in February, and after having made
himself familiar with the use of the instruments, should take them with him
to Gibraltar, and there await the arrival of the ' Novara ' on the passage from
Trieste to Rio Janeiro.

" I have the honour to remain, Sir,
" Your obedient Servant,
(Signed) " Edward Sabine,

Major- General"

" P.S. Several of the instruments above mentioned will be ready by the end
of the present month. Baron Rothschild's letter does not say anything
about Marine Meteorological instruments. Sliould instruments of this de-
scription, such as are now furnished to the British Navy, be desired, they
could be supplied by the Kew Observatory, and might accompany the mag-
netical instruments to Gibraltar."

" Dr. Karl Scherzer, Vienna."

The Magnetical Instruments for this Expedition have been prepared, and
the Constants determined at the Observatory. Dr. Hochstatter, of Vienna,
who has undertaken the superintendence of the Magnetical Observations to
be made during the voyage, visited the Observatory in the end of February
and beginning of March, to receive instructions in the use of the various
instruments.

A letter has been received by General Sabine from the Archduke Ferdi-
nand Maximilian, expressing his thanks, as Chief Officer of the Austrian

1857. c

XXXiv REPORT — 1857.

Navy, for the assistance aflForded to Dr. Hochstatter, who writes that he had
commenced his observations : — Dr. Hochstatter's letter is dated Gibraltar,

21st May, 1857.

In consequence of an application from the Hydrographer of the Admiralty,
Dr. Baikie and Lieut. Glover, who have recently sailed on an expedition to
Africa, were furnished witii Magnetical Instruments, whose Constants had
been previously determined at the Observatory. Dr. Baikie and Lieut. Glover
visited the Observatory, when detailed instructions were communicated to
them by Mr. Welsh, as to the practical use of the instruments.

Application having been made to the Royal Society by Her Majesty's
Secretary of State for the Colonies, relative to a supply of Magnetical In-
struments for an expedition to British North America, under the direction
of Mr. Palliser, Lieut. Blakiston, R.A., who accompanies the Expedition,
attended for some time at the Observatory for the purpose of manipulating
with the Magnetical Instruments, which have been prepared under the direc-
tion of Mr. Welsh for the use of the Expedition. The Constants of these
instruments were determined as in the other instances already referred to in
this Report.

At the request of the Council of the Royal Society, Mr. Welsh has pre-
pared the Magnetical Instruments required in the North Polar Expedition,
which has been fitted out at the expense of Lady Franklin : the cost of pre-
paration of these instruments is defrayed by the Royal Society. The instru-
ments themselves have been supplied from Major-General Sabine's establish-
ment at Woolwich.

General Sabine having communicated to the Committee that £200 had
been placed at his disposal by the Admiralty, for the purpose of conducting
the Magnetical Survey of Scotland, in connexion with the general Magnetic
Survey of the British Islands, as recommended at the last Meeting of the
Association, the Committee have arranged that Mr. Welsh shall undertake
such survey in the course of the present and following summer.

Sir James Clark Ross has already commenced the Survey of England,
taking Kew as his base station.

A new method, proposed by Dr. Lloyd, of determining the absolute total
magnetic force by means of the Dip Circle, will be employed in this Survey.
Dip Circles adapted for this method have been supplied to Sir James C. Ross
and Mr. Welsh, also to Lieut. Blakiston for his Survey in North America.

Photoh eliogr aph.
On the 20th of May, 1854, Benj. Oliveira, Esq., F.R.S., placed the sum of
£50 at the disposal of the Council of the Royal Society, to be appropriated
during that year in any manner the Council might consider most in harmony
with the interests of Science. Mr. Oliveira further stated, that he might pro-
bably in future years offer a similar sum if the mode of its disposal appeared
to him eligible ; and an application having at the same time oeen made by
the Kew Committee for the sum of £150, in order to erect a Photographic
Apparatus for registering the position of the spots in the Sun's disc, as sug-
gested by Sir John Herschel, the Council of the Royal Society devoted to
this purpose the donation of Mr. Oliveira, and proposes, should it be con-
tinued, to apply it for the next two years in replacement of the sum of £100
which the Council in the mean time advanced from the Donation Fund of
the Royal Society, in order that the undertaking might not be delayed. This
arrangement was approvc^d by Mr. Oliveira, and the apparatus has, under the
direction of Warren Do la Rue, Esq., F.R.S., been completed by Mr. Ross
at the cost of about £180.

BEPOBT OF THE KEW COMMITTEE. XXXV

The object-glass of this instrument is 3^ inches aperture and 50 inches
focal length ; it is not corrected for achromatism in the ordinary manner, but
so as to produce a coincidence of the visual and photogenic foci. The
secondary objectives for magnifying the image produced by the principal
object-glass are of the Huyghenian form. They are three in number, pro-
ducing respectively images of the sun 3, 4, and 8 inches in diameter. Between
the two lenses of each of these secondary object-glasses is inserted a dia-
phragm-plate carrying the fixed micrometer wires, which are of platinum ;
these wires are four in number, two at right angles to the other two. One
of the wires of each pair is in such a position that they may both be made
tangential to the sun's image, while the other two cross at a point situated
near the sun's centre. By means of these wires, the distance in arc between
each pair having been once for all ascertained astronomically for each
secondary object-glass, it will be easy to determine all the data necessary for
ascertaining the relative magnitudes and positions of the sun's spots. These
micrometer wires are under the influence of springs, so as to preserve a tension
upon them when expanded by the sun's heat, and thus to lieep them straight.

The principal and secondary object-glasses are not mounted in an ordinary
cylindrical tube, but in a pyramidal trunk square in section, 5 inches in the
side at the upper end, which carries the principal object-glass, and 12 inches
in the side at the lower end, which carries the photographic plate-holder and
the usual ground glass screen for focusing.

This trunk is firmly supported by a declination axis of hard gun-metal 2^
inches in diameter; it is furnished with a declination circle 10 inches in dia-
meter, reading to one minute of arc, and has a clamp and screw motion for
fine adjustment in declination.

The declination axis works in Y-bearings at the top of the polar axis, which
is 12 inches long; it is 4 inches diameter at its upper end and 1-| inch at
its lower end. The lower end fits with a slight taper into a brass collar up
to a shoulder, the friction being reduced by a steel spring plate pressing
against a hardened steel hemisphere at the end of the axis.

It will be seen by the above description, tliat every precaution has been
taken to secure stiff'ness in the telescope combined with freedom in the
motion of the polar axis. The polar axis is driven by a clock driver, which
answers perfectly, and is easy of regulation to the greatest nicety, so that tiie
sun's limb remains for a long period in contact with the tangential wires.
Near the lower end of the polar axis is fixed the hour-circle, which, like the
declination circle, is 10 inches indiameter ; it is graduated to read to 2 seconds of
time. An endless screw, making about two revolutions in one minute, geers
into the hour-circle and connects it with the clock. As it is generally ne-
cessary to make small corrections in right ascension after the tangent screw
has been geered with the driving clock, in order to bring the sun's image in
position with respect to the micrometer wires, a sliding plate is provided which
carries the bearings of the tangent screw ; this is acted upon by a second fine
screw parallel with the tangent screw ; so that by rotating the second screw,
the sliding plate and the tangent screw are moved through a small space,
and the hour-circle thus caused to rotate to the extent necessary for bringing
the sun's image in position.

The clock is driven by two weights, one pulling upwards over a pulley, the
other downwards, thus suspending the barrel and equalizing the pull and
avoiding friction on its bearings. By causing the click of the winding lever
to abut on the ratchet-wheel of the going part of the clock during the period
of winding, the clock goes at its normal speed while it is being wound.

The mode of regulating the clock is extremely simple and efficacious ; it is

XXXvi REPORT — 1857.

effected by approaching to, or withdrawing from, a hollow cone over a small
wheel, on which are attached, by means of flat springs, two small weights,
which expand by centrifugal force and come in contact with the inside of the
hollow cone.

The polar axis of the telescope is carried by a dial-plate, which fits on the
top of a hollow column of cast iron, the section of which is a parallelogram.
This column is securely fastened to the stone foundation. The instrument is
mounted within the rotating dome of the Kew Observatory, which has been
repaired and put in order for that purpose. The photographic dark room is
at present too distant from the telescope, but it is contemplated to construct
one close to it, as serious inconvenience has been already experienced in the
preliminary experiments in consequence thereof.

The telescope and its mechanical appliances may be said to be perfect so
far as they go, but experience will undoubtedly suggest several minor alter-
ations and additions before the telescope is brought practically to work. The
photographing of such minute objects as the sun's spots will require at all
times the utmost skill and care of an accomplished photographer, even when
the telescope has been fairly started. The difficulties yet to be mastered must
occupy some considerable time. The first attempts have been confined to the
production of negative photographs, but in consequence of the imperfections
always existing in the collodion film, it has been deemed advisable to make
attempts to produce positive pictures, and recourse may ultimately have to
be made to the Daguerreotype process.

The verification of Meteorological Instruments has been continued on the
same plan as in previous years. The following are the numbers of instruments
which have been verified since the leist meeting of the Association : —

Baro- Thermo- Hydro-
meters, meters, meters.

For the Admiralty 127 84-0 G05

For the Board of Trade 86 360 UO

For Opticians and others 65 324 6

Total 278 1524. 751

Mr. Stewart having left the Observatory, as mentioned in the last Annual
Report, the Committee in October last engaged Mr. Charles Chambers of
Leeds, on the recommendation of the Council of the Society of Arts. The
Committee report very favourably of the intelligence and assiduity with
which he has discharged his duties.

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xxxviii REPORT — 1857.

Report of the Parliamentary Committee to the Meeting of the British

Association at Dublin, i?i August 1857.

The Parliamentary Committee have the honour to report as follows : —

The questi(m discussed in the Report of your Committee, addressed to
the Meeting held at Glasgow in 1855, viz. "Whether any measures could be
adopted by the Government or Parliament that would improve the position
of Science and its cultivators," has been much considered by the Council of
the Royal Society. They assembled for this purpose in the autumn of last
year, and were then assisted in their deliberations by the replies received to
the circular of the 20th August last, agreed upon at Cheltenham, and issued
to all Members of the General Committee.

Of these replies an able digest has been prepared by Professor Phillips,
who was also a Member of the Sub-Committee appointed on behalf of the
Royal Society to consider this important subject.

The Council of the Royal Society, at their meeting held on the 15th of
January last, passed twelve Resolutions, which may be considered as
embodying their reply to the question above stated, and your Committee
are gratified by observing that most of the recommendations adopted in the
Glasgow Report have, in substance, received the sanction of the official
representatives of the most ancient and venerable of our Scientific Institu-
tions. At that meeting of the Council a resolution was passed, that the
President be authorized to communicate the twelve Resolutions to your
Committee, with a request that the same might obtain such support from our
Members as they might consider them entitled to receive. The Council of
the Royal Society likewise resolved that a copy of their Resolutions should
be forwarded to Lord Palnierston by their President, who by letter, bearing
date the 28th of January, transmitted the same accordingly.

The consideration of the steps proper to be taken in pursuance of the
above request addressed to your Committee, formed the chief subject of our
deliberations during the current year. We determined that it was not expe-
dient at present to take any steps beyond moving for the production of the
letter of the President of the Royal Society of the 28th of January above-
mentioned, with the copy of the twelve Resolutions enclosed therein ; and
this has been done accordingly, in the House of Lords by Lord Burlington,
and in the House of Commons by Mr. Robert Stephenson.

We were much influenced in this determination by the consideration of
the peculiar circumstances under which Parliament met, which have much
abridged the time at their disposal for the discussion of any measures of
importance, and by the further consideration that it might not be expedient
to precipitate a decision on matters which were new to the general public.

Again, though the Resolutions in question have received the general
approval of your Council, at a meeting held on the 16th January last, we
thought it right that the Committee of Recommendations should have an
opportunity of expressing their opinion upon them before any steps were
taken to urge their adoption on the Government or Parliament.

By the retirement of ]\Tr. Hey wood from Parliament, your Committee have
been deprived of the services of one of the most zealous of their members.
Mr. Heywood was not only most constant in his attendance, but no one had
the objects for which your Committee was constituted more sincerely at
heart.

The Duke of Argyll and the Earl of Rosse must, in pursuance of the
resolution adopted at Liverpool in 1854', be deemed to have vacated their
seats in your Committee, but we recommend that they should be re-elected.

BECOMMENDATIONS OF THE GENERAL COMMITTEE. XXXIX

Your Committee also recommend that the two vacancies caused by the
retirement from Parliament of Sir Charles Lemon, Bart., and Mr. Hey wood,
be filled by the election of the Right Honourable Joseph Napier, M.P. for
the University of Dublin, and Edward Cooper, Esq., F.R.S., of Markree
Castle, M.P. for the County of Sligo.

We have also to report the loss of the services of Mr. John Ball. His
scientific knowledge and zeal in the cause rendered him a valuable Member
of your Committee. This vacancy still remains to be supplied by the
General Committee.

14th August, 1857. Wrottesley, Chairman.

Recommendations adopted by the General Committee at the
Dublin Meeting in August and September 1857.

[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 £500 be placed at the disposal of the Council for the
maintaining the Establishment and providing for the continuance of Special
Researches at Kew Observatory.

That Professor Maskelyne, Mr. Hardwich, Mr.Llewellyn, and Mr.Hadow,
be a Committee to report on Researches on the Chemistry of Photography ;
with £10 at their disposal.

That Dr. A. Voelcker be requested to make Researches and Experiments
on the Constituents of Manures ; with £'2,5 at his disposal for the purpose.

That Professor Sullivan be requested to make Experiments on the Solu-
bility of Salts at temperatures above 100° Cent., and on the mutual action of
Salts in Solution ; with £20 at his disposal for the purpose.

That Mr. Robert Mallet, C.E., be requested to continue his Experiments
on Earthquake Waves; with £50 at his disposal for the purpose.

That Mr. E. P. Wright, Professor Melville, and Professor Kinahan, be a
Committee to report on the Dredging of the Coast of Ireland ; with £10 at
their disposal for the purpose.

That Mr. W= Keddie and Mr. Connal be requested to report on the Vege-
table Imports of Scotland ; with £10 at their disposal for the purpose.

That Professor Henslow, Professor Phillips, Sir W. Jardine, Mr. C. C.
Babington, Professor Balfour, Professor Owen, Dr. Hooker, Mr. J. S.
Bowerbank, Rev. M. J. Berkeley, Professor Huxley, and Dr. Lankester, be
a Committee to report on Typical Forms for Museums ; with £10 at their
disposal for the purpose.

That the Rev. C. P. Miles, Professor Balfour, Dr. Greville, and Mr. C.
Eyton, be a Committee to report on the Dredging of the West Coast of
Scotland ; with £25 at their disposal for the purpose.

That Professor Bell, Dr. Williams, and Dr. Lankester, be a Committee for
the purpose of completing a Report on the British Annelida ; with £25 at
their disposal.

That Dr. Daubeny be requested to conclude the Experiments on the
Growth and Vitality of Seeds ; with £5 5s. at his disposal for the purpose.

That Dr. Daubeny, Mr. C. C. Babington, Professor Buckman, and Dr.
Voelcker, be a Committee to report on Researches on the Growth of Plants ;
with £10 at their disposal.

That Professor Kinahan, Mr. E. P. Vv'right, Mr. J. R. Green, and Dr.
Carte, be a Committee to report on the Dredging in the Dublin district ;
with £10 at their disposal.

Xl REPORT — 1857.

That Mr. R. Patterson, Professor Dickie, Professor W. Thomson, and Mr.
Hyndman, be a Committee to report on the Dredging on the North Coast
of Ireland ; with £20 at their disposal.

That Mr. G. Rennie, C.E., be requested to continue his Experiments on
the production of Heat by motion in Fluids ; with £20 at his disposal for
the purpose.

That Mr. James Thomson, C.E., be requested to continue his Experiments
on the Measurement of the Discharge of Water ; with £10 at his disposal
for the purpose.

Involving Applications to Government or Public Institutions.

Resolved, — That it is of great importance to the progress of Science that the
Magnetic Observations which have already added so much to our knowledge
of terrestrial magnetism, should be continued. That the influence of the
Association will be well employed in attaining this object, and that it is
desirable to obtain the cooperation of the Royal Society. That a Committee
be appointed, consisting of the President, the Rev. Dr. Robinson, and Major-
General Sabine, to request, on the part of the British Association, the co-
operation of the President and Council of the Royal Society, and to take in
conjunction with them such steps as may appear necessary, including, if it
be thought desirable, an application to Government.

That Lord Wrottesley, Dr. Robinson, Mr. Osier, General Sabine, Mr.
Welsh, Sir W. S. Harris, and Dr. Whewell, be appointed a Committee to
express to the Board of Trade the wish of the British Association that self-
recording Anemometrical Instruments should be established on some of the
islands in the Atlantic Ocean, in aid of the Meteorological Observations now
being carried on on ship-board under the direction of the Meteorological
department of the Board of Trade.

That application be made to Her Majesty's Government to send a vessel
to examine and survey the entrance to the Zambesi River in South Africa,
and to ascend the river as far as may be practicable for navigation. That the
following Gentlemen be appointed a deputation to make the application : —
The President, Sir R. I. Murchison, Sir H. Rawlinson, General Sabine, Mr.
Macgregor Laird.

That the President, the Lord Wrottesley, the Right Honourable J. Napier,
Dr. Robinson, and Major-General Sabine, be a Committee for the purpose
of making application to the Government to send a vessel to the vicinity of
Mackenzie River, to make a series of magnetic observations, with special
reference to the determination of the laws now known to rule the magnetic
storms.

It having been found that the application of science to the improvement
of Steam-ships has been impeded by the difficulty of obtaining the necessary
data from the present registration, — Resolved — That a Committee be ap-
pointed and authorized to communicate, if necessary, with the Board of
Trade on the subject; — the Committee to consist of Admiral Moorsom,
Mr. J. Scott Russell, Mr. J. E. M'Connell, Mr. Charles Atherton, Mr. Wil-
liam Fairbairn, Mr. J. Perry, Mr. Henry Wright, Mr. Henderson.

Applications for Reports and Researches.

That Dr. Odling be requested to prepare a Report on the recent progress
of Organic Chemistry.

That Professor Haughton and Mr. David Forbes, F.G.S., be requested to
furnish a Report on the state of our knowledge of the Mineralogical and
Chemical composition of Rocks of an Igneous origin.

RECOMMENDATIONS OF THB GENERAL COMMITTEE. xU

That Professor Oldham be requested to prepare a Report on the state of
our knowledge of the Geology of India.

That Mr. A. H. Haliday, Professor Kinahan, and Mr. Wright, be requested
to prepare a Supplement to the Fauna of Ireland, comprising the additions
made thereto since the Report of the late Mr. William Thompson.

That Mr. W. Andrews be requested to report on the Species of Fishes
which occur on the West Coast of Ireland.

That Mr. J. R. Green be requested to report on the present state of our
knowledge of the Discoid Medusidse of the British Seas.

That Professor Kinahan be requested to prepare a Report on the Crus-
tacea of Dublin Bay.

That Mr. Oldham be requested to continue his researches on Steam-
Navigation at Hull.

Communications to be printed entire among the Reports.

Gustaf Plarr. — On some Transformations of a Series of Factorial Expo-
nentials.

Herren Schlagintweit. — On some Physical Observations made in India.

Mr. Commissioner Hargreaves. — On the Algebraic Couple.

Mr. A.Grubb. — On the Improvement of the Reflecting Telescope and the
Equatorial Mounting.

Mr. Oldham. — On Steam-Navigation at Hull.

Mr. C. Vignoles. — On Suspension Bridges.

Mr. P. Barlow. — On Suspension Bridges.

Synopsis of Grants of Money appropriated to Scientific Objects by the
General Committee at the Dublin Meeting in August and September
1857, with the name of the Member, who alone, or as the First of a
Committee, is entitled to draw for the Money.

Kew Observatory. £ s. d.

At the disposal of the Council for defraying expenses 500

Chemical Science.

Maskelyne, Prof. — Chemistry of Photography 10

VoELCKER, Prof. — On Constituents of Manures 25

Sullivan, Prof— Solubility of Salts 20

Geology.
Mallet, R., C.E — ^Earthquake Wave Experiments 50

Zoology and Botany.

Wright, E. P. — Dredging Coast of Ireland 10

Keddie, W. — Vegetable Imports of Scotland 10

Henslow, Prof. — Typical Forms for Museums 10

INIiLEs, Rev. C. P.— Dredging West Coast of Scotland ...... 25

Bell, Prof. — Report on Annelida , 25

Daubeny, Dr — Experiments on Vitality of Seeds 5 5

Daubeny, Dr.— Growth of Plants : 10

Kinahan, Prof. — Dredging near Dublin 10

Patterson, R. — Dredging North Coast of Ireland 20

Mechanical Science,

Rennie, G. — Production of Heat in Fluids 20

Thomson, J. — Discharge of Water 10

Grants .£760 5

xlii

REPORT — 1857.

General Statement of Sums which have been paid on Account of Grants for
Scientific Purposes.

£ s. d.

1834.

Tide Discussions 20

1835.

Tide Discussions C2

British Fossil Ichthyology 105

£167

1836.

Tide Discussions 163

British Fossil Ichthyology 105

Tliermometric Observations, &c, 50
Experiments on long-continued

Heat 17 1

Rain Gauges..... 9 13

Refraction Experiments 15

Lunar Nutation 60

Thermometers 15 6

£434 14

1837.

Tide Discussions 284 1

Chemical Constants 24 13 6

Lunar Nutation 70

Observations on Waves 100 12

Tides at Bristol 150

Meteorology and Subterranean

Temperature 89 5 3

Vitrification Experiments 150

Heart Experiments 8 4 6

Barometric Observations 30

Barometers H 18 6

£ s. d.
Meteorology and Subterranean

Temperature 21 11

Vitrification Experiments 9 4 7

Cast Iron Experiments 100

Railway Constants 28 7 2

Land and Sea Level 274 1 4

Steam-vessels' Engines 100

Stars in Histoire Celeste 331 18 6

Stars in Lacaille 110

Stars in R.A.S. Catalogue 6 16 6

Animal Secretions 10 10

Steam-engines in Cornwall 50

Atmospheric Air 16 1

Cast and Wrought Iron 40

Heat on Organic Bodies 3

Gases on Solar Spectrum 22

Hourly Meteorological Observa-
tions, Inverness and Kingussie 49 7 8

Fossil Reptiles 118 2 9

Mining Statistics 50

£1595 11

£918 14 6

1838.

Tide Discussions 29

British Fossil Fishes 100

Meteorological Observations and

Anemometer (construction) ... 100

Cast Iron (Strength of) 60

Animal and Vegetable Substances

(Preservation of) 19 1 10

Railway Constants 41 12 10

Bristol Tides 50

Growth of Plants 75

Mud in Rivers 3 6 6

Education Committee 50

Heart Experiments 5 3

Land and Sea Level 267 8 7

Subterranean Temperature 8 6

Steam-vessels 100

Meteorological Committee 31 9 5

Thermometers 16 4

£956 12 2

1839.

Fossillchthyology 110

Meteorological Observations at

Plymouth 63 10

Mechanism of Waves 144 2

Bristol Tides 35 18

1840.

Bristol Tides 100

Subterranean Temperature 13 13 6

Heart Experiments 18 19

Lungs Experiments 8 13

Tide Discussions 50

Land and Sea Level 6 11 1

Stars (Histoire Celeste) 242 10

Stars (Lacaille) 4 15

Stars (Catalogue) 264

Atmospheric Air 15 15

Water on Iron 10

Heat on Organic Bodies 7

Meteorological Observations 52 17 6

Foreign Scientific Memoirs 112 1 6

Working Population 100

School Statistics 50

Forms of Vessels 184 7

Chemical and Electrical Phaeno-

mena 40

Meteorological Observations at

Plymouth 80

Magnetical Observations 185 13 9

£1546 16 4

1841.

Observations on Waves 30

Meteorology and Subterranean

Temperature 8 8

Actlnometers 10

Earthquake Shocks 17 7

Acrid Poisons 6

Veins and Absorbents 3

Mud in Rivers 5

Marine Zoology 15 12 8

Skeleton Maps 20

Mountain Barometers 6 18 6

Stars (Histoire Celeste) 185

GENERAL STATEMENT.

xliii

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 C2

Railway Sections 38

Forms of Vessels 19.3

Meteorological Observations at

Plymouth 55

Magnetical Observations 61

Fishes of the Old Red Sandstone 100

Tides at Leilh 50

Anemometer at Edinburgh 69

Tabulating Observations 9

Races of Men 5

Radiate Animals .jj 2^

£1235

1842.

Dynamometric Instruments 113

Anoplura Britannise 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 Beleranites 50

Fossil Reptiles (publication of

Report) 210

Forms of Vessels 180

Galvanic Experiments on Rocks 5
Meteorological Experiments at

Plymouth 68

Constant Indicator and Dynamo-
metric Instruments 90

Force of Wind 10

Light on Growth of Seeds 8

Vital Statistics 50

Vegetative Power of Seeds 8

Questions on Human Race 7

£1449

1 6
12

18 8

1 10
6 3

10 11

11 2

12
8

14 7

17 6

8 6

1 11

17 8

1843.

Revision of the Nomenclature of

Stars 2

Reduction of Stars, British Asso-
ciation Catalogue 25

Anomalous Tides, Frith of Forth 120

Hourly Meteorological Observa-
tions at Kingussie and Inverness 77 12 8

Meteorological Observations at

Plymouth ., 55

Whewell's Meteorological Ane-
mometer at Plymouth 10

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 Co-operation 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 ofthe 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 10

Marine Zoology 2

Preparation of Report on British

Fossil Mammalia 100

Physiological Operations of Me-
dicinal Agents 20

Vital Statistics 36

Additional Experiments on the

Forms of Vessels 70

Additional Experiments on the

Forms of Vessels 100

Reduction of Experiments on the

Forms of Vessels 100

Morin's Instrument and Constant

Indicator 69

Experiments on the Strength of

Materials 60

£1565

4
8

4
3

6
8

10 2

1844.

Meteorological Observations at

Kingussie and Inverness 12

Completing Observations at Ply-
mouth 35

Magnetic and Meteorological Co-
operation 25 8 4

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 6

Maintaining the Establishment in

Kew Observatory 117 17 3

Instruments for Kew Observatory 56 7 3

xliv

REPORT 1857.

£ s. d.

Influence of Light on Plants 10

Subterraneous Temperature in

Ireland 5

Coloured Drawings of Railway

Sections 15 17 6

Investigation of Fossil Fishes of

the Lower Tertiary Strata ... 100
Registering the Shocks of Earth-
quakes 1842 23 11 10

Structure of Fossil Shells 20

Radiuta and MoUusca of the

^gean and Red Seas 1842 100

Geographical Distributions of

Marine Zoology 1842 10

Marine Zoology of Devon and

Cornwall 10

Marine Zoology of Corfu 10

Experiments on the Vitality of

Seeds 9 3

Experiments on the Vitality of

Seeds 1842 8 7 3

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 3 6

£981 12 8

1845.
Publication of the British Associa-
tion Catalogue of Stars 351

Meteorological Observations at

Inverness 30

Magnetic and Meteorological Co-
operation 16

Meteorological Instruments at

Edinburgh 18

Reduction of Anenioraetrical 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 1843 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 18 43 15

1^830

14 C

18 11

16 8

11 9

17 8

14 8

9 9

Fossil Fishes of the London Clay 100
Computation of the Gaussian

Constants for 1839 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 11

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

£G85

£.

6 3

1847.
Computation of the Gaussian

Constants for 1839 50

Habits of Marine Animals 10

Physiological Action of Medicines 20

Marine Zoology of Cornwall ... 10

Atmospheric Waves 6 9 3

Vitality of Seeds 4 7 7

Maintaining the Establishment at

Kew Observatory 107 8 6

£208 5 4

1846.
British Association Catalogue of

Stars 1844 211 15

1848.
Maintaining the EstabUshment 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 1 8

1849.
Electrical Observations at Kew

Observatory 50

Maintaining Establishment at

ditto 76 2 5

Vitality of Seeds 5 8 1

On Growth of Plants 5

Registration of Periodical Phae-

nomena 10

Bill on account of Anemometrical

Observations 13 9

£159 19 6

1850.
Maintaining the Establishment at

Kew Observatory 255 18

Transit of Earthquake Waves ... 50

GSNBRAIi STATEMENT.

xlv

£ s. d.

Periodical Phsenomena 15

Meteorological Instrument,

Azores ••• 25

£345 18

1851.
Maintaining the Establishment at

Kew Observatory (includes part

ofgrantin 1849) 309 2 2

Theory of Heat 20 1 1

Periodical Phsenomena 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 7

1852.

Maintaining the Establishment at
Kew Observatory (including
balance of grant for 1850) ... 233 17 8

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 6 7
1853. — — — —

Maintaining the Establishment at

Kew Observatory 165

Experiments on the Influence of

Solar Radiation 15

Researches on the British Anne-
lida 10

Dredging on the East Coast of

Scotland 10

Ethnological Queries 5

£205

1854.

Maintaining the Establishment at
Kew Observatory (including
balance of former grant) 330 15 4

Investigations on Flax 11

Effects of Temperature on

Wrought Iron 10

Registration of Periodical Phse-
nomena 10

£ a. d.

British Annelida 10

Vitality of Seeds 5 2 3

Conduction of Heat 4 2

£380 19 7

1855.
Maintaining the Establishment at

Kew Observatory 425

Earthquake Movements 10

Physical Aspect of the Moon 11 8 5

Vitality of Seeds 10 7 11

Map of the World 15

Ethnological Queries 5

Dredging near Belfast 4

£480 16 4

1856.
Maintaining the Establishment at
Kew Observatory : —

1854 £ 75 OT

1855 £500 OJ

Strickland's Ornithological Syno-
nyms 100

Dredging and Dredging Forms.

Chemical Action of Light

Strength of Iron Plates 10

Registration of Periodical Phseno-
mena 10

Propagation of Salmon 10

575

9 13
20

£734 13

1857.
Maintaining the Establishment at

Kew Observatory 350

Earthquake Wave Experiments 40

Dredging near Belfast 10

Dredging on the West Coast of

Scotland 10

Investigations into the Mollusca

ofCalifornia 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 7

Thermometers for Subterranean

Observations 5

Life-Boats 5

£507 15 4

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 Report 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-

Xlvi REPORT— 1857.

ciation expire at the ensuing meeting, unless it shall appear by a Report that
the Recommendations 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, John Taylor, Esq., 6 Queen Street Place, Upper Thames
Street, London, 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 Researches 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.

General Meetings.

On Wednesday, Aug. 26, at 8^ p.m., in the Rotunda, C. G. B. Daubeny,
M.D., F.R.S., Professor of Botany in the University of Oxford, resigned the
office of President to the Rev. Humphrey Lloyd, D.D., D.C.L., F.R.S, L. &E.,
V.P.R.I.A., who took the Chair and delivered an Address, for which see
page xlvii.

On Thursday Evening the Association was received by the Royal Dublin
Society.

On Friday, Aug. 28, at 8| p.m., in the Rooms of the Royal Dublin
Society, Prof. W. Thomson, F.R.S. , delivered a Discourse on the Atlantic
Telegraph.

On Saturday, Aug. 29, at 85 p.m., the Association was received by the
Royal Irish Academy.

On Monday, Aug. 31, at 85 p.m., in the Rooms of the Royal Dublin
Society, the Rev. Dr. Livingstone, D.C.L., delivered a Discourse on his recent
discoveries in Africa.

On Tuesday, Sept. 1, at 8^ p.m., the Association was received in the
Castle by His Excellency the Lord Lieutenant of Ireland.

On Wednesday, Sept. 2, at 3 p.m., the concluding General Meeting took
place in Trinity College, 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 Leeds*.

* The Meeting is appointed to take place on Wednesday, the 22nd of September, 1858.

ADDRESS

The Rev. HUMPHREY LLOYD, D.D., D.C.L.,

F.R.S.L. & E., V.P.R.I.A., Fellow of Trinity College, Dublin.

Gentlemen of the British Association,

Before I proceed to the task which devolves upon me this evening, in
virtue of the position in which your kindness has placed me, suffer me first
to thank you for the high honour you have conferred. But, highly as I
esteem the distinction, it was not without hesitation that I accepted it ; for no
one can feel more strongly than I do myself how unfit I am for some of the
duties connected with it, or how much more adequately they might have
been performed by others. But I knew, at the same time, that it has been
the desire of your Council, when practicable, to select your President from
among those local Members who had served in the ranks of the Association
and had shared in its labours ; and with such knowledge, and the conscious-
ness that I had, at least, that humble claim, I felt that I had no right to dis-
pute your choice.

I do not know whether I may venture to interpret further your motives, and
to assign another reason for your selection. Two-and-tvventy years have
elapsed since you visited this city. Upon that occasion my nearest relative
presided, and I myself had the honour of serving as one of your local Secre-
taries. Many concurring circumstances contributed to make that meeting
an agreeable one ; and if your Council has thought fit, on this occasion, to
associate th@ present with the memories of the past, the motive is, at least, a
pardonable one.

Gentlemen, this is to me a solemn occasion. Two-and-twenty years are
no inconsiderable portion even of the longest life ; and that man's moral na-
ture is not to be envied, who can contemplate the distant past thus vividly
recalled without emotion. These two decades have brought with them their
own large measure of change. The Body in which we are associated has

xlvili REPORT — 1857.

grown up from youth to maturity ; many of its honoured names are now
sought for only in the imperishable records of their toils ; the institutions
which welcomed it here upon its former visit to this city have all received
the impress of the changing times. And yet, amid all this change, we meet
once more in the same city, — in the same room, — to enter again on the same
labours ; our assemblage is now, as it was before, dignified by the presence
of the Representative of Majesty ; and I see around me, associated for this
task, many of those who shared it before; — the men whose sagacity first per-
ceived the want of such a Society as this, whose energy supplied it, and
whose wisdom directed its steps while it had need of guidance.

I trust I may be forgiven for dwelling thus far on the peculiar circum-
stances under which we are here assembled ; and I now hasten to discharge
the task which the usages of this Chair impose upon me, and proceed to lay
before you, as well as I am able, a brief sketch of the recent progress of some
of those Sciences to whose advancement we are pledged by our institution.
In doing so, I gladly follow the practice which has of late become the rule,
namely, that your President for each year should bring under your notice
chiefly, the recent additions to those departments of Science with which he
happens to be himself most familiar. It is plainly fitting that he who addresses
you should speak, as far as he can, from his own acquired knowledge. Partial
views are better than inexact ones ; and provision is made for their comple-
tion in the annual change of your Officer. In the present instance I derive
the full advantage of this arrangement, inasmuch as the subjects upon
which I could not thus speak have been, most of them, ably treated by ray
predecessor in this Chair.

To commence, then, with Astronomy : — The career of planetary discovery,
which began in the first years of the present century, and was resumed in
184-5, has since continued with unabated ardour. Since 1 846 not a single
year has passed without some one or more additions to the number of the
planetoids; and in one year alone (18,52), no fewer than eight of these
bodies were discovered. The last year has furnished its quota of five ; and in
the present three more have been found, one by Mr. Pogson of Oxford, and
the other two by M. Goldschmidt of Paris. Their known number is now
forty-five. Their total mass, however, is very small ; the diameter of the
largest being less than forty miles, while that of the smallest, Atalanta, is
little more than four.

These discoveries have been facilitated by star-maps and star-catalogues,
the formation of which they have, on the other hand, stimulated. Two very
extensive works of this kind are now in progress, — the Star-catalogue of M.
Chacornac, made at the Observatory of Marseilles, in course of publication
by the French Government, and that of Mr. Cooper, made at his Observa-
tory at Markree, in Ireland, which is now being published by the help of the
parliamentary grant of the Royal Society. It is a remarkable result of the

ADDRESS. xliX

latter labour, that no fewer than seventy-seven stars, previously catalogued,
are now missing. This, no doubt, is to be ascribed, in part, to the errors of
former observations ; but it seems reasonable to suppose that, to some extent
at least, it is the result of changes actually in progress in the Sidereal
Systems.

The sudden appearance of a new fixed star in the heavens, — its subsequent
change of lustre, — and its final disappearance, are phenomena which have
at all times attracted the attention of astronomers. About twenty such have
been observed. Arago has given the history of the most remarkable, and
discussed the various hypotheses which have been proposed for their expla-
nation. Of these, the most plausible is that which attributes the phenomenon
to unequal brightness of the faces of the star, which are presented success-
ively to the earth by the star's rotation round its axis. On this hypothesis
the appearance should he periodic. M. Goldschmidt has recently given sup-
port to this explanation, by rendering it probable that the new star of 1609
is the same whose appearance was recorded in the years 393,798, and 1203 ;
its period, in such case, is 405^ years.

The greater part of the celestial phenomena are comprised in the move-
ments of the heavenly bodies, and the configurations depending on them;
and they are for the most part reducible to the same law of gravity which
governs the planetary motions. But there are appearances which indicate
the operation of other forces, and which therefore demand the attention of
the physicist, — although, from their nature, they must probably long remain
subjects of speculation. Of these the spiriform nebulae, discovered by Lord
Rosse, have been already referred to from this Chair, as indicating changes
in the more distant regions of the universe, to which there is nothing entirely
analogous in our own System. These appearances are accounted for, by an
able anonymous writer, by the action of gravitating forces combined with
the efiects of a resisting medium, — the resistance being supposed to bear a
sensible proportion to the gravitating action.

The constitution of the central body of our own System presents a nearer
and more interesting subject of speculation. Towards the close of the last
century many hypotheses were advanced regarding the nature and constitu-
tion of the Sun, all of which agreed in considering it to be an opaque body,
surrounded at some distance by a luminous envelope. But the only certain
fact which has been added to science in this department is the proof given
by Arago, that the light of the Sun emanated, not from an incandescent
solid, but from a gaseous atmosphere ; the light of incandescent solid bodies
he'ing polarized hy refraction, while the light of the Sun, and that emitted by
gaseous bodies, is unpolarized.

According to the observations of Schwabe, which have been continued
without intermission for more than thirty years, the magnitude of the solar
surface obscured by spots increases and decreases periodically, the length of
the period being 11 years and 40 days. This remarkable fact, and the rela-
tion which it appears to bear to certain phenomena of terrestrial magnetism,
1857. d

1 REPORT — 1857.

liave attracted fresh interest to the study of the solar surface ; and, upon the
suggestion of Sir John Herschel, a photo-heliographic apparatus has lately
been established at Kew, for the purpose of depicting the actual macular
state of the Sun's surface from time to time.

It is well known that Sir William Herschel accounted for the solar spots
by currents of an elastic fluid, ascending from the body of the Sun, and pene-
trating the exterior luminous envelope. A somewhat different speculation
of the same kind has been recently advanced by Mosotti, who has endea-
voured to connect the phenomena of the solar spots with those of the red
protuberances, which appear to issue from the body of the Sun in a total
eclipse, and which so much interested astronomers in the remarkable eclipse
of 1842.

Next to the Sun, our own satellite has always claimed the attention of
astronomers, while the comparative sraallness of its distance inspired the hope
that some knowledge of its physical structure could be attained with the
large instrumental means now available. Accordingly, at the Meeting of
the Association held at Belfast in 1852, it was proposed that the Earl of
Rosse, Dr. Robinson, and Professor Phillips be requested to draw up a Re-
port on the physical character of the Moon's surface, as compared with that
of the Earth. That the attention of these eminent observers has been
directed to the subject, may be inferred from the communication since made
by Professor Phillips to the Royal Society on the lunar mountain, Gassendi,
and the surrounding region ; but I am not aware that the subject is yet ripe
for a Report.

I need not remind you, that the Moon possesses neither sea nor atmo*
sphere of appreciable extent. Still, as a negative, in such case, is relative
only to the capabilities of the instruments employed, the search for the indi-
cations of a lunar atmosphere has been renewed with every fresh augmen-
tation of telescopic power. Of such indications the most delicate, perhaps,
are those afforded by the occultation of a planet by the Moon. The occul-
tation of Jupiter, which took place on the 2nd of January last, was observed
with this reference, and is said to have exhibited no hesitation, or change of
form or brightness, such as would be produced by the refraction or absorp-
tion of an atmosphere. As respects the sea, the mode of examination long
since suggested by Sir David Brewster is probably the most effective. If
water existed on the INIoon's surface, the Sun's light reflected from it should
be completely polarized at a certain elongation of the Moon from the Sun.
No traces of such light have been observed ; but I am not aware that the
observations have been repeated recently with any of the larger telescopes.

It is now well understood that the path of astronomical discovery is ob-
structed much more by the Earth's atmosphere, than by the limitation of
telescopic powers. Impressed with this conviction, the Association has, for
some time past, urged upon Her Majesty's Government the scientific import-

ADDRESS.

ahce of establishing a large reflector at some elevated station in the Southern
Hemisphere. In the meantime, and to gain (as it were) a sample of the
results which might be expected from a more systematic search, Professor
Piazzi Smyth undertook, last summer, the task of transporting a large collec-
tion of instruments — meteorological and magnetical, as well as astronomical
— to a high point on the Peak of Teneriffe. His stations were two in num-
ber, at the altitudes above the sea of 8840 and 10,700 feet respectively ; and
the astronomical advantages gained may be inferred from the fact, that the
heat radiated from the Moon, which has been so often sought for in vain in a
lower region, was distinctly perceptible with the aid of the thermo-multiplier.

The researches relative to the Figure of the Earth, and the Tides, are in-
timately connected with Astronomy, and next claim our attention.

The results of the Ordnance Survey of Britain, so far as they relate to the
Earth's figure and mean density, have been lately laid before the Royal So-
ciety by Colonel James, the Superintendent of the Survey. The elHpticity
deduced is ;;g|-j. The mean specific gravity of the Earth, as obtained from
the attraction of Arthur's Seat, near Edinburgh, is 5*316, — a result which
accords satisfactorily with the mean of the results obtained by the torsion
balance. Of the accuracy of this important work it is sufiicient to observe,
that when the length of each of the measured bases — in Salisbury Plain, and
on the shores of Lough Foyle — was computed from the other, through the
whole series of intermediate triangles, the difference from the measured
length was only 5 inches in a length of from 5 to 7 miles.

Our knowledge of the laws of the Tides has received an important acces-
sion, in the results of the Tidal Observations made around the Irisli coasts
in 1851, under the direction of the Royal Irish Academy. The discussion of
these observations was undertaken by Professor Haughton, and that portion
of it which relates to the diurnal tides has been already completed and
published. The most important result of this discussion is the separation of
the effects of the Sun and the Moon in the diurnal tide, — a problem which
was proposed by the Academy, as one of the objects to be attained by the
contemplated observations, and which has been now for the first time solved.
From the comparison of these effects Professor Haughton has drawn some
remarkable conclusions relative to the mean depth of the sea in the Atlantic.
In the dynamical theory of the tides, the ratio of the solar to the lunar effect
depends not only on the masses, distances, and periodic times of the two
luminaries, but also on the depth of the sea; and this, accordingly, may
be computed when the other quantities are known. In this manner Professor
Haughton has deduced, from the solar and lunar coefficients of the diurnal
tide, a mean depth of 5*12 miles, — a result which accords in a remarkable
manner with that inferred from the ratio of the semidiurnal coefficients, as
obtained by Laplace from the Brest observations. The subject, however, is
far from being exhausted. The depth of the sea, deduced from the solar

lii REPORT — 1857.

and lunar tidal intervals, and from the age of the lunar diurnal tide, is some-
what more than double of the foregoing ; and the consistency of the indi-
vidual results is such as to indicate, that their wide difference from the former
is not attributable to errors of observation. Professor Haughton throws out
the conjecture tliat the deptli, deduced from tlie tidaXintervals and ages, corre-
sponds to a different part of the ocean from that inferred from the heights.

The plieiioineiia of Terrestrial Magnetism present many close analogies
witli those of the tides ; and their study has been, in a peculiar manner, con-
nected with the labours of this Association. To this body, and by the hands
of its present General Secretary, were presented those Reports on the dis-
tribution of the Terrestrial Magnetic Force which reawakened the attention
of the scientific world to the subject. It was in the Committee-rooms of
this Association that the first step was taken towards that great magnetic
organization which has borne so much fruit ; — it was here that the philoso-
phical sagacity of Herschel guided its earlier career ; — and it was here again
that the cultivators of the science assembled, from every part of Europe, to
deliberate about its future progress. It was natural, therefore, that the re-
sults obtained from such beginnings should form a prominent topic in the
addresses which have been annually delivered from this Chair ; and the same
circumstances will plead my excuse, if I now revert to some of them which
have been already touched upon by my predecessors.

It has been long known that the elements of the Earth's magnetic force
were subject to certain regular and recurring changes, whose periods were,
respectively, a day and a year, and which, therefore, were referred to the Sun
as their source. To these periodical changes Dr. Lamont, of Munich, added
another of ten years, the diurnal range of the magnetic declination having
been found to pass from a maximum to a minimum, and back again, in
about that time.

But besides these slow and regular changes, there are others of a different
class, which recur at irregular intervals, and which are characterized by a
large deviation of the magnetic elements from their normal state, and gene-
rally also by rapid fluctuation and change. These phenomena, called by
Humboldt " magnetic storms," have been observed to occur simultaneously
in the most distant parts of the earth, and therefore indicate the operation
of causes affecting the entire globe. But, casual as they seem, they are
found to be subject to laws of their own. Professor Kreil was the first to
discover that, at a given place, they recurred more frequently at certain
hours of the day than at others ; and that consequently, in their mean effects,
they were subject to periodical laws, depending upon the hour at each station.

The laws of this periodicity have been ably worked out by General Sabine,
in his discussion of the results of the British Colonial Observatories ; and
he has added the important facts, that the same phenomena observe also the
two other periods already noticed, namely the annual and the decennial
periods. He has further arrived at the very remarkable result, that the de-

ADDRESS. liii

cennial magnetic period coincides, both in its duration and in its epochs of
maxima and minima, with the decennial period observed by Schwabe in the
solar spots ; from which it is to be inferred that the Snn exercises a magnetic
influence upon the Earth, dependent on the condition of its luminous
envelope.

We are thus in the presence of two facts, which appear at first sight
opposed, namely, the absolute simultaneity of magnetic disturbances at all
parts of the Earth, and their predominance at certain local hours at each
place. General Sabine accounts for this apparent discrepancy by the cir-
cumstance, that the hours of maximum disturbance are different for the
different elements ; so that there may be an abnormal condition of the
magnetic force, operating at the same instant over the whole globe, but
manifesting itself at one place chiefly in one element, and at another place
in another. I would venture to suggest, as a subject of inquiry, whether the
phenomena which have been hitherto grouped together as " occasional "
effects, may not possibly include two distinct classes of changes, obeying
separate laws — one of them being strictly periodic, and constituting a part of
the regular diurnal change, while the other is strictly abnormal, and simul-
taneous. If this be so, it would follow that we are not justified in separating
the larger changes from the rest, merely on the ground of their magnitude ;
and that a different analysis of the phenomenon will be required.

The effects hitherto considered are all referable to the Sun as their cause.
Professor Kreil discovered, however, that another body of our System —
namely, our own satellite — exerted an effect upon the magnetic needle ;
and that the magnetic declination underwent a small and very regular varia-
tion, whose amount was dependent on the lunar hour-angle, and whose period
was therefore a lunar day. This singular result was subsequently confirmed
by Mr. Broun, in his discussion of the Makerstoun Observations ; and its
laws have since been fully traced, for all the magnetic elements, by General
Sabine, in the results obtained at the Colonial Magnetic Observatories.

The foregoing facts bear closely upon the debated question of the causes
of the magnetic variations. It has been usual to ascribe the periodical
changes of the Earth's magnetic force to the thermic action of the Sun,
operating either directly upon the magnetism of the Earth, or affecting it
indirectly by the induction of the thermo-electric currents. Here, however,
we have a distinct case of magnetic action, unaccompanied by heat ; and
the question is naturally suggested, whether the solar diurnal change may
not also be independent of temperature.

The most important fact, in its bearing upon this question, is the existence
of an annual inequality in the diurnal variation, dependent on the Sun's
declination, recently pointed out by General Sabine. If we deduct the
ordinate of the curve, which represents the mean diurnal variation for the
entire year, from those for the summer and winter half-yearly curves re-
spectively, the differences are found to be equal and opposite ; and the curves

Uv RKPOBT — 1857.

which represent them are, consequently, similar, but oppositely placed with
respect to the axis of abscissae. From this General Sabine draws the in-
ference, that the diurnal variation is a direct effect of solar action, and not a
result of its thermic agency.

The most important step which has been recently taken in this country
to advance the science of Meteorology, has been the formation of a depart-
ment connected with the Board of Trade, for the collection and discussion
of Meteorological Observations made at sea. The practical results of a
similar undertaking in the United States are now well known. The charts
and sailing directions, published by Lieutenant Maury, have enabled navi-
gators to shorten their passages, in many cases by one-fourth of the time,
and in some even to a greater extent. The commercial importance of such
results could not fail to attract general attention ; and accordingly, when
the United States Government invited other maritime nations to cooperate
in the undertaking, the invitation was cordially accepted. A conference was
held at Brussels in 1853, at which meteorologists deputed by those Powers
attended ; and a Report was made, recommending the course to be pursued
in a general system of marine meteorological observations. This Report
was laid before the British Parliament soon after, and a sum of money was
voted for the necessary expenditure. The British Association undertook to
supply verified instruments, by means of its Observatory at Kew ; and the
Royal Society, in consultation with the most eminent meteorologists of
Europe and America, addressed an able Report to the Board of Trade, in
which the objects to be attended to, so as to render the system of observa-
tion most available for science, were clearly set forth. With this cooperation
on the part of the two leading Scientific Societies, the establishment was
soon organized. It was placed under the direction of a distinguished naval
officer, Admiral FitzRoy ; and in the beginning of 1855 it was in operation.
Agents were established at the principal ports for the supply of instruments,
books, and instructions ; and there are now more than 200 British ships so
furnished, whose officers have undertaken to make and record the required
observations, and to transmit them from time to time to the Department. At
the present time TOO months of logs have been received, from nearly 100
merchant ships, and are in process of tabulation.

Holland is taking similar steps; and the Meteorological Institute of that
counti-y, under the direction of Mr. Buys Bellot, has already published three
volumes of nautical information, obtained from Dutch vessels in the Atlantic
and Indian Ocean.

For the purposes of Meteorological Science this system cannot be con-
sidered as complete, until observations on land are included. Most of the
greater atmospheric changes are due to the distribution of land and water,
and to the different effects of the Sun's rays on each. Observation alone
can furnish the data from which the effects of these agencies may be calcu-
lated ; and we can therefore probably make no great advance in the knowledge

ADDRESS. Iv

of the meteorology of the globe, without a concurrent investigation of its two
leading departnaents. Land observations exist in great numbers. In Prussia,
in Russia, in Austria, and in Belgium, such observations are organized
under Government direction, or at least with Government support ; in other
parts of Europe, as in Britain, the labour is left to individuals or scientific
societies. What is needed is to give unity to these isolated laboui-s — to con-
nect them with one another, and with the results obtained at sea ; and the
first step to this seeros to be, to give them, in each country, that permanence
and uniformity of system which can only be ensured in measures adopted
by the State.

Here, however, we encounter an objection, upon which it is necessary to
say a few words.

It has been objected to the Science of Meteorology, as it is usually studied,
that it proceeds upon a false method ; and that, consequently, it has led, and
can lead, to no results. I feel myself in a manner compelled to notice this
grave objection, in the first place, because it proceeds from men, whose
opinions on this (or almost any other scientific question) are entitled to the
highest deference ; and secondly, because this Association must bear no in-
considerable measure of the reproach, if it be %vell founded.

First, then, as to results. I am free to admit that the number of those
engaged in the discussion of meteorological observations is disproportioiiately
small, and that the results obtained probably fall far short of what may be
expected from the data already accumulated. But that the methods have
led, and can lead, to no results, is, I think, sufficiently disproved by the
labimrs of a single man — Professor Dove of Berlin. And if it be true that
the course pursued in the science has yielded much fruit, in proportion to
the labour bestowed on the discussion, it will hardly be deemed widely
erroneous. Still, as it is possible that the methods pursued — though not
fruitless — may be inadequate, it seems necessary to notice the objection
somewhat more minutely.

It is asserted, then, that the capital vice of tlie Science of Meteorology,
as at present pursued, is that it has no definite aim ; that it ought to embrace
an inquiry into the physical constitution of the objects with which the science
is concerned, and an investigation of causes as well as laws of phenomena.

It may be admitted, at once, in reference to this objection, that the phy-
sical constitution of the bodies whose changes we are investigating is a proper
object of study to the physicist ; but it does not seem to follow that it should
necessarily be conducted by the same individuals who are in search for the
laws of the phenomena, or even that the former knowledge is essential to the
progress of the latter. The noblest of all the physical sciences, Astronomy,
is little more than a science of laws — laws, too, of the simplest kind of
change; and the knowledge of these laws is wholly inde}iendetit of the physi-
cal constitution of the masses whose movements it studies. A similar obser-
vation may be made regarding the science of Terrestrial Magnetism; and

Ivi REPORT — 1857.

the case is one which brings us still nearer to the question at issue, inasmuch
as the laws which have been obtained — and they are numerous — have resulted
from a method of inquiry altogether similar to that adopted in Meteorology.
Time will not permit me to inquire whether there is not a misconception
of a metaphysical kind at the root of this objection. I may observe, how-
ever, before leaving the subject, that there are two modes of studying the
sequences of natural phenomena, — one in their relation to time, and which is
best accomplished by observations at stated periods, and the other in the
relation of the successive phases of the phenomenon to one another. Of these,
the latter, although not wholly neglected, has not been so much followed as
it deserves ; and I cannot but think that it would, if more systematically
followed, enrich the science of Meteorology with a new harvest of results.

The most important of the recent additions to the theory of Liff/it have
been those made by M. Jamin. It has been long known that metals differed
from transparent bodies, in their action on light, in this, that plane-polarized
light reflected from their surfaces became elliptically polarized ; and the
phenomenon is explained, on the principles of the wave-theory, by the
assumption that the vibration of the ether undergoes a change of phase at
the instant of reflexion, the amount of which is dependent on its direction,
and on the angle of incidence. This supposed distinction, however, was
soon found not to be absolute. Mr. Airy showed that diamond reflected
light in a manner similar to metals ; and Mr. Dale and Professor Powell ex-
tended the property to all bodies having a high refractive power. But it
was not until lately that M. Jamin proved that there is no distinction, in this
respect, between transparent and metallic bodies ; and that all bodies trans-
form plane-polarized into elliptically-polarized light, and impress a change
of phase at the moment of reflexion. Professor Haughton has followed up
the researches of M. Jamin, and established the existence of circularly-
polarized light by reflexion from transparent surfaces.

The theoretical investigations connected with this subject afford a re-
markable illustration of one of those impediments to the progress of Natural
Philosophy, which Bacon has put in the foremost place among his examples
of the Idola, — I mean the tendency of the human mind to suppose a greater
simplicity and uniformity in nature than exists there. The phenomena of
polarization compel us to admit that the sensible luminous vibrations are
transversal, or in the plane of the wave itself; and it was naturally supposed
by Fresnel, and after him by MacCullagh and Neumann, either that no
normal vibrations were propagated, or that, if they were, they were uncon-
nected with the phenomena of light. We now learn that it is by them that
the phase is modified in the act of reflexion ; and that, consequently, no
dynamical theory which neglects them, or sets them aside, can be complete.

Attention has been lately recalled to a fundamental position of the wave-
theory of light, respecting which opposite assumptions have been made.

ADDRESS.

Ivii

The vibrations of a polarized ray are all parallel to a fixed direction in the
plane of the wave ; but that direction may be either parallel, or perpendi-
cular to the plane of polarization. In the original theory of Fresnel the
latter was assumed to be the fact ; and in this assumption Fresnel has been
followed by Cauchy. In the modified theories of MacCullagh and Neumann,
on the other hand, the vibrations are supposed to be parallel to the plane of
polarization. This opposition of the two theories was compensated, as re-
spects the results, by other differences in their hypothetical principles ; and
both of them have led to conclusions which observation has verified. There
seemed, therefore, to be no means left to the theorist to decide between these
conflicting hypotheses, until Professor Stokes, recently, in applying the
dynamical theory of light to other classes of phenomena, found one in which
the effects should differ on the two assumptions. When light is transmitted
through a fine grating, it is turned aside, or diffracted, according to laws
which the wave-theory has explained. Now Professor Stokes has shown
that, when the incident light is polarized, the plane of vibration of the
diffracted ray must differ from that of the incident, the two planes being
connected by a very simple relation. It only remained, therefore, for ob-
servation to determine whether the planes of polarization of the incident
and refracted rays were similarly related, or not. The experiment was
undertaken by Professor Stokes himself, and he has inferred from it that the
original hypothesis of Fresnel is the true one ; but, as an opposite result has
been obtained by M. Holtzmann, on repeating the experiment, the question
must be regarded as still undetermined. The difference in the experimental
results is ascribed by Professor Stokes to the difference in the nature of the
gratings employed, the substance of the diffracting body being supposed to
exert an effect upon the polarization of the light, which is diffracted by it
under a great obliquity. I learn from Professor Stokes that he proposes to
resume the experimental inquiry, and to test this supposition by employing
gratings of various substances. If the conjecture should prove to be well
founded, it will, unfortunately, greatly complicate the dynamical theory of
light. In the meantime the hypothesis is one of importance in itself, and
deserves to be verified or disproved by independent means. I would venture
to suggest that it may be effectively tested by means of the beautiful Inter-
ference-refractor of M. Jamin, which the inventor has already applied to
study the effects upon light produced by grazing a plate of any soluble sub-
stance enclosed in a fluid.

It is well known that the refractive index of bodies increases with their
density ; and the theory of emission has even expressed the law of their
mutual dependence. That theory, it is true, is now completely overthrown
by the decisive experimentum crucis of MM. Fizeau and Foucault. It was
therefore probable, a priori, that this law — the only one peculiar to the
theory — would be found wanting. Its truth has recently been put to an ex-
perimental test by M. Jamin. Water, it is known, has its maximum of
density at about 40° of Fahrenheit ; so that, if Newton's law were true, its

Iviii REPORT— 1857.

refractive index should also have a maximum value at the saino temperature.
This has been disproved by M. Jamin, by observing the interference of two
rays, one of which has passed through air, and the other through water ;
and thus the last conclusion of the emission-theory has been set aside.

It Mould occupy too much of your time were I to touch, even lightly,
upon the subject of the chemical action of light, and the many beautiful and
important discoveries of the art to which it has given rise. I may, however,
mention, as one of the latest of the marvels of photography, that M. Poitevin
has succeeded in producing plates in relief, for the purposes of engraving, by
the action of light alone. The process depends upon the change in the
affinity for water, produced by the action of light upon a thin plate of
gelatine, which is impregnated with bichromate of potash.

In the whole range of experimental science there is no fact more familiar,
or longer known, than the development of Heat by friction. The most
ignorant savage is acquainted with it, — it was probably known to the first
generation of mankind. Yet, familiar as it is, the science of which it is the
germ dates back but a very few years.

It was known from the time of Black, that heat disappeared in producing
certain changes of state in bodies, and reappeared when the order of those
changes was reversed ; and that the amount of heat, thus converted, had a
given relation to the effect produced. In one of these changes, namely
evaporation, a definite mechanical force is developed, which is again absorbed
V hen the vapour is restored by pressure to the liquid state. It was therefore
not unnatural to conjecture, that in all cases in which heat is developed by
mechanical action, or vice versti, a definite relation would be found to subsist
between the amount of the action, and that of the heat developed or absorbed.

This conjecture was put to the test of experiment by Mayer and Joule,
in ] 84'2) and was verified by the result. It was found that heat and mechanical
pozver were mutually convertible., and that the relation between them was
definite, 111 foot pounds of motive power being equivalent to a unit of heat,
that is, to the amount of heat requisite to raise a pound of water through
one degree of Fahrenheit. The science of Thermo-dynamics, based upon
this fact, and upon a few other obvious facts, or self-evident principles, has
grown up in the hands of Clausius, Thomson, and Rankine, into large pro-
portions, and is each day making fresh conquests from the region of the
unknown.

Thus far the science of Heat is made to rest wholly upon the facts of ex-
periment, and is independent of any hypothesis respecting the molecular
constitution of bodies. The dynamical theory of heat, however, has mate-
rially aided in establishing true physical conceptions of the nature of heal.
The old hypothesis of caloric, as a separate substance, was indeed rendered
improbable by the experiments of Rumford and Davy, and by the reasonings

ADDRESS. liX

qf Young ; but it continued to liold its ground, and is interwoven into the
language of science. It is now clearly shown to be self-contradictory ; and
to lead to the result, that the amount of heat in the universe may be indefi-
nitely augmented. On the other hand, the identification of radiant heat with
light, and the establishment of the wave-theory, left little doubt that heat
consisted in a vibratory movement either of the molecules of bodies, or of
the ether within them. Still, the relation of heat to bodies, and the phenomena
of conduction, indicate a mechanism of a more complicated kind than that of
light, and leave ample room for further speculation.

The only mechanical hypothesis (so far as I am aware) which is consistent
with the present state of our knowledge of the phenomena of heat, is the
theory of molecular vortices of Mr. Rankine. In this theory all bodies are
supposed to consist of atoins, composed of nuclei surrounded with elastic
atmospheres. The radiation of light and heat is ascribed to the transmission
of oscillations of the nuclei ; while thermometric heat is supposed to consist
in circulating currents, or vortices^ amongst the particles of their atmospheres,
whereby they tend to recede from the nuclei, and to occupy a greater space.
From this hypothesis Mr. Rankine has deduced all the laws of thermo-
dynamics, by the application of known mechanical principles. He has also,
from the same principles, deduced relations (which have been confirmed by
experiment) between the pressure, density, and absolute temperature of
elastic fluids, and between the pressure and temperature of ebullition of
liquids.

The dynamical theory of heat enables us to frame some conjectures to
account for the continuance of its supply, and even to speculate as to its
source. The heat of the Sun is dissipated and lost by radiation, and must
be progressively diminished unless its thermal energy be supplied. According
to the measurements of M. Pouillet, the quantity of heat given out by the
Sun in a year is equal to that which would be produced by the combustion of
a stratum of coal seventeen miles in thickness ; and if the Sun's capacity for
heat be assumed equal to that of water, and the heat be supposed to be
drawn unilbrmly from its entire mass, its temperature would thereby undergo
a diminution of 2°"4' Fahr. annually.

On the other hand, there is a vast store of force in our System capable of
conversion into heat. If, as is indicated by the small density of the Sun,
and by other circumstances, that body has not yet reached the condition of
incompressibility, we have, in the future approximation of its parts, a fund
of heat probably quite large enough to supply the wants of the human
family to the end of its sojourn here. It has been calculated that an amount
of condensation, which would diminish the diameter of the Sun by only the
ten-thousandth part, would suffice to restore the heat emitted in 2000 years.

Again, on our own Earth, vis viva is destroyed by friction in the ebb and
flow of every tide, and must therefore reappear as heat. The amount of this
must be considerable, and should not be overlooked in any estimation of the

IX REPORT — 1857.

physical changes of our globe. According to the computations of Bessel,
25,000 cubic miles of water flow, in every six hours, from one quarter of the
earth to another. Tiie store of mechanical force is thus diminished, and the
temperature of our globe augmented, by every tide. We do not possess the
data which would enable us to calculate the magnitude of these effects.
All that we know with certainty is, that the resultant effect of all the thermal
agencies to which the Earth is exposed, has undergone no perceptible change
within the historic period. We owe this fine deduction to Arago. In order
that the date palm should ripen its fruit, the mean temperature of the place
must exceed 70° Fahr. ; and, on the other hand, the vine cannot be cultivated
successfully when the temperature is 72° or upwards. Hence the mean
temperature of any place, at which these two plants flourished and bore fruit,
must lie between these narrow limits, i. e. could not differ from 71° Fahr. by
more than a single degree. Now, from the Bible we learn that both plants
were simultaneously cultivated in the central valleys of Palestine, in the time
of Moses, and its then temperature is thus definitively determined. It is the
same at the present time ; so that the mean temperature of this portion of
the globe has not sensibly altered in the course of thirty-three centuries.

The future of physical science seems to lie in the path upon which three
of our ablest British physicists have so boldly entered, and in which they have
already made such large advances. I may therefore be permitted briefly to
touch upon the successive steps in this lofty generalization, and to indicate
the goal to which they tend.

It has been long known that many of the forces of nature are related.
Thus heat is produced by mechatiical action, when that is applied in bringing
the atoms of bodies nearer by compression, or when it is expended in friction.
Heat is developed by electricity, when the free passage of the latter is impeded ;
it is produced whenever light is absorbed ; and it is generated by chemical
action. A like interchangeability probably exists among all the other forces
of nature, although in many the relations have not been so long perceived.
Thus the development of electricity from chemical action dates from the
observations of Galvani ; and the production of magnetism by electricity
from the discovery of Oersted.

The next great step was to perceive that the relation of the physical forces
was mutual ; and that of any two, compared togetlier, either may stand to
the other in the relation of cause.

With respect to heat and mechanical force, this lias been long known.
When a body is compressed by mechanical force, it gives o\xiheat; and, on the
other hand, when it is heated, it dilates, and evolves jooM'er. The knowledge
of the action of electricity, in dissolving the bonds of chemical union, followed
closely upon that of the inverse phenomenon, and the discovery of electro-
magnetism by Oersted was soon followed by that of magneto-electricity by
Faraday. With reason, therefore, it occurred to many minds that the relations
of any two of the forces of nature were mubual; — that that which is the cause,

ADDRESS. M

in one' mode of interaction, may become the effect, when the order of the
phenomena is changed; — and that therefore, in the words of Mr. Grove, one
of the able expounders of these views, while they are " correlative " or reci-
procally dependent, "neither, taken abstractedly, can be said to be the
essential cause of the others."

But a further step remained to be taken. If these forces were not only
related, but mutually related, was it not probable that the relation was also a
definite one ? Thus, when heat is developed by mechanical action, ought we
not to expect a certain definite proportion to subsist between the interacting
forces, so that if one were doubled or trebled in amount, the other should
undergo a proportionate change? This anticipation, it has been already
stated, has been realized by Mayer and Joule. The discovery of the mecha-
nical equivalent of heat has been rapidly followed by that of other forces ;
and we now know not only that electricity, magnetism, and chemical action,
in given quantities, will produce each a definite amount of mechanical work,
but we know further — chiefly through the labours of Mr. Joule — what that
relation is, or, in other words, the mechanical equivalent of each force.

The first step in this important career of discovery — though long unper-
ceived in its relation to the rest — was, undoubtedly, Faraday's proof of the
definite chemical effect of the voltaic current. The last will probably be to
reduce all these phenomena to modes of motion, and to apply to them the
known principles of dynamics, in such a way as not only to express the laws
of each kind of movement, as it is in itself, but also the connexion and de-
pendence of the different classes of the phenomena.

A bold attempt at such a generalization has been made by M. Helmholtz.
The science of Thermo-dynamics starts from the principle, that perpetual
motion is impossible, or, in other words, that we cannot, by any combination
of natural bodies, produce force out of nothing. In mechanical force, this
principle is reducible to the known law of the conservation of living force ',
and M. Helmholtz has accordingly endeavoured to show that this law is
maintained in the interaction of all the natural forces ; while, at the same
time, the assumption of its truth leads to some new consequences in physics,
not yet experimentally confirmed. Expressed in its most general form, this
principle asserts that the gain of vis viva during the motion of a system, is
equal to the force consumed in producing it ; from which it follows, that the
sum of the vires vivce, and of the existing forces, is constant. This principle
M. Helmholtz denominates the conservation of force. A very important
consequence of its establishment must be, that all the actions of nature are
due to attractive and repulsive forces, whose intensity is a function of the
distance, — the conservation of vis viva holding only for such forces.

It is usually stated, in mechanical works, that there is a loss of vis viva in
the collision of inelastic bodies, and in friction. This is true with respect to
the motion of masses, which forms the subject of mechanical science as at
present limited ; but it is not true in a larger sense. In these, and such like

kii REPOttt— 1857.

cases, the movement of masses is transformed into molecular motion, and thlis
reappears as heat, electricity, and chemical action ; and the amount of the
transformed action definitely corresponds to the mechanical force which was
apparently lost.

In the cases just considered, mechanical action is converted into molecular.
But molecular actions of different kinds are themselves in like manner
interchangeable. Thus, when liffhf is absorbed, vis viva is apparently lost ;
but — not to speak of phosphorescence, in which the light absorbed, or a portion
of it, is again given out — in all such cases, heat and chemical action are
developed, and in amount corresponding to the loss. Hence the apparent
exceptions to the principle are in reality confirmations of it ; and we learn
that the quantity of force in nature is as unchangeable as the quantity of
matter.

This, however, is not true of the quantity of available force. It follows
from Carnot's law, that heat can be converted into mechanical work only
when it passes from a warmer to a colder body. But the radiation and con-
duction by which tiiis is effected, tend to bring about an equilibi-ium of tem-
perature, and therefore to annihilate mechanical force : and the same destruc-
tion of energy is going forward in the other processes of nature. Thus, it
follows from the law of Carnot, as Professor Thomson has shown, that the
universe tends to a state of eternal rest ; and that its store of available force
must be at length exhausted, unless replenished by a new act of Creative Powet.

Mr. Rankine has attempted, in another method, to combine the physical
sciences into one system, by distinguishing the properties which the various
classes of physical phenomena possess in common, and by taking for axioms
propositions which comprehend their laws. The principles thus obtained arfe
a.^n\\cd\i\e to all physical change; .and they possess all the certainty of the
facts from which they are derived by induction. The subject-matter of the
science so constituted is energy, or the capacity to effect changes ; and its
fundamental principles are— 1st, that all kinds of energy and work are homd-
treneous, or, in other words, that any kind of energy may be made the means
of performing any kind of work ; and '2nd, that the total energy of a substance
cannot be altered by the mutual action of its parts. From these principles
the author has deduced some very general laws of the transformation of
energy, which include the known relations of physical forces.

I have occupied your time so largely with the sciences of one section, that
I cannot do more than advert to one or two topics connected with the others,
which have struck my own mind, although, from my limited acquaintance
with the subjects, I could not venture to say that they are absolutely the
most deserving of notice.

Amon<T the most remarkable of the recent discoveries in inorganic che-
mistry are those of MM. Wcihler and Deville, relative to silicon and boron.
Each of these substances is now proved to exist in three very different states,

ADDRESS. ma

analogous to the three known states of carbon, to which they are thus closely
allied, namely charcoal, graphite, and diamond. The last of these states is,
of course, the most interesting. Crystallized boron possesses a hardness,
brightness, and refractive power comparable to those of diamond ; it burns
in chlorine, without residue, and under circumstances resembling those of
the combustion of diamond in oxygen ; it is not acted on by any of the acids,
and appears to be the least alterable of all the simple bodies. I have been
informed that its powder is already used in the arts, instead of diamond dust;
and it seems not improbable that, when obtained by the chemist in crystals
of larger size, it may rival the diamond as a gem.

The science of Geology appears, of late years, to have entered upon a new
phase of its development, — one characterized by a stricter reference of its
speculative views to the principles of those sciences with which it is con-
nected, and upon which it ought to be based. The able memoirs of Mr.
Hopkins, on what may be called dynamical geology, afford a remarkable
proof of this ; and we have another instance of the application of sound phy-
sical principles to this science in the explanations which have been recently
offered of the phenomena of slaty cleavage. A Report on this interesting
subject was presented to the Association by Professor Phillips at its last
Meeting, and will be found in the volume just published. These sounder
views originate, I believe, with himself and with Mr. Sharpe; but they have
been enlarged and confirmed by Mr. Sorby, Dr. Tyndall, and Professor
Haughton.

We have an interesting proof of the readiness of geologists of the present
day to submit their views to the test of exact observation, in the measure-
ments undertaken by Mr. Horner for the purpose of approximating to the
age of the sedimentary deposits. Of the geological changes still in opera-
tion, none is more remarkable than the formation of deltas at the mouths of
great rivers, and of alluvial land by their overflow. Of changes of the latter
kind, perhaps the most remarkable is the great alluvial deposit formed in the
valley of the Nile by the annual inundations of that river; and here it for-
tunately happens that history comes to the aid of the geologist. These sedi-
mentary deposits have accumulated round the bases of monuments of known
age, and we are therefore at once furnished with a chronometric scale by
which the rate of their formation may be measured. The first of the series
of measurements undertaken by Mr. Horner was made, with the coopera-
tion of the Egyptian Government, around the obelisk of Heliopolis, a monu-
ment built, according to Lepsius, 2300 years b.c. A more extensive series
of researches has been since undertaken in the district of Memphis ; but
Mr. Horner has not yet, I believe, published the results.

The problems now to be solved in Palceontology are clearly defined in the
enunciation of the problem recently proposed by the French Academy of
Sciences as one of its prize questions, viz. " to study the laws of distribution

Ixiv REPORT — 1857.

of organic beings in the different sedimentary rocks, according to the order
of their superposition ; to discuss the question of their appearance or disap-
pearance, whether simultaneous or successive; and to determine the nature
of the relations which subsist between the existing organic kingdom and its
anterior states." The prize was obtained by Professor Bronn, of Heidelberg ;
and his memoir, of which I have only seen an outline, appears to be cha-
racterized by views at once sound and comprehensive. The leading result
seems to be, that tiie genera and species of plants and animals, which geology
proves to have existed successively on our globe, were created in succession,
in adaptation to the existing state of their abode, and not transmuted or
modified, as the theory of Lamarck supposes, by the physical influences which
surrounded thera.

I must now pass from tiie results of science to the administrative measures
which have been adopted by this Association for its advancement, and more
especially to those which will be brought under your consideration at the
present Meeting.

One of the modes in which this Association most effectively promotes the
advancement of Science is, you are aware, by the preparation and publication
of Reports on the history, and actual state, of its several branches. With
the help of these, original investigators may, with little labour, ascertain all
that has been accomplished in each department, before they proceed to in-
crease the store ; and so not only prepare their own minds for their task, but
also avoid the waste of time and toil which has been too often incurred in
the re-discovery of the same truths.

To further the same objects, it was proposed by Professor Henry, of
Washington, at the Glasgow Meeting of the Association, that a Catalogue of
papers occurring in the Transactions of Scientific Societies, and in the
Scientific Journals, should be prepared by the Association, the Smithsonian
Institution undertaking to execute that part of the work whicii related to
American Science. A Committee, consisting of Mr. Cayley, Mr. Grant, and
Professor Stokes, was appointed to consider this proposal, and their Report
was submitted to the Cheltenham Meeting. The subject has since been under
the consideration of the Council of the Royal Society ; and a preliminary
Report has been drawn up by a sub-Committee of that body, which will
probably be brought before your Committee at this meeting.

A still more important question has been, for some years, under the con-
sideration of this Association and the Royal Society — the question, namely,
whether any measures could be adopted by the Government, or Parliament,
that would improve the position of Science or its cultivators in this country.

The Parliamentary Committee of the Association have taken much pains
in the attempt to arrive at a solution of this large and complex question.
They consulted, in the first instance, several of the most eminent scientific
men of this country ; and in their first Report, presented to the Meeting of

ADDRESS.

Ixv

the Association at Glasgow, they have analysed the replies obtained, and
have recommended certain general measures founded thereon. The most
important of these recommendations are the provision, at the cost of the nation,
of a central building in London, in which the principal Scientific Societies of
the metropolis may be located together ; and the formation of a Scientific
Board, to have the control and expenditure of the public funds allotted to the
advancement of science. This Report was brought under the consideration
of your Committee of Recommendations at the last two Meetings of the Asso-
ciation ; and the opinions of the members of the General Committee have been
since invited in reference to its suggestions. The Council of the Royal
Society have likewise deliberated on the same question, and have passed
certain resolutions on the subject, which accord in substance with the con-
clusions of the Parliamentary Committee. A copy of these resolutions
was forwarded by Lord Wrottesley, as President of the Society, to Lord
Palmerston ; and motions have been made in both Houses of Parliament for
the production of the correspondence.

The first of the objects above referred to — namely, the juxtaposition of
the Scientific Societies of London in one locality — has been since accomplished
by the grant of Burlington House for the use of the Royal, Linnsean, and
Chemical Societies ; and the result aff'ords a fresh instance of the readiness
of Her Majesty's Government to listen to, and comply with, the suggestions
of men of science, when deliberately and carefully made. I cannot but
think that this important step is fraught with consequences affecting the
promotion of science, and extending far beyond the external and obvious
advantages, which it ensures to the Scientific Societies more immediately
benefited.

Another mode in which this Association has materially aided in the
advancement of science is through the instrumentality of its Observatory at
Kew. The objects which are at present attained by that important establish-
ment are, the trial and improvement of instrumental methods, and especially
of those connected with the photographic registration of natural phenomena;
the verification of meteorological instruments, and the construction of stand-
ard barometers and thermometers ; the supervision of apparatus to be
employed by scientific travellers, and the instruction of the observers in their
use; and lastly, the conduct of special experimental researches, undertaken by
members of the Association at its request. In all these various ways, the
labours of the Kew Observatory have tended, in no small degree, to the
advancement of the sciences of Observation and Experiment in this country ;
and the result is due, not only to the sagacity of the Committee under whose
management it is placed, but also, and eminently, to the zeal and talents of
Mr. Welsh, and the gentleman who has the immediate charge of the esta-
blishment.

There is but one other topic connected with the administration of the

1857. e

Ixvi REPORT 1857.

Association to which I feel it necessary to invite your attention before I con-
clude, — I mean the change which has been made in the constitution of one
of the Sections, and which will come into operation at the present Meeting.
By a resolution of your Committee, adopted at the last Meeting, the scope
of the '* Statistical Section " has been enlarged, and it now embraces Econo-
mic Science in all its relations. I regard it as a fortunate circumstance for
the Association, that this important change will come into operation under
the Presidency of the distinguislied prelate, whose talents have been so long
devoted to the advancement of this science, and to whose nmnificence we
owe the Jbrmation of a shool of Political Economy in the University of
Dublin, which has already attained a high measure of celebrity. The
Section will have the aid, on this occasion, of more than one of those gentlemen
who have filled the Chair of the Whately Professorship, as well as of other
members of the Statistical Society of Dublin ; and its proceedings will receive
the countenance and support of many foreigners who have devoted them-
selves to the cultivation of Economic Science.

Gentlemen, suffer me now to thank you for the indulgent attention with
which you have favoured me. I am conscious that the sketch of the recent
progress of the Physical Sciences, which I have endeavoured to present, is
but a meagre and imperfect summary of what has been accomplished ; but
it is enough, at all events, to prove that Science is not on the decline, and
that its cultivators have not been negligent in their high calling. I now beg,
in the name of the Local Members of this body, to welcome you warmly to
this city ; and I pray that your labours here may redound to the glory of
God, and to the welfare and happiness of your fellow-men.

REPORTS

THE STATE OF SCIENCE.

REPORTS

THE STATE OF SCIENCE.

Report on the Recent Progress of Theoretical Dynamics.
By A. Cayley.

The object of the ' Mecanique Analj'tique' of Lagrange is described by the
author in the ' Avertissement' to the first edition as follows :— -" On a deja
plusieurs traites de mecanique, mais le plan de celui-ci est entierement neuf.
Je me suis propose de reduire la theorie de cette science et I'art de resoudre
tous les problemes qui s'y rapportent a des forniules generates dont le simple
developpement donne toutes les equations necessaires pour la solution de
chaqiie probleme." And the intention is carried out ; the principle of virtual
velocities furnishes the general formulae for the solution of statical problems,
and D'Alembert's principle then leads to the general formulaa for the solu-
tion of dynamical problems. The general theory of statics would seem to
admit of less ulterior development ; but as regards dynamics, the formulae
of the first edition of the ' Mecanique Analytique' have been the foundation
of a series of profound and interesting researches constituting the science of
analytical dynamics. The present report is designed to give, so far as I am
ablej! a survey of these researches ; there will be found at the end a list, in
chronological order, of the works and memoirs referred to, and I shall in the
course of the report preserve as far as possible the like chronological order.
It is proper to remark that I confine myself to the general theories of dyna-
mics. There are various special problems of great generality, and susceptible
of the most varied and extensive developments, such for instance as the
problem of the motion of a single particle (which includes as particular
cases the problem of central forces, that of two fixed centres, and that of the
motion of a conical pendulum, either with or without regard to the motion
of the earth round its axis), the problem of three bodies, and the problem
of the rotation of a solid body about a fixed point. But a detailed account
of the researches of geometers in relation to these special problems would
properly form the subject of a separate report, and it is not my intention to
enter upon them otherwise than incidentally, so far as it may appear desir-
able to do so. One problem, however, included in the first of the above-
mentioned special problems, I shall have frequent occasion to allude to: I
mean the problem of the variation of the elements of a planet's orbit, which
has a close historical connexion with the general theories which form the
subject of this report. The so-called ideal coordinates of Hansen, and the
principles of his method of integration in the planetary and lunar theories,
have a bearing on the general subject, and might have been considered in
the present report ; but on the whole I have considered it better not to do so.

1. Lagrange, 'Mecanique Analytique,' 1788.— The equations of motion
are obtained, as before mentioned, by means of the principle of virtual velo-

1857. s

2 REPORT — 1857.

cities and D'Aleniberl's principle. In their original forms they involve the
coordinates oc,y,z of the different particles m or dm of the system, quan-
tities which in general are not independent. But Lagrange introduces, in
place of the coordinates x,y,z of the different particles, any variables or
(using the term in a general sense) coordinates £, i//, 0, ... whatever, deter-
mining the position of the system at the time t: these may be taken to be in-
dependent, and then if ^', ;p', 0', . . denote as usual the differential coefficients of
^, di,(j),.. with respect to the time, the equations of motion assume the form

d dT_dT, ^__f. .
Jt'cU,' "di, '

or when S, '^', $, . . are the partial differential coefficients v^ith respect to
I,, yp, ip, . . . of one and the same function V, then the form

dt di, dS,' d^

In these equations, T, or the vis viva function, is the vis viva of the system
or sum of all the elements, each into the half square of its velocity, expressed
by means of the coordinates 4,1//,^,..; and (when such function exists) V,
or the force function*, is a function depending on the impressed forces and
expressed in like manner by means of the coordinates ^, -i/^, 0, .. ; the two
functions T and V are given functions, by means of which the equations of
motion for the particular problem in hand are completely expressed. In
any dynamical problem whatever, the vis viva function T is a given function
of the coordinates ^,\p,(p,..., of their differential coefficients ^', i//', ^', . . .
and of tiie time t; and it is of the second order in regard to the differential
coefficients I', 4/', cp', .. .; and (when such function exists) the force function
V is a given function of the coordinates ^, \^,<p,.. and of the time t. This
is the most general form of the functions T, V, as they occur in dynamical
problems, but in an extensive class of such problems the forms are less
general, viz. T and V are each of them independent of the time, and T is a
homogeneous function of the second order in regard to the differential
coefficients ^', ;//', 0', .. ; the equations of motion have in this case an integral
T4-V=/«, which is the equation of vis viva, and the problems are distin-
guished as those in which the principle of vis viva holds good. It is to be
noticed also that in this case since t does not enter into the differential equa-
tions, the integral equations will contain t in the form t-\-c, that is, in con-
nexion with an arbitrary constant c attached to it by addition.

2. The above-mentioned form '\s par excellence the Lagrangian form of the
equations of motion, and the one which has given rise to almost all the ulte-
rior developments of the theory ; but it is proper just to refer to the form
in which the equations are in the first instance obtained, and which may be
called the unreduced form, viz. the equations for the motion of a particle
whose rectangular coordinates are x,y,z, are

d/x y 1 x'^j. d^i

cU' " Ix Ix

where L=0, M=0, ... are the equations of condition connecting the
coordinates of the different points of the system, and X, yu, ..are indeter-
minate multipliers.

* The sign attributed to V is that of the ' Mecanique Analytique,* but it would be better
to write V= — U, and to call U (instead of V) the force function.

ON THEORETICAL DYNAMICS. d

3. The idea of a force function seems to have originated in the problems
of physical astronomy. Lagrange, in a memoir ' On the Secular Equation
of the Moon,' crowned by the French Academy of Sciences in the year
1774', expressed the attractive forces, decomposed in the directions of the
axes of coordinates, by the partial differential coefficients of one and the same
function with respect' to these coordinates. And it was in these problems
natural to distinguish the forces into principal and disturbing forces, and
thence to separate the force function into two parts, a principal force function
and a disturbing function. The problems of physical astronomy led also to
the idea of the variation of the arbitrary constants of a mechanical problem.
For as a fact of observation the planets move in ellipses the elements o
which are slowly varying; the motion in a fixed ellipse Avas accounted for
by the principal force, the attraction of the sun ; the effect of ihe disturbing
force is to produce a continual variation of the elements of such elliptic
orbit. Euler, in a memoir published in 1749 in the ' Memoirs of the Academy
of Berlin' for that year, obtained differential equations of the first order for
two of the elements, viz. the inclination and the longitude of the node, by
making the arbitrary constants which express these elements in the fixed
orbit to vary : this seems to be the first attempt at the method of the varia-
tion of the arbitrary constants. Euler afterwards treated the subject in a
more complete manner, and the method is also made use of by Lagrange in
his ' Memoir on the Perturbations of the Planets' in the Berlin Memoirs for
1781, 1782, 1783, and by Laplace in the 'Mecanique Celeste,' t. i. 1799.
The method in its original form seeks for the expressions of the variations
of the elements in terms of the differential coefficients of the disturbing
function with respect to ihe coordinates. As regards one element, the longi-
tude of the epoch, such expression (at least in a finite form) was first ob-
tained by Poisson in his memoir of 1808, to be spoken of presently ; but I
am not able to refer to any place where such expressions in their best form
are even now to be found ; the question seems to have been unduly passed
over in consequence of the new form immediately afterwards assumed by the
method. It was very early observed that the variation of one of the ele-
ments, viz. the mean distance, was expressible in a remarkable form by
means of the differential coefficients of the disturbing function taken with
respect to the time t, in so far as it entered into the function through the co-
ordinates of the disturbed planet. I am not able to say at what time, or
whether by Euler, Lagrange, or Laplace, it was observed that such diffe-
rential coefficient with respect to the time was equivalent to the difierential
coefficient of the disturbing function with respect to one of the elements.
But however this may be, the notion of the representation of the variations
of the elements by means of the differential coefficients of the disturbing
function tvith respect to the elements had presented il'ieM a posteriori, and was
made use of in an irregular manner prior to the year 1800, and therefore
some eight years at any rate before the establishment by Lagrange of the
general theory to which these forms belong.

4. Poisson's memoir of the 20th of June, 1808, 'On the Secular In-
equalities of the Mean Motion of the Planets,' was presented by him to the
Academy at the age of twenty-seven years. It contains, as already re-
marked, an expression in finite terms for the variation of the longitude of
the epoch. But the memoir is to be considered rather as an application of
known methods to an important problem of physical astronomy, than as a
completion or extension of the theory of the variation of the planetary
elements. The formulse made use of are those involving the differential
coefficients of the disturbing function with respect to the coordinates ; and

4 REPORT — 1857.

there is nothing which can be considered an anticipation of Lagrange's
idea of tiie investigation, d priori, of expressions involving the differential
coefficients with respect to the elements. But as well for its own sake as
historically, the memoir is a very important one. Lagrange, in his memoir
of the 17th of August, 1808, speaks of it as having recalled his attention to
a subject with which he had previously occupied himself, but which lie had
quite lost sight of; and Arago records that, on the death of Lagrange, a
copy in his own handwriting of Poisson's memoir was found among his
papers ; and the memoir is referred to in, and was probably the occasion of,
Laplace's memoir also of the 17th of August, 1S08.

5. With respect to Laplace's memoir of the 17th of August, 1808, it will
be sufficient to quote a sentence from the introduction to Lagrange's me-
moir : — " Ayant montre a M. Laplace mes forniules et mon analyse, il me
montra de son cote en meme temps des forniules analogues qui donnent
les variations des elemens elliptiques par les differences partielles d'une
meme fonction, relatives a ces elemens. J'ignore comment il y est par-
venu ; mais je presume qu'il les a trouvees par une combinaison adroite des
formules qu'il avait donne dans la 'Mecanique Celeste.'" This is, in fact,
the character of Laplace's analysis for the demonstration of the formulae.

6. In Lagrange's memoir of the 17th of August, 1808, 'On the Theory
of the Variations of the Elements of the Planets, and in particular on the
Variations of the Major Axes of their Orbits,' the question treated of ap-
pears from the title. The author obtains formulae for the variations of the
elements of the orbit of a planet in terms of the differential coefficients of
the disturbing function with respect to the elements ; but the method is a
general one, quite independent of the particular form of the integrals, and
the memoir may be considered as the foundation of the general theory.
The equations of motion are considered under the form, —

cPx_l+m _ rfii
di- r^ dx

d^y _\-\-m _dQ.

drz_\-\-m _dQ,
df- ~r^^~'d^'

and it Is assumed that the terms in fi being neglected, the problem is com-
pletely solved, viz., that the three coordinates, x,y,z, and their differential
coefficients, x', y\ z', are each of them given as functions of t, and of the
constants of integration a, b, c,f, g, h ; the disturbing function Q. is conse-
quently also given as a function of t, and of the arbitrary constants. The
velocities are assumed to be the same as in the undisturbed orbit. This
gives the conditions

Zx=0, hj=0, Sz=0;

and then the equations of motion give

^dx_dQ. ^dy _dD. ^dz _dD.

dt dx dt dy^ dt dz

equations in which Ix, &c. denote the variations of x, &c., arising from the

variations of the arbitrary constants, viz., dx=-^da + ~^U + , &c. The

da do

differential coefficients — , &c., can of course be expressed by means of

ON THEORETICAL DYNAMICS. 5

-— , &c. ; and, by a simple combination of the several equations, Lagrange

deduces expressions for — -, &c., in terms of —-, &c. ; viz. —
da at

in which, for shortness,

S(a;, «') i J f dxdx' dx' dx

^(^a, b) dadb da ab

The form of the expressions shows at once that (a,b)= — (6, a), so that
the number of the symbols (a, b) is in fact fifteen.

Lagrange proceeds to show, that the differential coefficient with respect
to f of the expression represented by the symbol (a, 6) vanishes identically ;
and it follows, that the coefficients (a, b) are functions of the elements only,
without the time t.

The general formulae are applied to the problem in hand ; and, in con-
sequence of the vanishing of several of the coefficients (a, b), it is easy in

the particular problem to pass from the expressions for ——, &c, in terms of

—-, &c. to those for — , &c. in terras of — -, &c. The author thus obtains
dt dt da

an elegant system of formulae for the variations of the elements of a planet's

orbit, in terms of the diflPerential coefficients of the disturbing function with

respect to the elements ; but it is not for the present purpose necessary to

consider the form of the system, or the astronomical consequences deduced

by means of it.

7. Lagrange's memoir of the 13th of March, 1809, 'On the General

Theory of the Variation of the Arbitrary Constants in all tlie Problems of

Mechanics.' — The method of the preceding memoir is here applied to the

general problem ; the equations of motion are considered under the form

dd^_d^dY_<Kl

dt dr^ dr dr dr

where T and V are of the degree of generality considered in the * Me-
canique Analytique,' viz., T is a function of r, 5.. »■', s', .. homogeneous of
the second order as regards the differential coefficients /•', s', . ., and V is
a function of r, s, . . only ; or, rather, the equations are considered in a form
obtained from the above, by writing T — V=R, viz., in the form

ddR_dR_d^

dt dr' dr dr '

and, as in the preceding memoir, expressions are investigated for the dif-
ferential coefficients -jt, &c, in terms of -^ &c. : these are, as before, of the

* These are substantially the formulae of Lagrange ; but I have introduced here and
elsewhere the very convenient abbreviation, due, I think, to Prof. Donkin, of the symbols

6 REPORT — 1857.

form '^=(o,6)f + , &c.

da at

where (a, b), &c., are in the body of the memoir obtained under a some-
what complicated form, and this complicates also the demonstration which
is there given of the theorem, that (a, i), &c., are functions of the elements
only, tvithout the time t ; but in the addition (published as part of the me-
moir, and without a separate date) and in the supplement the investigation
is simplified, and the true form of the functions (a, b) obtained, viz., Avriting

-^^=p,...then.

if, for shortness.

d(a,6) o{a,b)

d(r, p) dr dp dp dr „

5 (a, b) da db da db

The representation of — > — ^, &c. by single letters is made by Lagrange

in the addition, No. 26 (Lagrange writes _ = T', — = T", &c.), but quite

incidentally in that number only, for the sake of the formula just stated: I
have noticed this, as the step is an important one.

8. It is proper to remark that, in order to prove that the expressions
(a, b) &c., are independent of the time, Lagrange, instead of considering
the differential coefficients of each of these functions separately, establishes
a general equation (see Nos. 25, 34', 35 of the Addition, and also the Sup-
plement)

dt\ dr dr J

where, if Act, A6, .. denote any arbitrary increments whatever of the con-
stants of integration a, b, . . then Ar, &c., are the corresponding increments
of the coordinates r, &c. ; this is, in fact, a grouping together of several
distinct equations by means of arbitrary multipliers, and it is extremely
elegant as a method of demonstration, and has been employed as well by
Lagrange, here and elsewhere, as by others who have written on the
subject; but I think the meaning of the formulae is best seen when the
component equations of the group are separately exhibited, and in the
citation of formula3 I have therefore usually followed this course. Lagrange
gives also an equation which is in fact a condensed form of the preceding

d^
expression for -r-, but which it is proper to mention, viz. : —

dSl, dr^dK. _^ d dK

da da dr' da dr'

r r . • ., p 1 ^ dB. . J „ f d rfR da , d r/R db , \ ,^ ,
In fact, m the formula c — — stands for I — — — — - +— , — — 7-+ .. Vlt, and
dr \da dr dt db dr dt J

Ir for ( -^ -?+-^ — + V^; and, on substituting these values, the identity
\du dt dt dt J ° ^

of the two expressions is seen without difficulty.

9. Lagrange remarks, that in the case where the condition of vis viva
holds good, then if a be the constant of vis viva {T-\-v=-a), and c the

constant attached by addition to the time, then -r=-T-j which, he observes,

dt dc

ON THEORETICAL DYNAMICS. 7

is an equation remarkable as well from its simplicity and generality a8
because it can be obtained a priori, independently of the variations of the
other arbitrary constants : this is obviously the generalisation of the expres-
sion for the variation of the mean distance of a planet.

10. The consideration of Lagrange's function (a, b) originated, as appears
from what has preceded, in the theory of the variation of the elements ; but
it is to be noticed, that the function (a, b) is altogether independent of the
disturbing function, and the fundamental theorem that {a,b) is a function
of the elements onlj', without the time, is a property of the undisturbed
equations of motion. The like remark applies to Poisson's function (a, b),
in the memoir next spoken of.

11. Poisson's memoir of the 16th of October, 1809. The formulas of
this memoir are, so to speak, the reciprocals of those of Lagrange. The

relations between the differential coefficients — , &c., of the disturbing func-

tion and the variations — , &c., of the elements, depend with Lagrange,

upon expressions for the coordinates and their differential coefficients in
terms of the time and the elements ; with Poisson, on expressions for the
elements in terms of the time, and of the coordinates and their differential
coefficients. The distinction is far more important than would at first
sight appear, and the theory of Poisson gives rise to developments which
seem to have nothing corresponding to them in the theory of Lagrange.
The reason is as follows : when the system of differential equations is com-
pletely integrated, it is of course the same thing whether we have the
integral equations in the form made use of by Lagrange, or in that by
Poisson, the two systems are precisely equivalent the one to the other ; but
when the equations are not completely integrated, suppose, for instance, we
have an expression for one of the coordinates in terms of the time and the
elements, it is impossible to judge whether this is or is not one of the inte-
gral equations ; the? differential equations are not satisfied by means of this
equation alone, but only by this equation with the assistance of the other
integral equations. On the other hand, when we have an expression for
one of the constants of integration in terms of the time, and of the co-
ordinates and their differential coefficients, it is possible, by mere substi-
tution in the differential equations, and without the knowledge of any other
integral equations, to see that the differential equations are satisfied, and
that the assumed expression is, in fact, one of the system of integral
equations. An expression of the form just referred to, viz., c=(p {t,x,y,..
x\y' . ..), where the right-hand side does not contain any of the arbitrary
constants, may, with great propriety, be termed an " integral," as distin-
guished from an integral equation, in which the constants and variables
may enter in any conceivable manner ; it is convenient also to speak of such
equation simply as the integral c.

12. Returning now to the consideration of Poisson's memoir, the equa-
tions of motion are considered under the same form as by Lagrange, viz.,
putting T— V=R under the form

ddR_dR_da
dt d(j>' d'
but Poisson writes ;

dR_
d^~'"'
thus, in effect, introducing a new set of variables, s, . . equal in number to

9 REPORT — 1857.

the coordinates </>, .... but he does not complete the transformation of the
differential equations by the introduction therein of the new variables s, . . .
in the place of the differential coefficients <l>',..; this very important trans-
formation was only effected a considerable time afterwards by Sir W. R.
Hamilton. Poisson then assumes that the undisturbed equations are in-
tegrated in the form above adverted to, viz., that the several elements a,b..
are given as functions of the time t, and of the coordinates 0, &c., and their
differential coefficients (j)', Sec, or wiiat is the form ultimately assumed, as
functions of the time t, of the coordinates f, . ., and of the new varia-
bles s, &c. ; and he then forms the functions

where

d(o!, b)_da db _db da
d(s, (^) ds d<j> ds dip

(the notation is the abbreviated one before referred to), and he proves by
differentiation that the differential coefficient of {a, b) with respect to the time
vanishes : that is, that (a, b) which, by its definition is given as a function of t
and of the coordinates <p,..., and of the new variables s, ..., is really a
constant. Upon which Poisson remarks — " On conceit que la constante . . .
sera en general une fonction de a et b et des constantes arbitraires con-
tenues dans les autres integrales des equations du mouvement ; quelquefois
il pourra arriver que sa valeur ne renferme ni la constante a ni la con-
stante 6 ; dansd'autres cas elle ne contiendra aucune constante arbitraire, et
se reduira a une constante determinee ; mais afin," &c.

13. The importance of the remark seems to have been overlooked until
the attention of geometers was called to it by Jacobi ; it has since been
developed by Bertrand and Bour.

It is clear from the definition that (a, 6) = — (b,a). It may be as well to
remark that the denominator of the functional symboV is (s, (p) and not
(f, s), which would reverse the sign.

14. The equations for the variations of the elements are without difficulty
shown to be da . i^dQ, .

which have the advantage over those of Lagrange of giving directly — , &c.

in terms of ---, &c., instead of these expressions having to be determined
da

from the value of — , &c., in terras of — '-, &c.
da dt

i5. Poisson applies his formulce to the case of a body acted upon by a
central force varying as any function of the distance, and also to the case
of a solid body revolving round a fixed point. There is, as Poisson remarks,
a complete similarity between the formulEe for these apparently very dif-
ferent problems, but this arises from the analogy which exists between the
arbitrary constants chosen in the memoir for the two problems. The
forraulcE obtained form a very simple and elegant system, and one which,
although not actually of the canonical form (the meaning of the term will
be presently explained), might by a slight change be reduced to that form.

16. I may notice here a problem suggested by Poisson in a report to the
Institute in the year 1830, on a manuscript work by Ostrogradsky on

ON THEORETICAL DYNAMICS. 9

Celestial Mechanics, viz., in the case of a body acted upon by a central force,
the effect of a disturbing function, tohich is a function only of the distance
from the centre, is merely to alter the amount of the central force ; and the
expressions for the variations of the elements should thereibre, in the case
in question, admit of exact integration ; the report is to be found in Crelle,
t. vii. pp. 97-101.

17. The two memoirs of Lagrange and Poisson, which have been con-
sidered, establish the general theory of the variation of the arbitrary con-
stants, and there is not, I think, very much added to them by Lagrange's
memoir of 1810, the second edition of the ' Mecanique Analytique,' J 811,
or Poisson's memoir of 1816. The memoir by Maurice, in 1844', belongs to
this part of the subject, and as its title imports, it is in fact a development
of the theories of Lagrange and Poisson.

18. There is, however, one important point which requires to be adverted
to. Lagrange, in the memoir of 1810, and the second edition of the
'Mecanique Analytique,' remarks, that for a particular system of arbitrary
constants, viz., if a, ... denote the initial values of the coordinates ^, .. and

X,.. denote the initial values |of -7=-,f- then the equations for the varia-
tions of the elements take the very simple form

rfa__rfO d\_dil

'di~ dx"' dt~da'"'
This is, in fact, the original idea and simplest example of a system of can-
onical elements ; viz. of a system composed of pairs of elements, a, X, the
variations of which are given in the form just mentioned.

19. The ' Avertissement'to the second edition of the 'Mecanique Analytique'
contains the remark, that it is not necessary that the disturbing function £2

should actually exist; — -, -^, —— may be considered as mere conventional
■' dx' dy dz ■'

symbols standing for forces X, Y,Z, not the differential coefficients of one and

the same function, and then — - will be a conventional symbol standing for
da

do, dx , do, dy , d£l dz j • 1 1 r dQ. . j ^.u- u • n

— — —+ r-+-r- —, and similarly for — -, &c. ; and this being so, all

dx da dy da dz da do

the formulas will subsist as in the case of an actually existing disturbing

function.

20. Cauchy, in a note in the ' Bulletin de la Societe Philomatique' for
1819 (reproduced in the ' Memoire sur I'lntegration des Equations aux
Derivees Partielles du Premier Ordre,' ' Exer. d'Anal. et de Physique Math.,'
t. ii. pp. 238-272 (1841)), showed that the integration of a partial dif-
ferential equation of the first order could be reduced to that of a single
system of ordinary differential equations. A particular case of this general
theorem was afterwards obtained by Jacobi in the course of his investiga-
tions (founded on those of Sir W. R. Hamilton) on the equations of dyna-
mics, and he was thence led to a slightly different form of the general
theorem previously established by Cauchy, viz., Cauchy's method gives the
general, Jacobi's the complete integral, of the partial differential equation.
The investigations of the geometers who have written on the theory of
dynamics are based upon those of Sir W. R. Hamilton and Jacobi, and it is
therefore unnecessary, in the present report, to advert more particularly to
Cauchy's very important discovery.

21. I come now to Sir W. R. Hamilton's memoirs of 1834 and 1835,
which are the commencement of a second period in the history of the sub-

10 * REPORT — 1857.

ject. The title of the first memoir shows the object which the author pro-
posed to himself, viz., the discovery of a function by means of which the
integral equations can be all of them actually represented. The method
given for the determination of this function, or rather of each of the several
functions which answer the purpose, presupposes the knowledge of the
inteo-ral equations ; it is therefore not a method of integration, but a theory
of the representation of the integral equations assumed to be known. I
venture to dissent from what appears to have been Jacobi's opinion, tiiat
the author missed the true application of his discovery ; it seems to me, that
Jacobi's investigations were rather a theory collateral to, and historically
arising out of the Hamiltonian theory, than the course of development
which was of necessity to be given to such theory. But the new form ob-
tained in Sir W. R. Hamilton's memoirs for the equations of motion, is a
result of not less importance than that which was the professed object of
the memoirs.

22. Hamilton's principal function V. — The formulae are given for the
case of any number of free particles, but, for simplicity, I take the case of a
single particle. The equations of motion are taken to be

d'x_d\],
df dx

d'y_d\J

„.^=^.

df dz '

so that the vis viva function is

and the force function, taken with Lagrange's sign, would be — U. It is
assumed that the condition of vis viva holds, that is, that U is a function of
x,y,zon\y. The initial values of the coordinates are denoted by a,h,c,
and those of the velocities by a', b', c'. The equation of vis viva is
T=U + H, and this gives rise to an equation To=U„ + H of the same form
for the initial values of the coordinates. The author then writes

V=f 2Tdt,

an equation, the form of which implies that T is expressed as a function
of the time and of the constants of integration a, b, c, a', b', c'. The method
of the calculus of variations leads to the equation

lY=^m(x'hx+y'hj + z'hz)—m{a'la-irb'ib+c'Zc)^tlB.,

to understand which, it should be remarked that the coordinates x,y,z,
and the velocities a'', ?/', z\ being functions of t and of a, b, c, a', b', c', then
V is, in the first instance, given as a function of these quantities. But
'x,y,z being functions oi a,b,c, a',b',c',t, we may conversely consider
a',b',c' as functions of .r,y, r, a,b,c,t, and thus V becomes a function of
x,y,z, a,b,c,t. In like manner H is a function of x,y,z, a,b,c,t,and,
eliminating t, we have V a function of x,y, z, a,b, c, H, which is the form
in which in the last equation V is considered to be expressed. The equa-
tion then gives

ON THEORETICAL DYNAMICS. ll

dY , d\ , dV

ax dy dz

dV , dV ,, dV

— = — ma, ---=i—nio, -7- = — mc ,

da do dc

dV_.
dH~^'

and, considering V as a known function of x,y,z, a, b,c, H, the elimination
of H gives a set of equations vviiich are in fact the integral equations of
the problem, viz., the first three equations and the last equation give equa-
tions containing x,y,z, x',y\ 2', t and a,h, c, that is, the intermediate inte-
grals ; the second three equations and the last equation, give equations
containing x,y, z, t, a,b,c, a',b', c', that is, the final integrals.
The function V satisfies the two partial differential equations

i{(sy+(0+(s;}=°+«

which, if they could be integrated, would give V as a function of x,y, z,
a, b,c, H, and thus determine the motion of the system.

23. Hamilton's principal function S. — This is connected with the function
V by the equation

V=^H-|-S;

or, what is the same thing, the new principal function S is defined by the
equation

S=f(T + U)rf#;
Jo
but S is considered (not like V as a function of x,y,z,a,b,c; H, but) as
a function of x, y, z, a, 6, c, t. The expression for the variation of S is

l^= — \\lt^m{x'lx-\-y'ly-^z^lz)-m{a!la + Vlh-\-dcc)
which is equivalent to the system

-— = mx,
dx

dS
' dy

my':

dS
' dz

rfS

— ^—ma

dS
' db

—mb',

dS_
dc

f=-H;
dt

the first three and the second three of which give, respectively, the inter-
mediate and the final integrals; the last equation leads only to the expres-
sion of the supernumerary constant H in terms of the initial coordinates
a,b,c, and it may be omitted from the system.

The function S satisfies the partial differential equations

12 REPORT — 1857.

which, if they could be integrated, would give S as a function of x,y,z,
a,b,c, t, and thus determine the motion of the system.

24. Hamilton's form of the equations of motion. — This is in fact the
form obtained by carrying out the idea of introducing into the differential
equations, in the place of the differential coefficients of the coordinates, the
derived functions (with respect to these differential coefficients) of the
vis viva function T. Taking jj to denote any one of the series of coordi-
nates, then the original system may be denoted by

dt dt}' di] ~ dt]

(U is the force function taken with a contrary sign to that of Lagrange),
and writing in like manner cr to denote any one of the new variables con-
nected with the coordinates r) by the equations

rfT_

dr,'-""'

then T, in its original form, is a function of 77, . . . tj', . .., homogeneous
of the second order as regards the differential coefficients ??'..; and, con-
sequently, these being linear functions (without constant terms) of the new
variables -m, the vis viva function T can be expressed as a function of r;, . ..
w, ..,, homogeneous of the second order as regards the variables ct, ...
And when T has been thus expressed, the equations of motion take the form

dn_(m ^__^,^
dt rfra-' dt d>] dj]

which is the required transformation. The force function U is independent
of the differential coefficients »;', . . and, consequently, of the variables ot, . .,
hence, writing H=T— U, the equations take the form

dr] rfH d-ar dH ^

dt~ c?TO-' dt^ dr}'

which correspond to the condensed form obtained by writing T— V=R in
Lagrange's equations. It is hardly necessary to remark that H is to be
considered as a given function of ?;,... cr, ..., viz., it is what T — U be-
comes when the differential coefficients ?/, . . . are replaced by their values
in terms of the new variables or, . • .

25. I have, for greater simplicity, explained the theory of the functions V
and S in reference to a very special form of the equations of motion ; but
the theory is, in fact, applicable to any form whatever of these equations ;
and, as regards the function V, is in the first memoir examined in detail
with reference to Lagrange's general form of the equations of motion. The
function S is considered at the end of the memoir in reference only to the
special form. The new form of the equations of motion is first established
in the second memoir, and the theory of the functions V and S is there con-
sidered in reference to this form. The author considers also another
function Q, which, when the matter is looked at from a somewhat more
general point of view, is not really distinct from the function S.

* I find it stated in a note to M. Houel's ' These sur I'integration des equations differen-
tielles de la Mecanique,' Paris, 1855, that this form of the equations of motion had been
previously employed in an unpublished memoir by Cauchy,, written in 1831.

ON THEORETICAL DYNAMICS. 13

26. The first memoir contains applications of tlie method to the problem
of two bodies, and tlie problem of three or more bodies, and researches in
reference to the approximate integration of the equations of motion by the
separation of the function V into two parts, one of them depending on the
principal forces, the other on the disturbing forces. The method, or one of
the methods, given for this purpose, involves the consideration of the varia-
tion of the arbitrary constants, but it is not easy to single out any precise
results, or explain their relation to the results of Lagrange and Poisson. The
like remark applies to the investigations contained in Nos. 7 to 12 of the
second memoir, but it is important to consider the theory described in the
heading of No. 13, as "giving formulte for the variation of elements more
analogous to those already known." The function H is considered as con-
sisting of two parts, one of them being treated as a disturbing function ; the
equations of motion assume therefore the form

^_c?H rfY dm_ dH_dr
dt dvs dxa' dt drj drj

(I have written H, Y instead of the author's H„ Hj). The terms involving
Y are in the first instance neglected, and it is assumed that the integrals
of the resulting equations are presented in the form adopted by Poisson,
viz., the constants of integration a, b, &c., are considered as given in terms
of t, and of the two sets of variables tj, . . and ra-, ..; the integrals are then
extended to the complete equations by the method of the variation of the
elements. The resulting expressions are the same in form as those of
Poisson, viz. : —

da , ,xrfY ,

where

if, for shortness,

d(a, b) _da db db da
d(r;, -us) dt] dv: drj d-ar

and conversely the values of — -, &c. in terms of -— , &c. might have been

da dt

exhibited in a form such as that of Lagrange. The expressions (a, b), con-
sidered as functional symbols, have the same meanings as in the theories of
Poisson and Lagrange ; and, as in these theories, the differential coefficient
of (a, b) with respect to the time, vanishes, or (a, b) is a function of the
elements only.

27. It is to be observed that the disturbing function Y is not necessarily
in the same problem identical with the disturbing function H of Lagrange
and Poisson (indeed, in any problem, the separation of the forces into prin-
cipal forces and disturbing forces is an arbitrary one). Sir W. R. Hamil-
ton, in the second memoir, gives a very beautiful application of his theory
to the problem of three or-more bodies, which has the peculiar advantage of
making the motion of all the bodies depend upon one and the same disturbing
function*. This disturbing function contains (as in the last-mentioned

* Lagrange has given formulae for the determination of the motion of three or more
bodies referred to their common centre of gravity by means of one and the same disturbing
function. In Sir W. R, Hamiltoa's theory there is one central body to which all the others

14 REPORT — 1857.

general formulae) both sets of variables, and the consequence is that, as the
author remarks, the varying elements employed by him are essentially different
from those made use of in the theories of Lagrange and Poisson ; the ve-
locities cannot, in his theory, be obtained by differentiating the coordinates
as if the elements were constant. The investigation applies to the case
where the attracting force is any function whatever of the distance, and the
six elements ultimately adopted form a canonical system.

28. The precise relation of Sir W. R. Hamilton's form of the equations
of motion to that of Lagrange's, is best seen by considering Lagrange's
equations, not as a system of differential equations of the second order
between the coordinates and the time t, but as a system of twice as many
differential equations of the first order between the coordinates, their
differential coefficients treated as a new system of variables, and the time.
It will be convenient to write — U, instead of Lagrange's force-function V,
and (to conform to the usage of later writers who have treated the subject
in the most general manner) to represent the coordinates by q, . . ., their
differential coefficients by q', . .., and the new variables which enter into the
Hamiltonian form byjt;, . . .; then the Lagrangian system will be

dq_ , ^dT_dT_dV^
dt~^' dt dq' ~dq ~~ dq '

or putting T4-U=Z (this is the same as Lagrange's substitution, T — V— R),
the system becomes

dq , d dZ dZ

'di~^' didq' ~"dq

while the Hamiltonian system is

dt ~^dp ' dt~ dq dq'

or putting as before T— U=H, the system is
dq_dH dp__dH.
dt dp' dt dq '

where, in the Lagrangian systems, T and U, and consequently Z, are given
functions of a certain form of t,q,. . q', . ., and in like manner, in the Hamil-
tonian system, T and U, and consequently H, are given functions of a cer-
tain form of t, q,..p ., . The generalisation has since been made (it is not
easy to say precisely when first made) of considering Z as standing for any
function whatever of (,q, ,. , q', . ., and in like manner of considering H as
standing for any function whatever of t, q, . .p, ... It is to be noticed that
in Sir W. R. Hamilton's memoir, the demonstration which is given of the
transformation from Lagrange's equations to the new form depends essentially
on the special form of the function T as a homogeneous function of the
second order in regard to the differential coefficients of the coordinates ;
indeed the transformation itself, as regards the actual value of the new func-
tion T( = T expressed in terms of the new variables), which enters into the

are referred. The method of Sir W. R. Hamilton is made use of in M. Houel's ' These
d'Astrouomie : Application de la Methode de M. Hamilton an Calcul des Perturbations de
Jupiter.'— Paris, 1855.

ON THEORETICAL DYNAMICS. 15

transformed equations, depends essentially upon the special form just re-
ferred to of the function T, although, as will be seen in the sequel, there is
a like transformation applying to the most general form of the function T.

29. In the greater part of what has preceded, and especially in the above-
mentioned substitutions T + U=Z and T — U=H, it is of course assumed
that the force function U exists ; when there is no force function these
substitutions cannot be made, but the forms corresponding to the untrans-
formed forms in T and U are as follows, viz. the Lagrangian form is

dt~'^' dtdq' dq~^'

and the Hamiltonian form is

dq_dT ^__^, Q.
dt dp' dt dq '

that is, the only difference is, that the functions Q, instead of being the dif-
ferential coefficients with respect to the variables g ... of one and the same
force function U, are so many separate and distinct functions of the variables
g, •• ; or more generally of the variables g,..p,.. of both sets.

30. Jacobi's letter of 1836. — This is a short note containing a mere state-
ment of two results. The first is as follows, viz. the equations for the
motion of a point in piano being taken to be

fx_d\J ^_dV
dt' ~ dx ' d(- dy '

where U is a function x,y without # ; one integral is the equation of vis
viva ■|(a;'' + ?/'") = U+/i. Assume that another integral is a=¥(^x,y,x',y'),
then x',1/' will in general be functions of x,i/,a,h, and considering them as
thus expressed, it is stated that not only x!dx-\-y'dy will be an exact differ-
ential, but its differential coefficients with respect to a, h will be so likewise,
and the remaining integrals are

< +

a theorem, the relation of which to the general subject will presently appear.

The second result does not relate to the general subject, but I give it in a
note for its own sake*.

31. Poisson's memoir of 1837. — This contains investigations suggested by

* Jacobi imagines a point without mass revolving round the sun and disturbed by a planet
moving in a circular orbit, which is taken for the plane of x, y ; the coordinates of the point
are x, y, z, those of the planet a' cos n't, a' sin n't, m' is the mass of the planet, M the mass
of the sun ; then we have accurately

*{(S)+(l)"+(|)'}-<4-l)=

-£-) 1 (*'-+y"+2^ — 2a'(;i'Cos ji7+wsinw7)-|-a'2)A ^ cos ?i7+y sin raV J

(j;2-|-y2_|_£0^ L (*'-+y"+2^ — 2a'(;i'Cos ■i-i!t-\-yiva.n't)-\-a''^)\ ^ cos ?i7+y sin )

■which Jacobi suggests might be found useful in the lunar theory. The point being without
mass, means only that it is considered as not disturbing the circular motion of the planet ;
the problem is properly a case of the problem of two centres, viz. one centre is fixed, and
the other one revolves round it in a circle with a uniform velocity.

16 REPORT — 1857.

Sir W. R. Hamilton's memoir, and relating to the aid to be derived from a
system of given integral equations (equal in number to the coordinates) in

the determination of the principal function V. The equations —=mx',

&c. give dV = 111 (x' dx + 1/' di/ + z'dz), or in the case of a system of points,
dV ='^)ii(x'dx + i/'dy + z'dz). If the points, instead of being free, are con-
nected to"-etiier by any equations of condition, then, by means of these
equations, the coordinates x,i/, z of the different points and their differential
coefficients x',i/',z', can be expressed as functions of a certain number
of independent variables (j>, \p, d, &c., and of their differential coefficients
^', 4/', 0', &c. ; dY then takes the form dV=Xd, v//,0 . •; then, by the aid of these equations, ^',i//',0'..,
and, consequently, X, Y, Z . . can be expressed as functions (of the con-
stants of integration and) of the variables (p,\^,Q,... Hence, attending
only to the variables, d'V=Xrf(/) + Yrf;p+Zrf9+ . . is a differential expression
involving only the variables <j),\l/,d..; but, as Poi.<son remarks, this expres-
sion is not in general a complete differential. In the cases in which it is so,
V can of course be obtained directly by integrating the differential ex-
pression, viz. the function so obtained is in value, but not in form. Sir W.
R. Hamilton's principal function V, for, with him, V is a function of the
coordinates, and of a particular set of the constants of integration, viz. the
constant of vis viva h, and the initial value? of the coordinates. Poisson
adds the very important leniark, that V being determined by his process as
above, then /* being the constant of vis viva, and the constants of the other
given integral equations being e,f, &c., the remaining integrals of the
problem are *

dY dY ^ dY

where T,l,m,.. are new arbitrary constants. But, as before remarked, the
expression for dY is not always a complete differential. Poisson accord-
ingly inquires into and determines (but not in a precise form) the condi-
tions which must be satisfied, in order that the expression in question may
be a complete differential. He gives, as an example, the case of the motion
of a body in space under the action of a central force ; and, secondly, the
case considered in Jacobi's letter of 1836, which he refers to, viz., here
dY=x'dx+y'dy, and when the two integral equations are one of them, the
equation of vis viva ^{x""+y"-) — \5-{-h, and the other of them any integral
equation a = F {x,y,x',y') whatever (subject only to the restriction that a
is not a function o^ x,y,x'''+y'^-, the necessity of which is obvious) the con-
dition is satisfied per se, and, consequently, x'dx+y'dy is a complete
differential, and its integral gives (in value, although as before remarked
not iu form) the principal function V; and such value of V gives the two
integral equations obtained in Jacobi's letter.

32. Jacobi's note of the 29th of November, 1836, ' On the Calculus of
Variations, and the Theory of Differential Equations.' — The greater part of
this note relates to the differential equations which occur in the calculus of

dY
* Poisgou writes-TT =—t-\-e ; there seems to be a mistake as to the sign of h running

through the memoir. Correcting this, and putting —r for e, we have the formula ___. ^_|. ^
given in the text.

ON THEORETICAL DYNAMICS. 17

variations, including, indeed, the differential equationsof dynamics, but which
belong to a different field of investigation. The latter part of the note relates
more immediately to the differential equations of dynamics. The author re-
marlcs, that, in any dynamical problem of the motion of a single particle for
which the Y>fmciTp\e o( vis viva holds good, if, besides the integral of vis -viva,
there is given any other integral, the problem is reducible to the integration
of an ordinary differential equation of two variables, and that it is always
possible to integrate this equation, or at least discover hy a precise and
general rule the factor which renders it integrable. This would seem to
refer to Jacobi's researches on the theory of the ultimate multiplier, but the
author goes on to refer to a preceding communication to the Academy of
Paris (the before-mentioned letter of 1836), which does not belong (or, at
least, does not obviously belong) to this theory. He speaks also of a class
of dynamical problems, viz. that of the motion of a system of bodies which
mutually attract each other, and which may besides be acted upon by
forces in parallel lines, or directed to fixed centres, or even to centres the
motion of which is given ; and, he remarks, in the solution of such a pro-
blem, the system of differential equations being in the first instance of the
order 2w (that is, being a system admitting of 2/i arbitrary constants), then
if one integral is known, it is possible by a proper choice of the quantities
selected for variables to reduce the system to the order 2w— 2. If another
integral is known, the equation may in like manner be reduced to a system
of the order 2n — 4, and so on until there are no more equations to be in-
tegrated ; and thus the operations to be effected depend only upon quadra-
tures. All this seems to refer to researches of Jacobi, which, so far as I
am aware, have not hitherto been published. The results correspond with
those recently obtained by ^owr, post, Nos. 66 and 67.

33. Jacobi's memoir of 1857. — .Jacobi refers to the memoirs of Sir
W. R. Hamilton, and he reproduces, in a slightly different form, the inves-
tigation of the fundamental property of the principal function S. The case
considered is that of a system of n particles, the coordinates of which are
connected together by any number of equations ; but it will be sufficient
here to attend to the case of a single free particle. The equations of motion
are assumed to be

^_rfU d^_d\J <Pz_d\3
""de ~dx ' ""df ~dy ' "^dt^ ~dz '

But U is considered as being a function of x,i/, z and of the time t, that is,
it is assumed that the condition of vis viva is not of necessity satisfied. The
definition of the function S is

S-f Z' [\]+^(x''-\-y'-'+z'-')\dt, which,

when the equation oi vis viva is satisfied, that is, when T=^\m{x''^-\-y'^-\-z"')

= U+ /«, agrees with Sir W. R. Hamilton's definition S=2r \]dt+ht. The

function S is considered as being, by means of the integral equations as-
sumed as known, expressed as a function of t, of the coordinates x, y, z, and
of their initial values a, b, c. And then it is shown that S satisfies the equa-
tions

dS , dS , dS ,
^=mx , -j-=^my , ■j-=-mz ,

dS , dS ,, dS ,

da do dc

1857.

18 REPORT — 1857.

SO that the intermediate and final integrals are expressed by means of the
principal function S.

34.. But Jacobi proceeds, " the definition assumes the integration of the
differential equations of the problem. The results, tlierefore, are only
interesting in so far as they have reduced the system of integral equations
into a remarkable form. We may, however, define the function S in a
quite different and very much more general manner." And then, attending
only to the case of a system of free particles, he gives a definition, which, in
the case of a single particle, is as follows : —

Jacobi's principal function S.— The equations of motion being as before

di-x rfU ff-y rfU dh d\}
dt- dx df dy df dz

(where U is in general a function of x^y, z and #), then S is defined to be a
complete solution of the partial differential equation

-dt^^\\dx) +V^j -^\dz) i -^'

A complete solution, it will be recollected, means a solution containing as
many arbitrary constants as there are independent variables in the partial
differential equations; in the present case, tlierefore, four arbitrary con-
stants. But one of these constants may be taken to be a constant attached
to the function S by mere addition, and which disappears from the dif-
ferential coefficients, and it is only necessary to attend to the other three
arbitrary constants. S is consequently a function of t,x,y,z, and of the
arbitrary constants a, /3, y, satisfying the partial differential equation. And
this being so, it is shown that the integrals of the problem are

a-=^nx,-^=my,^=mz,

dS_ dS_ dS_
d^-^'dji-^"' dy""'

where X, ju, v are any other arbitrary constants, viz., the first three equa-
tions give the intermediate integrals, and the last three equations give the
final integrals of tiie problem.

Jacobi proceeds to give an analogous definition of the principal function
V as follows : —

35. Jacobi's principal function V. — First, when the condition of vis viva
is satisfied. Here V is a complete solution of the partial differential
equation

where h is the constant of vis viva. The partial differential equation con-
tains only three independent variables ; and since as before one of the
constants of the complete solution may be taken to be a constant attached
to V by mere addition, and which disaj)pears from the differential co-
efficients, we may consider V as a function of t,x,y,z, and of the two con-
stants of integration a and /3. But V will of course also contain the
constant h, which enters into the partial differential equation. The integrals
of the problem are then shown to be

ON THEORETICAL DYNAMICS. 19

dY , dY , dY

dY_ dY_. dY_

■where r, X, fi are new arbitrarj' constants.

36. Jacobi's principal function V. — Secondly, when the equation of vis
viva is not satisfied. Here U contains the time t, and we have no such
equation as T=U + /<, but along with the coordinates x,y,z there is intro-
duced a new variable H, and V is defined to be a complete integral of the
partial differential equation

where, in the expression for U, it is assumed that^ is replaced by -— -. There

are, consequently, four independent variables, and a complete solution must
contain, exclusively of the constant attached to V by mere addition, and
which disappears from the differential coefBcients, three arbitrary constants
a,/3, y. The integral equations are shown to be

-j—=mx.
dx

dY , dY

(la

dY dY

dH. '

where X, /x, r are arbitrary constants, viz., eliminating H from the first
three equations by the assistance of the last equation, we have the inter-
mediate integrals ; and eliminating H from the second three equations by
the assistance of the last equation, we have the final integrals. The substi-

tution of the above values -—, &c., in the partial differential equation gives
dx

T=U + H, that is, H( = T — U) is that function which, when the condition

of vis viva is satisfied, becomes equal to h, the constant of vis viva.

Jacobi's extension of the theory to the case where the condition of vis
viva is not satisfied, appears to have attracted very little attention ; it is
indeed true, as will be noticed in the sequel, that this general case can be
reduced to the particular one in which the condition of vis viva is satisfied,
but there is not it would seem any advantage in making this reduction ;
the formulae for the general case are at least quite as elegant as those for
the particular case.

37. Jacobi, after considering some particular dynamical applications, pro-
ceeds to apply the theory developed in the first part of the memoir to the
general subject of partial differential equations ; the differential equations
of a dynamical problem lead to a partial differential equation, a complete
solution of which gives the integral equations. Conversely, the integral
equations give the complete solution of the partial differential equation, and
applying similar considerations to any partial differential equation of the
first order whatever, it is shown (what, but for Cauchy's memoir of 1819,
which Jacobi was not acquainted with*, would have been a new theorem)

* Jacobi refers to Lagrange's ' Lemons sur la Theorie des Fonctions,' and to a memoir by
Pfaff in the ' Berlin Transactions' for 1814, as containing, so far as he was aware, every-

20 REPORT — 1857.

that the solution of the partial differential equation depends on the integra-
tion of a single system of partial diflPerential equations. The remainder of
the memoir is devoted to the discussion of this theorj' and of the integration
of the Pfaffian system of ordinary differential equations, a system which is
also treated of in Jacobi's memoir of 1844', ' Theoria Novi Multiplica-
toris,' &c. I take the opportunity of referring here to a short note by
Brioschi, ' Intorno ad una Proprieta delle Equazione alle Derivate Parziale
del Primo Ordine,' Tortolini, t. vi. pp. 426-429 (1855), where the theory
of the integration of a partial differential equation of the first order ia pre-
sented under a singularly elegant form.

38. Jacobi's note of 1837, 'On the Integration of the Differential Equa-
tions of Dynamics.' — Jacobi remarks that it is possible to derive from
Lagrange's form of the equations of motion an important profit for the
integration of these equations, and he refers to his communication of the
29th of November 1839 to the Academy of Berlin, and to his former note
to the Academy of Paris. He proceeds to say, that whenever the condition
of vis viva holds good, he had found that it was possible in the integration
of the equations of motion to follow a course such that each of the given
integrals successively lowers by two unities the order of the system; and
that the like theorem holds good when the condition of vis viva is not satis-
fied, that is, when the force function involves the time (this seems to be a
restatement, in a more general form, of the theorems referred to in the note
of the 29th of November 1836 to the Academy of Berlin); and he men-
tions that he had been, by his researches on the theory of numbers, led
away from composing an extended memoir on the subject. The note then
passes on to other subjects, and it concludes with two theorems, which are
given without demonstration as extracts from the intended work he had
before spoken of. These theorems are in effect as follows: —

I. Let

d'x d\J dry d\J d'z dU

'"5?=rfS' "'dP=d^' ""le^lb' ^'-

be the 3« differential equations of the motion of a free system, and

iSm(a;'- +2/'" + z'-)dt= U + h,

the equation of vis viva.

Let V be a complete solution of the partial differential equation

that is, a solution containing, besides the constant attached to V by mere
addition, 3n — 1 constants n(aj, a^... a3„_j), then first the integral equa-
tions are

<^V_. dY_ .

where /3(i(3p/32.../33„_,) and r are new arbitrary constants: this is in fact
the theorem already quoted from Jacobi's memoir of 1837, and it is in the
present place referred to as an easy generalisation of Sir W. R. Hamilton's

thing essential which was known in reference to the integration of partial differential equa-
tions of the first order ; he refers also to his own memoir ' Ueher die Pfaffsche Methode,'
&c., Crelle, t. ii. pp. 347-358 (1827), as presenting the method in a more symmetrical and
compendious form, but without adding to it anything essentially new.

ON THEORETICAL DYNAMICS. 21

formulae. But Jacobi proceeds (and this is given as entirely new) that the
disturbed equations being

d-x d\] do, dry dV da dPz rfU dD.
df dx dx' dt- dy dy' df dz dz

then the equations for the variations of the above system of arbitrary con-
stants are

da do, dh d€l

di~ d^""di~ 17'

d^__jKh ^__^.
dt~ da'" dt~ dh'

so that the constants form (I think the term is here first introduced) a
canonical system.

Jacobi observes, that in the theory of elliptic motion, certain elements
which he mentions, form a system of canonical elements, and he remarks,
that since one complete solution of a partial differential equation gives all
the others, the theorem leads to the solution of another interesting problem,
viz, " Given one system of canonical elements, to find all the other systems."
This is effected by means of the second theorem, which is as follows : —

II. Given the systems of differential equations between the variables
a(ai, Oj . . a J and h{h^, b^... b^)

da__dH. db_dn

dt~ db'"' 'di~da'"
M'here H is any function of the variables a,.., and b,...; and let
o(aj, ttj . . . a^) and /3(/3i, (i^ • • /?,„) be two new systems of variables connected
with the preceding ones by the equations

#=/3,... ^=-b,...
da da

where \^ is a function of a,...b,... without f or the other variables, then
expressing H as a function of t and the new variables a, . . . and ft, . -.,
these last variables are connected together by equations of the like form
with the original system, viz. : —

da^__dn dft__dH

dt~ dft"" dt~ da'"'
Jacobi concludes with the remark, that other theorems no less general may
be deduced by putting ;// + X\^j+/x»^2+ • • • instead of ;//, and eliminating the
multipliers X, /x, . . by means of the equations \/'i=0 ,\p2^=0, . ., and that the
demonstrations of the theorems are obtained without difficulty.

39. Jacobi's note of the 21st of November, 1838. — Jacobi refers to a
memoir by Encke in the Berlin ' Ephemeris' for 1837, ' iiber die Speciellen
Storungen,' where expressions are given for the partial differential coefficients
of the values in the theory of elliptic motion of the coordinates x,y, z and the
velocities x', y', z' with respect to the elements ; and he remarks, that if
Encke's elements are replaced by a system of elements a, ft, y, a', ft', y' which
he mentions, connected with those of Encke by equations of a simple form,
then considering first x,y, z, x',y', z' as given functions of t and the elements,
and afterwards the elements a, ft, y, a', ft', y' as given functions of t and
x,y,z, x',y',z', there exists the remarkable theorem that the thirty-six partial

differential coefficients -^, -^^ &c., and the thirty-six partial differential co-

22 REPORT — 1857.

efficients -r- -j^, &c. are equal to each other, or differ only in their sign, viz.
da, dj3

dx da dx' da' 'dx'

da~~

dx''

' M~d^" d^~d^' d^~

dx'

thirty-six equations in all, viz. the pair a, a' of corresponding elements may
be replaced by the pair /3, /3' or y, y' : and then in each of the twelve equa-
tions y,y or z,z' may be written instead of x,x'. Tlie like applies to a
system of constants which are the initial values of any system whatever of

coordinates p, . ., and the initial values of the differential coefficients 0'=—-,

-dp

&c. of the force function T with respect to p,.. ; and for every system of
elements which possess the property first mentioned, the form ulce for tlm varia-
tions assume the simplest possible form, inasmuch as the variatioji of each
element is equal to a single partial differential coefficient of the disturbiiig
^unction icith the coefficient +1 or —\, as is hnoton to he the case with the
last-mentio7ied system of elements ; in other words, if a,... and b,... be a
system of elements corresponding to each other in pairs, such that

dp db dp da dq db dq da

da dq' db dq' da dp'' db dp

(where a, b may be replaced by any other corresponding pair of elements,
and p, q by any other corresponding pair of variables), then the elements
a, . . . and b,... form a canonical system.

40. Jacobi's note of 1840 in the ' Comptes Rendus,' calls attention to the
theorem contained in the passage quoted above from Poisson's memoir of
1808, a theorem which Jacobi characterizes as " la plus profonde decouverte
de M. Poisson," and as the theorem " le plus important de la Mecanique et
de cette partie du calcul integrale qui s'attache a I'integration d'un systeme
d'equations differentielles ordinaires" ; and he proceeds, " le theoreme dont
il est question enonce convenablement est le suivant — un nombre quelconque
de points materials etant tires par des forces et soumis a des conditions telles
que le principe des forces vives ait lieu, si Ton connait outre que I'integrale
fournie par ce principe deux autres integrales, on en peut deduire une
troisieme d'une maniere directe et sans meme employer des quadratures.
En poursuivant le meme precede on pourra trouver une quatrieme une
cinquieme integrale et en general on parviendra a cette maniere a deduire
des deux integrales donnees toutes les integrales ou ce qui revient au meme
I'integration complete du probleme. Dans des cas particuliers on retombera
sur line combinaison des integrales dejd trouvees avant quon soit parvenu a.
toutes les integrales du probleme, mais alors les deux integrales donnees jouis-
sent des proprietes particulieres dont on peut tirer un autre profit pour Cinte-
gration des equations dynamiques proposees. C'est ce qu'on verra dans un
ouvrage auquel je travaille depuis plusieurs annees et dont peut-etre je
pourrai bientot faire commencer I'impression."

41. Liouville's addition to Jacobi's letter of 1840.-— This contains the de-
monstration of a theorem similar to that given in Jacobi's letter of 1836, and
Poisson's memoir of 1837, but somewhat more general; the sj'stem con-
sidered is a system of four differential equations of tlie first order: — •

dx_ d\]_ rfy rfU dy^_.d^ ^__X^

dt dx" dt ~ dx ' dt ~ dy" dt~ dy'

where U is a function of x,y,x',y', and X is a function of x,y,x',y' and t.

ON THEORETICAL. DYNAMICS.

One integral is U=:a, and if there be another integral Y=b where V is a
function oi x,y, x\y' only, then x',y' being by means of these two integrals
expressed as a function of x,y,a,b, it is shown that x'dx+y^dy is an exact

differential, and putting ^(x'dx+y'dy)=6, then that -tt=(^ is a new integral

of the given equations ; and in the case where \ is a function of t only, the

remaining integral is — =(\c?<4-a.
da J

42. Binet's memoir of 1841 contains an exposition of the theory of the
variation of the arbitrary constants as applied to the general system of
equations

^rfF_rfF rfL dM
dt dx' dx' dx ^ dx

where F is any function of ^, and of the coordinates x,y,z.. of the different
points of the system, and of their differential coefficients x',y',z\ &c., and
L=0, M=0, &c. are any equations of equation between the coordinates
x,y,z,.. of the different points of the system, these equations may contain
t, but they must not contain the differential coefficients x',y',z',.. The form
is a more general one than that considered by Lagrange and Poisson. The
memoir contains an elegant investigation of the variations of the elements of
the orbit of a body acted upon by a central force, the expressions for the
variations being obtained in a canonical form ; and there is also a discussion
of the problem suggested in Poisson's report of 1830 on the manuscript work
of Ostrogradslcy.

43. Jacobi's note of 1842, in the ' Comptes Rendus,' announces the general
principle (being a particular case of the theorem of the ultimate multiplier)
stated and demonstrated in the memoir next referred to, and gives also the
rule for the formation of the multiplier in the case to which the general
principle applies.

44. Jacobi's memoir of 1842, ' De Motu Puncti singularis': the author
remarks, that the greater the difficulties in the general integration of the
equations of dynamics, the greater the care which should be bestowed on
the examination of the dynamical problems in which the integration can be
reduced to quadratures; and the object of the memoir is stated to be the
examination of the simplest case of all, viz. the problems relating to the
motion of a single point. The first section, entitled, ' De Extensione quadam
Principii Viriumvi varum,' contains a remark which, though obvious enough,
is of considerable importance : the forces X, Y, Z which act upon a particle,
may be such that Xdx+Ydy + 7idz is not an exact differential, so that if the
particle were free, there would be no force function, and the equations of
motion would not be expressible in the standard form. But if the point
move on a surface or a curve, then in the former case Xdx-\-Ydy-\-Zdz
will be reducible to the form Fdp + Qdq, which will be an exact differential
if a single condition (instead of the three conditions which are required in
the case of a free particle) be satisfied, and in the latter case it will be
reducible to the form Fdp, which is, per se, an exact differential. In the
case of a surface, the requisite transformation is given by the Hamiltonian
form of the equations of motion, which Jacobi demonstrates for the case in
hand ; and then in the third section, with a view to its application to the
particular case, he enumerates the general proposition "quae pro novo prin-
cipio mechanico haberi potest," which is as follows : —

" Consider the motion of a system of material points subjected to anj

24 REVORT — 1857.

conditions, and let the forces acting on the several points in the direction of
the axes be functions of the coordinates alone: if the determination of the
orbits of the several points is reduced to the integration of a single differ-
ential equation of the first order between two variables, for this equation
there may be found, by a general rule, a multiplier which will render it
integrable by quadratures only."

And for the particular case the theorem is thus stated : —
"Given, three differential equations of the first order between the four
quantities q^iq^^PxiPv

dq, : dq, : dp, : dp,=— : ^^ : -^+Q. : -^+Q^'

in which Q,, Qj are functions of q,, q^ only ; and suppose that there are

known two integrals a,/3, and that by the aid of these PxtP^^i -j— , -5— are

dp, dp.^

expressed by means of the quantities q,, q^ and the arbitrary constants

a, /3; there then remains to be integrated an equation of the first order,

— dq^ — ——dq,=iO between the quantities q^^q.^, by which is determined
dp, dp^

the orbit of the point on the given surface : I say that the left-hand side of

the equation multiplied by the factor

dp, dp„ dp^ dp,
da dl3 da djS*

will be a complete differential, or will be integrable by quadratures alone,"
and the demonstration of the theorem is given. The remainder of the
memoir, sections ■i to 7, is occupied by a very interesting discussion of
various important special problems.

45- There is an important memoir by Jacobi, which, as it relates to a
special problem, I will merely refer to, viz. the memoir ' Sur 1' Elimination
des Noeuds dans le probleme des trois Corps,' Crelle, t. xxvii. pp. 115-131
(ISiS). The solution is made to depend upon six differential equations, all
of them of the first order except one, which is of the second order, and
upon a quadrature.

46. Jacobi's memoir of ISW, ' Theoria Novi Multiplicatoris,' &c — This
is an elaborate memoir establit-hing the definition and developing the pro-
perties of the "multiplier" of a system of ordinary differential equations, or
of a linear partial differential equation of the first order, with applications to
various systems of differential equations, and in particular to the differential
equations of dynamics. The definition of the multiplier is as follows, viz.
the multiplier of the system of differential equations

dx:di/:dz:dw...=X:Y:Z:W...

or of the linear partial differential equation of the first order

xf+Yf:zf+w|:+..=o

dx dy dz dw
is a function M, such that

rfMX , dUY , rfMZ c?MW

~ii — I--:? — +—^~+—i 1-..=0.

dx dy dz dw

One of the properties of the multiplier is that contained in the theorem of
the ultimate multiplier, viz. that when all the integrals (except one) of the
system of partial differential equations are known, and the system is thereby

ON THEORETICAL DYNAMICS. 25

reduced to a single differential equation between two variables, then t^^
multiplier (in the ordinary sense of the word) of this last equation is MV,
where M is the multiplier of the system, and V is a given derivative of the
known integrals, so that the multiplier of the system being known, the in-
tegration of the last differential equation is reduced to a mere quadrature.
To explain the theorem more particularly, suppose that the system of given
integrals, that is, all the integrals (except one) of the system are represented
byj9=a, 5'=/3, . . ., and let u, v be any two functions whatever of the variables,
so that jo, q,.,.u,v are in number equal to the system x, y, z, to, ... then if

ax ay az aw

X^+Yj^+Z^+wJi+..=V,
dx ay as aw

the last differential equation takes the form

\]dv—'Wdu=0,

where it is assumed that U and V are, by the assistance of the given in-
tegrals, expressed as functions of m, v and the constants of integration. The
multiplier of the last-mentioned equation is MV, where M is the multiplier
of the system, and V may be expressed in either of the two forms

_ ^(x,y,z,w,....)

'd{a,(i, u,v)

and

l'd{x,y,s,w,..

where the symbols on the right-hand sides represent functional determinants ;
in the first form it is assumed that x,y, z,w, . . are expressed as functions of
a, j3, . . . zi, V, and in the second form that p,g,...u,v are expressed as func-
tions of x,y,s,w,..,, but that ultimately p,q,... are replaced by their
values in terms of the constants and u, v ; the first of the two forms, from its
not involving this transformation backwards, appears the more convenient.

47. I have thought it worth while to quote the theorem in its general
form, but we may take for u, v any two of the original variables, and if, to
fix the ideas, it is assumed that there are in all the four variables x,y, z, w,
then the theorem will be stated more simply as follows : — given the system
of differential equations

dx-.dy.dz: dw=X : Y : Z : W,

and suppose that two of the integrals arep=:a,q=j3, the last equation to be
integrated will be

Wdz—Zdw=0,

where, by the assistance of the given integrals, W, Z are expressed as func-
tions of s, w. And the multiplier of this equation is MV, where M is the
multiplier of the system, and V, attending only to the first of the two forms,
is given by the equation

„ _ 5(a^>y)

^ 9(a,/3)'
which supposes that x, y are expressed as functions of a, /3, z, w.

26 REPORT — 1857.

48. Jacobi applies the theorem of the ultimate multiplier to the dif-
ferential equations of dynamics, considered first in the unreduced La-
grangian form, where the coordinates are connected by any given system of
equations of condition ; secondly, in the reduced or ordinary Lagrangian
form ; and, thirdlj', in the Hamiltonian form. The multiplier can be found
for the first two forms, and the expressions obtained are simple and elegant ;
but, as regards the third form, there is a further simplification : the multiplier
M of the system is equal to the unitj', and the multiplier of the last equation
is therefore equal to V. The two cases are to be distinguished in which t
does not, or does enter into the equations of motion ; in the latter case the
theorem furnished by the principle of the ultimate multiple is the same as
for the general case of a system, the multiplier of which is known, viz., the
theorem is, given all the integrals except one, the remaining integral can be
found by quadratures only. But in the former case, which is the ordinary
one, including all the problems in which the condition of vis viva is
satisfied, there is a further consequence deduced. In fact, the time t may
be separated from the other variables, and the system of differential equa-
tions reduced to a system not involving the time, and containing a number
of equations less by unity than the original system, and the theorem of the
ultimate multiplier applies to this new system. But when the integrals of
the new system have been obtained, the system may be completed by the
addition of a single diff'erential equation involving the time, and which is
integrable by quadratures ; the theorem consequently is, given all the
integrals except two, these given integrals being independent of the time,
the remaining integrals can be found by quadratures only. This is, in fact,
the ' Principium generale mechanicum' of the memoir of 1842.

The last of the published writings of Jacobi on the subject of dynamics
are the ' Auszug zweier Schreiben des Professors Jacobi an Herrn Director
Hansen,' Crelle, t. xlii. pp. 12-31 (1851): these relate chiefly to Hansen's
theory of ideal coordinates.

49. The very interesting investigations contained in sevei-al memoirs by
Liouville (' Liouville,' t. xi. xii. and xiv., and the additions to the ' Con-
naissance des Temps' for 1849 and 1850) in relation to the cases in which
the equations of motion of a particle or system of particles admit of integra-
tion, are based upon Jacobi's theory of the S Function, that is, of the function
which is the complete solution of a certain partial diff'erential equation of
the first order ; the equation is given, in the first instance, in rectangular
coordinates, and the author transforms it by means of elliptic coordinates
or otherwise, and he then inquires in what cases, that is, for M'hat forms of
the force function, the equation is one which admits of solution. A more
particular account of these memoirs does not come within the plan of the
present report.

50. Desbove's memoir of 1848 contains a demonstration of the two
theorems given in Jacobi's note of 1837, in the ' Comptes Rendus;' and, as
the title imports, there is an application of the theory to the problem of the
planetary perturbations ; the author refers to the above-mentioned memoirs
of Liouville as containing a solution of the partial differential equation on
■which the problem depends, and also to a memoir of his own relating to the
problem of two centres, where the solution is also given ; and from this
he deduces the solution just referred to, and which is employed in the
present memoir. Jacobi's theorem gives at once the formulae for the varia-
tion of the arbitrary constants contained in the solution. The material
thing is to determine the .signification of these constants, which can of
course be done by a comparison of the formulae with the known formulae of

ON THEORETICAL DYNAMICS. 2^

elliptic motion ; the author is thus led to a sj'stem of canonical elements
similar to, but not identical with, those obtained by Jacobi.

51. Serret's two notes of 1848 in the ' Comptes Rendus.' — These relate
to the theory of Jacobi's S function, that is, of the function considered as the
complete solution of a given partial differential equation of the first order.
In the first of the two notes, which relates to a single particle, the author
gives a demonstration founded on a particular choice of variables, viz.,
those which determine orthotomic surfaces to the curve described by the
moving point. The process appears somewhat artificial.

52. Sturm's note of 1848, in the ' Comptes Rendus,' relates to the theory
of Jacobi's S function, that is, of this function considered as the complete
solution of a given partial differential equation of the first order. The
force function is considered as involving the time t, which, however, is no
more than had been previously done by Jacobi.

53. Ostrogradsky's note of 1848. — This contains an important step in the
theory of the forms of the equations of motion, viz.. it is shown how, in the
case where the force function contains the time, the equations of motion
may be transformed from the form of Lagrange to that of Sir W. R. Ha-
milton. If, as before, the force function (taken with the contrary sign to
that of Lagrange) is represented by U, then putting, as before, T + U=Z
(the author writes V instead of Z), in the case under consideration Z will
contain not only terms of the second order and terms of the order zero in the
differential coefficients of the coordinates q, .. ., but also terms of the first
order, that is, Z will be of the form Z=Z2 + Zi + Zq, and putting H=Z2—Zq,
this new function H being expressed as a function of the coordinates q,..
and of the new variables j!?, .. ., then the equations of motion take the Ha-
miltonian form, viz. —

dq_dil dp _ dVi
dt~ dp' di~ dq '

In the theory of the transformation, as originally given by Sir W. R. Hamil-
ton, Z2=T, Z,=0, Zq=U, and, consequently, H=Z; — Zq=T — U as
before.

54. Brassinne's memoir of 1851. — The author reproduces for the La-
grangian equations of motion

d dZ dZ

dt d^' dE ~^'

the demonstration of the theorem

d f^dZ ^ ,. ^dZ^,. , X

and he shows that a similar theorem exists with regard to the system

_^ dZ d_dz _dZ_
de di!''^ dt di! d^ '

and with respect to the corresponding system of the mth order. The
system in question, which is, in fact, the general form of the system of
equations arising from a problem in the calculus of variations, had pre-
viously been treated of by Jacobi, but the theorem is probably new. In
conclusion, the author shows in a very elegant manner the interdependence

38 REPORT — 1857.

of the theorem relating to Lagrange's coefficients (a, b), and of the corre-
sponding theorem for the coefficients of Poisson.

55. Bertrand's memoir of 1851, 'On the Integrals common to several
Mechanical Froljlems,' is one of great importance, but it is not very easy
to explain its relation to other investigations. The author remarks that,
given the integral of a mechanical proijlem, it is in general a question ad-
mitting of determinate solution to find the expression for the forces ; in
other words, to determine the problem which has given rise to the integral ;
at least, this is the case when it is assumed that the forces are functions of
the coordinates, without the time or the velocities ; and he points out how
the solution of the question is to be obtained. But, in certain cases, the
method fails, that is, it leads to expressions which are not sufficient for the
determination of the forces; these are the only cases in which the given
integral can belong to several different problems; and the method shows
the conditions necessary, in order that these cases may present themselves.
It is to be remarked that the given integral must be understood to be one
of an absolutely definite form, such for instance as the equations of the
conservation of the motion of the centre of gravity or of areas, but not such
as the equation of vis viva, which is a property common indeed to a
variety of mechanical problems, but which involves the forces, and is there-
fore not the same equation for different problems. The author studies in
particular the case where the system consists of a single particle ; he shows,
that when the motion is in a plane, the integrals capable of belonging to
two or more different problems are two in number, each of them involving
as a particular case the equation of areas. When the point moves on a
surface, he arrives at the remarkable theorem — " In order that the equa-
tions of motion of a point moving on a surface may have an integral inde-
pendent of the time, and common to two or more problems, it is necessary
that the surface should be a surface of revolution, or one which is develop-
able upon a surface of revolution." When the condition is satisfied, he gives
the form of the integral, and the general expression of" the forces in the
problems for which such integral exists. He examines, lastly, the general
case of a point moving freely in space. The number of integrals common to
several problems is here infinite. After giving a general form which com-
prehends them all, the author shows how to obtain as many particular
forms as may be desired : it is, in fact, only necessary to resolve any pro-
blem relative to motion in a plane, and to effect a certain simple trans-
formation on the integrals ; one thus obtains a new equation which is the
integral of an infinite number of different problems relating to the motion
in space."

As an instance of the analytical forms on which these remarkable results
depend, I quote the following, which is one of the most simple : — " If an
integral of the equations of motion of a point in a plane belongs to two dif-
ferent problems, it is of the form

a='F(<j>',x,i/,t),

where 0' is the derivative with respect to t, of a function of x, y, which
equated to zero gives the equation of a system of right lines."

5^. Bertrand's memoir of 1851, ' On the Integration of the Differential
Equations of Dynamics.' — The author refers to Jacobi's note of 1840, in
relation to Poisson's theorem ; and after remarking that there are very few
problems of which two integrals are not known, and which therefore might
not be solved by the method if it never failed ; he observes that unfor-
tunately there are (as was known) cases of exception, and that, as his me-

ON THEORETICAL DYNAMICS. 29

moir shows, these cases are far more numerous than those to which the
method applies; thus for example tl c equation of vis viva, combined with
any other integral whatever, leads to an illusory result. The theorem of
Poisson may lead to an illusory result in two ways ; either the resulting
integral may be an identity 0=0, or it may be an integral contained in the
integrals already known, and which consequently does not help the solu-
tion. It appears by the memoir that the two cases are substantially the
same, and that it is sufficient to study the case in which tiie two integrals
lead to the identity 0=0. Suppose that one integral is given, the author
shows that there always exist integrals which, combined with the given
integral, lead to an illusory result, and he shows how the integrals which,
combined with the given integral, lead to such illusory result, are to be
obtained. For instance, in the case of a body moving round a fixed centre,
there are here two known integrals ; first, the equation oi' vis viva (but this,
as already remarked, combined with any other integral whatever, leads to an
illusory result) ; secondly, the equation of areas.

The question arises, what are the integrals which, combined with the
equation of areas, lead to an illusory result? The integrals in question
are, in fact, the other two integrals of the problem ; so that the inquiry into
the integrals which give an illusory result, leads here to the completion of
the solution. The like happens in two other cases which are considered,
viz. 1. the problem of two fixed centres, and the problem of motion i?i piano
when the forces are homogeneous functions of the coordinates of the degree.
2. Indeed the case is the same for all problems whatever, where the co-
ordinates of the points of the system can be expressed by means of two inde-
pendent variables.

The next problem considered is that where two bodies attract each other,
and are attracted to a fixed centre. Suppose, first, the motion is in piano,
then as in the former case all the integrals will be found by seeking for
the integrals which, combined with the equation of areas, give an illusory
result. When the motion is in spa'ce, the principle of areas furnishes three
integrals (the equation of vis viva is contained in these three equations) ;
the integrals which, combined with the integrals in question, give illusory
results, are eight in number, and, to complete the solution, there must be
added to these one other integral, which alone does not put the method in
default. The problem of three bodies is then shown to be reducible to the
last-mentioned problem ; and the same consequences therefore hold good
with respect to the problem of three bodies, viz., there are eight integrals
which, combined with the integrals furnished by the principle of areas, give
illusory results. To complete the solution it would be necessary to add to
these a ninth integral, which alone would not put the method into default.

57. The author remarks that it appears by the preceding enumeration
that the method of integration, based on the theorem of Poisson, is far
from having all the importance attributed to it by Jacobi. The cases of
exception are numerous; they constitute, in certain cases, the complete
solutions of the problems, and embrace in other cases eleven integrals out
of twelve. But it would be a misapprehension of his meaning to suppose
that, according to him, the cases in which Poisson's theorem is usefully
applicable ought to be considered as exceptions. The expression would not
be correct even for the problems, which are completely resolved in seeking
for the integrals which put the method into default ; there exists for these
problems, it is true, a system of integrals which give illusory results ; but
these integrals, combined in a suitable manner, might furnish others to
which the theorem could be usefully applied.

30 llEPOBT— 1857.

The author remarks, that, in seeking the cases of exception to Poisson's
theorem, there is obtained a new method of integration, which may lead to
useful results ; and, after referring to Jacobi's memoir on the elimination of
the nodes in the problem of three bodies, he remarks that, by his own new
method, the problem is reduced to the integration of six equations, all of
them of the first order ; so that he effectuates one more integration than had
been done by Jacobi ; and he refers to a future memoir (not, I believe, yet
published) for the further development of his solution.

58. To give an idea of the analytical investigations, the equations of
motion are considered under the Hamiltonian form

dq_dR dp__dH
dt~ dp'' dt~ dq'

where H is any function whatever of §-, . . . ja, . . . without t, and then a given
integral being

a=(l>{q,..p,...),
the question is shown to resolve itself into the determination of an integral
fi=^{q, . . . p, . . .), such that identically (a,/3)=0 or else (a,;3)=l, where
(a, /3) represents, as before, Poisson's symbol, viz.

if for shortness

S(a,/3) _da d^_da dfi
^(q, jo) dq dp dp dq

The partial differential equations (a, /3)=0 or(a, ^)=1, satisfied by cer-
tain integrals /3, are in certain cases, as Bertrand remarks, a precious method
of integration leading to the classification of the integrals of a problem, so
as to facilitate their ulterior determination : it is in fact by means of them
that the several results before referred to are obtained in the memoir.

b%. Bertrand's note of 1852 in the ' Comptes Rendus.' — This contains the
demonstration of a theorem analogous to Poisson's theorem (a, /3)=const.,
but the function on the left-hand side is a function involving four of the
arbitary constants and binary combinations of pairs of corresponding vari-
ables, instead of two arbitrary constants and the series of pairs of corre-
sponding variables.

60. Bertrand's notes, vi. and vii,, to the third edition of the ' M^canique
Analytique,' 1853, contain a concise and elegant exposition of various
theorems which have been considered in the present report. The latter of
the two notes relates to the above-mentioned theorem of Poisson, and places
the theorem in a very clear light, in fact, establishing its connexion with the
theory of canonical integrals. Bertrand in fact shows, that, given any in-
tegral a of the differential equations (in the last-mentioned form, the whole
number of equations being 1K), then the solution may be completed by
joining to the integral a a system of integrals /3i, ^.2---ftzk-\'> which, com-
bined with the integral «, give to Poisson's equation an identical form, viz.
which are such that

(a,/3„)=l («,/3,)=0,...(o,/3,,_,) = a
This, he remarks, shows, that, given any integral a, the solution of the pro-
blem may be completed by integrals /3i,/3o... /^a^-i, which, combined with
a, give all of them an identical form to the theorem of Poisson. But it is
not to be supposed that all the integrals of the problem are in the same case.
In fact, the most general integral is »j=w(a, /3i, ^^ . . I^2k-i)> ^"^ ^^ ** ^* ^"°^

ON THEORETICAL DYNAMICS. SI

seen that (a, jj)=(o, /3i) _^=— |-, consequently the expression (a, ?/) will

not be identically constant unless — ^ is so : but the integrals, in number

apj
infinite, which result from the combination of a, with /3o, /33... /Bg/j.-! com-
bined with the integral a, give identical results. Only the integrals which
contain /3, lead to results which are not identical. Tlie integrals a and /3p
connected together in the above special manner, are termed by the author
conjugate integrals.

61. Brioschi's two notes of 1853. — The memoir ' Sulla Variazione,' &c.
contains reflections and developments in relation to Bertrand's method of
integration and to canonical systems of integrals, but I do not perceive that
any new results are obtained.

The note, ' Intorno ad un Teorema di Meccanica,' contains a demonstration
of the theorem in Bertrand's note of 1852 in the ' Comptes Rendus,' and an
extension of the theorem to the case of a combination of any even number
of the arbitrary constants ; the value of the symbol is shown by the theory
of determinants to be a function of the Poissonian coefficients (a, /3), and as
these are constants, the value of the symbol considered is also constant.

62. Liouville's note of the 29th of June, 1853*, contains the enunciation
of a theorem which completes the investigations contained in Poisson's
memoir of 1837. The equations considered are the Hamiltonian equations
in their most general form, viz., H is any function whatever of t and the
other variables : it is assumed that half of the integrals are known, and that
the given integrals are such that for any two of tiiem a, /3, Poisson's coeffi-
cient (a, /3) is equal to zero ; this being so, the expression pdq+ ... —Hdt,
where, by means of the known integrals, the variables jo, . . are expressed in
terms o( q, . . . t, is a complete differential in respect to q,.. .t, viz. it will be
the differential of Sir W. R. Hamilton's principal function V, which is thus
determined by means of the known integrals, and the remaining integrals are
then given at once by the general theory.

63. Professor Donkin's memoir of 1854' and 1855, Part I. (sections 1, 2
3, articles 1 to 48). — The author refers to the researches of Lagrange,
Poisson, Sir W. R. Hamilton, and Jacobi, and he remarks that his own
investigations do not pretend to make any important step in advance. The
investigations contained in section 1, articles 1 to 14, establish by an inverse
process (that is, one setting out from the integral equations) the chief con-
clusions of the theories of Sir W. R. Hamilton and Jacobi, and in particular
those relating to the canonical system of elements as given by Jacobi's
theory. The theorem (3), article 1, which is a very general property of
functional determinants, is referred to as probably new. The most im-
portant results of this portion of the memoir are recapitulated in section 4,
in the form of seven theorems there given without demonstration ; some of
these will be presently again referred to. Articles 17 and 18 contain, I
believe, the only demonstration which has been given of the equivalence of
the generalised Lagrangian and Hamiltonian systems. The transformation
is as follows : the generalised Lagrangian system is

* The date is that of the communication of the note to the Bureau of Longitudes, but
the note is only published in Liouville's Journal in the May Number for 1855, which is
subsequent to the date of the second part of Professor Donkin's memoir in the ' Philosophical
Transactions,' which contains the theorem in the question. I have not had the oppor-
tunity of seeing a thesis by M, Adrien Lafon, Paris, 1854, where Liouville's theorem is
quoted and demonstrated.

32 REPORT — 1857.

dt dq' dq*

where Z is any function of t and of q, . . . q\ . . . And writing —=p, .. .,

then if lrl=—Z + q'p+ , , ., where, on the right-hand side, q',.. are ex-
pressed in terras of t,q,.. 2), . . ., so that H is a function of t, q, . . . p, ,. .;
then the theorems in the preceding articles sliovv that

dq_dU 4»__rfH
dt~dp'dt~ dq'

which is the generalised Hamiltonian system.

In section 2, articles '21 and 22, there is an elegant demonstration, by
means of the Hamiltonian equations, of the theorem in relation to Poisson's
coefficients (a,b), viz., that these coefficients are functions of the elements
only. And there are contained various developments as to the consequences
of this theorem ; and as to systems of canonical, or, as the author calls
them, normal elements. The latter part of the section and section 3,
relate principally to the special problems of the motion of a body under the
action of a central force, and of the motion of rotation of a solid body.

6^. Part II. (sections 4, 5, 6 and 7, articles 49-93, appendices). — Section
4 contains the seven theorems before referred to. Although not given as
new theorems, yet, to a considerable extent, and in form and point of view,
they are new theorems.

Theorem 1 is a theorem standing apart from the others, and which is used
in the demonstration of the transformation from the Lagrangian to the
Hamiltonian system. It is as follows : viz., if X be a function of the n vari-
ables a:,..., and ify, ... be n other variables connected with these by the
n equations

rfX

-d^-y-"

then will the values of x, . . ., expressed by means of these equations in
terms of y, . . ., be of the form

_rfY

and if/> be any other quantity explicitly contained in X, then also

dX dY

the differentiation with respect to p being in each case performed only so
far as jo appears explicitly in the function.
The value of Y is given by the equation

Y=-X+X7/+...

where, on the right-hand side, x,... are expressed in terms of y, . . .

Theorems 2, 3 and 4, and a supplemental theorem in article 50, relate to
the deduction of the generalised Hamiltonian system of differential equa-
tions from the integral equations assumed to be known. In fact (writing
y, q,.. . p, . .. b,... a, . . ., instead of the author's X, a:, . . . a;„, y, . . . y„,
a, . . . a„, ^1 . . . 5„), it is assumed that V is a given function of t, of the n va-

ON THEORETICAL DYNAMICS. 33

liables g, . . ., and of the n constants b, . . ., and that the n variables p, ...,
and the n constants a,.,., are determined by the conditions

g=„....(.)

so that in fact by viitiie of these 2m equations the 2w variables X, q, . . .
p,... may be considered as functions of t, and the 2n constants h, . . . a, . . .
(hypothesis l), or conversely, the 2m constants b, . . . a,..., may be con-
sidered as functions of t and of the 2m variables q, .. . p,. . . (iiypothesis 2).
Theorem 2 is as follows: viz., if from the 2m equations (1,2^ and their
total differential coefficients with respect to t, tiie 2m constants be elimi-
nated, there will result the following 2m simultaneous differential equations
of the first order, viz. : —

dq_ dH

dt dp "

dp__dR

dt dq "

where H is a function of q, . . . p, . . . (which will in general also contain t
explicitly), and is given by the equation

dV
where, on the right-hand side, the differential coefficient — is taken with

respect to t, in so far as t appears explicitly in the original expression for V
in terms of y, ...&,.. . and i, and after the differentiation, b, .. ., are to be
expressed in terms of the variables and t, by means of the equations (I).
Theorem 3 is, that there exists the following relations, viz. : —

dq da dq db

db~ dp' da~ dp ' '

dp da dp _^ db

db dq' da dq

where (jo, q^ are airy corresponding pair out of the sj itcn» / , . • • and
q, .. ., and (b, a) are any corresponding pair out of the systems b, .. . and
a, . . ., so that the total number of equations is 4w" : in each of the equations
the left-hand side refers to hypothesis 1, and the right-hand side to hypo-
thesis 2.

To these theorems should be added the supplemental theorem contained
in article 50, viz., that there subsists also the system of equations

rf6_ JH
dt~ da '"

da rfH

Tt~~'db"'

where the left-hand sides refer to hvpothesis 2, while the right-hand sides

dV
refer to hypothesis 1, as before H= — -^' but here H is differentially ex-
pressed, being what the H of theorem 3 becomes when the variables are
expressed according to hypothesis 1.

1857. »

34 REPORT — 1857.

In theorem 4 the author's symbol (i?, <?) has a signification such as
Poisson's (a, b), and if we write as before

■where

d(a, b)_da db db da
d(/?, q)~dp dq dp dq

(this refers of course to hypothesis 2), the theorem is, that the following
equations subsist identically, viz., b,a being corresponding constants out of
the two series b,... and a, . . ,, then

(b,a)=-(a,b)=l,

but that for any other pairs b, a, or for any pairs whatever b, b or a, a, the
corresponding symbol =0 : in fact, that the constants b, , . . and a, . . . form
a canonical system of elements.

Theorem 5 is a theorem including theorem 4, and relating to any two
functions u, v either of the two 2« constants or else of the 2w variables,
and which may besides contain t explicitly ; it establishes, in fact, a relation
between Poisson's coefficient (m, v) and the corresponding coefficient of
Lagrange.

Theorem 6 is as follows : viz,, li q, . . . p, . . . are any 2w variables con-
cerning which no supposition is made, except that they are connected by
the n equations

b-f{q,...p,...),

which equations are only subject to the condition of being sufficient for the
determination of j9, . . . in terms o^ q, . . . and a, . . ,, and they may contain
explicitly any other quantities, for example, a variable t. Then, in order
that the ^7i(n — l) equations

dpi_dpj

dq~dqi

may subsist identically, it is only necessary that each of the |«(72 — 1) equa-
tions (pi, bj)=0 may be satisfied identically.

Theorem 7 is, in fact, the theorem previously established in its general
form in Liouville's note of the 29th of June, 1853, viz., if, of the system of
2w differential equations

dq_dH dp_ dH

dt~ dp' dt~ dq'

there be given n integrals involving the n arbitrary constants b,..., so that
each of these constants can be expressed as a function of the variables
q,. . p,. . . (with or without f) ; then, if the |w(m — 1) conditions (6„ fi;) =
subsist identically, the remaining 7i integrals can be found as follows : — By
means of the ?? integrals, let the n variables p, ... be expressed in terms of
X, . . .b,. .. and t, and let H stand for what H, as originally given, becomes
when q, . . . are thus expressed. Then the values of j9, . . . and — H are the
differential coefficients of one and the same function of jo, .... and t; call
this function V, then, since its differential coefficients are all given (by the

. (?V dW

equations^— ^, .. -j- = — H), V maybe found by integration; and itia

therefore to be considered as a given function of p, . . . and t and of the
constants b,,... The remaining n integrals are given by the n equations

ON THEORETICAL DYNAMICS. 35

■where the n quantities a,... are new arbitrary constants.

65. Section 5 of the memoir relates to the theory of the variation of
the elements considered in relation to the following very general problem :
viz., Q, ... P, ... being any functions whatever of the 2n variables q,...
J9, ... and t; it is required to express the integrals of the system 2« dif-
ferential equations

in the same form as the integrals (sqpposed given) of the standard system
dg_dH. dp___<m
dt~ dp' dt dq

by substituting functions of t for the constant elements of the latter system.
And section 6 contains some very general researches on the general pro-
blem of the transformation of variables, a problem of which, as the author
remarks, the method of the variation of elements is a particular, and not
the only useful case. In particular, the author considers what he terns
a normal transformation of variables, and he obtains the theorem 8, which
includes as a particular case the second of the two theorems in Jacobi s
note of 1837, in the ' Comptes Rendus.' This theorem is as lollows:
viz., if the original variables ^, . . p, . . . are given by the 2n equations

dq_(m ^__^.
di~ dp' dt dq '

and if the new variables r,, ... cr, ... are connected with the original vari-
ables by the equations

^ dK dK

where K is any function of »?,... j», •• . which may also contain t explicitly,
then will the transformed equations be

^~ d'a' dt~ drj

in which $ is defined by the equation

IT d^

and is to be expressed in terms of the new variables, the substitution of the
new variables in ^ being made after the differentiation. In particular, if
K does not contain t explicitly, then ^=0 and $=H, so that, in this case,
the transformation is effected merely by expressing H i« X%WomT-
yariables. There is also an important theorem relating *« th« ^™{^X
tion of coordinates. To explain this, it is necessary to go back to tne
generalised Lagrangian form ^ 2

36 REPORT — 1857.

dt dq'~dq '

where the variables q,... correspond to the coordinates of a dynamical
problem ; if tiie new variables »/,... are any given functions whatever of the
original variables q, .. . and of t, this is wiiat may be termed a transformation
of coordinates. But tlie proposed system can be expressed, as shown in the
former jiai t of the memoir, in the generalised Hamiltonian form with tlie vari-
ables q,.,. and the derived variables j)> "• (the values of which are given by

'T--=p, . ..) : the problem is to transform the last-mentioned system by intro-
ducing, instead of the original coordinates q, . ... the new coordinates ?;, . ..,
and instead of the derived variables p,.... tlie new derived variables cr, . . .

defined by the analogous equations -t-=w, ..., in which Z is supposed to

be expressed as a function of jj, . . . and t. The method of transformation is
given by the theorem 9, which states that the transformation is a normal
transformation, and that the modulus of transformation (that is, the func-
tion corresponding to K in theorem S) is

K=qp+ ...

where q, . .. are to be expressed in terms of i] The latter part of the

same section contains researches relating to the case where the proposed
equations are symbolically, but not actually, in the Hamiltonian form,
viz., where the function H is considered as containing functions of q, •• •
p,... which are exempt from differentiation in forming the differential
equations (the author calls this a pseudo-canonical system), and where, in
like manner, the transformation of variables is a pseudo-normal transforma-
tion ; the theorems 10 and 11 relate to this question, which is treated still
more generally in Appendix C. The general methods are illustrated by
applications to the problem of three bodies and the problem of rotation ;
the former problem is specially discussed in section 7 ; but the results ob-
tained (and which, as the author remarks, affords an example of the so-
called ' elimination of the nodes') do not come within the plan of the pre-
sent report.

66. Bour's memoir of 1855, 'On the Integration of the Differential
Equations of Analytical Mechanics.' — It has been already seen that the
knowledge of half of the entire system of the integrals of the differential
equations (thfse known integrals satisfying certain conditions) leads by
quadratures only to the knowledge of the remaining integrals ; the re-
searches contained in this most interesting and valuable memoir show that
this theorem is, in fact, only the last of a series of theorems, here first
established, relating to the successive reduction which results from the
knowledge of each new integral. Speaking in general terms, it may be
stated that the author operates on the linear partial differential equation of
the first order, which is satisfied by the integrals of the differential equa-
tions ; and that he effectuates upon this equation a reduction of two unities
in the number of variables for every suitable new integral which is ob-
tained*. The author shows also that an equal or greater reduction may

* I have borrowed this and the next sentence from Liouville's report. It would, I
think, be more accurate to say, for every suitable new integral after the first one ; in the
case considered in the memoir, the condition of vis viva is satisfied, and there is always one
integral, the equation of vis viva, which is known ; but this alone, and in the general case
the first known integral, will not cause a reduction of two unitiei.

ON THEORETICAL DYNAMICS. 37

sometimes be obtained by means of integrals which appear at first foreio-n
to his method. Before going further, it maj^ be convenient to remark that
the author restricts himself to the case in which H is independent of the
time, and wliere, consequently, the condition of vis viva is satisfied ; it was,
however, remarked by Liouville that the analysis, slightly modified, applies
to the most general case where H is any function of t and the variables, and
it is possible that when the entire memoir is published (it is given in ' Liou-
ville's Journal' as an extract), the theory will be exhibited under this more
general form.

67. To give an idea of the analytical results, the equations are considered
under the ibrm

dpi dli dqi dH ...

(where, as already remarked, H is independent of t). The integrals admit,
therefore, of representation in the canonical form «, /3, Oj, a^, . . . a^n-z
where a(=H) is the equation of vis viva l3(_=^G~t) is the integral conju-
gate to this, and the only integral involving the time, and the remaining
integrals o, and a^, % and a^ . . a2n-a and a2n—2 are conjugate pairs, we
have (a„a) (=(«„H)) = 0, («„/3) (=(«„ G);=0, (a„a,) = l, (a„ a,)
=0, . . (a„ O2ra_2) = 0.

The integrals a,, a^... a2n-2 verify the linear partial differential equa-
tion

^i=n/dHdl_dR ^\ Q ^^ (j^ (J)

which is also satisfied by C=H> and of which the general solution is ^=
^(H, Op a^ . . . f<2»-2)) while, on the contrary, the first member of the equa-
tion (1), becomes unity for <f=G, in other words (H, G) = l. The equa-
tion (1) replaces the original differential equations; it is to the equation (1)
that the theorems of Poisson and Bertrand may be supposed to be applied,
and it is this equation (1) which is studied in the memoir, where it is
shown how the order may be diminished when one or more integrals are
known.

In the first place, the integral a=H which is known, may be made use of
to eliminate one of the variables, suppose /?„ ; the result is found to be

l=n-\(dp^ dC (¥ndC\,dX__^ x^x
^i=l \dq,d^, dp,dqj^dq,r ^^^'

which has the same integrals as the equation (1), except the integral of vis
viva C=H; it is this equation ('2) which would have to be integrated if
only the integral a were known.

Suppose now there is known a new integral a^\ this gives rise to the
partial differential equation

^l=n/da,d^_da^d^\

'^i=l\dqidpi dpi dqj ^"^^ ^ ^'

which is satisfied by i!^=H, G, a,, 03, u^... a^n-z, but not by a^, which gives
(a,,aj)=0. The equation {^) is satisfied ^=H, and it may be therefore
transformed in the same manner as the equation (1) was, viz. p„ may be
expressed in terms of the other variables and of o. The author remarks
that it will happen, what causes the success of the method, that this opera-
tion, the object of which is to get rid of the solution Z^=H, conducts to two
different equations, according as ^=G or ^= any other integral of the.

38 BEPOET — 1857.

equation (4) ; so that in the second form of the transformed equation the
unknown integral i=G is also eliminated. This second form is found
to be

l=n — \ {da^d'C da^d^\ r, / y\ n /cN

2^•=l W ¥r^5^J=^°'^"i'^^=^ (5).
which is precisely similar to the equation (1) (only the number of variables
is diminished by two unities), and is possessed of the same properties. Its
integrals are a^,a.,,a^...a2n-2j which are all of them integrals of the pro-
blem, and give (oj, Oi)=0. And the theorems of Poisson and Bertrand
apply equally to this equation ; the only difference is, that the number of
terms in the expressions (a, /3) is less by two unities. A new integral (og)
leads in like manner to an equation (8) similar to (5), but with the number
of variables further diminished by two unities, and so on, until the half
series of integrals a,a^,o.^..,a.2n-3 are known; the conjugate integrals
/3, 02,04... a2«-2 are then obtained by quadratures only, in the method ex-
plained in the memoir, and which is in fact identical with tliat given by the
theorem of Liouville and Donkin. Tlie memoir contains other results,
which have been already alluded to in a general manner ; some of these are
made use of by the author in his ' Memoire sur les problemes des trois
corps,' Journal Polyt., t. xxi. pp. 35-58 (1856).

68. Liouville's note of July, 1855, on the occasion of Bour's memoir,
mentions that the author of the memoir had recognized that, according to
the remark made to him, his formulae subsist with even increased elegance
when H is considered as a function of t and the other variables. But (it is
remarked) the general case can be always reduced to the particular one
considered in the memoir, provided that the number of equations is aug-
mented by two unities by the introduction of the new variables r and u, the
former of them, r, equal to ^-|- constant, so that

dr='
the latter of them, u, defined by the equation

du_ dU.
dr dt

Suppose in fact that

then, since r and u do not enter into H, which is a function only of t and
the variables g, . . . p, . . ., we have

dV__ _d^
du dr '

and, moreover, the differential coefficients with respect to t,q, . . .p, ... of
the functions H and V are equal. The system may be written

(U_dY du__dV_
dr du' dr dt

dp_dy ^-_dy_

dr d(i dr dp

which is a system containing two more variables, but in which V is inde-
pendent of the variable r, which stands in the place of t. The transforma-

ON THEORETICAL DYNAMICS. 39

tion is an elegant and valuable one, but it is not in anywise to be inferred
that there is any advantage in considering the particular case (which is thus
shown to be capable of including the general one), rather than the general
one itself: such inference does not seem to be intended, and would, I think,
be a wrong one.

69. Brioschi's note of 1855 contains an elegant demonstration (founded
on the theory of skew determinants) of a property which appears to be a
new one, of the canonical integrals of a dynamical problem, viz. if q,p stand
for a corresponding pair of the variables q,...p,... then

where the summation refers to all the different pairs of conjugate integrals
a, (3 of the canonical system, the pair q,p in the denominator being the same
in each term ; but if tlie variables in the denominator are a non-corresponding
pair out of the two series q, . . and jo, . . ., or else a pair out of one series only
(that is, both ^-'s or both jo's), then the expression on the left-hand side is
equal to zero. This is in fact a sort of reciprocal theorem to the theorem
which defines the canonical system of integrals. There are two or three
memoirs of Brioschi in Crelle's Journal connected with this note and tiie
note of 1853 ; but as they relate professedly to skew determinants and not to
the equations of dynamics, it is not necessary here to refer to them more
particularly.

70. Bertrand's memoir of 1857 forms a sequel to the memoir of 1651, on
the integrals common to several problems of mechanics. The author calls
to mind that he has shown in the first memoir, that, given an integral of a
mechanical problem, and assuming only that the forces are functions of the
coordinates, it is possible to determine the problem and find the forces which
act upon each point ; and (he proceeds) it is important to remark, that the
solution leads often to contradictory results, — that, in fact, an equation as-
sumed at hazard is not in general an integral of any problem whatever of
the class under consideration : and he thereupon proposes to himself in the
present memoir to develope some of the consequences of this remark, and to
seek among the most simple forms, the equations which can present them-
selves as integrals, and the problems to which such integrals belong. The
various special results obtained in the memoir are interesting and valuable.

71. In what precedes I have traced as well as I have been able the series
of investigations of geometers in relation to the subject of analytical dyna-
mics. The various theorems obtained have been in general stated with
sufficient fulness to render them intelligible to mathematicians; the attempt
to state them in a uniform notation and systematic order would be out of the
province of the present report. The leading steps are, — first, the establish-
ment of the Lagrangian form of the equations of motion ; secondly, La-
grange's theory of the variation of the arbitrary constants, a theory perfectly
complete in itself; and it would not have been easy to see a priori that it
would be less fruitful in results than the theory of Poisson ; thirdly, Poisson's
theory of the variation of the arbitrary constants, and the method of inte-
gration thereby afibrded ; fourthly. Sir W. R. Hamilton's representation of
the integral equations by means of a single characteristic function deter-
minable a jtjosferion by means of the integral equations assumed to be known,
or by the condition of its simultaneous satisfaction of two partial differential
equations ; fifthly. Sir W. R. Hamilton's form of the equations of motion ;
sixthly, Jacobi's reduction of the integration of the differential equations to
the problem of finding a complete integral of a single partial differential

40 REPORT— 1857.

equation, and the general theory of the connexion of the integration of a
system of ordinary differential equations, and of a partial differential equa-
tion of the first order, a theory, however, of which Jacobi can only be con-
sidered as the second founder; seventhly, the notion (arising from the
researches of Lagrange and Poisson) and ulterior development of the theory
of a system of canonical integrals.

I remark in conclusion, that the differential equations of dynamics (in-
cluding in tiie expression, as I have done throughout tiie repoit, the gene-
ralized Lagrangian and- Hamiltouian forms) are only one of the classes of
differential eqiialions which have occupied the attention of geometers. The
greater part of what has been done with respect to the general theory of a
system of differential equations is due to Jacobi, and he has also considered
in particular, besides the differential equations of dynamics, the Pfaffian
system of differential equations (including therein the system of differential
equations which arise from any partial differential equation of the first order),
and the so-called isoperimelric system of differential equations, that is, tiie
system arising from any problem in the calculus of variations. In a sys-
tematic treatise it would be proper to commence with the general theory of
a system of differential equations, and as a branch of this general theory, to
consider the generalized Ilamiitonian system, and in relation thereto to
develope the various theorems which have a dynamical application. It
would be shown that the generalized Lagrangian form could be transformed
into the Hamiltonian form, but the first-mentioned form would, I think,
properly be treated as a particular case of the isoperimetric system of dif-
ferential equations.

List of Memoirs and Works above referred to.

Lagrange. Mecanique Analytique. 1st edition. 17SS.

Laplace. Mecanique Celeste, t. i. 1799.

Poisson. Sur les iuegalites seculaires des moyens raouvemens des planetes.
Read to the Institute 20th June, 1808. — Journ. Polyt. i. viii. pp. 1-56.
J 808.

Laplace. Memoire Read to the Bureau of Longitudes 17th Aug.

1808. — Forms an Appendix to the Srd volume of the Mecanique
Celeste. 1808.

Lagrange. Memoire sur la theorie des variations des elements des planetes
et en particulier des variations des grands axes de leurs orbites. Read
to the Bureau of Longitudes the 17th Aug. and to the Institute the
22nd Aug., 1808.— Mem. de I'lnstit., 1808, pp. 1-72. 1808.

Lagrange. Memoire sur la theorie gcnerale de la variation des constantes
arbitraires dans tous les problemes de la Mecanique. Read to the
Institute 13th March, 1809.— Mem. de I'lnstit., 1808, pp. 257-302
(includes an undated adtlition), and there is a Supplement also without
date, pp. 363, 364'. 1809.

Poisson. Memoire sur la variation des constantes arbitraires dans les ques-
tions de Mecanique. Read to the Institute 16th Oct., 1809. — Journal
Polyt., t. viii. pp. 266-344. 1809.

Lagrange. Seconde memoire sur la variation des constantes arbitraires
dans les problemes de Mecanique, dans lequel on simplific I'application
des formules generates a ces problenus. Read to the Institute 19th
Feb., 1810— Mem. de I'lnstit., 1809, pp. 343-352. 1810.

ON THEORETICAL DYNAMICS. 41

Lagrange. Mecanique Analytique. 2nd edition, t. i., 1811 ; t. ii., 1813.
1811.

Poisson. Meinoire sur la variation des constantes arbitraires dans les ques-
tions de Mecanique. Read to the Academy, 2nd Sept., 1816. — Bulletins
de la Soc. Philom., 1816, p. 109; and also, Mem. de I'lnstit., t. i., pp.
1-70. 1816.

Hamilton, Sir W. R. On a general method in Dynamics, by which the
study of all free systems of attracting or repelling points is reduced to
the search and differentiation of one central relation or characteristic
function.— Phil. Trans, for 1834, pp. 24'7-308. 18S4.

Hamilton, Sir W. R. Second Essay on a general method in Dynamics. — •
Phil. Trans, for 1835, pp. 95-144. 1S35.

Poisson. Remarques sur I'integration des equations differentielles de la
dynamique. — Liouville, t. ii. pp. 317-337. 1837.

Jacobi. Lettre a I'Academie. — Comptes Rendus, t. iii. pp. 59-61. 1836.

Jacobi. Zur Theorie der Variations- Rechnung and der Differential-Glei-
chungen. Extract from a letter of the 29th Nov. 1836, to Professor
Encke, secretary of the mathematical class of the Academy of Berlin.
— Crelle, t. xvii. pp. 68-82. 1836.

Jacobi. Ueber die Reduction der Integration der partiellen DifFerential-
gleichungen erster Ordnung zwischen irgend einer Zahl Variabeln auf
die Integration eines cinzigen Systemes gewohnlicher Difierential-
gleichungen. — Crelle, t. xxvii. pp. 97-162, and translated into French,
Liouville, I. iii. pp. 60-96, and 161-201. 1837.

Jacobi. Note sur I'integration des equations differentielles de la dynamique.
— Comptes Rendus, t. v. pp. 61. 1837.

Jacobi. Neues Theorem der analytischen Mechanik. — Monatsbericht of
the Academv of Berlin for 1838 (paper is dated 2Ist Nov., 1836) ; and
Crelle, t. xxx, pp. 117-120. 1838.

Jacobi. Lettre adress6e a M. le President de I'Academie des Sciences a
Paris. — Comptes Rendus, t. xi. p. 529; Liouville, t. v. pp. 350-351
(with an addition by Liouville, pp. 351-355). 1840.

Binet. Memoire sur la variation des constantes arbitraires dans les formules
generales de la dynamique et dans un systeme d'equations analogues
plus etendues, — Journ. Polyt. t. xvii. pp. 1-94. 1841.

Jacobi. Sur un nouveau principe general de la Mecanique Analytique. —
Comptes Rendus, t. xv. pp. 202-205. 1842.

Jacobi. De motu puncti singularis. — Crelle, t. xxiv. pp. 5-27. 1842.

Maurice. Memoire sur la variation des constantes arbitraires conime I'ont
etablie dans sa generalite les memoires de Lagrange et celui de Pois-
son. Read to the Academv the 3rd June, 1844 Mem. de I'lnstitut,

t. xix. pp. 553-638. 1844."

Jacobi. Theoria novi niultiplicatoris systemati aequationum differential! um
vulgarium applicandi — Crelle, t. xxvii. pp. 199-268; and t. xxix.
pp. 213-279, and 333-376. 1844.

Desboves. Demonstration de deux theoremes de M. Jacobi, application
au probleme des perturbations planetaires. Thesis presented to the
Faculty of Sciences the 3rd April, 1848. — Liouville, t. xiii. pp. 397-
411. 1848.

Serret. Sur I'integration des Equations differentielles du mouvement d'un
point materiel — Comptes Rendus, t. xxvi. pp. 605-610. 1848.

Serret. Sur I'integration des equations differentielles de la dynamique

Comptes Rendus, t. xxvi. pp. 639-643. 1848.

42 REPORT — 1857.

Sturm. Note sur I'int^gration des equations generales de la dynamique. —
Comptes Rendus, t. xxvi. pp. 658-673. 1848.

Ostrogradsky. Sur les integrales des equations generales de la dynamique.
— Melanges de I'Acad. de St. Petersbourg, ^th Oct., 1848.

Brassinne. Theoreme relatif a une classe d'equations differentielles siniul-
tanees analogue a un theoreme employe par Lagrange dans la theorie
des perturbations. — Liouville, t. xvi. pp. 283-288. 1851.

Bertrand. Memoire sur les integrales communes a plusieurs problemes de
Mecanique. Presented to the Academy the 12th May, 1851. — Liou-
ville, t. xvii. pp. 121-174. 1851.

Bertrand. Memoire sur I'integration des equations differentielles de la
dynamique. — Liouville, t. xvii. pp. 393-436. 1852.

Bertrand. Sur un nouveau theoreme de Mecanique Analytique. — Comptes
Rendus, t. XXXV. pp. 698-699. 1852.

Bertrand's notes VL and VIL to the third edition of the Mecanique Analy-
tique, t. i. pp. 409-428, viz. note VJ. — Sur les equations dilferentielles
des problemes de la Mecanique et la forme que Ton peut donner a
leurs integrales; and note VII. — Sur un theoreme de Poi'sson. 1853.

Brioschi. Sulla vai'iazione delle costanti arbitrarie nei problemi della
Dinamica. — Tortolini, Annali, t. iv. pp. 298-311. 1863.

Brioschi. Intorno ad un teorema di Meccanica. — Tortolini, Annali, t. iv.
pp. 395-400. 1853.

Liouville. Note sur I'integration des equations differentielles de la dyna-
mique, presentee au Bureau des Longitudes le 29 Juin, 1853. — Liou-
ville, t. XX. pp. 137-138. 1853.

Donkin, Prof. On a Class of Differential Equations, including those which
occur in Dynamical Problems. Part I. — Phil. Trans. 1854, pp. 71-113.
Received Feb. 23rd, read Feb. 23rd, 1854. 1854.

Donkin, Prof. On a Class of Differential Equations, including those which
occur in Dynamical Problems. Part II. — Phil. Trans, 1855, pp. 299-358.
Received Feb. 17tli, read March 22d, 1855. 1855.

Liouville. Rapport sur un memoire de M. Bour concernant I'integration
des equations differentielles de la Mecanique Analytique. — Comptes
Rendus, t. xl. p. 661, seance du 26th Mars, 1855; Liouville, t. xx.
pp. 135-136. 1855.

Bour. Sur I'integration des equations differentielles de la Mecanique
Analytique (extrait d'un memoire presente a I'Academie le 5 Mars,
1855).— Liouville, t. xx. pp. 185-200. 1855.

Liouville. Note a I'occasion du memoire precedent de M. Edmond Bour. —
Liouville, t. xx. pp. 201-202. 1855.

Brioschi. Sopra una nuova proprieta degli integrali di un problema di
dinamica. — Tortolini, t. vi. pp. 430-432. 1855.

Bertrand. Memoire sur quelqu'une des formes les plus simples que puissent
prendre les integrales des equations differentielles du mouvement dun
point materiel. — Liouville, t. ii. (2*^ serie), pp. 113-140. 1857.

ON THE GROWTH AND VITALITY OF SEEDS.

Sixteenth and final Report of a Committee, consisting of Professor
Daubeny, Professor Henslow, and Professor Lindley, ap-
pointed to continue their Experiments on the Grotvth and Vitality
of Seeds.

When the summary, given in the Report for 1850, pp. 162 to 168, was
made up, many of the kinds of seeds set apart for the continuation of these
experiments had not ceased to germinate, which rendered a continuation of
periodical sowings necessary to arrive at a satisfactory result. Such sowings
have consequently been continued down to the present tune, and so few*
are now found to possess their vegetative powers, that it is deemed necessary
to consider the object attained, and thus close these investigations.

The Committee submit the annexed General Summary, which contains
all the results arrived at that are worth recording in this place.

Single sowings of a great many other kinds of seeds, mostly old, have
•been made during the time these experiments have been carried on; but as
in most cases the probable age at which they ceased to germinate could not
be traced, thej' are not inserted in the summary, but will be found entered
in the MS. Register submitted with this Report.

General Summary of the Experiments from 184;! to 1857 inclusive.

1. G-RAMINACEiB.

.Zea Mays

1.;

2. Phalaris canariensis

Panicum miliaceum.
Avena sativa

5. „ „

6. Triticmn asstivum ^y.

. Secale cereale ....
, Hordeum vulgare

1S46
lS-i8\
1853!
1842,
1844]
1849;
18541
1849
1857
1842
1844
1849
1854
1844
1857
1842
1844
1849
1844
•4857
1844
1857
1846
1848
1853
1842
1844
1849
1844
1857

198

127

nil.

194

3il47

8| 19

13 nil.

2178

lOlnil.

lilSO

3237

8| 37

13 nil.

3210

nil.

180

163

nil.

115

nU.

140

nil.

456

nU.

255

167

8!nU.

3:236

16 nil.

300

(300

1300

300

:300

1300

i600

600

200

300

300t

300

150t

150

soot

300

600

300

300t

300

2. PAL5IACEJ3.

9. Phoenix dactylifera

3. AMAEYLLIDACK.E.

10. Alstroemeria pelegriaa

„ aurantia

4. IniDACEiB.

1 1 . SisjTrachium bermiidianum

12. Grladiolus psittacinus

13. Iris sibirica

14. „ Bp

15. Tigridia pavonia

5. LILIACE.E.

16. Allium fragrans

1843
1845
1850

1843
1845
1850
1845
1847

1848
1843
1845
1850
1843
1845
1850
1846
1848
1853
1844
1846
1851

1844
1846
1851
1857
1847
1854

nil.

5
nil.
12
nil.

nU.

14
nil.
14
4
nil.
32
36
nil.

143

102

nil.

2
nil.

9
9
9

300

100

300

150

300

300
300
300
300
450
450

* Ulex, Dolichos, Malva, Ipomm.

t (In waxed cloth.)

i (In open jarg.)

REPORT — 1857.

5. LiLiACEJE, continued.

16. Allium senescens

17. Camassia esoulenta

18. Asphoclclus luteiis

19. Asparagus officinalis

6. PlNACE^E.

20. Pinus Pinea

21. Juuiperus commuuis

7. BETULACEiE.

22. Alnus glutinosa. .

8. Cannabinace.e.
23. Cannabis sativa

9. Horaces.
24. Morus nigra. . .

10. EUPHORBIACE.E.

!5. Euphorbia Lathyris . .

26. Croton, sp

27. Eicinus communis

11. COEYLACEJE.

28. Fagus sylvatica. . .

29. Quercus Eobur.

12. CuCUEBITACEiE.

30. Momordica Elaterium.

31. Cucurbita Pepo

32. Bryonia dioica .

1848
1847
1854
1844
1846
1851
1857
1845
1847
1852

1846

184;

1845

1846
1853
1857

1842
1849

1854

1843
1845
1850

1844
1846
1851
1844
1843
1845
1850

1846
1848
1845
1850

1845
1855
1857
1843
1845
1850
1855
1845
1847
1852

13. PASSIFLORACEiE.

33. Passiflora Herbertiana

34. Tacsonia pinnatistipula . .

14. ViOLACEiE.

35. Viola lutea

3
1

nil.
52
32
1
nil.
251
97
ml.

28
nil.

Ill

nil.

45
13
nil.

82
59
nU.

20
46
nil.
30
21
15
nil.

1842
1842

1844
1846
1851

nil.

13
4
nil.
35
37
19
nil.
81
5
nU.

nil.
nil.

202

60
300
300
150
150
150
150
450
,450
450

19
300
300

450
450
450

150
150
150

300
300
300

150
150
150
50
45
45
45

300

75
75
75
45
45
45
45
300
300
300

375
150

450
450
450

14. ViOLACB.E, continued.

35. Viola lutea

15. CRUCIFER.E.

36. Mathiola annua

37. Turritis retrofracta

38. Arabis hirsuta

•39. „ lucida

40. Koniga maritima . . .

41. Lunaria biennis

42. Vesicaria grandiflora

43. Iberis umbellata

44. Biscutella erigerifolia

45. Malcohnia maritima.

46. Hesperis matronaUs .

47. Erysimum Peroffskianum

48. Lepidium satiTum

1857

49. .Sithionema saxatUe .

50. Isatis tinctoria

51 . Brassica Napus

oleracea

Rapa

52. Crambe maritima .

53. Bunias orientaUs

1844
1846
1851
1842
184S
1842
1844
1846
1851
1844
1846
1851
1845
1847
1843
1845
1850
1844
1846
1851
1843
1845
1850
1844
1846
1851
1857
1843
1845
1850
1842
1844
1849
1854
1848

1848

1842

1844

1849

1854

1842

1844

1849

1844

1857

1842

1844

1849

1854

1845

1847

1852

1847

1849

185711

nil.

203
3 236

nU.

nil.

nil.
202
170

nil.
143
114

nil.
299

nil.
280
150

nU.

nil.

252

3178

nil.
222

14 nil.

1234

3 82

8 nil.

1262

8
13

3
16

8
13

195

300

',00

nil.

300

100

340

450

323

450

nil.

450

150

1.50

nU.

150

150*

nil.

150

483

900

335

900

nil.

900

105

300

nil.

.300

150

nil.

150

* (In waxed cloth.)

ON THE GROWTH AND VITALITY OP SEEDS.

15. Cruciper/e, continued.
Heliopliila araboides

54.

55. Schizopetalon Walkeri

08,

16. Cappaeidace^.
Cleome spinosa

17. Byttneriace^.
Hermannia, sp

18. TROP^OLACEiE.

Tropseolmn majus .

,, peregrmum
Lymnanthes Douglasii

19. Malvace^e.
Malope grandiflora

Kit aibelia vitif oKa . . .
Lavatera trimestris
Malva mauritiana. . .

... sp

Hibiscus, sp

Sida, sp

20. TiLIACEJ!.

Corcliorus, sp

Triumfetta, sp

21. SAPINDACEiE.

Cardiospermum Halicaca'
bum

69.

74,

1844
1846

1851
1846
1848
185.3

1857

1844
1846
1851

1844

1843
1845
1850
1848
1846
1848

1843
1845
1850
1855
1848
1848
1845
1847
1852
1857
1844
1844
1844

1844
1844

1848
1857

22. Hypericacbjj.
Hypericum Kabnianum ... 1842

„ hirsutum 1844

1846

, 1851

23. MAGNOLIACE.B.

MagnoHa, sp 11845

„ 1850

Liriodendron tulipiferum 1843
1845

24. Eanuncxjlacej!.

Clematis erecta 1842

ThaUctrum minus 'l847

1849

'1849

„ _ 1857

Anemone coronaria 1 847

1849

600
600
600
1.50
1.50
150
150

300
300
300

150

75
75
75
30
150
150

300
300
300
300
200
100
600
600
GOO
600
100
100
150

450
450
450
450

45
45
50
50

150
300
300
600
600
300
300

24. Eanunculace^, cont

75. Adonis autumnalis

76. Eanunculus caucasicus

77. Nigella nana

78. Helleborus foetidus

79. Delphmium flexuosum

80. Aconitum Napellus

)) J.

81 . Pseonia, sps. mixt

25. Papaverace.e.

82. Argemone alba

83. Papaver amoenum

„ orientale

84. Grlaucium rubrum

85. Eschscbioltzia californica .

86. Chryseis crocea
87.

26. PUMAEIACE^.

Hypeooum procumbens
Fumaria spicata

92,

93,

27. BERBERIDACBiE.

Berberis aquifolium . . . ,

28. Anacardiace.e.
Ehus, sp

29. Xanthoxylace.e.
AUantus glandulosa ...

30. LiNACE.E.

Linum usitatissimum

„ perenne

31. Balsaminace.e.
Balsamina hortensis.,

1843
1845
1850
1855
1847
1849
1843
1845
1850
1845
1847
1842
1848
1845
1850
1855
1842
1844
1849

1845
1847
1852
1857
1843
1845
1850
1842
1843
1845
1850
1845
1847
1852
1857
1842
1847

1842
1846
1848
1853

1842

1844

1846
1848
1853
1857

1842
1844
1849
18.54
1848

1846

86
79

7
nil.

9
nil.
110
40
nil.
63
nil.
ml.

1
13
12
nil.

30
nil.

109

159

nU.

179

nil.

nU.

ml.

174

124

nU.

nil.

nU.

63
3

8
ml.

397

202

nU.

REPORT~1857.

31. Bal.«A3[inace.e, cont.
94. Impatiens glandiiligera . .

32. Geraniace.e.

95. Pelai'goniiim, sp

33. CARYOPnYLLACEj;.

96. Buifouia annua

97. Cerastium perfoliatiun ..

98. Dianthus barbatiis

99. Saponaria annua

100. Gypsophila elegans

1845 3
1850 8
1855 13

101. Silene inflata

„ quadridentata

„ pendiila

„ armeria alba
102. Viscaria oculata

103. Pbamaceum, sp. . .

34. PoRTCLACACEiE.

104. Talinum eiliatum . .

105. Calandrinia grandiflora.

106. „ speciosa ....

35. POLYGONACE-E.

107. Polygonum Fagopyrum.

108. Eumex obtusifoUum

3G. Nyctaginace^.
109. Mirabilis jalapa —

1844

1843

1845

1850

1848

1857

1844

1846

1851

1857

1845

1847

1852

1844

1846

1851

1857

1844

1846

1851

1857

1848

1846

1848

1853

185

1844

1844
1846
1851
1857
1842
184'
1843
1845
1850
1855

1842
1844

1849
1854
1844
1846
1851
185'

1843
1845
1850

34
11
ml.

109
16
nil.
14
nU.

242

181

nil.

247
38
nU.

140

143
6
nil.
58
88
2
nU.
31
41
31

1.30

nil.

196

188

nU.

58
nU.
117
171

18
ml.

nU.

226

3162

nil.

150
150
150

300
.300
300
300
300
300
300
300
300
450
450
450
600
600
600
600
150
150
150
150
100
200
100
450
450
4.50
450
100

600
600
600
600
600
600

;oo

300
300
300

150
150
150
1.50
450
450
4.50
450

75
75
75

37. Phytolaccace.e.
1-10. Phytolacca deeandra .

38. AsfARANTACBiE.

111. Amaranthus caudatus

39. Che:nopodiace.e.
112. Chenopodium Botrys.

Quinoa

113. Beta vulgaris

40. SAUEUEACEi).

114. Saururia, sp

41. MESEMBRYACEiE.

115. Mesembryanthemum cry-
stallinum

1844
1846
1851

1843
1845
1850
1855

1845
1847
1849
1857
1846
1848
1853
18.57

1844

42. Tetragoniace.e.
116. Tetragonia espansa

43. THYMELACE.E.

117. Gnidia, sp

44. Proteaces.

118. Leucadendron, sp.

45. LEGniiNosiE.

119. Podalyria, sp

120. Pultensea, sp

121. Lupinus lucidus . . .

,, rivularis

polyphyUus .

succulentus

grandifolius .

122. Ci'otalaria, sp...
12.3. Aspalathus, sp.
124. Ulex europsea . .

125. Spartium scoparium

21
nil.

210

178

nil.

1220

3: nU.
2471
lOl nil.
1446
3155
23

1843

1845
1850
1855

1843
1845
1850

1844

1844
1844
1842
1842
1847
1842
1854
1857
1843
1845
1850
1847
1854
1857
1844
1844
1843
1845
1850
1855
1857
1846
1848
1853

nil.

94
112
nil.

38
22
ml.

113
2

nil.

1
nU.

1
11
nil.
215
85
nU.

1
nU.

113

4
122
38
80

ON THE GROWTH AND VITALITY OP SEEDS.

45. Leguminos.e, cont.
Spartium scoparium . .
Cytisus Laburnum

albus

127. Tetragonolobus purpureas

128. TrifoUum repens

129. Melilotus ccenilea

130. Trigonellafoenum-grsecum

131 . Medicago inaculata

132.
133.
134.

Ononis angustifoHa

Indigofera, sp

Psoralea bifcuminosa

139.
140.

Galega, sp

Sutlierlandia, sp.

Colutea, sp

Pisum sativum ,

Ervum, sp. .
Vicia sativa .

1857
1843
1845
1850
1855
1846
1848
1853
185'
1843
1845
1850
1842
1844
1849
1844
1846
1851
1857
1843
1845
1850
1843
1845
1850
1855
1857
1842
1844
1847
1849
1857
1844

184426

1844

184443

1842

1844

1849

141

„ grandiflora

„ lutea

Paba vulgaris

142. Lathyrus lieteropliyUus . . .

fl43

„ annuus.

„ sativus .

Orobus niger

1854
1846
1842
1844-
1849
1854
1848
1848
1842
1844
1849
1854
1843
1845
1850
1855
1857
1848
1848
1845

80
21
2
nil.
85
24
13
nil.
58
40
nil.

119
22

nil.

106

149
19

nil.

122
89

nil.
73
71

113

101
8

nn.

28
54
46
nil.

107
16
5
1
92
94
15
uH.
90

129

120
8
nil.
18
91
71
71
40

nil.
44

105

nO.

600
150
150
150
150
300
300
300
300
75
75
75
450
450
450
300
300
300
300
150
150
150
300
300
300
300
300
300
150
150
150
150
200
100
100
75
150
150
150
150
100
160
150
150
1.50
25
100
75
75
75

150
150
1,50
150
150

6
150

45. LEGtTMiNos.E, cont.
Orobus niger

143

144. Seorpim'us sulcata

145.
146.

147.
148.

149.
150.
151.

Coronilla, sj)

^schynomene, sp.

Hallia, sp

Hedysarum, sp.

CUtoria, sp

Erythrina, sp

Pliaseolus multiflorus.

162,

153.
154.
155.
156.

DoHchos lignosus

Caesalpinia, sp. ..

Cassia, sp

Tamarindus, sp. . .
Cercis canadensis

158.
1.59.
160.

Mimosa, sp

Adenanthera, sp

Eobinia pseudacacia

157. Gleditschiatriacanthos ..

163.

104.
165.

46. POMACE/E.

Cotoneaster rotundifolia

Crataegus maorantha
„ pimetata . . .

47. EOSACE^E.

Potentilla nepalensis .

„ sp. from Douglas
Geum, sp

48. LyxiiRACEJ!.
Cupbea procumbens

1850

1855

1843

1845

1850

184442

1844

1842

1844

1849

1854

1844

1843

1845

1850

1855

1857

1844

1844^27

1844126

1844'25

1843

1845

1850

1846

1853

1857

1844

1843

1845

1850

1843
1845
1850
1843
1845
1850
1843
1845
1850

1842
1843
1845
1850
1842
1847
1854

1843
1845

nil.

nil.
49
52
nU.
nU.
3
nil.

46
45

REPORT — 1857.

Name.

Sown
in \

'^1

Name.

Sown
in %

s
1

48. Lythracej:, cont.

165. Cuphea prociimbens

49. Eha.mnace-e.

166. Trichocephalum, sp

167. Phylica, sp

1850 i

1844 ^

1844 '■
18442

1843

1845 .

1846

1848

1853

18471

1842

1844

1850

1849

18541

1853

1845

1850

18551

1843

1845

1850

1843

1845

1850

18563

18571

1845

1847

18.52

18571

1846

1847

1844
1846
1851
18571

1843

1845

1850

1842

1844

1849

18.541

1842

1844

1846

1851

1842

1844

1846

1851

I nil.

1 2
1 1

1 9

L 2
3 ml.

1141
3
B 4

2 nil.
1152
3109
5 20

3 30
3 nil.
1 5
3 7
8 4
3 nn.
1 66
3 33
8 nU.
1243
3143
8142

1 08
5 nil.
1140
3

8 12
3 nil.

9 76

2 31

1 29

3 41
8 9

4 1

1135
3 64
8 nil.
1125
3204
8 1
3 nil.

7 nil.
1131
3121

8 nil.

7 ml.
1 125
3 78

8 2

150

25
17
50

300
300

450
450
450
450
300
300

50
300
300
300
300
300
300

75
300
300
300
300
300
600
600
600
600
100

150
160
150
150

300

000

600

000

1500

600

375

300

54. POLEMONIACE^, COUt.

182. Polemonium Cferuleum ...

1857 1^
1845 i
1850 i

1848 '.
1843;
1845[ ;
1850 i
1843

1845 .

1850 f

1844

1846 .

1851 I

1843
1845 ,
1850
18551

1843
1845
1850

1843
1845
1850
1844
1846
1851
1848

1843
1845
18551
1857 1

1843

1845

1850

1842

184;3

1845

1850

18551

1848

1847

1843

1845

1850

18651

1847

1849

1846
1848

1 nil.
I 3
I nil.

I 62
168
3 84
3 nH.
L131
3122
3 nU.

1120
3130
5 nil.

1 71

3 89
3158
3 nil.

1120
3150
3 nil.

nil

3 79
8 nil.
1201
3135
8 nH.

2 3

1 25

3 45
3 3
5 nil.

1101
3 44
8 nil.

7 nil.

1 14
3 43

8 2
3 nil.

2 3

3 24

1165
3 78
8 5
3 nil.
1 2
3 nU.

1 65
3 nil.

300
9
9

200
300
300
300
300
300
300

450
450
450

300
300
300
300 •

300
300
300

150
150
150
300
300
300
100

300
300
300
300

300
300
300
1.50
300
300
300
300
100

260

300

.300'

3001

3001
3000

— i

55. Hydropiiyllace/E.
184. Nemophila atomaria

50. A(lUIFOLIACE.E.

" "

51. Solan ACE^!.

186. Phacelia tanacetifolia

56. JPlantaginace.e.

" j>

" ''

171. Datxira Stramonium

" "

57. PRIMVLACE.E.

" "

*' '

58. NOLANACB.E.

189. Nolana atriplicifolia

59. B0RAGINACE.E.

" "

174. Nlcandra physaloides

" "

191 . Echivmi grandiflorvmi

192. Amsinckia angustifolia . . .

193. Cynoglossimi glochida-

" "

176. Lycopersicum esculentum

52. AsCLEl'IADACEiE.

177. Aselepias verticillata

53. CONVOLVULACE^.

00. LABIAT.E

" "

)> ))

" "

195. Horminum pyrenaicum. . .

54. POLEMONIACE^.

" "

180 Gilia achilleaefolia

197 „ citriodora

198. Dracocephalmn denticula-

" "

199. Leonm'us cardiaca

181. Leptosiphon ancli-osacea. .

182. Polemonium gracile

„ cajruleum . .

J» 3)

" "

01. VerbenacevE.

, "

ON THE GROWTH AND VITALITY OP SEEDS.

202

62. Selaginace^e.
Hebenstreitia tenuifolia . .

203

204.

G3. Pedaliacb^e.
Martynia probosoidia

64. BiGNONIACE.E.

Eccremocarpus scaber

205. Catalpa cordifolia
206.

65. SCROPHULARIACE.E.

Browallia elata

207.
208.

Choenostoma polyantha .
Schizanthus pinnatua. . . ,

209. Verbascuin Thapsus

210. Alonsoa incisa

211. Iiinaria Prezii

212
213

214.

215.

1216

217

218,

J219

1844
1846
1851

1843
1845
1850

1846
1848
1853
1857
1843
1845

1846

1848

1853

1848

1857

1844

1846

1851

1857

1842 1

1844

1849

1846 1

1848

1853

1845 I

1847

1852

1848 3

1848 3
1842 1

„ |1844 3

11849

„ calycinum J1848 3
Collinsia heterophylla ..J 1842 1

'1844 3

...1849 8
...1185413

Pentstemon dilfusus 1842 6

„ pubescens ...1 1842 6

„ pulchellus ...1842 6

„ atropurpureus 1842 6

„ digitalis il842 6

„ Isevigatus ...'l842 6

„ graciUs 1842 6

„ procerus 1842 6

Mimulus moschatus 1842 6

Digitalis lutea 1843 1

1845 3
1850 8
Veronica peregrina 1847 1

1849 3

Linaria spartea

„ bipartita . .
Antirrhinum majus

175
102
nil.

27
10
nil.

41
3
1

ml.

nil.

66. CampanulacejE.
Campanula Medium

1844

nU.

398

240

nn.

430
126
nU.
48

5
nil.
167

1
nU.

6
517
475
nil.

9
322
578

1
nU.
nU.
nil.
nil.
nil.
nil.
ml.
nil.
nil.

4
213
46
nU.
34
nil.

125

300
300
300

60
60
60

300
300
300
300
50
50

150
150
150
300
300
600
600
600
600
500
1500
1500
300
300
300
600
600
600
100
100
900
900
900
25
900
900
900
900
900
1500
750
750
900
750
1500
1200
3000
300
300
300
300
300

300

66. Campanulace^, cont.

219. Campanula Medium

67. Valerianace^e.

220. Valeriana officinalis

221. Fedia dentata

68. DiPSACACE.E.

222. Dipsacus laciniatus.

223. Knautia orientaHs .

69. COMPOSIT,E.

224. Ageratum meiieanum

225. Aster tenella

226. Callistemma liortensis

227. St«nactis speciosa

228. KauifussiaameUoides.

229. Buphthalmum cordifolium

230. Zinnia multiflora

1846
1851

1844
1846
1851
1850

1843
1845
1850
1846
1848

grandiflora .

231. Sanvitalia procumbens ..

232. Eudbeckia amplexicaulis

233. Coreopsis atrosanguinea. .

„ Atkinsoniana ,
234. HeliantliuB indicus

235. Bidens diversifolia.

236. Tagetes patala
„ lucida

1844

1846

1851

1857

1844

1846

1851

1844

1846

1851

1843

1845

1850

1844

1846

1851

1857

1843

1845

1850

1844

1846

1857

1846

1848

1853

1845

1847

1843

1845

1850

1845

1850

1842,

1843;

1845

1850

1844

1846

1851

1857

1848

1846;

1848

1109
nil.

17
nil.

63
60
nU.
39
nil.

300
300

300

30O

300

150
150
150
150
150

12
135

3
nil.
184
120
nil.
70
161
nU.
113
18
nil.
181
114

1
nil.
77
26
nil.

37
nil.
86

2
nil.
154
nil.
10
55
nil.

142
nil.
nil.
70
68
nil.
39

124

nil.

139
6

600
600
600
600
600
600
600
600
600
600
300
300
300
300
300
300
300
300
300
300
450
450
450
300
300
300
600
600
450
450
450
100
300
300
900
75
75
75
450
450
450
450
200
450
450

1857.

REPORT — 1857.

69. CoMPOSiT.E, continued.

236. Tagetes lucida

237. Gaillardia aristata

238. Heleniiim Douglasii

239. Callichroa platyglossa

240. Galinsogea trilobata

241. Sphenogyne speciosa .

242. Oxyvira chrysanthemoides

243. Madia splendens.

244, Cladanthus arabicus

245. Lasthenia glabrata . . .
„ californica .

glabrata .

1853

1846

1848

1844

1846

1851

1843

1845

1850

1843

1845

1850

1843

1845

1850

1843

1845

1850

1847

1854

1845

1847

1852

1857

1844

1846

1851

1848

1842

1844

1849

1854

1844

1857

246. Chrysanthemum corona-
rium

247. Athanacea, sp

248. Ammobium alatiim

249. Xeranthemvim annuum . .

250. Calendula pluTialis

,, officinalis
„ maritima
251. Aj'ctotis, sp

1846

1848

1853

1857

1844

1845

184'

1852

1846

1848

1853

185

1844

1846

1857

1842

1844

1849

1848

1844

lul.
87
nU.
192
186
nU.
92
92
nil.
94
100
uH.
157
75
ml.
54
67
nil.
1
nil.
235
nil.
2
nil.
200
175
nil.
53
343
363
4
nil.
270
nH.

450

300

600

300

225

600

100

600

600*

600

69. CoMPOSiTiE, cotitinued.
252. Centaurea depressa

253. Centrophyllum taiu-icmn

254. Carthamiis tiuctoiius

255. Arctium Lappa

256. Cnicus arvensis

257. Ehagadiolus stellatus.

172

122

nil.

131

nil.

nil

nil.

401
nil.
53
26

450
450
450
450
25
600
600
600
300
300
300
300
600
600
600
600
600
600
200
100
100

1844 1

1846 3

1851

18.57

1848

1845

1847

1852

1844

1846

1851

1857 14

1844

1846

1847

1849

1857

1845

1847

1852

1843

1845

1850

1855

1845

1847

1852

261. Aronopogon Dalechampii 1847

1849
1857

262. Scorzonera hispanica 1845

184-

258. Catauanche ccervilea

259. Cichorium Endivia

260. Tragopogon porrifolium

112

nil.

106

nU.

nil.

nU.

286

nil.

228

260

263. Picris echioides

264. Lactuca sativa. . .

265. Borkhausia rubra

„ foetida

70. ONAGEACE.E.

266. CEnothera tcnella

267. CEnothera, sp. from Dou-
glas

268. Godetia Lindleyana

„ lepida
269. Clarkia elegans

1852
1848
1842
1844
1849
1844
1846
1851
1857
1848

1848

1847
1854
1843
1845
1850
1842
1847
1842
1847
1854

300
300
300
300
25
300
300
300
300
300
300
300
150
150
150
150
150
GOO
600
600
450
450

139 450
450
600
600
600
150
30
150
150
600
600
600
100
150
150
150
300
300
300
300,
100

nil.
267

138

nU.
77
10
12

nil.

131

196
2

nil.
35

nil.

139

nU.

nil.

100

180
180
300
300
300'
750
750
15C
15C
15G

* (In open jar.)

ON THE GROWTH AND VITALITY OF SEEDS.

270.
271.

272.
J73.

$74.

575.
J76.

J77.
!78.

179.

70. Onagrace.e, cont.
Eucharidium coucinnum

Lopezia racemosa . . . .

j» »» •■•'

71. Myetacejs.
Eucalyptus, sp

72. LOASACE/B.

Loasa lateritia

„ nitida

>» »)

Bartonia aurea

») »>

» ij

» »

73. TjAIBELLIPERyE.

PetroseUiium sativum

Carum Carui

» i>

>» »

Slum Sisarum

Bupleurum rotundifoHum

CEnantlie crocata

1844
1846
1851
1846
1848
1853

1844

1844
1846
1851
1843
1845
1850
1844
1846
1851
1857

1842
1844
1849
1854
1845
1847
1852
1849
1854
1845
1847
1843
1845
1850
1844
lg46
1851

110
256

nil.
212
208

nil.

14
112

nU.
153

nH.

182

160

nil.

nU.

334

nil.

nU.

nil.

242

106

600
600
600
450
450
450

450
450
450
300
300
300
600
600
600
600

150
150
150
150
600
600
600
600
600
600
600
300
300
300
300
300
300

281.

282.

283.

284.
285.
286.

287.
288.

73. Umbellifer^, cont.

(Enanthe crocata

iEthusa cynapioides . . .

Fceniculum diilee

Ligusticum Levisticum

Angelica Archangelioa

Pastinaca satiya

Heracleum elegans

Daucus Carota

Scandix brachycarpa
Conium maculatum

289. Smyrnium Olusatrum

1857

1842

1844

1849

1854

1847

1849

185'

1842

1844

1849

1854

1844

1846

1851

1842

1844

1849

1843

1845

1850

1842

184-1

1849

1845

1847

1854

1848

1843

1845

1842

1847

1844

1840

1851

1857

nil.

22
3
1

nU.
192

nil.
156

35
2

nil.

ml.
157

nil.
1

nil.
155

79
1

nU.

nil.

159

144

nil.
102

66
2

ml.

300
300
300
300
300
00
300
300
300
300
300
300
300
300
300
300
300
300
150
150
150
300
300
300
900
900
300
150
300
300
450
450
300
300
300
300

From the above summary, the accompanying Table, showing the greatest
ages at which the seeds therein named were found to vegetate, ha.f beeu
prepared.

E 2

REPORT — 1857.

Table showing the Greatest Ages at which the Seeds named in the General
Summary germinated.

Age.

Graminaceee.

Zea Mays

Phalaris canariensis

Aveiia sativa

Triticum aestivum

Secale cereale

Hordeum vulgare

Palmacetp.
Phoenix dactylifera

Amaryllidacece,
Alstroemeria pelegrina ....

Iridacece.
Gladiolus psittacinus ....

Iris sibirica

Tigridia Pavouia

Liliace<e.

Allium fragrans

Caraassia esculenta

Asphodelus luteus

Asparagus officinalis

Conifer<E.
Pinus Pinea

Betulacece.
Alnus glutinosa

Cannabinace<p.
Cannabis sativa

Moracem.
Morus nigra

Euphorbiaceee.

Euphorbia Lathy ris

Croton, sp

Riciuus communis

Corylaceae.
Quercus Robur

Cucurbitaeece.
Momordica Elaterium ....

Cucurbita Pepo

Bryonia dioica

FiolacecB.
Viola lutea

Cruciferce.

Mathiola annua

Arabis hirsuta

Koniga maritima

Lunaria biennis

Iberis umbellata

Biscutella erigerifolia ....

Malcolmia maritima

Hesperis matronalis

Erysimum Peroffskianum.

Lepidiura sativum

iSthionema sasatile

Isatis, sp

Brassica Napus

Brassica oleracea

Brassica Rapa

8 9 1012 13 1415 18 2125 26 27 42 43

ON THE GROWTH AND VITALITY OF SEEDS.

Crambe maritima

Bunias orientalis

Heliophila araboides ...
Schizopetalon Walkeri...,

CapparidecB.
Cleome spinosa

ByttneriacecB.
Hermannia, sp

Tropxolacece.
Tropseolum majus

Malvacea.

Malope grandiflora

Kitaibelia vitifolia

Malva mauritiana

Malva, sp

Hibiscus, sp

Sida, sp

TiliacecB.

Corchorus, sp

Triuinfetta, sp

HypericacecB.
Hypericum hirsutum ....

Magnoliaceoe.
Magnolia

Ranunculace<2.

Adonis autumnalis

Nigella nana

Delphinium, sp

Aconitum Napellus

Paeonia, sp

PapaveracecB.

Argemone alba

Papaver amcenura

Glaucium rubrum

Eschscholtzia californica .
Chryseis crocea

FumariacecB.
Fumaria spicata

Anacardiacea,
Rhus, sp

Xanthoxylaoece.
Ailantus glandulosa

Linacece.
Linum usitatissimum ....

Balsaminacem.

Balsaraina hortensis

Impatiens gland uligera....

Geraniacem.
Pelargonium, sp

Caryophyllacea.

Buffonia annua

Dianthus barbatus

Saponaria annua

Gypsophila elegans

Silene infiata

Viscaria oculata

Pharnaceum, sp

Portulacacece.

Talinum ciliatum

Calandrinia speciosa

3 4 5

1213

REPORT — 1857.

Age.

3 4

1012

26 27'

Polygonaeece.

Polygonum Fagopyrum

Rumex obtusifoliuin

Nyctaginacecs,
Mirabilis Jalapa

Phytolaccacecs.
Phytolacca decandra

Amarantacea.
Amarantus caudatus

Chenopodiacets.
Beta vulgaris

Saururaceoe.
Saururus •

Mesemlryacem.
Mesetiibryanthemum crystalliaum

Tetragoniacece.
Tetragonia expansa

Thymelaceee.
Gnidia, sp

Proteacem.
Leucadendron, sp

Leguminosce.

Pultenaea, sp

Lupinus polyphyllus

Crotalaria, sp

Aspalathus, sp

Ulex europaeus

Spartium scoparium

Cytisus albus

Melilotus cserulea

Medicago raaculata

Psoralea biturainosa

Galega, sp

Colutea

Pisum sativum

Vicia sativa

Faba vulgaris

Lathyrus heterophyllus

Orobus niger

Coronilla, sp

jEschynomene, sp

Hedysarum, sp

Clitoria, sp

Phaseolus multiflorus

Dolichos, sp

Csesalpiiiia, sp

Cassia, sp

Tamarindus, sp

Gleditschia, sp

Adenanthera, sp

Robinia

PomaceoB.

Cotoneaster rotundifolia

Crataegus punctata

Rosacem.

Potentilla nepalensis

Geura, sp

Lythracece.

Cuphea procumbens

RJiamiiacex.
Cryptandra, sp •

ON THE GROWTH AND VITALITY OF SEEDS.

Age.

SolanacecB.

Petunia odorata

Datura Stramonium

Hyoscyamus niger

Nicandra physaloides

Solanum ovigerum

Lycopersicum esculentum

Convolvulace<2.
Convolvulus major

PolemoniacecB.

CoUomia coccinea

Gilia achilleaafolia

Polemonium caeruleum

HydrophyllacecB.

Eutoca viscida

Phacelia tanacetifolia

PlantaginacetB.
Plantago media

Primulacem,
Anagallis arvensis

Nolanacea.
Nolana atriplicifolia

Boraginaceee.

Cerinthe major

Ecliium grandiflorum

Cynoglossum glochidatum

Labiatm.

Elsholtzia cristata

Nepeta cataria

Leonurus cardiaca

Selaginacecs.
Hebenstreitia tenuifolia ...

PedaliaceeB.
Marty nia proboscidia

Bignoniacex,
Eccremocarpus scaber

ScrophulariacecB.

Schizanthus pinnatus

Browallia data

Verbascum Thapsus

Alonsoa incisa

Linaria Prezii

Antirrhinum majus

Collinsia heterophylla

Mimulus moschatus

Digitalis lutea

Campanulacem.
Campanula Medium

Valerianacem.

Valeriana officinalis

Fedia dentata

Dipsaeacece.
Dipsacus laciniatus

Compositce.

Ageratum mexicanum

Aster tenella

Callistemma hortensis

Stenactis speciosa

Kaulfussia amelloides

Buphthalnium cordifolium

3 4 5

6 8

1012,13

1415

2125

2627

REPORT — 1857.

Zinnia niultiflora

Kudbecki^ amplexicaulis

Coreopsis atrosanguinea

Heliaiitlius indicus

Bidcns diversifolia

Tapetes lucida

Helcnium DougUsii ■

Callicliroa platvglossa

Galinsogca trilobata

Splienogyne speciosa

Oxyura chrysanthemoides .

Madia splendcns

Lasthenia caiUfornica . . . . •

Chrysanthenura coronarium.

Amraobium alatum ■••

Xerauthemum annuum

Calendula pluvialis

Centaurea depressa

Cartliamus tinctorius

Arctium Lappa

llhagadiolus stellatus

Catananche cserulea

Cichorium Endivia

Tragopogon porrifolium ....
Arnopogon Dalecliampii ....

Lactuca sativa

Barkhausia rubra

Onagraceoe.

(Enothera, sp

Godetia lepida ■

Clarkia elegans

Eucharidium concinnum ...

Lopezia racemosa

Myrtacem.

Eucalyptus, sp

LoamceeB.

Loasa lateritia

Bartonia aurca ■

Umbellifera.

Petroseliniim sativum

Carum Carui •

Bupteurum rotundifolium...

(Enanthe crocala

yEtbusa cynapioides

Foeniculum dulce

Ligusticum levisticum

Angelica Arch angelica

Pastinaca sativa

Heracleum elegans

Daucus Carota

Conium maculatura

Smyrnium Olusatrum

Age.
3 4 5 6 8 9 10 12 13 14'l5Jl8'2l|25 26 27142143

W. H. Baxter.

Oxford, 20th August, 1857.

ON STEAM NAVIGATION AT HULL. 57

Continuation of Report on Steam Navigation at Hull. By James
Oldham, C.E. Hull, M.I.C.E.

On the occasion of the Meeting of the British Association at Hull in 1853,
I had the honour of reading a short paper " On the Rise, Progress, and present
Position of Steam Navigation at Hull," and thinking that a continuation of
the subject might be interesting to the Association, to show the increase or
advance which has taken place since 1853, I have prepared a second Report
as a Supplement, which I beg now to present, but as it consists chiefly of
Tables of Statistics, 1 shall only read to you the summary of the Tables, com-
paring them with those of 1853 ; before doing so, however, I will just refer
to one other point introduced in my former paper, I allude to the facilities
offered in the Port of Hull to iron ship-building. I then called upon ship-
owners of tiiat Port to encourage their fellow-townsmen in this important
branch of art, and the result has been, that, since the Meeting of 1853, about
fifty-six iron ships have been launched and completed, and by the end of the
present year that number will be increased to sixty iron vessels of various
descriptions, which will have been built in Hull by two houses, viz. Messrs,
Charles and William Earle, and Messrs. Martin Samuelsou and Co., in about
four years, — varying in tonnage from about 1600 downwards, but producing
an aggregate of about 27,000 tons burthen. Several of the above were built
for other British Ports, and some for foreign Companies. The result is
highly encouraging, and although a mere fraction of what has been effected
throughout the United Kingdom, yet it illustrates the spirit which animates
the determined and onward movement of commercial enterprise. Our
builders too have made rapid improvements in both ships and machinery,
and have proved, that, by following out the principles laid down by Mr. Scott
Russell, the results will always be satisfactory. 1 may mention as a proof of this
remark, that in one case a steam-ship of upwards of 1100 tons register, and
only of 135 nominal horse-power, has made the passage from Cronstadt to
Hull with a full cargo of goods, of upwards of 1500 tons weight, in 5^ days.

It will be seen by the summary of the Tables of Statistics, compared with
1853, that there is under each head, except one, that of B, a great increase
of steam shipping, viz. — A gives an increase of 10,564 tons and 2755 horse-
power. B a decrease of 1317 tons, and a decrease of 733 horse-power;

but this is chiefly owing to some of the steamers having been placed in the
list B, when they ought to have been in list D of 1853. C gives an in-
crease of 15,363 tons and of 3066 horse-power. D gives an increase of

1275 tons and of 676 horse-power.

The total number of steamers, leaving out several tugs and other boats,
but some of which were included in 1853, has increased from 81 to 131.

The total increase in tonnage is 25,885, and of horse-power 5764.

Tables of Statistics.

The following Tables show the present position of Hull in regard to the steamers which
belong to, or trade from the Port : — (A.) Sea-going steamers belonging to the port. Total

tonnage, 19,841 ; horse-power, 5554; averaging 3'57 tons per horse-power. (B.) River

steamers belonging to the port. Total tonnage, 901 ; horse-power, 402 ; averaging 2-24

tons per horse-power. (C.) Sea-going steamers belonging to other ports, but trading to

Hull. Tonnage, 21,272; horse-power, 5302; averaging 4-01 tons per horse-power.

(D.) River steamers belonging to other ports, but trading to Hull. Total tonnage, 2431 ;
horse-power, 1102 ; averaging 2-20 tons per horse-power.

The total number of steamers trading to Hull amounts to 131, of the aggregate burthen
of 44,445 tons, and 12,360 horse-power; averaging on the whole 3*60 tons per horse-
power ; giving also an average on the total number of steamers of 339"198 tons each.

Note. — 68 screw and 63 paddle-steamers = 131.

REPORT — 1857.

-^ -s

•H 'S

«u

a "3 S S

■a

bert Napier, Glasgow,
vid Napier, Glasgow,
tterley Company, Aberdeen
rrester and Co., Liverpool,
ownlow and Co., HuU.
nion and Co., Leeds,
pier and Crichton, Glasgow
ird and Co., Greenock,
sston and Co., Liverpool.
OS. Wingate and Co., Whit
ownlow and Co., Hull.
D.Marshalland Co., South S
ownlow and Co., Hull,
ates and Young, Belfast,
and W. Earle, HuU.
Samuelson and Co., HuU.
lock and Denney, Dumbar
lock and Denney, Dumbar
Samuelson and Co., HuU.

le, Hull,
and Co., HuU.
Greenock,
le, HuU.
le, HuU.
le, Hull,
and Co.
le, HuU.
and Co., Hull,
le, Hull.
Co., HuU.
Wood.
Renfrew.
le, HuU.

a
&

C. and W. Eai
M. Samuelson
Caird and Co.,
C. and W. Eai
C. and W. Ear
C. and W. Eai
R. Hawthorne
C. and W. Ear
M. Samuelson
C. and W. Eai
Brownlow and
Thompson auc
Hoby and Co.
C. and W. Eai

«QQa&Haafc.ZocuH23HM'_)oSfefc.S

"o :

3
o

•a

§> :

^ "tb^i

3 S

— o
"3 t.

•g

a
1

c;
3

"2 1" t:

Co., HuU
0., Thorne
chton, Gla
, Greenock
d Co., Live
Co., HuU
1. Hi.U

, South Sh
Gainsborou
ung, Belfas
le. HuU ..

rS 3

-"2 Si
ca <u H

d
o

all

Co., Hull
le, HuU ..
rs, Newcas
le. Hull ..

~ a .

Robert Napier
Brownlow and
Duffles and Co
John Laird, Bi
Brownlow and
Pearson and C
Napier and Cn
Murris and Co
Motteshead an
Brownlow and
Edward Gibsoi
T. D. Marshall
Henry Smith,
Coates and Yo
C. and W. Ear
M. Samuelson
Denney, Broth
A. Denney, Dl
M. Samuelson

C. and W. Ear
M. Samuelson
Denney Broth
C. and W. Ear
Brownlow and
G. and W. Eai
Palmer Brothe
C. and W. Eai
M. Samuelson
C. and W. Ear
Brownlow and
Richardson an
Hoby and Co.,
C, and W. Eai

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62 REPORT — 1857.

Report of a Committee, consisting of The Rt. Hon. Earl of Hard-
wiCKE, Chairman; Mr. Andrew Henderson, Mr. John Scott
Russell, Mr. James Robt. Napier, Mr. Charles Atherton,
Mr. Arthur Anderson, Rev. Dr. Woolley, Admiral Moor-
SOM (vice Mr. W. Mann), Mr. John Macgregor (vice Mr. G. F.
Young), Captain J. O. Owen, Professor Bennett Woodcroft,
James Perry, and Mr. James Yates, Secretary, appointed to
inquire into the Defects of the present methods of Measuring and
Registering the Tonnage of Shipping, as also of Marine Engine-
Power, and to frame more perfect rules, in order that a correct and
uniform j^rinciple may be adopted to estimate the Actual Carrying
Capabilities and Working-Poiver of Steam Ships^.

The Committee, having held its sittings weekly, for the purposes of in-
quiry and the reception of information, beg leave to present the following
Report : —

Your Committee think it necessary, at the outset, to state the difficulties
they met with (incidental, no doubt, to all private committees that attempt
to inquire into laws affecting particular classes) in inducing individuals to
appear before them to give evidence on this subject, or to give information
by writing or correspondence.

The chief information now derived is from members of the Committee,
who, being personally interested in the subject, were naturally biassed in
their views by the circumstances that surround them.

The mode, therefore, your Committee thought it best to adopt, for the
purpose of eliciting information, was that of circulating the annexed letter
(see No. I. in Appendix), specially referring to eight points of inquiry bear-
ing on the subjects.

Copies of this Circular were sent to the Admiralty, Navy Board, Board of
Trade, Custom House, and Treasury, with a request that copies might be
forwarded to the vai'ious Officers under Government connected with the
scientific and working departments.

Your Committee received from all the Government Departments a refusal
to forward those questions.

Copies of the Circular were also sent to all the Local Marine Boards, to
the offices of the public newspapers, at shipping ports, and to many gentle-
men connected with science and trade.

The Local Marine Boards declined to entertain the question.

Answers were returned from several individuals, including members of
your Committee.

Your Committee proceed to give a short summary of the replies, which
they received from their own members, and which are inserted in the
Appendix.

Mr. John Scott Russell considers the object of registered tonnage is the
taxation of their contents ; the present is a mere standard of taxation ! that
all tonnage dues should be abandoned, and the same should be levied on
freight.

For scientific purposes, he considers that the register tonnage measurement
cannot be of any service — does not consider that it would be tolerated, that

* See Report for 1856, p. 458.

ON THE MEASUREMEMT OP SHIPS FOR TONNAGE. 63

lines of construction and scientific calculations should be demanded to be
given up under an Act of Parliament.

Considers (on tlie question of steam power) that it would be neither politic
nor expedient to attempt to define power in a form more absolute than the
nature of the subject practically admits.

The results of his reflections are, that nothing is necessary to be now done
except to rectify the allowance for engine room, which remains fictitious and
arbitrary.

Dr. WooUey thinks it hopeless to look for information from legislative
enactments that would be useful in a scientific point of view.

Thinks that in the levying of dues on shipping it is impossible to devise a
general rule fairer than that which is now in force.

Does not think the public much interested in the question.

Does not doubt that the more science is brought to bear in shipbuilding
the greater will be the economy, both as regards the first cost and the
management of vessels ; and owners will consequently be able to charge a
lower price for carrying goods and passengers.

Considers that an enforced registration should have for its object —

1st. To secure a fairness in levying Government dues,

2ndly. To give a fair idea of the amount of tonnage or roomage employed
for mercantile purposes.

Thinks the present registration sufficient for merely statistical pur-
poses.

Thinks the present law makes too great a difference between steamers and
sailing ships.

Sees no valid reason for making distinctions based on the difl^erent mate-
rials of which ships are built, or making discriminative distinctions between
vessels based on the difl^erent principles of machinery with which they may
be fitted.

He agrees with Mr. Napier in thinking an enforced registration of engine-
power needless.

Mr. James Robert Napier considers the objects of registration to be the
levying of dues, and simplifying the process of transferring the property
from one owner to another.

Thinks the present system of tonnage measurement is more minute than
is necessary, and of little or no use to the shipbuilder ; is inclined to take
Mr. Russell's view of the subject, and not limit the load-draft of water.

Does not see any reason for making a distinction between vessels built of
wood or iron.

Considers nominal horse-power a useless terrtl. Instead of nominal horse-
power, he would substitute simply the capacity of the cylinders, or area of
cylinders, multiplied by length of stroke. This would be positive informa-
tion, and would be useful in buying and selling, and might be inserted in
the registry of a vessel.

Thinks a legal standard of power would remove some confusion which at
present exists.

Mr. Atherton considers that the present registration of shipping, as re-
spects tonnage and nominal horse-power, affords no definite measure of
quantity, either as to ship or engines, available for judging of the relative
capabilities of steam ships.

Thinks the statistics of trade, based on the present expression of "ton-
nage," does not indicate the amount of trade, as respects the weight of goods
conveyed.

Considers that there is no constant ratio between " Tms Burden " and

64 REPORT — 1856.

" To7is Begister," and the capability for carrying tons weight of cargo ; and
therefore the present official registration does not fulfil the advertising
requirements of trade.

Considers that no definition of tonnage, and no mode of determining it,
can adequately embrace both the capability of a ship for carrying weight and
its capacity lor holding hulk. The weight-tonnage and the bulk-tonnage
must therefore be distinct.

Considers that, as the present scheme of registration does not set forth
any of the principal dimensions, as length, breadth, and depth, or the load-
line-draught, or give the displacement either at light-draught when rea<ly to
receive cargo, or at tlie load-draught or submerging-draught, it cannot, on
any definite principle, constitute the base of scientific inquiry into the com-
parative displacement and consequent dynamic performances and merits of
ships, nor a reliable base for statistical inquiry into the imports and exports
of the country.

Does not consider that the science of naval -architecture would be in-
terfered with by the constructor's deep draught of water forward and
aft, or some regulation limit to be assigned as such, being made an item
in the official registration of every ship, and duly marked on the ship
herself.

Considers that, in forming a rule for placing this mark to regulate the
freeboard limit, an investigation into existing practice (as to the ratio which
actually exists between the freeboard and the length, breadth, and depth of the
hull^ will be the best means of deducing a rule for determining the position
of the mark in question. Proposes a rule to exemplify this method of deter-
mining the freeboard limit.

Considers that, if the registration be based on admeasurements compre-
hensively adequate for deducing therefrom the iveight-tonnage and hulk-
tonnage, then no occasion will exist for discriminative protection in favour
of any particular class of vessel, whether sailing-ship or steamer, or descrip-
tion of material with which a ship may be built, or systems of machinery by
which ships may be propelled.

Considers the present registration of engine-power a delusion, because no
definite measure of power has been assigned, either by the legislature or by
the practice of trade, to the term " Nominal Horse-power," as indicating the
working-power of marine engines.

Considers that a legalized unit of horse-power is a requirement only of
secondary importance to a comprehensive tonnage registration.

Considers there can be no objection to a system prescribed by law, whereby
ships are to be measured for tonnage registration, to include their capability
for carrying weight, in addition to the bulk-tonnage prescribed by the pre-
sent law, and considers that all official admeasurements should be made on
one uniform principle, to be sanctioned by scientific authority. Shows that
weight-tonnage would assimilate closely with metrical tonnage.

Admits Sterling's rule, as prescribed for the measurement of ships, by the
Act of 185t, to be based on strictly scientific principles, but regards its
practical application as inconvenient, and not self-detective of error, and a
pirating of the lines of ships.

Considers Mr. Peake's system, for various reasons stated, as the best for
common use in determining cubical admeasurements, whereby the roomage
and tonnage of a ship may be ascertained and registered, without affording
data for pirating tlie constructor's lines.

INIr. Henderson states the objects of registering tonnage; gives a table
that shows the mode that has been in use, and the measurements for ascer-

ON THE MEASUREMENT OF SHIPS FOR TONNAGE. 65

taining displacements at certain specified draughts that are in addition
desirable ; gives a proposed form of certificate.

Considers the plan of measurement (at present used under the Act of 1854)
practically inefficient for obtaining a correct mensuration of vessels, in con-
sequence of equal divisions not being ahvaj's attainable.

Considers that, to obviate certain defects (stated in his paper given in the
Appendix, No. 6), all measurements, besides that of the measuring officers,
should be attested by the builder and owner, &c.

Considers that, after a trial of two years, the present tonnage measure-
ment and registration system has proved deficient and non-eflfective for the
attainment of most of the objects of public utility which registration ought
to afford.

Gives a comparison of four modes of measurement, on paper ruled to a
scale, i inch to a foot, for facilitating the process of admeasurement.

Thinks tliat the book of instructions given to measuring surveyors should
contain practical directions and diagrams of each of these four modes of
measurement.

Thinks that the measuring officers should be shipbuilders or nautical men,
experienced in taking measurements.

Admiral Moorsom is of opinion that every vessel should incur a penalty
which is loaded so as to sink below a certain draught of water.

That her registered tonnage should comprise the weight of water between
her assigned load-draught and that draught which she would have when fit
for sea, with crew and stores and everything on board, except that by which
she earns her freight.

He proposes a plan for obtaining the results required for registra-
tion*.

Considers that the public have great concern in the improvement of
engines, and improvement can make but slow and fitful progress when the
poiuer exerted and power given out are not known.

Considers that any measure of power must be incomplete without the
weight of fuel which is the originator of the power, and in any general
system for the registration of engine capability we must include the con-
structive details of the boiler as well as the cylinder.

Such an expression would mean a given weight moved through a certain
space in a certain time with a certain weight of coal.

Admiral Moorsom forwarded also a pamphlet, by himself, bearing on this
subject, which will be found in the Appendix.

Mr. James Yates shows the points of agreement between the party, as
represented by Mr. Moorsom, Registrar-General of Tonnage, and that repre-
sented by those who consider the present sj-stem of registration imperfect.
Recommends the adoption of the " Metrical Ton " as the base of a ship's
registered tonnage.

The foregoing is a brief summary of the answers given to the eight
questions circulated by your Committee, which were received from mem-
bers of the said Committee, and will be found in the Appendix to this
Report.

Letters from Mr. James Peake and Admiral Laws, bearing on the subject,
were received.

That from Mr. Peake gives a full explanation of his method of calcu-
lating the tonnage of ships, both internally and externally.

Your Comjiiittee have also received answers from gentlemen connected
with Science and Trade to the effect, as follows: —

* Appendix, No. 7.
1857. »

66 REPORT — 1857.

Mr. Mansel considers that the registration of the carrying capability of a
vessel should be viewed in reference to weight alone, and is strictly propor-
tional to her external volume between the load and light-draught water-lines,
but has no definite relation to the capacity inside of the inner lining.

Considers that, at the commencement, the desire to foster the growth of
steam-shipping led to the adoption of a discriminating tonnage, to an extent
injurious towards sailing vessels, and erroneous in principle.

Considers that the capacity sacrificed to fuel alone ought to have been
exempted from dues.

Thinks that the difference between the displacement at the light-draMght
and the displacement at the /ocrrf-draught, would be the weight-carrying
capability of the ship for cargo and stores, in the case of a sailing vessel, and
for cargo, fuel, and stores, in the case of a steam-ship ; and that it is impe-
rative that this difference should be registered, even though it might not be
taken as the basis for levying dues.

Considers that the present law for measuring ships is objectionable, inas-
much that it does not directly imply the external volume of the vessel upon
which the carrying capability, cost of construction, and propulsion, directly
depend. Also, supposing equal strength, it is our interest that the difference
between the external and internal volume shall be a minimum. At present,
with equal displacement, the vessel with this difference greatest pays least
dues, and thus an indirect premium is given to the worst ship. Again, tlie
method of allowing engine deduction is still more objectionable, for if we
fill a certain portion of the internal volume with an inefficient mechanism,
we get the same deduction from gross tonnage, as if the same portion of
the same vessel had been filled with the most perfect mechanism, working
up to a much greater power, to the disadvantage of the better mechanised
ship.

Considei's that nominal horse-power implies a certain area of piston moving
through a certain space, &c. Indicated horse-power has no very definite
relation to the above. The fii'st represents more nearly the commercial
value of the material and workmanship; the second, the evaporative power
of boiler, fuel, and cost of working, &c.

Thinks that the simplest divisor for indicating horse-power, in foot lbs.
per minute, should be 100,000. Sees no objection to retaining the old and
well-known unit of 33,000 font lbs. per minute equal to one-horse power,
and thinks it absolutely essential that both nominal horse-power and indi-
cated horse-power should be defined and recognized by legal enactment,
and form part of the registered elements of ships — the first, or engine
register of nominal horse-power, being essential for the valuation of the
engine, and the second, or indicated power, for the working expenses of the
engine.

Mr. Greenhow thinks it would be of great value to acquire a true estimate
of the capability for carrying weight of cargo, and advances his reasons for
so thinking : —

Scientifically. — The register ought to be a decided gauge, by which to
ascertain her capability for carrying weight of cargo.

Statistically. — The returns of tonnage now published afford no criterion
by which to judge of the amount of produce conveyed.

Considers that the present system of tonnage measurement, as prescribed
by the Merchant Shipping Act of 1854, gives very incorrectly "the internal
roomage of ships."

Sees no difficulty in a change towards truth, in re-arranging the tonnage
dues, by which no greater amount will be paid by the shipowner.

ON THE MEASUREMENT OP SHIPS FOR TONNAGE. 67

Thinks there ought to be a limit to the amount of lading.
States that he has established a rule, by which to establish the position of
the light and load line, suited to the varying dimensions of different ships.
He gives the plan of his rule.

Mr. Lawrie does not think that any restriction should be laid on the
draught of water in a ship, but that it should be left in the hands of the
insurers. Thinks a radical change should be made in the mode of measuring
engine-power.

Mr. Schoneijder finds that he has been foiled in his search for knowledge
in England, as regards the size and tonnage of ships, as well as their engine-
power; the present system of registration giving him no information on this
important subject.

Mr. Miller thinks that the present rule (Sterling's) is sufficient for all
purposes of measurement, and gives correct data for whatever measurements
may be required ; yet he considers that, in addition to the same, there should
be supplied a correct scale of displacement; also the proper position of the
centre of gravity of displacement; centre of effort of sails, and the length of
the meta-centre, or centre of stability; — thereby determining the ship's
proper trim.

Does not think it equitable or advisable to make a discriminative distinc-
tion (to the extent given by the present law) between sailing ships and
steamers.

Thinks it desirable that some definite system be adopted that might deter-
mine the actual working-power of steam-engines for marine purposes.

Mr. Baxter writes on the loss of ships at sea, and thinks that the capability
of a ship to convey a cargo safely through the sea is in no way defined, or
capable of being judged of, by the present system of tonnage.

Mr. Henry Wright states that, in 1839, before a Committee of Inquiry into
the cause of the Wrecks of Timber Ships, it was found that in 1836-7-8, out of
5427 vessels which cleared from British North America, there was an aggre-
gate loss of 226, or 4*164 per cent, by wreck, of which upwards of 150 were
at sea, the remainder being wrecked on shore. It was remarked that there
were lost as many good as bad ships, showing that the frailty of the vessels
was not the sole cause, but owing to improper over-stowage. The result
was " interference" and the loss was reduced one-half.

Mr. Wright demonstrates the weakness of the present law io prove the
overloading of a ship, and that insurance offers no safeguard whatever.

Mr. George Rennie states that he agrees generally in the views of Mr.
Atherton.

Your Committee, having duly weighed the character of the evidence, and
the opinions given therein, are of opinion, — 1st, That the present method of
measuring and registering the tonnage of shipping, gives a very close
approximation to the internal capacity of a ship ; but that it gives no mea-
sure of the poM'er of a ship to carry weight.

2ndly. Engine Power (Horse-power), though an item of registration, yet
has no practically definite or legalized signification, as a measure of marine-
engine capability for working power; no unit of power is given, and there
are no registered data by which the working capability of an engine can be
approximately ascertained.

Your Committee differ in opinion as to the capability of ships for carrying
weight being made an item of registration, but if one denomination of
tonnage only is to be recognized, concur in the opinion that "tonnage"
(though a misnomer as applied to space) should be continued, as under the
present law, to be based on the internal roomage of ships. Consider it

F 2

68 REPORT — 1857.

incompatible with the principles of unrestricted competition to make arbi-
trary discriminations, in the measurements for tonnage, between vessels built
of timber or iron, or fitted with the paddle or the screw (c. 22 and 23), for
the following reasons : —

The internal capacity of iron ships (ships built upon the cellular principle,
like the ' Great Eastern ') has not necessarily a greater ratio to the external
bulk, than is the case with wooden ships (ships built on the diagonal plank
principle, like the ' Nankin,' ' Niger,' and ' Banshee') ; but the very reverse
may be the case, and the space required for the machinery of a screw-ship, of
given power, is not necessarily either greater or less than the space so
occupied by engines of the same power constructed for a paddle-wheel
vessel.

Then, again, the law, in its present discriminations between the paddle
and the screw, does not meet the case of the paddle and the screw combined
(as in the ' Great Eastern'), or, indeed, any other combination.

It therefore appears to your Committee, that discriminations, as regards
the material of which ships are built, or different mechanical contrivances
by which ships are propelled, should be abolished.

As negards the discriminations between sailing vessels and steamers (sec-
tion 23), whereby, in certain cases, steamers propelled by paddle are allowed
37 per cent, and when by screw, 32 per cent., to be deducted from the gross
tonnage, in consideration of the space occupied by machinerj^ which arbi-
trary deduction gives no consideration to space actually/ appropriated to
engine room, or to the actual power or weight of the machinery, without
which consideration such space may be occupied by cargo, this discrimina-
tion, and the mode of assessing it, appears to your Committed devoid of
principle, and not just even between steamers themselves. For example,
a sailing vessel and a steamer may be of the same gross tonnage (say 1000
tons), but in consequence of the steamer being fitted with auxiliary ma-
chinery, not weighing possibly more than 100 tons, including coals, there is,
by law, in the special cases now referred to, a reduction from its tonnage of
37 per cent., or 370 tons; and again, the reduction of the steamer's tonnage
may be 370 tons, whether the weight of the machinery and coals be actually
100 or 500 tons.

That in making a deduction for propelling-machinery and fuel, the deduc-
tion for tonnage based on space, as by the present law, should be rated on
actual space occupied; and as respects tonnage based on weight, the reduc-
tion would in effect be rated on the weight of machinery, the same being
included in the light-displacement, which would be deducted from the load-
displacement.

Your Committee, considering that the question of Government dues or
private dues assessed on shipping is a question between parties in the state
(which, though indirectly bearing on this inquiry, yet is not put to your
Committee as a question for their consideration and report), does not feel
itself called upon in the Report to enter into its merits.

On the subject of Engine Power, your Committee cannot find that any
statute unit of power has ever been recognized in any legislative enactment
for fixing standard units of quantity (such as the standard yard, gallon,
pound-weight, <S:c.). The registration of horse-power is prescribed by the
Act of 1854, but no legalized definition is given of the term as a measure of
mechanical power, nor has the term "Nominal Horse-power" any definite
signification in trade as a measure of working power ; and consequently
the registration of the engine-power of a steam-ship affords no certain indi-
cation of her engine capabilities.

ON THE MEASUREMENT OF SHIPS FOR TONNAGE, 69

It is found in practice that the actual working-power of marine engines,
with reference to their nominal horse-power, fluctuates upwards of 100 per
cent., and on the general average of the practice of the present day, it
appears that the unit of marine engine horse-power is equivalent to 100,000
lbs. raised one foot high per minute of time, being equal to three times the
unit denominated " Indicated Horse-power" (viz. 33,000 lbs. raised one foot
high per minute).

It appears to your Committee that the legalization by statute of some
standard unit of power is an indispensable requirement of the age ; and the
question is, whether 33,000 lbs. or 100,000 lbs. raised one foot high per
minute, shall be recognized and legalized as the standard unit of power to
which the registration of marine engine-power should have reference.

That the unit designated by 100,000 lbs. raised one foot high per minute,
would nearly approach the working capability per nominal horse-power of the
present marine engines, is admitted ; but conceiving that a registration of
engine capability would still not give all the information as to the engines
which registration ought to embrace, your Committee recommend that the
registration of marine engines should, in addition to their capability, embrace
the number and diameter of the cylinders, and length of stroke, or other indi-
cation of the size of engine, according to its construction, as well as the number
and size of the boilers, and total area of the fire-grates, whereby the size
and quantity of the machinery on board, irrespective of its capability for
working power, may be at any time compared with the registered description
thereof.

The Committee supposed it important to confine the Report to those points
on which a definite aiid almost unanimous opinion could be given. With
respect to the question relating to the registration of weight-tonnage and
displacement, after maturely considering the evidence, the Committee did not
agree in such a manner as to be able to recommend this portion of the subject
for legislative enactment.

(By order of the Committee) Hardw^icke,

May 27, 1857, Chairman,

APPENDIX.

No. I. — Circular. — To the respective Members of the Committee appointed
by the British Association " to inquire into the defects of the present methods,
and to frame more perfect rules for the Measurement and Registration of
Ships and of Marine Engine Power, in order that a correct and uniform
principle of estimating the actual Carrying Capabilities and Worki7ig Power
of Steam Ships may be adopted in their fuhire Registration^

Sir, — Rear-Admiral the Right Honourable the Earl of Hardwicke having
been nominated by the members of the Tonnage Committee, "to officiate as
permanent chairman for conducting (with the assistance of a private secre-
tary, whom hisLordship may be pleased to nominate) the proceedings of this
Committee," his Lordship has directed me as Secretary (pro tern.') to request
that the members of this Committee will be pleased to meet at the Hall of the
Society of Arts, Adelphi, London, on Thursday, 1st January next, at eight
o'clock P.M., to take into consideration the business assigned to this Com-
mittee, especially with a view to concerting as to the points of statistical
inquiry on which this Con>mittee may require to avail themselves of the co-

70 REPORT — 1857.

operative assistance of the Statistical Section of tlie Britisli Association, in
accordance with the recommendation and resolution of the General Com-
mittee of the British Association to that effect.

Preparatory to this meeting on Thursday, the 1st January, and in order
that the opinions of each of the members of the Committee, whetiier present
or not, may be known and duly noticed, it is requested that each member
will be pleased to communicate in writing, on or before Monday, 1st De-
cember next, addressed to " The Secretary of the Tonnage Committee, Society
of Arts, Adelphi, London," his opinions on the following points, and on such
other points as may especially occur to respective members in relation to
the matters submitted by the British Association for the consideration of
this Committee: —

1 . To particularize the objects of public utility, fiscal, mercantile, scien-
tific, and statistical, sought to be attained, or which may be promoted by a
complete system of measurement, and comprehensive registration of the
tonnage capabilities of ships, and the engine capabilities of steam ships.

2. Admitting that the present system of tonnage admeasurement, as pre-
scribed by the Merchant Shipping Act of 1854, giving the internal roomage
of ships, affords useful data for registration so far as it goes, what are the
additional details of admeasurement which are required to give the capability
of ships for carrying weight of cargo, and in other respects necessary to render
the official registration of shipping, as periodically published by authority in
the Mercantile Navy List, complete and effective for the objects of public
utility above referred to?

3. To particularise in what respects the present system of tonnage and
engine-power admeasurement and registration, as prescribed by Part 2 of the
Merchant Shipping Act of " 1854," is deficient and not effective for the
attainment of the objects of public utility above referred to.

4. Following the example of limitations commonly prescribed by Govern-
ment in matters wherein public safety is concerned, such, for example, as
protection from fire in Building Acts, what are the objections to the official
assignment of some limit to the load-draught of water, based on ordinary
conditions of protection from wreck, at which ships may leave port; and
presuming on the necessity for some limit being assigned which the draught
of water may not exceed, by what rules may this limit be most correctly
determined, and by what regulations may it be most efl^ectually enforced
without involving unnecessary interference with mercantile shipping trans-
actions ?

5. In what respects is it commercially equitable, or in other respects
advisable, to make a discriminative distinction between sailing ships and
steamers in the measurement of the registered tonnage on which dues may
be charged on shipping?

6. In what respects is it commercially equitable, or in other respects advi-
sable, in the measurement and calculation of registered tonnage, to make a
discriminative distinction, based on the different materials (whether wood or
iron, or a combination of both) with which ships may be built, or on the
diff"erent principles of machinery (whether paddle-wheels, screw-propeller,
paddle and screw combined, water-jet, or other appliance) with whicii ships
may be fitted ?

7. Seeing that no definite measure of power has been specifically fixed by
law as the statute unit of mechanical power (as has been done to regulate all
other measures of quantity, as in the cases of the statute yard, the statute
acre, the statute gallon, the statute pound, &-c.), and seeing, moreover, that
in the practice of trade, the " nominal horse-power" of a steam-ship does not

ON THE MEASUREMENT OF SHIPS FOR TONNAGE. 'jfl

define the measure of power available for the propulsion of the ship (the
capability of engines for the production of working power with reference to
their nominal horse-power being notoriouslj', in some cases, the double of
what it is in others), what steps should be taken to remedy this incongruity ;
and, presuming on its being determined to adopt some specific measure of
power as the legalized standard unit of power, what definition, measure, or
amount of power, should (in the opinion of the respective members of this
Committee) be adopted as the statute unit of marine engine-power, and by
what name should it be called, viz. whether " horse-power," or "marine horse-
power," or " statute-power," or " units of power," or other denomination ?

8. The respective members of Committee are requested to state their
opinion whether it be advisable that any particular mode of prosecuting the
details of measurement and working out the calculations thereof (such, for
example, as Sterling's rule) should be prescribed by law for the measurement
of ships, as is done by the Merchant Shipping Act of " 1854;;" or, ought
the system of taking the measurements and working out the calculations to
be left to the discretion of the chief officer of the department on wJiom the
responsibility for the scientific prosecution and accuracy of the calculations
will professionally rest, as in the case of the astronomical calculations for the
Nautical Almanac published by Government, but for which the system of
prosecuting the observations and deducing the calculations is not prescribed
by law, but determined and improved from time to time, as may be, by the
astronomer ; and if it be considered that a prescribed mode of working out
the calculations ought to be fixed and enforced by law, is the rule (Sterling's)
now enforced by the Merchant Shipping Act the best rule now known and
practised for calculating the cubature of ships?

It is not expected that the respective members of this Committee will indi-
vidually express opinions on each and all of the various points above sub-
mitted for their consideration, but it is requested that each member, according
to his special avocation, experience, or acquirements, will address himself to
those points on which he may be regarded as an authority ; and as the com-
plete elucidation of the matters referred to this Committee, with a view to the
public good, is the duty assigned to this Committee, it is requested that each
member will not only express his own opinion, but seek information and confer
with others within his sphere conversant with the matters referred to, though
not members of this Committee ; and for the purpose of aiding in this object
of obtaining information, duplicate copies of the points of investigation above
propounded are enclosed herewith.

It is further purposed, that as soon as the written opinions or answers of the
respective members of the Committee, to be given in on or before Monday,
the first day of December, shall be received by the Secretaiy, addressed as
above directed, copies thereof will be forwarded to each of the members of
this Committee for mutual information, and in order that further confirma-
tion, or correction, or amendment of the original opinions, may be thus
elicited, to constitute the base of the general report to be discussed and
settled at a future meeting of this Committee, preparatory to being presented
to the British Association at their ensuing meeting.

I am, Sir, your obedient Servant,

Charles Atherton,
Woolwich Dockyard, Nov. 6, 1856. Secretary, jtfyo te7n.

No. 2 Mr. J. Scott Russell {Member of the Committee).

1st, 2nd, 3rd. The original object of legislation for tonnage appears to

72 REPORT — 1857.

have been the taxation of their contents. A keel of coals was a vessel of
given size, carrying a given bulk and weight of coals. The present imperial
tonnage scale is still a mere standard of taxation. It is, however, much more
common to tax tlie ship iiccording to this imperial tonnage, than to levy the
tax on her contents, as originally intended. Taxation by tonnage is, there-
fore, arbitrary ; to distribute taxation, or to exact tonnage dues equitably,
they should be levied on the actual freight or cargo, and not on the mere
vehicle %vhich conveys them. If this were done, tlie present tonnage-laws
might be altogether repealed, or retained for statistical purposes merely. It
would tend much to the promotion of the commerce of this country, if
shipping were thus emancipated frovn the present inequitable restrictions, by
the abandonment of all tonnage dues and tonnage registration for ^^ fiscal
purposes." Dues for lights and harbours, if levied on actual freights and
cargoes, would be much more equitably, and not less efficiently, levied than
at present. I agree with Mr. Napier in thinking this the best solution of all
the difficulties connected with the tonnage question.

If this were done, register tonnage Avould remain as a mere record of the
internal capacity, or of the room inside of ships, an imperial ton being
retained, as now, to indicate a space of 100 cubic feet, or a space of 5 feet,
by 5 feet, by 4 feet. Such measure, used for mere statistical jniiposes, would
be unobjectionable.

For mercantile jfurposes, that is, for chartering or hiring ships, the present
law is most convenient. The bulk of the room which the charterer hires,
and the owner receives payment for, is measured with sufficient precision for
such practical purposes.

For scientijic piirposes, at least for purposes of naval architecture, it does
not appear to me that anything of the nature of register tonnage or measure-
ment can be of any service. The construction plans, or lines of a ship given
by a shipbuilder, with all the elements of her construction, if combined with
a record of her performance, and an authentic account of lier sailing quali-
ties, would be of great value. Anything short of this, recording some of
her elements, and excluding others, would be more likely to mislead than
inform. Shape is a principal element in the performance of a ship, and the
lines of the ship are required adequately to give that. I do not think that
it would be tolerated in this country by shipbuilders that their lines of con-
struction and scientific elements and calculations should be demanded to be
given up under certain clauses by Act of Parliament; neither, if this diffi-
culty were overcome, could records of qualities be obtained compulsorily, to
give the compulsory elements of construction — the scientific value which
they would only obtain by an equally compulsory record of performance.
Careful experiments, made by individuals or associations, can alone be
expected to afford scientific data of this nature.

4. The example of Government interference in such matters, is so bad an
example, that it should be avoided rather than followed, in imposing restric-
tions on the shipping trade. There is no reason to regard the Government
of our country as either more interested in enabling a ship to perform her
journey safely, or more able to judge of the conditions of such sal'ity, than
her captain and her owner. As every different form of ship, and every
different quality of ship, and various species of cargo and each different
voyage would admit of, and require, a different degree of loading' — this must
be left to the captain and owner, who know their ship and their business,
instead of being consigned to officers who cannot know it.

5. It is a mistake to suppose that, in giving to steam-ships an exemption
from payment of tonnage dues on their engine-room and coal-bunkers, they

ON THE MEASUREMENT OF SHIPS FOR TONNAGE. 73

are obtaining a preference over sailing vessels. On the contrary, it is essen-
tial to fairness that such exemption should be given. Sailing ships already
possess such exemption in the existing tonnage-law. The divisor 100, in
the tonnage-law, gives that exemption. The real ton of freight is 4-0 cubic
feet in most things, and, in some, 50 feet. The difference between the mer-
cantile ton of 40 feet, and the imperial register ton of 100 feet, is designed
to give the shipowner ample exemption for that portion of the internal room
of a ship which is occupied by captain's cabins, sailors' berths, sails, cables,
cordage, chains, anchors, sea-stores, provisions, and all the requisites of
mooring and working the ship. This exemption has been recognized in all
the tonnage-laws of this country. It has been merely extended to the steam-
ship on the same footing — the propelling power, and all provisions for it,
being included in a similar exemption. The error of the present law con-
sists in making that exemption on an arbitrary tonnage, instead of the actual
tonnage of engine room — an error which no time should be lost in re-
medying.

6. I do not see, and cannot imagine, why any exemption should be made
other than that of the actual room occupied by engines, boilers, and fuel.

7. The only true measure of power is the work actually performed by a
marine engine; this work will vary with the talent of the maker, with the
care and intelligence of the keeper of the engine, with the age and condition
of the boiler, and with the qualities and loading of the ship. In the absolute
sense of true power, two engines, in whicli all the main dimensions are alike,
and both perfectly new, will give out a totally different practical result. This
is why the engine of one maker is well worth £60 per horse-power, and of
another not worth £30. Yet, under varying circumstances, a given engine
will perform double at one time from another.

Owing, therefore, to the great variety in kinds and qualities of engines, it
is neither politic nor expedient to attempt to define power in a form more
absolute than the nature of the subject practically admits. The scale com-
monly used among engineers for buying and selling engines is just as good as
any other, so long as the talent of the builder and the knowledge of the uses
is a main element of power of a marine engine. It is a question of name
and character more than of dimensions and measure. Legislation cannot
safely try to trammel such elements.

8. Practically, Sterling's rule, or Attwood's rule, or Chapman's rule, or
any ordinary intelligent rule, will tell very accurately the cubic contents of
the inside of a ship. I do not see any grave fault in the present rule, though
I will not assert that some more minutely precise rule for purposes of abstract
science might not be given.

Conclusion. — The result of considerable thought and pains given to this
examination is that, in my opinion, we need not ask any alteration of the law
regulating Imperial Register Tonnage, except the rectification of the allow-
ance for engine-i-oom, which remains fictitious and arbitrary. Neither should
I recommend any further interference of Government officers with the ret^is-
tration or working of ships or steam-vessels. I look for the advancement of
naval architecture rather to the association of naval constructors and men of
science with each other, and the mutual communication of their notions and
knowledge, than to empirical efforts of legislation ; and I hope for progress
in navigation, rather from the general advancement of education and know-
ledge, among all who are concerned in shipping, than from any trammels
which, in the disguise of assistance and regulation. Government might be
induced to impose on the captains and owners of ships.
February 17, 1857.

74 REPORT — 1857.

No. 3. — Rev. Dr. Woolley {Member of the Commi(tee').
To the Hon. Secretary of the Tonnage Committee.

Portsmouth Dockyard, Feb. 27, 1857.

Sir, — I regret that so few members of the Committee have put us in
possession of their opinions on the subjects on which we have to report;
especially that no actual builder of sliips has given us the benefit of his
experience.

As regards the report, I am of opinion that we should keep in view two
objects ! — 1. The particularising of the useful objects which an interchange
between shipbuilders of information witii regard to ships actually built by
them, might be expected to produce. 2. Those objects which an enforced
registration ought to attain.

1. On a careful consideration of the whole subject, I have embraced the
decided opinion that it is hopeless to look for such information as would be
useful in a scientific point of view from legislative enactment. There are so
many points beside light and load displacement, indicated horse-power. Sec,
which must be known in order to form a sufficient scientific estimate of the
value of a ship, tliat I fear an enforced registration of certain particulars
would be found to be a delusion. Our scientific objects can best be attained
by the voluntary association of persons interested in shipbuilding and the
science of naval architecture. If the British Association would lend the
sanction of its authority to tlie recommendation of the institution of a Naval
Architectural Society, it would, I think, be conferring a greater boon on
science than by any other means.

Legislative interference is very much to be deprecated, except to serve an
object in every way commensurate with the evils which all restrictions impose
upon trade. We cannot too jealously guard against unnecessary restraints,
and should be very chary of calling lor Government assistance. The well-
known maxim of Horace applies M'ith great force to legislative interference
with matters of this kind —

Ncc Deus intersit nisi clignus vindice nodus
Inciderit.

I cannot say that it appears to me that any adequate object has been pro-
posed in the various answers to the eight queries of which I have received
an abstract. On one point all seem agreed, viz. that absolute fairness in the
incidence of tolls can only be secured by charging in every case on the actual
freight. Short of this, and if it be not feasible to make the actual freight
the basis of levying the dues, then I am of opinion that it is impossible to
devise a general rule fairer than that which is now in force.

I cannot see that the public are much interested in this question. The
ownership of ships is in a sufficient number of hands to protect the public
from anything like a monopoly, and to render the application of the princi-
ples of supply and demand secure. The competition existing among ship-
owners is a sufficient security that the carriage of goods will be fixed at the
lowest remunerative price. No doubt the more science is brougiit to bear
on shipbuilding the greater will be the economy, both as regards the first
cost and the management of vessels, and owners will consequently be able
to charge a lower price for the carriage of goods and passengers. But I do
not think that the application of science is to be sought by legislative
enactment.

2. An enforced registration would have for its object — First, to secure
fairness in levying Government dues (in case dues should continufe to be
levied on tonnage) ; and secondly, to give a fair idea of the amount of ton-

ON THE MEASUREMENT OF SHIPS FOR TONNAGE. 75

nage or roomage, or whatever it may be called, employed for mercantile
purposes. The space available at the usual rate of 40 cubic feet to a ton, is
quite sufficient for the purpose ; and as the internal roomage divided by 100
does on the average bear a definite ratio to this space, I am inclined to think
that the present registration is sufficient for merely statistical objects.

Among the reasons which have weighed most with me, in arriving at the
above conclusions, are the following : —

In all the rules which have been established by Act of Parliament for the
measurement of tonnage, the legislature has had one object in view, viz. to
provide for the fair incidence of tolls.

If measurement by weight were taken as the basis of registration, external
measurement, as proposed by the Tonnage Committee of 184^9, viz. up to
the deck, would not be more correct than the present legalized internal
measurement ; and it would have the disadvantage of offering an induce-
ment to build ships of insufficient strength — as the greater the ratio of the
internal to the external capacity for the greater number of cargoes, the more
advantageous would the arrangement be to the owner. It is generally
acknowledged that a comparatively large interior space or roomage, is of prin-
cipal importance in the eyes of shipowners; and that it would not be a recom-
mendation generally, that, with a small internal capacity, a vessel possessed
large capacity for carrying weight. If, therefore, the registration were based
on external measurement, it would become the interest of the owner to
reduce the scantling of the vessel to the lowest possible dimensions — even
verging upon danger.

The ' Great Eastern,' now building at Millwall, will have a large external
displacement compared with its internal roomage, owing to its being built on
the cellular principle. I cannot think this an advantage, viewed merely in a
commercial or economical point of view, as the prime cost is greater, and the
vessel when built is not as available for the ordinary run of merchandise as
others which have a proportionably larger internal roomage.

The strength of a vessel is a very important element in its construction ;
and it appears to me that the registration of tonnage for dues on the external
instead of the internal measurement up to the deck would operate greatly to
the detriment of this element.

The carriage of passengers cannot be considered as among the least
lucrative of the uses to which a ship may be put. The room required for
each passenger is out of all proportion greater than the weight of himself
and luggage. Passenger ships, with a comparatively small displacement,
require large internal roomage ; and as all covered spaces are included in the
present internal measurement, the incidence of dues is far more just on the
present law than it would be on a law which established a system of mere
external measurement.

It has been urged that the prevalence of shipwrecks and consequent loss
of life must be laid to the door of the present defective state of shipping
registration. I do not, however, find that the result of the inquiries of per-
sons most competent to judge corroborates this view. Among the causes
which the seamen themselves (no incompetent judges) urge, such as the
enormous competition of late years, insufficiency and incompetency of crews
and officers, I do not find the overloading of ships. I cannot but infer from
this significant silence that such a cause is not in operation, at least to any
considerable extent.

To appreciate the qualities of a vessel in a scientific point of view, a know-
ledge of the light and load displacements, as well as of the area of midship
section, and of the form of the ship, especially towards the bows and stern,

76 REPORT — 1857.

is absolutely indispensable. The qualities of the vessel, as shown at sea, are
also necessary elements to forming tins estimate. Of these none but the
load and light displacements have been proposed to become the subjects of
registration ; and these alune would by no means supply that information
which must form tlic basis of all scientific estimate.

External measurements up to the deck, as proposed by the Commission of
J 849, would afford no data for obtaining a knowledge of the light and load
displacement. The first requisite for this purpose is to fix a definite load
water-line. The impracticability of defining such limit, openly avowed by
one Koyal Commission, has been felt and acted on by all. There is no rule
of science which can establish it — it is always to a certain extent a matter of
judgment, and it varies not only with every different condition of lading and
trim, but also with the season of the year. It may be, or it may not be, that
a rule for the defining of free-board, in other words, the distance between the
load water-line and the deck, expressed in definite parts of the principal
dimensions, may answer tolerably well for the actual practice, with regard
to a considerable proportion of our present mercantile navy; but such a
rule can be nothing but the merest empiricism, would certainly not satisfy a
majority of persons at present interested in shipping, and might be found
absolutely inapplicable to vessels built on some improved principle, which
not only maj', but probably will, be introduced into naval architecture within
a few years. The fixing of the load water-line on other than strictly scien-
tific principles (and no such exist), would in all probability check improve-
ment and progress ; and would certainly be very unworthy of the recom-
mendation of a professedly scientific body like the British Association.

I think also that an official assignment of a limit to the load-draught of
water would be attended with vexatious interference on the part of local
officials most inimical to trade ; and I think, with Mr. Laurie, that this is a
matter which may be safely left to be settled between the insurers and the
insured. It is difficult to conceive any mode of determining legally this
limit, which cannot be assigned on any scientific principle that would not
operate as a check to the progress of science in the art of shipbuilding, which
must be free if it is to flourish with vigour.

On the fifth question I am now prepared to state my opinion, that the
present law makes too great a difference between steamers and sailing ships.
For the very same reason that a fractional part only of the contents of a
sailing ship is taken as the registered tonnage, which in the first instance was
undoubtedly to allow ample room for the crew and all the necessary stores
and equipment of the vessel, I think that the excepting from the tonnage the
space actually occupied by the engines, boilers and coals, is equitably fair.
The measurement, however, should be limited to the space actually occupied
by the engines, &c. It would be unfair to include the space in that on
which dues are paid. Not only are the first cost and the expenses of work-
ing a steam-ship much greater than those of a sailing vessel of the same
capability of carrying cargo, but, in consequence of the motive power, the
dues of the one are paid three or four times for each payment by the other.
With regard to the sixth question. In the absence of any information
from practical shipbuilders, I can see no valid reason for making any distinc-
tion whatever, based on the different materials of which ships may be built.
A wooden ship and an iron ship built on the same lines, and calculated for
the same deep draught, would differ somewhat in capability of carrying
cargo, the difference being in favour of the iron ship, which would also pay
a somewhat higher rate of dues, having a larger internal capacity. On the
whole I believe by registration of internal capacity the assessment is pretty

ON THE MEASUREMENT OP SHIPS FOR TONNAGE 77

fairly apportioned between vessels, whatever be the material of whicli they
are composed. Nor can I see more reason for making a discriminative
distinction between vessels, based on the different principles of machinery
with which they may be fitted.

With regard to the seventh point. Although the term horse-power, and
the measure of useful effect which it represents, have not been specifically
fixed by law, I apprehend that, in case of a question arising between builder
and purchaser, with regard to the term indicated horse-power, the law-courts
would have no difficulty in arriving at a definite meaning of this term.

Not only in England, where it originated, but in America, and generally
throughout the civilized world, the measure of useful effect, to which the
name horse-power is given, viz. 33,000 lbs. raised one foot high per minute,
has long been accepted. The confusion which would be introduced by the
adoption of any other measure would be much more than equivalent to any
advantage which would attend its adoption, this advantage being, at the
most, the approximate assimilation of the indicated horse-, as at present deve-
loped by engines on the average, to the nominal horse-power. The great
name of Watt has given a value and currency to the present measure, which
have placed it beyond all rivalry ; nor could any new measure hope to come
into competition with it.

The object of the proposal to fix the statute power by Act of Parliament,
seems to be, to require that the registered power should be a real measure
of the power exerted. It appears to me that nothing could be more difficult
than to subject this to an eft'ective measurement, depending, as it does, upon
so many different qualities. If it be proposed to register the horse-power as
indicated, on trials of ships under certain specified circumstances, nothing
could well be more delusive, as it would be by no means difficult, according
as it suited the interest of the owner or maker, to make this power, so deve-
loped, vary within almost any assignable limits, on one side or other, of the
power which Avould be usually exerted. Nothing can be imagined more
inquisitorial than to require private individuals to make such trials of their
engines — and all merely to serve scientific purposes — which trials, after all,
could not be in the least depended on.

The present nominal horse-power is useful as giving the dimensions, &c.
of the engine, which must form the basis on which contracts are to be made.
It is indifferent whether this be retained in its present form, or the several
items be given under the name of " Engine Register." I agree with Mr.
Napier in thinking an enforced registration of engine-power needless. I
cannot see what the public have to do with it. It is the business of the
customer to enter into such a contract with the engine-maker, as to secure
his obtaining the article he wants. The terms of a contract are of course
open to arrangement between the parties interested ; and if in addition to
the dimensions, &c. of the engine, the contract includes the stipulation that
on a trial trip, under certain specified conditions, the engine shall work up to
some defined limit of indicated horse-power, I apprehend that, in case of
litigation, a jury would experience no difficulty arising from indefiniteness
in the term Indicated Horse-power. There never has been more than one
measure of this important element, and there seems no necessity of calling
in the aid of Parliament to fix it. I apprehend that no practical difficulty
has been felt on this score.

With regard to the eighth query: — 1st, I see no comparison whatever
between the calculations for the ' Nautical Almanac' and the calculations for
ships. Astronomical science embraces a wide field ; and many of the acutest
minds in Europe are employed on it. In the vast variety of methods in use

78 REPORT — 1857.

in practical astronomy, it is to be expected that improvements sliould be
continually made ; and it is of course advisable that the officers charged with
the responsibility of" bringing out the 'Nautical Almanac' should be able to
avail themselves of improved methods. Moreover, the Astronomer Royal,
who is always one of the most eminent men of science in this country, and
it may also be said in Europe, is the superintendent-in-chief of the ' Nautical
Almanac' The reputation and acknowledged ability of the scientific officers
concerned in this case are a sufficient guarantee of the accuracy of the
methods they employ.

The rule or rules employed for the calculation of tonnage or displacement
are of a very different nature. As a matter of fact, no real improvement
has been made in the method, in a scientific point of view, since the days of
Newton, the rule called Simpson's or Sterling's having in reality been invented
by Newton. The great merits of this rule are, that it is as accuiate as any
rule for the measurement of a figure not strictly geometric can be, and that
it is simple and easy of application. As applied to obtain internal roomage,
Stirling's rule requires only measurements to be taken at certain intervals,
and these measurements are very easily made. The whole process, after the
measurements are made, is simply arithmetical. The accuracy of the mea*
surements can be tested by laying them down to a fixed scale on paper, and
passing a curve through them ; but this curve is not required for the purpose
of making the calculations.

Mr. Peake's method is founded on the very same principle; but, in the
points wherein it differs, it is, in my opinion, no improvement. First areas
of sections are calculated as usual ; then two sets of calculations are after-
wards required to complete the operation. The areas of sections are repre-
sented on paper by lines set off to a certain scale, and an elaborate system of
exhausting the area so formed is employed. This is evidently a far more
complex and difficult process than to make simple calculations from ordi-
nates at once. In taking, also, the greatest distances from various base-
lines of points in the curved portion, Mr. Peake assumes that he obtains the
areas more correctly than Sterling's rule gives them. This is a mere assump-
tion, founded on no known property of the parabola, which is the curve
supposed to pass through any three points.

We know that a parabola may be made to fulfil five conditions; if it pass
through three points it fulfils three of these — and its having its axis parallel
to a fixed line, is equivalent to the fulfilment of the other two. We know
also, that a parabola so drawn, subject to the ordinary conditions under which
this (Sterling's method) is applied, is palpably, to the eye, coincident with
the section of the ship. It is, at all events, impossible to draw a regular curve
more nearly coincident with it.

It would be very dangerous, as it would be unnecessary, to leave subordi-
nate agents to exercise their own discretion in the use of methods for calcu-
lating tonnage, when a rule so simple and correct as Sterling's is at their
command. 1 conceive, therefore, that no alteration is required, or advisable,
in the rule now in force under the Merchant Shipping Act of 1854.
I have the honour to be. Sir, your obedient Servant,

J. Yates, Esq. JoSEPH WoOLLEY.

No. 4. — Mr. James Robert Napier {Member of the Committee).

Glasgow, March 2, 1857.

Reply to Tonnage Committee's Circular of 6th November, 1856, by

James R. Napier.
1. The objects of registering shipping I believe are, — 1st. For the purpose

ON THE MEASUREMENT OF SHIPS FOR TONNAGE. ^9

of levying such dues as to reimburse the proprietors of docks, harbours,
rivers, lighthouses, &c. &c., for the expenses they may have been at in pro-
viding such accommodation. 2nd. For the purpose of simplifying the process
of transferring the property from one owner to another. 3rd. The shipbuilder
and shipowner might wish to know the efficiency of a vessel, but I cannot
conceive that any public registration is necessary for this purpose, as the
shipbuilder or engineer has all the elements in his possession for finding,
what may be called, the scientific efficiency, and the shipowner's cash account
will soon show him the mercantile efficiencj-, by the profits he is making
upon his capital ; and I do not see that the public have anything to do with
the question.

3. The present system of tonnage admeasurement is more minute than is
necessary, and of little or no use to the shipbuilder, as his designs, calcula-
tions, «&c. are based almost exclusively upon the weight of ship and cargo,
and seldom upon her internal roomage.

4. I am inclined now to take Mr. Russell's view of this subject, and not
to limit the load-draft of water.

5. I have not sufficiently considered this question.

6. I cannot see any reason for making a distinction between vessels built
of wood, iron, or of any other material, in their measurement. In the re-
gistration, the material may be named ; it would be useful to do so.

7. Nominal horse-power is a useless term. It has no relation whatever to
the power the machine may be exerting, and is a very round-about and even
indefinite way of expressing the size of a steam-engine, or rather of its
cylinders. According to the Government ideas of the subject, even where
every length of stroke (in paddle-wheel engines) has a different velocity for
the piston to travel, the size of cylinders for a given power is quite indefi-
nite. It is useless for the purposes of buying and selling, for the cost of
construction does not vary as the nominal horse-power. Instead of nominal
horse-power, I would substitute simply the capacity of cylinders, or area of
cylinders, X length of stroke. This is positive information, and would be
useful in buying and selling, and might be inserted in the register of the
vessel. A legal standard of power would remove some confusion which at
present exists, and as the elements of such a standard are already recognized,
viz. the lb., the foot, and the minute or second, there can be little difficulty
in combining them, and calling the unit " foot pounds," or " ft. lbs.," per
minute or per second. A horse-power is already known to be 33,000 foot
lbs. per minute, and I see no good reason for changing this term.

8. Sterling's rule is very good, but all vessels, large and small, ought to
be divided into the same number of ordinates, and five ordinates would give
a near enough approximation to the capacity of the ship for all the ordinary
purposes of trade.

No. 5. — Mr. Charles Athkrton {Member of the Committee).

General Summary of his Report.

The foregoing matters touching the Merchant Shipping Act of 1854, have
been thus generally gone into for the purpose of opening up those points of
inquiry which bear especially on the limited duties assigned to this Com-
mittee by the British Association, namely, " To inquire into the present
methods, and to frame more perfect rules for the measurement and regis-
tration of ships and of marine engine-power, in order that a correct and
uniform principle of estimating the actual carrying capabilities and working-
power of steam-ships may be adopted in their future registration," and the

80 REPORT— 1857.

conclusion at which I arrive on the points thus referred to this Committee
are, — that the Merchant Shipping Act of 1854' is an admirably conceived
base of legislation, intended to concentrate all the objects for which legisla-
tion, in its protection of public interests, can be called upon to take cogni-
zance of shipping affairs; that, so far as the inquiries assigned to tiiis Com-
mittee are concerned, and which relate exclusively to Part 2 of the Act,
there appears to be no absolute necessity for the cancelling any part of the
existing clauses ; but it is necessary that the provisions of the Act be
extended to meet the following requirements, which are indispensable to the
protection and promotion of public interests.

1. The Act of 1854 is defective, in so far that the prcscribeil registration,
though called tonnage, takes no direct cognizance whatever of the tons
weight of cargo that will either sink the ship, or that will immerse a ship
down to any definite gauge-mark. The consequence is, that a ship chart-
ered for the conveyance of merchandise may be filled with some descrip-
tions of goods without being half-loaded, or sunk with other descriptions of
goods without being half-filled. To remedy this deficiency, it is necessary
not only that the registration shall give the capacity of a ship for holding
cargo, as is done by the present law, but also the capability for carrying
weight of cargo as determined by the weight that will sink the ship down to
a given gauge-mark, to be fixed upon the stem and stern or amidships of
every ship.

2. The Act of 1854; is defective, in so far that it prescribes no regulations
whereby the draught of water at which ships actually put to sea may be
officially inspected and recorded, with reference to a statute gauge-mark, as
above described, to be fixed upon every ship, such record to be received as
evidence in the case of questions subsequently arising as to the condition in
which ships put to sea; for the want of which record many of the provisions
of the Act, evidently intended for the protection of life, become futile for
want of proof as to the freeboard with which ships put to sea.

3. It is submitted that the official imposition of a gauge-mark to be fixed
on the stem and stern of ships, or amidships, for the purposes above referred
to, would, of itself, without any interference whatever on the part of Govern-
ment officers in the loading of ships, tend greatly to the prevention of over-
loading, whereby ships are rendered unmanageable and life endangered.
The provisions of the Act for the protection of life would then become
operative instead of being a dead letter as respects the overloading of ships.

4. The Act of 1854 is deficient, in so far that it does not prescribe the
measure of the unit by which the registered engine power of steam-ships is to
be determined, nor has any other Act of Parliament prescribed the unit of
power by which engine-power may be legally ascertained and designated ;
nor has engineering practice adopted any specific unit as the measure by
which marine engine-power is bought and sold. It is admitted that the
working-power of marine engines, as supplied to Government bj- the most
eminent engineers under contract at the nearly uniform price of £50 per
nominal horse-power, fluctuates upwards of 100 per cent, with reference to
their nominal power, which regulates the cost. Under these circumstances,
the registration of engine power, without reference to any legalised statute
unit, is an imposition on public credulity.

.5. It is submitted that the legalisation of a statute unit of power, and the
legislative obligation that the registered power or engine capabilities of
steam-ships shall be ascertained and registered with reference to the said
statute unit, will be no more of government interference with mercantile and
engineering aflPairs, than is the imposition of the statute lineal foot, the statute

ON THE MEASUREMENT OP SHIPS FOR TONNAGE. 81

gallon, or the statute ton weight. A legalised statute unit of power is a
positive requirement of the age. It is not proposed that there shall be any
obligation as to engines being woi'ked up to the full power that thej' are
capable of developing, any more than that ships shall not put to sea without
being fully loaded.

6. It is further submitted that the deficiencies of the Act of" ISS^," in
respect of the defective registration above referred to, vitiate the public
statistics of the country so far as based on the registration of shipping; for,
as shown in the foregoing pages, the ratio between the registered tonnage
of a ship, and its capability for safely carrying weight of cargo, depends in
great measure on the dimensions or proportions of length, breadth and depth
of the ship ; so much so, that (as shown) a ship of 2000 tons register may be
so proportioned as to have no displacement available for cargo without
encroaching on the freeboard necessary to the safety of the ship, whilst an-
other ship may be so proportioned externally and constructed internally as
to carry safely the double of her registered tonnage, especially in the case
of auxiliary powered steam-ships, which now threaten to supersede sailing
ships altogether. Hence the mere registered tonnage of ships is not of itself
a statistical criterion of the extent of trade, excepting in so far as respects
the carrying power of similarly proportioned and similarly built vessels.

7. Registration under the Act of " 1854?" does not meet the requirements
of commercial operations, as shown by shipping advertisements, which fre-
quently ignore the legalised registration under the Act of "ISM'," and refer to
other designations of tonnage, such as gross tonnage, tons burden, tonnage
O.M., tons (without designation), all which terms are made use of irrespec-
tive of the register ton, and not one of all these five terms for tonnage
expresses or has any constant ratio whatever to the one thing needful, namely,
the tons weight of cargo that a ship will carry with reference to any statute
gauge mark. Then, again, we see engines advertised as 100 H.P. nominal,
but 450 H.P. effective, and neither nominal H.P. nor effective H.P. have
any statute signification or definite ratio to each other.

8. The Act of "1854" in respect of its r(>gistration deficiencies, is obstruc-
tive of the application of science to maritime engineering and architecture,
as respects all investigations into the comparative dynamic performances of
steam-ships as a means for practically determining the best type of form for
the respective purposes or services for which ships may be required. The
extent to which this exclusion of science for so important a part of naval
engineering and architecture as that of developing the dynamic economy of
different types of ships, is adverse to public interests, may be judged of from
the fact, that on estimating the comparative dynamic capabilities of ships of
given size, and required to steam at a given speed, but of different types of
form, by any recognised law of scientific comparison, a vast difference of
dynamic merit is found to be prevalent. The great majority of ships are
found to be of a low order of dynamic merit, below what has been found to
be practically realisable ; so much so, that the average of the generality of
shipping requires probably 25 per cent, more power to attain a given speed
than is required (cceteris paribus) by vessels of the superior type, whicli is
occasionally produced ; and when it is considered that the trade and navi-
gation returns for " 1856" show that the foreign import and export trade of
Great Britain, as indicated by the registered tonnage of shipping, amounts to
18 millions of tons per annum, whilst the home trade amounts to 26 millions,
being a total of 44 millions of tons per annum, sea-borne trade (that is, if
the weight-carrying capability of ships be on the average equal to the
register tonnage), and as the cost of all merchandise to the consumer,

1857. ' G

82 REPORT — 1857.

such as corn and cotton, depends considerably on the cost of transport, it
must be admitted that the registration of tonnage and engine power, though
required only for the exclusive purpose of rendering science available for
improving the dynamic performances of steam-ships, is, of itself, a considera-
tion which demands the interference of the legislature as the guardian of
public interests in all public affairs.

In conclusion, therefore, it is submitted that the defective condition of our
shipping registration under the Act of " 1854," is such as demands the con-
sideration of parliament with a view to the extension of the Act to meet the
following I'equirements : —

1 . That a statute gauge-mark shall be affixed on each side, amidships of
every ship, for indicating the statute freeboard, the exact position of said
mark to be determined by a rule based on the length, breadth and depth of
the ship taken in such proportions as the legislature shall determine, and
corresponding marks shall be fixed on the stem and stern at such position in
line with the midship mark as the approved water-line trim of the vessel
shall indicate, and the dimensions of length, breadth and depth by which
the position of the midship mark is determined shall be registered.

2. That in addition to the present registi-ation of tonnage, based on inter-
nal measurement, the registration shall include the displacement of the vessel
when light ready to receive cargo equipped in all respects ready for sea, but
not including coals and other consumable stores, also the displacement when
immersed down to the statute gauge-marks before referred to, and the total
displacement measuring up to the deck ; these displacements taken iu cubic
feet, to be rated at 35i cubic feet to the ton weight, and the difference
between the light displacement, and the statute gauge-mark displacement,
to constitute the registered weight-tonnage of the ship.

3. That the draught at which ships actually put to sea shall be inspected
and recorded with reference to the statute gauge-mark on the stem and
stern of the ship.

4-. That a standard measure of power be determined and legalised as the
statute unit, to which the registration of the engine power of steam-ships shall
have reference ; the registered power shall be that which engines and boilers
shall, for the time being, be capable of continuously exerting, the same being
ascertained by means of the indicator, as usual in the trial of steamers, and
calculated by the statute unit.

Charles Atherton.

Woolwich Dockyard, 3rd March, 1857.

No. 6. — Mr. Andrew Henderson (Member of the Committee).
General Summary of his Report.

The British Association having appointed a Committee " to inquire into
the defects of the present methods, and to frame more perfect rules for the
measurement and registration of ships and marine engine power, in order
that a correct and uniform principle may be adopted in their future regis-
tration," the following review of the opinions and information is submitted,
premising that the members of the Committee, being unanimous in opinion
that the removal of all fiscal dues levied on tonnage would be the best solu-
tion of all the difficulties connected with the tonnage question. Although
not included in the above, it was considered so important, that the writer was
deputed by the Committee to seek information on the subject.

The result of this inquiry shows that, although the original object of
register tonnage may have been the taxation of the cargoes of ships, it baf

ON THE MEASUREMENT OF SHIPS VOR TONNAGE. 83

long since ceased to be used as a basis of taxation, inasmuch as all fiscal
dues or duties are levied by the Custom-house on the cargoes imported and
exported.

The only dues or rates levied on tonnage are for harbour and dock accom-
modation and light dues, for maintenance of lights on the coast ; the former
being mostly paid to local trusts or dock companies, while the light dues,
although levied by the Custom-house, are paid to the Trinity-house for the
maintenance of the lights ; so that these dues cannot, in point of fact, be any
longer considered as fiscal or government.

Many of the light-houses, previous to 1835, were private property, till
purchased by the Trinity-house Corporation, who thereby incurred a debt
of £1,200,000. The shipowners have paid oif both principal and interest.
The light dues now charged on tonnage amounts to £313,208, and the cost
of maintenance amounts to £214,700, the surplus revenue from light dues,
£98,508, being received by the Board of Trade for the Mercantile Marine
Fund-

The coasts of France and America are lighted by their respective govern-
ments without charge on shipping. Both equity and policy dictate the
expediency of relieving the shipowners of this country from all tonnage dues
for lights, and transferring the charge to the cargoes and passengers carried
by ships, or to the Consolidated Fund.

A bill in parliament proposes to abolish all passing tolls and town dues
levied on shipping, the latter at Liverpool amounting to £125,000 a-year,
being raised by a small rate levied on all cargoes imported or exported on
the Mersey. A similar rate on cargo levied at all other ports would provide
the£250,000 annually required for maintaining the lights, buoys and beacons,
and for the conservancy of the ports and rivers on our coasts. The substi-
tution of light dues levied on cargo and passengers for the present tonnage
dues levied on shipping, would entail no additional labour on the Custom-
house officers, as they must necessarily keep a record of all goods imported
and exported at each port. This is a more legitimate occupation than the
measurement of ships, which is stated to be " an extraneous duty thrown
upon their oflicers," in a report from the Commissioners of Customs recently
published.

Both economy and efficiency would be efiected by the transfer of the duty
of measuring ships from the Custom-house officers and department, to the
shipwright and engine surveyors, now employed by the Board of Trade for
all ships carrying passengers, whose certificate of survey would furnish the
Custom-house with the dimensions, register, and gross tonnage, and other
particulars required for the various forms of register and transfer of vessels ;
these also forming the record for compiling the statistics of the shipping of
the country, which comprises the only remaining usefulness of tonnage
registration for statistical purposes at the Custom-house, tliere being no
longer any fiscal dues or Government duties levied on the tonnage of shipping,
notwithstanding which, up to the present time, the Board of Trade and Go-
vernment have only considered the measurement of tonnage and registration
in a purely fiscal point of view.

The reasons for these conclusions will be found in the facts of the work-
ing of the present system, detailed in the foregoing paper, in which it was
found necessary to refer to the proceedings of former committees, and the
different principles of measurement in use.

In 1835 an Act was passed adopting the principle of internal measurement
for register tonnage.

In 1849 the Bubject was again investigated by a committee, consisting of

84 REPORT — 1857.

Lord J. Hay and a body of shipowner.*, vvlio reported that " the equi-
table basis on wiiich charges for dock, light, harbour, and other dues,
is that of the entire cubic contents of a vessel measured externally." A bill,
based on this recommendation, was brought in, computing the tonnage by
means of diagrams of section, and curves of areas, with a scale of dis-
placement.

This bill was opposed by the owners of timber ships and the builders of
iron vessels, and from this and political causes was deferred.

At that time I proposed that the principle of the bill of 1850, and of the
plan recommended by Mr. Moorsom for internal measurement, should be
embodied in one bill, and the mean of the two measurements be taken as
the basis for register tonnage; and before the bill was actually passed, I
submitted that this could still be accomplished by combining the Rule No. 1
of the bill of 1850 as well as Rule No. 2, which already forms part of the
bill, by an alteration of the clauses 20, 21, 22, of the present act.

Register tonnage is necessary for statistical purposes, but should approxi-
mate the old builder's tonnage, in Avhich the statistics of shipping have,
from the earliest times, been kept, and which more nearly assimilates that
of other nations. There are, however, objects to be attained by a more
comprehensive system of tonnage registration, viz. the saCety and efficiency
of the ships, their mercantile capabilities, and to supply scientific data
for facilitating a comparison of the various types of ships, including a record
of their burthen in weight or displacement, capacity, strength of material and
steam-power. The practicability of obtaining this record is exemplified by
the annexed table of the dimensions and proportions of ships and engines
and comparative analysis of their capacity, resistance, and the result of test-
trials and performance at sea ; the particulars recorded of many affording
data for estimating the comparative dynamic merits of ships by the co-effi-
cient of their displacement or index number. The additional measurement
and data required are shown in the table. (Appendix A.)

With this view it is proposed to substitute for the forms now sent to the
Custom-house, the record, on the present builder's " certificate, of all parti-
culars of dimensions, old tonnage and measurement by new rule, mentioned
in the accompanying form, giving the builder's construction, load, draft,
displacement, and area of midship section, as well as the launching draught,
and estimated weight of hull and fittings as the light water-line, from which
a scale of displacement and area of midship section may be formed at any
draught of water." (Vide Appendix B.)

These particulars relating to the external bulk and internal space, with
the draught, displacement, and area, would not oidy give the internal capa-
city, but also the capability for carrying weight of cargo, as well as the data
forming a scale for displacement and area of midship section at any draught
of water, whence may be deduced the relative efficiency of different vessels.
I consider the present plan of taking and recording the internal measure-
ment, and the mode of computation to be practically inefficient for obtaining
a correct mensuration of vessels, and that the formula and mode of calcu-
lating are extremely liable to error, without the means of testing their cor-
rectness, as was suggested by the Tonnage Committee of 1849.

Tiie Act of 1851', though nominally adopting the same scientific rule, in
effect abandoned the most important part, viz. tlie use of the diagram and
curves of areas.

By using paper ruled to a scale in the formation of the diagram, the com-
putation is rendered both easy and correct, and a record of these measure-
ments, &c. in the certificate of the surveyor would furnish the owuer or

ON THE MEASUREMENT OF SHIPS FOR TONNAGE. 85

government with the means of ascertaining the weight of cargo carried or
the capacity for light goods.

All measurements, however made, ought to be attested by the builder or
owner, <S:c. and recorded on the certificate.

The correctness of Sterling's rule is entirely based on the assumption
that the sections should be measured at exactly equal distances, but experi-
ence ])rovcs that in practice it is almost impossible to obtain these measure-
ments at the exact intervals required.

It is, however, of comparatively little importance by what method a vessel
is measured, provided means are at the same time used to check the calcu-
lations, and the most simple and practical mode of accomplishing this is by
the method so long used by Mr. James Peake, viz. by a system of vertical
sections and curves of areas, measured by a series of triangles. Annexed is
a comparison of four modes of measurement. (Appendix C.)

The black lines on the right side show the plan as recommended by the
Tonnage Commission of 1849, and the measurement proposed in Bill of
1850.

The triangular lines on the extreme right represent Mr. Peake's method
for displacement to load-line.

The dotted lines on the left represent Mr. Moorsom's mode, adopted in
the present act, as shown in formula No. 1, p. 30, in substitution of that
recommended by the Tonnage Commission, of which he was secretary.

The diagonal lines on the left represent M. Norman's on the French
plan, useful in correcting other measurements, or if built true to design.

For statistical purposes, owing to the great decrease, as above shown, of
from 8 to 10 per cent, in the Register Tonnage, below the average of the
same vessel under the late law, this must impair the object of statistical
returns, and injure the harbours, piers, and docks, maintained for shipping,
while it reduces the charges and light dues only, and is consequently very
popular with shipowners.

Two years' experience in the practical working of the present tonnage
measurement and registration system, has proved deficient and non-effective
for the attainment of most of the objects of public utility sought for.

The advantages of internal over external measurement have been stated to
be, that inasmuch as the greatest number of cargoes carried by our mer-
chant shipping consist of stowage goods, not doad weight, equal to at least
three-fourths of the whole, and as ships' sides and bottoms are of various
scantlings and thickness, and are constructed of materials of different weight,
external measurement would give advantage to some ships over other's, of
i.5 to 20 per cent.

This is, however, not the fact, as an examination into the trade returns of
1850 exhibits the following results of the trade of the United Kingdom,
amounting to 10,760,297 tons of imports and exports; of which 7,483,214
tons, or 69^ per cent, were of heavy goods (coal, metal, grain, and sugar),
and 3,277,083 or 30^ per cent, of light goods, of which a timber-built ship
will carry 10 per cent, less than iron vessels.

With respect to the working of the Act of 1854, it appears that in Sep-
tember 1855, a great many vessels were remeasured under the new act, it
being found that the Rule No. 1 for internal measurement reduces the register
tonnage from 5 to 10 per cent., an important saving of dock and light dues
to coasting steamers, besides some increase in the deduction for engine-room;
while by Rule No. 2, for external girthing, the gross tonnage was increased
5 per cent, on the late measurement, and ranged from 5 to 15 per cent, more
than by Rule No. 1.

86 REPORT — 1857.

The war caused a great demand for screw steamers hired by the ton, and
induced the numerous remeasurements under the new act ; thus the anoma-
lies of our tonnage laws are exemplified by there being three or four different
measurements in use, all nearly equally indefinite as to the real built effi-
ciency or tonnage capacity of vessels transferred.

With respect to the fixing the load limit ; — at present we can obtain from
the builder his construction load line and launching draught, and if in addi-
tion we obtain the draught of water, the scale of displacement, and area of
midship section, we have sufficient data for assigning a proper limit of
loading, and marking it on the register as in Appendix B.

Should the builder assign a load draft and displacement, such as nautical
science may not justify, and as the safety limit must also depend much on
the proportions and form of the vessel, the load draught of water and height
of freeboard may be ascertained as follows : — For example, take one-
twentieth of the length, one-fifth of the breadth, one-fifth of the depth, and
divide by three — the result will be the safety freeboard measured from the
deck or gunwale and the mean draft of load water, which should be men-
tioned in the register and never exceeded.

In conclusion, all that is requisite is, to alter the three clauses given in
the present act of 1854, as it embodies the principles recommended by the
Tonnage Committee of 1849 (and contained in the Bill of 1850), together
with all the advantages derived from internal measurement, as given in the
present act ; and bases the register tonnage on the mean of the external
bulk and internal space, thereby affording internal capacity and a displace-
ment measurement, from which the weight of cargo carried could be as-
certained.

Alterations w? the Clauses of the Merchant Shipping Act, 1854, appertaining
to the Measurement of Ships for Tonnage, proposed by A. Henderson *.

Clause 20. Throughout the following rules the tonnage deck shall be
taken to the upper deck in ships which have less than three decks, and to
be the second deck from below in all other ships; and in carrying such
rules into effect all fractions of feet shall be expressed in decimals. " It
being considered that the equitable basis on which charges for dock, light,
harbour, and other dues should be made, is that of the entire cubical con-
tents or external bulk to the medium height of the tonnage deck, together
with the internal space or capacity under the tonnage deck (within the
ceiling planking, exclusive of lower deck beams and fixtures of hull); the
mean of the two being taken as the basis of registered tonnage. These
quantities to be expressed in cubic feet and decimals on the register and
certificate. The difference between the external bulk and internal space to
be considered the cubical contents of the hull of the vessel ; the per centage
or ratio the cubic contents of the hull bear to that of the internal capacity,
and of that quantity to the bulk, giving a fair criterion of the relative capa-
city of timber and iron ships for light goods and passengers."

Clause 21. The tonnage of every ship to be registered, with the excep-
tions mentioned in the next section, shall, previously to her being registered,
be ascertained by the l"ollowing rules hereinafter called Rule I. " for External
Measurement and Internal Measurement "; and the tonnage of every ship to
which such rule can be applied, whether she is about to be registered or not,
shall be ascertained by the same rule.

* The additions shown in italics or inverted commas.

TAiiULAR COMl'AltiyoN, TUE OLD, THE rnESENT, AND PROPOSKD MEASURBMENT FOR TuNNAGE, AND AN^iiYSIS I

APPENDIX A.

' &HIPS AND STEAMERS, THEIR rHOPORTIONS, DISPLACEMENT. WEIGHT, AND RE-^ISTANOE, ENGINES AND 8TE.UI PO^YE^I, AND RESULTS 01' SPEED REALIZE!

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Appekdix B.— Prj|io«eJ Scale of Tonnage and Area of M. S.

I ol' four modes ul' >

3I1S un papor ruled to a scale (
, Esq., 1857-

which tu funu t

s of areas and scalp

'.adopting the

Mr. MOORSOM'S MEASUREMENTS.;

(Internal.)
As adopted in the Shipping A

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1086

12932

Represents

M. NORMAN'S FRENCH PLAN
MEASUREMENTS,

(Ext

laL)

i 16-3 X 5-8 = 47-27

i 150 X 5-3 = 4134

i 13-3 X 6-8 = 4522

i 11-8 X 4-4 = 25-96

i 11-8 X 1-3 = 7-50

J 67 X l-O - 3-35

i 4-3 X -75 = 1-61

Ekienial area HcctiQii 172-25

I A.HENDERSON'S MEASUREMENTS.

(External.)
. Area of 1 l)resdih a

1 height. 1
)X 11-9 J

External area of i section ..
; Ditto, ditto, measured iiuide, i.

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r Represents A.. Hender-
< son's intema] mea-

Do. iron ships. Do. Do.

Do. A. H.'s BxiemaJ |
Measuremeut to I
Load Water Line J

ON THE MEASUREMENT OF SHIPS FOR TONNAGE. 87

Rule I 1. Measure the length of the ship in a straight line along the

upper side of the tonnage deck from the inside of the inner plank (average
thickness), at the side of the stem to the inside of the midship stern timber
or plank there, as the case may be (average thickness), deducting from this
length what is due to the rake of the bow in the thickness of the deck and
what is due to the rake of the stern timber in the thickness of the deck, and
also what is due to the rake of the stern timber in one-third of the round of
the beam ; to be termed the length for tonnage. " The height for tonnage to
be taken from a base line at the underside of the false keel to the medium
height of the tonnage deck. The breadth for tonnage to be the extreme
breadth, exclusive of doubling. Divide the length so taken into the follow-
ing number of vertical sections required for the measurement of transverse
areas at nearly equal distant divisional points."

Table.

Class 1 . Ships of which the tonnage deck is 50 feet long or under, into
four parts, for the measurement of " three transverse areas at the mala
breadth section, and other divisional points of the length."

Class 2. Ships of which the tonnage deck is above 50 feet, and not exceed-
ing 120 feet, " into sections for measuring five transverse areas."

Class 3. Ships of which the tonnage deck is above 120 feet, not exceeding
180 feet, "into sections for measuring seven transverse areas."

Class 4. Ships of which the tonnage deck is above 180 feet, not exceeding
225 feet, " into sections for nine transverse areas."

Class 5. Ships of which the tonnage deck is, according to the above mea-
surement, above 225 feet, into 12 sections, for measuring eleven transverse
areas at the point of division. " The length of the tonnage deck from stem
to stern, on a scale of quarter-inch to a foot as a base line, from which the
transverse areas being set off" on a scale of ten square feet to quarter-inch at
each point of division and marked on the scale. A curve, run fair from the
stem through these marks to the stern, will form the curve of areas of exter-
nal bulk."

(Rule 1.) " For external measurement to be ascertained when the vessel is
on the stocks during the progress of building, or in dry dock, or otherwise
on the ground, and according to the following rule. No. 1, (that is to say)
determine the length between the perpendiculars by setting up from the
under side of the false keel two-thirds (|^) the medium height of tonnage
deck, to cut the outside of the rabbets (or these produced) of the stem and
stern post, these intersections squared down to the keel to give the positions
of the perpendiculars, and having taken off the number of transverse sections
of the hull, stated in the table."

" Compute the correct external bulk (exclusive of any wooden sheathing
which may have been brought on to the proper planks of bottom) to the
medium height of the tonnage deck, by means of a curve of areas constructed
from the areas of the aforesaid sections ; in the case of a break on the deck,
the medium height to be ranged fair through in continuation of the deck,
as if there had been no break. Record the correct mensuration in cubic
feet thus obtained as the external bulk, to medium heiglit of tonnage
deck."

"To form scale of displacement. — Divide this bulk by 35, the quotient will
represent the tonnage displacement of the hull immersed to that height
above keel. By similar areas and curves, compute the tonnage displace-
ment loaded to 2-3rds the height of deck, or between the perpendiculars, as
■well as the light line, immersed l-3rd from the keel. These three quanti*

86 REPORT — 1857.

ties, set off on a horizontal scale of 10 tons to the quaiter-inch, at their
respective heights on a perpenilicular scale of quarlcr-inch to a foot, a curve-
run from the keel through the tliree, will form a scale or table upon the
tohpage displacement or weight of cargo carried."

Rule I. — Internal Measurement.

2. Then the hold, being first sufficiently cleared to admit of the required
depths and breadths being properly taken, find tiie transverse area of such
ship at each point of division of the length, as follows : — Measure the depth
at each point of division, from a point at a distance of one-third of the round
of the beam below such deck, or, in case of a break, below a line stretched
in continuation thereof, to the upper side of the floor timber at the inside of
the limber strake, after deducting the average thickness of the ceiling ; then,
if the depth at the midship division of the length do not exceed sixteen feet,
divide each depth into four equal parts; " then measure tiie inside horizontal
breadth at each of the three points of division, and also at the upper and lower
points of the depth, extending each measurement to the average thickness of
that part of the ceiling which is between the bilge planks and limber strake ;
also marking at the end of each horizontal breadth measured, the average
thickness of the side, i. e. ceiling, frame timber, and outside plank, from
which to compute the external area of each transverse section ;" number
these breadths from above (?'. e. numbering the upper breadth One, and so
on, down to the lowest breadth); multiply the second and fourth by four,
and the third by two; add these products together, and to the sum add the
first breadth and the fifth ; multiply the quantity thus obtained by one-third
of the common interval between the breadths, and the product shall be
deemed the transverse area; but, if the midship deck exceed sixteen feet,
divide each depth into six equal parts instead of four, and measure, as before
directed, the horizontal breadths at the five points of division, and also at
the upper and lower points of the depth ; number them from above as before ;
multiply the second, fourth, and sixth, by four, and the third and fifth by
two ; add these products together, and, to the sum, add the first breadth and
the seventh ; multiply the quantity thus obtained by one-third of the com-
mon interval between the breadths, and the products shall be deemed the
transverse area.

S. Having thus ascertained the transverse area at each point of division
of the length of the ship as required by the above table, procued to ascer-
tain the internal space of the ship in the following manner: — " Number the
areas successively, 1 , 2, 3, &c.. No. 1 being at the extreme limit of the length
at the bow, and the last No. at the extreme limit of the length at the stern ;"
then, whether the length be divided, according to the table, into four or
twelve parts, as in classes 1 and 5, or any intermediate number, as in classes
2, 3, and 4, " multiplying the second and every even-numbered area by four,
and the third and every odd-numbered area (except the first and last) by
two; add these products together, and, to the sum, add the first and last, if
they yield anything ;" multiply the quantity thus obtained by one-third of the
common interval between the areas : record the product thus ascertained in
cubic feet as the internal space under the tonnage deck.

To compute Register Tonnage.
" Add together the external bulk to the medium height of tonnage deck,
and the internal space under the tonnage deck in cubic feet; divide the sum
by 2, taking the mean of bulk and space in cubic feet as the basis of re-
gistered tonnage, to be deduced by the use of the factor '30, '31, or '32

ON THE MEASUREMENT OF SHIPS FOR TONNAGE. 89

(hundredths) of that mean as the registered tonnage, approximating the
old or builder's tonnage by the use of the divisor 35^."

" All measurements to be recorded on paper ruled to a scale of a quarter of
an inch to a foot on the section of the length at which they are measured,
diagrams of each section to be formed at the line of measurement, these
areas to be computed by any two of the four modes contained in the instruc-
tions, the correct areas to be formed into a curve of areas from the length
of the tonnage deck, A scale of displacement, the area of midship section,
and draft of water, to be formed on the certificate of survey, which is to be
recorded in the diagrams of sections and curves of areas, and formed from a
section of the frame ruled on a scale half an inch to a foot. A specification
of the quality and scantling of the various materials used in the vessel to
be filled in on the back of the certificate of survey ; to be signed by the
builder or owner, as well as the surveying officer."

22. Ships which, requiring to be measured for any purpose other than
registry, have cargo on board, and ships which, requiring to be measured
for the purpose of registry, cannot be measured by the rule above given,
shall be measured by the following rule hereinafter called Rule 11. : —

Rule II. — 1. Measure the length on the tonnage deck from the outside of
the outer plank at the stem to the aftside of the stern-post, deducting there-
from the distance between the aftside of the stern-post and the rabbet of the
stern-post at the point where the counter plank crosses it ; measure also the
greatest breadth of the ship to the outside of the outer planking or wales,
and then, having first marked on the outside of the ship on both sides thereof
the height of the tonnage deck at the ship's sides, girt the ship at the greatest
breadth in a direction perpendicular to the keel from the height so marked
on the other side by passing a chain under the keel ; to half the girth thus
taken add half the main breadth ; square the sum ; multiply the result by
the length of the ship taken as aforesaid ; then multiply this product by the
factor '0018 (eighteen ten-thousandths) in the case of ships built of wood,
and by '0021 (twenty-one ten-thousandths) in the case of ships built of iron,
and the product shall be deemed the register tonnage of the ship, subject to
the additions and deductions hereinafter mentioned.

2. If there be a break, a poop, or other closed-in space on the upper deck,
the tonnage of such space shall be ascertained by multiplying together the
mean length, breadth and depth of such space, and dividing the product by
100, and the quotient so obtained shall be deemed to be the tonnage of such
space, and shall, subject to the deduction for a closed-in forecastle mentioned
in Rule I., be added to the tonnage of the ship under the tonnage-deck as-
certained as aforesaid ; and if the ship has three or more decks, the tonnage
of each space between decks above the tonnage-deck shall be ascertained in
the same manner as for the like spaces in Rule I., and added to the tonnage
aforesaid.

No. 7. — Admiral Moorsom (^Member oftlie Committee).
In answer to the Circular of Nov. 6th, 1856.

Highfield, Birmingham, Feb. 23, 1857.
My Dear Sir, — I shall not be able to attend your Committee to-morrow.
I have considered the questions in Mr. Atherton's printed paper, and I
cannot afford you much help in the form of categorical reply.

There does not seem to be much disposition on the part of owners of sailing
vessels or steamers to stir against the present system of registration.

On many grounds, however, I think that every vessel should incur a penalty

90 BEPORT--1857.

•which is loaded so as to sink, below a certain draught of water ; and that her
registered tonnage should comprise the weight of water between her assigned
load draught and that draught which she would have when fit for sea, with
crew and stores and everything on board, except that by which she earns
her freight. Supposing such a principle to be admitted, the method of de-
termining such tonnage would not be difficult.

I annex an example. But the question at this moment is, how is this
principle of registration to be tested, and, if sound, carried out ?

The agitation of it, so that the public may some day see they have an
interest in it, must do good, and I shall, tlierefore, be glad to subscribe towards
the expenses of your association.

Next, as to the unit of HP. When a person wishes to buy an engine, he
need not trouble himself about the nominal HP, but specifying the nature
and extent of the work it is to do, he can bind the engine builder to results.
The contractor, on his part, has his own rules for making the instrument.
It then becomes a question of specific performance between the parties, with
which the public is not concerned. But with the question of the improve-
ment of engines and the improvement of vessels, the public has every con-
cern, and improvement can make but slow and fitful progress when the power
exerted and the power given out in any case are not known, or knov,'n only
to a few persons, and that by special experiment only, and not by stated
performance.

In the pamphlet I have had printed for private circulation, of which you
have a copy, I have expressed my opinion on this question of the improve-
ments of engines and vessels, and your Committee may probably coincide
in my views.

I think then, that it is of little consequence to what unit we refer the ex-
pression HP, if in any given case we can know the power exerted ; and it is
the indicator power and its results, including the consumption of fuel, that is
wanted.

Any measure of power must be incomplete without the weight of the fuel
which is the originator of the power, and in any general expression we must
include the boiler as well as the cjdinder.

Such expression would consequently mean a given weight moved through
a certain space in a certain time with a certain weight of coal.

Now, as yet we have no data for such an expression. I must apologise
for so hasty and incomplete a statement, but I would not let the day pass
without an acknowledgment of your note. Having returned home only on
Saturday, and leaving home again tomorrow, I have not at present time to
proceed further with the subjects of the printed letter.

I am, Sir, yours truly,

J. Yates, Esq. C. 11. Moorsom.

(Enclosure.)

Let the dimensions of a vessel at her light draught ready for sea, except
cargo, be —

Length 300 feet.

Breadth 50 „

Draught 15 „

Assume the coefficient of displacement, = 45.

Then, L^i^iiP X , 45=2892-825 tons.
35

ON THE MEASUREMENT OP SHIPS FOR TONNAGE. 91

Let the dimensions at load draught be —

Length 325 feet.

Breadth 53 „

Draught 22 „

Assume the co-efficient of displacement, = 62.

Then, ^^f^^^ X, 62=6712-74
2892-825

Tonnage for dues 3819-915

The builder's displacement scale would furnish these particulars, and it
should be the duty of the Customs Department to check that scale and
verify the facts.

A table of co-efficients might be constructed on the ratios of length to
breadth, and breadth to draught of water, which would enable every owner
to ascertain the displacement at all draughts.

Memorandum on the Questions submitted in the Circular of Nov, 6th, 1856.

Having read the papers transmitted with Mr. Wright's letter of the 19th
inst., I have something to qualify in my letter to Mr. Yates of the 23rd of
February, and not much to add to it.

1st. I concur in the opinion that science has nothing to gain by legislation,
except the repeal of the laws which impede her progress ; and believing that
the interference of authority in things which can be matter of bargain
between man and man must always be pernicious, I would tolerate such in-
terference only where no other security can be had against misdoing. On
these principles I am disposed to let the present system of registration stand
for all purposes of voluntary contract, but I think a shipowner should be
taxed only in the measure in which he can receive freight; and as the dis-
placement is the measure of the freight which a ship can take, it should also
be the measure of tolls and dues. Moreover, as the public ultimately pay
these charges, they are interested in the question.

In so far also as the system of registration may interfere with the best form
of construction of vessels, it impedes science, in which also the public are
concerned.

I adhere, however, to my opinion that for each vessel there should be a
draft of water beyond which she should not be loaded, but, instead of a
penalty, I would merely withhold the clearance. On this point, it would be
useful to obtain facts as to any differences of opinion between the govern-
ment agents and the other parties in cases of vessels with passengers.

I have heard of such differences.

The case of the Royal Charter is somewhat in point ; after getting into
the Bay of Biscay, she was compelled to return to port to be re-stowed.

When on board this ship, before she received her cargo, I pointed out to
the authorities of the ship then on board, the risk of such a contingency,
and how to guard against it; for, if I understood the letters of Dr. Scoresby,
(himself a seaman and on board), which appeared in the Times, the ship was
not only two feet too deep but was overweighted in her fore-body. Now, how
could the underwriters protect themselves in such a case ?

Would the policy be vitiated ? Was the premium higher in consequence
of such a known contingency as overloading and misleading ?

How could the second-class passengers, who were represented as washed

92 REPORT — 1857.

out of tlicir bcrtlis, protect themselves beforehand ; and what remedy had
they after the tact, or what compensation ?

If the displaceiuent principle were adopted, tables might be constructed
for all known forms of vessels, which would give the displacement at any
draught of water, and upon the difference of light and load draught the
dutic's should be payable : this would set at rest the question between sailing
vessels and steamers.

Secondly. — As to a unit of HP. Here the commercial part of the question
resolves itself into a matter of bargain, and neither buyer nor seller can be
benefited by interference. The buyer has but to specify the work he requires,
and to make his contract accordingly. But the scientific part of the ques-
tion assumes another aspect.

Improvement can make but slow and fitful progress when the power exerted
and the power given out are known only to a few of the initiated. What
science wants to know in each case is, the indicator power and its results, in-
cluding the consumption of fuel. Any measure of power which does not em-
brace the weight of fuel, which is the originator of the power, must be
incomplete.

Any general expression must include the boiler as well as the cylinder,
and it would mean a given weight moved through a certain space in a cer-
tain time, with a certain weight of fuel. We have not as yet data for such
an expression.

The accompanying pamphlet, which I have had printed for private circu-
lation, may perhaps throw some light upon this subject, and I have marked
the passages bearing on the immediate question of power.

I have now before me a table printed by the Admiralty last year, and
showing "results of trials made in her Majesty's screw ships and vessels."
These results are useful as far as they go, but they do not go far enough,
and the particulars of the table might be simplified and amended. They
involve a theory, whereas facts alone are wanted. The trials were made in
smooth water only, and do not contain any account of the consumption of
fuel.

The passages marked in the pamphlet and the tables A and B will show
how necessary it is to have the performances of vessels and engines at sea,
in order to institute any comparisons towards the deduction of laws, and
that the consumption of fuel is indispensable.

March 24', 1857. C. R. Moorsom, Rear Admiral.

No. 8 Mr. James Yates (Member of the CommiUee)-

To the Shipping Registration Committee of the British Association.
I am very desirous of directing the attention of the Shipping Registration
Committee to the following considerations : —

The party, if it may be called a party, which we considered as opposed to
ourselves, and which" we may probably regard as represented by Mr. G.
Moorsom, do not appear to be in such entire opposition as may at first be
imagined, and certainly, we are not entirely opposed to them. On the con-
trary, we appear to agree in the most important and fundamental points.

1. We aorree in regard to the necessity of internal measurement as an
element of tonnage registration, being the space inside a vessel, or under
cover, which may be used to carry either cargo or passengers.

2. We agree in regard to Sterling's rule as a recognized method of ad-
measurement, available for calculating the entire contents of a ship of any
form, measured either internally or externally.

ON THE MEASUREMENT OF SHIPS FOR TONNAGE. 93

3. We agree that neither internal nor external measurement does, of itself,
provide any security against the construction of weak thin-sided ships,

4. We agree with the remarks in Mr. Moorsom's Treatise on Tonnage, in
regard to the great advantages of the registration of displacement, or outward
measurement between the light and load water-lines, as showing the actual
weight which any vessel will carry.

These advantages cannot be more distinctly stated than they are by Mr.
Moorsom, in the following remarks on the measurement of keels, and the
method of marking the load water-line with nails, according to weights
actually placed on board, as prescribed by 6 and 7 William and Mary, a.d.
1694, and by 15 George III. c. 27.

" This being a measure of pure and unerring displacement, free from the
possibility of evasion, and giving the exact dead weight of the cargo shipped,
whatever may be the form or construction of the vessel, it offers no induce-
ment to the building of one kind of form more than another; and the conse-
quence is, that many of these peculiar vessels are remarkable for their sailing
capabilities.

"Although the process of 'admeasuring and marking,' to which these
vessels are still legally directed to be submitted, involve neither the taking
of measurements nor computation, and can therefore, it may be supposed,
scarcely be termed a mode of admeasurement in the usual acceptation of the
operation ; yet it is, nevertheless, essentially and absolutely, the most correct
measurement possible of the displacement, or external cubature of that part
of the vessel which lies, or is contained, between the light and load lines of
floatation, that is, of the cargo shipped ; and is, therefore, not only an assu-
rance of the security of the public revenue to be derived from the export of
coals, but is found also to tend greatly to the general accommodation of the
trade in which these vessels are engaged ; and from what has been already
predicated of their sailing capabilities, the process is, moreover, an eminent
and satisfactory, though it may appear an humble example, that an operation
founded on truth, without the possibility of evasion, is an operation without
influence in the formation of ill-formed vessels*."

In a subsequent chapter, Mr. Moorsom treats with great ability the sub-
ject of displacement, showing how it is in practice calculated by Sterling's
rule, and with how great advantage this registration of displacement may be
applied to merchant ships, as is already done in men-of-war by recording the
scale of displacement of all ships in the Royal Navy. See ch. V., p. 113-
148. These statements of Mr. Moorsom clearly establish the practicability
of ascertaining the weight that ships will carry as based on the measurement
of displacement, and recording the same, together with the measurement of
internal roomage.

5. Another principle of the utmost importance, in which, I trust, we are
agreed, and with the statement of which I shall conclude these remarks, is,
that the measurement of tonnage should be international, in other words,
that, as far as possible, it should be the same for all nations, and adopted
with the consent of all. Mr. Moorsom asserts the value of the principle, and
quotes an American author, GriflSths, a ship-builder of great experience,
who entertains the same cosmopolitan views. He quotes that admirable
memorial of the Council of the Society for the Encouragement of Arts,
Manufactures, and Commerce, which recommends to the Lords of the Trea-
sury, A.u. 1853, the consideration of the best means of promoting the adop-
tion throughout the world of a uniform decimal system of measures, weights,

* ' A Brief Review and Analysis of the Laws for the Admeasurement of Tonnage,' by G.
Moorsom. 2nd edition. London, 1853, pp. 15, 16.

94 EEPORT — 1857.

and coins, and which especially insists on the great advantage and conve-
nience of the Metrical System. As Mr. Moorsom also alludes, in encoura-
ging language, to the sentiments " of our active-minded Transatlantic rivals,"
I will add, that not a few of the most distinguished among them have urged
upon their government an examination of the merits of the same system*.
Moreover, Mr. Allan Gilmour points out the necessity " of having a law,
under which the tonnage of all vessels entering our ports, whether British or
foreign, shall be computed in the same wayf ."

In pursuance of these "cosmopolitan views" of Mr. Moorsom and Mr.
Gilmour, I wish to offer some considerations in favour of the adoption of the
metrical ton in place of the British ton, for the registration of the weight ton-
nage of ships. It is probable that this mode of registration, if adopted by Great
Britain, would lead in a short time to perfect uniformity throughout the world.
The metrical ton of 1000 kilogrammes is now recognised, and in part practi-
cally adopted by a considerable number of the principal mercantile nations. It
is established in France, Belgium, Holland, Prussia, Hamburg and the other
Hanseatic ports, Denmark, the kingdom of Sardinia, Lombardy, Algeria,
Greece, and several South American States. Its adoption after a few years
has been decreed by the governments of Spain and Portugal.

Besides Great Britain and its dependencies, the only commercial nations
of importance, which do not already use the metrical ton, are the United
States of America, Russia, Sweden, Turkey, and Egypt. There can be no
doubt that these latter countries would adopt it, if Great Britain led the way.
The metrical ton being the weight of a cubic metre of water equal to 1000
kilo"-rammes, while the British ton is nearly 1015 kilogrammes, or 1^ per
cent in excess, it is evident that no objection can arise from the adoption of
the former as the unit of ship's tonnage by weight except the temporary in-
convenience which accompanies every change whatsoever. A ship of 1000
tons British weight would simply be 1015 metrical tons.

According to a return issued by the Board of Trade, the exports from the
United Kingdom in 1855, consisting of British and Irish produce and manu-
factures, amounted in value to £95,688,085, or nearly £96,000,000. The
countries which use the metrical ton, and are included in this statement of
exports, are as follows : —

Prussia, Hanover, and the Hanseatic £

Towns 9,787,600

France 6,012,658

Holland 4,558,210

Sardinia 853,916

Lombardy 717,713

Belgium 1,707,693

Portugal 1,4.75,713

Spain 1,268,815

Denmark 759,656

New Grenada 588,935

Mfexico 585,898

£28,315,207

* See my ' Narrative of the Origin and Formation of the International Association for ob-
taining a Uniform Decimal System of Measures, Weights and Coins.' I have republished at
pp. 51, 52, the memorial referred to; and at pp. 9 — 11, 47 — 49, 1 have given an account of
similar efforts in the United States by President Adams, the Hon. George Bancroft, and others.

t ' Remarks on the Tonnage Admeasurements of Ships,' published in Moorsom's ' Brief
Review,' pp. 175—179.

ON THE MEASUREMENT OP SHIPS FOB TONNAGE. 95

Thus, the portion of these exports sent to countries using the metrical
ton amounts to above s628,000,000. A considerable proportion of the
countries to which the remaining 3668,000,000 of goods were exported
does not use either the English or the metrical ton, but some other weight.
So large a proportion of our foreign commerce being already carried on with
nations using the metrical ton, it appears highly probable that the adoption by
Great Britain of the metrical ton as the unit of weight tonnage, would speedily
lead to its universal adoption throughout the world. Nor can it be questioned,
that this would be a most proper adjunct to the recent alteration of the Navi-
gation Law, by which the ships of all countries are permitted to carry goods
and passengers to and from Great Britain with unrestricted freedom. A
common method of computing the carrying powers of ships, would be a
manifest and indisputable advantage. For statistical information, the adop-
tion of the metrical ton weight is indispensable. At two great statistical
congresses, Brussels, 1853, and Paris, 1855, it was recommended that the
weights and measures of the Metrical System should be universally employed
as common terms of comparison, reference being made more especially to the
tonnage of ships*.

Let us now consider the advantages of the metre as a linear measure, and
of the metrical ton based upon it, independently of their extensive adoption
throughout the world. According to the English method, the measures of
length are generally computed in feet, inches, and eighths of an inch ; or, if
recourse is had to decimals, as directed by the late Mercantile Shipping Act,
in feet and hundredths of a foot. The use of a measuring-line, divided into
metres and centimetres, appears to present at least equal advantages, and
would be simple, easy, and commodious in the extreme for tonnage measure-
ments, having all the recommendations of a decimal system.

If the metrical ton be adopted as the base of ships' tonnage, the displace-
ment between the light and load water-lines, expressed in cubic metres and
centimetres, will give the metrical tonnage without any further trouble and
with perfect exactness, because a metrical ton is the weight of a cubic metre
of water. This remarkable facility is obtained, because in constructing the
Met-ical System, care was taken to adjust the weights so that they might
have a direct and simple relation to the measures. In the English weights
and measures this principle has been disregarded.

Suppose now that we follow the new law, the Mercantile Shipping Act of
1 854, which, however, is never likely to extend itself to the world at large,
because in this law " the ton " is a palpable misnomer, not being a weight of
any kind, but a certain extent of internal space. Under this law the cubic
contents of every part of a vessel, adapted to carry passengers or cargo, are
ascertained either by Stei'ling's rule or some other approved formula, and
are expressed in cubic feet. The number of cubic feet is then divided by
100, this number having been adopted as the divisor in order to assimilate
the new tonnage registration to the former tonnage registration.

If we apply the metre as the unit of linear measure, we shall find the in-
ternal space in cubic metres instead of cubic feet, and we can easily reduce
the one measure to the other, because a cubic metre being equal to 25'32
cubic feet, the number of cubic metres multiplied by the decimal '3532, will
give the number of tons measure at the rate of 100 cubic feet to the ton,
according to the principle of the new law.

It thus appears tliat the metrical ton, differing from the British weight of
the same name only by about 15 parts in 1000, whereby a ship capable of

* See Rouher and Legoyt, ' Compte Rendu de la Deuxieme Session du Congres Intena*
tionale Statistique.' Paris, 1856, 4to., p. xv., 169-172, 192, 193, 256, 257,

REPORT — 1857.

carrying 1000 tons weight British, would carry 1015 metrical tons, and be
registered accordingly, recommends itself, not only by its use among many
of the chief trading nations, but by its adaptation to the requirements of in-
ternational commerce, to the convenience of mariners, and, most especially,
to the measurement and registration of vessels of all kinds as respects their
capabilities for carrying weight : to which it must be added, that the system
of weights and measures to which this ton belongs, and which is every year
extending through the world, is tlie only system which appears at all likely
to become universal ; so that tiie metrical ton weight must be adopted as the
basis of tonnage registration, if international tonnage is to be pursued as an
indispensable part of a really good method.

James Yates.

Lauderdale House, Highgate, Feb. 14, 1857.

Rejiort on the Temperature of some Deep Mines in Cornwall.
By Robert Were Fox, F.R.S., G.S.

In compliance with the request of the Committee of the British Association,
I have had further experiments made on the temperature of some deep mines
in Cornwall by careful observers, and I have now to report the results of
their investigations*. But before I do this, it may perhaps be well to allude
to the method of working, or rather exploring a metalliferous vein or "lode"
in this county. The horizontal bearing of most of the lodes is from east to
west, or rather from northward of east to southward of west; and they
descend into the earth to an unknown depth, and much more often in an
inclined than a. vertical direction, intersecting the different rocks which occur
in their courses. The miners work a lode by means of shafts, and galleries or
"levels," which latter, being on the course of the lode, do not usually succeed
each other in a vertical, but in an inclined direction.

FiK. 1.

Fis. 2.

Let fig. I, a,h, represent a north and south section of a lode inclined to-
wards the north ; c, d an engine-shaft through which the water is pumped

* I am indebted to my friend \YilIiani Hustler of Rosemorryn, near Falmouth, for the
results obtained iu the United Mines, and most of those in Fowey Consols ; — to Captain
J. Puckey, Manager of Fowey and Par Consols, for experiments in those mines ; — to Captain
Charles Thomas, Manager of Dolcoath, for an experiment there; to Captain Jennings of
Tresavean, for some made in that mine in 1853 ; and to Henry Peters of Lanner, near Red-
ruth, for the other experiments in Dolcoath, iu Levant, and Cotallack Mines.

ON THE TEMPERATURE OP DEEP MINES IN CORNWALL. 97^

up to the adit e,/, from the bottom or "sump" d(hgs. I & 2), and from
cisterns placed at various intervals in the shaft, the water which enters the
levels being conducted into the cisterns, and thereby prevented from falling
to the bottom of the shaft. From the adit, the water is discharged into a
valley, or near the sea shore. The horizontal lines in fig. 1 represent " cross-
cuts" or N. and S. levels, which connect the engine-shaft with the levels at
right angles to them, as shown in fig. 2. These latter, on the course of the
lode, are usually about ten fathoms apart, and they are connected together
by many short shafts inclined with the lode. There are also other shafts
from the surface to the deep levels, through which the ore is drawn up,
ventilation promoted, &c. In most of the deep mines several lodes are
worked, and each by means of a similar series of levels, shafts, &c., which
are connected with the former series by " cross-cuts," so that one engine-shaft
may often serve for two or more lodes. The deepest levels in a mine are
generally much less extended than those above them, as shown in fig. 2, and
the quantity of water in them is often comparatively small, the upper water
being in a great degree cut off by the superior levels, and conveyed to the
cisterns through the latter. The temperature of the water that flows into
the ends of the deepest levels is generally as high, or nearly so, as that of the
rocks and lode, and more often higher, which it may be presumed it would
not be if much of the upper water were mixed with it. Most of the experi-
ments were made at or near the ends of the deepest level in each of the
respective mines, as at E. and W., fig. 2.

The thermometers employed were obtained for me by Professor Phillips,
from Casella, and were, I need scarcely say, accurately graduated.

They were placed in holes from 15 to 20 inches deep in the rocks and
lodes, which were carefully closed up with clay, tow, or cotton. After
the thermometers had been so left from half an hour to an hour, they
were withdrawn for an instant for the temperature to be read off, and
were often again left in the holes for some time longer ; but as no further
change was observed at the second reading, this precaution was latterly
dispensed with.

In taking the temperature of the water, the most copious springs at their
sources or influx into the levels were selected, if near the stations where the
other observations were made ; and the temperature of the surrounding air
was also ascertained.

The mines visited are situated in different parts of the county, ranging
from near Fowey, to St. Just, a little to the north of the Laud's End, a distance
of about fifty miles.

To begin with Fowey Consols* copper mine, situated near Fowey, as
being the most easterly one.

The deepest level in this mine was reported to be 328 fathoms under the
surface, and about 298 fathoms below the sea-level ; but the influx of water
interfered with any experiments being made in this part of the mine, which
is the more to be regretted, as perhaps there are few if any mines elsewhere
so deep in reference to the level of the sea, although there are many deeper
from the surface of the ground.

At 268 fathoms below the surface, water issued from a copper lode at

* Capt. J. Puckey calculates that the total length of all the levels on

the courses of the lodes in this mine amounts to 153 miles.

Of the erossccourses or levels, N. and S 22 miles.

And of the shafts 7 mUes.

182 miles in all,
1857. "

98 REPORT — 1857.

96°'5 Fahr. ; the lode * was 95°'5 and the air 95°'2 : no persons at work near
the place.

In a level 288 fathoms deep, another lode was Q-i", the adjoining rock
93", and the air 91°'5: no water, and the containing rock "killas."

Par Consols is situated near Par on the shores of the English Channel, and
produces copper and tin in " killas." Its deepest level, when visited, was
208 fathoms from the surface, and about 178 fathoms under the sea-level:
the lode in it was at 84°, the rock 84-°, and the air 82°. The part of this mine
which produces tin was 128 fathoms beneath the surface at its deepest level,
and there the lode was at 74'°, the rock near the lode 74°, the air 75°, and
the water 72°.

The United Mines in the parish of Gwennap have yielded much copper
ore in " killas." At the eastern end of a level, 255 fathoms under the surface,
and nearly 200 fathoms below the sea-level, a stream of water gushing out of
a rich copper lode, called the north lode, was lately found to be at the tem-
perature of 116° Fahr., and the neighbouring rock and air were at 106°. In
another level, also 255 fathoms deep, worked on a parallel lode, southward of
the former, in which there was very little water, the rock was 82°'5, and the
air 82°.

I have had no recent information relative to the temperature at the bottom
of the mine, but in 1853 the rock was 94°, the air 90°, and the depth 275
fathoms. At that date the stream of water in the eastern end of the level,
255 fathoms deep, was at 109°, or 7° less than now that the level has been
further extended. In 1846, when the level was still less advanced towards
the east, the spring of water, discharging as was then estimated 94 gallons
in a minute, was at 106°"3, and the air 104°'2. At that time I examined
some of the water and found 15 grains of common salt and chloride of lime
in a quarter of a pint of it, in nearly equal proportions ; but no metallic salt
could be detected. This mine is several miles from the sea.

In 1853 I had some observations repeated in Tresavean, to ascertain in
what proportion the temperature had increased with the increased depth
since 1837. This mine is in the parish of Stythians, about eight miles to
the N.W. of Falmouth, and has been very productive of copper, found mostly
in granite, and but very little in killas. The bottom level was 352 fathoms,
or 2112 feet under the surface, which is more than any other mine in Corn-
wall, and about 1750 feet below the sea-level, or rather less in this respect
than Fowey Consols. The lode in this deep level, at its eastern extremity,
was at 90°"5, the thermometer having been long kept in a dry hole, closed
at the top; the contiguous granite 91°*5, the hole rather moist, the air
91°*5, and a small spring of water flowing from the lode into the level, 93°'5.
In 1837 the deepest level in this mine was 262 fathoms, or 1572 feet beneath
the surface, and the rock there was then found at 82°-5.

Dolcoath, in the pari>h of Camborne, has been a very productive mine of
copper and tin ores, and now yields much of the latter from its deepest parts,
the containing rock there being granite, with killas nearer the surface. The
deepest level on the north lode was 272 fathoms below the surface, and ex-
tended only about four fathoms on each side of the engine-shaft. The rock
near the eastern end of this level was at 73°*5, the air 71°*7, and the water
73°. At tlie western end the rock was 73° on one side of the level, and 73°*5
on the other, the air 73°, and the water, the quantity of which was leri/ small,
72°'7. At about three fathoms further south, and the same depth, another

* When the temperature of the rods or of the lodes is mentioned in this Report, it is
meant that the thermometers were placed in holes in them for half an hour or more, and
that the other precautions already referred to were observed.

ON THE TEMPERATURE OF DEEP MINES IN CORNWALL. 99

lode was worked, the level extending to about fourteen fathoms to the west-
ward of the engine-shaft. There the granite was found to be at 79°'5, and
the water, which was much more abundant than in the other level, 79°'5,
while the air was at 78°. Two men at a time worked near each of the
stations in both levels. The pumps discharged only about 190 gallons of
water per minute from the mine.

In 1821-1822 the deepest level in Dolcoath was 230 fathoms from the
surface, and I then had an accurate thermometer, 4 feet long, kept in it
more than a year and a half, with the bulb sunk 3 feet in the lode, and
it varied from 75° and 75°*5 to 76°*5 and 77° ; an occasional influx of water
having caused a temporary rise of the mercury to the extent of a degree or
more. This temperature being from two to three degrees higher than the
rock, was lately found by H. Peters to be at an increased depth of 42 fathoms :
I begged Captain Charles Thomas, the manager of the mine, to have a ther-
mometer left for some days in a hole in the rock near one of the ends of the
deepest level on the north lode. This he has done, and he reports that
the temperature did not vary from 73°, although the thermometer was left
there a week, and the top of the hole was well closed, thus confirming
H. Peters' observations.

The water near the bottom of the engine-shaft in 1822 was at 82°, at 239
fathoms below the surface, and this year (1857) it was at 82°-5, at 278
fathoms deep.

Levant copper and tin mine, in St. Just parish, is nearly twenty miles to
the west of Dolcoath, and is close to the sea. Its deepest level is 255
fathoms below the surface of the ground, and nearly 230 fathoms beneath
the sea-level, having been horizontally extended under it through killas.
The temperature of the rock near the end of this level was 84°'7 on one side
of the latter, and 85°-5 on the other ; the water 85°'5, and the air 85°. No
men had been employed in this level for some time. There was very little
water there, and indeed only about 60 or 70 gallons were discharged per
minute from the mine.

In 1853 the temperature of the rock in this level, when it was not ex-
tended so far westward under the sea, was reported to me to be 87°> and the
granite rock at the same level, eastward of the shaft, 74°.

Botallack copper and tin mine is situated at the north-western extremity
of Cornwall, in the parish of St. Just, and the engine-house is built on a
rock which is washed by the sea. The western levels have been worked
through killas far under the Atlantic, one of them extending more than half
-a mile from the shore. Two men and a boy were employed in the deepest
level, which was less advanced from the shore. It was 188 fathoms below
the ground, and about 180 fathoms under the sea-level. The rock near the
end of the level was 79° on one side of it, and 79°*5 on the other, the air 81° :
no water at that station, and but little comparatively in the mine.

The foregoing results exhibit great differences in the rates of increase in
the temperature in different mines, and also in different parts of the same
mine. If we arrange the mines in the order of their respective depths, in-
cluding those only in which experiments were made in the rocks or lodes at
their deepest levels, the following will be the ratios in feet, in descending
from the surface, in which the temperature was augmented one degree Fahr.
from 50°, the mean temperature of the climate.

100

REPORT — 1857.

Mines.

Depths
in feet.

Dates.

Temperatures.

Increase of 1°
in descending.

Hocks.

Par Consols (tin part) ...

Botallack, C. and T

Par Consols (copper part)

Dolcoath, C. and T

Levant, C. and T

768
1128
1248
1380
1530
1530
1530
1572
1632
1632
2112

1837
1S37
1837
1822
1853
1853
1857
1837
1857
1857
1853

74° -50 = 24°
79 -50 = 29

84 -50 = 34
75-5 -50 = 25-5
74 -50 = 24
87 -50=37

85 -50 = 35
82-5 -50 = 32-5
73 -50 = 23
79-5 -50 = 29-5
90-5 -50 = 40-5

32 feet
39 „
36-7 „
54 „
63-7 „
41-3,,
43-7 „
48-4 „
71 „
55-3 „
521 „

Killas.

Granite.

Killas.

Granite.

Levant, C. and T

Dolcoath, C. andT

Dolcoath, another lode...

On comparing the results obtained in Dolcoath in 1821-1822 and 1827>
it appears that the temperature was increased only 4° in one level with an
increased depth of 252 feet, giving a ratio between the stations of 1° increase
in 63 feet ; and in another level the temperature was actually 2° to 2°"5 less
than in 1822, although 252 feet deeper than the mine was then. These
experiments were made with great care, and this exceptional case may pro-
bably be due to the greater hardness and compactness of the lode in the
deeper level, and the diminished quantity of water.

The depth of Tresavean was increased 540 feet between 1837 and 1853,
and the temperature 8°'5 in the deepest level, or in the ratio of 1° in 63*5
feet.

I have not included in the Table the results recently obtained in the United
Mines or Fowey Consols, the experiments not having been made in their
deepest levels; but the hot spring at 116°, at the depth of 255 fathoms in
the United Mines, gives a ratio of 1° increase in 23"2 feet, and the rock in
another level, also 255 fathoms deep, 1° in 47 feet.

In 1853 the bottom of the United Mines was 275 fathoms below the sur-
face, and the rock 94", or in the ratio of 1° in 37'5 feet. At Fowey Consols,
the rock, in a level 288 fathoms deep, was at 93°, or in the ratio of 1° in-
crease in 402 feet.

Widely as the ratios differ from each other in different mines and in dif-
ferent parts of the same mine, the results tend to confirm the statement that
the temperature in general increases less rapidly in deep mines tiian in those
which are of inferior depth ; and this is more especially observable when ex-
periments are made from time to time at the bottom of a mine as the depth
increases, unless the results be modified by an increase of water coming from
greater depths. It is not, however, to be inferred that the diminishing ratio
of temperature in descending into the earth extends to an indefinite depth;
it may, on the contrary, and probably does, increase much more uniformly
at depths where the circulating water has little or no influence. A copious
spring of warm Avater gushing from a vein, is hailed by the miners as a
favourable indication of the proximity of ore, and so is a pervious, or
" hollow " lode ; but the former clearly results from the latter, the warm
water rising from greater depths through the lode.

These subterranean springs are often nearly as free from saline matter as
those occurring at the surface ; in some I have found common salt and
chloride of lime, especially in water taken from the deep levels of Poldice
and Wheal Unity, and the hot spring at the United Mines. My friend
William Hustler has recently examined the latter, and he reports that it
" still contains a large quantity of chloride of sodium, and a considerable
quantity of chloride of calcium, with traces of the sulphates of lime and

ON CERTAIN TRANSFORMATIONS. 101

magnesia ; no iron or copper." All these mines are several miles from the sea.
The water from the deepest level in Levant and Botallack also contained
some common salt, and was slightly saline to the taste ; but the proportion
was much less than might have been expected in excavations extending so
far under the sea. I have examined the water from numerous mines, taken
immediately from the springs at their entrance from the veins into the levels,
and I have not detected the presence of any metal, except in some instances
a very little sulphate of iron, and traces of the sulphate of zinc, on two or
three occasions. On the other hand, it may be observed, that the water not
coming directly from the springs, but which is collected more or less in
pools in the levels, often contains metallic salts derived from the ores in
the levels broken from the lodes, and exposed for a time in heaps to the
joint action of air and water.

The phenomena observed in mineral veins, however, afford strong pre-
sumptive evidence that the water circulating through them has, from time to
time, varied much in its properties, sometimes depositing minerals, and at
others decomposing them.

Captain J. Puckey has, at my request, made an experiment on the tem-
perature of the rock at the end of a "cross-cut" in Fowey Consols. The
end was dry, 60 fathoms from the lode, distant from other workings, and 140
fathoms deep. He thinks that they will have to extend the cross-cut 20
fathoms further to intersect another lode. The thermometer remained an
hour in a hole of the rock, the top of which was closed with clay ; and on
being withdrawn, the mercury was found at 82°, and in the air it stood at 78°.
Captain John Kitto has also made experiments in Swanpool lead mine near
Falmouth; temperature of rock 58° at the end of a dry cross-cut, 34 fathoms
northward of the lode, and 55 fathoms deep. In another cross-cut, the end
of which is 14 fathoms to the south of the lode, and 60 fathoms below the
surface, the rock was at 60°, air 64°, and the water 59°. The presence of
the latter probably indicated the proximity of another lode. This mine is
80 fathoms deep, and both the mines are in killas.

I may remark, in conclusion, that on comparing the specific gravities of
pieces of different rocks taken from the deepest parts of some of the mines,
with others of the same kind occurring at or near the surface, I have not
found any decided differences between them in this respect.

De quelques Transformations de la Somme 2j ^i+i ^i+i ti+i ' " ^^'^^^

entier negatif, et de quelques cas dans lesquels cette somme est ex-
primable par une combinaison de factorielles, la notation «''+' desig-
nant le produit des tfacteurs «(a-f l)(« + 2) ^c. .. (a-f t— 1). Par
G. Plarr, Docteur es Sciences de Strasbourg.

[A Communication ordered to be printed entire among tlie Reports of the Association.]
Dans un memoire sur la s6rie

J\>r,rj l.y^ 1.2.y.(y-i-l + i3l + yi + i

Gauss a doime une expression de la somme de cette serie pour des valeurs

102 REPORT — 1857.

quelconques de a/3y, satisfaisant seulement a la condition de convergence
y— a— /3>0.

Dans le cas ou a est entier negatif (et que du reste, y, s'il est de meme
entier negatif, est en valeur absolue plus grand que —a), laseriese termine,
et pent s'expriraer par uu quotient de deux factorielles,

X«.Ar)=^5^^^ISr^ 0)

Disignons par analogic par F( ' ) la s6rie proposee de six factorielles,
c'est a dire, posons

\ y,€ J « it\ + i^t\+i^t\+i'

Dans le cas ou a est entier negatif (et que y et e, s'ils I'ont I'un ou I'autre
entiers negatifs, sent en valeur absolue plus grands que —a), la serie se ter-
mine au 1 — a'^iie terme, et son expression est susceptible d'un certain nombre
de transformations, dont voici quelques unes: —

^/a,/3,a\_ (y-/3)-l-^- / a,/3,e-a \
\y,ey-y-a| + l ^ \a+fi-y+l, e) ^^

f/ «» a ^ \ (y-/8)-"l+'(e-/3 )-"i+' / a,/3, a+/3 + g-y-f+l \
\y,e/ y_a! + i^_«u+ t \a+/3-y+l, a + /3-e+lJ '^^

/ «,/3, A _ /3-°'l + ^a-'" + ^ /«, «-y+l, g-e + ll ,.

V'rrry"^" '^ y-«l+>e-«'+» I a-/3+l,a-a+l /• ' * ^'>

Les forniules (6), (c) sont des consequences de (a).
Dans le cas ou e — 2 est entier negatif, et en valeur absolue plus petit que
— a, la formule (a) donne celle-ci:

/ g, /3, a \ (y + e-^-g)«l ^' / e-S, a, e-/3 \ .

A r,e ; y-a|+l 1 ^ + e-/3-S, e J ' ' * ' ^""^

Lorsque a+/3 + S— y— e+l=0, la formule (b) donne le resultat suivant,
base sur la remarque que Ff '^'f'' ) = 1 lorsque ^'=0; savoir,

p/a,/3,g\_ (y-/3)-°'l^'(e-/3r«'^' ,,

V y. e / y-al + lg-al+l ^^ W

Le cas ou les bases a, /3, &c. satisfont a la relation a+/3 + S — y—e+ 1=0

est done un des cas dans lesquels la fonction F( ' ^' — j peut se sommer

V y. e /

sous forme monome, et s'exprimer par un quotient de factorielles.

Voici maintenant la demonstration de la formule (a). La formule (1)
donne

./«, b\ -a a^l+'^,^'+i ^ (c-z,)-''l+'

Identiilons avec le 3^ membra le quotient — — dans I'expression de

F( — — ~ J. Nous devious poser

— a=:t, c — 6=a, c=e.

ON CERTAIN TRANSFOKMATIONS.

103

DeU

Intervertissons I'ordre dans la sommation par rapport a, tet a s. A cet effet
donnons une signiBcation glometrique a la double sommation exprimee par

^i°''2j(t>s).

Concevons les valeurs (p(t, s) disposes par points dont les abscisses soient
t, et les ordonnees s. L'ensemble de ces points est limite par un triangle

dont I'hypotenuse a pour Equation s-=t, et les deux cadettes sont s=0 et
«=— a; car pour chaque valeur de t considere comme indice indepeudautj
11 faudra donner ^ s les valeurs depuis s=0 jusqu'a s=^. Si Ton con-
sidere f

/. .

comme indice independant, il faudra pour chaque valeur de s donner a t les
valeurs depuis <=« jusqu'a <= —a. On aura done

d'ou

Introduisons un nouvel indice u lie a s, < par «=s + m. Les liraites de u
seront pour <=s, m=0 ; pour f=—a, m= —a,—s. De plus,

(-<yl+i (-1)'
2 t\+\ — 2«l+i

a<l+i=a»l+ix(a+5)"'+S&c.
D'ou

\ y. f /~ » i.i+iy.|+vi+i ^<> ^^^0 l«l+»(y +«)"'■"

104 REPORT — 1857.

La somme 2" 0(") ^^^ ^^ ^* forme

Cetto quantite, toute reduction faite, devient

y-«l + i (a + /3-y+l)+*l + '

En la substituant dans rexpression precedente de Fl -^-^ — J, et en remar-

quant que ( — 1)^'= + 1, il en resulte la formule (a).

Pourque la formule («) ne soit pas illusoire, il faut que « + /3 — y+l? s'il
est en tier negatif, ne sort pas en valcur absolue moindre que —a, ou moindre
que e— 2 si par hasard cette derniere quantite est entiere negative moindre
que — a en valeur absolue.

La formule (b) se deduit de (a) si Ton identifie F < ' ^' ^ > avec

La + /3 — y+1, eJ

F I "') ^'' f \ en posant a=a.>, /3=/3', e-a=g', a+jS-y + l = e', €=y' ; et
L (y', e' J

que Ton applique la formule (a) aux lettres a', /3', &c.
La formule (d) se deduit de (a) en posant

e-g=a', /3=S', a=/3',

e=e', a + /3-y+l=y',

a' /3' S'
appliquant la formule (a) a F ' , ' , et transformant le facteur en de-

y, e'

hors de F.

Report on the Marine Zoology of Strangford Lough, County Down,
and corresponding part of the Irish Channel. By G. Dicki e, M.D.,
Professor of Natural History, Queen's College, Belfast.

The entrance to Strangford Lough is less than two miles in breadth ; it gra-
dually becomes narrower, forming a channel half a mile broad with a length
of about three miles. The tidal current in this channel is estimated as
havino- a velocity of nine miles per hour ; as a consequence of such pecu-
liarities, we find near Portaferry a depth of twenty-nine to thirty-five fathoms
in the centre of the channel, and a gradual slope upwards from mid-channel
to both shores. The bottom, in the deepest part, consists of rock with large
and small stones interspersed ; near the shore we find a mixture of small
stones and gravel, and in the small bays sand or mud, or both intermixed.

The wider expansion of the Lough itself presents very much the same
characteristics of bottom, with this difference, that the proportion of hard
material is very much less, a large part consisting of mud. These pecu-
liarities give rise to corresponding differences in the distribution of animal
life, as the following facts testify : —

The fauna of parts of Strangford Lough has been examined by the late

ON THE MARINE ZOOLOGY OF STRANGFOBD LOUGH.

105

Mr. Thompson and Mr. Hyndman, during excursions in 1832, 184'6, and
1851. Some of the results of these dredgings, found among the papers of
Mr. Thompson, will be given separately ; the exact places dredged by these
gentlemen are not in every case recorded.

About the middle of June of the present year (1857) I began the exa-
mination of the Lough ; fortunately the weather was so favourable that
during fifteen days' stay at Portaferry, twelve dredging excursions were
made, each occupying five to eight hours. At the end of the first week. I
was joined by E. Waller, Esq., and received valuable aid from him in
recording the lists of species.

It may be necessary to state that species designated as common or very
common are those of which a considerable number of specimens were brought
up at every haul of the dredge ; of those called rare, not more than four or
five were procured, either at one haul or as the result of several trials ; the
species marked very rare, are those of which not more than four or five
specimens (generally not so many) were found among the entire products
of all the excursions : as examples, may be mentioned Chemnitzia scalaris and
Terebratula caput-serpentis.

These symbols have been used for brevity's sake : —

Very common **

Common , *

Rare f

Very rare %

Living /

Dead d

Strangford Lough, Castle Ward Bay ; a quarter of a mile from the shore,
depth seven to twenty fathoms ; three and a half miles from the sea ; bot-
tom mud, small stones, gravel.

Aplidium fallax

TUNICATA.

Clavellina lepadiformis f

Molgula tubulosa *

Lamellibranchiata.

Pholadidce. Pholas Candida f d. Cyprinidcs.

Gastrochcenida. Saxicava arctica ... t I. Cardiadce.

rugosa * I.

MyadcB. Mya truncata f d.

Corbulida. Corbula nucleus * I,

AnatinidcB. Thracia phaseolina . . . t d.

Solenidce. Solen ensis * d.

pellucidus f I. Lucinidce.

SolecurtidcB, Solecurtus coarctatus X d.

TellinidcB. PsammobiaFerroensis * d. Kelliada.

■ tellinella f I- MytilidiB.

Syndosmya alba t I.

prismatica | I.

Mactridce. Mactra elliptica t ?• ArcadcB.

Veneridce, Tapes virginea * I,

puUastra f I,

aurea t d. Ostreada.

Venus casina f I.

fasciata * I,

— — ovata ** I.

striatula | I.

striatula ** d.

Cyprinidce, Cyprina Islandica ... t l-

Astarte sulcata f I.

Astarte triangularis... | I.
Cardium echinatum . * d.

edule * d.

nodosum * I,

fasciatum J d,

pygmaeum f I.

Suecicum j d.

Lucina borealis * I.

flexuosa t d,

Kellia suborbicularis . t I.
Modiola modiolus ... * I.

• phaseohna? t U

Mytilus edulis * I,

Nucula nucleus * /.

nitida | h

Leda caudata j I,

Lima Loscombii t d.

Pecten striatus % d.

maximus * d.

opercularis * /.

tigrinus t d.

Ostrea edulis t d,

Anomia ephippium... * /.
striata t d.

106

REPORT — 1857.

Gasteropoda.

ChitonidtB. Chiton asellus * I.

fascicularis ... | I.

Isevis t i-

niber t I.

Patellidm. Patella pellucida ... * /.

Acmrea virginea * I.

testudinalis ... t d.

Dentaliadec. Dentalium entalis ... * I.

CalyptraidcB. Pileopsis Hungaricus t d.

Fissurellida.
TrochidtB.

Fissiirella reticulata
Emarginulareticulata
Trochus cinerai'ius...''

magus

millegranus . . .

Montagui

tumidus * I.

LiittorinidcB. Rissoa striata * d.

Turrit ellid(B. Tui'ritella communis * I.

Cerithiadee. Aporrliaispes-pelecani * /.

Cerithium reticulatum * d.

Pyramidellidce.^ulima bilineata ... % I.

polita j d,

Chemuitzia scalaris . j d.

elegantissima... I d.

indistincta % d.

t d. Naticidce. Natica nitida * l.

sordida % d.

Cypra;a Europaja ...** d.

Mangelia tm'ricula... t d.

rufa t d.

septangularis... f ^'

linearis t d.

Nassa incrassata * d.

Buccinum undatum . t I-

Fusus antiquus t I-

Trophon clathratus . % d.

• muricatus * d,

Murex erinaceus ... t d.

Cylichna cyliudracea t d.

obtusa \ d.

Tomatella fasciata... j d.

.** I.
t I.
* I.

Cypraadx.
Coiiidw.

Euccinida.

Bullidce.

zizypbinus

var. Lyonsii ..

Phasianella pullus ..

Littorinidce. Lacuna crassior J d,

vincta ** I.

Rissoa Beanii * d.

. costata t d.

crenulata t d,

labiosa * d.

rufilabrum * d.

The dead shells so abundant in this locality were chiefly Tapes pullastra,
T. virginea, Cytherea lincfa, Venus ovata, V. striatula, Cardium nodosum,
Corbula nucleus and Nucida nucleus.

Wellstream Bay, west of Chapel Island ; five miles from the sea ; half a
mile from the shore ; chiefly mud ; fifteen fathoms.
Lamellibranchiata.
VeneridcB

Cyprinida.

CardiadcB.

Lucinidcs.
Arcades.

Artemis lincta * I.

exoleta t d,

Astarte sulcata t I.

Cyprina Islandica ... f d.

Cardium echinatum . t d.

nodosum t I.

Lucina borealis f t.

Nucula nucleus * I.

nitida f J.

Myada. Mya arenaria t d.

CorbulidcB. Corbula nucleus * I.

Anatinidte. Thraciaphaseolina... t d.

convexa t d,

Solenida. Solen pellucidus t I-

Solecurtid(B. Solecurtus coarctatus t d.

TellinidcB. PsammobiaFerroensis * d.

Syndosmya intermedia t I-

Veneridce. Tapes virginea t I.

Venus ovata t ^•

Gasteropoda.

Chitonidce. Chiton asellus * I. Trochidce.

Patellidce. Patella ]5ellucida ... t I. Turritellidcs.
Dentaliadce. Dentalium entalis .. . t d. Naticidce.
Trochidce. Trochus zizypbinus . t d. Muricidce.

tumidus t I.

Upper part of Wellstream Bay, six miles from the sea ; a mile from the
shore ; mud chiefly ; four to eight fathoms.

Trochus Montagui...
Turritella communis

Natica nitida

Trophon muricatus . .

t I.

f I.

+ d.

Lamellibranchiata.
Gastrochcenidce. Saxicava arctica ... t l. Solenidce.

Myadce. Mya truncata J d. Soleciir tides.

CorbulidcB. Corbula nucleus * I. Tellinidce.

Pandoridcc. LyonsiaNorvegica ... | d.
Anatinidce, Thracia convexa j d. VeHeridce,

Solen pellucidus t t.

Solecurtus coarctatus t d.

Tellina donacina t d.

PsammobiaFenoensis t d.
Tapes virginea * d.

ON THE MARINE ZOOIiOGY OP STRANGFORD LOUGH. 107

Lambllibhanchiata (continued).

Venerida.

MytilidcB.

Arcadee.
Ostreadce.

Cardiadce,
Lucinidce.

ChitonidcB
Patellidce.
Dentaliadcs.

Modiola modiolus ... * d.
Modiola phaseolina . \ I.
• marmorata ... "Y I.

Nucula nitida + I.

■ nucleus * d.

Lima subauriculata .. % d,

Loscombii % ^>

Ostrea edulis t d.

Anomiaephippium..-. * I,

Troehus zizyphinus . t I'

var. Lyonsii ... t I.

Turritella communis * d.
Aporrhais pes-pele-

cani * I-

Natica nitida t ^«

Buccinum undatum . t i'
Cyprsea Europaea ... t d.

Bay opposite KiUilergh ; six miles from'the sea ; half a mile from the land ;
mud; six fathoms.

Myatmncata t d. Venerida.

Corbula nucleus ... * I. Mytilidcs.
Solecurtus coarctatus t d. Arcades.
Psammobia Ferroensis * d. Ostreadce.

Syndosmya alba + I.

Gasteropoda.

Chiton asellus t I. Turritellida.

Troehus cinerarius... * I,

Near the centre of Strangford Lough, two to two and a half miles from
either shore (in a line between Kircubbin and Killinchy) ; seven miles from
the sea ; chiefly mud; depth fifteen to twenty-five fathoms.
Lamellibranchiata
Solecurtus coarctatus + d. Kelliadce.

Venus striatula * d.

■ ovata * i.

fasciata * d.

Artemis Uncta * d.

exoleta ......... t d.

Cyprina Islandica ... + d.

Isocardia cor t ^•

Cardium echinatum . t d.

Lucina flexuosa t d.

Gasteropoda.

Chiton asellus * I. TrocUdes

Acmsea virginea * ^■

Dentalium entalis ... * d.
Fissurellidce. Emarginula reticulata * d.
Trochidce. Troehus cinerarius... * I.

' ~ umbilicatus ... t d.

tumidus * I-

millegranus ... t

Myadts,
Corbulidce.
Solecurtid(S.
Tellinidce.

CerithiadcB.

Naticidce.
MuricidcB.
Cyprccadis.

Venus casina t d.

Modiola modiolus ... * I.
Nucula nucleus * /.

Pecten opercularis . . .
Anemia ephippium. , .

Chitonidte.
TrocMdcB

Turritella communis * d.

Solecurtidce.
Pandoridce.

Corbulidce.
Venerid(e.

Cyprinidce,
Lucinidce.

Patellidce.
Fissurellidcs.

Trochidce.

Lyonsia Norvegica . X ^•

Thracia convexa t d.

Corbula nucleus * I.

Tapes virginea * /.

Venus casina t d.

ovata ** I.

■ striolata t I.

Cyprina Islandica ... * I.

Astarte sulcata I.

Lucina borealis ' I.

flexuosa.... t d.

Arcadce.
Ostreadce.

Gasteropoda.

Acmaea virginea * I.

Fissurella reticulata . t I.
Emarginula reticulata t d.
Troehus millegranus . t I.

zizyphinus t ^-

cinerarius * I.

tumidus * I.

Turritellidce.
Naticidee.

Muricidce.

Bullidce.

KeUia suborbicularis t ^.
Modiola modiolus ... * I.

Nucula nucleus * /.

nitida..... t I.

Pecten maximus ... t I,

■ striatus t ^'

opercularis......** I.

pusio * l-

varius * I,

Anomia ephippium... * I.

striata t h

Ostrea edulis * I.

Turritella communis * I.

Natica sordida % d.

moniUfera ^ t d,

Nassa incrassata t d.

Buccinum undatum . * I.
Trophonmuricfatus... t d,
AkerabuUata t I-

The broken ghelh in this locality were chiefly Venus ovata, Tapes virginea,
Peeten opercularis, Modiola vulgaris, and Ostrea edulis.

Bay to the north of Gun Island, in the Irish Channel, at south entrance
of Strangford Lough ; . a mile from the shore ; mud and sand ; seven fatboms.

t;o8

REPORT — 185 7.

Cardium nodosum .

Natica nitida * /.

Nassa incrassata * d.

Lamellibbanchiata

Tellmida. Tellina fabiila * /. Cardiadcs.

Veneridce. Venus striolata * d.

Gasteropoda.
Fissurellid<e. Fissurella reticulata . t d. NaticidcB,
Trochidce. Trocbus cinerarius... * d. MuricidcB.
tumidus * d.

In the open channel opposite to the entrance of Strangford Lough, the
results of dredging indicated very regular distribution of materials through-
out a distance of seven miles from the bar.

1. From the bar to one mile — more or less — large stones with a mixture of
fragments about the size of the fist.

2. Two miles — more or less — from the bar, gravel, small stones, and
shell sand.

3. Three miles — more or less — from the bar, gravel with dead and living
moUusca, and fine debris of shells.

4. Four to five miles from the bar, sand and mud, with a smaller pro-
portion of dead and living mollusca.

5. Six miles — more or less — from the bar, fine mud and sand.

6. Seven miles from the bar — more or less — fine black tenacious mud,
with one living bivalve (^Syndosmya intermedia), and Brissus lyrifer.

It need scarcely be stated, that the powerful currents which issue from the
narrow opening of the Lough, in some measure account for these pecu-
liarities, the lightest materials being carried farthest and deposited at a
distance from the bar.

Mollusca of First Zone, \1 fathoms.
Chiton ruber, f I. \ Chiton asellus, * I. \ Acmsea virginea, * I.

Mollusca of Second and Third Zones,

Lamellibbanchiata,

Gasf rocAeenirfcs. Saxicavarugosa... * I. Cyprinidce.

• arctica + I.

M3^a truncata \ d.

Corbula nucleus f d.

Pandora obtusa % d.

Thracia phaseolina... f d.

Solen sifiqua f d.

ensis \ d.

Solecurtus coarctatus j d.

candidus % d,

Tellina crassa f d.

fabula + I.

PsammobiaFerroensist d.

tellinella * I.

Syndosmya prismaticaj I.

Mactra elliptica * I.

Lutraria elliptica ... * I.

Tapes virginea * I.

Venus casina f d.

fasciata t I.

striatula ...... f d,

ovata * d.

Artemis exoleta f d.

lincta t ^«

Myadce.

Corhulid(e.

Pandoridce.

Anatinidce.

Solenidce,

Solecurtidce.

TelUnidee.

Mactridte.
Veneridce.

Cardiadce.

Lucinida.
Kelliadcs.

Arcades.

Ostread(S.

12 to 15 fathoms.

Cypiina Islandica ... + I,

Circe minima J I.

Astarte sulcata -f d.

triangularis ... J I.

Cardium nodosum... * I.

pj'gmaeum f d.

Norvegicum ... J d.

Lucina borealis -f" /,

Kellia suborbicularis X ^»

Montacuta substriata i /,

Nucula nucleus * d.

Pectunculus glycymeris **/.
Modiola modiolus ... * I.

phaseolina? ... f i.

Lima Loscombii X ^•

Pecten similis | d.

varius f d.

opercularis * d.

maximus f d,

• tigrinus * I.

Ostrea edulis f I.

Anomia striata f /.

epbippium * I,

patelliformis ... -f I,

Bbachiopoda.
Tere6rofM/Jd«.Terebratulacaput-serpentis,t I. Craniadce. Crania anomala..

ON THE MARINE ZOOLOGY OF STRANGPORD LOUGH.

109

Gasteropoda.

Pyramidellidce.^ulima distorta (var.

gracilis) t d.

Chemnitzia elegantissima J d.
Odostomia unidentata ... J d.

spiralis f d.

Naticidcs. Natica monilifera ... f d.

nitida * d.

Velutinidce. Lamellaria perspicua X d.
Cancellariad(S.TnchotroY>is borealis + d.

Nassa incrassata * d.

Buccinum undatum . * /.

Fusus antiquus f I.

Trophon muricatus . f d.

clathratus f d.

Barvicensis ... J d.

Mangelia lineai-is ... j d.
costata j d.

Solenides.
Tellinidce.

Mactridfe.
Veneridce.

CardiadcB,

Arcades.
Ostreadce.

I.
t d.

Chitonidee. Chiton asellus * I.

ruber t ^•

Patellida. Patella pellucida f d.

Acmaea virgin ea f I.

Dentaliadee. Dentalium entalis . . . * d.
Calyptrmdce. Pileopsis Hungaricus J d.
Fissurellidee. Fissurella reticulata . j d.

Emarginula reticulata f I,
Trochidce. Trochus zizyphinus . f I.

Montagui * I. Muricidce.

cinerarius ** I.

tumidus * d.

Liftorinidce. Rissoa labiosa * d.

striata * d.

«— crenulata J d.

Cerithiadce. Cerithium adversum j d. Conidce,

reticulatum ... * d.

Eulima bilineata f d. • purpurea j a.

Pyramidellidce. polita J I. rufa \ d,

Mollusca of Fourth Zone, 18 to 20 fathoms.
Lamellibranchiata.

CorbuUdee. Corbula nucleus f I. Cyprinidce,

Pandora obtusa J I.

Solen pellucidus t I.

Psammobia tellinella f d.

Ferroensis f d. Mytilidce,

Mactra elliptica * d.

Tapes virginea \ d.

Venus casina f I.

• fasciata f d.

—' — ovata * d.

Gasteropoda.
Dentaliadee. Dentalium entalis ... * d. Naticidcs.
Fissurellidee. Emarginula reticulataf d.
Trochidce. Trochus cinerarius... * d. Muricidce.

Montagui * d.

tumidus * I.

Littorinidee. Rissoa striata * d. Conidce,

PyramJc?eZZi(/(«.ChemnitziaindistinctaJ d,

Mollusca of Fifth Zone, 15 fathoms.
Solenidce. Solen pellucidus ... * I. Dentaliadee. Dentalium entahs ... * d.
Tellinidce. Syndosmya intermedia* I. Turrit ellidcs. Turritella communis * I.

Veneridce. Venus ovata t I. Naticidee, Natica nitida f I.

Mollusca of Sixth Zone, 9,6 fathoms.
Tellinidce. Syndosmya intermedia* I. Conidce. Mangelia linearis ... \ d.

Along with these a single living specimen of the rare Brissus lyrifer was
procured.

In Strangford Lough 103 species (dead or living) were dredged : 58 Bi-
valves and 45 Univalves. The locality which produced the largest number
is near the junction of the narrow channel with the wider part of the Lough
itself, viz. Castle Ward Bay; the general result being —

Lamellibranchiata. Living 29 species 1 .-
Dead^l8^„ 1=^7

Gasteropoda Living 22 „ l_cq

Dead 31 „ J-^''

Circe minima

Cyprina Islandica ...
Cardium echinatum .

nodosum % I.

Modiola modiolus ... * d.

Crenella decussata ..XI.

Pectunculus glycimeris * d.

Pcctenopercularis... * d.

tigrinus \ I.

varius \ d.

Natica nitida f I.

sordida % d.

Nassa incrassata ... * d.

Fusus antiquus \ I.

Trophon muricatus . -f" d.
Mangelia attenuata

Xd.

100 species.

110 REPORT — 1857.

The next locality worth mentioning is Wellstream Bay, about two miles
■within the wider part of the Lough, or that distance from the upper end of
the narrow channel, and five to six miles from the sea. Contrasted with the
former locality, the number of species is reduced to one-half, viz.

Lamellibranchiata. Living 10 species \ o,-,

Dead 22 „ /— ^^

Gasteropoda Living 10 „ "1 ,q

Dead 8 „ S=^^

50 species.
In the widest part of the Lough, near its centre, and farther from the sea
than the previous locality, we find a still greater reduction in the number: —

Lamellibranchiata. Living 21 species \ ne

Dead 5 „ ] "^^

Gasteropoda Living 8 „ l^id

Dead 6 „ J

40 species*.

In the open Irish Channel, outside the Lough, 96 species were dredged,
in the following proportions : —

Lamellibranchiata. Living 31 species \ rr

Dead 24 „ /"^^

Gasteropoda Living II „ \ >,

Dead 30 „ J"^^

96 species.

It may be worthy of notice, that the dead shells found in the outside
Channel, and those dredged in the Lough, presented an aspect so different,
that if the two were mixed together, I could easily point out those found in
the one or the other locality. Those dredged at sea were peculiarly fresh in
external appearance, and generally retained their original consistence, and
in many cases their colour ; whereas those found in the Lough had almost
universally lost their colour, and in many instances were so decayed that
they could be easily crushed by the fingers.

On taking a general view of the MoUuscan fauna of Strangford and that
of the Irish Channel opposite its entrance, we remark the absence of species
belonging to the Lusitanian and South British typesf, and the general oc-
currence of those of the European type, with a large proportion of those
called Celtic. Some of those considered as more peculiarly British (British
type), are also not uncommon, as Trochus Montagui, T. millegranus, Pecten
tigrinus. Those of the Atlantic type are generally rare, the only species
found in abundance being Cerithiimi reticulatum, Mangelia gracilis, and
Psammobia tellinella ; others being rare, as Cerithium adversum, Circe mi-
nima, Fissurella reticulata, JSIatica sordida, Terebratula caput-serpentis, &c.
Those of the Boreal type are represented by Cyprina Islandica, which is
not uncommon, and by a few others which are rare, as Cardiuvi suecicum.
Crania anomala, Leda caudata, Syndosmya intermedia, and Trichotropis
borealis.

The general conclusion is, that the Mollusca recorded here belong mainly
to the European and Celtic types, with a moderate proportion of species be-
longing to the Atlantic type, and a very few Boreal forms.

* Species procured by the dredge only are recorded here; littoral species, commoQ
everywhere, are not included.
t Forbes and Hauley'e British Molluscs, Yoh i. Introduction.

ON THE MARINE ZOOLOGY OF STRANGFORD LOUGH. Ill

EcHiNODERMATA of Strangford and corresponding part of the
Irish Channel.

Comatula rosacea. Abundant in various parts of the Lough in 10 to 15 fathoms.
Rare outside in 20 fathoms.

Ophiura texturata. Plentiful in Lough and Channel, in 10 to 20 fathoms.

albida. Less common than the last, and along with it.

Ophiocoma neglecta. In Channel, 25 fathoms, rare.

granulata. Velvety black. Common in different parts of the Lough, 10 to

20 fathoms. Rare in the Channel.

hellis. Abundant in 20 fathoms, chiefly in upper part of the Lough, be-
tween Kircubbin and Killinchy. Also in the Channel, but rare.

rosula. Very common in all parts of the Lough ; less so in the Channel.

filiformis. In the Channel, six miles off; rare.

Uraster glacialis. Occasionally inside and outside the Lough, at different depths.

rubens. Occasionally in the Lough.

hispida. Occasionally in the Lough and Channel.

Solaster endeca. In upper part of the Lough, between Kircubbin and Killinchy,
not unfrequent.

papposa. In different parts of the Lough, but rare.

Palmipes membranaceus. In upper part of the Lough, between Kircubbin and Ard-
millan; rare.

Echinus splicera. In the greatest profusion at low-water mark in the lower part of
the Lough, also in 10 to 25 fathoms everywhere.

miliaris. Abundant in the Lough and in the Channel, 10 to 25 fathoms.

Echinocyamus pusillus. In the Lough and outside, in 15 to 25 fathoms, rather rare.

Spatangus purpureus. Occasionally, between Ardmillan and Kircubbin, 25 fathoms.
Also outside the Lough, but rare.

Brissus lyrifer. A single specimen (very fine), in mud, seven miles outside Strang-
ford Bar, 25 fathoms.

Amphidofus cordatus. Not uncommon in the Lough, in 10 to 20 fathoms ; rare in
the Channel.

roseus. Off Strangford Bar, rare, 20 fathoms.

Cucumaria fusiformis. In the Lough, 15 fathoms, very rare.

Ocnus brunneus. In the Lough, 10 to 15 fathoms ; abundant.

In addition to these, the following are recorded in 'Notes of Dredging,' by
the late Mr. Thompson and Mr. Hyndman : —

Cribella oculata. A few, 15 to 20 fathoms,

Thyone papulosa. In 15 to 20 fathoms.

Cucumaria hyalina. In 15 to 20 fathoms.

Syrinx Harveii. In 15 to 20 fathoms.

TUNICATA.

The following list of Strangford species is compiled from the results of
dredging by the late Mr. Thompson and Mr. Hyndman ; most of them were
also dredged by myself in June last (1857) : —

Ascidia mentula. Abundant, 4-6 fathoms, Cynthia microcosmus. Common, A-Q fa-

■ venosa. Several, ditto. thoms.

prunum. With the last. claudicans. Rare, ditto.

parallelogramma. On shelh. mora. Rare, ditto.

scabra. Several, 4-6 fathoms. rustica. Common, ditto.

canina. Ditto, ditto. Clavellina lepadiformis. Not uncommon.

orbicularis. Rare, ditto. Botryllus Schlosseri, Rare.

echinata. Very rare. polycyclus. Common.

intestinalis. Not uncommon. LeptocUnum aureum. Occasionally,

vitrea. Very rare. Aplidiumfallax. Common,

Molgula tubulosa. Not uncommon.

112 REPORT — 1857.

Crustacea.

Dredged by Mr. Thompson in September ] 851, in 4 to6 fathoms, near Ring-
dufferin and Ringhaddy Islands ; most of these were also got in June 1857 : —

Stenorhynchus phalangium. Eurynome aspera. Porcellana longicornis.

Inachus Dorsettensis. Portunus pusillus. Galathea squamifera.

■ dorynchus. arcuatus. Hippolyte varians.

Hyas araneus. Pagurus Bernhardus.

Sponges of Strangford Lough.
These were mostly all got in one locality, upon oyster and scallop beds,
in about 20 fathoms, near the centre of the expanded part of the Lough,
between KiUinchy and Kircubbin. These were long since dredged by
Messrs. Thompson and Hyndman, and nearly all were found in 1857 : —
Tethya lyncurium. Halichondria hirsuta. Cliona chelata.

Halichondria hispida. suberea. Grantia lacunosa.

fucorum. mainmillaris. fistulosa.

sanguinea. carnosa. Dysidea fragilis.

• macularis.

Suggestions for Statistical Inquiry into the extent to which Mercantile
Steam Transport Economy is affected by the Constructive Type of
Shipping, as respects the Projjortions of Length, Breadth, and
Depth. By Charles Atherton, Chief Engineer of Her Majesty's
Dockyard, Woolwich.

At the Cheltenham Meeting of the British Association in August 1856, I
had the honour to present a paper on " Mercantile Steam TransportEconomy."
The principal objects of that paper were, in the first place, to expose the
difficulty which attends all investigation and even all discussion on maritime
affairs, in consequence of the technical terms in which shipping, especially
steam shipping, is spoken of, and officially registered as respects the size or
magnitude of vessels and machinery, having no definite meaning expressive
of the capability of ships for carrying weight of cargo, or the capability of
the machinery for the production of working power ; and in the second place,
after getting the better of the foregoing difficulty by rejecting the records of
tonnage and nominal horse-power as being indefinite, and basing my calcu-
lations on load displacement, as expressing the actual magnitude and weight
of the mass propelled through the water, and assigning an arbitrary but defi-
nite amount of working power based on indicator measurement to the term
horse-power, and availing myself of maritime statistics already published as
to the actual performances of vessels, and of the received laws which are re-
cognized as expressing the mutual relations of displacement, power, and speed
under definite conditions of practical application, I was enabled to demon-
strate approximately the proportional increased rate of pecuniary cost which
attends an increased rateof speed at which cargo per ton weight may be con-
veyed by steam-ships of any definite size and type, according to the length
of passage and speed that may be required : for example, assuming a passage
of 3250 nautical miles to be performed by a vessel of 2500 tons load dis-
placement, and of which the coefficients of dynamic duty were assumed to be
known and equal, and of a comparatively high order, the vessels respectively
being fitted for speeds of 8, 10, and 12 knots per hour, it was shown that the
cost of transport per ton weight at the speed of 12 knots per hour would be
about 50 per cent, above the cost that would be incurred by a speed of
10 knots, and about 100 per cent., or double the cost incurred by a speed of

ON MERCANTILE STEAM TRANSPORT ECONOMY. 11^

8 knots ; and if the vessels be of a certain comparatively inferior type of
build, as indicated by a lower coefficient, but still of such type as is commonly
employed, the rate of freight per ton weight of cargo conveyed at the 12 knots'
speed on the passage referred to, was found to be about double the rate if
conveyed at the speed of 10 knots per hour, and about three times the rate
incurred by a speed of 8 knots an hour.

Applying this estimated difference of cost incurred by difference of type
to the aggregate trade of the country, as shown by the statistical returns of
the Customs' House, it was suggested that the pecuniary interest of the great
paymaster " the public," is involved to the extent of millions per annum,
simply by the difference of type of build and condition of the ships and
engines, and administrative management by which the foreign trade of the
country, as respects transport, may be prosecuted. These points of my
former paper are now referred to by way of introduction to the following
paper, in which it is purposed to continue the subject-matter of my former
dissertation, by showing the extent to which the weight-carrying capability
of ships of given tonnage, whether rated by the gross register tonnage (new
measure), under the Merchant Shipping Act of ISo't, or by the tonnage
builders' measure O.M. (also commonly called " burden," and still generally
in use, though legally superseded in 1835), is dependent on the relative pro-
portions of length, breadth, and depth to which ships may be constructed ;
and it is submitted for the consideration of the Association that this point of
inquiry comes to be of special importance, seeing that the tendency of the
present times to build vessels of great magnitude as respects length and
breadth, whilst the load«draught is restricted by local circumstances within
the definite limit of the minimum depth of water of the ports to be fre-
quented, has a direct tendency to involve a condition of things as respects
proportions of build adverse to public interests, for the public will have
to bear the brunt of freight charges proportional to the cost expenses that
may be incurred in the general administration of shipping affairs. We may
just as well assert that the public have no interest in the efficiency of our
army and navy, as that it has no interest in the efficiency of our commercial
shipping. Rates of freight (excepting on occasions of national emergency)
must be ruled in the aggregate by the general average cost at which the
general service of mercantile transport is actually performed, whether it be
well or ill performed ; and the general introduction of proportions of build
which can only perform their service at high rates of freight above the prime
cost rates which would duly remunerate vessels of superior type, involves
pecuniary considerations that may well form the subject of special statistical
inquiry to be prosecuted at the instance of the British Association. The
application of statistical science in connexion with shipping as a means of
inquiry into the principles of Mercantile Steam Transport Economy, is, I may
say, a new subject of inquiry, to which the British Association, and, I must
add, the Society for the Promotion of Arts, Manufactures, and Commerce,
have given public vitality. The question of Maritime Transport Economy
has a bearing on public interests analogous to the operation of the rail and
the telegraph.

A further object of this paper is, that by means of the following Table (A),
•which has been prepared to show the mutual relations which subsist in ships
of given variations of build between Tonnage Builders' Measurement O.M.,
Gross Register Tonnage, Weight Tonnage, or the capability of ships to carry
weight of cargo, and the corresponding displacement when ships are loaded
down to a determinate load line ; and Table B, showing the mutual relations
of displacement, power, and speed, we may thus have the means of connect-

1857. «

}14 REPORT 1857.

ing (that, is, within the limitations of the variations of build referred to in
Tables A and B), througli the intermediate element " displacement," the two
Tables A and B thus establishing the mutual relations within the limits afore-
said, between builders' tonnage, gross register tonnage, and weight or cargo
tonnage, with the power required to attain a given speed, thus enabling us
to show the bearing of proportions of build as affecting mercantile steam
transport economy.

In the first place, therefore, before entering on this exposition, and in con-
sideration that persons generally, even amongst those who devote their time
to popular and statistical studies, and to scientific pursuits, and even assume
the responsibilities of legislation on shipping, are not familiar with the technical
meaning of the terms "tonnage" and "burden," which are of such frequent
recurrence in discussing the properties of shipping, as compared with the
ordinary and unsophisticated meaning of those words, and are actually and
unconsciously misled by those terms, when used technically in shipping so-
phistry, having a signification quite at variance with their ordinary meaning,
I will endeavour to dispel this mystery by a few remarks in explanation of
the terms " tonnage " and " burden," which, above all other terms, are most
amenable to the foregoing singular imputation, namely, that their technical
meaning is directly at variance with the ordinary signification of the said
words : for example, ship's "tonnage" is not spelt with a u, " tunnage," and
we all know that a " ton," as distinguished from " tun," popularly signifies
2240 lbs. weight, or 20 cwt., each cwt. being 11 2 lbs. The ordinary accep-
tation of the word " ton " implies a unit of weight, not of measure. Thence
it is popularly inferred that the "tonnage" of a ship means the number of
tons weight which constitute the proper load of a ship ; but what is a ship's
tonnage as implied in the terms " tonnage O.M.," " tons burden," " register
tonnage" ? It has nothing whatever to do with weight. By the old law, termed
*' builders' measurement O.M.," which, though legally superseded in 1835, is
still practically in use, and constitutes to this day the rule which, even in
the Government service, generally regulates the builder's contract price of
shipping, the measurement of this tonnage is regulated by the length of the
ship and its breadth only, taking no cognizance of depth. It has nothing
whatever to do with the load-draught of water for which a ship may be
constructed. Provided that the length and breadth of two ships be the
same, the builders' tonnage O.M. will be the same, though the load-draught
of one ship be 30 feet and of the other only 3. This same tonnage, builders'
measure O.M., is also frequently called by the equally delusive term "burden,"
though, as above shown, it has nothing to do with burden : for example, in
shipping advertisements we see daily that " tons burden " is a designation by
which ships are conmionly advertised. It is true that Parliament abolished
that law of tonnage, builders' measurement O.M., or the so-called " burden,"
in 1835, but nevertheless the Government have continued to uphold the
rule (builders' measurement) as the base of their ship-building contracts, and
ships, as respects their comparative size, are still only known to the world
generally by their so-called tonnage or tons burden, or builders' measure-
ment O.M. No steps having been taken by the Government to discontinue
and forbid the use and adoption of the old law of measurement, though
repudiated by statute in 1835, it has continued to prevail, and merchants,
following the example of the Government, make it the general base of build-
ing contracts to the present day.

It is therefore submitted for the consideration of the British Association,
that the statute abolition of tonnage builders' measurement O.M., also called
" burden," ought not to be permitted to lie dormant. It should be expressly

ON MERCANTILE STEAM TRANSPORT ECONOMY. 115

decreed that the said builders' measurement O.M. is not legally binding in
any contract, either for the building, or freighting, or chartering of ships, and
that the definition and measurement of " tonnage " shall be in accordance
with the existing law, viz. the Merchant Shipping Act of 1854, subject to
such amendments thereof and additions thereto as may be found necessary
to render the Act complete for all the purposes of shipping registration.

And now, what is tonnage registration under the new law — the Merchant
Shipping Act of ISS^? To begin with: vessels constructed previously to
1854 are permitted, at the option of their owners, to retain their former ton-
nage or be measured under the new law, and be registered accordingly, and
the statistics or Parliamentary returns of shipping do not show to what extent
this privilege, of optionally withholding the former registration, has been
acted upon ; so that our present registration under the new law, the Act of
1854, is a mixed registration, and we do not know the ingredients thereof or
tlieir proportion ; but the measurement under the new law of all ships built
since May 1855, is an internal measurement, no notice whatever being taken
of external measurement, or of the light draught line or constructor's load
line, or any limitation thereof assigned by reference to " freeboard ; " and
consequently tonnage under the new law, the Act of 1854, does not give
the weight-carrying capability of ships, nor any comparison thereof, if of dif-
ferent types of form, and of different build as respects the weight of the
materials employed ; but if the law does not give the weight-carrying capa-
bility of the ship, the question is — what does it give ? It gives an admis-
sibly correct measurement of the internal capacity of ships, but calls this
capacity " tonnage," giving a new signification to the word ton ; for each
100 cubic feet of this internal space of the ship available for holding cargo
is called a ton of tonnage. Tonnage is therefore a mere measurement of
space, not of weight. Then, again, as regards cargo, even a ton of cargo is
not always rated as 20 cwts. The freight of goods is charged either by
measurement or by weight, and the same word " ton" is applied in all cases ;
100 cubic feet constitute a ton of shipping ; 40 cubic feet of some kinds of
goods, and 50 feet of others, constitute a ton of measurement goods ; and
cargo is rated accordingly for freight, provided the said measure do not
weigh a ton. 100 cubic feet of light goods may therefore be stowed in
1 ton of shipping, and be rated for freight at 2^ tons ; that is, a ship of
1000 tons register tonnage may be expected to stow 2500 tons of measure-
ment cargo, or, better still, 1000 tons weight of heavy goods, and fill up with
2000 tons measurement of light cargo, and thus go to sea with this 3000 tons
of freight, no limitation being assigned to draught. Such are the anomalies
of tonnage, and yet we talk of statistics based on tonnage ; and what is the
consequence of this abuse of the word " ton " ? Why, in times of war, our
tonnage registration of shipping not only affords no reliable data, but actually
deceives as to the capabilities of vessels for carrying ordnance and such
like heavy military stores. Experience of the past three years has abun-
dantly shown how great would be the advantage to the public if, in times of
war and emergency, when there is no time for the readmeasurement of
shipping, and when shipping must be chartered or purchased at any price,
our registration of shipping were available, like a tabular ready-reckoner, for
giving the Government a correct idea of the capability of every ship for
conveying weight of cargo, in addition to the present registration of capa-
city for holding cargo, and consequently a comprehensive view of the value
of ships for military transport service embracing both weight and roomage.

The statistical insufficiency of the present system of shipping registration
as a record of the capability of ships, is shown by the following Table (A) :— .

ox MERCANTILE STEAM TRANSPORT ECONOMY. 11/

In this Table it will be observed that the twelve vessels, A, B, C, &c-
to M, are all of the same builders' tonnage O.M., namely 1000 tons; that
we have three vessels (A, B, C) whose length is four times the breadth of
beam ; three vessels (D, E, F) whose length is six times the breadth ; three
vessels (G, H, I) whose length is eight times the breadth ; and three vessels
(K, L, M) whose length is ten times the breadth ; and that, in each set of
three vessels, the load-draught of water is taken at two-thirds of the breadth,
half the breadth, and one-third of the breadth ; so that in this Table we have
a gradation of proportions, the length varj'ing from four times to ten times
the breadth, and the load-draught varying from two-thirds to one-third of
the breadth, which limits embrace nearly all the proportions of shipping in
mercantile use. The arbitrary elements of construction on which the calcu-
lations (Table A) have been prosecuted, are explained in the various head-
ings. It will be observed that the freeboard (column 5), or non-immersed
depth above the load-draught line, has in each case been taken at one-
fortieth of the length, plus one-twelfth of the breadth of beam. There is no
recognized rule for the determination of this element. Constructors of ship-
ping follow their own rules or their own caprice in determining freeboard, or
the position of the construction load-line. The above combined proportions
of length and breadth have been adopted, as giving a progression, which, it
is believed, will meet the ordinary allowance of freeboard at which loaded
ships of all sizes are sent to sea. The various elements of construction
(columns 7 to 16) are believed to be closely approximate to ordinary prac-
tice ; and the ratios of nominal tonnage to actual weight-carrying capabilitj',
shown in columns 1 7 to 20, are therefore approximately such as would result
from the ordinary build of shipping.

Now, on comparing the ratios which result from the constructive propor-
tions of the ships A, B, C, &c., M, we have the following results : — 1st, it ap-
pears (see columns 17 to 20), that, taking builders' tonnage at 100, the ratio
of register tonnage varies from 85 to 51 in ships (A, B, C) of which the
length is four times the beam, and from 9i to 63 in ships (K, L, M) of which
the length is ten times the beam ; that is, taking the extreme cases embraced
within the limits of this Table, a ship of type K will have a register tonnage
of 94 tons for every 100 tons builders' measure; but a ship of type C will
have only 51 tons register for each 100 tons builders' measure. It also ap-
pears (see columns 17 and 19), with reference to builders' tonnage O.M.,
taken at 100, that the capability for carrying weight fluctuates from 131 tons
weight down to 33 tons weight per 100 tons of builders' measure O.M., or a
ship of 1000 tons builders' tonnage of the type A will have four times the
weight-carrying capability that is afforded by a ship of 1000 tons builders'
tonnage of the type M.

With reference to register tonnage (gross), new measure, under the Act of
1854, taken at 100, it appears (see columns 21 and 23) that the capability
for carrying weight varies from 177 tons down to 52 tons per 100 tons of
register tonnage; or a ship of 1000 tons gross register tonnage of the type
A will have nearly 3\ times the weight-carrying capability that is afforded
by a ship of 1000 tons gross register tonnage of the type M.

With reference to weight tonnage, or the capability of ships to carry
weight, it appears (see columns 25, 26, 27) that, with the proportions of
ship A, each 100 tons of weight- carrying capability will require a vessel of
76 tons builders' measure O.M., or 65 tons gross register tonnage ; but
with the proportions of ship M, each 100 tons of weight-carrying capability
will require a vessel of 303 tons builders' measure O.M., or 191 tons gross
register tonaage.

118 REPORT — 1857.

With referencf! to tlie mutual relation of the load displacement and weight
tonnage, it appears (see columns 29 and 32) that with the proportions of
ship A, eacli 100 tons of load displacement will give 57 tons of weight
tonnage, but with the proportions of ship M, each 100 tons of load displace-
ment will give only 29 tons of weight tonnage ; that is, a ship of 1000 tons
load displacement, on the type of ship A, will carry double the weight that
would be carried by 1000 tons of displacement on the type of ship M.

It might possibly be objected that the foregoing variations, which have all
been calculated with reference to ships of 1000 tons builders' measure O.M.,are
not applicable to vessels of a different magnitude ; therefore, to test the validity
or otherwise of this remark, the same constructive elements have been applied
to a ship X of 20,939 tons builders' measure O.M., and 25,000 tons load
displacement, the length of this ship X being six times the beam, and the
load-draught one-third of the beam, this type or proportion being the same
as that of ship F. On comparison of the ships X and F (see columns 29,
30, 31 and 32), it will be found that the ratios of builders' tonnage, register
tonnage, weight tonnage, and load displacement, are closely similar through-
out: for example, in ship F, each 100 tons load displacement gives 42 tons
of weight tonnage, but in ship X each 100 tons of load displacement gives
39 tons of weight tonnage. Hence we may infer that the results of these
calculations, showing the extent to which the weight-carrying capabilities of
ships is irrespective of the nominal tonnage, whether it be builders' tonnage
O.M., or gross register tonnage N.M., and is approximately dependent on
the constructor's proportions of build, admit of general application to vessels
of all sizes of the types referred to in Table A. Surely the above exposition
is sufficient to establish the necessity of some legislative enactment under
which builders' tonnage O.M., and register tonnage N.M., should not be
permitted to co-exist as recognized measurements of the mercantile capa-
bilities of shipping. Under existing circumstances, it is respectfully sub-
mitted for the consideration of the British Association, that a clause be in-
troduced into the Merchant Shipping Act, that the only legal signification
of the word "tonnage" shall be the measurement prescribed by the said Act,
and that no other signification of that term shall be legally binding in com-
mercial transactions. Also, that the capability of ships for carrying weight,
as measured with reference to some determinate freeboard, be made an item
of registration.

The ratios above set forth, as expressing the Aveight-carrying capability
of ships, include the whole weight available for engines, boilers, coal, con-
sumable stores, and cargo ; so that, as applied to steam-ships, these ratios, as
respects weight-tonnage for cargo chargeable for freight, assume a new phase
of great importance as affecting mercantile steam transport economy ; and,
for the purpose of inquiring into the modification thus introduced, the fol-
lowing Table B has been calculated, sliowing the mutual relations of dis-
placement, power, and speed, for vessels up to 25,000 tons load displacement,
the speed varying from 6 knots up to 25 knots per hour.

The element " Load Displacement " being common to both Tables A
and B, we have, by the aid of these Tables combined, the means of showing
the mutual relations between builders' tonnage O.M., gross register tonnage
N.M., weight-tonnage, load displacement, speed, and power of all vessels
within the limits of the types or proportions of build referred to in Table A,
and thus showing to what an extent mercantile transport economy by steam
is affected by the proportions of length, breadth, and depth to which steam-
ships may be built. For example : let us compare a ship of the type D,
namely, length six times the beam, and load-draught two-thirds the bea.in,

120 REPORT 1837.

having weight-carrying capability or weight-tonnage of 2000 tons, with a ship
of the same capability for carrying weight, but of the type I, namely, length
eight times the beam, and load-draught one-third the beam. By Table A
(columns 25, 26, 27 and 28), it appears that the ship of type D, of 2000
tons weight tonnage, will be 1680 tons builders' tonnage O.M., 1400 tons
gross register tonnage N.M., and 3680 tons load-displacement ; and by Table
B, it appears that 950 ind. h.p. would propel this ship at the speed of 10 knots
per hour; the consumption of coal at the rate of 3^ lbs. per indicated horse-
power per hour, would be SO cwts. per hour; and supposing the engines,
boilers, &c. to weigh one ton weight per fis'e ind. h.p., the weight of these
will be 184' tons; this ship may therefore be expected, on the data of the
said Tables, to make a passage of 3500 nautical miles in 350 hours, consu-
ming 525 tons of coal, and carrying 1291 tons weight of freight cargo. But
what would be the case with the vessel of 2000 tons weight tonnage of type
I? It appears that the builders' tonnage O.M, would be 5120 tons, the re-
gister tonnage N.M. 2720 tons, and the load-displacement 54-80 tons ; and by
Table B, it appears that to propel this vessel at 10 knots per hour Avould
require 1240 ind. h.p., these engines weighing 248 tons, and the consump-
tion of coals 39 cwts. per hour ; so that, on the data of the said Tables, this
ship on the type I may be expected to make the passage of 3500 nautical
miles in 350 hours, consuming 682 tons of coal, but carrying only 1070 tons
of freight cargo. Hence it appears that with vessels of type D, we have ex-
penses proportional to 1400 tons register N.M., and 950 ind. h.p., with in-
come proportional to 1291 tons weight of freight ; while with the ship of type
I we have expense proportional to 2720 tons register N.M., and 1240 ind.
h.p., with income proportional to only 1070 tons weight of freight; that is,
the comparative prime cost expenses of transport in these two cases (assu-
ming the cost incidental to one ind. h.p. to be equal to that of one ton of gross
register tonnage) will be in the proportion of

1400 -1- g.TO , „^ 2720 + 1240

1291 = '-^^ ^« 1070 = 3-70'

or in the proportion of 1 to 2. Such is the effect of mere difference of pro-
portion or type of build on mercantile steam transport economy. This
example of a difference or extra cost of 100 per cent, on the prime cost rates
of freight per ton weight of cargo conveyed on the same passage, and at the
same rate of speed, is evidently occasioned by the load-draught of water being
two-thirds of the beam in one case, that of the vessel D, and only one-third
of the beam in the other case, that of the vessel I ; and yet we see that the
type or proportion of small load-draught in proportion to beam is a type or
proportion of build, towards which the progressive increase in the size of
shipping is gradually leafling mercantile practice, as exemplified in the most
extraordinary maritime enterprise of the present day, the ' Great Eastern.'

The mechanical advantage which attends progressive increase of size as
measured by load dis])lacement, is conspicuously shown by Table B, whereby
we observe tiiat a vessel of 250 tons displacement requires 274 ind. h.p. to
attain the speed of 12 knots per hour, being very nearly in the ratio of one
ton displacement to one h.p.; but, if the ship be 2000 tons, the ratio of dis-
placement to power to attain the same speed (12 knots) will be 2 to 1 ; Avith
I a ship of 9000 tons it will be 3 to 1 ; and with a ship of 20,000 tons it will
be 4 to 1. Hence a ship of the reputed size of the ' Great Eastern,* viz. about
25,000 tons load displacement, Mill require proportionally only aborat one-
fourth of the power to attain a given speed that would be required by a ship
of 500 tons displacement. Hence the great advantage of size, provided the

ON THE VITALITY OF THE SPONGIADiE. 121

ship be of good type and can be always fully loaded; but seeing that load-
draught is limited by local circumstances and other considerations which may
not limit the length and breadth, it becomes a matter of calculation to deter-
mine at what point the admitted advantages of size become neutralized with
reference to any particular service by the limitation of loud-draught in pro-
portion to beam. Let us have all the advantages we can get, without running
into extremes, by which those advantages become sacrificed.

Are not public interests involved in this matter, and is it not a matter of
grave importance, meriting the attention of the British Association ? I beg
to conclude with the suggestion, that it is only by statistics that the deficiencies
of our present maritime system can be properly searched into and brought
to light; and it is only by the force of statistical exposition that the re-
quired remedies can be devised. It is therefore respectfully submitted, that
the constructive type of shipping as respects the proportions of length, breadth,
and depth, constitutes a subject of inquiry which merits the notice of the
Statistical Section of the British Association.

Further Report on the Vitality of the Bpongiadcs.
By J. S. BowERBANK, LL.D., F.R.S. &^c.

[With a Plate.]

In the Report on the Vitality of the Spongiadae which I had the honour of
reading to the Association at Cheltenham last year, I detailed a series of ob-
servations on the inhalation through the pores and the exhalation of water
through the oscula of a marine British sponge, Hymeniacidon caruncula,
Bowerbank, MS., and I was enabled to determine with certainty the capa-
bility which that sponge possesses of opening and closing the oscula at its
pleasure; but I could not in that series of observations satisfactorily deter-
mine the nature and powers of the imbibing pores, as these organs can onh'
be seen distinctly in operation in very young and transparent specimens. I
therefore determined to confine my researches on this subject more especially
to Spongillajluviatilis, specimens of which may readily be obtained of small
size and under very favourable circumstances for the observation of the
porous system. On the 13th October, 1856, my friend Mr. H. Gilbertscn,
of Hertford, brought me several young specimens of this species, one of which
nad attached itself to a watch-glass, in which it had been kept for observation.
The point of attachment was a thin membrane projected from the edge of the
sponge {a, fig. 1, Plate I.), having in it a few single spicula irregularly dis-
posed, and with very little appearance of sarcode upon it ; and above the thin
attached membrane there was a second one, which was a prolongation of the
upper surface of the sponge. The body of the sponge was thin, concave at
the upper and convex at the lower free surface. It was nearly circular in
its outline, and rather exceeded half an inch in diameter. Atone portion of
the margin it had been recently extending its dimensions, and the space in-
tervening between the old surface and the new one had the appearance of
being one large cavity, the new dermal membrane being forced outward and
supported from the points of the radial lines of the spicula of the newly
produced portion of the skeleton, the outer surface of the membrane curving
inward, from point to point, in a manner that plainly indicated the forcible

123 REPORT — 1857.

pressure outward of the newly-formed radial lines of the skeleton. At a short
distance within the margin, and in the neighbourhood of the newly-produced
portion of the sponge {b, fig. 1), there was a single oscuium situated on a
large oval bladder-shaped projection of the dermal membrane, which varied
considerably in its form according as the sponge was inert or in action.
When in the former state it was frequently in a semi-collapsed condition,
the apex being considerably attenuated, so that the whole assumed an ovate
form, the smaller end being the distal one, and in that condition not the
slightest orifice was visible, the oscuium being entirely closed, and what was
very remarkable, its place was not even indicated by an apparent thickening
or corrugation of the membrane. On the contrary, when in action the blad-
der-shaped projection was dilated at the apex so as to cause it to assume a
regular oval form, and the oscuium was apparent in the form of a large cir-
cular orifice, about one-fourth the size of the diameter of the bladder-like
portion on which it was situated (fig. 2). From this orifice a powerful
stream of water was continuously ejected, and large and small patches of
faecal matter were frequently thrown out with considerable force.

When a small portion of pure indigo was rubbed up in water, and a
drop or two of the water laden with this substance was mixed with that in
the watch-glass, and it was placed beneath the microscope with a power of
130 linear, and a strong light passed through it from a concave mirror,
at first no action was apparent, the oscuium was in a completely closed
condition, and although I searched the surface of the newly-formed portion
of the sponge with the greatest care and attention, I could not detect a single
open pore. In rather more than half an hour I found one open, and in a
short period others gradually and successively made their appearance, until
at last, in one of the spaces between two of the radial lines of the skeleton, I
readily counted as many as 10 in a fully expanded and active condition, and
in other similar spaces they were apparent in considerable numbers. The
action presented to the eye was exceedingly interesting. The molecules of
indigo approached the surface of the sponge at first slowly, their motion
beiu" gradually accelerated as they became nearer, until at last they sprung
as it were with avidity into the pores ; within the sponge some passed to the
right hand, while others took their course to the left, and they often passed
other molecules which had entered by other pores, and which were passing
in a contrary direction. Many of these molecules might be readily followed,
as they meandered through the interior of the sponge, and might be seen
flowing in every direction. During the maintenance of this action in full
force, when I directed my observations to the oscuium, it was seen pouring
forth a continuous stream of water and along with it masses of fiocculent
matter, and many of the larger molecules of the indigo that had entered by
the pores ; but it is remarkable that although the finer molecules of indigo
were being imbibed by the pores in very considerable numbers, very few
indeed of them were ejected from the oscuium ; and if the imbibition of the
molecules continue for half an hour or an hour, and then cease, the sponge
is seen to be very strongly tinted with the blue colour of the indigo, and it
remains so for at least 12 or 18 hours, after which period it resumes its ori-
ginal pellucid appearance, the whole of the imbibed molecules having under-
gone digestion in the sarcode lining, the interior of the sponge and the efi'ote
matter having been ejected through the oscuium. After having watched
the active operations of the sponge for nearly an hour, I set to work to sketch
the field of view in the microscope, in order to mark the position of the
pores ; but by the time the outline of the sketch was completed, about half
an hour, the action had ceased, the pores were entirely closed, and my further

ON THE VITALITY OP THE SPONGIADiB. 123

proceedings, as regarded their delineation, were deferred to a more favourable
opportunity.

On the 14th the sponge was in a quiescent state, and strongly tinted by
the indigo imbibed on the previous evening.

15th October. — I examined the Spongilla at ^ past 10 a.m.; there was ^lo
action to be detected, and a considerable tint of colour was still visible : at
9 P.M. 1 placed it under the microscope ; it was then free from colour and
in full action. The tube bearing the osculum was very different in form
from what it was on the evening of October the 13th, when at 11 p.m. it
was in form and proportions like an olive (fig. 2) ; at 9 p.m., on the 15th, it
was in form and proportions like the last two joints of a man's finger, slightly
bent at the last joint (fig. 3). At 10-30 of the same evening, when the
action had grown very languid, the basal portion was very much expanded,
and the whole assumed the form of a cone, the apical portion of which had
fallen over on one side, and the excurrent stream was directed towards the
body of the sponge at an angle of about 45 degrees to its plane (fig. 4) ; it
is evident, therefore, that this organ assumes a great variety of forms.

At 9 P.M., when I commenced my observations, the portion under exa-
mination was crowded with pores in a fully expanded condition, and I imme-
diately mixed a drop of water charged with indigo, with that in the watch-
glass, and the imbibition of the molecules continued steadily until 10*30 p.m.,
when it suddenly became very languid ; at this period I directed my atten-
tion for a few moments to the osculum, and on again returning to the obser-
vation of the pores, I found nearly the whole of them completely closed. I
examined some of the largest of the pores with the utmost care for more than
an hour with a power of 260 linear, but I could not detect cilia either at the
margins or within the entrance. When the incurrent action became rather
languid, I observed that the molecules within the sponge were performing a
sort of cyclose circulation, frequently rising up and passing across the open
pores, but never coming out through them ; but while this action was going
forward, now and then a molecule of indigo would pass languidly into the
pore. It would seem, therefore, to indicate that the organs of incurrent
action were situated, as I have long suspected, within the large intermarginal
cavities, as in Granlia ciliata, and not immediately around or within the
pores.

During the continuance of vigorous incurrent action, the water charged
with indigo is in continual motion, flowing from all quarters towards the
open pores ; many of the molecules come in contact with the portions of the
skeleton projected through the dermal membrane, and wherever they touch,
tliey adhere tenaciously to the adhesive matter coating those parts, in the
same manner as they do to the sarcodous membranes within the sponge ; but
the same results do not seem to follow with those without, that occur with
those within. On the evening of the 15th, when I terminated my observations,
I left the sponge with an abundance of molecules attached to the internal
tissues, and a considerable quantity of similar molecules fixed to the external
fasciculi. On examining the same sponge at 11 a.m. on the 16th, I found
the external tissues with the molecules still adhering in considerable quan-
tities, but the internal ones were perfectly free from the coloured particles.
The excurrent tube still retained much the same form that it had on the
termination of my observations on the previous evening, but it was in a more
collapsed condition, and instead of the osculum being a well-defined circular
orifice, it had assumed a much smaller and more irregular shape, and was
puffed out from the end of the excurrent tube in the form of a loose hemi-
spherical appendage to its apex, from which a, molecule now and theu came

124 REPORT — 1857.

languidly forth (fig. 5). On examining the pores I could not find a single
one open.

I again examined the same sponge at 8 p.m. of the 16th October. » The
excurrent tube bearing the osculum was nearly erect (fig. 6), and the stream
was slowly pouring forth. I examined the usual part for the pores, and found
very few that were in a slight degree opened. I then directed my attention
to the thin stratum by which the sponge was attached to the watch-glass.
Hitherto I had not detected any pores in that part of the sponge, but tiiis
evening I saw several which were open, and into which the floating mole-
cules were steadily entering. I selected one spot for observation, where
there were several pores indistinctly visible : in about 5 minutes they became
very much more distinct, fully expanded, and the margins assumed a thick-
ened and well-defined outline ; others made their appearance, and at last
fourteen were in a fully expanded and active state (fig. 8). I immediately
put a drop of water charged with indigo over the pores ; the molecules were
absoi'bed with great rapidity, and the rush of the indigo to the pores became
so great that its accumulation rendered the sight of them indistinct, and to
clear the sponge from the indigo I sent a puflP of air from my mouth on to
the surface of the water in the watch-glass, but doing this rather too roughly,
I turned the sponge over on its flexible base, as it were on a hinge ; I there-
fore removed it and placed it in a basin of fresh water to float it back again
into its proper position, and immediately replaced it under the microscope,
the whole operation not occupying more than a minute; but on getting the
precise spot into focus, I found not a single pore open : the sudden violence
done to the sponge had caused a complete cessation of action and a perfect
closing of the inhalent pores. This result is curious, in contrast with tho
fact, that the sponge endures a large Vibrio, which is continually crawling
with considerable activity over its surface, and frequently biting large mouth-
fuls out of the soft tissues, without appearing to create the slightest alarm,
although passing immediately across the pores while in full action.

18th October. — At 11 p.m. I resumed my observations at the precise spot
which I had examined on the evening of the 16th, and of which I then took
a sketch. Not one of the pores that I had carefully diagrammed opened
during an hour and a half that I constantly observed them, but several others
close by the spot were fully expanded, and were steadily imbibing the mole-
cules of indigo with which I supplied them. I selected three of these for
observation, but with a power of 260 linear I could not detect cilia. The
mode of the entry of the molecules was regular and very remarkable : they
approached the pore by a steadily accelerated motion, and when they reached
the margin rushed suddenly into the orifice ; but although entering thus
forcibly, their course was not straight downwards, but eacii one seemed to
slip as it were round the margin and pass rapidly off' at an angle of 45 degrees
immediately beneath the dermal membrane, and their course might be traced
for a considerable distance in a straight line, and with a gradual decrease of
speed from the moment of their entrance. These circumstances would seem
to indicate the position of the motive power to be immediately within the
margin of the pore, but I could not in any case detect them ; I sometimes
saw a hazy rim immediately within the pore, but I believe this was due to
parallax arising from a slight change in the position of the dermal mem-
brane. The peculiar mode of the entry of the molecules, combined with the
cyclose circulation that I have previously noted as occurring when the in-
halent action became languid, induces me to believe that the seat of the cilia
is confined to the large intermarginal cavities of the sponge, and that they are
not appendages of either the pores or the oscula. At the end of an hour and

ON THE VITALITY OF THE SPONGIAD.«. 125

a half of close observation with the hope of detecting the act of the closing
of the pores, I was rewarded for my patience by seeing that the clear tense
rounded margin of one of them, which was black by the aberration of the rays
of light passing through it, began to lose its distinctness, and at the same
time it assumed an irregularly oval instead of a circular form. The margin
melted away, as it were spreading gradually inward towards the centre, and
this action continued until the orifice became entirely closed, and not the
slightest mark remained to indicate the place a minute previously occupied
by a fully expanded pore. When thus closed, the membrane presented pre-
cisely the same irregularly granulated appearance that characterized the sur-
rounding tissue. Two other pores in the immediate neighbourhood under-
went precisely the same process in the course of less than a minute.

October 19th. — At 9 p.m. I found the sponge in very languid action, and
completely clear internally of molecules and indigo. The excurrent tube bear-
ing the osculum had assumed a new aspect. In addition to the usual conical
projection of membrane, the apex was dilated into the form of a supplementary,
obtusely oval bladder, terminated by the usual osculum in a fully dilated
condition (fig. 7). Through this orifice, in consequence of its favourable
position, I could focus clearly, down to the body of the sponge, and had
there been cilia lining the interior surface of the tube, I could not possibly,
I think, have missed seeing them ; but I failed in detecting the slightest in-
dication of their presence : very few pores were open, and none of those which
I had diagrammed carefully on the 16th, nor any of those which I had
observed on the 18th.

I continued to observe this and several other small specimens of Spongilla
for several weeks, but as the results were with very little variation the same
as those I have previously described, it is unnecessary to detail them.

The observations on Spongilla, as regards the forcible and the languid
exhalation, are in perfect accordance with my description of those actions in
the marine sponge Hymeniaddon caruncula, recorded in my report " On the
Vital Powers of the Spongiadae," published in the Reports of the British As-
sociation for 1856, p. 438. The vigorous imbibition and ejection of the
surrounding water is as strikingly indicative in the freshwater sponge as it
was in the marine one, of the period of feeding ; while the languid action in
either case distinctly marks the aerating process only, during which the
digestion of the nutritive particles previously imbibed is gradually effected,
and the effete matter partially ejected. In the performance of these instinct-
ive acts, Spongilla possesses the same degree of control over these actions
that I have described in my former report as existing in the marine sponge ;
sometimes the rapid ejection of the excurrent stream in the Spongilla was
suddenly brought to a conclusion, while at others there was a very gradual
decline in the rapidity of the action until it assumed the degree of force that
marks the excurrent streams of the breathing action only.

The structure of the pores, and the perfectly plastic nature of the dermal
membrane, as exhibited in these observations, are very remarkable. The
sensitiveness of the sponge to injury, the rapidity of the act of closing those
organs, and the power they appear to possess of opening new ones to any
extent and in any direction they please, attest an astonishing amount of vital
energy in a membrane in which I have been unable to trace any indication
of the existence of fibrous tissue.

126 REPORT — 1857.

On Flax. By John P. Hodges, M.D., F.C.S., Professor of Agri-
culture, Queen's College, Belfast, and Chemist to the Chemico-Agri-
cultural Society of Ulster.

Composition of the Unsteeped Flax Stem and of the Dressed Fibre.

For the purpose of studying the nature of the proximate compounds which
arc contained in the cells of the flax-plant, and which are in part removed in
tlie steeping process, several analyses, both of unsteeped and of dressed flax,
i.e. of the fibre in the condition in which it is brought into the market,
deprived of the portions unsuitable for spinning, have been made by the
Reporter. By operating upon large quantities of material, he was enabled to
separate considerable quantities of some of the most important constituents
of the plant, and had hoped to be ready to communicate the results of the
investigations in which, at various periods during the past three or four
years, he has been engaged ; but, froni the interruption of pressing profes-
sional duties, he has been obliged to remain content with merely a partial
survey of the subject. As, however, the chief labour of the investigation
has been removed, he expects that, in the course of next year, he may con-
clude the inqiiiry. In the mean time, a summary of some of the results ob-
tained will be found interesting, and in some degree useful, as a contribu-
tion to the chemical history of a material of so great importance to the sta))le
industry of Ireland. For the proximate analyses of the plant, various methods
of investigation were tried ; but that which was preferred, as affording the
most reliable results, was conducted as follows: — The flax, cut into small
pieces, was in the first place repeatedly treated with cold water, so long as
anything was dissolved. The solution was strained through linen, and after-
wards filtered and heated to ebullition. The coagulum which was produced
on boiling the liquid was separated by the filter, and a few drops of acetic
acid added, which produced a precipitate of caseine, which, after twelve
hours' subsidence, was collected, washed, dried, and weighed. In the liquid
from which the caseine was separated, when evaporated to an almost syrupy
consistence, alcohol, when added, produced a bulky gelatinous precipitate of
a greyish colour, which was collected on a filter, washed with alcohol, and
dried. The alcoholic liquids, on concentration, afforded rich orange-coloured
solutions, and afforded, on evaporation, reddish-brown extracts, which, in the
case of the dressed flax, weie found to contain a considerable amount of
grape-sugar. The several precipitates and residues, after being weighed,
were carefully incinerated, and the weight of ash obtained in each case de-
ducted. The amount of nitrogen contained in the samples was determined
by the method of Varrentrapp and Will, and in each case two estimations were
made — first, of the total amount of nitrogen contained in the specimen dried
at 212°; and secondly, of the amount of nitrogen which was retained, in the
form of insoluble azotized compounds, in the specimen from which all soluble
matters had been removed by treatment with water as described. The
amount of fatty matter and oil present was obtained by treating the specimen
dried at 212° in a simple, but exceedingly effective, extraction apparatus,
which for upwards of ten years has been in use in the laboratory of the Re-
porter, and has been found of great service in facilitating the treatment of
substances with alcohol and aether. It is formed by attaching a thin glass
flask, capable of containing about 6 oz. of liquid, by means of a small
glass tube and sound corks, to a glass vessel of about 12 oz. capacity pro-
vided with two openings, one being at the top and the other at the side, as
close as possible to the bottom of the vessel. To the opening at the top of
the vessel, a glass tube bent at right angles is affixed by means of a cork,

ON FLAX. 127

and its longer limb made to pass to the bottom of a loosely-closed vial
which is placed in a beaiicr containing some cold water. The apparatus thus
constructed consists of three vessels; and the material to be extracted, reduced,
if possible, to coarse powder, or cut into small pieces and bruised, is placed
in the intermediate vessel, tlie lower tubulure of which should be loosely
filled with a piece of cotton which has been previously boiled with aether
and alcohol. A little flask, in which about an ounce of aether has been
placed, is then attached, and the bent tube inserted, with the long limb
passing into the vial, in which also there is some aether. The apparatus
being thus arranged, a spirit-lamp is held under the little flask, and the
heat continued until nearly all the aether is volatilized. The flask is then,
without being detached, cooled by immersion in a basin of cold water,
Avhen the asther in the intermediate vessel, and also that in the condenser,
is forced into it by atmospheric pressure. The flask is then dried by blotting-
paper, tiie heat of the lamp again applied, and the process continued until
the aether which passes through the little bent tube connected with the flask
is entirely (ree from colour. By this method of extraction, nearly all the
aether employed can be recovered by applying heat to the flask, so as to cause
the liquid to accumulate in the condenser, and a concentrated solution of the
matter dissolved is collected in the flask. By placing the flask (the weight
of which has been ascertained) in the water-bath, so as to remove all traces
of the solvent, the amount of the extract can readily be determined.

The total amount of matters extracted by aether, in five experiments, with
samples of flax-straw, the produce of crops in this country, in different years,
and all of first-rate quality, gave an average of 2'068 per cent, on the flax
dried at 212°. The residue of the flax, after extraction with water, and the
subtraction of the amount of wax, &c. extracted by aether, and of the in-
soluble nitrogenized compoimds, as calculated from the amount of nitrogen in
the washed fibre, and assumed to possess the composition of albumen, and
of the insoluble inorganic matters which it was found to contain, was regarded
as fibre.

The following is a statement of the results obtained in the examination of
samples of dressed flax fibre, of average quality, and also of a sample of un-
steeped flax-straw which had been taken from the field when fully matured,
and had remained for some weeks in the stack. The samples of fibre dried
at 212" contained, respectively — No. 1, 9"10, and No. 2, 8'61 per cent, of
M'ater; and the unsteeped straw 12 per cent.: —

Unsteeped

No. 1. No. 2. Straw.
Wax volatile oil, lino-tannic acid, and

resinous matter 2200 2-620 1'360

Sugar and colouring matter, soluble

in alcohol 1-541 0-624 5-630

Inorganic matters, soluble in alcohol 0281 0116 2-830

Poctine 0-698 0-280 0360

Salts, insoluble in alcohol 0076 0-044 0080

Nitrogenized compounds, soluble in

water, cascinc, &c 3-560 ]-380 0-834

Nitrogenized compounds, insoluble

in water 2-940 4-310 4-269

Inorganic matters, united with the

fibre 0-730 1-490 2-500

Fibre 87-974 89-136 82-137

100-000 100-000 100-000

128 REPORT~1857.

The total araoiint of inorganic matters present in the samples was ob-
tained by the careful incineration of tiie flax in platinum dishes. The
specimens of fibre dried at 212° gave, respectively, in No. 1, I'-tO per cent.,
and in No. 2, I'oi per cent, of ash. The ash had a brick-red colour. The
unsteeped flax left, on incineration, 5'23 per cent, of an almost white ash.
The ash from the fibre had the following composition : —

No.l. No. 2.

Potash 7-94 ... 1-85

Soda 2VJ ... 7a-2

Chloride of sodium ... 2"75 ... 1"77

Lime 29-24 ... 2708

Magnesia 464 ... 070

Peroxide of iron 3'72 ... 7'40

Phosphoric acid 5-23 ... 1040

Sulphuric acid 6*00 ... 3'12

Carbonic acid 28-17 ... 1910

Silica 10-45 ... 21-31

100-33 100-36

By distilling the straw of the flax plant with water, there is obtained in
the receiver a slightly acid distillate, from which, when saturated with com-
mon salt, by treatment with tether, there is procured a small amount of an
exceedingly fragrant oil, of a yellow colour, which possesses an intense
honey-like odour. This oil, when heated, evolves a penetrating smell, with
a somewhat turpentine odour. It soon solidifies on exposure to the air,
forming irregular granules, and acquires an acid reaction. Its dilute solution
evolved the characteristic agreeable odour which is perceived in rooms in
which large quantities of dressed flax are stored. It may also be separated
by adding water to the solution, obtained by treating the straw with alcohol
in the extraction apparatus, and subjecting the mixture to distillation. By
the action of £Ether upon both the unsteeped and dressed flax, rich green-
coloured solutions are obtained. These solutions possess a strongly acid
reaction, and, on partial cooling, bulky, flocculent white deposits separate,
leaving the supernatant liquid of an emerald-green colour. The deposited
matter soon collects in transparent granules, and, when repeatedly washed
with cold aether, which separates from it a yellow colouring matter, it dries
over the water-bath to a slightly yellow brittle pulverulent extract, which
in the cold is scarcely at all acted upon by absolute alcohol, but dissolves
by the assistance of heat in spirits of turpentine and in ammonia, and is
saponified by heating with solution of caustic potash. Fixed on a loop
formed on a piece of platinum wire, and exposed, with the usual precautions,
to water heated over a lamp, it was observed, in several trials, to soften at
the temperature of 182° Fahr., and to melt at 184'°-5 Fahr. ; strongly heated
in a platinum capsule, it runs along the dish, then melts and evolves an
odour of wax, and when placed in its melted condition on paper, produces a
greasy stain. The amount of wax separated from the unsteeped flax amounted
to 0"27 per cent.

When the solution obtained by treating the flax-straw with tether is evapo-
rated to dryness, a residue is left which consists of a deep olive, almost black
extract, mixed with a substance of a rich orange colour. This extract, on
being dissolved by the assistance of heat in aether, and distilled water added
to it, produces a brown turbid solution, on the surface of which a dark brown
sticky matter collects, which, when removed by filtration, leaves the liquid
of a bright golden-yellow colour, and affords, on evaporation, an orange

ON FLAX. 129

strongly acid extract, which was found to consist chiefly of a peculiar tannic
acid, which strikes a deep green colour with the persalts of iron. This acid,
which may provisionally be termed lino-tannic acid, was also obtained in white
needle-shaped crystals, by adding neutral acetate of lead to the aethereal solu-
tion of the plant, and decomposing the lead compound diffused in alcohol by
sulphuretted hydrogen. The filtrate from the sulphuret of lead, which had
an orange colour, when evaporated to dryness, afforded on treatment with
aether, a solution from which, when the aether has spontaneously evaporated,
crystals of the acid separated. The acid, though existing in minute quantity
in the plant, has been detected both in the unsteeped and dressed flax, and
possesses considerable interest in connexion with the technical preparation
of the fibre, as its presence explains the discoloration which is frequently
observed when the flax-straw has been steeped in water containing salts of
iron. In addition to the lino-tannic acid, the straw of the flax plant was
found to contain a considerable amount of malic acid, and also an acid yellow
colouring substance of a resinous nature, which can be extracted by alcohol,
and yields, with basic acetate of lead, a rich chrome-yellow-coloured preci-
pitate, which, when suspended in alcohol and decomposed by sulphuretted
hydrogen, and the sulphuret of lead removed, yields a straw-coloured liquid,
from which, on evaporation, the resin is obtained in the form of a tenacious
orange-brown extract, which is insoluble in aether, but dissolves readily in
alcohol, and is precipitated from its solution in the form of a buflF-coloured
mass, which is dissolved by alkalies, with the production of a rich orange-
coloured solution.

From the green plant, and also from the dressed fibre, water extracts a
gelatinous substance which is thrown down as a bulky precipitate on the
addition of alcohol. This precipitate was found to consist of pectine with
malate and sulphate of lime. In the unripe plant, and also in the stems, as
pulled from the field in the usual state of maturity, when the seeds contained
in the capsules have commenced to assume a brown colour, starch was dis-
covered, and could readily be extracted by placing the stems in a powerful
lever press, and moistening them with a small quantity of water. By allow-
ing the expressed liquids to remain at rest, the starch subsides, and can be
recognized by the microscope as consisting of extremely minute corpuscles,
which assume a purple colour on the addition of a watery solution of iodine.
When, however, the flax-straw is examined after it has remained exposed to
the air for several days in the stook, the liquid obtained by subjecting it to
pressure and washing with water was found to afford no indication of the
presence of starch. In the dressed flax, no starch could be detected, but
the presence of a considerable amount of grape-sugar was demonstrated.
The discovery of grape-sugar in the fibre is in many respects exceedingly
interesting, as it serves to afford an explanation of the statement frequently
made by experienced steepers, that, by storing up the steeped flax as imper-
fectly dried, by exposure to the air for some weeks before proceeding to re-
move the adherent woody matters by mechanical means (by scutching), the
separation of the fibre is found to be greatly facilitated, and its qualities
improved.

Examination of the Steeping Process.

As stated in former communications to the Section, experiments, which
were conducted by immersing flax in water, both at ordinary temperatures,
and also in vats filled with water, heated and steadily maintained at from
80° to 90° Fahr., have shown that in both cases the series of decompositions
which ensued might be regarded as identical, and that the fermentation

1857. K

180 REPORT — 1857.

which takes place resembles the so-called butyric acid fermentation. Thus,
when the gases which are evolved from the surface of the steeping vats are
collected, which is most conveniently effected by filling the receivers with
the flax water and supporting them over the surface of the liquid, the
mixture of gases obtained, when transferred to the mercurial trough, and
examined by the introduction of pellets of potash, explosion of the residue
with oxygen, &c., according to Bunsen's excellent methods, was found, in
numerous trials, to afford merely carbonic acid, hydrogen, and nitrogen. In
no case could traces of carbonic oxide, carburetted hydrogen, nor of sul-
phuretted hydrogen be detected. The absence of sulphuretted hydrogen
was carefully ascertained by the employment of various methods; not the
least indication of its presence could be detected, though papers moistened
with acetate of lead were exposed to the gases evolved during the entire
progress of the fermentation. This fact is important, as it has been asserted
that the disagreeable odour of the flax-pool depended upon the copious evo-
lution of sulphuretted hydrogen ; and its presence in the gases evolved has
been reported by a French chemist, though upon insufficient evidence,
afforded by the examination of flax-water, conveyed in bottles from remote
parts of the country to Paris. The production of a large amount of sul-
phuretted hydrogen has been urged as a serious objection to the adoption of
Schenck's hot-water process.

The corrected composition of 100 volumes of the mixed gases evolved
from the fermenting vats was found to be as follows : —

Carbonic acid 22-29

Hydrogeu 44-30

Nitrogen 33-41

10000

At the Belfast meeting of the Association, it was stated by the Reporter
that, during the fermentation, a very considerable amount of butyric acid was
produced. Since that period, the experiments have been repeated on a con-
siderable scale, and it has been found that, though, when the fermentation
has fairly commenced, after the straw has been about twenty-four hours
immersed, the distillate from the fermenting liquid contains formic acid and
butyric acid; yet, as the process continues, and especially towards its con-
clusion, the formic acid almost entirely disappears, and the butyric acid de-
creases in amount, and is replaced by valerianic acid. In some cases, indeed,
the distillate, towards the conclusion of the period of steeping, afforded nearly
pure valerianic acid.

Beport of the Committee on the Magnetic Survey of Great Britain.
By Maj 01-- General Sabine.

The author gave a brief review of the important researches connected with
the magnetism of the globe by MM. Kreil and Lamont, on the Continent of
Europe, Dr. Bache and others in America, and by our own observers in
various parts of the earth. He adverted to the Magnetic Survey of the British
Islands, executed at the request of the British Association in 1837 and 1838,
published in the ' Reports ' for 1838, as the first national work of this descrip-
tion which had been executed in any country, and to the similar works
since completed in Austria and Bavaria, at the expense of the Governments
of those countries, in proof of the value of the example. It is on such

A CATAIiOGUK OF OBSERVATIONS OP LUMINOUS METEORS. 131

surveys that we must in great measure depend for the materials on which
correct delineations of the three magnetic elements on the surface of the
earth can be satisfactorily based ; and it is to the repetition of such surveys,
from time to time, th^ we must look for the data on which a true theory of
the secular variation of terrestrial magnetism may be founded. Twenty
years having elapsed since the execution of the iormer Magnetic Survey
of the British Islands, the General Committee had deemed that the proper
time had arrived for its repetition, and named a Committee for the purpose,
consisting of the same five members of their body by whom the former survey
was made, with the addition of Mr. Welsh, the Director of their Establishment
at Kew. The present Report stated the progress which the Committee had
already made, chiefly in England and in Scotland, and their expectation that
at the next meeting of the Association they should be able to report that the
work was drawing near to its completion.

Report on Observations of Luminous Meteors, 1856-57- -By the Rev.
Baden Powell, M.A., F.R.S., F.R.A.S., F.G.S., Savilian Pro-
fessor of Geometry in the University of Oxford.

In submitting to the British Association ray tenth Report of Observations
on Luminous Meteors, I could have hoped that it might have contained
some attempt at least towards the classification and generalization of the
vast mass of results which have now been communicated. But while the
actual contribution of fresh observations for the year which has elapsed since
my last communication is not very extensive, I am also constrained to admit
that I have as yet attempted very little towards the greater object in view.

In the present communication, nevertheless, besides the mere detail of
observations, I am able to include notices of one or two important specula-
tions on the subject which have been pursued by some eminent men who
have turned their attention to this inquiry, and have followed out some
generalizations on certain points connected with it, which seem eminently
valuable towards the gradual establishment of a solid theory of meteoric
phaenomena.

I. Some generalizations respecting the causes of meteor-phaenomena, espe-
cially the averages of their horary variation in numbers through the night,
have been advanced by Mr. G. C. Bompas, founded on the observations of
MM. Coulvier-Gravier and Boguslawski.

The general result of those observations is, that the number of meteors
varies through the successive hours from 6 p.m. to 6 a.m., by a regular
inc7-ease up to the last-named hour.

The number which appear in the East is more than double the number
originating in the West; those from North and South nearly equal. In
other words, nearly two-thirds of the whole number originate in the Eastern
hemisphere of the sky.

From the observations of Boguslawski and others, it appears that the crre-
raffe velocity/ of meteors is about double that of the earth in its orbit.

Mr. Bompas, combining these facts, deduces the following theory, derived
solely from the conditions of the earth's motion. The greatest number of
meteors is encountered when the observer s meridian is in the direction of the
earth's motion, which is at 6 a.m. ; and then decreases to 6 p.m., when he
looks the opposite way. If the earth were at rest, meteors (supposed equally

132 REPORT — 1857.

distributed) would converge on it equally from all quarters. But the earth,
in fact, being in motion with a velocity half that of the average velocity of the
meteors, it encounters nearly two-thirds of the number on the side towards
which it is moving.

II. A considerable series of results has been investigated by M. A. Poej',
respecting the colours of luminous meteors, derived from extensive sets of
observations collected by M. Ed. Biot from those made in China from the
7th century b.c. to the 17th a.d. ; — those collected in the Reports of the
British Association ; — and those made at Paris by INI. Coulvier-Gravier.
Among these generalizations we may remark the following : —
In the Chinese observations meteors of simple primitive colours are very
rare, the great majority being of compound tints ; in the European observa-
tions the reverse is the case.

The Chinese observations show a remarkable constancy of tints during a
long period of years, when an equally constant but different scale of colour
prevails ; and this for several successive periods.

Cases of complementary colours in the body of the meteor and the train,
or fragments, are often noticed,

Changes of colour during the course of the meteor are observed, being
most usually from ivhite near the zenith to blue near tlie horizon, but some-
times from tchite to red. This, the author observes, agrees with the law of
INI. Doppler, that a luminous body moving towards the observer will change
its colour from white, in succession to the violet end of the spectrum ; —
ino\i\igfrom the observer, to the red. This law, he states, is especially con-
firmed by the Paris observations. He remarks on the necessity for attend-
ing to ^er^owa/ differences in observers' estimate of colour; a remark fully
confirmed by the great contradictions existing in the descriptions of the
colour of many of the brightest meteors, at the same time and place, by dif-
ferent observers.

He gives the results of the various observations cited, in tables exhibiting
the number of meteors of each tint for each month; and adds others of
meteors arranged under several heads, of physical peculiarities.
The details are given in the Appendix No. 4.

III. One point of the highest interest and importance towards forming
any sound theory of meteors, is the estimate of their actual size from their
apparent diameters and calculated distance. In all the results usually given
this calculation is made on acknowledged geometrical principles, assuming
that the apparent disk is the real one, diminished only by the effect of
distance.

Prof. J. Lawrence Smith of the U. S. has adduced some very remarkable
optical experiments to show the entire fallacy of any conclusion from the
apparent diameter of a highly luminous or incandescent body seen at a
distance.

These experiments exhibit a singular apparent enlargement of the visible
disks of intensely luminous bodies of known size, when observed successively
at distances of 100 yards, of a ^ mile, and -J- mile; at which distances re-
spectively, for example, the body of electric light of carbon points (actually
0-3 inch diameter) appeared i, 3 times, and 3^ times the diameter of the
moon ; and other incandescent bodies in a similar proportion dependent on
the degree of ignition.

These results seem dependent on some optical or ocular cause, of greater
energy than we can ascribe readily to simple irradication ; but in a rough way
they admit of some degree of verification by looking at a row of street lamps
seen nearly in a line from the eye, the apparent diameters of which do not

A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. ]33

decrease at all for a considerable distance ; and even then by no means in
proportion to the law of perspective.

This subject appears to be one eminently deserving of more full and
precise investigation, whether in a meteorological or an optical point of
view.

IV. Prof. Lawrence Smith's paper is, however, mainly devoted to other
points of not less importance respecting the nature and theory of meteors, and
especially of those which fall either wholly or in portions, producing meteoric
stones.

He gives a minute account of five specimens found in America, accom-
panied by chemical analyses, from which it appears that they all contain the
mineral called Schreibersite, not known as a natural compound on the earth.
He enters largely on theoretical views, and in the course of these specula-
tions examines various hypotheses which have been put forth, and eventually
endeavours to revive the theory of the origin of these bodies from the lunar
volcanoes supposed at some remote period to have been in a state of activity.

Without discussing such a question, which will perhaps be generally viewed
with suspicion at the present day, and passing to the general subject of
shooting stars, which the author is inclined to distinguish entirely from those
masses which have fallen to the earth, we may notice the apparently favour-
able mention he makes of the general admission of the cosmical nature of the
former, and of that view of their nature which regards them as nebulous
masses revolving in our system.

It has been further supposed that such masses, being in a high state of
electric tension, on approaching the earth, a discharge might take place by
which their metallic elements might be reduced : dependent on the size of
the nebulous mass, the force of the discharge, the consequent intensity of
the fusion, and other conditions, larger or smaller metallic or earthy masses
might be precipitated, and might fall entire or shattered into fragments.
The author, however, considers these latter effects as incompatible with the
conditions of observed meteorites.

But probably, on the whole, all such speculations are as yet premature.
We must obtain a larger amount of data and better classification of observa-
tions before we can hope to follow out such inferences successfully.

For the details of Prof. L. Smith's paper see Appendix No. 5.

V. In some of the earlier of this series of Reports, reference was made to
the theory proposed by Sir J. Lubbock, of meteors shining by reflected light
and being simply darkened by entering the earth's shadow, and to some ob-
servations of meteors which coincided with it. It is much to be regretted
that other observations of a kind capable of such application have not been
more frequent. One remarkable instance observed by Capt. Jacob, at
Bombay, was considered some years ago by Prof. C. P. Smyth, and a com-
munication on the subject made by him to the Royal Society of Edinburgh
(184'9), of which a short notice in the Proceedings of that body is the only
remaining record — the details having unfortunately not been preserved.
The results, however, are stated to accord exactly with the theory.

The essential parts of the notice are given in Appendix No. 6.

VI. Of the August meteors for the present year, the only notice which
has reached me has been an account published by Dr. T. Forster, of
Brussels, in the Times. He observed great numbers, some of them pre-
senting unusual appearances, especially in regard to colour.

His letter is given in Appendix No. 7.

134

REPORT — 1857.

Meteors communicated by

Date.

1856.
Jan. 7

Hour.

h m

4 50 p.m.

4 60 p.m.

Oct. 18 Mean time
at the place,
9 4 p.m.
5 58 p.m.

A fire-ball

Nov. 15

22 7 16 p.m

1857. I
Jan. 2 Between
{2a.m.&5 3D
1856. I
Aug. 10 From 9 p.m.
to 10 p.m

Oct. 19

6 24 25
(g.m.t.)

Oct.

Nov. 30 7 17 p.m.
I (g.m.t.)
30. 8 1 p.m

281

29 I

30 r

3VJ

Appearance and
Magnitude.

luminous vertical
band expanded at
the middle, with
a bright centre
tapering to the
ends, intensely
bright and white
Nearly = Tf. ,

Brighter than any
stars visible through
the rain.

Just visible through
clouds.

A number of small
meteors.

Five bright meteors
at different inter-
vals of time. Seve
ral smaller.

A very brilliant
meteor. = 2nd mag
Increased to — it-
and exploded with
sparks.

= aLyra;

Bright ; = 4 ; disap-
peared suddenly
near i Ursa Major.

Brightness
and Colour.

Bright and red

Left a column of thiu va-. Visible for 20 mins.

pour which wavered and

gradually vanished. I
The middle expanded and Disappeared after

Two very
bright.

Bluish. In-
tense at ex-
plosion.

Light orange.
Colour of J|..

Brilliant meteors '
over the sky."

all

29; 6 30 p.ra.iA fine meteor

30 30 p.m.iPassed near ? ..

Nov. 9i 3 a.m. Six meteors within
an hour of eacl
other.

Train or Sparks.

Velocity or
Duration.

ends curved opposite
ways, became faint and
vanished.

Small train of sparks left
behind.

about 10 minutes.

Slow..

The brightest left a train, Rapid
whichremained 1 or 2 se-
conds. The head moved
on separately, became
stationary, and vanished
by gradual diminution.

Left a bearded train behind.

No train

Very little train

Slow ; about 3 sec.

Rapid

Moderate velocity
2 or 3 sees.

About = ? ..

Bright yellow
ish.

Exploded fragments " pur-[Sparks remained

sued the path the meteor visible some time

itself liad takeufor about

10°."
No explosion, train, or

sparks.

Sparks : no explosion,

after the body'^
had vanished.

Appeared 30° from:
zenith & moved.
About same time
on other nights
many meteors.

A CATALOGUE OF OBSERVATIONS OF I<UMINOUS METEORS. 135

Various Observers.

From S. to W. parallel to hori-
zon. Altitude 40°; passed
near 2^.

From E. to N. at inclination of
40° to horizon.

Nearly S., vanished within 30'
of %.

Direction or Altitude.

In the S. at low altitude, de-
scended from S. to E.

Nearly S.

All the accounts
nearly similar.

Rain at the time .

2/. barely visible
from clouds.

In the N., all at small altitudes
midway below Ursa Major
and Cassiopeia ; directions
nearly horizontal but incliiicd
towards W. ; one inclined
nearly at 45'. All moved
from E. to W.

Just below Ursa Major, forming
an equilateral A vWlii /3 and y.
From W. to E. about 3°.

Prom N. to S.; disappeared near

the Pleiades.
From S.E.to N.\V.,from a Per-
■ sei to £ Ursa Major. Straight

course.

Altitude 25° in N.E., moved
through 30° upwards.

From a little N. of zenitli to
wards S.E., disappeared af
20° alt.

3 to S.E., 3 to N.W

General remarks.

Sky partially cloud-
ed.

Place.

East Knoyle,

Wilts.

Blackheath,
Southampton,
Brighton, Ri-
ver Hill near
Sevenoaks.

Wrottesley Ob-

servatory,
Wolverhampton
Ibid

Ibid

Ibid ,

Margate

Tavistock Place,
London.

Tavistijck Place.

London.
Oxford

Bombay.
Bombay .

Kandallah
Bombay .

Observer.

A correspondent
to Lord Wrot-
tesley.

Mr. J. Rogers,
Mr.T. Kimber,
and Corre-
spondents to
several Jour-
nals.

Observatory As-
sistant.

Id.

Prof. Powell and
Mrs. Powell.

F. V. Easel, Esq.

id Ibid.

Mr.G A.Rowell.Ibid.

Reference.

MS. communication
from Lord Wrot-
tesley.

SeeAppendixNo.2,

MS. communication
from Lord Wrot-
tesley.

Ibid.

MS. communica-
tion.

A Correspondent
to Bombay
Tinies.

Bombay Times,
Nov. 1.

Ibid.

Ibid. Nov. 6.

Ibid. Nov. 11.

136

REPORT — 1857.

Date.

Hour.

Appearance and
MaKnitude.

Brightness
and Colour.

Train or Sparks.

' Velocity or
Duration.

1856. h
Nov. 2811 45 p.m.

1857.
Feb. 9

Several shootingstars,
One remarkable.

9 35 p.m

(g.m.t.)

One very
bright; illu
minated ob
jects around
" like a flash
of light-
ning."

Bluish white
Intensely
bright and
sparkling.

Bright train from a few
degrees from the zenith
to about a degree W. of
h , seen after the meteor
had disappeared ; re-
mained a few seconds.

Left a whitish serpentine
train for an inappreci-
able instant.

Less than 1 sec.

Luminous Meteors observed in 1855-56-57, by J. King Watts,

1855.
Oct. 6
Nov. 30
Dec. 6

1856.
Aug. 25

Oct. 21

1 3 p.m.

7 p.m.

7 15 p.m.

10 45 p.m.

Large

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

10 46 p.m.

7 16 p.m.

7 6 p.m,

8 25 p.m

Nov. 5
18

27
Dec. 20

1857,
May 14

July 20

Large

= lst mag.*.

= 2nd mag.*
Large ,

10 46 p.m.
7 58 p.m.

7 30 p.m.

10 30 p.m.
9 45 p.m.

10 15 p.m.

11 5 p.m.

Small

Very large

Small

= 2nd mag.*

Large

Large meteor

White
White
White

No sparks

Sparks

No sparks

Reddish

Sparks .

White

Bluish-red

White
White

Slow..,
Slow..,
Slow...
Rapid

Slow.

'WV/.''

Many sparks and longiSlow

train.

Many sparks Quick

Long train and sparks afterj Rather slow,

it had become invisible.

None

Red with pur-
plish tint.

Sparks ,

White
White

Rapid
Rapid

No sparks

Slow.

Quick
Quick

Slow

Rather slow.

A CATALOGUE OF OBSERVATIONS OP LUMINOUS METEORS. 137

Direction or Altitude

General remarks.

Place.

Observer.

Reference.

Jkloved vertically downvrards
; through'about 8°; disappear-
; ed 20° W. of Sirius.

Light clouds con
cealedeverything
except Sirius.

A little N. of
Whittington,
near Oswestry.

Near Glasgow ,

Rev. A. R. Lloyd. MS. communica-
tion.

W. J. Macquom
Rankine, Esq.,
C.E.

MS. communica-
tion.

Esq., F.R.G.S., F.E.S., St. Ives, Huntingdonshire.

From E. to W

From N. to S

From a, Ursa Major to Pleiades

A beautiful object,.

From a. Cygnus passing « Lyrae
i to the W.

jFrom Draco to Pegasus .

From Ursa Major to Ursa Minor
From Polaris to a Cygnus . .

[Prom Cepheus to Westward
From « Andromedae towards

Cygnus.
[From Cassiopeia to a. Lyrae

[Prom Pleiades to a Persei

From a Aries towards Pegasus.

Fell from' a Andromedae down

towards the W.
iFrom Ursa Minor down towards
I CamelopardaUs.

Had a very beautiful
appearance with
a long whitish-
red line running
from it, emitting
sparks.

Emitted a strong Ibid.,
light. I
Ilbid.,

A very bright and Ibid.,
brilliant meteor,
leaving a strong
light.

St. Ives, Hunts..

Ibid

Had the appearance
of a strong flash

Unusual brilliancy,
and was very
startling.

Bright ,

Very bright. It rose
in sight suddenly
andverybrilliant,
remainedstation-
ary for upwards
of 5 minutes, then
slowly passed
downwards.

J. King Watts.

Id.

Ibid,
Ibid

Ibid

Ibid,
Ibid,

Ibid,

Id.

138

REPORT — 1857.

Meteors observed by-

Date.

1856.
Aug. 2

,j Appearance and Brightness

"""''• I Mat'iiitiKle. and Colour.

Train or Sparks.

h m I

12 4 a.m. = 1st mas'.'

112 10 a.m. = 2nd mag.*
5 9 p.m.j = 3rd mag.*

Oct. 18

21
28
31

Nov. 20

Dec. 20
9

1857.
Jan. 9

8 55 p.m. =1 size C

9 15 p.m.

9 31 p.m.

9 37 p.m.

9 22 p.m.

large meteor

9 p.m. till

10 p.m.

7 40 p.m.
9 p.m.

2 20 a.m,
718 30p.m

8 19 p.m.
8 54 p.m
8 10 p.m

9 7 30 p.m
11 15 p.m

= lst mag.*
red.

Colourless ...

Reddish}' ellow

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

= 8th mag.*

2nd size 1st mag.*

Six meteors above 3rd
mas;.*

= 2nd mag.*
Very small ..

= 2nd mag.*

Larger than Saturn.

None

Velocity or
Duration.

Slow, duratioul sec.

Streaks iRapid

Streak

No train

Rapid, duration 0*1

sec.
2 sec

Streak Rapid

Blue Streak 0-3 sec.

Yellowish.

All colourless

Colourless

Yellowish.
Yellowish.

Streak

AU streaks

Streak

Streak ....
Train ...

H sec, slow

Exceedingly rapid.
Rapid

Instantaneous .

Slowly, duration 2
sees.

2nd mag.* Colourless ...Streak

2nd mag.* Colourless ...|Streak

2nd mag.* Yellowish Train

2nd mag.* Yellowish .

Large Bluish ....

, 'Train

Yellow tail

Not rapid.
Moderate .
Rapid ....

Tolerably rapid, du-
ration 0'3 sec.

A CATALOGUE OF OBSERVATIONS OF LUMINOUS MBTEOKS. 139

E. J. Lowe, Esq.

Direction or Altitude.

General remarks.

Place.

Moved horizontallyimmediately Circular

under Aries and only 4° above!

the horizon. j

Fell down from o Ursse Majoris Two meteors close

j together.
Fell from direction of Polaris

towards Capella. I

Started at ft. Ophiuchi, and Rapidly increased,

Hightield House.

Ibid.,
Ibid.

Ibid.

passed midway between
» Serpentis and Z, Ophiuchi,
passing across No. 52 Ser-
pentis and fading 3° lower.

Moved exactly in the same path

as the last.
From M Ursse Majoris towards

W. horizon at an angle of

SO''.
From No. 13 Delphini almost

perpendic. down.
From about a Cygni passing 5°

N. of Altair.

All perpendic. down

Fell perpendic. down from

between Capella and « Aurigae.
Same path as tlie last

Fell down and ending at m Ursae
Minoris.

From /S Auriga; down at an angle
of 45° towards N., fading
away 8° immediately above C

Perpendic. down from /3 Cygni

Down from i Auriga;

From tt. Andromedae up towards
zenith.

From a, Draconis downwards at

an angle of 50" towards W,
InS.E

without altering
its form, from 3rd
mag.* to I size
of C , and sud-
denly vanishing
when at its maxi-
mum brightness.

Ibid.,
Ibid.

Seemed very near

the earth.
Moonlight

Many meteors .

Many meteors
mostly in Ursa
Major, Ursa Mi
nor, and Draco.

Several meteors ...

Kite-shaped, and
had many streaks
left which linger-
ed and seemed to
ignite after the
meteor had pass
ed by. Moved
behind several
cirri.

Ibid.
Ibid.

Stars very bright Ibid,
and scintillating
considerably.

Ibid.,

Beeston

Ibid.,
Ibid.,
Ibid.,

Ibid..

Ibid.,
Ibid.
Ibid.,

Ibid..

Ibid.,

Moon bright, but
her light was
nothing whilst
the meteor lasted

Observer.

Id.

Reference.

E. J. Lowe Mr. Lowe's MS.

Ibid.
Ibid.
Ibid.

Ibid.
Ibid.

Ibid.

Ibid.
Ibid.
Ibid.

Ibid.

Ibid.
Ibid.
Ibid.

Ibid.

Broomfield F.Waketield,Esq.

House, near
Ashford,AVick-
low.

Ibid.
Ibid.
Ibid.

Ibid.
Ibid.

140

REPORT — 1857.

Date.

1857
Feb. 26

April 16

Hour.

h m

8 12 p.m

11 3 p.m.

Appearance and
Magnitude.

= lst mag.=

= 3rd mag.*

11 36 p.m. 8 times size of If. ...

8 30 p.m. = 1st mag.'
10 30 p.m. = 2^

Brightness
and Colour.

Bluish

Colourless ...

Colourless ...
Colour steel
blue.

Train or Sparks.

Train

Streak

Leaving a long train of
light for several seconds

Streak

Small tail

Velocity or
Duration.

Rapid, duration 0'3
sec.

Rapid .
Slowly .

Slowly

Slow, duration 5 to
6 sees.

f The August meteors have been badly seen here, owing to much cloud on the one hand, and full
cricket-ball, fell N. of Nottingham. It is probably a meteor, and has been promised to me : the person

APPENDIX.

No. 1. Details of a Meteorite mentioned in a former Report, which fell at

Cirencester in 1 835. Extract of a letter to Prof. Powell from Thos. C.
Brown, Esq.

" Copy of a notice of the Meteorite entered in the Book of Donations of
the Permanent Library, Cirencester, by the late Mr. Arnold Merrick, Cura-
tor to the Museum. — ' A specimen of a meteorite which fell about half a
mile from Aldsworth in a field occupied by Mr. Waine, within twenty yards
of his workmen, who were sitting against a wall at the time, on the 4th of
August 1835, a sunny afternoon without a cloud. A meteor was seen at
Cirencester proceeding eastward, and a remarkable noise was heard at half-
past 4 in the afternoon. The noise was heard in most parts adjacent.

" ' The workmen saw no unusual light, but heard the aerolite rush through
the air, and felt it shake the ground by striking it with great violence. It
fell on a swarth of oats, and drove the straws before it down into the earth
for six inches, till opposed by rock. When the men got it up, it was not hot,
but the part of the surface which appeared not to have been broken was
quite black and soiled the fingers. It weighs about 9270 grains. It contains
a great deal of iron, but is not magnetic. Its specific gravity is 3-4.

" •' Mr. Waine states that a shower of small pieces fell about half a mile
south of the spot where this fell. Children thought it was a shower of
black beetles, and held out their hands to catch them as they fell.'

" My niece. Miss Anna Sophia Brown, now Mrs. Pooley, about 4 p.m. on
the same day, being in her father's garden at Cirencester, perceived a meteor
passing from W. to E., apparently about twice the height of Cirencester
tower,''which is upwards of 100 feet high, looking like a copper ball larger
than an orange [?], and having a tail or stream of light behind it. In its
passage it made a rumbling noise heard by many persons, reminding her of
thunder, and the people of the town marvelled that it should thunder in a
serene day with a cloudless sky. On the same day at Aldsworth, 13 miles
E. of Cirencester, the meteoric stone fell, the particulars of which are before
ctiyen, " Thos. C Brown."

No. 2. — From the Express, Wednesday, January 9, 1856.
Bemarhable Meteor.— A correspondent writes, under date Southampton,
January 8, 1856 :— " The meteor observed here yesterday made its appear-

A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 141

Direction or Altitude.

General remarks.

Place.

Observer.

Reference.

Nearly perpendic. down, incli-
ning to W., and passing
through Polaris.

)ownwards from S. of Saturn..

Aurora Borealis ...

E. J. Lowe

Ibid.

Ibid.
Ibid.

Ibid

'rom n Ursse Majoris to 10°
below the nebula in Andro-
medse.

Highfield House.

Capt. A. S. H.
Lowe.

Mrs. E. J. Lowe.
F.Wakefield.Esq.

'ell from the S.E. towards the
W.

Sky clear, after
much thunder and
rain.

Broomfield
House, near
Ashford.Wick-
low.

lOon on the other. — On Aug. 13th, a ball as smooth and round as a biUiard-ball, and larger than a
'ho found it concluded it was a thunderbolt. — E. J. Lowe.

ance during twilight. It descended perpendicularly. The light which
heralded the fire-ball was at first not unlike the streak of brilliant sparks
that precedes the bursting of a sky-rocket. The fire-ball likewise originated
apparently very much as the fire-balls of a sky-rocket originate, from some
explosive and combustible agency. But the light after the discharge of the
fire-ball became gradually whiter, and persons who looked at it through a
telescope saw shining in its centre what appeared like a star. The shape of
the streak or band of light was not unlike the blade of a huge flaming sword
suspended in the heavens with the flat surface towards the north. That its
substance was remarkably dense and firm is evident, since its shape was un-
altered and its edges were sharply defined for more than five minutes. In
fact, so stable did it appear in the heavens, that numbers of people were
overcome with wonder and dismay, and shed tears. After a time it became
more cloud-like and tenuous ; its edges gave out, and its straight and perpen-
dicular direction became less firm. At one time its colour was not unlike
the very white steam forced from a boiler, and it assumed a serpentine form.
Before it vanished, however, it was cloud-like in its appearance and move-
ments. A few stars were visible in the heavens when the meteor appeared."

A paragraph in the Brighton Examiner shows that the remarkable meteor
above described was visible in that town : —

" About five o'clock on Monday evening a very brilliant and extraordinary
meteor was observed by several of the inhabitants over the sea in a south-
easterly direction. The ball, apparently of fire, was exceedingly splendid,
leaving a brilliant ribbon, as it were, behind it, as bright as molten silver.
It fell nearly perpendicularly, the ribbon assuming a spiral form, till it finally
vanished, in about ten minutes after its first appearance. The sky at the
time was beautifully clear and cloudless. When first seen it was considerably
more than 45 degrees in height, and extended 10 or 12 degrees."

Another Account. — "A very beautiful meteoric phsenomenon was ob-
served in the S.S.W. part of the heavens this evening just after five o'clock.
My attention was first arrested by the appearance of a very brilliant light
darting suddenly towards the earth, apparently proceeding from a star, which,
I think, is the planet Jupiter, at present an evening star, taking an easterly
direction. My first impression was that an immense sky-rocket had been
discharged into the air, but instead of the train of fire proceeding upwards,
it rapidly descended towards the earth, or rather the Channel, for it must
have been several miles from land ; and as it extended in length, lost some-

142 REPORT — 1857.

portion of its brilliancy and became nearly stationary. At first the appear-
ance was like a long oblique line of fire, '.vhich gradually swelled out towards
the centre, and curved itself not unlike a huge gilded serpent. Its apparent
length was between 20 and 25 feet[?J. The phaenonienon was visible about
fifteen minutes — becoming more attenuated, and at length entirely dissipated
or diffused in the atmosphere." — Briyhton Examiner.

" To the Editor of the Times.

" Sir, — Having just witnessed a very remarkable meteor, I hasten to send
you the particulars of it as observed from this place. At nine minutes to 5
(4'51 P.M., or, perhaps, 4'' 51"" 30^) a brilliant ball of white light fell from a
point in the S.S.W., 3° or 4° south and east of Jupiter. It grew brighter as
it fell, but did not appear to burst, and vanished about 12° from the horizon ;
its course was nearly perpendicular, but slightly inclined to the east. It left
behind it a brilliant streak of white liglit, tapering to both ends, about 6° in
length, which immediately assumed a curved or spiral form, exceedingly like
a serpent rearing itself up. The middle part of this tapering band of light
gradually expanded, taking the form of small fleckering clouds (cirro-cuinuli).
This became gradually more curved, or rather spiral, and the whole mass
drifted very slowly towards the south-east, the middle part having apparently
a more rapid motion than the extremities. It continued distinctly visible for
upwards of 10 minutes, when some heavy mist clouds drii'ting up from the
north-east obscured it. Being near the house, I got out an astronomical
telescope with a glass of low power, but was unable to decide whether the
ligh,t seen was vapour in the atmosphere (which it much resembled), or dif-
fused nebulous light.

" The sky at the time the meteor appeared was perfectly clear and briglit
with the rays of twilight. Its size was somewhat difficult to estimate, but I
should guess it at about four times the apparent diameter of Jupiter, which
was close at hand.

" Whatever wind there was came from E.N.E., but there were no clouds
in the tipper sky to indicate the direction of currents there. Not the slight-
est sound was perceptible. The point at which it first became visible was,
as nearly as possible, 20° above the horizon, ascertained by an altitude circle.
I had not time to get out an azimuth instrument to verify its position in
azimuth ; but the foregoing pai'ticulars may be useful for comparison, as it
has, doubtless, been observed in many places.

" I am, Sir, yours faithfully,

"River-hill, Sevenoaks, Jan. 8, 5'15 p.m." " John Rogers."

" To the Editor of the Times.

" Sir, — Nearly due south a meteor of a most remarkable and brilliant cha-
racter was observed this evening. The sky was clear overhead, but not
bright, and there arose from the horizon, to the height of about 10°, black
and jagged clouds. A falling star was said to have been first seen, and im-
mediately afterwards the writer had an uninterrupted view of the meteor,
which at first seemed to emerge from the dark clouds in a strictly vertical
direction, and stretched at least to a height of 30° from the horizon. In form
its first appearance was that of a wand, and it gradually tapered at the ends
and expanded in the middle, at which time its appearance was most brilliant,
its edges distinct and smooth ; and it was of such intense whiteness as to seem
an opake body, though bright as the new moon. As the expau.^ion at the
centre increased, the ends were bent in contrary directions, and Hogarth's
• line of beauty' was inscribed in the heavens on a gigantic scale.

" After a short time the meteor seemed to be broken at regular intervals.

A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 143

aiid it had then the appearance of dislocated vertebrae. At this time the
light was deep yellow, inclined to red, — probably a reflection from the sun,
not far below the horizon. Its edges at last lost their character, its light
became pale, and very gradually it vanished altogether without the slightest
noise of any kind, which was attentively listened for. From its first being
noticed to its final disappearance, a period of about ten minutes elapsed. Ail
the changes seemed to be produced slowly, and only in its sudden appearance
had it at all the character of a gaseous explosion.

" I remain. Sir, your obedient servant,
" Blackheath, Jan. 7, 4-50 p.m." "T. Kimber."

No. 3. — A paper " On the Horary Variation of Meteors," by G. C.
Bompas, Esq., was communicated to the Royal Astronomical Societv, and
of which an abstract appears in their Notices for March 1857, p. 147.

These researches relate to the law, and to the probable cause, of the liorary
variation in the number of meteors, established by the observations of
Coulvier-Gravier, Saigey, and others. (Recherches sur les Etoiles Filantes,
Paris, 1845, and Humboldt's Cosmos, iii. 440.)

From these various researches the following table gives a summary of the
number of meteors at difi'erent hours of the night: —

Hours p.M j 6 to 7

7 to 8

8 to 9 9 to 10

10tolllltol2

Mean No. of Meteors. . . 1 3-3

3-5

3-7 4

4-5

Hours A.M

12tol

lto2 2 to 3

3 to 4

4 to 5 5 to 6

Mean No. of Meteors...

5-8

6-4

7-1 7-8

8-2

It thus appears that from 6 p.m. through the night to 6 a.m., the number
of meteors seen regularly increases. But it is assumed that this is a fair
representation of the number actually occurring, or which would be seen, if
daylight permitted, in those hours of which no mention is made in the obser-
vations, a circumstance which may be open to question.

Again, if we estimate the numbers observed as coming from different
quarters of the heavens, designating the numbers which come from the
several points of the compass by those initials respectively, then the average
of the observations gives —

E. greater than 2 W.
N.=S. nearly,
butE. + W.=N. + S.

Coulvier-Gravier observes, " But for the cause which transfers from the
West to the East nearly one-half the number due to each of these directions,
there would come exactly the same numbers of shooting stars from the four
points of the compass."

He does not, however, appear to assign what that cause is.

As to the heights of meteors, it appears that the greatest heights which
have been ascertained bear but a very small proportion to the earth's radius.
The altitudes of the greatest number lie between 16 and 140 miles, though
some reach 200 or 400 miles. (See Herschel's Outlines, 904.)

The velocities of meteors have been variously assigned as from 18 to 36
miles per second ; but some have been 90 miles. (Herschel, ibid.)

Boguslawski considers that 5 out of 6 have a velocity about double that

144 REPORT — 1857.

of the earth in its orbit, which he talces as a fair average. (6toiIes Filantes,
p. 102.)

Mr. Bompas observes, that, as already seen, the observations indicate a
maximum of meteors at 6 A.yi., and a minimum at 6 p.m.; he also adverts
to the fact, that the part of the lieavens towards which the earth is moving
at any time is always 90° or 6'' from the direction of the sun. Thus at 6 a.m.
the observer's meridian is in the direction of the earth's motion, and at 6 p.m.
in the opposite. In other words, tiie law is this : that the greatest number of
meteors is encountered wiien the observer's meridian is in the direction of the
earth's 7notion, and the number diminishes thence regularly to 6 p.m., when
he looks the opposite way.

Combining these considerations the author explains the facts on a very
simple principle, expressed by a construction of which the essential points are
here represented.

m, nil, &c. being meteors eqtmlly distributed in space would converge to the
earth at C if at rest, equally on all sides.
But if the earth move in the direction

— * EC with a velocity half\\\a.i of the

average velocity of the meteors, they will
converge to the earth at E half-way from
the extremity to the centre; and thus "»>
two-thirds nearly will fall on the side
towards C, or would have an apparent
motion more or less opposed to that of
the earth, and diverging from the point
towards which the earth is moving.

The author gives this only as a general explanation of the principle. He
admits that the exact amount is more difficult to determine, and will chiefly
depend on the proper velocity of meteors, which seems at present not well
ascertained, and on their average direction, if ascertainable. It will also be
materially affected (as he points out) by the inclination of the earth's axis;
but these points remain for further investigation.

No. 4". — " On the Colours of Luminous Meteors," by M. A. Foey, Director
of the Physical and Meteorological Observatory at Havannah.
(From the Coraptes Eendus, vols, xliii. and xHv.)

The author observes, that, being much interested in the differences of
colour of luminous meteors, he has drawn up three tables, one of which
comprehends all the shooting stars and globes recorded as observed in China,
the second those observed in England (including some other countries), and
the third those at Paris. For tlie first table, he has made use of the well-
known catalogue by Edouard Biot * of the shooting stars and globes ob-
served in China during 2^ centuries, since the 7th century before Christ to
the middle of the 17th of our era. For the second table, he has had
recourse to catalogues published annually in England, from 184-1 to 1855,
by Prof. Baden Powell, in the Reports of the British Association for the
Advancement of Science. Lastly, for the third table, he has used the cata-
logue of shooting globes observed at Paris, from 1841 to 1853, by M. Coul-
vier-Gravier. Thus these three tables together comprise 2145 cases of
coloured shooting stars and globes observed in these several localities. With
respect to coloured shooting stars and globes, he has found nothing in the
catalogues of Messrs. Quetelet, Herrick, Chasles and Perry. In the three
tables is given the monthly distribution of the different colour of shooting
* Memoires des Sarauts Etrangers, vol. \. pp. 129 and 415.

A CATALOGUE OF OBSERVATIONS OP LUMINOUS METEORS. 145

stars and globes. This notice appears to the author important, both as
regards atmospherical optics, and the relative dependences which may exist
between particular colours and the appearances or modifications of other
meteorological phienomena, as well as the variations of time according to
the seasons.

(1) Colours of shooting stars and globes observed in China from the 7th
Century B.C. to the 17th a.d.

(Comptes Rendus, vol. xliii., Dec. 15, 1856.)

Colour.

1-5

3
<

1
O

Red

8
1

5
1

51
5

Whitish red

Yellowish red ...

525

Yellow

1
1

2
1

6
5

Whitish yellow...

Reddish yellow...

Blue

1
11

1
35

1
11

5
305

Whitish blue

Bluish white

Reddish blue

Blackish blue ...

White

Total ...

994

There is also one case of a bluish-red meteor, one of a bluish one, one
of blue and white, one of yellow and blue, two of M'hitish, and one of the
colour of a stork's feather. Total 1004; shooting stars and globes observed
in China in the space of 24 centuries.

In the above table, it appears that the primitive or simple colours are as
rare as the compound colours are numerous ; such as the yellowish red and
the whitish blue. This result is contrary to that which we obtain from the
table of observations made in England, where, out of a total of 1065 coloured
meteors, 326 are of a pure blue, 151 of a pure yellow, and 129 of a pure red.

It is an important fact, that in the 1004 meteors observed in China during
so long a period as 24 centuries, we do not find a single indication of a green
shooting star or globe. This circumstance is the more remarkable, since a
.scientific English observer, Dr. Buist, had already stated in 1849, that the
finest meteors resembling a star of the first magnitude, which are observed
in India, are generally of an orange, bluish, or greenish colour. In the
above table of the 24 centuries of observations in China, the colours orange
and greenish are entirely wanting. However, in the 1065 meteors observed
in England, there are 78 of a pure orange colour, and 33 cases of colours
compounded with orange. Then there are 5 meteors of a pure green, and 8
cases compounded with green. In the catalogue of M. Coulvier-Gravier,
of 76 coloured shooting globes, we observe 8 cases of green globes, and 4 of
globes which broke up into green-coloured fragments.

(2) Colours of shooting stars and globes observed in England from 1841
to 1855.

(From the Comptes Rendus, ibid. Dec. 29, 1856.)

In the observations made in China given in the preceding table, the author
1857. L

146

REPORT 1857.

observes one peculiarity as deserving of notice: — viz. that the number and
constancy of the same tints in the observations of one period or dynasty
differ from those whether in the preceding or succeeding period. The same,
he says, holds good with respect to the colours observed when meteors
explode, whether breaking up into fragments or not.

In making his inferences from the titles of observations in China as well
as of those in England and Paris, the author excludes those cases where the
body of the meteor and its train exhibit complementary tints, like some of
the double stars : this relation of tints he also finds in many cases of meteors
which break up mto fragments as compared with the original colour ; and in
meteors simultaneously accompanied by others, as well as in the coloured
light sometimes projected by them on the earth. He also observes that the
colour often changes in the course of a meteor through the atmosphere,
from tvhiie near the zenith to blue near the horizon. He also excludes from
his comparisons those meteors which have trains of the same colour witk the
body.

Colours of meteors observed in England from 1841 to 1855 (including
some in other parts of the world).

Coloiu-.

p.
<

Red

1
2
1
6
1
1
1
' 6

1
3

2
4
3

1
3

1
2
2

17
1

1
5
1

2
1
1
7

14
6
1
1

1
1

31
4
3

2
5

13
4
4

138

23
3

45
1
1
2

15
4

16
3

36
4

26
1
1

20
4

16
7

14
2

26
3
1

15
2
1

5
1

3
5
3

2
1

129

151

326

158

Reddish

Orange-red

Yellow

Blue

Bluish

Whitish blue

White

Whitish

Uncoloured

Total ...

1040

Besides the coloured shooting stars and globes indicated in the above table,
there are also the following : — reddish white, 3 cases in April, June, and
August ; orange-yellow, 2 cases in September and December ; slightly orange
tinged with white, 1 case in June; yellowish red, 1 case in December;
greenish white, 2 cases in November and December ; greenish blue, 1 case
in December; purple and green, 1 case in May; reddish blue, 2 cases in
April and November ; violet, 1 case in February ; pale rose-coloured, 1 case
in November ; purple, 2 cases in August and November ; yellow and violet,

1 case in September ; orange and prismatic, 1 case in November ; coloured,

2 cases in January and November; dull-coloured, 1 case in September;
brown, 1 case in September ; yellowish white, 1 case in July ; brilliant white
tinged with brown and silver, 1 case in August. Total 1065 coloured shoot-
ing stars and globes principally observed in England from 1840 to 1855.

We see in the above table that the simple or primitive colours most

A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 14/

predominate, and that the compound blue-coloured meteors are twice as
numerous as those of a pure yellow and red colour ; a result contrary to that
obtained from the preceding observations in China. We observe that the
meteors comprised in the tints belonging to the lower part of the spectrum,
from green to red, are in number 465 cases, while those comprised in the
tints of the upper part of the spectrum, from green to violet, embrace 401
cases. Now, in applying to the colouring of shooting stars and globes the
theory of M. Charles Doppler on the colour of single fixed stars, of the
double stars, and stars periodically variable, it would be necessary to con-
clude from the facts, that 64 coloured meteors have been moving from the
observer, from the moment of their appearance ; supposing, which is not
always the case, that the meteors have followed the right line which joins
them with the eye of the observer. However, on the other hand, meteors of
a pure blue, which are of an ascending tint and approach towards the observer,
are twice as numerous as those of a pure red and yellow, which belong to
the descending tints and recede from the observer. According to the
theory of M. Doppler on the colour of fixed stars, an object luminous by
itself, or from a borrowed light, increases in intensity as it approaches the
observer, while the colour passes, rapidly ascending from white to green, then
to blue, and at last to violet. By receding, the intensity diminishes in all
cases, and the white light passes successively to yellow, to orange, and at last
to red. Perhaps we ought still to take account, in the colour of fixed and
shooting stars, of the differences of perception and appreciation of luminosity
and colour, of diff'erent observers.

(3) Colours of shooting stars and globes observed at Paris from 1841 to
1843, with notices of trains, fragments, &c., differently coloured, observed
in China as well as in England.

(5rom the Comptes Rendus, xliv., Jan. 12, 1857.)

The author now proceeds to give a list of coloured shooting globes ob-
served at Paris fiom 1841 to 1853 by M. Coulvier-Gravier*. This skilful
observer has given with great precision as many as three or even four suc-
cessive shades assumed by meteors in their transit through the air. These
tints almost entirely follow the law deduced by M. Dopplerf, on the variation
of colour of a luminous point in motion. The greater part of the shooting
globes appear blue on approaching the horizon or the observer, after having
passed through all the tints corresponding to the upper part of the spectrum.
Some terminate with red, probably in receding from the observer. Besides
the law of M. Doppler, which may be applied to the colours of meteors, we
ought still to take account of the particular state of the atmosphere in a
twofold point of view, as regards electro-chemistry and the modificators of
meteorological agents.

Colours of globe meteors observed at Paris from 1841 to 1843.

January. — Bluish ; bluish towards the horizon, 2 cases,

February — Bluish ; bluish towards the horizon, 2 cases ; fragments yellow,
red, then greenish-yellow globe, and three fragments bluish towards the
horizon.

March. — Yellow-orange, then green ; bluish towards the horizon.

April. — Bluish towards the horizon ; white, orange-yellow, orange, then
blue-green.

May. — Bluish towards the horizon ; white, then bluish towards the hori.
zon ; clear yellow, then bluish ; clear yellow, then yellow-orange.

* Annales dc Chimie et de Physique, vol. xl. (January 1854).
t Repertoire d'Optique Moder'ne de M. I'Abbe Moigno, 3rd part, p. 1165-1203.

148 REPORT— 1857.

June. — A little bluish; bluish; reddish towards the horizon; yellow;
greenish towards the horizon.

July. — Bluish towards the horizon, 4 cases; very white, then bluish
towards the horizon ; yellow, green, blue, tlien red; fragments greenish yellow,
bluish, then reddish ; fragments clear yellow, then yellow-red.

August. — Reddish, 2 cases ; bluish ; bluish towards the horizon, 6 cases ;
whitish, then blue towards the horizon; whitish, then bluish ; very white;
broke itself into bluish fragments near the horizon.

September. — Bluish ; bluish towards the horizon, 4 cases ; copper-red,
then bluish towards the horizon ; yellow-red ; then bluish ; reddish, bluish,
then greenish blue, as also the fragments.

October. — Red towards the horizon ; bluish ; bluish, red, then greenish;
brilliant yellow, then yellow-red ; copper-red, white, then greenish at the
horizon ; yellow, bluish yellow, then reddish ; clear yellow, then copper-red.

November. — Bluish, 2 cases ; bluisli towards the horizon, 2 cases ; frag-
ments bluish ; yellow-orange towards the horizon ; fragments yellow, red,
greenish blue; yellow-white, yellow-orange, then greenish, very white, being
broken into fragments ; two only passed from white to the colour of red-hot
iron ; reddish,

December. — Reddish towards the horizon ; bluish towards the horizon, 2
cases ; bluish ; copper-yellow ; yellow, then bluish towards the horizon ;
whitish, then blood-red.

Total of coloured shooting globes, 76 cases.

Globes with trains differently coloured from the body.

July.— -Globe bluish towards the horizon, with a deep red train ; white,
then bluish, with a remarkable red-white train ; white, reddish, then bluish
towards the horizon with reddish train.

August. — Globe bluish towards the horizon with greenish train.

September. — Globe very brilliant white, with train reddish on the west
side, greenish in the middle, and whitish on the east side.

Total of globes with different-coloured trains, 5 cases.

Globes with trains similarly coloured.

July. — Greenish train.

August. — Bluish trains, 3 cases; greenish train.

September. — Clear yellow train, then deep red.

October. — Very white train, then at the end of its duration of a less
splendid whiteness.

November. — Reddish trains, then greenish, 2 cases.

December. — Reddish train, bluish, then greenish.

Total of globes with uniquely-coloured trains, 10 cases.

The author states that these meteors correspond to the period of the ob-
servations made in China and in England described in the preceding notices.

Changes of colour.

In China. — April: colour of fire, then white. December: red, then white.

In England. — February : green, red, then violet ; globe green, red, then
violet. April : red, then blue, 2 cases, July : brilliant orange-red, almost
white, then very brilliant red. August: reddish, then brilliant blue. Septem-
ber : straw colour, then purple. November : orange, then orange-yellow,
pale orange, and after 15° of transit, bluish.

Shooting stars accompanied by coloured tails of the same tints.
In China. — November : red star, divided itself into 5 stars, of which the
first had a red tail.

A CATALOGUE OF OBSERVATIONS OP LUMINOUS METEORS. 149

lu England. — August : blue star, bluish train ; stars accompanied by trains
differently coloured.

In China. — June : a star (witli a train) 200° in length ; bad the front
part black, the termination red, and the middle white.

In England. — February : a brilliant red star surrounded with the tints of
the rainbow, with a bluish train. March : red star, train blue. April : star
surrounded by a rich colour of purple, then blue, orange, and clear yellow ;
considerable train, clear yellow. July : cream-colourecl, train purplish red
in the centre and greenish blue at the latter part; blue star, train of pale
red sparks. August : bluish white, train red. September : orange, train
red ; brilliant white, reddish train ; blue, then brilliant I'ed, throwing out
sparks leaving a blue nraik, visible during several seconds.

Shooting stars with similarly coloured trains.

In China. — Trains yellowish red: June, July, August, and November, 2
cases each ; October and September, 1 case. Yellow : January, 1 case.
Reddish yellow : May and October, 1 case. Whitish blue : August and
October, 2 cases ; February, April, May, November, and December, 1 case,
lleddish blue : June, 1 case. Blue and yellow : October, 1 case.

In England. — Red : July, 1 case. Reddish : August, I case. Blue :
February, April, and December, 1 case each ; August, 2 cases. Bluish :
November, 1 case. Of different colours: February, 1 case. With train of
pale brilliant sparks : June, 1 case.

Change of colour of stars when they break into fragments.

In China the star divided itself into 1 blue and 2 red stars ; at the moment
when a globe of fire fell, a flame appeared, and a score of lit.tle red stars
spouted out of it. This case, marked by M. Abel Resumat, is not noticed
by M. Biot.

In England. — March : green star, fragments red ; white star, gave greenish
and red flashes in exploding. April : bluish red, fragments prismatic ; star
blue at the moment of explosion. July : yellow or pale orange star, three
dull red fragments. October: brilliant globe separated into fragments M'ith
several colours.

Shooting stars accompanied by others differently coloured.

In China. — Winter and October : one red, the other white, 2 case?. No-
vember : one yellow, the other red.'

In England. — July : fine orange-red globe, followed by a multitude of
little blue globes, afterwards purple.

Stars with reflexions of a different colour.
In China. — July : blue star threw out a reddish light which illuminated the
earth. December : reddish-blue star, ibid. ; bluish light.

Various other effects.
In China. — October : red star, whose tail changed itself into a bluish-
white vapour. May : a train dispersed itself slowly and became a greenish-
black cloud. A tail divided itself into little whitish-blue stars.

No. 5. — "A Memoir on Meteorites : and Description of five new Meteoric
Irons," &c., from the American Journal of Science, May 1855, vol. xix., by
J. Lawrance Smith, M.D., Professor of Chemistry in the University of Louis-
ville, U.S.

In this communication the author describes in detail specimens of meteor-
ites found in North America — 2 in Tennessee and 3 in Mexico. Figures
are given representing their general appearance, and chemical analyses of

150 REPORT — 1857.

their composition. It does not appear that any of them were seen to Tall, or
known to have been accompanied by any meteoric appearances, except in
one instance, in which a very vague tradition of this kind is mentioned.
He notices their irregular and fragmentary form and crystalline structure,
wiiicii he conceives evince the agency of intense heat, and show tiem to be
fragments of larger bodies.

The presence of metallic iron in so large a proportion as that in which it
is found with respect to the other ingredients, he conceives to indicate a
proof of tlie absence of oxygen (in its gaseous state, or in that of water) in
the body from which the fragments are derived.

The stony portions of the meteorites resemble exactly volcanic products;
in which the presence of iron also furnishes a point of analogj^ He also
comments on the usual presence of phosphorus, which is derived from the
nuneral Schreibersite, constantly occurring in these masses. The metallic
nickel, cobalt and phosphorus show equally the absence of oxygen. Carbon
is often found, contrary to the assertion of some observers.

The Sclircibcrsite, which is observed as almost constantly present, the
author remarks, is wholly ^jec?i//aj' to meteorites ■, no natural |)liosphuret of
iron, nickel, or other metal being found as a terrestrial mineral.

Hence he considers meteorites as having a common origin exterior to the
earth, which he believes to be from the lunar volcanoes.

A^ialyses.
No. 1. Meteorite from Tazewell County, Tennessee.

Coirespondlng to

Iron 83-02 Nickeliferous iron 9S-97

Nickel 14.-62 Schreibersite . . 1'03

Cobalt -5

Copper ....... '06

Phosphorus "19

Chlorine -02

Sulphur -08

Silica -81.

Magnesia •24

99-57 100-00

In which Nickeliferous iron contains —

Iron 82-59

Nickel .... 17-4.1

100-00
Schreibersite —

Phosphorus . . . 15-47

Nickel 29-17

Iron 55-36

100-00
No. 2. Meteorite from Campbell County, Tennessee.

Iron 97-54

Nickel 0-25

Cobalt -06

Copper .... (a trace)
Carbon .... 1-5
Phosphorus ... -12
Silica ...... 1-05

100-52

A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS.
No. 3. Meteorite from Coabuila, Mexico.

151

No. 4-.

Iron . .
Cobalt . .
Nickel . .
Copper
Pliosphorus

Iron . . .

Nickel . . .

Cobalt . . .

Copper . .

Phosphorus .
Chromic oxide

Magnesia . .

Silica . . •

Alumina . .

95-82

•35

3-18

(a trace)

■24-

Corresponding to

Nickeliferous iron 98*45

Schreibersite . . 1*55

99-59

1 0000

on, Mexico.

85-54

Nickeliferous

iron 93^81

8-55

Chromic iron

. . •*!

•61

Schreibersite

. . -84

•03

Olivine . .

, . 5-06

•12

•21

2-04

3-02

'a trace)

100-12

No. 5. From Chihuahua, Mexico. Not analysed.

The other details as to the structure, form, physical characters, &c., of
these meteorites are not susceptible of abridgement. But they all present
evident marks of fusion or igneous action ; while the author's mierence as to
the fragmentary nature seems somewhat doubtful.

« Experiments on Light, referring to the apparent magnitudes
of Luminous Meteors."
(Prof. L. Smith's Memoir, p. 30.)
In the author's experiments three solid bodies in a state of vigorous in-
candescence were used: 1st, charcoal points transmitting electricity; 2nd,
lime heated by the oxy-hydrogen blowpipe ; 3rd, steel in a state of mcan-
descence in a stream of oxygen gas. They were observed on a clear night
at different distances; and the body of light (without the bordermg rays)
compared with the disk of the moon, then nearly full, at 45° above the hori-
zon. The results are given in the following table :—

Actual
diameter.

Apparent

diameter

at 100 yards.

Apparent
diameter
at \ mile.

Apparent
diameter
at i mile.

•3 inch
•4 inch
•2 inch

^ diam. of 1>
^ diam. of J
i diam. of 5

3 times T)
2 do.
1 do.

3i times 3)
2 do.
1 do.

Incandescent steel globule

If then, the author argues, the apparent diameter of a luminous meteor at
a o-iven distance is to be accepted as a guide for calculating the real size of
these bodies, they would be (according to the table given by Prof. Olmsted
(Am. Journ. of Science, vol. xxvi. p. 155) for estimating the diameters of
meteors in comparison with the moon),

Charcoal points 80 feet diameter.

Lime light 50 „ „

Incandescent steel globule 25 „ »

152 REPORT — 1857.

A large meteor observed at Wilton was estimated bj' Mr. E. C. Herrick
(Am. Journ. of Science, vol. xxxvii. p. ISO) to be about 150 feet in diameter.
It appeared to increase gradually in size until just before the explosion, when
it was at its largest apparent magnitude of i the moon's disk : exploded at
25° or 30° altitude with a heavy report, which was heard 30 seconds after
the explosion was seen. One or more of the observers saw fragments descend
to the ground. When it exploded it was three or four miles from the surface
of the earth ; immediately after the explosion it was no longer visible. The
large size of the body is inferred from the fact of its appearing A of the moon's
diameter about six miles' distance.

After the experiments above recorded, the uncertainty of suclj a con-
clusion is evident. A body in a state of incandescence might exhibit the
apparent diameter of the Wilton meteor at six miles' distance and not be
more than a few mches or afoot in actual size, according to the intensity of
the incandescence.

It ought to be added that Mr. Herrick (in the paper referred to) expressly
allows for some uncertainty of this kind.

The author furtlier instances another large meteor observed at Weston,
and estimated by the same kind of calculation at a mile and a half in dia-
meter', on the principle of these experiments it need not have been more than
one or two feet.

No. 6. — Extract of a Notice of a Shooting Star, by Prof. C. Piazzi Smyth.
From the Proceedings of the Royal Society of Edinburgh, No. 34', Feb. 5,
1849.

This instance, the rare one of an ascending shooting star, was furnished
by Captain W. S. Jacob, Bombay Engineers ; and he having given the place
where the body first appeared, that where it disappeared, and the time, with
great exactness, it was considered by the author to afford a good case for
testing the theory of Sir J. Lubbock.

Allowing that many phsenomena of an atmospheric kind may have been
confounded with true shooting stars, still, the author observes, a great pro-
portion are undoubtedly of a cosmical nature, and belong properly to astro-
nomy ; and these may be divided into two classes of small bodies. 1st, Those
which are circulating round the sun as a primary ; and, 2ndly, Those which
are revolving round the earth as such. The first we may occasionally sec
when passing near them in their orbits, but are not likely to come within
sight of the same again, unless, indeed, they approach so near the earth as
to gravitate towards it instead of the sun, and so become satellites or shoot-
ing stars of the second class.

Sir J. Lubbock's theory is, that the shooting stars shine by reflected light,
and are extinguished by entering the earth's shadow ; and he has given for-
mulse on this supposition for computing the distance of the body from tiie
spectator by noting the place in the sky where, and the time when, the ex-
tinction occurs.

These formulai have been rendered more convenient for computation by
Mr. Archibald Smith, Phil. Mag., March ISIQ; and, computed according
to them. Captain Jacob's observation gives, for the distance of the body from
the observer, 1721 miles: and that entry into the earth's shadow was the
true cause of the disappearance, is borne out by the fact that the direction
of motion was toicards the axis of the earth's shadow. And, on account of
the extremely small distance of the body, its change of place during flight
would sufficiently account for its gradually appearing in the lower part of
the sky when coTuing out of conjunction, increasing in brilliancy during its

A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 153

flight (reaching, at its maximum, the brightness of Venus), and then slowly-
vanishing as it entered first the penumbra and then the umbra of the earth's
sliadovv, in a slanting direction ; and lastly, the body can hardly fail of being
a satellite, as its distance is so much less than that of a shooting star, which
M. Petit of Toulouse has pretty well identified as revolving about the earth
in 3'' 20'", or at about 3000 miles from the surface.

No. 7. — Letter from Dr. Forster, Times, August 17, liS57.
" Extraordinary Coloured Meteors.
" To the Editor of the Times.

" Sir, — I venture once more to trespass on your valuable time and paper
to communicate the following extraordinary phsenomena to the public, since,
if similar meteors should have been seen in different latitudes, such registers
may tend to useful results, as well as to solve the long-disputed question of
the cause of meteors. Monday, being the 10th of August, astronomers were
all on the look-out for the periodical falling stars. I began my watch on the
9th, when some few brilliant examples occurred. On the 10th they were
more numerous, as also on the lltli ; but on the 12th, that is, last night, they
assumed very unusual forms and colours. Being at Ostend I returned late
to a good position above the sea, and watched them great part of the night.
Many hundreds fell in various directions, but particularly towards S.W. and
W., not N.W. as usual. They did not in general move fast and leave the
white trains behind them, as is usual, but descended slowly with a bi'ight
yellow flame ; others were splendidly crimson, and some bright blue and
purple. This fact is very curious, as favouring the hypothesis of ignited
gases, adopted by M. De Luc of Geneva ; and it would be interesting to
ascertain whether this coloration of the meteors has been observed in other
places far from the influence of the sea. I have ascertained that during the
whole of this month meteors have been numerous all along the Rhine and
in Germany. Such numbers have not fallen since the 10th of August, 1811,
nor have we any record of such a quantity as on the present occasion, extend-
ing over four days consecutively, and exhibiting such very brilliant and
diversified tints of light.

" Collaterally with these meteors the following phaenomena should be
noticed, proving the highly electric state of the air. In the storm which
raged in Holland on the 5th of July, the hailstones were larger than pigeons'
eggs, and broke nearly all the windows in Arnheim. The same occurred at
Spa on the 5th of August, when every pane of glass exposed to the hail was
beaten to pieces. All the electrical instruments indicate a high positive
charge. A tromhe or waterspout was witnessed by me in the distance on the
11th. The showers have not cooled the air, as they usually do. A new
weathercock with several horizontal and vertical fans and wheels, which I
have put up in order to test the wind, shows that the varying gales have not
blown horizontally, but slanting, or in undulations, and the thermometer has
risen again to Indian heat. All these circumstances point to some cause of
the changes of temperature not at all depending on the place of the sun, and
which future observations may more fully develope, if astronomers will accu-
rately observe them in various parts of the world. We may possibly derive
therefrom what has long been a desideratum in science — a table of true indi-
cations of the changes of weather.

"I submit all or any of these observations to your better judgment foi*
insertion, and have the honour to remain,

" Your obedient servant,

" Brussels, Aug, 13." " T. FoKSXEB."

154 REPORT — 1857.

On the Adaptation of Suspension Bridges to sustain the passage of
Raihvay Trains. By C. Vignoles, CE., P.R.S.

The following observations are submitted to the British Association as ap-
pearing to possess sufficient interest for discussion, from tlie circumstance
of differences of opinion amongst civil engineers having thrown doubt upon
the feasibility of applying the principle of suspension to the purpose of
railway transit.

But the practical success in America of this principle on a large scale
may be quoted as an example in its favour, and is a striking set-off against
the failure in this country, which occurred upwards of five-and-twenty years
ago, under circumstances which have militated against any attempt to
repeat the experiment. Some debate on this question took place in the
Institution of Civil Engineers of London, at a meeting last spring, from which
many engineers were absent ; and as the subject was on the intended appli-
cation of a suspension bridge to carry a railway across a navigable river
in the North of Ireland, a further inquiry may not be wholly uninteresting
at a meeting held in the Irish capital, where many engineers and other
practical and scientific men may be present, and who, not having had a pre-
vious opportunity of joining in the inquiry, may be disposed to propound
their opinions.

A further reason for bringing the subject forward, and one which will
naturally create a more extended interest in the discussion, is, that the recent
events in India cannot fail to produce, among the remedial measures to be
applied, a general and a more rapid extension of railways, even to the most
remote parts of our Asiatic dominions, and in the course of this extension
many rivers of great breadth must be bridged.

It is desirable to condense the matter into a few salient and important
points, and it may be generally assumed that the whole inquiry is comprised
under the following heads, viz —

1st. The maximum load to pass the bridge.

2nd. The velocity of the train. And these being given, there are then
to be determined —

3rd. The strength of the chains.

4th. The rigidity of the platform ; which having been duly provided for,
the additional considerations will be as to —

5th. Prevention of undulation, vibration, and oscillation.

1st. Maximum load to pass the Bridge. — This load may be taken as equal
to the weight of the locomotive engine and tender, and of as many carriages
as will extend on a single line of railway along the platform of one wiiole
opening between the suspension piers ; to the consideration of such a single
line the inquiry may be confined.

The length of the train, and consequently the weight on the platform of
the bridge, will therefore be in proportion to the span or opening. The
weight of an engine and tender may be taken, speaking roundly, at one ton
per lineal foot of the railway over which they pass, and the weight of loaded
carriages at half a ton per lineal foot. For a bridge with a clear opening
of ■iOO feet, the weight of a train extending the whole length of the platform
would average little more than half a ton per lineal foot ; but as it has been
generally customary to compute the insistent load on railway bridges at one
ton per lineal foot of single line, this weight will be the one assumed.

2nd. Velocity of the Train It would be opening too wide a field upon

the present occasion to inquire into or to attempt to solve the complex
ppoblem of what additional gravitating eflfect is produced upon railway

ON RAILWAY SUSPENSION BRIDGES. 155

Btrvictures by the percussive action of trains moving at different velocities.
It must be admitted, in limine, that we have not at present sufficient justi-
lication to recommend that railway trains should be allowed to pass over
the platforms of suspension bridges except at moderate speed ; nor, as a
matter of every- day practice, should the locomotive engine be allowed to act,
except slowly, while passing over such a bridge.

With these limitations of speed, and of action of the driving-wheels, of the
locomotive, the resistance to weight which must be provided for in a railway
suspension bridge, need not be more than to meet the maximum load above
assumed, namely, one ton per lineal foot of the platform, in addition to the
weight of the platform itself, of the chains and their accessories, and of the
suspension-rods, all of which are matters of strict calculation dependent
upon the span.

3rd. Strength of the Chains. — The mathematical theory of suspension
bridges has been so fully entered into by the best foreign and English
authors, more particularly by the French, amongst whom M. Navier is the
most distinguished, that little need be said now, except to give the best
admitted ybrwjwte for calculation. There is so little practical difference in
the form of the curve which the chain of a suspension bridge assumes when
freely suspended without a load, and when fully loaded, that is, the difference
in form between a catenary and a parabola, that the most esteemed writers
on this subject have, by common consent, agreed to consider the curve of
the chain of such a bridge to be a parabola rather then a catenary, on
account of the very much greater simplicity of the mathematical calculations.
Perhaps it may not be irrelevant to enter very briefly into this.

When a heavy chain, freely suspended from two fixed points, is acted on
by the force of gravity only, the foi'm of curve which it assumes is called
the cateiiary. If, however, the chain be loaded with weights, distributed in
such a manner that for each unit of length {ex. gr. for each foot), measured
along the horizontal tangent at the lowest point of the curve, the weights
should be equal to each other, the effect of such a distribution is to cause
the curve of the chain to approach in form to another curve called the
parabola. If the disti'ibuted weights become so great that the weight of
the chain may be neglected in comparison with them, the form which the
curve assumes in this case is accurately that of the parabola.

In most, if not all ordinary cases, the weight of the chain is, however,
never inconsiderable in relation to that of the platform and of the testing-
load together; and consequently the form of the chain is never exactly
that of the parabola, though it approaches more nearly to this curve than to
the catenary ; so near, that for all practical purposes it may be considered
to have attained that form, viz. of the parabola.

In the case where the curve of the principal openings has a chord, say
for instance of 424 feet, and a versed sine of 29^ feet, or the proportion
between the chord and versed sine of between 14 and 15 to 1, the two
curves (catenary and parabola) passing through the points determined by
these conditions approach so near to each other in form, that their greatest
distance, measured in a vertical line intersecting both of them, is only 0-6
(3)5th) of an inch.

4th. The Rigidity of the Platform. — This is perhaps the most important
point of the subject, and has probably hitherto been least considered, and,
strictly speaking, the novelty of the inquiry is confined to this alone. In
all the earlier examples of suspension bridges, the object of the engineer
appears to have been to construct the jilatform as light as possible. In
many instances this was carried to a most dangerous extent ; even in the

156 REPORT — 1857.

case of the great suspension bridge over the Menai Straits, tiie platform has
been repeatedly damaged by storms of wind, which twisted it as if made of
pasteboard. The late Mr. Rendel was the first engineer wlio perceived the
mistake which had been hitherto committed in this resjject. When the
suspension bridge at Montrose had been destroyed about twelve or fourteen
years ago, lie reconstructed the platform and stiffened it by bracings
so effectually that it has since remained uninjured. This principle of
strengthening the suspended platform was carried out to a greater extent by
the writer of these observations at the bridge over the Dnieper at Kieff, in
llussia, and the successful resistance of this well-braced platform to the
effect of hurricane winds, and to vibration, oscillation, and undulation, has
been very remarkable.

The desideratum is, that the platform of a suspension bridge intended to
sustain a railway train should be made as stiff as possible; and the first
natural consideration is, how is this stiffness or rigidity to be best obtained ?
The mode in which this has been effected in the great Niagara sus]Densiou
bridge, is on the system of a deep trellis frame, — in fact, a timber tube, the
sides of which are of lattice-work, the railway passing on the top.

It is generally understood, and a print published at the time seems to
confirm this, that the oiiginal iutention of Mr. Stephenson was to have
added suspension chains for supporting the tubular platform of the Britannia
Bridge, although that intention was subsequently abandoned, and the tubes
made sufficiently stiff not to require their assistance.

Another great point in this discussion seems to relate to the adapting of
suspension bridges for passing railway trains in localities and under circum-
stances where fixed bridges could not be erected except at an unjustifiable
expense, or not at all, from the onerous conditions naturally or judicially
imposed.

According to the locality, timber or iron may be best suited for con-
structing the jilatform, the platform being made as deep and as stiff as
possible, and thus becoming a girder held up by suspension chains ; and the
stiffness being augmented by the increased depth of framing, it will be
advisable that the rails should be attached thereto as high up as practicable.
But the weight of the platform must be kept within reasonable limits, to
avoid too great an increase in the sectional area and weight of the chains,
which would otherwise become necessary ; and further i)recautions have to
be taken as regards the distribution of the load on the platform, and to guard
against oscillation and undulation, for all which due consideration must be
given as to the proper breadth of the platform.

The weight of the platform of an ordinary suspension bridge was formerly
scarcely more than 36 lbs. to the square foot of the area of the whole platform ;
the present weight of the Menai Bridge platform, after having been strength-
ened, is about 58^ lbs. to the square foot ; the weight of the platform of the
Montrose Bridge, as reconstructed by Mr. Rendel, is 41-^ lbs. to the square
foot; and the weight of the platform of the Kieff Bridge is 49i- lbs. to tlie
square foot, including the two footpaths which are corbelled out from the
main part of the framing ; but the weight of that part of the platform
between the chains, and which sustains the roadway, is about 60 lbs. to tiie
square foot. The ordinary test-load for a suspension bridge was about
62 lbs. to the square foot; the proof-load put upon the Kieff Bridge was
really about 84 lbs, to the square foot.

Now a railway-load passing over a suspension bridge being taken at one
ton per foot forward, the weight per square foot upon the platform will
vary as the breadth of the bridge : if the bridge be 20 feet, the passing load

ON RAILWAY SUSPENSION BRIDGES. 157

will be one cwt., or 112 lbs. to the square foot; if 27 feet wide, it will be
83 lbs. ; and if 30 feet wide, 75 lbs, to the square foot. The Kieff Bridge
is 52^ feet wide, and therefore a passing load of one ton per lineal foot
spread over this area, is only 43 lbs. per square foot, whereas the test-load
was 84 lbs. to the square foot, which is about double what would have been
the weight of the heaviest railway train ; or taking 42 feet, exclusive of
footpaths, the railway-load would have been 52 lbs. per square foot, or less
than two-thirds of tlie test-load, which, it may be remarked, lias remained
on forty-eight hours without the platform showing any deflection visible to
the eye, although some deflection really took place.

It appears therefore most undoubted, that suspension bridges of modern
construction may be perfectly adapted to sustain the passage of railway
trains, and that the chief consideration has to be given to tiie character and
dimensions of the platform ; and as a general rule 1 would suggest, that not-
Avithstanding the advantage to be gained by depth, this should not be carried
too far, more especially if the lattice-girder system be adopted, as it presents
too much surface to the wind, and thus induces increased lateral oscillation.
Also, that the breadth of the platform for a single line should not be less
than 25 feet, in order to spread the load and reduce the insistent weight per
square foot of platform.

It might be interesting to establish a comparison of the expense of various
descriptions of platform, but this wovxld lead too much into detail, and the
materials for this purpose have yet to be collected. Still, as a contribution,
and by way of illustration, the present opportunity may be taken to state
the cost of the platform of the Kieff Bridge, already mentioned as so re-
markably stiff, and capable of sustaining the transit of a railway train.

In a length of 12 feet of the whole breadth of 52^ feet of the platform,
the quantity of materials was as follows : —

Timber, 600 cubic feet £150

Iron, 30 cwt 30

Total. ... £180

for a length of 12 feet, or £15 per lineal foot of the whole breadth of the
platform, which is something less than six shillings per square foot of a
platform such as that at Kieff (of which the drawings were shown).

5th. Prevention of Undulation, S^c. — The effects upon a suspension bridge
of passing loads and of strong winds, cause vibration, oscillation, and un-
dulation. Of these, the undulation is considered to be the most serious.
The vibration may be assumed as produced by what may be called the per-
cussive action of the passing load, and when the platform is not sufficiently
stiff, and the passing action is irregular over the surface, as, for instance, by
the impetuous rush of a drove of cattle, or of a multitude of people, oscil-
lation and undulation ensue ; the first producing a lateral swing of the
platform, the latter arising from the bending of the platform in its longi-
tudinal direction.

The remedy for vibration and oscillation is provided by a sufficiency of
stiffness, not to say absolute rigidity, in the platform, which will also, to a
certain extent, counteract the propagation of the undulation, but not entirely.

The experience, however, of four years on the Kieff Bridge, has proved
that the mode adopted in that construction of disposing the suspension rods
alternately (in the manner shown on the exhibited drawings) has completely
counteracted the undulation ; and many very heavily-laden carriages together,
—artillery, cavalry, and large bodies of troops, — have been continually

158 REPORT — 1857.

passed over the platform of this bridge without the slightest undulatory or
oscillating motion having been produced.

We are hence enabled to infer, without looking to improvements in detail,
which will naturally be introduced, that a platform so constructed and so
suspended as the one at Kieff', is capable of sustaining the passage of railway
trains at a moderate velocity, and within a reasonable cost of construction ;
and taking the example of the wire bridge in America, and of this wrought-
iron chain bridge in Russia, it may be legitimately concluded, that the
adajjting of suspension bridges to railway purposes is perfectly practicable.

The extent to which tiiis application may be made can scarcely be defined
a priori, but the writer ventures, from his own experience, to state his
opinion, that where the span of the required bridge must exceed 300 feet,
the suspension principle should be adopted for the sake of economy.

It would be extending these obsei-vations far beyond the bounds assigned
to such meetings as these, to go further into the details, and therefore, how-
ever tempting the opportunity, we must abstain from entering upon the
subject of the modern mode of obtaining foundations and forming river-
piers, which mode would greatly influence any selection between a fixed or
a suspension bridge. Neither must we even touch upon the choice between
the wire-rope and the wrought-iron plate chain, as the means of suspending
the platform, though it is obvious that where the span becomes very large,
the superior lightness of the wire is a great inducement to decide the pre-
ference for it over the wrought iron.

The proportion between the chord and the vers^ed sine of the curve of the
suspending chain is another point of the highest interest, as i-elating to the
questions of more or less oscillation, and of increase or decrease in the
amount of tension, as this proportion varies.

It is sufficient to have brought the general subject of the practicability of
adapting suspension bridges to sustain the passage of railway trains before
the Mechanical Section of the British Association ; and it is to be hoped
that this opportunity will not pass away without engineers and the other
scientific and practical men now assembled, bringing their judgement and
experience to an examination of this very important question.

On Electro-Chemistnj. By Professor W. A. Miller, M.D., F.R.S.

In reporting upon the recent progress of electro-chemical research, the
author stated that the inquiries made of late years in the field of electro-
chemistry were characterized rather by modifications of the laws previously
admitted, than by any fundamental additions to the existing stock of know-
ledge upon the subject.

Faraday's observations on the exceptional conducting power of solid sul-
phide of silver, and one or two other substances wiien heated, had been
traced, by the researches of Beetz and Hittorf, to tiue electrolytic decompo-
sition, which is rendered possible by the somewhat viscous condition pro-
duced by heating these bodies. The true electrolytic nature of the decompo-
sition was proved, first by the rise in conducting power, occasioned by rise
of temperature (whereas in metals the effect is exactly the reverse) ; and
secondly by the effects of polarization observed upon the electrodes between
which such bodies are placed.

Allusion was then made to the experiments by Bunsen on the insulation

THERMOMETRICAL OBSERVATIONS AT POINT BARROW. 159

of metallic bodies by electricity ; in the course of which he had shown that
in many instances, as in the decomposition of a solution of sesquichloride of
chromium, the deposit upon the negative electrode could be made to assume
the metallic form by reducing the surface of this plate to dimensions consi-
derably smaller than those of the positive electrode, a result probably owing
in part to the secondary decomposition produced in the limited portion of
liquid around the wire, whereby the sesquichloride was reduced to the proto-
chloride of chromium and subsequently the metal itself was deposited. This
view was rendered probable by observing the effects obtained during the
electrolysis of sesquichloride of iron, in which these successive steps could be
distinctly observed. In cases in which, like the chloride of manganese, the
compound was already in the condition of protochloride, it was unimportant
whether or not the negative electrode presented a smaller area than the
positive electrode. Attention was called to the fact pointed out by Faraday
of the non-existence of more than one electrolyte in a multiple series ; thus
in the case of the two chlorides of tin, the fused protochloride is an electro-
lyte, but the bichloride, although a liquid at ordinary temperatures, is not an
electrolyte if anhydrous. Yet the bichloride when dissolved in Water, itself
also not an electrolyte, conducts freely; and a similar result is obtained in
other analogous cases.

Referring to the decomposition of salts in solution, the bearings of elec-
trolysis upon Davy's binary theory of the composition of salts were briefly
alluded to, and some of the difficulties attending the adoption of this tlieory
in the case of the subsalts were mentioned; these facts, taken in conjunction
with those already alluded to in the case of the bichloride of tin, leading the
author rather to the view that a salt is to be regarded as a whole, susceptible
of decomposition in various modes (just as a crystal may admit of cleavage
in two or three different directions according to the method in which the
force is applied), and therefore admitting of representation under two or three
different rational formulae, each of which may, under particular circumstances,
be advantageously employed.

Results of Thermometrical Observations made at the ' Plover's ' Winter-
ing-place, Point Barrow, latitude 71° 21' N., long. 156° 17' W.,
in 1852-54. By John Simpson, Esq., R.N., F.R.C.S., F.R.G.S.,
Surgeon of H.M.S. 'Plover.'

[With a Plate.]
At p. 331 of the ninth volume of the 'Royal Geographical Society's Journal,'
1839, Sir J. Richardson, in reference to Sir David Brewster's discussions of
an hourly register of the temperature at Leith Fort, says: —

" Convinced of the importance of investigating the phaenomena of diurnal
temperature in various latitudes, I have thought that a discussion of the
thermometrical observations made on Sir E. Parry's several voyages would
be a service rendered to science." Following the lead thus indicated, it has
appeared to me that the results of the observations made at Point Barrow
would be a valuable though small addition to those given by Sir J. Richard-
son, to whose form of tables 1 have adhered, only making additions, as the
means of the decades or three divisions of each month, where I thought this
could be done without marring the original purpose of the table.

Thn observations now offered were made with great accuracy, and possess
the advantage of having been registered every hour at one spot from the 3rd
of September 1852 to the 7th of August 1853, and for a few days before

160 REPORT — 1857.

and after these dates in the neighbourhood, making a complete year, less 21
days. Again, in precisely the same locality, from the 7th of September 1853
to the 19th of July 1851', to which have been added the six first days of Sep-
tember, and one day, the 20th of July, during which the ship was in tVe im-
mediate neighbourhood, making a second complete year, less 42 days. The
ship returned again to the same spot on the 27th of August 1854, and
remained four whole days, for which the hourly register gave a mean tempe-
rature of 39°'448, serving as a fair guide in estimating the temperature of the
last eleven days of August, which accordingly has been assumed to be 39°'448,
thus reducing the interval in the last year to thirty-one days.

To fill up the interval of twenty-one days' absence in 1853, the mean tem-
perature of these has been assumed at something between the decades last
preceding and first following that period. Thus, the first ten days of August
giving a mean of 3B°441, and the first ten of September giving a mean of
32°*146, the second and third decades of August have been assumed as 37°
and 35° respectively. In the same manner, to fill up the interval of thirty-one
days in the summer of 1854, the second decade of July giving a mean of
3S°"287, the mean of the last eleven days is assumed to be 39°. The last
eleven days of August having been calculated to give a mean of 39°"448, as
already stated, the intervening two decades can, without much risk of error,
be assumed at 40°.

The thermometers used throughout the period of observation were made
by Adie and Co. of Edinburgh, in February 1848 ; and having been returned
to the Hydrographer's Office, Admiralty, in April 1855, I have no doubt
some of them could be obtained there, if required for comparison with any
acknowledged standard. There were six of them, numbered from 10 to
15, and remarkably alike in appearance and size. To each was attached a
graduated glass scale, on which, besides the number, was cut the maker's
name. On application at Messrs. Adie's establishment, Edinburgh, I ob-
tained the following information as to their mode of construction : —

" For spirit thermometers constructed February 1 848, —
Before use, colourless alcohol, sp. gr. '79465.
Before use, coloured „ ,, '79537.

After use, „ „ „ -79541.

"Points fixed from standard mercury thermometer 62° and 32°. Scale then
run down to —56°."

They were on several occasions exposed together to different degrees of
cold, and were very uniform in their indications down to the lowest tempera-
tures registered. Subjoined is a table of thermometers compared (p. 161).

It appears from this Table that five of the instruments by Adie indicated
a mean of 35°"5 nearly as the freezing-point of mercury, whilst that by Cox
of Dcvonport stood at —41°, and that by Pastorelli at —48°.

Pastorelli, No. 419, had an error of — 1°-5 at the freezing-point of water;
and at our lowest temperature its indications were 13° below Adie's.

Cox's thermometer, No. 1, had an error of 2° at the freezing-point of water,
but at lower temperatures corresponded much more nearly with Adie's. Like
Pastorelli's, however, it had the disadvantage of a heavy box-wood scale, pre-
venting it from indicating rapid changes of temperature, which the glass scales
of Adie's instruments permitted. Both these were rejected for ordinary use.

The mercurial thermometer used as a standard was Pastorelli, No. 406.
This also had a heavy box-wood scale, but I believe was otherwise a good in-
strument, and, if sufficiently long exposed to a uniform temperature, could
be trusted as low as 32° below the zero of Fahrenheit. At that point the

THERMOMBTRICAL OBSERVATIONS AT POINT BARROW. 161

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162 REPORT — 1857.

tube seemed to become irregular; and on solidifying, the mercury sank com-
pletely into the bulb.

A curious circumstance happened with this instrument on one occasion.
Believing the quicksilver in it to be pure, I placed it beside one of Adie's, ex-
posed to the air at a temperature about the freezing-point of mercury, for the
purpose of ascertaining the exact degree indicated by Adie's at the moment
of solidifying. Whilst attentively watching it, to my surprise the column of
mercury suddenly shot up the stem to — 4°, then slowly but steadily de-
scended into the bulb. Though I heard no sound of the glass cracking, I
thought the bulb had given way, and the entrance of air had forced the mer-
cury up the tube; but in this I was mistaken, for having taken it on board
and thawed it, nothing wrong could be detected, and it worked as well as
before. The explanation which offered itself to my mind was, that the sur-
face of the mercury in the bulb becoming at once solidified, its contracting
pressed the central and still fluid portion of the metal into the stem with a
jerk, and thence again gradually absorbed it as the process of freezing ap-
proached the centre.

Whether these instruments by Adie were absolutely correct seems doubtful.
In my Journal I find the following remarks regarding them : —

"Feb. 2, 1854'. — Temperature fell to —39° in the night, when I had a good
comparison of the thermometers, those of Adie's remaining within a degree
of — 39°, whilst a quantity of quicksilver in a teacup partially froze. The
quicksilver remained out all night, and did not become completely fluid again
until 9 a.m., when the temperature had been some hours at — 36°, —35°, and
—34-°. A mercurial thermometer placed in it also stood at —34°, and the
same one now blackened for exposure to the sun's rays and enclosed in a
glass case has fallen to — 52°, i. e. become solid, whilst the one (Adie, 11)
in constant use shows only — 37°*5."

"Feb. 3, 1854. — One of the new thermometers was kept in the vessel in
which the quicksilver was exposed; and it remained all day at — 36°, whilst its
fellows showed — 39° and —40°. On removing it a small portion of the soli-
dified metal adhered to the bulb and still remains attached, although the tem-
perature indicated by it and the others is -37°. The result of this is either
that the mercury is impure, which I believe is not the case, or the instru-
ments have an error of 3 or 4 degrees."

" Feb. 4.^ — The mercury adhering in the solid state to the bulb of the spirit
thermometer remained in the same state until half-past two this morning,
when it dropped off, that and the four other thermometers by Adie showing
-36°."

From these experiments, I incline to the belief that an error of 3 or 4
degrees will be found to exist in these instruments at the freezing-point of
mercury. The quantity of metal in the teacup was several ounces, and there-
fore too large, unless its indications be taken while partially solid either in
freezing or melting. I have considered the dropping off of the small portion
adhering to the bulb of the spirit thermometer as the best index.

The mercurial thermometer alluded to as descending to — 52°, was one at-
tached to a scale apparently graduated regardless of accuracy ; but from some
experiments made with it, I considered the tube was tolerably uniform in
calibre ; I therefore removed the scale, and attached another reaching down
to within half an inch of its bulb. This scale was graduated by comparison
with Pastorelli (mercurial), as low as — 32°, and thence the graduation was
continued to the bottom of the scale in the same proportion, bringing it down to
— 50°, about two degrees below which the mercury always stood when solid.

The spirit thermometer for use was placed in a tin cylinder 2^ inches in

THERMOMETRICAIi OBSERVATIONS AT POINT BARROW. 163

diameter, with a longitudinal opening through which it could be easily read ;
this cylinder was kept in another of the same material which was painted
white, seven inches in diameter, having a conical projecting roof, and a flat
bottom, with numerous small openings in both, and a door opening like a
common tin lantern : this again, with its door facing the north, was fixed to
a stout stake, placed in the ice at a distance of 90 feet to the eastward of the
ship. The arrangement so made was to protect the instrument from the wind
and snow-drift, and from the influence of the sun, while admitting the easy
access of air. To have placed it further from the ship would have been to
put it in the way of natives, who might steal or break it ; and as the ship's
hull was banked round with snow, and the prevailing winds came in from
the N.E., it was thought the effect of her presence on the thermometer at that
distance would be little or none.

The position of the ship at Point Barrow was at the extremity of a narrow
point or spit of gravel, which at no part rose more than 6 feet above the
ordinary sea-level, and about five miles distant from the mainland of the
American continent. The coast trended on one side to the S.W., and on the
other to the E.S.E., and was uniformly low and flat in the latter direction for
150 miles, whilst to the S.W.there was no elevation near the coast approaching
100 feet for a like distance. Tlie mainland to the south had not been explored
for more than twenty or thirty miles, to which extent it was perfectly flat,
and the natives described it as quite level for several days' journey further,
beyond which it became hilly, and far south mountainous. The climate,
therefore, may be described as maritime or almost insular, and was not sub-
ject to such extremes of temperature as the land. This was ascertained by
the register kept by Capt. Maguire on a journey to the hunting-grounds
during the coldest part of the year, the temperatures recorded by him being
generally lower than those taken at the ship during his absence. In the
summer the shooting-parties recorded higher temperatures on the land than
were observed at the ship.

The long polar night, or observed absence of the sun, was 69 days, from
November to January ; and the continued presence of the luminary in the
summer, owing to refraction, embraced a period of 74 days.

The calculations for the following Tables were made at intervals of leisure,
and, though simple enough, were very tedious and open to error; but this, I
think, has been successfully avoided by the various cross checks I used.
Each mean in the first twelve Tables is deduced from the sums of the obser-
vations, and in no instance from results already obtained. Some exceptions
to this rule were made in producing the means of the two years combined.

Table I. gives the mean temperature of each day, and the mean of every
10 days (or, when the month consists of 31 days, the last division is the meaij
of 11, and the latter portion of February is the mean of only 8 days) ; at the
foot of the table the mean of each month, and at the foot of the page the mean
temperature of the whole year, as ascertained from 8760 observations, those
of tiie last 21 daj-s of August having been intercalated as already stated.

In this Table a remarkable rise of temperature will be observed before
and after the winter solstice. The month of December set in cold the first
10 days, giving a mean of 22i degrees below zero, whilst the second decade
presented a mean of only half a degree below that point ; and the last 1 1 days
rose to 6^ above it. The mean of December is little more than one-tenth of
a degree lower than that of October, and is nearly 4 degrees higher than
November : this was owing to a southerly gale which almost produced a thaw
for 3 days at the winter solstice, and had the effect of driving the ice com-
pletely off" the coast, leaving nothing visible from the beach to the furthest

M 2

164 REPORT — 1857.

range of vision, east, north and west, but the open ocean and a water sky.
This was succeeded bj' intense cold in January, when the sea speedily froze
over again.

The periods at which the mean temperature of the year occurred in spring
and autumn were at the middle of October and April, or rather more than
20 days after the equinoxes; but the period of greatest cold was a month
after the winter solstice, and the greatest summer heat appears to have oc-
curred in the beginning of August, or 40 days after midsummer.

Table II. gives the highest and lowest single temperatures of each month,
the means of the highest and lowest daily temperatures for each month, and
the means of these or of the daily extremes.

This Table shows that the greatest monthly range of temperature occurred
in April, and was no less than 73 degrees, only 22 short of the range for the
whole year, which was 95 ; running from +52° in summer to — 43° in winter.
The mean of these two single temperatures was 3 degrees below the true
mean of the year, whilst the mean of the daily maxima and minima accorded
with the true means to nearly within half a degree.

Table III. shows the mean temperature of every hour for each month.
By this, the hottest and coldest periods of the day may be seen, as well as
the mean daily range for the month. The coldest and hottest times of the
day were usually a little after 2 o'clock a.m., and a little before 2 o'clock
p.m. ; but the time at which the mean temperature of the month occurred
was rather before 7 a.m. and p.m. In this the daily changes of temperature
corresponded with the annual, in the intervals between the periods of the
extremes and the means following being sliorter than the intervals between
the periods of the extremes and the means preceding them. The greatest
range between the day and night temperatures took place in April, and was
11 degrees.

Table IV. shows the mean temperature of every pair of opposite hours.
From this Table it does not appear at first sight that any pair of similar hours
can be selected as corresponding to the monthly mean ; but on closer exami-
nation, the pairs of 3 and 9 generally give a mean nearer that of the month
than any others. This appears more distinctly in the succeeding tables, where
the whole year is given.

Table V. gives the hourly mean for the seasons, for the summer and
winter halves of the year, and for the whole 344 days, at the same locality.
From the omission of the 21 days in August, the summer temperatures ap-
pear somewhat below the truth, and the same remark applies to the summer
half and to the whole year. But this does not materially affect the main
object of the Table, which is to exhibit the progressive change of temperature
from hour to hour.

Table VI. shows the mean temperature of every pair of similar hours for
the seasons, half-years, and year, as in the last Table. In the last column it
will be seen that the pairs of hours giving a mean nearest the mean of the
year are 3 and 9, or a little after ; or at very nearly equal periods before and
after noon and midnight, and not intermediate between the periods of the
extremes and evening and morning means.

These first six Tables i-efer to the year 1852-53, beginning with Septem-
ber and ending with August ; and the six following are corresponding ones
for the year 1853-54.

Table VII. differs from No. I. in the periods before referred to being
generally later, in the extremes being more marked, and in the mean tempe-
rature of the whole year being lower than that of the preceding one. Thus
the periods of the mean temperature in the autumn and spring were nearer

THERMOMETRICAL OBSERVATIONS AT POINT BARROW. 165

the end of October and April, or about 24 to 30 days after the equinoxes ;
the extreme of cold was experienced in the first part of February, and the
extreme of summer heat was probably about the end of the first decade of
August.

The usual interruption to the winter cold was less decided, and took place
at the beginning of the second decade of January, raising the mean of that
month above December, as December in the preceding season had been
raised above November.

Table VIII. corresponds to Table II. By it the range between the
highest and lowest single temperatures will be seen to be 1 degree more than
the previous year, and give a mean 3 degrees below the true one of the year,
whilst the means of the daily extremes accord very nearly with it. The
greatest monthly range took place in March, and was 65 degrees : 1 1 less
than that of April of the preceding year, and 31 less than the annual range.

Table IX. is similar to Table III., from which it presents no very re-
markable difference. In it April again shows the most marked range between
the day and night extremes, amounting to more than 12|- degrees.

Tables X., XI. and XII. agree in their general features with Nos. IV.,
V. and VI., and are defective in the July and August columns from the
absence of the ship.

The succeeding Tables are compiled to give the means of two years, for
which purpose the observations for the omitted summer intervals have been
intercalated.

Table XIII. gives the means of the decades or third parts of each month,
and of the whole month. Also, the highest and lowest single temperature
noted during the two years, the extreme thermometric range being 97 de-
grees. The mean of these two extremes w"as + 3°*5, and the true mean of the
two years was +6°"882, or 2,5 degrees below the freezing-point of water. The
autumnal and vernal periods at which these temperatures occur, by tiiis Table,
are about 14 and 23 days after their respective equinoxes; but the extremes
of heat and cold, which occur on the 8th of August (probably) and on the
8th of February, are more than double that number, or about 48 days, after
the solstice. Here the interval between the summer extreme and the occur-
rence of the annual mean in autumn is 67 days, and from the latter to the
time of the winter extreme is 117 days; from the winter extreme to the
vernal period at which the annual mean occurs is 74 days, and from this to
the summer extreme 107 days.

Table XIV. gives the mean temperature for two years, of every hour for
each month.

Table XV. gives the mean of every pair of similar hours of Table XIV.

Table XVI. gives the mean temperature for two years of every hour for
each of the four seasons, for the half-years, and for the year. In this Table
it will be observed that the interval of time between the extremes and that
at which the annual mean folloivinff takes place is perceptibly shorter than
between either extreme and the time of the mean preceding it.

Table XVII. gives the mean of every pair of similar hours in Table XVI.

Table XVIII. gives the mean temperature of every hour for the month of
June, for 22 days in July, and for the 21 days both before and after the 21st
of June, from hourly observations taken with a blackened thermometer ex-
posed to the sun's rays. This Table, though so limited, maj'^ be of some in-
terest in regard to the growth of vegetation during the short summer of the
Arctic regions.

Table XIX. gives the means of the pairs of similar hours in the first and
third columns of Table XVIII.

166

REPORT — 1857.

— 1

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►.MHIHiHIHIHIMHIcJ

THERMOMETRICAL OBSERVATIONS AT POINT BARROW. 167

o
o

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The highest single temperature occurred 31st Julv,
and was + 52°.

The lowest single temperature occurred 19th Jan.,
and was— 43°.

tc
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00

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t^ VO r^vo M
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_— ^^....„. .__„„ —

168

REPORT — 1857.

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r» :^ ^ N ^ r** .^ r* 7^ 5^ r* r^

r^r^r^t^vbvb mm^-^j-coco
fototocococorototorototo

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vo O covo O VO O f^ O vo to%p
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to c< oo ^ .'i- ^ 0^ r F^7^ y^ 9
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M tJ ro ■* u^vO t-^00 On O I-" rt

i g

t-i tJ ro ^ mvo 1^00 On O w cj
M M M

THBBMOMETRICAL OBSERVATIONS AT POINT BARROW. 169

b S

>- ^

-M

O O vn in
wn t^ t^ _in

u-> tn O

u^ »n

CO OO

TC OO GO OO

OO oo oo 00

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to M C^ t^

to n CO to

CO CO

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in -<j- ON f*

to «n lO t^

o t-~

M M

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_M _t) n to

CO CO

to M

In u^ lo lo

in lo u^ »n

in in

m CO en m

to CO CO to

CO CO

vo tn w oo

to CO to oo

OO vo

m M

O M oo vp

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CT\ 0\

M o

V) 'c4 M '^

en en CO en

M M M M

M M

t« 'm

to to to to

CO CO

to to

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^ M H -.j-

On O

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O CTs p t^

ON l^ t^ >X)

vp ,j-

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00 ON 0\ ON

'o\ b\

ON On

^ M M M

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oo w vo IH

M 00

m M

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to tl- 0\ H

m o

in in

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vn vn

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to OO fl NO

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to O

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M M M r»

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rt N

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t-^

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t^ t-^ c^ t^

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00 00

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to CO to to

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to to

« r* c< e<

M tl O «

C^ O

c< d

c«

■^

OS CO 0\ »-<

t< m ci »n

m CO

ON ►<

in vo !>. vo

to to to f)

to M

tl VO

in in vn »J^

in In vn »o

m m

in in

»i^

oo vn 00 >-•

in vD to vo

OO CO

CO OO

ON pN t^ J^

« CO ^ to

r ."=•■

to Tt-

00 oo do ON

0\ 0\ 0\ <J\

On on

On On

o t^ o vo

yo ^ ti ti

VO ^

M 00

00 t^ ^ p

M t4 HI M

OO «

5gr VN

\n \rt \n xrt

to in «n vn

'■* "m

in in

m o\ m vo

CO On w O

On 00

OO to

oo t^ t^ oo

OO OO 00 00

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00 00

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OO OO

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r< r) O rt

c4 n c« M

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c< «

S M rt CO •*

«n vo t>. 00

ON O

w c»

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M M

13 T3 n3 TS

'tf 'O ^13 '^

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a la a ca

a ct

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4 S cs cd S

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CS C9

>n vo t~ 00

ON O

M M

170

REPORT — 1857.

cyiMvo r^ o^ ir, m u^ moo o\ •*
Vh V*- V ^ Vt- In iovb vb Koo oo

0r»)i-iioc^0t<vo*r-«O\

n p ^ p\^ p <> TO

oo cxj 00 00 t^ K*^ m Iri u-» ^ Vj-

o
vb

M c» CO <^ v^vO t^OO On O « N

■< o

w c) ri >J- "1VO t^oo o\ O " N

M M M

a
g

rot^t^rit^«M»l-t?\e)0>«

tJ- M M cv-too (7s ON M en ui un OS

m m m Vn *m ^ tn t^oo ON b On

KO 00

O ^^ O fo Ov^o oo o *J^
<n t^ o\vo in t-^ cs ro OS
b OsOO r^vb in ^ ri- ro

r)l-li-ci-i«iMnn>-i

OO »0 "d* W1VO tooo -si- On u^ O (^

oo oo On OS r-v*^ u-1 vo CO t-i OnOO

OS O
'H TO

•^^so >n M Os m w O "
N Th U-, t^yj 00 ps p _rt
Vo Vo m to Vn rn to Vl- 'tI-

corococococococococort to

M rt to Ti- m\o t^oo OS O >-i M

c< ro

■sj- mvo t-.00 OS O 11 fj

oo N « vo moo On O m'O
to .^ inso to osvo »n M oo

to -i-
vn r^

I-~w OstoOvO -+"10 Os + M
•1 -;t- O t-^ O moo O m t^ c) OS

i c S>

„ „ „ „ V, -^ to Vh m m
rototocototototocoto

\0 VO

to to

t-^ t^ t'-so so mrj-^toc) f4 »H
tototototototocoro»ototo

en §3

iiS. ■
m 3

M M OS ■>j-0O oo O to l^ "
Ln Os OsOO to OS rl C^ ^ OS

? ^

tn in M oo t~^ mso c« to m t^ Os
O !-• <?NOO t^Otowi-irls^o

b b b b b b « to Vosb

1 +

00 00

OS bsoo K Kvb Vh to t) M b b

oo OsO O t-~>n^>*-tort

o o>

vo vo t^ ■+VO 1-1 m M to in to «
oo OS o o to mso vo m r^so Cs

In \j-\\o so in v> tn In *n in

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elf.
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\0 M U-l^M^O t^lH ^VO

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tr.

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1-1 r)

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a
o
o

THERMOMETRICAL OBSERVATIONS AT POINT BARROW. l7l

r~.

•*

»H

■+

•"1-

I^S

>'^

i »

•+

CTv

r-f

l-t

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■ri

■d

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u-i

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u-i

u-»

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S

t-^

t-~

t*i

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n ci

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c»

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c« 'I-

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ro CO

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VO VO

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■<1-

VO VO

w t-«

f-(

t-«

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'l-

tl M

c»

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S M

■+

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t^ 00

„

t-t

-B

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Ts m

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■n

C/3

a a

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cS cS

-i-

t^ 00

C?v

172

REPORT — 1857.

«*" CO

U I— I

fcfi

o ..

s->

iCQ

- ,

crt

t>-.

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■+

ri-OO O VO t-- N ^OO I^O

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t4 M ci »^ cr\ o oo u-,\o oo

NO -^NO M O »^ NnNO "-' +

-»

cnc*^r^rocoTj-c-^c^roro

comrOTj- + cococ*i + Tj-

Ni^

O "NO t^l-~ONOOO ONO

M t^rJ-o->r^'-« OOO tr>rt

O ON^O CO OO vriNO u-1 r^ iH

rt en Onoo 00 no no oo c< CO

-^j-concocoror^N c» t»

mcoMrtciclnclcoco

trv

t^^

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176

REPORT — 1857.

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178

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N d rt rl n ri r» ri ri n rl rJ
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c» ti tJ rt rt ci ci d c» ci cl c^
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180

REPORT — 1857.

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THERMOMETRICAL OBSERVATIONS AT POINT BARROW.

181

a g;

3 o

O &4

CO QJ

00 oo oo o cnoo -^ o "^ rt r^ 0\

vo in w

O O oo

00 rl O ^ Cv *oo oo
^ O "100 m c^ >n «

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o\ OsOO

oo oo t^\0 \£) in lo u-1

11 H CI «i- lOVO t^OO Cv O w H

w cl c^

^ too t^oo 1:^. o tH

A.M.

Noon.

•4

fl rt ^VO m O M covo -^ O On

■^ O to tovo oo VO tl M rl ON
cl On -"i- O-OO '^ r-. ON tH ^o CO

in m m invo t-^oo on O t-" cJ N

Ml-ll-ll-ll-ll-ll-ll-.rtrt««

CO fi rt "-t o ooo t-^ r-^vc vo

COOO O »^rt -^-^M ioi-^t^u-»
p ON p _C\oo t^«^ y^ -^ N p p

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r ."^ ^ t~^^ p 5^p p p r

In U-) u-i u-i VnvJD i>-,<o »i) 'i: vi)

«3
OO

M M CI ^ m\o t^co 0\ O M cl

i i

t< CO <4- m«^ l^OO On O ti pi

M W M

ON COVO O '-' ONVO ON tJ- l>. O
On 00 p rt OS t-- CO c^ r^ CO t^ ON
f< Cl CO CO CO Vh Vtvb 'is V-. t--- t^

COCOCOCOCOCOCOCOCOCOCOCO

COVO CO O t--- CO l>. CO COOO O CO
•t CO p r-. « so On COVO On *n cJ
oo OO OO t-- K-vb u-> tr> Vh CO CO CO

NO
NO

•-2

'Ms

to 2
5

vo in«ntor)-o-'*-M T^•+T^-o^
^\0 in moo c» vo c» t^ .^ c< oo
M 'w 'i-i in b O 'm m V>i5 "t^ t^

1 +

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c<«c^wcoo-^»-«clclc»-^
00 oo K ^^^b t^ CO rt w b b b

vr\ On inoo ON r^ On en t^NO t^OO
tn m in en O onoo oo r-^v^ -"i- <4-
00 00 00 00 oo 't^- K 'r^ 't^ 'i^ 'i^ t^

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182

REPORT 1857.

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THERMOMETRICAL OBSERVATIONS AT POINT BARROW. ISSi,

Table XVIII. — Showing the Mean Temperature of every Hour for the
month of June, part of the month of July and for June, and the twelve
first days of July combined, ft-om observations taken hourly with a black-
ened Thermometer at the ' Plover's ' winter quarters, Point Barrow.

1853,

June.

July 22nd.

42 days of
June and July.

A.M. I

34-50

+ 3572

+ 35-02

36-26

36-90

36-85

38-66

39'09

39-62

43 '4 3

42-54

44-19

48-66

43'3i

48-14

53-90

46-59

53-28

59-26

52-59

58-57

63-00

54-90

61-92

66-00

58-36

64-67

67-66

62-31

65-21

72-03

65-00

70-30

Noon. IX

71-86

64-99

70-30

P.M. I

72-16

63-31

69-83

71-43

62-72

69-30

69-40

65-81

68-21

67-56

63-18

65-95

63-14

56-13

61-07

58-10

50-68

56-04

54' 13

52-09

53-38

49-06

46-13

48-40

47-06

37-31

45-45

42-26

37-40

41-26

37-20

35-63

37-12

36-16

34-54

35-95

Means ....

S4'994

54-120

Table XIX. — Showing the Mean Temperature of every Pair of similar
Hours in first and third columns of Table XVIII.

Hours.

1853.

June.

July 22nd.

June and July.

A.M. P.M.

I and I

+ 53-33

+ 52-42

2 and 2

53-85

S2'57

3 and 3

54-03

53*41

4 and 4

55-50

54*57

5 and 5

54-50

54*55

6 and 6

56-00

54-86

7 and 7

56-70

55-47

8 and 8

56-03

55-16

9 and 9

56-53

55-06

10 and 10

54-80

53-23

1 1 and 1 1

54-61

53*71

12 and 12

54-01

....

53-12

Means

54*994

54-120

Highest single temperature in the sun +106* on 7th June 1853.

184 REPORT — 1857.

Explanation of Plate II.

Fig. 1 represents the mean daily curve for each month, as deduced from
Table XIV. From among the almost straight lines representing the winter
months, March is observed to rise in a bold curve, showing tiie rapidly in-
creasing power of the solar rays, which had hardly produced any effect in
shaded places during February. April exceeds March by 2 degrees in the
height of its curve; but that of each summer month in succession becomes
flatter in consequence of the summer warmth being attended by more cloudy
weather, and a lessened fall of temperature during the nights. September
presents a curve of great flatness, the difference of temperature between noon
and midnight scarcely exceeding 1 degree. The almost continued foggy state
of the weather then prevents the sun effecting much rise in the day, and the
great extent of sea, river, and lake surface, still unfrozen during the earlier
))art of the month, prevents any great fall of temperature during the night.
With the exception of a slight rise in the October curve, the whole six repre-
senting autumn and winter are remarkably flat.

Fi(j. 2 shows the mean daily curves of the four seasons, deduced from
Table XVI. ; also the curve of the winter half of the year, or the autumn and
winter combined, the curve of the summer half, which is spring and summer
combined, and the curve of the whole year, each being the mean of two years.
The flat curve of autumn has nearly the same form as September, and in
position occupies the place of the mean temperature of the year. The winter
line nearly coincides both in form and position with January, and is very
flat. Spring has nearly the form of March and the position of April ; and
the summer cui've, either in shape or position, does not differ much from
July. With the exception of autumn, the curve of each season bears a
striking resemblance to that of its middle month.

Fifi- 3 indicates the curve of mean daily temperature shown by a black-
ened thermometer exposed to the sun. The black line represents the month
of June, and the dotted one three weeks before and after the 21st of June. In
both, the extremes seem to be very near noon and midnight, and the bold
character of the curve is very striking.

On the Algebraic Couple ; and on the Equivalents of Indeterminate
Exj)ressions. By Charles James Hargreave, LL.D., F.R.S.

In a paper entitled " Analytical Researches concerning Numbers," which
was published in the Philosophical Magazine some years ago (vol. xxxv.
p. 36), 1 had occasion to avail myself of a principle, which, though it has not
yet taken rank amongst recognized forms of mathematical reasoning, appears
to be capable of extensive application and calculated to lead to true and use-
ful results. This principle may be expressed by stating simply, that the ana-
lytical equivalent of an indeterminate expression is the arithmetical mean of
all its possible values. The accuracy of the results to which I was conducted
bytiie application of this principle in the pajjer above referred to, led me to
the conclusion, that the princijile might probably to some extent be intro-
duced into mathematical science, without departing from or unduly extend-
ing doctrines heretofore admitted. Since that period, I have not had the
opportunity of pursuing this interesting subject ; but I find that it is one

ON THE ALGEBRAIC COUPLE. . 185

which has not failed to attract the attention of eminent mathematicians ; and
I trust I may be permitted to avail myself of this Meeting of the British Asso-
ciation in Dublin, as a convenient opportunity for the publication of the
views which I had in contemplation on the occasion of my former paper.
These views having suggested themselves in the course of a brief investiga-
tion relating to the interpretation of the Algebraic Couple, I propose to in-
troduce this subject also, in the hope that it may prove interesting to tliose
Avho have given their attention to the various systems of Multiple Algebra
which have been from time to time propounded.

On the Geometrical Interpretation of the Algebraic Couple.

The object of this section is to apply and interpret the Algebraic Couple
to and by means of the geometry of angular magnitude and position.

The couple in its ordinary form, x-\-y^ — \, is the argument of the arbi-
trary function,/(a'+?/'V/ — 1), which represents a value of u in the partial
differential equation

cPu (Pu „

If we take the corresponding differential equation of three variables,

d^u d-u d?u_^
d^^df'^dF''
and effect its integration, not generally, but under the restrictive condition

.r- + »/-+ir-=7^(a constant),
we obtain

?<=./,Aan-» J^ + tnn-' ^v-l 'j

whidli may be regarded as an integration of the equation upon the surface of
a sphere whose radius is r. If / be the longitude of a point computed from
anv origin, and X its distance in latitude from the equator, the integral
assumes the form

2< = 0[ Z+cos~' . ),

^\ - cos Ay

M=^^/q:/i:ilogtan^).

whore ju is the co-latitude. The argument of this function is now in the
form of an ordinary algebraic couple, the constituents of which are an-
gular magnitudes ; and my object will be to show that the couple in this
form is an adequate symbolical representation of position on a sphere, or of
angular position in space, in the same manner as the ordinary couple ade-
quately represents position on a plane.

It will be convenient for the sake of comparison to consit!or the algebraic
couple, when geometrically interpreted, rather as an operation, than as a
quantity or result. Let us regard x-\-y*^ — 1 not merely as denoting the
position of a point (x, y), but implying also the process of arriving at such a
point from the origin by progressing along an unvarying course, viz. that
course which is constantly inclined lo the unit-line at an angle whose tan-
gent is ^.

186 REPORT — 1857.

On a plane the direction of unvarying course is the straight line; and its
equation is

y=^x tan/3,

and the symbol denoting the point (a;, -y), involving its distance along the
unit-line, x, and the angle defining its course, /?, is

,(l+,/_ltan/3),or--^

-'L.,/?^^.

Now if, on a sphere, we consider the equatof as the unit-line on which real
angles are measured, the line of unvarying course, or the line which is always
inclined to the unit-line at the same angle, is the rhumb line; and its equa-
tion is

/tan 0=log cot ^,

where is the angle of direction. Introducing this value of 9 into the couple
in its new form, /± -/^ log cot ^. we obtain simply

/(I + s/'^\ tan 0),or -^e^''~;
^ — -" cos

which is a couple of precisely the same form as the ordinary ])laue couple.

If we lay down the definitions that two lines of unvarying course (or
rhumb lines) are parallel when they are inclined at the same angle to the
equator, and that parallel lines are equal when they traverse the same amount
of longitude, we easily obtain the proper rules for adding and multiplying
two or more angular positions.

To find the sum of two positions P or (/, 0) and P' or (/', 0'). From the
origin O draw the unvarying courses OP and OP' ; from P draw the course
PP" equal and parallel to OP'; then P" is the resultant position. For the
algebraic sum,

/(I + -v/ZTi tan 0) -I- Z' (1 + v/:^ tan 0') equals /" (1 ± VHi tan 0"),

if l-\-l'=l", and /" tan 0"=/ tan 0-f/' tan 0'.

Now in the construction above given, (which the reader will easily imagine
without diagram,) we have

l"z=l+V;

and since the equation of the line PP" is
i\
V tan 0'=log cot ^ — log cot tL,

° c) ° cy

we also have

/"tan0" = /tan0 + /'tau0'.
Similarly, to find the difference of two positions P' and P" : fron) P" draw
the course P"P parallel to OP' and equal to it, but in the opposite direction ;
then P will be the difference of the two positions.

Considering the couple in the form e^"^-!, it will be seen that the

cos

amplitude denotes, as on a plane, the direction of the position, or the angle

defining the course ; but the modulus does not denote the angular distance

traversed, or the length of the course, for that is ; but it denotes the

sin

line into which the course would be projected if the sphere were opened out

ON THE ALGEBRAIC COUPLE. 187

after the fashion of Mercator's chart. The product of two positions (/, 6)
and {V d'), (that is, the fourth proportional to the unit.of angular magnitude
and the two positions,) is evidently the position (Z",0"), where e"=0' + 6, and

^' — ^ ; that is to say, the amplitude of the product is the sum

cos 0" cos cos 0'

of the amplitudes of the factors ; and the projection of the modulus of the
product is the product of the projections of the moduli of the factors. We
thus see that as a plane angle bears a sort of logarithmic relation to linear mag-
nitude, so the dihedral angle (denoted here by 0) bears a similar logarithmic
relation to plane angular magnitude.

It will be at once apparent that in this method of representing angular
position, every point has an infinite number of symbolical representations,
inasmuch as it may be reached from the origin by an infinite number of per-
fectly distinct courses. The longitude which we have denoted by I may be
denoted also by any value of /±2 « tt ; each value of which has a correspond-
ing and distinct value of d. In eiFect, the couple becomes

l± 2mr ^Qn^—j
cos 0,1
where 0„ is determined by the equation

(l+2mr) tan 0„=log cot ^.

If the point be at the pole of the sphere, the values of 0„ are continuous ;
that is to say, every angle is a value of 0„ ; which is well known, for it is ob-
vious that the pole may be reached by an unvarying course at whatever angle
we start from the equator. In this case the longitude traversed is infinite ;

except when 0„is -, in which case the longitude traversed assumes the form

OC-i-OC, and is any arbitrary quantity. This also is geometrically evident,
since if the pole be regarded as having a longitude, that longitude is per-
fectly arbitrary. In this case the couple assumes the form /n + \/ — 1 tan ^J.

Comparing this with the form we started from, tan-^ ^-f-tan-i — lll^

and remembering that at the pole z=r, we have tan-* ( V^ — l)=OCv' — 1,
e infini
Since

the infinity employed being an arbitrary multiple of tan — .

tan-'ffl + tan-i(V-l)=tan-i-^+ — ^=tan-i'/-l,

l-a-/— 1

it follows that, if either of two positions be at the pole, their sum is at the
pole ; unless indeed the other point be at the opposite pole, (in which case
a= — \^ — 1,) when their sum is any point on the equator, or rather every
point on the equator at the same time. In like manner, since

tan-i«!-tan-i(i/'^)=tan-i-^II — -ZL=tan-i(- V^l),

it follows that if a position at the pole be deducted from any other position,
the resultant position is at the opposite pole; and since n tan-' (-V^— 1)
==taa-'( V' — 1), the sum of any number of polar positions is a polar posi-
tion.

188 REPORT — 1857.

On Infinite Angles, and on the Principle of BIcan Values,

The exemplification of these subjects by the foregoing theory depends mainly
on the distinction above pointed out, between considering a position merely
as a point I'eached, and having one fixed relation witii the origin, and consi-
dering it with reference to tlie course by which it has been reached. The
former mode of consideration is merely a limiting view of the latter. If we
conceive a point on a sfihere starting from the origin of longitude and tra-
versing an unvarying course inclined to the meridian, and if we at any mo-
ment inquire, first, what amount of longitude has it traversed; and secondly,
in what longitude is it now posited, the answers to the two questions must
obviously be, in an algebraic sense, the same ; and in a geometrical sense also
they must be the same wherever they are intelligible, that is, for every po-
sition from the equator up to and exclusive of the pole. The assertion of
this geometrical proposition (the identity of the answers to the two queries),
extended by the substitution of inclusive for exclusive, does not involve any
principle other tlian the axiom, that, what is quantitatively true up to the
limit, is quantitatively true at the limit; for in this case the passage from ' up
to the limit' to 'at the limit,' may be considered in such a light as not of
necessity to involve any change in the character of the subjects or ideas with
which we are dealing, or to transfer our conceptions from calculable magni-
tude to something no longer the subject of calculation. The passage from
the equator of a sphere to the pole by an unvarying course does not of
necessity involve the consideration of infinite magnitude, for the linear space

traversed in getting up to the pole is — ; — -, where a is infinitely small ; and

2 sni

the linear space traversed in actually attaining the pole is , both of

2 sm y

which are finite and calculable. It is true that an infinite amount of angular
longitude is traversed, but this considei'ation does not interfere with the cer-
tainty of our actually attaining the pole in a finite time at a finite rate of
progress ; and there is nothing in the geometrical character of the problem
which could lead us to believe that the above inquiries are of totally difl^erent
natures when applied to the pole, and when applied to a point indefinitely
near to the pole. Let us then consider the point as having reached the pole
in this manner, and propose the two inquiries above suggested.

If we ask, what amount of longitude has been traversed ; the answer is, an
infinite amount. If we ask the geometrical question, in what longitude does
the point now exist; the answer is, that it is in every possible longitude
throughout the whole cycle of longitude.

We are thus led by these considerations to the inference that the idea (as
applied to geometry) of an angle which in an analytical sense is infinite, and
the idea of an angle whicli has at one and the same time every real magnitude,
are one and the same idea. An angle in geometry, when made to vary by a
uniform process, is of necessity periodic in its magnitude ; but when the sym-
bol representing an angle is imported into algebra by the introduction of its
trigonometrical functions into general analysis, then the angle or its symbol
must of necessity be considered as having a progressive magnitude, and as
being capable of having every real value from negative infinity to positive
infinity ; and the foregoing considerations tend to the conclusion, that an in-
finite angle, in the latter sense, is the same thing as that angle in the former
sense, which has at the same time and in one conception every real value ;
an idea, the perception of which is facilitated by the circumstance that we
can geometrically depict a position whose angular distance in longitude from

ON THE ALGEBRAIC COUPLE. 189

a fixed origin has this singular value. If the conception of such an angle be
difficult, the difficulty exists to the analyst alone : to the geometrician the
idea is easy and even elementary ; for to assert that the pole has at once
every possible longitude, is merely to say that it is the intersection of all the
meridians, or that it exists at once on every meridian, which is in truth the
definition of the pole.

The considerations here developed seem to derive additional weight from
a view of the subject which we have hitherto excluded ; where the point
passes to the pole directly in latitude, without any geometrical change of

longitude; that is, the case where 0=-. This is a limiting case. For all

values of 6 up to this value, the longitude traversed is infinite ; at this point
the infinity changes sign. What is the value through which it passes? The
analytical expression for the longitude, in all cases, is '■

/=cot01ogcot^=cot— log tan - at the pole.

This then assumes the form OC-rOC) where the elements producing the two
infinities are independent of each other ; a kind of expression wliich we know
to be the algebraic symbol for that which has every value within the whole
range of value. It is indeed generally said to be the representative of inde-
terminate value, or that it means, "any real quantity we please:" but the
language appears inadequate, the thing represented being manifestly, " every
real quantity at once." Here then we have a case in which, without passing
from the field of analj'sis, we find the conception of an angle having every
possible value at once ; and it presents itself to us as the limiting idea of a
series of infinities, and as the mode of transition from a series of positive in-
finities to exactly the same series of negative infinities.

The series of infinite angles which represents the longitude traversed in
reaching the pole, is a series of functions of 0, of such a nature that their rate
of increase can be ascertained and their relative magnitudes compared, with
as much ease as if they were all finite quantities ; for they vary directly as
cotan Q.

If (X.Q denote the longitude of the pole as reached at the angle Q, we have

^(OCe)_ logco'2_ Ztan0_ 2 OC9 ;

d^ siiTy sin-0 sin 12

an equation which marks the rate of decrease as advances from towards

- : at that point it passes through the phase of analytical indeterminateness,

and then passes through the stages of negative infinity at the same rate of
progress as it had manifested on the positive side. The general result may
be thus recapitulated : that having in analysis met with angles of various de-
grees of infinite magnitude, they are interpreted geometrically into angles,
each of which has at the same time every possible value ; that having also in
analysis met with an angle which has an absolutely indeterminate value, or all
values at the same time, we find that it is the mode by which a series of de-
creasing positive infinite angles passes without discontinuity to an exactly
similar series of negative infinite angles.

The series of infinite angles with which we are dealing is evidently at its
positive maximum when 0=0, and at its negative maximum when Q=ir.
At these points we pass through what would appear to be the most trans-
cendental of all infinite angles ; which resolves itself in geometry into the

190 REPORT— 1857-

almost irrational idea, of the amount of longitude wliicli it would be neces-
sary to traverse before we reach the pole, the condition of the problem being
that we are never to quit the equator. It is useful, however, not to neglect
this transitional infinitj-^, for it is evidently of a different kind from those on
each side of it. It is the infinitely remote limit of a series of increasing in-
finities, just as the other transitional point appeared to be the nearest approach
to finite quantity that infinity admits of, the minimum point of a series of
decreasing infinities.

Before proceeding to consider the trigonometrical functions of OC9, it will be
convenient to point out another series of infinite angles which presents itself
in the course of this investigation, and which may perhaps throw some light
on the nature of an infinite angle, though it is not so readily susceptible of
geometrical illustration as the case already considered. It has been observed
that any angular position furnishes an infinite number of values of f<„, and
that the longitude has a corresponding number of values, connected by the
equation

(/ + 2«7r) tan 07»=log cotan ^.

By increasing n (which denotes the number of circuits which the course
makes round the sphere) without limit, 0„ diminishes without limit; and the
course approximates to an infinite number of circuits i-ound the equator.
The series of infinite longitudes now intended to be brought under considera-
tion, consists of the limits of the values of the longitude traversed when Q^ ap-
proaches 0, for all positions on the sphere from the equator to the pole.
When the point is at the pole, the infinite angle under consideration is that
■which we have already noticed as being of a very high order of magnitude ;
its value is infinite, not merely because tan 0„ is zero, a circumstance which
■for our present pyrpose is common to all other positions, but also because

logcotan ^ being log tan- is infinite. As the position descends from the

pole towards the equator, the limit of the longitude traversed assumes still an

infinite value, but diminishes in proportion to log cotan L, until the point

falls upon the equator itself, in which case the value is a transitional phase of
the series of infinite angles, and it assumes the form 0-f-O, where the two ele-
ments of which the zeros are the limits are independent of each other; from
which we are to infer, what is indeed geometrically evident, that the course
consists of an arbitrary number of complete revolutions 2w7r, in addition to
the original longitude of the point I. On the other side of the equator, the
longitude traversed passes through an exactly similar series of values, but
without any change of sign. We have thus another point of view from which
we perceive that the limiting conception of a series of infinite angles of vary-
ing magnitudes proves to be an angle possessing an infinite number of values.
Having thus acquired some idea of the meaning of an infinite angle, by ob-
serving its demeanour through the various phases of the above geometrical
illustrations, the next question which suggests itself is, how are we to deal
with its trigonometrical functions. Confining ourselves to the set of angles
which we have denoted by OC^ (the longitude traversed in reaching the pole
at the angle Q), we may safely assert that these functions are independent of
0; for whatever may be the value of 0, all the values of OCg corresponding to
them are geometrically identical ; and we are here dealing with purely geo-
metrical functions. It follows that a trigonometrical function of an infinite

ON THE ALGEBRAIC COUPLE. 191

angle is the same function of that angle which lius at once every possible
value, or which is the same thing, every possible value within one complete
period. We should therefore be inclined to say, that, speaking geometrically,
cos OC or sin OC has no particular individual value, but that it possesses at
once every value between — 1 and +1, both inclusive. We shall not, I ap-
prehend, arrive by any process of abstract reasoning at an analytical equiva-
lent for these and similar expressions. We may, however, interpret them by
reference to particular problems, the solution of which involves principles not
purely algebraical; and the question will then arise, how far it is safe, having
regard to the nature of these principles, to consider the interpretation as uni-
versal.

Suppose a point placed upon a sphere whose equator is horizontal, and such
point descending by the force of gravity, and that a person is entitled to re-
ceive, (or obliged to pay, as the case may be,) such a fraction of a pound as is
denoted by the cosine of the longitude of the place at which the point tra-
verses the plane of the equator. For every position of the point up to, but
exclusive of the pole, the value of this person's interest is simply the fraction
cos of a pound, d being the longitude of the original position. If the point
be actually on the pole, the problem considered as a physical one fails ; and
the answer assumes the form of a trigonometrical function of an angle which
has no one value in particular more than another. If we bring this limiting
case within the scope of the problem by proposing it in this form : — a material
point I'oUs from the pole of a sphere to the equator down a meridian, de-
termined by some impulse extraneous to the problem ; what is the value of
the interest of a person who is to receive, (or pay, if the result be negative,)
the fraction of a pound above indicated ? — the algebraical answer is the same
as before, viz. the cosine of an angle which has any or every value, no one in
particular more than another ; but the problem is not now purely algebraic,
but belongs to the Theory of Probabilities, which tells us that the answer is
(cos w + cos(2?2)-t-...-t-cos(mn))^OT, where n diminishes without limit and

m n=2 ii, that '\s, T^^ cos Odd; and this, which is the mean of all the possi-
ble values of cos 6, is therefore, in this problem at least, the interpretation of
the cosine of the indeterminate angle which denotes the longitude of the pole.
Perhaps this doctrine of the interpretation of indeterminate values may be
stated as follows : — If a problem when treated analytically give an indetermi-
nate result of which all the individual values are calculable, and if the same
pi'oblem when treated by the principles of the science to which it belongs
give a specific result, we are warranted in saying that the latter is quoad sub-
jectam materiam the interpretation of the former, and may be treated as its
analytical equivalent ; this doctrine being subject to the implied condition
that the science to which the problem belongs, and which gives us the spe-
cific result, is a science whose fundamental principles do not rest on induc-
tion in any other sense than the axioms of algebra do.

A and B engage in a game in which they will win alternately, A winning
first : what is the present value of A's ultimate winnings when they rise ?

\ / 1 )*

The only answer given by algebra is — ^^ — -, where x is the number of

games about to be played ; but the real answer is evidently i, so that \ ought
to be the arithmetical interpretation of ^^ ^ ; or the equivalent of

( — 1)^ is if X be indeterminate and integer ; and that of ( — 1)" is the same,

provided the infinity used be the limit of the ordinal series 1, 2, S, 4 ,

and not the limit of any partial series, as 1, 3, 5, 7.... or 2, 4', 6, 8

192 REPORT— 1857.

It would appear that problems of this sort are not soluble by algebra alone,
when the problem itself contains an indeterminate element ; but if it contain
an infinite in lieu of an indeterminate element, it is soluble by algebra, as a
limiting case of some more general problem. Suppose a person plays a
succession of games, of which, when divided into sets of three, he wins in
every first game a pounds, in every second b pounds, and loses iu every third
game a + h pounds; what is the present value (apart from any considerations
of time) of what he will gain, supposing that he plays until the happening of
some event unconnected with the game and which may never happen ? The
answer given by the Theory of Probabilities \s^(2a + b), being the mean .of
the three possible results of one set of games. If the conclusion of the play-
ing be indeterminate, algebra gives only an indeterminate result ; but if the
conclusion of the playing be indefinitely postponed, the answer to the problem

is, the value to which the series ai' + 6.r- + c.r^+a.r^+&.r^+c.i'^+ (c being

—>(a-\-b)) approximates as x approximates to unity; and this also is
^ {2 a-\-b). The problem is in fact brought within the domain of algebra by
considering it as the limiting case of another problem, in which an algebraic
relation exists between the values of the winnings of each game ; and the value
of the limit depends upon the nature of the connexion. In the problem pro-
posed, the a pounds won in the first game has no kind of connexion with
the a pounds won in the 4th, 7th, &c. games ; but in the extended problem
a connexion exists, inasmuch as we consider that when ax\s the value of
a pounds at the end of the first game, ax*, ax'' ... represent the values of
a pounds at the end of the 4th, 7th, &c. games ; and it is this consideration
which renders the problem an algebraical one.

Considerations of this nature seem to tend to the conclusion, that we are
not to expect from algebra alone, as that science is at present constituted, the
discovery or proof of the principle that the analytical equivalent of an inde-
terminate expression is the arithmetical mean of all its values, or any prin-
ciple of this character ; for algebra being the science of symbols irrespective
of their meanings, knows nothing of symbols which are of their own nature
periodic or alternating, or otherwise limited as to the values they are capable
of having, or of symbols which are indeterminate in point of value ; except
indeed when they occur as limiting cases of particular problems ; in which
cases their values are to be learnt from the specialties of the problem, or in
other words, the science to which the data of the problem belong.

Returning to the consideration of infinite angles, it will be readily seen that
OCg and (X.„_q are identical in every particular except sign. Considering
these angles as longitudes attained, they possess a species of identity which
OCg and OCg- do not possess ; the former pair have passed through precisely
the same values, have traversed every meridian the same number of times ;
the latter pair have not. Viewing the two pairs of infinities as angles im-
pressed with every value through which they have passed, now that they have
arrived at an indifferent or neutral value, the former pair possess an absolute
identity (except in sign) with reference to our mode of interpretation. If we
take two infinities which difl^er otherwise than in sign, and if we permit our-
selves to say that (— 1)'^=:0 and ( — 1)°' =0, yet we could not thence infer
that ( — 1)°'=(— 1)°'' ; but since — 1 = — 1""' identically, we maybe sure
that ( — 1)°'0=(— l)«''-s since OCfl= — OC^_o ; and if these quantities are to
be interpreted each into zero, we may be sure that it is the same zero. But
whether it be, or be not, safe to affirm that (— 1)°'=0 universally, we may cer-

tainly affirm, (the three infinities being the same,) that- — -^ — -^ — fTzr""^-

ON THE ALGEI^RAIC COUPLE. 193

This consideration enables us to obtain the following results, without the ap-
plication of the principle of mean values, wiiich, however, gives the same
results : —

X _x

Since 2 sin .r=— a/HT((— i)^— (— 1) 'i^), we have sinOC=0.

Since tan .r= — -/^ \~ _x ^ '^^e havetanOC= - '^^{h—^)-^ '■

and generally, the odd functions and their odd powers will be found to be zero.
The value of the even functions is not immediately perceived, unless we con-
as ~ iC

ceive ourselves at liberty to assume that ( — 1)'^ and ( — 1) '^ become when
a; is infinite. If, however, we bear in mind, that in speaking of OC as an angle,
we are using the symbol in its ordinary algebraical sense of a number which
is larger than any number we can name, and which does not admit of alte-
ration by the mere addition or subtraction of any finite quantity, and con-
cerning whose value nothing further can be predicated, we shall easily per-
ceive that cos OC must have the same value as sin OC ; for since

.=sin(^+l) = -sin(.r-g

we have, with the above meaning of infinity,

cos 0C= +sin OCj and therefore =0 ;
from which we are to infer that ( — 1)°' and ( — l)"*^? or e^^^^-^ are both
zero, since they are equal and their sum is zero.

o- , sin X , . cos X i , __ 1

Smce tan x= =- when x is 0C= — -. — » we have tan 0C=-

cos a; —sin x tan OC

By taking the powers of 2 cos,r=( — 1)'' + ( — 1) ",
and of 2sina;=-V'^((-l)'^ — (-1) "),

X X

and observing that ( — 1)" and (—1) " are both zero when .r=OC, we ob-
tain

cos2«QC=-L 2»(27^-l)(2^^-2). ..(« + !) .
22»' 1.2.3.... «

cos2»+ioc=0;
and the powers of the sines are the same. The assertion that tan OC=0 is at
variance with the result given by Professor De Morgan in his treatise on di-
vergent series in the Cambridge Phil. Trans, (vol. viii. part 2). The result
deduced in that paper by two methods is tan 0C= + '^ — 1. The first me-
thod depends on the assertion that log (— ) = 7r'/^, and log (— )

:=7r V — 1 ; but inasmuch as the two fractions whose logarithms are required
are, from their derivation, reciprocals of each other, I apprehend that the sura
of their logarithms is simply the logarithm of 1, or zero; which would lead
to tan OC=0. The second method leads to the equation above deduced,

tan 0C= — , from which however we are not at liberty to deduce

tanOC

tanOC=i V — \. Independently of the a priori difficulty of believing that

the mean value of an odd function can be other than zero, I conceive that any

1857. o

194 REPORT — 1857-

pi'ocess of mean values giving an ambiguous result, such as + V — 1, would
imply that the real result is the mean between the two values of the ambi-
guous expression, which in the present case would be zero. That

(tan + tan n + tan n + tan (2 w) + . . . . + tan(m n))-T-m,

where mn=2 n, approximates without limit to zero as n diminishes without
limit, may be shown by causing w to diminish in such a manner as never to

be an aliquot part of — or This may be effected by making n an odd

aliquot part (as small as we please) of tt. It is then certain that the terms
of the above series cancel each other, and we are not embarrassed with the

difficulty of proving that tan - + tan — =0 ; for we never fall on these va-
lues. Moreover, it has already appeared that the angle whose tangent is
^ — 1 is OC^ — 1 ; which corresponds with the value derived from the ex-
pansion of tan^i a; when x is made equal to \^ — 1; while the equation
tan~* ■%/ — 1=0C would be at variance with this expression.

In conjunction with tan (OC V — ])= V—l it may be useful to notice,

sin(a:^— 1)=— 2- («''— e-'O; sin (OC^— 1)=0C^— 1 ;

and to compare these expressions with the hyperbolic tangent, cosine, and
sine of a real angle which are respectively 1, 0C» and OC-

We have already remarked that the results here contemplated, whether
arrived at by the principle of means, or by reference to the problems producing
them, are to be regarded not as unique values, but as interpretations quoad

the particular subject in hand. It is not true that 1 — 1 + 1 — 1+ equals

I generally, or that this series has any unique value ; for it may be made to

represent any proper fraction — by making it the limit of the series
n

1 vfn

J ^m ^ ^n a;"* + " + 3?^" jj;)n+2n_j_^3n ^m+3n J_ gr - .

1 — xn

If A and B play, and win alternately, A winning the first, the value of A's
Avinnings is ^; but that is only on the assumption that there are no drawn
games; for if there be ?« — 1 drawn games after each game won by B before

A wins again, the value of A's winnings is — , being the limit of the f.bove

series ; and if the number of games played be indefinite, the doctrine of means

leads to this identical result.

It has been suggested by Mr. De Morgan in the memoir above referred to,

that the fabric of periodic series and integrals raised by Fourier, Poisson,

Cauchy and others would be exposed to great danger by the production of

any case in which 1 — 1 -f .... should differ from -^ when it is the limit of a

series A^, — Aj + If this suggestion should prove to be well-founded, it

would lead to great doubt as to the truth of the results obtained by these

analysts ; for although I am not able to adduce any instance in which the

known analytical envelopment of such a seriesasa;'?^*') — ar^O-j-a^-JCa; — a;'P(^^ + ..,

differs from ^ when a:=l, yet it is easy to adduce cases in which the doctrine

of mean values applied to such a series fails to produce |^ as the limiting value.

This doctrine gives as the limiting value,

ON TELESCOPES AND EQUATORIAL MOUNTINGS. 195

.^(O)-0(l) + ?)(2)-0(3)+ ±<t>(n) ^

fin)
n being made infinite. If </)(w) be n", so that the series becomes l—x + x'*

— .r' + a;'"— this mean value is (1+5 + 9+ 13 + 17+ . +(4'J0 + 1))

+ (2p + l)S which, asj9 increases, approaches ^; and in this case the ana-
lytical envelopment, which can be found in the shape of a definite integral,
also gives i. The doctrine of means gives the same result for any other in-
teger powel- of n ; and probably, if the analytical envelopment were found, it
would give the same value. But if (j)(n) be of the form a", the doctrine of
mean values gives as the limit of the series

^_^(«)-|-^(a2)_^(a3)_j__j,(a4)_ ^

noti, but ; and this circumstance of itself would induce me to require

1+-
a

to sec the analytical envelopment of the series before I pronounced its limit-
ing value to be ■^. There are algebraic considerations which would rather
tend towards the" conclusion that this limit is a function of a ; for when a is
1, its value is^L; and if a be infinite, its value appears to approximate to
unity. It is perilous, however, to hazard surmises as to the value of this limit,
so long as no finite equivalent for the series is produced.

lieport on the Improvement of Telescope and Equatorial Mountings.
By Thomas Grubb, M.R.LA. ^c.

The labours of the Earl of Rosse, now only perhaps receiving due appre-
ciation, have placed beyond doubt the practicability of producing specula
for reflecting telescopes of dimensions equalling, if not exceeding, those
which the conditions of our atmosphere permit of being used with advan-
tage, combined with an accuracy of surface and consequent excellence of
definition which we can scarcely either hope or desire to surpass.

Meantime the achromatic objective has received but small increment of
dimension, and is now probably for ever distanced, in this respect, by its
competitor the reflector. The spirited exertions of the Messrs. Chance of
Birmingham have indeed produced a pair of discs suited to the formation of
an object-glass of abour. 29 inches diameter, but these exertions have not
been seconded by a corresponding spirit in Great Britain, either public or
private. A few years since, the possible acquisition of an achromatic tele-
scope, of corresponding gigantic size, was looked forward to as a national,
triumph, if ever accomplished; but our Government, retaining its character
of pr<)V(ubial supineness (if not apathy) in such matters, has allowed tliese
splendid discs to be transmitted to a more congenial kingdom ; yet even there
the work seems to progress but slowly, and 1 apprehend that their formation
into an object-glass is still a work for the future. Four years have now passed
since the production of these discs, and nearly three years since, on being
applied to by Messrs. Chance, I offered to form them into an object-glass.
Under such circumstances it is desirable that attention should be turned to
the reflecting form of telescopes as that alone suited for instruments of the
largest dimensions, and important that these should receive from time to
time such accessions of improvement as the progressive steps in arts or
science place at our disposal.

196 REPORT — 1857.

Now the two points in which inferiority may be at present held as against
the reflector are — the greater liability of the surf\ices to tarnish, and the
less intrinsic brilliancy of the pencil. In respect of the first, I hold the
objection to be much less in amount, with good specula, than usually sup-
posed. If we have to infer that Sir J. Herschel frequently repolished his
mirrors at the Cape, we know that some specitnens of optical glass have
rapidly deteriorated. It was stated by Professor Moll, of Utrecht, at the
former Meeting of the British Association in Dublin, that there was then in
Paris an object-glass through which we might in vain attempt to look ; but
it is manifest that neither a low quality of speculum metal, nor glass carrying
its own destruction within its substance is fitted for optical instruments, and
that both should be equally avoided. As a proof of the permanence of good
specula metal, I may mention that on a recent occasion, a surface twelve
years polished showed an increase of only six per cent, of reflecting power
on being repolished.

In respect of the second point of inferiority of the reflector, viz. the greater
absorption of the incident light, and consequent lesser intrinsic brightness of
its pencil, as compared with that of the achromatic. I would observe, m« limine,
that this difference decreases as the size of the object-glass increases, so that
an object-glass of 4 feet diameter, and of a thickness adequate to resist
flexure, would transmit little, if any, more light to the eye than a reflector of
equal aperture as it is now possible to construct it. Such considerations do
not however lessen the importance of obtaining for the reflecting telescope
every possible accession as well to the permanence as to the reflective power
of its surfaces, compatible with their general accuracy and perfection of
figure. To the improvement of the reflecting telescope in these respects, I
have lately devoted some attention ; how far 1 have realized what is valuable
remains to be shown.

So far as the Cassegrain and Gregorian forms are concerned, these im-
provements are based upon the employment of one or more silvered (not
quicksilvered) surfaces ; and my first application of it has been to that form
of the reflecting instrument which I have long preferred (not perhaps without
good reason) to all others, viz. the " Cassegrain." Convinced, from previous
practical working of both speculum metal and glass, that both were capable
of receiving equal degrees of accuracy of surface, I conceived it unnecessary
to stop to consider whether the failure of a recorded attempt to construct a
reflecting telescope of quicksilvered surfaces was due to the errors of work-
manship of the artist, or the formula by which he was guided, and selected
the small mirror of the Cassegrain telescope for experiment.

Now the most obvious construction for a silvered mirror for such, was to
form a lens (so to speak) of equal thickness throughout, having no disper-
sion, and therefore requiring no correction of colour, and to silver the con-
cave surface. This construction I rejected, notwithstanding its simplicity,
on considering that there would be a secondary image (coinciding nearly
with tiie primary) formed by the outer or unsilvered surface, and producing
what is called a " ghost " in the field of view.

I therefore assumed a radius of curvature for the outer surface differing
considerably from that of the inner or silvered surface ; and as this would
produce refraction and therewith colour, it became necessary to adopt an
achromatized compound of crown and flint glass. This being constructed,
has proved altogether satisfactory : the inner surfaces being cemented, no ap-
preciable loss of light occurs from using two lenses instead of one ; the re-
flecting surface being as yet only quicksilvered, no increase of light should
be expected : still, when the combination is used in a telescope, the image

ON TELESCOPES AND EQUATORIAL MOUNTINGS. 19?

appears both brighter and whiter than when using the ordinary small spe-
culum; the image also appears perfectly free from chromatic dispersion.
When the quicksilver shall have been replaced by a surface of pure silver,
the increase of light will of course be equivalent to the proportionably higher
reflective power of the latter, which, in the absence of good photometric ob-
servations, may be estimated at the least at a fourth. The same principles I
propose to apply to the improvement of the Gregorian telescope, with in-
verted surfaces.

In the case of the Newtonian reflector, and where the aperture does not
exceed 12 inches, the prism of total reflexion with plane surfaces, as at pre-
sent occasionally used, seems hardly to admit of improvement ; but for much
larger apertures, and especially when we approach the size of Lord Rosse's
great telescope, where the requisite size of the prism would involve the pass-
ing of the rays through about 6 inches of glass, the case is widely different,
and if the difficulty, not to speak of the expense, of procuring prisms of
homogeneous and perfectly annealed glass of adequate dimensions did
not prevent their use, their thickness would go far to neutralize their use-
fulness.

The arrangement which here first presented itself, as affording some spe-
cial advantages and permitting of a great reduction in the size of the reflect-
ing prism, was to construct the prism with a converging power, and place it
beyond the focus of the large speculum, so that the reflected pencil would
form a secondary image to be viewed by the eye-glass instead of the primary.
By adopting an aplanatic construction for the prism, the distinctness would
be preserved, and the entire arrangement better (as having fewer surfaces)
than the more obvious one of a small plane prism placed a short distance
within the focus, and reaching (so to speak) this image with a long com-
pound eyepiece of four lenses. Both constructions, however, include two
obvious disadvantages ; viz. a secondary image, illuminating the surfaces and
making the field less dark than otherwise ; and secondly, and which is of
more consequence, a very reduced field of view.

That form of the reflecting prism which I propose for adoption in the case
of large Newtonian reflectors, is as follows : — the prism is an aplanatic com-
pound o^ negative or diverging power ; this power is of course arbitrary or ad
libitum, but I prefer that it be such as will about halve the angle of con-
vergence of the pencil passing through it from the large speculum. As-
suming this proportion to be adopted, the practical effect will be as follows: —
the requisite size of the prism will be just halved (linearly), the resulting
image will be doubled in linear dimensions, and the magnifying power (with
any given eyepiece) augmented in the same proportion. The length of the
telescope will indeed be increased, but only by one-fourth of a diameter of
the large speculum. This arrangement has the obvious advantages of the
fewest possible surfaces, and no secondary image. It has been objected that
the field of view is by it lessened. I cannot consider such to be the case in a
practical sense ; for even with Lord Rosse's telescope of 54? feet focus, the
lowest eyepiece in general use may be doubled in all its proportions, and with
such lower-power eyepiece and the proposed prism, the magnifying power and
angular extent of field would correspond with these same as obtainable from
the combination of the higher eyepiece and ordinary plane mirror or plane
prism.

It will be observed that my proposed improvements, so far as described,
relate only to substitutes for the small mirror of reflecting telescopes ; and
for so far I consider they may be confidently and advantageously applied. I
see, however, no reason why the same may not be applied to the large specula

198 REPORT — 1857-

of the smaller reflecting instruments, and, assuming that cither the Cassegrain
or Gregorian form is selected, a beautiful principle of correction is indicated,
viz. : let both large and small mirrors be made each of a single piece of glass,
let the outer surface of the larger lens (that which when silvered becomes
the larger speculum of the telescope) differ in its radius of curvature from
that of the silvered surface by the least quantity which will sufficiently dis-
sipate its reflected image in the field, and let the outer surface of the smaller
lens (that which when silvered becomes the small speculum) diff'er from the sil-
vered surface of the same in an opposite manner, i.e.(allowing for the distance
between the two lenses) so that the colour produced by the refraction of the
larger lens shall be balanced by the colour of an opposing refraction in the
smaller. This done, the combination as a whole will be achromatized, and
the secondary images (or " ghosts ") so far dilated as to be insensible in the
field.

For the great speculum of instruments of the largest class we probably
must retain the speculum metal ; there is, however, a construction which is
possibly practical up to a considerable size, viz. that of a comparatively thin
lens, silvered at the back, and supported throughout its back (or nearly so) by
a thick or ribbed disc or casting of glass or metal, ground to fit with ade-
quate accuracy.

It may be useful, in concluding this section of the subject, to make a rough
comparison of the achromatic and reflector. A 15-inch reflector, in which the
suggested improvements were carried out so far only as the small metal is
concerned, would equal a 12-inch achromatic in light, and a reflector of 36
inches in diameter, similarly circumstanced, would be more than equivalent
to an achromatic of the size of the 29-inch discs already spoken of, while,
the length of the telescope being in each instance, for the achromatic, more
than double that of the reflector, the expense of the mounting may be
estimated as fourfold.

In passing to the second division of my subject, viz. the improvement of
the equatorial mounting of large telescopes, I would first briefly advert to
the several constructions in use, and which may be classed under three
varieties, two of which are of English, the third of German origin. We have,
then, the long-polar axis variety, which has the great disadvantage of the un-
steadiness resulting from the telescope being attached to nearly tlie toeakest
part of an axis longer than itself. Secondly, we have the overhanging con-
struction, consisting of a cone of great comparative w-eight and dimensions,
and prolonged beyond its upper bearing in a biforked manner, thereby ad-
mitting of the telescope turning on bearings within the projecting fork. This
construction requires for steadiness an unwieldy mass of moving matter in
proportion to the optical power it supports, four tons being used in the case
of a telescope of 8 inches aperture, a mass tenfold that required with a
better construction.

The third variety, or German form of equatorial, has the advantage of the
telescope being supported as close as possible to the strongest part of its
polar axis ; and the efficiency of such mounting is placed beyond doubt by
the well known Dorpat instrument, and subsequently by the Avorking of
still larger instruments, for example, that erected many years since in this
country for E. J. Cooper, Esq., where the telescope is 13^ inches aperture
and 24|^ feet focus, and which has remained in effective use, with scarcely any
repair, from the time of its erection, although unprovided with a dome or
other roof, — a point of no slight importance when we consider the expense of
such for so large an instrument, not to speak of the labour and time con-
sumed in moving it during observation.

ON TELESCOPES AND EQUATORIAL MOUNTINGS. 199

It will be seen, from this short mention of the several varieties of equato-
rial mountings, that I give a most decided preference to the general form or
principles of construction of the German instrument, in which preference it
cannot be supposed that there is any undue element of partiality, as none of
the forms are of my own devising. The British Association, it will be re-
collected, long since impressed with the importance to science of having a
powerful instruuient sent to a southern latitude, urged the British Govern-
ment to contribute to the work, and appointed a committee to examine and
select the most effective form of instrument, &c. &c. Anxious to be a suc-
cessful competitor in such an undertaking, I applied myself to remove the
only apparent objection to the German form of instrument, and also to devise
such modi K cation of its details as would suit it pre-eminently for a large re-
flecting telescope. Both these objects were accomplished with entire success.
My plan, as also estimates, had the honour of being approved of by the
Committee before referred to ; and although it would now appear as if, from
some occult cause, the distinction of being the constructor of the proposed
instrument is likely to remain an honorary one, still, as the improvements
sjjoken of are applicable to instruments of much smaller dimensions, it may
not be unprofitable to lay the general principles and results of these before
the Association.

Til at which the German form of equatorial seemed alone to require, was
a system of equipoise inter se, unobjectionable in itself, and which would
reduce the nature of the pressures of the declination axis on its bearings to
the same which these would be if the polar axis were vertical instead of in-
clined to the co-latitude of the observatory. The declination axis of a large
instrument of the German type has necessarily great diameter, and its bear-
ings, if ground in to fit without shake, as they may be in a small instrument,
M'ould have too much friction ; it is therefore desirable that the bearings
should be in effect Y^y, and in order that such bearings shall be as admissible
as in a meridional instrument, the pressure of the axis on each side of its Y
bearing should be equal in every position of the instrument ; moreover, it is
desirable that the end pressure of the declination axis, in all positions of the
instrument out of the meridian, shall be neutralized. These important condi-
tions are perfectly fulfilled by a system of internal counterpoise, which, being
applied, then permits of an external system of anti-friction rollers, relieving
the Y bearings of all but a fractional portion of the remaining pressure of
the declination axis and its appendages (viz. the telescope and its counter-
poise). The result of such arrangement may be readily anticipated; an
achromatic telescope of 12 inches aperture and 20 feet focus, so mounted
and with perfect steadiness, is moved by a force of about one pound applied
at the eye end.

Secondly, and for the equatorial mounting of the largest reflecting instru-
ments up to 6 feet diameter (the size of Lord Rosse's), if required, I modify
the German type, as shown in the drawings exhibited, by placing the decli-
nation axis within instead of beyond the larger end of the polar, and I invert
the whole. Thus the previous steadiness is rather increased; the bearings of
tlie polar axis may both be of minimum size, and the centre of gravity of the
whole instrument is brought as close to the ground-level as can be desired,
instead of being considerably aloft ; also, the settings and readings of the
largest instrument are rendered most convenient, and the observer is gene-
rally close to the ground, and never more than a few feet from it.

The subjoined Table contrasts the weights to be moved and power required
for the same, in the second English and improved German forms of equa-
torials, for telescopes of several sizes, viz. —

200

REPORT- — 1857.

C D

No.

u
1}
1}

Size of Instrument.

Forms of Jlounting.

Weight to Force required,
be moved, acting at a
in lbs. radius of 5 feet.

For a 4-feet reflector....
For .in 8-inch refractor..
For a 12-inch refractor..

(•English form No. 2

\ German form improved.

r English form No. 2

\ German form improved.

J English form No. 2

\ German form improved.

45,000 250
19,000 20

8,000 45
600 1

16,000 90
1,200 2

In respect to the foregoing Table, it is right to state, that, so far as Nos. 1
and 2 are concerned, the data in columns C and D are the results of cal-
culation ; and the same is to be understood of column D in the case of No. 3.
The data for No. 5 arc taken directly from those of No. 3, while the numbers
appended to No. 6 give the result of actual experience.

Report on the Experimental Plots in the Botanical Garden of the Royal
Agricultural College at Cirencester. By James Buckman, F.L.S., F.A.S.,
F.G.S., S)-c., Professor of Geology and Botany, Lecturer on Geology, (^c.
at the Cheltenham Proprietary College.

The experimental plots in tlie garden of tlie Royal Agricultural College
rest partly on a thin bed of forest marble clay and partly on the brashy soil
of the underlying Great Oolite, so that, although most of the soil is of a
heavy tenacious ciiaracter, stiil a large portion is that of the porous Stone-
brashes so prevalent in the district, the nature of the geology being readily
made out (rom the following section.

a. Forest Marble Clay.

b. White Freestones of the Great Oolite.

Neither the staple of the land itself, nor any method of cultivation that has
as yet been adopted renders this part of the Royal Agricultural College Farm
better, if indeed equal, to the land of the best part of the farm ; so that the
agricultural experiments at least are not likely to suffer in value from being
carried on too exclusively under the conditions of garden culture.

The garden is for the most part divided into plots, the greater portion of
which are 2^ yards square — many however are double that size, — whilst small
borders are occupied with single specimens of flowering plants, the latter
being mostly grown for assisting demonstrations in the lecture room.

With merelv agricultural experiments, the method I have adopted is to
first use a small plot, and then adopt either a 5-yard plot or four of these
united, after which the matter is transferred to the farm ; so that as time pro-
gresses, and facilities for carrying on these experiments increase, it is hoped
that this garden may be the means of introducing new and valuable varieties
of crops to the farmer, as well as of elucidating some interesting facts and
principles in Botanical science.

The plots for the present year, 1857, are employed in the growth of plants
in the following groups : —

EXPERIMENTS ON THE GROWTH OF PLANTS,

201

Plots.

1. Meadow and pasture grasses 66

2. Cereal grasses — Corn crops 16

3. Papilionaceous plants 30

4. Green feeding crops 20

5. Esculent vegetables 9

6. Economic and medicinal plants 16

7. Weeds 5

8. Flowering, ornamental, and other plants ... 50

Total 212

1. The Grasses. — These may be very conveniently divided into the
following groups.

a. Grasses of value in meadow and pasture.

b. Grasses which are but pasture or agrarian weeds.

c. Grasses which indicate certain conditions of soil, climate, &c.

As regards the plots of grasses generally, I may state that last year these
consisted to a great extent of two sets, one planted five years before, and a
new lot now just coming to perfection, the difficulty of keeping species un-
mixed, and other circumstances attendant upon growing specimens in small
plots, rendering frequent renewal absolutely necessary. As respects the
purity of a crop, the older beds offered some most interesting observations,
as they show how in a short period one species may be entirely lost, and the
ground be taken possession of by others ; hence the following : —
Original Crop*. Possessed by

Phleuni pratense. Arrhenatherura avenaceum.

Alopecurus pratensis. Dactylis glomerata.

Loliura Italicum Poa pratensis.

perenne. Poa pratensis and others.

Cynosurus cristatus. Holcus lanatus.

Poa trivialis. Poa nemoralis.

Three beds, side by side, have become mixed in the following manner.

Triticum caninum.

Wheat

Last year.

Hordeum murinum.

Observations of this nature are interesting in a practical point of view, as,
from cultivation or the want of it, meadows are constantly changing their
contents, good grasses gaining the ascendant in the former, and bad in the
latter. In my plots, bad grasses, that is those of a poor feeding quality,
take possession of plots originally sown with better kinds ; this arises from
the circumstance of the general poverty of the soil, which is assisted by these
crops never being depastured like those of meadows, but on the contrary are
left to perfect themselves for the teaching of the students, and consequently
are annually cut down as ripened or seeded grasses, thus affording a practical
example of the injury arising from exhausting crops, besides showing that

* These and most of the older beds have this year been occupied by totally diflferent crops,
the old crops of grasses being gradually destroyed.

202 REPORT — 1857.

many of the grasses only maintain a perfectly perennial habit by being crop-
ped off before tliey have seeded. This consummation having been attained,
many species, such as the Loliums, Hordeums, Dactylis, and Alopecums, die
out the same, or at best the second year afterwards ; and indeed in cultiva-
tion, even when cut before it is ripe, the old plants gradually die out.

Grasses indeed differ so much in the species that prevail and the well or
ill doing of these according to circumstances, that the practical observer of
them, either in a wild or cultivated shape, or, better, both, may become
acquainted not only with the broad features connected with the conditions
of soil, but all their inflections, such as its value, the cultivation it has
experienced or that should be adopted, mechanical texture, want of draining,
and the like.

As regards particular Botanical facts that have received illustration from
ray experiments, I would shortly comment upon the following genera : —
Alopecurus, Dactylis, Affrostis, Poa, Feshtca and JBromus*. Of the first two
genera, I received packets of seed from the seedsman with the following
names : —

Alopecurus pratensis. Dactylis glomerata.

„ nigricans. „ gigantea.

The A. nigricans I take to be but a variety of A. pratensis ; and indeed,
after three years of growth, it may almost be pronounced as identical. Both
do well ; and I can see no reason for preferring the one to the other, so alike
are they in growth and habit.

As regards the two names of Dactylis, for they are nothing more, they are
here inserted to note with reprehension a practice too often adopted by seeds-
men, of giving a new name from some accidental enlargement of form per-
haps arising from suitable soil — or other unimportant distinctions ; and tiius
disappointment results to the cultivator, while works are burdened with
synonyms.

Agrostis. — The last year's plots of this were as under : —

Plot A. Agrostis vulgaris. Plot B. Agi-ostis stolonifera.

These were sown in 1855, and at the last meeting they presented the follow-
ing appearances : —

A. "Presents the usual delicate A. vulgaris of the grass meadows with
a few plants of A. stolonifera intermixed."

B. "The general plant is A. vulgaris having ?i feiv A. stolonifera inter-
mixed; and these latter present more of the A. alba form than of the con-
gested inflorescence and true stolon growth of the A. stolonifera."

This seems to favour the view that the three forms are all referable to a
single speciesf , as when cultivated in a like position their broader features
of distinction are lost, and the seed of one, though for the most part coming
true, will still send up exceptional examples of each of the others ; but the
diversity of conditions under which the three forms occur in nature seems
sufHcient to account lor the different aspect which they assume, such as —

A. vulgaris, common to upland meadows.

A. alba, in ditches and damp places.

A. stolonifera, in stony brashes, mostly an accompaniment of agrarian con-
ditions.

* Avena and iEgilops to be noticed in the Cereal list.

f This is more strongly confirmed in the present year, 1857, as now

Plot A is attaining the size and appearance of A. alba.

Plot B is nearly all A. alba. These plots are on a thin clay bed.

EXPERIMENTS ON THE GROWTH OF PLANTS. 203

PoA. — Of this genus, among other species the two following were sown
side by side.

P. aquatica {Glyceria). P.fluitans {Glyceria).

These were sown in the autumn of 1855. During 1856 stiff and sturdy
sliort-and rigid-leaved plants were forming ; these leaves were so harsh as to
cut the flesh on the slightest touch. During the present year, 1857, they
have flowered, and to my utter astonishment the plants of both plots are the
same ; the culms were as much as a yard in height, and the flowers so small
and ovate as quite to justify the retaining of the generic name of Poa for the
whole group.

While these grasses were flowering, I watched them from day to day with
great interest, as in all their parts they differed so much from any known
species; the short rigid leaves with the angular sheath, and the elegant panicle
of flowers from their size, and the rigidity of the whole plant removed these
far from the P. pratensis, and the whole details differed so much from the
forms whose seed was sown as well as from all other recognised forms, that
while it showed me I could not have mistaken my seed, it also was con-
vincing that I had obtained a new and singular variety. This indeed is not
to be wondered at when we consider that both the forms, the aquatica and
fluifans, absolutely grow in the water ; but here I had got them to grow in an
upland situation, and to manage like other upland grasses with only water
from rain. Still the change was so curious, that I was anxious to re-examine
the seeds as sown ; and fortunately some of the packets were saved, and I
can pronounce them true as named*.

Here then I cannot help concluding that even such dissimilar grasses as
the typical forms of P. aquatica and P.fluitans are not specifically distinct ;
and though the former in its wild state bears a large and diffuse panicle of
flowers, and the latter is almost as spicate as a Lolium, yet we may, I think,
connect the evidence here presented to us with that obtained in the growth
of the Festiica loliacea pratensis and elatior presently to be detailed.

However, I shall not conclude my experiments upon this subject without
sowing some new plots with seeds of the hitherto supposed species gathered
by myself for the express purpose ; not that I in the least doubt these experi-
ments, but in order, if possible, to note the changes more clearlyf.

Festuca. — The species to be communicated upon I shall divide into two
groups.

a. Festuca ovina. b. Festuca loHacea.

„ j8 duriuscula. „ p pratensis.

„ y rubra. „ y elatior.

„ Itenuifolia.

(I. These were sown six years since in three distinct plots, and they soon
established themselves in a separate tufted method of growth. The first two
years they were readily distinguishable; now, however, the follo\ving facts
are observable.

F. ovina is about eighteen inches high; F. tenuifolia, duriuscula and
rubra differ but slightly in size, and scarcely in details, and the creeping
habit of root of the latter is entirely lost J.

It may be remarked that the F. rubra is not amongst our wild forms at
Cirencester, but I have occasionally met with specimens of F. duriuscula in

* The two packets were sent for examination,
t Specimens of the new Poas are sent for examination.

X Certainly not so much as regards the width and length of the leaves, as the same form
takes on in bushes when compared with the open ground.

204 RErORT — 1857.

the road dirt with which the tops of our stone walls are frequently capped,
having a decidedly creeping habit which, if shown as a tendency " in light
sandy pastures near the sea" which is given by Hooker as the habitat of the
F. rubra, may account for the difference.

As respects the varieties F. ovina, ienuifoUa and duriuscula, it may be
remarked that poor uplands present the first, the bushes and hedgerows
around these the second, and meadows examples of the latter ; but seldom
are they greatly intermixed, which, perhaps, may be taken as an argument
that these forms are but varieties induced by different circumstances. From
long observation and experiment I can only so consider them ; and had I a
choice of names for the typical form, 1 should choose that of duriuscula, as
the departure seems to be from that type, of which F. ovina is a mountain
form, and F. rubra a seaside or arenaceous one.

b. Festuca loliacea varieties.

Six years since, I sowed the seeds of the three forms as below, and in the
following order.

Festuca loliacea.

Festuca pratensis.

Festuca elatior.

These plots the first year of flowering presented appearances as under: —

1st. Festuca loliacea. — Most of the plants of the true spicate type, but
sparingly mixed with paniculate flowers : the herbage of which was of the
rich green which characterizes F. loliacea.

2nd. Festuca pratensis. — All true, but with a tendency to a rigidity of
leafage.

3rd. Festuca elatior, scarcely distinguishable from (2).

In three years great changes had been wrought as under : —

1st. F. loliacea. — No spicate flowers.

2nd. F. pratensis. — More rigid and larger, in fact none of the true mea-
dow type.

3rd. F. elatior. — A little larger, but otherwise not distinguishable from
(2).

In the fifth year the F. elatior prevailed in all the beds.

These plots are destroyed, as in 1855 the same experiments were recom-
menced in another part of the garden, the plots, however, being placed at a
distance apart; and the present year they were plainly observed to be taking
the same course as the others.

Here then, I think it satisfactorily proved by experiment that these three
forms are all of them referable to a single species, as the changes indicated
have taken place in individuals ; they, however, maintain their distinctive
characters under the following circumstances.

In meadows by the sides of rivers subject to occasional floods, as the Isis
at Oxford, or irrigated meadows, as on the banks of the Churn at Cirencester,
F. loliacea is constant in its characters, and is a most valuable grass for hay
or pasture.

In rich meadow flats, as in the Vale of Berkeley — the celebrated country
of the " double Gloucester cheese," — the F. pratensis is a common and valu-
able denizen, and any meadow where it maintains its character may be consi-
dered as of good quality.

EXPERIMENTS ON THE GEOWTII OF PLANTS. 205

On the alluvial sandy clay banks by the seaside, or poor siliceous clays
inland, the F. elatior rears its tall coarse form. In Gloucestershire the
banks of alluvial mud thrown up to prevent the encroachments of the water
in the Severn estuary are always occupied by this grass, which I look upon
only as the extension of the prafensis from the rich flats within this boundary.

The F. prafensis is a grass which is usually recommended for admixture
in forming new pastures, on which account there can be but little doubt that
it was used in the glades laid down within the last few years at the entrance
of Oakley Park, the seat of the Earl Bathurst. When first sown it came up
true enough, though with a disposition to reediness ; the last four years it has
become wholly F. elatio?- in all its features, and is now in such large coarse
" hassocks" as to be dissightly as a lawn, and much impairs the hay or pas-
ture. The secret of all this appears to be that here it was sown on the forest
marble sandy clays, the texture of which as a soil is similar to that in the
favourite habitat of this form of grass, and this too, though in a less degree,
no doubt, favoured the changes as observed in ray botanical garden.

Here then we see, in these forms of Fescue, plants which assume what
have been taken as specific characters, not only from change of circum-
stances giving rise to varieties which have been obtained from different
generations by seeding, but these have assumed the form of varieties from
the same seed and plants, and absolutely becoming F, pratensis, and after-
wards F. elatior from the typical F. loliacea : and so certain is this in my
experimental garden, that the result of twice sowing these three forms from
seed from different seedsmen has been the permanent establishment of F.
elatior in all three plots.

JBromus mollis varieties.

My experiments and observations upon the annual forms of Brome, though
still in progress, yet seem to warrant a diminution in specific names; for
example, B. mollis and B. racemosus of authors are sure to be intermixed to
a greater or less extent from the same seed ; thus the seed of the B. mollis
will have a sprinkling of the racemosus, whilst seed of the latter will present
exceptional examples of the former; and, besides, all distinction is lost in
every shade of intermediate form by which the hairy and smooth varieties
are connected.

Again, as regards B. eommutatus, this is by far too common a grass in pas-
tures subject to floods and in irrigated meadows, in which situation the
B. mollis is quite exceptional. Now, as I have watched the laying out
of poor pastures as irrigated meadows, I have always observed that two or
three years is often sufficient to change the B. mollis which was alone before
into B commulatus. Of course it may be considered that this was in virtue
of that law of substitution of one species for another which so universally
occurs on a change of soil and other conditions ; but I incline to the belief
that much of this is after all due to a change of form and specific character,
and as regards the grass under consideration our chain of evidence is nearly
complete when it is stated that the B. eommutatus from the irrigated mea-
dows, most certainly in experiments in my garden, has resulted in fine exam-
ples of B. secalinus, a form not before known there, and therefore not liable
to have led me into error, as would be the case where the diflPerent varieties
are wild natives near the spot.

I have not been able to experiment upon the whole of the forms of what
I would term the B. mollis group, but I suspect that the B. arvensis which I
this year found so abundantly on the c"halk about Avebury, in Wiltshire, is
but a form of the same ; and though in all probability a foreign one intro-
duced with "seeds," yet its individuality may have been implanted by

206 REPORT — 1857.

growth in a foreign soil, as I observed when in America most of the natural-
ized liritish plants had, to say the least, a different expression from the same
grown at home.

2. Ceiieal Grasses — Corn Crops. — The experiments in this list to
which I would direct attention are as under : —

Plots.

a. Peruvian Barley succeeding Swede Turnips — manured

with different manures G

b. Sowing of wheat at different depths "2.

c. Transmutation of oats 5

d. Experiments with ^^gilops 3

a. The Peruvian Barley was sown on account of the interest of this variety,
and also to occupy six large plots which were last year planted with Swede
Turnips : five plots with different manures, and one without manure for
comparison. The whole of the Turnip experiments, when complete, will
form a substantive report, I hope, next year. It may be enough here to
state that the result in the Turnips was widely different, but I could trace
no difference in the Barley.

h. For two autumns past I have sown wheat at different depths, from one
to seven inches. My crop of 18.56 came up tolerably regular, and that from
two to four inches in depth was certainly the best, the deeper sown being
thin, and tillering but indifferently : this year, however, the deeper sown is
very thin, and consequently with fine large ears, whilst that at less depth
is still more irregular and weaker, probably arising from injury caused by
wire worms. These experiments will be again repeated, and they are now
only noted, not to show any conclusions that have been arrived at, but to
point out how unsafe it is in agricultural experiments to generalize from a
single set of experiments, as these are so liable to be interfered with by in-
sects, climate, and a variety of causes.

c. When last year I had the pleasure of laying my notes upon these
experimental plots before the Section of the British Association, the early
period at which we met and the general lateness of the season prevented my
being enabled to report upon some experiments in oat transmutation which
the ripening of my crops subsequently showed to be of great interest ; and
as the interest consists in the fact that the Avena fatua has been made to
assume the forms of different varieties of cereal or cultivated oats, I shall now
detail the steps taken in bringing about this change*.

It is now six years since on a neighbouring farm, in a patch of seeding man-
gold wurtzels grown on forest marble, I observed an abundance of Avena
fatua; and as this wild grass is a great pest, especially in clay districts, such as
those on the Lias of the Vale of Gloucester and the Oxford Clay in Wilts, but
comparatively rare on the Oolite brashes, I took a class of students to exa-
mine it and gather specimens for the Herbarium, at the same time giving
them a field lecture upon this pest, in which I adverted to a tradition among
the farmers of the Vale of Gloucester, that " they were prevented from grow-
ing oats because they degenerated into wild oats;" and it was with a view
of determining if possible from experiment whether this notion was correct,
that I afterwards gathered some of the ripe seed of the wild oat, which in the
following spring I sowed in one of my plots. It came up very well, and the
process was repeated the following season in another part of the garden, and
in the autumn of 1855 I thought I remarked the following changes : — ■

1. A lighter-coloured fruit.

* Specimens of these changes accompanied the Report.

EXPERIMENTS ON THE GROWTH OF PLANTS. 207

2. A less degree of hairiuess when compared with the fruits of iho true
A.fatucu

3. A greenish coloured, straight and slight awn. instead of the black, bent
at right angles, and twisted at the lower part of the very rigid awn of the
wild plant.

4. The fruits were more frequently two than three perfect ones to each
glume.

5. The fruits were much more plump, arising from a greater development
of grain than in A. fatua.

6. The ripe fruits separated from the floral envelope less readily than in
A. fatua.

In following out the experiments in the spring of 1856, the best specimens
having been selected for seed were again sown ; and in the month of September
following, when this crop was gathered, the results were as under.

1st. Avena/atua, tolerably true, though perhaps not so coarse and strong
as is usual on heavy clays.

2nd. Avena fatua, var. sativa, with a diffuse, spicate, pyramidal panicle,
allied to the form called " Potatoe Oat," by farmers.

3rd. Avena fatua, var. sativa, with a compact panicle of flowers tending
to one side, allied to the agricultural form known as " Tartarian Oats."

The two latter presented various shades of advance ; a few of the more
changed were awnless, but most of them possessed awns which were very
coarse and rigid for what we may terra " tame oats ;" and the grain was by
no means so plump as (when compared with its thick envelope) to entitle it
to be called a good oat. However, it was sufiiciently striking, and, on the
whole, much more sudden in its advance than I had calculated upon. But
to proceed.

In the present year, 1857, I planted the sorts, carefully separated, in
separate patches of larger size, with the following result as to the crops.

a. The plot of Avena fatua is again mixed with many examples of the
Potatoe form of oat, but none of the Tartarian type.

b. The Potatoe oats have a plumper seed and are much less awned ; some
examples are however still rigidly awned.

c. The Tartarian form is much larger than is usually grown in the best
cultivation, its grain very fine, some awned, but mostly awnless.

Thus far then have these curious experiments proceeded. Next year they
will be transferred to the field, in the hope of perpetuating these new
varieties, as they promise to be much more vigorous than the older ones ;
and this indeed is one of the advantages in agriculture of new sorts, as, for a
time at least, they usually succeed better than the older ones. But this is a
matter I must not stop now to discuss.

It should be remarked that the shed seeds of the plot of 1856 were care-
fully dug in, in the hope that, by being allowed to deposit their seeds as in
nature, the whole may again degenerate into wild oats ; but only one speci-
men, and that of Afatuu, came up, for, having been so long submitted to
cultivative processes (and the gathering and storing of seed previously to
sowing is a very important one), they have little disposition to come up
wildly afterwards, a fact which is more observable in some situations than in
others ; and acting upon this hint, I am not quite sure whether the best way
to get rid of some weeds would not be to carefully cultivate them.

These experiments are of interest as showing what may be done in this
direction towards elucidating some curious facts in vegetable physiology.
They are no less so to the agriculturalist, as the remark of the old farmer,
which was never a favourite one with the botanist, is now known to be true ;

208 REPORT— 185/.

for if we can by experiment advance tiie vvild oat to the cultivated state, so
the cultivated by degenerating may relapse into the wild state. That the
latter position is true, I iiad long known from an examination of the produce
of shed oats around riclcs and in fields, as some of these in a single year will
be seen to possess a few hairs at the base of the fruit*, the awn will get longer
and more rigid witli a darker colour, and the seed niucii smaller. It would,
however, take too long to pursue an inquiry into the agricultural speculations
which these experiments might illustrate, and this perhaps may be better
done when our crops are still further advanced; and I need therefore only to
advert to such subjects as those involved in the growth of new sorts, the
reasons for their value, and the facts connected with their maintenance, to
prove this position.

d. ^gilops. — My three plots of this grass may be described as follows: —

1st. A permanent plot that is allowed to seed itself and groiu sporadically,
which it does v/ith great freedom.

2nd. A plot of carefully picked seeds sown in autumn.

3rd. The same seeds sown in spring.

In reporting upon JEgilops last year, I remarked upon the difficulty of
ripening the seeds. However, this is obviated, as the present condition of
Plot 1 shows it to have become perfectly acclimatized. I had last year some
reason to think I had made an advance towards proving the truth of M.
Fabre's statement as to this being the parent of the cultivated wheat; but
this year my examples have, if anything, retrograded. I shall therefore repeat
the experiments in my own private garden, which is a distance from the
College, and on a perfectly different soil. If M. Fabre's views be correct, I
should have little hope of success where the plant grows so well and the cir-
cumstances seem so suitable for its maintenance in a wild condition, cul-
tivation indeed consisting in the growing of plants in soils and situations
unsuitable for them in their wild nature.

3. Papilionaceous Plants. — As regards this family, my experiments
tend to show that many species may be made available for agricultural feed-
ing purposes more than are at present employed; these however need not now
be commented upon. I shall therefore confine myself to an account of ex-
periments and observations on the following ; —

Vicia angustifolia. Narrow-leaved vetch.

Trifolium pretense. Broad-leaved clover.

„ tnediujn. Ziczac clover.

Melilotus officinalis. Common melilot.

„ Taurica. Cabool clover.

In 1852 I collected seeds of Vicia angustifolia from the neighbourhood of
Cirencester, which I sowed in a plot. In the spring of 1853, it came up well;
but on flowering, only a few plants could be said to present the characters of
the species as laid down in books, or indeed as afforded by the parents of
these very specimens. The chief differences were much larger foliage, a
greater length of stem, a tendency to two flowers in the axils of the leaf
instead of a solitary one, and a great increase of size in the seeds. Now these
distinctions did not exist in more than 20 per cent, of the plants; and as
regards the difference in the seed, it may be remarked that it is rare to get a
sample of seed of the cultivated vetch but will be very variable.

In 1854-, I planted the seeds that were largest and most changed from

* I this year gathered a specimen from an old oat field on the Royal Agricultural College
Farm with four white hairs at the base, and the seeds had a tendency to separate with the
oblique scar, the grain still being plump.

EXPERIMENTS IN THE GROWTH OF PLANTS. 209

the original, the resulting crop being in all particulars the Vicia saliva of
authors.

In the autumn of the same year was planted a plot of the like selected seed
and with the same result, affording stems as much as 2^ feet in length, with
leaflets half an inch broad, its original size being about 6 inches long, with
leaflets a little more than the eighth of an inch broad.

From 18.'55, I have kept up a plot of each set, thus developing a winter
and spring variety of V. sativa from V. angustifolia, whilst at the same time
I have a plot in which the crop is permanently maintained by self-sown seeds;
these, though larger than in wild nature, still preserve the rounded pods
and small seeds with but little variation. The spring- and autumn-sown
varieties are about as distinctive in appearance as are the agricultural forms
of these.

Trifolium pratense. — This form in cultivation undergoes great changes,
particularly in size and colour ; it becomes many times larger, and its heads
of flowers increase in size but are less bright in colour. This plant is found
wild in all rich meadows and pastures ; its place however in poor sandy soils
where lime is absent is supplied by the Trifolium medium, on which account
the latter plant was some few years since introduced into agriculture, to
ensure a crop where the T. pratense usually failed. The seedsmen used to
supply it under the name of Trifolium medium, its proper botanical designa-
tion; but it is a curious circumstance that all the samples of this seed now in
the market are only those of a variety of T. pratense, and hence at present
the best-informed seedsmen no longer send it out under the original desig-
nation of T. medium, the " cow grass" of the farmer, but Avith the name of
Trifolium pratense perenne, the fact being now well established that we have
two varieties of broad clover in cultivation, whilst the true T. medium * has
been lost to agriculture until it be again introduced from wild plants ; and
the whole evidence with regard to this subject tends to show that it has not
been lost from neglect, as it has been in constant cultivation ; but it has
gradually merged into the T, pratense; and at this present moment the so-
called " broad clover" on the one hand and cow grass on the other are
scarcely distinguishable, and seedsmen are constantly threatened with actions
for supplying the wrong seed. This therefore remains as a matter for ex-
periment, not only on account of the practical advantage of reviving the lost
form to the farmer, but in order to settle the botanical question, as hitherto
the botanist has never had a doubt of the distinctness, as species, of the T.
pratense and T. mediumf.

Melilotus. — Of these the M. officinalis and M. Taurica are kept up from
self-sown seeds, as well as a plot of each drilled in rows the latter ; J received
some years since under the name of " Cabool clover," and I have since
obtained the same from the seedsman with the designation of " Buchara
clover:" they are probably only exotic forms of M. leucantha of the British
flora.

The Melilots among the Papilionacea and the Anthoxanthum odoratum
in the list of British grasses are alike remarkable for containing a peculiar
aromatic principle, to which as it occurs in the latter the sweet smell of

* It may be well bere to note that during the past week I have received some " cow-
grass" from Cheshire, which has more of the details of the true T. medium than any I have
yet seen : this case proves my position, because a great part of Cheshire has a subsoil of
marine sand, the bottom of the old strait which separated England from Wales, and on this
it continues ; and hence I view it only as an arenaceous form of T. pratense. But this fact
points out the propriety of getting cow-grass seed from the Cheshire sands.

t Seeds of T. medium from different localities would be highly valued by me. No seeds-
man can now supply the true form.

1857. ■ p

210 REPORT 1857.

meadow hay is due, and is probably the cause of the superior quality of pas-
ture hay when compared with that of the irrigated meadow, where this grass
is seldom present, as also with hay of artificial grasses technically called seeds.
If flavour and, with this, superior quality, be imparted to hay by the pre-
sence of an aromatic species, would it not be well to mix a portion of melilot
with clover and seeds ? Cattle are exceedingly fond of it, and it is a plant
which will grow readily and yield a large return in produce. To this end I
have cultivated the common melilot, and should prefer it to the M. Taurica,
on account of its less woody structure when mature.

These plants may be considered as biennial ; however, by frequent cutting
they may be made to last many years ; and the following experiments in
reference to this subject may be interesting, as showing the evil to the farmer
of letting clovers (for it is the same with the Trifolia) remain too long before
cutting.

A plot of M. Taurica of two years last summer had one-half of its rows
kept cut down and not allowed to seed, the other half was seeded ; and on
the ■ith of September, 1856, I made the following note : —

" Cabool Clover. — The cut-down rows about 18 inches high, fresh and
green, and fit for cattle food ; the rest in seed."

On the 1st of May, 1857, I made the following note : —
" Cabool Clover. — Tlie cut portion a tine succulent plant, 8 inches high ;
the seeded part very thin, 3 inches high."

This year each of my clover plots will perform double experiments, as in
them I am carrying on the same observations.

4. Green Feeding Crops. — In this list I would only advert to the
Symphytum, and Sanguisorba officinalis.

The Symphytum asperrimum was introduced to this country as an orna-
mental plant from the Caucasus, by the Messrs. Loddige, as long ago as 181 J,
since when it has been recommended as a profitable green feeding or soiling
crop for cattle, for which it seems adapted from its luxuriant growth and
good feeding properties. It is a handsome plant, growing as much as 4 feet
high, with an abundance of bright-blue bell-shaped flowers.

While experimenting on the growth of this plant, it struck me that the
Symphytum officinale of our ditches would be equally valuable if it could be
made to grow away from its natural habitat. With the view of testing this, I
introduced an example of the white form of S. officijiale from the River
Churn in Cirencester, into my garden, which year by year has so nearly
approached the asperrimum in its details, as to induce me to communicate
the experiment to the British Association at a former meeting ; and it was
again commented upon in my notes of last year before this Section, when it
was elicited from the Rev. J. L. Jenyns that " the S. asperrimum and <S'.
officinale were growing together near Bath, and that it was now impossible
to distinguish the one from the other." Here then I think I am justified
in now saying that there can be no doubt of the specific identity of these two
forms of plant.

Sanguisorba officinalis, on account of its astringent properties, may per-
haps be considered as a useful plant for admixture with sainfoin and clovers,
and to this end I have for years been anxious to try it as one of my experi-
ments; but it is a curious fact as showing the position of the seed trade, that
with as many as a dozen trials to procure it from as many seedsmen, and
always under its botanical designation, I have never been able to obtain it,
and all my plots have turned out Poterium sangicisorba, a plant of a different
character, and which can only be considered as a weed : indeed the buyer of
foreign sainfoin seed should be careful as to this plant, as in some samples

EXPERIMENTS IN THE GROWTH OF PLANTS. 211

a large per centage of Poterium will be present. Three plots are now occupied
with Poterium, the seed in all cases being labeled Sanguisorba officinalis, a
circumstance showing either a great want of knowledge or a wilful substitu-
tion of the one for the other on account of a similarity of aspect and English
name.

5. Esculent Vegetables. — A constant change in vegetable diet has
always appeared to me to be a matter of such great importance, that I seldom
miss an opportunity of making myself acquainted with the growth and ca-
pabilities of any new kind that may be introduced, as well as such as have
nearly passed away on account of the favouritism shown from time to time
towards new introductions ; and as examples of what I am doing in that way
I would notice the following : —

Potato Yam iDioscorea Batatas) . 1 ^ introductions

A wild Potato y »° iu-

The Yellow Lima Potato . . . ./ to this country.

o . ^ ^ Among the ail-but ex-

bchorzonera v i j j ^ ui

p , I ploded vegetables.

The potato yam is so much like our Tamus communis, as almost to lead
to the inference of specific identity, judging from the vine and foliage, for I
have not yet seen it in flower, much less in fruit. Its yearly increase of
tubers seems to me too small to warrant its displacing the potato, for which
it was recommended in the height of the disease of the latter plant. My plot
in the Botanical Garden is not nearly so luxuriant as some specimens in my
private garden, the latter being so much warmer and the soil considerably
better. Here my plants of this year are climbing up sticks and are as much
as 2 yards high ; what the tuber will be remains to be seen ; however, from
my present experience I can only recommend it as an addition to the list of
our culinary vegetables.

Last winter I was gratified at receiving a box of potato tubers which had
been sent me by my friend Jenkin H. Thomas, Lieut. R.N., consisting of
tubers of a " wild potato," and also some of a " Lima potato." The former
appears to be a Solanum ; but if of the species tuberosum, it is very different in
all particulars from our cultivated form, the tubers of the latter are more like
small kidney potatoes. But from the leaves and the slight indication of flower,
I do not think it can be a Solanum at all : but I am informed that they are
usually sold in Lima, so that I must make further inquiries into their previous
history. I would now remark that a plot of them in my experimental garden
has got on very badly, not more than five per cent, of the tubers growing, and
that in a feeble state ; however, three tubers planted in my private garden,
though they were a long time coming up, are now very large plants, and in
full vigour of growth.

As regards the wild potato, Lieut. Thomas writes as follows : — " I pro-
cured them from the top of a small island called San Lorenzo, opposite the
anchorage of Callao and town of Lima, in Peru, and I have not the slightest
doubt in my own mind but that they are the original potatoe, as the island
is uninhabited, and fertile only at the top (an elevation of about 900 feet),
where these potatoes grew : there is generally a mist over the top, and I think
the temperature from 68° to 70°. The blossom is the same as our domestic
one, but the leaf is prickly and rough ; I cooked several of them when I was
in Peru, but found them bitter and strong, but expect that cultivation and
a couple of years' trial will totally eradicate that." — In a letter to the author
of this report, Aug. 17, 1857.

212 REPORT — 1857.

The experiments with these in niy garden at the College have been a com-
parative failure — however, about a tenth of them have come up, — whilst in
ray private garden the six tubers which Iplanted all came up well, and flowered
and fruited too freely to expect much advance in the tubers ; they came up
quickly, and were in flower before the " Lima potatoes" (planted at the same
time) showed above ground. They are now before rae, and present the
following appearance : — the original tuber has much enlarged, and small and
imperfect young tubers stud the sides of the old one; they are very rough
externally, and of a decidedly bitter taste. I have preserved the roots, and
also a quantity of seeds, in order to carry on further experiments, as I see no
reason why, in a short time, I should not procure a new variety ot cultivated
potato from this stock ; but if these should afterwards present pinnate and
bipinnate leaves, it will be interesting to mark the progress of change from
the curious lobate leaf it now possesses.

The arriving at fresh potatoes from this source may do much to settle
some questions regarding potato disease. It has been recommended to grow
new varieties of this tuber from the apple or seeds, in order to procure a
sound stock ; but this in practice has failed, as seedling potatoes have been
found to be as prone to disease as others. It is, however, possible that this
may arise from the fact that the apples after all contain the seeds of an
unsound race; and I shall therefore look with great interest to the result of
the next few years in the growth and advance of this wild potato, and I
hope I shall have two races going, one derived from the tubers, and another
from the seeds.

Salsafy and Schorzonera are two capital roots, easy of cultivation, and
which readily store during the winter. They are not, perhaps, so produc-
tive as carrots and parsnips ; but they offer a good variation to these, both as
a change of crop and also as food : formerly they were highly esteemed, but,
like several other vegetables, they are now only found in the gardens of the
curious.

Cardoons. — This is a vegetable very little grown in England, and yet it is
of excellent quality, and not difficult of cultivation. Professor Lindley, in his
'Guide to the Orchard and Kitchen Garden,' p. 535, says, "The Cardoon
{Cynaru Cardunculus,) is greatly admired by many, and ought to have a place
in every gentleman's garden ; and yet it is curious how few of even gardeners
have ever seen it." It progresses well on my plots, and I hope to experiment
largely upon it in another season.

It may be well in this place to refer to some experiments which I have
now been carrying on for nearly ten years in the ennobling of the wild parsnip.
Of course it was known that our garden esculent was derived from the Pas-
tinaca sativa of our fields ; but the progress of the experiments has been
marked by some interesting facts relating to malformations of roots known
as finger-and-toe, and which will be found detailed in the ' Journal of the
Royal Agricultural Society ;' and at the same time it was a matter of no small
interest to myself and pupils to note the great changes that took place as the
experiments proceeded. The result has been the production of a good-sized
parsnip of a regular shape, but containing more flavour than is perhaps de-
sirable* ; but, inasmuch as some people complain of the want of flavour in the
ordinary cultivated parsnip, time may tone down my specimens to the re-
quisite degree. I would remark that I sadly want a change of soil for con-
tinuing the experiments, and I have this year grown a quantity of seed ; I

* During the time that my experiments have been in progress, I have been enabled to
■watch the downward progress of parsnips left from an abandoned garden ; and though these
have not even yet lost all traces of their civilization, they are essentially wild parsnips.

EXPERIMENTS IN THE GROWTH OF PLANTS. 213

shall be happy to forward some to any members of the Association on appli-
cation, only asking for the sake of information, any notes that may be made
on its progress.

It is not a little curious that experiments of a like kind with tlie carrot have
resulted in a failure. Upon reporting upon this last year, it was stated by
Mr. Bentham, that Villemain had succeeded in advancing the carrot and
some others, but had failed in all his experiments with the parsnip. This is
curious, as showing that we cannot always command success in experiments
of this nature — some circumstance or other may be wanting, and therefore we
must not pronounce a thing impossible that we have tried ourselves without
success ; and at the same time it shows us that there are certain laws which
operate to produce the changes we have noted, so that from a repetition of
experiments of this kind we may hope to become acquainted with some new
facts connected with vegetable growth.

An observation of some practical importance may be here noted. As a rule
it may be laid down that neither parsnips nor carrots yield good roots in field
cultivation in a district where these plants abound as wild natives, as they
usually grow small and very much forked, digitated, " finger-and-toed ;" and
therefore, if grown as an agricultural crop under such circumstances, a much
more careful preparation of the soil, even than that usually employed, will
be necessary to ensure success ; and thus it is that success is much more
general with these roots in garden than in field culture.

But, besides, this own-grown seed tends much to degeneracy, especially in
the field crop; and in the choice of seed we should always, if possible, choose
that from a poorer soil and backward climate rather than in poor root soils
to introduce a seed that had been grown in a district so much richer. These,
indeed, may almost be considered as general laws.

6. Economic and Medicinal Plants. — The success which has attended
my growing of many useful plants of this list in rough bits of ground, and
otherwise waste corners of my garden, as well as in poor unmanured plots, is
a matter of great interest, inasmuch as it shows that every bit of what is too
frequently waste ground may be turned to account, and made to yield at
least sufficient to pay the expenses, if not an overplus of profit ; one item,
however, the mere one of not losing, is gain, as cropping tends to get the land
in workable condition.

In the economic class, such plants as flax, hemp, teasels, chicory and
sunflower are all worthy of attention as being capable of yielding a good
return, and often in most unpromising positions. I shall now, however, in
this department only dwell upon some experiments in the growth of Linum
perenne (perennial flax).

In ISS^ I sowed one of my plots with seed of the L. atigustifolium
gathered at Hele in Cornwall. It came up very well, and in 1855 might
have been seen its plants in rows with branches a few inches long trailing
along the ground, some with light, others with dark- blue coloured flowers
somewhat small when compared with the L. usitatissimum or L. perenne;
in this state it presented little to recommend it as a cultivated plant. In the
past year it had advanced to a strong and vigorous upright plant somewhat
more than two feet in height, with handsome dark-blue flowers, indeed
rivalling the L. usitatissimum in size and beauty. As regards its fibre I
have as yet had no opportunity to make experiments ; but if in this respect
it should equal the annual flax, I cannot help thinking that we shall have
in the Linum perenne a plant of great economic value.

As regards the specific distinction of the L.angustifolium and L. perenne,
I must after thrse experiments express great doubts; nay, I am almost inclined

214 REPORT — 1857.

to think that L. usitatibsinmm is but an annual form oi L. perenne, so that
this year I shall collect the seeds of my perennial patch with a view of com-
mencing an annual cultivation. At all events, should I fail in proving this
point, we may fairly expect other changes of great interest, seeing that so
much has already been done in bringing a little straggling linseed from its
wild habitat, and cultivating in a different soil and climate, not by imitating
its wild conditions, but by making for it a new soil, and planting in rows so
that one row has the effect of inducing the upright growth to its neighbour,
— a fact readily seen in examining the growth of my plant as its shoots first
start in a trailing method — a circumstance which shows that in order to test
the capabilities of some plants for a crop, we can only do so not by growing
single specimen examples, but by planting a quantity side by side.

As subjects for experiment, it fortunately happens that the linseeds are
readily affected by cuitivative processes, so that we possess in them subjects
capable of affording much information as the result of carefully conducted
experiments, which leads me to remark that, as there are some tribes of
plants which we cannot so easily act upon, permanency of our appointed
species must not be concluded from the failure of our limited experiments,
though, on the other hand, species must give way in those cases where as the
result of properly conducted experiment the seed of one plant can be made
to produce what has been considered as a distinctly specific form.

As regards medicinal plants, such specimens as Hyoscyamus, Datura,
Papaver album, Coriander, and Caraway seem to do remarkably well in a
not over-good soil and with but little trouble, so that where a market can be
got for the produce, it might be worth while to attend to their cultivation,
especially in corners.

I shall here only remark upon experiments with the Datura Stramonium
and D. Tatula. A plot of each of these species was sown side by side, the
former from seed grown in the district ; the latter from seed kindly commu-
nicated by Mr. Savory the eminent apothecary and chemist, of New Bond-
street. Of the former not one seed came up, whilst of the latter several
plants at the time of my writing are in great perfection. I am informed by
Mr. Savory that this species is highly valuable as a remedial agent, it being
much more active and uniform in its action than the D. Stramonium ; and
he recommends it in the shape of cigars. Though these plants have been
referred to under distinct names, there can, I think, be but little doubt that
they are only varieties. The flowers of my specimens are but very slightly
tinctured with purple. These plants are very abundant in the United States,
the tinctured variety being much more common towards the South than in
the Northern States, and it is not at all improbable that the want of colour in
my specimens is the result of the cold, exposed climate of my garden, and
poor soil in which I have planted them*.

7. Weeds. —In this class I would notice the following plots : — a. Allium
vineale ; b. Carduus acaulis and others.

a. A plot was planted in the spring of 1856 with young plants oi Allium
vineale with the view of showing my class its method of growth, 1 pointing
out to them how to get rid of so direful a pest. In the summer it had
grown to good flowering heads, when, fearing lest it should overrun the
garden, I had them pulled up and put into a weed fire to burn. The
plot was left untouched until the spring of 1857, when to my astonishment
young plants shot up, and the rows of this plot were as complete as in the
former season. Upon reflection I saw in this a lesson which I had not my-

* Beck in his ' United States Botany' gives the D. Tatula as a variety of D. Stramo-
nium. The former is called the Indian, and the latter the American thorn-apple.

RESISTANCE OF TUBES TO COLLAPSE.

215

self sufficiently studied ; in order to explain which it will be necessary to
point out that around the bulb of this plant, will be found from one to four
bulblets, which at the time the plants begin to dry are easily separable from
the parent : it therefore happened that upon pulling up the stem, the bulblets
became detached and caused a thicker plant to spring up where I had
thought it destroyed. This shows how even the pulling of a plant of this
character is inefficacious for its destruction ; and it may further be appealed
to as one of those accidental experiments which almost every plot presents,
for it may be observed that in these plots many facts (of agricultural interest
especially) are daily unfolded by the College Garden experiments, that I
have not commented upon in this report.

As regards the Carduus acaulis, it will here only be necessary to say that
having found a new locality in Wilts, for Carduus tuberosus, I have brought
a few specimens into my garden, and as will be seen from a separate paper
which I have laid before the Section on this discovery, I have an idea that
the C. tuberosus is but a hybrid. I am cultivating the C. acaulis and C.
acanthoides side by side, in the hope of being able to prove this by experi-
ment.

8. Flowering and Ornamental Plants. — These for the most part
consist of such specimens as may be of use for teaching, or ornament in the
lecture-room ; and many of them afford interesting examples of departure
from recognized typical forms as to be of value in teaching, whilst others
seem to grow wildly and lose their whole cultivative characters. As yet I
have not attended to the cultivation of flowers merely as illustrations of trans-
mutation of species ; but I am convinced that such genera as Primula, Viola,
Myosotis, and Malva, &c., would furnish a vast amount of interesting matter
as the result of time and attention bestowed on their investigation.

Here then, for this meeting, must end my notes ; if, however, the Section
should deem them, or the class of experiment they have reference to, worthy
of continuation, the subject offers a field sufficiently wide, and, I think,
important for much future investigation and description, as it appears to me
that it is upon the noting and collecting such facts as can only be obtained
where the subjects of them are under constant observation, that we can hope
for much light being thrown upon the at present obscure subject of specific
distinctions ; and here, whilst experiments are being made upon this matter,
it is not too much to state that other facts of great interest are constantly
presenting themselves, so that while we are collecting evidence of a scientific
kind we may also expect to make experiments tending to useful practical and
economic discovery.

On the Resistance of Tubes to Collapse.
By William Faibbaikn, F.R.S.

At the joint request of the British Association and the Royal Society, a
series of experiments was undertaken to determine the laws which govern
the resisting powers of cylindrical tubes exposed to a uniform external
pressure, and from them to determine their strength, and deduce rules for
proportioning the internal flues of boilers and similar vessels.

Hitherto it has been considered as an axiom of boiler-engineering, that a
cylindrical tube placed in the position of a boiler flue, M'as equally strong in
every part when subjected to a uniform external pressure, the length not

216

REPORT 1857.

affecting the strength of a Hue placed in such circuuistances. This rule is,
however, applicable only to tubes of infinitely great length, or to tubes
unsupported by rigid rings at the extremities ; it is very far from true
where the length of the tube does not exceed certain limits, and where the
ends are retained in a cylindrical form by being securely fastened in rigid
frames to prevent their yielding to external pressure. Some experiments
upon large boilers, with flues 20 to 30 feet long and about 3 feet diameter,
first led to misgivings on this subject, by indicating the greater strength of
the shorter flue. This anomalous result induced further inquiry, which not
proving satisfactory, it was determined to submit the question to experiment,
in order to prove how far these doubts were entitled to credit

To attain the objects of the experiments in a satisfactory manner, it was
necessary that the apparatus for conducting them should be of great strength
and large dimensions. For this purpose a cast-iron cylinder C, 8 feet long,
28 inches in diameter, and 2 inches thick of metal, was prepared for the

reception of the tubes to be experimented upon. A small pipe, a, was
connected with a force pump, and by means of this, water was injected into
the cylinder and the requisite pressure obtained. A second pipe, b, com-
municated with two steam pressure gauges, by which the force required for
collapse was registered ; and the indications of these were checked by a small
and accurately fitted safety valve d. The large cylinder was fitted at top

RESISTANCE OP TUBES TO COLLAPSE. 217

and bottom with heavy ribbed covers, screwed to strong flanges on the
cylinder, calculated to sustain great pressure. The tube to be experimented
upon was fixed in the position shown at D, having cast-iron ends riveted
and soldered to it to render it perfectly water-tight. The small tube m,
communicating with the interior of the tube D, was for the purpose of
allowing the escape of the contained air at the moment of collapse. The
whole of the experiments were effected by means of the hydraulic pump, by
which water was forced into the cylinder C ; and the air, driven in a com-
pressed state into the upper part, became highly elastic as the pressure was
progressively increased until rupture took place. At very high pressures,
the air in the cylinder C was permitted to escape, and collapse effected by
water pressure only.

The tubes upon which the experiments were made varied from 18 inches
to 60 inches in length ; from 4 inches to 18f inches in diameter, and from
•OtS to '25 inch in thickness of metal. They were composed of plates of
riveted sheet-iron, and the thinnest were carefully brazed at the joints to
make them tight and prevent the entrance of water under pressure.

The results of the experiments may be stated under three heads : strength
as affected by length, as affected by diameter, and as affected by thickness
of metal.

1. Strength as affected by Length. — The results under this head are sin-
gularly interesting and conclusive. Within the limits of from 1*5 foot
to about 10 feet in length, it is found that the strength of tubes similar in
other respects, and supported at the ends by rigid rings, varies inversely as
the length.

Thus, taking the four-inch tubes of different lengths, we have the following
mean results derived from experiment : —

(1.) Resistance of four-inch Tvhes to Collapse.

Diameter. Thickness of Plates. Length. Collapsing Pressure.

ins. ins. ins. lbs. per sq. in.

4. -043 19 137

4 -043 60 43

4 -043 40 65

The remarkable differences which exist in the resisting powers of the above
similar tubes will be at once apparent. Assuming the experiment upon the
tube 60 inches long to be correct, we may easily calculate the strength of
the other 19- and 40-inch tubes, by the above-stated law of inverse pro-
portion.

Thus, for the 40-inch tube, we have 40 : 60 : : 43 : a:=64 lbs. And for the
19-inch tube,

19:60::43: j:=lS5lbs.,

where the calculated differ from the experimental results by ^jth in one case,
and xfy^'is i" ^^^ other.

(2.) Resistance of six-inch Tubes to Collapse.

Diameter. Thickness. Length. Collapsing Pressure,

ins. ins. ins. lbs. per sq. in.

(1.) 6 -043 30 55

(2.) 6 -043 59 32

Here, from the data of experiment (1.), we may calculate the strength of a
tube similar to that in experiment (2.)

59 : 30 :; 55 : a; =28 lbs.,
where the calculated differs from the experimental result by ^th.

218 REPORT — 1857-

(3.) Resistance of eight-inch Tubes to Collapse.
Diameter. Thickness. Length. Collapsing Pressure,

ins ins. ins. lbs. per sq. in.

(1.) 8 -043 39 32

(2.) 8 -043 30 39

where from (1.) we have

30 : 39 : : 32 : a;=41 lbs.

differing from the result in (2.) by /^ths.

(4.) Resistance of ten-inch Tubes to Collapse.

Diameter. Thickness. Length. Collapsing Pressure,

ins. ins. ins. lbs. per sq. in,

(I.) 10 -043 50 19

(2.) 10 -043 30 33

whence from (1.) we have

30: 50:: 19 : a-=3l§ lbs.
or \^ lb. less than experiment (2.). In the same manner all the experiments
might be taken and compared, and the law will be found to hold true in
every case. The discrepancies are comparatively small, and, as they appear
to follow no law, are evidently to be accounted for from defects in the con-
struction of the tubes and difficulties in the mode of conducting the expe-
riments, inseparable from such a mode of research.

II. Strength as affected by Diameter. — A precisely similar law is found
to hold in relation to the diameter. Tubes similar in other respects vary in
strength inversely as their diameters. Testing this law in the same manner
as the last, we may at once place the calculated pressure beside that derived
from experiment. Hence we have the following table: —

(1.) Resistance to Collapse of Tubes Jive feet long.

meter.

Collap

ing

Pressure.

lbs.

per sq. in

ins.

By Experiment.

Calculation.

Variation

4 ...

lbs.

6 ...

32 . . .

28-6

. . . -3-4

. . . 20-8 .

21-5

. . . +0-7

10 . .

16-0 .

17-2

14-3

1-2

12 .. .

12-5 .

1-8

The above variations are slight when compared with the resisting powers of
the tubes. They were no doubt caused by the varying rigidity of the iron
plates, or defects in the cylindrical form. Similarly we may take the results
on tubes 30 inches long, and tabulate them in a similar manner.

(2.) Resistance to Collapse of Tubes 2 feet 6 inches in length.
Diameter. Collapsing Pressure.

lbs.

per sq. in

Variation

ins.

By Experiment.

Calculation.

lbs.

4 ...

.... -6

6 ...

8 ...

. 39

10 . . .

. 31

. 26

12 ..

.... 4-4

As before, the variation between the results calculated by the law from

RESISTANCE OP TUBES TO COLLAPSE. 219

the data of one experiment and those arrived at by actual collapse, will
be seen to be very slight, and within the limits of error which might be
anticipated.

III. Strength as affected by the Thickness. — It is found that the tubes vary
in strength according to a certain power of the thickness, the index of which,
taicen from the mean of the experiments, is 2*] 9, or rather higher than the
square.

Combining the above laws into a general expression, we get as the formula
for the strength of tubes subjected to a uniform external force,

where P is the collapsing pressure, k the thickness of the plates, L the length
of the tube, which should not be less than 1*5, or greater than 10 feet; D
the diameter, and C a constant to be determined from the experiments. For
tubes of greater length than above specified, a variable quantity dependent
upon the length must be introduced ; and the value of this has yet to be
determined.

For ordinary practical calculations the following formula will probably
afford the needful accuracy,

a'
P=806,300Xj^^^.

Thus, for instance, take a flue 10 feet long, 2 feet in diameter, and com-
posed of ;^-inch plates. Here the collapsing pressure

•25'
P =806,300 X ,/^ =210 lbs.
10x24

per square inch nearly.

Some experiments have also been made upon elliptical tubes; and the
results have been most conclusive as to the weakness of this form in resisting
external pressure. No tubes in use for boilers should ever be made of the
elliptical form.

With regard to cylindrical flues, the experiments indicate the necessity of
an important modification of the ordinary mode of construction, in order to
render them secure at the high pressures to which they are now almost con-
stantly subjected. If we take a boiler of the ordinary construction, 30 feet
long, 7 feet in diameter, and with one or more flues 3 feet or 3 feet 6 inches
in diameter, it will be found that the outer shell is from three to three and a
half times as strong in resisting an internal force, as the flues which have to
resist the same external force. This being the case, it is evident that the
excess of strength in those parts of the vessel subjected to tension, is actually
of no value, so long as the elements of weakness are present in the other parts
subjected to compression. To remedy these defects of construction, it is pro-
posed that strong rigid rings of angle-iron should be riveted, at intervals, along
the flue, — thus practically reducing its length, or in other words, increasing its
strength to uniformity with that of the exterior shell of the boiler. This
alteration in the existing mode of construction is so simple, and yet so
efl'ective, that its adoption may be confidently recommended to the attention
of those interested in the construction of vessels so important to the success
of our manufacturing system, and yet fraught with such potent elements of
disaster when unscientifically constructed or improperly managed.

220 REPORT — 1857.

Report of the Proceedings of the Belfast Dredging Committee.
By George C. Hyndman.

In the comprehensive Report of the late Wm. Thompson, Esq., made in 1843,
the MoUusca of Belfast Bay were so far elucidated that but few species have
since been added, and it may be considered that little now remains to be
done in that department but to generalize the results, which may be summed
up at present by stating the numbers to be, of

Bivalves, Acephala lamellibranchiata, 96 species.

Brachiopods, Acephala palliobranchiata, 2 species.

Univalves, Gasteropoda prosobranchiata, 96 species.

Univalves, Gasteropoda opisthobranchiata, 1 1 species.

In all 205 species.

Of the Tunicata,the Nudibranchs, and the Cephalopods, little or no further
observations have been made since Mr. Thompson's report.

The Bay of Belfast is a wide open estuary, without any minor inlets and
not diversified with any islands, except the Copelands, which lie at its
entrance on the southern side. It is about seven miles wide between the
extreme headlands, and within that space its depth does not exceed 10
fathoms. It is only beyond this line that the depth increases to 20 fathoms,
and does not reach 50 fathoms till beyond the outermost of the Copeland
Islands.

The only river of any magnitude deserving notice that flows into the Bay,
is the Lagan, which enters at the extreme southern point, and has in the course
of ages considerably changed that portion of the Bay, by the deposits of gravel,
sand, and mud carried down. A very large area over which the tide once
flowed has thus been gradually filled up ; on it now stands a great portion of
the town of Belfast, with its numerous manufactories, places of business, and
the abodes of its stirring population. Evidence of this change occurs wherever
excavations have been made for wells and foundations of buildings, sea sand
and shells being generally found, sometimes at the depth of 30 feet and more
in places further up the valley than where the town stands. Further down
on either side of the Bay extensive changes have also taken place, by the
gradual rising of mud banks covered with Zostera, where so lately as sixty
or seventy years ago, people were in the habit of travelling along the strand at
low water between Belfast and the villages of Holywood and White Abbey.

Whilst these changes had been going on at the upper end of the Bay,
alterations of an opposite character were taking place on both sides still
further down, where, as at Cultra and Ballyhome Bay on the Down side, and
near Carrickfergus on the Antrim side, large portions of the land have been
undermined and swept away. Without supposing any variation in the winds
and tides, these latter changes may in part be accounted for by the continued
drawing away of gravel and sand, and the removal of numerous detached
rocks and reefs for building and other purposes, by which the shores have
been more exposed to the action of the waves than formerly.

These changes in the bed of the sea must have had a corresponding influ-
ence upon the Mollusca, many species which inhabited the sandy and muddy
tracts of shore having been covered up and killed ; and several species have
probably thus become extinct, as they are no longer found living : but on
this point as yet there is only negative evidence, and the subject requires
further investigation.

BELFAST DREDGING COMMITTEE.

MoLLUscA of Belfast Bay.

221

Species.

Observations.

Lamellibranchiata
Teredo Norvagica

Pholas dactylus

parva

crispata

Candida

Saxicava rugosa

arctica

Mya truncata

^~^ 9t

arenaria

Corbula nucleus

Pandora obtusa

Lyonsia Norvegica

Thracia pbaseolina

villosiuscula ,

pubescens ,

convexa

distorta

Cochlodesma praetenue...

Solen marginatus

sUiqua

ensis

pellucidus

Solecurtus coarctatus ..

Psammobia Ferroensis . .

tellinella

Tellina crassa

incarnata

tenuis

fabula

solidula

Syndosmya alba

dead

living
dead

living

dead

living
living
living
living
dead

living
living
living

living
dead
dead
dead
dead

dead
dead

dead

living

&dead

dead

dead
dead

dead
living
dead
living
living
dead

Not knovpn as living in the Bay. Found frequently in
drift wood dug up in making sewers in Belfast, and in
the excavations for the Harbour improvements.

In variegated marl between high and low water near
Carrickfergus : also on the County Down shore.

In submerged peat at the mouth of Conn's water, at the
upper end of the Bay on the County Down side, by
the late Dr. Drummond ; at White House Point on
the Antrim side by the Ordnance Survey Collectors.

In submerged peat at extreme low water in Bangor
Harbour, County Down, and in other places.

In the alluvial deposit at the head of the Bay, of very
large size.

On both sides of the Bay ; between tide marks common.

Common from low water mark to 25 fathoms.

Not uncommon in the deeper water.

Littoral, in mud.

At various depths to 25 fathoms. Of very large size in
the alluvial deposit.

Littoral in sand and mud.

In mud at 15 to 20 fathoms ; not abundant.

Off Castle Chichester and Black Head, in 15 to 20
fathoms ; rare.

On both sides of the Bay, in from 8 to 12 fathoms.

In the deeper water, scarce.

Off Groomsport, Edward Waller, Esq.

Recorded in Mr. Thompson's Report.

Not uncommon in the alluvial deposit cut through in
forming the new Channel, at a depth of 10 to 15 feet.
Not known to be now living in the Bay ; two spe-
cimens have been dredged oflf Black Head, broken,
but with ligament fresh, so that it is probably still
living ; its habit of burrowing places it out of reach
of the dredge.

In limestone near Belfast, Mr. Grainger.

In 20 fathoms off Black Head, valves united, rare.
Recorded by Brown as found in the Bay.

Off Bangor, County Down, and in alluvial deposits at
the Quays.

On both sides of the Bay. Very large and fine speci-
mens from Ballyhome Bay, Mrs. Clealand.

On both sides of the Bay, and of very large size at the
same place with the last.

Not uncommon in 6 to 20 fathoms.

Rare, in 20 fathoms off Black Head ; valves fresh and

united.
Rare, ofif Castle Chichester and Bangor, with valves

united. In the alluvial deposits.
Rare, off Castle Chichester.
Rare, in 10 fathoms off Castle Chichester, and also off

Groomsport.
Very rare, off Castle Chichester.
Not uncommon on sandy shores, both sides of the Bay.
Rare, off Bangor.

Common in mud between tide marks.
Rare in 8 to 10 fathoms.
In the alluvium near Belfast.

222

REPORT — 1857.

Species.

Observations.

Lamellibranchiata.
Syndosmya intermedia ...

living
living
dead

dead

living
living
dead
dead

dead
dead

living
dead
living
dead

living
living
dead
living

Rare, in the deeper water.

Rare, in 20 fathoms off Black Head.

Common in the alluvial deposit. At a depth of 30 feet,
in sinking a well at Durham Street Mill. At 18 feet
at Linfield Mill. On the muddy banks of the river
Lagan nearly as far up as the tide now flows. Has
not been found living, but is probably to be found.

A single valve dredged up off Castle Chichester, and
odd valves off Bangor.

On sandy shores between tide marks.

In 20 fathoms, not uncommon.

In shell sand from deep water, common.

On both sides of the Bay and in the alluvium, not un-
common. Probably living, but inaccessible to the
dredge. Common in the alluvium.

Rare, in the alluvial deposit.

Rare, in the alluvial deposit, of large size. Not
known to be now living in the Bay.

Common on both sides of the Bay.

Abundant in the alluvium.

Not common, in from 10 to 20 fathoms.

Common throughout the Bay at various depths, with
the valves fresh and united, and also in the alluvium.

Rare, off Bangor.

Common in sandy beaches between tide marks.

In the alluvial deposits.

Freouent in 20 fathoms.

Scrobicularia piperata ...

var. Saniiensis

dead Common in the deener water. Not found in the allu- 1

living
living

living
dead
dead

dead

living
dead
dead

living

living
dead

dead

living

dead
dead
dead
dead

vium.
Common from low water mark to 20 fathoms.
Not uncommon from 10 to 20 fathoms on both sides

of the Bay.
Rare, in 20 fathoms off Black Head.
Abundant in shell sand from deep water.
Scarce, in about 10 fathoms on both sides of the Bay.

On the shore at Cultra single valves are thrown up

by the tide. Probably still living.
Not uncommon with the valves united on both sides

of the Bay. Also in the alluvial deposits. Probably

living.
Not uncommon in 5 to 10 fathoms. Of very large

size in the alluvial deposit.
Rare, in 20 fathoms.
Frequent, of various sizes.
Rare, in shell sand from deep water.
Common in 10 to 20 fathoms, both sides of the Bay.

Rare, with the last.

Abundant in shell sand from deep water.

A smooth-edged variety of this, as well as of the
preceding. Query. — Can the difference be
sexual .'
Not common. In from 10 to 20 fathoms, valves often

united.
Common on sandy shores, but not in sufficient numbers

to be gathered for sale.
Rare, in 10 to 20 fathoms.
Rare, in 10 fathoms.
Rare, in shell sand from deep water.
Rare, in 10 to 20 fathoms.

lincta

var. Scotica, smooth-

Cardium echinatum

BELFAST DREDGING COMMITTEE.

223

Species.

Observations.

Lamelmbranchiata,
Lucina borealis

spinifera

flexuosa

Montacuta substriata —

bidentata

Turtonia minuta

Kellia suborbicularis .

rubra

Mvtilus edulis

dead

dead
dead
living

dead
living

dead
living
living

Modiola Modiolus.

Tulipa

Crenella discors.

' marmorata

decussata .

Nucula Nucleus.

nitida ....

radiata ....

living

living
living

living

dead
living
dead
living

Not uncommon in 6 to 12 fathoms. Of large size in
the alluvial deposits at Belfast.

Very rare, in 20 fathoms off Black Head, valves united.

Rare, in 5 fathoms, and in the alluvial deposits.

Rare, on Spatangus purpureus, in 20 to 25 fathoms off
Black Head.

Rare, off Bangor.

Abundant between tide marks. Found in great quantity
in the stomachs of Mullet taken in the Harbour near
Belfast. In one fish taken in Larue Lough and the
contents of the stomach given to me by W. Darragh,
Curator to the Belfast Museum, I estimated 35,000
of these little shells.

Rare, in mud from 10 fathoms.

Common between tide marks.

Very abundant on banks uncovered by the tide on both
sides of the Bay. They were in former days very
abundant on the banks off Holy wood,when they were
used as food, and also for bait. Now they have be-
come less plentiful and not so good in quality, and
are not so much sought after. Captain White, Har-
bour Master, tells me that in his early days it was a
common saying that " Mussels and Hemp paid the
Holywood rent." The Hemp was then grown for
making fishing gear, but has long ceased to be so
used. In Benn's History of Belfast, it is stated that
in 1739 and the following year, in consequence of the
great frost, crowds of wretched people from Belfast
and other places assembled on the Warren at Holy-
wood, and, pitching tents there, lived on the Mussels
found on the banks.
Mr. Patterson in his ' Zoology for Schools ' records a
similar case as having happened in 1792 or 1793,
when about 20 families of poor people came from the
interior of the country and encamped along the road-
side and on the beach a short way to the west of
Holywood. They remained there about five weeks,
subsisting principally upon the mussels from the
banks.
Mussels grow very rapidly, as a vessel lying in the Old
Channel for less than three months was found to be
covered with them, fully an inch in length. They
also attach themselves to the buoys, and even to
the pUot-smack which is kept sailing through the
Harbour.
Common at various depths from 6 fathoms. They are
dredged up in from 6 to 10 fathoms off Groomsport,
and used extensively as bait for Haddock and other
fish. They are also eaten by the fishermen. Very
commonly occupied by Pinnotheres pisum, the Pea
Crab.
Rare, in about 10 fathoms and deeper.
Rare, at the roots of Antennularia and other zoophytes

in from 10 to 25 fathoms.
Very common imbedded in Ascidia mentula, and some-
times moored by a byssus to shells and seaweed.
Rare, in shell sand from 27 fathoms ; valves united.
Common in muddy ground from 5 fathoms and deeper.
Rare, in shell sand from 27 fathoms.
Rare, off Groomsport. Edward Waller, Esq.

224

REPORT 1857.

Species.

Observations.

Lamellibranchiata.

Ledacaudata

Area tetragona

lactea ,

Pectunculus glycimeris . ,

Pinna pectinata .

Lima subauriculata
Loscombii

' hians .

Pecten varius.
Pusio .

• tigrinus .

' similis ..
' maximus

opercularis

Ostrea edulis ,

dead
living

dead
dead
living

dead

living

dead
living

dead
dead

living
living

living
dead

dead
living

living

Rare, in 20 to 25 fathoms off Black Head.

Imbedded in a pebble of black limestone in 50 fathoms,
off the Copeland Islands.

Rare, in shell sand from 27 fathoms.

Rare, with the preceding.

Rare, in 10 to 20 fathoms off Castle Chichester and
Black Head.

Abundant at the same place. Small-sized single valves
common in shell sand from deep water.

Rare, in 25 fathoms off Black Head. Pearls were
found in one specimen, of a brown colour like the
shell.

Very rare, in shell sand from 27 fathoms.

Rare, in 20 fathoms and deeper. Makes a nest for
itself like hians, but often occurs without any. The
animal swims vigorously through the water. The
late James Rose Clealand, Esq., of Rathgael House,
discovered this shell many years ago off the Copeland
Islands, and was aware of its making a nest. He
was one of the earliest dredgers in this bay.

Common in shell sand from deep water.

i\. single valve found in the alluvial deposit by Dr. Wm.
M'Gee; also recorded as found by the Ordnance
Survey Collectors in 7 fathoms ; but the shell has
never occurred in any of our late dredgings.

Not common, in about 10 fathoms.

Not uncommon among dead shells from 10 to 12
fathoms. Sometimes found inside a bivalve shell
closely fitting to its concavity.

Rare, in 20 fathoms and deeper.

Single valves not uncommon in shell sand from deep
water.

Rare, in shell sand from 27 fathoms.

Not uncommon in some localities. Mr. Hugh Gray, an
intelligent and experienced dredger and fisher from
Groomsport, tells me that these shells may be taken
in great numbers off Ballycormick Point close to the
shore in 7 to 10 fathoms, and also along the Antrim
coast and round the Copeland Islands. They are
seldom sought for exclusively, but taken in the search
for oysters, as they bring a very small price in the
market.
Abundant in some places and generally diffused through
the Bay, at various depths from 7 to 20 fathoms.
Mr. Gray says they are sometimes taken in great
numbers in trawling, by their shell fastening upon
the net. They are also sometimes taken by the
dredge and brought to market, but the price is so
low as not to remunerate the fishermen.
Abundant at various depths from near low water mark
to 25 fathoms. Attains a very large size and a great
age, if the number of layers of shell be taken as a
criterion. Those that are taken in this Bay have
long been esteemed for their good quality under the
name of Carrickfergus Oysters. The following in-
formation has been given me by Mr. Hugh Gray.
There are various beds through the Bay on which
Oysters may be had. One near the Lighthouse in
about 1 to 1;^ fathom. Other beds are from 2 to 8
fathoms. About four years ago a bed was discovered

BELFAST DREDGING COMMITTEE.

Species.

Observations.

Lamellibranchiata.

Anomia ephippium . .

aculeata

patelliformis

striata

Brachiofoda. Acephala

PaLLIOBRANCH I ATA

Terebratula caput ser-
pentis.

Crania anomala

Gasteropoda Pkoso
branchiata.

Chiton fascicularis

ruber

cinereus

asellus

albus

cancellatus

Itevis

mfirmoreus

Patella vulgata

living

living
living
dead
dead

living

dead
dead

living
living
living
living
living
living
living
living
living

• pellucida

living

near the Copeland Islands in 14 fathoms, now nearly
dredged out. This is the greatest depth at which
Oysters are generally taken for sale, but Mr. Gray
has known them brought up on the long lines from
45 fathoms, of large size and good quality. Oysters
generally prefer hard ground, that is, where stones
and dead shells are to be found to which they can
attach themselves ; they are of better quality on such
ground than on mud. He has seen their spawn, but
knows nothhig of their age, nor how long they are
in attaining their full size. The number of boats
employed in dredging has diminished of late years,
more owing, Mr. Gray thinks, to a falling off in price
than to any scarcity of the Oysters, which are now
imported in considerable quantitiesfrom Greencastle,
Stranraer, and Whitehaven. The highest price he
has known the fishermen to obtain was 21s. per 120.
They are now down to 7s. for the best, and have
been so low as 3s. when not of the best quality.

No attempt has been made to establish artificial beds
in Belfast Bay.

Common on oysters, scallops, and other shells at va-
rious depths. Upper valves of large size are some-
times found with laminaria attached.

Not very common, on laminaria.

Frequent on shells from 10 to 20 fathoms.

Common in shell sand from deep water.

Same as the last.

Very rare. Recorded as having been taken by the Ord-
nance Survey Collectors off White Head. Has not
occurred to any of us since within the Bay, although
found in deeper water outside.

Rare, in shell sand from deep water.

Rare, in shell sand from deep water, found living in the
deep water north of the Bay.

Determined by the late W. Thompson, Esq., and
published in his Report under the names by which
they were then known.

Common on rocks and stones between tide marks.
Within the Bay they are not much sought after as
food ; but at Groomsport Mr. Gray informs me they
are so used, and also as bait for Codling. Captain
White, Harbour Master, tells nie that they are found
to be good for eating and wholesome on the outer
coast of County Down, but that in Strangford Lough
they are found not to be wholesome, and are avoided
by the people there.

Common,h\\no'vimgmtot\iestemsoi Laminariadiyitaia.
Intheyoungstate on the leaves of the same plant. The
thin variety seems only to be found on rocky shores.

1857.

226

REPORT 1857.

Species.

Gasteropoda Proso-
branchiata.
Acmoea tcstudinalis

millegranus

Montagui

tumidus

■ cinerarius . . .

umbilicatus
•magus

helicinus ....

Phasianella pullus .

Adeorbis subcarinata.
I Scissurella crispata .
I lanthina communis .

Littoriua Neritoides
littorea

virginea

Propilidiuni ancjioide

Dentaliura entalis

Pileopsis Hungaricus..

Fissurella reticulata . .
Puncturella Noachina
Emarginula reticulata

crassa

Trochus ziziphinus ..

granulatus

Observations.

living Frequent on both sides of the Bay on rocks and stones
near low water mark.
First discovered as a British shell by the late James
Rose Clealaiid, Esq., and named after him by Sovrerby,
but it vras afterwards found to have been previously
described and named by Miiller.

living Rare, on oysters and dead shells from 10 fathoms.

dead Scarce, among the shell sand from 27 fathoms.

living In 90 to 100 fathoms off the Maidens.

living Common in from 5 to 20 fathoms.

living Rather scarce, among oysters and dead shells in 10 to
20 fathoms.

Uving Scarce, in similar situations with the last.

dead Rare, in shell sand from deep water.

living Common at various depths from 5 to 25 fathoms.

dead Frequent in shell sand from deep water.

living Very rare, in 60 fathoms off the Copeland Islands.

dead iRare, in shell sand from 20 fathoms and deeper.

living Common from Larainarian zone to deep water. The
white variety, Lyonsii, is occasionally found.

dead Very rare. Two broken specimens dredged up at
separate times in the Bay ; but as there are only two
other examples known of its being found so far from
its usual southern habitat, these have been no doubt
introduced accidentally.

living Rather scarce, in from 10 to 20 fathoms.

dead Abundant in shell sand from deep water. First taken
in this neighbourhood by the late J. R. Clealand,
Esq.

living Off Groomsport. (Edward Waller, Esq.)

dead Rare, in shell sand from deep water.

living Rare, in from 10 to 20 fathoms.

living Common between tide marks and a little deeper.

living Common between tide marks.

living Common in some situations on both sides of the Bay
from low water mark to 10 fathoms.

living Common on Laminaria digitata, &c.

living Frequent near low water mark.

dead Common in shell sand from deep water.

dead Rare, in shell sand from deep water.

dead Very rare, in same shell sand as last.

living Rarely found so far south in the Channel, but occasion-
ally abundant on the shore at Portrush and the
Giant's Causeway.

living Common near high water mark.

living Common on rocks between tide marks on both sides of
the Bay. Very abundant on banks on both sides of
the channel leading to the Harbour, from whence
the Periwinkles are gathered and exported in large
quantities to London. Mr. Getty, Secretary to the
Harbour Commissioners, informs me that this trade
has been carried on for the last 25 years by one per-
son, who employs three horses and a mule to draw
them, besides employing boats, &c., paying about
jE60 weekly in wages during the season. The Peri-
winkles are assorted and put into sacks, of which one
liundred are often shipped by one steamer weekly.
The quantity exported in 1854 amounted to 400 tons,
and in 1855 to 459 tons. During this long period

BELFAST DREDGING COMMITTEE.

227

Species.

Observations.

Gasteropoda Proso-
branchiata.

Littorina littorea

rudis .

patula ..
iittoralis

Lacuna pallidula

vincta

crassior

Rissoa striatula .

Zetlandica.

crenulata .

calathus .

Beanii ....

pur.ctura .

costata ....

striata ....

parva .

interriipta .
■ labiosa ....
rufilabrinn.
ciugillus .
ulvK

Slienea planorbis ....
Turritella communis .

Caecum glabrum

Aporhais pes pelecani
Ccrithium reticulatum

adversum .,

Scalar! a Turtoni

communis

clathratula

Aclis uiiica

Eulima polita

distorta

bilineata

Cliemnitzia riifescens..,
Odostomia uuidentata

plicata

eulimoides

there appears to have been no diminution in the
supply until this last season, when it is stated they
are not so plentiful as formerly,
dead In the alluvial deposits. I have found these shells in
a sandy beach on the banks of the Blackwater
(Blackstaflf), nearly two miles beyond the present
highest reach of the tide,
living Common on rocky ground a little below high water

mark,
living Common in similar localities as the last,
living Common among fuci on rocks and stones between tide

marks,
living Common on laminaria.
living Same as the last,
living Rather rare, on laminaria, &c.,in deeper water than the

two preceding,
dead Rare, in shell sand from deep water,
dead Rare, with the last,
dead Rare, do.

dead Rare, do.

dead Abundant, do.
dead Scarce, do.
dead Scarce, do.
dead Abundant, do.
living Common between tide marks,
living Common on sea- weed,
dead Common in shell sand,
living Common between tide marks,
living Abundant on banks where Zostera grows,
living Scarce on seaweed between tide marks,
living Common under stones near low water,
living Profusely scattered over the muddy shores left dry be-
tween high and low water.
In summer it is the chief food of the grey Mullet, which
is taken in the channel leading to the Docks. In
winter various sea-birds feed upon it.
living Common on seaweed near low water. Foand also in

the stomachs of grey Mullet,
living Frequent in from 10 to 20 fathoms,
dead In the alluvial deposits, of much larger size than any

now found living,
dead Rare, in shell sand from deep water,
living Common in 10 to 25 fathoms,
living Abundant on the muddy banks between tide marks,
dead Common in the alluvial deposits,
dead In shell sand from deep water.

dead Rare. In the alluvial deposits ; in one instance several
were found together. Not known as no\v living in
the Bay.
dead Rare in shell sand from deep water,
dead Rare, with the last,
dead Very rare, same as last.
dead Rare, in deep water,
dead Rare, in shell sand from deep water,
dead Not uncommon, with the last,
dead iRare, off Groomsport. (Edward Waller, Esq.)
dead jRare, in shell sand from deep water,
dead 'Rare, Bangor,
dead jRare, in shell sand from deep water.

228

REPORT — 1857.

Species.

Observations.

Gasteropoda Proso-
bran chi ata.
Odostomia interstincta ..,

spiralis

Natica monilifera

nitida

Montagui

Velutina laevigata

Lamellaria perspicua

Tricliotropis borealis

Cerithiopsis tubercularis

Mures erinaceus

Purpura Lapillus

Nassa reticulata.
incrassata .

Fusus Islandicus.
antiquus .

Trophon clathratus

muricatus

Barvicensis ..

Mangelia turricula..

rufa

septaiigularis

purpurea ...

linearis

nebula

costata

Cypra;a Europsea

moneia

dead
dead
dead
living
dead

dead
living
living
dead
dead
living
living

living
living
dead

Buccinura undatum living

dead

living
living

living

dead

living

dead

living

dead

Rare, vfith the last.

Rare, with the last.

Not common, off Bangor.

Rare, in about 10 fathoms.

A small white polished variety, or a distinct species, is
common in shell sand from deep water.

In 20 fathoms.

Rare, in 15 to 20 fathoms.

Rare, on Laminaria.

Rare, in shell sand from deep water.

Rare, with the last.

Rare, in deep water.

Common on rocks between high and low water mark,
sometimes found in deep water.

Occasionally found in 10 to 20 fathoms.

Comuion in 8 or 10 fathoms.

Common in deep water. In 30 fathoms off the Cope-
lands, many specimens were found very bright in
colour, and fresh, but all inhabited by Paguri.

Abundant from low water to 50 fathoms,

In the alluvial deposit and at various depths. At
Groomsport they are taken by means of baskets
baited with fish garbage, and sunk in any convenient
depth, and are used as bait for taking codfish. They
are never eaten here by the fishermen or poor people.
In this locality they are called Buckies, as are also
Fusus antiquus.

Not uncommon at various depths.

Common at various depth, principally in the deep water.
Taken for bait along with Buc. undatum.

A singular convoluted variety was dredged off Grooms-
port this season by Samuel Vance, Esq. No part of
the spire is visible except the few solid whorls at
the apex. Exhibited at the Meeting of the Associa-
tion, and since published in the Dublin Natural His-
tory Review.

Occasionally found in 6 to 10 fathoms on both sides of
the Bay.

Rare, off Groomsport and in the deeper water.

Rare, in 8 or 10 fathoms.

Frequent in 5 to 6 fathoms.

Rare, oft' Groomsport. (Edward Waller, Esq.)

Rare, in 10 fathoms.

Occasionally in deeper water.

Rare, in shell sand.
Rare, in same.
Rare, in same.
Rare, in 1 fathoms.

Not uncommon from low water to 20 fathoms.
Frequent at various depths.

Specimens of this shell have been frequently found on
the shore near Bangor, County Down. Although
not indigenous, its occurrence may be worth noticing,
as there is a tradition that a ship engaged in the slave
trade was wrecked there, and thus the Cowries are
accounted for.

BELFAST DREDGING COMMITTEE.

229

Species.

Observations.

Gasteropoda Opistho-
branchiata.
Cylichna cylindracea

dead
dead
dead
dead
dead
living

living

dead
living
living

living

Rare, in shell sand.

With the last.

Rare, off Bangor, and in shell sand.

Abundant on the Zostera banks. Sometimes thrown

up on the Kinnegar, Holywood, in great numbers. I

have sometimes seen it swimming in the channel

leading to the Quays, giving out a purple liquid when

touched.
Very rare. A single specimen from Groomsport many

years ago ; none since.
Not uncommon of large size off Groomsport in 6 or 8

fathoms, and in other places.
Occasionally found at various depths.
Plentiful, occasionally in a few fathoms.
Rather scarce, in 8 or 10 fathoms, off Bangor and

Groomsport, and in Castle Chichester Bay.
Scarce, off Groomsport in 6 or 8 fathoms and in other

places.

Akera buUata

Bulla Crauchii

Scaphander lignarius

Pleurobranchus membra-
naceus.

In the course of their various proceedings in dredging, the Committee
were aided by several gentlemen amateurs, who lent their yachts for the
purpose and otherwise assisted; and in the year 1856 they were joined in
their labours by Edward Waller, Esq., whose cooperation has proved of
great service in determining species.

In 1850 Mr. Getty and Mr. Hyndman had first become aware of a deposit
of fine shell sand in about 27 fathoms at the entrance of the Bay, which
produced several rare species of shells, Propilidium ancyloide, Puncturella
Noachina, Scissurella crispata, Adeorbis subcarinata, Rissoa Beanii, Tere-
bratula caput serpentis, and Crania anomala, all dead; and in 1852 further
research led to the discovery of a great submarine bank known to the fisher-
men as " the Turbot Bank," lying a short distance out from the cliffs called
the Gobbins, on the coast of Antrim, and extending from the Isle of Muck
across the entrance of Belfast Bay towards the Copeland Islands. Fishing
by means of long lines had formerly been successfully carried on upon this
bank within the recollection of some of the fishermen, but has been given up
for several years, as the fish, from whatever cause, do not now frequent the
bank.

This locality having been further explored in 1856 during a dredging
excursion, a quantity of sand was brought up so rich in shells that it was
thought desirable to have a list made out. With this view the sand was
examined by Mr. Waller, Dr. Dickie, and Mr. Hyndman. Some of the species
more difficult to determine have been named for Mr. Waller by the kindness
of Joshua Alder, Esq. ; such species are marked A, including Mangelia
Holbollii, an interesting addition to the British fauna.

The Turbot Bank lies in about 25 to 30 fathoms ; the ridge is composed
of gravel and broken shells, more or less fine, the finer being in the top,
while the edges towards the deeper water are made up of coarse rolled
pebbles derived from the rocks of the adjoining coast, and found by Messrs.
McAdam and Bryce to consist of Trap, Marl, Grey wacke. Porphyry, Quartz,
Flint, Sandstone, and Coal, — the last no doubt from the passing vessels.

230

REPORT — 1857.

The following is a summary of the species : —

Acephala lamellibranchiata 83

palliobranchiata 2

Gasteropoda prosobranchiata 97

opisthobranchiata 11

In all 193

List of Shells from the Turbot Bank.
Those marked A. determined by J. Alder, Esq.

Species.

Observations.

Pholas striata

very rare

scarce
frequent
scarce
scarce
scarce

rare

rare
scarce
scarce

rare

rare
scarce

rare

rare
scarce

rare

rare
scarce
scarce
scarce
common

rare

scarce.

common

rare.

common

frequent

scarce

frequent

scarce

common

scarce
frequent
frequent

dead

dead.

dead

dead.

living.

dead.

dead

dead.

dead

dead
dead
living
dead

dead,
dead,
dead,
dead

dead.

dead

2 single valves only found. It is not ad-
mitted as a British shell by Forbes and
Hanley, and it is no doubt an intro-
duced species in shipwrecked Maho-
gany.

Fragments mostly.
Fragments only.

Valves united.

A few living, dead shells common.
Fragments only.

Sometimes with valves united.

Sometimes with valves united.
Sometimes with valves united.
Single valves not uncommon.
Occasionally living, single valves very
frequent.

From the smallest size up to full-grown,
valves often united.

Livingoccasionally, single valvescommon.
Single valves of small size.

Saxicava arctica

Sphoenia Binghami, A

Cochlodesma praetenue...
Solecurtus coarctatus ...
Psammobia FeiToensis ...

Tellina crassa

solidula....,

Syndosmj'a alba

prismatica

Mactra elUptica

striatula

ovata

Artemis exoleta

lincta

BELFAST DREDGING COMMITTEE.

231

Species.

Astarte triangularis

Cardium echinatum ...

edule

nodosum

fasciatum

pygraaeura

Suecicum

Norvegicum

Lucina borealis

spinifera

flexuosa

leucoma

Montacuta substriata...,
Turtonia minuta.
Kellia suborbicularis.

rubra.

Mytilus edulis

Modiola Modiolus

tulipa?

Crenella discors

marmorata

decussata

Nucula Nucleus

nitida

Leda caudata

Area tetragona

lactea

Pectunculiis glycimeris.

Piuna pectinata .

Lima Loscombii ..

subauriculata

Pecten varius

• pusio

' striatus .
■ tigrinus .

Danicus?

similis

maximus

opercularis

Ostrea edulis

Anemia ephippium

aculeata

patelliformis

striata

Terebratula caput serpen
[tis

Crania anomala

Chiton asellus

Patella vulgata

pellucida

Acmaea virginea

Pilidium f ulvum

very frequent

rare

frequent

not common

frequent

scarce

not common

rare

common

scarce

frequent

scarce

common

frequent
rare

frequent

rare

scarce

common

frequent

scarce

frequent

scarce

not common

frequent

rare

dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
living

living
dead
dead,
dead,
dead,
dead
dead,
dead,
dead,
dead,
dead

Observations.

Living, rare; valves united common,

single valves very frequent.
Like sulcata, there is a smooth-edged var.

of this. Quaere, is the difference sexual ?

On Spatanffus purpureas.

Small-sized single valves.
On the edge of the bank.
Single valves.

Both valves entire, frequent.]

living,
dead,
dead,
dead,
dead

Full-sized with valves united frequent.
Single valves of various sizes abun-
dant. Very rarely alive, and only small-
sized specimens.

Living specimens have been taken by
trawling. Fragments sometimes found.

Single valves and fragments common.

Single valves.

Single valves (Dr. Dickie).

Living on the edge of the bank. Single
valves common.

(Dr. Dickie).

Single valves.

Single and broken valves.

Small-sized single valves common.

Fragments and broken shells.

Single valves.

Living in the deep water, single valves
not uncommon.

Same as the last.

Dr. Dickie.

232

REPORT — 1857.

Species.

Observations.

Propilidiuin ancyloide ...

frequent

frequent
scarce

rare

rare
common

rare
frequent
abundant

frequent

not common

scarce

frequent

scarce

very rare

not common

scarce

very frequent

scarce

rare

abundant

scarce

common

frequent

scarce

frequent

rare.

frequent

rare

scarce

frequent

scarce

very rare

rare

very rare

rare

frequent

scarce

rare

dead

dead,
dead
dead,
dead,
dead,
dead,
dead,
dead.

dead,
dead,
dead,
dead.

dead,
dead,
dead
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead,
dead.

In the fine shell sand taken in 1850
merous. Scarce ever since.

Of small size only.
Dr. Dickie, doubtful.

In the fine shell sand only.
Determined also by Mr. Hanley.

A single specimen by Mr. Waller.

nu-

Pileopsis Hutigai-icus

Fissuvella reticulata

Puncturella Noacliiiia ...
Emarginula reticulata ...

Troclius zizyphinus

cinerarius

magus.

heliciuus.

Adeorbis subcarinata

Scissurella crispata

Zetlandica, A

inconspicua, A

Turritella communis

Aporhais pes pelecani ...
Cerithium rcticulatum ...

Scalaria communis

distorta, var. gracilis

Chemnitzia elegantissima
fulvocincta, A

indistincta, A

Odostomia conspicua, A...

BELFAST DREDGING COMMITTEE.

233

Species.

Observations.

Odostomia unidentata ...

dead.

acuta, A

dead,
dead.

eulimoides, A

plicata, A

dead.

interstincta, A

dead.

spiralis, A

frequent
scarce
rare

dead,
dead.

Natica nit ida

tnouilifera

dead,
dead.

Montagui

Velutina ItGvigata

scarce
scarce

dead,
dead.

Trichotropis borealis

Cerithiopsis tubercularis..

scarce

dead.

Murex erinaceus

rare
not common

dead,
dead.

Purpura lapillus

Nassa reticulata

scarce
scarce
rare

dead,
dead,
dead

(Dr. Dickie.)
Fry very common.

incrassata

pygmsea ?

Buccinum undatuin

frequent

dead

Fusus Islandicus

frequent

dead

Very common.

antiquus

frequent
frequent

dead.

Trophon clathratus, A

dead.

muricatus, A

frequent
scarce

dead,
dead.

Barvicensis, A

Mangelia turricula, A. ...

scarce

dead;

rufa, A.

septangularis.

teres

rare

dead

Fragments.

linearis, A.

nebula.

striolata.

costata, A.

Holbollii,A

rare

dead

This rare shell, new to the British list,
was first discovered in shell sand

dredged up in 1856. It vyas distin-

guished at once by hoth Mr. Waller

and Mr. Hyndman as diflFering from

any species described by Forhes and

Hanley, and vcas determined by Mr.

Alder.

Cyprsea Europsea .*••

frequent

very rare

rare

dead.

Ovula patula

dead

A single specimen (Mr. Waller).
Ditto (ditto).

acuminata

dead
dead.

Cylichna cylindracea

scarce

very rare

dead,
dead,
dead,
dead

A single specimen each to Dr. Dickie and

Tornatella fasciata

Bulla Cranchii

Scaphander lignarius

rare

dead.

G. C. H.

Philine aperta

scarce
rare

dead,
dead.

It will be seen from the foregoing list that with few exceptions the shells
are dead and many of them inhabitants of deep water ; it therefore became
an object of interest to discover the locality from whence they were derived,
and this may now be considered to be ascertained. In Admiral Beechey's
Hydrographic Survey there is indicated a deep recess in the Channel not
far distant from an extensive ridge of rocks lying off the entrance to Larne
Lough, on which the two Maidens Lighthouses are erected. Here in a
limited area is a depth of from 80 to 100 fathoms; but it is difficult for

234

REPORT — 1857.

dredging operations, owing to the strong current of the tides and the eddies
formed by the sunken rocks. After several unsuccessful attempts to reach
this region by Mr. Getty and Mr. Hyndman, the latter was at length, in
1856, enabled to accomplish his object through the kind assistance of Captain
Hoskyn, R.N., then engaged in completing the Survey, and who brought to
the task the experience gained under the late Captain Graves, R.N., while
dredging in the TEgean. A few hauls of the dredge produced Terebratula caput
serpentis and Propilidium ancyloide alive, besides some rare Crustacea and
Zoophytes. In 1857 a steamer was engaged, and a day spent in further
explorations, the result of which is now given ; but it is evident that further
investigation in this locality is desirable and likely to repay the labour.

List of Species taken in deep water, 70 to 100 fathoms, off the
Maidens Lighthouses, 1856 and 1857.

Species.

Observations.

dead
dead,
dead,
dead,
living
dead,
living
living
dead,
living
dead,
dead,
living
living
living
dead,
dead,
dead,
dead,
living
living
living
living
dead,
living
dead,
living
dead.
Uving
living
dead,
living
living
living
dead
dead,
living
living
dead,
living
living
dead.

A single broken specimen.

Small sized, 70 to 100 fathoms.

90 fathoms, several dead with Paguri.

90 fathoms.

100 fathoms.
100 fathoms.
100 fathoms.

100 fathoms.
70 fathoms.
70 to 1 00 fathoms.
70 to 90 fathoms.

70 fathoms.

75 fathoms, very fine.

75 fathoms.

90 fathoms, small size.

90 fathoms.

In Ascidia mentula, 75 fathoms.

90 fathoms.

Valves united, 75 fathoms.

70 to 90 fathoms.
70 to 90 fathoms.

70 fathoms.
70 fathoms.

clathratus «

DentaUum entalis

Propilidium ancyloide

Terebratula caput serpeutis

Pectunculus glycimeris

Crenella marmorata

var. Scotica

BELFAST DREDGING COMMITTEE.

235

Species.

Observations.

living
living
living
dead,
living
living
living
living
living
living
living
dead,
living
living
living
living
living

75 fathoms, at roots of Sertularia.
75 fathoms.
90 fathoms.

75 fathoms.

70 fathoms, small sized.

90 fathoms.

90 fathoms, very small sized.

90 fathoms.

100 fathoms, very small size.

70 fathoms.

Balanus porcatus (Scoticus)

Pagurus Thompsoni ?

Amphidotus roseus

Echinocyamus pusillus

living 75 fathoms,
living 75 to 100 fathoms,
living 175 fathoms.

Several Zoophytes taken with the foregoing have yet to be fully examined,
for which purpose they are in the hands of Professor Wyville Thomson, who
has observed among them a new form of Sertularia.

Zoophytes received from the North of Ireland.

By Professor Wyville Thomson, Queen's College, Belfast.

ZOOPHYTA HYDROIDA.

TUBULARINA.

Fam. 1. CorynidcE.
Clava (Gmelin).
C. multicornis, Font. Very common on seaweed between tide-marks.
Belfast Bay, Strangford Lough, &c. Constantly dioecious. The males dis-
tinguished from the females by the lighter and brighter colour of the repro-
ductive organs. In this species the Medusoid zooid is not developed. A
very variable species.

HVDRACTINIA.

H. echinata, Flem. sp. Common on old shells, usually associated with a
Pagurus.

CORYNE.

C.pusilla, Gaut. Abundant on seaweed between tide marks and on
Zoophytes in the Coralline zone.

EUDENDRIUM.

E. rameum, Pall. Frequent in Belfast Lough. A specimen dredged off
the Gobbins. Mr. Hyndman.

E.ramosum, Ellis. Frequent in Belfast Lough. Off Crawfordsburn, male
and female. In this species both male and female individuals developed
Medusoid zooids. These zooids sometimes become early disengaged, and
sometimes remain attaclied until the male and female generative products
are fully matured.

i have met with one or two other small species of this genus, but have not
had an opportunity of examining them fully.

236 REPORT — 1857-

TUBULARIA.

T. indivisa, L. In deep water. Common.

T. Dumertieri. On Fbisfra truncata. Belfast Bay.

T. Larynx. " Belfast and Strangford Loughs."— Wm. Thompson.

Sertulariadce.
TnoA.
T. halecina, L. Common. Belfast Bay, &c.

T. Beanii, Johnst. Common. Belfast Bay, &c. ^c. In the male the
aperture of the vesicle is placed at or near the apex ; in the female near the
centre of the capsule. , /^ „

T. muricata, Ellis. A specimen in the late Wm. Thompsons Collection,
marked "Newcastle, Co. Down."

Sertularia.

S. polyzonias, L. Common.

S. rugosa. Common.

S. rosacea. Not very common. Belfast Lough.

S. Allied to rosacea. Dredged off Bangor, Co. Down.

S. Allied to rosacea. A specimen dredged by Mr. Hyndman off

the Gobbins, Co. Antrim. A specimen procured previously by myself in
Lamlash Bay, Arran.

S. pumila. Very common. In some cases, at all events, the testes of
this species, developing parent-cells and spermatozoa, are thrown out in a
gelatinous envelope from the mouth of the capsule ; and the female organs
forming ova without intermediate " zooids," are retained within the ovarian
vesicle till mature.

S. Pinaster. Frequent in Belfast Bay, &c.

S. Tamarisca, L. Belfast Bay, &c.

>S'. abietina, L. Common.

S.filicula, Ellis. Rare. In the late Wm. Thompson's Collection.

S. operculata, L. Common.

S. argentea, Ellis. Common.

>S'. cupressina, L. Magilligan Strand. (Templeton.)

Thuiaria.
T. Thuia, L. North Coast of Ireland. (Wm. Thompson.)
T. artieulata, Pall. Belfast Lough, Coast of Co. Down.

Antennularia.
A. antennina, L. Common.
A. ramosa, L. Common.

Plumularia.

P.falcata, L. Common.

P. cristxiia, Lam. On Halidrys siliquosa. N. Coast of Ireland. (Wm.
Thompson.)

P. pinnata, L. Frequent.

P. setacea, Ellis. Frequent.

P. Catharina, Johnst. Belfast Bay.

P. myriophyllum, L. White Head near Carrickfergus. M'Calla.

P. frutescens, Ellis. A specimen dredged off the Gobbins by Mr.
Hyndman.

BELFAST DREDGING COMMITTEE.

237

CampanulariadcB.

Laomedea.
L. dichotoma, L. Common.
L. geniculata, L. Very common.
L. gelatinosa, Pall. Common.
L. Flemingii, Milne-Edwards. Common.
L. lacerata, Johnst. Deep water.

Campanularia.
C. volubilis, Ellis. Common.
C. Johnstoni, Alder. Common.
C. Hinchsii, Alder. In deep water. Common.
C. verticillata, L. Not common. Belfast Bay.
C? ? dumosa, Flem. Very common.
Coppinia arcta, Dalyell, sp. On Plumidaria falcata.
Halia reticulata, Wy. T. On Sertularia abietina. Common.

The following Polyzoa, from the deep water near the Maidens Rocks,
have been determined by the Rev. Thomas Hincks: —

Tubulipora hispida.
• ' serpens.
Cellepora pumicosa.

. Skenii.

Hippothoa catenularia.

divaricata.

Flustra foliacea.
Membranipora Flemingii.

coriacea.

Lepralia Malusii.

Hyndmanni.

simplex.

Lepralia reticulata.

fissa.

ciliata.

labrosa.

annulata.

innominata.

auriculata.

Brogniartii.

linearis.

coccinea.

pertusa.

spinifera.

FoRAMiNiFERA. Belfast Bay.

Professor Williamson having expressed a wish to be supplied with some
of the sand dredged up from different depths and localities in order to ascer-
tain the Foraminifera of the district, a quantity was accordingly forwarded
to him ; and the following list has been obligingly furnished of the different
forms obtained by him from the sand, which he pronounces not rich in these
organisms : —

Lagena vulgaris.
— — var. clavata.

— var. perlucida.

var. striata.

Entosolenia marginata, young.

squamosa..

Polystomella crispa.

umbilicatula.

Rotalina Beccarii.

globularis.

Globigerina bulloides.
Planorbulina vulgaris.

Truncatulina lobatula.
Bulimina pupoides, var. fusiformis.
Polymorphina lactea.
Textularia cuneiformis.
Biloculina bulloides.

var. carinata.

var. Patagonica.

Spiroloculina concentrica.
Miliolina seminulum.

var. oblongum.

bicornis, var. angulata.

Spirillina' foliacea, young.

The Belfast Dredging Committee for 1858, are Professor Dickie, Profes-
sor Wyville Thomson, Mr. Patterson, and Mr. Hyndman.

238 REPORT — 1857.

On the Mechanical Effect of combining Girders and Suspension Chains,
and a comparison of the weight of Metal in Oi-dinary and Suspension
Girders, to proditce equal defections with a given load. By Peter
W. Barlow, F.R.S.

My attention has been recently directed to this subject from having been
required to investigate, as engineer of the Londonderry and Enniskillen, and
Londonderry and Coleraine Railways, the best mode of effecting a junction
between the lines at Londonderry, to be combined with an improved road
communication, for which an Act has been obtained by the Corporation of
the city ; and the Commissioners having determined to advertise for plans,
leaving the decision to Sir William Cubitt, an engineer justly occupying a
position so eminent, and in whose judgment I had the greatest confidence, I
determined to submit the result of my investigation to him, although the
principle which I concluded would best meet all the circumstances of the
case, viz. the suspension girder, was one with reference to which consi-
derable prejudice had existed.

Sir William Cubitt, after devoting much attention to the subject, has fully
sanctioned the principle, and recommended the Bridge Commissioners to
carry out my design, with some modifications suggested by hnn.

In order to verify my calculations, I have caused a series of experiments
to be made, the results of which are of so much practical importance, and so
fully confirm my investigations, that I determined to lay them before the
British Association, in order that the simple question of the mechanical effects
of combining a girder with a suspension chain, on which no difference of
opinion ought to exist, should be fully decided ; but before describing these
experiments I will make a few general remarks upon the systems which have
been adopted in bridge constructions.

General remarks upon the construction of Bridges of large span. — Bridges
may be divided into three classes : —

1st. The Arch, a structure in which the supporting material is subjected to
compression alone, but which contains no rigidity in itself.

2nd. The Suspension Bridge, in which the supporting material is sub-
jected to extension alone, which also contains no rigidity in itself; and

3rd. The Girder, in which the material is subjected to both extension and
compression, of which there are two varieties; one, which is subjected to
diagonal strains, as the lattice, Warren, and tubular girders ; and a second,
in which all the strains are confined to the upper and lower webs, as in the
bow and string ; and Mr. Brunei's new girder, which is a combination of
an arch and a suspension chain, each doing half the supporting duty.

This second variety is the most simple form, but has no more rigidity in
itself than an ordinary arch or suspension bridge.

Of these three systems, the girder necessarily requires, from combining
compressive and extensive resistances, a much larger amount of metal than
either of the other systems, which will be rendered evident by a simple inves-
tigation, and by reference to existing structures.

In an ordinary arch the compressive force is resisted by the abutments,
which in no way add weight or strain to the metal ; but if the arch is converted
into a girder, it can only be done by adding a tie-bar, the arch having then
to support its own tie or substitute for an abutment, in addition to its own
weight.

In a suspension bridge the tensile force is resisted by back chains, and
if these are taken away to make it a girder, a compression-tube or bar has to
be used as a substitute for them (as in the Chepstow bridge), which tube

GIRDERS AND SUSPENSION CHAINS COMBINED. 239

becomes in large spans, with its supports, by far the largest portion of tlie
structure, and destroys the bridge by its own weight, the weight of metal
being fully doubled to produce equal strength, and quadrupled to produce
equal stiffness, if loaded equally all over.

The great difference in weight produced by this and other causes will be
seen by comparing suspension girder bridges with ordinary girder bridges ;
and I will take as an example the case of the two largest railway openings
yet constructed, the Niagara suspension girder bridge, and compare its weight
of metal with that of the Britannia Tube.

The quantity of material in the Niagara Bridge, having a roadway and a
single railway of three gauges in a span of 820 feet, is in round numbers
1000 tons, and the weight in the Britannia Tube of 460 feet span 3000 tons
for a double line.

If the Britannia Tube had been made on the same principle as the Niagara
Bridge, the quantity of material to give the same strength and rigidity would
not have exceeded ^th part of what has actually been employed.

So great a difference in the weight renders it obvious that the principle of
an ordinary girder involves great extra material, and it became an interesting
and important inquiry to ascertain the cause of this difference.

The view that has hitherto been generally adopted on this subject, is that
advanced by Mr. E. Clark in his work on the Britannia Tube, in which he
states, speaking of the proposal to use the Menai suspension bridge for
railway purposes, — "With respect to the use of the present suspension bridge
for the proposed traffic, it was found difficult to devise any means of suffi-
ciently strengthening it that did not involve an almost entire reconstruction,
and great difficulty M'as similarly found in attempting to render any suspension
bridge sufficiently rigid for railway traffic, by means of ordinary trussing.

" When the passing load is small compared to the weight of the chains and
of the structure itself, there is indeed no difficulty ; but the construction of a
platform 450 feet long, sufficiently rigid for railway traffic, almost amounts
to the construction of the tube itself."

Although unsupported by fact or experiment, this theory has been received
and acted upon, not only by a large portion of the public, whose impressions
of suspension bridges are derived from what had hitherto been constructed
of insufficient strength, and without being combined with a girder, but it has
been received and acted upon by engineers of eminence in this country.

These experiments, however, distinctly prove that a suspended girder, as
designed for the Londonderry Bridge, is rendered equally rigid with less than
^th of the metal required in the girder alone, so that the most important
economy arises from the combination of a girder with a chain.

Experiments on Suspe?mon Girders. — I have had the model accurately
made, which is now submitted to the meeting, on a scale of ^rd part of the
actual span, the length being 13' 6" between the bearings, — a length exceed-
ing that of the average of the models used by the Iron Commissioners in their
experiments, and is amply sufficient, due allowance being made for the scale,
to determine with accuracy the deflections on the actual girder, although the
deflections of the chains will be somewhat more on the model than on the
girder, from the weight not being sufficient to bring the surfaces into perfect
contact.

The principal object of the experiments was to ascertain the deflection of
the wave of a girder attached to a chain, as compared with the deflection of
the same girder detached.

This being obtained, it was perfectly easy to arrive at the deflection of the
wave of the Londonderry Bridge, because we have sufficient experiments on
girders to enable a calculation to be made of what the Londonderry girder

240 REPORT — 1857.

would deflect without the chain, which being obtained and reduced in the
ratio of the girder attached to the girder detached, gave the true deflection.
My first intention was to maice the experiments with a girder which was a
correct model of the actual bridge, which would have indicated ^rd of the
actual deflection, but I found the deflection of the wave to be so small that
it was difficult to measure it with sufficient accuracy, and I therefore had a
wooden box made of the correct depth, with the sides as thin as it would stand,
viz. ^ deal plank, in order to obtain greater deflection of the wave, with the
correct depth of the girder, and with the chain attached to it as in the pro-
posed bridge.

I could no longer obtain the actual deflection of the Londonderry Bridge
by multiplying the experimental deflections by 33, but knowing that the de-
flection of a model on the correct scale would be ^rd of the Londonderry
girder, and knowing by experiment how much the model was deflected when
unattached, the actual deflection of the Londonderry girder is obtained by
reducing the observed experimental deflection in the ratio of the rigidity of
the actual model to a true model, and then multiplying by 33.

The deflections of this girder, taken without the chains attached, with a
weight of 168 lbs. on the centre, was -Jo of an inch ; with the chain attached,
and M'ith the weight placed ^ from the high tower, it was as follows: —

Centre. |- from Low Tower.

in. in.

•010 -010

•040 -010

•040 •OlO

•020 -000

•040 •OO.'i

•050 -005

The ratio of the deflection of the wave at |th the distance, where the
greatest amount arises when the chain is attached, to that in the middle
when not attached, is as 1 to 10 only ; but it was evident from the large
deflection at the centre and from no rise occurring at the opposite end, that
the girder was too rigid to indicate the wave, and that the deflection observed
was greatly due to the chain not coming to its bearing.

I therefore decided, in order to magnify the wave and make its amount
more distinct, to have a girder made of angle-iron 1 inch thick and a quarter
the depth of the former girder, but simply suspended from and not attached
to the chain.

The deflection of this girder without the chains, with a load of 42 lbs.
placed on the centre, was r2 inch.

The deflections of the wave with the chain attached, and 227 lbs. distributed
over the girder when the weights were placed at 1 from the high tovrer,
were with —

lbs.

^ from High Tower

in.

•030

112

•060

168

•075

Experin
•030

112

•050

168

•075

lbs.

5 from High Tower.

Centre.

3 from Low Tower.

in.

-•10

-•01

+ •05

112

-•20

-•04

+ •12

168

-•28

-•06

+ •16

Experiment 2. — In this case the weights were placed \ from the low tower.

56 +-06 -•Ol —-12

112 +^15 -^05 -^25

168 +^18 -^07 --36

The deflections here averaged "32 inch with 168 lb?., equal to •OB inch with

42 lbs., or yljth the deflection of the girder without the chain.

from

^ from

f from

:V from

i. T.

11. T.

"H. T.

-•31

-•48

-•32

-•02

GIRDERS AND SUSPENSION CHAINS COMBINED. 241

The deflection of the Londonderry girder, deduced from the mean results
of the deflections of the Boyne Viaduct and Newark Bridge and the Britannia
Tube (see Appendix A), was 33 inches with 100 tons in the centre, ^'f =2^20
inches, the deflection here indicated in the Londonderry Bridge with 100
tons placed at a quarter the length of the girder.

It was still obvious from the deflection at the centre and little rise exhi-
bited in the wave, that the stretching of the chain to bring the metal surfaces
to bear, still sensibly influenced the result, and I had another wooden girder
made, consisting of a plank 7^ inches in width and |th of an inch thick, in
order still more to magnify the wave, and to diminish the error from the
stretching of the chain.

The deflection without the chain attached was I'lS inch with 10 lbs.

Experiments loith the Chain attached. — With 56 lbs. placed at \ from tlie
high tower on the girder which was previously quite unloaded, the deflec-
tions were at —

I from % from i from

II. T. H. T. H. T.

+ •22 +^29 +-15

Experiment 2. — 70 lbs. being equally distributed over the girder, and
56 lbs. at \ from high tower —

-•28 —^42 —-25 +*04 +^23 +-28 +-20
Experiment 3. — 150 lbs. all over weight in same place —

—•20 -•So — -20 +^02 +-20 +^23 +'14

Experiment 4. — 193 lbs. equally distributed, 56 lbs. as before —
-•18 --31 -•I? +-05 +-IS +^20 -l-^H

The deflection here indicated with the model loaded with a weight repre-
senting 96 tons on the bridge (which experiment was several times repeated),
was '31 with 56 lbs. = ^055 with 10 lbs., or ^^^yth of the deflection of the girder
without the chain ; #|-= 1 "27 is therefore the deflection of the wave indicated
by the experiment of the Londonderry Bridge, with a load of 100 tons at -L
from the toAver.

To obtain the comparative rigidity of the experimental girder, we have
here as —

2061bs. : lOlbs. : : 1 in. : '0485, the deflection of a true model with 10 lbs,;

•0485 ^^ 30^ represents the rigidity of the experimental girder; 2^x33 =

•335, the deflection by a weight on the bridge of 56 X 33-=27 tons.

27 : 100 : : "335 : r27, the deflection as previously calculated.

This result being so much at variance with the general view of the subject,
although very nearly in accordance with my calculations, I determined to
verify it by a smaller girder, 6 inches by -|ths of an inch thick, whicli would
render the wave still more visible, the observations being made with great
nicet}'.

The deflection at the centre when not attached to the chain was 2*375
inches with 8 lbs.

Girder attached to the chains, 193 lbs. being equally distributed over it.
The deflection, with the weight placed 1 from the high tower, was —
lbs. -^frora H. T. Centre. i from L. T.

56 --64 +*13 +^53

Experiment 2. — With 56ibs at the centre of the bridge the deflection was
—SO.

The deflection of the wave here exhibited at ^th of the lengtii with the
bridge loaded to a weight equivalent to 100 tons on the actual bridge, which

1857. R

242 REPORT— 1857.

experiment was repeated several times with the same result, was O'Gi inch
with 56 lbs., the deflection without the chains being 2'375 with 8 lbs., or 25
times the amount.

In determining; how far this result was effected by the resistance produced
b}' the change of figure in the curve of the chain, I removed all the weights
from the plank, and found the result as follows, with 56 lbs. at -\ from the
high tower : —

■J from H. T. Centre. \ from L. T.

—•85 +-20 +'75

With 56 lbs. placed 1 from low tower —

+ •81 +-12 --86

From this experiment it appears that the deflection is decreased by loading
the bridge to ^th of that ol the girder unattached, and if the chain were
M'ithout weight it would be still further reduced ; in practice, however, the
weight on the bridge will much exceed that on a model, and ^th will be the
least amount that will arise, a result so at variance with the preconceived
notions of many engineers, that it is to be expected in some instances it
will be received with incredulity ; but an investigation will show that the

result is in accordance with the law T-^-^a constant quantity.

If the girder were supported only in the middle, the deflection of the half
girder would be ^th, but as one half of the girder cannot deflect without the
other half rising, from the action of the chain, it is reduced to -j^th ; but the
girder is not supported at one point only, but at various points, which will
still further reduce the deflection.

However, whether this view is precisely the correct one or not, the fact is
established, that the deflection of the wave of a girder attached to the chain
and loaded as in the actual bridge, will not exceed -j^th of the same girder
without the chain, from which we may estimate the weight of girder sufficient
to produce in a suspension bridge or arch the requisite rigidity.

In order to show the impoi'tance of this result in the cost of bridges, I will
compare the deflection and weight of metal in a bridge similar to the Lon-
donderry Bridge, with a girder of equal span, in each case assuming that
3 tons per foot on the bridge will bring no strain exceeding 5 tons per inch
on the metal.
The weight of chain, such that 3 tons per foot on the girder will

not exceed 5 tons per inch, is (see Appendix B) 150 tons.

The weight of girder suflScient to give no wave or deflection

greater than P32in. with 100 tons (see Appendix A) .... 150 „
The weight of metal in cast-iron columns, so that the greatest
compression with 3 tons per foot is 4 tons per inch (see Ap-
pendix C) GO „

Weight of suspension ban, so that the tensile strain does not ex-
ceed 5 tons per inch with 3 tons per foot load (see Ap-
pendix D) 15 „

375
To this must be added the value of the cost of the anchorage
of the chains, which in the Londonderry Bridge will be 15
per cent, of the iron-work of the main girder portion of the
bridge, so that I iiave added 57 tons to represent the value
of the cost 57 »

4'32 tons.

GIRDERS AND SUSPENSION CHAINS COMBINED. 243

To compare this weight with that of a girder alone of the same length and
depth as that used, which would be equally rigid with the suspension girder,
we have to multiply 150x25 = 3750 tons, or more than eight times the
amount of metal ; but it may be correctly argued that a simple girder would
be made deeper, and it is therefore fairer to make the comparison with an
actual girder, of which we have an example nearly the same span in the
Britannia Tube.

The weight of the pair of the Britannia Tubes is 3100 tons, or more than
seven times the amount, a difference which will be received with surprise;
but it is perfectly consistent with the fact that the Derry Bridge has nearly
three times the depth, and has 2660 tons less of its own weight to support.

The weight of metal in the Londonderry Bridge does not in fact exceed
that of the sides of one of the Britannia Tubes without the top and bottom
webs.

It should be observed that the proportion of the cost of anchorage will
vary under different circumstances, but in the case of the Londonderry
Bridge it will be under 15 per cent.

It should also be noticed, on the other hand, as a set-off to the cost of
anchorage, that the foundations Avill be increased in a girder bridge, from
their having to support 3110 tons as compared with 432 tons in the suspension
bridge, Avhich will produce an amount in saving in average cases equal to
the anchorage.

We will now compare the rigidity of the suspension bridge with that of
the tube.

The deflection from 1 ton per foot all over the suspension bridge (see
Appendix A) will be 1^ inch.

The deflection of one of the Britannia Tubes from 1 ton per foot all over
is 3-\ inches.

The greatest wave that will be produced by a ti-aiu of 200 tons covering
one-half of the Londonderry Bridge, the other portion being unloaded, will
be readily found from the experiments.

The calculated extreme deflection of the girder with 200 tons all over,

41'25
separate from the chain, is 41 "25 inches (see Appendix A) : „. =r65, the

greatest deflection of the wave if simply suspended from the chain ; but, as
the chain in the actual bridge is attached to the girder for nearly one-half
the length, the rigidity will be much greater than here indicated.

It thus appears that the deflection of the Londonderry Bridge, with a sus-
pended girder and loaded all over, equals the wave when the bridge is half
loaded, and they are each about half the deflection of one of the Britannia
Tubes when loaded all over with the same weight per foot.

It is necessary to explain, that the estimate given of the deflection of the
Britannia Tubes assumes that they act separately ; when united at the top
they become suspension girders, and the deflection is reduced ; on the other
hand, it has to be noticed that I have not taken into account the increased
rigidity from uniting the girder to the chain, instead of simply suspending it,
which will have a most material influence.

I will also call attention to the fact, that in estimating the deflection of the
Londonderry Bridge, I have treated the point of support as a fixed point,
which is the case if all the spans are equally loaded ; but in the event of one
span being loaded and the adjoining span unloaded, the point of suspension
will not be a fixed point, and the deflection will be greater than I have
estimated.

Thus with one span loaded and the second span unloaded, the girder bridge

244 REPORT — 1857-

will show a comparatively better result than with the entire bridge loaded,
but not to any sensible amount, as the same property which renders the
suspended girder rigid will prevent the movement of the point of suspension.

The weight on one opening will create a disposition to straighten the chain
in the adjoining opening, which will be resisted by the girder so effectually
from being united with it, that little motion of the point of suspension will
occur, even if no assistance Avere given by the tower.

We may make a similar comparison deduced from other large girders, of
which the next largest actually erected is the Boyne Viaduct: here the

Span is 264' feet.

Weight of effective metal 300 tons.

To find a girder of equal depth and rigidity of 44-0 feet span, we have
as —

264* : 440* : : 300 : 1388 tons; the weight of a girder being continuous
that would deflect 1*9 inch with 540 tons all over, or about two-thirds of the
rigidity of the Londonderry Bridge.

The Boyne Viaduct thus indicates a much more favourable result than
the tube ; and, as the system would admit of greater depth, much less metal
would suffice for this span.

A similar deduction may be made from the Newark Dyke Bridge, which
has —

Span of opening .... 240 feet.
Weight of metal .... 244|^ tons.

Here we have as —

240'^ : 440'' :: 244^ : J 506 tons, the weight required to construct a girder
that will deflect 2^ inciies with 240 tons, and indicates also a more favourable
result than the solid-sided girder, but not equal to the Boyne Viaduct.

I must not conclude these comparisons without referring to Mr. Brunei's
new system of combining an arch and a suspension chain, giving each half
the duty.

There is no doubt, in the case of the proposed Londonderry Bridge, if the
chain was reduced to half the section, and an arch of the depth of tiie chain
was substituted, and the suspension rods extended to the arch, that theoretically
with the same metal there would be equal strength and rigidity ; but the real
difficultj' is the impracticability of such a construction : the metal in an arch
of 451 feet span and 80 feet rise cannot be measured by the section as in a
chain, from the tendency to buckle, and from having to contend with its
own weight.

Thus in the Saltash Bridge, which is now in course of construction on this
principle of 451 feet span, the depth is only 56 feet, or little more than ird
of the Londonderry Bridge if of that construction, and thus nearly three
times the metal is required to give equal strength, and nearly nine times to
give equal rigidity, from the deflection varying as the cube of the depth.

It will be observed that there will be no difficulty in giving even a greater
depth to a suspension bridge ; the vertical pressure or weight of the bridge is
small compared with the pressure on the arch of Mr. Brunei's girder, and as
the height is only 88 feet no practical difficulty arises.

Concluding Observations.

The important practical results of the preceding experiments are: —
1st. That in suspension bridges it is essential that the platform should be
stiffened with a girder to prevent vertical undulation.

2nd. That the deflection of the wave of a girder attached to a chain similar

GIRDERS AND SUSPENSION CHAINS COMBINED. 245

to the Londonderry Bridge, will not exceed ^th of the deflection of the same
girder not attached to the chain.

3rd. That theoretically the saving of metal to give equal strength in a
suspension bridge is only one-half of that of a girder ; but as it can be made
of great depth without practical difficulty, and as the deflection varies as the
cube of the depth, a bridge on this principle of such span as the Londonderry
Bridge may be made under average circumstances with at least one-fourth
of tiie metal of an ordinary girder bridge having equal rigidity.

The results Nos. 1 and 2, although at variance with the general practice of
engineers, are still in accordance with such experience as we possess.

Suspension bridges, with a few exceptions, have been not only built of
small depth without stiffening girders, either vertically or horizontally, but
the points of suspension have not been fixed, but simply resting en rollers,
so as to give every facility for movement ; and thus arises the motion generally
complained of in suspension bridges.

Moreover, suspension bridges have been built without any rule or super-
vision, and as they will bear their own weight, however lightly constructed,
they have been in most cases of insufficient strength, many now existing
not having -^th or ^th the strength given in the Derry Bridge.

In a few cases where a girder has been used, the results accord with my
experiments. The Niagara Bridge of 820 feet span has a gird^ very little
deeper than the Derry Bridge, and is built of timber only ; yet the deflection
from a train is not more than 5 inches, as appears from the Report of Mr.
Roebling ; an amount much less than my experiments would indicate, when
it is considered that the girder is of timber only.

Another case is that of the Inverness Bridge, which has a wrought-iron
parapet 3 feet 6 inches deep, and is nearly represented by the small wrought-
iron model.

This bridge has been subjected to the test of a locomotive passing over it
on a truck drawn by fourteen horses, which produced so little deflection, as
appears from the Report of Mr. Rendel, that a member of the Institution of
Civil Engineers, when the subject was mentioned at the recent discussion,
expressed his doubt of the fact.

It is however satisfactorily explained by the preceding experiments, which
prove that such a parapet is sufficient to render a suspension bridge so nearly
rigid that no deflection would be observable without measurement.

There are other cases of suspension girder bridges, viz. the Montrose
Bridge in Scotland, the Kief Bridge in Russia, and more recently the Chelsea
Bridge over the Thames at London, in all of which it is reported that objec-
tionable movement is cured ; and I am informed by Mr. Vignoles, the engi-
neer, that the Kief Bridge has been passed over by Russian artillery at a
gallop without any objectionable oscillation or deflection. In America sus-
pension bridges have been used for aqueducts, the trough acting as a girder,
the success of which proves that all vertical and horizontal oscillation has
been cured.

I will conclude my paper by remarking, that it has been necessary in the
preceding investigation to make reference to the existing works of eminent
engineers. I am desirous to observe that such comparisons have been
essential to the elucidation of the question, and that I have no intention for
one moment to detract from the engineering merit of these great works. The
genius exhibited in overcoming the various difficulties which presented them-
selves during their execution must be evident to all, but especially to those
whose profession renders them acquainted with what had to be contended
with.

246 REPORT — 1857.

At the time they were designed, the popular objections to suspension
bridges were niucli greater than at present, and no example existed of a rail-
way suspension bridge.

An engineer might then have been as little justified under such circum-
stances in adopting a suspension bridge for railway traffic, as he would now
be in error in disregarding the experience which has since been obtained.

It is still, however, asserted, but w ithout any assigned reason, that suspen-
sion bridges are not adapted for trains at speed ; my own view on this point,
from large experience in railway construction, from observing the effect pro-
duced on bridges crossed by contractors' waggons drawn by horses, and by
experiments made on trains at speed with the Iron Commissioners, is, that
road traffic gives as severe trial by troops marching in step, by herds of
cattle, or by cavalry trotting or galloping, as the heaviest trains at full speed
on railways.

This is not, however, the subject I now submit for discussion ; the first
step in the inquiry is the simple mechanical problem of the strength and
deflection with stationary loads, on which no doubt should exist ; and when
it is remembered that the extension of the railway system is much governed
by the cost of construction, of which the crossing of valleys and rivers forms
so considerable an item, that in some cases a single bridge costs as much
as 75 or 100 miles of line, I hope the inquiry will be deemed of sufficient
importance by the Association to elicit a full investigation and discussion.

APPENDIX.

Estimate of Deflection of the Londonderry Girder, from experiments on the

Boyne Viaduct.

The centre opening is 264- feet. Weight of girder 300 tons. 540 tons all
over produces a deflection of 1*9 inch.

The deflection, if of the length of the Londonderry Bridge, would have
been 264.'' : 440^ : : 1-9 : 8-79 inches.

To ascertain the deflection, if of the same depth as the Londonderry
Bridge, we have 16-5^ : 22-5^ : : 8*79 : 22-289 inches.

This assumes a weight per foot forward equal to the Boyne Viaduct. The
Boyne Viaduct, if of the same length as the Londonderry Bridge, would
weigh 512 tons.

The following will therefore be the deflection, if of the same weight as the
Derry Bridge :— 150 : 512 : : 22-289 : 76-078 inches, which is the deflection
with 540 tons all over. 200 tons all over will therefore be 28-17 ; 100 tons
in the middle, 23'53 inches.
Estimate of the Deflection from Experiments on the Newark Dyke Bridge.

Span, 240 feet ; weight of girder, 244|^ tons ; deflection with 240 tons all
over, 2-75 inches. As 240' : 440' : : 2-75 : 17 inches.

The depth of the Newark Dyke being the same as the proposed London-
derry Bridge, 17 inches will indicate the deflection, if it was equal in weight
to the Newark Dyke Bridge ; but the weight, if of the same length, being
450 tons, we have, — 150 : 450 : : 17 : 51 inches, the deflection with 240
tons all over. With 200 tons all over, 42-5 inches.

With 100 tons in the middle it will therefore be 34 inches.

Estimate of the Deflection from Experiments on the Britannia Tube.
The Britannia Tube weighs 1600 tons, and deflects with 200 tons all over
1*25 inch,

GIRDERS AND SUSPENSION CHAINS COMBINED. 247

The deflection of the Britannia Tube^ if reduced to 150 tons, would be 12*5
inches.

The depth, practically, of the proposed Londonderry Bridge is 16^ feet, and
of the Britannia Tube 28 feet,— 16' : 28'^ : : 12-5, or 449-21 : 2195-20 : :
12-5 : 6-07 inches, which has to be reduced in the ratio of the cube of the span,
460' : 440' : : 60*7 : 53-08 inches, the deflection of the Londonderry girder
with 200 tons all over.

The mean of the three results indicates 41-25 inches as the deflection of a

girder of 150 tons, loaded all over with 200 tons, and US inches wlien loaded

33
in the middle with 100 tons: —=1-32 will therefore be the deflection when

attached to the chain *.

B.
Dimensions of Londonderry Bridge, and calculation of Strains and Deflection.

Span between points of support, 451 feet; length of the girder, 440 feet;
depth at high tower, 88 feet ; depth at side tower, 59 feet ; centre catenary
half horizontal length, 246 feet ; side catenary, half horizontal length, 205
feet; length, half chain (centre), 266-2 feet; length, half chain (side),
215-5 feet.

Strain on cables at high tower with 3 tons per foot load, assuming ^th to
be supported by the girder and 2| tons by the chain, according to the for-
mula

T= ^ V4^x'+f=^ X \^4x88=^ + 246-^ = 1031 tons,

X being the depth of catenary, y the half span, tv the weight equally distri-
buted, and T the tension.

Section of the cable at high tower, so that no strain exceeds 5 tons per
inch, 206 inches.

Strain of the cable at the side tower,

1000 ■ ;

4x59^ ^^4X59- + 205^ = 1 000 tons.

Section of cable at side tower, 200 inches; horizontal strain, 840 tons;
section of iron at bottom of chain, 168 inches.

Deflection from Expansion and Contraction.
This calculation assumes that the expansion between sunimer and winter
is YoVu*-'^ P^'*- ^'^ *^'^ length, and that it produces a strain ol" 5 tons per inch.
The exact length of the chain from the formula

z= ^/y'Jr^x'oY v'246'+f88'=266-16,

z being half length of catenary,

y being half chord,

X being versed sine.

Add elongation of half the cable -133

266-293

x= -v/fz^— y= 'v/|266-2932— 246*= 88-3.
The deflection, therefore, from tiie temperature will be Jrd of a foot, or 4
inches, a deflection much under that of ordinary suspension bridges, arising

* The deflections are here estimated to vary as the cube of the depth, ia order to obtain
the extreme amount. The more correct result in a beam of this form will be from the
square, so that the means here given of 41'25 and 33 inches will considerably exceed the
actual deflection.

248 REPORT — 1857.

from the great depth. From this has to be deducted the expansion of the
cast-iron towers, which will amount to ^ an inch.

The same deflection of course indicates the effect of 3 tons per foot on the
bridge, as tliis Aveight produces 5 tons per inch strain on the cable. One foot
per ton all over will therefore cause a deflection under 1^ inch.

In the design for the proposed Londonderry Bridge, ornamental cast-iron
towers arc proposed. As a mechanical question, we must estimate them as
cast-iron columns acting simply to carry weight, which, ifthey were sodesigned,
would be as follows : —

The weight to be supported by the high tower when the bridge has its
extreme load, is 1500 tons. To give 4 tons per inch, we require 375 inches,
or 3750 lbs. per yard.

The high towers being 30 yards high, the weight of metal will be 50 tons.

The low tower will have 1320 tons with a full load, 1^^^= 330 inches, or
3300 lbs. per yard ; the height being 20 yards, the weight will be 20 tons.

The mean of the two towers will require for direct strain 40 tons. Add
50 per cent, for bolts and ineffective material, 20 tons =60 tons.

Estimate of the Weight of Suspension Bars.

The weight to be carried is 1100 tons, if we allow 5 tons per inch ; the
section required is 220 inches, or 2200 lbs. per yard; tlie average length is
10 yards, and weight 10 tons. Add 50 per cent, for ineffective metal 5 tons
= 15 tons.

Evidences of Lunar Influence on Temperature.
By J. Park Harrison, M.A.

[A Communication addressed to Major-General Sabine, General Secretary to the British
Association, and ordered to be printed among the Reports.]

A FALL in temperature having been found to recur with some frequency
between 9 and J), and a corresponding rise shortly after ]), tables and]
curves were formed in the early part of 1857; for a series of lunations, and!
a careful comparison instituted between the temperatures of the days at)
the period of suspected action. The result of the inquiry was satisfactorj\'
It appeared beyond question that decided effects (depending on lunar in-
fluence) occurred at the time referred to ; and even that a single day — the
third before J), — was on the annual mean of considerably lower tem-
perature than another day, viz. the second after }) ; the difference between
the two temperatures being by far the greatest in the winter months. These
facts I had the pleasure of communicating to you soon after they had been
ascertained ; and they were shortly afterwards laid before the British Asso-
ciation at Dublin.

The following Table was then formed of the mean annual temperatures of
eight fixed days, viz. the third before and the second after the four principal
phases of the moon in each lunation, for 21 years. The observations chiefly
used were those made at Dublin under the direction of the Ordnance Survey
in 1836-1852, and were well adapted to my purpose from being collected
in a single volume; the remainder were from the Greenwich results of
1852-1857.

EVIDENCE OF LUNAR INFLUENCE ON TEMPERATURE. 249

Table I — Mean Annual Temperatures of certain fixed days in the
Lunations of 1836-1857.

,-i

'SI

Cf)

r/1

1--

r-i

1(5

(75

7-1

Tfl

-rf

-TT^

-ril

•^

•*

■*

;

1 \

;

1/5

1(5

!>•

•*

"7^

-f

Ti<

1(5

■*

l-l

T~<

<-)

.•^

(->

<r>

(75

■^

1(3

-:<

«5

-*...

i-i

l-l

(»

•*

r-i

(»

■^

•*

TJ(

■^

v<5

TI<

•^

TJH

115

r-\

i~-

rr>

<J5

•rf

■T<

•*

-3<

■^

TJH

Til

1(3

■*

/■

J>-

115

■^

■*

r-i

rrt

TT(

'I'

TjH

■^

TJH

'5<

■^

•^

rjH

■*

Tjl

■*

1
*

"ii

1-1

■^

»ra

T-^

(53

*»

•*

-T

TTl

■^

-=i<

■*

«3

■

1-1

«5

—{

«5

iTi

(Tl

(05

(T)

-Tl

«■!

■*

•^

v(5

Tf(

■^

'Jl

•*

•

ira

(^3

i-i

-*l

(Tl

1-(

(35

1— 1

■*

Tj<

TI<

Til

«5

■*

-3 :

^ t^

(-1

,_(

1(5

•p (?5

•rtH

1(5

»^

'^ti

■*

1(5

-? 00

f/i

GT)

Of)

rf)

a 00

Of)

1-1

i-i

I— i

7-1

§ '"'

1-1

« CO

im"

>c"

(75

6 if

(50

1(5

-f

-tl

■rM

-T,*

'TlH

1(3

!T>

rr>

(T)

Of)

-« 00

CCi

1-1

'"'

•^

'"'

<tj 1-1

'"'

From this Table it will be seen, —
At the period of < ? > there was I ^ ^f^^ | in thirteen years out of twenty-one.

250 REPORT — 1857.

And in five of the eight years in which there are exceptions to the (assumed)
rule of a higher temperature preceding •, exceptions are also found at the
period of O-

And so with the quarters : —

At the perioC of { J ) there wa, { » ^^ i"/'-;- ^ } „u.oft„e„.y.„ue.

Only two exceptions occurred at ) , and in both cases they are found in the
same years at ^ .

2. Winter lunations to all appearance exercising a considerable influence
upon the mean temperature of the two days at the period of D , inquiry was
next extended to individual months. The results evidence the same marks
of system that have been already observed in the yearly means.

In the months of October, November, December, and January, the pro-
portion in which a rise or fall occurred from the third day before to the
second day after the syzygies and quarters, during the same twenty-one
years, was as follows : —

T /-v i u ^ f • a rise in 13 out of 21 .

In October, . . at < ^ „ ,. ,, ■ , ^ ,. e cm

(^ O a tall in 15 out ot 22.

T XT 1 .^ f • a fall in 16 out of 23.

In November, at < ^ p „ . , ,, ^ n „,,

' \ O a fall in 13 out ot 22.

T T-v I t r • the rise and fall equal.

In December, at < _ . • , . ,. Pan
' [ O a rise in 14 out ot 22.

In January, . . at < ^

a fall in 17 out of 22.
a rise in 16 out of 21.

. ^ , , if]) the rise and fall equal.

In October,., at < ^ ,. „ . ,„ . ^poi
(da tall in 16 out ol 21 .

y XT 1 i. f ]) a rife in 14 out of 21.

In November, at -^ ^ ^ ,, . ,„ . „ ^,.
' [ C a fall m 13 out of 20.

T T-i 1 i. f D a rise in 13 out of 21.

In December, at < ^ ,, . j *■ n i

L ([ the rise and tall equal.

, , .^ f B a rise in 16 out of 21.

In January, . . at < ^ p ,, • m .. c nn
•' \ C a fall in 13 out of 23.

In the summer months a rise prevailed in the proportion of about 3 : 2,
at all the periods, excepting in May, at the time of J), when it was as 4 : 1.

At the period of d, there occurred in the same 21 years the following
remarkable alternations of temperature : —

In March,., a rise in 12 out of 21.
In April,. . a fall in 13 out of 21.
In May, . . a rise in 13 out of 21.
In June,. . a fall in 13 out of 21.
In July, . . a rise in 13 out of 21.
In August, a fall in 13 out of 21.

Strong indications of similar reciprocity were traceable in separate lu-
nations and at different periods of the same lunations.

3. Further evidence of system was next obtained from the highest and
lowest mean temperatures of each month. These were found in a tabular

EVIDENCE OF LUNAR INFLUENCE ON TEMPERATURE. 251

form, with the dates attached, for 22 years, in the results of the Dublin Ob-
servations. And although it was scarcely to be expected that monthly
maxima and minima would coincide to any extent with the annual mean tem-
peratures (or means of tiie means) of the eight days at the different lunar
periods, in the first iialf of the lunation they appeared in a great measure
to do so.

At the periods of the syzygies and quarters, upon the days of the change,
and for the three days before and after, the proportion in which maxima and
minima mean temperatures occurred in each month, is shown approximately
in the following Table ; the iigns + and — before the figures indicating the
predominance of maxima or minima : —

Table II.

Slonths.

November .
December .

January

February

March

April

May

June

July

August

September .
October ....

+ 5
+ 3
+ 2
+ 3
+ 2
+ 5
-3

- 5

- 3

- 2

+ 2^:1

+ 2':1
+ 3:2

— 2

— 3
+ 3

— 5
+ 2

— 5

+ 3:2

— 3

— 2
+ 5

— 3

— 3
+ 5
+ 3;

— 3
+ 3

2: 1
2: 1

Thus, in winter, for six consecutive months^ maxima predominate at # ;
for the other six months minima, and that in much the same proportion.
In four of the winter months, viz. December, January, February, and March,
in which maxima preponderate at the period of %, minima are in excess at O-
In July, August, and October, the converse holds good. At the quarters, a
similar reciprocal action takes place in the months of October, November,
January, April, June, and July.

i. Not the least striking fact which has been elicited during the progress
of this investigation, is the systematically unequal distribution of the maxima
and minima mean temperatures over the several days of the lunation. At
Dublin, for the period under consideration, the greatest number of high and
low temperatures at each quarter, excepting at O. occur upon the day fol-
lowing the change. In the annexed Table this will be clearly seen, as well
as an apparent increase in the numbers as they approach the four days of
greatest action — more particularly at the quarters.

Table III. — Showing the distribution of the 530 maxima and minima mean
temperatures of day in each month for 22 years at Dublin.

•

O
26

24 12 18

4
9

<L
25

23|9

15 23' 7

11 14 15 18

• 1

1527

15 18 19

26 20

The other points to which I wish to direct attention in this Table are the
excess of maxima and minima upon the third day before and third day after
#, and the regular progression of effects at the octants.

252 REPORT — 1857-

At J, out of the 13 maxima and minima, on the second day after the day
of chan^^e, the proportion of the former to the latter was as 2 : ] . No maxmia
or minima, however, were found to occur for 22 years on any of the three
days following on ]) in the months of April, May, June, July, September, or
October ; wlnLst on the 4 th day after J (or the 2nd octant), seven out of the
eii'lit maxima and minima occurred in these very months.

°At (I there is the following alternation, —

d.
+ 12 —12 +14—20-15.
-6+7 -11 +6+5.

5. By the courtesy of Mr. Glaisher I am able to give additional evidence
of system of considerable value from his tables of mean temperatures of
each day at Greenwich for 43 years.

It will be interesting to compare the maxima and minima mean tem-
peratures, which I have^extracted for the earlier half of this period (from
1814 to 1835), with the Dublin results (from 1830 to 1852). Thus the
number of maxima and minima of the month which occurred at Dublin
on the three days preceding 9 were, +13 — 10; +3—6; +5—3. At
Greenwich +11—6; +3—6; +8-7. On the three days before ]), at
Dublin,+6— 5; +6 — 8; +7—8. At Greenwich, +8—7 ; +9-11; +8
—9. On the first and second days after ]) , at Dublin, +12—9; +9—4.
At Greenwich, +8—6; +15—6. On the three days before O, at Dublin,
+ 8 — 7; +6— 9; +15-12. At Greenwich, +15 — 10 ; +10 — 8 ; +5 — 6.
On the second day before and after (I, at Dublin, +13 — 5; +4 — 16. At
Greenwich, + 10 — 9 ; + 8 — 20. The due proportion of maxima and minima
would have been +9— 9/o7' each of (he above days. This, in the following
Table of maxima and minima in the month for the days of the change, will
be found to be very nearly the case at • and J) .

Table IV.

f ^ !• p To ~ I (I I

At Dublin, 1830-1852 2l{+;j;| \^[tiQ. 26{+q 24{1J5; !

At Greenwich, 1814-1836,...'20 1 +52;! 18 {+ ^ 23|l^^| 23(1^*; j

It will be noticed also, that with the single exception of the day of 0> the
regularity in the proportion of maxima to minima which runs through these
figures is far greater than could a priori have been thought possible.

6. Though time has not permitted me to enter on an examination of the
remaining mean temperatures at Greenwich, I am able to give the highest
and lowest maxima and minima in the month for the wiiole series of 43 years
from the notes at the foot of Mr. Glaisher's Tables ; the days of the moon's
age being obtained from the Nautical Almanack. The following was found
to be the grouping of the highest and lowest temperatures at the period
of }), to which attention was originally drawn :—

])

+ +

That is to say, on nearly 16,000 observations, eleven out of tiic twenty-four
highest and lowest mean temperatures occurred at the above period, and

EVIDENCE OF LUNAR INFLUENCE ON TEMPERATURE. 253

minima only before the day of change. The just expectation would be
about 3 maxima and 3 minima for the whole period of seven days.
The results at Dublin for twenty-two years were at —

•-•+ + +•

In this case also minima precede the day of the change.

For the rest more than half of the whole number of the superior maxima
and minima occurred on the following eight days, both at Greenwich and
Dublin, viz the third day before, and the third day after % ; the second day
before, and the second day after ]) ; the day before d ; and the days on
which the moon entered on her tirst, second, and third quarters.

Of the six days of the lunation on which no superior maxima or minima
occurred, either at Greenwich or Dublin, three were found at #, two at 0>
and one at (T.

Many other details of interest might be enumerated ; but when it was
considered that the observations on which they depend are ordinary daily
means, taken irrespective of the hour of the moon's changes, it seemed
hardly worth while to dwell on minute points which would at present only
complicate the question.

7. The dissolution of clouds in presence of O) first announced as a
meteorological fact by Sir John Herschel, has since been confirmed by
observations made by Mr. Piazzi Smyth on the Peak of TenerifFe, at which
altitude sufficient heat was detected in the lunar rays to make it possible that
evaporation might cause the phoenomenon in still higher regions of the air.
It had been noticed previously, and independently, by Baron Humboldt in
America.

A still more remarkable fact has been noticed by Mr. M. J. Johnson, the
Radcliffe Observer at Oxford, viz. that the cloud-dispelling power of the moon
extends beyond the period of O ; or as it would perhaps be more correct
for me to say, is not confined to it. From repeated observations it appears
tiiat at Oxford the influence begins after the moon is four or five days old,
and lasts till she approaches the sun again the same distance on the other side.
So frequently had this been noticed by Mr. Johnson, that during a course
of observations on which he was engaged a few years ago, he felt that his
attendance at the observatory could not be dispensed with, however unpro-
mising might be the appearance of the night, until the moon had fairly risen ;
and over and over again when this has occurred, the sky, before com-
pletely obscured, has become clear.

Mr. Johnson has furnished me with a comparative statement of the number
of observations of the sun and moon taken beween the day of ]) and the day
after O) in the years IS^i, 1845, and 1846, which shows that the moon was
visible on an average 137 times on the meridian, while the sun is seen only
100 times. In the year 184-4 the preponderance in favour of the visibility
of the moon was as l'S2 : 1.

A clearing of the atmosphere, to whatever attributable, by increasing solar
as well as terrestrial radiation, and so producing extremes of heat and cold,
■would, it is evident, be sufficient to account for some of the results enume-
rated in this communication.

The importance of Mr. Johnson's facts, in connexion with the peculiar
action which it has been shown exists at the period of J) , will be at once ap-
parent; and however little required, the latter in a measure strengthens the
probability that the eff'ects which have been observed are not accidental.

254 REPORT — 1857.

8. Before concluding, it will be necessary to explain the mode in which
my results were obtained.

The average length of a lunation being a little more than 29^ days, and
the difference between the quarters varying from three or four hours to two
days and even more, with a view to secure as much uniformity as the circum-
stances of tl)e case, in the absence of a sufficient number of hourly obser-
vations, would admit, the mean temperatures of the days on which the moon
entered on her four principal phases were first set down as centres, and then
the mean temperatures of the days immediately before and after them, each
in its proper order ; and so with the maxima and minima of the month.

By this method it will be seen that the numerically imperfect observations
in each quarter fell upon the intermediate or octant days ; and my results, I
think, show that this was a proper method to adopt. Otherwise, and if there
had been any indications of a regular progression of effects from 9 to O. it
would have been better to take tiie latter as a centre, and to have arranged
the observations accordingly.

The investigation is now being carried out further by means of the
highest and lowest readings of the self-registering maximum and minimum
thermometer.

Garlands, Ewhurst, Surrey.

P.S. Dr. Buys Ballot, Director of the Royal Meteorological Institute of
the Netherlands, informs me that he has found the highest temperature to
follow on O, which he attributes to the greater amount of heat reflected
from the moon's surface at that period. M. Ballot's results are formed
from observations made at Haarlem, extending over 120 years. The efl^ects
were there too most conspicuous in the winter months.

Report on the Animal and Vegetable Products imported into Liverpool
from the year lb51 to 1855 {inclusive).

In consequence of a suggestion from Professor Balfour at the Glasgow
Meeting 1855, it was considered a very desirable object to obtain some
information relative to the species of animals and vegetables which furnish
the articles of commerce, and the extent to which the demand on each is
carried. The General Committee therefore recommended as an experiment,
that Committees should be appointed for this purpose in Liverpool and
Glasgow to collect the necessary particulars and report thereon. The gen-
tlemen chosen for Liverpool were Professor T. C. Archer, Queen's College,
Liverpool, and Joseph Dickenson, M.D., F.R.S., F.L.S., &c.

Unfortunately the serious indisposition of Dr. Dickenson obliging him to
travel, he was unable to take any active part in preparing the following
Report, to which his great experience would have been so valuable; but as
it was seen that the sum voted by the General Committee would be insuffi-
cient to meet the expenses of clerical assistance, Dr. Dickenson liberally
undertook to pay any excess of expenditure, thus giving valuable aid to its
completion.

The plan pursued in obtaining the results was as follows : —
In each large port there is published daily, a paper called " The Bill of
Entry," which gives, besides a variety of other particulars, the arrival of

ANIMAL AND VEGETABLE PRODUCTS.' 256

every vessel, the port from whence she sailed, and a copy of her manifesto,
giving an account of the cargo she brings. By the kind cooperation of Mr.
Robert MacAndrew, a complete file of these papers for the five years was
obtained, and, books being prepared for the purpose, a clerk was employed
to go over the file and transcribe every importation under its proper heading,
and to make inquiries of the merchants or brokers whenever it was doubt-
fully expressed, as was very frequently the case. One thousand five hundred
and sixty-five of these mercantile newspapers were thus collated, and every
package imported in the five years was recorded. The next step was to as-
certain the average weight of each package, or the entire weight of each
consignment, which was done chiefly by personal application to the con-
signees, who in every instance, when appbed to and informed of the cause
of inquiry, readily gave the required information.

It cannot be doubted that the connexion of Science and Commerce in this
practical way, if followed out, will have a most important effect upon human
progress. The man of science, by learning the particular species which aff"ord
valuable products, will by his knowledge of affinities be enabled to direct
the merchant to new fields of enterprise ; and when science thus shows its
power of being practically useful, the respect for it will be increased, which
must greatly assist in its advancement.

But the method pursued in the present instance is too laborious and too
partial to be of any great use, except as indicating the important information
which is lost to the country for want of a more complete system of statistics.
The Board of Trade " Returns" would appear to supply the deficiency to a
great extent; but a comparison of the following tables with that voluminous
production will show that very many things are never mentioned in the
Official Returns, except under such general denominations as " Drugs not
otherwise enumerated," &c. Now it is to the unknown articles that most
attention should be given : intelligent people abroad see natural productions
which they believe would be most useful to our manufactures, or in our
Materia Medica ; they send a small quantity for experiment, which being
unknown, is entered under some general term similar to the above, and the
Revenue is satisfied. The broker, if a man of extensive business, does not
like to be troubled with small matters ; and the article is laid aside until value-
less, and then consigned to the dust-cart. In this way the importation of the
valuable Hydroborate of Soda, now extensively imported as borax from South
America, was in abeyance for at least six years; and almost numberless
instances of a similar kind might be collected in our largest sea-ports.

The remedy for this would be the appointment of an official in the landing
department of each port, to ascertain and record every new importation.
The merchant in all such cases would willingly give a specimen for examina-
tion ; and as there are now Industrial Museums in London (Kew), Liverpool,
Edinburgh, and Dublin, the specimens could be determined there, and remain
for public inspection. It ought also to be imperative upon the Landing Officers
to return every ia-iportation by its correct name, a difficulty which would be
very trifling if either of the above Museums were referred to. One other
reason cannot be objected to : — if National Statistics are worth collecting,
they can only be so when correct ; and correct statistics must be more
essential to a great commercial nation than to any other.

T. C. Archer.

Tables,

256

REPORT 1857'

O M .

lO D rj

-w _N —

C.2 =;

§>

>*.

"3
o
to

1
bO

^ „ 3

S ° ;^

.2
1

i'5

coo

Oj *-H

•"•

a ■»

o .2

■5 ''^

■Mm

B
C

.Sea

•2 a
oi8

>»

O) O

CS.S

o i-o

O j^

-a o
eg

a
t/i

§
-3

"c
£

*-3

t/3

iii

■S=5 -

S 3

■^ HH t^

o ""

^-^

'•^

^5.

t/3

■*j

"Si

•1

-C 3

3 .j!

•fS 3

,_!,

:::»

: ^^ '3

%■% ^

« £ 53

e X

to «?

) ^

"55

"=?§

*fl

r 1

■<

•esnr

•B8U©V[0]T[

ANIMAL AND VEGETABLE PRODUCTS.

267

•2 o s

'ft? >

^1^ :

^^ •

"•^a-ap

"oh

Si, g _>• „ .rt

a-^

i> « .2 q"-^ ,a

^ §

fco'c fcp^

a:.s

•ssoHTJ

s "^

■e«=

a- o ea ^ ^ <
.&■ o "" 'S

- 2 J2 <u -s

« <" s s a 3

S 13 a p.<! <!j
Em

^ s

a-^

£ ? s

•sseoisujureaQ

268

REPORT — 1857.

—

e •

•a «i

l«

-^ "•

b B

3 .

_S9

"^ rr

a a,

|ja

o
o

■* O IN 00 l^ CD

o
to

CP
O

E CO

2 -2S

^ .2

00 —1 -H <N ^

d '*^

—1 •«

t>.

i-^

O to

o
o

1 ' ' i '

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o

C7>

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o

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<>■ f2

era ■* O r-H rt CJ

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- b

ci:

?i, a

o :

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o J

in rt r-H «o o

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lO
00

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o
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CO

00 '-'

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'I"

■*

H-l

1—4 l-H .

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i'-i

^ ^

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CO^

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t>.

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^ O —

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CO CO

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ta
<u

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a; 13

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cq
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1 1

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:2;qd:

^'^

t II

^ 2

: 2 =«

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o 5

• 1

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a> '''*'

j£

1-3

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o 1

c S 5»

s S'tsO

•fi 'S.

■ -II

13
O

1 1 a>

•IS 1

1 u =

S-i

: o

a> bo
bi o

bO «

"°'2 ^

".SE

3 ^

1 0.3

• S.2

, '3

^ ii

JS2

' ==• bO

<u 2

js fib

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P "

: H

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;£,

S
3
o

:1
'1

•s

■is*

•S
1

J-l

2>> ,

|| .1

Q p:

tsl

•aeoo'Btt

ANIMAL AND VEGETABLE PRODUCTS.

269

-^<«-

[3 S

g g'^ 3

« SJ s
" -a •£ '

1^ «

g-^ > _ Q J2 JJ

^ r« _

i cs c OJ •

; cs «

3 C S S

3<« a ^

: o 3 S .

2 'f?

■js 3 ca B

a S o .2

= a

UJS f=• CT*

sl-^oS

870

REPORT — 1857.

es of this
root arrive
ssels from
vci as regu-

:rally manu-
iiis, baskets,
1 decorated
aoiBupres-

i a

a ^

.52 o

3
1

3 a

sed in Ame-
h valued for
other grasses

1-.

o S -a
S o

■^3 "5 « M

g to

.ts h

Si
o

-^ 03 > ;;

^ « ^ «

a 1 =!>=

*3 XI

a S

a
to

o
u

3
O

13 •a

<S .2 "*" o3 eg

J3 2

coo

<;s

a-^

3 '-'

-o

x.^

t-.

o *«

^ (N

coo

■^

X. "3

•s

° ^

■ss

0.00

1:^

"Srt

t-.

■S CO

•s

CT*

-So

0,00

.£3

o ^

CT"

0,00

3 W

Ui <— '

■^

S o

'S _•

_«

g ca

t- C8 C

•Si

Ola

-5

°a4S

•a

'^'

3 ^->

sf
s o

<; oj

<4 «)

"a
to

"3 e ~..

^^1
w"'^

;

'S"

Si.

•a

■|

■l

'o,

£;•

fc-

3 .

« .

S .

ca ,

-«

u-d

a r^

"«

«T3

Urc

<i» S^

<o ^

4) S

« 3^

s. «

J3 S

•^ M

-C M

^ S

P-l

J-^

• ^

: ^

• ^

►j

: a

" —

• S

• ea

jj^

•a

Jd-

:6.

• £

1 s

: e
: S

.2^

• .o

i.s

S «

1-, -3

•g-

i ^

i 'a'

III

V3 O

"^1

3 's

= <--

a^.

•aeso'BU

!^<5

ANIMAL AND VEGETABLE PRODUCTS.

271

•a « 3 S ""

a o m u a

cr* £3 ,, to o

- ■ a> E ■

-1 i «

rs ^ <" c

to (U o t«

a a -a "

4i 4) 53 o

£.2-

g -^ ..

s s -s 3 - as

c<5

- w a
J* 1-. O -

-2 . « S

•3 c

Is^talll^.^iM-S'?

goaS^ti^,„

^ s s; J is p.^ .2
H

3 <» -w 3 .;

to >

« c (u £ S mT Z
'£ 's ^2 ^-^ - :a c c

^«x-5 oi^ ^ § « ^-a

•2 "5 .S ~ S « -S ^ S- s

'3 "S -2 "3 -^ "

a-'S

! -= t -f; 2 -r; « .0

■5 b

„ 5f O O ^

= ;rs 2 a 3

^ -a j; o «

a £ c « to^

§ <u o . <u c ,a

t- "^ O) o ^ -*:? ^5

ft.p, 5 S-c

S-S^

272

REPORT — 1857.

^■5 o fe-g

C Jji o

is ,

c s- _ to.

>;>.>, es

to 3 S TS
5 O - °

1 >, t" to

' .2 2 c5 c S
' Cm u a a

' i3

tp'E, E '-S "2 B'

^ 3 '- -^ &o

^ s

>-3 .

oj 2 S

- o =
to *j ca

per 100.
Used only as
sticks ; the nati
them by hang
in the smoke
tires.

£ CO
5»^

■Co

O "O
0.00

c^ 6

coo

a--

coo

O lO

coo

1-H T3 ■<f U

^ a

c c

go -I

steo

-a ^

a i

its »5

& s

s a

•c.§<«

"•3.

(■jg -a) (-ssnf)

•aeao^jQcLtQ •aeapioj-y

(•ip«n)

-seaol I D

ANIMAL AND VEGETABLE PRODUCTS.

273

rl -

.0 « §1 4) tS

"?T3 ^-d V

all palm-
h value

sticks
id polishe
3 are eat

is import
rch in th
s ; Pearl
od.

er of pac

in 1851

f all kin

1 = L"^

£ « « « V

5^3
^3

go flour
se as sta
ufactoric
nly as fo
e numb
eceived
1,800
ago.

s*5 S ^ -d J=

t3 <»

asao:Pu,-n'V3

•r-i

Z^ u

3 bO B

a gre
what h

titles
manufa

3 a eo
.= -3

-2^

•a

of
some
ol.

quai
ves

o'i to

»,

■*^

-s^-s

-M

0.
J

penment ;
very fine
colour anc
sheep's wo
Very large
Palm lea

tured int
their way
try, and arc
for contai

3
'■3

-2

gc^

■s «•

J= .5 M X2

§)S

S iSi -=5

TS J3 " ^ .

3 e~i .

OS Q

?74

REPORT — 1857.

■s-s-i

i3 a, p.--'

2 5 £-S "-2

(- fco o d D .-a

to c ^ « I* .J^ p

^ ^ • - « o o-

O S ca -

:~ — 5 «

B = ^-H

, Oh J= J3 CO

O.00

O C -M v^ C/3 A

"£■*

o ^

0.00

«2

cOi

0.00

o ^
p. 00

a'"

a i;

c «5

S 2

•s c
5"

e «

■o a,

eS T3

a «5

o% ">.2

a. 2

■2 I.t5
H

.2 8

(2 I

(U h]

•{panntfuoo) ai&ovva\vi

ANIMAL AND VEGETABLE PRODUCTS.

275

« ? 3 .5 ^

*> a «i 'a "5
i« 01 .S a c -c

3 s: M ■« ^ .2 g
o -2* 3 * ^- "-^

H 5 'C S ^ '5 p.

^ ^ o
e3 O « 5

|e|I s

^' to

C C c

■ -^ CO c -, .

5 D ♦; ~ _

I-

.9 T:

£ ^ = 1^1 ig !

S 3.= S^Sj^JSH I

S E S ^ g-'

MO ■—

M <-'•-"

22 <^

&: S

o o g •

t^ C O QJ

5 E *"H

« S'

•'a H

; g _rt

E-t

2 °.tt

a; O

S ^
I — Q

pi"*

if^

.5^

•aeao'Bixauioja

276

REPORT — 1857.

S .S .t: -d- 1«

S.S5 £

*; j=

i
1

: w

: S
:

1 i g i
^ ^ " i

: c
: 2

: a

': ^

: 00

1 ^

!>. 1-1

00 IN
(N

: <N

: °

I 1

1 1

<M IN

■ c
: °

00
CO

- o

c
c

.2 .2
B s .

w fr

B
c

2r.

si;- '==

3
V3

^ S g

JH 'S. to

la'? '§-

■a

"E.
S

J bo V U CS

fc, H t- fa H

" P • :

1 i-S i ^=
1 s-g 1 1

"S
43

• c

: s

• S =
•| :

■ii i

5 J
"~;r'

2
§ K

1 S

a
a

S :

1 1

'3 •
^ :

s :

P :

1 . :

§2; c
^ i

:
g :

I \

t 1
'1 i

1 I 12

.5 «? ^ ^

B OS S u
^ • - £ <»

S S3 0^ g S»-

« -a

A -^ ^-^ ^ N.

•aeao'cp •aeao'epTJi ■aeaoi3snK[ •aeso'CjaqtiuTZ

ANIMAL AND VEGETABLE PRODUCTS.

§.2

J; to

.S 3
-« g .

o 'S CO "£ -r
c fe o ?

« i « 2 -

2 ° B"" ~-
□ a. I

" 3 to £P

^ '° "S "C «

^ . « o ? to u

= ^

itities
rougl
idlta
1 the

5-^5 —

^^l|

S C B "■

73 ■" ""w

C8 "^

^ 5^ §

•S 3 >.

a.ti

2 S
IS o-

3 a

r" =a r'

O B

s *»

J s

"B^

? a,

.2 S

4)^

"5^

«J! H >

(Z)

H O

^^ ^^

^ A

■aeoo'BiuuxEiii

•seao'BpixioJO

•aeao'Bi'iuoJO

•SBQO'BIXt'I

278

REPORT — 1857.

bo S

S « c

■a a..2.S
o t- +j >

o "^ 5 !3

fc^ 'S ^ "eS
 « B S

I 5
So

c ^
.2 5

s s
C i2

- *^

. « £•
M-i: *

•a- a>

— '5 '3 O* S, c

'aeacyBtxiT

•aeao'Bajoosoia: •aeao'BiTuis

■*

^ CD

*s ^

o to

^ to

3 O

« o

£ O

■<»<

«^

t> c»

^ «

■*

3 O

Otf>

ii o

^ o

U IN

x: o

3 M

U«J

,4"

**" c<5

U -J

.a •*

3 l-»

t~.

O to

-J

^ • h

5) a; g
3 4>

.2 2 3

ANIMAL AXP VEGETABLE PRODUCTS.

379

a. .

>..s

XI 5,

•s

>■!

•3

"Si

TS-a

-o

»§
& *

£3

to
00

»— i

§2

i
00

c
c

6,347,43

to"

C5_
to

to
to
to
in
<N

in
o»

JO
eo

■*

00_

to
to

to
CO

3
•*

c
c

in
eo

•^

in
00

CO
CO

in
"^
in

CO
CO

cm"

3."

~""

^ a;
-tJ

p- 5

10 .

"c3

etf

ctf

„(»

._s ^

■a

Si?

pa c

1c3

-a

4> ca

-a

- =»

ca
"C

a.3

r 1 °

B
es

■3

.* '"

-5

■SbS

-5

i^o

.S aS

•1 S

I- >.

»-

■^

I ^

"n. 1

a
J

c
a

.5 "
"" " ■«

S5 g
^ S
tM ^

0-3

1^1

a
3
3

J
c

E-

^ " ca

1 :

/---^

^->»

1 ;^

a
c

ea a)

1 a

.a »

2 i

-a

s
a

1
5

1
a

.1
S

■&
a

< e
■S

Hoi

III

S S T3

"it
K

•2
"a

^ — r-1

sea

3JTUO£

1 .J,.

280

REPORT — 1857.

ANIMAL AND VEGETABLE PRODUCTS.

281

making
g cali-
engra-

s
■3

.S "

C s-
w o

,i2

<2
S

1.1

.5 ""
■^ 3
o *

3
n
fcp

•S'

2-60
*- S

■^

43 m

M""

s t>

■?

c
c

- ^0

-*J

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.H '-'

■w

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CO
CO

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3 tC

o»

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- .20

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o

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■5

|°!

S ■='"

„

- .20

DO
J3 00_

«o

t-^

»>.

^ 3 oT

— ^^

«>.

J5:

-t

<£

.— *

•M

CO "^

1/:

3 ii

- .20

4.9

2 00

to 3 ^f

g^';

t£>

CO ^ ■»»<

r-<

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n "

•— <

C-1 "^

a
a

; <S

s "tn

- .20

flj

.3 CO

3 to

£^

-.3*

»^ XI -^

<— *

rl -

■n

(M ■"

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4;
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3 .

= «

'3.

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C/3

III

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_ =

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es 3

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t.ij

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_v.

3 3

~T3 .

«11

■

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■S's
s

<2 J

■£

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ST s;

S-f

.ii

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to ^

's a<§ 3

_ p

„

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H"^ H

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c

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c
c

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s

c
c

oqdn[

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UKl'OllT — 1857.

3 «

M 1

- M

« .9

O.U

•^3 i^

O 4J

O M

-g «

s-5 =

-1