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THE ROYAL SOCIETY

OF

EDINBURGH

r PROCEEDINGS

Volume 9

NOVEMBER 1875— JULY 1878

PROCEEDINGS

THE ROYAL SOCIETY

EDINBURGH.

VOL. IX.

NOVEMBER 1875 to JULY 1878.

PRINTED BY NEILL AND COMPANY.

MDCCCLXXVIII.

Reprinted with the permission of The Royal Society of Edinburgh

NSON REPRINT CORPORATION JOHNSON REPRINT COMPANY LTD.
dfth Avenue, New York, N.Y. 10003 Berkeley Square House, London, W. I

By arrangement with the original publishers, any
material that appeared in color in the original,
has been reproduced in black and wrhite.

First reprinting, 1966, Johnson Reprint Corporation
Printed in the United States of America

80201 G1401

CONTENTS.

Election of Office-Bearers, ......

Opening Address. Session 1875-76. By the Senior Vice-President,
David Milne Home, Esq. of Wedderburn, LL.D.,

The Volcanic Eruptions of Iceland in 1874 and 1875. By Captain
Burton. (With two Maps of Iceland), ....

Vortex Statics. By Sir William Thomson, ....

Experiments illustrating Rigidity produced by Centrifugal Force.
By John Aitken, Esq., ....

On the Electrical Conductivity of Stretched Silver Wires. By J. G-.

MacGregor, M.A., B.Sc. Communicated by Professor Tait,

On the Defoliation of the Coniferae. By Dr Stark, .

On Diamagnetic Rotation. By George Forbes, Esq., M.A., F.R.A.S.,
On the Linear Differential Equation of the Second Order. By Pro-
fessor Tait, ........

On Two-dimensional Motion of mutually influencing Vortex-
columns, and on Two-dimensional Approximately Circular Motion
of a Liquid. By Sir W. Thomson, ....

On the Origin of Language — Max-Miiller, Whitney. By Professor
Blackie, ........

Note on Certain Formulae in the Calculus of Operations. By Pro-
fessor Stokes, Hon. F.R.S.E. (In a Letter to Professor Tait),

A Further Contribution to the Placentation of the Cetacea ( Monodon
Monoceros ). By Professor Turner, ....

Observations on the Zodiacal Light. By C. Michie Smith. Com-
municated by Professor Tait, . . . . .

Note on the Volcanoes of the Hawaiian Islands. By J. W. Nichol,
F.R.A.S. Communicated by Professor Tait,

New General Formulae for the Transformation of Infinite Series
into continued Fractions. By Thomas Muir, M.A.,

Laboratory Notes. By Professor Tait —

a. On a Possible Influence of Magnetism on the Absorption
of Light, and some correlated subjects,

PAGE

1

2

44

59

73

79

85

85

93

98

98

101

103

110

113

117

118

1Y

Contents.

PAGE

b. On a Mechanism for Integrating the General Linear Differ-

ential Equation of the Second Order, . . .118

c. The Electric Conductivity of Nickel. By C. Michie Smith

and J. Gordon MacGregor, . . . .120

On the Structure of the Body-wall in the Spionidae. By W. C.
MTntosh, M.D., ....... 123

Note on Circular Crystals. By E. W. Dallas, . . .129

Preliminary Note on the Flame produced by putting Common Salt
into a Fire. By C. M. Smith. Communicated by Professor
Tait, ........ 133

The Annual Periods of Thunder (with Lightning), Lightning (only),
Hail, and Snow, at Oxford. By Alexander Buchan, M.A., . 135

Note on the Origin of Thunderstorms. By Professor Tait, . . 136

An Application of Professor James Thomson’s Integrator to harmonic
Analyses of Meteorological, Tidal, and other Phenomena, and to
the Integration of Differential Equations. By Sir W. Thomson, 138
Note on the Thermo-Electric Position of Cobalt. By Professor Tait, 138
On a Glass Digester in which to Heat Substances under Pressure.

By Dr E. A. Letts, ....... 139

On the Connection between Cohesion, Elasticity, Dilatation, and
Temperature. By Professor George Forbes, . . .141

Notice of the Completion of the Works designed by Sir Charles A.
Hartley, F.B.S.E., for the Improvement of the Danube. By
David Stevenson, Y.P.B.S.E., . . . . .142

Chapters on the Mineralogy of Scotland. By Professor Heddle.
Chapter I. — On the Rhombohedral Carbonates. Communicated
by Professor Tait, . . . . . . .144

On Thermo-Dynamic Motivity. By Sir W. Thomson, . . 144

On the Vortex Theory of Gases, of the Condensation of Gases on
Solids, and of the Continuity between the Gaseous and Liquid
State of Matter. Bv Sir W. Thomson, . . . .144

On two new Laboratory Apparatus. By William Dittmar, . . 144

On an Improved Form of Galvanic Battery. By J. Cook. Com-
municated by Professor Tait, . . . . .148

On the Properties of the Perigon Versor. By G. J. P. Grieve.

Communicated by Professor Kelland, . . . 149

Descriptions of some new or imperfectly understood Forms of
Palaeozoic Corals. By H. Alleyne Nicholson, M.D., D.Sc.,
F.R.S.E., Professor of Natural History in the University of St
Andrews, and James Thomson, F.G.S., .... 149

On a Stable and Flexible Arch. By Professor Fleeming Jenkin, . 151
Is the Gaelic Ossian a Translation from the English ? By Professor
Blackie, ........ 151

Notes on Dredging in Madeira. By the Rev. Robert Boog Watson,

B.A., F.R.S.E., F.G.S., \ .153

Contents.

V

PAGE

Note on a New Fossil Foot-Print from the Permian Sandstone of
Dumfriesshire. By Patrick Dudgeon, F.R.S.E. (Plate I.), . 154

On the Decennial Period in the Mean Amplitude of the Diurnal
Oscillation and Disturbance of the Magnetic Needle and of the
Sun-spot Area. By J. A. Broun, F.R.S., . . . .155

On the Parallel Roads of Lochaber. By David Milne Home, LL.D., 159
Physical Observations in Northern Asia. By Professor G. Forbes, . 161
On Parallel Motions. By the Rev. John Wilson, M.A., Bannock-
burn Academy. Communicated by Professor Kelland, . .161

Laboratory Notes. By Professor Tait —

a. On the Passage of the Electric Current from Amalgamated

Zinc Sulphate Solution. By J. G. MacGregor, M.A., . 170

b. On the Thermo-Electric Properties of Cobalt, &c. By

Messrs Knott, MacGregor, and C. M. Smith, . .170

c. Measurements of the Potentials required for Long Sparks

of a Holtz Machine. By Messrs Macfarlane and Paton, 170

Note on Orthogonal Isothermal Surfaces. By Professor Tait, . 170
Notice of some Recent Atmospheric Phenomena. By Professor Tait, 170
Report by the Society’s Boulder Committee. (Plates II. and III.), 170
Election of Office-Bearers, ...... 203

Opening Address by the Rev. W. Lindsay Alexander, D.D., . . 204

On the Roots of the Equation V ptpp = 0. By Gustav Plarr. Com-
municated by Professor Tait, ..... 237

Applications of the Theorem that Two Closed Plane Curves intersect
an even number of times. By Professor Tait, . . . 237

On the Distribution of Volcanic Debris over the Floor of the Ocean,

— its Character, Source, and some of the Products of its Disintegra-
tion and Decomposition. By J ohn Murray, Esq. Communicated
by Sir C. Wyville Thomson, ..... 247

On New and Little-known Fossil Fishes from the Edinburgh Dis-
trict. No. I. By R. H. Traquair, M.D., F.G.S., . . . 262

On the Ruff ( Machetes Pugnax). By Professor Duns, . . 272

Communication from the President relative to the Administration
of the Government Fund of £4000, . . . .275

On New and Little-known Fossil Fishes from the Edinburgh Dis-
trict. No. II. By R. H. Traquair, M.D., F.G.S., . . 275

Note on Clapeyron’s Formula. By Professor Dewar, . . 283

Note on the Specific Gravity of Ocean Water. By J. Y. Buchanan, 283
Note on the Manganese Nodules found on the bed of the Ocean.

By J. Y. Buchanan, ...... 287

Note on the Measure of Beknottedness. By Professor Tait, . . 289

Note on the Effect of Heat on Infusible Impalpable Powders. By
Professor Tait, . . . . . . .298

Abstract of Additional Memoir on the Parallel Roads of Lochaber.

By D. Milne Home, LL.D., ..... 299

VI

Contents.

PAGE

On Some Effects of Heat on Electro-Static Attraction. By Prof. Tait, 302
On the Curves produced by Reflection from a Polished Revolving
Wire. By Edward Sang, Esq., ..... 302

On an Ammonia- Cupric Zinc Chloride. By E. W. Prevost, Ph.D., . 302
On a Peculiarity of the Diurnal Hygrometric Curve at Geneva. By
Alexander Buchan, Esq., ...... 304

On Knots. By Professor Tait, ..... 306

Presentation of the Makdougall-Brisbane Prize to Alexander Buchan,
M.A., ....... 319, 486

On the Action of Sulphuretted Hydrogen on the Hydrate and on the
Carbonate of Trimethyl- Sulphine. By Professor Crum Brown, . 319
On Links. By Professor Tait, . . . . .321

Laboratory Notes. By Professor Tait —

a. Measurement of the Potential required to produce Sparks

of various lengths, in Air at different pressures, by a
Holtz Machine. By Messrs Macfarlane and Paton, . 332

b. The Thermal Conductivity of Gas Coke. By Messrs Knott

and Macfarlane, ...... 333

c. Preliminary Experiments on the Currents produced by

contact of Wires of the same metal at different Tempera-
tures. By Messrs Knott and Macfarlane, . . 333

d. On the Relative Percentages of the Atmosphere and of the

Ocean which would flow into a given Rent in the Earth’s
Surface. By Professor Tait, .... 333

On the Biliary Secretion with reference to the Action of Cholagogues.

By Professor Rutherford, F.R.SS. L. and E., and M. Vignal, . 334
Specimen of Auriferous Quartz. By Patrick Dudgeon, . . 338

On a Problem of Arrangements. By Professor Cayley, . . 338

On the Construction of the Canon of Sines, for the Decimal Division
of the Quadrant. Edward Sang, Esq., .... 343
On the Precautions to be taken in recording and using the Records
of Original Computations. Edward Sang, Esq., . . . 349

On an Unnamed Palaeozoic Annelid. By Prof. Duns. (Plate IV.), 352
On Eisenstein’s Continued Fraction. By Thomas Muir, M.A., . 359

Note on an Infinitude of Operations. By Thomas Muir, M.A., . 359

Note on Determinant Expressions for the Sum of a Harmonical
Progression. By Thomas Muir, M.A., .... 361

Sevenfold Knottiness. By Professor Tait, .... 363
Exhibition of a Large Map showing the Progress of the Geological
Survey of Scotland. By Professor Geikie, . . . 367

Notice of a Saline Water from the Volcanic Rocks of Linlithgow.

By Professor Geikie, F.R.S., . . . . . 367

On the Arrangement and Relations of the Great Nerve-Cords in the
Marine Annelids. By W. C. MTntosh, M.D., F.R.S.E., F.L.S., . 372

Contents.

Vll

PAGE

On the Application of Graphic Methods to the Determination of the
Efficiency of Machinery. By Professor Fleeming Jenkin, . 381

On Professor Tait’s Problem of Arrangement. By Thomas Muir,
M.A., . . . . . . . .382

On Mr Muir’s Discussion of Professor Tait’s Problem of Arrange-
ments. By Professor Cayley, ..... 388

On Amphicheiral Forms and their Relations. By Professor Tait, . 391
On the Toothing of Un-round Discs which are intended to roll upon
each other. By Edward Sang, ..... 393

On the Mineralogy of Scotland. Chapter II. By Professor Heddle, 393
Least Roots of Equations., By J. D. Hamilton Dickson, . . 393

On New and Little-known Fossil Fishes from the Edinburgh Dis-
trict. No. III. By Dr R. H. Traquair. ( See Appendix), . 394

On Ocean Circulation. By John Aitken, .... 394

On a New Investigation of the Series for the Sine and Cosine of an
Arc. By Edward Sang, ...... 400

Note on the Bifilar Magnetometer. By J. A. Broun, F.R.S. Com-
municated by Professor Tait, ..... 402

Addition to the paper “ On the Establishment of the Elementary
Principles of Quaternions.” By G. Plarr. Published in Yol.
XXVII. of the Transactions of the Society. Communicated by
Professor Tait, ....... 402

Note on Mr Muir’s Solution of a “Problem of Arrangement.” By
Professor Cayley, ....... 402

Preliminary Note on a New Method of Investigating the Properties
of Knots. By Professor Tait, ..... 403

On the Cranial Osteology of Rhizodopsis, and on some points in the
Structure of Rhizodus. By Dr R. H. Traquair. ( See Appendix), 403
Notice of Recent Earthquake Shocks in Argyleshire in 1877. By

David Stevenson, Civil Engineer, ..... 403

Additional Remarks on Knots. By Professor Tait, . . . 405

On the Structure and Relations of the Genus Holopus. By Sir C.
Wyville Thomson, F.R.S., ...... 405

On the Diurnal Oscillations of the Barometer. Part II. By
Alexander Buchan, M.A., . . . . . .410

On the Air Dissolved in Sea- Water. By J. Y. Buchanan, . .412

Why the Barometer does not always indicate real Vertical Pressure :

A continuation of the Paper laid before the Royal Society of
Edinburgh in July 1875, in which, in addition to several other
points, this was attempted to be shown. It is now more fully
written out. By Robert Tennent, . . . . .412

Laboratory Notes. By Professor Tait —

a. On an Effect of Heat on Electro-Static Action, . .415

b. On Dr Blair’s Scientific Aphorisms in connection with the

Ultra-Mundane Particles of Le Sage, . . .415

viii Contents .

PAGE

Note on an Identity. By Professor Tait, . . . .416

Appendix : —

The Thermo-Electric Properties of Cobalt. By Messrs C.^G.

Knott, J. Gordon MacGregor, and C. Michie Smith, . .421

Notice of some Becent Atmospheric Phenomena. By Professor
Tait, ........ 425

On New and Little-known Fossil Fishes from the Edinburgh
District. No. III. By R. H. Traquair, M.D., F.G.S., . 427

On the Cranial Osteology of Rhizodopsis, and on some points in
the Structure of Rhizodus. By Dr R. H. Traquair, . . 444

Election of Office-Bearers, . . . . . .471

Opening Address by the Vice-President, Principal Sir Alexander
Grant, Bart., . . . . . . .472

Remarks by Sir William Thomson on delivering the Makdougall-
Brisbane Prize to Mr Buchan, ..... 486

Report of the Deputation to Upsala. By Alexander Buchan, M.A., 521
On a Method of Determining the Cohesion of Liquids. By J. B.
Hannay, F.C.S., ....... 526

Note on Vector Conditions of Integrability. By Professor Tait, . 527
On Gladstone’s Theory of Colour-Sense in Homer. By Professor
Blackie, ........ 533

Note on a Geometrical Theorem. By Professor Tait, . . 533

On the Tabulation of all Fractions whose values are between two
prescribed limits. By Edward Sang, .... 536

Can the Law of Multiple Proportions be demonstrated from
Analytical Data ? By W. Dittmar, .... 536

On the Solid Fatty Acids of Coco-Nut Oil. By G. Carr Robinson, . 537
Suspension, Solution, and Chemical Combinations. By William
Durham, ........ 537

Note on the Surface of a Body in terms of its Mass. By Professor
Tait, . . . . . . . .541

On a White Sunbow. By Sir Robert Christison, Bart., Professor
Tait, Mr J. Christison, Mr Buchan, and Dr Ferguson, . 542-48

Letter on the Phonograph. By H. E. Rosevelt, . . . 548

Address by Sir Wyville Thomson oil delivering the Neill Prize to
Dr Traquair, ....... 549

Chapters on the Mineralogy of Scotland. Chapter III. — The Garnets.

By Professor Heddle, ...... 550

On the Strength of the Currents required to work a Telephone , By
Professor Tait, . . . . . . .551

Experiments with the Telephone. By James Blyth. Communicated
by Professor Tait, ....... 553

On the Theory of the Telephone. By Professor George Forbes, . 555
Some Experiments with the Telephone. By John G. M‘Ken-
drick, M.D., ........ 558

Contents.

IX

The application of the Graphic Method to the determination of the
efficiency of a direct-acting Steam-Engine. By Professor Fleeming
Jenkin, ........ 563

On the Disruptive Discharge of Electricity. By Alexander Macfar-
lane, M.A., B.Sc. Communicated by Professor Tait, . . 563

On the Compressibility of Water, Sea- Water, a four per cent.
Chloride of Sodium Solution, Mercury, and Class. By J. Y.
Buchanan, M.A., F.R.S.E., ..... 565

On the Action of Heat on some Salts of Trimethyl-Sulphine. By
Professor Crum Brown and J. Adrian Blaikie, Esq., . . 565

Extracts from two letters on the Refractive Indexes of Glass and
Quartz, as tested by Reflection from the Surface. By Professor
Quincke. Communicated by Sir William Thomson, . . 567

Mr Gott’s and Professor Bell’s Explanation of the Action of the
Telephone, . . . . . . . .570

Proposed Theory of the Progressive Movement of Barometric Depres-
sions or Storms ; being in continuation of the Paper read before
the Society on July 5, 1875. By Mr Robert Tennent, . .570

On the Thermo-Electric Properties of Charcoal and certain Alloys,
with a supplementary Thermo-Electric Diagram. By C. G. Knott,
B.Sc., and J. G. MacGregor, D.Sc. Communicated by Professor
Tait, . . . . . . . .579

On the Auriferous Quartz of Wanlockhead. By Dr Lauder Lindsay, 579
On the Discharge of Electricity through Turpentine. By A.
Macfarlane, B.Sc., and Mr R. J. S. Simpson. Communicated by
Professor Tait, . . . . . . .579

Remarks on the Phonograph. By Professor Fleeming Jenkin and
Mr J. A. Ewing, . . . . . . .579

On Thermal Conductivity. By Professor Tait, . . .581

On the Wave Forms of Articulate Sounds. By Professor Fleeming
Jenkin and Mr J. A. Ewing, ..... 582

On the Action of the Chlorides of Iodine upon Acetylene and
Ethylene. By George M‘Gowan, ..... 588

On some Definite Integrals. By Professor Tait, . . . 594

Chapters on the Mineralogy of Scotland. Chapter IV. — Augite
Hornblende, and Serpentinous Change. By Professor Heddle, . 595
On the Old Red Sandstone of Western Europe. By Professor
Geikie, F.R.S., . . . . . . .596

On Beats of Imperfect Harmonies. By Sir William Thomson, . 602
On Vortex Vibrations, and on Instability of Vortex Motions. By
Sir William Thomson, . . . . . .613

On the Theory of Vowel Sounds. By Professor M‘Kendrick, . 613
Preliminary Note on a Method of Detecting Fire-Damp in Coal
Mines. By Professor George Forbes, . . . .613

Note on Electrolytic Conduction. By Professor Tait, . .614

Note on Thermal Conduction. By Professor Tait, . . .615

h

x Contents.

PAGE

On the Indications of Molecular Action in the Telephone. By R. M.
Ferguson, Ph.D., ....... 615

Sketch of the Arrangement of Tables of Ballistic Curves in a
Medium resisting as the Square of the Velocity, and of the Appli-
cation of these Tables to Gunnery. By Edward Sang, . . 637

On some Physical Experiments relating to the Function of the Kid-
ney. By David Newman, Glasgow. Communicated by Professor
M‘ Kendrick, ....... 648

Note of a Method of Studying the Binocular Vision of Colour. By
John G. M‘Kendrick, M.D., ..... 654

On the Genus Rhizodus. By Dr R. H. Traquair, . . .657

On the Anatomy of a recent Species of Polyodon, the Polyodon
gladius (Martens), taken from the river Yangtsze-Kiang, 450 miles
above Woosung. Part III., being its Viscera of Organic Life. By
P. D. Handy side, M.D., . . . . . . 660

A Mechanical Illustration of the Vibrations of a Triad of Columnar
Vortices. By Sir William Thomson, .... 660

Fourth Report of Boulder Committee, with Remarks. ByD. Milne
Home, Esq., ....... 660

Remarks by David Milne Home, LL.D., Convener of the Society’s
Boulder Committee, on presenting the Committee’s Fourth Report
at a Meeting of the Society, 20th May 1878, . . . 692

On the Splitting up of Electric Currents, as detected by the Tele-
phone, and the founding thereon of a Sounder to call attention
from one Telephone to another. By R. H. Bow, R.E., . . 707

An Account of some Experiments on the Telephone and Microphone.

By James Blyth, M.A., . . . . . .711

Note on a Variation of the Microphone. By R. M. Morrison,
D.Sc., . . . . . . . .712

On the Action of Heat on some Salts of Trimethyl-Sulphine.

Part II. By Professor Crum Brown and J. Adrian Blaikie,
B.Sc., . . . . . . . .712

On a Class of Determinants. By Mr J. D. H. Dickson, Tutor of St
Peter’s College, Cambridge, . . . . .714

On the Wave-Forms of Articulate Sounds. By Professor Fleeming
Jenkin, F.R.S., and J. A. Ewing, B.Sc., .... 714

On the Electric Conductivity of the Bars employed in his Measure-
ments of Thermal Conductivity. By Professor Tait, . .718

On the Biliary Secretion, with reference to the Action of Chola-
gogues. Part II. By Professor Rutherford, F.R.SS. L. and E.,
and M. Vignal, ....... 718

On a New General Method of Preparing the Primary Monamines.

By R. Milner Morrison, D.Sc., . . . . .721

On the Preparation and Properties of Pure Graphitoid and Adaman-
tine Boron. By R. M. Morrison, D.Sc., and R. Sydney Marsden,
B.Sc., . . . . . . . .721

On Colour in Practical Astronomy, spectroscopically examined. By
Professor Piazzi Smyth, . . . . . .721

Contents.

xi

PAGE

On the Disruptive Discharge of Electricity. By Alexander Marfar-
lane, D.Sc., and P. M. Playfair, M.A., .... 721

On the Wave-Forms of the Vowel Sounds produced by the Appa-
ratus exhibited by Professor Crum Brown. By Professor
Fleeming Jenkin, F.R.S., and J. A. Ewing, B.Sc., . . 723

Notes on the Fungus Disease affecting Salmon. By A. B. Stirling,
Assistant Conservator of the Anatomical Museum in the Univer-
sity of Edinburgh. Communicated by Professor Turner, . .726

On some New Bases of the Leucoline Series. Part I. By G. Carr
Robinson, Esq., ... .... 732

On the Crystallisation of Isomorphous Salts. By G. Carr Robin-
son, Esq., ........ 732

On a New Method for the Separation of Yttrium and Erbium from
Cerium, Lanthanum, and Didymium. Part I. By J. Gibson,
Ph.D., and R. M. Morrison, D.Sc., .... 734

On certain Effects of Periodic Variation of Intensity of a Musical
Note. By Professor Crum Brown and Professor Tait, . . 736

Note on a Mode of Producing Sounds of very great Intensity. By
Professor Tait, . . . . . . .737

Donations to the Library of the Royal Society, . 178, 446, 739

Index, ........ 767

Errata to be corrected in Table at top of page 607 opposite.

Column 1, second row of figures, for “ 286-75,’’ read “ 288.”

ninth „ „ “573*50,” ,, “ 576.”

Column 3, second „ ,, “ +0-60,” ,, “ -Q-65.

>> ninth „ ,, “+1*20,” „ “-1*30.’

5)

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

VOL. IX.

1875-76. No. 93.

Ninety-Third Session.

Monday , 22 d November 1875.

Sir ROBERT CHRISTISON, Bart., Hon. Vice-President,

in the Chair.

The foRowing Council were elected :■ —

President.

Sir WILLIAM THOMSON, Knt., LL.D.

Honorary Vice-Presidents.

His Grace the DUKE of ARGYLL.

Sir ROBERT CHRISTISON, Bart., M.D.

Vice-Presidents.

David Milne Home, LL.D.
Professor Kelland.

Rev.W. Lindsay Alexander, D.D.

David Stevenson, Esq., C.E.

The Hon Lord Neaves.

The Right Rev. Bishop Cotthrill.

General Secretary — Dr John Hutton Balfour.

Secretaries to Ordinary Meetings.
Professor Tait.

Professor Turner.

Treasurer-— David Smith, Esq.

Curator of Library and Museum — Dr Maclaoan.

Councillors.

Dr Arthur Mitchell.

George Forbes, Esq.

Principal Sir Alex. Grant, Bart.
Professor Geikie.

Dr Andrew Fleming, H.M.I.S.
Dr Charles Moreread.

Alexander Buchan, A.M.
Robert Wyld, Esq.

Dr Ramsay H. Traquair.
Dr Thomas Harvey.

Dr John G. M‘Kendrick.
Dr J. Matthews Duncan.

vol. IX.

A

2

Proceedings of the Royal Society

Monday, §th December 1875.

DAVID MILNE HOME, Esq., of Wedderburn, LL.D.,
Senior Vice-President, in the Chair.

The Chairman delivered the following opening Address: —

Gentlemen, Fellows of the Royal Society of Edinburgh, — In
compliance with a request of the Council, I have the honour to
come before you this evening to give an address, on this the first
night of our Winter Session, in pursuance of the custom prevalent
in this and most other Societies.

I need not say how much 1 regret, for your sakes as well as my
own, that this duty is not to be discharged by our eminent Presi-
dent.

The first point which I will submit to your notice, is the nature
and amount of the work we as a Society are doing, and our means
of doing it.

The second and concluding part of my Address will have
reference to the present aspect and prospects of science generally
ip the country.

With regard to the work we are carrying on, it may be suffi-
cient to refer to the proceedings of our last winter’s session. Our
Secretary tells me that it was the longest session he remembers —
it having been prolonged beyond mid-summer.

You are aware that our Society was intended by its founders to
embrace literature as well as science ; and that in regard to science,
we encourage investigations in any of nature’s various fields. The
following abstract, under different heads, of the papers read during
last session, indicates the range and variety of the Society’s
operations : —

In Applied Mathematics or Physics, we had 11 papers read; in
Pure Mathematics, 9 ; Notes from Professor Tait’s Physical Labo-
ratory were read at five meetings ; of Geological papers, 4 were read ;
of Chemical papers, 3 ; of Physiological papers, 3 ; of Anatomi-
cal papers, 3 ; of Meteorological papers, 2 ; of Literary papers, 2 ;
separate Biographical Memoirs of eleven deceased Members were

of Edinburgh, Session 1875-76.

3

read. Many interesting experiments were shown at our meetings;
and in particular, our President, at one of our meetings, exhibited
and explained his wonderful tide-calculating machine, by means of
which there can be obtained in a few seconds, results which hitherto
have required minute and laborious calculations.

The three Prizes which the Society has at its disposal, were
awarded as follows : —

The Keith Prize was awarded to Professor Tait, for his paper on
a “ First Approximation to a Thermo-Electric Diagram.”

The Makdougall Brisbane Prize was awarded to Professor Lister,
for his paper u0n the Germ Theory of Putrefaction and Fermenta-
tion.”

The Neill Prize was awarded to Mr Charles William Peach, for

A

his “ Contributions to Scotch Geology and Zoology.”

Gentlemen, an important part of our work as a Society is to
publish in a volume of Transactions the most deserving of the
papers read at our meetings. A copy of these Transactions is, as
you know, obtained gratis by every member. Copies also, to tbe
extent of considerably above a hundred, go to foreign libraries,
foreign universities, and foreign societies. Many of these papers
are necessarily not of so popular a character as to pay, by the
sale of them, the cost of printing. But these papers, though not
interesting to the general community, may be of the highest
importance for the advancement of science. Fortunately our
Society is sufficiently wealthy to be able to defray the expense,
not only of printing, but of a large gratuitous circulation. X
believe that it is a knowledge of this fact which obtains for our
Society so large a membership, and so satisfactory a revenue.

With regard to our membership, we have now 358 Ordinary
Fellows. X observe from the address which I had the honour of
giving five years ago, that the number then was 326, so that there
has been in the interval an increase of 32 members.

The number of members whom we have lost by death is, I am
sorry to say, larger than usual, being altogether 14. The follow-
ing are the names alphabetically arranged : —

4

Proceedings of the Royal Society

1 . Foreign Honorary Fellow. — Le Comte de Remusat.

2. British Honorary Fellows. — Sir Charles Lyell, Bart, of
Kinnordy; Sir William Edmund Logan, LL.D.; Sir Charles
Wheatstone, D.C.L.

3. Ordinary Fellows. — Rev. Dr D. Aitken ; John Auld, Esq. ;
Professor Hughes Bennett, Edinburgh University; Rev.
Professor Crawford, Edinburgh University; Colonel Seton
Guthrie, Thurso ; Sir William Jardine of Applegarth, Bart. ;
Professor William Macdonald, St Andrews’ University; the
Hon. Lord Mackenzie; Edward Meldrum, Esq., Dechmont;
the Venerable Archdeacon Sinclair.

I propose to give an obituary notice of several in this list, with
regard to whom I have succeeded in obtaining information, chiefly
through the good offices of our Secretary, Professor Balfour.

Charles, Comte de Remusat, a distinguished French poli-
tician, philosopher, and man of letters, was horn at Paris on
the 14th of March 1797. His father held various public
offices under the first Empire. His mother was an intimate
friend of the Empress Josephine. The young Remusat, after a
brilliant course at the Lyc6e Napoleon, betook himself at first
to the study of law, but he soon turned to literature, and wrote
as a journalist in newspapers and reviews from 1818 till 1830.
In company with Guizot, Cousin, and Jouffroy, he was on the
staff of the “ Globe,” a periodical founded by Dubois in 1824,
which struggled against the growing absolutism of the Restoration.
He continued afterwards, in concert with Guizot, to support doc-
trinaire constitutionalism, and in philosophy he was on the whole
of the school of Cousin. His name appears in the list of journalists
who protested against the ordinances which brought about the
Revolution of July. In 1830, he was chosen deputy by Toulouse,
and soon followed the leadership of Thiers in the Chamber. In
1838, he was for a short time Under-Secretary of State in the
ministry of Count Mole, and in 1840 he was Minister of the
Interior, under Thiers. After the Revolution of 1848, he continued
a member of the Constituent Assembly, and supported the party of
order. During the whole period of the second Empire, he withdrew

of Edinburgh, Session 1875-76.

5

from political life, and devoted himself to literary and philosophical
labours, sceptical of the possibility of an Imperial government
restoring liberal institutions. The Revolution of 1870 brought the
Count de Remusat back to public life, as Minister of Foreign Affairs
under M. Thiers, with whom he fell in May 1873, and with whom
he agreed in regarding the Republic as, if not the political ideal,
at least the best practical solution of the difficulties of France. He
died at Paris on the 6th of June 1875.

The Count de Remusat was a copious, solid, and eloquent writer.
Besides his large contributions to the periodical press, especially
the “Revue des Deux Mondes,” he was the author of many valuable
works. One of his earliest essays was connected with his legal
studies, and appeared in 1820 (“ Sur la procedure en Matiere Crimi-
nelle ”), followed by other tracts on the responsibility of ministers of
State, the liberty of the press, and the law of elections. His most
brilliant and productive period as a writer was after 1840. Among
his other works are the following : —

Essai sur la nature de Pouvoir,

1840.

Essais de Philosophie,

1842.

Abelard, ....

1845.

Melanges Philosophiques, .

1847.

St Anselm,

1852.

Bacon— Sa Vie, son Temps,

1858.

La Philosophie Religieuse, .

1864.

David Hartley,

1874.

Philosophie Anglaise — Bacon jusqu’a Locke,

1875.

As may be inferred from the subjects of his studies, M. de
Remusat was deeply interested in England. Probably no eminent
Frenchman of his time unders ood English institutions and
national character so well. The practical philosophers and states-
men of this country, and their readiness to accept the teaching of
experience and to recognise the tendencies of the age, in a spirit
of wise compromise, were all in harmony with his temper; which
always inclined to moderation, and was averse to fanaticism,
whether political or speculative, religious or anti-religious. In
philosophy, he belonged to the school opposed to Materialism.

In M. de Remusat we have lost one of the most eminent of the

6

Proceedings of the Royal Society

French politicians and thoughtful men of letters of the nineteenth
century, and the philosophy of mind has lost one of its ablest
expositors, though he may not have ranked among its discoverers
and leaders.

Charles Lyell was born at Kinnordy, in Forfarshire, on 14th
November 1797, and died in London 22d February 1875. He was
on our list of British Honorary Fellows. His early education was
obtained at Midhurst, in Sussex. He went thereafter to Oxford, and
there obtained his A.M. degree in 1821. Whilst at Oxford he had
the advantage of attending Dr Buckland’s lectures, then Professor
of Geology. On leaving the university, he studied for the English
bar; but finding this line of life not likely to be congenial, and
having the means of living without the aid of a profession, he
betook himself to geology. The seed sown by Dr Buckland had
been dropped into soil fitted to its germination and rapid develop-
ment.

Probably Lyell’s first paper was an account of a “ Recent
Formation of Freshwater Linn stone in Forfarshire,” his native
county. This was very soon Allowed by many other papers,
written at places visited by him in Hampshire and Dorsetshire.
These were read before the Geological Society of London, of which
he had become member. In the year 1824 he had shown such
knowledge of geology, that he was elected one of the Honorary
Secretaries of the Society.

In 1827 he contributed to the “Quarterly” a review of Mr
Poulett Scrope’s “ Geology of Central France.”

Shortly afterwards, he published his “ Principles of Geology,”
the work in which he first showed his distrust of old geological
maxims, and started his own original conceptions. Most geologists
before his day had attempted to explain many things by assuming
that the natural agencies of bygone times had been much more
powerful than now. On the other hand, Lyell maintained that the
natural agencies now on our planet were capable of producing
all the effects observed, if only sufficient time was allowed for
their operation.

These new views attracted great attention. The demand for the
book in which they were explained was so great, that it went

of Ed in b urgh , S^ss io i i 1875-76.

7

through five editions in a very short time— each edition contain-
ing a large amount of new matter. The work, by these numerous
additions, became so changed in character, that he reconstructed
it, and brought out a new work called “Elements of Geology,”
and greatly altered his “ Principles ” as regards arrangements.
In the latter, he presented explanations of the various forces at
work in the earth and in the universe likely to affect the earth.
In the former, he described the observed effects. Subsequently he
brought out the “Student’s Manual of Geology,” in which he
brought together most of the facts mentioned in the two previous
works.

No geologist before LyelPs time had devoted himself so exclu-
sively and so laboriously to the science. He not only kept himself
acquainted with the discoveries made by others, but he travelled
over large portions of the earth’s surface, with the view of verify-
ing alleged facts, and making di coveries himself.

He went to Norway, Sweden, Belgium, Switzerland, Germany,
Spain, Catalonia, and the Danish islands of Seeland and Monen.
He was twice in America. On the first occasion, in 1841, he went,
in compliance with an invitation, to deliver a course of lectures at
Boston. He then remained in the New World a whole year, his
explorations extending from Canada through the States to the
mouths of the Mississippi. On returning to England, he pub-
lished his “ Travels in North America,” in which, whilst geological
information chiefly is given, some useful views occur on other
subjects also. In 1845 he paid a second visit to America, and
examined more particularly the Southern States and the coasts
bordering the Gulf of Mexico. On his return to England, he
published his “Second Visit to the United States,” — a companion
to his former work.

The most recent of Lyell’s important works was his “ Antiquity
of Man,” which went through four editions, the first having come
out in 1863, the last in 1873. But beside these elaborate works,
he published numerous memoirs, most of which had been read at
meetings of the Geological Society and British Association for the
Advancement of Science.

In 1836, and also in 1850, he was President of the London
Geological Society. The "Royal Society’s Copley Medal was awarded

8

Proceedings of the Royal Society

to him in 1858, and the Geological Society’s Wollaston Medal was
awarded to him in 1866.

In the year 1864 he presided at the Bath Meeting of the
British Association for the Advancement of Science. He was
Patron of the Scotch Geological Society. In the year 1848 he
was knighted, and in the year 1864 he received a baronetcy in
recognition of his services to science.

Sir Charles Lyell was married in 1832 to Mary Elizabeth, eldest
daughter of the late Leonard Horner, himself a distinguished
geologist. Lady Lyell was a devoted wife, and sympathised with
her husband in his pursuits, accompanying him in all his travels,
and assisting him in literary work.

During the last five or six years, Sir Charles Lyell lost his eye-
sight to such an extent that he could neither read nor recognise
his friends. The last time that I was in his house, Harley Street,
London, Lady Lyell had to lead him, and make known to him the
presence of several friends who came in.

Lady Lyell’s death in the year 1874 was a severe shock to her
husband. After that event, Sir Charles’s health rapidly failed. His
death was caused by a severe fall on the staircase of his house, he
having, owing to his blindness, missed the uppermost step.

Probably few men were ever so devoted to any special object, as
Sir Charles Lyell was to geology, through his whole life. He was
inspired by a genuine love of truth, and for its sake did not
hesitate to retract opinions when he found he was mistaken. In
the three first editions of his “ Antiquity of Man” he had expressed
his concurrence in the opinion of some Scotch geologists, that the
land near the Firth of Forth had risen 25 feet since the Homan
occupation. In the last edition of the work, he revoked that
concurrence. In the account given by him of the Glen Roy terraces,
he published his belief, that they were due to fresh water lakes.
In a letter which I received from him shortly before his death,
adverting to some facts recently discovered, he allows, that perhaps
after all, Darwin’s theory of the terrace having been made by the
sea, might prove to be correct. Sir Charles Lyell in this respect
showed an example to all men of science, in caring more for the
interests of truth, than for mere consistency.

9

of Edinburgh, Session 1875-76.

William Edmond Logan, another Honorary Fellow of the Society,
was bora at Montreal, Canada, in the year 1798, and died on 22d
June 1875.

His father was originally a landed proprietor in Stirlingshire, and
emigrated to Canada. He sent his son from Canada, when very
young, to Scotland, to be educated in the High School, and after-
wards in the University of Edinburgh.

When young Logan was in Edinburgh, geological investigations
and speculations were exciting much interest, in consequence of
the discussion between the Huttonians and Wernerians. Mr Logan
then acquired a taste for geology; and having occasion to go to
South Wales, he began to study the rocks in the coal-fields there,
at this time, beginning to be more extensively worked. Having
procured an Ordnance Survey map on a large scale, he was at the
trouble to trace out and lay down upon it the outcrop of all the
coal seams worked through extensive tracts of country. Seeing
where the outcrops ceased to be continuous, he ascertained the
amount and direction of the dykes and slips by which the strata
had been dislocated. He descended into the mines, and studied
for himself the structure of the coal, and examined particularly the
fossils found in the coal. He was then struck bv the fact, that
every coal seam lay upon a bed of blue-coloured clay, in which
apparently the plants had grown, now found petrified in coal.
In several instances he discovered that some of the fossil trees
which had their trunks in the coal-bed had their roots still
stretching into the underlying bed of clay.

About this time Sir Henry de la Beche, who was directing the
Geological Survey of England and Wales, happened to come into
South Wales. Having heard of Mr Logan, he became acquainted
with him; and having seen the work he had been carrying on, he
at once put him on the staff of the survey.

Mr Logan having permanently adopted geology as a profession,
became a Member of the Geological Society of London. Frequently
joining in the discussions there, he made the acquaintance of Sir
Charles Lyell, Sir Roderick Murchison, and other leading geologists.

Having obtained leave of absence to visit his father in Canada,
he went there in 1841, and spent much of his time in exploring
the great coal-fields of Nova Scotia and Pennsylvania.

VOL. IX.

B

10

Proceedings of the Uoyal Society

In the spring of 1842 he returned to England, and in the
Gi-eological Society gave an interesting account of his survey in these
American coal-fields. He had been particularly anxious to obtain a
confirmation of his discovery, that coal seams everywhere rested
on fire-clay; and he was able to afford these proofs from what he
bad seen in Nova Scotia.

He had made another discovery in these coal-fields. He had
discovered the footprints of a reptile; and he brought to London
with him the sandstone slab which contained these prints. This
slab was submitted to Professor Owen, who expressed a clear
opinion, that the impressions had been made by an animal which
had four claws on the two fore feet, and three claws on the hind
feet. The interest attaching to this discovery was, that no reptile
had been discovered in rocks so old, it being at the bottom of the
Carboniferous formation; — whereas, previously, no reptiles had
been found below the Permian rocks.

I mention this discovery of Logan’s, because I see that my friend
Principal Dawson of Montreal, in his “ Book on Acadian Geology,”
mentions that discoveries of similar reptiles, made in the year 1844
in Sweden and the United States, -had been asserted to be prior
to others of the same kind.

Logan’s reputation as a geologist was now established. It led
to his being entrusted with the charge of the Canadian Geological
Survey, on the recommendation of Sir Roderick Murchison and
Sir Henry de la Beche. The Canadian Legislature had wisely
resolved to have the mineral riches of the country ascertained by
competent surveyers. F or nearly thirty years Sir W illiam conducted
the Canadian Survey,, and drew most important conclusions regard-
ing the whole series of rocks in that part of the world — conclu-
sions universally accepted by geologists as correct.

At the Paris International Exhibition of 1855, he showed a large
collection of specimens, besides magnificent m^ps and diagrams,
which attained much attention, and received great commendation.
It was on this occasion, that the British Government, in recogni-
tion of his eminence as a geologist, and of his services in Canada,
bestowed on him the honour of knighthood.

Sir William did not publish anything beyond the official reports
of his survey. He was not ambitious of fame, either as an author

of Edinburgh, Session 1875-76.

11

or otherwise. He stuck closely to the work he had undertaken,
and continued at it till the year 1869, when failing health led him
to resign.

He, however, continued to take an interest in geological pursuits,
and gave, from his private funds, a donation of L.5000, for the
endowment of a chair of' geology in the M‘Gill College, Montreal.

Charles Wheatstone was born at Gloucester in 1802, and died
in Paris 19th October 1875. He was on the list of our British
Honorary Fellows.

The rudiments of education were obtained by him at a private
school. Whether he afterwards went to a university, I have not
discovered.

His youth and early manhood were devoted to the construction
of musical instruments, and to experiments with the view of dis-
covering more exactly the laws of sound. He paid special attention
to the instruments depending on vibrating springs. The present
improved Concertina is due to his invention.

His first scientific memoir was in the year 1823, when he pub-
lished in the “ Philosophical Annals” an account of some “ New
Experiments on Sound.” It excited considerable attention among
physicists, and was translated into several foreign periodicals. In
1827, in the “ Quarterly Journal of Science,” he published farther
“ Experiments on Audition,” accompanied by a description of the
Kaleidophone, an instrument to illustrate both acoustical and optical
phenomena.

During the next eleven years, he continued to produce papers and
to invent instruments for illustrating the properties of sound.

In 1838 he seems to have entered on a different subject of inves-
tigation altogether, viz., light. He had discovered relations be-
tween waves of sound and waves of light. He communicated to
the Royal Society of London, and also to the British Association^
an account of some hitherto unobserved phenomena of binocular
vision, illustrating them by means of the instrument vhich he
invented, called the “ Stereoscope.'1 To Wheatstone is due the
discovery, that the conception of solidity is due entirely to the
mental union of two dissimilar perspectives.

In 1852 he invented an instrument called the u Pseudoscope ,”

12

Proceedings of the Royal Society

which still farther illustrated the mental action in certain optical
phenomena. An article in the “Edinburgh Review” of October
1858, describes thus the effect of the Pseudoscope: — “When an
observer looks with it at the interior of a cup or basin, he not un-
frequently sees it at first in the real form, but by prolonging his
gaze, he will perceive the conversion within a few minutes ; and it
is curious, that while this seems to take place quite suddenly with
some individuals, as if the basin were flexible and were suddenly
turned inside out, it occurs more gradually with others, the con-
cavity slowly giving place to flatness, and the flatness gradually
rising into convexity.”*

Wheatstone was exceedingly interested in this discovery of the
interference of mental action with optical phenomena, and invented
several instruments with the view of ascertaining the principles on
which it depended. The subject led him to study the subject of
nervous organisation ; but it is believed, that he effected no special
discoveries in that field.

In 1834 the science of Electricity began to occupy Wheatstone’s
attention. He endeavoured to ascertain the velocity of the elec-
trical current. He invented many most ingenious machines with
that view. He seems to have made only an approximation to the
truth, viz., that the current travelled through a mile of wire in less
than the 360th part of a minute.

It now occurred to him that electricity might be employed in
conveying intelligence along great distances by moving a magnet.
By this time an idea of the same kind had occurred in G-ermany.
Mr Cooke, when there, had become informed of the investigations
by Schilling, and having come to London, made these known to
Wheatstone. A proposal for a partnership between the two, was
suggested, and was carried out. Messrs Cooke and Wheatstone

A curious circumstance, analogous to the phenomena here described,
was, without the help of any instrument, observed by me and other friends
lately, in watching the revolutions of a cup anemometer on the top of Alnwick
Castle. On looking at the instrument, it was seen revolving in a direction
consisting with the truth ; but on continuing to look at it, in about half a
minute the anemometer suddenly appeared to change the direction of its
rotation, and to continue so to rotate. We remained for some time looking at
the instrument to repeat the experiment. The same result on every occasion
followed, and to every one of the party, eight or nine in number.

13

of Edinburgh, Session 1875-76.

soon thereafter were employed to establish electric telegraphs on
most of the great English railways.

In 1837 the five-needle telegraph was invented; in 1840, the
alphabet dial telegraph; in 1841, the type-printing telegraph; and
the automatic telegraph between 1858 and 1867. By this last
machine it was found possible to transmit words at the rate of
from 100 to 160 words per minute.

In 1840 Wheatstone conceived the idea of a submarine telegraph
cable, and pointed out both the difficulties and the means of
obviating them.

His last work was to contrive a new recording instrument for
submarine cables, formed by a globule of mercury moving to and
fro in a capillary tube containing acid, or by a drop of acid in a
tube containing mercury, and which was found to be 58 times more
sensitive than any recorder previously employed. He had gone to
Paris to exhibit this invention to his colleagues of the Academy of
Science, when he was attacked by the fatal illness — bronchitis—
which terminated in his death.

This brief notice of Wheatstone’s discoveries in the science of
sound, optics, and electricity gives but a poor idea of the immense
amount of brain work which he went through in the long life
accorded to him. The papers which he contributed to Societies
both in Great Britain and on the Continent are very numerous.
They were always characterised by great lucidity of style and by
copious and telling illustrations, which made them both attractive
and instructive.

Wheatstone was elected a Fellow of the London Royal Society
in 1836, a Chevalier of the Legion of Honour in 1855, a Foreign
Member of the French Institute in 1873. In 1868 the Govern-
ment of Lord Derby conferred on him a knighthood.

In private life Sir Charles Wheatstone had 'the reputation of
being reticent and unsociable. The fact probably was, that his
mind was constantly absorbed with the problems which were con-
stantly presented to it. He was so nervous and bashful, that
though always ready and pleased to describe his discoveries to any
single individual, he entirely broke down when he attempted to
address an audience. Hence, his Professorship of Natural Philo-

14

Proceedings of the Royal Society

sophy in King’s College, London, was little better than a title ; for
he never had a class.

There was no physicist of his time so universally respected. His
remains were brought from Paris for interment in the family burial
place at Kensal Green. The procession was followed by a vast
number of carriages, including many of the nobility; and even the
shops in the streets along which the funeral cortege passed were
shut, whenever it was known whose it was.

David Aitken, D.D., who had been seven years an Ordinary Fellow
of this Society, was born about the beginning of this century. He
died on the 27th March last, in his own house in Charlotte Square,
Edinburgh. He was educated at the High School and University
of Edinburgh, and became a licentiate of the Church of Scotland.

I believe that he had been tutor in the family of the Earl of
Minto, by whom, or through whose influence, he was in the year
1829, presented to the parish of Minto. There he remained
minister for thirty-seven years ; and on resigning his charge, pur-
chased a house in Edinburgh, where he- lived till his death.

Being fond of travel, he visited Norway, Italy, Egypt, and
Syria. As he suffered extremely during the winter season from
delicacy of chest, he often spent the winter abroad. Possessing an
independent fortune, he was able to obtain the services of an
assistant during his absence.

He was a person of literary tastes, was well acquainted with the
German language, and was a friend and correspondent of the
German philosopher Hegel. In the year 1827 he wrote an
article in the “Edinburgh Review” on German literature. He
also drew up the Statistical Accounts of Minto Parish, embodying
an excellent account of its geology, botany, and zoology.

His knowledge of Church history was so considerable that he
was offered the Chair of Church History in the University of Edin-
burgh. On his declining it, the late Dr Welsh was appointed.
His sermons were in composition marked by great elegance and
clearness ; but owing to delicacy of chest, his voice was weak, and
his manner in the pulpit had not the earnestness necessary to
create interest.

He was exceedingly fond of natural history, and took great

of Edinburgh, Session 1875-76. 15

interest in his garden, which was always kept with scrupulous
neatness.

John Hughes Bennett was born in London 31st August 1812,
and died at Norwich 25th Sept. 1875. He had joined our Society
in 1842.

He was educated at the Grammar School, Exeter. It is stated,
however, that he was indebted for the early part of his education
to his mother, a lady of brilliant intellectual attainments. Being
a great admirer of Shakespeare, she caused her son to read aloud
to her many of his plays, and as he did so, taught him the art of
emphasis and rhetorical action. Probably to this tuition of his
mother, Dr Bennett was indebted for the elegance of his composi-
tion, and for the impressiveness of his delivery when he lectured
or spoke in public.

He commenced the study of medicine at Maidstone, in the year
1829, under the guidance of a practitioner there. It was there
that he acquired the art of dispensing, and even obtained a certain
amount of medical practice. He assisted also in post-mortem
examinations.

To acquire better medical instruction and training, he removed
to Edinburgh in the year 1833, — unacquainted with any one in
that city or in Scotland. By his talents and assiduity he soon
attracted the notice of his professors, and obtained the esteem
of numerous fellow-students. His attention was devoted chiefly
to anatomy, physiology, and pathology. Having joined the
Royal Medical Society, and shown his abilities and knowledge
at its meetings, he ultimately became President of the Society.
Whilst still a student, in the year 1836, he published two papers
which obtained for him considerable credit.

In the year 1837, he received the degree of M.D. with the
highest honours, obtaining at the same time a gold medal for his
thesis.

After obtaining all the knowledge which Edinburgh could
supply, Dr Bennett repaired to Paris, where he studied for two
years. Being able to speak and write the French language fluently,
he wrote in the French medical journals, and ultimately became
President of the Parisian Medical Society.

16

Proceedings of the Royal Society

He also went to Germany, spending some time in the principal
University cities, and endeavouring to acquire knowledge beyond
what he had already obtained. One of his acquisitions on the
Continent was ability to use the microscope in practical medicine.
Nor was his pen idle, for whilst abroad, he contributed no less than
seventeen articles to Tweedie’s “ Library of Medicine.”

In 1841 he returned to Edinburgh, and commenced a course of
lectures on histology. He there took the opportunity of showing
to what an extent the microscope might and should be used. It
was at this time that Dr Bennett published a treatise on the use of
cod-liver oil as a therapeutic agent in certain forms of gout, rheu-
matism, and scrofula, — dedicating the treatise to Sir Robert
Christison. In Germany he had seen the good effects of using this
medicine in these cases.

From 1842 to 1848 he continued to give lectures on various
medical subjects. In the last named year he was appointed to
the Chair of Institutes of Medicine, vacant by the transference of
Dr Allen Thomson to Glasgow.

For several years Dr Bennett was proprietor and editor of the
“ Edinburgh Monthly Journal of Medical Science,” in which,
besides editorial articles and reviews, he inserted multitudes of
separate memoirs.

In the “British Medical Journal,” where a detailed account of
Bennett’s life and labours is given, and from which I have culled
the foregoing notices, I see a list of no less than 105 memoirs on
various anatomical and pathological subjects.

In July 1848 Dr Bennett was unanimously elected to the Chair
of Institutes of Medicine.

Whilst teaching in the University and in the Infirmary, Pro-
fessor Bennett found time for literary work, and published his
highly appreciated “ Clinical Lectures on the Principles and
Practice of Medicine.” This book passed through five editions in
this country, and six in the United States, besides being translated
into French, Russian, and Hindoo.

The following additional works flowed from his ready pen.
Their titles were, “Pulmonary Consumption,” “Cancerous and
Cancroid Growths,” Introduction to Clinical Medicine,” “Outlines

of Edinburgh, Session 1875-76. 17

of Physiology/’ “ Text-Book of Physiology — General, Special, and
Practical.”

Professor Bennett had conferred upon him numerous honours and
distinctions. He was President for two years of the Medico-Chirur-
gical Society of Edinburgh ; Hon. Secretary and emeritus President
of the Royal Medical Society of Edinburgh ; and Fellow of numerous
medical societies on the Continent. He bad sent to him, about a
year before bis death, a special licence from the French Govern-
ment entitling him to practise medicine in France. This honour
was probably suggested by the fact of his having, two or three
years before his death, resided in the south of France for the
benefit of his health.

The enormous amount of work, both mental and physical, which
Professor Bennett undertook, probably shortened his life. About
1865 his first illness appeared in the form of a throat affection.
Having recovered by a sojourn in the south of France, and returned
to Edinburgh, he was again prostrated in 1869. After an interval
he recovered, but in the winter of 1871-2 he was obliged to return
to Mentone. During the following summer, he resumed work in
Edinburgh, and gave some clinical lectures. The winters of
1872-3 and of 1873-4 again forced him into a warmer climate,
but each time with less benefit. In the year 1874, he resigned the
Chair of the Institutes of Medicine. Last winter he spent in Nice.
His last illness was owing to disease of the bladder. In August
last he returned to Norwich, the place of his birth, where an
operation was performed, and a stone was extracted. The debility
caused by this operation, combined with previous exhaustion of
constitution, brought on death.

Undoubtedly, Professor Bennett was in the medical profession
a person of great eminence. He introduced many very important
changes in medical practice, and made known many new principles.
His devotion to study and investigation probably led to his having
the character of being somewhat unsociable and austere. But
those who had the privilege of intimacy with him, know that he
was truthful, honest, honourable, and earnest in every relation of
life.

The Rev. Dr Thomas Jackson Crawford joined our Society in

vol. IX.

c

18

Proceedings of the Royal Society

1871. He was born in 1812, and died lltli October 1875, at G-enoa,
at which place, when he died, he was sojourning for the benefit of
his health.

His father was Professor of Moral Philosophy in the United
College of St Andrews.

His son Thomas received the earlier part of his education at the
Edinburgh High School. To St Andrews he went back for his
more advanced studies. Intending to be a clergyman of the Scotch
Church, he took his degree in 1831, and in 1834 was licensed as a
preacher of the gospel by the Presbytery of St Andrews. Whilst
at college he attracted the special notice of the professors by the
superiority of his talents, his assiduity to learn, and the excellence
of the essays which he produced. The patronage of the parish of
Cults being in the gift of the Principal and Masters of the United
College, he was presented to that parish.

When the Royal Commission on Church Patronage in Scotland
sat, it inquired into the way in which the University of St Andrews
exercised its ecclesiastical rights.

On that occasion the Rev. Dr George Cook, one of the Professors
of St Andrews, explained to the Commissioners the circumstances
attending Mr Crawford’s presentation ; adding, that though his
own son was then desirous of obtaining it, and though there was
a party in Cults parish wishing his appointment, he did not hesitate
to prefer young Crawford to his own son.

Whilst minister of Cults, he wrote a Statistical Account of the
parish, which, besides other information, contains several interest-
ing anecdotes regarding the youthful career of Sir David Wilkie,
the painter, whose father had been minister at Cults.

From Cults, Mr Crawford was translated to Glamis, and six years
later he was promoted to Edinburgh, to be minister of St Andrew’s
Church, jointly with the late Rev. Dr Thomas Clark.

About this time he received from his alma mater University, the
degree of D.D. He also, shortly thereafter, was made Convener of
the General Assembly’s Committee on Psalmody, an appointment
for which he was well fitted, on account of his knowledge of and
fondness for music.

Having preached a sermon in 1847 on Jewish Missions, which
was afterwards published, that circumstance led to his being selected

of Edinburgh, Session 1875-76.

19

to take the oversight of the G-eneral Assembly’s Scheme for the
Conversion of the Jews.

In 1853 he entered the arena of controversy by publishing first
a pamphlet, entitled “ Presbyterianism Defended against the Exclu-
sive Claims of Prelacy,” and thereafter another pamphlet, entitled
“Presbyterianism or Prelacy; which is the more conformable to
the pattern of the Apostolic Churches.” His views on these sub-
jects were reiterated by Dr Crawford in the Address which he
delivered from the Chair of the G-eneral Assembly, as Moderator, in
the year 1867. This public advocacy of Presbyterianism, to the
prejudice of Prelacy, drew forth some letters from Bishop Words-
worth, which were published in the “ Scotsman ” newspaper,

“The Fatherhood of God” was Dr Crawford’s first important
contribution to purely doctrinal subjects. Dr Candlish, some of
whose views were controverted, replied to this publication.

At this time Dr Crawford was Professor of Divinity in Edinburgh
University, having succeeded the Rev. Principal Lee in the year
1859.

He published also a volume on the “ Atonement,” in the year
1871.

In the year 1874 he was appointed the Baird Lecturer. His
lectures, first delivered in Glasgow, were afterwards, by special
request, re-delivered in Edinburgh, and were published in a volume
under the title of “ Mysteries of Christianity.”

The immense amount of study which these lectures entailed, I
have heard, weakened Dr Crawford’s health, and prepared his con-
stitution for the illness to which he ultimately succumbed.

In the winter following the publication of these lectures, he was
obliged to reside in the milder climate of the south of England.
He suffered from great delicacy of lungs. But he returned to
Edinburgh last spring, whilst the sharp east winds were still pre-
vailing, and moreover betook himself again to College work, against
the advice of his medical friends.

During the summer of 1875 he went to Germany, sojourned a
while in Switzerland, and then went to Italy. There he so far
recovered his strength, that he could walk considerable distances,
and even up steep hills, without suffering inconvenience. But the
weather in the north of Italy is often dangerous to persons with

20

Proceedings of the Royal Society

weak lungs, especially when the wind is from the north. After a
short illness of ten days, caused by inflammation of the lungs,
lie died.

Dr Crawford, besides being a man of great eminence, and most
highly respected in his own profession, was a person of varied
attainments. Besides having a knowledge of music, he often took
his part at amateur vocal concerts, with others — some of whom are
probably now present among us to-night — and who, I am sure will
bear me out when I say, and I say it from a long personal
acquaintance with him, that Dr Crawford was a person of most
amiable disposition, and most conciliatory in all the relations of
life. Though he entered into controversy he ever avoided personal
aspersions ; and those with whom he fought, were always ready to
admit the fairness with which he wielded his weapons.

I learn from Dr Crawford’s son, what I had not been aware of,
that Dr Crawford kept up to the last, his knowledge of mathematics;
and that frequently, when he was in want of recreation, nothing
pleased him more than taking a problem and working it out.

Sir William Jardine, Bart, of Applegarth, in the county of
Dumfries was born in February 1800, and died 21st November
1874, He had been fifty years a member of this Society.

He was the son of the sixth baronet, by a daughter of Thomas
Maule, the representative of the Earls of Panmure.

Born in Edinburgh, he was educated partly at home, partly at
York. With a view to the medical profession, he attended the
medical classes in Edinburgh. But he did not carry out these
professional views. Having succeeded his father when he was
scarcely twenty-one years of age, he took up his residence at his
family dwelling-place, Jardine Hall. By this time he had evinced
a strong taste for scientific pursuits, especially natural history in
all its branches.

He was a good botanist, a good geologist, and a good ornitho-
logist. He was also a keen sportsman, both with the gun and the
rod. Very many specimens in the large and valuable museum
which he formed at Jardine Hall, were collected by himself.

In the year 1825 he commenced, in conjunction with the late
Mr Selby of Twizell, in Northumberland, the publication of the

21

of Edinburgh, Session 1875-76.

“ Illustrations of Ornithology.” In 1833 he undertook a still
more important work, “ The Naturalists’ Library,” forty volumes of
which appeared in the course of the next ten years — a work for
which he obtained contributions from the best scientific naturalists
in the kingdom; — but of this work, no less than fourteen volumes
are made up of contributions by Sir William exclusively. He also
published a new edition of Alexander Wilson’s “ American Orni-
thology;” started and carried on for some time a magazine of
zoology and botany ; and was also for some years a joint editor of
the “Edinburgh Philosophical Journal.”

Here is a list of other works which flowed from his pen New
edition of “White’s Selborne,” “British Salmonidse,” “ Ichthyo-
logy of Annandale.”

A still more important work by Sir William Jardine was en-
titled “Contributions to Ornithology,” in three volumes, extend-
ing from the year 1848 to 1852. This work contains descriptions
and coloured figures of many species of birds previously unknown.
Another publication was “ Memoirs of the late Hugh Edwin Strick-
land,” in the year 1858. Mr Strickland had married a daughter
of Sir William. He was a good geologist. He unfortunately was
killed in a railway tunnel, the rocks of which he was examining
when a train came on him unexpectedly.

Jardine’ s frequent visits to Northumberland, to co-operate with
his friend Mr Selby of Twizell, brought him into acquaintance witli
Dr Johnston of Berwick-on-Tweed, who was well versed in botany
and marine zoology. Dr Johnston having about this time founded
the Berwickshire Naturalists’ Club, Sir William Jardine joined it
in September 1832, and in that year contributed papers of some
value on the “Parr” and the “Silver White,” small fish of the
salmon species, which frequented the Tweed and many other
rivers. At that time, the true nature of these fish was not known,
though it has since been well ascertained that the parr are the
young of the true salmon in their first year’s growth.

Sir William Jardine was President of the Berwickshire Natura-
lists’ Club in the year 1836, and frequently attended its meetings
in subsequent years.

In the year 1860 he was one of the’ Royal Commissioners
appointed to investigate the Salmon Fisheries of England and

22 Proceedings of the Royal Society

Wales. The evidence collected by these Commissioners is of
great value. Legislation followed on their report.

Shortly before his death, Sir William occupied himself in pre-
paring a catalogue of the various objects of interest in his museum.
This catalogue was in proof, and awaiting revisal when he died.
The list of birds contains no less than 6000 species, and probably
not less than 12,000 specimens. Sir William was most obliging
in lending specimens to friends. I remember on one occasion
obtaining from him on loan the skull of a fossil bear found in this
country, on the occasion of a popular lecture which I was giving
in Berwickshire.

Sir William Jardine was during the last ten years of his life
constantly resident at Jardine Hall, enjoying the sports of country
life, discharging the duties of a proprietor, and taking his share
of county and parochial business.

William Macdonald was born in the year 1798, and died on
1st January 1875. He was the oldest member of our Society, in
the class of Ordinary Fellows, having joined the Society in the year
1820. There is, however, one older member, my venerable friend
Sir Richard Griffiths, who is an Extraordinary Fellow of the
Society. He was ninety-one years of age last September, and is
still in excellent health, residing near Kelso. I believe that Sir
Richard would have been here to-night, had the weather been
less stormy.

Dr Macdonald at an early age inherited a good estate in Argyll-
shire. He applied himself to the execution of extensive works
in that county, for the improvement of his property, and of the
district where it was situated. Unfortunately he involved him-
self in financial difficulties, and was obliged to sell his estate.

He then studied medicine, passed with honours, but never
practised.

In 1820 he joined a number of Societies. He was the oldest
member not only of our Society, but also of the Royal College of
Physicians and of the Linnean Society.

Dr Macdonald frequently read papers to us on various subjects.
He held peculiar views on some points of anatomy, which were

23

o f Edin burgh , Session 1875-76.

entirely at variance with those generally held ; but he never would
concede that he was in error.

He was very partial to natural history, and wrote upon “ The
Structure of Fishes,” “ The Unity of Organisation, as exhibited in
the Skeleton of Animals,” and “On the Vertebral Homologies, as
applicable to Zoology.”

In the year 1849 he accepted an appointment to that somewhat
anomalous professorship of “Civil and Natural History” in St
Andrews, but I am not sure whether he ever had any students.

He had formed a large and interesting collection of specimens
in natural history and anatomy.

Principal Shairp informs me that, a few years before his death,
Dr Macdonald made over this collection to the University Museum.

Donald Mackenzie became a Fellow of this Society in 1870.
He was born 19th June 1818, and died 17th May 1875, at Nor-
wood, near London, where he had gone on account of ill health.

Though born in Edinburgh, his father was from Sutherlandshire,
and a Captain in the Royal North British Fusiliers. His mother
was Robina Jamieson, one of the seventeen children of John
Jamieson, D.D., who wrote the well-known Dictionary of the
Scottish language.

Donald was the eldest of seven children, all of whom he survived,
though he, too, died at the comparatively early age of fifty-seven.

At first he studied for medicine, and received the degree of
M.D. from the University of Edinburgh in 1838. He was also a
Fellow of the Royal College of Surgeons.

But he abandoned that profession, and came to the Scottish bar,
influenced, it is believed, by the expectation that as his uncle,
Robert Jamieson, advocate, had a large amount of practice in the
Courts, he would be able to give him a lift. Robert Jamieson I
remember well in the Parliament House, being the most con-
spicuous figure there for height and breadth, and a lawyer of great
acuteness. His sister, Donald’s mother, lived to the age of eighty-
four.

Donald, to whom this notice refers, did not inherit the Jamieson
constitution. He was narrow-chested and slim, but walked with
elastic step.

24 Proceedings of the Royal Society

Having come to the bar in 1842, he soon got into considerable
practice, and was popular among his brethren in the Parliament
House. He was appointed Advocate-Depute in 1854, an office
which he held till 1858, when he lost it on a change of Grovern-
ment. He was reinstated in 1858, and was appointed Sheriff of
Fife in 1861. In the discharge of this office, he is said to have
given great satisfaction, both to the practitioners in the Sheriff-
Court and to the resident gentry.

Mr Mackenzie was raised to the Bench in 1870, and was not
only most conscientious in his attention to the judicial duties, but
was successful in pronouncing judgments which were seldom
reversed. It is related that on two occasions, when they were
reversed in the Inner House, they were, by an appeal to the House
of Lords, adhered to.

Lord Mackenzie was exceedingly fond of all country sports. A
serious illness was contracted, about two years before his death, in
consequence of his continuing to fish in wet clothes, till he got a
severe chill. In November 1874 he became so ill, that he was
obliged to ask leave of absence for the winter. During the subse-
quent Christmas holidays, he attempted to return to his work in
the Bill Chamber, but he was obliged to give it up, and confine
himself to bed. Disease of the heart, aggravated by rheumatism,
had set in. He continued more or less an invalid for a whole year
before his death, seldom discharging any judicial work.

Lord Mackenzie was universally respected for his close attention
to duty, his sound knowledge and judgment as a lawyer, his
freedom from guile, and his conciliatory disposition toward all
with whom he was brought in contact. His life was shortened by
a determination to perform any duty incumbent on him, though
probably conscious that he was thereby weakening his constitu-
tion.

John Sinclair was born 20th August 1797, and died 22d May
1875. He was the third son of the Right Hon. Sir John Sinclair,
Bart, of Ulbster, in the county of Caithness, author of that
valuable repertory, the Statistical Account of Scotland. His
mother was Diana, daughter of Alexander, the first Lord Mac-
donald.

25

of Edinburgh, Session 1875-76.

His education commenced in Edinburgh University; but he
went afterwards to Pembroke College, Oxford.

In the last book which he published, entitled “ Old Times and
Distant Places,” he mentions that, when at Edinburgh University,
he was the chief means of forming what was called the “ Rhetorical
Society,” among the members of which were the present Earl of
Wemyss, the late Adam Anderson (afterwards Lord Anderson), and
David Robertson, who, whilst on his death-bed, was created Lord
Marjoribanks.

When he went to Oxford, he proposed a similar society; but
“the Dons” (he says) “ frowned upon him, and prevented it.”
The project was renewed some years after. The “ Oxford Union
Club” was then formed, embracing among its members the present
Archbishop of Canterbury, Mr Gladstone, Mr Lowe, and others
who afterwards became men of distinction.

Having gone through the necessary forms for taking orders in
the Episcopal Church, he was ordained by the Bishop of Lincoln
in 1820. He was shortly thereafter appointed to St Paul’s Episco-
pal Chapel, Carrubbers Close, where he remained till he became
assistant to the Rev. Mr Alison, the officiating clergyman of the
then new and handsome chapel of St Paul’s, in York Place.

It was in the year 1820 that Mr Sinclair joined our Society. I
see from his little book, that he took a considerable interest in our
proceedings, as he mentions our Dinner Club, of which he was a
member, and specifies several duties which he undertook as a
member of Council.

Thus he was selected by the Council to endeavour to induce Dr
Williams, rector of the English Academy, to shorten the length
of a paper he was to read on Greek particles, a subject on which
he had read several long papers before, much to the ennui of the
majority of members. Dr Williams, it seems, was not a person
who could be easily diverted from bis purpose ; Mr Sinclair under-
took to try his hand upon the inflexible Welshman. He explains,
in an amusing way, how he succeeded.

Another more important work with which Mr Sinclair was
entrusted by our Council, was the arrangement of the unpublished
MSS. of Hume, the historian. These MSS. had been left as a
legacy to the Society by the late Baron Hume, the historian’s

VOL. XI.

D

26

Proceedings of the Royal Society

nephew. In this duty he was conjoined with the late Lord
Meadowbank and Dr Abercrombie; but the chief part of the work
fell on Mr Sinclair.

He mentions that it was in the year 1828 that he became
acquainted with Dr Thomas Chalmers, when the latter resigned
his professorship of Moral Philosophy at St Andrews, to become
Professor of Divinity in E linburgh University. Having a great
admiration for the doctor’s character and writings, he attended his
first course of lectures, and describes the intense interest with
which he and the other students listened to the professor’s exposi-
tions. The salary of the professors being then very small — only
£200 — the idea of offering a testimonial to Dr Chalmers, at the
end of his first course, occurred to Mr Sinclair. According^ a
sum of £200 was raised from the voluntary students, and presented
to the new professor.

In the year 1839 Mr Sinclair went to London, apparently to
consult Mr Wardrop, the celebrated occulist, about his eyes. He
had to submit to a painful operation and to severe discipline,
which confined him to a room in London for some weeks.

Whilst he was there, a vacancy occurred in the office of Secre-
tary to the National Society — a great Society, established, among
other things, for the encouragement and support of schools con-
nected with the Church of England. Mr Sinclair was asked to
fill the vacant office. At first he refused, as it would oblige him
to leave Edinburgh altogether, and he could not be certain of being
so well received in London as he had been in his own country.
But finding that the two London Archbishops and other persons
of influence were anxious that he should accept, he consented.
He was at the same time appointed to be examining chaplain to the
Bishop of London.

Immediately after entering on this new office, he found himself
involved in a great public controversy, which called for the utmost
exertion, with great tact on his part. The controversy had reference
to the schools of the National Society receiving aid from Gfovern-
ment. After the administration of the Education Grant was
transferred from the Lords of the Treasury to the Privy Council
Committee, a system of inspection, to see that the schools were
properly conducted as regards teaching, was resolved on. The

of Edinburgh, Session 1875-76.

27

Church of England did not object to inspectors; but inasmuch as
the religious instruction in the schools was to be reported on by
Government inspectors, the Church desired to have some security
as to the qualifications of the inspectors to judge of that in-
struction.

The National Society, at the suggestion of Mr Sinclair, resolved
to intimate to Government that they would recommend the
managers of all Church of England schools to refuse the Govern-
ment grants, unless some arrangement satisfactory to the Church
was made on that point. The Government having at first refused to
make any concession, notice was sent to the Privy Council from the
managers of about 200 schools, that they would not in future
receive the grant. Mr Sinclair, in support of the National Society’s
views, appealed to the Universities of Oxford and Cambridge, and
secured their help. He preached on the subject ; he induced
several of the leading London newspapers to advocate the views of
the Church; he obtained the assistance of Lord Ashley and other
influential public men. At length the Privy Council Committee
yielded, — agreeing that no inspector should be allowed to examine
any Church of England School whose name had not first been sub-
mitted to the Archbishops of Canterbury and York for their
sanction. This privilege was extended also to the schools in Scot-
land connected with the Church.

The grants to the Church of England Schools were paid to the
Treasurer of the National Society, and were by him distributed to
the schools. When the above arrangement had been completed,
the office of treasurer was held by a Mr Watson, who was so averse
to the proceedings of the Privy Council, that to avoid touching the
unclean thing, he refused to receive the Government grant, or grant
a receipt for it, and sent in his resignation. Mr Sinclair on this
occasion was appointed to be treasurer, so that he was installed
into the two most important and laborious offices of the Society.

In the year 1843 Mr Sinclair, in addition to these duties, was
called on to undertake important pastoral work. In that year he
was appointed Vicar of Xensington, and in the following year
Archdeacon of Middlesex.

The population of that new part of London had immensely out-
grown the means of public worship, so he set himself to work on

28 Proceedings of the Royal Society

behalf of Church Extension. He remained Vicar and Archdeacon
for the last thirty years of his life. When he came into the dis-
trict there were three parishes ; before the close of his career, he
had been the means of forming in it twenty-three parishes.

Whenever Mr Sinclair found it necessary to carry any important
measure in later years, he seems to have acted on a hint given to
him by the late Dr Chalmers, on the last occasion, as he says, that
he saw this great and good man. This was in the year 1843. He
had been telling the Doctor of wrhat he was doing for the support
and extension of the Church of England National Schools, and
in particular, how' he had received promises of support from
hundreds of influential people, including members of the Cabinet
and of both Houses of Parliament. Dr Chalmers, he says, “heard
me patiently for some time, and then replied, ‘ Mr Sinclair, I per-
ceive you are an enthusiast; your National Society must, under
G-od, depend upon the nation for support, and not on Cabinets or
Parliaments.’ ”

After this conversation, very little is said by Mr Sinclair in his
autobiography about applications by him to influential individuals;
whilst a good deal is said about the public meetings which he
resorted to when he wanted to raise money, or to influence public
opinion. He never spoke from the platform himself; for after leav-
ing the University, he lost the fluency of speech, which he says, he
had acquired there ; but he had great tact in arranging meetings
and providing speakers who were likely to be listened to.

Several amusing stories of this kind are told in his little book.
One may be mentioned. Mr Thackeray had recently come to
reside in Kensington, and Mr Sinclair thought his name would be
a powerful attraction. Mr Sinclair called upon him. Thackeray
was unwell, and in his bedroom. Mr Sinclair having sent up his
card, Thackeray came down stairs, when Mr Sinclair explained his
object. Thackeray at once declined, saying he had never in his
life made a speech in public, and that he only wrote for the public;
and besides he was too ill to leave the house. Mr Sinclair said
that he would not insist on a speech, but that it wras very difficult
to get up a meeting in Kensington, and that if Mr Thackeray would
only allow his najne to be printed in the handbills, he would not
insist on his saying much, and would have the speaking done by

29

of Edinburgh, Session 1875-76.

others. Mr Thackeray was amused, and said, (c Well, if I am alive,

I will come to your meeting.” The handbills were accordingly
issued with Thackeray’s name in them. A great crowd assembled.
Mr Thackeray appeared on the platform. He found when there
he could not avoid saying something. His words were few but
telling, and they were received with enthusiasm. Mr Sinclair
adds, that this was the only time that the rhetorical powers of the
great novelist were proved at a public meeting.

It was not merely in London that Mr Sinclair was of use.
During general periods of great distress in the manufacturing and
mining districts of Wales and Lancashire, the bishops of these
dioceses obtained his services to enable them to raise funds and
devise measures of relief ; his services in these respects being
thought of, on account of his well-known business habits, and also
his sympathy with the working classes.

In the year 1853 he was sent out to the United States as one of
a deputation from the Church of England to the General Conven-
tion of the Protestant Episcopal Church in New York. When
there, he made acquaintance with Mr Washington, the nephew of
the great man who had founded the American Republic, and with
whom his father, Sir John Sinclair, had corresponded.

I have had sent to me a long list of pamphlets, books, and
sermons, published by the Archdeacon. The largest work is one
in two volumes, published in 1837, on the Life and Times of his
father.

From what I have said, it will be perceived that Mr Sinclair, by
the energy with which he threw himself into every work he under-
took, justified Dr Chalmers’ opinion, that he was an enthusiast.
But his enthusiasm was — which is rarely the case — tempered with
great good sense and sound judgment. His untiring industry, his
practical usefulness, and his benevolence of character, showed that
he was no unworthy son of a most excellent and patriotic Scotchman.

Having concluded all that it has occurred to me to state
regarding ourselves — I mean regarding the work we are doing, and
our means of doing it — I proceed to submit to you a few remarks
regarding the present state of science generally in our own country.

It appears to me that a great educational movement, amounting

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Proceedings of the Royal Society

almost to a revolution, is at present taking place in our land, and
especially in that branch of public education which relates to
science. I will not say that old institutions are being subverted;
but undoubtedly new institutions are rising up very different from
the old, and the old are undergoing considerable changes. I believe
that the seed from which all these changes have sprung, and are
springing, was planted by one man — the late Prince Consort. I
know of no other person of weight and influence who so constantly
took every opportunity of urging on the people of this country
the introduction into our universities and schools of scientific
instruction.

This opinion is shared by others more entitled than me to
speak on this subject ; to whom I will now shortly refer.

Three weeks ago, at Oxford, His Royal Highness Prince Leopold
agreed to perform the duty of distributing prizes to students of the
School of Science and Art established in that town. The prince
was introduced on that occasion by the Duke of Marlborough, lord-
lieutenant of the county, and who, some years ago, was President
of the Government Department on Education. His G-race, on in-
troducing the prince, said that “it was not surprising that His
Royal Highness should take a warm interest in every thing that
belonged to Science and Art, when they remembered that he trod
in the steps of the illustrious prince to whom the development
of Science and Art in this country was mainly if not wholly
attributable.”

Prince Leopold responded to this sentiment. “ I do not forget,”
said His Royal Highness, “ that there is devolved upon me, as well
as upon other members of my family, a sacred trust, to foster, in
such manner as we are able, the general study throughout the
kingdom of Science and Art. From the passage I am about to read,”
be continued to say, “ you will perceive that only a few years ago,
and even in our university, Science and Art studies received little,
if any, support. I will quote from an address by my revered father
on the occasion of his laying the first stone of the Birmingham and
Midland Institute, almost exactly twenty-four years ago.” The
passage quoted by Prince Leopold, was a remarkable one. Its first
sentence was as follows : — “ The study of the laws by which the
Almighty governs the universe is our bounden duty.” Prince

31

of Edinburgh, Session 1875-76.

Albert, in the passage so read by his son on this occasion, went on
to show that, besides being our duty as human beings, it was for
our interest as citizens to attend on these studies. “I advise you,”
said the prince, “ to follow, in undivided attention, the sciences of
mechanics, physics, and chemistry, and the fine arts of painting,
sculpture, and architecture. You will thus confer upon your
country an inestimable boon, and in a short time have the satis-
faction of witnessing the beneficial results upon our national powers
of production. Other parts of the country will emulate your ex-
ample, and I live in hope that all these institutions will some day
find a central point of union, and thus complete the national
organisation.”

Weighty as these words of Prince Albert were, and coming from
an authority so much respected, I am not sure that they would
have been universally listened to, had it not been for the great
international exhibition of works of industry held in London in the
year 1851 — itself a measure due to the sagacity of that excellent
prince. There the people of this country first saw, with their own
eyes, what were the fruits of the superior schools for scientific in-
struction existing in Germany, Austria, Switzerland, and France.

Shortly afterwards, royal commissions were issued to ascertain to
what extent any of the sciences specified by the Prince Consort
were taught in our schools.

The result of these inquiries was sufficiently remarkable.

In the year 1864 the Public Schools’ Commission, after special
inquiry, reported that from all the first class schools in England,
the teaching of science was practically excluded.

This official exposure had some effect ; for in the year 1868
another Government commission, the Endowed Schools’ Commis-
sion, reported, that a majority of the endowed schools in England
had intimated their willingness and their intention to introduce
science teaching.

To how very small an extent this promise was fulfilled, may be
judged of by the revelations of the Oxford and Cambridge school
examinations made throughout England during the last three or
four years. Even in this very year of 1875 what has been ascer-
tained? Out of 461 candidates for certificates of good scholarship
from 40 first-class English schools, there were only 28 scholars in

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Proceedings of the Royal Society

chemistry, 21 scholars in mechanics, 15 in physical geography, and
6 in botany; whilst for Greek there were 433 scholars, for Latin
438, and for elementary mathematics 458.

The small amount of scientific instruction given in the English
endowed schools was ascertained, still more precisely, by the Royal
Commission, which has only recently framed its report. I mean
the commission over which the Duke of Devonshire presided.
From that report it appears that a circular was sent out by this
commission two years ago to about 250 endowed schools, requesting
them to fill up a sohedule showing what amount of scientific
instruction, if any, was given in them.

Only 128 answers were received'. That fact alone was significant.
But when these answers came to be examined, it was found that out
of the 128 answers, only 87 gave any definite information. Of these
87, 65 confessed to giving no science teaching whatever ; of the
remaining 22, the utmost time allotted to any kind of scientific
instruction, was four hours per week, in eighteen of the schools.

But though it was right to ascertain the truth in this matter
through the authentic inquiries of royal commissions, the people of
this country, knowing well enough, from their own experience and
observation how the matter stood, would not wait for these official
inquiries. They took the matter into their own hands, and set to
work at once to supply what was required. I do not know any
stronger proofs of public patriotism in our country, than what this
educational movement affords. In all the great centres of industry,
arrangements were made for having institutions established in
which not only science in its various branches should be taught,
but the arts and literature also.

At Manchester, John Owens bequeathed about L. 100, 000 for the
endowment of a new college. No part of that money, however,
being allowed to be expended on buildings, his fellow-citizens
supplied what was needed. A sum of L. 250,000 was raised; and in
the year 1870 the foundation stone of a magnificent edifice was laid
for a Science and Art College, the Duke of Devonshire presiding.

In the year 1871, a physical science college was established in
Newcastle, for which L. 35, 000 was raised; and as it was to be
affiliated with Durham University, that university agreed to give
L.1000 a year out of its revenue for the institution.

33

of Edinburgh, Session 1875-76.

In the year 1873, Josiah Mason, who had made a large fortune
as a manufacturer at Birmingham and Kidderminster, gave the
princely sum of L.250,000 (or the erection and endowment of a
College of Practical Science in Birmingham.

In January 1874, an association was formed for the promotion of
scientific industry in Lancaster, at which the Earl of Derby pre-
sided— an association formed chiefly at the instance of Lancaster
manufacturers and artizans, who, having visited the Vienna Inter-
national Exhibition held in the autumn of 1873, had seen there
the rapid and alarming progress of Continental nations in many of
the arts.

In the same year, the Yorkshire College of Science was begun in
Leeds, of which college Lord Frederick Cavendish is president,
there being L. 100,000 subscribed for it.

In the course of last summer, steps were taken to establish in
Bristol a College of Science, to be affiliated to Oxford University,
for which L. 26,000 has been already subscribed. Nottingham,
Sheffield, and other towns, not so wealthy as to found colleges, are,
however, stirring for the establishment of schools and societies for
the teaching of classes.

In Scotland, Dundee is stirring, wishing to have a college which
is to be affiliated with St Andrews University, and for which it is
proposed to raise as much as L. 200,000.

Nor are our old, time-honoured national universities, in the
midst of this great educational movement, asleep. Asleep or in-
different they could scarcely remain, for very obvious reasons.
Both at Cambridge and at Oxford, science lectures and fellowships
have been at length introduced ; and the Chancellor of Cambridge,
the noble Duke of Devonshire, has, from his own funds, presented
that university with a splendid chemical and physical laboratory,
having a most complete apparatus, at a cost of L. 10, 000.

Our own University of Edinburgh has during the last five years
had three new chairs created and endowed for engineering, geology,
and political economy; and farther measures of extension, on a
large scale, are being adopted, for which above L. 85, 000 have been
already subscribed.

Even the farmers , who are not generally proverbial for moving
out of old paths, or even for moving in them, except at a slow pace,

VOL. IX.

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34

Proceedings of the Royal Society

are showing signs of progress. The Royal English Agricultural
Society last year set apart L.500 to be given yearly in scholarships
to encourage instruction in the sciences bearing on agriculture.

The Highland and Agricultural Society has this year set apart
L.250 for a similar purpose.

But I must here offer a word of apology for the managers of the
English endowed schools, which, in their programmes of studies,
made no provision whatever for science. I remember when my son
was at one of these schools, that I went to the head master and
ventured to hint the disappointment I felt at the want of such pro-
vision. His answer was— “ We are obliged to suit our teaching to
university requirements. Only certain subjects are taught at
Oxford and Cambridge ; and we endeavour to prepare our scholars
in the subjects taught in these universities.”

I thought the excuse satisfactory ; but now that the old univer-
sities have introduced science teaching, and now that new colleges
are being established all over the land with the same view, and
bursaries are given by societies, corporations, and associations, in
almost every large town, these secondary endowed schools will have
no longer an excuse for not giving science instruction ; they will
be even under a necessity to give it for their own sakes.

Here again, however, I have to observe that the country refused
to wait this slow progress of school amelioration. The G-overnment,
with the entire approval of Parliament, by means of a special
department at Kensington, encouraged the establishment through-
out England and Scotland of schools and classes for the teaching of
science and art. This encouragement was and is now given by
prizes to scholars, remuneration to teachers, and loans of apparatus
to the schools. The result has been marvellous. The scheme has
been in operation for only nine years. At first it was little known
and not well understood; but now these schools are extending
rapidly; for whilst in the year 1869, that is three years after the
scheme was started, there were in G-reat Britain only 523 schools
with 24,865 scholars, there were in 1874 (since which date I have
seen no reports), 1336 schools and 53,050 scholars.

It is also proper to mention that the national elementary schools
which are recognised by the Education Act for England and for
Scotland, are encouraged to include various sciences in their pro-

of Edinburgh , Session 1875-76.

35

gramme of lessons; there being capitation grants of money to the
managers of these schools for scholars who, at the annual inspec-
tions, pass satisfactory examinations in various branches of
science.

I have thus at some length explained what has been done during
the last ten, and more particularly during the last five years, for
increasing the means of scientific instruction in our universities,
colleges, and even in elementary schools, because of the import-
ant bearing of these measures in promoting such objects as this
Society aims at. When vast multitudes of our population become
conversant with science, who knew nothing of science before, who
can doubt that investigation will be stimulated, and that discoveries
and inventions will be made with a speed hitherto unprecedented ?

But there is another measure of even greater importance to
science, which is about to be taken in this country. Our schools,
colleges, and universities are institutions for teaching truths, and
explaining facts already known. It is now proposed to establish
colleges of research, as they have heen called, for aiding in the
discovery of truths, facts, and principles not yet known.

In the year 1868, the British Association for the advancement
of science appointed a committee of some of its most eminent
members to report on the two following questions

“Does there exist in the United Kingdom of Great Britain and
Ireland, sufficient provision for the vigorous prosecution of physical
research ?”

“ If not, what farther provision is needed, and what measures
should be taken to secure it”

In the following year that committee gave in a report, answer-
ing these questions thus : —

“ The provision now existing in the United Kingdom is far from
sufficient for the vigorous prosecution of physical research.

“ Whilst greatly increased facilities for extending physical
research are required, your committee do not consider it expedient
to define how these facilities should be provided.” The committee
added, that “ as the whole question of the relation of the State to
Science is at present in a very unsatisfactory position, they urge
that a Royal Commission alone is competent to deal with the
subject.”

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Proceedings of the Royal Society

That report having been approved of by the Association, an
influential deputation waited on Her Majesty’s G-overnment, to
suggest the appointment of a Commission ; and accordingly in May
1870 such a Commission was appointed.

This Commission has been most diligent in its investigation and
discussion of the several points remitted to it. They have exa-
mined several hundred witnesses, and have issued no less than
eight reports.

Besides ascertaining the condition of our universities, colleges,
and endowed first-class schools, as regards their teaching power, and
suggesting in many cases that assistance should be given to them
by the State, the Commissioners took up the other important
question, to which the British Association specially had called
attention — viz. this, whether the State ought not to aid researches
for discovering new scientific facts and truths.

As the report of the Commissioners on this question is of great
interest alike to men of science and to scientific bodies in this
country, 1 quote a few sentences to show the opinion of these
Koyal Commissioners, and the advice they give to Her Majesty’s
Government : —

(‘ The great advances in physical science which have been made
in this country, and within this century, by such men as Dalton,
Davy, and Faraday, without aid from the State; the existence of
numerous learned societies ; and the devotion of some few rich
individuals to the current work of science, at first sight appear to
reduce the limits within which State aid to research is required in
this country.

“ But whilst we have reason to be proud of the contributions
of some great Englishmen to our knowledge of the laws of
nature, it must be admitted that at the present day scientific
investigation is carried on abroad to an extent, and with a com-
pleteness of organisation to which this country can offer no parallel.
The work done in this country by private individuals, although of
great value, is small when compared with that which is needed in
the interests of science ; and the efforts of the learned societies,
not excepting the Boyal Society, are directed merely to the dis-
cussion and publication of the scientific facts brought under their

37

of Edinburgh, Sessio7i 1875-76.

notice. These societies do not consider it any part of their corporate
functions to undertake or conduct research. .....

“But whatever may be the disposition of individuals to conduct
researches at their own cost, the advancement of modern science
requires investigations and observations extending over areas so
large, and periods so long, that the means and lives of nations are
alone commensurate with them.

“ Hence the progress of scientific research must in a great
measure depend upon the aid of Governments. As a nation, we
ought to take our share of the current scientific work of the world.
Much of this work has always been voluntarily undertaken by
individuals, and it is not desirable that Government should super-
sede such efforts ; but it is bound to assume that large portion of
the national duty, which individuals do not attempt to perform, or
cannot satisfactorily accomplish.”

The sentences which I have now read are the preamble and the
basis of the conclusions to which the Commissioners unanimously
came. These conclusions are as follows : —

1. “ The assistance given by the State in this country for the
promotion of scientific research is inadequate; and it does not
appear that the concession or refusal of assistance takes place upon
sufficiently well-defined principles.”

2. “ More complete means are urgently required for scientific
investigations, in connection with certain Government departments.
Physical as well as other laboratories and apparatus for such in-
vestigations ought to be provided.”

3. “ Important classes of phenomena relating to physical meteor-
ology, and to terrestrial and astronomical physics, require observa-
tions of such a character, that they cannot be advantageously carried
on otherwise than under the direction of the Government .”

4. “ Whilst national collections of natural history are accessible
to 'private investigators , it is desirable that they should be made
still more useful for purposes of research than they are at present.
We would now express the opinion that corresponding aid ought
to be afforded to persons engaged in important physical and chemi-
cal investigations ; and that, whenever practicable, such persons
should be allowed access , under proper limitations, to such labora-
tories as may be established or aided by the State.'1

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Proceedings of the Royal Society

5. “ It has been tlie practice to restrict grants of money made to
private investigators for purposes of research, to the expenditure
actually incurred by them. We think that such grants might be
considerably increased. We are also of opinion, that the restriction
to which we have referred, however desirable as a general rule,
should not be maintained in all cases, but that, under certain cir-
cumstances and with proper safeguards, investigators should be
remunerated for their time and labour. ”

6. “ The grant of L.1000 administered by the Eoyal Society, has
contributed greatly to the promotion of research, and the amount
of this grant may with advantage be considerably increased.’’

“In the case of researches which involve, and are of sufficient
importance to deserve, exceptional expenditure, direct grants, in
addition to the annual grant made to the Royal Society, should be
made in aid of the investigations.”

7. “ The proper allocation of funds for research ; the establish-
ment and extension of laboratories and observatories ; and generally,
the advancement of science, and the promotion of scientific instruc-
tion as an essential part of public education, would be most effec-
tually dealt with, by a Ministry of Science and Education , and we
consider the creation of such a ministry of primary importance .”

8. “ The various departments of the Government have from time
to time referred scientific questions to the Council of the Royal
Society for its advice. We believe that the work of a Minister of
Science, even if aided by a well-organised scientific staff, and also
the work of the other departments, would be materially assisted, if
they were able to obtain, in all cases of exceptional importance or
difficulty, the advice of a Council representing the scientific knowr-
ledge of the nation.”

9. “ This Council should represent the chief scientific bodies in
the United Kingdom. With this view, its composition need not
differ very greatly from that of the present Government Grant
Committee of the Royal Society. It might consist of men of
science selected by the Council of the Royal Society, together with
representatives of other important scientific societies, and a certain
number of persons nominated by the Govenment.”

Such, gentlemen, are the conclusions and recommendations of
these Royal Commissioners on a subject deeply interesting not only

of Edinburgh , Session 1875-76.

39

to all scientific bodies, and men of science in this country, but to
the nation at large. The Commissioners are men eminently
qualified by social position, by enlightened knowledge, and by a
thorough investigation of the subject, to pronounce an opinion,
and I feel very confident that when their report comes before
Parliament, their conclusions will be accepted, the organisation
recommended by them agreed to, and the necessary supplies
ungrudgingly voted.

I have, before concluding, only one other point to mention. No
great measure, whether political or educational, can be adopted in
this country by the G-overnment, or even by Parliament, which has
not obtained previously the general assent of the community.
Now it is a gratifying circumstance, that during the last few
months, many distinguished men, good judges of public opinion,
and who also themselves influence public opinion, have recently
taken occasion to advert to the question of scientific instruction.
I have already mentioned the names of His Royal Highness Prince
Leopold and his Grace the Duke of Marlborough. It so happens
that the same page of the “ Times” newspaper, of the 12th Nov.,
which reports what they said, gives speeches in the same direction
by Sir Alexander Cockburn, Lord Chief- Justice of England, and
by Mr Gladstone, the ex-Premier. Going back a few weeks, I
find speeches by the Duke of Devonshire, the Marquis of Harting-
ton, the Earl of Derby, the Marquis of Ripon, Lord Winmanleigh,
Lord Frederick Cavendish, Sir Stafford Northcote, the Right Hon.
Lyon Playfair, and Mr Bell, M.P. for Hartlepool, one of our most
extensive and intelligent iron-masters.

These names I mention to show that the great landowners of
the country, and also many distinguished statesmen, are responding
heartily to the appeal made to them by our manufacturers and
merchants, who feel that their own interests, and the continued
prosperity of the country in trade and commerce, require institu-
tions which will give to their sons, and also to the working classes,
a more technical education than they have hitherto received. With
such combined action, who can doubt that an immense impetus
will be given both to scientific teaching and to scientific research ?
Wonderful indeed have been the discoveries during the last half
century, even with the scanty appliances whicli men of science

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Proceedings of the Royal Society

have hitherto had at their command. These discoveries, the
Lord Chief-Justice Cockburn said, “ perfectly overwhelmed him
with astonishment,” and as the Royal Commissioners said, may
justly invoke national pride, that so many of them should be due
to the unaided efforts of individuals. What, then, may we look
forward to in the next half century, with the additional appliances
which these Commissioners recommend ?

But, perhaps, here a word of caution, even from so humble an
adviser as myself, may be allowed. Lord Chief- Justice Cockburn,
on the occasion to which I have referred, says — “ No one bows with
a more profound and reverent worship at the shrine of science
than I do. No one values more than I do classical attainments.
Nevertheless, allow me to say, that I know of no study more valu-
able to an Englishman than the study of English. Nothing is more
valuable than the power of English composition, English oratory,
and English elocution; and greatly as I* value classical knowledge,
and the knowledge of foreign languages, I still say, that the
English language and English composition are of the first impor-
tance to Englishmen.” These remarks he followed up by
announcing his wish to give a prize of twenty guineas annually
for a piece of English composition.

Much to the same purpose, our distinguished colleague Mr Lyon
Playfair, when assisting the other day to inaugurate the Science
College at Leeds, expressed a hope that the institution would
not be confined to science, but would embrace letters and the
arts.

These views suggest one danger to be avoided by those who are
anxious to establish colleges and schools for scientific teaching.
The country, willing as it undoubtedly is to supply deficiencies
in this respect, will certainly not agree that a knowledge of science
shall be all that a well-educated Englishman or Scotchman ought
to possess.

But there is another danger, and one more serious. Mr Glad-
stone, when distributing the prizes of the science and art classes at
Greenwich, three weeks ago, made these impressive remarks: —
“ Whatever I may think of the pursuits of industry and science,
and of the triumphs and glories of art, I do not mention any one
of these things as the great specific for alleviating the sorrows of

of Edinburgh, Session 1875-76.

41

human life, and meeting the evils which deface the world. I
believe firmly in science and art, for their own purposes. I be-
lieve in their reality, their efficacy, and their value ; I believe
they are efficacious and valuable for the purposes for which
they are ordained, but not for purposes for which they were not
ordained. If I am asked what is the remedy for the deeper
sorrows of the human heart — what a man should chiefly look to
in his progress through life, with which to sustain him under trials
nd affliction — I must point to something very different, to some-
thing which in a well-known hymn is called ‘the old, old
story/ It is this ‘ old, old story, told in a good old book, with
the teaching to be found there, which is the greatest and best gift
ever given to mankind, a gift carrying with it and imposing upon
all alike, the most solemn trusts and responsibility, because arousing
the fullest recollections of the past and the brightest hopes of the
future. I venture upon this observation for myself, lest, in speak-
ing of the immense value which is to be attached to the subjects
with which we are dealing to-night, it should be supposed I was
setting them up as having some exclusive right to allegiance upon
your minds and hearts, or, at any rate, a right paramount to every
other.”

I much fear that this warning of the ex-Premier is needed. I
fear it may be said, not merely of men of science, but of others
also, that they often allow their hearts and minds to be so occupied
— so engrossed with pursuits and studies, as to leave no room for
other things which should find a place there also.

Men of science have sometimes been charged, not merely with
allowing their minds to be too much engrossed in this way, but
with conceit and arrogance, engendered by the consciousness of
possessing wisdom above the great bulk of their countrymen. The
true man of science, is fairly amenable to no such charge. So
far from possessing that “pride, and arrogance, and fro ward mouth,”
which is condemned in the good old book referred to by Mr Glad-
stone, be is , and at all events should he , the reverse of all this ; for
whatever amount of knowledge he acquires, whatever the dis-
coveries he achieves, no one sees so clearly the immensity of what
still remains to be discovered. Even in our own planet, how little
do we yet know of the composition of the earth’s interior, how

VOL. IX.

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Proceedings of the Royal Society

little of its deep oceans, how little of ne great atmosphere which
surrounds us! And even if we knew and understood all and every
part of our own habitation, what is that, when we think what a
tiny atom that habitation is in the great system of the universe,
seen and unseen!

The true man of science, knowing all this, is humble-minded,
not arrogant or supercilious; diffident, not presumptuous; forbear-
ing, not intolerant.

If these are the qualities which men of science possess and
show, whilst prosecuting their studies and researches, they will
secure favour for themselves and for their noble pursuits. They
will be accepted and respected as the expounders of the grand and
beautiful laws by which God governs the universe — laws , a know-
ledge and a right application of which will assuredly conduce,
alike to the prosperity of nations and to the happiness of the
human race.

The following statement in regard to the number of the present
Fellows of the Society was laid on the table by the Secretary : —

1. Honorary Fellows —

Royal Personage —

His Royal Highness the Prince of Wales, . . 1

British Subjects —

John Couch Adams, Esq., Cambridge; Sir George
Biddell Airy, Greenwich; Thomas Andrews, M.D.,

Belfast (Queen’s College); Thomas Carlyle, Esq.,

London; Arthur Cayley, Esq., Cambridge; Charles
Darwin, Esq., Down, Broomley, Kent; John An-
thony Froude, Esq., London; James Prescott Joule,

LL.D., Cliffpoint, Higher Broughton, Manchester;

William Lassell, Esq., Liverpool; Rev. Dr Hum-
phrey Lloyd, Dublin; William Hallowes Miller,

LL.D., Cambridge; Richard Owen, Esq., London;

Lieut. -General Edward Sabine, R.A., London;

George Gabriel Stokes, Esq., Cambridge; James
Joseph Sylvester, LL.D., London; William Henry
Fox Talbot, Esq., Lacock Abbey, Wiltshire; Alfred
Tennyson, Esq., Freshwater, Isle of Wight, . . 17

Carry forward,

18

of Edinburgh , Session 1875-76.

Brought forward,

Foreign —

Claude Bernard, Paris; Adolphe Theodore Brong-
niart, Paris: Robert Wilhelm Bunsen, Heidelberg;
Michael Eugene Chevreul, Paris; James D. Dana,
LL.D., Newhaven, Connecticut; Heinrich Wilhelm
Dove; Jean Baptiste Dumas, Paris; Charles Dupin,
Paris; Christian Gottfried Ehrenberg, Berlin; Elias
Fries, Upsala; Herman Helmholtz, Berlin ; August
Kekule, Bonn; Gustav Robert Kirchhoff, Heidel-
berg ; Herman Kolbe, Leipzig ; Albert Kolliker,
Wurzburg ; Ernst Edward Kummer, Berlin ;
Johann von Lamont, Munich; Richard Lepsius,
Berlin ; Rudolph Leuckart, Leipzig ; Urbain
Jean Joseph Leverrier, Paris; Joseph Lionville,
Paris ; Henry Milne-Edwards, Paris ; Theodore
Mommsen, Berlin ; John Lothrop Motley, United
States; Louis Pasteur, Paris; Professor Benjamin
Peirce, United States Survey; Adolphe Pictet,
Geneva; Henry Victor Regnault, Paris; Angelo
Secchi, Rome ; Karl Theodor von Siebold,
Munich; Bernard Studer, Berne; Otto Torell, Lund;
Rudolph Virchow, Berlin; Wilhelm Eduard Weber,
Gottingen; Friedrich Wohler, Gottingen,

Total Honorary Fellows at March 1875,

18

35

The following Foreign Honorary Fellows were elected in
March 1875 —

Dove, Kekule, Kolbe, Kummer, Lionville, Motley.

The following are the Honorary Fellows deceased during
the year —

Foreign — M. Comte de Remusat, ... 1

British — Sir Charles Lyell, Bart., Sir W. E. Logan,

Sir Charles Wheatstone, 3

2. Non-resident Fellow under the Old Laws —

Sir Richard Griffiths, ....

Total Honorary and Non-resident Fellows, 6th Dec. 1875,

44

Proceedings of the Royal Society
3. Ordinary Fellows —

Ordinary Fellows at November 1874, . . . . 345

New Fellows , 1874-75. — John Aitken, Esq. ; The Hon.

James Bain ; Dr Ludwick Bernstein ; James Bryce,

LL.D.; John Christie, Esq.; Robert Clark, Esq.; Dr T.

S. Clonston ; Dr William Craig ; Daniel G. E. Eliot,

Esq.; Thomas Fairley, Esq.; Robert Gray, Esq.; Sir
John Hawkshaw; William Jack, Esq.; Archibald Kirk-
wood, LL.D.; John Ramsay L’Amy, Esq.; C. H. Millar,

Esq.; John Milroy, Esq.; E. W. Prevost, Esq.; Ralph
Richardson, Esq.; Michael Scott, Esq.; James Syme,

Esq.; James Thomson, LL.D.; Charles Wilson Vincent,

Esq. ; Professor Daniel Wilson, .... 24

B. Baden Powell, formerly elected, but not admitted
till 1874; Dr Alexander Wood (re-admitted), . 2

Total New Fellows, . . 26

371

Deduct Deceased. — Rev. Dr Aitken; John Auld, Esq.; Dr
J. Hughes Bennet ; Rev. Dr Crawford ; Col. Seton
Guthrie; Sir William Jardine,Bart. ; Professor Macdonald;

Hon. Lord Mackenzie; E. Meldrum, Esq.; Ven. Arch-
deacon Sinclair, 10

Resigned. — Rev. Thomas M. Lindsay ; John L.

Douglas Stewart, Esq., . . ... 2

Cancelled. — Charles Lawson, Esq., .... 1

33

Total number of Ordinary Fellows at November 1874, . 358

Add Honorary and Non-Resident Fellows, ... 50

Total Ordinary and Honorary Fellows at commencement
of Session 1875 (6th December), 408

The following Communication was read : —

The Volcanic Eruptions of Iceland in 1874 and 1875. By
Captain Burton. (With two Maps of Iceland).

Shortly after reading “Volcanic Eruptions in Iceland” (the
“ Scotsman,” May 21), and “ An Appeal for Iceland ” (the “Times”
July 1), I made a trip to Arctis, partly with a view of inspecting
and inquiring into the last outbreaks. Perhaps your energetic
Society may not be unwilling to have an unprejudiced account of
what was seen and heard.

N° 1,2,3, Eru

M'Swlane Si Eis'idine . LiiH? Efe?

Eruption 29 tK March 1875.

N° 1,2,3, Eruptions with intermissions during the years 1867,1869, 1870-72. N° 4, Eruption about Christmas 1874. U? 5. Eruption 29 March 1875.

The brown shading mark the Ashes thrown S.E. to East.

"William P Nimmo, London 4 Edint>ur£h

William E "Nrmmo, London Sc. Edinburgh

Dttsilbss -

Skplualr

indirect mllet
From Tyre)'/

M'y-

r thro a

dJudl

tonp low snowy dew

i Ik. '“^ViS

leant? said to ha.fi been seen- Prom
nd. supposed, cause oP Veru/jord, Pop
Re,v* Siouriur Gurinarson places it
"Lone. (G.) 30 ° 20. |

Vaj,U4ui4t ^

William P "Nimmo, London <t Edinburgh

IF.Tslani, E3inr

45

of Edinburgh, Session 1875-76.

The accompanying maps, prepared for my forthcoming volume,
(“ Ultima Thule ”), mark the four paroxysmal eruptions which
took place upon the same area during 1867, 1869, 1870 (to 1872,
at which last date all activity had subsided), and about Christmas
1874. Number five, the latest phenomenon, broke out on March
29, 1875.

These movements may or may not be connected with the five
days’ eruption of Skaptar Jokull (January 9, 1873), recorded by
all the journals of Europe ; but they certainly occupy the heart
and the southern outskirts of the Od&fta Hraun, the great lava field
subtending the north of the Yatna Jokull, and extending to the
N.N.E., almost as far as the Lake Region — My-vatn and its
oasis. The name is variously translated “Terrible wilderness”
(Henderson), and “ Desert of the Evil Deed ” (Baring Gould),
whilst the area is differently calculated at 1160 to 1500 square
miles; in fact, one half of the Yatna Jokull. Viewed from the
nearest heights — Bl&fjall, for instance — it is a grim and ghastly
picture, a region of ruin and desolation, a fitting mise en scene for
the Last Man : my companions remarked that such a spectacle
would soon give them the horrors. I see no difficulty beyond a
certain expense in crossing and exploring this waste: at the same
time, I doubt that the feat would yield any results ; and explora-
tion purely for * exploring appears to me like “climbing for
climb.”

This “ great and terrible wilderness,” so small and mean in com-
parison with the Sahras of Africa, Asia, and South America, and
yet so grisly in its brown-black desolation, is supposed by Baring
Gould to be the gift of the Trolladyngjur and of HerSubreifc, while
Mr W. L. Watts would derive it solely from SkjaldbreiS. I find it
to be the produce of a multitude of craters which opened in and
south of it, before the days when Qraefi and other lofty peaks,
attracting rain and snow, built up the mighty neve , which mono-
polises the south-eastern corner of Iceland. The peculiarity of the
latest outbreaks (1867-1875) is the distance, not to say isolation,
of the vents from any large body of water, suggesting the un-
pleasant fact that we must modify received opinion. For instance,
the eruption of Christmas 1874 upon the south-eastern flank of the
distorted horseshoe Askja (oval-shaped wooden casket) or Dyng-

46 Proceedings of the Royal Society

jufjoll (Cubilia or “Chamber Hills”), are at least thirty-eight
direct geographical miles from My-vatn (midge -water), and forty-
live from the nearest seashore. Nos. 1, 2, and 3 vents are more
distant from the lake, and but little nearer the coast. The
non-maritime Andine volcanoes are popularly supposed to be con-
nected by fissures and strata-faults with the Pacific. Here, how-
ever, the foci are separated from the Atlantic eastward by the
valley of the broad and deep Jokulsd 1 Axarflrfii, the longest, if
not the largest, river in Iceland. To the west they are guarded by
the Skjalfandi Fljdt, and south by the huge Yatnajokull, whilst
palagonite is not a rock which maintains permanent fissures like
porphyry. I can only suggest that the eternal snows of the
mighty neve take the place of lake and sea water.

Our approach to Iceland was heralded by volcanic phenomena.
On Friday, July 8, as my shipmates were recovering from the
sufferings which began in Pentland Firth, we found the milky
blue sea patched and streaked with what many supposed to be rye
— the cargo of some wrecked vessel — but which proved to be
pumice, the largest piece hardly equalling a bean. On the return
voyage (August 9) we passed through a similar discharge, and we
heard of dense and choking ash-showers. Landing (July 10) at
Husavlk, the old export harbour of the great Northern Brimstone
Mines, we found burned stone thrown up in tons on the beach
north-east and south-west of the factory. A few of the bits were
equal to a man’s fist : some were slightly vitreous, and others had
a fibrous texture like asbestos ; they much resembled those brought
from the Askja by Mr W. L. Watts. Lastly, when we approached
the focus of eruption we picked up common specimens of an inter-
mediate size, where certainly none existed in 1872. Our maximum
distance then was 70 or 80 miles, and the line of our direction was
from south-west and west to north-east and east. As will presently
appear, a single morning (March 19) is supposed to have discharged
3840 tons in four hours. All authorities are agreed that the ashes
fell in Norway within twenty-four hours — a rapid but not an
unusual rate of progress. In the Hekla eruption of 1693 the
scoriae were also carried by the winds in one day to the Foeroe
Islands ; the same was the case with the Skaptar outbreak of
1783; and in 1845 the goodwives of Shetland, when bleaching

47

of Edinburgh, Session 1875-76.

their linen, were surprised to find it covered with pepper from
Hekla. But instances of this nature need not be multiplied.

On July 17, while collecting specimens of brimstone from the
great My-vatn mines, a select company of the expedition rode over
the N&maskarb (“ Fountain-scaur ”), the gap in the Montes
Phlegrcei, east of My-vatn, and thence we took the highroad, or
rather the bridle-path, leading eastwards over the My-vatnsoroefi
(Desert of the Midge- water) to the greatest of the three Jokuls&rs.
After some three hours of sharp canter, which covered more than
half-way, we sighted to the south of the road and north-east of
Burfell, a low black-blue mound with white patches. It was about
a mile long ; and a solitary puff, escaping every quarter of an hour,
told us that it was burning low. Nothing could be meaner than
this outbreak, which I will call the My-vatn eruption : it looked
by the side of older formations as if Vulcan had struck work, and
the underground furnace of Iceland were being “ drawn.” Shortly
after our departure, however, Mr W. L. Watts here observed a
huge Grjd, and an active eruption, which he briefly noticed in the
“ Times ” newspaper, and which I hope he will presently describe
at greater length, accompanying his description with a ground-plan
and elevation.

This No. 5 is connected by a band of old lava with No. 6, a
mound to the north of the road. It was first seen (Feb. 18) from
the Grimstbair farm, erupting to the west of the Sveinagjd, in what
is called the Austurfjoll or My-vatnsfjoll. The great smoky fire
(jarbeld) springing from 14 or 16 mound craters (gosborg) lying
on a meridian, formed, say the natives, a molten river 300 to
400 fathoms broad and one vegarleid ( = 3 English miles) long,
throwing up lava, pumice (vikur) and stones, often the size of a
man, which fell down upon the crater lips. Some of the hot
material melted the snow. The lava soon set, but the ground was
too hot for walking, and the stone flood glowed white beneath 2 to 4
feet of the upper black stratum which had cooled in a few minutes.
The plain around was split with hideous Gjar (fissures); the fre-
quent hornitos, blisters, and hillocks on the run probably the
effects of steam, were hollow, with a capacity of 2 to 4 hogsheads,
and the smoke (vapour?) hung upoh the horizon like a cloud. On
March 10 the eruption lasted all night, and the most violent effort

48

Proceedings of the Royal Society

was on April 13. By that time the area of the foci (eldgigar) was
about 40 square fathoms; and where the ground before was level,
rose a lava hill 30 to 60 feet high. The greatest flow was to the
north, and southwards a fire stream (eldgos), one mile long and 500
fathoms broad, was covered with high and rough blisters ; and was
overhung with whitey-blue fumes. The view was confined by the
fine dust to 300 feet : during daylight it wore the semblance of a
mirage (Landjoldu or TitSbrd), and at night it became a pillar of fire.

Our disappointment was tempered by meeting a party of three
Icelanders driving two ponies, whose imitation Icelandic coffers
bespoke the English owner. The head guide introduced himself
as P&ll P&lsson ; I recognised him as the godfather of u Mount
Paul” in the heart of the V&tnajokull. Led by Mr W. L. Watts,
he and five other islanders set out from the Nupstaftir farm on
June 24, and after twelve nights and days (July 7) in the snow,
the adventurous band issued from the great neve between Kis-
tufell and Kverkfjoll, and on July 10 — a fortnight and more —
they reached G-rimstaftir, whither their horses had been sent
round via the Eastern path. This is, indeed, a unique
feat of travel which I hope will not be its own reward. Paul,
who was physically as well as morally the best type of an
Icelander, accompanied us to our head-quarters at ReykjahlfS
and gave me a detailed account of the southern outbreaks. He
saw south-east of the Kistufell and north of the Yatnajokull, but
not in the snow, two small smokes, remnants of Nos. 1 and 2, dis-
tant some six hours’ ride, and three others appeared in the Dyng-
jufjoll. This account was confirmed by Dr P. E. Julius Hall-
ddrsson, government physician of the Thingeyjar Sysla. Both
agreed that No. 4 was still active, and they placed the site on
the south-eastern bend of the Askja or southern Dyngjufjoll
the curious horseshoe of the map which they would break up
into detached hills, and would moreover open to the N.E.
instead of the N.N.E. The lava on April 10 was about three
(Danish) miles long by a maximum of half a mile broad. At night
tne farm rooms were completely illuminated by the fire-blush
(EldroSi), and when this ceased violent earthquakes came on.
Showers of ashes fell north of My-vatn (Thingeyjar Sysla), and
more copiously in the Jokulsdal (Miila Sysla), covering the ground

of Edinburgh , Session 1875-76.

49

with a stratum a quarter of an ell thick.* The darkness during the
dust showers prevented the Jokulsdaelingar (people of Jokulsdal)
reading by day, and many of them left their farms and drove their
cattle to grass on the Vopnafjorftr. This outbreak is supposed to
have come not solely from the Dyngjufjoll, which, since April 5,
emitted only heavy smoke, but from several other places in the
northern, the north-eastern, and the north-western faces of the
Vatnajokull. In addition to this movement, which may be called
the “ Dyngjufjoll eruption,” and which is frequently referred to
in the local and in our home papers, Dr Jnlius places another
vent, hitherto unnumbered, about seven miles to the S.S.W.
of HerbubreiS, the “ broad-shouldered ” and perpendicular-sided
mountain of palagonite, which I had attempted to ascend in 1872.
I am happy to say that Mr W. L. Watts also noted the projecting
buttress from the south-west, which, descried too late, appeared to
me the only place for successful climbing. Here was the outbreak
of May 29, 1875, and hence, according to my informant, the greater
part of the ashes and pumice had been carried to the north-east.
On the other hand, Mr W. L, Watts saw no erater south-west of
Her<5ubrei<5, and would derive the pumice and ashes from Askja.
The Medico placed a suplementary crater in the old lava-field on a
meridian between HerbubrerSarfell and the BeykjahlfS-Jokulsa road.
Thus we have five several vents: — A and B, north and south of the
road (March 29); C, continuing the line southwards; D (May 29),
near Herftubreift; and E, the Askja or southern Dyngjufjoll

On July 29 the expedition received, at Husavik, a visit from Mr
W. L. Watts, who was fresh from the conquest of the Vatnajokull,
and he gave us the first intelligent account of the movement. He
had found fresh ashes, but no pumice, on the snows of the Vatna-
jokull, about the middle or in N. lat. 64° 25'. Kistufell was quiet;
smoke or vapour issued intermittently from Kverkfjoll, which I
saw in 1872 vomiting a glacier, and about SkjaldbreiS rose a large
mound of old lava, but no new signs of action appeared. He walked
over layers of pumice, extending a score of miles, from the Svarta

* The Danish measures are:--

12 inches = 1 foot (= 12-356 English).

24 thumblungar or 2 feet = 1 alen (ell).

24,000 feet = 1 mile (=: 4£ English statute miles in round numbers).

VOL. IX.

G

50

Proceedings of the Royal Society

to Iierbubreib, the deepest drifts measuring some eight feet, being
north-east of Vabalda to five miles south of the “Broad-shouldered.”
The explorer’s chief work was about the Askja or southern
Dyngjufjoll — I must warn my readers not to confound these
“ Chamber hills” with the “ Trolladyngja (sing.), perhaps better
known as Skjaldbreib, the “Broad shield. As Mr Watts intends
to publish his discoveries, I must not abuse the liberality with
which he gave his information. He would break up the fanciful
horseshoe of the great map, which in these parts is a mere field-
sketch, into a heart-shaped series of hills, mounds, and cones, here
connected, there separated, by “ Gils ” and broad passes : on the
western side the Odaba lava has penetrated into the enceinte , and
a latitudinal bar of heights traverses the southern quarter. By
walking over the eastern hills Mr Watts came in sight of the centre

i

of eruption ; the aneroid stood at 25'05 ( = 5000 feet in round num-
bers, whilst the northern plain is about 1000 feet lower. Various
angles to Herbubreib (80° to 40° for mag. var., west = 40), and
the Skjaldbreib (170° to (04° = 130°) placed the Gja-site inside the
horseshoe in N. lat. 64 45' and about W. long, (f.) 17

The centre of the eruption, which we will call the OskjugjA,
was a mere fissure, an acute-angled triangle with the apex to S.S.W.;
stepping the base gave a little more than a mile, and the
circumference would be about five. The three arms were deep
and perpendicular crevasses opened in the hills by the eruption,
and the lips readily fell in. The heights around it, especially
those to the east, were strewn with thick strata of pumice, ejected
wet, and decomposing under atmospheric action ; they also showed
that surface-streams of water had lately flowed over the new matter.

The most curious part of this
Gja is that it contains a triangle
within a triangle, both similar in
all their accidents ; moreover,
there is a series of smaller fissures
extending from the centre to the
apex, and to the two other angles,
north-western and north-eastern.
At the eastern arm, a deep pit
about a quarter of a mile in circumference discharges volumes of

The Oskjuyja

51

of Edinburgh, Session 1875-76.

steam and fatty fetid loam, which falls in granules. At the base
is another pit-crater, opening in high and broken ground; it is
also covered with pumice and offensive loam, which the depths
continue to vomit. The explorer distinctly saw a pit of hot water
spouted from the western side of the inner triangle : he could
trace, through the volumes of steam, its shaft or column, and
he heard the rain fall upon the rocks, bringing down with it an
avalanche of stone. The Askja is not a Jokull, and only a few
streaks of snow lay upon the flanks. This, therefore, may be
considered a crucial instance of water erupted from a fire vent.

Meanwhile there are no reports of any outbreak at HerSubreiS,
nor in the Trolladyngur, the inadequate features from which
Baring Gould would derive the 0d&3a Hraun. I have taken the
liberty in my map of counter-marching the “Troll’s Bowers,” from
a meridian to a diagonal, beginning south of Blafjall and abutting
almost upon Herftubreib. In local history we read dreadful accounts
of Trolladyngjur’s seven eruptions; of a.d. 1150 (the earliest);
of 1180; of 1340, when the “Broad-shouldered” is said to have
vomited for the first time; of 1359; of 1475; of 1510 (when the
second outbreak of Herftubreib is reported); and, finally, of 1862,
when there was an eruption of ashes, concerning which we have
few and uncertain details. Thus the ratio of outbreaks from Trol*
ladyngjur was 7 to 26 Heklas, 13 Katlas, 11 submarines, and 5
Orsefas.

The local papers, especially the “ Norftanfari ” of Akreyri
(February 19, March 3, April 9 and 17, and May 13 and 19 ; and
the “Isafold,” of March 27), give ample accounts of the late
movements. The My-vatn eruptions have been visited by many
parties of farmers, but only one has yet reached the Oskjugjd
(Askja or Dyngjufjoll Gj&). The relations are chiefly from the pen
of Jon Sigurbsson, of Gautland near My-vatn, Knight of the
Dannebrog, and Althingismaftur (M.P.), whom some Englishmen
have lately confounded with another “ White John,” the celebrated
agitator who lives at Copenhagen. Much of the matter has been
translated and published by our home press, but there are interest-
ing details which have not been noticed. Generally — allow me to
remark — the accounts, though utterly unscientific, bear an aspect
of sobriety and truthfulness wholly wanting in the older Icelandic

52

Proceedings of the Royal Society

descriptions recorded by Mackenzie and Henderson, and they show
that the spirit of enterprise has not wholly died out of Iceland.
It must, however, be borne in mind that both features are mere
crevasses opened by the tension of gases, and that due allowance
must be made for “hills and hillocks,” for “cliffs and preci-
pices.”

The “ Isafold,” a new paper published twice or thrice a month by
Hra Bjorn Jonsson, and printed by Einar Thorftarson of Reykjavik,
gives (No. 2, of March 27) a letter from My-vatn, which well de-
scribes the outbreak nearest the lake. It owes its chief interest to
the fact that it is the only one which corroborates the testimony of
Mr Watts, in mentioning torrents of hot water that cannot be
melted snow. At 11 a.m., on February 16, an expedition
ascended and crossed in half-an-hour the eastern flank of the
volcano, which in that direction sends out a long spit. After
mounting a low hill with a steep cliff to the south, the explorers
reached a narrow crevasse lying on a parallel of latitude, and form-
ing a “ vinkil,” apex, or angle to the south. Here they found a
deep flat recess about half a (Danish) mile in diameter, surrounded
by heights with perpendicular scaurs to the east and south ; west
and north-west the land was lower and flatter. Snow covered the
whole country. Hard by to the south-east and on plain ground
rose the crater which vomited the densest smoke, but there was no
new lava except upon the lips. The stone-rain, and hot ground burn-
ing their shoes, prevented them approaching it nearer than 70
fathoms, but they computed the diameter at 40 to 50 fathoms, and
the cone sides were bo steep that the breadth above and below was
about the same. The crater jetted in paroxysms. The thick
smoke made the ejected matter appear like torn fragments of coat
lining — evidently melted stone or burnt mud, most of which fell
back into, or on the edges of the bowl. The smaller rapilli were
thrown to a minimum height of 100 fathoms. No fire appeared in
the crater. Some 80 to 90 fathoms to the west was a cliff probably
formed by the eruption ; it measured a tenfold area (8000 to 9000
square fathoms)* The rocky edge, except to the north-west where
it was lowest, stood some 6 fathoms high. Below and south of the
cliff rose a second and a somewhat smaller crater. It jetted
steadily, but not so high as the other : discharging a lava-rain

53

of Edinburgh, Session 1875-76.

to the south-west; and a rivulet of almost transparent water flowed
to the north-west , where it formed a little basin under the rocks.

The expedition did not attempt the cliff because they had no
ropes, and both rocks and snow were cracked and crevassed. A
little further west rose the third crater, which vomited only
smoke. Its “Vinkil” or apex was a horseshoe, with the two
heels to the north and the toe facing south.

It is perhaps a little higher than the level of
the My-vatnssveit (the adjoining midge-lake N-
country). If much more lava flow, it must be
filled up, and then the fiery torrent will run over
and along the cliff to the sandy waste on the left
bank of the Jokulsa. East of the new mountain and the recess was
an old Hraun or lava stream, which seemed to have discharged east-
wards ; the bed showed no signs of craters nor volcanic vents, but
the snow will prevent till next summer any examination of the
Steintegundir (minerals).

Ash showers have been blown to the north-east of the Austur-
f j oil and, falling on the grass, which was bare of snow, they will
probably injure the pastures. It is reported that stone-rain ex-
tended to Kelduhver east of the Reykjarheifti. About New Year’s
day, an earthquake opened great crevasses where formerly the
ground was smooth. These movements were numerous near the
volcano. The expedition built a snow-house under the ravine-
cliff, but the falling stones compelled them to abandon it.

The “Norftanfari” of February 19, relates that during the winter
of 1874-5, a strong earthquake, proceeding from the southern or outer
Dyngjufjoll (hin fremri), shook the farms of Viftidal, Grrimstaftir, and
MoSrudal dFjollum, in the latter levelling some buildings. From No.
13 of March 3, we learn that four men of My-vatn (My-vatningar) set
out on Feb. 15, directly southwards, and after walking 24 hours,
hearing frightful subterranean thunders (dunur) like cataracts from
a mountain, and smelling sulphur fumes (eldlykt), they reached the
Askja, which has been incorrectly laid down on the map. The jets
of stone and lava, thrown many feet high, prevented them approach-
ing nearer than 60 to 70 fathoms. The vents consisted of one
large focus and of many small parasites, a single one discharging
lava. In early February smoke appeared every day, and presently

54 Proceedings of the Royal Society

came a slight earthquake. In April 9th, Jakob Hdlfd&narson, the
farmer of G-rimstaSir on the My-vatn, reports his visit to the My-
vatnsfjoll, where, on March 10th, the eruption lasted all night ;
and next day the smoke, hanging for a full eiktarlengd (three
hours) upon the horizon, was dispersed by. a storm. He walked
northwards over the lava hill (Hraunmalarkamb), and saw the
molten stone in the crevasses as if a fire had been built with wood
and charcoal. East of the Kamb (coombe), he inspected two big
crevasses erupting large stones, which fell back into them. The
lava had flowed for two days, and small fragments lay 300 fathoms
distant from the fire stream : 160 fathoms to the west smaller bits
were found ; but the greatest quantity was heaped up within ten
fathoms of the vent (eldsupptok). An anonymous account of the
same eruption, supposed to be by old Peter Jonsson of ReykjahltfS,
father-in-law to Jakob H&lfd&narson, is given in the “ Nor'Sanfari”
of April 17, 1875. He reports that sundry Lax&rdalers rode some
six hours from Reykjahli'S to explore the new volcano, via Hvann-
fell, where they heard loud thunderings. A storm raging at the
time in the north-west made them mistake the cause : these
rumblings became fiercer as they approached the focus. The earth-
fire springing out of three places in a meridianal line, formed high
lava hills npon the level ground. The greatest altitudes were to
the north : 50 to 80 fathoms west of the northernmost, upon a
tract which had sunk more than three mannahmftir (stature of
man), lay a great “ gil ” or crevasse. About the three foci, which
owned from 20 to 30 parasites, the lava had run mostly to the
south-east, but now he saw it flowing from the southernmost to
the S.S.W. The northern was an elongated rise, and from
its crater, about 300 fathoms in length, hot lava jetted 200 to
300 feet aloft, and fell in small cold drops upon a scanty area
No fire appeared during the day, only white mist (gufa), growing
whiter as it rose in the air ; it was so thick that it towered many
fathoms high, and the direction was perpendicular, although a strong
wind was blowing. In the darkness of the night conflagrations
became visible. No ashes fell at My-vatn, though they were thickly
spread by a strong north wind, and were strewed together with
pumice over the eastern regions, especially at Jokulsdal, Fljotsdal,
and Sey<5isfjor5. In the first-mentioned place candles were lit for

55

of Edinburgh, Session X875-7t>.

five, in the second for three, and in the third for four hours. The
layer of pumice and ashes measured some 4J inches deep in the
Jokulsdal, and 1J in the Seyfiisfjorb. This was the sixth explosion
since the outbreak, and about every tenth or twelfth day the violence
increased. The line extended through the Od&fiahraun to a little
north of Reykjahlifi-Grimstafiir- road.

About Easter-day a thick smoke was seen at Mofirudal a Fjollum ;
it rose south of Herfiubreifi, and many erroneously thought that it
came from Mofirufialsland. Others supposed it to rise from the
Dyngjufjoll, but it was certainly from Yatnajdkull, or from the
Tungu (Boab or Mesopotamia), formed by the westermost forks of
the Jokulsa. The discharge of pumice ( Danice u Pimpsteen ”) was
so abundant that for days the ferry boats could not cross the stream.

The “ Norbanfari ” of May 13 contains an unsigned article,
bringing up the account of our My-vatn eruption to May 5. Loud
thunderings with thick smoke were noticed on the last “ Tuesday
in the winter,” that is, on April 13; the summer beginning with
“ Sumarm&l,” April 17. On the “ first summer day ” (April 22)
four men took horse to visit the volcano. From Kollottafjall they
saw a fiery crevasse, made like a mountain u fjargyd,” or sheep
fissure where the animals take refuge during bad weather; and
on the borders of the SveinagjA, where a fine grassy plain formerly
extended, they found a high hill of lava pierced with three craters
lying on a meridian. These vents roared loudly, and threw up
rocks, which returned to the earth after 45 seconds. The smaller
rapilli rising like smoke disappeared in the air, and presently fell
like snow. From the largest focus, which lay south of the road,
a fiery flood ran westward : it had been reported three (Danish)
miles long, but it proved to be about 1000 fathoms, with a breadth
of 300 to 400. The people of My-vatnssveit have lost a little
grass, chiefly to the north of the road, and their ponies may suffer
during the winter. Some convulsion has taken place in the
Dyngjufjoll, whence, for a long time, more smoke issued than
during the winter. There was a great eruption close to the Od4<5a-
liraun on March 18 and 19, and the concussion of the air drove
the farm peeple from their beds. On March 23 fire was reported
to have proceeded from forty places lying close to the Holsfjoll
road, but it lay west, not east, of the Jokulsa.

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Proceedings of the Royal Society

Extracts from the letter of my friend, Sira Sigurftur Gunnarsson,
the priest of Hallormsta'S, addressed to the “ Norftanfari ” of April
24, appeared in the “ Times ” of July 1, 1875. It is dated March
29, 1875, and headed “ Fall of Pumice and Ashes in Mulasyla.”
The author, I may remark, has more than once visited the Vatna-
jokull. The following interesting details may be added to the
abstract : — “ During the Yule of 1873, and in early 1874, an earth-
quake shook the eastern regions, after which the people of the
Fjoll country saw two tall pillars of thick smoke apparently
proceeding from the Askja or Dyngjufjoll; and viewed from
Hallormsta<5arh&ls they rose at a considerable distance from each
other. Early in the year there was no fire in the My-vatnsoroefi, and
the earthquake became less violent towards the end of the winter. ”

After noticing the thunderings and the ash and pumice rain of
March 29 (Easter Monday) reported in the “ Times,” my reverend
friend continues : — “ The movement appears to have taken place
in the southern part of the Dyngjufjoll, westward of Herftubreift,
and a short way north of the winter Grjd. The direction of the
ashes was on both sides of a line to Modrudal and Fossvellir, as
far as the Undos in Hjaltarstaftarthingd and the Vatnsdalsfjall.
Another shower, travelling from west to east, and extending four
(Danish) miles, fell at Bru, and a mile and a half east of Aftalbol
(Rrafnkelsdal), Kleif (Fljotsdal), Skriftdal, and as far as Fdskrufts-
fjorft to the south-east. The amount which fell east of that line
in Breiftdal and Stoftvarfjorft was trifling. If we draw one straight
line from the focus of the eruption eastward between Fdskrufts and
Stoftvarfjorft, and a second from Vatnsdalsfjall near Njarftvik, also
to the east, the area upon which the ashes and pumice rained
would hardly be less than 100 square miles. Also assuming
the average depth of the layer at 3 inches, we must assign to the
discharge of March 19 a weight of 3840 tons.”

“It is reported that the ash showers have ruined twenty farms in
the Jokulsdal (between the Lagarfljot and the eastern Jokulsa)
and in the northern Mula Sysla, where the owners are preparing to
abandon their property. The position of the Fljotsdalsherad, where
the scoriaceous rains fell thickest, are the Jokulsdal, Fell, Fljostdal,
Skogar, SkriSdal, Vellir, and EySathinghA Heavy and terrible
showers also desolated Norftfjorti, Reyftarfjorft, Myvafjorft, and

57

of Edinburgh, Session 1875-7G.

LoftmundarfjoriS. Where the land has abundance of water, as in
parts of SkriSdal, Vellir, and EySathinghd, the farmers hope that
the ashes will disappear during the spring, and that they will be
dissolved by the rains.” This interesting letter concludes with
an exhortation “ not to abandon the holdings for good,” and with
excellent advice about the measures to be taken. Yet it owns that
“ from this fearful visitation all husbandry in the east country
must come to utter ruin,” and the less Icelanders are advised not
to emigrate the better for the island.

The writer of “An Appeal for Iceland” (“Times,” July 1,
1875), compares this mild and harmless eruption, which has not
destroyed a single life, with the terrible convulsions of 1783, which
killed some 14,000 human beings. He also calculates the destruc-
tion of pastures to the extent of 2500 to 3000 square miles, while
popular computations make 4000 square miles the habitable area
of Iceland.

According to PHI PHs^on only four farms on the west of the
Jokulsd have suffered severely. These are, going from south to
north, Bru, EyrikstaSir, H&konarstaSir, and Arndrstaftir. Ilerra
Thorftur Grudjonsson, factor at Husavik, never even heard of the
eruption till I showed .him the nepawspers. Finally, the brown
shadings in my chart, marking the eastern and north-eastern limits
of the ash showers, and copied from an Iceland map obligingly
lent to me by my friend, Mr Hubert Mackay Smith, may be allowed
to prove that the damage extends over a small area.

Mr Jon A. Hjaltalln, of the Advocate’s Library, Edinburgh,
received (June 26) trustworthy accounts of the ash and pumice
rain. “ It extended over several parts of Norftur Mulasysla and
SucSur Mulasysla, depositing a layer about 1J inches thick. In some
places the winds have carried it off, but sundry parishes will be
unable to keep their live stock at home this summer. Next hot
season, however, it is expected that the pastures will be all right.”

Mr W. L. Watt, who has just ridden over the ground, found the
pumice and ashes beginning about the middle course of the Svarti,
(N. lat. 64° 50'), and extending northwards to Her'SubreitS (65° 10').
or a total depth of 20 to 25 miles, bounded eastward by the
Jokulsa, where the country is not, and never has been, habited
by man.

VOL. IX.

n

58 Proceedings of the Royal Society.

The limits of this paper do not permit me to enter into all the
details of the last eruption in Iceland ; but the reader may be
assured that the outline and the main features of the subject are
correctly drawn.

The following Gentlemen were elected Fellows of the
Society: —

Bruce Ailan Bremner, M.D.

Rev. Francis Edward Belcombe.

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

vol. ix. 1875-76. No. 91.

Ninety-Third Session.

Monday , 2CBA December 1875.

Sir WILLIAM THOMSON, President, in the Chair.

The following Communications were read : —

1. Yortex Statics. By Sir William Thomson.

(Abstract.)

The subject of this paper is steady motion of vortices.

1. Extended definition of “steady motion.” The motion of any
system of solid or fluid or solid and fluid matter is said to be steady
when its configuration remains equal and similar, and the velocities
of homologous particles equal, however the configuration may
move in space, and however distant individual material particles
may at one time be from the points homologous to their positions
at another time.

2. Examples of steady and not steady motion

(1.) A rigid body symmetrical round an axis, set to rotate round
any axis through its centre of gravity, and left free, performs
steady motion. Not so a body having three unequal principal
moments of inertia.

(2.) A rigid body of any shape, in an infinite homogeneous liquid,
rotating uniformly round any, always the same, fixed line, and
moving uniformly parallel to this line, is a case of steady motion.

(3.) A perforated rigid body in an infinite liquid moving in the

VOL. ix.

i

60

Proceedings of the Boyal Society

manner of example (2.), and having cyclic irrotational motion of
the liquid through its perforations, is a case of steady motion
To this case belongs the irrotational motion of liquid in the neigh
bourhood of any rotationally moving portion of fluid of the same
shape as the solid, provided the distribution of the rotational mo
tion is such that the shape of the portion endowed with it remains
unchanged. The object of the present paper is to investigate
general conditions for the fulfilment of this proviso ; and to inves
tigate, farther, the conditions of stability of distribution of vortex
motion satisfying the condition of steadiness.

3. General synthetical condition for steadiness of vortex motion. —
The change of the fluid’s molecular rotation at any point fixed in
space must be the same as if for the rotationally moving portion
of the fluid were substituted a solid, with the amount and direction
of axis of the fluid’s actual molecular rotation inscribed or marked
at every point of it, and the whole solid, carrying these inscrip-
tions with it, were compelled to move in some manner answering
to the description of example (2). If at any instant the distribu-
tion of molecular rotation * through the fluid, and corresponding
distribution of fluid velocity, are such as to fulfil this condition, it
will be fulfilled through all time.

4. General analytical condition for steadiness of vortex motion. —
If, with (§ 24, below) vorticity and “ impulse,” given, the kinetic
energy is a maximum or a minimum, it is obvious that the motion
is not only steady, but stable. If, with same conditions, the
energy is a maximum-minimum, the motion is clearly steady, but
it may be either unstable or stable.

5. The simple circular Helmholtz ring is a case of stable steady
motion, with energy maximum-minimum for given vorticity and
given impulse. A circular vortex ring, with an inner irrotational
annular core, surrounded by a rotationally moving annular shell
(or endless tube), with irrotational circulation outside all, is a case
of motion which is steady, if the outer and inner contours of the

* One of the Helmholtz’s now well-known fundamental theorems shows
that, from the molecular rotation at every point of an infinite fluid the velocity at
every point is determinate, being expressed synthetically by the same formulae
as those for finding the “ magnetic resultant force” of a pure electro-magnet.
■ — Thomson’s Reprint of Papers on Electrostatics and Magnetism.

61

of Edinburgh, Session 1875-76.

section of the rotational shell are properly shaped, but certainly
unstable if the shell be too thin. In this case also the energy is
maximum-minimum for given vorticity and given impulse.

6. In these examples of steady motion, the “ resultant impulse”
(V. M.* § 8) is a simple impulsive force, without couple; the cor-
responding rigid body of example 3 is a circular toroid, and its
motion is purely translational and parallel to the axis of the toroid.

5. We have also exceedingly interesting cases of steady motion
in which the impulse is such that, if applied to a rigid body, it
would be reducible, according to Poinsofs method, to an impulsive
force in a determinate line, and a couple with this line for axis.
To this category belong certain distributions of vorticity giving
longitudinal vibrations, with thickenings and thinnings of the core
travelling as waves in one direction or the other round a vortex
ring, which will be investigated in a future communication to the
Koyal Society. In all such cases, the corresponding rigid body of
§ 2 example (2) has both rotational and translational motion.

7. To find illustrations, suppose, first, the vorticity (defined below,
§ 24) and the force resultant of the impulse to be (according to the
conditions explained below, § 29) such that the cross section is
small in comparison with the aperture. Take a ring of flexible
wire (a piece of very stout lead wire with its ends soldered together
answers well), bend it into an oval form,
and then give it a right-handed twist
round the long axis of the oval, so that
the curve comes to be not in one plane
(fig. 1). A properly-shaped twisted
ellipse of this kind [a shape perfectly
determinate when the vorticity, the
force resultant of the impulse, and the rotational moment of the
impulse (V. M. § 6), are all given] is the figure of the core in what
we may call the first f steady mode of single and simple toroidal

* My first series of papers on vortex motion in the “ Transactions of the
Royal Society of Edinburgh,” will he thus referred to henceforth.

t First or gravest, and second, and third, and higher modes of steady mo-
tion to be regarded as analogous to the first, second, third, and higher funda-
mental modes of an elastic vibrator, or of a stretched cord, or of steady
undulatory motion in an endless uniform canal, or in an endless chain of
mutually repulsive links.

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Proceedings of the Iioyal Society

vortex motion with rotational moment. To illustrate the second
steady mode, commence with a circular ring of flexible wire, and
pull it out at three points, 120° from one another, so as to make it
into as it were an equilateral triangle with rounded corners. G-ive
now a right-handed twist, round the radius to each corner, to the
plane of the curve at and near the corner; and, keeping the cha-
racter of the twist thus given to the wire, bend it into a certain
determinate shape proper for the data of the vortex motion. This
is the shape of the vortex core in the second steady mode of single
and simple toroidal vortex motion with rotational moment. The
third is to be similarly arrived at, by twisting the corners of a
square having rounded corners ; the fourth, by twisting the corners
of a regular pentagon having rounded ‘corners ; the fifth, by twisting
the corners of a hexagon, and so on.

In each of the annexed diagrams of toroidal helixes a circle is
introduced to guide the judgment as to the relief above and
depression below the plane of the diagram which the curve repre-
sented in each case must be imagined to have. The circle may
be imagined in each case to be the circular axis of a toroidal core
on which the helix may be supposed to be wound.

To avoid circumlocution, I have said, “give a right-handed
twist ” in each case. The result in each case, as in fig. 1, illus-
trates a vortex motion for which the corresponding rigid body
describes left-handed helixes, by all its particles, round the central
axis of the motion. If now, instead of right-handed twists to the
plane of the oval, or the corners of the triangle, square, pentagon,
&c., we give left-handed twists, as in figs. 2, 3, 4, the result in
each case will be a vortex motion for which the corresponding
rigid body describes right-handed helixes. It depends, of course,
on the relation between the directions of the force resultant and
couple resultant of the impulse, with no ambiguity in any case,
whether the twists in the forms, and in the lines of motion of the
corresponding rigid body, will be right-handed or left-handed.

8. In each of these modes of motion the energy is a maximum-
minimum for given force resultant and given couple resultant of
impulse. The modes successively described above are successive
solutions of the maximum-minimum problem of § 4; a determinate
problem with the multiple solutions indicated above, but no other

of Edinburgh, Session 1875-76. 63

solution, when the vorticity is given in a single simple ring of the
liquid.

9. The problem of steady motion, for the case of a vortex line
with infinitely thin core, bears a close analogy to the following
purely geometrical problem : —

Find the curve whose length shall be a minimum with given

resultant projeetional area, and given resultant areal moment (§ 27
below). This would be identical with the vortex problem if the
energy of an infinitely thin vortex ring of given volume and given
cyclic constant were a function simply of its apertural circum-
ference. The geometrical problem clearly has multiple solutions
answering precisely to the solutions of the vortex problem.

10. The very high modes of solution are clearly very nearly
identical for the two problems (infinitely high modes identical)
and are found thus : —

Take the solution derived in the manner explained above, from
a regular polygon of N sides, when N is a very great number. It
is obvious that either problem must lead to a form of curve like
that of a long regular spiral spring of the ordinary kind bent round
till its two ends meet, and then having its ends properly cut and
joined so as to give a continuous endless helix with axis a circle
(instead of the ordinary straight line-axis), and N turns of the
spiral round its circular axis. This curve I call a toroidal helix,
because it lies on a toroid * just as the common regular helix lies

* 1 can a circular toroid a simple ring generated by the revolution of any
singly-circumferential closed plane curve round any axis in its plane not
cutting it. A “tore,” following French usage, is a ring generated by the
revolution of a circle round any line in its plane not cutting it. Any simple

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Proceedings of the Royal Society

on a circular cylinder. Let a be the radius of the circle thus
formed by the axis of the closed helix ; let r denote the radius of
the cross section of the ideal toroid on the surface of which the
helix lies, supposed small in comparison with a; and let 0 denote
the inclination of the helix to the normal section of the toroid.
We have

~ 27 ra a

taD 6 = NlSn7 = Nr ’

because is as it were the step of the screw, and 2ttt is the cir-
cumference of the cylindrical core on which any short part of it may
be approximately supposed to be wound.

Let k be the cyclic constant, I the given force resultant of the
impulse, and /x the given rotational moment. We have (§ 28)
approximately

Hence

I — - K7ra2, /x = KN7rr2a .

\J K7r’ \f Nk^ttHs ’

= /i.

\/ N/XK57T5

tan 6

11. Suppose, now, instead of a single thread wound spirally
round a toroidal core, we have two separate threads forming as it
were a “ two-threaded screw,” and let each thread make a whole

ring, or any solid with a single hole through it, may be called a toroid ; but
to deserve this appellation it had better be not very unlike a tore.

The endless closed axis of a toroid is a line through its substance passing
somewhat approximately through the centres of gravity of all its cross sec-
tions. An apertural circumference of a toroid is any closed line in its surface
once round its aperture. An apertural section of a toroid is any section by
a plane or curved surface which would cut the toroid into two separate toroids.
It must cut the surface of the toroid in just two simple closed curves, one of
them completely surrounding the other on the sectional surface : of course, it
is the space between these curves which is the actual section of the toroidal
substance, and the area of the inner one of the two is a section of the
aperture.

A section by any surface cutting every apertural circumference, each once
and only once, is called a cross section of the toroid. It consists essentially
of a simple closed curve.

65

of Edinburgh, Session 1875-76.

number of turns round the toroidal core. The two threads, each
endless, will be two helically tortuous rings linked together, and
will constitute the core of what will now be a double vortex ring.
The formulae just now obtained for a single thread would be appli-
cable to each thread, if k denoted the cyclic constant for the circuit
round the two threads, or twice the cyclic constant for either, and
N the number of turns of either alone round the toroidal core.
But it is more convenient to take N for the number of turns of
both threads (so that the number of turns of one thread alone is
JN), and k the cyclic constant for either thread alone, and thus for
very high steady modes of the double vortex ring

I = 2/c7ra2, fx = KN7rr2a,

tan 0

= 11
sj N

m

N/XK^7r5 *

Lower and lower steady modes will correspond to smaller and
smaller values of N, but in this case, as in the case of the single
vortex core, the form will be a curve of some ultratranscendent
character, except for very great values of N, or for values of 6 in-
finitely nearly equal to a right angle (this latter limitation leading
to the case of infinitely small transverse vibrations).

12. The gravest steady mode of the double vortex ring corre-
sponds to N = 2. This with the single vortex core gives the case
of the twisted ellipse (§ 7). With the double core it gives a sys-
tem which is most easily understood by
taking two plane circular rings of stiff
metal linked together. First, place them
as nearly coincident as their being linked
together permits (fig. 5). Then separate
them a little, and incline their planes a
little, as shown in the diagram. Then
bend each into an unknown shape deter-
mined by the strict solution of the transcendental problem of
analysis to which the hydro-kinetic investigation leads for this
case.

13. Go back now to the supposition of § 11, and alter it to
this : —

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Proceedings of the Royal Society

Let each thread make one turn and a half, or any odd num-
ber of half turns, round the toroidal core : thus each thread will
have an end coincident with an end of the other. Let these
coincident ends he united. Thus there will he but one endless
thread making an odd number N of turns round the toroidal core.
The cases of N = 3 and N = 9 are represented in the annexed
diagrams (fig. 9).*

Imagine now a three-threaded toroidal helix, and let N denote
the whole number of turns round the toroidal core, we have

I = 3/<7ra2, fji = kN irr2a ,

tan 6 =

Suppose now N to be divisible by 3 : then the three threads
form three separate endless rings linked together. The case of
N = 3 is illustrated by the annexed diagram (fig. 6), which is
repeated from the diagram of Y. M. § 58. If N be not divisible
by 3, the three threads run together into one, as illustrated for the
case of N = 11 in the annexed diagram (fig. 7).

14. The irrotational motion of the liquid round the rotational
cores in all these cases is such that the fluid velocity at any point is
equal to, and in the same direction as, the resultant magnetic force
at the corresponding point in the neighbourhood of a closed gal-

* The first of these was given in § 68 of my paper on vortex motion. It has
since become known far and wide by being seen on the back of the “ Unseen
Universe.”

of Edinburgh, Session 1875-76.

67

vanic circuit, or galvanic circuits, of the same shape as the core or
cores. The setting forth of this analogy to people familiar, as
modern naturalists are, with the distribution of magnetic force in
the neighbourhood of an electric circuit, does much to promote a
clear understanding of the still somewhat strange fluid motions
with which we are at present occupied.

15. To understand the motion of the liquid in the rotational
core itself, take a piece of Xndian-rubber gas-=pipe stiffened internally
with wire in the usual manner, and with it construct any of the
forms with which we have been occupied, for instance the sym-
metrical trefoil knot (fig. 8, § 13), unit-
ing the two ends of the tube carefully
by tying them firmly by an inch or two
of straight cylindrical plug, then turii
the tube round and round, round its
sinuous axis. The rotational motion of
the fluid vortex core is thus represented.

But it must be remembered, that the
outer form of the core has a motion per-
pendicular to the plane of the diagram,

and a rotation round an axis through the centre of the diagram,
and perpendicular to the plane in each of the cases represented by
the preceding diagrams. The whole motion of the fluid, rotational
and irrotational, is so related in its different parts to one another,
and to the translational and rotational motion of the shape of the
core, as to be everywhere slipless.

16. Look to the preceding diagrams, and, thinking of what they
represent, it is easy to see that there must be a determinate parti-
cular shape for each of them which will give steady motion, and I
think we may confidently judge that the motion is stable in each,
provided only the core is sufficiently thin. It is more easy to
judge of the cases in which there are multiple sinuosities by a
synthetic view of them (§ 3) than by consideration of the maxi-
mum-minimum problem of § 8.

17. It seems probable that the two- or three- or multiple-
threaded toroidal helix motions cannot be stable, or even steady,
unless I, fx, and N are such as to make the shortest distances
between different positions of the core or cores considerable in

VOL. IX.

K

68

Proceedings of the Poyal Society

comparison with the core’s diameter. Consider, for example, the
simplest case (§ 12, fig. 5) of two simple rings linked together.

18 Gro back now to the simple circular Helmholtz ring. It is
clear that there must be a shape of absolute maximum energy for
given vorticity and given impulse, if we introduce the restriction
that the figure is to be a figure of revolution, that is to say,
symmetrical round a straight axis. If the given vorticity be given
in this determinate shape the motion will be steady, and there is
no other figure of revolution for which it would be steady (it being
understood that the impulse has a single force resultant without
couple) . If the given impulse, divided by the cyclic constant, be
very great in comparison with the two-thirds power of the volume
of liquid in which the vorticity is given, the figure of steadiness is an
exceedingly thin circular ring of large aperture and of approximately
circular cross section. This is the case to which chiefly attention is
directed by Helmholtz. If, on the other hand, the impulse divided
by the cyclic constant be very small compared with the two-thirds
power of the volume, the figure becomes like a long oval, bored
through along its axis of revolution and with the ends of the bore

'

rounded off for trumpeted) symmetrically, so as to give a figure
something like the handle of a child’s skipping-rope, but sym-
metrical on the two sides of the plane through its middle
perpendicular to its length. It is certain that, however small
the impulse, with given vorticity the figure of steadiness thus
indicated is possible, however long in the direction of the axis
and small in diameter perpendicular to the axis and in aperture
it may be. I cannot, however, say at present that it is certain
that this possible steady motion is stable, for there are figures
not of revolution, deviating infinitely little from it, in which,
with the same vorticity, there is the same impulse and the same
energy, and consideration of the general character of the motion
is not reassuring on the point of stability when rigorous demon-
stration is wanting.

19. Hitherto I have not indeed succeeded in rigorously demon-
strating the stability of the Helmholtz ring in any case. With
given vorticity, imagine the ring to be thicker in one place than in
another. Imagine the given vorticity, instead of being distributed
in a symmetrical circular ring, to be distributed in a ring still,

of Edinburgh, Sessio7i 1875-76.

69

with a circular axis, but thinner in one part than in the rest. It
is clear that with the same vorticity, and the same impulse, the
energy with such a distribution is greater that when the ring is
symmetrical. But, now let the figure of the cross section of the
ring, instead of being approximately circular, be made considerably
oval. This will diminish the energy with the same vorticity and
the same impulse. Thus, from the figure of steadiness we may
pass continuously to others with same vorticity, same impulse, and
same energy. Thus, we see that the figure of steadiness is, as
stated above, a figure of maximum-minimnm, and not of abso-
lute maximum, nor of absolute minimum energy. Hence, from
the maximum-minimum problem we cannot derive proof of
stability.

20. The known phenomena of steam rings and smoke rings
show us enough of, as it were, the natural history of the subject
to convince us beforehand that the steady configuration, with
ordinary proportions of diameters of core to diameter of aperture,
is stable, and considerations connected with what is rigorously
demonstrable in repect to stability of vortex columns (to be given
in a later communication to the Koyal Society) may lead to a
rigorous demonstration of stability for a simple Helmholtz ring
if of thin enough core in proportion to diameter of aperture. But
at present neither natural history nor mathematics gives us perfect
assurance of stability when the cross section is considerable in
proportion to the area of aperture.

21. I conclude with a brief statement of general propositions,
definitions, and principles used in the preceding abstract, of which
some appeared in my series of papers on vortex motion com-
municated to the Royal Society of Edinburgh in 1867-68 and 69,
and published in the Transactions for 1869. The rest will form
part of the subject of a continuation of that paper, which I hope
to communicate to the Royal Society before the end of the
present session.

Any portion of a liquid having vortex motion is called vortex
core, or, for brevity, simply “ core.” Any finite portion of liquid
which is all vortex -core, and has contiguous with it over its
whole boundary ir rotation ally moving liquid, is called a vortex . A
vortex thus defined is essentially a ring of matter. That it must

7 0 Proceedings of the Royal Society

be so was first discovered and published by Helmholtz. Some-
times the word vortex is extended to include irrotationally moving |
liquid circulating round or moving in the neighbourhood of vortex
core ; but as different portions of liquid may successively come
into the neighbourhood of the core, and pass away again, while
the core always remains essentially of the same substance, it is
more proper to limit the substantive term a vortex as in the
definition I have given.

22. Definition I. — The circulation of a vortex is the circulation
[V.M. § 60 (a)] in any endless circuit once round its core. What-
ever varied configurations a vortex may take, whether on account
of its own unsteadiness (§ 1 above), or on account of disturbances
by other vortices, or by solids immersed in the liquid, or by the
solid boundary of the liquid (if the liquid is not infinite), its
“ circulation ” remains unchanged [V. M. § 59, Prop. (1)]. The
circulation of a vortex is sometimes called its cyclic constant.

Definition II. — An axial line through a fluid moving rotation-
ally, is a line (straight or curved) whose direction at every point
coincides with the axis of molecular rotation through that point
[V. M. § 59 (2)].

Every axial line in a vortex is essentially a closed curve, being
of course wholly without a vortex.

23. Definition III. — A closed section of a vortex is any section
of its core cutting normally the axial line through every point of
it. Divide any closed section of a vortex into smaller areas ; the
axial lines through the borders of these areas form what are
called vortex tubes. I shall call (after Helmholtz) a vortex
filament any portion of a vortex bounded by a vortex tube (not
necessarily infinitesimal). Of course, a complete vortex may be
called therefore a vortex filament ; but it is generally convenient
to apply this term only to a part of a vortex as just now defined.
The boundary of a complete vortex satisfies the definition of a
vortex tube.

A complete vortex tube is essentially endless. In a vortex
filament infinitely small in all diameters of cross sections “ rota-

71

of Edinburgh, Session 1875-76.

tion varies [Y. M. § 60 (e)] from point to point of the length
of the filament, and from time to time inversely as the area
of the cross section. The product of the area of the cross section
into the rotation is equal to the circulation or cyclic constant of
the filament.

24. Vorticity will be used to designate in a general way the
distribution of molecular rotation in the matter of a vortex. Thus,
if we imagine a vortex divided into a number of infinitely thin
vortex filaments, the vorticity will be completely given when the
volume of each filament and its circulation, or cyclic constant, are
given; but the shapes and positions of the filaments must also be
given in order that, not only the vorticity, but its distribution, can
be regarded as given.

25. The vortex density at any point of a vortex is the circula-
tion of an infinitesimal filament through this point divided by the
volume of the complete filament. The vortex density remains
always unchanged for the same portion of fluid. By definition it
is the same all along any one vortex filament.

26. Divide a vortex into infinitesimal filaments inversely as their
densities so that their circulations are equal; and let the circula-

tion of each be — of unity.
n

Take the projection of all the fila-

ments on one plane. — of the sum of the areas of these projections

n

is (Y. M. §§ 6, 62) equal to the component impulse of the vortex
perpendicular to that plane. Take the projections of the filaments
on three planes at right angles to one another, and find the centre
of gravity of the areas of these three sets of projections. Bind,
according to Poinsot’s method, the resultant axis, force, and

couple of the three forces equal respectively to — of the sums of

the areas, and acting in lines through the three centres of gravity
perpendicular to the three planes. This will be the resultant axis ;
the force resultant of the impulse, and the couple resultant of the
vortex.

The last of these, that is to say, the couple is also called the
rotational moment of the vortex (V. M. § 6).

72

Proceedings of the Royal Society

27. Definition IV. — The moment of a plane area round any axis
is the product of the area multiplied into the distance from that
axis of the perpendicular to its plane through its centre of
gravity.

Definition V. — The area of the projection of a closed curve on
the plane for which the area of projection is a maximum will be
called the area of the curve, or simply the area of the curve. The
area of the projection on any plane perpendicular to the plane of
the resultant area is of course zero.

Definition VI. — The resultant axis of a closed curve is a line
through the centre of gravity, and perpendicular to the plane of
its resultant area. The resultant areal moment of a closed curve
is the moment round the resultant axis of the areas of its pro-
jections on two planes at right angles to one another, and parallel
to this axis. It is understood, of course, that the areas of the
projections on these two planes are not evanescent generally,
except for the case of a plane curve, and that their zero values are
generally the sums of equal positive and negative portions. Thus
their moments are not in general zero.

Thus, according to these definitions, the resultant impulse of a
vortex filament of infinitely small cross section and of unit
circulation is equal to the resultant area of its curve. The
resultant axis of a vortex is the same as the resultant axis of the
curve, and the rotational moment is equal to the resultant areal
moment of the curve.

28. Consider for a moment a vortex filament in an infinite
liquid with no disturbing influence of other vortices, or of solids,
immersed in the liquid. We now see from the constancy of the
impulse (proved generally in Y. M. § 19) that the resultant area,
and the resultant areal moment of the curve formed by the
filament, remain constant, however its curve may become con-
torted ; and its resultant axis remains the same line in space.
Hence, whatever motions and contortions the vortex filament may
experience, if it has any motion of translation through space this
motion must be on the average along the resultant axis.

i

of Edinburgh, Session 1875-76.

73

29. Consider now the actual vortex made up of an infinite
number of infinitely small vortex filaments. If these be of
volumes inversely proportional to their vortex densities (§ 25), so
that their circulations are equal, we now see from the constancy
of the impulse that the sum of the resultant areas of all the
vortex filaments remains constant ; and so does the sum of their
rotational moments: and the resultant areal axis of them all
regarded as one system is a fixed line in space. Hence, as in the
case of a vortex filament, the translation, if any, through space is
on the average along its resultant axis. All this, of course, is on
the supposition that there is no other vortex, and no solid
immersed in the liquid, and no bounding surface of the liquid near
enough to produce any sensible influence on the given vortex.

2. Experiments illustrating Rigidity produced by Centrifugal
Force. By John Aitken, Esq.

If an endless chain is hung over a pulley and the pulley driven
at a great velocity, it is well known that the motion so communi-
cated to the chain has almost no tendency to change the form of
the curve in which the chain hangs, and that the principal effect
of the motion is to confer on the chain a quasi-rigidity which
enables it to resist any force tending to alter its curvature.

This is only true in a general sense, and possibly may be true of
some ideal form of chain ; but in all chains we can experiment on
there are forces in action in the moving chain which tend to cause
the chain to depart from the form which it has while at rest.

I shall refer to these disturbing forces later on. As the disturb-
ing forces in most chains are very small, we shall neglect them,
and for the present suppose the centrifugal force just balances the
tension at all points. The following experiments were made to
illustrate the balance of these forces, to show that into whatever
curves we may bend the chain when in motion, the centrifugal force
has no tendency to alter these curves: that all forms are forms of
stability, as far as the centrifugal force is concerned.

The first experiments were to show the effect of destroying the
balance between the tension and the centrifugal force. In these
experiments the links on the descending side of the loop were

74

Proceedings of the Royal Society

allowed to fall on a platform, so that part of the chain lay loose on
the platform, thus destroyed the tension produced by the centrifugal
force at the lower part of the chain. The chain was made to take
the same velocity as the driving pulley, by being pressed into
contact with it by means of an elastic wheel.

I. When the chain was pressed at the point where it leaves the
pulley there was no alteration in the path of the chain, because
the chain after it leaves the pulley is moving in a straight line, and
as there is no deviating force, there is no centrifugal force, and
therefore, removing the tension in the chain has no effect on the
direction of the motion of the links.

II. When the chain was pressed at a point a little higher up
the pulley, then the centrifugal force of the curved part of the
chain resting on the pulley at the descending side, being unba-
lanced by the tension, rises from the pulley, and is shot in a direc-
tion away to one side of the pulley. Of course the curved part of
the chain on the other side of the pulley has also a tendency to
rise, but is kept in its place by the tension produced by putting
the chain in motion after being stopped by the platform.

III. When the chain is pressed on the ascending side of the
pulley, then the chain rises up off the pulley and forms itself into
a somewhat irregular curve resting on the platform, and touching
the pulley at only one point. When the velocity is sufficient to
raise it to a certain height, the conditions become altered. The
chain in rising takes up all the slack chain lying on the platform,
and a tension is produced in the chain by the centrifugal force, and
unless we keep increasing the speed of the chain, it can no longer
keep in its elevated position, because the centrifugal force is now
balanced by the tension, and as the force of gravitation is now
unbalanced, it gradually flattens the curve till the chain again
comes to rest on the top of the pulley and spreads itself out in an
irregular curve on the platform.

IV. At the beginning of the previous experiment the centrifugal
force being unbalanced by the tension, it overcomes the force of
gravitation and causes the chain to rise into the air. After all the
slack chain has been taken up, and a tension is produced in the chain
by the centrifugal force, then the centrifugal force is balanced by
the tension and is no longer capable of opposing gravitation, and

75

of Edinburgh , Session 1875-76.

the chain begins to fall; but at this point its fall may be stopped,
or the chain may be made to rise again by destroying the tension
at the lower part of the chain. If we cause the chain, instead of
meeting the platform at an acute angle, to strike it as near as pos-
sible at right angles, then the motion of the chain where it strikes
the platform is partly destroyed, and the chain again rises and may
be kept balanced for a long time resting on the platform, and only
touching the driving wheel at one point. The reason for this being,
that if we partially stop the motion of the links by causing them
to strike the platform, or if we alter the direction of their motion
by causing them to strike the platform, then there will be less
tension in the lower part of the chain than in the upper, as the
tension in the lower part will be only that due to partially changing
the direction of the motion of the links. The centrifugal force of the
upper part of the chain will be therefore unbalanced, and will cause
the chain to rise and keep its elevated position against the force of
gravitation. If a quick upward motion is given to the platform,
the chain may be thrown up in the air, and again dropped on the
platform like a solid body.

The next experiments are to show that centrifugal force may
produce sufficient rigidity to cause a chain to run along a platform
like a wheel. A short endless chain was put over a pulley which
was driven at a great velocity; the chain was then dropped on the

I platform, along which it ran for some distance. It is not necessary
that the chains form circular loops to do this. The loop may be
tall and narrow, and will, while running along, keep the longer
axis of the curve in its original upright position. Nor need the
chain be heavy. A watch-guard was hung over a pulley about eight
inches diameter; it then formed a loop about eight inches broad
by about two feet high. When thrown off the pulley it glided
along the platform for some distance. The chains were also
dropped on an inclined polished surface, on which they remained
standing in rapid motion for some time.

All these experiments only illustrate the balance of the centri-
fugal force, and the tension when the motion is all in one plane.
The next experiment is to illustrate this balance when the motion
takes place in different planes. This is easily illustrated by means
of a circular disc of paper, or any other flexible material. If we

VOL. III.

L

76 Proceedings of the Royal Society

bend the disc while it is rotating, we find that the bent part does
not rotate with the disc, and that the disc only slowly regains its
original flat form. If we load the outside of the disc with a row
of flattened pellets of shot, we increase the resistance or rigidity
of the disc while in motion, and if the weight is such that it just
balances the elasticity of the paper, then the bend will remain in
the same place for a very long time while the disc is rotating
rapidly. The disc may even be bent till the circumference touches
the centre, and while the bend keeps its place the chain of shot is
passing through many planes, and the tension at the different
points just balances the centrifugal force.

Before proceeding to experiment with the horizontal chain, I
must refer to the disturbing forces in action causing the chain to
change its form while in motion. When looking at these endless
chains in motion, the most marked effect of this motion is to cause
a curious reverse curve just after the chain has turned at the lowest
point of its path and has begun to ascend. This reverse curve was
supposed to be produced by friction from the great tension produced
by the centrifugal force; but that it is not really so, is easily
proved by taking two precisely similar chains and oiling one and
passing the other through a flame to remove all grease. The only
difference between the two chains now is that the friction in the one
is greater than in the other. If we hang these two chains over two
pulleys of the same diameter on the same shaft so as to drive both
chains at the same velocity, we find that the oiled chain has the
reverse curve well marked, while the friction in the other chain
causes the loop to open out and take up a curve approaching a circle
and shows no reverse curve, and when both chains are compelled to
have the same curvature at bottom, the reverse curve is much the
least where the friction is greatest. The reverse curve seems to be
due to the change of motion which takes place in the links when
moving in a path of varying curvature. For instance,, when the
links are descending along the flat part of the curve, their motion is
almost simply one of translation, whereas when passing round the
curves they have a motion of rotation as well as a motion of transla-
tion, the result of which is, that the links resist this rotation at the
entrance of the curve, and thus flatten out the curve on that side,
aud after the rotation has been communicated to them, they tend to

77

of Edinburgh, Session 1875-76.

keep this rotation, and thus continue the curve at the lower end
of the chain much farther round than if the chain was not in
motion. And, for very evident reasons, the quickest part of the curve
is not at the bottom, but a short distance up the ascending side; and
farther, the rotation of the link at the bottom is quicker than that
corresponding to the curvature. These points may all be illustrated
by a chain in which the links are short and the chain as thick as
possible, so that the moment of inertia of the links round an axis
perpendicular to the plane of the motion of the links is as great as
possible. Such a chain when properly made gives a series of large
and well-marked waves all the way up the one side of the loop and
down the other. The length of the links also tends to change the
form of the curve. If we have two chains of the same material
and same size every way, except in the length of the link, then the
larger the link the more the chain tends to open out the curves
and take the circular form, and the smaller the links the nearer
it approaches the form it has while at rest, and the more marked
the reverse curve becomes.

An elastic band in rapid motion will also tend to take up a
circular form, because the strain at the quick part of the curves
will tend to open them out, in the same manner as when the band
was at rest. An elastic chain while in motion does not show the
reverse curve like a chain, probably because the strain on the
material prevents it doing so.

In the previous experiments gravitation acted on the chains, so
that whatever form we might impress on them, gravitation con-
stantly tended to change that form and bring it back nearly to the
form it would have if gravitation alone acted on it. An attempt
was therefore made to get quit of the disturbing effect of gravita-
tion. Different ways were tried of effecting this, but none of
them were thoroughly successful. The next experiment shows the
most successful method tried, namely, suspension. The chain is
hung by means of a number of fine cords to a circular disc, capable
of rotating about a vertical axis placed as far above the chain as
possible. The chain is driven by means of a rapidly revolving
horizontal pulley running on a vertical axis, and to give sufficient
friction the chain is pressed to the pulley by means of an elastic
wheel. The centre of suspension is so arranged that it can be

78

Proceedings of the Royal Society

brought over the driving pulley, or removed to some distance
from it, so as to be able to bring the centre of suspension over the
centre of gravity of the chain, whatever shape the chain may be
caused to take. The chain so suspended, when in rapid motion,
retains for a considerable time whatever form we please to give it.
It may be moulded into a most complicated series of curves, and
though it resists any effort made to alter these curves, it has
itself but little tendency to do so. If we observe the chain closely,
we will however find that the disturbing forces, which I have
already referred to, are acting on the chain, tending to change its
curvature. For instance, if we keep the point of suspension over
the centre of gravity of the chain, we will find after some time
that the chain will take up a circular form. This is caused by the
friction in the chain, and other causes. Again, the effect of the
varying rate of rotation of the link on its own axis is also well
marked, but is quite different from what wo get when the chain is
hung over the driving pulley. When the chain is hung over the
pulley, there is a tension due to the wreight of the chain. This
tension gives rise to the wave form which certain chains take up
when in motion. The tension due to the centrifugal force has no
such effect. When, therefore, the chain is suspended and gravita-
tion removed, there is no tension preventing the chain from con-
tinuing to curve always in the same direction; and if we use a
chain specially prepared to show this effect, such as the one
already referred to, the chain goes on bending further and further
round till it comes against the part of the chain coming in the
opposite direction and stops the motion, even though the chain
at that point is also bending out of the way on account of the
resistance offered by the links to rotation on their axis.

of Edinburgh, Session 1875-76.

79

Monday, 3 d January 1876.

Sir WILLIAM THOMSON, President, in the Chair.
The following Communications were read : —

1. On the Electrical Conductivity of Stretched Silver Wires.
By J. G. MacGregor, M.A., B.Sc. Communicated by
Professor Tait.

The apparatus which I used in a few experiments on silver wires
was as follows : — To a beam, supported in stonework, a plate of
copper was fastened, upon which a smaller plate could be tightly
screwed. Between the two plates a very thick copper wire was
secured, vertically. Its lower end was provided with a small plate
of copper, fastened by screws. This plate served to make fast one
end of the silver wire under investigation. The other end was
joined in the same way to a second thick copper wire; this was
provided with a horizontal round brass plate, through the centre of
which it passed, and which acted as weight-carrier. A length of
about 8 mm. at the end of the part of the copper wire which projected
below the weight-carrier was amalgamated, and, while hanging
quite free, dipped into a glass cup containing mercury, which, by
means of a long screw, could be elevated or depressed by any desired
amount. When measurements of resistance were made it was
always placed in such a position that the amalgamated part of the
copper wire was just beneath the surface of the mercury. The
glass cup served also to support the weight-carrier during the
adjustment of the weights, that the silver wires might be sub-
jected to no jerks. After putting on weights the cup was lowered
very slowly and steadily until the weights hung free. A copper
wire (4 7 mm. thick and 30 cm. long), dipping in the mercury,
joined up the silver wire as one of the arms of a Wheatstone’s
bridge. At the upper end of the copper wire, which was fastened
to the beam, two other copper wires were fastened by binding
screws. One of them went to the galvanometer; the other was the
standard wire, with whose resistance that of the silver wires was

80 Proceedings of the Royal Society

compared. For all the observations on a single wire, it had, in all
cases, as nearly as possible the same temperature. That it might
not be affected by warm or cold currents of air it was defended by
a coating of gutta percha, and made to pass through a tube of water
whose temperature could readily be noted. By dipping into a mercury
pool it was joined up as a second arm of the Wheatstone’s bridge.
A length of about 5 mm. of the end which dipped in the mercury was
well amalgamated. Above that the wire was varnished by a non-
conductor, so that contact began always at the same point of the wire.
The other two arms of the bridge consisted of the segments of a Ger-
man-silver wire, — Kirchhoff’s form of the Wheatstone bridge being
used exactly as described by Wiedemann in his “Galvanismus.”*
The galvanometer used was Wiedemanns mirror galvanometer, f
the deflections of the mirror being observed by means of a telescope.
The current employed was that of a Bunsen’s cell of great internal
resistance. The length of the wire was determined by a very delicate
cathetometer, which could measure accurately to *02 mm. The
lower end of the copper wire which was fastened to the beam, was
smooth and flat, and cut at right angles to its vertical axis. The
edge of the small plate was correspondingly cut, so that the exact
point at which the silver wire was seized and compressed by the
copper plate could be seen through the telescope of the catheto-
meter. The clamp which seized the lower end of the silver wire
was arranged in the same way. The wires, of whose resistance
measurements were made, were of pure silver, and were carefully
drawn by M. E. Stohrer, philosophical instrument maker of Leipzig.
They were always raised to a red heat before being subjected to
tension, care being taken that fusion did not occur in any part. In
order to determine the effect of tension on the conductivity of the
wires, it was necessary to know the relation of their diameter before
to their diameter after being stretched. This was estimated by a
careful measurement of lengths and specific gravities. For the latter
purpose a chemical balance was employed, which could weigh accu-
rately to ’0001 grm. As the wires had to be rolled up to prevent
their touching the sides of the vessel containing the distilled water
in which they were weighed, the measured specific gravity was pro-

* “ Galvanismus,” vol. i. pp. 251-255, 2d German ed., 1872.

t “ Galvanismus,” voL ii. pt. 1, pp. 227-230, 2d Ger. ed., 1873.

81

of Edinburgh, Session 1875-76.

bably not exactly that of the wire of measured resistance. The
error, however, must have been very slight.

The course of procedure was as follows : — The wire was heated
red hot in an alcohol flame. After cooling, its specific gravity was
determined. It was then fastened by the copper plates to the
thick copper wires, and a slight weight was attached just sufficient
to straighten the wire, that its length might be accurately ascer-
tained (it was straightened as much as possible by being drawn
between the fingers before being fastened in the apparatus). When
straight enough for the determination of its length, its resistance
was also measured by the method of double observation, as de-
scribed in the u Galvanismus ” (see above).* After the determina-
tion of resistance, weights were carefully piled upon the carrier,
which during the operation was held fast from below. They were
then allowed to stretch the wire gradually until it hung quite free,
and its elongation had ceased. Then the length, the resistance,
and finally the length a second time, were determined, the second
measurement of length being made in order to be certain that there
had been no further elongation. The weights were now carefully
taken off, the carrier being again supported from below, and the
specific gravity of the wire was measured as before, the compressed
ends, however, having been cut off. A large number of experiments
were rendered useless by the fact that too great weights were attached.
Either the wires broke, or they were found on inspection to have
too variable a diameter to be regarded as uniform. In the result
given below such small weights were used that almost no difference
of diameter throughout the whole length of the wire could be noticed
by means of a magnifying instrument. Thus the wire could be
treated as uniform, and the specific gravity method assumed to
give its diameter.

The results of the examination of three wires are given in the
following table: —

* Instead of the formula given in u Galvanismus,” the following was used: —
s*+ - d2) + s(d1d12 + d%d12 - Zdxd^~ d^d^d^ — 0.

The length of the German-silver wire as found by this formula was 1108795
mm. As measured by the cathetometer its length was 1108:8 mm.

82

Proceedings of the Royal Society

Length

(mm.)

Weight

(grms.)

d*

(mm.)

Resistance
(standard
copper wire
=unity).

Length
(length be-
fore stretch-
ing=unity).

Resistance

(resistance

before

stretching

=unity).

Wire 1. 1

777-62

809-56

2246

5075

198-8

239’8

1-4369

1-5519

1

1-0411

1

1-0800

Wire II. |

830-82

890-04

1246

6746

234-9

311-2

1-5376

1-7803

1

1-0713

1

1-1579

Wire III. |

660-86

729-14

1246

7911

114-7

216-9

1-2308

1-4864

1

1-1033

1

1-2105

These results agree, as might be expected, with those which
Moussonf has published on steel, iron, and copper wires, in the
fact that the resistance increases very much faster than the length.
This must be the case unless there be a diminution of resistance,
due to tension, sufficient to neutralise the increase of resistance due
to decrease of the cross section of the wire. It is interesting to
ask, then — Does the decrease in the diameter of the wire account
for that part of the increase of its resistance which is not due to
the increase of its length? The following table answers this ques-
tion. The column headed “ calculated resistance ” contains the
resistance as it ought to have been if its increase had been due only
to change of dimensions; —

Specific Gravity

Observed
resistance after
stretching.

Calculated

resistance.

Before stretching.

After stretching.

Wire I.

10-4784

10-5330

1-080

1-092

Wire II.

10-4967

10-5646

1-157

1*155

Wire III.

10-5051

10-5394

1-210

1-220

The agreement of the figures in the observed and calculated
columns is very close, notwithstanding the many sources of error
to which the experiments were liable, such as the change in

* See Wiedemann’s “ Galvanismus,” vol. i. p. 255.

t “Galvanismus,” vol. i. p. 310; “Neue Schweizerische Zeitschrift, ” vol.
xiv. (1855), p. 33.

83

of Edinburgh, Session 1875-76.

specific gravity produced by the rolling up of the wires, their
extension by weight between the first determination of specific
gravity and the first determination of resistance, the irregularity in
their cross section produced by stretching, and the slight contrac-
tion of the wires after the removal of the weights and before the
second determination of specific gravity,— all of which, however,
must have been exceedingly slight. It seems to warrant the state-
ment that if tension has any effect upon silver wires at all the effect
is exceedingly small. This differs from Mousson’s conclusion as
to steel, iron, and copper wires. He found that the increase in
their resistance produced by stretching was not fully accounted for
by the change of their dimensions.

In the course of the experiments I found that by raising a silver
wire, which had been stretched, to a red heat, its resistance was
very slightly diminished. A wire of about the dimensions of No.
III., which, after having been stretched by 6985 grms. had a re-
sistance of 1-8135, had, after being heated red hot, a resistance of
1-8103. This is again different from what Mousson has found to
be true of steel, iron, and copper wires, but it agrees with a deter-
mination made by Becquerel on silver wires.*

The following tables contain series of observations made for the
purpose of finding the relation between the stretching weight and
the total increase in the resistance of the silver wires used. In
these determinations, the constant resistance with which the resist-
ances of the stretched wires were compared was that of a silver
wire. Both wires were surrounded by a coating of steam. The
stretched wire, in order that, by its being kept at a high tempera-
ture, greater elongations might be produced by the same weights ;
the constant wire in order that thermo-electric effects might be
eliminated. The steam coating was formed by enclosing the wires
in glass tubes, and these tubes in a much larger tube, and conduct-
ing steam between them. In other respects the apparatus and
mode of procedure were quite the same as before. The observa-
tions were made when the appended weights had ceased to produce
any appreciable elongation, and with the steam coating half-an-
hour was generally found to be a sufficient length of time for the
production of the total stretching effect.

* “ Ann. de Chimie et de Physique” (3), xvii. 1846, p. 253.

M

VOL. IX.

84

Proceedings of the Royal Society

able I.

Weight

(grms.)

d

mm.

Resistance

(Constant Silver Wire
= unity).

500

102-0

•8315

750

99-8

•8348

1000

99-6

•8351

1250

98-8

*8363

1500

95-8

•8409

1750

91-4

•8477

2000

82-0

•8623

2250

63'0

•8925

Table II.

1285

60-6

•8963

1535

52-6

•9094

1785

426

•9260

2035

26‘6

•9531

2285

— *6

10011

2535

—42-2

1-0791

Table III.

873

4-2

•9924

1285

— 24-6

1-0453

1535

— 48-2

1 -0909

2035

—121-4

1-2459

Table IV.

1873

678-6

*2407

2873

676-8

•2419

3214

670-6

•2463*

4857

663-0

•2516

5171

659-6

•2540

5921

647-2

•2629

6490

635*0

•2717

6964

623-4

•2802

7650

600-8

•2971

8176

578-8

•3141

8307

567-0

•3233

8842

532-0

•3515

* This measurement is marked in my notes as “ inaccurate, owing to an
error of observation.”

85

of Edinburgh , Session 187 5-7 6.

It will be seen that the relation between appended weights and
thereby increased resistances is not that of simple proportion. In
this respect silver wires appear again to differ from copper wires.
Some experiments made by Messrs Meik and Murray * having
shown that the changes of resistance of copper wires, when
stretched by weights, are directly proportional to the weights.

I am deeply indebted to Professor Wiedemann of Leipzig, in
whose laboratory these experiments were performed, for the excel-
lent apparatus which he kindly placed at my disposal, and for the
advice and assistance with which he favoured me.

2. On the Defoliation of the Coniferse. By Dr Stark.

3. On Diamagnetic Rotation. By George Forbes, Esq.

M.A., F.R.A.S.

Faraday’s discovery of the magnetic rotatory polarisation of
light may be expressed in the following manner : — Let two electro-
magnets, in the form of iron tubes, surrounded by helices of wire, be
placed end to end, so that in the spaoe between them the lines of
force are very intense. Let a rod of dense glass be placed in this
space, so that a ray of light may pass through the two tubes and
the rod of glass. Let such a ray on entrance be plane-polarised,
so that the direction of vibration is in a vertical direction. If the
electro-magnet be now magnetised, the emergent ray will be
polarised, so that its vibrations are inclined to the vertical at a
small angle. The direction in which the line of vibration has been
rotated is the same as the direction of the positive current in the
helices.

The same effect might be produced without the aid of mag-
netism if the rod were rotated round the axis of the ray of light
with great velocity. The rotation of the plane of polarisation

* Proc. Roy. Soc. Edin., Session 1869-70, p. 3.

86

Proceedings of the Royal Society

would be the angle rotated whilst the light traverses the glass rod.
This is on the assumption that the ether within the rod is likewise
rotated. In the magnetic experiment it is easy to produce a
rotation of 1° in a piece of glass three inches long. Light takes
T.Tnrff, trmr, 777777 a seco,n6 to traverse this distance. Hence, to
produce an effect equal to the magnetic effect, the glass rod would
require to be rotated 10,000,000 times in a second. We cannot
determine with great precision the plane of polarisation of a ray of
light, hence we cannot measure any rotation of the plane of polari-
sation which might be thus produced.

In the same manner, if we suppose the molecules of glass and
the accompanying ether to be rotated round the lines of magnetic
force, and in the direction of the positive current producing the
given magnetic field, then the phenomena observed by Faraday
would be explained ; and we should be able to determine the
number of rotations per second induced in any specimen of glass
wiih a given intensity of magnetic field.

So soon as the electro-magnet is demagnetised, the rotation of
the molecules ceases. It seems, then, that there is a friction
among the molecules tending to stop the rotation. Hence we
should be led to conclude that the energy of the magnet is gradu-
ally used up by the presence of the piece of glass.

Assuming, then, that there is a friction among the molecules
of glass, it follows that when the electro-magnet is magnetised the
rod of glass has a tendency to turn bodily round an axis through
its centre of gravity parallel to the lines of force ; and if the rod
of glass were free it would turn round this axis.

In the winters 1872-3 and 1873-4, I made a number of
experiments to put this hypothesis to the test. The general idea
of the experiments was this. A rod of glass was suspended by a
fine skein of silk fibres between two poles of an electro-magnet,
one pole above, the other below. A small mirror was fixed on the
rod, and a lamp and scale arrangement was mounted for measuring
rotations. Readings were taken when there was no current, and
also in the two positions of the commutator.

The result of these experiments seems to be that there is an
effect of the kind anticipated. Sometimes, it is true, a deflection
was produced by a diamagnetic repulsion, owing to a want of

87

of Edinburgh , Session 1875-76.

absolute symmetry in the arrangements. This rotated the glass
rod slightly, and produced a little confusion. But beyond this
there was an undoubted effect, for the nature of the deflection was
found to depend upon the polarity of the two poles, the effect being
different according as the upper pole was a north or a south one.
I was sometimes able, simply by timing the reversals of the com-
mutator, to get up a very large rotation-swing, and by the same
means I was able to stop the rotation swinging.

I delayed the publication of these experiments with the view
of establishing more certain results. But much time has elapsed,
and I have still been unable to find time for this. Hence, I am
unwilling any longer to withhold their publication. I will now
give the experiments in detail, and will conclude by collecting the
general results.

Description of the Apparatus.

A rod of glass was suspended by a strand of silk fibres attached
to one end. This was supported on a stone imbedded in the wall
of the laboratory. The rest of the apparatus was on a separate
stand. A horse-shoe electro-magnet was placed so that the poles
were vertically over each other, and as nearly above and below the
axis of the glass rod as possible. Thus the axis of the glass rod
lay along the lines of magnetic force. The electro-magnet was
connected through a commutator with a battery of Grove cells.
Upon the glass rod was attached a small piece of silvered glass, by
means of which the light reflected from a paraffin lamp fell upon
a scale divided to millimetres. The distance of the scale from the
glass rod was about seven decimetres. The apparatus was arranged
so that the glass rod was suspended within a glass jar or bottle, to
get rid of currents of air.

During the session 1872-73 thick flint glass tubes were
employed for suspension, and an electro-magnet weighing about
6 lbs. After that a rod of Faraday’s heavy glass was used, and an
electro-magnet weighing about 50 lbs.

88

Proceedings of the Boyal Society

Details of Experiments.

The first experiments were made in 1873, March 28, and
they were continued regularly until April 16. The rod of flint-
glass was suspended in air, water, and oil. A rotation was nearly
always communicated to the rod when contact was made with the
electro-magnet. When the magnetism of the electro-magnet was
reversed I sometimes got a rotation in the opposite direction, and
sometimes a rotation in the same direction, but to a different
extent. The apparatus was repeatedly dismounted and set up
again with all the parts changed. The effects were generally
unaltered. In noting the experiments, I used the terms “no
contact,” “right contact,” and “left contact,” as being least liable
to lead to error. “ No contact ” means that the circuit was broken.
“ Right contact ” means that the lower pole of the electro-magnet
would, if free, point to the north. “ Left contact ” means that the
lower pole of the magnet would, if free, point to the south. When
the readings of the scale are increasing the glass is rotating in the
direction of the hands of a watch with the face upwards. The
glass was sometimes put into water or oil, and in this case also
rotation was generally observed.

The rotation oscillations in air were so great as to necessitate
reading the scale at the end of each half oscillation, and taking a
mean. In the following table each reading is a mean of many
observations : —

March 29. — Flint-Glass in Air.

No contact, .

245 scale reading.

Means.

Right „

155

L = 146,

Left „

146

R = 155.

No „ . ,

235

N = 240.

Flint-Glass in Water.

No contact, .

415

Right „

268

L =

248.

Left ,,

248

R -

268.

No „

410

N =

412.

89

of Edinburgh, Session 1875-76.

Flint-Glass in Oil.

Rio-ht and left contact each continued to diminish the scale

o

reading during twenty-two minutes. The change from left to
right contact diminished the readings with a jump. “ No con-
tact” again reversed the rotation.

Flint-Glass in Water.

No decided effect.

No contact,
Right „
Left ,,

Flint-Glass in Air.

370 scale reading.

523

478

370

Means.
N = 370.
L = 478.
R = 523.

The poles of the electro-magnet were now put so far to the east
of the glass as possible, and again as far to the west. The same
kind of results were obtained.

Oil was again used, and no certain effect was observed. March
31. — The apparatus, as left last day, with 'oil in the jar, showed no
effect. No effect was shown with air. But on trying a new rod of
flint-glass the old effects were observed. The oil seemed to have
destroyed the effect.

Flint-Glass in Air.

Right contact, steady rise from 400 to 543
No contact,

Left

Right

Left

No

Right

No

Left

V

558

567

546

556

540

531

529

533

in about 4 minutes.

R = 538.
N = 542.
L = 552.

No contact,
Right ,,
Left „
Right „
Left ,,

Half-an-hour interval.

522 x
512

523
497
519
508 )

R = 509.
N - 515.
L = 521.

VOL. IX.

N

90

Proceedings of the Royal Society

By keeping right contact for decreasing rotation- swing, and
left for increasing, the range of swing increased after 6 swings to
123 divisions. On reversing this action for 6 swings the range
was reduced to 12 divisions.

Note. — These are the most striking experiments. It will be
noted that here the “ right ” gives lower readings than the “ left ”
contact. But I cannot be sure that the commutator arrangements
had not been changed. Here all disturbing effects are done away
with, and the right and left contacts produce deflections on
opposite sides of the “ No contact ” reading.

No contact,
Right „
Left „

No

5)

Flint-Glass in Water.

„ . 541 scale reading. Means.

531 R = 531.

551 N = 541.

540 L = 551.

A new rod was now prepared, which also showed a very decided
difference between right and left contact, right being lowest.

Numerous experiments under various conditions were now tried,
but no new effects were discovered. It is desirable, however, to
record the following, which were made to be certain as to the
direction of rotation under different conditions of polarity : —

No contact, .......

850

Upper pole would point to north if free,

840

No contact, .......

848

Lower pole,

854

Upper pole,

835

Lower pole,

850

No contact, .......

845

The general result of the experiments of the winter is, that
when a 'pole tending to point to the north is above the glass rod , and a
pole tending to point to the south is below , the rod turns in the opposite
direction to the hands of a watch with the face upwards.

On placing the magnet with the poles in a horizontal plane,
rotations were sometimes observed. This is in direct contradiction
to the theory that led to these experiments. I can offer no
explanation, but merely record the fact.

In the session 1873-74 similar experiments were made with a

of Edinburgh, Session 1875-76.

91

piece of Faraday’s heavy glass. But in this case the glass was
inserted in a hole in a cork, to which also the mirror was attached.
On examining the cork it was found to be magnetic. This
accounted for all the phenomena observed.

But in the previous session this would not account for the
phenomena. There was no cork employed ; and experiments
made to test this by altering the position of the magnet showed
that there was no magnetism in the arrangement.

It was the doubt that hung over the last winter’s experiments
that made me wish to delay publishing any results until I should
have finally settled the matter. I have been unable to do so
hitherto, and offer the original experiments in the meantime.

Note on the preceding paper.

[The first statement is that a rotation of the plane of polarised
light might be produced by rotating a transparent body about the
ray as an axis.

It is improbable that no such effect would be produced, but that
the question is by no means a simple one may be seen by looking at
Sir W. Thomson’s paper on this subject (Proc. R. S. Bond., 1856).

I have also tried a great many hypotheses besides those which I
have published, and have been astonished at the way in which
conditions likely to produce rotation are exactly neutralised by
others not seen at first.

There can be no doubt, however, that a rotation of some kind is
going on in a diamagnetic medium under magnetic force, and this
may be of the molecules of the glass of the ether or what not,
and this probably goes on in all media whether transparent or not.

This rotation, as Prof. G-eorge Forbes says, stops as soon as the
magnetic force is removed. He supposes that it is stopped by
friction, and therefore, that energy is being dissipated at all
times as long as magnetic force acts on a medium.

But we know that a magnet will retain its magnetism for a long
time, and it has never been shown that a magnet must necessarily
lose its magnetism. Hence we must admit that the molecular
rotation is not accompanied with friction, but that it is set up by

92

Proceedings of the Royal Society

electro-motive force, and exerts electro-motive force when it is
stopped, like a rotating body having inertia.

(a) If the friction supposed by Prof. Forbes exists, it would act
as an accelerating force on the glass, so that if free it would rotate
faster and faster up to a certain great velocity, and if suspended by
a fibre, it would rotate till the moment of friction was balanced by
the moment of tortion of the fibre.

(J3) If there is no friction the only effects possible would be those
due, not to the maintenance, but to the starting and stopping of
the molecular rotation.

To investigate (a) experimentally we must observe the elongations
of the oscillation as follows : —

Make + ve observe three turning points A. B C, break for nearly
half a complete vibration. Make - ve observe three turning points
D E F, break again, and make +ve, and so on. Then the result is
obtained by taking

I S { A + 2 B + C-(D + 2 E + F) }
on

when n represents the number of repetitions of the series of six
observations.

To investigate (J3) experimentally we must make and break when
the mirror is passing the point of equilibrium.

In Prof. Forbes’s experiments there is a disturbing effect due to
the ordinary diamagnetic action of the electro-magnet on the tube,
which, if the tube is not perfectly symmetrised about the axis of the
fibre, will tend to produce rotation. This force, however, is the
same whether the current be + or — , provided the position of the
tube is the same. Hence, if the + and — currents are exactly equal,
it may be possible to distinguish this effect from the effect sought
by Prof. Forbes.

J. Clerk Maxwell,]

of Edinburgh, Session 1875-76.

93

4. On the Linear Differential Equation of the Second
Order. By Professor Tait.

( A bstract. )

This paper contains the substance of investigations made for the
most part many years ago, but recalled to me during last summer
by a question started by Sir W. Thomson, connected with Laplace’s
theory of the tides.

A comparison is instituted between the results of various pro-
cesses employed to reduce the general linear differential equation
•of the second order to a non-linear equation of the first order.
The relation between these equations seems to be most easily
shown by the following obvious process, which I lit upon while
seeking to integrate the reduced equation by finding how the
arbitrary constant ought to be involved in its integral.

Let u and v be any functions of x,

du dv
dx ^ dx
A u + Bv

u + Cv'
u + Cv

■ ■ (i),

where B and A, and therefore their ratio C, are arbitrary constants.
The elimination of C from (1) must of course give a differential
equation of the first order in £•

We have

_ u" + Cv" A/ + (V\2

* ~~ u + Cv \w + Cv/

Now we have, by adding and subtracting multiples of (1), &c.,
j., u + Pu + Qw + C(u -fPu+Qy) /u -\-Cvf ^

1 Alf+cL/- *

whence, if u and v are independent integrals of the equation

2/" + iy + Q</ = 0 (2),

we have the required equation

£'+£2+PM-Q=o

and the process above shows why it takes this particular form.

But (2) gives

y = A u -f* B#

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Proceedings of the Royal Society

as the complete integral, so we see that

i

y

y

=

Various classes of cases in which this form is integrable are
given, of which the following is one : —

Let $=rj J Q, then the equation becomes integrable in the form

7]

2 , ~ + fJQ — 0
>z + mrj + 1 ^

(3),

provided

Q'

p ^ + * 7W = m(^

i.e..

€-/Pdx

~jw

- mf€ '

fFdx c lx ,

The next subject treated is the effect of the alteration of sign
of P or Q in (2). This is illustrated by the equation

y" ±xy' ±y = 0,

which is integrable or at least reducible to quadratures for any of
the four combinations of sign.

The always integrable case where

P = (C-a>)Q

is next examined.

Another portion of the investigation deals with certain infinite but
convergent series, whose sums can always be expressed in terms of
the integral of a linear differential equation of the second order.
Consider, for instance, the expansion

€ X =

+ px +...•+■

1+V

X

+

+ . .

= 2 P nXn , suppose.

Obviously we have

Pn = p*P_n=^ +

From this at once

•)n+ 1

\n

+

P

n + 2

|1 n + 1 j2 \n 4- 2

= Pn _ i , whence Pra = (/ dp)n P(
dp

• (5)-

of Edinburgh, Session 1875-76.

95

Also

d /Pn\ Pn + l | ^ 1

TV\Y)=Y+'' whence v'~*

Yd

dp\pn / p

Eliminating Pw between (5) and (6), we obtain

\dpj

0 \dpj

Ip J

(6).

(7).

This equation is thus true for all positive integral values of n,
and its form at once shows that it is true for negative integral
values also. It is very singular that such a series of equations of
all orders should have a common solution. But it depends upon
the fact, which I do not recollect having seen in print, that

\dx ax/ \cLxJ \dxj

This can be verified at once by applying it to xm\ as can also the
companion formula

( d Y fd\* n

[x — x) = x>h — ) xn .

\ ax J \dx/

Suppose we had, instead of (5) and (6),

f/Q/i

d

dq

dq

( qnQn )

_ — Qn + 1

n— 1

Q» — ;

(51),

(61),

we should find the same equation (7) for Q0 as for P0. In fact, as
is easily seen,

Q, = P».

Other pairs which alike give the equation

K,

are

and

dr

dSn
ds

= R

n- f- 1

dr

d / Pn\ _ R» — 1

\ rn J ~ rn — 1

(71)

’ dr

d

— Sre_i , ^s(sn Sw) — sn+1 Sn+i .

We thus get the two distinct particular integrals of each of the
corresponding differential equations.

96

Proceedings of the Royal Society

More generally,

and

P n _ ( df Pn-i/

whence

\dpj pn~v ’

P = (1_Y pn(±Y
” v \dpj “ \dpj pn~v

Changing n - v to ra, this becomes

— m p

m
m i

which, when ra = 0, agrees with (7). Here n may have any posi-
tive integral value not less than m. When we write n~m we have
merely a truism. If we put n = m-f 1, we arrive at the same result
as we should have obtained directly from the first forms of the
equations (5) and (6). All these series satisfy differential equations
of the form

x

cPy
dx 2

= *•

Corresponding properties are easily proved for the series forming
the co-efficients of the various powers of x in the expansions of
expressions like

€^W + ^, €^ + ^\ &C, &C.

It is easily seen that what has been called P0 above is the
infinite series

po= ^ + 12^32 + • • • = f(p) • • (8)>

and that quite generally if

n

m

_l+_P _j__£

I "I MiOm i

pm 1 pm^pm

&C.

we have

“-(4)V(4W'"

n

m

whatever positive integer be represented by n. Of this the simplest
case is U1 = €p > where of course

of Edinburgh, Session 1875-76.

97

ni = ni •

Again, just as the solution of this equation has the property

cp _ cp + q

€ c — e ,

so it is easy to see that we have in (8)

Ap) /(?) = ZO+2)i

where the bracket over p + q is employed to indicate that in the
expansion we must square the numerical co-efficients of each term
of a power of this binomial, i.e .,

P + q = p + q ,

p + q2- p2 + q2-\- 2 2pq ,

p -f- <f = p3 + f -f- 32 ( p2q -f pq 2) ,

p + f = p4 + + 42 ( qpq + p$3) + 62p2^2 ,

&c., &c.,

and a similar property, though of course involving higher powers
of the co-efficients, holds for each of the functions ILm above.

For the product of any two similar expansions (with different
variables) is easily seen to have all its numerical co-efficients raised to
any given power when those of the separate expansions are so raised.

The paper contains also an account of various attempts to solve
the general equation of the second degree, of which the following
may be noted.

a. Transform to

S-x^=°’

and evaluate

JJ y tlx1

at once , just as

r^dx

J y ax

is evaluated.

The difficulty is reduced to finding the value of

where a sinyle operation is to be effected.

VOL. IX.

0

98

Proceedings of the Royal Society

b. Transform to

f +«2=X>

and express this by the help of an auxiliary operation in terms of
a merely artificial quantity z, so that

^ + £2 = e*s Z
ax

so that all equations of the kind considered can he reduced to
the very simple form

C$ + i2 = kcax

ax

If this were integrated, the only remaining difficulty would lie in
the separation of symbols from the quantities they operate upon.

5. On Two-dimensional Motion of mutually influencing Vortex-
columns, and on Two-dimensional Approximately Circular
Motion of a Liquid. By Sir W. Thomson.

Monday , Yitk January 1876.

The Bight Rev. Bishop COTTERILL, Vice-President,

in the Chair.

The following Communication was read : —

On the Origin of Language— Max -Muller, Whitney.

By Professor Blackie.

Professor Blackie stated that though the origin of language might
be considered by some more a metaphysical than a philological ques-
tion, it was yet so closely connected with philology, that whatever
opinions a philologer held on this question could not fail to exer-
cise a strong secret influence on his philological procedure. The
primary elements out of which language grew were admitted by all
to be three, viz., cries or interjectional exclamation, mimetic re-
production of audible sounds, technically but stupidly called onoma-
topoeia, and gesture. But while agreeing on this threefold basis
the most distinguished writers on this subject, such as Max-Miiller,
Wedgwood, Whitney, Bleek, Schleicher, and Steinthal, disagreed
fundamentally, or at least seemed to be at daggers drawing, with
regard to the course which language pursued in its further develop-

99

of Edinburgh, Session 1875-76.

ment. On the one hand, Muller, who had had a great influence in
guiding public opinion in this region, stoutly asserted that out of
the three primal elements, as from a root, no further growth of
what we called human language, for reasonable social purposes,
could take place; while, on the other hand, Wedgwood — who in
this whole matter had, in his opinion, received scant recognition
from the scholars of his own country — as stoutly maintained that
from these three elements, as their natural root, the whole organism
of the beautiful growth of language, stem, leaf, and fruit, could be
satisfactorily explained. After carefully studying the arguments
of the learned Oxford Professor, he was of opinion that Wedgwood
was in the main right. To this conclusion he came from a course
of independent investigation some years ago, and when, curiously
enough, he had only used Wedgwood’s dictionary for occasional
consultation, without having read and pondered the discourse prefixed
to the last edition of that work. The grounds of his opposition to
Muller were stated to be simply these : — While in perfect agree-
ment with him that roots significant of ideas are the ultimate facts
in the analysis of languages as we now have them, and believing
also that such conceptional roots are the natural and necessary ex-
pression of reason in a reasoning animal, and explicable only on the
supposition of an indwelling plastic reason in man, I am at the
same time unable to see why this plastic reason in the formative
process of language-making should not have used the materials so
amply supplied by the interjectional and mimetic elements of the
simplest germs of speech. The interjectional element, I call the
principle of significant vocal response ; and the onomatopoetic prin-
ciple, I call the mimetic, dramatic, or pictorial element in language;
and I am prepared to show that, even under the many defacements
and obliterations which spoken words, like old sixpences or wave-
worn pebbles, suffer from the tear and wear of time, they yet show
in hundreds of cases on their face the manifest superscription of
their mimetic origin. For we must take note, first, that not only
pigs and cuckoos, cats, curs, and crows, but all nature, is full of
sounds, and that there is no absolute silence anywhere but in death ;
and, further, that not only an immense variety of sounds can be
approximately expressed by imitation in articulated vocal breath,
but that by an easy transference the impressions of the other senses
can be analogically expressed in the flexible material of significant

100 Proceedings of the Royal Society

sound. It is also not only an easy but a natural and necessary pro-
cess of the human mind in the formation of general concepts to use
the material presented by mere sensuous impressions ; and thus,
while we expressly deny the perverse doctrine of the sensationists
that mind can be explained from sense, or the imperial unity of
thought be generated from a multiplicity of external impressions,
we can see no difficulty in deriving such general concepts as char-
acter and type , for instance, from the roots \apao-croi and TuVrco,
which originally were mere mimetic reproductions of an external
sound, as in our word scratch. Language, therefore, was formed by
the gradual extension of words originally expressing sensations and
feelings to intellectual purposes ; and there is nothing ignoble in
this, for the mind uses the materials supplied by sense just as the
architect uses the stones dug by the quarryman or the lime carried
by the hodman. Neither can one at all see the logical justice of
Max-Miiller when he exposes the historical falsehood of some of
Wedgwood’s onomatopoetic etymologies; for the erroneous applica-
tion of a principle does not in the least imply that the principle
itself is erroneous; and, besides, the oldest roots to which certain
very recent forms of Komanesque words may be traced back in
Sanscrit can be shown in not a few cases to have been the product
of that very mimetic process which Muller so persistently ignores.
But while Muller seems actuated by some strange prejudice in his
stout determination to make no use of the onomatopoetic element so
thickly strewn in language, Professor Whitney has introduced no
little confusion into this matter by talking of language as an insti-
tution, and reviving the doctrine of the old Greek Sophists, that
language is tfeVei, not cret. Every simile limps; but if we must
have similes, it is far nearer the truth to talk of language as a
growth and a living organism than to call it an institution. In
some sense language is certainly a growth ; in no sense is it an in-
stitution. Institutions like the Sabbath, for instance, are then
creatures of positive law ; but language is a direct efflux of plastic
reason, and no more an institution than the song of the nightingale
or a sonata of Beethoven. As to the connection between Darwinism
and the origin of language, while the Darwinian philologers, with
Schleicher at their head, will no doubt find a special delight in
tracing the splendid roll of a Platonic period from the grumph of

101

of Edinburgh, Sessio7i 1875-70.

the primeval pig, and the mew of the pre-Adamitie kitten, those
who with me look on Darwinism as a mere pleasant conceit of men
besotted in the one-sided study of physical science, can, so far as
philological conclusions are concerned, leave the conceit to shift for
itself, being firmly convinced that whenever reason does show itself
whether on the original appearance of man or at some after-stage
of his development, it appears as a force altogether different from,
and in some of its functions, as Professor Ferrier wisely maintained,
essentially contradictory of, and antagonistic to, every kind and
degree of mere sensation ; and in this character brings forth lan-
guage as the natural manifestation and organised body of itself.

Monday , 1th February 1876.

Sir WILLIAM THOMSON, President, in the Chair.

The following Communications were read : —

1. Note on Certain Formulae in the Calculus of Operations.
By Professor Stokes, Hon. F.R.S.E. (In a letter to Pro-
fessor Tait.)

“ January lith, 1876.

“Formulae like those you sent me* are readily suggested by
supposing the function operated on to be of the form %Axa, or say,
for shortness, *«, with the understanding that no transformations
are to be made which are not equally valid for 2Ar«.

Thus

fdL%dL\xa = a2(a— l)2 . . . (a — n -f Y)‘1xa~ n
\dx ax)

= a (a — 1) . . . (a — n + 1)^-^^ xu

-(s)v(a)v‘

and

(x x^ xa = (a+ l)(a + 2) . . . (a + n)xa + n

= (a + ii)(a -j- n — 1) . . . (a+l)<rft‘*‘”

nf d \ n n a
= X ( -~ ) X X .

\dxj

See ante , p. 95.

102

Proceedings of the Royal Society

The direct transformation may readily be effected by noticing,
in the first instance, that any two operations of the form

x-m+iAxm

dx

are convertible. We find, in fact,
d

dx ' dx

x

-m+lfcc . x~n+1 i Xn = xi

(S2+(m+n+1)4+nm>

into which m and n enter symmetrically.

Replacing the operations in the left hand member of the first
formula by convertible operations, which will be separated by
points, we find

d d

-i

d

d

7 J ^ X 7 • X i )

dx dx dx dx

d d - 1 _2 2 d _i 2 d _i

~r x~r x — x 7-a; . x — x

dx dx dx dx

and so on. Hence,

f f\n _ r~n( rn f r- n + !

dx x dx) \ dx

x«-\ d x-n+2 V
dx J

Again,

nLn-

\ dx

x

X

-n + 1 . n-lA «-n + 2

t *J 7 it/

dx

= x

— n

n ( d Y ) 2 ( d\n n ( d\l

Ms)

<fa) (

<ir/

X X = X X ~r X ,

dx dx ’

^ o 2 -1^2

tAs f t b “ tv A d/ 7 JO a

dx dx ’

and so on. Hence

dx

x — aS* - xn x r~n+l — rn r~n + 2 — r*-1

cA/ 7 w/ | w A iA/ -j i/y * lA/ -i <As

dx dx

d

1 ^ o

— X ' X -r- x . a? —

6/

d ) 2

X J-
dx

r-

a;

dx

dx

dx

r - n + 1 —

W • • • tv ^ IV j

= x

d \n
dx

n >»

of Edinburgh, Session 1875-76.

103

2. A Further Contribution to the Placentation of the Cetacea
( Monodon Monoceros). By Professor Turner.

In the year 1871, I read before this Society a memoir on the
Gravid Uterus of Orca gladiator , in which I discussed the placenta-
tion of the Cetacea. This memoir was published in the Transac-
tions for that year. On the present occasion I purpose describing
the placenta in a Cetacean genus in which it has not hitherto been
examined.

In the month of December 1875 I received, through the inter-
mediation of my friend Mr C. W. Peach, from Mr John
Maclauchlan, the chief Librarian and Curator to the Free Library,
Dundee, a cask containing the gravid uterus of a Narwhal (. Monodon
Monoceros ), which had been procured by the captain of the Dundee
whaling steamer “Erik.” The uterus had been preserved in strong
brine, and was in good condition for anatomical examination.

The uterus was two-horned, and contained a foetus 5 feet 5 inches
long in the left cornu. The gravid horn measured 7 feet 4 inches
along its great curvature ; the non-gravid, 4 feet. The girth of the
gravid horn, at its thickest part, was 4 feet 4 inches. The length
of the corpus uteri was 1 foot ; that of the vagina, 1 foot 8 inches.
The os was occluded by an extremely viscid mucus.

The uterine cornua were opened into by a longitudinal incision
along the greater curvatures. The uterine wall was comparatively
thin, and the chorion was closely adherent to its mucous lining.
By an incision through the chorion, along the greater curvature of
the gravid horn, the sac of the amnion was opened into and the foetus
exposed. The foetus lay with its back in relation to the greater
curvature of the cornu, its belly to the lesser curvature, its head
close to the corpus uteri; whilst its caudal end was directed to the
narrow end of the horn, but did not reach to within two feet of the
Fallopian tube. The tail was curved forwards under the hinder
part of the ventral surface of the foetus. The pectoral flipper was
directed backwards parallel to the long axis of the body. The
umbilical cord was 3 feet long, spirally twisted, and bifurcating
where it reached the sac of the allantois. The amnion formed an
immense bag, which reached to 5 inches from the free end of the
gravid horn of the chorion, but it did not extend into that part of

104 Proceedings of the Royal Society

the chorion which occupied the non-gravid horn. The amnion
was closely adherent to the greater part of the chorion in the
gravid cornu ; but that portion of the chorion which was attached
to the mucosa lining the lesser curvature of the cornu, and which
lay opposite the abdominal aspect of the foetus, was in relation
to the wall of the sac of the allantois. The allantois formed a
large funnel-shaped bag at the place of bifurcation of the cord.
It was prolonged along the concavity of the chorion to within 2
inches of its free end in the gravid horn, and to within 9 inches of
the free end of the prolongation of the chorion into the non-gravid
horn. The length of the sac of the allantois was therefore much
greater than that of the amnion, though its capacity was much
less. The allantois was prolonged as a slender tubular urachus
into the umbilical cord, which also contained two large arteries and
two veins. The amnion investing the cord had numerous brownish
corpuscles, resembling those I have described in Orca gladiator ,
projecting from it ; and similar corpuscles were scattered over that
part of the amnion which was in apposition with the wall of the
sac of the allantois, and a few were seen on the amnion beyond the
border of the allantois. In addition to these brown corpuscles,
numerous other bodies of a dull white appearance were found.
Sometimes these were slender rods, from j^th to j^-th inch long,
arranged end to end like the links of a chain, at other times they
were globular, like minute shot. The rods were most numerous
on the abdominal half of the cord, whilst the globules were most
numerous at and near its bifurcation. The surface of the amnion
adjacent to the cord had a few of these globules scattered over it.
These white bodies were covered by the smooth amnion, which with
a little care could be stripped off as a distinct pellucid membrane.
They consisted of crowds of squamous epithelial cells, so that in
structure they resembled the whitish bodies which are so
abundantly developed in connection with the amnion of the cow.
Between 3 and 4 inches of the abdominal end of the cord was
covered with cuticle, which had the purplish-grey colour of the
cuticular investment of the adjacent surface of the wall of the
belly.

The two uterine cornua became continuous with each other
through the corpus uteri, and were partially separated by an

of Edinburgh, Session 1875-76.

105

imperfect septum, which projected from the inferior wall. Owing
to the great distension of the left cornu, this septum was pushed to
the right, so that the os uteri opened directly into only the gravid
horn. The chorion extended from the end of the gravid to that of
the non-gravid cornu. As it passed through the corpus uteri it
was somewhat constricted by the projecting septum. In the whole
length of the non-gravid horn, and at the free end of the gravid
horn, the chorion was raised into strong longitudinal folds, which
corresponded in reverse order with a similar series of folds of the
uterine mucosa radiating from the orifices of the Fallopian tube.
At the os uteri the mucosa was raised into strong folds, which radi-
ated into the gravid chorion for a considerable distance, and in some
parts of their extent projected as much as 3 inches from the general
plane of the mucosa, though at the os they had not more than one
half that projection. The chorion in apposition with this part of
the mucosa was also folded. In the gravid horn opposite the
foetus, where the expansion both ot chorion and uterus was the
greatest, the folds were not present. Except in a few localities, to
be immediately specified, the whole of the extensive surface of the
chorion was so covered with vascular villi that, to the naked eye at
least, no non-villous intervals could be recognised. The chorion
was adherent to the uterine mucosa, so that gentle traction was
needed to draw them asunder; and, as the one was peeled off
the other, the villi of the chorion were seen to be drawn out of
multitudes of crypts opening on the free surface of the mucosa.

The chorion, which lay opposite the os uteri and the immediately
surrounding mucous membrane, was for the most part not villous,
but presented a smooth, feebly vascular appearance, which con-
trasted strongly with the adjacent villous chorion. This smooth
spot was irregular in form, measured 6 inches by 4 inches, and
from it narrow bands of smooth chorion radiated outwards for
from 2 to 3 inches between the villous covered folds of the chorion.
It was similar to, but much larger, than the corresponding spot in
Orca and the Mare. Small isolated patches of villi were scattered
irregularly over the surface of this smooth spot. The inner surface
of the chorion at the bare patch was lined by the amnion and not
by the allantois. Three inches from this large spot a bare patch,
1 inch by inch, was completely surrounded by villous chorion,

VOL. IX.

P

106 Proceedings of the Royal Society

The uterine mucosa opposite these smooth portions of the chorion
was smooth and free from crypts, except where the isolated patches
of villi were in apposition with it. Eadiating for about 1 inch
from the pole of the chorion in the gravid horn were narrow non-
villous bands of the chorion separated by intermediate villous
surfaces. These hands corresponded to folds of the mucosa free
from crypts, which radiated from the orifice of the Fallopian
tube, and were continuous with the longitudinal folds of mucosa
in that tube. In the non-gravid horn the chorion was devoid of
villi for about 5 inches from its free end, and for even a greater
distance the villi were irregularly scattered so that well-defined
smooth patches could be traced as far as 10 or 12 inches from the
pole. On some parts of the chorion pedunculated hydatid dilata-
tions of the villi, about the size of small peas, were irregularly
scattered.

When examined microscopically, the villi were seen to be
arranged in tufts, which varied in size and in the number of villi.
Some tufts had not more than two or three villi, but more usually
numbers were collected together, though occasionally short single
villi arosefrom the chorion in the intervals between the tufts. The
villi had as a rule a club-shaped form, but some divided into fili-
form branches. They were highly vascular, and a beautiful extra-
villous layer of capillaries was distibuted, as in Orca, beneath the
free surface of the chorion.

The free surface ofthe uterine mucosa had, as in Orca, a delicate
reticulated appearance, and was pitted with multitudes of recesses
and furrows, which again were subdivided into innumerable crypts.
In the polar regions of the cornua and in the corpus uteri the
mucosa was more spongy and succulent than in the greatly dis-
tended part of the gravid horn, in which the mucosa was obviously
more stretched, so that the pits and furrows were almost obliterated,
and the crypts opened on the general plane of the mucosa. In
their general arrangement, and in the vascularity of their walls, the
crypts in the Narwhal resembled so closely the corresponding
structures in Orca, that I need not give a special description. The
layer of cells which lined them was a well-defined cylindrical
epithelium, many of the cells of which, however, were so swollen
that the breadth almost equalled the length.

of Edinburgh , Session 1875-76. 107

Scattered over the surface of the mucosa in the more distended
part of the cornu were numerous smooth, depressed, circular or
ovoid spots, the largest of which was not more than ~th inch in
diameter, though as a rule they were less than -j^th inch; so that to
the naked eye they were apt to escape observation. Each spot was
surrounded by a minute fold of the mucosa, sub-divided into crypts.
On an average from twenty-five to thirty of these spots were found in
each square inch. They resembled the smooth depressed spots de-
scribed by myself* and some other anatomists in the uterine mucosa
of the gravid pig. On the surface of the chorion adapted to this part
of the mucosa, occasional smooth patches from -Ayth to-^th inch in
diameter were seen surrounded by villous tufts which were in
apposition with the smooth depressed spots on the mucosa, but
they had not the definite stellate form which one sees on the
chorion of the pig. The extra-villous layer of capillaries ramified
beneath these non-villous spots of the chorion. In the succulent
parts of the mucosa the smooth depressed spots could not be seen
with the naked eye, but only after a careful search with a pocket
lens were they found at the bottom of some of the trenches or pits
in the membrane.

From the general resemblance between these spots and those
met with in the uterine mucosa of the pig, one was naturally
inclined to think that they, would have a relation to the mouths of
the utricular glands. I proceeded, therefore, to examine the glan-
dular layer of the mucosa. The glands were very numerous, and
branched repeatedly. Many of the branches formed short diver-
ticula, others were much longer; sometimes they were tortuous, at
others a considerable length of straight gland tube could be seen.
In the deeper part of the mucosa the glands lay almost parallel to
the surface; but as they approached the crypts, they were directed
more obliquely, so as to be frequently divided in vertical sections.
The glands were subjacent not only to the crypts, but to the smooth
depressed spots, numerous examples of which I carefully examined.
In one instance, I saw a tube lined by epithelium lying obliquely
beneath the membrane of a spot, and opening near the middle by a
distinct orifice bounded by a crescentic fold of the membrane. In

* “Journal of Anatomy and Physiology,” Oct. 1875. Also Lectures on the
Comparative Anatomy of the Placenta, Edinburgh, 1876.

108 Proceedings of the Iloyal Society

a second instance, the end of a gland passed from under cover of
the surrounding crypts, and then seemed to open by an obliquely
directed mouth near the free edge of the spot. But upwards of thirty
other spots examined with equal care gave me no evidence of gland
mouths opening on them. Hence it would appear that these smooth
surfaces on the mucosa are by no means necessarily associated with
the mouths of the utricular glands, and one is disposed to conclude
that the gland orifices are usually concealed amongst the crypt-like
foldings of the mucosa. The very much greater number of the crypts
than of the stems of the glands, negatives the idea of the crypts
being merely dilatations of the mouths of the glands, so that in the
Narwhal, as in Orca, the Pig, and Mare, the crypts are to be
regarded as interglandular in position and produced by a hypertrophy
and folding of the mucosa.

Through the kindness of my friend Dr Allen Thomson, I have
had the opportunity of examining a portion of the gravid uterus
and chorion of a Narwhal, the foetus in which measured only 3J
inches long. The free surface of the mucosa was gently undulating
and traversed by shallow furrows, but no definite crypts could be
seen. The gland-tubes were remarkably numerous, tortuous, and
branching. I made a comparative measurement of their size, with
that of the glands in my much more developed specimen, and found
them to have only one-half the transverse diameter. The gland-
stems inclined obliquely to the surface of the mucosa on which
their orifices could occasionally be seen. The free surface of the
chorion was not villous, but traversed by faint ridges, which without
doubt fitted into the shallow furrows of the mucosa. Patches of
epithelium-cells could be seen covering the surface of the chorion.
It is clear therefore that in the Narwhal, as I have elsewhere de-
scribed in the pig, the villi do not form on the surface of the chorion,
nor the crypts on the surface of the mucosa, until the embryo has
reached a stage of development in which its body, though small,
has assumed a form which enables its ordinal characters to he
recognised.

When I published my memoir on the placentation of Orca, I
was under the impression that the crypts were lined by a pavement
epithelium, and was not disposed to regard the crypts in the
mucosa of that cetacean as secreting organs; but a re-examination

of Edinburgh , Session 1875-76.

109

of the epithelium-cells lining its crypts has convinced me, that
they are not a pavement epithelium, in the sense of being
squamous cells, but have an intermediate or transitional form
between the columnar epithelium and the tesselated epithelium.
In the Narwhal, again, the cells are cylindrical, as in so many
mammals, so that I believe the Cetacea to offer no exception to
the view that these cells are a secreting epithelium, and they
doubtless elaborate a secretion for the nourishment of the foetus.
From the fact that the utricular glands had a much greater
calibre in my specimen than in the one belonging to Dr Thomson,
one may infer that even after the crypts are fully developed the
glands still play a part in foetal nutrition.

The foetus in my specimen had an almost uniformly purplish-grey
colour, but with a patch of yellowish-white on the belly near the
anus. The snout was rounded; the fissure of the mouth 1J inch
long; eye-slit inches behind the snout, and surrounded by a
faint circle; ear orifice very minute, 3 inches behind the eye-slit;
blow holes above and a little anterior to eye slit. Length of
flipper 7 inches, its anterior edge 12 inches behind the snout.
Funis was attached to the belly about midway between the
anterior and posterior end of the foetus. A low, but distinct dorsal
ridge, the rudiment of a dorsal fin, commenced a little in front of
a point midway between tip of snout and end of tail, and ex-
tended backwards for between 10 and 11 inches along the middle
line of back. It had a lighter greyish tint than the surrounding
skin. Breadth of tail was 15J inches. In a profile view of the
foetus a slight depression in the contour of the top of the head
was seen in the region of the blow-holes. The foetus in utero
differed therefore very materially in colour from such a half-grown
specimen as Dr Fleming described*, in wdiich the upper part of
the body was a dusky black, the belly white, and numerous oblong-
spots extended horizontally along the sides ; still more did it
differ from old specimens, which have a whitish marbled colour.
The presence of a dorsal ridge is also of interest, as the Narwhal
is described as without a dorsal fin.

I availed myself of the opportunity of examining the dentition
of the foetus. On May 20th, 1872, I described to the Society the
* Memoirs Wernerian Socy., 1811.

110 Proceedings of the Royal Society

dentition of a foetal Narwhal 7J inches long, in which I found two
dental papillae developed in the gum, on each side of the upper,
jaw, but the early stage of development of the foetus did not
permit me to say whether the anterior or posterior denticle would
have been the one to become the maxillary tusk, though I thought
it probable that the more anterior would become the tusk.

In this much larger foetus the superior maxilla was 8| inches
long. At the anterior end of each of these bones were two well
marked sockets, one opening immediately behind the other. The
anterior socket contained a cylindriform rudimentary tusk. The
posterior socket contained an aborted tooth J inch long, and
inch in its widest diameter. The hinder half of the aborted tooth
was attenuated, and had several short irregular processes projecting
from it ; the anterior half was smooth and rounded. This tooth
was inclosed in a distinct sac, formed of fibrous tissue, which, like
the sac of the rudimentary tusk, was firmly united to the fibrous
tissue of the gum. There can be no doubt, therefore, that I was
right in my conjecture that the more anterior dental papilla
becomes the tusk of the Narwhal.

3. Observations on the Zodiacal Light. By C. Michie Smith.
Communicated by Professor Tait.

While engaged in cable work in the West Indies, I had, during
the winter and early spring of 1875, a number of very favourable
opportunities of examining the zodiacal light,

Before leaving this country I had, under the advice of Professor
Tait, and with a note of recommendation from Professor Jen kin,
applied to the Royal Society for the loan of a spectroscope, to make
observations with during the voyage ; but unfortunately I was
unable to obtain one, and so had to content myself with a small
pocket-spectroscope. On the outward voyage I did not notice the
light at all till we got well to the south, near Cayenne, on the 8th
of January ; and, owing to the very bad weather we had about that
time, I was not able to make any satisfactory observations till we
were again somewhat farther north. The general appearance of
the zodiacal light has been so often described, more or less faith-
fully, that I need not attempt any description of it here. I wish,

Ill

of Edinburgh , Session 1875-76.

however, to mention one feature with which I was much struck,
and which I have never seen remarked on — namely, that, on
watching the western sky from sunset onwards, it is impossible to
tell when the diffused sunlight ends and the zodiacal light begins
till it becomes so dark that the form of the latter can be traced to
a considerable altitude, when it is seen to be longer and narrower,
and inclined to the vertical at a considerable angle. I am strongly
inclined to believe that near the sun it is very much wider than at
some distance from it, for I have very good reason to think that
what by people generally would be taken as simply the last of the
sunset glow is really due to the zodiacal light. This part, of
course, can only be seen in places where the twilight is very short.
The best time for making observations I found to be about two
hours after sunset, when all traces of twilight had certainly dis-
appeared, and consequently all risk of confusion with it was gone.

On January 31st, in lat. 8°N., long. 56° W., the light was very
bright, and I made some spectroscopic observations. At two hours
after sunset the light was visible for 90° from the horizon, and so
bright was it towards the horizon that I was able to get a distinct
spectrum. I first opened the slit very wide, when I observed a
broad strip of light, nebulous at the extremities, with a distinct
reddish tinge at the one end ; then, by gradually closing the slit,
I obtained a narrower but tolerably pure continuous spectrum, in
which I could distinctly see reddish, orange, and greenish-blue, and
on making comparison with the spectrum of a lamp (placed at the
far end of the ship so as not to dazzle my eyes), I estimated that
the spectrum extended from the red to past the position occupied
by the F line in the solar spectrum. A large number of observa-
tions taken on other nights, whenever the circumstances were
favourable, entirely confirmed these first observations. On several
nights, and especially on February 27th, when off Ponce, in the
Island of Puerto Eico, I observed the spectrum from a short time
after sunset till long after the last traces of twilight had dis-
appeared, hut no change was noticeable after the spectrum had
become so faint that the Fraunhofer lines could not be distin-
guished, except in the brightness of the spectrum, as I was still
able to see colour distinctly, but no traces of any bright lines.

On February 26th and 27th I took a number of sextant measure-

112

Proceedings of the Royal Society

ments of the zodiacal light. These are, of course, only approxi-
mate, as the light has no definite boundary-lines, but gradually
fades off at the borders. The measurements were made by the
help of stars, as it was quite impossible to measure the light itself.
On the 26th sunset was at about six o’clock, the light was very
bright for 30° from the horizon, having at the horizon a breadth
of about 25°, and at an altitude of 30° a breadth of about 20°. At

9 p.m. the light could be traced quite round to the eastern horizon,
a phenomenon which I observed on several other occasions. At

10 p.m. the light was scarcely, if at all, visible. That this sudden
disappearance was not caused by any change in the atmospheric
conditions was clearly shown by the undiminished brightness of
the stars. On February 27th the breadth at the horizon was 30°,
while at an altitude of 30° it was only about 20°. The centre of
the band passed a little to the south of the Pleiades. I endeavoured,
by means of the sextant, to measure the inclination of the band to
the vertical. For this purpose I chose two bright stars near the
centre of the band — one at a considerable altitude, the other close
to the horizon ; I then measured the angle between these and the
angle between the upper one and the horizon ; these angles were
respectively 55° 30' and 51°, giving the value of 31° 30' for the
inclination of the centre of the band to the vertical. I had un-
fortunately no access to star-charts, else I could have fixed the
direction more accurately ; but even these rough observations con-
firm the ordinary statement that the direction is slightly inclined
to the ecliptic.

The spectroscope used was one of Mr Ladd’s admirable small
direct-vision spectroscopes, with five prisms and a single lens.
Behind the slit is a small round hole, through which the light may
be made to enter by opening the slit very wide, and which is very
convenient for examining monochromatic light. With this in-
strument it is easy to see a number of the Fraunhofer lines on a
tolerably clear moonlight night. And such an instrument, though
in some respects inferior to a simple large prism and slit, will, I
believe, be found very suitable for work such as that described
above, especially when it has to be carried on on board a ship
much given to rolling.

of Edinburgh, Session 1875-76.

113

4. Note on the Volcanoes of the Hawaiian Islands. By J. W.
Nichol, F.RA.S. Communicated by Professor Tait.

The late Transit of Venus Expedition gave the writer some
opportunities of visiting several islands of the Hawaiian Archi-
pelago, some details of which may prove interesting.

They form a group of islands about 10J hours west longitude
from Greenwich, and about 20° to 22° north of the equator, and
differ in size from 10 miles long by 6 or 7 broad, to 90 miles by GO,
which are about the dimensions of the most easterly and largest,
viz., Hawaii (the Owyhee of Cook). The general lie of the islands
is from north-west to south-east, those in the east displaying the
most recent traces of volcanic activity. In the older or western
portion the main mountain ranges run in the same direction as the
islands, rising in many places to a height of 3000 to 4000 feet, and
having lateral ridges branching off at right angles, with an occa-
sional crater of oval shape thrown up at a distance from them, and
evidently of more recent origin.

The putting up of a meridian mark on one of these ridges in
the island of Oahu was attended with some difficulty, the narrow
space along which one had to ride, sometimes not more than a yard
or two wide, with precipitous descents of 500 to 1000 feet on
either side, not rendering it comfortable to any one with weak
nerves.

The two most easterly islands, viz., Maui and Hawaii, although
having their greatest length in the north-east and south-west
directions, are composed only of mountains standing singly, and
present no appearance of ranges. Maui, indeed, is nothing more
than a couple of mountains joined by a very low neck of land, on
the top of the eastermost of which (Mount Haleakala), at a height
of 11,000 feet, is found one of the largest and most perfect extinct
craters in the world, being some 10 miles in diameter, which unfor-
tunately time would not admit of our visiting. The sides of
Haleakala are not precipitous, and the general view from the sea is
that of a huge hog-backed mountain. Traces of flows of lava so
recent as to be quite black, and not covered with vegetation, are
also seen coming down from what had been openings in its sides a
short distance above the sea-level.

VOL. IX.

Q

114 Proceedings of the Royal Society

The island of Hawaii, or the most recent and easterly, is composed
of four mountains — the Mauna Kea, 14,500; Mauna Loa, 13,800,
Huallalei, 8000, and Kohala, about 5000 feet in height, with large
valleys of 2000, 3000, to 6000 feet above the sea-level between.
The slope of the mountains is usually gentle, and numerous small
craters of 100 to 300 feet in height are found distributed on their
sides, and also in the intermediate valleys. On the west side pre-
cipitous rocks face the sea, with a height of 3000 feet, which have
valleys opening seawards that are almost inaccessible from the land
side, owing to the precipitous character of their sides. It is on
this island that the most recent displays of volcanic activity are
seen, the country having been overrun in many places by lava
flows, which have left large tracks quite useless for agricultural
purposes. Earthquakes are common, and the summit crater of
Mauna Loa, 13,800 feet up, is frequently, and that of Killauea (on a
level plateau on the side of Mauna Loa, about 3000 feet above the
sea) is almost always in a state of activity. The crater of
Killauea is on the north-east of Hawaii, about 32 miles from the
bay of Hilo, which is the most convenient starting-point for those
wishing to visit the volcano. In the ride of 32 miles one has
an ascent of some 3000 feet, but the ups and downs are so numerous
that one can hardly detect it. During some portion of the way
one passes through very dense tropical vegetation, palms, tree
ferns, &c., with creepers and ferns clustering around, but for the
most part the path lies over lava flows, so recent as to be almost
devoid of vegetation, which render it so rugged as to compel one
to walk his horse the greater part of the way. When approaching
the volcano the visitor is at first struck by the sight of hundreds of
steam jets rushing up in all directions, some of which are utilised
as vapour baths, by putting a wooden box over them with a hole
in the top large enough to admit the neck of the bather. On going
some hundred yards further, an immense pit appears, at the further
end of which during the day are seen large volumes of smoke,
while at night a red flare is visible in the sky, with an occasional
piece of white hot lava getting tossed up high enough to be seen
above the edge of the inner crater. This large pit or outer crater
is of oval shape, and some 3 miles long by 1^ to mile broad in
the widest part. The sides are precipitous, and from 600 to 700

115

of Edinburgh, Session 1875-76.

feet in height, being in many places divided into close parallel
ridges, showing the height to which the lava had reached before
breaking out at a lower level. There were two large sulphur beds
at the side of the outer crater, about 2 miles distant from each
other, and pieces of native sulphur could be picked up, each with
a hole in its centre, showing that the vapour had solidified round
the hole from which it had emerged. The floor of the outer crater
was composed of black lava, several acres of wdiich were covered
over one night by the lava breaking out at a side of the lowermost
edge of the outer crater, quite distant from the inner one.

Our first descent was made at night by means of some rustic
staircases cut in the sides of the ridges, and assisted by whatever
brushwood might be growing on the sides. At last our party
were landed on a floor of black lava, all seamed with cracks and
contorted into curious shapes, sometimes like a mass of cable ropes
mingled together, at others showing large pudding-like excrescences,
which are dangerous to walk upon, since they are simply large
bubbles with a thin covering, to guard against which each visitor
carries a thick stick wherewith to test the ground before him.

After walking for about half an hour on this black lava, and
crossing innumerable cracks of from three inches to a foot in width,
some of which showed a white line of fire about 6 feet beneath, the
gradual ascent to the inner crater was reached. Its position in
regard to the general form of the outer crater may be said to be in
one of its foci, and its size, by estimation, about a ^ mile long by J
broad. The increasing glare and smoke now warned us of our
proximity to the more active parts, while here and there on the
outer side of the inner crater were some bright red streaks, which,
on our closer approach, turned out to be red hot lava flowing through
holes in the outer side of the inner crater on to the general surface
of the outer one.

The ascent of some 70 feet to the top of the inner crater is a
gradual one, and considerable detours bad to be taken to get round
the parts which were being overflowed. The lava of its sides was
twisted about and broken up in a most ugly manner, besides being
so rotten as to break away in flakes whenever a foot was put upon
it. The greatest caution was needed to test the ground before
treading on it, and frequent play had to be made wdth our thick

116

Proceedings of the Royal Society

sticks. Tumbles were frequent, from which the writer escaped
unharmed by having a thick pair of dogskin gloves on his hands.
One of our party, however, a professor from Indiana, managed to
fall into a crack up to his middle, and got his hands severely cut
and burnt.

The view from the top, however, amply repaid the trouble.
Four lakes of molten lava, the largest some 200 yards in length,
and of kidney shape, and the others of smaller size, were seen in
full activity. In the largest lake seven to eight fountains of white
hot lava were playing up at once to a height of 30 to 40 feet, one
sometimes stopping and another commencing at a different part of
the side of the lake.

The lava in this lake was about 50 feet below the inner edge of
the crater, and appeared to be slowly advancing toward the tunnels
from which we had seen it issuing on the road up. The lakes were
not at the same level, and you might see one brimful and another
60 to 70 yaids off at a level of some 30 or 40 feet below it. On
another of the lakes, about 50 yards wide, was a single fountain,
bursting from a cavern in its side, and throwing lava half-way
across its surface, while from the roof and sides of the cavern hung
down lava stalactites.

After looking at this for some time, the claims of our injured
friend became so strong, as to oblige us to take him back to the
crater house, resolved next da}^ to have a more deliberate inspec-
tion.

The next day proved wet, but the writer explored his way through
the driving mist formed by the rain coming in contact with the
heated lava, the only disagreeable incident being his getting to
the leeward of a blow-hole, and having to run to get clear of the
suffocating sulphur vapours. This blow-hole was about the size of
a man’s body, and as you went forward to it you heard a gurgling
sound beneath. Smoke was coming out in considerable volumes,
and on looking in, the sides were seen to enlarge beneath and be
at a white heat.

Having at length got seated comfortably upon an upheaved
block of lava about 20 feet above the larger lake, and 8 to 10 yards
from its side, a new fountain sprung up suddenly from the side of
the lake quite close at hand, which immediately forced a retreat to

117

of Edinburgh, Session 1875-76.

a more respectful distance. About the same number of fountains
continued to play up as on the preceding evening, and looked red
by day. Daylight, however, drowned out the redness of the lakes
as seen by night, and made them appear quite black.

After watching for a considerable time, a red hot crack was seen
to start suddenly from one side of the lake to the other, then other
cracks in different directions, and first one-half of the lake and
then the other was covered with a fresh coating of red hot lava, the
former tumbling out of sight as it got shrunk and cracked in cooling.

A curiosity called Pele's* hair is found round the sides of these
lakes. This is composed of fine fibres of lava cooled, broken off
from the molten liquid while being spouted up in the fountains,
carried away by the wind, and lodged in the cracks around.

The summit crater of Mauna Loa, some 15 miles off, and 10,000
feet above Killauea, was in activity about a month previous to our
visit to the island, but limited time prevented our seeing it. Some
points of curiosity may be noted before ending.

1. The lakes are not at the same level, although quite close to
each other.

2. The summit crater of Mauna Loa is 10,000 feet above
Killauea, and frequently in violent eruption, while Killauea is com-
paratively undisturbed.

3. The outer crater of Killauea appeared to act as a receptacle
for the lava, which, as soon as it arrived at a sufficient height, and
got the assistance of an earthquake, broke through below and
covered the country, sometimes running in a broad stream for 25
miles, and leaving an indication of the level which it had reached
in form of a new ridge within the lip of the outer crater.

4. The necessity of an earthquake to enable it to break through
is shown by the great difference of heights of the lava even within
short distances.

5. The fountains were in every case playing round the edges of
the lakes.

5. New General Formulae for the Transformation of Infinite
Series into continued Fractions. By Thomas Muir, M. A.

* The name of the Hawaiian Fire-Goddess.

118

Proceedings of the Royal Society

6. Laboratory Notes. By Professor Tait.

(a) On a Possible Influence of Magnetism on the Absorption
of Light, and some correlated subjects.

Professor G. Forbes’ paper, read at a late meeting of the Society,
and some remarks made upon it by Professor Clerk-Maxwell, have
once more recalled to me an experiment which I tried for the first
time rather more than twenty years ago, in Queen’s College, Belfast.
I have since that time tried it again and again, whenever I suc-
ceeded in getting improved diamagnetics, a more powerful field
of magnetic force, or a more powerful spectroscope. Hitherto it
has led to no result, but it cannot yet be said to have been fairly
tried. I mention it now because I may thus possibly be enabled
to get a medium thoroughly suitable for a proper trial.

The idea is briefly this, — The explanation of Faraday’s rotation
of the plane of polarization of light by a transparent diamagnetic
requires, as shown by Thomson, molecular rotation of the lumini-
ferous medium. The plane polarized ray is broken up, while in
the medium, into its circularly-polarized components, one of which
rotates with the ether so as to have its period accelerated, the other
against it in a retarded period. Now, suppose the medium to ab-
sorb one definite wave-length only, then — if the absorption is not
interfered with by the magnetic action — the portion absorbed in
one ray will be of a shorter, in the other of a longer, period than if
there had been no magnetic force ; and thus, what was originally a
single dark absorption line might become a double line, the com-
ponents being less dark than the single one.

Other allied forms of experiment connected with this subject
were discussed.

(6) On a Mechanism for Integrating the General Linear Differen-
tial Equation of the Second Order.

I am anxious to explain to the Society a kinematical device for
the solution of the General Linear Differential Equation of the
Second Order before I become acquainted with the principle of the
integrating machine which, I understand, was described last Thurs-
day by our President to the Boyal Society.

119

of Edinburgh, Session 1875-76.

My arrangement consists of a combination of two equal modifica-
tions of Ammsler’s Planimeter, ABC, AB'C', the wheels of which
are attached at the joints B, B'. O' slides along AC, and the length
of AC can be altered by turning either of the heads I), D', of coaxal
screws of equal pitch. Now, if we suppose D connected with the

wheel at B, and D' with that at B', by means of universal flexure
joints (Thomson & Tait’s “ Natural Philosophy,” § 109), it is obvious
that the length of AC will depend upon its angular position, and
upon the motion of C' along AC.

Let AB = AB' = a, BC = B'C'=6, AC = r, AC' = r15 / ABC = £,
and let 0 denote the position of AC. Then, if the whole turn through
an angle dO , the motion of B perpendicular to CB is the same as
if it had rotated about 0, where [_ AOB is a right angle. Hence,
if p be the radius of the wheel at B, dif/ the angle through which it
rotates,

^2 ^

pd if/ = — a cos </> dO — ^ dO

A similar expression holds, of course, for B'. Now, if a be the
inclination of the threads of the screws, one right, the other left,
handed,

dr = p (dif/ — dif/f tan a ,

Now C' may be made to move along any curve we choose, so that
r1 may be any assigned function of 0. Hence, by introducing the

constant factor

tan a

~w

for r, we may give the equation the form

dr

dO

r2 — ©

120

Proceedings of the Royal Society

to which the solution of the general linear differential equation of
the second order can always be reduced.

(c) The Electric Conductivity of Nickel. By C. Michie Smith
and J. G-ordon MacGregor.

Pure nickel foil, obtained in Paris by Dr Andrews, was cut into
a spiral about 20 inches long, and it was on this spiral that all the
following experiments were made. During the month of November
1875 a large number of experiments were made as to its thermo-
electric properties, and these were found to be almost identical with
that of the specimen from observations on which the line was laid
down on the “ thermo-electric diagram.” (Trans. R.S.E., 1872-3.)
This line, it will be remembered, is a peculiar one, and is very similar
to that of iron, with this difference, that the peculiar changes take
place at much lower temperatures in nickel than in iron. Having
thus finally determined the position of the line in the thermo-electric
diagram, we were anxious to discover whether, like iron, it exhibited
other peculiarities about the same temperature, and for this end we
made the following experiments on the electric conductivity at dif-
ferent temperatures. The method of observation was as follows : —

To the two ends of the nickel spiral stout copper wires were
soldered, and the whole was carefully fastened together in such a
way that no two coils of the spiral could touch each other. Side
by side with this nickel spiral was placed a similar spiral of soft
platinum wire of approximately equal resistance. This platinum
was part of a wire the electric conductivity of which had been
formerly carefully tested, and had been found to obey very strictly
the law of being proportional to the absolute temperature. These
spirals were then placed in a large pot of oil, care being taken that
they hung quite free from the sides of the pot, and the ends of the
thick copper wires were led to the pools of a mercury commutator,
so arranged that either the nickel or platinum could be made to
form one of the arms of a Wheatstone’s bridge, in connection with a
very delicate Thomson’s dead-beat mirror galvanometer. In
making the observations the oil was heated by a powerful Bunsen
burner, and constantly stirred. By this means it was found per-
fectly practicable to keep the oil sensibly at the same temperature
during the time necessary to find the resistance of the two wires

121

of Edinburgh , Session 1875 76.

by the ordinary balance method. That no errors were caused by
thermo-electric effects was proved repeatedly during the experi-
ments by completing the circuit without the galvanic cell, when no
current was shown on the galvanometer. The results obtained for
the nickel entirely agreed with what had been anticipated from the
thermo-electric properties. For, when the conductivity is plotted
in terms of the temperature, the curve shows a sudden change in
direction at a temperature of about 149° C. (300° F.), indicating
that there is at that point a sudden change in the rate of alteration
of the conductivity with change of temperature. The curve ob-
tained for nickel can be very well represented by two straight lines
inclined to each other at an angle of about 9°, while the curve got
for the platinum wire is strictly a straight line.

That no part of the effect was due to the conductivity of the
oil was amply proved by the following experiment : —

Two pieces of platinum foil, each having a surface of 2*5 square
inches, fastened to the ends of copper wires, were plunged in
the oil when it was at a temperature of 550° F., and were kept
a quarter of an inch apart; the resistance of the oil between them
was then measured, and was found to exceed 9 megohms, while
the resistance on causing them to touch fell to a small fraction of
an ohm.

After a series of experiments had been made with the nickel,
the whole spiral was heated to a white heat in the flame of a Bun-
sen burner, and allowed to cool in the air ; another series of ex-
periments was then made on the conductivity, but no change was
observed.

The following tables contain the observations for two of the
experiments, side by side with the values of the conductivity, calcu-
lated on the supposition that the curves are best represented
by straight lines — the platinum being represented by a single
straight line, while the nickel is represented by a broken line.
The calculated and observed values, it will be seen, agree very
closely with each other, except where a divergence is to be ex-
pected, namely, at the intersection of the two lines (nickel). The
equations were taken from the lines obtained by plotting the con-
ductivity in terms of the temperature. R is the resistance in
thousandths of an ohm, t the temperature in degrees F. : —

VOL. IX.

R

122 Proceedings of the Boyal Society .

January 14th, 1876.

O o

Nickel.

Platinum,

Formula up to t= 2729. R.='525 1 + 131.

Formula R = -34 t + 176. 1

<v a>

s-i

Resistance = °^ms.

Resistance =-

ohms

Ep

1000

1000’

Observed.

| Calculated.

Difference.

Observed.

Calculated.

Difference.

+

—

+

—

53

159

159

• • •

• • •

192

194

...

2

69

168

167

1

200

199

1

...

99

183

183

...

...

210

210

...

• • •

132

200

200

• • •

• • •

221

221

...

• • •

162

215

216

• • •

1

230

231

...

1

194

233

233

• . .

...

242

242

...

• • •

218

247

245

2

...

250

250

• • •

• • •

247

265

261

4

• . •

260

260

...

• • .

Formula above 1

= 272°.

R

= *775 t + 64.

279

285

280

5

...

271

271

• • •

...

307

305

302

3

• • •

281

280

1

• • •

345

331

331

• • •

• • •

293

293

...

• • •

376

354

355

• • •

1

303

304

• • •

1

440

401

405

...

4

323

326

...

3

January 18 th, 1876.

Nickel.

Platinum.

O .4

P

Formula up to t = 306°. R = '58 1 + 133.

Formula R = '326 t + 187.

Resistance =

ohms -7- 1000.

Observed.

Calculated.

Difference.

Observed.

Calculated.

Difference.

102

194

192

+

2

• • •

219

220

+

1

136

212

212

• • •

• • •

230

231

...

1

169

230

231

• • .

1

242

242

• • •

• • •

229

266

266

• • •

• • •

262

262

• • •

...

301

312

308

4

...

285

285

...

. . .

Formula above t = 306°.

R

= -775 1 + 74.

363

356

355

1

...

305

305

• • •

• • •

407

386

389

• • •

3

319

320

• • •

1

447

420

420

• • •

...

333

333

...

• • •

502

466

463

3

• • •

348

351

...

3

An attempt was made to discover whether or not the conductivity
curve had another peculiar point corresponding to that in the

123

of Edinburgh, Session 1875-76.

thermo-electric curve at a high temperature. For this an arrange-
ment was used similar to that employed for the iron wire in the
experiments formerly described (“ Proc. R. S. E.” 1874-75, pp.
629-631). But no results were obtained, owing to the breaking
of the nickel ribbon when exposed to the great heat of the white hot
cylinder.

The following Gentlemen were elected Fellows of the
Society: —

William Skinner, Esq.

J. Ballantyne Hannay, Esq.

Peter Denny, Esq.

Monday , 21 st February 1876.

Sir WILLIAM THOMSON, President, in the Chair.

The following communications were read : —

1. On the Structure of the Body-wall in the Spionidse. By

W. C. MTntosh.

In regard to external form, Nerine foliosa , Sars, is generally taken
as the type of the family, and therefore it may be selected for
structural examination in the first instance. Anteriorly the pointed
snout is completed by the intricate interlacing of the muscular
fibres beneath specially thickened cuticular and hypodermic layers.
As soon as the body-wall assumes a rounded form, a layer of circular
and oblique muscular fibres occurs beneath the hypoderm, the
majority having the latter (i.e., the oblique) direction. In the
centre of the area the oesophagus is suspended by strong muscular
bundles (the most conspicuous of which are vertical) passing from
the hypodermic basement-layer in the middle line superiorly to be
attached to the oesophagal wall. A second series, as they descend
to their insertion at the ventral surface, give lateral support to the
tube; while a third group interlace in a complex manner, and, with
the blood-vessels, fill up the space between the oesophagus and the
wall of the body.

Toward the posterior part of the head is found — on the dorsal
surface — a slight hypodermic prominence, which indicates the
position of the central ganglia of the nervous system ; the latter

124 Proceedings of the Royal Society

being quite external to all the muscular layers, and covered only
by the cuticle and hypoderm. In a line with the first bristles, the
layers have assumed a more definite appearance. Beneath the
hypoderm is a circular muscular coat, which, however, is somewhat
irregular in its arrangement ; for, toward the dorsal region, the
layer spreads out at each side, and the fibres mix with the oblique
muscles of that part, while only a very thin layer stretches across
the middle line of the dorsum. Within the former is a more or
less developed longitudinal layer — best marked at the ventral aspect.
A long oblique muscle extends from the lateral dorsal region on
each side to the middle of the body-wall; and an important feature
is the situation of the nerve-cord in close proximity to the inferior
attachment of this muscle to the hypodermic basement-layer.
Various muscular fasciculi, as before, attach the oesophagus to
the body-wall, and the bristle-muscles and those of the lateral
appendages have made their appearance.

A little behind the foregoing it is noticed that the circular
muscular layer is less continuous (though strong inferiorly), and
that the longitudinal has been grouped by the other fibres into
certain definite bands, the most conspicuous being a double dorsal
and two lateral. The former fibres, indeed, have now assumed
considerable bulk, a thin circular layer only intervening between
them and the hypoderm. The formation of the lateral longitu-
dinal muscles, again, is interesting on account of their homological
bearings. From the inferior bristle-tuft, and from the region on
each side of it, a strong series of muscular fibres converges toward
the side of the oesophagus, and then splits into two bands. The
outer bundle is the more powerful, and at the infero-lateral region
of the body it bends somewhat sharply outward to be attached to
the wall. The fibres thus arch over a chamber on each side for
the lodgment of the ventral longitudinal muscle. In ordinary
transverse sections they are much stronger than the other, and,
moreover, have the nerve-cords at their insertion. The second
series slants downward and inward, and is chiefly composed of fibres
passing from the dorsal arch by the side of the oesophagus to
mingle with the circular fibres at the ventral surface. A thin layer
of longitudinal fibres also occurs on the internal aspect of the
ventral transverse band (a part of the circular coat).

of Edinburgh, Session 1875-76. 125

As we proceed backward, the lateral longitudinal muscles gradu-
ally increase in breadth, while the great oblique bands nearly meet
in the central line interiorly. The dorsal longitudinal fibres are
grouped in two symmetrical masses, and a strong band passes
between the edges of the ventral longitudinal muscles, — the median
longitudinal fibres formerly indicated lying immediately within
this layer. The nerve-cords have now descended quite to the
ventral surface, and have a pale intermediate area.

As soon as the body assumes a transversely-elongated form, the
dorsal longitudinal muscles become much extended, and are, be-
sides, intersected by the powerful vertical bands, which sweep from
the dorsal basement-layer to the ventral surface, through the lateral
longitudinal muscles (now for the most part ventral in position).
The oblique muscle on each side is more horizontal, passing from
the inferior bristle-bundle to the median line at the ventral surface,
and going right through the vertical bands before insertion. The
nerve-cords lie close together below the transverse muscle, and a
small neural canal exists at the inner and upper border of each.
There are still a few longitudinal fibres between the ventral attach-
ments of the oblique muscles. The alimentary canal shows internal
circular and external longitudinal fibres.

It is very soon apparent, in proceeding backward, that the
vertical muscles descending from the dorsal to the ventral surface
do not interdigitate with the great longitudinal muscles through-
out their whole extent. They leave, as observed by the lamented
M. Claparede, at the external border of each dorsal muscle a con-
siderable mass, which bends downward, and presents in transverse
section a distinctly pennate appearance. A similar arrangement
occurs at the outer and inner extremities of the ventral longitu-
dinal muscles. Finally, the nerve-cords now have a single and
very large intermediate neural canal. The foregoing condition
continues with little modification to the tip of the tail ; though the
dorsal pennate process disappears, the muscle itself being separated
from its fellow, and considerably diminished in bulk, while the
transverse fibres between it and the hypodemi have greatly in-
creased.*

* The late M. Claparede, in his “ Structure des Annel, S4dentaires,” p. 15,
&c., pi. xv., gives the structure of the hypoderm, and notices the pennate

126 Proceedings of the Royal Society

In Scolecolepis vulgaris , Johnst., the body-wall is similarly con-
structed. Anteriorly the central ganglia of the nervous system lie
outside the muscles on the dorsum, and the cords rapidly pass
downward to the inferior attachments of the oblique muscles. In
this region there is also a dense mass of longitudinal muscles. As
soon as the oral aperture is completed posteriorly by the frilled
hypoderm, the following arrangement occurs : — Within the hypo-
derm is an irregular circular coat, the most conspicuous part being
a broad belt, which hounds the mouth at the ventral border, and
stretches between the great longitudinal muscular masses on each
side. Superiorly a short but distinct band also appears under the
central hypodermic elevation. A fasciculated longitudinal muscle
(dorsal) lies below the latter on each side, its inferior surface being
attached to a chitinous sinuous band, which forms a space by
its upward curve from a raphe. A somewhat triangular interval
occurs, moreover, between the muscles in the median line. The
form of this chitinous arch is maintained by strong transverse
fibres, which curve from raphe to raphe. At the latter, on each
side, there is almost a rosette of muscular fibres, the chief fasciculi
being directed downward and outward in transverse section. Out-
side the foregoing dorsally are various oblique bands, the superior
stretching from the dorsum downward and outward to the lateral
hypoderm, while the lateral pass downward and inward. The
chitinous arch gradually disappears as the dorsal muscle becomes
fully developed. Behind the preceding region the arrangement
consists, as in N.foliosa , of a double dorsal and two lateral longitu-
dinal muscles, with the vertical and oblique bands, the latter passing
through the former near the ventral attachment. There is also a
very strong transverse ventral muscle, with a series of longitudinal
fibres internally. Each nerve-cord in transverse section presents
a distinct though small neural canal. The hypoderm, as well
as the muscles, seems to be more largely developed than in N.
foliosa , a feature corresponding with the increased size of the
nerves.

After the dorsal muscles have expanded into a broad layer, the
same interlacing with the vertical bands occurs, but the pennate

muscles and the arrangement of the nerve-cords of this form, but the fore-
going observations do not interfere with his remarks.

127

of Edinburgh , Session 1875-76.

arrangement formerly noticed does not appear in this form. The
two neural canals soon increase in size, and approach each other in
the middle line. With the exception of the great development of
the ventral longitudinal muscles posteriorly, little further change
takes place in the structure of the body-wall.

The situation of the central ganglia in Scolecolejois cirrata, Sars.,
corresponds with the preceding, and the nerve-cords follow the
progress of the oblique muscles toward the ventral surface, each
trunk having a small neural canal. When the body wall is com-
pletely formed (for instance about ^ in. from the snout), the great
size of the longitudinal muscles is conspicuous. The dorsal form a
thick superior arch, and proceed a considerable distance down the
lateral wall; while the ventral muscles constitute two great curved
masses in transverse section, the inner border of each being so
carried upward that a deep ventral sulcus is formed for the nerve-
trunks and their hypodermic external investment. For the same
reason the strong oblique muscles are rendered nearly horizontal.
The rounded firm nature of the alimentary canal gives little scope
for the development of vertical fibres.

The structure of the body-wall in Spio, and the position of the
ganglia and nerve-trunks correspond with the foregoing in general
features. The same may be said of the rarer Prionospio, which
has two neural canals interiorly.

In Polydora ciliata, Johnst., the body-wall anteriorly is charac-
terised by the great development and bifid nature of the median
ridge, which is flanked on each side by a prominent process of the
hypoderm. In transverse section, the snout a little behind the
tip presents, on each side of the dorsal process, a large rounded
lobe, which projects downward to the oral aperture. Exter-
nally, the lobe is composed of a thick layer of hypoderm, having
internally a series of circular fibres, which come from the transverse
dorsal arch in the form of a loop on each side. The fibres pass
downward within the hypoderm, curve inward ventrally, and then
proceed upward over the oesophagus to the point of commencement.
A well-marked series of longitudinal fibres lines the outer division
of the loop, and afterwards merges into the ventral longitudinal
muscle of the side. The dorsal arch of transverse fibres cuts off
the hypodermic process, containing the nerve-ganglia, and in the

128 Proceedings of the Royal Society

cavity which forms therein is superiorly a small group of longitu-
dinal fibres.

Behind the foregoing a transverse dorsal layer is found beneath
the central and now solid hypodermic process, next the dorsal lon-
gitudinal muscles (the fasciculi of which, in the middle line, are
directed downward and outward, while the outer are directed down-
ward and inward); then a kind of X shaped process occurs in the
centre, the legs of the X being prolonged horizontally, so that the
whole resembles a figure of oo, the two spaces containing muscular
fasciculi. The lateral and oblique muscles are largely developed,
the latter having the nerve-cord on each side below its ventral
attachment.

The most interesting point in this form, perhaps, is the structure
of the fifth body-segment, which bears the remarkable hooks
characteristic of the genus, besides peculiar bristles with spear-
shaped heads, and a minute fascicle of the ordinary structure.
Immediately in front of the hooks, the body in transverse section
shows externally a circular coat, which is thin at some parts, but
greatly developed at others. Dorsally a very powerful series of
fibres spread outward from the middle line on each side — some be-
coming continuous with the circular coat, others passing obliquely
outward and downward to the superior bristle-bundle. Inferiorly
a strong transverse band lies over the nerve-trunks, and forms an
external investment to the ventral longitudinal muscles. The
oblique muscle comes from the lower bristle-bundle, and joins the
former over the nerve-trunk, after piercing the vertical bands.
The superior longitudinal muscle forms a great mass on each side,
and it interdigitates with the fibres of the vertical muscle. The
latter is greatly developed, especially at its inner border, next the
oesophagus. The same (vertical) fibres pierce the ventral longitu-
dinal muscle in the compartment formed for it by the circular and
oblique bands. The size of the ventral is less than that of the
dorsal longitudinal muscles. A somewhat strong group of longitu-
dinal fibres lies within the ventral transverse band. Finally, each
fascicle of the ordinary bristles has a V shaped series of fibres
extending from the base of the tuft to the lateral wall, and inter-
digitating with those from the transverse and other muscles of the
region.

129

of Edinburgh, Session 1875-76.

As soon as the powerful hooks of the fifth segment appear, the
entire area — from the alimentary canal to the body wall — is occu-
pied by their muscular apparatus. This consists of a dense series
of fibres, which slant from the matrix of the bristles superiorly
upward and outward to decussate with the fibres at the upper and
outer angle of the body-wall. A still stronger series of fibres occur
in the inferior division ; the inner are nearly vertical, the rest
incline downward and outward. It would appear, therefore, that
this powerful muscular mass chiefly acts on the hooks, so as to
bring their curved points against the wall of the tube or tunnel.
The strong inferior fibres likewise gain additional purchase by
passing through the ventral longitudinal layer to be attached to
the basement-tissue of the hypoderm. In this region the nerve-
cords form two almond-shaped bodies in transverse section in the
ventral hypoderm, and they are separated by a distinct interval.

Posteriorly the nerve-cords still remain separate, and a large
neural canal lies between them. A well-marked pennate process of
the ventral longitudinal muscle occurs at its inner (median) edge.

The foregoing forms, in conclusion, were compared with the
structure of Mcea mirabilis , Johnst., an aberrant member of the
Spionidas.

2. Note on Circular Crystals. By E. W. Dallas.

At long intervals notices of circular crystals have appeared before
this Society. In 1853 Sir David Brewster read a paper on the
subject, which followed one by Mr Fox Talbot in 1836, and which
again had been preceded by one from Sir David Brewster about twenty
years before. It is not easy to account for these long intervals,
unless they may be attributed to difficulty and uncertainty in
manipulation, for except in very few instances the crystals observed
by Sir David Brewster are of microscopic size, and, he remarks, require
the perfection of optical appliances for their observation, and natu-
rally so when crystals of the 200th of an inch in diameter are looked
upon as of respectable size.

Some time ago, being occupied with the subject, I found that by
impeding crystallisation by means of gum arabic, circular crystals
were formed of a greater size.* This took place with certain salts,

* Perfect crystals were exhibited up to two inches in diameter.

VOL. IX.

s

130 Proceedings of the lioyal Society

but not with all that were tried. Among the successful instances
may be mentioned sulphate of copper, binacetate of lead, muriate
of morphia, and other similar salts, which afford beautiful crystals,
and are very easily manipulated. The method of proceeding is
similar in all ; for instance, to a solution of sulphate of copper,
let gum arabic or common dextrine be slowly added until it pours
oily, then tried, and more gum or more salt added until the result
is satisfactory. No precise general rule can be given, as each salt
will be found different in the quantity of gum required. The
solution is then to be spread thinly over a plate of glass, and dried
rapidly before a clear fire, or, if the plate is small, it may be dried
over a gas-burner. Upon cooling, the plate, if left to itself, soon
shows numerous small specks, which will gradually develope them-
selves into circular crystals. The process is hastened and a better
result obtained by breathing on the plate, when, after a short time,
they may be observed to start out very beautifully. These crystals
while growing are extremely sensitive, any variation in the moisture
applied for their formation resulting in the production of rings.

The growth of the crystals once begun is extremely regular.
When the centre is of inappreciable size they are circular, and they
proceed onwards in that form until stopped by other crystals, or
until the whole vacant space is oceupied by them. Should the
origin have a definite shape, then that is carried on by the crystals
arranging themselves always perpendicularly to the outline of that
origin, while, should it be a straight line, they form beautiful
fringes perpendicular to the line, and terminate at each extremity
in semicircles.

The centres round which the crystals arrange themselves maybe
either some foreign body in the film, or be determined by some
molecular arrangement of the salt at a particular point in the film.
They seem to originate spontaneously, and subject to no apparent
rule, for foreign particles, and even minute crystals, will not always
determine centres ; in fact a film may be full of little crystals of the
salt, and to very few of them can the circular arrangement be traced.

The crystals present themselves under two aspects in all the
salts that I have examined, — a true and an abnormal form. I
designate the true form as that in which the crystallisation proceeds
by the formation of spicular crystals radiating from a centre and

131

oj Edinburgh , Session 1875-76.

in optical contact, while in the other many different forms may be
observed, in which the component crystals are more or less of a
laminate structure, often presenting most beautiful appearances.
I have made this distinction, having observed that in some cases
at least the true crystals are permanent, while the laminate are not
so under like conditions, but change into the true form by time, or
may become altogether disintegrated in a damp atmosphere into a
confused mass, having few optical properties. The crystals also
possess distinctive optical properties.

The production of either of these classes of crystals appears to
depend on two conditions, namely, on the thickness of the film, and
on the amount of moisture applied in their production, — a thin
film and a moderate supply of watery vapour inducing the true
form, while a thick film and an increased quantity so alter the
structure that at last, although the crystallisation may proceed
from a centre, the circular character .is entirely lost.

Spherical crystallisation, to which the circular is to be referred, is
veryfrequent in mineral substances. It may be seen also in the well-
known experiment of the rapid crystallisation of a supersaturated
solution of acetate of soda, by the introduction of a centre round
which the salt forms a spherical mass, and the surface, when the
action has ended, presents all the appearance of a circular crystal.

However difficult it may be to account for the origin of crystals,
their growth in a circular form, when once the centre is determined
in a film, is very obvious in those cases where they are produced.
In the preparation of the film, not only is the superfluous solvent
rapidly evaporated by heat, but a considerable part of the water of
crystallisation is also driven off, and there is left on the glass plate
a film of an amorphous substance, which, either by attracting
moisture spontaneously from the atmosphere, or by having it added,
allows the salt, whatever it may be, to resume its crystalline form.
That this is the case may be seen from the fact that the crystallisa-
tion will take place, and that in a circular form, if the drying of a
plate is stopped just at that point when there is sufficient water
left to enable the crystals to form when the plate is cooled. In
this case their formation is a repetition of the acetate of soda ex-
periment already alluded to. A plate may sometimes also be dried
and crystallised, and on being again exposed to heat the crystals

132

Proceedings of the Royal Society

will disappear, and the plate may be re-crystallised, but not so well
as at first, and not from the same centres. This is the case with
the binacetate of lead.

There is one remarkable form of these crystals which is of fre-
quent occurrence, and which Sir D. Brewster seems to have observed
only in mannite. The form looks very extraordinary, a properly
prepared plate presenting the appearance of being covered with
paraboloids. These are simply circular crystals which have been
formed in the film while the general crystallisation has proceeded
from one side, and is caused by the crystals overtaking one another
in their onward progress in one direction. Taking this case in its
simplest form by supposing equal rates of crystallisation proceeding
from the edge of a plate and from a centre near the edge, their line
of contact will necessarily be a parabola, for it is evident the
edge is a directrix and the centre the focus of such a figure, but
this will very seldom occur, since the growths are not only generally
unequal, but also vary in themselves.

The question may be put whether gum arabic is the substance
best suited for these experiments. I have not tried many, and
with those that I have experimented upon the results were not so
satisfactory. That other agents may be employed, according to
the salts or other substances to be treated, is certain ; for example,
collodion, as may be seen in a coated photographic plate that has
been allowed to dry after excitation in the nitrate of silver bath,
when circular crystals of iodo-nitrate of silver arQ often produced.
This salt, be it observed, although produced through the agency
of water, being at once decomposed by that element.

Having confined my observations mainly to a very small number
of salts, it would be premature to offer any general conclusion on the
structure of their circular crystals or on their optical properties ; be-
sides, from the great interest Professor Tait has shown in the subject,
I am in great hopes that he maybe induced to make some investiga-
tion in it. I shall only mention one point that I have observed in
the effect of some crystals on the black cross, something in their
structure producing a more or less spiral arrangement of the arms
in a horizontal direction, while on one occasion a vertical arrange-
ment was observed, in which the arms seemed to be raised one
above the other like four quadrant steps. This effect I have only

133

of Edinburgh, Session 1875-76.

seen once in a crystal of sulphate of magnesia, and have not been
able to reproduce anything of the kind, hut the crystallisation of
that salt is so varied and irregular that many things may pass
unobserved.

The only other point I shall lay before the Society is, that I have
succeeded in producing a crystallisation very similar to that of frost-
pictures on a window pane, and I hope to be able to make the
imitation more perfect. For this purpose I have employed the
sulphate of copper and magnesia, — a salt that crystallises under the
rhombohedral system, the same with that of ice. This salt crystal-
lises in the films from centres in a most remarkable manner in four
different modes, viz., the true circular, the laminate, a branched or
dendritic form, and another that I hardly know how to designate,
unless it may he called the ostrich plume form. All these different
forms may be observed on the plates, either simply or in combina-
tion, and produce most varied and singularly beautiful effects.

3. Preliminary Note on the Flame produced by putting
Common Salt into a fire. By C. M. Smith, Esq. (Com-
municated by Professor Tail).

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

vol. ix. 1875-76. No. 95.

Ninety-Third Session.

Monday , tith March 1876.

Sir WILLIAM THOMSON, President, in the Chair.

The following Communications were read : —

1. The Annual Periods of Thunder (with Lightning), Light-
ning (only), Hail, and Snow, at Oxford. By Mr Buchan.

During the twenty-one years ending 1873, the maximum period
of thunder with or without lightning, at Oxford, extended from
about 9th April to the end of October, the middle of the period
being the first week of July; the three highest days taken
consecutively being those immediately preceding the summer
solstice. During the five months from November to March, only
thirteen cases had occurred during the period. Lightning, on the
other hand, had its maximum period from May to November, —
particularly during August, September, and October. The maxi-
mum period of hail was during the first six months of the year ;
whereas, during the second half of the year, very few cases
occurred. The snow period extended from the middle of October
to the middle of May, — most falling from December to March, —
the absolutely highest month being March.

Thus, thunder with lightning , at Oxford, closely follows the sun,
the middle of the period being only about ten days after the

VOL. IX.

T

136

Proceedings of the Royal Society

summer solstice; lightning (only) has its maximum period during
that time of the year when the humidity of the air is at its
maximum; hail is most frequent during that period of the year
when the temperature is rising, or when the vertical layers of the
atmosphere is in most unstable equilibrium ; and snow during the
coldest months of the year, with this striking peculiarity, that
the maximum period is not in the depth of winter, but in March,
in the end of winter; immediately after which the curve abruptly
falls.

The intimate connection of the thunderstorm with summer
rainfall, and the important bearing of the whole four curves on
climatology, was referred to.

2. Note on the Origin of Thunderstorms. By Prof. Tait.

This Note does not refer so much to those great thunderstorms
which extend over hundreds of miles in each direction, as to those
small local storms which are often seen of from two to five or
six miles only in diameter.

It refers particularly to those which are seen, in summer and
autumn, to pass down the Tay valley. They almost invariably
come from the westward, and I am told each is almost always
accompanied by a storm of similar dimensions passing eastwards
down the valley of the Forth. So far as I can ascertain, they
seem both to commence almost abruptly somewhere in the district
about Ben Ledi and Ben Lomond.

Seen from St Andrews, which they frequently pass at a few miles
distance to the northward, they usually appear to be in a state of
rotation about a vertical axis. It is not very easy to judge of the
relative distances of the various clouds, so as to ascertain the sense
of the rotation ; but, in one case which I observed carefully last
autumn, the rotation appeared to be in the positive direction, — i.e .,
opposite to that of the hands of a watch whose face is turned
upwards.

If this be generally the case, and if it should be found that the
direction of rotation of the companion storm in the Forth valley
is negative , it would seem that their common origin may be
explained on the following very simple hypothesis, which has the

of Edinburgh, Session 1875-76. 137

additional recommendation of easily accounting for certain other
singular phenomena.

It is known from balloon ascents that, in general, the atmo-
sphere is arranged in horizontal strata of considerable depth or
thickness, alternately moist and dry, — temperature diminishing
steadily with increase of height in the moist, and remaining
nearly constant throughout the dry, strata. These strata have
usually horizontal velocities, differing (sometimes considerably)
both in magnitude and direction. Thus near the common bound-
ary of two such strata, fluid friction will in general tend to produce
vortex motion, — the vortex columns being at first nearly horizon-
tal, with their ends at the boundary, which is a surface of discon-
tinuity.

A complete investigation of the possible circumstances would
show four quite different cases : —

Vortex formed

into a stratum of

dry )
moist j

. f drj
m ( moi
( moist 1
t dry 1

air.

air.

with its ends

turning }

down )
up J

The half vortex-ring thus formed tends, so far as it can, to
become semicircular. It may thus extend downwards to the earth
or upwards into the higher regions of the atmosphere.

If it extend downwards nearly to the earth, the lower portion will
soon be destroyed by friction, and we shall have a couple of vertical
vortex columns, with their ends respectively in the surface of dis-
continuity, and on the ground. They will of course rotate in
opposite directions about the vertical, and their mutual influence
will tend to cause them to progress in directions parallel to one
another, the motion of each being in the same direction as
that of the rotatory motion of the side which it at the moment
turns to the other. This is exactly the presumed case of the little
storms in the Tay and Forth valleys above referred to ; the south
side of the Tay column (that turned towards the Forth), moving
eastward about the axis, while the axis itself moves to the east.

This theory is evidently capable of at once explaining the ap-
parently sudden occurrence of such storms (of which waterspouts
must be looked upon as small but quickly rotating examples),
when the lower atmosphere has for hours been in a dead calm.

138

Proceedings of the Royal Society

The disturbance has, in fact, its origin above the lower stratum,
and works its way downwards into it.

It is also competent to explain the production of similar rotat-
ing storms in the higher regions of the atmosphere — many miles
above the earth’s surface — and thus to account for that by no
means small number of cases of so-called “ summer-lightning,”
which obviously cannot be explained by the occurrence of an ordi-
nary thunderstorm at such a distance as to be below the specta-
tor’s horizon.

I have already explained to the Society that a possible source of
at least a large part of the electric charge of a thunder-cloud is
the contact-electricity of water-vapour and air. Thus while the
precipitation of the vapour develops heat, the water particles pre-
cipitated are strongly electrified. And the aggregation into one
of a number of equal little drops all charged to the same potential
may increase the potential in any ratio whatever. Thus the
charge on each drop in a large cloud may become so great that the
electricity is driven entirely to the particles at its surface. This
is supplementary to, and does not interfere with, Sir W. Thomson’s
explanation of the process by which the vapour is condensed.

It is possible that taking place in greatly larger spaces of air,
but to a much smaller extent in each cubic foot, this sudden pro-
duction, and as sudden scattering in all directions, of considerable
quantities of electricity, may account for some of the main pheno-
mena of the Aurora.

3. An Application of Professor James Thomson’s Integrator
to harmonic Analyses of Meteorological, Tidal, and other
Phenomena, and to the Integration of Differential Equa-
tions. By Sir W. Thomson.

A first rough Model of Professor J. Thomson’s Integrator was
shown.

4. Note on the Thermo-Electric Position of Cobalt. By
Professor Tait,

139

of Edinburgh, Session 1875-76.

5. On a Glass Digester in which to Heat Substances under
Pressure. By Dr E. A. Letts.

The objections to the use of sealed tubes are known to every
practical chemist, and are a serious drawback to their employ-
ment. The chief of these are the time expended in the manu-
facture of the tubes, the amount of skill in glass-blowing re-
quired, the danger experienced in opening them, and above all,
the fact that only a small quantity of material can be heated at
one operation. Moreover, the same tube can seldom be used for
more than three or four experiments, as each time it is sealed up
its neck must be drawn out, and its length thus considerably
decreased. These disadvantages were especially felt by me whilst
preparing bromacetic acid, which was required in considerable
quantities, and where as many as half a dozen tubes of bromine
and acetic acid had to be heated before 100 grammes of the acid
could be obtained. To obviate these objections I have had an
apparatus constructed, which consists of a cylinder of glass, the
walls of which are about half an inch thick. Its length is fifteen
inches, its external diameter three inches, and its capacity about
600 cubic centimetres. At one end it is drawn out to a tube,
whose aperture is only about one-sixth of an inch in diameter,
though its walls are as thick as the rest of the apparatus. Origin-
ally this tube was provided with a stopcock, but at Professor Brown’s
suggestion, I have substituted a glass plate, which is ground fiat,
and accurately adapted to the top of the tube.

In order to keep the glass plate pressing on the tube the whole
apparatus is placed in a frame, consisting of three brass wires
arranged symmetrically around the cylinder, and attached by means
of nuts, below, to a brass ring, and above, to a brass plate, through
which latter a screw passes, which, when turned, presses on a brass
plate placed on the glass cap.

As any experiments with such an apparatus would be attended

140

Proceedings of the Royal Society

with danger, were it necessary to be in its neighbourhood, it
occurred to me that an automatic arrangement might be employed
to give notice that the temperature had been reached to which it
was intended to subject the digester.

For this purpose I employed a thermometer with a somewhat
wide tube and large bulb. A platinum wire is sealed into the
bulb, and touches the mercury, whilst a brass wire passes down
the tube, and is held in position by a binding screw. The two
wires are connected with an electric bell, the brass wire being so
adjusted, that when a particular temperature is reached the mer-
cury touches its end, and thus completes the circuit, and causes the
bell to ring.

In order to test the digester, about 200 grammes of a mix-
ture of two-parts bromine and three of acetic acid was placed
in it, and after fixing it in its frame, the whole apparatus was
immersed in an oil bath and heated to 150° C., the temperature
at which reaction in this case takes place. The experiment was
made in a cellar, and the bell placed in a room some distance
off. The gas to heat the oil bath was led by a tube from another
cellar, so that it could be regulated without going near the digester.
In about an hour and a half the bell rung, and thereupon the gas
was shut off; and on examining the digester next day, it was
found that the reaction had taken place, and that only twelve
grammes of product had been lost — a very inconsiderable quantity.

As the action of bromine on acetic acid is very sudden, and
accompanied by the disengagement of a large volume of hydro-
bromic acid, the apparatus may be considered to have undergone a
very severe test, and that its efficacy for all ordinary purposes is
established.

Should the digester come into general use, it will certainly save
chemists much time and labour.

The following Gentlemen were elected Fellows of the
Society : —

Rev. Francis Le Grix White, M.A.

James Duncan, Esq., Benmore.

Rev. Norman Macleod.

J. S. Fleming, Esq.

James Douglas H. Dickson, M.A. Glasg., B.A. Camh.

of Edinburgh, Session 1875-76.

141

Monday , 20 th March 1876.

Sir WILLIAM THOMSON, President, in the Chair.
The following Communications were read : —

1. On the Connection between Cohesion, Elasticity, Dilatation,
and Temperature. By Professor George Forbes.

(. Abstract .)

At various times there have arisen supporters of one or other of
two extreme hypothesis concerning the nature of what we define
as force. These are the hypothesis of u action at a distance” and
of “ no action at a distance.”

According to the latter hypothesis, the centre of gravity of no
body, however large or however small, can be moved from a posi-
tion of rest, nor can its motion be altered in direction or amount,
except by direct collision with another portion of matter.

Starting from this supposition as a basis of argument, and without
assuming anything further as to the manner in which the different
physical forces are caused by collisions, it is possible to arrive at
some very general theorems; and from these theorems conclusions
may be drawn as the nature and connection of some of the physical
forces, which are necessarily true if the hypothesis of no action at
a distance be true.

The principal result of these theorems is the following: — Let a
rod be chosen of any substance whose cohesion and elasticity do
not vary enormously with the temperature. Let a be its expan-
sion, in terms of its length, when the temperature is raised 1°.
Let /3 be the compression of the same rod, in terms of its length,
when a unit weight is supported at its summit. Let c be the
number of these units which, when suspended by the rod, suffice
to break it by sudden rupture. Let 0 be the absolute temperature
at which all these experiments are made. Then the theory leads us
to the conclusion that

Only a few experiments have been made by which we can test

142 Proceedings of the Royal Society

this law. But the following values are the most accurate, and
tend to prove the truth of the law. The apparent discordance in
the case of iron is in part due to the variations in the qualities of
that metal in different specimens.

/8c

e

a

Gold,

•00001484

•00001358

Silver, ....

•00001796

•00001809

Copper, ....

•00001511

•00001481

Platinum, . . .

•00001006

•00000851

Iron,

•00001573

•00001220

In calculating this table, the values of c from the experiments
of M. Wersheim are used; those of a from the experiments of Mr
Mathiessen (except iron); those of ft from the experiments quoted
by Prof. Balfour Stewart in his Text-Book; and the assumed
temperature is 18° C., or 283° absolute temperature.

2. Notice of the Completion of the Works designed by Sir
Charles A. Hartley, F.R.S.E., for the Improvement of the
Danube. By David Stevenson, Esq., V.P.R.S.E.

In 1868 I presented to the Society, on behalf of Sir Charles A.
Hartley, a memoir published by the European Commission of the
Danube, on the improvement of that river, and at the same time
gave a notice of the works designed by Sir Charles Hartley for
effecting that important object. These works have now been com-
pleted, and Sir Charles Hartley has again asked me to present to
the Society a second memoir published by the Commission, which
brings the history of the works constructed under their charge down
to the time of their completion in 1873.

In supplement of the notice formerly communicated, which
referred to a work in progress, it may not be uninteresting, now
that the work is completed, to state briefly what has been effected
by this most important and successful example of hydraulic
engineering.

of Edinburgh , Sessio7i 1875-76. 143

The engineering problem to be solved by the European Com-
mission was the removal of the bar which obstructed the Sulina
mouth of the Danube, which, in 1856, had a varying depth of
channel never exceeding 11 feet. The design of Sir Charles
Hartley — the engineer to the Commission — consisted in piers so
constructed as to confine the current of the river in its passage into
the Black Sea. At the date of my last notice the north pier had
been extended to the length of 4640 feet, and the south pier to
3000 feet, and a maximum depth of 17J feet instead of 11 feet had
been obtained. I, however, suggested in that notice, that as the
Danube must continue to bring down an enormous mass of detritus,
so in course of time the works which had proved so successful must
be extended; and it appears that this has been found necessary, as
the south breakwater, completed in 1871, has been extended to 3457
feet in length, and even with this additional length it is, I think,
not improbable that in the course of time still farther extension
may be required, for the Sulina mouth of the Danube will still dis-
charge the same amount of water, bearing with it the same amount
of alluvial matter, estimated in high floods at about 70,000 tons in
twenty-four hours, the deposit of which at the extremity of the
piers will still have a tendency, though in deeper water, to form a
bar.

The works have, however, proved most successful, and reflect the
highest credit on Sir Charles Hartley, by whom they were designed
and executed, and the following is a summary of the results that
have been obtained.

The total length of piers executed is 8789 feet, at a cost of
L. 185, 352, being L.21 per lineal foot, in an average depth of 14 feet
at low water. The navigable depth of the channel over the bar
has been increased from 11 feet in 1856, to 20 feet in 1873. In
1853,2490 vessels, of 339,457 aggregate tonnage, left the port;
in 1869 there were 2881 vessels, with a tonnage of 676,960.
Thus, while the number of vessels increased only at the rate of
16 per cent., the tonnage, due to the greater draught, had been
increased at the rate of 50 per cent., a good practical proof of the
value of the improvements. The number of shipwrecks at the
mouth of the Danube has also been greatly diminished.

VOL. IX.

u

144

Proceedings of the Royal Society

Monday , 3 d April 1876.

Sir WILLIAM THOMSON, President, in the Chair.

The following Communications were read : —

1. Chapters on the Mineralogy of Scotland. By Professor
Heddle. Chapter I. —On the Bhombohedral Carbonates.
Communicated by Professor Tait.

Professor Heddle read a paper on the 11 Bhombohedral Carbonates
occurring in Scotland,” the first of a series of Chapters intended to
embrace the analytical results of an investigation of all unknown
or insufficiently determined Scottish species.

In this paper many analyses of the carbonates were submitted ;
and the pseudomorphic changes taking place in these were referred
to in a special manner.

2. On Thermo-Dynamic Motivity, By Sir W. Thomson.

3. On the Vortex Theory of Gases, of the Condensation of
Gases on Solids, and of the Continuity between the
Gaseous and Liquid State of Matter. By Sir W.
Thomson.

4. On two new Laboratory Apparatus. By William Dittmar.

The object of this communication is to submit to the notice of
the Society two little inventions of mine, which, whatever may be
the degree of originality which they can claim, will, I venture to
hope, prove useful additions to the catalogue of chemical-laboratory
appliances. The one is a new form of the precision balance,
which pretends to execute exact weighings with a hitherto un-
attained degree of rapidity ; the other is a contrivance for main-
taining a constant pressure in a supply of gas, and thus making it
possible, with comparative facility, to keep, say an air-bath, for
any length of time, at a constant temperature.

The new balance differs from the instrument in its customary

145

of Edinburgh , Session 1875-76.

form only in two points, of which the more important is a modifi-
cation of the centre of gravity “ bob” arrangement, which enables
one, at a moment’s notice, to shift the centre of gravity of the
instrument from a certain definite position, I., to .a certain
other (higher) position, II., matters being arranged so that in
passing from I. to II., the sensibility, i.e. the deviation, correspond-
ing to an overweight of, say 1 milligramme, is increased in an
exactly pre-determined ratio, such as of 1 : 10, for instance. For
this purpose the “bob” is made very light, so that the distance
through which it has to travel in order to effect the desired change
of sensibility is not too small, and, instead of to a screw as usual,
is fixed by mere friction to a vertical triangular steel rod forming
part of the needle. The other new feature in the balance is,
that the rider-principle, besides being discounted in a slightly
different manner from the customary one, is extended to the
determination of differences of weight up to 100 (instead of 10)
milligrammes.

The arrangement adopted is represented in the accompanying
sketch, for the interpretation of which it is only necessary to say
that C (10) and (10) O are equal to C (0)x and (0)1 (10)j respectively,
and that both O (10) and (10)j are each divided into 10 equal
parts, the former by notches filed into the beam, the latter by
marks ; and to add, that there are two riders, one weighing^ centi-
grammes for the left arm, and another weighing p milligrammes

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Proceedings of the Royal Society

for the right arm, the balance being adjusted so that, when both
riders are at their zero-points, it is in equilibrium, and p being
chosen so, that, supposing the large rider to be shifted to the
n mark, and the small one to the m mark, this virtually amounts
to the addition of lOn + ra milligrammes to the charge in the
right pan.

There is no need of my explaining how the balance is meant to
be used; I will rather avail myself of this opportunity for drawipg
the attention of readers interested in the subject to a few inferences
from the theory of the balance, which, obvious as they are, have
hitherto not been sufficiently appreciated by either the authors of
our physical handbooks or by practical balance-makers.

I. Given a balance in which everything is constant except the
distance s of the centre of gravity of the empty instrument from
the axis of rotation, and it is easily shown that (for a constant
charge) the deviation a of the needle for a given over-weight A, and

consequently the

“sensibility” a — is the greater the less

s. This, of course, is duly stated by all authors; but what is
always forgotten to be pointed out are two things, viz. — 1st, That
the “ sensibility ” has nothing to do with the inherent precision of
the instrument ; and 2dly, That supposing the sensibility to be
increased, all the other good qualities of the balance get less ; we
diminish the rate of vibration (this rate being proportional to

we diminish the range of differences of weight deter-

minable by the method of vibration ; we diminish the relative
constancy (in opposition to variations in the charge) of the
sensibility and the time of vibration. Considering now, —

II. The case of a balance to be constructed , the arm-length l and
weight w of the empty beam also become variables, related to
each other, according to some equation like w = const. l7 and
(assuming each of the pans to bear a certain medium charge p) we
have

t i— -

— t== const. J l v const. + const. I ,
sja

i.e ., by diminishing l we can increase the sensibility without
diminishing the rate of vibration (or vice versa)) but the other

147

of Edinburgh , Session 1875-76.

disadvantages mentioned under I. must be taken into the bargain,
and, besides, the inherent precision of the balance gets less.* To
pass to an example: What we gain by substituting a 7-inch for a
14 inch bea,m is that, for the most convenient t, the sensibility
becomes 2 to 4 times greater; but this advantage is secured with-
out expense in good qualities by placing before the graduated
limb a lens magnifying the excursions of the needle into 2 to 4
times their natural size. This is the theory of the u short beams”
which have lately come so much into fashion.

To come back to my own balance, I must not forget to thank
Messrs Becker Sons of Rotterdam for the readiness with which
they have, at their own risk, tried to realise my ideas in an
actual instrument, which, by the way, is now being exhibited at
South Kensington. To increase the usefulness of the instrument,
I have caused Messrs Becker to add to it a glass plunger, which
is adjusted so that it displaces exactly 10 grammes of water at
15°, and which consequently enables one with great rapidity to
determine the specific gravities of liquids by tbe method of
immersion.

To pass now to the new gas- governor , its most essential part
consists of a mercury-manometer (fig. 2), of which one limb. A, is

about 20 mms. wide, and stands vertical ; while the other, C, is of

the width of a thermometer tube, and is placed horizontally.

* For fuller explanations, see my article “ Balance ” in the “ Encyclopaedia
Britannica.”

148 Proceedings of the Royal Society

The empty part of the wider limb communicates, through F,
with the gas-supply, through G- with the gas-lamp serving to
heat the air-bath; and the quantity of mercury is adjusted so
that, when the gas is at the lowest pressure which, in the course
of the experiment, it is likely to “assume, the mercurial index
in C occupies a certain convenient position a.

The manometer is connected with a constant battery (the circuit
of which includes an electro-magnetic arrangement for opening or
shutting the gas-tap), in such a manner that, as soon as, through
ah increase of pressure in E, the index in C travels ever so little
towards the right of a, the current is closed, and the gas cut off.

The following Gentlemen were elected Fellows of the
Society : —

John Macmillan, M.A.

John Gibson Cazenove, D.D.

The following Gentlemen were elected Honorary Fellows
of the Society : —

1. Foreign Honorary.

Carl Ludwig, Leipzig.

Ferdinand de Lesseps, Paris.

2. British Honorary.

Henry John Stephen Smith, Oxford.

Thomas Henry Huxley, London.

Thomas Romney Robinson, D.D., Armagh.

Monday, 17 th April 1876.

Professor FLEEMJNG JENKIN in the Chair.

The following Communications were read : —

1. On an Improved Form of Galvanic Battery. By J.
Cook, Esq. Communicated by Professor Tail.

I wish to direct attention to a simple improvement on battery
cells, whereby porous cells are dispensed with, and the incon-
veniences of gravity batteries avoided.

149

of Edinburgh, Session 1875-76.

I may say it is a year or two since I first tried the plan.

It consists in first filling the outer glass cell one-third or one-
half with fine silver sand, then pushing a ring of glass (which I
cut from a common ale pint-bottle with a hot soldering bolt)
down an inch or so into the sand. The zinc element forms a ring
round the glass, and the copper lies as a plate on the sand within
the glass. Its superiority to the gravity batteries, and to those,
such as Sir William Thomson’s, where the sand forms a dividing
layer between the copper with its sulphate below and the zinc with
its liquid above, will be obvious. I did not find the cupric sulphate
solution to diffuse into the zinc division. It so readily admits of
inspection that it would be infinitely preferable' to the Meidinger
and other plans.

2. On the Properties of the Perigon Yersor. By G. J. P.
Grieve, Esq. Communicated by Professor Kelland.

3. Descriptions of some new or imperfectly understood
Forms of Palseozoic Corals. By H. Alley ne Nicholson,
M.D., D.Sc., F.R.S.E., Professor of Natural History in the
University of St Andrews, and James Thomson, F.G.S.

(. A bstract).

In this communication the authors gave descriptions of several
new or imperfectly understood forms of Paheozoic corals. After
giving a general account of the method of investigation employed
by them, the genus Heliophyllum , Hall, was discussed at length.
The external structure of this genus is very peculiar, and it was
shown that the genus is not by any means as nearly related to
Cyathophyllum as has been generally believed. The new genus
Grepidophyllum was proposed for a group of forms possessing the
extraordinary and characteristic endothecal dissepiments of Eelio-
phyllum, but with the remarkable character that the central tabu-
late area of the corallum is shut in by a well-developed accessory
wall or inner mural investment. Sometimes this secondary
investment constitutes a complete circular sheath to the central
tabulate area, and in this case all the primary septa become

150 Proceedings of the Royal Society

directly connected with the outer surface of the cylindrical tube
thus formed. More commonly, the secondary investment is open
all down one side, and becomes directly continuous with two of
the primary septa, thus constituting a horse-shoe shaped space,
formed by the central tabulate area together with a wide fossula
containing three short septa. It was shown that the fine coral
described by Mr Billings under the name of Diphyphyllum Archiaci
was truly a Crepidophyllum. It was further shown that two
different forms, of very similar aspect, had been included by one
of the authors under the name of Heliophyllum sub-ccespitosum.
One of these forms, the typical one, is a Crepidophyllum, and will
stand as G. sub-ccespitosum. The other is a Heliophyllum , and the
authors described this under the name of H. elegantulum.

The name of Thysanophyllum was proposed for a genus of
gestrseiform corals from the Carboniferous rocks of Scotland.
This genus is related to Lonsdaleia in the general form of the
corallum, in the presence of an exterior vesicular zone of large-
sized cells, and in the possession of septa, which have no con-
nection with the outer wall. It differs from Lonsdaleia , how-
ever, in the fact that the columella, so conspicuous in the latter
genus, is wholly wanting, and the central area of the visceral
chamber is occupied by strong remote, transverse tabulae. Two
species of the genus were described, under the names of Thysano-
phyllum orientate and T. minus.

Finally, the genus Lindstromia was proposed for a group of
small corals, in which the corallum is simple and conical, with an
extremely deep calice. The septa are well developed, and meet
in the centre of the visceral chamber, where they coalesce to a
greater or less extent, and form a strong twisted pseudo-columella,
which projects into the floor of the calice, and occupies a large
portion of the entire visceral chamber. There are no tabulae, but
the septa are furnished with more or less strongly developed
dissepiments, which, however, are remote, and do not give rise to
any vesicular zone. The genus may, perhaps, be regarded as
belonging to the Aporosa. The species L. columnaris was described
from the Devonian rocks of North America, and it was mentioned
that the authors were in possession of other forms of the genus,
still undescribed, from the Carboniferous rocks of Scotland.

of Edinburgh, Session 1875-76.

151

4. On a Stable and Flexible Arcb. By Professor
Fleeming Jenkin.

Monday , May 1876.

Professor KELLAND, Vice-President, in the Chair.

The Council have awarded the Keith Prize for the biennial
period 1873-75, to Professor Crum Brown, for his Re-
searches on the Sense of Rotation, and on the Anatomical
Relations of the Semi-circular Canals of the Internal Ear.

The following Communication was read : —

Is the Gaelic Ossian a Translation from the English X
By Professor Blackie.

The recent revival by a distinguished Celtic scholar of the theory
of Laing that Macpherson’s Gaelic Ossian is a translation from the
English, affords an opportunity of examining that question in a
more strictly philological fashion than it has hitherto had the
fortune to enjoy. Parts of the question were no doubt touched by
Mackenzie in the Report of the Highland Society, published in
1805 by Graham in his dissertation on the authenticity of Ossian,
by Dr Clerk of Kilmalie, the distinguished author of the new
version of Ossian in the late splendid edition published at the
expense of the Marquis of Bute ; but systematically grappled with
the question has never been. Having recently gone through the
whole of the originals, I have made careful notes of whatever
might tend to settle this question, and have come to the conclusion,
in the face of the statement of Mr Campbell — whose authority, no
doubt, is one of the highest on the subject, that the Gaelic is
unquestionably the original. The tests by which a translator’s
hand seems clearly discoverable are the following five: — (1) In
the English version, awkward, forced, and unidiomatic expressions
frequently occur, which can be clearly traced to the influence of a
Gaelic original. (2) In all poems of any antiquity handed down

VOL. IX.

x

152

Proceedings of the Royal Society

in manuscripts, difficulties will occur arising from obsolete words,
errors in transcription, confused connection, and other causes. In
such cases it is a common practice with translators to skip the diffi-
culty, gloss over the matter with some decent commonplace, and
sometime to make positive blunders, which is not difficult for a
philologer to expose. All these signs of a translator’s hand are
frequent in Macpherson’s English, and would be more so bad he
not indulged in such a habit of skipping generally that it is difficult
to say in certain cases decidedly that the skip was made because
the writer of the English wished to shirk a difficulty. (3) It is a
common practice with translators, when they find a passage a little
obscure, to remove the obscurity by some manifest alteration of
the phrase, or even by interpolating a line, or interlarding a com-
mentary. This also occurs in Macpherson. (4) It is not always
that a translator writes under the same vivid vision, or the same
fervid inspiration as the original poet; and the consequence is that
he will occasionally degrade poetry into prose, and specially fail to
bring out that individuality of character in his word-painting which
Ruskin has so triumphantly insisted on in the case of the sister
art. The instances of failure to seize the most striking features of
the original, and the substitution of generic for specific epithets,
are frequent in Macpherson. (5) Most translators y ie — some-
times, no doubt, wisely — to the temptation of improving on their
originals; and Macpherson, from what we know of him, was the
last man in the world to think of resisting such a temptation.
How much of the G-aelic, as we now have it — that is, his clean
copy of his own originals — was subjected to this process of beauti-
fication, as we may call it, no one can now tell, but 1 have traced
in several instances departures from the simplicity of the original
Gaelic, which can be explained most naturally on the supposition
that they proceed from a translator who has yielded, without any
just cause, to this flattering seduction. When the results obtained
by the detailed application of these tests are combined with the
amount of external evidence to be found in the Highland Society’s
report to the effect that Macpherson actually did translate from
Gaelic originals, and was seen by various parties for weeks and
months employed in the work of traslation, a cumulative proof was
produced that he was most anxious to see by what arguments Mr

153

of Edinburgh, Session 1875-76.

Campbell could rebut. If that gentleman, to whom Celtic litera-
ture owes so much (and who in fact is the Wolf of the Ossianic
question), or any Galician who thinks with him, shall succeed in
leading a counterproof, I can only conclude that, considering the
scrappy and fragmentary nature of some of the materials in Mac-
pherson’s hands, it might possibly have been the case that the
translator filled up some of the gaps in his tale in English, with
the intention that they might be done into Gaelic before publica-
tion by Strathmaskie, Captain Morrison, or some other of his High-
land coadjutors; but that the English, as a whole, is a translation
from the Gaelic, and not a translation of the best quality in many
respects, may be accepted as one of the best ascertained facts in
the whole range of philological investigation.

The following Gentlemen were elected Fellows of the
Society

Professor M. Forster Heddle.

J. F. Rodger, S.S.C.

William Thomson, F.C.S., Manchester.

Monday , Ibth May 1876.

Sir WILLIAM THOMSON, President, in the Chair.

The Keith Prize for the biennial period 1873-75, which
has been awarded to Professor Crum Brown for his Re-
searches on the Sense of Rotation, and on the Anatomical
Relations of the Semi-circular Canals of the Internal Ear,
was presented by the President.

The following Communications were read

1. Notes on Dredging in Madeira, by the Rev. Robert Boog
Watson, B.A., F.R.S.E., F.G.S.

The difficulties in the way of dredging at Madeira are many
and considerable. This has probably prevented any of this work
having been done since the publication of Mr Macandrew’s list of
Mollusca, presented to the British Association in 1854. The author

1 54 Proceedings of the Boyal Society

having dredged for several years at Madeira, confirms Macandrew’s
generalisation of the Mediterranean character of the Mollusca —
excludes 12 of Macandrew’s named list as having crept in by mis-
take, and to the 115 remaining species identified by Macandrew
as Madeiran has added 200 to 250 more, making nearly 400 in all,
of which 80 or perhaps 100 are probably new. These he hopes
soon to publish.

2. Note on a New Fossil Foot-Print from the Permian
Sandstone of Dumfriesshire. By Patrick Dudgeon, Esq.,
F.E.S.E. (Plate I.)

What appears to be an entirely new foot-print has lately been
found in the red sandstone of this district. I have seen many of
the foot-prints from the various quarries in the neighbourhood,
but have not before observed this one, nor is it like any figured in
Sir William Jardine’s splendid work on the “ Ichnology of Annan-
dale.” The foot-prints in question were found in a bed about
20 feet from the surface, at Locharbrigg’s Quarry, three miles
from Dumfries. They exhibit the usual large hind and smaller
fore foot; the impression of the hind foot measures '*5 x 2'’6, the
fore foot 2'3 x 1'- 9 ; the stride of the animal appears to have been
about 10'. The impression of the hind foot does not interfere with
that of the fore foot, as is the case with several of the foot-prints
figured in Sir William Jardine’s work, the interval between them
being 2' : the hind foot, therefore, must have been put down in the
rear of the fore foot when the animal was walking. The impres-
sion of the foot shows five toes, the thumb being placed far back.
The most characteristic features in these foot-prints are the well-
developed claws, and the oblique position of the toes, i.e., they are
placed to march one behind the other. In almost all the foot-
prints I have seen, where the toes can be made out, the middle one
appears the most prominent ; this foot-print is markedly distinct
in this respect.

As yet I have only been able to obtain one good specimen of
this foot-print — a hind foot ; the rest of the slab on which the casts
were impressed was unfortunately used for a paving stone in a
cottage in the neighbourhood. I got it lifted ; but the rough

Proc. Roy Soc.Ednf PlI.Yol.IX.

Farlane 2c Erakine . LibkTS EAmT

155

of Edinburgh, Sessio7i 1875-76.

usage it had been subjected to had greatly injured the impressions
on it ; they were, however, sufficiently distinct to enable me to
give the above particulars.

The accompanying photograph is a good one of the hind foot in
my possession, about half the size of the original. The posterior
pad of the foot is not quite complete, and it, together with the pads
of the toes, are somewhat broken.

I would propose for these foot-prints the provisional name of
Herpetichnus loxodactylus , the oblique-toed Herpetichnus, with the
following abbreviated character: —

Genus Herpetichnus, Jardine (“ Ichnology of Annandale,”
1853, p. 14).

Herjpetichnus loxodactylus , sp. nov.

Sp. chars. — Fore foot = 2'*3 x l'*9 ; hind foot = 3'‘5 x l/#6 ; stride
about 10'; impressions free ; toes 5, oblique; thumb far back;
claws well developed.

Locality and horizon. — Permian Sandstone, Locharbriggs Quarry,
three miles from Dumfries.

P.S. — In the discussion which followed this paper, Professor
Huxley stated that so far as he could judge from the photograph
exhibited, the markings closely resembled a foot-print he had
described some years before in a paper read before the Geological
Society of London, “ On tbe Stagonolepis Robertsoni (Agassiz) of
the Elgin Sandstones ; and on the recently discovered Foot-marks
in the Sandstone of Cummingstone ” (“Quart. Jour. Geol. Soc.,”
1859, xv. p. 440). The resemblance of these Cummingstone foot-
marks to the Chelichnus of the Dumfriesshire flags was noticed by
Professor Huxley in the paper referred to.

3. On the Decennial Period in the Mean Amplitude of the
Diurnal Oscillation and Disturbance of the Magnetic
Needle and of the Sun-spot Area. By J. A. Broun, F.R.S.

(Abstract.)

The author, in presenting results relating to the decennial period
derived from observations made at Trevandrum during twenty-two
years, has sought a redetermination of the mean duration of that

156 Proceedings of the Royal Society

period, as shown by preceding magnetical observations connected
with bis own. The relation of the frequency and area of sun-spots
to the amplitude of the diurnal movements of the magnetic needle
gives an increased value to this investigation.

Two very different results have been obtained ; — one by Dr
Lamont, showing a period of 104 years ; the other, by Dr ft. Wolf,
gives 11J years. Dr Lamont’s result depends on the assumption
that three periods occurred between 1787 and 1818 — an assump-
tion which is opposed to the conclusions which have been deduced
from the sun-spot, auroral, and magnetic observations for that
interval. Dr Wolfs result has therefore been accepted very gene-
rally by many of the most eminent scientific men in England and
on the Continent.

The author determines the epochs of maximum and minimum
range of the diurnal oscillations of the magnetic needle by the
more exact method, in which the mean for twelve months corre-
sponding (at its middle point) to each month of the year is obtained.
Commencing with the Trevandrum observations, from the present
time, proceeding backwards to the earliest series, showing a maxi-
mum, that of Cassini (Paris 1784-1788.) The maximum at this time
(1787'25) is confirmed nearly by Gilpin’s observations (London,
1786-1806). The latter do not show the minimum in 1792 and
maximum in 1797, which should satisfy Dr Lamont’s assumption,
and they are considered by him, like the observations of sun-spots
at the time, as worthless for this investigation. Dr Wolf, on the
other hand, finds support in both for a minimum in 1798.

It is concluded by the author, from an examination of Gilpin’s
observations, that a maximum really happened in 1797*7, but so
little marked as to make it probable that any slight corresponding
increase of sun-spots would not be noticed by the single, not very
accurate, observer at the time. Evidence, however, of a slight
maximum is also found in Professor Loomis’s investigation for the
frequency of the aurora borealis. As it is certain that another
maximum occurred about 1804 to 1806, the author finds that
Gilpin’s observations, which agreed with Cassini’s at the commence-
ment of the series, showed in all probability the true magnetic
variations afterwards.

It results from these investigations that the mean duration of the

157

of Edinburgh, Session 1875-76.

period is 10-45 years ; but that it appears to undergo a variation
between 8 and 12J years in an interval of 42 years. The small
maximum of 1797*7, if a true result, may be expected to repeat
itself at some future time, a result which could not fail to aid in
the search for the cause of these variations.

The author shows, that according to the long period of 42 years,
a maximum should have happened in 1776 ; but that year Dr Wolf
has concluded to be one of minimum sun-spot frequency. That
1776 was really a year of maximum is confirmed by the observa-
tions of Van Swinden, who, it is shown, appears to have been the
first to obtain a variation due to the decennial period, and to have
pointed out the appearance of a law : it is also confirmed by the
observations of Cotte at Montmerency.

The ratio of the ranges of the diurnal variation in the years
when it is a maximum to that in the years of minimum, is com-
pared for different parts of the world, and found nearly the same
in both hemispheres. It is also found that the law of the diurnal
variation is the same in the year of maximum as in the year of
minimum. The author concludes that the increase of the diurnal
variation is not due to a different cause from that which produces
the variation at the minimum, and that this cause acts when there
are no sun-spots in the same way as, though with less intensity
than, when the latter have their maximum frequency and area.
The magnetic variations are therefore not due to the sun-spots ; the
latter appearing only when the common cause produces diurnal
variations having at least two-thirds of the maximum amplitude.

The results derived from the sun-spot area are compared with
those from the magnetic observations. While a general agreement
is found in the decennial variations from year to year, it is evident
that the attempt to calculate the amplitude of the diurnal varia-
tion from the sun-spot frequency (as has been done by Dr Wolf)
must give results frequently deviating widely from the truth, as
might be expected from the previous conclusion.

The decennial period of disturbance of magnetic declination at
Trevandrum, deduced from hourly observations in the eleven years,
1854 to 1864, is next considered. It is found that the mean disturb-
ance at each hour of the day shows the decennial period; but that
the range of the mean value, from the minimum to the maximum

158 Proceedings of the Royal Society

year, is different for each hour, while the maximum and minimum
do not happen at exactly the same time for all hours of the day.
Secondary maxima and minima are also shown, which vary in
their epochs gradually from midnight to noon.

No clear law appears to connect the amount of the maximum
disturbance for any hour with that of the minimum for the same
hour in the 11 years ; the ratio of the first to the second is least
for the hours near noon, and greatest for those near midnight. It
is found, however, that the maximum and minimum mean dis-
turbance in the diurnal variation for each year, as well as in the
decennial variation for each hour, are connected by the following
relations : — Dm being the maximum and D0 the minimum dis-
turbance.

^/Dm — JD0 = Constant.

The monthly mean disturbance at Trevandrum in each of the
years 1854 to 1864 is compared with the monthly mean sun-spot
areas deduced by Messrs De La Hue, Stewart, and Loewy, from
Carrington’s and the Kew Observations, with the following re-
sult : — The monthly mean disturbance in the years 1854-56 had
a considerable value, and marked variations when there were few
or no sun-spots. In 1857 to 1862 there are found several maxima
and minima of disturbance and sun-spots which occur simulta-
neously. In some cases, and especially in June 1862, there is a
well-marked sun-spot area maximum without any corresponding
change of magnetic disturbance. The cause of the solar disturb-
ance did not then extend its action to the earth at that time.

The author concludes with a notice of the hypotheses proposed
to explain the decennial period of magnetic variations and of sun-
spot frequency, as well as of the cause of sun-spots. It is pointed
out that no theory of sun-spot formation can be accepted which
does not explain their non- (or very rare) appearance every 10 or
11 years, and therefore the cause of the decennial period is bound
up with this explanation. A planetary action which disturbs the
equilibrium of the solar gases has been proposed ; no other seems
to present itself, and this the author believes will be found ulti-
mately to be in question ; and though he has not himself been able
to find any satisfactory evidence in its favour, yet remarkable
results have been obtained by Messrs De De Eue, Stewart, and
Loewy.

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of Edinburgh , Session 1875-76.

4. On the Parallel Roads of Lockaber. By David Milne

Home, LL.D.

( A bstract .)

The author referred to the papers written on the subject, begin-
ning with that by Dr Macculloch, in the year 1817 ; and he
explained the various theories suggested.

He intimated his adoption of the Lake theory, and expressed his
adherence to the view he took in the memoir read by him in this
Society in the year 1846, that the blockages of the lakes had been
effected by detrital matter.

In support of this view, he pointed out that all over this district
of the Highlands there were immense beds of clay, sand, and
gravel up to the tops of the hills, at even 2000 feet above the
present level of the sea.

These deposits he considered to be undeniable proofs of the
prevalence of the sea over this part of the earth’s surface to a
height of 3000 feet at least.

When the sea retired, so as to expose to atmospheric action the
higher parts of the country, there would be depressions in the sur-
face of the land, where lakes would be formed. These lakes would
continue at high levels, till the streams issuing from them cut
through the detritus. In some cases, the process of erosion would
be so gradual, that the lakes would subside without producing any
conspicuous beach-lines on the mountain sides. In other cases,
the removal of the blockages would be on a large scale, owing to
the looseness of the detritus ; and if these removals were separated
from one another by a considerable interval of time, beach-lines
of a permanent character would be formed on the sides of the
mountains enclosing the valleys.

The author referred to the existence in this district of the High-
lands, now, of several lakes at high levels, which were kept up by
detrital blockages. He instanced, in particular, Loch Earba, in the
Lochaber district, at a height of about 1150 feet, which was kept
up by such means, and on whose banks there was evidence that
the lake had once stood 30 feet higher than at present. Near
Kingussie there was Loch Gwynae, at a height of 1015 feet above
the sea, on whose sides there were traces of five terraces, the highest
of which is 132 feet above the present surface of the lake.

VOL. IX.

Y

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Proceedings of the Royal Society

He referred to the ample means of cutting through and remov-
ing detrital matter possessed by streams and rivers, mentioning
particularly the enormous cliffs of detritus cut through by the
Rivers Spean and Spey.

He next proceeded to discuss the theories of other geologists.

With regard to the theory that the parallel roads were formed
by the sea, he adduced arguments to show, that this view was im-
possible, inasmuch as the “roads” should in that case have all
stood at the same level ; whereas, in the different glens, they stood
at different levels. Moreover, it had been found, that old river
courses existed, by which the water in G-len Gfluoy flowed into the
water in Glen Roy, and that the water in Glen Roy flowed through
Glen Glaster into Loch Laggan, — a state of things utterly fatal to
the marine theory.

With regard to the blockage of the lakes having been formed

ice , the following objections were stated : —

ls£, The improbability that some of the glens were filled with
water, whilst others were filled with ice, the temperature of those
glens being all much the same, in consequence of nearly equal
altitudes above the sea.

2d, The impossibility of getting a glacier to come to the exact
spot, where the lakes stopped, to form barriers several miles long,
so solid and permanent in structure, as to prevent the escape of
the water from lakes above 300 feet deep.

The author concluded by referring to the numerous examples in
the Lochaber district, of boulders perched on tops of hills, and of
rocks smoothed and striated. These phenomena had been ascribed
by some geologists to the action of land-ice. But, coupling with
these high-perched boulders, the occurrence of kaims or eskars on
the sides of the hills (above the parallel roads), and therefore
formed before the Lake period, the author was inclined to ascribe
these phenomena to one agent — viz., a sea loaded with ice, when
the land was submerged, and to a strong current in the sea, from
the north-west, which swept over the submerged land, and through
such valleys as Glen Spean and Glen Roy. The lakes, he referred
to the period when the land was rising out of the sea. Their
beaches were formed on the marine detritus; — which also for a time
dammed back the lake waters.

of Edinburgh, Session 1875-76.

161

Monday , 5th June 1876.

D. STEVENSON, Esq., C.E., Vice-President, in the Chair.
The following Communications were read : —

1. Physical Observations in Northern Asia. By
Professor G. Forbes.

2. On Parallel Motions. By the Rev. John Wilson, M.A.,
Bannockburn Academy. Communicated by Professor

Kelland.

It has been well said that the transmission of force is an ‘‘essen-
tial condition in machinery.” It is no less true that directness in
transference is important; that the fewer links in the chain bind-
ing driver and follower together, the less likely is the machine to
be put out of gear. There is no question here as to the compara-
tive values of the different modes of conveying motion from a
prime mover, — rolling contact, sliding contact, wrapping connec-
tors, or linkwork. Each has its own excellencies ; each its special
advantages ; and one is to be preferred to another only according
to the nature of the work to be done.

I. Watt's Parallel Motion. — The general problem is the “com-
mutation of circular with rectilinear motion.” The importance of
the question began to be felt soon after the introduction of the
steam-engine; and Watt, in 1784, patented an invention which
not only had the credit of being the earliest, but up to recent
times, the most reliable and accurate parallel motion in existence.
This system was a great advance on the huge chains and arches
which were affixed to the working beam of the engine for the pur-
pose of obtaining the desired motion; and it has proved to be suf-
ficiently accurate for all practical purposes. The construction is
simple, consisting of three bars : two, rotating round fixed centres,
and connected at their other extremities to the third bar. A point
in this bar, either within or without the points of junction, accord-

162

Proceedings of the Royal Society

ing as the centres are on opposite sides, or on one side of the con-
necting rod, moves in a straight line. The simple explanation of
the underlying principle is that the curvature in one direction is
modified by the curvature in an opposite direction, due to the
motion of the other bar. In both the original and the modified
form of this three-bar motion there is a divergence from the straight
line, which though inappreciable for small angles, becomes some-
what more apparent for larger ones.

The determination of the parallel point is given in the formula

QF : FP : : AP : BQ

In the figures 1 and 2, A.P and BQ are the arms; PQ the con-

Fig. 1. Fig. 2.

necting link. Let the centres A and B be chosen so that the line
mM shall bisect the versed sines of BQ and AP; the throw QK
being equal to PT.

163

of Edinburgh, Session 1875-76.

QF : FP : : Lm : MK : Lq : Kp

: : BQ (1 - cos 0) : AP (1 - cos <p)

: : BQ • 2 sin2? : AP ■ 2 sin2 £

A A

: : BQ • O2 ■ AP • f . . . . (1J)

: : BQ • AP2 : AP ■ BQ2 ... (2)

: : AP : BQ

0 0

(] ) For small angles, sin ^ =-^ nearly.

(2) Ultimately, BQ sin 0 = AP sin <p, or, BQ : AP : : sin : sin 0 : : <p : 0.

In connection with Watt’s system we are led to consider the
motion of the pantagraph, which has been a means of extending
the parallel motion. Thus, while to the point F is attached the
air-pump rod of an engine; by means of the pantagraph, whose
property is that it describes similar curves on a smaller or larger
scale, another point will trace another parallel line, and to it there-
fore may be fixed the end of the piston-rod. By superadding the
parallelogram of bars to the Watt parallel motion, and making
E, — the angle of the parallelogram — the connecting point of the
piston rod, so as to concentrate the force ; we have the point E
describing a curve similar to F, when

QF : BQ : : PQ or HE : BH. (Fig. 3.)

H
E

Fig. 3.

The problem of the pantagraph may be proved as follows. Let
the initial position be at an angle of 90°, the arms lying along the
axes of x and y. (Fig. 4.)

Given the fulcrum A and the ratio AB : AC, to find B1? the posi-
tion which B the pencil assumes when the tracer C moves to Cr
When the position of Cn is given, the angle CjDjA is known, for
ADj and CDj are constants. Join BBj and CCj ; ABX and ACj
(which latter are not assumed to be coincident).

In the triangles CjDjA and BjFjA, the angle BjFjA is equal
to the angle CjDjA; and the sides about these angles are propor-

164

Proceedings of the Royal Society

tional, viz., BjFj :F2A : : CjDj : D:A. Therefore the triangles are
equiangular (Euc. VI. : 6).

Wherefore the angle F1AB1 is equal to the angle D1AC1, that is

they are identical ; and AB^ is a
straight line. Now in the triangle
ACCj, — AB : AC : : ABX : ACr
Therefore BBX is parallel to CC^
and BB: : CCl : : AB : AC, which
is the given ratio.

Wherefore the position of Bx is
found. And any other position
such as C n will have its projec-
tion in similar ratio to the given
one AB : AC or AF : AD.

II. The Reciprocator.— About
1864 M. Peaucellier communi-
cated to the SocietePhilomathique a paper anent a newly-discovered
means of producing parallel motion; but, at the time, little notice
was taken of the subject. When Lipkin, a pupil of Tchebicheff,
rediscovered it a few years later, it awakened the attention of the
most eminent mathematicians of the day ; and now it promises to
become a power in the field of higher analytical investigation. The
marvellous extension of the problem is due chiefly to the research
of Professor Sylvester, who was the first in this country to direct
attention to it.

The fact of pure linkwork constituted the difference between
Peaucellier’s and all other attempts at parallel motion. These
have been only approximate, or if exact, the slot has been called
into action ; while in the case before us the motion is entirely due
to the grouping of links around fixed centres.

The system consists of seven links. (Fig. 5.) A cell or rhombus
MPNC is jointed at two opposite angles to two links AM and
AN, which are called connectors. To one of the remaining angles
is attached a radial bar BP. Of the two fixed points, A is called
the fulcrum ; B, the pivot. The points C and P are the poles of
the cell. The variable distances CA and AP are called the arms
of the cell, while the difference between the squares of AM and
MP is termed the modulus.

165

of Edinburgh, Session 1875-76.

When A, the fulcrum, lies without the rhombus, the cell is called
a positive cell ; when it falls within, the cell is negative.

The following results can easily be verified : —

(1.) APC is a straight line.

(2.) AP . AC is a constant quantity (Euclid III. 36), N being
at every moment the centre of a circle with a radius NP or NC.
This result is expressed
by saying that the
curves described by P
and C are tbe inverse
of one another. Now
the inverse of a circle
is generally another A
circle. If, then, one of
the poles of the cell be
made to revolve in a
circle round B, the
other pole will describe
a circle. There is however an exception, for when the fulcrum is
in the circumference of the circle described by P or C, the other
pole describes a straight line.

The following is the geometrical proof : —

Let the positions of P be pv p2, p3, &c., and the corresponding
positions of C, cv c2, c3, &c. ; and suppose that the initial position
of the system is when AC lies along the axis of x , that is, in a
straight line with the centres A and B. Join P and pl ; C and cr
Join the corresponding pairs P p2, Cc2, &c.

ByEucl. II.: 12. AM2 = MP2 + AP2 + 2AP • PK

Am2 = mp 2 + Ap2 + 2 A p * pk
.-. AP [AP + 2PK] = A p [Ap + 2 pk]
AP • AC = Ap * Ac.

AP Ac
°r Ap ~ AC

In the triangles APp and ACc the angle A is common ; and the
sides about it are proportional, viz.,

AP : Ap : : Ac : AC

166

Proceedings of the Royal Society

Therefore the triangles are equiangular (Euc. VI. 6), wherefore the
angle qCA = P^qA . But P/qA, the angle in a semicircle, is a
right angle (Euc. III. 31), therefore qCA is also a right angle.

With any other position p2 ofP, C will take up a corresponding
one c2, by joining which with C a right angle is formed. Where-
fore the point C moves in a straight line at right angles to AB
produced.

When the ratio subsisting between the length of the radial bar
and the distance of the pivot from the fulcrum is not one of
equality, the position of the parallel point is a circle, which is
concave or convex with respect to the fulcrum, according as BP is
greater or less than AB. The results, as determined by methods
of analysis, show that the equation is the same for both the sym-
metrical and non-symmetrical forms of the cell ; that is, for both
the ordinary cell, where the pivot B in the initial position lies in
a line with the fulcrum and the poles, — and for that form where
the line passing the poles makes in the initial position a tangent
to the circle described by the radial bar. Thus, if R were the centre
of the circle described by C, its distance from the fulcrum A,

is RA =

AB [AM2 - MP2]
BP3 - AB2 ;

and the length of the radius

BP [AM2 - MP2]

IS iiu - Bp2 _ AB2

The determination of the position of R, which is evident in the
non-symmetrical form of the cell, is simply given in the ratio
RC : RA : : BP : AB.

Thus, if AM = 7; MP = 5; BP = 3; andAB = l

th„ BP [AM2 - MP2] 3(49 - 25)

tuen JUj - Bp2 _ AB2 - 9 _ j =9

RA = ~ • RC = 3

One form of the cell has given rise to a discussion of the question
whether the parallel motion of Peaucellier is not simply a modifi-
cation of the pantagraph. The resemblance between the two
systems is not noticeable at first sight ; and one would be inclined
to deny any connection between them.

167

of Edinburgh, Session 1875-76.

In this system the connectors are joined not at the opposite
angles of the rhombus but at such points in the adjacent sides
produced that at every moment they are parallel to the remaining
sides (fig. 6). APC
is a straight line.

AM = CMsince AM||LP.

Let LP be produced to
F, makingLF = LM,and
complete the rhombus
LFKM* The bars AN,

ON, and IP can be re-
moved without interfer-
ing with the motion of
C and P. Thus AM, Fig. 6.

MC, with LF, FK form a pantagraph, and for every position of
C, P takes another, equiangular and proportional.

III. The Gorgon Linkage . — The parallel motion of Mr Scott
Bussell is exact, and constitutes a two-bar motion. From the fact
that it was fitted by Mr Seaward to the engines of the “ Gorgon,”
it may conveniently be called a Gorgon Linkage. A link AB is
bisected in C, and at this point another link CD, equal to CA or
CB is attached. D is the centre of revolution. If one end A of
the link AB be guided along the axis of x, the motion of B is at
every moment in the axis of y from D.

For every position C is the centre of a circle ADB, and ADB is
the angle in a semi-circle, that is, a right angle. Hence B de-
scribes a straight line.

This system of links derives additional interest from the dis-
covery of the Peaucellier cell, as by it the motion of the parallel
point can be thrown in a direction at right angles to itself ; that
is, parallel to the line joining fulcrum and pivot ; and this can be
transferred to the line of centres by means of the pantagraph.

IV. Hypocycloidal Parallel Motion . — Another very interesting
case of the problem of Parallel Motion is that produced by a hypo-
cycloidal movement. When one circle is made to revolve on the
concave circumference of another circle, any point in it describes
a curve, which is called the hypotrochoid or hypocycloid. If the
diameter of the revolving circle be equal to the radius of the circle

VOL. IX.

z

168

Proceedings of the Royal Society

Fig. 7.

in which it revolves, the hypotrochoid becomes an ellipse ; and if
the point be on the circumference of the smaller circle, the ellipse
degenerates into a straight line.

Let the circle BPO (fig. 7), diameter BC = AC, revolve in
the circle ABM, radius AC. If the initial position of the describ-
ing circle be such that AC
be its diameter along the
axis of y, the point A will
move along the diameter
AM. When the circle has
moved round to B, let P
be the position of A ; then
AB = BP. Join BKC and
KP. Let ACB = 0;
BKP = <p. The arc BP =
AB .* . BK- <p = KC-6 =
2 BK • 0. Hence <p = 2 6.
Hence P must lie on AC.
(Euc I. 32).

The difficulty of constructing, and the inconvenience experienced
in using an arrangement in which the annular wheel comes into
action, are so great that it is seldom employed. The following is
a simple method of obtaining the hypocycloidal motion without
requiring the annular wheel. On the arm ACB (fig. 8),

which is made to revolve
in a circle MLP round A,
attach two toothed wheels
LNF and FEM, in gear with
each other and with a fixed
wheel EOH, whose radius
AE is double that of NLF.
The centre wheel EEM is
used merely for the purpose
of reversing the motion of
NFL, hence it is immaterial
how many teeth it has; the
only postulate of the pro-

Fig. 8.

blem being that LFN revolve on its axis at double the speed of the

169

o f Edin b urgh , Session 1875-76

arm AC, and in a contrary direction. The number of teeth on HEO
is twice the number on NLF. Hence NLF makes two revolutions
round its axis, while the arm causes it to revolve round the fixed
centre-circle HEO. The axis C is rigidly connected with a wheel
XWP, revolving on the upper surface of the plate-arm ABC, whose
circumference continually passes through A. Thus while the plate-
arm ABC makes one revolution round A in the direction of the
hands of a watch, XWPA, which is rigidly connected to the axis
C of NLP and partakes of its motion, makes two revolutions in
the opposite direction. Thus it revolves round an imaginary
annular wheel XYZQ, whose diameter ZQ is double that of its
own ; and in virtue of hypocycloidal motion, if XWP be the
initial position, the point A in the circumference of XWPA will
move along ZQ.

In the annexed figure (fig. 9), the modus operandi of the machine
is sketched. The system is analogous to the sun and planet wheel
invented by Watt.

It would be going beyond the limits of this paper to direct
attention to the two modifications of the Peaucellier cell, which
have been called respectively the Quadratic-binomial Extractor,
and the Conicograph. The introduction of these into the sphere
of mathematical investigation has given several indications of
valuable results to be obtained therefrom. For a brief outline of
these, we refer the reader to the pamphlet of Professor Sylvester,
who not only was the first in this country to direct attention to
the general problem, but also had the credit of demonstrating the

170

Proceedings of the Royal Society

higher vantage ground opened to the mathematician by means of
Peaucellier’s discovery. The extent of our own obligation to him
is great.

Not less are we indebted to Professor Kelland, whom we have
known both as a teacher and a friend. The valuable hints and
suggestions he has given us on this subject we are glad to take
this opportunity of acknowledging.

3. Laboratory Notes. Ity Professor Tait.

(«.) On the Passage of the Electric Current from Amalgamated
Zinc to Zinc Sulphate Solution. By J. G-. MacGregor,
M.A.

(5.) On the Thermo-Electric Properties of Cobalt, &c. By Messrs
Knott, MacGregor, and C. M. Smith.

(c.) Measurements of the Potentials required for Long Sparks of a
Holtz Machine. By Messrs Macfarlane and Paton.

4. Note on Orthogonal Isothermal Surfaces. By

Professor Tait.

5. Notice of some recent Atmospheric Phenomena.

By Professor Tait.

6. Keport by the Society’s Boulder Committee. (Plates

II. and III.)

Mr David Milne Home gave in the Third Report of the Society’s
Boulder Committee, from which the following are extracts : — In
November 1875, on the invitation of Sir John Douglas of Glen-
finnart, the Convener went to visit him at that place, to have an
opportunity of examining several remarkable boulders reported to
the Committee as situated in that part of Argyllshire.

1. On the east side of Lochlong, opposite to Ardentinny, there
is the farm of Peaton. On this farm, a burn descends from a
steepish hill which faces the north. A gneiss boulder lies in a
gorge cut by the burn through rocks of clay slate. The boulder

Proc Roy. Soc.Rdm- PLATE II. Vo l IX.

Same Boulder viewed from opposite side.

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171

of Edinburgh, Session 1875-76.

rests on the rocky sides of the burn, jammed in between the sides.
The boulder has some local name like “Jenny Meullen,” meaning
“ House on a knoll.” The height of the boulder above the sea is
about 226 feet. Its distance from the sea-beach is about three-
quarters of a mile. The size of the boulder is about 24 x 18 x 12
feet. It is most probable that the boulder was transported across
the loch from the north or north-west, and was arrested in its
further progress southward by the hill, on the north side of which
it stands.

Two sketches of this boulder are given on Plate II. figs. 1 and 2.

2. Between the site of this boulder and the sea-beach an old sea
margin occurs at a height of about 45 feet above the sea (medium
level). A number of boulders lie along the line of this sea margin.
There is an old sea margin on the opposite or west side of the
loch, at exactly the same height — viz., 45 feet.

3. Close to the beach in this part of Lochlong — i.e., about 8 or
9 feet above high-water mark — at a place called “ Letter,” there
lies another gneiss boulder, 12 x 8 x 8 feet. Its long diameter
points N.W. by N.— viz., to Grlenfinnart Valley.

4. Very near this boulder (about 100 yards to the north) the
clay slate rocks have been ground down and smoothed. Their
smoothed surfaces show numerous striae pointing N., 2° or 3° W.
(magnetic). The smooth surface dips towards the north at an
angle of 3° or 4°.

5. On the hill above Carrick Castle, situated on Lochgoil, there
is a boulder called “Clach udelain,” or the “Stone nicely balanced.”
It is at a height of 1526 feet above the sea. This boulder is of
gneiss, and lies on rocks of clay slate. It lies on a bare rock, the
face of which slopes to N.N.E. — i.e., towards Lochgoil. The
boulder is within three or four yards of the edge of a precipitous
rocky cliff, which goes vertically down about 500 or 600 feet. The
block is of enormous size. Unfortunately the note taken of its
dimensions has been lost. This boulder, from its position, could
not have fallen from any hill. There is no hill near it from which
it could have fallen.

A sketch of this boulder is given on Plate II. fig. 3.

6. The next boulder visited is about two miles to the eastward of
the last-mentioned, and is within a quarter of a mile of Lochgoil,

172

Proceedings of the Royal Society

near its junction with Loclilong. It is about 450 feet above the sea.
It may be observed, that all the rocks in this district have their
smooth faces towards the north, their rough faces towards the
south. This boulder has received the name of the “ Giant’s Put-
ting-Stone,” from a legend which alleges that in former times
there were giants who inhabited the district on both sides of Loch-
long, and who were in the practice of amusing themselves by throw-
ing these huge boulders across the loch. The rock on which it rests
slopes gently N. by E. This rock presents a large surface, ground
down and smoothed. The space of rock occupied by the superimposed
boulder is only 18 inches by 12 inches. It would not be difficult
for two men with strong levers to move the boulder from its narrow
resting-place, in which case the boulder would probably roll down
the steep hillside into the loch.

Two sketches of this boulder are given on Plate III. figs. 4 and 5.

7. To the north of Knap Farm-house, there is a small hill, on or
very near the top of which eight or ten boulders are clustered.
They suggest the idea that this hill has arrested or interrupted
the body, whatever that body was, which transported the boulders,
and caused them to be stranded here.

8. There is another hill lower down the valley of Knap (about
480 feet above the sea), the top of which consists of clay slate
rocks, rounded and smoothed by some agent passing over from the
north. It has received the popular name of the u Pig’s Back.”
Several boulders lie on this ridge. The largest rest on a very small
portion of rock.

A sketch of this ridge of rock, with boulders on it, is given on
Plate III. fig. 6.

9. Pulag boulder is near the top of a hill to the west of Glen-
finnart, about 824 feet above the sea. It is a large block of gneiss,
about 7 feet high. There are many other smaller boulders lying
near it. The large boulder is almost on the edge of a precipice
which goes down at least 200 feet. It could not have been rolled
or pushed to its present position. The levels of the district show
the greatest openings towards the north — a circumstance which
suggests that the boulder came from the north. Moreover, its
south end rests on a smaller boulder, which seems to have stopped
its progress further south.

173

of Edinburgh, Session 1875-76.

A sketch of this boulder is given on Plate III. fig. 7.

10. Along various parts of the hills in this district where their
highest ranges are seen against the sky, and at a height of about
2000 feet above the sea, boulders are discernible from a distance,
lying on the ridges. It would he very desirable to obtain particular
accounts of boulders at so high an elevation.

11. In the last Report of the Committee, notice was taken of a
boulder in Ayrshire called the u Hun terston Boulder.” Along the
same coast, and especially on the property of Mr Alexander of
Boydstone, several very large boulders may yet be seen. One,
called the “ Boydstone Rock or Stone,” is situated about two miles
north-west of Ardrossan. Some chips of the boulder, sent to the
Convener in a letter, show that it is porphyritic. The rocks on
this part of the coast are Old Red Sandstone. The boulder is in
length about 19 feet, and in breadth about the same. It is partly
buried in the mud of the shore. Its highest point is 9J feet above
the shore. It is said to contain 40 cubic yards above the shore
line. It is supposed that the boulder is buried to the depth of
5 feet. The tide at high water leaves about 3 feet of the boulder
visible. This boulder has inspired the poetic genius of an Ayrshire
letter-carrier (Malcolm Kerr, post-messenger between Ardrossan
and West Kilbride), who, through Mr Weir of Kirkhall, has sent
to the Convener the following stirring address : —

To the Great Boulder on the shore opposite to the lands of Boydstone,
two miles north of Ardrossan, Ayrshire.

“ Can’st thou speak, old grey stone,

Unto me ?

List thou to the ocean’s moan,

I to thee :

Music sweet ! Spirits string
Wild ditties, as they cling
To the big waves which swing
Around thee.

Stranger ! whence didst thou come
To this shore ?

Art thou an Arctic crumb,

Which of yore

174 Proceedings of the Royal Society

On some huge iceberg side
Prom thy first home did glide,

A wanderer on the tide,

To this shore ?

Many eyes with wonder,

Ages gone,

Looked on thee ! What number
Yet unknown,

Will gaze with curious eye,

Seeking to know thy history,

And solve a hidden mystery,

Old grey stone.”

Besides the boulder which inspired these verses, there are two
others, also on Mr Alexander's property — one of them, as Mr Weir
states, “ even larger than the big stone at Brigurd, at Hunter-
ston.” This larger one it was proposed to split up for building
purposes at Ardrossan ; but Mr Alexander interfered, and saved
it. There are many other boulders along the Ayrshire sea-coast,
but none so large as the Boydstone boulder. A chip of one of these
sent, shows that it is of gneiss, indicating a northern origin.

12. A report has been received of a gneiss boulder near Dun-
blane, on the property of Cromlix, belonging to the Hon. Captain
Drummond. The length of the boulder is stated to be 17J feet,
its breadth (on an average) 10, its height about 5 feet. Its
longer axis lies in a direction south-west and north-east. At its
south end it dips into the ground at an angle of 45°. Its weight
above ground is estimated at 34 tons. Its height above the sea is
about 450 feet. It is about four miles south from the G-rampians.
The same, reporter (Henry Wilkie, Ashfield Works, Dunblane)
refers to a group of four boulders in the parish of Bedgorton, at the
west end of a gravel ridge on the farm of Bertha, the property of
Murray Graham, Esq. of Murrayshall. Three of these Bedgorton
boulders are within an area of 30 yards. They are angular; flat
on the top, and some of them square. They seem to be Silurian
rocks. They are distant about twelve miles from the Grampians.

13. Notice has been received by. the Convener from Mr Bobert-
son, C.E., who is in charge of the Albert New Docks at Leith,
that boulder clay was found in excavating for the docks beneath
the shore line, to the depth of about 70 feet. The clay was full of

175

of Edinburgh, Session 1875-76.

large blocks. Some of these were of sandstone, weighing 10 or
12 tons, and appeared to be of the same rock as that worked at
Granton and Craigleith Quarries to the westward. Beneath the
boulder clay, there was found what the engineers call a “running
sand ” lying over strata of shale and sandstone.

Before concluding, the Committee may advert to the circumstance
that a part of the district comprehended in this Report was. many
years ago described by an eminent Scotch geologist — the late Charles
M‘Laren — and with reference to the very matters embraced in this
report. Mr M‘Laren read papers in this Society, in the years
1846-47, describing the boulders then existing on the shores of
the Gairloch, and on the hills between that loch and Lochlong.
Even then the destruction of boulders in that quarter had begun,
being appropriated, as Mr McLaren states, to building purposes ;
and probably by this time they have all been annihilated.
Mr M‘Laren in these papers described also the striation and
smoothings of the rocks, which he found from the sea-shore
up to the tops of the ridges, between the Gairloch and Lochlong,
at heights of about 1000 feet above the sea. It is due alike to
the memory of our Associate, and to the interests of geological
science, to mention, that the boulders referred to by him, as
found on the Gairloch, consisted of grey granite, of which he
counted above a hundred, one-third of them exceeding 30 tons in
weight; as also mica slate, which, though less numerous, had
had among them blocks of 60 and 80 tons in weight. As
the rocks of the Gairloch in situ , are of a more recent kind — viz.
clay slate-— Mr M'Laren justly inferred that the boulders were of
northern origin. For those of granite, he pointed to Ben Cruachan,
a mountain exceeding 3000 feet in height, situated to the N.N.W.,
and distant about thirty miles. The mica slate hills are also in
the same direction, somewhat more distant. From his study of the
boulders and other phenomena in this district, Mr McLaren drew
two important conclusions. One conclusion was, that the boulders
must have been brought to the district from the parent moun-
tains, across valleys and ranges of hills, on ice floating on a sea
which stood from 1500 to 2000 feet above the present sea-level, and
in which a strong current had prevailed from the N.W. This con-
clusion, it will be noticed, is confirmed by the facts specified in the

2 A

VOL. IX.

176 Proceedings oftlie Royal Society

present Report, and also in former Reports by the Committee. The
numerous instances given in these Reports of huge boulders shown
by their composition to be of northern rocks, clustered frequently
on the summits or peaks of hills, at heights of 1500 and 2000 feet
above the present sea-level, seem to leave no doubt regarding the
soundness of that conclusion to which Mr McLaren had come to
thirty years ago.

The other conclusion to which Mr M£Laren came, and which
many good geologists of the present day hold, was this, that local
glaciers had at one time existed in all those valleys. This he
inferred from observing, that the striations on the rocks were all, as
he thought, exactly parallel with the axis of the valley, and which
here generally runs in a direction north-west and south-east ; and
also from discovering accumulations of gravel and clay in the
form of elongated embankments — some across the valleys, others
parallel with the valleys, reminding him of the lateral and terminal
moraines of Switzerland.

As to the soundness of this second conclusion, or the correctness
of the observations on which it was founded, the Committee give no
opinion. None of the members of the Committee have visited the
localities, and their function as a Committee has been chiefly to
collect facts connected with the boulders. Rut it may not be out
of place to record the fact, that another of our Associates, the late
Robert Chambers, who had also given much attention to this
branch of geological science, went to examine the districts referred
to by Mr M‘Laren, and expressed doubts regarding these last-
mentioned views. In two papers read by him in this Society in
December 1852, Chambers states, that on the rocky ridge between
Lochlong and Holy Loch, at a height of 600 feet above the sea,
the direction of the striations was not parallel with the valley, but
“ slanting over the hill ; ” and as the striations were not merely on
the sides of the valleys, but on the tops of the hilly ranges dividing
the valleys, he thought they were more probably due to a general
glaciation of the country than to local glaciers. Chambers quotes
also the opinion of Sir Roderick Murchison, “ that there is no
imaginable centre for the issue of glaciers of the ordinary kind down
the G-airloch.” On this point the Committee offer no opinion, and
wish only to advert to the investigations of eminent Scotch geolo-

177

of Edinburgh, Session 1875-76.

gists who in former days attempted a solution of these difficult ques-
tions. The Committee would venture to suggest a re-examination
of the localities, as the fuller knowledge now possessed on these
subjects may possibly throw a clearer light on the phenomena.

The Committee wish only to add, that if any geologists, whether
fellows of this Society or not, happen, in the course of their rambles
through the country, to fail in with or hear of any boulders re-
markable for size, position, or composition, not yet mentioned in
the Committee’s Reports, the Convener will be happy to receive a
notice of them.

After some conversation, in which Mr Ferguson of Kinmundy,
Dr Bryce, the Rev. T. Brown, and others took part, the Report was
adopted, and the proceedings terminated.

178

Proceedings of the Royal Society

Donations to the Royal Society Library during Session

1874-75 : —

I. Authors.

Abbt (Dr Ferdinand). IJeber die Spontanen Rupturen des Herzens.
Erlangen, 1875. 8vo. — From the Author.

Armstrong (Sir William) and others. Recent Discussions on the
Abolition of Patents for Inventions in the United Kingdom,
France, &c. London, 1869. 8vo. — From R. A. Macfie , Esq.

Banner (E. G-.). Sanitary Appliances and System of Sanitation.
London, 1876. 8vo. — From the Author.

Bartoli (Dottore Adolfo Gr.). Sopra i Movimenti Prodotti dalla
Luce e dal Calore, e sopra il Radiomentio di Crookes.
Firenze, 1876. 8vo. — From the Author.

Becker (Franz) . Beitrage zur Kenntniss des Tellurs. Erlangen,
1875. 8 vo. — From the Author.

Beilby (J. Wood). Reasons suggestive of Mining on Physical
Principles for Gold and Coal. Melbourne, 1875. 8vo. — From
the Author.

Bidder (Roderich). Ueber Koheleths Stellung zum Unsterblich-
keitsglauben. Erlangen, 1875. 8vo. — From the Author.

Birnbaum (Rudolph). The Sanitary Powers of the Iron Springs
of Schwalbach. Berlin, 1876. 8vo. — From the Author.

Bogler (Dr F.). Klinische Beobachtungen bei Offenbleiben des
Foramen Ovale. Erlangen, 1875. — From the Author.

Braun (Wilhelm). Die Singularitaten der Lissajous’ schen Stimm-
gabelcurven. Erlangen, 1875. 8vo. — From the Author.

Bretschneider (Wilhelm). Ueber Curven vierter Ordnung mit drei
Doppelpunkten. Stuttgart, 1875. 8vo. — From the Author.

Brimmer (Carl). Ueber die Chemischen Bestandtheile der Angel-
ike- Wurzel. Erlangen, 1875. 8vo. — From the Author.

Bruns (Dr Heinrich). Ueber die Perioden der Elliptischen Inte-
grale. Dorpat, 1875. 4to. — From the Author.

179

of Edinburgh, Session 1875-76.

Buchner (Dr Ludwig Andreas). IJeber die Beziehungen der
Chemie zur Rechtspflege. Munchen, 1875. 4to.— From the

Author.

Burmeister (Dr Hermann). Description physique de la Repub-
lique Argentine. Tome Premier. Paris, 1876. 8vo .-—From
the Author.

Die fossilen Pferde der Pampas-formation. Buenos Aires,

1875. Fol. — From the Author.

Charles (P.). The G-eographical Distribution of Animals and
Plants in their Wild State. 1876. Salem, Mass. 4to. —
From the Author.

Chevreul (M. E.). L’Enseignement devant 1’Etude de la Vision.
La loi du Contraste Simultane des Couleurs. Paris, 1875.
4to. — From the Author.

Explication de Nombreux Ph4nomenes qui sont une Con-
sequence de la Vieillesse. Paris, 1875. 4to . — From the

Author.

—— Etudes des Procedes de 1’Esprit Humain dans la Recherche
de ITnconnu a Faide de Observation et de FExperience, et du
moyen de savoir s’il a trouve l’Erreur ou la Verite. Paris,

1874. 4to. — From the Author.

Croizier (Le C. De). La Perse et les Persans. Paris, 1873. 8vo.
— From the Author.

Day (St John V.). A Paper on Recent Arrangements of Con-
tinuous Brakes. 1875. 8vo. — From the Author.

Diehl (Dr G.). Bietrage zur Pathologie und Therapie des Diabetes
Mellitus. Erlangen, 1875. 8vo. — From the Author.

Disse (Dr Joseph). Beitrage zur Anatomie des Menschlichen
Kehlkopfs. Bonn, 1875. 8vo. — From the Author.

Dana (Prof. A.). II Passaggio di Venere sul Sole, Osservato a
Muddapur. Palermo, 1875. 4to. — From the Author.

L’Aneroide a Vite Micrometrica Sperimentata colie diffe-

renze di livello della Strada Eerrata delle Alpi. Torino,

1875. 8 vo. — From the Author.

Eidam (Dr H.). (Jeber die Bildungsweise intraperitonealer tumo-
ren im Kleinen Becken. Leipzig, 1875. 8vo. — From the
Author.

180 Proceedings of the Royal Society

Ennis (John), A.M. The Origin of the Stars, and the Causes of
their Motions and their Light. London, 1876. 8vo. — From
the Author.

Faber (Dr J.). Die Embolie der Arteria Mesenterica superior.
Erlangen, 1875. 8vo. — From the Author.

Fleischmann (Johann Karl). Kritische Studien fiber die Kunst
der Charakteristik bie iEschylos und Sophokles. Nurnberg,
1875. 8vo. — From the Author.

Forster (Dr S. von). Ueber congenitale Hypoplasie des Uterus.
Erlangen, 1875. 8vo. — From the Author .

Friertag (Isaac). Ueber die Bildung der Ilare. Dorpat, 1875.
8 vo. — From the Author.

Fries, E. leones Hymenomycetum. Fasc. 7-10. 4fco. — From the
Royal Academy of Sciences , Stockholm.

Furbringer (Dr Max). Beitrag zur Kenntniss der Kehlkopf-
muskulatur. Jena, 1875. 8vo. — From the Author.

Gtarstin (J. R.). Facts and Reasonings adduced in support of the
course taken by the Royal Irish Academy respecting the recent
action of certain G-overnment Departments. Dublin, 1876.
8 vo. — From the Author.

Geer (Louis de). Minnestekning ofver Hans Jarta. Stockholm,
1874. 8vo. — From the Author.

G-erichten (Dr E. Yon). Die Theorie der Sasuren und Salzbildung
und die Electrochemische Theorie. Erlangen, 1875. 8vo. —
From the Author.

Thesen welche zur Erlangung der Yenia Legendi in

der Philosophichen Facultat, &c. Erlangen. 1875. 4to. —
From the Author.

Gordan (Dr Raul). Ueber das Formensystem binmrer Formen.
Leipzig, 1875. 8vo. — From the Author.

Gresbeck (Berthold). Ursache der Irritation cerebri infantum und
deren Behandlung. Erlangen, 1875. 8vo. — From the
Author.

Griinewald (Max). Ueber den Kaiserschnitt". Munchen, 1876.
8vo. — From the Author.

Hamilton (H.). Minnesteckning ofver Jacob August von Hart-
mansdorff. Stockholm, 1872. 8vo. — From the Author.

181

of Edinburgh, Session 1875-76.

Harneck (Axel.). Ueber die Verwerthung der elliptischen func-
tionen fiir die G-eometrie der Curven dritten Grades. Leipzig,
1875, 8vo. — From the Author.

Hartley (Walter Noel). Air, and its Eelations to Life. London,
1875. Second edition, 1876. 8vo. — From the Author.

Hartung (Dr E.). Ueber einen Fall von Mamma accessoria. Er-
langen, 187. 8vo. — From the Author.

Hayter (H. H.). Victorian Year-book for 1874. London, 1875.
8 vo. — From the Author •

Herzog (Wilhelm). Beitrage zur Naheren Kenntniss der Structur
der Seline. Erlangen, 1875. 8vo. — From the Author.

Hess (Dr Otto). Ueber einen Fall von Heterotaxie der Brust-
und Bauckeingeweide. Erlangen, 1875. 8vo. — From the

Author.

Hoerner (Dr C.). De extremo Graecorum discrimine quomodo in
Xliade descriptum sit. Erlangen, 1875. 8vo. — From the
Author.

Hooker (Dr J. D.), C.B.. The Flora of British India. Part IV.
8 vo. — From the India Office.

Hornberger (Richard). Einige Verbindungen des Zirkoniums.
Erlangen, 1875. 8vo. — From the Author.

Hornstein (Carl). Astronomische Magnetische und Meteorolo-
gische beobachtungen an der K. K. Sternwarte zu Prag im
Jahre, 1875-76. 4to. — From the Author.

Jakowicki (Anton). Zur Physiologischen Wirkung der Bluttrans-
fusien. Dorpat, 1875. 8vo. — From the Author.

Johanson (Edwin). Beitrage zur Chemie der Eichen- Weiden und
Ulmennride. Dorpat, 1870. 8vo. — From the Author.

Kaulbars (Franz). Trophische und vasenmotorische Storungen
peripherer Nervenverletzungen. Jena, 1874. 8vo. — From
the Author.

Kiesselbach (Wilhelm). Beitrage zur Naheren Eenntniss der
Sogenannten Grauen Degeneration des Sehnerven bie Erk-
rankungen des Cerebrospinalsystems. Erlangen, 1875. 8vo.
— From the Author.

Kuhn (Moriz). Ueber die Beziehung Zwischen Druck, Volumen
und Temperatur bei Gasen. Wein, 1875. 4to .—-From the
Author.

182 Proceedings of the Boyal Society

Lassel (W.). On Publishing the Specula of Reflecting Telescopes.

1874. 4to. — From the Author.

Leuckart (Rudolf). Die Menschlichen Parasiten und die von
Ihnen Herruhrenden Krankheiten. 1876. 8vo. — From the
Author.

Luvini (Jean). Le Di^theroscope. Turin, 1876. 8vo. — From the
Author.

Lyman (Theodore). Commemorative Notice of Louis Agassiz.
8 vo. — From the Author.

Macdonald (James). The Origin and Destiny of Comets. Prah-
ran, 1869. 8vo. — From the Author.

Maison (Dr Otto). Ueber die Resection des Unterkiefers. Er-
langen, 1875. 8vo. — From the Author.

Mandelstam (Dr N.). Ueber den Einfluss Chemischer Agentien
auf die Erregbarkiet der Nerven. Erlangen, 1875. 8vo. —
From the Author.

Mazzola (G-iuseppe). Effemeridi del Sole, della Luna. Torino,
1874-75. 8vo. — From the Author.

Mehlis (Christian). Die G-rundidee des Hermes von Standpunkte
der Vergleichenden Mythologie. Erlangen, 1875. 8vo. —
From the Author.

Meissner (Dr A.). Ein Fall von Yerengerung der Pfortader durch
chronische Peritonitis bei Gallensteinerkrankung. Erlangen,

1875. 8 vo. — From the Author.

Michel (Dr J.). Die Histologische Structur des Irisstroma. Er-
langen, 1875. 8vo. — From the Author.

Molitor (Eduard). Die Behandlung des Fiebers bei Typhus
und Pneumonie. Munchen, 1875. 8vo. — From the
Author.

Monteiro (Joachim John). Angola and the River Congo. Yols.

I. and II. London, 1875. 8vo. — From the Author .

Muller (Baron Fredinandus von). Fragmenta Phytographias.
Yol. IX. Melbourne. 8vo. — From the Author.

Descriptive Notes on Papuan Plants. Melbourne. 8vo. —

From the Author.

Naumann (Alexander). Jahresbericht iiber die Fortschritte der
Chemie fur 1873. Heft 3. 8vo. — From the Editor.

183

of Edinburgh, Session 1875-76.

Mussbaum (Heinrich). Beitrage zur Kenntniss der Anatomie
und Physiologie der Herznerven und znr Physiologischen
Wirkung des Curare. Dorpat, 1875. 8vo. — From the

Author.

Oudemans (Dr J. A. C.). Die Triangulation von Java Ausgefuhrt
vom Personal des Geographischen Dienstes in Niederlandisch
Ost-Indien. Batavia, 1875. 4to. — From the Author .

Paolo (Riccardi). Annuario della Societa dei Naturalisti in
Modena, 1875. Anno IX., X. 8vo.— From the Author.

Paulus (Franz). Verhartung und Verknocherung des Haematoms
der Dura mater und ihre Beziehung zur Heilung desselben.
Erlangen, 1875. From the Author.

Penzoldt(Dr F.). Die Magenerweiterung. Erlangen, 1875. 8vo.
— From the Author.

Pfeuffer (Dr P.) Experimented beitrage zur Resorption gefarbter
fette. Erlangen, 1875. 8vo. — From the Author .

Pleyte (W.). Les Peintures murales de FEglise dedi4e a Saint
Jaques a Utrecht. 1874. Fol. — From the Author.

Popp (Friedrich). Ueber Embolie der Arteria centralis retinas.
Regensburg, 1875. 8vo.- — From the Author.

Quetelet (M. Era), La Tempete du 12 Mars. 1876. 8vo. — From
the Author.

Raab (Dr Jos.). Die Tetanie. Erlangen, 1875. 8vo,— From the
Author.

Ribot (F.). Revue Philosophique de la France et de FEtranger.
Paris, 1876. 8vo. — From the Author.

Richardson (Ralph). The Ice Age in Britain. Edinburgh, 1876.
8vo. — From the Author.

Rothhaupt (F. R.). Die Pulsformen der Paralysis progrediens.
Mellrichstadt, 1874. 8vo. — From the Author.

Sandon (Lord). Letter to the President of the Royal Irish Aca-
demy. 1876. 8vo. — From the Royal Irish Academy.

Schmidt (Alfred). Das Russische Geldwesen Wahrend der Finanz-
verwaltung des Grafen Cancren von 1823-1844. St Peters-
burg, 1875. 8vo. — From the Author.

“ Searcher,” a Truth in Extremis; A Plea against the Murder of
Science by the Gold Poison. Oxford, 1876. 8vo.— From the

Author.

2 B

VOL. IX.

184

Proceedings of the Royal Society

Steinmann (F.). Ueber Retroversionen und Retroflectionen der
Gebarmutter und deren Behandlung. Erlangen, 1875. 8vo.
— From the Author.

Steubing (Dr W.). Ueber des Schragverengte Becken und seinen
Emfluss auf die G-eburt. Erlangen, 1875. 8vo. — From the
Author.

Stewart (C. M. A.). International Correspondence by means of
Numbers. London, 1874. 8vo. — From the Author.

Sudhoff (Karl). Ueber das Primare Multiple Carcinome des
Knochensystems. Erlangen, 1875. 8vo. — From the Author.
Treub (Dr M.). Driemaandelijksch Botanish Literatuurdverzicht.

Nijmegen, 1874. 8vo. — From the Author.

Trumpp (Ernst). Einleitung in das Studium der Arabischen
Grammatiker. Munchen, 1876. 8vo. — From the Author.
Veh (Friedrich). Ueber die Wirksamkiet klar filtrirter faulender
Flussigkeiten. Dorpat, 1875. 8vo. — From the Author.
Vincent (Charles W., F.R.S.E.). The Year-Book of Facts in
Science and the Arts for 1875. London. 8vo. — From the
Author.

Vinclion-Thiesset (Artus). La Cause des Effets. Saint Quentin,
75. 8vOi — From the Author.

Vogt (Dr Gunther). Zur Statistik und Casuistik der Progressiven
Muskelatrophie. Erlangen, 1875. 8vo. — From the Author.
Wedekind (L.). Beitrage zur Geometrischen interpretation
Binarer formen. Erlangen, 1875. 8vo. — From the Author.
Wikszemski (Adam). Beitrage zur Kenntniss der giftigen Wirkung
des Wasserschierlings. 8vo. — From the Author.

Zielonko (Justus). Pathologish-Anatomische und experimentelle
Studien uber Hypertrophie des Herzens. Dorpat, 1875. 8vo.
— From the Author.

II. Transactions and Proceedings of Learned Societies,

Academies, etc.

Amsterdam. — Flora Batava. Nos. 227-231. 4to. — From the King
of Holland.

Jaarboek yan de Koninklijke Akademie van Wetenschappen
gevestigd te Amsterdam voor 1774. 8vo. — From the
Academy •

185

of Edinburgh, Session 1875-76.

Amsterdam. — Processen-verbaal van de G-ewone Yergaderingen der
Koninklijke Academie van Wetenschappen, 1874-
1875. 8 vo. — From the Academy.

Verhandelingen der Koninklijke Academie van Wetens-
ckappen. Deel VIII.-iXY. 4to.— From the Academy.

Yerslagen en Mededeelingen der Koninklijke Academie van
Wetenschappen. Afdeeling Naturkunde. Deel IX. 8vo.
— From the Academy.

Baltimore. — First Annual Report of the Provost to the Trustees of
the Peabody Institute. 1868.

Ninth Annnal Report (1876) of the Peabody Institute. 8vo.
— From the Institute.

Basel. — Yerhandlungen der Naturforschenden G-eseilschaft. Sech-
ster Theil, Zweites Heft. 8vo. — From the Society.

Berlin. — Abhandlungen der Koniglichen Akademie der Wissens-
chaften zu Berlin. 1874-1875. 4to.— From the Aca-

demy.

Die Fortschritte der Physik im Jahre 1870. Dargestellt
von der Physikalischen G-eseilschaft zu Berlin. XXYI.
Jahrgang, Abth. 1-2; 1871, XXYI. Jahrgang, Abth.
1-2. 8 vo* — From the Society .

Jahresbericht der Commission zur Wissenschaftlichen
Untersuchung der Deutschen Meere in Kiel fur die Jahre
1872-73, 2 und 3 Jahrgang. Fol. — From the Com-
mission.

Monatsbericht der Koniglich. Preussischen Akademie der
Wissenschaften zu Berlin. 1875 — Juni, Juli, August,

September, October, November, December. 1876— -Januar,
Februar, Marz, April, Mai. 8vo. — From the Academy.

Bet me. — Mittheilungen der Naturforschenden Gesellschaft in Bern
aus dem Jahre 1874. Nos. 828-873, 878-905. 8vo.—
From the Society.

Bombay.— Census of the Bombay Presidency, taken on the 21st
February 1872. Part 3d. 4to. — From the Bombay

Government.

The Indian Antiquary. Yol. IY. from September to Decem-
ber 1875; Yol. Y. from January to July 1876. 4to—
From the Publishers .

186 Proceedings of the Royal Society

Bombay. — Journal of the Bombay Branch of the Royal Asiatic
Society, 1875. Yol. XI, Nos. 31, 32. 8vo. — From the Society.
Bonn. — Yerhandlungen des Naturhistorischen Yereines der Preus-
sischen Rheinlande und Westfalens. Jahrgang XXXI.
Folge 3 ; XXXII. Folge 4. 8vo. — From the Society.
Bordeaux.^ Memoires de la Societe des Sciences Physiques et
Naturelles de Bordeaux. Tome I. Second Series; Second
Caher. 8vo. — From the Society.

Boston. — Annual Report of the Trustees of the Museum of Com-
parative Zoology at Harvard College in Cambridge 1874-
1875. 8 vo. — From the Trustees.

Appalachia. Yol. I. No. 1. 8vo. — From the Appalachian
Mountain Club.

Memoirs of the Boston Society of Natural History. Yol.

II. Part 4; Nos. 2-4. 4to. — From the Society .
Proceedings of the Society of Natural History. Yol. XVII.

Parts 3, 4 ; XYIII. Parts 1, 2. 8vo. — From the Society.
Occasional Papers of the Boston Society of Natural History.
8vo.' — Prom the Society.

Proceedings of the American Academy of Arts and Sciences.

New Series, Yol. II. 8vo. — From the Academy.

The Complete Works of Count Rumford. Published by the
American Academy of Arts and Sciences. Yol. IY. —
From the Academy.

Brussels. — Bulletin de l’Academie Royale des Sciences, des Lettres
et des Beaux-Arts de Belgique. Tome XII. Partie 1 ;
XXXI. No. 5; XXXII. No. 11; XL. Nos. 7-12;
XLI. Nos. 1-6. 8 vo, — From the Academy.

Memoires de l’Academie Royale des Sciences, des Lettres et
des Beaux-Arts de Belgique. Tome XLI. Part 1, 2.
4to. — From the Academy.

Memoires Couronnes et Memoires des Savants Etrangers
Publiees par l’Academie Royale des Sciences, des Lettres
et des Beaux-Arts de Belgique. Tome XXXYIII.,
XXXIX. Part 1. 4to. — From the Academy .

Memoires Couronnes et Autres, Memoires Publiees par
1’Academie Royale des Sciences, des Lettres et des Beaux-
Arts de Belgique. Tome XXIY., XXY., XXYI. 8vo.
— From the Academy.

187

of Edinburgh, Session 1875-76.

Brussels. — Biographie Nationale publie par I’Academie des Sciences,
des Lettres et des Beaux-Arts de Belgique. Tome
Cinquieme, Part 1. 8vo. — From the Academy.

Notices Biographiques et Bibliographiques. 1871. 8vo. —
From the Academy.

Annuaire de l’Academie Boyale des Sciences, des Lettres
et des Beaux-Arts de Belgique. 1876. 8vo .—From the
Academy.

Budapest. — A Magyar Tudomanyos Akademia Ertesitoje A. M. T.

Akademia Kendelelebol Szerkeszti A Fotjtkar. 1873,
Szam 8-11 ; 1874, Szam 1-14-17. 8vo. — From the
Academy.

Mathematekai es Termeszett-udomanyi Kozlemenyek vonatk-
azolagAslaziaViszonyokra Kiadja AMagyar Tudomanyos
Akademia. • Kotel VII., VIII., IX., X. 8vo. — From
the Academy.

leones Selectm Hymenomycetum Hungarian Magyar-orszag
Harty Agombainak Valogatott Kepel. No. 2, 3, 7-10.
Fob — From the Academy.

Az Emberi vese Visszere-Rendszere Dr Senbossek Jozsef.
Evk. XIV. Kot. 4. 4to. — - From the Academy.

Adatok a Szem Perczhartyaja Szovet es Elettanaboz Dr
Hanhoffer Lajos, Evk* XIV. Kot. 5. 4to. — From the
Academy.

Ertezesek A Mathemat, Tudomanyok, Korebol Kiadja A
Magyar Tudomanyos Akademia. A III. Osztaly Rende-
letebol Szerkeszti Szabo Jozsef Osztalytkar. 1873,
Kotel II. Szam 3-6; 1874,111. Szam 1-8, 15; 1873,
IV. ; 1873, Szam 3-6 ; IV. 1875, Szam 1-3 ; V. 1874,
Szam 1-9; VI. 1875, Szam 1-6. 8vo .—From the Academy.

M. Tudem Akademiai Almanack Ossillagaszati es Kozen-
seges. 1873-75. 8vo. — From the Academy.

Buenos Aires.— Acta de la Academia Nacional de Ciencias exactas
existente en la Univsraidad de Cordova. Tom I. 4to. —
From the Author.

Calcutta. — Memoirs of the Geological Survey of India. Vol. XI.

part 2, 8vo. Palseontologia, Vol. I. Parts 2-4. 4to. —
From the Survey .

188

Proceedings of the Royal Society

Calcutta.— -Records of the G-eological Survey of India. Yol. VIII.
Parts 1-4. 8 vo. — From the Survey.

Journal of the Asiatic Society of Bengal. 1875, Nos. 2-4,
Part 1 ; Part 2, No. 1-3, extra No. 8vo. — From the

Proceedings of the Asiatic Society of Bengal. 1875, Nos.

6-10 ; 1876. Nos. 1, 2. 8vo. — From the Society.

Report of the Meteorological Reporter to the Government
of Bengal for the years 1867 to 1874. By W. G. Wilson,
M.A.L.C.E. Fol. — From the Government of Bengal.
Report of the Midnapore and Burdwan Cyclone of the 15th
and 16th of October 1874. By W. G.Wilson, M.A.L.C.E.
Fol. — From the Government of Bengal.

Report of the Commissioners appointed to Inquire into the
Origin, Nature, &c., of the Indian Cattle Plagues, with
Appendices. 1871. Fol. — From the Commissioner.
California. — Proceedings of the California Academy of Sciences.

Yol. Y. Part 3. 8vo .—From the Academy.

Cambridge ( U.S .) — Catalogus Universitatis Harvardianas. 1875.
8vo. — From the University.

The Harvard University Catalogue. 1874-75. 8vo. —

From the University .

Forty-Ninth Annual Report of the President of Harvard
College. 1873-74. 8vo. — From the College.

The Treasurer’s Statement of Harvard College. 1874.
8 vo. — From the College.

Illustrated Catalogue of the Museum of Comparative
Zoology at Harvard College. No. VIII. Part 2. 4to. —
From the College.

Canada.- — Report of the Progress of the Geological Survey of
Canada for 1874-75. 8vo. — From the Geological
Survey.

Cape of Good Hope. — Observations made at the Magnetical and
Meteorological Observatory at the Cape of Good Hope.
Yol. II. 1841-1846. 4to. — From Her Majesty's Govern-
ment.

Catania. — Atti dell Accademia Gioenia de Scienze Naturali de
Catania. Tomo VI., IX. 4to.-— From the Academy.

189

of Edinburgh , Session 1875-76.

Cherbourg. — Memoires de de la Soci4te Nationale des Sciences
Naturelles de Cherbourg. Tome IX. 8vo. — From the
Society.

Chur. — Verhandlungen der Schweezeriscben Naturforschenden
Gesellschaft in Chur. Jahresbericht 1873-74. 8vo. —
From the Society.

Copenhagen. — Oversigt over det Kongelige danske Yidenskabernes
Selskabs Forhandlingar og dots Medlemmers Arbejder i,
Aaret 1874, No. 3; 1875, No. 1. 8vo. — From the So-
ciety .

Memoires de l’Academie Royale de Copenhagen. 5th
Serie, Yol. X. No. 7-9 ; Yol. XI. No. 1, 2 ; XII.
No. 1, 2. 4to. — From the Academy.

Dehra Boon. — General Report on the Operations of the Great
Trigonometrical Survey of India during 1874-75. Fob
— From the Survey.

Dublin. — Journal of the Geological Society. Yol. I. Part 1 ; II.
Parts 3, 4. 8vo. — From the Society.

Journal of the Royal Dublin Society. Yol. VII. Part 1.
8 vo. — From the Society.

Proceedings of the Royal Irish Academy. . Yol. II. Nos. 1-3.
8 vo. — From the Academy.

Transactions of the Royal Irish Academy (Science). Yol.
XXV. Parts 10-18. 4to. — From the Academy.
Edinburgh. — Proceedings of the Royal Physical Society. Session
1874-75. 8vo. — From the Society.

Transactions of the Highland and Agricultural Society of
Scotland. Yol. VIII. 8vo. — From the Society.

Catalogue of the Printed Books in the Library of the
Faculty of Advocates. Yol. IV. 4to.— From the

Library.

Transactions of the Royal Society of Arts. Yol. IX. Parts
2, 3. 8vo. — From the Society.

Transactions and Proceedings of the Botanical Society.

Yol. XII. Part 2. 8vo.-— From the Society.

Forty-Eighth Annual Report of the Council of the Royal
Scottish Academy of Painting, Sculpture, and Architec-
ture. 1875. 8vo. — From the Academy.

190

Proceedings of the Itoyal Society

Edinburgh. — Journal of the Scottish Meteorological Society. Nos.
47—48. 8vo. — From the Society.

Erlangen, — Sitzungsberichte der Physicalish-Medizinischen Societat
zu Erlangen. Heft 6. 8vo. — From the Society.

Frankfort.-*- Abhandlungen herausgegeben von der Senckenber-
gischen Naturforsckenden G-esellschaft. Band IX. Heft
3, 4 ; X. Heft 1-4. 4to. — From the Society.

Bericht iiber die Senckenbergische Naturforschende Gesells-
chaft. 1873-74; 1874-75. 8vo, — From the Society.

Geneva. — Memoires de la Societe de Physique et d’Histoire
Naturelle de Geneva. Tome XXI Y. Part 1. 4to. —

From the Society.

Glasgow. — Proceedings of the Philosophical Society. 1875-76.
8 vo. — From the Society.

Gottingen. — Abhandlungen der Koniglichen Gesellschaft der Wis-
senchaften zu Gottingen. Band XX. 4to. — From the

Society.

Nachrichten von der K. Gesellschaft der Wissenchaften
und der Georg- Augusts-Universitatj aus dem Jahre 1875.
12mo. — From the University.

Gratz. — Mittheilungen des Naturwissenschaftlichen Vereines fur
Steiermark. Jahrgang 1875. 8vo. — From the So-

ciety.

Greenwich. — Astronomical and Magnetical Observations made at
the Royal Observatory in the year 1873. 4to. — From the
Observatory.

Haarlem. — Archives Neerlandaises des Scienees Exactes et
Naturelles publiees par la Societe Hollandaise & Haarlem.
Tome X. Liv. 1-5 ; XI. Liv. 1-3. 8vo. — From the
Society.

Archives du Musee Teyler. Vol. IY. Fasc. 1. 8vo .-—From
the Society.

Naturerkundige Yerhanderlingen der Hollandsche Maats-
chappij der Wetenschappen. Deel II. No. 5. 4to. —

From the Society.

Hamburg. — Verhandlungendes Vereines fur Naturwissenschaftliche
Unterhaltung zu Hamburg. 1875. 8vo. — From the

Society.

191

of Edinburgh, Session 1875-76.

Helsingforsia. — Acta Societal Scientiarum Fennicae. Tome X.
1875. 4to. — From the Society.

Innsbruck. — Berichte des Naturwissenckaftlich - Medizinischen
Vereines in Innsbruck. Jabrgang VI. 1875, Heft 1.
8 vo. — From the Society.

Jena. — Jenaiscbe Zeitscbrift fur Naturwissenschaft berausgegeben
von der Mediciniscb-Naturwissenscbaftlicben G-esellscbaft
zu Jena. Band IX. Heft 4; X. Heft 1-3. 8vo. —

From the Society.

Kasan. — Beports of the University of Kasan. 1875. Nos. 1-6.
8vo. — From the University.

Kiel . — Schriften der Universitat zu Kiel aus dem Jahre 1874.
Band XXI., XXII. 4to.— From the University.

Leeds. — Annual Beport of the Leeds Philosophical and Literary
Society. 1874-75. 8vo. — From the Society.

Leiden. — Annalen der Sternwarte, berausgegeben von Dr H. G. Van
de Sande Bakbuyzen Verter. 4to. — From the Obser-
vatory.

Leipzig . — Ueber die Darstellungder Geraden Aufsteigung des Mondes
in Function der Lange in der Babn und der Knotenlange.
Band X. No. 8. P. A. Hansen. 8vo. — From the Royal
Saxon Academy.

Dioptriscbe Untersucbungen mit Berucksicbtigung der
Farbenzerstreuung und der Abweichung wegen Kugel-
gestalt. P. A. Hansen. Band X. No. 9, 8vo. — From
the Royal Saxon Academy.

Ueber das Aelius und Sabinus System wie iiber Einige
Verwandte Bechts — Systeme von Moritz Voigt. Band
VII. No. 4. 8vo.-= From the Royal Saxon Academy.

Von der Bestimmung der Tbeilungsfehler eines Gradlinigen
Maassstabes.* P. A. Hansen. Band X. No. 7. 8vo. —
From the Royal Saxon Academy.

Preisscbriften gekront und berausgegeben von der Furstlich
Jablonowskischen Gesellschaft zu Leipzig. 8vo. — From
the Royal Saxon Academy.

Ueber die Storungen der Grossen Planeten insbesondere
des Jupiter. P. A. Hansen. Band XI. No. 4. 8vo. —
From the Royal Saxon Academy.

2 c

VOL. IX.

192

Proceedings of the Royal Society

Leipzig.— Elektrische Untersuchungen iiber die Thermaelektrischen
Eigenschaften Des G-ypses des Diopsids des Orthoklases,
des Albits und des Periklins. W. G. Hanket. Band XI.
Nos. 3, 5. 8 vo. — From the Royal Saxon Academy.

Bericht iiber die Verhandlungen der Koniglich. Sachsischen
G-esellschaft der Wissenschaften zu Leipzig. Math.
Phys. Classe, 1873, Nos. 3-7; 1874, Nos. 1-5; 1875,
Nos. 1. Phil.-Hist. Classe, 1873 ; 1872, Nos. 1, 2 ; 1871,
No. 1. 8vo. — From the Royal Saxon Academy.

IJeber den Ausgangswerth ker Kleinsten Abweichungs-
summe Dressen Bestimmung Verwendung und Verallge-
meinerung. G. Th. Fechner. Band XI. No. 1. 8vo. —
From the Royal Saxon Academy.

Ueber das von Weber fur die Elektrischen Krafte Aufges-
tellte Gesetz. Carl Neumann. Band XI. No. 2. 8vo. —
From the Royal Saxon Academy.

Erster Jabresbericbt der Zoologischen Statien in Neapel.
8vo. — From the Society.

Die Geschichtschriebung iiber den Schmalkaldischen Krieg,
von Georg Yoigt. Band VI. No. 6. 8vo. — From the
Royal Saxon Academy.

Die Epheten und der Areopag vor Solon von Ludvig Lange.
Band VII. No. 2. 8vo. — From the Royal Saxon Aca-
demy.

Zur Charakteristik Konig Johann’s von Sachsen in Seinen
Verhaltniss zu Wissenschaft und Kunst, von Dr Johann
Paul, von Falkenstein. Band VII. No. 3. 8vo. — From
the Royal Saxon Academy.

Liverpool. — Proceedings of the Literary and Philosophical Society,
No. 29. 8 vo. — From the Society.

London. — Calendar of the Royal College of Surgeons of England.
1875. 8vo. — - From the College.

Report of the Meteorological Committee to the President
and Council of the Royal Society. 1875. 8vo. — From
the Meteorological Committee of the Royal Society.

Contribution to the Meteorology of Japan, by Staff-Com-
mander Thomas H. Lizard, H.M.S. “ Challenger.” 4to.
— From the Meteorological Committee of the Royal Society.

193

of Edinburgh, Session 1875-76.

London. — On the Physical Geography of the part of the Atlantic
which lies between 20° N. and 10° S., and extends from
10° to 40° W. By Captain Toynbee, F.R.A.S., F.R.G.S.
8 vo. —From Meteorological Committee of the Royal Society.
Statistical Report on the Health of the Navy for the year
1874. 8vo. — From the Admiralty .

H.M.S. “Challenger” Report on Ocean Soundings and
Temperatures — Pacific Ocean, No. 5 ; H.M.S. “ Valo-
rous ” Deep-Sea Soundings and Temperatures — North
Atlantic Ocean. 1875. Fob — From the Lords Commis-
sioners of the Admiralty .

Memoirs of the Royal Astronomical Society. Vol. XLII.

1873-75. 4to. — From the Society.

Proceedings of the Royal Society. Vol. XXIII. Vol. XXIV.

Nos. 164-170 ; XXV. No. 171. 8vo. — From the Society.
Transactions of the Royal Society. Vol. CLXV. Part 1.

List of Fellows, 1874, 4to. — From the Society.

Quarterly Weather Report of the Meteorological Office.
1874, Part 2. 8vo. — From the Meteorological Committee
of the Royal Society.

Results of the Monthly Observations of Magnetic Dip,
Horizontal Force, and Declination, made at the Kew
Observatory, from April 1869 to March 1875. By the
Kew Committee. 8vo. — From the Royal Society.
Transactions of the Clinical Society. Vol. VIII. 8vo.~
From the Society.

Transactions of the Pathological Society. Vol. XXVI.
8 vo. — From the Society.

Transactions of the Linnean Society. Second Series
(Botany), Vol. I. Part 2; Second Series (Zoology),
Vol. I. Part 2. 4to. — From the Society.

The Anatomy of the Lymphatic System. By E, Klein,
M.D. — The Lung, II. 8vo. — From the Royal Society.
Proceedings of the Chemical Society. Vol. XIII., October,
November, December; XIV., January, February, March,
April, May, June, July. 8vo. — From the Society.
Proceedings of the Royal Geographical Society. Vol. X.
Nos. 1, 2; Vol. XX. Nos. 3-6. 8vo. — From the Society.

194 Proceedings of the hoyal Society

London.— Journal of the Statistical Society. Vol. XXXVIII.

Part 4; Vol. XXXIX. Parts 1, 2. 8vo. — From the Society.
Journal of the Linnean Society. Botany, Vol. XV.
Nos. 81-84; Zoology, Vol. XII. No. 60-63. List of
Members. 8vo. — From the Society.

Journal of the Geological Society. Vol. XXXI. Part 4 ;
XXXII. Parts 1, 2. List of Members. 8vo. — From the
Society.

Transactions of the Linnean Society. Second Series.
(Botany), Vol. I. Part 3 ; (Zoology), Vol. I. Part 3.
8vo. — From the Society.

Proceedings of the Linnean Society of the Session 1874-75.
8vo. — From the Society .

Journal of the Royal Asiatic Society of Great Britain and
Ireland. Vol. VIII. Part 1. 8vo. — From the Society.
Proceedings of the Royal Institution of Great Britain.
Vol. IV. Parts 7, 8; Vol. VII. Parts 5, 6. List of Mem-
bers. 8vo. — From the Society.

Proceedings of the Geological Association. Vol. IV.
Nos. 4-7. Annual Reports, 1875. 8vo. — From the Asso-
ciation.

Proceedings of the Mathematical Society. Nos. 83-92.
8 vo. — From the Society.

Proceedings of the Society of Antiquaries. Vol. VI. No. 5.
8 vo. — From the Society.

Journal of the Royal Institution. Vol. V. No. 27 ; VI.

No. 28.— 8vo. — From the Institution.

Transactions of the Zoological Society. Vol. IX. Parts 5-7.
4to. — From the Society.

Proceedings of the Zoological Society, 1875. Parts 2, 3.
8vo.— From the Society.

Revised List of the Vertebrated Animals now or lately living
in the Gardens of the Zoological Society of London.
Supplement. 8vo. — From the Zoological Society.
Transactions of the Royal Medical and Chirurgical Society.

Vol. LVIII. 8vo. — From the Society.

Proceedings of the Royal Medical and Chirurgical Society.
Vol. VIII. Nos. 1, 2. 8vo. — From the Society.

of Edinburgh, Session 1875-76. 195

London. — Journal of the East India Association. Yol. IX
Nos. 4, 5. 8 vo. — From the Association.

Journal of the Royal Geographical Society. Vol. XLV,

8 vo. — From the Society.

Proceedings of the Institution of Civil Engineers. Vols.
XLII., XLIII. Parts 1, 2. 8vo. — From the Institution .
Lucern. — Yerhandlungen der Schweizerischen Naturforschenden
Gesellschaft in Andermatt den 12, 13, und 14 September
1875. 8vo. — From the Society.

Lund. — Acta Universitatis Lundensis Lunds Universitets Ars-
Skrift Mathematik och Naturvetenskap far ar 1871-73.
Tom. IX., X. — Philosophi Spakvetenskap och Historia.
1872-73 — Tom. IX., X. 1871 — Theologie. 4to. — From
the University .

Madrid . — Memorias de la Real Academia de Ciencias Exactas,
Fisicas y Naturales de Madrid. Tomo VI. Parts 1,
4to. — From the Academy.

Manchester. — Transactions of the Geological Society. Yol. XIV
Parts 1-3. 8vo. — From the Society.

Proceedings of the Literary and Philosophical Society. Yol.
XIY. Nos. 11, 12. 8vo. — From the Society.

Mexico. — Boleten de la Sociedad de Geografia-y-Estadistica de la
Republica Mexicana. Tomo II. Nos. 5-7. 8vo. — From
the Society.

Montpellier. — Mdmoires Academie des Sciences et Lettres de Mont-
pellier; Section des Sciences. Tome VI. Fasc. 2, 3; Tome
VII., VIII. Fasc. 1, 2. De la Section de Medecine — Tome
IV. Fasc. 3-6. De la Section des Lettres — Tome IV.
Fasc 2-4. Tome V. Plates. 4to. — From the Academy.
Moscow. — Bulletin de la Societe Imperiale des Naturalistes 1875,
Nos. 1-4; 1876, No. 1. 8vo. — From the Society.

Munich. — Catalogus Codicum Latinorum Bibliothecae Regiae
Monacensis. Tomi II. Pars 2. 8vo. — From the Editors.
Abhandlungen der koniglich. bayerischen Akademie der
Wissenschaften. Philosophisch-Philologischen Classe —
Band XIII. Abth 3. Math.-Physik Classe — Band XII.
Abth 2. Historischen Classe — Band XIII. Abth. 1, 2.
4to. — From the Academy.

196

Proceedings of the Royal Society

Munich. — Catalogus Codicum Mann Scriptorum Bibliothecae Recias
Monacensis. Tomi Primi, Pars Primi, Pars Quarta. 8vo.
—From the Academy.

Almanach der koniglichen Bayerischen Akademie der Wis-
senschaften. Jalir 1875. 12mo. — From the Academy .
Sitzungsberichte der konigl. bayer. Akademie der Wissen-
scbaften. Philosophisch-Philologischen und Historis-
cben Classe 1875 — Band II. Heft 1-4; Band I. Heft 1.
Matkematisch-Phisykalischen Classe — 1875, Heft 2, 3;
1876, Band I. Heft. 8vo. — From the Academy.

Neuchatel. — Bulletin de la Societe des Sciences Naturelles de Neu-
chatel. Tome X. Part 2. 8vo. — From the Society.

New Haven (JJ.S.) — Journal (American) of Science and Art, con-
ducted by Benjamin Silliman. Vol. X. Nos. 58-60 ; XI.
Nos. 61-66 ; XII. Nos. 67, 68. 8vo. — From the Editor.
Transactions of the Connecticut Academy of Arts and
Sciences. Vol. III. Part I. 8vo. — From the Academy.
New York. — Fifty-Sixth Annual Report of the Trustees of the New
York State Library for the year 1873 ; Fifty-Seventh An-
nual Report for the year 1874. 8vo.— From the Trustees.

Eighty-Sixth Annual Report of the Regents of the Univer-
sity for 1873; Eighty-Seventh Annual Report for 1874.
8vo. — From the University.

New Zealand. — Statistics of the Colony of New Zealand, 1874.
Folio. — From the New Zealand Government.

Tenth Annual Report of the Colonial Museum and
Laboratory. 1874-75. By Dr Hector. 8vo. — From the
Geological Survey.

Nijmegen. — Nederlandsch Kruidkundog Archief. Deel II. Stuk 1.
8vo. — From the Editors.

Oxford. — Astronomical and Meteorological Observations made at the
Radcliffe Observatory, Oxford, in the year 1873. Yol.
XXXIII. 8vo. — From the Observatory .

Paris— -Annales des Mines. Tome VIII. Liv. 4e, 5e, 6e; Tome
IX. Liv. le. 8 vo. — From the Ecole des Mines.

Bulletin de la Societe de Geographie. 1875, Septembre,
Octobre, Novembre, Decembre ; 1876, Janvier, Fevrier,
Mars, Avril, Mai, Juin. 8vo. — From ilie Society.

197

of Edinburgh, Session 1875-76.

Paris . — Bulletin de la Societe Matbematique de France. Tome III.
Nos. 3, 5, 6. 8 vo. — From, the Society.

Nouvelles Archives du Museum d Histoire Naturelle. Tom
X. Fasc. 1-2. 4to. — From the Natural History Museum .
Publications of the Depot de la Marine (with Charts). 8vo.
— From the Depot.

Revue Historique Dirigee. Par M.M. Gr. Monod et Gr.
Fagniez. Tome Primier, No. 1. 1876. 8vo. — From the

Editors.

Revue Philosophique de la France et de l’^tranger Dirigee.
Par Th. Ribot. Premiere, No. 1. 1876. 8vo .-—From

the Editor.

Philadelphia. — Proceedings of the American Philosophical Society.
Vol. XIV., Nos. 94 and 95. 8vo. — From the Society.
Transactions of the American Philosophical Society. Vol.
XV. New Series, Part 2. 4to .-—From the Society.

Rome. — Bolletino del Comitato Geologico dTtalia. Nos. 1-6.
8vo. — From the Society.

Salem (U.S.) — The American Naturalist. Vols. VIII. and IX.
8vo. — From the Peabody Academy of Science.

Memoirs of the American Association for the Advance-
ment of Science. Vol. I. 4to. — From the Associa-
tion.

Memoirs of the Peabody Academy of Science. Vol. I.

No. 4. 8 vo. — From the Academy.

Sixth Annual Report of the Trustees of the Peabody
Academy of Science, for the year 1873. 8vo. — From the
Academy.

Sidney. — Proceedings of the Linnean Society of New South Wales.

Vol. I. Part 1. 8vo. — From the Society.

Stockholm. — Kongliga Svenska Ventenskaps-Akademienes Hand-
lingar Ny Folja Attonde. Bandet 1870-71-73. 4to .
— From the Academy.

Meteorologiska Jakttagelser i Sverige utgifna of Kongl.
Svenska Vetenskaps-Akademiens Anstallda och Bear-
betade af Er-Edlund. Tolefte Bandet 1870; Trellonde
Bandet 1871 ; Fjertonde Bandet 1872. 4to. — From the
Academy.

198

Proceedings of the Royal Society

Stockholm. — Ofversigt af Kongl. Vetenskaps Akademiens Forhand-
lingar Tjugondeattonde. Argangen 1871-1872; Tretionde
Argangen 1873; Tretiondeforsla Argangen 1874. 8vo.
— From the Academy.

Bihang till Kongl. Svenska Yetenskaps- Akademiens Hand-
lingar. Forsta Bandet, Hafte 1-2 ; Andra Bandet, Hafte
1-2. 8vo. — From the Academy.

Lefnadsteckningar ofver Kongl. Svenska Yetenskaps- Aka-
demienstefter ar 1854, Aflidna Ledamoter. Band I. Hefte
3. 8vo. — From the Academy.

St Petersburg. — Annalen Physikalischen Central Observatoriums.

1874. 4to. — From the Russian Government.

Bulletin de l’Academie Imperiale des Sciences de St Peters*
bourg. Tome XXI. No. 5. 4to. — From the Academy.
Repertorium fiir Meteorologie. Band IY. 4to. — From the
Royal Academy.

Tableau G-eneral Metbodique et Alpbabetique des Matieres
Contenues dans les Publications de l’Academie Imperiale
des Sciences de St Petersbourg. 1872, lre Partie. 8vo.
— From the Academy.

Toronto. — Canadian Journal of Science, Literature, and History.

Yol. XIY. Nos. 5, 6; Vol. XY. Nos. 1, 2. 8vo .—From

the Editor.

Turin. — Atti della Reale Accademia della Scienze de Torino.
Vol. X. Dispensa 1-8. 8vo. — From the Academy.
Bolletini dell Osservatorio della Regia Universita de Torino.

1875. 4to. — From the University.

R. Osservatorio Astronomico di Torino Effemride del Sole,
Della Luna e die Principal Pianeti calcolate per Torino,
in Tempo Medio Civile di Roma, per l’Anno 1876-1877.
8vo. — From the University.

Bolletino Meteorologico ed Astronomico del Regio Ossor-
vatorio della Universita di Torino. 1873-1874. 4to. —
From the University.

Upsala. — Nova Acta Regise Societatis Scientiarum Ups'aliensis.
Yol. IX. Fasc. 2. 4to. — From the Society.

Bulletin Meteorologique Mensuel de l’Observatoire de l’Uni-
versite d’Upsal. Vol. YI. Annee 1874. 4to .—From the
University.

199

of Edinburgh, Session 1875-76.

Utrecht. — Nederlandsch Meteorologisch Jaarboek voor 1870 and
1874. 4to. — From the Meteorological Institute.

Verslag van het Verhandelde in de Algemeene Yergadering
van het Provinciaal Utrechtscke genootscap van Kunsten
en Wetenscbeppen. 1874. 8vo. — From the Society of
Sciences and Arts.

Victoria. — Statistical Register of the Colony of Victoria for 1874.

Fol. Population — Part 6. Statistical Register Inter-
change— Part 5. Reports on the Mining Surveyors and
Registrars, 1875. — Fol. Patents and Patentees —

Vol. VIII. — 4to. Statistics of Friendly Societies,

1874.

Statistical Register of the Colony of Victoria. — -Part 7.
Accumulation. Fol. — From the Registrar General.

Vienna. — Das Gebirge um Hallstatt. Eine Geologisch-Palaontolo-
gische Studie aus den Alpen. Ahhundlungen der k. k.
Geologischen Reichsanstalt. Band VI. Heft 2. Edmund
Mojsisvocs v. Mojsv&r. 4to. — From the Society.

Die Congerien und Paludinenscichten Slavoniens und Eeren
Faunen, von D. M. Neumayl und C. M. Paul. Band VII.
Heft 3. 4to. — From the Society.

Denkscriften der kaiserlichen Academic der Wissenschaften.
Math.-Natur. Classe. Band XXXIV. 4to. — From the
Academy.

Sitzungsberichte der kaiserlichen Academie der Wissen-
schaften.— Min. Bot Zool. Geo. Pal. Classe. Band LXX.
Hefts 3, 4, 5. LXXI. Hefts 1, bis 5. — Phys. Anat.
Classe. Band LXX. Hefts 3, his 5 ; LXXI. Hefts 1, 2.
—Phil. Hist. Classe. LXX VIII. Hefts 2, 3; LXXX.
Hefts 1, 2, 3 ; LXXIX. Hefts 1, 2, 3. — Math. Nat. Classe.
LXX. Hefts 3, 4 his 5 ; LXXI. Hefts 1, bis 5. 8vo.-—
From the Academy.

Almanach der Kaiserlichen Academie der Wissenschaften.

1875. 8vo. — From the Academy.

Jahrbuch der kaiserlich-koniglichen Geologischen Reich-
sanstalt. Band XXV. Nos. 3, 4; XXVI. No. 1. 8vo. —
From the Society.

2 D

VOL. IX.

200

Proceedings of the Royal Society

Vienna. — Verhandlungen der kaiserlich-koniglichen Zoologisch-
botanischen Gesellsschaft in Wien. Band XXV. 8vo. —
From the Society.

Verhandlungen der kaiserlich-koniglichen Geologiscben
Beichsanstalt. 1875, 1-5; 11,12, 13. Nos. 14-18. 1876.
8vo. — From the Society.

Festschrift zur feierdes Funfundzwanzigjahrigen Bestehens
k. k. Zoologisch-Botanischen G-esellschaft in Wein. 4to.
— From the Society.

Warwick. — Fortieth Annual Report (1876) of the Natural History
and Archaeological Society. 8vo. — From the Society.

Proceedings of the Warwickshire Naturalists’ and Archaeo-
logists’ Field Club. 1875. 8vo. — From the Society.

Washington. — Annual Report of the Board of Regents of the Smith-
sonian Institution, for the year 1874. 8vo. — From the
Institution.

Astronomical and Meteorological Observations made during
the year 1873. 4to. — From the U. S Naval Observatory.

Bulletin of the United States Geological and Geographical
Survey of the Territories. 1875. Nos. 2, 3. 8vo. —

From the Geological Survey.

Report of the Geographical and Geological Surveys West
of the Mississippi. 1875. 8vo. — From the Geological

Survey ,

Report of the United States Geological Survey of the Terri-
tories. By F. V. Hayden. Vol. II. 4to. — From the

Geological Survey.

Annual Report of the United States Geological and Geo-
graphical Survey of the Territories, embracing Colorado
and parts of adjacent Territories, being a Report of the
Exploration for the year 1874. By F. V. Hayden. 8vo.
— From the Geological Survey.

Watford. — Transactions of the Watford Natural History and Hert-
fordshire Field Club. Vol. I. Part 1-3. 8vo. — From
the Society.

Wellington (N.Zi)— Reports on the Durability of New Zealand
Timber in Constructive Works. 8vo. — From the Agent
General.

of Edinburgh, Session 1875-76. 201

Wellington (N.2.) — Transactions and Proceedings of the New
Zealand Institute. 1875. Yol. VIII. 8vo. — From the
Institute.

Whitby . — Report of the Literary and Philosophical Society. 1875.
8 vo. — From the Society.

York. — Annual Report of the Yorkshire Philosophical Society for
1874. 8 vo. — From the Society.

Zurich. — Schweizerische Meteorologische Beobachtungen. 4to. —
From the Observatory .

Vierteljahrschrift der Naturforschenden G-esellschaft in
Zurich. Neunter Jahrgang, Heft 1-2. 8vo. — From the
Society.

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

vol. ix. 1876-77. No. 96.

Ninety-Fourth Session.

Monday , 27 tli November 1876.

Sir WILLIAM THOMSON, President, in the Chair.

The following Council were elected

President.

Sir WILLIAM THOMSON, Knt., LL.D.

Honorary Vice-Presidents , having passed the Chair.
His Grace the DUKE of ARGYLL.

Sir ROBERT CHRISTISON, Bart., M.D.

Vice-Presidents.

Professor Kelland.

Rev.W. Lindsay Alexander, D.D.
David Stevenson, Esq., C.E.

General Secretary — Dr

The Hon LordNEAVES.

The Right Rev. Bishop Cotterill.
Principal Sir Alex. Grant, Bart.

John Hutton Balfour.

Secretaries to Ordinary Meetings.
Professor Tait.

Professor Turner.

Ti ' easurer — David Smith, Esq.

Curator of Library and Museum— Dr Maclaoajn.

Councillors.

Dr Andrew Fleming.

Dr Charles Morehead.
Alexander Buchan, M.A.
Robert Wyld, LL.D.

Dr Ramsay H. Traquair.
Dr Thomas Harvey.

vol. ix.

Dr John G. M‘Kendrick.

Dr J. Matthews Duncan.
Sir T. C. Wyville Thomson.
D. Milne Home, LL.D.
Professor Crum Brown.
James Bryce, LL.D.

2 E

204

Proceedings of the Hoy at Society

Monday , 4 th December 1876.

The Rev. W. Lindsay Alexander, D.D., one of the Vice-
Presidents, at the request of the Council, gave the following
Opening Address : —

Gentlemen, — The Council having appointed me to deliver the
address at the opening of this the ninety-fourth session of the
Royal Society of Edinburgh, I have not felt myself at liberty to
decline the appointment, though deeply conscious of my inability
to discharge adequately the duty which has thus been laid upon
me.

I have, in the first instance, to advert to the changes which have
taken place in the fellowship of the Society in the course of the
past year. During that period the Society has lost by death nine
of its Ordinary Fellows and three of its Foreign Honorary Fellows.
These are by name —

Thomas Login, Esq., C.E., India.

Sir G-eorge Harvey, Kt., P.R.S.A.

James Warburton Begbie, M.D., F.R.C.P.E.

Lewis D. B. Gordon, Esq., C.E.

David Bryce, Esq., Architect.

George Stirling Home-Drummond of Blair-Drummond, Esq.

Alexander Russel, Esq.

Thomas Laycock, M.D., F.R.C.P.E.

The Most Noble the Marquis of Tweeddale, K.T., G.C.B., &c.

Adolphe Pictet, Geneva.

Adolphe Theodore Brongniart, Paris.

Christian Gottfried Ehrenberg, Berlin.

Fifteen new members were elected during the past year.

The total number of Fellows of the Society at this date is 419,
viz.—

Ordinary Fellows, .... 363

Honorary Fellows, .... 55

Non-resident Fellow under the old law, 1

419

205

of Edinburgh , Session 1876-77.

Following a practice which has grown to be a usage and a rule,
I proceed to lay before the Society brief biographical sketches of
the deceased members, so far as I have been enabled to gather
materials for this purpose. I shall take them in the order in which
they have been enumerated above.

Thomas Login,* born at Stromness, in Orkney, in 1823, studied
engineering at Dundee. In 1814 he obtained an appointment in
the Public Works Department in India, and was engaged from
1847 to 1854 in the construction of the Granges Canal under the
late Sir P. T. Cautley, who has most cordially acknowledged that
to Mr Login’s advice and assistance “ he wras greatly indebted in
designing and executing that work.”

After this period Mr Login was invalided and came to England.
In 1857 he returned to India, where he acted successively as
executive engineer of the Darjeeling and Roorkee Roads and of the
Northern Division of the Granges Canal. In 1868 he again came
to England, returning to India in 1870 to occupy the post of offi-
ciating superintending engineer at Umballa, where his labours
were varied and arduous, and a return of his illness cut short his
useful career on 5th June 1874, while engaged in an inspection of
the Thibet Road in the Punjaub.

While resident in India Mr Login made several communications
on engineering, among which may be mentioned his paper on the
“ Benefits of irrigation in India, and on the proper construction of
irrigating canals,” for which he received a Telford Premium from
the Institution of Civil Engineers ; his “ Description of the Ganges
Canal,” and recommendations for “ Roads, Railways, and Canals for
India;” and his paper “ On the Delta of the Irrawaddy,” com
municated to this Society in 1857.

Mr Login was a member of the Institution of Civil Engineers,
and was elected a Fellow of this Society in 1857.

George Harvey was a native of St Ninians, near Stirling, where
he was born February 1806. His father, a respectable tradesman
in that city, and a man of intelligence and piety, trained up his
children in the fear of God, and in a strict regard to the claims of
* This sketch has been furnished by David Stevenson, Esq., C.E.

206 Proceedings of the Boyal Society

honour and duty, and sent them forth to the business of life well
educated and thoroughly imbued with upright and virtuous prin-
ciples. From an early period Gteorge showed that his bent was
towards the pictorial art ; and his boyish efforts in that direction
proved that he had the natural gifts which, under due cultiva-
tion, promised to lead to eminence. In order to obtain this
necessary culture he came in 1823 to Edinburgh, where he studied
at the drawing school connected with the Institution. His first
pictures were exhibited in 1826, and attracted much attention.
In his earlier efforts he seems to have had Wilkie before him as
his model; at any rate, his subjects were selected from scenes of
humble Scottish life, such as Wilkie delighted to delineate. These
Harvey reproduced with scrupulous truthfulness, and his pictures
show a keener sense of the more humorous side of his subject
even than those of Wilkie. The scenes he preferred to delineate
were such as he had himself witnessed, and the features of which
remained vividly impressed on his memory. One of his earliest
pictures represented a village school during school hours, — the
respectable master engaged in hearing a lesson from a class of boys
and girls, and the rest of the pupils employed either in working
at their slates or conning their lessons, or in weary vacuity waiting
for the season of dismissal, or, as their bent inclined, playing tricks
and working mischief out of the master’s sight. This picture
attracted the attention of an eminent patron of art, who desired
to purchase it ; but Harvey, having promised it to a friend, would
not consent to sell it, even though his friend urged him not to
lose the advantage, so important to a beginner, of getting his pic-
ture placed in the gallery of a celebrated collector. To the village
school Harvey resorted oftener than once, even in the more ad-
vanced stages of his career, for the subject of a picture, as his well-
known pictures of “ The Examination ” and “ The Skule Skailin’ ”
show. Other scenes of ordinary Scottish life were depicted by him
at this time, such as “ The Leisure Hour,” “ Disputing the Billet,”
“ The Small-Debt Court,” and in later years his u Curlers,” his
“ Highland Funeral,” his “ Penny Bank,” show the undying in-
terest which the habits, pursuits, and manners of his countrymen
had for him. As a religious man, the religious history of his
country could not fail powerfully to engage his regards, and in

207

of Edinburgh, Session 1876-77.

connection with this some of the noblest efforts of his pencil were
produced; his Covenanter pictures — The Preaching, Baptism, and
Communion, as well as “ The Battle of Drumclog ” — attesting how
deep was his sympathy with those who in evil days had to seek
their spiritual sustenance and contend for their spiritual liberty at
the peril of their lives ; while his “ Beading of the Bible in Old St
Paul’s,” his “ Bunyan in Prison,” and his “ Bunyan selling laces
on Bedford Bridge,” show that it was not to the religious history
of his own country, or the struggles and sufferings of his own
countrymen, that his sympathies were restricted. In the ecclesi-
astical movements of his own time, also, he took a deep interest;
and his “ Quitting of the Manse ” remains to show how he could
appreciate a noble sacrifice for conscience’ sake on the part of those
with whom he himself had no ecclesiastical connection. In the
wider field of general historical painting Harvey did not attempt
the delineation of great and stirring events, but contented himself
with depicting scenes and actions of individual life or personal
enterprise. As among his most powerful efforts in this wider field
of his art may be mentioned his “Dawn revealing the New World
to Columbus,” his “ Shakespeare before Sir Thomas Lucy,” his
“ Bobbers melting Plate,” his “ Castaway,” and his “ Dr Guthrie
Preaching in the Highlands.” He was fond also of painting groups
of children, whose ways he had carefully observed, into whose
affections and sympathies he lovingly entered, and from whose
mimic sports he could draw lessons which by his pencil he sought to
impress on older folks. It is only necessary to name his “ Children
blowing Bubbles in Greyfriars’ Churchyard,” and his “ Wise and
Foolish Builders,” to illustrate his success in this department of
his art. In his later years he betook himself to the painting of
landscapes; and here, in the judgment of those most qualified to
judge, he was at his best. As a delineator of Scottish pastoral
scenery, whether in the Lowlands or in the Highlands, he in many
respects stands without a rival. In portrait-painting he was less
successful ; still some noble portraits, that, for instance, of the late
Professor Wilson, came from his easel ; and in several of his his-
torical pictures characteristic likenesses of eminent men living
at the time are introduced.

I cannot pretend to offer a critical estimate of Harvey’s merits

208 Proceedings of the Royal Society

as an artist. Even an unskilled observer, however, could not fail
to be struck with the more prominent qualities of his works, — the
truthfulness of representation, the clearness of conception, the power
and precision of execution, and the freshness and thoughtfulness
by which his pictures are characterised. A peculiar excellence
attaching to the productions of his pencil is derived from their high
moral character. Of his historical paintings each depicts some
scene of deep moral interest, or illustrates and enforces some great
moral or religious lesson ; and when he ceased to occupy himself
with such subjects, it was to Nature in her serener and grander
aspects that he turned, or among the dwellers in quiet pastoral
regions that he sought the objects of his art. In scenes of calm
natural beauty, amidst the solemn silence of the everlasting hills,
he delighted to roam, and such scenes he sought especially to
transfer to his canvas. They lifted up his own soul to (rod, and
he sought by his art to make them the means of producing the
same effect on others. He delighted also to depict scenes in the
common life of men, scenes which had powerfully touched that
chord of human sympathy which so strongly vibrated in his own
soul. With a deep sense of humour, and with an eye for the
ludicrous both in form and action, he never stooped to cater for
the mere amusement of the public, nor did he ever use his skill
in such a way as to offend the sensibilities of the least refined.
Nothing mean, nothing trivial, nothing fantastic, engaged his pencil.
In all ho did a high moral purpose is discernible, and his works, if
they have secured for him the reputation of a great artist, no less
commend him as a great moral teacher. This is wholly in keeping
with his general character. Endowed with genius and keen sus-
ceptibilities, he was at the same time a man of high principle, of
a vigorous and manly intellect, of simple and natural tastes, of
broad sympathies, of warm affections, and of a kindly and genial
spirit.

Not long after exhibiting his first pictures Harvey became an
Associate of the Academy. From that time forward he took a
lively interest in that Institution, and to his zeal and energy it
was in no small measure indebted for its establishment and early
success. In 1870 he appeared as its historian in a volume in which
the origin and progress of the Academy are narrated, and many

209

of Edinburgh, Session 1876-77.

interesting documents connected with its history are given ; the
volume is entitled “Notes on the Early History of the Royal
Scottish Academy.” In due time he became an Academician and
a member of Council, and on the death of the late Sir John Watson
Gordon he succeeded him as President of the Academy. Some
time afterwards he received the honour of knighthood from the
Queen.

Endowed with a constitution robust and sound, Sir George Harvey
was able up to an advanced period of life to pursue without serious
interruption the work of his profession. As he approached his
seventieth year, however, his health began to give way, and symp-
toms of a serious kind soon showed themselves. In the spring of
1874 his illness assumed so serious a form that his life was despaired
of; and though he rallied so far as to be able to leave his room,
take short drives, and receive his more intimate friends, it became
increasingly manifest that his work was done, and that his earthly
career must soon reach its close. Calmly, serenely, surrounded by
loving friends, and tended with affectionate solicitude by those
nearest and dearest to him, he for several months awaited his end.
This came to him on the evening of the 22d of January 1876,
when he peacefully breathed his last.

Sir George Harvey became a Fellow of this Society in 1867.

James Warburton Begbie was born at Edinburgh on the 19th of
November 1826. He was the second son of Dr James Begbie, for
many years well known and held in much repute as a consulting
physician in this city. Destined to follow his father’s profession,
young Begbie was carefully educated with that view. His profes-
sional studies were prosecuted at the University and the Surgeons’
Hall, Edinburgh, and afterwards at several of the continental
schools, including those of Paris, Vienna, and Italy; and he had
all along, while pursuing his studies, the advantage of his father’s
constant superintendence, instruction, and counsel. His degree of
M.D. was taken in 1847, and in 1852 he was elected a Fellow of
the Royal College of Physicians. In 1855 he was appointed a
physician and clinical lecturer in the Royal Infirmary; and much
about the same time he began to lecture on the practice of physic
in the Extra- Academical School. His period of service at the Infir-

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Proceedings of the Royal Society

mary expired in 1865, and at this time he gave up lecturing, as his
private practice had so increased that he could no longer give the
time required for this. For the same reason he was obliged to
resign the office of Examiner in Medicine for the Edinburgh Uni-
versity, to which he had been appointed in 1869. On relinquish-
ing his connection with the Infirmary he devoted himself to private
practice as a physician ; but after the death of his father, which
took place in 1870, he found it necessary to retire from ordinary
practice and devote himself to the work of a consulting physician.

In this capacity he continued to labour till the close of his life;
and in it he attained a position which has been described as almost
unique in his profession, his consulting room, on days when he was
to be seen at home, being crowded with patients of all classes, and
his services being in request, not only in all parts of Scotland, but
frequently also in England. For this he was indebted, in some
degree, to the urbanity and kindliness of his manner, in a greater
degree to the excellent footing on which he stood with members
of his own profession, but most of all to his undoubted skill, know-
ledge, and experience as a physician.

In the midst of his professional engagements, Dr Warburton
Begbie found time to furnish several valuable contributions to the I
literature and science of his profession. These appeared, for the
most part, in the pages of the “Edinburgh Medical Journal,” to
which he was for many years a frequent contributor. He published
also, at an early stage in his career, a little work, entitled “ Handy
Book of Medical Information and Advice. By a Physician.” This,
though published anonymously, speedily obtained an extensive
circulation, which was much increased when the authorship of the
work became generally known. In the literature of his profession
he was deeply versed, and his extensive knowledge of the history
of medicine enabled him to illustrate his own writings by appro-
priate citations from his predecessors in the same field of inquiry
and observation. To his other accomplishments he added that of
being an excellent linguist; with the classical writers of Greece
and Borne he was familiar, and he was able to converse freely in
several of the modern European tongues. As a lecturer on medi-
cine he was distinguished by the accuracy and fulness of his know-
ledge, by the perspicuity of his style, and by the minuteness with

211

of Edinburgh , Session 1 875-7 6.

which he entered into the exposition of his subject, both in its
theoretical aspects and in its practical details; and the same features
are discernible in the published productions of his pen. When the
British Medical Association met in Edinburgh in the autumn of
1875 Dr Begbie was selected to act as orator of a section of that
body, and on that occasion he delivered an address on the practice
of medicine in ancient and modern times, which displayed all the
excellent qualities of his manner as a lecturer and a writer, and
was not only well received by his professional brethren, but wel-
comed with hearty applause by the general public.

The incessant demands made upon him in the exercise of his
profession, and his unsparing devotion to the case of all who sought
his aid, his innumerable and often exhausting journeys, and the
toil, physical and mental, which he endured, began to tell upon a
constitution originally sound and healthy but not remarkably robust.
For some years before his death he had, at intervals, suffered from
weakness in the action of the heart; and these attacks had come to
be so frequent that he found it necessary, in the beginning of the
present year, to seek relief by retiring for a season from the active
duties of his profession. With this view he left Edinburgh in
the beginning of February last, intending to proceed by easy stages
to the south of England and ultimately to Italy. He had not,
however, reached farther than to Carlisle, when the symptoms of
his illness showed themselves in so aggravated a form that he saw
his case had become one of imminent danger. He accordingly
returned home. Here, at first, he seemed to rally, but after a few
days his strength gradually sank, and though several of the most
eminent of the medical practitioners in the city were in constant
attendance upon him, it soon became evident that a fatal issue could
not be averted. He died on Friday the 26th of February 1876.
His funeral took place on the following Thursday, and was attended
by some of the most distinguished members of the legal and medical
professions, and by a large company of the citizens.

Dr Warburton Begbie had all the qualifications of a great phy-
sician. To natural abilities and excellent general culture he added
profound knowledge of his profession, extensive experience in the
practice of it, great skill in the discernment of disease, and a happy
facility in suggesting fitting methods of treatment. His high moral

VOL. ix. 2 F

212

Proceedings of the It o gal Society

character also, and the known conscientiousness with which he
devoted himself to the case of those who consulted him, tended to
inspire confidence in him on the part of the public, as well as to
encourage his professional brethren to appeal to his advice incases
of emergency; nor were there wanting that “ hilaris vultusf that
kindly demeanour, and that gentle manner, which Celsus tells us
are such excellent qualities in the “ peritus medicus.”* Pleasant
looks and cheerful words will not of themselves, it is true, effect a
cure; but every experienced physician knows how materially they
are helpful to the end he seeks to gain with his patient : —

11 Sunt verba et voces quibus hunc lenire dolorum
Possis, et magnam morbi depellere partem ” +

Few men have passed away more sincerely lamented than was
Dr Warburton Begbie, as well by his professional brethren as by
the general public. As a skilled physician, as a man of varied
culture, high moral character and amiable manners, as a sincere
Christian and a generous benefactor to the poor, he has left behind
him a reputation which will not soon be obliterated.

Dr Begbie became a Fellow of this Society in 1870.

Lewis D. B. Gordon, J son of Joseph Gordon, writer to the Signet,
was born at Edinburgh in 1815, and received his early education
at the High School and University of Edinburgh.

Having determined to follow the profession of engineering, young
Gordon was first sent to Dundee, where he had the benefit of work-
ing at the bench and studying engine-fitting at the Dundee Foundry.
His next introduction to practical work was at the Thames Tunnel,
where, by the kindness of Mr Brunei, he had an opportunity of
seeing all the details of that unique work. Finally, he completed
his studies at the Royal Mining Academy, Fribourg, and the Ecole
Polytechnique at Paris.

* Periti medici est non protinns ut venit apprehendere manu brachium,
sed primum residere hilari vultu, percunctarique quemadmodum se habeat,
et si quis ejus metus est eum probabili sermone lenire. — Cels. De Re Medica,
b. iii. c. 6.

t Hor. Epist. I. 1. 35.

X This sketch has been contributed by D. Stevenson, Esq., C.E.

of Edinburgh, Session 1875-76.

213

On his return to Scotland he commenced practice as a civil
engineer in Glasgow, in partnership with Mr Lawrence Hill.

In 1840 the Government determined to establish a professorship
of civil engineering in the University of Glasgow, for which Gordon
became a candidate, and so high were his recommendations that
he received the appointment. There can be no doubt that at so
young an age, and with the strict sense of duty which ever animated
him, Gordon felt the task of organising the new chair to be one
that called forth all his energies. No man could be more fully
alive to the importance of his new office, or knew better the large
amount of knowledge — scientific and practical — that was required
of its occupant, and his sensitive mind felt the responsibility he
had undertaken very keenly. But he had a spirit that was not
easily daunted by difficulties, and in anticipation of his appointed
work he produced the syllabus of a course of study, embracing a
very wide field of engineering, under the following general heads:—

The Mechanical Effect produced by Forces and its Measure.

Physical and Mechanical Properties of Materials.

Results of Experiments on the Resistance of Materials.

Friction.

Doctrine of Mechanics.

Animal-power and its Recipient Machines.

Water-power and its Recipient Machines.

Steam-power and the Steam-engine.

After delivering his lectures he had the satisfaction to find that
he had got through the first session with comfort to himself and
profit to his pupils.

It may here be noticed that the skeleton syllabus of his opening
course of lectures was afterwards, in more matured form, published
in 1847, under the unassuming title of “ Engineering Aphorisms
and Memoranda,” and ultimately, in 1849, with further additions,
it was published, under the title of “ A Synopsis of Lectures on
Civil Engineering and Mechanics.”

He, however, knew that he had to make his professional character
as an engineer, and that this was not possible were all his energies
to be given to his professorial duties, and therefore, during the
time he occupied the chair, he invariably, when the session was
completed, devoted his whole time to the practice of his profession

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Proceedings of the Royal Society

as an engineer, — first in conjunction with Mr Lawrence Hill, and
latterly with Messrs Liddell and Newall, with whom he entered
into a second copartnery.

He ultimately found, as his engineering business increased, that
he could not fulfil the duties of his chair to his own satisfation,
and, in 1855, he resigned his professorship, in which he was suc-
ceeded by the late Professor Pankine.

During the time of his first partnership he, in conjunction with
Mr Hill, was employed in general engineering business in Scot-
land, and reference may, in particular, be made to the investigation
for the water supply of Glasgow in 1845, when they came to the
conclusion “ that the nearest adequate supply of pure water, that
can be brought to Glasgow by gravitation, is what is afforded by
the overflow of Loch Katrine.” This project was revived in 1852
by Professor Eankine and Mr John Thomson, and was ultimately,
as is well known, successfully carried out by Mr J. F. Bateman.
Among other works, Messrs Gordon and Hill were employed in
advising the Marquis of Breadalbane in his mining operations at
Tyndrum, and in constructing the great chimney for Messrs
Tennants’ works at St Rollox, which was, at that early period,
considered to be a work as bold as it was successful.

But it was in connection with Messrs Liddell and Newall that
most of Gordon’s engineering work was done. Liddell and Gordon
were engineers for several railways in England and Wales, and
designed and executed many iron bridges, among which may be
mentioned the Hereford, the Usk, and especially the Crumlin Via-
duct in South Wales, consisting of 10 spans of 150 feet, — a structure
of marvellous lightness, and withal of requisite strength and rigidity.
Their firm was rendered famous by the introduction of wire ropes,
which Gordon had seen in use at the mines in Germany, and intro-
duced into England in 1840, under a patent taken out by Gordon,
Newall, and Liddell. The uses of these ropes became highly import-
ant when they were ultimately so largely employed in protecting the
electric wires for submarine cables, — a new and large field of work
was thus opened up for the firm, which was designated P. S Newall
and Co. of Gateshead. The firm manufactured and laid upwards of
4500 miles of cable in different parts of the world. It was on one
of his numerous voyages in connection with marine telegraphs that

215

of Edinburgh, Session 1875-76.

he, in 1859, had the misfortune to he shipwrecked in the Red Sea,
when he suffered exposure on a barren rock for four days, and con-
tracted illness from which he never recovered. Latterly he suffered
from paralysis, which for many years prevented his engaging in
active business.

In preparing his lectures for the Glasgow professorship, Gordon
felt that at his early age he had much knowledge to acquire, and
he seems to have had no difficulty in giving the result of his inves-
tigations to the Glasgow Philosophical Society, of which he was a
member, and to which he communicated, between 1840 and 1844,
many papers.

In 1841, in a paper “ On the Determination of the Melting Points
of Metals,” he gave an account of the experiments of Plattner of
Fribourg. In the same year, under the title of “ Dynamometrical
Apparatus,” he detailed the investigations of M. Morin of Metz,
and, under the u Temperature of the Earth,” he gave an elaborate
account of the thermometric observations of Forbes and Herr
Dove. He also made communications on “ The Flow of Water
through Pipes,” the “Measure of Impact by Pressure or Weight,”
and other subjects of interest to the Society.

Of papers and pamphlets, on subjects of general engineering,
the following imperfect list may be given : —

“ Description of the Great Chimney of St Rollox at Glasgow.”
1844.

“ On the Supply of the city of Glasgow with Water from Loch
Katrine.” 1845.

“ Railway Economy, — an Exposition of the advantages of Loco-
motion by Locomotive Carriages instead of the present
system of Steam-tugs.” 1849.

“ Railway Economy, — Use of Counter-pressure Steam in the
Locomotive Engine as a Brake. Translated from M. L.
Le Chatelier, Ingenieur en Chef des Mines.” 1869.

“ Exposition of a Plan for a Metropolitan Water Supply.”

“On the most Advantageous Use of Steam.” 1845.

“ Short Description of the Plans of Captain J. Vetch, R.E.,
for the Sewerage of the Metropolis.” 1851.

In 1848 he translated from the German the tl Principles of the
Mechanics of Machinery and Engineering,” by J. Weisbach, of

216

Proceedings of the Royal Society

the Royal Mining Academy, Fribourg; and as a supplement added
some original appendices “On the Strength of Materials,” “Tubular
Bridges,” and the “ Rigidity of Cordage.”

Even after being laid aside from active business he continued
to take a lively interest in engineering, and never failed to answer,
in carefully considered letters, whatever his friends in the profes-
sion submitted for his friendly advice, which was always promptly
and ungrudgingly given.

In proof of what I may call the disinterested interest he took in
his profession and his professional brethren, it is pleasant to know
that the latest work in which Gordon was engaged was a labour of
love and regard for the memory of a professional brother.

About the close of 1875 it occurred to Mr James R. Napier of
Glasgow and Gordon, that a memoir of the late Professor Rankine,
and a republication of his contributions on scientific subjects to
Societies and journals would be a task agreeable to his friends, use-
ful to his former pupils, and acceptable to men of science. His
last letter to Mr Napier on the subject is dated 24th February
1876, just two months before his death. But his correspondence,
which had been going on three months, then ceased, and his friendly
desire — so like his nature — to give his time and strength as one of
the editors of the works of his successor in the chair of engineering
at Glasgow came to an end. He died at Poynters Grove, near
London, on the 28th April 1876. He became a Fellow of the
Society in 1845.

Resignation to the will of God was the ruling principle of the
last years of Gordon’s long illness, and this gave cheerfulness to his
daily intercourse, which was the admiration, and indeed the envy,
of the many friends who now lament his death.

David Bryce was a native of Edinburgh, where he was born in
1803, and where he received his early education, principally at the
High School. The son of an architect he determined to follow his
father’s profession, for which from an early age he had shown special
aptitude. After serving an apprenticeship in his father's office,
where he laid the foundation of his future eminence as a designer,
and acquired that technical skill by which he was distinguished, he
while yet young became assistant to Mr Burn, a well-known archi-

of Edinburgh, Sessio?i 1875-76.

217

tect, by whom he was soon after received into partnership. On Mr
Burn’s removal to London in 1844, Mr Bryce commenced business
for himself, and soon earned a high reputation in his profession.
For a short time he was in partnership with Mr Robert Anderson,
and a few years before his death he was joined by his nephew, Mr
John Bryce, in conjunction with whom he carried on business to the
close of his life.

During his lengthened career Mr Bryce executed many important
works, which remain to attest his ability and skill. In style he was
cosmopolitan, and, accordingly, the buildings he designed are in
various styles of architecture. In Edinburgh the Life Assurance
Company’s Office, the Scottish Widows’ Fund Office (originally the
Western Bank), the Subscription Library, the Surgical Hospital,
the Standard Assurance Office, the Sheriff Courts, the Union Bank
and Free St George’s Church are in the Italian style, as are also
the Western Bank and the Scottish Widows’ Fund Office in Glas-
gow; the British Linen Company’s Bank and the Clydesdale Bank,
in Edinburgh, are in the Palladian manner; and the Fettes College,
Edinburgh, and the Dundee Exchange, are in French Gothic. For
churches he generally adopted the Gothic, rarely the Norman,
and still more rarely the Italian. For a few public buildings he
employed the old Scottish style, as in the New Royal Infirmary,
Edinburgh, and the Sheriff Courts, Kirkwall ; but he reserved this
chiefly for private mansions. Of these he erected and altered a
vast number throughout the country; indeed, it has been affirmed
on good authority, that “ perhaps no man in the kingdom has
altered more mansion-houses than Mr Bryce.” * Here, it may be
said, his chief success was achieved, and here his peculiar genius
was chiefly manifested. “ Many an inconvenient, comfortless
dwelling has been by him converted into one of the most comfort-
able residences, and many a tame, uninteresting, commonplace
mansion rendered a picturesque feature in the landscape.”! Of
the houses of which he was the architect the most noteworthy are
Cortachy House, the seat of the Earl of Airlie ; Glen House, the
property of Mr C. Tennent; Ballinkinrain House, the property of
Mr Orr-Ewing, M.P. ; Hartrig House, near Jedburgh, the residence
of Lord Campbell ; Castlemilk, near Lockerbie, the property of Mr
* “ The Builder,” for May 27, 1876, p. 607. t Ibid.

218 Proceedings of the Boyal Society

Robert Jardine; Kimmerghame, the residence of Mr Campbell
Swinton ; Broadstone, the residence of Mr J. Birkmyre ; and Wood-
croft, the residence of Colonel Davidson. All these are in the old
baronial style. In other styles are Panmure House (Elizabethan):
Langton, near Dunse, the seat of Lady Elizabeth Pringle (Eliza-
bethan) ; Portmore, the residence of Mr Mackenzie (Elizabethan);
Kinnaird Castle (French); Belladrum, the property of Mr Merry,
M.P. (French) ; Eastburgh, the residence of Mr Carnegy (French) ;
and Kincaid Castle, the seat of the Earl of Southesk. In adopting
these different styles MrBryce was not a mere copyist ; he impressed
upon all his work the stamp of his own taste and genius. Essen-
tially an artist, he had a fine perception of harmony, and he sought
always to bring his buildings into fitness for the place they had to
occupy, and into harmony with the surrounding scenery, so as to
make them part of one great picture. “ When he had a work on
hand where anything like scope was allowed to his powers, he
wrought upon it as a painter does upon his easel, recurring to it
again and again, altering proportions and rearranging the grouping
of masses, and in doing this he did not hesitate occasionally to
obliterate what had cost him much labour.”*

Mr Bryce stood high in his profession, and his name will remain,
along with those of Adam, Hamilton, and Playfair, among those
of the greatest of modern architects. He was Grand Architect for
Scotland, a Fellow of the Royal Institute of British Architects,
and a member of the Royal Scottish Academy, as well as a Fellow
of this Society. He was a man of varied acquirements, of high integ-
rity, and of a genial disposition. Under a blunt manner, and some-
what rough exterior, there lay in him a kindly nature and a generous
heart; and, whilst his society was much sought after by his friends,
he drew to him the esteem alike of his servants and his employers.

He died on the 7th of May last, in his seventy-fourth year. He
became a Fellow of the Royal Society in 1856.

George Stirling Home-Drummond was the eldest son of the late
Henry Home-Drummond, Esq. of Blair-Drummond, and great-
grandson of the celebrated Henry Home Lord Karnes. His father
was for many years member of Parliament, first, before the passing

« The Builder,” as above.

219

of Edinburgh , Session 1876-77.

of the Reform Bill, for Stirlingshire, subsequently for Perthshire ;
in which capacity he rendered important services, particularly by
the laws which he procured to be enacted, of which the Act for the
Regulation of Public Houses in Scotland, and that for the Small
Debts Jurisdiction in the Sheriff Courts, may be mentioned as
specially valuable. He died in 1867, and was then succeeded in
his estates by his son, the subject of this notice. This gentleman
was born in Edinburgh on the 1st of March 1813. He received
his university education at Oxford, where he was entered at Christ
Church College. Some time after leaving the university, he tra-
velled through Palestine and other parts of the East. Of this
tour he wrote an account, which was printed for private circula-
tion, but never published.

Mr Horn e-Drummond was a man of extensive culture and varied
pursuits. With the languages and literature of ancient Greece
and Rome he was familiar; of several of the languages of modern
Europe he was accurately master, especially French and Italian,
which he wrote and spoke with ease and fluency ; and in several
branches of natural science, he was proficient. He was chiefly
interested in antiquarian research, and became especially skilled
in the deciphering of ancient documents. One of the fruits of his
labours in this field was the collection of a mass of notes and
papers relative to the Earldom of Monteith, which, it is under-
stood, is now in the possession of a learned legal antiquary, with
the view of being used in the preparation of a historical volume.

Though interested in literary and scientific pursuits, Mr Home-
Drummond did not neglect the duties of a large landholder and
country gentleman. In this capacity as well as in the relations
of private life, he was much respected and esteemed. He died
somewhat suddenly in London, on the 3d of June in the present
year. He was elected a Fellow of this Society in 1869. He was
also a Fellow of the Society of Scottish Antiquaries and a Fellow
of the Geological Society.

Alexander Russel was a native of Edinburgh, where he was
born on the 10th of December 1814. His father was a solicitor
practising in that city, and his mother, from whom it is said he
derived much of his mental vigour and character, was the daughter

2 G

VOL. IX.

220

Proceedings of the Royal Society

of a Mr Somerville, whose interest in politics and stanch adherence to
his party may be said also to have been inherited by his descendant.
After receiving education at several schools in Edinburgh Mr Russel
was apprenticed to the printing trade with Mr John Johnstone, a
gentleman well known in connection with literature as an editor
and author still more than as a printer. To young Russel the
acquaintance and society of this gentleman and his gifted and
accomplished wife were of great advantage. They soon discovered
his abilities, and they did much to foster his taste for literature as
well as to direct his studies. By them he was encouraged to the
use of his pen in composition, and several of his early essays were
introduced by Mrs Johnstone into “ Tait’s Magazine,” of which
she was at that time the editor. From the outset, however, his
bent was to politics rather than to literature ; and having been at
an unusually early age appointed editor of the “ Berwick Adver-
tiser,” he was enabled thenceforward to devote himself to a career
to which his tastes inclined him, and for which he was by natural
abilities and acquired facilities and resources peculiarly fitted.
After some years he exchanged the editorship of the “Advertiser”
for that of the “ Fife Herald,” which post he continued to hold
till towards the close of 1844. By this time his reputation as an
able writer and skilful editor was established ; and in 1845 he,
after a connection of short duration with a paper in Kilmarnock,
was invited to become the colleague of the late Mr Maclaren as
editor of the “ Scotsman,” then, as it is still, the leading political
journal in Scotland. In connection with Mr Maclaren he con-
tinued to edit this journal, taking upon him almost the entire
management, until 1849, when Mr Maclaren retired, and Mr
Russel became sole editor. In this position he remained up to
the time of his death, though latterly, through failing health,
he Was obliged to devolve upon others much of that work which
for many years he had with Herculean vigour done alone.

The “ Scotsman ” newspaper is, as is well known, the recognised
principal organ of the Whig party in Scotland ; and for the advocacy
and diffusion of the principles held by that party it was designed.
Of that party Mr Russel was a stanch adherent, of its principles
he was the bold, uncompromising, and consistent advocate, and its
interests he zealously laboured to advance. The services he ren-

221

of Edinburgh, Session 1876-77.

dered to his party were immense. Nor were the members of the
party slow to acknowledge this ; as was attested in many ways,
but especially by the testimonial which was presented to him in
1859, “ in recognition of his services and as a mark of respect for
his honourable and independent conduct in public and private
life,” and by his being spontaneously elected a member of the
Reform Club in London, which has been described as “ the
central organisation of the Liberal party.” Nor was it by persons
of that party alone that his merits were acknowledged, and the
tribute of respect to his consistency and integrity rendered. Per-
haps no provincial newspaper was so generally read by men of all
parties as the “ Scotsman ” whilst under Mr Russel’s management ;
and however much some of its readers might dissent from his
opinions or dislike his principles, there were none who did not
admire the boldness, the steadfastness, and the consummate ability
with which these were maintained and advocated. For the con-
duct of a public journal he was eminently qualified as well by the
brilliancy of his faculties as by the extent and variety of his know-
ledge, his sound sense, and the manly vigour which characterised
all his utterances on questions of public interest. Of him may it
be said, with much greater justice than of the person to whom
Addison first addressed the line, that he was

“ For wit, for humour, and for judgment famed.”

If sometimes his wit was over keen, if now and then in his humour
there was a flavour of coarseness, if occasionally he jested where jest-
ing was (i not convenient,” if the showers of ridicule with which he
assailed the objects of his criticism were often more copious than
deserved, there is this to be said on the other side, that his judgment
was seldom at fault, that in his satire there was no malevolence,
that kis antagonism was open and manly, that he scorned to use any
base arts of insinuation, vituperation, or slander, and that when he
wielded the scourge there was so much cleverness in his manipula-
tion, such felicity of expression and illustration, and withal such a
joyous hilarity pervading the whole, that even those who were the
objects of his most pungent strictures found it impossible to with-
hold their admiration, or to resent with bittei-ness the castigation
they had received.

222 Proceedings of the Royal Society

Those who have been born and brought up in towns, and whose
avocations restrict them to a residence in “ the busy haunts of
men,5’ have often little or no relish for natural scenery, and no
inclination towards the pursuits or pastimes of country life. Dr
Johnson, it is well known, thought Meet Street much to be pre-
ferred to Greenwich Park, and maintained that no man would live
in the country who could help it. Boswell, in recording this with
approval, “ shelters ” himself under the authority of one whom he
describes as a man of fashion, but distinguished also by a love of
literature, who declared that he preferred the smell of a flambeau
at the playhouse to the fragrance of a May evening in the country.*
Madame de Stael, when an enthusiastic friend was expatiating on
the delight which such a heart as hers must take in green fields
and gentle streams, replied — “ Ah ! il n’y a pour moi de ruisseau
qui vaille celui de la Bue de Bac,” a street in the Faubourg St
Germain, through which a paltry rivulet flows. There are many
who, without having a distaste for the country so pronounced as
this, are yet supremely indifferent to it, and either never care to
visit it, or if they are seduced into it, are never happy till they
turn their back on it and find themselves once more among streets
and houses. Mr Russel was not of this class. Though born in a
town, and from his youth up a dweller in towns, he had a passion-
ate love for the country, and found no relief from his toils so
refreshing and exhilarating as a ramble among the hills and by
the streams of his native land. He was also enthusiastically
devoted to angling, and there are few of the angling waters of
Scotland with which he was not acquainted. With the Gala
and the Tweed he was especially familiar, and often sought on
their banks that recreation which their streams afforded to him in
the pursuit of his favourite pastime. With the habits of the
tenants of the waters he was careful to make himself acquainted,
and he knew them all well, from the trout to the salmon. His
observations were embodied in an article which appeared in the
“ Quarterly Review,” and which he afterwards expanded into a
volume ; and on the subject of fishing he became so much of an
authority, that he was repeatedly examined before Parliamentary
Commissions appointed to inquire into this matter. Besides tra-
* Life of Dr Johnson, i. n. 438. 8vo edit. Lond. 1807.

of Edinburgh, Session 1876-77.

223

versing widely his own country, Mr Russel in 1850 made a tour
in Ireland ; in 1863 he for the first time visited the Continent ;
and in 1869 he went to Egypt, and was a witness of the ceremony at
the opening of the Suez Canal. In 1872, after his first serious ill-
ness, he made a lengthened tour through the south of Europe, visit-
ing several places in France, Portugal, Spain, and N orthern Italy.

The illness under which Mr Russel suffered was a form of heart
disease, and by this he was for some years before his death so
seriously affected that he was obliged to retire to a great extent
from the literary work of the “ Scotsman.” Towards the end of
last year the attacks became more frequent and severe, and his
strong constitution at length sank under them. He died on the
18th of July last.

Mr Russel became a Fellow of the Royal Society in 1870.

Thomas Laycock was horn at Witherby, in Yorkshire, on the
10th of August 1812. He was the son of a Wesleyan minister,
and received his early education at the Wesleyan Academy, Wood-
house Grove. Destined for the medical profession, he was, when
fifteen years of age, apprenticed to Mr Spence, surgeon, of Bedale.
He afterwards prosecuted professional studies at University College,
London, where he followed the full curriculum ; subsequently, he
went to Paris, where he studied under Velpeau and Lisfranc ; and
from this to Gottingen, where he took his M.D degree “ summa cum
laude.” On his return from the Continent he settled at York as a
general medical practitioner. In 1841 he was appointed physician
to the York Dispensary; in 1844 he acted as Statistical Secretary
to the British Association, which met that year at York; and in
1846 he became Lecturer on the Theory and Practice of Medicine
in the York Medical School. On the retirement of the late Pro-
fessor Alison in 1855, he was elected Professor of the Practice of
Medicine and of Clinical Medicine in the University of Edinburgh.
In 1869 he was appointed Physician to the Queen in Scotland.
He was a Fellow of the Royal College of Physicians as well as of
the Royal Society of Edinburgh.

Endowed with great mental ability, and possessed of indomitable
energy, Dr Laycock contributed largely to the literature and science
of his profession. He was an excellent linguist, and kept himself

224

Proceedings oj the Royal Society

abreast of the most important advances in medical science and
speculation on the Continent. He translated Prochasta’s Treatise
on the Nervous System and Unger’s Physiology. His own con-
tributions to various branches of medical science were many, and
most of great value. Besides numerous papers in the medical
journals and in the transactions of learned societies, he published a
Treatise on the Nervous Diseases of Women, in which he first de-
veloped his views as to the scientific data of unconscious and in-
voluntary brain function, and explained thereby the phenomena
of mesmerism, dreaming, and insanity. The views advanced in
this work he afterwards extended and completed as a system of
Practical Philosophy, in a work in two volumes, entitled “ Mind
and Brain, or the Correlation of Consciousness and Organisation,”
of which the first edition appeared in 18G0 and the second in 1869.
He also devoted much attention to the subject of epidemiology,
and his papers on this and on questions of sanitary reform contri-
buted much to turn attention to the important matter of public
health, and to direct to the use of measures best fitted to secure and
promote it.

The natural bent of Dr Laycock’s mind was towards speculation
and theory; but he had what many theorists and speculative thinkers
have not, a capacity of minute observation and a patience of details
which have enabled him to give to his writings a value and im-
portance independent of the theories which they are intended to
advocate. As to the soundness of these theories there may be, and I
presume are, differences of opinion, but there can be but one
opinion as to the conscientious carefulness and exactitude of his
observations, and as to the value of the facts which he has collected
and described. His doctrine concerning the reflex function of the
brain is now, I believe, universally recognised by physiologists, and
its importance both in a scientific and a practical relation acknow-
ledged to be great. To the subject of mental disease Dr Laycock
devoted much attention ; and he did not a little to advance the
science of mental pathology, and thereby to place on a firmer basis
the theory of the treatment of the insane. As a professor his aim
was not merely to communicate knowledge to his students, but still
more to awaken them to thought, to stimulate them to inquiry, and
to urge them to use their faculties in the independent pursuit of

225

of Edinburgh, Session 1876-77.

truth. Complaints have sometimes been made of his want of
lucidity as a lecturer, but the fault here may have been rather on
the part of the student than on the part of the professor; for where
the mind has not been previously trained to processes of thinking,
the most lucid exposition of doctrines which are speculative and
abstract will fail of conveying to the hearer a clear and just concep-
tion of the teacher’s meaning. Dr Laycock’s lectures were always
thoughtful and instructive, and if they often required an effort of
close attention and thought on the part of the student to appre-
hend them, this was never rendered without great advantage to the
student thence accruing.

In outward manner Dr Laycock was somewhat cold and formal,
and there was in his addresss what had the appearance, though
slight, of hauteur. But under all this there lay an extreme kindli-
ness of disposition, which manifested itself in many acts of gene-
rous beneficence and tender sympathy.

For some years before his death Dr Laycock’s health had begun to
fail. In 1857 he had been visited with a threatening of phthisis; and
though he seemed entirely to recover from this, the insidious malady
continued lurking in his system. In 1866 disease of the left knee-
joint rendered amputation of that limb necessary; and this gave a
shock to his system from which he never wholly recovered. He was
able, however, in the enjoyment of an apparently fair measure of
health and strength, to continue his ordinary avocations and to fulfil
his professorial functions up to the close of last winter session, when
an accession of his old malady laid him aside. As the summer
advanced pulmonary consumption gradually extended its ravages in
his frame, and on the 21st of September he breathed his last.

Dr Laycock became a Fellow of this Society in 1856, the year
after his appointment to the Chair in the University.

George Hay, Marquis of Tweeddale, was born at Yester House,
on the 1st of February 1787 ; and succeeded his father as eighth
marquis in 1804. In the same year he entered the army, and he
was engaged in active service during the whole of the Peninsular
War. He served as aid-de-camp to the Duke of Wellington, by
whom he was highly esteemed as a brave soldier and an able officer.
He afterwards served in Canada. He was wounded at the battle of

226 Proceedings of the Royal Society

Busaco, and be received other wounds in subsequent engagements ;
and when, in 1814, he returned home invalided, he was so lame from
the effects of his wounds that he was obliged to use crutches. As
a young man he was remarkable for his great strength, and many
stories are told of his powers both on the field and in pugilistic
encounters. He wielded a sabre longer by several inches than the
regulation standard; he was an excellent horseman, and a notable
whip. It is recorded of him that he once drove the mail coach from
London to Haddington without leaving the box or resigning the
reins for a single stage. Even in extreme old age he was to be
seen on the streets of this city driving a pair of spirited horses
with the vigour and skill of an experienced charioteer.

In 1842 the Marquis went out to India as Governor and Com-
mander-in-Chief at Madras. Here he remained for six years faith-
fully discharging the duties of his high and responsible office. As
one who had been trained under Wellington he could not but set
himself to restrain and cure the lax discipline which had been
allowed to creep into the Indian army; and the severity of some
of the measures he took with this view exposed him to no small
obloquy and censure. Events, however, proved that he was right
in the course he pursued, and that his action was alike necessary
and salutary.

On his retirement from active service in the army the Marquis
devoted himself to the duties and occupations of a country gentle-
man, and these he continued to pursue to the end of his life with
the exception of the six years he was in India. He engaged largely
in agricultural pursuits, retaining in his own hands an extensive
farm, which he cultivated with the utmost assiduity, sparing no
expense of money, or labour, or skill, not only to render it produc-
tive to the highest possible degree, but to make it a model of
scientific farming, from which others engaged in the same pursuit
might derive profitable instruction. He introduced many im-
portant improvements both in the practice of farming and in the
implements used in agriculture; so great, indeed, were the im-
provements he introduced, both in the methods and in the means
of tillage, that he may be said to have revolutionised Scottish
agriculture. In 1836 he received the gold medal of the High-
land and Agricultural Society for the invention of a machine for

227

of Edinburgh, Session 1876-77.

the making of tiles to be used in drainage. He invented also
the Tweeddale plough, an implement which has been found of
immense use, as enabling the cultivator with the minimum of
draught to turn up the subsoil so as to break it up and subject
it to the action of the atmosphere. The system of deep ploughing
which he introduced prepared the way for the use of the steam-
plough, which he was the first to bring under the notice of the
Society and to introduce into general use. As has been justly said,
“ the agricultural world was under a deep obligation to the Marquis
for the time, research, and large pecuniary expenditure he devoted
to the practical solution of the steam plough question.”*

To the agriculturist the condition and changes of the atmo-
sphere are hardly of less interest than is the soil which he has to
till. As might be expected, therefore, in one so interested in
agriculture, the Marquis of Tweeddale attached great importance
to meteorology, and devoted much time, labour, and money to the
fostering of that science. Of the National Meteorological Society
of Scotland he was from the first, and continued to be, the main
support. From time to time he offered prizes for the best essay
or series of observations on meteorological phenomena; which had
the effect of engaging the attention of competent inquirers to
these phenomena, and drawing forth some communications of
the greatest importance to those engaged in agriculture and allied
pursuits.

Besides holding the hereditary honours and dignities of his house,
some of which had come down to him from a remote ancestry, Lord
Tweeddale possessed many personal distinctions. He was a K.T.
and G.C.B., a representative Peer of Scotland, Lord-Lieutenant of
Haddingtonshire, Colonel successively of the 30th Regiment, the
42nd Regiment, and the 2nd Regiment of Life Guards, a General
in the army, and a Field Marshal. He died at Tester House on
the 10th of October last, in his 90th year.

The Marquis of Tweeddale became a Fellow of this Society in
1849.

Adolphe Pictet was born at Geneva on the 1 1th of September
1799. He received his education at the Hofwyl institution
* Stephens & Slight, Book of Farm Implements.

2 H

VOL. IX.

228

Proceedings of the Royal Society

founded by Fellenberg, who was an intimate friend of his father
Charles Pictet de Rochamont. He afterwards studied at Paris;
and from that he went to Germany, where he made the acquaint-
ance of Schlegel, Schelling, Hegel, and Goethe, as he had at Paris
that of Victor Cousin and other men of eminence. A vast mass
of letters remain to testify to the intimacy of his relations with
these and other distinguished men among his contemporaries.

He began to write in the “ Bibliotheque Universelle,” a journal
founded by members of his own family, and of which he became
the proprietor in 1825. In 1838 or 1839 he commenced to lecture
on aesthetics in the Academy at Geneva, and three years after-
wards he was appointed professor there of aesthetics, modern litera-
ture and linguistic. This appointment he did not hold long;
circumstances led to his engaging in other pursuits, and for a time
he left Geneva and fixed his abode at Turin. Obliged, as every
Swiss citizen is, to serve as a soldier, he for some time was in the
army, where he rose to the rank of colonel of artillery. Directing
his attention to the implements of artillery warfare, he introduced
such improvements in these that the Austrian Government pur-
chased for 25,000 francs the secret of bombs of his invention.
Returning to Geneva, he devoted himself to his favourite studies,
and from time to time issued works in various branches of philo-
sophy, and especially in comparative philology, which brought him
reputation much more in other countries than his own. In Geneva,
indeed, he was very little known, the abstruse character of his
writings rendering them acceptable only to the few, and the deaf-
ness with which he was afflicted preventing him from mingling in
general society. In 1839 the Institute of France adjudged to him
the Volney prize for an essay on the affinity of the Celtic language
with the Sanscrit ; and twenty years afterwards the same prize was
assigned to him for a work in which he developed at length his
views as to the primary relations of the Indo-European tongues
generally. This work, which is entitled “ Les Origines Indo-
Europeennes, ou Les Aryas primitifs ; Essai de Paleontologie lin-
guistique,” is one of great learning and acuteness, and has com-
manded the applause of philologists and ethnologists in all parts
of the learned world. In 1856 he published a work scarcely less
remarkable in its kind, entitled “ Du Beau dans la Nature, Part, et

229

of Edinburgh , Session 1876-77.

la poesie, etudes d’Esthetique.” Ilis other works are, u Course a
Chamonix, conte fantastique” (1838); “ Essai sur les proprietes et
la tactique des fusees de guerre” (Turin, 1848); “ Mystere des
Bardes de l’lsle de Bretagne;” two “ Essais sur des Inscriptions
G-auloises,” and many articles in reviews and other periodicals.

M. Pictet was a Member of the Koyal Irish Academy, of the
Ethnographic Society of New York, of the Academie Stanislas of
Nancy, as well as a Fellow of this Society. From Napoleon III.
he received the decorations of the Legion of Honour and of St
Maurice and St Lazare. He was elected an Honorary Fellow in
1804. He died 20th December 1875.

Adolphe-Theodore Brongxtart was born at Paris on the 14th
January 1801. He was the son of Alexandre Brongniart, the
celebrated naturalist and associate of Cuvier, who died in 1847.
Devoted from childhood to the study of the natural sciences, in
which he was encouraged as well by the example as by the counsels
of his father, Adolphe, while preparing to take his degree of doctor
of medicine, cultivated at the same time with earnestness and suc-
cess botany and geology. In 1822 he published a monograph on
the classification and distribution of fossil vegetables ; three years
later he published a work on Champignons , in which he embraced
the whole of that family in a natural classification of its genera;
and in 1826 he presented to the Academie des Sciences a “ Memoire
sur la generation et le d^veloppement de Fembryon vegetal,” for
which he received the first prize for experimental physiology. In
this work a new light was thrown on the most important fact in
the life of plants; and if it cannot be said that he entirely lifted
the veil which had hitherto covered the mystery of fecundation,
he advanced very near to the complete explanation of that phe-
nomenon. The course on which he had thus entered of scientific
investigation he pursued with unabated energy to the close of his
life. The number of investigations which he conducted, and the
papers which he presented to scientific societies and to the scientific
world through the press, indicate an almost unprecedented amount
of activity on his part. His most important work is his “ Histoire
des Vegetaux Fossiles,” which unfortunately was left unfinished
by him. In this work new light is thrown on both botany and

230 Proceedings of the Royal Society

geology, and it may be regarded as a work of standard authority
on vegetable palaeontology.

M. Brongniart was elected professor of botany and vegetable
physiology in the Museum of Natural History at Paris in 1833;
and from 1852 he was inspector-general of the University for the
sciences. He was a Member of the Academie des Sciences and
an officer of the Legion of Honour. He was elected an Honorary
Fellow of this Society in 1872. He died in February last.

Christian Gottfried Ehrenberg was born at Delitsch, in Prussia,
on the 19th of April 1795. He studied chiefly at Leipsic, where
he took his doctor’s degree in medicine. At Berlin, in 1815, he
devoted himself to microscopic researches in physiology, and through
these became known to the scientific world. In 1820 he was sent
by the Academy of Sciences, along with Hemprich, on a scientific
expedition to Egypt, in the course of which he traversed Egypt,
Abyssinia, and a considerable part of Africa. His companion
having succumbed under the fatigues of the journey, Ehrenberg
prosecuted it alone, and returned bringing with him a large collec-
tion of animals and plants until then unknown. He was named
professor extraordinary in the Faculty of Medicine at Berlin; but
he preferred going with Humboldt to explore Central Asia, and
more particularly the plateau of the Altai. On his return he settled
at Berlin, where he was in 1842 made principal secretary to the
Academy of Science. Here he devoted himself chiefly to micro-
scopic researches on the Infusoria, and in this field made many
discoveries, which added materially to the knowledge of these minute
forms of animal life, and suggested the explanation of many pre-
viously unexplained phenomena, such as phosphorescence on the
sea, blood-rain, red snow on the Alps, and the blood-red spots which,
to the terror of the ignorant and superstitious, sometimes appear on
bread. To the heaps of infusoria, also, he attributed “the exist-
ence of vegetable soil, and according to his observations these
infinitely small creatures have formed entire mountain-chains, and
played an important part in the formation of the crust of the
earth.”* His great work, entitled “ Die Infusiorsthierchen als
vollkommen Organismen ” (Leipz. 1838), contains his classification
* Men of the Time, p. 328, 8th edit.

231

of Edinburgh, Session 1876-77.

of these minute organisms, a classification, however, which natural-
ists have not universally adopted.

Herr Ehrenberg was a member of most of the learned Societies
of Europe. He was elected an Honorary Fellow of this Society in
1845. He died in April of this year.

In the course of the past session the number of “ papers ” read
at the meetings of the Society was forty-five, besides the address
delivered at the opening of the session by the senior Vice-Presi-
dent, Mr Milne-Home. Of the papers read, twenty-three were in
the department of mathematics and physics, three in chemistry,
four in meteorology, one in anatomy, five in geology, two in geo-
graphy, five in botany and natural history, and two on literary
subjects. Some of these papers were of considerable length, and
most were of importance and permanent interest.

The Keith Prize for the biennial period 1873-75 was awarded
to Professor Crum Brown for his “ Researches on the Sense of
Rotation and on the Anatomical Relations of the Semi-Circular
Canals of the Internal Ear;” and was presented to him by the
President at the meeting on the 15th of May.

The Society is to be congratulated on the evidence which the
number and variety of the papers read last session afford of the
continued zeal and activity of its members in various spheres of
scientific inquiry and literary research. At the same time, I ven-
ture to express a wish that the range of the Society’s activity were
widened, so that incursions were made into fields of inquiry and
research which, so far as our Proceedings show, are wholly ne-
glected by the members of the Society. With the exception of
the two literary papers, all the papers read last session have to
do either with the exact sciences or the sciences of observation.
Besides these, however, there are the moral sciences, the science
of experience or consciousness, and the history of science, in all
of which there are questions of high interest and importance which
yet remain unsettled, and which await and invite the investigation
of members of a learned body such as this. How little, for in-
stance, is known of the history of philosophic thought and scientific
speculation among the Arabians and the Jews in the Middle Ages,
or among the theosophists, mystics, and speculatists of the East !

232

Proceedings of the Royal Society

In ethics, in political economy, in jurisprudence, in international
law, how many points of profound interest are still in dispute or
are involved in obscurity ! In psychology, how many new theories
and methods have recently emerged, both in this country and on
the Continent, which may change the entire aspect of that science,
and which, at any rate, challenge the careful consideration of all
philosophic thinkers! A new science, indeed, has of late sprung
up in this department, — the science, so-called, of physiological
psychology, — an infelicitous designation, as I cannot but think, see-
ing that as physiology can never become psychology nor psycho-
logy physiology, the union of the two words in one designation
is almost tantamount to a negation of the possibility of the science
so designated. This science has found so many enthusiastic and
able cultivators that its claims on the attention and study of Scien-
tific inquirers cannot be neglected. I confess I am not myself
sanguine of any great advantage accruing to psychology from its
being approached through the medium of physiology, for this, were
there no other reason, that, as on the one hand, the physiologist
must first learn from consciousness or experience the existence of
any faculty before he can search for or find an organ for that
faculty in the body ; so, on the other hand, he is unable from the
mere observation of the bodily organs or functions to throw any
light upon the mental faculties, seeing all he can accomplish at the
utmost is to point to a connection of some sort between the mental
faculty and the bodily organ. At the same time, I defer to the
judgment of the eminent men who have appeared as the cultivators
of this science, and claim for it a place among the objects which
engage the attention of the members of this Society.

“ Through desire a man, having separated himself, seeketh and
intermeddleth with all wisdom ” (Prov. xviii. 1). This saying of the
Hebrew sage might be adopted as a fitting motto for such a Society (
as this. By joining it the members separate or set themselves
apart, under the impulse of a master desire, to the pursuit of
knowledge; and it beseems them, as so separated, to take all wis-
dom for their province. It is true that in the present day know-
ledge is no longer confined to the few, or locked up within Societies
of those who give themselves to the pursuit of it as their business
and occupation. It is true that “science has now left her retreats,

233

of Edinburgh, Session 1876-77.

her shades, her selected company of votaries” (Channing) ; and
that many who are engaged in other occupations are at the same
time diligent cultivators of science, and often come forward to add
contributions to its stores. Still, it is to those who set themselves
apart as men of science or as literary men that the world looks for
the steady pursuit of knowledge, and for the guidance of others to
the solution of those questions which from time to time press upon
the interest or affect the welfare of the community. And where
Societies of such are formed men look to them to intermeddle with
all wisdom, and leave no part of the wide field of knowledge un-
explored.*

On the value and utility of such Societies it would be idle in me
to expatiate in such an assembly as this. Who knows not that by
intercourse with others men have their faculties sharpened, are
helped better to understand themselves, and to bring to precision
and definiteness their own cogitations, as well as stimulated to
explore new fields of inquiry and guided to make new discoveries?
It is long ago since Homer said —

“ By mutual confidence and mutual aid
Great deeds are done and great discov’ries made.

The wise new wisdom from the wise acquire,

And one brave hero fans another’s fire” — +

and ample experience has showed that this holds true no less of
those who go in quest of truth than of those who engage in mili-
tary adventure ; for as Plato, after referring to this passage in
Homer, says, “ in society we all are somehow more alert in deed
and word and thought ;”J and Aristotle, also referring to this pas-
sage, says that by society “ those engaged in great undertakings
are rendered more potent to think and to act.Ӥ I content myself
with congratulating the Society on its past achievements and its
present flourishing condition; and expressing my confidence that
the energy which has characterised the members in the past will
be no less displayed, and with equally satisfactory results, during
the session on which we now enter.

* Naturae rerum vis atque majestas in omnibus momentis fide caret si quis
modo partes ejus ac non totam complectitur animo.— Plin. Hist. Nat. vii. 1.

t Iliad, x. 265, in Pope’s version.

X Protag., p. 348, D.

\ Nicom. Eth., viii. 1.

234 Proceedings of the Royal Society

We need have no misgivings as to the worthiness of the pursuits
to which this Society is devoted. To search after truth, to strive,
as “ the minister and interpreter of Nature,” not only to discover
all her facts but to elicit their meaning, to educe the principles
which underlie them, and to arrive at the apprehension of the laws
which they obey, —

“ Und was in schwankenden Erscheinung schwebt
Befestigen mit dauerden Gedanken”* —

is an occupation than which none can be more noble, more worthy of
the faculties with which we have been endowed, or more pleasing to
Him by whom these faculties have been conferred, — for He Himself
is Truth; and in proportion as men with sincerity and earnestness seek
after truth, in that proportion do they put on the similitude of God
and come into sympathy with Him. The visible universe, moreover,
is as Goethe has expressed it, “ Der Gottheit lebendiger Kleid” (the
living mantle of the Deity) ; and by it He, who is himself invisible,
reveals himself to us, making known to us, as the apostle tells us,
by the things that are made his eternal power and Godhead (Rom.
i. 20). Philosophy, if it follow its normal tendency, leads up to
God ; for the progress of all true philosophic thought is from the
many to the one, from facts to principles, from the relative to
the absolute, from phenomena to essence ; and it is illegitimately
arrested in its proper course, and defrauded of its proper issue, if
it be stopped short of the Supreme Essence in whose infinite mind
are the archeal types of all existences — “ the forms eternal of
created things.” Nor is the value of literary and scientific study
as a moral discipline to be overlooked. To those engaged in such
pursuits there arises an influence which, like some subtle essence,
pervades their whole inner nature, and unconsciously, perhaps, to
themselves elevates, purifies, and refines it. The study of philo-
sophy, of literature, and of science thus becomes a great moral
therapeutic, an instrument of spiritual culture : — “ Animum format
et fabricat, vitam disponit, actiones regit, agenda et omittenda
demonstrat, sedit ad gubernacubum et per ancipitia fluctuentium
dirigit cursum.”f

“ The true philosopher (I use the words of Sir Humphry Davy)
sees good in all the diversified forms of the external world. Whilst
*- Goethe, Faust, Prol. t Seneca, Ep. xvi.

235

of Edinburgh, Session 1876-77.

be investigates the operations of infinite power guided by infinite
wisdom all low prejudices, all mean superstitions disappear from
bis mind. He sees man an atom amidst atoms fixed upon a point
in space, and yet modifying the laws that are around him by under-
standing them ; and gaining, as it were, a kind of dominion over
time and an empire in material space, and creating on a scale
infinitely small a power seeming a sort of shadow or reflection of
a creative energy, and which entitles him to the distinction of
being made in the image of G-od and animated by a spark of the
Divine mini.” *

The following statement, in regard to the number of the present
Fellows of the Society, has been drawn up by the Secretary: —

1. Honorary Fellows: —

Royal Personage —

His Royal Highness the Prince of Wales, . . 1

British Subjects —

John Couch Adams, Esq., Cambridge; Sir George
Biddell Airy, Greenwich ; Thomas Andrews, M.D.,

Belfast (Queen’s College) ; Thomas Carlyle, Esq.,

London; Arthur Cayley, Esq., Cambridge ; Charles
Darwin, Esq., Down, Bromley, Kent; John An-
thony Froude, Esq., London; Thomas Henry
Huxley, London; James Prescott Joule, LL.D.,

Cliffpoint, Higher Broughton, Manchester; William
Lassell, Esq., Liverpool ; Rev. Dr Humphrey Lloyd,

Dublin; William Hallowes Miller, LL.D., Cam-
bridge ; Richard Owen, Esq., London ; Thomas
Romney Robinson, D.D., Armagh; Lieut.-General
Edward Sabine, R. A., London; Henry John Stephen
Smith, Oxford ; George Gabriel Stokes, Esq., Cam-
bridge; James Joseph Sylvester, LL.D., London;

William Henry Fox Talbot, Esq., Lacock Abbey,

Wiltshire; Alfred Tennyson, Esq., Freshwater, Isle
of Wight. ........ 20

Foreign —

Claude Bernard, Paris; Robert Wilhelm Bunsen,

Heidelberg ; Michael Eugene Chevreul, Paris ;

James D. Dana, LL.D., Newhaven, Connecticut;

Heinrich Wilhelm Dove, Berlin; Jean Baptiste

Carry forward, 21

* Consolation in Travel, Works, vol. ix. p. 3G1.

2 i

VOL. IX.

236

Proceedings of the Royal Society

Brought forward, 21

Dumas, Paris; Charles Dupin, Paris; Elias Fries,

Upsala ; Herman Helmholtz, Berlin’; August
Kekule, Bonn ; Gustav Robert Kirchhoff, Heidel-
berg; Herman Kolbe, Leipzig; Albert Kolliker,

Wurzburg; Ernst Eduard Rummer, Berlin ; Johann
von Lamont, Munich ; Richard Lepsius, Berlin ;

Ferdinand de Lesseps, Paris ; Rudolph Leuckart,

Leipzig; Urbain Jean Joseph Leverrier, Paris;

J oseph Liouville, Paris ; Carl Ludwig, Leipzig ;

Henry Milne-Ed wards, Paris ; Theodore Mommsen,

Berlin ; John Lothrop Motley, United States ;

Louis Pasteur, Paris ; Prof. Benjamin Peirce, United
States Survey ; Henry Victor Regnault, Paris ;

Angelo Secchi, Rome ; Karl Theodor von Siebold,

Munich ; Bernard Studer, Berne ; Otto Torell,

Lund ; Rudolph Virchow, Berlin ; Wilhelm
Eduard Weber, Gottingen; Friedrich Wohler, Got-
tingen, 34

The following are the Honorary Fellows deceased during
the year : —

British — Sir William E. Logan.

Foreign — Adolphe-Theodore Brongniart, Christian
Gottfried Ehrenberg.

2. Non-Resident Fellow under the Old Laws: —

Sir Richard Griffiths, 1

Total Honorary and Non-Resident Fellows at 4th
December 1876, .56

3. Ordinary Fellows: —

Ordinary Fellows at November 1875, . . . . 358

New Fellows , 1875-76. — Rev. Francis Edward Belcombe;

Bruce Allen Bremner, M.D. ; Rev. John Gibson Cazenove,

D.D. ; Peter Denny; James Douglas H. Dickson, M.A. ;

James Duncan; J. S. Fleming; J. Ballantine Hannay;

M. Forster Heddle ; Rev. Norman Macleod, D.D. ; John
Macmillan, M.A. ; J. F. Rodger, S.S.C. ; WillianrSkinner,

W.S. ; William Thomson, F.C.S. ; Rev. Francis Le Grix
White, M.A., 15

Carry forward, 373

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of Edinburgh, Session 1876-77.

Brought forward, 373

Deduct Deceased — Dr James Warburton Begbie ; David
Bryce; G. Stirling Home Drummond; Lewis D. B.
Gordon, C.E. ; Sir George Harvey ; Dr Laycock ; Thomas
Login, C.E. ; Alexander Russel ; The Marquis of Tweed-
dale, ......... 9

Resigned — Hon. Charles Baillie (Lord Jerviswoode) . 1

_ io

Total number of Ordinary Fellows at November 1876, . 363

Add Honorary and Non-Resident Fellows, . . 56

Total Honorary and Ordinary Fellows at commencement

of Session 1876-77, ....... 419

Monday , ltith December 1876.

Sir WILLIAM THOMSON, President, in the Chair.
The following Communications were read : —

1. On the Hoots of the Equation Y pcf>p = 0. By Gustav
Plarr. Communicated by Professor Tait.

2. Applications of the Theorem that Two Closed Plane Curves
intersect an even number of times. By Prof. Tait.

( A bstract. )

The theorem itself may be considered obvious, and is easily
applied, as I showed at the late meeting of the British Association ,
to prove that in passing from any one double point of a plane closed
curve continuously along the curve to the same point again, an even
number of intersections must be passed through. Hence, if we sup-
pose the curve to be constructed of cord or wire, and restrict the
crossings to double points, we may arrange them throughout so that,
in following the wire continuously, it goes alternately over and under
each branch it meets. When this is done it is obviously as com-
pletely knotted as its scheme (defined below) will admit of, and
except in a special class of cases cannot have the number of crossings
reduced by any possible deformation. The excepted class is that in

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Proceedings of the Iioyal Society

which the intersections are either wholly or partially nugatory, i.e .,
not in reality contributing to the knot, whether on account of the
order of their arrangement or their signs. All nugatory intersec-
tions can be detected at once by the scheme itself, and may be
struck out. As will be understood from what follows, the schemes

AABBCC and ACBBCA

are wholly nugatory, while in

ACBDCBDAEGFEGF

only the intersection A is necessarily nugatory. In fact a group
like C B D C B D, when not itself nugatory by reason of its signs,
is self-contained, and forms a special knot which may be drawn tight
so as to present only a roughness in the string. The following
sketches illustrate these essentially nugatory crossings: —

I. Given the number of its double points, to find all the essen-
tially different forms which a closed curve can assume.

(a.) Going round the curve continuously, call the first, third,
&c., intersections A, B, C, &c. In this category we evidently
exhaust all the intersections. The complete scheme is then to be
formed by properly interpolating the same letters in the even
places ; and the form of the curve depends solely upon the way in
which this is done.

(6) It cannot, however, be done at random. For instance, the
scheme

ADBECADBEC | A

is lawful, but

ADBACEDCEB | A

is not.

The former, in fact, may be treated as the result of superposing
two closed (and not self-intersecting) curves, both denoted by the
letters A D B E C A, so as to make them cross one another at the
points marked B, C, D, E, then cutting them open at A, and joining
the free ends so as to make a continuous circuit with a crossing at A.

239

of Edinburgh, Session 1876-77.

But in the latter scheme above, we have to deal with the curves

A D B A and C E 0 E, and in the last of these we cannot have the

junctions alternately -4- and — as required by our fundamental prin-
ciple. In fact, the scheme would require the point C to lie simul-
taneously inside and outside the closed circuit A D B A.

Or we may treat ADB A and 0 E D C as closed curves inter-
secting one another and yet having only one point, D, in common.

(c) Thus, to test any arrangement, we may strike out from the

whole scheme all the letters of any one closed part as A A ,

and the remaining letters must satisfy the fundamental principle.

Or we may strike out all the letters of any two sets which begin
and end similarly, e.g ., A...X,X...A, the two together
being treated as one closed curve, and the test must still apply.

More generally, we may take the sides of any closed polygon
as A - X, X - Y, Y - Z, Z - A, and apply them in the same way.
But in this, as in the simpler case just given, the sides must all
be taken the same way round in the scheme itself.

(d.) Such schemes as the latter of the two in (6) above may be
made algebraically possible by slightly changing our assumptions.
Thus, for instance, we might admit of a triple point, and agree not
to reckon it as an intersection on a continuous oval provided one
of the remaining branches goes into the oval, and the other comes
out of it, these two not necessarily intersecting one another. In
the case specified the triple point would be E supposed to lie on
the oval ADB A, and not to be counted as an intersection while
we pass round that oval. But this is a mere algebraic escape from
a geometrical difficulty, and will not necessarily help us when we
deal with knots on actual cords or wires.

II. A possible scheme being thus made, with the requisite
number of intersections, let it be constructed in cord, with the
intersections as above alternately + and — . Then [since all schemes
involving nugatory points, like those above mentioned, must be got
rid of, as they do not really possess the requisite number of inter-
sections] no deformation which the cord can suffer will reduce,
though it may increase, the number of double points. If it do
increase the number, the added terms will be of the nugatory
character presently to be explained. If it do not increase that
number, the scheme will in general still represent the altered

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Proceedings of the Royal Society

figure. Hence the scheme is a complete and definite statement
of the nature of the knot.

(a.) One illustration depends upon the fact that all deforma-
tions of such a cord or wire may be considered as being effected by
bending at a time only a limited portion of the wire, the rest being
held fixed. This corresponds to changing the point of view finitely
with regard to the part altered, and yet infinitesimally with regard
to all the rest. This, it is clear, can always be done, as the relative
dimensions of the various coils may be altered to any extent without
altering the character of the knot All such deformations may be
obtained by altering the position of a luminous point, and the plane
on which it casts a shadow of the knot. Any addition to the
normal number of intersections which may be produced by this
process is essentially nugatory.

Another mode, really depending on the same principles, consists
in fixing temporarily one or more of the crossings, and considering
the impossibility of unlocking in any way what is now virtually
two or more separate interlacing closed curves, or a single closed
curve with full knottings, but with fewer intersections than the
original one.

Another depends upon the study of cases of knots in which one
or more crossings can be got rid of. Here, it is proved that con-
tinuations of sign are in general lost when an intersection is lost;
so that, as our system has no continuations of sign, it can lose no
intersections.

(6.) Practical processes for producing all such deformations gra-
phically are given at once by various simple mechanisms. Thus,
taking 0 any fixed point whatever, let p} a point in the deformed
curve, be found from its corresponding point, P, by joining PO
and producing it so that

PO * Op = a2,

or so that

PO -pOp — a, Ac., Ac.

The essential thing is that points near 0 should have images
distant from 0, and vice versa. And p must be taken in OP produced,
else the distorted knot is altered from a right-handed to a left-
handed one, and vice versd. This distinction is shown in the cuts

241

of Edinburgh, Session 1876-77.

1 and 3 below, where it will be seen that one turn of the coil may
be regarded as wound round the other — the screw being right-
handed in 3 and left-handed in 1.

3.

It is easy to show that these methods give merely different
views of the same knot. The simplest way of doing this is to
suppose the knot projected on a sphere, the eye being at the centre.
Arrange so that one closed branch, e.g., A— A , forms nearly
a great circle. Shifting the eye to opposite sides of the plane
of this great circle the coil presents exactly the two appearances
related to one another by the deformation processes given above.
What was inside the closed branch from the one point of view
is outside it from the other, and vice versa.

Thus 1 and 2 above are the only forms with three non-nugatory
intersections. 2 may be formed from 1 by putting 0 in either of the
three border areas, each of which has two sides only. If 0 be placed
in external space, or in the inner three-sided area, 1 is reproduced.
Similar remarks apply to the deformation of 2.

Figures 4 and 5 are the only forms with four valid intersections.
Like 1 and 2, the first of them is a clear coil (see below), the second
not clear. And, of course, any deformation of either produces the
other, or reproduces itself. 6, 7, 8, 9, are forms of an essentially
not-clear arrangement, with five intersections. The numbers
inserted in 6 show which form is produced by placing 0 in the
corresponding area. The only other forms having five intersec-

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Proceedings of the Royal Society

tions, are the clear coil of two turns, whose scheme is the first
given in I ( b ) above, and its solitary deformation.

(c.) Hence to draw a scheme, select in it any closed circuit, e.g.,
A ... . A — the more extensive the better, provided it do not
include any less extensive one. Draw this, and build upon it the
rest of the scheme ; commencing always with the common point A,
and passing each way from this to the next occurring of the junctions
named in the closed circuit. [It is better to construct both parts
of the rest of the scheme inside , and then invert one of them, as we
thus avoid some puzzling ambiguities.] Inversions with respect
to various origins will now give all possible forms of the scheme.

III. Thus the scheme is. perfectly definite as to the general
shape of the curve, if we take the possible deformations into account.
And the spherical projection, already mentioned, will in general
allow us to regard and exhibit the knot as a more or less perfect plait.
It does so always when the coil is clear , i.e., when all the turns
of the cord maybe regarded as passing in the same direction round
a common axis thrust through the knot. When the coil is not
clear some of the cords of the plait are doubled back on them-
selves. Thus by drawing the plait from a given scheme we can
tell at once whether one of its forms is a clear coil or not.

From this point of view another notation for clear coils is given
in the form

a y a

P ay /? " "

243

of Edinburgh, Session 1876-77.

Here a, /3, y . , . are, in order, the several strings plaited— so that
in the coil (3 is the prolongation of a, y that of } 3 , &c., and a that of

the last of the series. The expression ^ means that a crosses over

(3. It is sometimes useful to indicate whether a crossing takes

place to the right or left. This is done by putting + or - over

the symbol. Thus the four crossings above may be more fully

written as H 1 —

a y (3 a

(3 ay/?'**’

The properties of this notation are examined in detail. It is
shown, that the combination just written cannot be simplified in
itself ; but that

a y y a

(3 a (3 (3

VV,&C.

p

a

This notation requires care. For instance, the terms

a a

(3(3

are simply nugatory, and may be written off. But, on the other
hand, the terms

a (3
(3 a

usually add to the beknottedness of the whole scheme.

When the scheme is not compatible with a clear coil there occur
terms of the form

a

a,

and the application of this method becomes very troublesome.

(a.) When the scheme has no merely nugatory intersections,
the most complete knotting is secured by alternate crossings above
and below ; or, as we may write,

A X B Y C &c.

H + — +

and here there is no continuation of sign.

(b.) Cases in which there is no knot at all may be obtained for
any scheme by making each letter positive on its first appearance.
The various coils are then, as it were, paid out over one another.
This process will give rise, in general, to but few changes of sign :

2 K

VOL. IX.

244

Proceedings of the Royal Society

but the number of such will usually depend upon the particular
intersection with which we commence the scheme.

Additional changes of sign, still without any knotting, may be
introduced by various processes, of which the following is the
simplest: — When two letters appear together twice, not necessarily
in the same order, but with like signs, these signs may be changed.
Thus, the following parts of a scheme

may be changed to

PQ....QP

+ +

PQ . . . . QP

+ +

and the statements already made about nugatory intersections can
be applied to these and other combinations even when they occur
separately once only in each of two separate knots on the same
cord. This, and a great number of similar theorems, allow of a great
special extension of the nugatory test already given — but an exten-
sion which cannot be made in any case until the signs of the
intersections are given as well as the order of their occurrence.

Again, though, as has been said above, continuations of sign
disappear when an intersection is lost, it does
not follow that if a scheme have continuations
of sign it must necessarily be reducible. The
annexed diagram is an excellent instance. Its
scheme contains fourteen continuations, and
only twelve changes, of sign, and yet the knot
is irreducible. But if we suppose it cut across
twice at the single unsymmetrieally placed crossing, and the ends
joined so as still to preserve continuity in the string, the scheme

has still fourteen continuations, but only ten
changes, of sign ; and it does not involve any
real beknottedness.

The remaining figure illustrates a fully
knotted scheme, where there are no continu-
ations of sign, but in which the mere change
of sign of one of the intersections produces four continuations of
sign, and the whole beknottedness disappears. Similar remarks
apply to most of the preceding figures.

of Edinburgh , Session 1876-77.

245

IV. A great many other deductions from the fundamental pro-
position are given — for instance,

A closed plane curve, intersecting itself, divides the plane into
separate areas whose number is greater by 2 than the number of
intersections.

Regarding the curve as a wall, dividing the plane into a number
of fields, if we walk along the wall and drop a coin into each field
as we reach it, each field will get as many coins as it has corners,
but those fields only will have a coin in each corner whose sides are
all described in the same direction round. The number of coins
is four times the number of intersections — and two coins are in
each corner bounded by sides by each of which you enter— none
in these bounded by sides by each of which you leave.

Cut off at any intersection and remove a portion of the curve
forming a closed (not self-cutting) circuit. You thus abolish an odd
number of intersections. Hence if there is an even number of
coils, whether the whole be clear or not, there is an odd number of
intersections, and vice versd.

To form the symmetrical clear coil of two turns and of any (odd)
number of intersections, make the wire into a helix, and bring one
end through the axis in the same direction as the helix (not in
the opposite direction, as in Ampere’s Solenoids ), then join the ends.
[The solenoidal arrangement, regarded from any point of view, has
only nugatory intersections.] An excellent mode of forming this
coil is to twist a long strip of paper through an odd number of
half-turns, and then paste its ends together,- — the two longer edges
become parts of one continuous curve which is the clear coil in
question. This result is applied to the study of the form of soap-
films obtained by Plateau’s process on clear coils of wire.

Y. Another question treated is the numbers of possible arrange-
ments of given numbers of intersections in which the cyclical order
of the letters in the 2nd, 4th, 6th, &c. places of the scheme shall be
the same as that in the 1st, 3rd, 5th, &c., i.e, the alphabetical.
Instances of such have already been given above. In the first of
I (5), for example, the letters in the even places are

D E AB C.

Here the cyclical order of the alphabet is maintained, but A is
postponed by two places.

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Proceedings of the Royal Society

Whatever be the number of intersections a postponement of no
places leads to nugatory results.

A postponement of one place is possible for three and for four
intersections only.

Postponement of two places is possible only for ( four ), five, and
eight — three for seven and ten — four for nine and fourteen — five
for (eight), eleven and sixteen, — six for (ten), thirteen, and twenty,
&c. Generally there are in all cases n postponements for 2n + 1
intersections: — and for 3n + 2, or 3w + 1 intersections, according
as n is even or odd. The numbers which are italicised and put in
brackets above, arise from the fact that a postponement of r places,
when there are n intersections, gives the same result as a postpone-
ment of n-r-1 places. [It will be observed that this cyclical
order of the letters in the even places is possible for any number
of intersections which is not 6 or a multiple of 6.]

When there are n postponements with 2^4-1 intersections the
curve is the symmetrical double coil — i.e., the plait is a simple
twist.

The case with 3rc + 2 or 3n+ 1 intersections is a clear coil of
three turns, corresponding to a regular plait of three strands.

VI. Numerous examples are given of the application of various
methods of reduction. For instance, the scheme

A^BTCG!D4EIFI(ji)H5KCLi7| A

- + + + -P- + - + - + - + - 4- - 4-

which is rendered irreducible by changing the sign of B, is reduced
by successive stages as follows : —

ABC(?D4AIfii)HKBC'LF| A,

- + - + -+ + 4---+- 4- - 4-

BC A GD AGcDYLBC H\ B,
+__+_+_+__++

CA(rDdGBC| C;

1 1 1-4.

and, finally,

AGVAGrD\A,

-+-+-+

which is the simple irreducible knot of figures 1 and 3 above.

of Edinburgh, Session 1876-77.

247

3. On the Distribution of Volcanic Debris over the Floor of

the Ocean, — its Character, Source, and some of the Pro-
ducts of its Disintegration and Decomposition. By John

Murray, Esq. Communicated by Sir C. Wyville Thomson.

Daring the present session I propose to lay before the Society
several papers on subjects connected with the deposits which were
found at the bottom of the oceans and seas visited by H.M.S.
Challenger in the years 1872, 1873, 1874, 1875, and 1876.

Instruments in use for obtaining information of the Deposits.

It will be convenient to introduce this first communication with
a brief description of the instruments and methods employed on
board H.M.S. Challenger with the view of obtaining information
and specimens of these ocean deposits. The instrument in most
frequent use was the tube or cylinder forming part of the sounding
apparatus.

During the first six months of the cruise this cylinder was one
having less than an inch bore, and was so arranged with respect to
the weights or sinkers that it projected about six inches beneath
them. The lower end of the cylinder was fitted with a common
butterfly valve. This arrangement gave us a very small sample of
the bottom.

In July 1873 this small cylinder was replaced by one having a
two-inch bore/ and it was also made to project fully eighteen inches
below the weights. This was a great improvement, as it gave a
much greater quantity of the bottom in most soundings.

The tube was, in the clays, frequently forced nearly two feet into
the bottom. On its return to the ship, the butterfly valves w'ere
removed, and a roll of the clay or mud, sometimes eighteen inches
in length, could be forced from it. In this way we learned that
the deeper layers were very frequently different from those occupy-
ing the surface.

In the organic oozes— as the G-lobigerina, Pteropod, Radiolarian,
and Diatom oozes — the tube did not usually penetrate the bottom
over six or seven inches, these deposits offering more resistance than
the clays and muds. Occasionally the tube came up without any-
thing in it, but the outside was marked with streaks of the black

248

Proceedings of the Royal Society

oxide of manganese. In about thirteen out of nearly four hundred
soundings we did not get any information of a reliable nature about
the deposit.

The dredge in use was a heavy modification of Ball’s naturalists’
dredge, and the trawl was the ordinary beam trawl of the fishermen.

Both of these instruments had generally a bag of canvas or other
coarse cloth sewed into the bottom of the netting, to prevent the
soft clay or ooze from being entirely washed out. In this way we,
at many stations, got, along with animals, a large quantity of
ooze, clay, stones, or manganese nodules.

While trawling or dredging the ship often shifted her position a
mile or two, but we could not tell whether the dredge or trawl had
been working over all that distance, or had merely taken a dip
into the deposits. This should be remembered when comparing
the captures in one locality with those of another.

Altogether there is much uncertainty about the behaviour of the
trawl and dredge in deep water. It occasionally happened that
when the greatest care was taken, and when it was believed that
the trawl had been dragging for some hours, it came up without
anything in it, or any evidence upon it or in the attached tow-nets
to show that it had been on the bottom.

During the last year of the cruise a tow-net was attached to the
dredging line just below the weights, which last were placed a few
hundred fathoms in front of the trawl or dredge. Tow-nets were
also attached to the trawl and dredge. These nets frequently
came up nearly full of mud, and almost always contained minute
things and fragments from the surface layers of the bottom.

At times the water-bottle attached to the sounding line came up
with clay or ooze in it, or had some of the deposit adhering to its
under- surface.

These then were the means and methods employed for getting
information concerning ocean deposits, and collectively they have
furnished us with a large amount of material. A careful examina-
tion of the specimens procured has already much increased our
knowledge of the nature and distribution of ocean deposits, of the
sources of the materials of which they are built up, and of the
chemical processes taking place in the deep waters and on the floor
of the ocean.

249

of Edinburgh, Session 1876-77.

The Volcanic Debris in Ocean Deposits and some of the Products
of its Disintegration and Decomposition.

In a preliminary report to Professor Wyville Thomson, which
has been published in the Proceedings of the Royal Society of
London, I pointed out the wide-spread distribution of volcanic
debris in ocean deposits and its probable influence in the formation
of deep sea clays, and manganese nodules or depositions. In this
paper I propose to treat of these subjects in more detail, and to
give some of the results of observations which have been made
since the above report was written.

Pumice Stones.

The form of volcanic debris most frequently met with in ocean
deposits is pumice stone.

Specimens of these stones, varying from the size of a pea to that
of a foot-ball, have been taken in dredging at eighty of our
stations. I have placed the position of these stations on a map,
from which it will be seen that they occur all along our route.

Near volcanic centres the dredge has frequently brought them
up in great numbers, as off* the Azores in the Atlantic, oft* New
Zealand and the Kermadec Islands, at several places among the
Philippine Islands, off the coast of Japan, and elsewhere. As a rule,
they are not numerous in shore deposits when these are distant
from volcanic regions. In deposits far from land they are most
abundant in deep-sea clays, from which the shells and skeletons of
surface organisms have been all or nearly all removed.

In the North Pacific the trawl brought up bushels of them from
depths of 2300 and 2900 fathoms. Perhaps in no single instance
have we trawled successfully on any of our deep-sea clays without
getting numbers of these stones. If there be an exception it is in
the North Atlantic. But here it is to be remembered that while
we were investigating the conditions of the North Atlantic our
attention had not yet been directed to the importance of detecting
the presence of pumice, and we have not preserved such large
samples of the North Atlantic deposits as of those of other regions.

On the whole, pumice stones are more numerous in the Pacific
than in the Atlantic deposits.

In the Globigerina and other organic oozes, they are abundan

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Proceedings of the Royal Society

or otherwise according as the deposit is near or far removed from
volcanoes. In these oozes they never occur so abundantly as in the
clays. They are more or less masked and covered up by the accumu-
lated remains of foraminifera, diatoms, or other surface organisms.
In like manner they are obscured in shore deposits by river and coast
detritus. Besides those specimens which are sufficiently large to
be examined by the hand, we detected with the microscope minute
particles of feldspar in all our ocean deposits.

An inspection of the specimens which I have placed on the table

appearance. Some of them have undergone much decomposition,
while others are little altered. Some are coated with the peroxide
of manganese, or have streaks of this substance running through
them. They are the most frequent nucleus of the manganese
nodules, to which I shall presently refer. Some specimens which
were dredged from a depth of over three miles will, when dried,
float for weeks in a basin of water; others, which have undergone
partial decomposition, sink at once.

They present a great variety of texture and composition. They
are white, grey, green, or black in colour. They are highly vesi-
cular, or rather compact and fibrous. There would appear to be every
gradation from common feldspathic to dark green pyroxenic kinds.

We find in them crystals of sanidin, augite, hornblende, olivine,
quartz, lucite, magnetite, and titaniferous iron. Magnetic iron ore
was found in all the specimens examined, either in crystals or in the
form of dust. The other minerals vary in kind and abundance in
the different specimens. The same crystals which we find in the
pumice occur in all the kinds of ocean deposits.

Sources of the Pumice Stones.

The pumice stones which we find at the bottom of the sea have
most likely all been formed in the air. Some of them may have
fallen upon the sea; but the great majority seem to have fallen on
land, and been subsequently washed and floated out to sea by rains
and rivers. After floating about for a longer or shorter time they
have become water-logged and have sunk to the bottom. Both in
the North Atlantic and Pacific small pieces of pumice were several
times taken on the surface of the ocean by means of the tow-net.

of Edinburgh , Session 1876-77.

251

Over the surface of some of these serpulm and algae were growing,
and crystals of sinadin projected, or were imbedded in the feldspar.
During our visit to Ascension there was a very heavy fall of rain,
such as had not been experienced by the inhabitants for many
years. For several days after, many pieces of scoriae, cinders, and
the like were noticed floating about on the surface of the sea near
the island. Such fragments may be transported to great distances
by currents.

On the shores of Bermuda, where the rock is composed of blown
calcareous sand, we picked up fragments of travelled volcanic rocks.
The same observation was made by G-eneral Nelson at the Bahamas.
Mr Darwin noticed pieces of pumice on the shore of Patagonia, and
Prof. L. Agassiz and his companions noticed them on the reefs of
Brazil. During a recent eruption in Iceland, the ferry of a river
is said to have been blocked for several day by the large quantity
of pumice floating down the river and out to^sea. All the pumice
which we find need not be of quite recent origin. Mr Bates informs
me that great quantities of pumice are continually being floated
down the Amazon. These come from near the foot of the Andes,
where the head-waters cut their way through fields of pumice stones.
In the province of Wellington, New Zealand, two of the rivers run
through areas covered with pumice, and during floods bear great
quantities out to sea.

Prof. Alex. Agassiz has kindly furnished me with the following
note : —

“The river Chile, which flows through Arequipa, Peru, has cut
its way for some thirty miles through the extensive deposits of
volcanic ashes which form the base of the extinct volcano Misti.
Some of the gorges are even 500 feet in depth, forming regular
canons. The whole length of the river bottom is covered by well-
rolled pieces of pumice from the size of a walnut to that of a man’s
head. In the dry season (winter) there is but little water flowing,
but in the summer, or rainy season, the river, which has a very
considerable fall (7000 feet in a distance of about 90 miles), drives
down annually a large mass of these rolled pumice stones to the
Pacific. The volcanic ashes are not recent. There is no tradition
among the Indians of any eruption within historic times.”

Captain Evans, the present hydrographer to the navy, informs

2 L

von. IX.

252 Proceedings of the Eoycd Society

me that he frequently picked up pumice on the Great Barrier Beef
of Australia.

Volcanic Ashes.

Near volcanic centres, and sometimes at great distances from
land, we find much volcanic matter in a very fine state of division
at the bottom of the sea. This consists of minute particles of
feldspar, hornblende, augite, olivine, magnetite, and other volcanic
minerals. In the South Pacific, many hundred miles from land,
and from a depth of 2300 fathoms, the trawl brought up a number
of pieces of tufa entirely composed of these comminuted fragments.
These particles appear to me to have been carried to the areas
where we find them, by winds, in the form of what is known as
volcanic dust or ashes. Sir Bawson Bawson sent to Sir Wyville
Thomson a packet of the volcanic ashes which fell on the Island of
Barbadoes, after an eruption in 1812 on the Island of St Vincent,
W. I., one hundred and sixty miles distant. I have examined this,
and find it made up of fragments of the same character as those in
the tufa to which I have just referred, some of the particles being
perhaps a little larger. We have sometimes found this ash in con-
siderable abundance mixed up with the shells in a globigerina ooze.
In the deposits for hundreds of miles about the Sandwich Islands
there are many fragments of pyroxenic lava, which I believe have
been borne by the winds, either as ashes, or in the form of Pele’s hair.

At Honolulu we were informed that threads of Pele’s hair were
picked up in the gardens there after an eruption of Kilauea, one
hundred^and eighty miles from the volcano. This Pele’s hair bears
along with it small crystals of olivine.

Obsidian and Lava Fragments.

Small pieces of obsidian and of feldspathic and basaltic lavas were
frequently found in deposits near volcanic islands.

At two stations in the South Pacific, many hundred miles from
land, we dredged pieces of this nature of considerable size larger
than ordinary marbles. It is difficult to account for the transfer-
ence of these fragments to the places where they were found. It
is, however, in this region, and this alone, that it may be necessary
to bring in a submarine eruption to account for the condition of
things at the bottom.

of Edinburgh , Session 1876-77. 253

A consideration of these observations, and the specimens which
are laid on the table, will, I think, justify the conclusion that vol-
canic materials, either in the form of pumice-stones, ashes, or other
fragments, are universally distributed in ocean deposits.

They have been found abundantly or otherwise in our dredgings,
according as these have been near or far from volcanoes, or as there
has been much or little river and coast detritus, or few or many re-
mains of surface organisms in the deposits.

Some of the Products of the Decomposition of Volcanic Debris.

Clay. — Pure clay, as is well known, is a product of the decom-
position of feldspar, and the clay which we find in ocean deposits
appears to have had a similar origin.

In the deposits far from land the greater part of the clay origi-
nates, I believe, from the decomposition of the feldspar of frag-
mental volcanic material, which we have seen to be so universally
distributed.

Pumice-stone is largely made up of feldspar, and from its areolar
structure is peculiarly liable to decomposition. Being permeated
by sea water holding carbonic acid in solution, a part of the silica
and the alkalies are carried away, water is taken up, and a hydrated
silicate of alumina or clay results.

Like most clays our ocean clays contain many impurities, these
last being as varied as the sources whence the materials of the
deposits are derived.

Let us briefly enumerate the sources of these materials.

We have first the matters derived from the wear of coasts, and
those brought to the sea by rivers, either in a state of suspension or
solution. The material in suspension appears to be almost entirely
deposited within two hundred miles of the land.

Where great rivers enter the sea, and where we have strong cur-
rents, as in the North Atlantic, some of the fine detritus may be
carried to a greater distance, but its amount can never be very
large. In oceans affected with floating ice we have land debris
carried to greater distances than above stated; for instance we can
detect such materials in the deposits of the North Atlantic as far
south as the 40th parallel N., and in the South Pacific as far north
as the 40th parallel S.

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Proceedings of the Royal Society

Some of the substances in solution, as carbonate of lime and silica,
are extracted by animals and plants to form their shells and ske-
letons ; these last, falling to the bottom, form a globigerina, a pte-
ropod, a radiolarian, or a diatom ooze. We have also the bones of
mammals and fish mixed up in different kinds of deposits. These,
as well as animal and vegetable tissues, generally are a source of
phosphates, fluorides, some oxide of iron, and possibly of other inor-
ganic material.

Sir Wyville Thomson, early in the cruise, suggested that much
of the inorganic material in deposits is derived from the source to
which I have just alluded. Our subsequent observations have, I
think, shown that originally Sir Wyville gave too much importance
to this as a source of the materials in our deep deposits.

Second . — We have the dust of deserts, which is carried great
distances by the winds, and which, falling upon the ocean, sinks to
the bottom and adds to the depositions taking place. In the trade
wind regions of the North Atlantic we have a very red-coloured
clay, in deep water, which is largely made up of dust from the
Sahara. Such dust frequently falls in this region as what is called
blood-rain.

Third. — We have the loose volcanic materials, which have been
shown to be universally distributed as floating pumice, or as ashes
carried by the wind.

This short review shows that the clay in shore deposits is chiefly
derived from river and coast detritus. As we pass beyond about
one hundred and fifty miles from the shores of a continent the
character of the clayey matter changes. It loses its usual blue
colour, and becomes reddish or brown, and particles of mica and
rounded pieces of quartz give place to pumice, crystals of sanidin,
augite, olivine, &c. All this goes, I think, to show that in depo-
sits far from land the clay is chiefly derived from volcanic debris,
though in the region of the North Atlantic trade winds much of it
may be derived from the feldspar in the dust of the Sahara.

The pumice which floats about on the surface of the sea must
be continually weathering, and the clay which results and the
crystals which it contains will fall to the bottom, mingling with
the deposit which is in course of formation. In our purest globige-
rina ooze this clay and these crystals are present. If a few of the

255

of Edinburgh, Session 1876-77.

shells, say thirty foraminifera, are taken from such a deposit, and
carefully washed, and then dissolved away with weak acid, a residue
remains which is red-brown or grey in colour, according to the
region from which the ooze came. If the same number of shells
be collected from the surface and dissolved away in the same
manner, no perceptible residue is observed. The clayey matter
would therefore seem to have infiltrated into the shells soon after
they fell to the bottom.

I have already mentioned several instances of pumice-stones
having been found on coral reefs. Many more instances could be
given. These stones, undergoing disintegration in these positions,
add clay, crystals of augite, hornblende, magnetic iron ore, &c.,
to the limestones which the coral animals are building up.

I have found these crystals in the limestones and red earth of
Bermuda, and in a specimen of the limestone from Jamaica.

This observation, it appears to me, points out that the red earth
of Bermuda, Bahamas, Jamaica, and some other limestones, may
originally have been largely derived from fragmental volcanic
materials, which were carried to the limestone while yet in the
course of formation. There are also small particles of the peroxide
of manganese in the red earth of Bermuda.

Peroxide of Manganese.

Peroxide of Manganese occurs widely in ocean deposits, either
as nodules, incrustations, or as depositions on the bottom itself.
It has been found most frequently in the nodular form in the deep-
sea clays far from land. It also occurs in the organic oozes, when
these contain much volcanic debris, or are near volcanic centres.

In shallow water, near some volcanic islands, it covers shells
and pieces of coral or pumice with a light brown incrustation. It
has been met with very sparingly, if at all, in shore deposits
removed from volcanic centres.

In my preliminary report above referred to, I stated that further
investigation might show that manganese nodules and depositions
abound :in these regions where we have much of the debris of
augitic or heavy lavas.

A re-examination of specimens since our return confirms this
view. Wherever we have pumice containing much magnetite,

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Proceedings of the Roycd Society

olivine, augite, or hornblende, and these apparently undergoing
decomposition and alteration, or where we have evidence of great
showers of volcanic ash, there we find the manganese in greatest
abundance. This correspondence between the distribution of the
manganese and volcanic debris appears to me very significant of
the origin of the former. I regard the manganese, as we find it,
as one of the secondary products arising from the decomposition of
volcanic minerals.

Manganese is as frequent as iron in lavas, being usually asso-
ciated with it, though in very much smaller amount. In magnetite
and in some varieties of augite and hornblende the protoxide of
iron is at times partially replaced by that of manganese.

In the manganese of these minerals, and in the carbonic acid
and oxygen of ocean waters, we have the requisite conditions for
the decomposition of the minerals, the solution of the manganese,
and its subsequent deposition as a peroxide.

The carbonic acid converts the silicates of the protoxides of
manganese, and the protoxides of manganese into carbonate of
manganese, and thus prepares the way for oxidation by the oxygen
of the water.

It is probable that the action of the carbonic acid is not apparent,
and that the manganese is at once deposited as a high oxide if not
as the peroxide. This theory is essentially the same as that which
Bischof gives for manganese ores generally. I have laid a series of
these manganese depositions on the table. An inspection of these
and their localities will show that in the clays and oozes the depo-
sitions are nodular in form. If a section be made of one of these,
a number of concentric layers will be observed arranged around a
central nucleus — the same as in a urinary calculus. When the
peroxide of manganese is removed by strong hydrochloric acid,
there remains a clayey skeleton which still more strongly resembles
a urinary calculus.

This skeleton contains crystals of olivine, quartz, augite, magne-
tite or any other materials which were contained in the clay from
which the nodule was taken. In the process of its deposition
around a nucleus, the peroxide of manganese has inclosed and
incorporated in the nodule the clay and crystals and other materials
in which the nucleus was imbedded. The clayey skeleton thus

257

of Edinburgh, Session 1876-77.

varies with the clay or ooze in which it was formed. Those from
a fine clay usually adhere well together; those from a globige-
rina ooze have an areolar appearance; those from a clay with
many fine sandy particles usually fall to pieces. Mr Buchanan
informs me that the purest portions of these nodules, that is those
portions made up of closely packed concentric layers, contain from
30 to 34 per cent, of the peroxide.

Taking the nodule as a whole, it will of course contain very much
less than this. The nucleus varies in each nodule, 'and that part of
a nodule which is made up of concentric layers will vary with each
locality, and with the depth from which it comes. We may expect
therefore that analysis will show considerable variations in the
amount of alumina, silica, and metals, lime, &c., in the nodules
from different stations. At some places in the Pacific the nodules
show periods of deposition very distinctly. We have first a very
compact nodule which may have a shark’s tooth for a nucleus, and
which appears to have been formed slowly. Then there would
seem to have been a shower of ashes. After a time manganese
was again deposited, inclosing in the nodule a layer of these ashes.
The most frequent nucleus in the nodules is a piece of pumice or
other volcanic fragment.

In deep-sea clays, far from land, sharks’ teeth, ear-bones of whales,
and fragments of other bones are very often the nucleus around
which the manganese is deposited. In one instance a piece of
siliceous sponge forms the nucleus. In a globigerina ooze a por-
tion of the deposit has apparently formed the nucleus. In these
we have perfect casts of the foraminifera, but all the carbonate of
lime has been removed. The volcanic fragments which have
formed the nuclei of nodules appear frequently to have undergone
peculiar alterations. For instance, obsidian is usually surrounded
by beautiful agate bands.

When we found the bottom composed almost entirely of volcanic
ashes, or so hard from other reasons that the sounding tube did not
penetrate it, the manganese was deposited in layers over the
bottom itself. Large pieces of this nature were taken several times.

The escape of carbonic acid through the floor of the ocean near
volcanic islands may in these regions greatly accelerate the pro-
cesses which end in the deposition of the peroxide of manganese,

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Proceedings of the Royal Society

and account for the great abundance of it in some such localities
where we found it.

Native Iron and Cosmic Dust .

While examining the deposits during the cruise I frequently
observed among the magnetic particles from our deep-sea clays
small round black coloured particles which were attracted by the
magnet, and I found it difficult to account for the origin of these.

On our return home I entered into a more careful examination
of the magnetic particles. By means of a magnet carefully
covered with paper I extracted these particles from the deposits,
from the pumice-stones, and from the manganese nodules of many
regions. The great majority of these magnetic particles are
magnetic iron ore and titaniferous iron, either in the form of
crystals, or as line dust. In the clays, and in the manganese nodules
from stations far from land and in deep water, there were again
noticed many small, round spheres among the magnetic particles.

On mentioning this to Professor G-eikie, he suggested that I
should try the method employed by Professor Andrews of Belfast
for detecting minute particles of native iron.

This process consists in moistening the magnetic particles, which
have been extracted by means of the magnet, with an acid solution
of sulphate of copper, when copper is at once deposited on any
native particles which may be present. In this way I have detected
native iron in many of our deposits, in the powdered portions of
manganese nodules, and in pumice-stones.

Professor Andrews tells me that there can be little doubt that
the particles on which copper is deposited are native iron, as he has
found that it is not deposited on nickel, and the chances of cobalt
being present are very slight. Professor Andrews warned me on
the extreme precautions necessary in conducting these observations,
that no iron from a hammer or other instrument should get at the
specimen under observation.

It is true that all specimens of our deposits have been obtained
by means of dredges and iron gear, and some of these particles
may be from this source.

Many of the particles must have another origin. I have taken
two of our manganese nodules, and washing them carefully, taking

259

of Edinburgh, Session 1876-77.

care to let no iron instrument come near them, have broken them
by rapping them .together. Then taking only the interior parts of
these nodules I have pulverized them in a porcelain mortar. The
magnetic particles were afterwards extracted by a magnet covered
with paper. Now, placing these particles on a glass slide under
the microscope, and adding the sulphate of copper solution, there
was in a few moments a deposit of copper on several small perfect
spherules, varying in size from the y^o to the qJq °f an *n
diameter. I have placed some of these spherules under the micro-
scope and now show them to the Society. It will be noticed that
on one the copper is not deposited all over the sphere, but in
ramified spider-like lines. On the cut surface of a meteorite, from
Professor Sir Wyville Thomson’s collection, which I also exhibit,
the copper is precipitated in precisely the same manner as on the
little sphere from the manganese nodule. Besides the spherules
on which the copper is deposited, there are others generally of a
larger size and dark colour. These are, so far as microscopic ex-
amination shows, quite like the particles on the mammillated outer
surface of this Cape meteorite, also from Sir Wyville’s collection.

These spherules have hitherto only been noticed in those deposits
in deep water far from land, and where for many reasons we believe
the rate of formation of deposits to be very slow.

They occur also only in those manganese nodules which come
from the same deep-sea clays or deposits far from land.

The particles of native iron found in pumice-stones are not
numerous, and never take the form of spherules so far as observed.
Some of these particles of native iron may then come from the
dredge. Other particles come from the pumice and the volcanic
materials. Professor Andrews long since showed that minute par-
ticles of native iron existed in basalt and other rocks. And lastly
the spherules of which I have been speaking appear to have a
cosmic origin.

The reason, for these spherules occurring only in deposits far
from land and in deep water, may be more apparent by reference
to the annexed diagram, which might represent a section from
the west coast of South America out into the Pacific 500 miles.
Along the shores of the continent as at a we have an accumu-
lation of river and coast detritus. At b in depths from 1400

2 M

VOL. IX.

260

Proceedings of the Royal Society

to 2200 fathoms we have a globigerina ooze mostly made up of sur-
face shells. At c, in a depth of 2300 to 3000 fathoms, all the surface
shells are removed from the bottom. No coast detritus reaches this
area, and we find in the deposit pumice stones, some volcanic
ashes, manganese nodules, sharks’ teeth, and ear bones of whales.
It is only in areas like this that we find sharks’ teeth and ear bones
of cetaceans in any numbers. Some of them from the same haul
are deeply surrounded with manganese deposit, and contain little
animal matter ; while others have no deposit on them, and seem
quite recent. These, and other facts which might be mentioned,
all argue for an exceedingly slow rate of deposition. Now it is in
these same areas that the spherules of native iron and other
magnetic spherules are found, both in the deposits and in the
manganese nodules from them.

Finding them in this situation favours the idea that they are of
cosmic origin, for in such places they are least likely to be covered
up or washed away. It is certainly difficult to understand why the
spherules on which the copper is precipitated have not become
oxidised. If nickel be present in them, this may retard oxidation
to some extent.

The manganese depositions in our ocean deposits are very dif-
ferent in structure and composition from any of the ores of man-
ganese I have had an opportunity of examining, and the deposits
of the deep sea far from land have not, so far as I know, any equi-
valents in the geological series of rocks.

All the subjects treated of in this paper are still under investiga-
tion, and at some future time I hope to present a much more
detailed account.

These observations seem to me to give ground for the following
conclusions : —

of Edinburgh, Session 1876-77. 261

First, That volcanic debris, either in the form of pumice stones,
ashes, or ejected fragments, are universally distributed in ocean
deposits.

Second, That pumice stones are continually being carried into
the sea by rivers and rains, and are constantly floating on the sur-
face of the ocean far from land.

Third, That the clayey matter in deposits far from land is prin-
cipally derived from the decomposition of the feldspar in fragmental
volcanic rocks, though in the trade wind region of the North
Atlantic the dust of the Sahara contributes much material for
clay.

Fourth, That the red earth of Bermuda, Bahamas, Jamaica,
and other limestone countries, is most probably originally derived
from the decomposition of pumice stone, while these limestones
were in the process of formation.

Fifth, That the peroxide of manganese is probably a secondary
product of the decomposition of the volcanic rocks and minerals
present in the areas where the nodules of manganese are found.

Sixth, That there are many minute particles of native iron in
deposits far from land; that some of these particles are little sphe-
rules ; that these last, as well as some other spherules which are
magnetic, have probably a cosmic origin.

Seventh , That the peroxide of manganese depositions in the
deep sea are different in structure and composition from known
ores of manganese.

Eighth. — That we do not appear to have equivalents of the rocks,
now forming in the deep sea far from land, in the geological series.

In conclusion, I have to acknowledge much assistance in these
investigations from all my colleagues, especially my indebtedness to
Sir Wyville Thomson and Mr Buchanan.

Since my return I have received many hints from Professors Tait,
Gfeikie, Turner, Dr Purves, Mr Morrison, and other gentlemen.

In much of the mechanical work which an examination of these

b

deposits has entailed, I have, both during the cruise and since my
return, had the assistance of Frederick Pearcey.

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Proceedings of the Royal Society

4. On New and Little-known Fossil Fishes from the Edin-
burgh District, No. I. By K. H. Traquair, M.D., F.G-.S.

FAMILY PALiEONISCIDiE.

Genus Nematopty chins, Traquair, 1875.

This genus was instituted by the author for the reception of the
Pygopterus Greenockii of Agassiz, and characterised in the “ An-
nals and Magazine of Natural History ” for April 1875. It differs
from Pygopterus in the form of the scales of the flank, which are
much higher than broad, and having their articular spine arising
from the whole, or nearly the whole of the upper margin ; in the
structure of the pectoral fin, in which all the rays are articulated
for the greater part of their extent ; and in the form of the anal,
which is in shape like the dorsal, and is not produced backwards
in the peculiar fringe-like manner characteristic of Pygopterus .

Since the publication of the notice above referred to, remains of
N. Greenockii have turned up in two other localities near Edinburgh,
viz., near Juniper Green in the horizon of the Wardie Shales
(Museum of Science and Art), and at Baw Camps, near Mid Calder,
in that of the Burdiehouse Limestone (Collection of the Geological
Survey of Scotland).

The following is new to science.

Nematopty chius gracilis , sp. nov. Traquair.

Of this two specimens have occurred at Gilmerton. The
more perfect of these, compressed on its side, displays the entire
contour of the fish, including all the fins, and measures 9 inches in
total length, by 1J inch in depth between the head and the ven-
trals ; the length of the head is contained about 4J times in the
total. The ventral fins arise opposite a point 3J- inches distant
from the tip of the snout ; the commencement of the anal is mid-
way between that of the ventral and of the caudal ; the dorsal is
situated nearly opposite the anal, commencing only \ inch in front of
it. The form of the fish is thus elongated and slender, gradually
tapering from behind the shoulder towards the tail, the dorsal fin
being situated very far back. The other and slightly longer spe-

263

of Edinburgh, Session 1876-77.

cimen lies compressed on its back, and shows the under surface of
the head, both pectoral and both ventral fins, with traces also of
the dorsal, anal, and caudal. Its length is 9J inches, but the fish
must originally have been a little longer, as its caudal extremity is
imperfect.

The scales are very small, and much disarranged, as. is the case
in nearly all the fishes occurring in the same bed, but their confi-
guration is apparently the same as in N. Greenochii , and their ex-
ternal ornamentation consists, as in that species, of very fine oblique,
thread-like, branching, and anastomising ridges; the median ridge-
scales, extending from behind the dorsal fin along the upper margin
of the caudal body- prolongation, are very large and pronounced.
The bones of the head are much crushed and broken, so that only
a few of them can be made out. The suspensorium is very oblique
and the gape extensive, the length of the lower jaw being, in the
first mentioned specimen, inch. The external surface of the
lower jaw is ornamented with a minute and very close tubercula-
tion; the dental margin of the maxilla is also tuberculated, but the
rest of its surface is marked with delicate ridges, which run for the
most part parallel with its superior and posterior margins. Large
conical teeth occur in both jaws, with a few of the external series
of smaller ones. One of the larger teeth in the mandible of speci-
men No. 2 measures a little over J inch in length by — in diameter
at the base; its form is regularly and acutely conical, with well-
marked smooth enamel-cap at the apex, below which the surface
is delicately and beautifully striated, the striae being more pro-
nounced than is usually the case in N. Greenochii. The opercular
bones are not visible, but some of the branchiostegal rays may be
detected ; their outer surfaces are ornamented by very fine flexuous
ridges. The paired fins are moderate in size; indeed Jhey might
safely be termed small. The pectoral of No. 1 measures one inch
in length ; in neither specimen can its number of rays be ascer-
tained, but it is evident that the principal ones were unarticulated
for about ^ of their length. Tire length of the ventral in the first
specimen is § inch ; its rays, probably 25 in number, are delicate,
smooth, and with their transverse articulations rather far apart.
The dorsal and anal fins resemble each other in form, but the latter
is apparently slightly the larger; both are triangular, acuminate,

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Proceedings of the Royal Society

high in front, with concavely cut out posterior margin ; the height
of the dorsal in front is 1 J inch, its base of origin is disturbed ; the
apex of the anal is imperfect, its base measures inch. Their
rays are numerous, slender, and smooth, dichotomising only near
their extremities, and having their transverse articulations compa-
ratively distant. The caudal, as it lies before us, can hardly be
called inequilobate, but as the upper lobe appears somewhat
crumpled, its entire length is probably not accurately exhibited.
It is deeply bifurcated, the lower lobe being narrow and of great
length, measuring 1 J inch, though its extreme point is cut off ; its
rays are like those of the dorsal and anal, being slender, smooth,
and with rather distant articulations, the joints being at first more
than twice as broad, but getting a little closer towards the end of
the rays ; in the upper lobe the rays are, as usual, short and very
delicate. Small and closely set fulcra are observable on the ante-
rior margin of all the fins.

Remarks. — It is of course at once evident that the present species
is closely allied to the powerful Nematopty chins Greenockii , A g. sp.,
of the Wardie Shales; it differs, however, from the latter in several
particulars beside its smaller size. The transverse articulations of
all the fin-rays are considerably more distant ; and the principal
rays of the pectoral are unarticulated for a greater distance than is
the case in N. Greenockii. The form of the laniary teeth differs
also somewhat in the two species. In N. gracilis these are more
regularly conical, gradually tapering from the base to the apex;
whereas in N. Greenockii they assume a more slender form, owing
to the more sudden narrowing of the base upwards into the body
of the tooth, although the relative proportion of the diameter of
the base to the length of the tooth is about the same. The specific
name “ gracilis ” is bestowed on the present species in allusion to
the slender and elegant shape of the body.

Geological Position and Locality. — The two specimens above de-
scribed were found in the blackband ironstone at present wrought
in Yenturefair Colliery, Gilmerton, near Edinburgh, and are both
preserved in the Museum of Science and Art, Edinburgh. This
ironstone, well known for its Rhizodus remains, is a member of the
Lower Limestone group of the Carboniferous Limestone series of
the Lothians, and occurs along with the North Greens coal-seam,

of Edinburgh, Session 1876-77. 265

the lowest wrought coal in the Edinburgh district, between the
first and second Marine Limestone beds in ascending order.

Gonatodus, gen. nov., Traquair.

Amblypterus, Agassiz (pars.).

The body is fusiform, the scales rather large, rhomboidal, orna-
mented with striae and punctures, sometimes nearly perfectly
smooth. Rays of pectoral fin articulated ; base of ventrals short ;
dorsal and anal large, triangular, dorsal situated behind the middle
of the back so that the middle of its base is opposite the commence-
ment of the anal ; caudal following closely on the anal, powerful
and deeply cleft with well developed body-prolongation along the
upper lobe ; rays in all the fins numerous, and closely jointed.
Suspensorium not quite so oblique as in Palceoniscus, Elon-
ichthys , and most other genera of the family, but more so than in
Amblypterus ; operculum large, oblong, suboperculum wanting,
interoperculum * quadrate ; branch iostegal rays numerous, with a
median lozenge-shaped plate behind the symphysis of the mandible.
Jaws stout ; teeth closely set and of very peculiar form, being
cylindro-conical, first inclined slightly inwards, then bent outwards
at an obtuse angle, the apex coming then by another curvature to
point upwards (or downwards in the case of the upper jaw).

Gonatodus punctatus , Agass. sp.

Amblypterus punctatus (pars.) Agassiz, Poissons Fossiles, vol. ii. pt. 2, p.
109 ; Atlas, vol. ii. tab. 4 c, fig. 4, but not figs. 3, 5, 6, 7, 8.

(?) anconocechmodus, Walker, Trans. Geol. Soc. Edin., vol. ii.

pt. 1 (1872), pp. 119-124.

The length of the entire specimens varies from 5| to inches,
but in none is the extreme point of the upper lobe of the tail pre-
served. The length of the head is contained about four times, the
greatest depth of the body about three times in the total length up
to the bifurcation of the caudal fin. The head is short, with bluntly

* The bony plate which I here denominate “ interoperculum ” is the same
as that which, in the Palgeoniscidse, has hitherto been considered as “sub-
operculum.” In Rhabdolepis there occurs between it and the operculum
another and smaller plate, which I interpret as “suboperculum,” and which
is wanting in most of the genera of this family. (See the author’s account of
the structure of the Palaeoniscidae in the Mem oirs of the Palaeontographical
Society for 1877).

266 Proceedings of the Royal Society

rounded snout; the external ornament of the hones of the cranium
proper is rugose in character. The operculum is oblong, broader
above than below, and ornamented with delicate ridges which
radiate from the anterior-superior angle downwards and backwards
over its surface ; the interoperculum is nearly square, and marked
with ridges which for the most part pass horizontally over its surface
from before backwards; the prasoperoulum is well developed. The
jaws are stout; the broad part of the maxilla is ornamented with
delicate and not very closely placed branching and anastomosing
ridges, which for the most part tend to run parallel with its superior
and posterior borders ; the striation of the mandible is close, the
ridges running longitudinally, but the dentary margin is finely
tuberculated. The teeth with which the jaws are armed are most
peculiar in form and arrangement ; they are about to inch
in length, slender-cylindrical in shape, but suddenly narrowed
near the extremity to a sharply conical apex. Each tooth is first
inclined a little inwards, then bent outwards at an obtuse angle,
and again bent so that the apex comes to point upwards (or down-
wards in the case of the maxillary teeth). They are nearly
uniform, and arranged in one closely set row, inside which there
are no larger teeth, nor have I seen any evidence of smaller ones
outside. The branchiostegal rays are thirteen on each side, the ,
anterior of each series being broader than those behind, besides
which there is a median lozenge-shaped plate in front. The bones
of the shoulder girdle are well shown in most of the specimens,
and like those of the face are ornamented externally with flexuous j
branching and anastomosing ridges.

The scales of the flank are slightly higher than broad, with
gently concave upper, and convex flower margin ; the articular
spine is well marked. On the under surface, the socket for the
spine of the scale below is distinct, but the keel is obsolete ; the
latter appears as we proceed backwards towards the tail, while
the spine and its socket diminish and ultimately disappears. The
posterior margin of the scale is finely and obliquely serrated. On
the outer surface the margin overlapped by the scale next in front
is very narrow ; the exposed area is in the most anteriorly situated
scales, is ornamented with delicate and rather feebly marked ridges,
best marked along the anterior and inferior margins with which

267

of Edinburgh, Session 1876-77.

they run parallel, and usually becomiug speedily obsolete over the
rest of the scale, so as to leave a considerable space above and
behind, marked only with tolerable coarse punctures, though in
many cases shallow grooves also extend for some distance forwards
from the notches between the denticulations of the posterior border.
These' striae are much more pronounced in some specimens than
in others; except on the small scales at the base of the dorsal fin,
where they are pretty well marked, they cease to be observable
before the origin of the ventrals, whence backwards the only scale-
ornament consists oT scattered punctures passing into short oblique
furrows, especially near the interior margin, these punctures and
furrows being persistent even on the small lozenge-shaped scales
clothing the sides of the caudal body-prolongation. The scales
also vary considerably in size on different parts of the body, becom-
ing rapidly smaller posteriorly. One from the middle of the flank
between the head and ventral fins in a specimen of 6 inches, mea-
sures nearly inch in height by in breadth, while the breadth
of one from the side of the posterior part of the body opposite the
termination of the dorsal fin is only equal to one-half that of the
former. The scales immediately below and adjoining the base of
origin of the dorsal fin are of particularly small size. The usual
large scales are seen in front of the dorsal and anal fins, and the
squamation of the prolongation of the body axis along the upper
lobe of the caudal present nothing specially worthy of note.

The pectoral fins are acutely pointed, and of considerable ex-
panse. The length of each is equal to about three-quarters that of
the head ; the ventrals are smaller ; the base of each is rather
short. They are likewise pointed in shape, and have their posterior
margins considerably cut out. The dorsal is placed behind the
middle of the back, so that the centre of its base is nearly opposite
the commencement of the anal ; both these fins are large and
triangular ; the caudal is powerful and deeply cleft. The rays of
all the fins are very numerous and delicate ; in the pectoral these
cannot be less than 30 ; in the ventral, 23; in the dorsal and anal,
45 each ; those of the caudal cannot be counted. The articulations
of the fin rays are also tolerably close, especially in the finer rays
of the posterior part of each fin, where the joints appear nearly
square, being in the other rays rather longer than broad ; the arti-

2 N

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Proceedings of the Iioycd Society

culations are more than usually distant towards the proximal ex-
tremities of the principal rays of the pectoral, and also, though to
a less extent, in the lower lobe of the caudal. The joints are scale-
like in general aspect; the distal margin of each is notched or !
concave, the proximal correspondingly convex ; and the outer sur-
face is in most cases marked with at least one delicate furrow
parallel with the anterior and posterior borders; near the bases of
the dorsal and anal fins the joints present indeed an appearance as
of fine striation. The fulcra of the anterior margins of the fins are
closely set and very minute, being only observable with the aid of
a lens.

Remarks. — Under the name of Amblypterus punctatus , three im-
perfect specimens of fossil fish from the shales of Wardie were de-
scribed and figured by Agassiz in the “ Poissons Fossiles.” One
of these is a head with the anterior part of the body (Atlas, vol. ii.
tab. 4 b, fig. 4) ; the second (ib. fig. 5) wants the head and
shoulders and the extremity of the tail ; the third (ib. fig. 3) dis-
plays the entire caudal fin, but is obliquely cut off just in front of
the dorsal and anal. The principal characters which he assigned
to this species were — the considerable depth of the anterior part of
the body; the character of the teeth, which had the form of small
obtuse cones apparently disposed in several rows; and the orna-
ment of the scales, which consisted, in those in front, of oblique un-
dulating lines closer together at the anterior part of each scale and
mingled with punctures, the latter more numerous towards the
posterior margin ; while on the scales of the hinder part of the
body those lines were less crowded, and the punctures more numer-
ous, the former entirely disappearing on the scales of the pedicle
of the tail, where only a few scattered points were left.

For some time after commencing the study of the fossil fishes of
Wardie, this species “ punctatus stated by Agassiz to he common
in that locality, was to me a complete enigma, as among the
numerous entire specimens of fish which I had the opportunity of
examining, I could not find one which agreed in all its characters

with Agassiz’s description, though in some the anterior , and in
others the posterior part of the fish answered well enough. The
mystery was, however, at once cleared up by an examination of
the figured specimens, of which two, collected by Lord Greenock,

269

of Edinburgh, Session 1876-77.

are in the collection of the Boyal Society of Edinburgh ; while the
third, collected by Dr Buckland, and contained in the Oxford Uni-
versity Museum, was forwarded to me with great liberality by Pro-
fessor Prestwick. A comparison of these specimens with a series
of entire fishes from the Wardie beds establishes the fact, that the
Amblypterus punctatus of Agassiz was founded upon fragments of
two distinct species, the specimen with the head, but without the
hinder part of the body, being even generically distinct from the
other two, which display the hinder part, but without the head,—
the fishes to which they respectively appertain differing not only
in dentition, but also in many other particulars connected with the
head, the scales, and the fins.

The peculiar form and arrangement of the teeth in the first of
these render necessary the institution of a new genus, to which I
have given the name Gonatodus * These teeth were somewhat in-
correctly described by Agassiz as being “ en cones obtus,” this
appearance in the specimen he examined being due to their being
there only seen in antero-posterior vertical section, their pecu-
liar flexures and pointed apices being invisible ; their being dis-
posed “sur plusieurs rangdes ” seems also to be an error as far as
the mandibles and maxilla are concerned, though probably there
were additional teeth on the margin of the palate. Perfect
examples of the species to which the other two type specimens
belong show that the teeth are in it acutely conical, incurved, and
of different sizes, large and small, and that in these and other
respects the fish is closely allied to the Amblypterus nemopterus ,
Palceoniscus striolatns , and P. Robisoni of Agassiz, along with
which forms it is, in my opinion, referable to the genus Elonichthys
of Giebel.f It now, however, becomes a question for which of
these two fishes the specific term “ punctatus ” should be retained.
Now, although the enlarged representations of scales given by
Agassiz (Pois. Foss. Atlas, vol. ii. tab. 4 c. figs. 6 and 7) are taken
from the second species ( Eloniclitliys ), yet the term is indeed
applicable to both, and as the characters of the head and teeth are

* yow , knee; and odovs, tooth.

t The reasons for removing these forms from the genera Amblypterus and
Palceoniscus, and uniting them with Elonichthys, will be given in my next
communication.

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Proceedings of the Royal Society

those which more especially distinguished Agassiz’s conception of
“ Amblypterus punctatus” from his A. nemopterus with which he
contrasted it as occurring in the same beds, it seemed to me more
appropriate to relain his name u punctatus" for the species of which
these peculiarities are characteristic. For the other I propose the
name Elonichthys intermedins ; it is very closely allied both to E.
nemopterus and E. striolatus, and will be described in my next com-
munication on the fossil fishes of the Edinburgh district.

The peculiar dentition of Gonatodus was, however, first correctly
described by Mr E. Walker* in a fish from the oil shales of Pitcorthie,
Fifeshire, to which he gave the name of Amblypterus anconocech-
modus} the horizon in which it occurred being probably that of the
Burdiehouse Limestone. Mr Walker’s fish undoubtedly belongs to
the same genus with that described above, and may possibly he
the same with G. punctatus — if not, it is certainly very closely allied,
— but I have had no opportunity of instituting a comparison by
means of actual specimens. Mr Walker, however, makes no men-
tion of punctures as a scale ornament, and his figures represent the
entire surface of the scale covered — as he says in the text — “ with
fine striae which run parallel with the anterior and lower margins,”
and “are more conspicuous on the scales of some specimens than on
those of others.” f Eegarding the arrangement of the teeth in the
lower jaw, Mr Walker also states that they “ are placed alternately
one close to the outside margin, the next to it is fully half its own
thickness farther in, and so on the whole length of the bone,” — an
appearance of which I have observed some slight indications in
G. punctatus , but not with the regularity described.

Geological Position and Locality. — The specimens from which the
above description of Gonatodus punctatus has been drawn up are in
the Museum of the Eoyal Society of Edinburgh and in the private
collection of the author. They are all preserved in nodules of clay

* “On a New Species of Amblypterus and other fossil fish remains from
Pitcorthie, Fife.” Trans. Edin. Geol. Soc. vol. ii. pt. 1 (1872), pp 119-124.

t In the Wardie specimens the scales appear for the most part dull, and deli-
cately striated all over ; this is, however, internal structure , not external sculp-
ture, and is due to the flaking off of the external ganoine layer. When this
is preserved in situ, as it is here and there in many specimens, the surface of
the scale is brilliant, largely punctured, and the appearajice of striation more
or less limited or obsolete, as already described.

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ironstone, from the lower Carboniferous shales of Wardie, near
Edinburgh, belonging to the Cement-stone group of the Calciferous
sandstone series.

The next species is new, and from a higher horizon.

Gonatodus macrolepis sp., nov. Traquair.

Description. — The usual length of examples of this species is
from four to six or seven inches, hut although a considerable
number of specimens more or less perfect have occurred in no two
do the proportional measurement agree, owing to the greater or less
amount of alteration of form, frequently amounting to positive dis-
tortion, which they have undergone, apparently both soon after
death, and also during the consolidation of their ironstone matrix.
Seldom do the scales, save on the caudal body-prolongation, remain
in their original relations to each other on any considerable part of
the body, but are always more or less jumbled up, even though the
contour of the fish may remain tolerably regular, and the shape
and structure of more or fewer of the fins be quite intact, As
remarked in the description of Nematopty chius gracilis , this con-
dition affects nearly all the small fishes occurring in the Gilmerton
ironstone. In one example of the present species in my collection,
the apex of the anal fin appears neatly cut off, and dislocated a
quarter of an inch forward from the rest of the fin.

The most perfect specimen in my collection is 6J inches in
length by If in depth at the ventral fins, and is nearly perfect.
In no specimens are the bones of the head well shown, these
being always more or less crushed and broken ; what can be seen
of them shows that they were conformed essentially as in the pre-
ceding species, and sculptured much in the same way, though per-
haps a little more coarsely. The configuration of the teeth is also
essentially the same, though they appear to be a little more clumsy
in shape, and not quite so regular in arrangement. But the most
salient peculiarity of the present species lies in its scales, which
are considerably larger than in G. punctatus, except on the caudal
body-prolongation, where they are equally small. Their outer and
brilliantly-polished surfaces are also devoid of ornament, and might
indeed be described as completely smooth, only a few delicate
punctures being discernible by careful examination with the lens ;

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their posterior margins are finely denticulated as in the preceding
species. The form and position of the fins is the same as in G.
punctatus, but their rays are slightly coarser and proportionally
fewer in number, though it is difficult to ascertain with accuracy
their numbers in the various fins. The articulations of the rays
are also a little closer, but the configuration of the joints is the
same, these being emarginate distally, convex proximally, and with
a little furrow parallel with their anterior and posterior margins,
but I have not observed any additional furrows or strise than those
near the bases of the dorsal and anal as in the Wardie species.

Geological Position and Locality. — A considerable number of
examples of this species have occurred in the Blackband ironstone
at Yenturefair Colliery, Grilmerton, and are contained in the Edin-
burgh Museum of Science and Art, and in the private collection of
the author. A fragment in the Hunterian Museum of the Uni-
versity of Glasgow, from the ironstone of Possil, also a member of
the Carboniferous Limestone series, though higher in position than
that of Gilmerton, is probably also referable to the same.

5. On the Huff (. Machetes pugnax). By Professor Duns.

I

The exceedingly beautiful bird now on the table was forwarded
to me on the 1st of September last by Mr Wilson, Edington Mains,
Chirnside, Berwickshire. It had been shot two days previously.
Mr Wilson says, “ On comparing it with all the Waders figured
by Bewick (the only work of the kind which I possess), I find
none that correspond ; whence I infer that it is really a rara avis.”
He adds, “ When noticed by the edge of the pond by my children
it had a young one with it, which they saw it feeding. The young
one, they said, was much lighter in its plumage, but was old enough
to fly strongly.” The note led me to expect a full-grown female
wader and young one. But the size of the bird and its general
features of maturity showed it to be a male, in full winter plumage.
Its companion, described as young, doubtless from its size, seems
to have been the female, or reeve, which is little more than half
the size of the male. In this respect the ruff differs from most of
the sub-family Tringince, in which the females are generally larger
than the males.

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of Edinburg! l, Session 1876-77.

The ruff is polygamous. After the breeding season a separation
takes place between the sexes, which continues till the approach
of the following spring. The example now before us is thus
exceptional, as occurring along with one female long after the
breeding season was past, which is late in the spring, or in
May. At one time these birds were met with in great numbers
in the low-lying districts of Norfolk and Lincoln, where they
bred. Even in these localities they are now seldom met with.
There are no instances on record of their nesting in Scotland,
where they are even more rare than in England. “ On the
east coast of Scotland,” says Macgillivray, u they usually appear
about the middle of September and depart in about a fortnight ;
but I have never seen an adult male killed there, the little flocks
that occur being young birds and females.” “ Except in a very
few instances,” says Mr Gray, “ I have never met with the ruff in
the western counties. One or two occasionally penetrate as far as
the Clyde, but these are mere stragglers.”* The forms now noticed
appeared at a considerable distance from the coast, in a district,
however, which at one time must have presented as good nesting
ground as could be found in Norfolk or Lincoln, but which by
drainage and many other features of high farming has become
almost free from conditions suitable to their habits. It would
almost seem as if some birds have a transmitted instinct towards
certain localities, which at long intervals finds high expression in
certain pairs. Might not this account for the occasional occurrence
of the bittern, the night heron, and many other forms in districts
where they are now regarded as stragglers ? I know, moreover,
one locality where the names of places show' how common the raven
had been at one time, but where only one pair is known to have
appeared in forty years. Many instances of this kind might be
given. The habits of the ruff have been, I might almost say, so
exhaustively described by Montague, Bennie, Selby, and others,
as to make it unnecessary to refer to them here. I have, however,
placed on the table other specimens than that now noticed, with

* Dr John Alexander Smith has noticed specimens from Carnwath, Alloa,
Portobello, and Fenton Barns, East Lothian. As many as a dozen were
recently seen near Grangemouth by Mr Harvie Brown, five of which were
shot.

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Proceedings of the Royal Society

the view of indicating the relative size of male and female, of
pointing out the profuse and almost grotesque ornamentation of
the males at the breeding season, and of showing the wide variation
in the plumage of male birds especially. During the breeding
season numerous papillaa, or fleshy tubercules, appear on the face,
a couple of ear tufts slope gracefully to the hind head, and a large
frill or ruff of elongated feathers surrounds the neck. These fea-
tures continue till about the middle of June, when the birds moult.
They then put on the autumn and winter garb. It is next to im-
possible to find two males ornamented alike. But it is known that
the colouring of the frill first assumed is retained through all the
changes of plumage that follow in after years. If red originally,
it will have that colour as successive breeding times come round.
If black, or white, these colours reappear in their season. The
fact is curious and interesting from the physiological point of view.
The theory of sexual selection does not help to explain it. The
birds are polygamous, and the male has to fight to obtain the
female. It is not, however, the size or colour of the frill, but the
strength of beak and of leg that conquers. Then what is it that
determines the colour of the frill in different birds of the same
species, and what keeps the hue persistent throughout all the yearly
changes of plumage? The questions are easily put. One would
like if they were as easily answered.

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

vol. ix. 1876-77. No. 97.

Ninety-Fourth Session.

Monday , 1 5th January 1877.

Sir ’WILLIAM THOMSON, President, in the Chair.

The following Communications were read : —

1. Communication from the President, relative to the
Administration of the Government Fund of £4000.

2. On New and Little-known Fossil Fishes from the Edin-
burgh District. No. II. By R. H. Traquair, M.D.,
F.G.S.

Genus Elonichthys , Giebel, 1848.

Amblypterus (pars), Agassiz.

Palceoniscus (pars), Agassiz.

Pygopterus (pars), Agassiz.

Body fusiform, sometimes rather deep; median fins large, the
caudal deeply cleft, inequilobate ; dorsal and anal triangular, acu-
minate, the dorsal situated nearly opposite the interval between the
ventrals and the anal ; base of ventrals not extended ; pectoral rays
articulated (except a varying amount of the commencement of the
principal ones). Fin rays ganoid, closely set, striated ; fulcra
closely set, minute. Scales sculptured, of moderate size, rhom-
boidal, their posterior borders frequently denticulated or serrated ;
the anterior overlapped area very narrow, reduced to a mere mar-
gin. Suspensorium very oblique ; gape extensive ; operculum well

2 o

VOL. IX.

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Proceedings of the Royal Society

developed, oblong ; interoperculum square-shaped ; no subopercu-
lum. Branchiostegal rays numerous ; the anterior one of each
lateral series broader than the rest a median lozenge-shaped plate
in front. Jaws stout ; teeth acutely conical, sharp, of two sizes,
large and small, the larger ones being placed in a row internal to
the more closely set outer series of smaller teeth. Ornament of
cranial bones tubercular or rugose-tubercular; facial bones, and
those of the shoulder-girdle striated; the jaws usually also tuber-
culated just at the dental margin.

The name Elonichthys was first proposed by Giebel* for certain
fishes ( E . Germari , crassidens and loevis) from the coal-measures
of Wettin, near Halle, which he considered intermediate in generic
character between Amblypterus and Palceoniscus, as defined by
Agassiz. They were said to resemble Palceoniscus in their ful-
crated fins, but to differ from it in the absence of the scaly covering
to the rays, affirmed by Agassiz to exist in some Palmonisci, while
to certain “ Amblypteri ” they showed an affinity in the striation
of their scales, and to “Amblypterus" in general in the large size of
the fins. Their special characteristics were to be found in the
dentition, which consisted of an external series of minute teeth
comparable to the “ Biirstenzahne 1 of Amblypterus , between which
there were large conical teeth, “ wie ich dieselben weder bei den
Palasonisken noch Amblypteren finde.” Unfortunately, however,
for this diagnosis, the fin-rays of Palceoniscus are no more covered
with scales than those of any other genus belonging to this family;
nor are the fins of Agassiz’s “ Amblypteri ” destitute of fulcra
except on the upper lobe of the tail,” as has been so repeatedly
stated by compilers, who, copying this error from the “ Tableau syn-
optique des Genres et des Especes” have apparently overlooked the
correction of it made by Agassiz himself a few pages further on in
his general description of the genus.f The dentition, too, of Gie-
bel’s Elonichthys is essentially similar to that of Agassiz’s Ambly-
terus macropterus ( Bhabdolepis Troschel) in which large conical
teeth were shown to exist by Goldfuss in 1847,J and again by

* Fauna der Vorwelt, 1, 3, p. 249.
t Poissons Fossiles, vol. ii. pt. 1. p. 29.

+ Beinage zur vorweltlichen Fauna des Steinkohlen-gebirges. Bonn 1847,

p. 20.

277

of Edinburgh, Session 1876-77.

Troschel in 1857,* the latter author using this character to separate
the striated-scaled “ Amblypteri ” of Saarbriicken and Lebach,
under the name of Rhabdolepis (i?. macropterus , R. eupterygius)
from their smooth-scaled associates with minute slender teeth, for
which the term Amblypterus was retained (A. latus , A. lateralis).

An examination of the type-specimens of Elonichthys in the
Mineralogical Museum at Halle has, however, convinced me that
the genus is tenable, and that to it is referable an extensive series
of Paheoniscidae, which will include, besides Giebel’s originals
and several new species, various forms referred by Agassiz and
other writers to Amblypterus , Palceoniscus, and Pygopterus. Several
species also, whose position, from want of sufficient information, is
somewhat doubtful, may best be placed here provisionally.

Elonichthys most closely resembles Acrolepis and Bhabdolepis ,
but differs from the former in the anterior covered area of the scales
being reduced to a very narrow margin, and from the latter in the
absence of the subopercular plate. From Amblypterus , as restricted
by Troschel, the greater obliquity of the suspensorium, and the
dentition, are obvious marks of distinction ; the teeth in the
true Amblypteri being minute, slender, without differentiated lani-
aries, and more meriting the title “ en brosse” than those of any
other genus of Palaeoniscidae. From Palceoniscus it is distinguished
by the large size of the median fins, and by the possession of large
conical teeth in the jaws, the teeth of Palceoniscus , as that genus
must now be restricted, being small, and though, of different sizes,
without conspicuous laniaries. It is also widely separated from
Pygopterus by the structure of the pectoral fin, in which the prin-
cipal rays are articulated for the greater part of their length, where-
as in the last-named genus, they are unarticulated till towards their
terminations; by the position of the dorsal fin, which, in relation
to the anal, is further forward ; and by the form of the anal, which
is not produced backwards in a fringe-like manner along the lower
margin of the body.

Accordingly Amblypterus nemopterus of Agassiz, and one of the
two species included in his A. punctatus , must be transferred to
Elonichthys , as well as his Palceoniscus Robisoni, P. striolatus , P.
Egertoni , and Pygopterus Bucklandi. The mutual resemblances of

* “Verh. des naturhist. ver. d. preuss. Rheinlande,” xiv. (1857) p. 12.

278 Proceedings of the Royal Society

these forms are so close that it seems almost unaccountable that
they should have been placed by Agassiz in different genera ; his
having done so seems, indeed, to indicate the arbitrary nature of the
distinction which he drew between Amblypterus and Palceoniscus ,
as well as his not having fully realised the nature of the essentially
distinctive characters of the true Pygopteri.

Amblypterus Portlockii of Sir Philip Grrey-Egerton * seems to
belong to this genus, as probably also does Palceoniscus Brownii of
Jackson, judging from the figure given. f The same must also be
said of P. peltigerus of Newberry, | which was indeed first described
by that author as an Elonichthys .§

As above defined, Elonichthys is pre-eminently a carboniferous
genus, and well represented in strata of that age in G-reat Britain
and other countries. The necessary restriction of the limits of the
genera Palcecniscus, Amblypterus , and PygopteruSj and the transfer-
ence of the carboniferous species formerly referred to them to
Elonichthys and other genera (Nematopty chius, Rhadinichthys ) leave
the three first named without representatives in the carboniferous
formation, so far as our present knowledge goes, — a conclusion which
may appear at first somewhat startling to geologists, who have
been so long accustomed to look upon them as characteristic of that
era, as well as of the succeeding Permian. |]

Elonichthys nemopterus , Agass. sp.

Amblypterus nemopterus, Agassiz, Poissons Foss. vol. ii. p. 1 p. 107;

Atlas, vol. ii. pi. 46, figs. 1 and 2.

To Sir Walter C. Trevelyan, Bart., of Wallington, Northumber-
land, I am indebted for the loan of the original example of this
species figured by Agassiz ; the only other specimen, which I can
with certainty identify with it, is contained in my n collection.
Its principal specific characters may be summed up as follows : —

Length from 4 to 5 inches ; scales rather small, their posterior

* Quar. Jour. Geol. Soc. vi. 1850, p. 2.

t Report on the Altert Coal Mine, New Brunswick, ‘p. 52, pi. i. fig. 2.

J Geol. Survey of Ohio, Palaeontology, vol. i. p. 345, pi. xxxviii. fig. 1.

§ Proc. Acad. Nat. Sc. Philad., 1856 ; pp. 96-100.

|| The strata at Saarbriicken and Lebach, containing the typical Amblypteri,
as well as the fish-bearing beds of Munster- Appel, Kreuznach, Goldlauter, &c.,
in Germany, and of Autun in France, long believed to belong to the carboni-
ferous formation, are now referred by continental geologists to the Lower Per-
mian (“unteres Rothliegendes ”).

279

of Edinburgh, Session 1876-77.

margins finely denticulated, ornamented with delicate ridges, which
are mostly parallel with the anterior and lower margins, some
above being parallel with the upper one, and which in the hinder
part of the fish, tend, on the posterior part of the scale, to become re-
placed by punctures ; dorsal and anal fins very high in front sharply
acuminated ; the rays of all the fins delicate, with rather distant
articulations (in the principal rays at least twice as long as broad).

By Agassiz the rays of the dorsal fin are described as being
“ tous bifurques a plusieures reprises jusque vers leur milieu.” It
seems to me, however, that the dichotomisation of the longer rays,
as is usual in this genus, does not commence till towards their ter-
minations. He also described the surface of the scales as being
“ornee de petites rides saillantes, disposees a-peu-pres comme les
lignes d’accroissement en losanges concentriques plus on moins
regulieres et un peu obliques, de telle sorte que leurs angles aigus
sont tournes vers les angles superieur-anterieur et inferieur-poste-
rieur de chaque ecaille,” — a description which is hardly correct,
as there are no striae parallel with the posterior margin of the scale.
The scales of the type-specimen are, however, in very bad preser-
vation, the exterior ganoine layer having everywhere disappeared,
and their markings can only be made out from the impressions on the
counterpart. Agassiz seems also to have been much struck by its re-
semblance to the Amblypterus ( Rhabdolepis ) macropterus of Saarbriic-
ken ; to me, however, although the bones of the head are very badly
preserved, its affinities to the following species seem so plain and
obvious, that I have no hesitation in referring it to the same genus.

Geological Position and Locality. In ironstone nodules from the
Lower Carboniferous shales of Wardie, near Edinburgh.

Elonichtliys intermedins , sp. nov. Traquair.

Amblypterus pundatus (pars) Agassiz “Poissons Fossiles,” vol. ii. pt. 2, p. 109.

Atlas vol. ii. tab. 4c. figs. 3, 5, 6, 7, 8, but not fig. 4.

Eliminating from the three figured specimens of “ Amblypterus
pundatus ” A g., the one showing a head, and which in my last com-
munication to the Society I have made the type of a new genus,
Gonatodus, retaining the original specific name pundatus , the two
remaining headless specimens seem undoubtedly to agree with each
other, and also with a series of more or less perfect fishes in my

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Proceedings of the Royal Society

own collection, which belong to a species perfectly distinct, even
generically, from the first. The presence in the jaws of this species of
sharp conical teeth of different sizes, as well as its entire aspect, shows
that it is referable to the same genus as Elonichthys striolatus ,
(. Palceoniscus striolatus, Agassiz) with which it is indeed closely allied.

Description. — The largest specimen in my collection measures6 £
inches in length, but, as it is a little contorted laterally, it must have
been originally somewhat longer; the more ordinary length is from 5J
to 6J inches. The form of the body is fusiform, but as hardly any
specimen is absolutely free from some amount of distortion, it is
difficult to ascertain the proportional measurements with absolute
accuracy; two very good examples, however, agree in this, that
the length of the head is contained a little more than four times,
and the greatest depth of the body (just in front of the dorsal fin)
a little more than three times in the total length, up to the bifurca-
tion of the caudal fin.

Many of the details of the structure of the head are clearly
shown. The outer surfaces of the bones of the cranial shield dis-
play a fine tubercular ornamentation, the tubercles frequently
passing into short rugae; the superethmoidal forms as usual a
blunt prominence projecting over the front of the mouth. The
suspensorium is very oblique, and the gape consequently of great
extent. The operculum is rather narrow, its posterior-superior angle
is rounded off, the posterior-inferior one acutely pointed, its outer
surface is marked with delicate and somewhat distant ridges,
which mostly follow the direction of the lines of growth. The
interoperculum is square-shaped and apparently similarly orna-
mented, though it is difficult to obtain a satisfactory view of its
external surface. The exact number of the branchiostegal rays is
hardly ascertainable ; in many specimens the anterior one of each
lateral series is distinctly shown to be much broader than the rest,
and a median lozenge-shaped plate is also conspicuously present
between these, and behind the symphysis of the mandible. The
maxilla is of the usual form ; its broad portion is ornamented with
delicate raised striae placed rather widely apart, and mostly parallel
with the superior and posterior margins; they are closer and more
pronounced along the dentary margin. The mandible is moder-
ately stout, and closely striated externally with delicate ridges,

281

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which run in a direction slightly oblique to its upper border. The
teeth are rarely seen, being usually covered up by the matrix, whose
intense hardness defies all attempts at working them out; in some
specimens, however, a few are exhibited both on the mandible and
maxilla. They are conical, sharp, and incurved, and of different
sizes, the largest measuring about inch in length, though in one
specimen a broken tooth is perceptible which must have been
larger, probably attaining about — inch in length. The bones of
the shoulder girdle, usually well seen, present nothing remarkable
in their configuration ; they are ornamented externally with closely
set, wavy, branching, and anastomosing ridges.

The scales of the body are of medium size ; as usual they
diminish from before backwards, but not in so very marked a
manner as in Gonatodus punctatus. Externally they are marked
with oblique furrows passing into isolated coarse punctures in the
posterior part of the scale. In the anterior part of the fish, and
along the line of the back in front of the dorsal fin, these furrows
are closer, producing sometimes a ridged appearance between them,
and extend more over the surface than is the case further back,
where they are shorter, and more limited to the anterior margin, so
that the greater part of the exposed area of the scale is simply
punctured; the furrows become, indeed, almost entirely lost on the
scales of the tail pedicle. The posterior margins of the scales are
finely denticulated.

The length of the pectoral fin is equal to about § that of the
head; it is sharply acuminated, and contains about 30 rays-, which
at the medial edge of the fin become very short and delicate. The
first three rays on the lateral edge, which are short and do not
reach the apex, seem entirely unarticulated; the articulations of
the others are distant proximally, but becoming rapidly closer dis-
tally, so that over the greater part of the expanse of the fin the joints
are square-shaped, becoming at length even shorter than broad.
The ventrals are situated midway between the pectorals and the
anal; they are also acuminate in form, each containing about 15
rays, articulated from their origins, their joints also diminishing in
length from their proximal towards their distal extremities. The
dorsal is situated nearly opposite the interval between it and the
anal; both of these fins are very similar in shape, being triangular,

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very high in front, acutely pointed, and with the posterior border
gently concave. Their rays appear coarse, compared with those of
Elonichthys nemopterus , and especially with those of Gonatodus
punctatus , so that had Agassiz only seen the fins of the latter he
could not have confounded it with the present species. Each con-
sists of about 30 rays, finely striated externally in the direction of
their length; their transverse joints are conspicuously longer than
broad in the principal rays, but become shorter in the posterior
part of the fin, and also in the longer rays towards their extremities.
The longer rays begin also to bifurcate towards their terminations,
the process gradually creeping up on the posterior part of the fin
till in the delicate hindermost rays it takes place about their
middle, — a very general characteristic of the fins in the species of
this genus. The caudal is very powerful ; the rays of its lower lobe
are divided by rather distant articulations, and dichotomise towards
their extremities ; those of the upper lobe divide about their middle,
and are characterised by the extreme closeness of their articulations,
the joints being rather shorter than the rays are broad. The
fulcra of all the fins are minute and closely set.

Remarks. — The close resemblance which this species bears to E.
striolatus is quite apparent}; their specific distinction is also suffi-
ciently pronounced. In E. striolatus the articulations of the prin-
cipal rays of the dorsal and anal fins are much closer; the dorsal and
anal fins do not seem to be quite so sharply acuminate in form ; the
laniary teeth are larger; the scale ornament, though belonging to
the same general type, is more delicate in character. To E. nemop-
terus its resemblances are also very strong ; it differs, however, from
it in the greater coarseness of the fin rays, with closer articulations,
this being especially marked in the case of the pectoral, as well as
in the nature of the scale ornament. The aspect of the fin rays is
somewhat intermediate between their condition in the two other
species named, hence the specific term which I have adopted
for the present fish.

Geological Position and Locality. — In ironstone nodules from
the Lower Carboniferous shales of Wardie, near Edinburgh. In
the collection of James Linn, Esq., there is also a specimen from
Dechmont in Linlithgowshire, in very indifferent preservation, but
which I am inclined to refer to the same species.

of Edinburgh , Session 1876-77.

283

3. Note on Clapeyron’s Formula. By Professor Dewar.

4. Note an the Specific Gravity of Ocean Water. By

J. Y. Buchanan.

During the cruise of the Challenger the specific gravity of the
surface water was observed daily while at sea, and that of water
from the bottom and intermediate depths as often as opportunity
offered. These observations were almost entirely confined to the
region between the parallels of 40° N. and 40° S. latitudes, which,
including as it does the regions of the equatorial calms, of the
trade winds, and to a certain extent of both the northern and
southern westerly winds is decidedly the most interesting field for
such investigations. Many valuable observations have been made
by other observers, and I have availed myself more especially of
the series of observations made by Lenz during Kotzebue’s voyage
to the Pacific and back. His observations were almost entirely
confined to the surface water.

The density of sea water depends on the amount of salt which it
contains, on its temperature, and on the pressure to which it is
subject. Away from the disturbing influences of the shore, the
water of the ocean is subject to comparatively slight variations in
saltnesss, so slight indeed that different waters may without
sensible error be assumed to be equally affected by changes of tem-
perature and pressure. As the remarks which are offered in the
present paper have reference to the salinity or concentration of
the water, the specific gravities have all been reduced to their
value at 60° F., the unit being that of distilled water at its tem-
perature of maximum density. The pressure is that of one atmo-
sphere.

There are two meteorological causes which affect the saltness of
the sea; the one is the formation of vapour and the precipitation of
it as rain, and the other is the freezing of the water and melting of
the ice thus formed. Vast quantities of solid matter, chiefly car-
bonate of lime and silica, are removed from the water by living
organisms, and these substances form the chief components of the
solid matter brought down in solution by rivers. Although this is

2 p

VOL. IX.

284 Proceedings of the Royal Society

a very important cause of the transmigration of rock, it does not
sensibly affect the specific gravity of the sea-water, because only a
very limited amount either of silica or of carbonate of lime can be
in solution at any one time. The general distribution of saltness,
as indicated by the specific gravity of the water at a common tem-
perature of 60° F. at the surface, is shown on a chart on which
localities of equal saltness are connected by lines, and the spaces
between successive lines coloured distinctively. The vertical dis-
tribution is shown in diagrams in sections along certain lines of
route, the depths at which the same saltness is observed being also
connected by lines. The variations of saltness at the surface on
the lines of section are further shown by curves having for ordi-
nates the reduced specific gravity, and for abscissae degrees of
latitude or longitude according to circumstances.

These diagrams show at once how great are the differences in the
saltness of the water in different depths and at different localities
on the surface, and it must be remembered that we are here con-
sidering bona fide ocean water, litoral waters so much influenced by
the drainage of the land being reserved for separate treatment.
Looking at the chart we see that specific gravities above 1-0270
occur in three localities only — namely, in the trade-wind regions
of the North and South Atlantic, and of the central South Pacific.
In the North Pacific the specific gravity was nowhere as high as
1*0265, whereas large tracts both of the North and South Atlantic
reached 1-0275. The greater part of the year 1873 was passed in
the North Atlantic, and the central part was crossed on the home-
ward voyage. On the eastern side and in the track of outward bound
ships, the maximum of 1 -02763 was reached in latitude 24°. In the
central part the maximum was 1-02768 in latitude 25°, and in the
western part it was 1*02743 in 27°30'; so that between the meri-
dians of 20° W. and 70° W. the line of maximum saltness would
appear to run nearly due east and west, with a slight northerly in-
clination towards the west. In the central South Atlantic the
maximum of 1*02768 was observed in latitude 17°26', and in the
western part 1*02783, in latitude 15°15', so that here also the line
of maximum saltness would appear to have a slight northerly trend.
Between these two lines the specific gravity falls off until a mini-
mum of 1*0260 is reached at about 3° N. latitude, and following the

285

of Edinburgh, Session 1876-77.

equator from east to west the specific gravity appears to increase
pretty steadily. In the Central Pacific the maximum saltness is
observed in latitude 18° S., where the specific gravity is 1*02725;
in the north the maximum is 1*0263, in latitude 22° N. The
minimum of 1*02488 was found in latitude 7°26' N. In the
Western Pacific the series of observations was not so continuous,
there being a considerable gap between latitude 15° S. and 2 S. ;
the northern portion, however, is complete. Here, again, the
absolute maximum is in the south, reaching 1 *0268, in 22°30° S. ;
in the north the maximum is 1*0263 in 22° N., but the dense water
of the Southern Pacific penetrates into the northern part of the
ocean, giving another and higher maximum of 1*0266 in lat. 2' N.
The actual maximum observed was 1*0242 close to Humboldt Bay,
in New Guinea. Other very low specific gravities were observed
occasionally even at considerable distances from the coast; but the
fact that there was frequently drift-wood floating about, and that
the light water was confined to a stratum of 10 to 20 fathoms thick-
ness, showed that we had here to do with shore water. If the
general run of the curve be followed, the oceanic minimum will be
found to occur about 10° N., marking 1*0258.

The saltness, which increases on both sides of the equator until
a maximum is reached in the trade wind districts, decreases again
towards the poles and the whole of the ocean to the southward of
latitude 40° S., has a specific gravity below 10260, and for the
greater part below 1*0255. In the neighbourhood of ice in sum-
mer great and sudden variations are frequently observed, the specific
gravity amongst loose park ice frequently falling as low as 1*0240,

Confining our consideration, then, in the meantime, to the
surface, we find that the maxima in the Southern Pacific and
Atlantic are situated nearer the equator than those in the northern
parts of these oceans; that the maxima in the Atlantic are higher
than the corresponding ones in the Pacific ; and that the maximum
maximorum occurs in the South Atlantic about latitude 15° S.
The equatorial minima in both oceans are to the northward of the
equator ; and from all these facts we see how intimately the con-
centration of the sea-water is connected with the distribution of
the trade winds.

If we turn now to the consideration of the vertical distribution

286 Proceedings of the Royal Society

of density, we see that the influence of atmospheric conditions does
not cease when we leave the surface. In the trade-wind districts
we find the excessive concentration extending to greater or less
depths, according to the ocean which we are considering, and,
as might have been expected, this effect is much more sensible in
the Atlantic than in the Pacific. In the Atlantic, again, the
amount of concentration is much greater in the northern than in
the southern portion, while in the Pacific the reverse is the case.
The great amount of concentration in the North Atlantic is doubt-
less due chiefly to the form of its basin. The south-east trade
which blows with a preponderating force drives constantly fresh
supplies of water in to the northern basin, where a large portion of
it is kept constantly circulating by the prevailing winds in a region
where the atmosphere is ever greedy of moisture. This circulation,
assisted by the yearly oscillations of temperature, bring about a
constant concentration of the deep waters, and at the same time,
as I have pointed out, a heating of the deeper waters by convec-
tion. The effect of this concentration of the water is to render it
heavier than an equal bulk of water further to the south, and con-
sequently it forces its way southwards along the bottom. This
under outflow from the North Atlantic was conjectured by Cap-
tain Tizard from a consideration of the temperature of the deep
water of the western basin of the South Atlantic, and a glance
at the vertical section of the Atlantic is sufficient to show the
great likelihood of its existence. From a consideration of this
section it would appear probable that at some position about 40°
north latitude a tolerably uniform density of from 1*0265 to 1*0270
will be found, and, indeed, in the neighbourhood of the Azores
the following bottom specific gravities were observed : —

Depth in fathoms, . . 1675 1000 900 750

Specific gravity at 15*56, . 1*02670 1*02693 1*02691 1*02679

Although we find that in all tropical and temperate regions the
temperature of the water is highest at the surface, and decreases
as the depth increases, we do not by any means invariably find the
highest specific gravity at the surface, nor does it decrease regu-
larly with increasing depth. The water is usually least salt
at between 500 and 1000 fathoms from the surface. The maximum
specific gravity at any locality is .frequently observed at depths of

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of Edinburgh, Session 1876-77.

from 25 to 150 fathoms from the surface, and it is not unusual to
find besides the normal minimum between 500 and 1000 fathoms,
a second minimum at 25 or 50 fathoms from the surface. These
maxima and minima are caused in some cases by currents, and in
others are the evidence of past wet or dry seasons. In the Southern
Ocean the surface specific gravity varies between 1-0240 and 1*0250,
being nearly constant at 1*0250 in localities free from ice; it in-
creases, however, with the depth, the bottom specific gravity being
usually T0255 or 1*0256.

The following Gentlemen were elected Foreign Honorary
Fellows, to fill up the vacancies caused by the death of
Adolphe Theodore Brongniart and of Christian Gottfried
Ehrenberg : —

Alphonso De Candolle, Geneva.

Professor Carl Gegenbaur, Heidelberg.

The following Gentlemen were elected Ordinary Fellows
of the Society : —

John Murray.

Walter Noel Hartley, Chemical Demonstrator,
King’s College, London.

Walter Weldon, F.C.S., London.

Monday , 29 th January 1877.

Professor KELLANI), Yice-President, in the Chair.

The following Communications were read : —

1. Note on the Manganese Nodules found on the Bed of the
Ocean. By J. Y. Buchanan.

The manganese nodules occur in greater or less quantity all
over the ocean-bed, and most abundantly in the Pacific. They
occur of all sizes, from minute grains to masses of a pound weight,
and even greater, and form nodular concretions of concentric shells,
round a nucleus, which is very frequently a piece of pumice or a
shark’s tooth. Their outside has a peculiar and very characteristic
mammillated surface, which enables them to be identified at a
glance. When freshly brought up they are very soft, being easily

288 Proceedings of the Royal Society

scraped to powder with a knife. They gradually get harder on
exposure to the air.

The powder, heated in a closed tube, gives out water which re-
acts alkaline, and has an empyreumatic odour. Heated with strong
hydrochloric acid, it liberates abundance of chlorine, and the
residue which remains is white, consisting of silica, clay, and
sand, the sand being the same as is found in the bottom mud from
the same locality. Their composition varies greatly, different
nodules containing different quantities of mechanically admixed
mud, and the number of different elements found in them is very
large. Copper, iron, cobalt, nickel, manganese, alumina, lime,
magnesia, silica, and phosphoric acid have been detected in a
large number ; but I have not as yet been able to make a com-
pleted analysis of any of them. I have, however, made a few
determinations of the most important component substances. For
this purpose the outside and densest layers of the nodules were
selected, and portions of them pulverised and dried for ten or
twelve hours at 140° C. The amount of chlorine liberated on
treatment with hydrochloric acid was determined by Bunsen’s
method, and the iron was determined by titration with stannous
chloride. The samples analysed were from four different localities.

Nos. 2, 4, and 5 were from the same place, No. 2 being the
matter collected round a shark’s tooth as nucleus ; Nos. 4 and 5
being the outside rinds of ordinary nodules.

The results are given in the following table, the numbers being
in many cases the means of several observations : —

Locality.

A

B

C

D

E

F

G

Lilt.

Long.

No.

Insoluble

Residue.

0

Mn02

MnO

Fe203

AI2O3

H20

Na20

13° 52' S.

149° 17' W.

2

1755

6-13

33-30

2718

...

...

• • •

• • •

...

4

15-30

5-92

32-23

• ••

23-86

...

• . •

...

...

5

15-30

6-49

35-28

...

24 85

...

10-2

• ••

37° 52' N.

160° 17' W.

6

36-24

6.49

24 41

...

2016

3-83

7-70

5-98

42° 42' S.

134° 10' E.

7

17-98

7-54

41-11

33-53

18-04

2-55

7-31

...

22° 21' S.

150° 17' W.

8

21-74

5.19

28-20

...

24-52

7-67

8 54

8.5

A is the residue which remains undissolved after treating the
mineral with strong hydrochloric acid, evaporating to dryness and
redissolving. In No. 5 it contains 85T6 per cent, silica, and in
No. 6, 82-27 per cent.

B is the available oxygen determined by Bunsen’s method.

289

of Edinburgh, Session 1876-77.

C is the Mn02 equivalent to the available oxygen.

D is the MnO found by weighing as Mn304.

E is the Fe203 found by titration with SnCl2.

F is the alumina found by subtracting the Fe203 found in E
from the weight of the precipitate with acetate of soda.

G-is the water expelled on ignition; it is obtained by deducting two-
thirds of the oxygen found in B from the loss of weight by ignition.

It will be seen from the results given in the above table that the
nodules from different localities vary greatly in composition, though
in the same locality they have similar composition, irrespectively
of the nature of the nodules. The insoluble residue contains,
besides silica and clay, sand of the same mineral nature as is found
in the bottom at the same locality. The manganese is present
wholly as Mn02, and the iron as Fe203 . In No. 6 there is 3 per
cent, of cobalt ; this metal, along with copper and a little nickel,
is present in all of them. Zinc was not found in any of the above
specimens.

2. Note on the Measure of Beknottedness. By Prof. Tait.

In drawing the various closed curves which have a given number
of double points, I found it desirable to have some simple mode of
ascertaining whether a particular form was a new one, or only a
deformation of one of those I had already obtained. Of course
the schemes (as described in my former paper) contain the desired
information, but it may sometimes be difficult to obtain in this
way; for, when the number of intersections is large, we may have
to change the crossing which is taken as the initial one several
times before we hit upon the same notation for like crossings (if
such exist) in the two schemes compared. And the methods of
deformation already given often present their results in forms so
distorted that it is not easy at once to recognise their identity with
other drawings of the very same curves.

The method of treatment described in my paper, which depends
upon the study of the plait , supplies (by the + and - signs over
the various crossings) exactly the sort of information we require,
though it may leave ambiguities. But some simple mode of apply-
ing it is requisite.

I first tried a modification of the process (formerly described) of

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Proceedings of the Royal Society

going round the curve and pitching a coin into each field or cell as
it is reached. To make the required distinction between crossing
over and crossing under , we may suppose the two coins to be of dif-
ferent kinds, — silver and copper for instance. Let the rule be : —
silver to the right when crossing over, to the left when crossing under.
Then, however the path be arranged, of the four angles at each
crossing, one will have no coins, th'e vertical or opposite corner will
have two silver or two copper coins, the others one copper or one
silver coin each.

It is easily seen that a reversal of the direction of going round
leaves the single coins as they were, but shifts the pair of coins
into the angle formerly vacant; also that in the deformed figures
the circumstances are exactly the same as in the original. Hence
we may divide the crossings into silver and copper ones, according
as two silver or two copper coins come together. And the excess
of the silver over the copper crossings, or vice versa, furnishes an
exceedingly simple and readily applied test (not however, as will
soon he seen, in itself absolutely conclusive of identity, though
absolutely conclusive against it), which is of great value in arrang-
ing in family groups (those of each family having the same number
of silver crossings), the various knots having a given number of
intersections.

I soon saw that this process, so limited, was intimately connected
with that required for the estimation of the work necessary to carry
a magnetic pole along the curve, the curve being supposed to be
traversed by an electric current, and it occurred to me that we
might possibly obtain a definite measurement of beknottedness in
terms of such a physical quantity: as it obviously must be always
the same for the same knot, and must vanish when there is no
beknottedness. The measure may be made more complete by
recording the numbers of non-nugatory silver and copper cross-
ings separately, with the number to be deducted as due merely to
the coiling of the figure. I shall recur to this point later.

When unit current circulates in a circuit, the work required to
carry unit pole once round any closed curve once linked with
the circuit is ± 47t. Instead of the current we may substitute a
uniformly and normally magnetised surface bounded by the circuit.
The potential energy of the pole in any position is always measured

291

of Edinburgh, Session 1876-77.

by the spherical opening subtended by the circuit ; but its sign
depends upon whether the north or south polar side is turned to the
pole. Hence there is no potential energy when the pole is situated
in the plane of the circuit but external to it, and the value is
± 27r when the pole just reaches the plane of the circuit internally.
G-auss gave from these results the value of a remarkable double
integral extending over each of any two closed curves linked
together in space. Clerk-Maxwell ( Electricity , § 422) has shown
that this integral may vanish even for a complex linking of the
two circuits; and a similar difficulty is met with in the single
circuits with which we are now dealing, so that a special set of rules
must be made for determining the beknottedness in terms of the
silver and copper junctions. But the difficulty just mentioned
leads, as will be seen, to a very curious result.

To construct the magnetised surface which shall exert the same
external action on a pole as a current in any given closed circuit
does, we may either suppose a surface extending
to infinity in one direction (say, for definiteness,
upwards from the plane of the paper), and having
the circuit for its edge ; or we may form, as in
the figure, a finite autotomic surface of one sheet,
having the circuit for its edge. The only diffi-
culty in estimating the work lies in the definite statement of how
the pole is to move along the curve itself. For, if its path screw
round the curve, ± 47r must be added to the work for each such com-
plete turn. As an illustration,
suppose we bend an india-rubber
band coloured black on one side, as
in the figure, so that the black is
always the concave surface, we find on pulling it out straight that
it has no twist. If both loops be made by overlaying, when pulled out
it becomes twisted through two whole turns. This is an instance
of the kinematic principle that spiral springs act by torsion.

Perhaps the most simple definite condition is that which I first
employed, viz., to make the pole move along the curve, keeping always
in the osculating plane and on the convex side. But we have then
to arrange beforehand what is to be done at a point of inflexion.

A practical rule, however, may easily be given from the con-

vol. ix. 2 Q

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Proceedings of the Royal Society

sideration of the magnetised surface above mentioned. Go round
the curve, marking an arrow head after each crossing to show the
direction in which you passed it. Then a junction like the fol-
lowing gives + 2tt at each time of crossing ;
or, if we use the infinite surface spoken of
above, it gives + 4nr for the upper branch,
and nothing for the lower (which, on this
supposition, does not pass through the magnetic sheet). Change
the crossing from over to under , and these quantities change sign.
The junction figured above would, in our first illustration, be a
silver one. But a still simpler process is to go round putting a
dot to the right after each crossing over , and vice versa. Silver
crossings have two dots in one angle ; copper one in each of two
vertical angles.

Now, in order that our rule may be such as to give no work
where there is no beknottedness, we must make the required ex-
pression such as to vanish whenever all the intersections are
nugatory. Those which are nugatory only in consequence of
their signs are in pairs, silver and copper, and will take care of
themselves, as we see by special examples like the following, in
which the reversal of one of the directions simply reverses the

signs. Hence the only part to correct for
is that depending on the number of whole
turns, and the sketch of the india-rubber
band above shows that the work at the
vertex of each such partial closed circuit is simply not to be
counted-— i.e., that the ± 47r , which would be reckoned for each
crossing by our rule, is to be considered as made up for by the cor-
responding screwing of the pole round the curve.

To illustrate the application of this process, let us consider again
the two distinct forms with five non-nugatory intersections

1.

(the first being a modified form of the “pentacle,” the second, fig. 6

293

of Edinburgh, Session 1876-77.

of my paper, which, for the comparison below, must be supposed to
have all its signs changed) whose schemes are, respectively —

APBECAPBEC

— + — + — -b — + — +

A,

ADBECADCEB
- + - + -+•- + - +

A.

The lower signs refer to over or under, the upper to the electro-
magnetic work, or to the silver-copper distinction. These two
instances, in which both series of signs are absolutely identical,
each with each, show at once that we cannot take the two sets of
signs alone as fully descriptive of the knot.

To determine the electromagnetic work for any knot, we must
divide the scheme into independent circuits, no one of which in-
cludes a less extensive one ; and omit from the reckoning the work
for the terminal of each such circuit, and for each of the intersec-
tions which is not included in any one of the feparate circuits. The
particular closed circuits chosen do not affect the final result, as is
easily seen by thinking of the various deformations of each figure.

In the first of the two schemes above there is but one independent
non-autotomic circuit, which may be taken as

ADBECA.

In this all the intersections are included, so that the whole work is
to be found by leaving out that for A only ; i.e., it is - IGtt.

But in the second scheme we may take the two circuits

BADBand CADC,

and E is not included in either. Hence we must leave out of count
the work for B, C, and E ; and thus the whole work is only

— 87T.

In fact, the figures show that to untie the first knot we must not
only have the signs such that we can slip off B and E, but also C
and P, i.e., two signs must be changed; while the second loses all
its beknottedness if A and P could be got rid of, that is if one sign
only be changed. This is an instance in which the estimate by the
electro-magnetic process exactly agrees with the result of simpler

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Proceedings of the Royal Society

considerations. And it is probable after all that the true measure
of beknottedness is the smallest number of signs in a scheme which
must be altered in order that the wire may cease to be knotted.

It will be found that the alteration of five signs is sufficient to
remove the knotting from the annexed figure, and the stages of

operation of the various modes of reduction show that this form can
be regarded as made up of simpler knots intersecting one another
on the same string. In such a case it is not easy to give a strict
definition of the beknottedness in any other way than by defining
it as the smallest number of changes of sign which will take off all
the knotting. For the separate knots are virtually independent,
and to change all the signs in any one of them does not in every
case necessarily simplify the knot. Uncorrected the work is
- 13 x 47t. Corrected it is - 10 x 47r, which agrees with the
removal of the beknottedness by change of five signs only.

If the sign of the one unsymmetrical crossing be altered, four
changes of sign will suffice; for the uncorrected work is - 11 x 47r;
corrected it is - 8 x 47r, corresponding to four changes of sign.

The various modes alluded to in my paper of adjusting the
(lower) signs so that there shall be no beknottedness, follow at once
from these remarks. For we may make all the free letters in
each circuit +, save those which we have taken, in pairs, in some
previous circuit.

This test, though extremely useful as above explained in classi-
fying knots with the same number of intersections, is not fully
descriptive of a knot, being ambiguous whenever there is more
than one class of knots with the same number of intersections and
with the same excess or defect of silver as regards copper crossings.
This consideration, which promises to clear up some obscure and
difficult parts of the subject, has led me to some very curious re-
sults. The most important of these is when a knot, whatever be
its number of intersections, has equal numbers of silver and of

295

of Edinburgh, Session 1876-77.

copper crossings, or when the uncorrected expression for the electro-
magnetic work vanishes. Thinking of this in connection with the
fact that a change from right-handed to left-handed in a knot simply
changes silver to copper, or vice versa, i.e., reverses the sign of the
electro-magnetic work, 1 was led to see that there is a class of knots

which are capable of being changed from right to left-handed , without

*

change of form , by the ordinary processes of deformation. Of course
this implies that there is a mode of interchanging the letters, two
and two, in the scheme, so that their order remains unaltered ; or,
what comes to the same thing, that we shall get exactly the same
scheme (signs not included) by taking either of two different
crossings as A, and lettering as usual from it in the same direction
round the curve.

It will be readily found by trial that this can be done with the
only forms which have four valid intersections — as they are figured
in my former paper — if only the wire or cord be so twisted about
that, wThile the form is preserved, the junctions B, D be brought into
the positions relative to the figure which were formerly occupied
by A, C. For the scheme

+ + + +

ADB ACBDC | A
— + — I 1 — +

remains the same, so far as the letters are concerned, if we keep
the same cyclical order of letters, but write A for B, B for C, &c.
In estimating the electromagnetic work, by the rule above, w?e find
we may leave out either A, C, or B, D. So that the work is ± 8?r,
i.e., one degree of beknottedness.

The following case, with six intersections, is very instructive.
Either figure is formed from the other by throwing the lower coil
over the top of the whole.

3 4

It will be seen that each of these forms may be regarded as a

296 Proceedings of the Royal Society

simple loop passed unsymmetrically through a simple knot of
three intersections (figures 1 and 3 of my former paper), and that
the knot and loop are interchangeable between two groups of
three intersections. The knot is right-handed when transferred
to the second group ; left-handed in the first. But the figures
plainly show that they may also be regarded as a right nnd a
left-handed simple knot having a part common to each, so that
neither can be pulled tight, subject to our convention that there
shall be nothing higher than a double point. And here the peculiar
difficulty associated with the amphicheiral forms comes in ; for, in
estimating the electromagnetic work, we find we must leave out one
copper and one silver junction — the result being + 877- - 877-. This
is to be treated as ± 167t (or two degrees of beknottedness) because
the portions with different signs belong to what are, virtually at
least, two separate knots.*

The possibility of such amphicheiral forms is obvious from one
of the first illustrations in my former paper; where we have
only to suppose the irrelevant crossing removed, and one of the
separate simple knots (which are both right-handed in the cut)
made left-handed. But I was not at first prepared to find this
property in any knot not separable into detached, self-contained
portions ; so that it is possible that some of my former statements
may require modification.

It may be well to notice that when, in a slight variation of the

* Feb. 19. — This is not correct. There is but one degree of beknottedness,
for the two knots are not “ virtually separate,” as they have a part in
common, while one is right-handed and the other left-handed. In fact, the
figures above are mere transformations of the last cut in my former paper
— which is shown to be capable of being opened up by a single change of
sign. This can be done in the figures above, at either end of the lower
coil where it forms part of the external boundary. But if, without altering
the outline of the figure, we change all the signs in either of the two com-
ponent knots, so as to make them both right-handed, or both left-handed, the
whole acquires the double degree of beknottedness wrongly assigned to it in
the text. But it has now continuations of sign, and in virtue of these it hap-
pens to be reducible. In fact, when we make it into a clear coil after these
changes of sign it becomes the pentacle (fig. 1 above), the only knot with
fewer than six crossings which possesses, as we have seen, two degrees of be-
knottedness. I stated in my first paper, that when the signs in any non-
nugatory arrangement are alternately + and - the cord “ is obviously as
completely knotted as its scheme will admit of.” This completeness must

297

of Edinburgh, Session 1876-77.

arrangement just described, the loop passes symmetrically through
the simple knot, we have another six- crossing form, very much
resembling the last, but which is essentially not amphicheiral.
It is figured below in one of its forms — the others may be got by
deformation — and the schemes of the two kinds are appended for
comparison.

Figs. 3 and 4 A. D¥> E G AD F CH? B \ A..

Fig. 5 ADBFCFDiECF.BI A.

It will be seen that the sole difference between the amphicheiral
knot and that last figured, lies in the inversion of the positions
of A and F in their even places in the scheme.

It appears, then, that none of these abbreviated methods, how-
ever useful as temporary aids to classification, can take the place
of the scheme in fully describing the form of a knot and in
measuring the amount of beknottedness in general. Especially is
the scheme required in order to calculate the beknottedness in
terms of the electromagnetic work. And this conclusion might, I
think, have been inferred from the prominent part which the
arrangement of the letters in the even places plays in determining
the form of a knot; an arrangement of which only traces are left
when we substitute the sign of the work at each junction for the
letter attached to it, thus losing all control of the amount to be
added or subtracted on account of the mere number of coils.

[ Added Jan. 27th.'] — Professor Clerk-Maxwell, to whom I sent
some of the above results (and to whom, as well as to Sir W.

be understood of what may be called Knottiness , not of Beknottedness. For it
has just been shown by a particular case that we can occasionally increase
the degree of beknottedness, while diminishing knottiness, i.e., losing crossings
by so altering their signs as to make some of them nugatory. The point
thus raised, i.e., the distinction between Knottiness and Beknottedness, is a
very troublesome and delicate one, and is obviously related to several of the
difficulties pointed out in the present paper.

298 Proceedings of the Royal Society

Thomson, I am indebted for various hints, usually in the especially
valuable form of criticisms and reasons for doubt), has lately called
my attention to a paper by Listing, of date 1847, part of which is
devoted to the subject of knots. I have this morning obtained it
from the Cambridge University Library, but have not yet thoroughly
read it. As was to be expected, I find that the author has antici-
pated some of the contents of my papers ; and he mentions at least
one very curious fact, which I had thought possible, but had not
observed, though it is very directly connected with one of the results
of the present note. He virtually shows, by giving a particular case,
that the method of deformation which I employ does not always
give all possible forms of a completely knotted wire. I believe
that this depends on the fact that a part of the scheme is amphi-
cheiral. I propose to give the Society an account of Listing’s
method and results on the earliest opportunity.

3. Note on the Effect of Heat on Infusible Impalpable
Powders. By Professor Tait.

Several years ago Professor Dewar gave me a specimen of silica
in a state of exceedingly minute division, which had been produced
in Dr Playfair’s laboratory in the preparation of fluosilicic acid. I
noticed at the time how much its great mobility is increased by
heating — so that it behaves almost like a liquid. And I fancied
that I observed close to the surface a thin stratum of what might
by the same analogy be called a vapour ; consisting of particles
thrown up and falling back again, like the little drops thrown up at
the surface of soda-water. I was inclined to ascribe these pheno-
mena to heat directly — supposing that the particles were fine
enough to behave, though in a very imperfect way, as the kinetic
theory assumes the particles of a gas to behave. However this may
be, the extreme mobility of such powders when heated on a plati-
num dish ; and the fact, noticed by chemists, that a bath of calcined
magnesia is capable of propagating waves when heated ; seem to
show that valuable results might be obtained by seeking for evi-
dence of inter-diffusion as the result of experiments made by very
long-continued heating of vessels containing fine silica and mag-

299

of Edinburgh, Session 1876-77.

nesia originally in separate strata. I have brought this before the
Society in the hope that (as it can hardly be classed as a laboratory
experiment) some of the Fellows, who may have access to a suit-
able furnace which is in activity the greater part of the year, may
be induced to give the experiment a fair trial.

4. Abstract of Additional Memoir on the Parallel Eoads
of Locliaber. By D. Milne Home, LL.I).

Mr Milne Home stated that he had been induced to resume his
researches in the Lochaber district, in consequence of a lecture,
in June last, by Dr Tyndall of London, at the Royal Institution,
Albemarle Street, and subsequently printed and published. In
this lecture, Dr Tyndall controverted the detrital theory of lake
barriers, and advocated the glacier theory ; — supporting his views
by a reference to observations which Dr Tyndall said he had
recently made on a special visit to the Parallel Roads.

Mr Milne Home said that on account of Dr Tyndall’s reputation
as a man of science, and his great knowledge of glacier action, he
had thought it right to reconsider his own opinions, and go back
to Lochaber with Dr Tyndall’s lecture in his hand.

During this recent visit, Mr Milne Home said he had obtained
farther information bearing on the question, which he hoped might
be deemed sufficiently important to be communicated to the
Society.

He would first mention the import of this information, and then
offer remarks on Dr Tyndall’s lecture.

After recapitulating the grounds on which he had in his last
Memoir suggested that the barriers of the old lakes had been com-
posed of the natural detritus of the district, he mentioned the fol-
lowing facts, in corroboration of these grounds —

1. He specified several additional cases of lakes, in Stratherrick
(a district not far from Lochaber), now kept in by detrital block-
age, and which, owing to a partial lowering of this blockage, had
subsided from higher levels, — these higher levels being indicated
by horizon al lines of cliff.

2 r

VOL. IX.

300

Proceedings of the Royal Society

2. He specified the occurrence of thick beds of detritus, consist-
ing of clay, gravel, and sand, along the hills between Stratherrick
and Strathspey, at levels of from 2000 to 2500 ft. above the sea,
— heights far greater than the sites of the barriers of the old
Lochaber lakes.

3. He next indicated on a map the probable sites of the barriers
by which the lakes of Gflen Roy and Glen Spean had been respec-
tively confined, till the barriers were broken down, and gave
reasons for fixing on these sites.

4. While in his last Memoir he had attributed the breaking
down of the barriers to the agency of the rivers discharging from
the lakes, and also of streams flowing upon the barriers from the
adjoining mountains, he now added another probable cause of
injury, to the barriers at the mouths of Glen Spean and Glen Glusy
in the agency of the sea, there being probable evidence that when
these barriers existed, the sea was standing at a level of about 500
or 600 feet higher than at present ; and that the blockages of
these two glens were so near the sea, when at that height, as to
form sea-cliffs.

He explained that this evidence consisted, first, in the occurrence
of sea shells, said to have been found at two places outside the
Glen Spean barrier, in beds of clay from 200 to 500 feet above the
sea, by persons whose trusworthiness he had ascertained ; and,
second , in the existence of a series of terraces, in the district about
Spean Bridge, from 400 to 500 feet above the sea, which he con-
sidered to be marine.

5. Mr Milne Home then adverted to the grounds on which the
glacier theory rested, and stated that by another visit made
last autumn to Corry N’Eoin and Glen Treig, the only two
valleys, where a glacier is supposed to have existed, when Glens
Spean and Roy were occupied by lakes, he had discovered that
these valleys, instead of being then filled with ice, must have been
occupied by water, viz., the water of the Glen Spean Lake ; inas-
much as there are beach lines round the whole of L oc Treig, and
also at the mouth of Corry N’Eoin.

6. Referring to what had been called the Moraines of the
alleged Treig glacier — viz., at Murlaggan, and in the district be-
tween the Rough Burn and Fersit, — he said that at Murlaggan

301

of Edinburgh, Session 1876-77.

the knolls referred to were composed entirely of beds of sand and
fine gravel, — manifestly deposited by water, and not brought by
a glacier.

The supposed Moraines, between Rough Burn and Fersit, con-
sist of enormous embankments of gravel, apparently sub-marine,
and formed when the sea stood some thousands of feet above its
present level. The boulders strewed over this district, and heaped
on these embankments, had probably been brought by floating ice,
in a current from the westward, flowing up the valley of Spean
towards Strathspey.

7. In regard to Dr Tyndall’s lecture, Mr Milne Home pointed
out, that when impugning the soundness of the detrital barrier
theory, Dr Tyndall had given a representation of that theory only
from Sir Thomas D. Lauder’s Memoirs, written fifty-nine years
ago, and not from the more recently published Memoirs, which
stated facts and arguments not to be found in Sir Thomas Lauder’s
paper. Moreover, Dr Tyndall had unfortunately misapprehended
Sir Thomas Lauder’s views regarding the formation of the barriers,
ascribing to him views on this subject disparaging to the detrital
theory, which neither Sir Thomas nor any other author entertained.

The only specific objection to the detrital theory suggested by
Dr Tyndall, was the alleged absence of any traces of barriers.
Mr Milne Home stated that he thought there were traces; and
that, even if there were none, the want of them would be no valid
objection to the theory.

With regard to the grounds on which Dr Tyndall maintained
the glacier theory, Mr Milne Home stated that Dr Tyndall ought
to have shown, how there could be such a difference in the climatic
condition of the two sides of Spean Yalley, that while the glens on
the south side were filled with ice, the glens on the north side were
filled with water; — this, however, Dr Tyndall had failed to do.

Mr Milne Home farther stated that though it was undoubtedly
true that some traces of glacier action were visible in various parts
of Lochaber, these, as it seemed to him, belonged to a period in the
world’s history long antecedent to the lakes of Glen Roy and Glen
Spean. When these lakes existed, the water of the Spean lake
penetrated into the two glens (Corry N’Eoin and Treig), supposed
to have been occupied by glaciers. It was therefore a physical

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Proceedings of the Royal Society

impossibility, that there could have been glaciers in these two glens
at the time that there were lakes in Glen Roy and G-len Spean.

Even if there had been glaciers in these glens, these glaciers,
to reach the position of the G-len Roy barriers, would, after emerging
from their parent glens, have had to travel seven or eight miles
across uneven ground, push themselves round the corners of several
hills, and rise up to a level several hundred feet above these glens.
If it was possible to suppose that the tongues of these glaciers could
reach the required spots, the notion of their forming solid and
permanent barriers at these spots seems quite untenable.

Monday , 5th February 1877.

Sir WILLIAM THOMSON, President, in the Chair.

The following Communications were read : —

1. On some Effects of Heat on Electrostatic Attraction.

By Professor Tait.

2. On the Curves produced by Reflection from a Polished
Revolving Wire. By Edward Sang, Esq.

When a polished thin straight wire turns on a fixed point in
space, the point at which light coming from a fixed source is re-
flected, moves in a curved surface. In this paper the motion of
the wire was supposed to be restricted to the plane passing through
the eye and the source of light. The curve was shown to be of the
third order, having a straight line as a symptote both ways, and to
depend for its form upon a characterising angle. The interest of
the subject lay chiefly in the remarkable transformations of the
curve.

3. On an Ammonia-Cupric Zinc Chloride. By
E. W. Prevost, Ph.D.

The following is but a short and incomplete account of a com-
pound formed on the carbon and binding screws of a makeshift
Leclanehe battery. The cells employed were ordinary Bunsen ele-
ments, of which the carbon was embedded in manganese dioxide ;

of Edinburgh, Session 1876-77. 303

the substance in question grew on the brass binding screws, and as
a thin layer on the carbon. The external appearance of the mass
was reniform, the colour ranging from a pale blue to a dark purple
and lilac tint; the portions from the carbon were of a pale green
shade, and of no special shape. The quantity being small, it was
impossible to make more than one analysis of each substance and
that only with very small quantities. The exterior portions which
showed no crystalline structure, and were efflorescent, appeared to
contain less water than the interior portions, which possessed a
paler colour, the composition being otherwise the same. The in-
terior was not homogeneous, as particles of some white substance
could be distinguished scattered through the mass. The dark purple
and green portions, when heated to 100° C, give off ammonia and
water in varying quantities (NH3 2-02-0*87 per cent.), and left a
bluish green powder, which was only slightly soluble in water or
in dilute sulphuric acid, but easily dissolved with effervescence by
nitric or hydrochloric acid. The original substance treated with
water formed a blue alkaline solution, resembling that produced by
the solution of cupric hydrate in excess of ammonia, a green residue
being left undissolved, which, with potassium hydrate, yielded
ammonia.

The analyses point to a formula,

Cu2Zn4Clc(NH3)4C03 .

If the carbonic anhydride be present as zinc carbonate, and in all
probability the above-mentioned white particles are (ZnC03), we
have present the substances,

(2NH3Cu)C12 + (2NH3Zn)Cl2 + ZnC03 + ZnCl2 .

Also was found (NH4)2(NH3)3Cl5Cu2Zn3C03 ,

And in another analysis, no carbon dioxide being present,

Cu2Zna(NH3)3Cl4 .

In contact with a portion of the substances analysed was metallic
copper; this may probably account for the varying quantities of
combined copper in its immediate neighbourhood, some of the
results obtained indicating the presence of an ammonio-cuprous,
as well as of an ammonio-cupric compound. No trace of metallic
zinc could be found.

304

Proceedings of the Eoyed Society

Anal yses.

The following are analyses of the substances, but much re-
liance cannot be placed on them, as they are each from a single
analysis of a very small quantity of substance.

I. Purple and lilac portion from interior, changing on exposure,
giving off ammonia, insoluble in water, and depositing brown
powder.

II. Pale blue, interspersed with white particles.

I.

II.

Cu .

21-67

26-77

Zn.

32-62

33-76

Cl .

27-08

2634

C03 (from C02)

10-10

6T6

NH4 ....

6-39

6 84

NH3 . •

212

...

99-98

99-87

On a Peculiarity of the Diurnal

Hygrometric

Curve at

Geneva. By Alexander Buchan, Esq.

In a work recently published by Professor Plantamour on the
climate of Geneva, the hourly means of the aqueous vapour of the
atmosphere for each month is given, deduced from observations
made during the twenty-seven years ending with 1875. The curves
drawn from these figures are undoubtedly the most remarkable of
the meteorological specialties of the climate of Geneva.

Professor Plantamour endeavours to explain the facts of the
diurnal hygrometric curves at Geneva by the ascending and
descending currents of air consequent on the diurnal march of the
temperature. These systems of air currents serve to explain a part
of the phenomena in question, — but only a part, and we think a
very small part. A reference to the curves at other places is suffi-
cient to show that this explanation is insufficient. There is
another cause to which the characteristic feature of the curves
is due, and that cause is the diurnal changes of the wind, which

305

of Edinburgh, Session 1876-77.

occur at Geneva, arising from its position with reference to Lake
Geneva, and from the qualities of these winds as determined by
the relative size of the lake.

The hourly variations in the direction of the wind show that the
land and lake breezes are strongly marked — the breeze from the
lake prevailing during those hours of the day when the tempera-
ture of the land is in excess of that of the lake, the land breeze
during the rest of the day. In December, when the land is at no
hour of the day warmer than the lake, no breeze from the lake sets
in over Geneva, and also in January the breeze from the lake is
but slight and of short continuance. These breezes leave their
impress in a most distinct manner on the curves of the hourly
variation of the vapour tension. During the winter months, when
no breeze from the lake, or but a feeble one, sets in, the vapour
curves show only one daily minimum, occurring about sunrise, and
one maximum, about 2 p.m., whereas during the other months, from
March to October, the vapour curves exhibit two daily minima, one
about or shortly before sunrise, and the other from 2 to 4 p.m., and
two maxima, one from 8 to 11 a.m., and the other from 6 to 10 p.m.,
according to season. Equally marked are the curves of the hourly
variations of cloud, the maximum during the winter months occur-
ring about sunrise, and the minimum about sunset. On the other
hand, during the warm months there are two maxima and minima
— the first maximum occurring about or shortly after sunrise, and
the second, but by far the larger maximum, about 6 p.m., and the
two minima shortly after midnight, and from 9 to 11 a.m.

The explanation of these instructive phenomena is doubtless to
be found in the size of Lake Geneva, which is large enough to
occasion a strong breeze during the day from the lake all round its
shores. On the setting in of the breeze, the air conveyed by it,
having been resting sometime previously on the surface of the lake,
is necessarily moist, and while this state of matters continues the
first daily maximum of vapour tension is reached. As the breeze
continues, the current is necessarily drawn from higher strata of
the atmosphere, and being thus but a brief interval in contact with
the lake the air becomes constantly drier till the second daily mini-
mum occurs, from 2 to 4 p.m. The breeze then gradually diminishes
in force, and the air consequently becomes moister, till the maxi-

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Proceedings oj the Royal Society

mum vapour tension of the day occurs about the time when the
breeze from the lake falls to a calm, and before the land breeze
springs up.

A cursory examination of the curves suffices to show that there
is a close connection between their critical phases and the corre-
sponding phases of atmospheric pressure and temperature; and the
idea is suggested that in this great contribution of Plantamour’s to
the meteorology of Geneva, we are put in possession of data of the
utmost importance as regards the relations of the vapour of the
atmosphere and its movements to changes of atmospheric pressure
in a way such as could be done by the observations of few observa-
tories.

5. On Knots. By Professor Tait.

(Abstract.)

At the last meeting of the Society I stated that I had just pro-
cured a remarkable essay by Listing, part of which bears on the
subject of knots, and that I had found in it an example of a change
of form not producible by the modes of deformation I had employed.

It had for some time struck me as very singular that, thoug I
could easily prove that (when nugatory intersections are removed)
a knot in which the crossings are alternately over and under is not
farther reducible, I could not prove all its possible deformations to
be producible by inversions or projections of the kinds specified in
my paper; but, as soon as I recognised the existence of amphi-
cheiral forms, I saw that it was probable that they would furnish a
key to my difficulty. I immediately set to work to classify the
simpler of such forms; and while I was thus engaged I got the
Gottinger Studien for 1847, in which is Listing’s paper, with the
title Vorstudien zur Topologie.

By this title Listing means qualitative as distinguished from
quantitative space-relations. He commences with a study of inver-
sion ( UmJcehrung ) and perversion (Verkehrung'), — the first being the
effect of a rotation through two right angles about any axis, the
second the result of reflexion in a plane mirror.

He next treats of screwing of all kinds, including twisting and
plaiting.

307

of Edinburgh, Session 1876-77.

He then applies the notion of lines winding or screwing round
one another to the projection of a knot on a surface, and shows that
we can thus obtain a knowledge of the relative situation of the
various coils. At each crossing portions of the two branches may
be regarded as small parts of lines twisted round one another. Of
the four angles so formed, two vertical or opposite ones are bounded
towards the right , the other two towards the left , by that line which
passes over the other. We thus distinguish these pairs of vertical
angles into right- and left-handed. [Listing uses right-handed for
what we should call left-handed in screwing, but the difference is
of no importance, so far as his results are concerned.]

Next he shows that perversion, but not inversion, changes right-
handed into left-handed angles.

He then gives the complete knot with three intersections, and
shows that when it is in a reduced (as distinguished by him from
a reducible ) form, all the angles in each separate mesh have a
common character; but that, when it is reducible, some of the
meshes have angles of both kinds. He distinguishes between the
right- and left-handed forms of the reduced knot, and shows that
they are not convertible into one another; also that (including
external space, or the Amplexum ) there are three meshes with two
corners each, and two with three corners; one class being right-
handed, the other left. And he states that the Amplex may be
made to change its character from right to left by being changed
from a three-cornered to a two-cornered mesh, or vice versa.

He points out that a loop (i.e., a mesh with only one corner) does
not appear in the reduced form, and then writes, as the type-
symbol of the reduced right-handed knot of three intersections, the
expression

3 r2 'i

2P ) ’

denoting three right-handed meshes with two corners each ( Oesen ),
and two left-handed meshes with three corners each ( Mascheri ).
[The perverted, or left-handed, form is of course represented by the
same symbols, with the interchange of r and l .]

The sum of the numerical coefficients in the symbol is the
number of meshes (the Amplex included), and is greater by two

2 s

VOL. IX.

308

Proceedings of the Royal Society

than the number of crossings. The sum of the products of the
coefficients into the corresponding exponents gives, in each of the
two parts of the symbol, double the number of crossings. These
symbols contain the topologic character of any particular knotting.

Listing next points out that the reduced three-crossing knot may
he obtained by three half-turns about one another of two originally
parallel cords whose ends are afterwards joined into one ring,
and that the character depends upon the direction of the torsion.

He proceeds to give a symmetrical knot, with seven crossings, in
two different reducible, and one reduced, forms. The reduction of
the first gives the three crossing knot, that of the second the four
forms of the essentially non-clear coil of five intersections. (Figs.
6-9 of my first paper.)

Their common symbol he writes as

2 >-4 + r2 |

2/3 + 2/2 j ,

and he points out that, in this case, the Amplex belongs to each
in succession of these four kinds of meshes.

He then states that the symbol

2r4 + 3r2 )

2Z5 + 2 12 I

gives five different reduced forms, each with seven crossings; while
the symbol

r5 + 3r3
Z4 + 2/3 + 2/2

has six distinct forms.

But he adds the following extremely important remark : — u In
certain cases one symbol is equivalent to another, so that the
reduced forms of the one can be transformed into those of the other.”
He states that this is the case with the last written symbol and the
following: —

2r4 + 2/’3
/4 + 2/3 + 21“

which has five reduced forms.

Thus there are, in all, eleven reduced forms of these kinds, all
equivalent to one another, and all having seven crossings. The

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of Edinburgh , Session 1876-77.

following are his figures: the first and second belonging to the
former of the two equivalent symbols, the third to the latter —

He concludes this part of his Essay by saying that u these
examples (confined as they are to single, closed lines), and the
remarks made upon them, serve to show that the fundamental
conception of twisting of lines is capable of being applied to the
most complex space relations.”

It may be added that these very elegant and important results
are given as statements merely, without any hint of how they were
arrived at, or how they may be extended. In fact brevity has
been sedulously studied, for all that is given about knots forms a
comparatively small part of the whole of Listing’s extremely valu-
able, but too brief, Essay.

The rest treats, rather more fully, the whole subjects of inver-
sion and perversion, screws of various kinds, plaiting and twisting,
(with their applications to vegetable spirals, &c.), the numbers of
jines joining given sets of points, the extensions of the meaning of
the word Area , &c., &c.

The above abstract, which contains almost all of Listing’s remarks
on knots, shows that he has long ago anticipated a very great deal
of what I have lately sent to the Society. For myself, however, I
may say that I have had to learn only two things (about knots) from
Listing, viz. (1), a special case (which will be examined imme-
diately), in which two forms are equivalent, though not transform-
able into one another by the methods given in my first paper; and
(2), to value more highly than I had hitherto done the method of
classifying forms by the numbers of each kind of mesh, and the
right-handed or left-handed character of each.

My first paper, as sent to the Society, was essentially confined
(as indeed its title indicates) to the results deducible from a special
elementary theorem, — one of two which occurred to me long ago

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Proceedings of the Royal Society

when designing Vortex- Atoms of various forms, and which I gave
to Section A at the late meeting of the British Association. The
second of these theorems (as will be seen by reference to my British
Association paper, Messenger of Mathematics , Jan. 1877), was virtually
the same as Listing’s division of the meshes of a reduced knot into
right- and left-handed, — only I called them black and white , but.
as I did not see how to connect this theorem directly with the measure
of beknottedness, I did not formally introduce it into my papers read
to the Society. It is, of course, virtually included in the state-
ments regarding coins thrown into the corners of cells, — for, taking
the case of the silver and copper coins, the pair of left-handed
vertical angles are those in which, or in one of them, there is
silver — the right-handed, copper.

Nothing can be clearer than Listing’s statements on several
parts of the subject : it is greatly to be desired that he had made
many more. Still, with a cordial recognition of the great value of
all that is to be found in Listing’s paper, I adhere to what I said
in my last communication, to the effect that the full character of
a knot cannot be learned except from its “ scheme,” or some-
thing equivalent to it. That the type- symbol (when such a repre-
sentation is possible) is ultimately equivalent to the scheme may
possibly be true,* especially when we consider that it virtually
contains two independent descriptions of a knot ( i.e . in terms of its
right-handed and its left-handed meshes separately) ; that for pur-
poses of classification it is superior is, I think, obvious, but I think
it equally obvious that for the purpose of drawing the knot it is
inferior. And the scheme for a reducible knot is quite as simple
as that for a reduced one, while it is not easy to see what would be
called the symbol of a reducible knot. Nor can I represent by

* (Added Feb. 7.) — I have just found symbols for which this is not the case.
The following single instance is sufficient, for the present, to show that the
type-symbol is not always equivalent to the scheme. The symbol

r4 + 2 r3 4- 2 r2 )

P+P+P+P ]

may represent either a continuous curve with 7 intersections, or a complex
system consisting of a circle intersected at six points by a skewed figure of
8. I shall discuss the subject fully in a paper “ On Links,” which I have
in preparation.

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of Edinburgh , Session 1876-77.

Listing’s notation the double trefoil knot which has appeared in
each of my papers ; for, although irreducible (at least so far as I
am aware), it contains several meshes which have angles of essen-
tially different characters. Listing’s avowed object was to simplify
notation as far as possible. My impression is that, in one respect
at least, he has carried simplification a little too far; for it cost
me some little time and trouble to draw, from his type-symbol,
the one knot which he speaks of, but leaves undrawn, viz., as
above, —

2r4 + 3r2 )

2Z5 + 2l2 J

Here is one of its forms: transformation will give the four
others.

In fact the type-symbol, even in this specially simple and symme-
trical case, where it is much condensed, contains just as many sepa-
rate typographical characters as the scheme ; and I think there can
be no doubt whatever that it is almost incomparably more easy to
draw the figure from the scheme than from the symbol. Given the
scheme, the symbol can be formed from it in a moment; while the
finding of the scheme from the symbol is very troublesome. But in
such a matter experience is the only guide, and I have had almost no
practice in trying to draw from the symbol. Listing’s type-symbol
leads directly, however, to an inquiry not even suggested by the
scheme; (for the latter, as I have given it, is essentially confined to
a single closed curve), — viz., the forms of more than one closed
curve, intersecting one another or not, which jointly divide an
unlimited plane into given numbers of meshes with given numbers
of sides.

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Proceedings of the Royal Society

The first idea of this was suggested to me when I endeavoured to
draw the curve with six intersections, whose type symbol is

This symbol obviously satisfies the three numerical conditions;
but, on trying to draw the corresponding figure, I found that it
always came out as a species of endless chain of three separate
links. One of its forms, from which the others can be found by
transformation, is three circles, every two of which intersect.

Two figures of 8, linked together at each end. give the symbol

And by shifting the twist from one to the other, as explained in

I have not as yet studied the theory of type-symbols, as it differs
so much from my own method; but it is obviously desirable to find
the criterion by which to distinguish from one another the type-
symbols necessarily denoting one closed curve, and those neces-
sarily denoting two or more intersecting curves. It is probable that
there are symbols which may represent either kind of figure. The
inquiry will no doubt be found very simple, if only approached from
the proper side.

I now pass to the sole point of Listing’s paper which (so far as
knots are concerned) was thoroughly new to me, though not unex-
pected ; and I shall lead up gradually to the special case which he
gives, using for the purpose the properties of the amphicheiral knots
mentioned in my last paper.

To apply the amphicheiral property to the production of new
forms, we may begin by studying under what conditions the internal
arrangements of a knot can be altered while four points of its con-
tour, and two of the parts of the cord or wire joining pairs of these,
are fixed. [The reason for the number four is, that when two only

3r4

2*3 + 3*I 2

the latter part of this paper, the symbol may be changed to

r4 + 2r3 + r2
2Z4 + 2 12

}■

of Edinburgh , Session 1876-77.

313

are employed to mark off separate parts of a knot, it is either (a)
virtually unconstrained, or ( b ) it is divisible (and is actually divided)
into two separate knots.] If, under these circumstances, changes
can he made on one side of the fixtures, they will be practicable
also in whatever way these points be connected by the rest of the string
provided always that it be not led through the amphicheiral part.
Hence, if there be an amphicheiral part of any knot, it may often
be transformed in situ ; the rest of the knot being unaltered, but
the amphicheiral part being made to present, as it were, another
hand to the rest.

To begin with a very simple case, let us take the simplest amphi-
cheiral form — the complete knot with four crossings—as below.

1. 2.

When the first of these is inverted, 0 being within either of the
interior three-sided meshes, the second is produced : if 0 be in one
of the boundary three-side meshes the perversion of the second is
produced. But we may easily convert 1 into 2 by fixing the lower
crossing (i.e., by fixing a point near it in each of the four lines
diverging from it, so that the dotted part remains fixed), and making
the upper loop rotate so as to banish the upper crossing* Thus
the upper parts of these two figures are equivalent.

And we can now suppose the (dotted) portions between the fixed
points to be cut open and reknotted in any way we choose, —subject,
of course, always to the rule of alternate over and under, else the
knot would in general be reducible. Of course, unless we wish to
study linking , the ends must be joined so as to preserve con-
tinuity throughout the string.

The simplest modes of joining (without additional intersections)
give us at once two different aspects of the same “ trefoil5’ knot :
— with one crossing additional we have the original figures

314

Proceedings of the Royal Society

(1 and 2) above: with two additional we have the following, —
figured in my first paper.

With three we have two apparently different forms,

These are, however, only transformations of the six-crossing amphi-
cheiral form (figs. 3 and 4 of my last paper), and are directly trans-
formable into one another. They are, of course, unchanged if the
lower part be reversed, for the upper parts are symmetrical.

But when we add four new crossings, as below, instead of the
single crossing removed, we get the two equivalent figures

which are not transformable into one another by the processes of
my first paper. In fact the schemes will be found to be incom-
patible, begin each where we choose. In Listing’s notation their
type-symbols would stand respectively, thus —

2h -f- 2r3 'j C r5 _j_ ^4 _j_ r3 _|_

2? + 3 P j and (2^ + 3^

The schemes are

AEBFCBDABGBCGD I A and ADBFGABGBBBFGC | A.

j

But even this simplest amphicheiral form has other applications.

315

of Edinburgh, Session 1876-77.

Thus, it will easily be seen that the figures below are mere distor-
tions of fig. 2 above ; and that, the dotted parts being fixed, they
can be changed on an actual cord into one another, and even
reversed (as from left to right), thus giving four distinguishable
forms, of which I figure only two,-—

Each of these may be changed without undoing the fixtures to its
reverse (from left to right) by the first simple process just described,
the loop, in fact, being transferred from one branch of the (undotted)
cord to the other.

Of course the number of ways in which the dotted part can be
varied is infinite. I therefore give here only that which reproduces
the forms already quoted from Listing as equivalent.

r5 + 3r3 ) f 2r4 + 2 r3

Z4 + 2Z3 -f 2P j an tZ4 + 2t3 + 2Z*

which are those already quoted from Listing.

In fact, looking at Listing’s figures above, we see that in each
there is a part of the curve, containing four crossings, exactly the
same as one or other of the two (partly dotted) distortions of the
4-crossing knot above.

The paper contains many other instances of these applications of
amphicheiral forms.

In conclusion, it appears that the problem of finding all the abso-
lutely distinct forms of knots, with a given number of intersections, is
a much more difficult one than I at first thought; and it is so because
the number of really distinct species of each order is very much less
than I was prepared to find it. The question now belongs more to

VOL. ix. 2 T

316

Proceedings of the Royal Society

quantitative than to qualitative relations. It resembles, in fact,
the species of problem originally suggested by Crum Brown, and
resolved by Sylvester and Cayley, of determining the number of
conceivable Hydrocarbons under given conditions of limitation.
And here I am glad to leave it, for at this stage it is entirely out
of my usual sphere of work, and it has already occupied too much
of my time.

[April 1 Uh. — Prof. Listing, to whom I sent in “ proof” the
above abstract of part of his paper, has kindly written some re-
marks upon it, from which I extract the following very interesting
passages, which increase our regret that such a master has pub-
lished so little on a subject which he has evidently made his own : —

“ [n dem . . . proof . . . sollte die Aufmerksamkeit vorzugs-
weise auf den allerdings sehr kurzen Theil gelenkt werden, welcher
sich auf die Knoten oder Curvenverschlingungen bezieht. Ander-
enfalls wiirde ich gewiinscht haben, dass das — obwohl sehr ele-
mental — Capitel iiber die ‘ Position ’ etwas nalier besprochen worden
ware, zumal darin das Motiv zu finden, warum ich uosere gewohn-
liche Schraube laeotrop nenne statt dexiotrop, wie Sie p. 307 riigen.
Ich habe langst die Benennungen rechts und links bei Schrauben-
windungen, sowie die lateinisclien oder griechischen Ausdriicke,
welche stets zu den widerwartigsten Yerwechselungen Anlass
geben, durch die Namen Delta- und Lambda- Windung ersetzt,
welche, wie p. 42 meiner Schrift erwahnt ist, mnemonish und in-
tuitiv die Vorstellungen fixiren. Der Botaniker — und einige haben
in der That diesen Modus befolgt — wiirde also dem Humulus lupu-
lus Deltawindung, dem Convolvulus Lambdawindung zuschreiben,
so wie unsere kiinstliche Schrauben der Technik meistens Lambda-
Schrauben und nur in seltneren Fallen Delta-Schrauben sind.
Die Untersckeidung zwischen Inversion und Perversion im An-
schluss an sogenannte positive und negative Positionen ist nur ein
gelegentliches specielles Ergebniss.”

“Die Yerschlingungen cyclischer Curven im Baume d. h. die
Knoten betreffend, so sollten, wie in den ‘Yorstudien’ es nicht
anders erwartet werden durfte, die G-eometer auf die Bedeutsam-
keit dieses iiberaus schwierigen Theils der Topologie durch Auf-
zeigung einiger der einfachsten Anfange aufmerksam gemacht

of Edinburgh, Session 1876-77.

317

werden, z. B. durch Andeutungen iiber mogliche Bezeichnungs.
methoden, Symbole und dgl. durch welche wir, wie es die Wissen-
schaft in alien analogen Fallen zu erstreben hat, von der Intuition
zu den Begriffen fortzuschreiten vermogen. Die von mir em-
pfohlenen Symbole sollen nichts weiter sein als ein derartiger Fin-
gerzeig, und wenn ich auch ganz mit Ihnen darin xibereinstimme
dass das Schema einen Nodalcomplex leichter construirbar macht
als das Symbol, so bleibt doch das Schema viel weiter von dem
Begriffe entfernt als das Symbol, auch abgesehen von den auf
beiden Seiten noch iibrig bleibenden Vieldeutigkeiten. Wie frag-
mentar das, was ich vor 30 Jahren dariiber angedeutet habe,
gewesen, kann ich Ihnen unter vielen an dem einen Punkte
erlautern, dass ich mich dort nur auf die Yerknotung einer einzigen
cyklischen oder einer cyklodischen Curve beschrankte, und nur auf
solche Verschlingungen unter der Benennung * reducirt ’ einging,
deren sammtliche Parcellen (inch Amplexum) monotyp sind, wie-
wohl Ihnen selbst bekannt ist, dass es Knoten giebt mit Maschen,
deren Ecken promiscue 8 und A heissen, ohne auf einfachere For-
men, d. h. eine geringere Zahl von crossings reducirbar zu sein.
. . . Es verstekt sich von selbst, das die in den Vorstudien ange-
fuhrten Symbole nur auf monotype reducirte Complexe anwendbar
sind, hnd durch Verallgemeinerung andere Gestalten annehmen,
worauf ich indessen hier weiter einzugehen unterlasse.”

I have thought it better to give Listing’s own comments on my
remarks than to seek permission from the Council to alter these
remarks in the text.]

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH

vol. ix. 1876-77. No. 98.

Ninety-Fourth Session.

Monday , 19 th February 1877.

DAVID STEVENSON, Esq., Vice-President, in the

Chair.

The Chairman reported that the Council had awarded the
Makdougall-Brisbane Prize for the biennial period 1874-76,
to Alexander Buchan, M.A., for his paper “ On the Diurnal
Oscillation of the Barometer,” which forms one of an
important series of Contributions by Mr Buchan to the
Advancement of Meteorological Science.

The following Communications were read : —

1. On the Action of Sulphuretted Hydrogen on the Hydrate

and on the Carbonate of Trimethyl-sulphine. By Professor

Crum Brown.

(. Abstract .)

The investigation, of which this paper contains the first part, was
undertaken with the view of throwing light on the constitution of
salts of trimethl-sulphine.

These salts have been represented in two different ways — 1st,
as compound of tetratomic sulphur, and 2d, as molecular combi-
nations of sulphide of methyl with methylic ethers, just as the
ammonia salts have been represented as compounds of pentad nitro-
gen, or as molecular combinations of ammonia with hydric salts.

2 u

VOL. IX.

320

Proceedings of the Royal Society

It appeared to the author that facts having an important bearing
on the question, which of these is the better representation of the
constitution of such bodies, might be obtained by the study of the
sulphur compounds of trimethyl-sulphine, of the corresponding
selenium compounds, and of the intermediate substances.

The following list, in which each substance is formulated — a,
on the assumption of tetrad sulphur and selenium, and b , on the
supposition of molecular union illustrates this idea.

h.

(CH3)2S, ch3hs.

(CH3)2S, (CH3) 2S , (CHJ2S.
(CH3)2Se , CH,HS .

(CH3)2Se', (CH3)2Se, (CH3)2S.

(CH3)2S, CH3HSe.

(CH3)2S , (CH3)2S , (CH3)2Se .
(CH3)2Se , CH3HSe .

(CH3)2Se , (CH3)2Se , (CH3)2Se .

(CH3)_S , (CH3)2Se , (CH3)2Se .

(3) and (6), (5) and (7), and (4) and
(10) form three pairs of isomers.

Upon any theory (3) and (6) may be expected to be different, but
it is not so with the other two pairs. They ought to be different,
if the assumption of tetrad sulphur and selenium is correct, but
on the theory of molecular combination it is difficult to see how a
difference of properties could be accounted for.

The hydrate and also the carbonate of trimethyl-sulphine are
readily acted upon in the dry condition by sulphuretted hydrogen,
and the product is colourless if air has been rigidly excluded. The
characteristic reaction with nitroprusside shows the product to be
a sulphide or sulphhydrate, but the action of oxygen upon it is so
rapid that it has not yet been obtained in a condition fit for
analysis. Before attempting to prepare it in a state of purity, it
was thought best to examine the products of its oxidation. These
are — (1), an orange polysulphide, which in the presence of moisture

(CH„)2S , (CH3)2Se , (CH3)2S .

(1.) (CH3)3S— SH
(2.) ((CH3)3S)2S
(3.) (CH3)3Se — SH
(*■) ((CH3)3Se)2S

(5 ) S

W (CH3XSeb

(6.) (CH3)3S— SeH

(7.) ((CH3)3S)2Se

(8.) (CH3)dSe — SeH

(9.) ((CH3)3Se)2Se

(CH3)3Se

Of these it is obvious that

321

of Edinburgh , Session 1876-77.

and oxygen is further oxidised, with separation of yellow sulphur,
yielding (2) hyposulphite of trimethyl-sulphine.

The action is thus similar to that of sulphuretted hydrogen on
potash or carbonate of potash, but takes place with much greater
rapidity.

The examination of the sulphide and polysulphide of trimethyl-
sulphine will form the subject of the next part of the paper.

2. On Links. By Professor Tait.

(Abstract.)

Though in my former papers on knots I have made but little
allusion to cases in which two or more closed curves are linked
together, the method I have employed is easily and directly ap-
plicable to them. I stated to the British Association that the
number of intersections passed through in going continuously
along a curve, from any intersection to the same again, is always
even — whether it be linked with other curves or not Hence, even
when a number of closed curves are linked together, the intersec-
tions may be so arranged as to be alternately over and under along
each of the curves.

When this is done, each of the meshes has all its angles right or
left handed ; so that Listing’s type-symbols may be employed, just
as for a single knotted curve. The scheme, however, consists of
as many parts as there are intersecting curves — each part contain-
ing, along with each of its own crossings twice, each of its intersec-
tions with other curves once.

represents a couple of ovals linked together.

When three ovals are joined, so as to form an endless chain, we
have

Thus

AB | A AB | A

or

2r2

2P

A B C D | A DCEFjD FEBA | F

or

322 Proceedings of the Boyal Society

Of course such figures can be transformed or deformed according
to the methods given in my first paper — the scheme and the type-
symbol alike remaining unaltered. And alterations of both scheme
and symbol are, in various classes of cases, producible by the pro-
cesses of my last paper without any change of links or linking.

The genesis of the scheme of a link may be most easily studied
by forming a knot into a link. This is done by cutting both turns
of the wire at any junction, and joining them again so as to make
two closed curves instead of one. No intersections are lost by this
process, except that which was cut across, provided, of course, that
the original knot had no nugatory intersections, and that none are
rendered nugatory by the operation of cutting the whole across.

Any crossing with four adjacent crossings when the turns of the
coil pass alternately over and under one another will appear in a
scheme as follows : —

AXB C X D . . . .

— I — + - +

implying that from X through B and C back to X forms one con-
tinuous circuit; similarly from X through D and A back to X.

There are but two ways in which continuity can be kept up if
we cut the cord twice at X, and reunite the ends in a different
arrangement from the original one.

It is obvious that if we pass from C to B, by way of X (abolished),
and similarly with the rest, we divide the continuous closed curve
into two separate (but generally inter-linked) closed curves. If
we pass from A, by way of X (abolished) to C, we pass thence in
time to B, and finally by way of D to A. Thus the curve remains
continuous, but with one intersection less than at first. And, in
either case, the alternate order of the signs of the crossings will be
maintained throughout.

In the former of these modes we take the part containing C and B
(and we may, if we please, also take the rest) in the same order as
before the change. The scheme is therefore, without any other
change, simply divided into two parts, which are separated from
one another by the (abolished) junction X in its two positions.

In the second mode, it is obvious that the letters in one of the
two parts separated from one another by the mark X in its two
places are simply to be inverted in order without change.

323

of Edinburgh , Session 1876-77.

The process presents no difficulties, so that I shall give only two
simple examples. Thus the scheme of the pentacle, viz. : —

ADBEC ADBEC | A

is divided at A (in this case it does not matter which junction we
take) into the two superposed non-autotomic ovals

DB EC | D, DBEC | D,
by the first mode : — , and is simplified into

DBECCEBD | D

(• i.e ., a wholly nugatory scheme) by the second.

The type-symbols in the original state, and in the two altered
states, are, respectively,

2r5 I

5 l2 1

2 r4 1
4 l2)

r' ' \

2>l2 + 21 )

The last of these is virtually nothing. In fact, terms in
r or l to the first power are rejected by Listing. And, when
these loops are taken off by untwisting or by opening up, the scheme
becomes

r4 )

l2 + 21 )

and a second application of the process removes the whole.

Operating in a similar way upon the only other figure with five
non-nugatory intersections — viz. : —

A4D4B2E2C2A4D4C2E2B2 I A
2 v*4 + r2 )

2P + 12 i

we find three classes of cases, according to the particular intersec-
tion operated on.

[I may here introduce, though it involves a slight digression, a
method which I have found very convenient as an assistance in
finding which intersections have similar properties as regards the

324

Proceedings of the Royal Society

figures which will be obtained when they are made in turn the
point of section. In the scheme above written the suffixes express
the numbers of letters which intervene, in the scheme, between the
two appearances of the same letter. If n be the whole number of
letters, the suffix may of course be either 2 r or 2n - 2r - 2. It is
convenient to write always that one of these two numbers which is
not greater than the other. When a particular suffix occurs only
once, the corresponding crossing has evidently different properties
from the others ; if twice, we find in general that the corresponding
crossings have similar properties. If three times, two of them have
usually like properties, but the third not — and so on. This method
is useful, but it is in certain cases misleading. In fact, we must
look not only at the suffix itself, but at the place which it occupies
relatively to the whole group of suffixes, in order to obtain absolutely
definite information. Something similar to this is obviously hinted
at in Listing’s paper, where he seems to determine the number of
possible transformations of the figure representing a symbol, by
treating the numerical coefficients much as I have here treated the
suffixes. But this is mere conjecture on my part.]

By this method then, or by examining the diagram, we see that
A and D are similar, so are B and C, while E may possibly possess
distinct properties of its own. We need, therefore, take only three
cases, A, B, and E,

a.) Divide at A. Then we have either
DBEC | D DCEB | D

two ovals crossing one another, one taken right handed, the other
left ; or

DBECBECD | D = BECBECIB

2r3 )

3 12 I

the trefoil knot ; for D becomes nugatory.

b.) Divide at B. We have either
A D | A ECADCE | E = DA |

2r2 )

2 12 1

D

325

of Edinburgh, Session 1876-77.

two linked ovals, C and E having become nugatory ; or

ECADCEDA | E

2 r3 + r2 )

2Z3 + Z2 1

an amphicheiral knot, the only knot with 4 intersections,
c.) Dividing at E we find the same results as for B and C.

From the rules just given for removing an intersection, it is of
course easy to pass to those required for the introduction of a new
intersection.

In endeavouring to frame a general method of determining
whether a particular type-symbol necessarily denotes one continuous
curve, or a superposition of two or more curves, I was completely
unsuccessful. But, as indicated in a note to my last paper, I found
the reason to be that no such distinction necessarily exists. And by
the application of the methods of adding or removing intersections
given, I found a number of instances in which the same type-sym-
bol may represent many entirely different kinds of figures. Thus
the following

are all represented alike by the symbol

r5 _j_ ^4 r3 + r2 |

Z4 + 2Z3 + 2Z2 j

But I have since succeeded in obtaining cases in which the same
type-symbol represents two perfectly distinct single closed curves.
One instructive example is the following

326 Proceedings of the Royal Society

The common type-symbol is

r5 + r4 + r3 + 2 r2 I
P+l* + P + 2P /

But the schemes are

A,E6B4G8C6H6D6B4EoA0F!Cea6F2HliD8

and

A 6D4B2H4C6F4D4A8E4G2F4C6G2E4A ,b.

Now no change in lettering can affect the suffixes, so that the
two schemes are essentially different. In fact the sum of the suf-
fixes is 84 in the first scheme, but only 64 in the second. The
first has only one degree of beknottedness, the second has two.
The first is not amphicheiral, the second is.

There is no connection between the type-symbol, as Listing gives
it, and the singleness or complexity of the curve represented, but it
is possible to make analogous symbols capable of expressing every-
thing of this kind. Only we must now adopt something very much
resembling Crum Brown’s Graphical Formulae for chemical compo-
sition. Some very remarkable relations follow from this process, but
I can only allude to a few of the simpler of them in this abstract.

The only necessary relations among the numbers forming the
right or left part of a symbol are satisfied if no one is greater than
the sum of the others, and if the sum of all is even. With any set
of numbers subject to these conditions, we can form the right or
left-hand side of a symbol-— and from that we can form the other
when we know the grouping.

An example or two will make this clear. Take, for instance, the
symbol

2r4 + r2 )

W + P J

which represents the five-crossing knot of p. 242 above.

A glance at the figure shows that the following is the arrange-
ment of the right-handed meshes.

2

/ \

yA — — p4

the single mesh with two corners having one of these corners in
common with each of the two four-sided meshes, which again

327

of Edinburgh, Session 1876-77.

have three corners in common. Hence in this notation the joining
lines represent the crossings. Hence also the characters of the left-
hand meshes are obvious from the figure. Outer space has the
three external lines for corners — inside there is one triangle and
two spaces bounded by two lines each (i.e.9 with two corners). Thus
we reproduce the left-hand part of Listing’s symbol. But the
figure also shows us which lines (corners) each pair of these has in
common, and enables us at once to draw the annexed figure

which gives us exactly the same information as the first, only from
a different point of view.

The connections in the former figure cannot be varied, so that,
in this particular case, Listing’s symbol for the right-handed meshes
alone suffices to draw the figure; at least if nugatory crossings be
rejected. Such would arise, for instance, if we tried to draw the
symbol in the form

r2

II

7*4

11

r4

O

which would give three ovals joined like the links of a chain— the
last having an internal nugatory loop. In this case the second part
of the symbol would be

P + 2P + 1

where the nugatory character of one intersection is clearly ex-
hibited.

But, if we had merely the left-hand part of the symbol given us,
we might adjust it thus

1 2

3 28 Proceedings of the Royal Society

which would correspond to

r4 + 2 r3

for the right-handed part, and would give us the form

or one of its deformations.

The criterion by which to distinguish at once whether such
symbolic representations as those just given represent knots or links
is easy to find. If we remember that each of the (even number of)
crossings lying on a closed curve is a corner of one black and of one
white mesh (contained within the curve) — while each of the crossings
lying within it is a corner of each of two white and of two black meshes
— we see that unless we can enclose a part of the graphic symbol in
such a way that the sum of the exponents within the enclosure,
and that formed by the doubling of the number of the joining lines
which are wholly within the enclosure, and adding it to the number
of those which cut the boundary, are equal even numbers — the figure
is necessarily a knot. But if we can enclose such a part, it requires
to be farther examined to test whether the figure consists of links
or is a single knot.

Thus, in the example just given, the part

/\
p — p

\/

is a simple oval divided by two intersecting chords into three-
cornered meshes — but in the following formula

r2

Z\

/v* 3

although the par

seems to fulfil the conditions above, it does not represent a separ-

— -

329

of Edinburgh, Session 1876-77.

ate closed curve. In fact, the upper line represents a crossing on
the boundary , at which there is (internally) only a left-handed
mesh, which is impossible if the boundary were a closed curve.

And the lowest line in the figure is a point in the boundary
which forms- a common vertex of three (internal) meshes, two right
and one left-handed. This, also, is inconsistent with the boundaiy’s
being a closed curve.

There is only one other case which may cause a little trouble.
It can easily be seen by the fig. of last page. For we may take out
the following part of the symbol

P

which must obviously represent the lemniscate in the figure. Its
exponents and lines do not satisfy our condition : but they will
do so if we remove the diagonal line— which corresponds to what
is (in the lemniscate when alone) a nugatory intersection.

I conclude by giving the representations, according to the
method just explained, of some of the preceding figures. Thus
the three first figs, of p. 325 are, respectively,

/

P — P = P

\ /
W

73

II \
l4_P

while the pair of common-symbol knots on the same page are
P—P r2

Z5=Z4

and

It may be observed that the present method gives great facilities
for the study of cases in which knots are reduced, or are changed

330

Proceedings of the Royal Society

into links, by the removal of an intersection. For, to take off an
intersection is easily seen to be equivalent simply to rubbing out
one connecting line in the figure, and simultaneously diminishing
by unity each of the exponents at its ends. If it be the only line
connecting these exponents, they are (after reduction by unit
each), to be added together. And this consideration enables us
to obtain, even more simply than before, the rules for distinguish-
ing a knot from a link. I propose, when I have sufficient leisure,
to re-investigate the whole subject from this point of view.

Meanwhile I may notice that it is exceedingly easy to draw the
outline of any knot or link by this method. All that is necessary is
to select a point in each of the lines in the figure, and join (two and
two) all these points which are in the boundary of each closed area.
The four lines which will thus be drawn to each of the chosen
points must be treated as pairs of continuous lines intersecting at
these points, and at these only. When there are only two sides —
and, therefore, only two points — in an area, two separate lines must
be drawn between them, and these must cross one another at each
of the two points.

The annexed diagram shows the result of this process as applied
to the following symbol

5 r— rf 5

fy» 5 /v»5

This method also clears up in a remarkable manner the whole

331

of Edinburgh, Session 1876-77.

subject of change of scheme of a given knotting which was dis
cussed in my last paper. To give only a very simple instance,
notice that the first of the changes there mentioned is merely that
from

/ 2 \

m - n

ii ii

to

m — n
llX2/||

where the double lines may stand for any numbers of connection
whatever.

I conclude by stating, in illustration of the remarks made at
the end of my last paper, that I have hastily (though I hope cor-
rectly) investigated the nature of all the valid combinations among
720 which are possible in the even places of a scheme correspond-
ing to 6 intersections (only 80 of these are not obviously nugatory)
— and that'I find only four really distinct forms . They are

1. Two separate trefoil knots. Here there are two degrees of
beknottedness.

2. The amphicheiral form. (Figured on p. 295 of my Note on Be-
knottedness. Also in a clear form in the last cut of my first paper.)

3. Fig. p. 297 of the same paper. These two forms are essen-
tially made up of a trefoil knot and a loop intersecting it.

4. The following knot, which belongs to a species found with
every possible number of crossings from 3 upwards. This species
furnishes the unique knots with 3 and with 4 crossings, and one of
the only two kinds possible with 5.

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Proceedings of the Boyal Society

Its symbol is always of the form

2 r3 + (n ~ 3 )r2
2 +

| or more fully

/i\

0*-l) = (w-l),

there being n — 2 lines in the lower group.

The three last forms have each essentially only one degree of be-
knottedness. In certain cases (see the foot note ante p. 296) we may
give two degrees of beknottedness by altering some of the signs
— but the knot has then one nugatory intersection, and falls into
the class with five crossings.

A number of curious problems are suggested by the process
which I employed in the investigation of these six-crossing forms.
I give the following as an instance.

Take any arrangement whatever of the first n letters : — Say, for
instance,

CND A . . . LE.

change each to the next in (cyclical order, so that A becomes B,
B becomes C, . . . . , N becomes A) and bring the last of the
row to the beginning. The result is

FDAEB . . . . M.

After performing this operation n times we obviously get back the
arrangement from which we started. [Thus in seeking all the
different forms of knots of a given number of crossings, one alone of
this set of n need be kept.] The problem is to find sets such that
the original combination is repeated after m operations like that
above. It is obvious that if m is to be less than n it must be an
aliquot part of it, and thus n must be a composite number.

\_Ayril 11. — The references to Listing’s type-symbol here given
must be taken in connection with the extracts from his letter, ante ,
p. 316.]

3. Laboratory Notes. By Professor Tait.

(a.) Measurement of the Potential, required to produce Sparks of
various lengths, in Air at different pressures, by a Holtz
machine. By Messrs Macfarlane and Paton.

The general result of these strictly preliminary experiments
appears to show that for sparks not exceeding a decimetre in length

333

of Edinburgh, Sessio?i 1876-77.

(L), taken in air at different pressures (P), between two metal balls
of 7mm,5 radius, the requisite potential (V), is expressed by the
formula

V ccP JL.

The Holtz machine employed is a double one, made by Ruhm-
korff, and it was used with its small Leyden jars attached. The
measurements had to be made with a divided-ring electrometer,
so that two insulated balls, at a considerable distance from one
another, were connected, one with the machine, the other with the
electrometer. With P constant the curve for V closely resembles
a parabola between L = 0 and L = 60ram, but for higher values of L
it appears to tend towards an asymptote at a finite distance from the
axis. Thus it would seem that to double the length of very long
sparks under these circumstances, a comparatively small percentage
increase of potential will suffice. This may enable us to explain
some singular peculiarities of lightning. Mr Macfarlane intends
to work up this subject very thoroughly, with the help of Thom-
son’s Long Range Electrometer.

(6.) The Thermal Conductivity of Gas Coke. By Messrs Knott

and Macfarlane.

The method employed was the same as that described (Proc.
VIII. 623) , but the high conducting power of gas coke for elec-
tricity made the experimental work very difficult. The results, so
far, are not very consistent with one another, but they appear to
point to a diminution of conductivity by rise of temperature.

(c.) Preliminary Experiments on the Currents produced by contact
of Wires of the same metal at different Temperatures. By
Messrs Knott and Macfarlane.

These experiments, so far as they go, confirm the results
formerly obtained by Mr Durham, Proc. VII. 788.

(d.) On the Relative Percentages of the Atmosphere and of the
Ocean which would flow into a given Rent in the Earth’s
Surface. By Professor Tait.

The note had reference to some sensational statements recently

334

Proceedings of the Royal Society

made under the the title “ Are we drying up.’' But it led also to
a curious hydrostatical question as to the equilibrium arrangement
of water poured into a shaft already full of air, and supposed to be
so deep that in its lower parts the air is compressed to a density
exceeding that of water. This suggested numerous questions,
such as : What addition to the atmosphere would raise the sea
from the earth’s surface ?

Monday , 5 th March 1877.

Sir WILLIAM THOMSON, President, in the Chair.
The following Communications were read : —

1. On the Biliary Secretion with reference to the Action of
Cholagogues. By Prof. Butherford, F.R.SS. L. & E.,
and M. Yignal.

(Abstract.)

Notwithstanding the fact that substances supposed to affect the
flow of the bile have been administered to man for more than 2000
years, there is still very great uncertainty as to what does and what
does not augment the biliary excretion. The indefinite state of
knowledge regarding this point is due to the circumstance that
variations in the flow of bile from the human liver are estimated by
simply observing the colour of the dejections, — a method that is of
necessity exceedingly rough, for it is impossible thus to detect
slight variations in the excretion of bile, especially when, as in the
case of rhubarb, the substance gives to the dejections a colour
similar to that of the bile, and where, as in the case of sodium
sulphate, the substance gives rise to copious dejections of a watery
character, whereby the colour is diluted.

Even in the case of those substances generally believed to
augment the biliary flow, e.g., podophylline, observations on man
have entirely failed to determine whether they merely occasion an
expulsion of bile from the gall bladder, or an increased secretion
by the liver. The determination of the point is of great import-
ance in scientific medicine, for it is calculated to advance our

335

of Edinburgh, Session 1876-77.

knowledge of the nature of the diseased condition relieved or cured
by the cholagogue.

By experiments on animals, both of the above-mentioned diffi-
culties may be overcome, and definite knowledge arrived at.

The want of precise knowledge in this department of thera-
peutics induced Nasse, Kolliker, and Muller, Scott, Hughes
Bennett, and Rohrig to perform some experiments ; but the results
have been limited and unsatisfactory, owing to the faultiness of
the experimental methods adopted.

In the present research the experiments have been performed
on dogs, fasting and curarised, in order that the secretion of bile
might be rendered constant. The bile was continuously collected
from the common bile duct, and measured every fifteen minutes,
and the flow of bile into or out of the gall bladder was eliminated
by clamping the cystic duct. The results obtained are as follows: —

1. In a curarised dog that has fasted 18 hours, the secretion of
bile is tolerably uniform during the first four or five hours after the
commencement of the experiment, but falls slightly as a longer
period elapses. Its composition remains constant.

2. Croton oil is a cholagogue of feeble power. The high place
assigned to it by Rohrig was probably the result of his imperfect
method of experiment.

3. Podophylline is a very powerful stimulant of the liver. During
the increased secretion of bile, the percentage amount of the special
bile solids is not diminished. If the dose be too large, the secre-
tion of bile is not increased. It is a powerful intestinal irritant.

4. Aloes is a powerful hepatic stimulant. It renders the bile
more watery, but at the same time increases the excretion of biliary
matter by the liver.

5. Rhubarb is a certain though not a powerful hepatic stimulant.
The bile secreted under its influence has the normal composition.

6. Senna is a hepatic stimulant of very feeble power. It renders
the bile more watery.

7. Colchicum increases to a considerable extent the amount of
biliary matter excreted by the liver, although it renders the bile
more watery.

8. Taraxacum is a very feeble hepatic stimulant.

9. Scammony is a very feeble hepatic stimulant.

2 Y

VOL. IX.

336

Proceedings of the Royal Society

10. “Euonymin,” an impure resinous matter prepared from the
bark of Euonymus atropurpureus , is a powerful hepatic stimulant.
It is not nearly so powerful an irritant of the intestine as
podophylline.

11. “ Sanguinarin,” an impure resinous matter prepared from
the Sanguinaria canadensis , is a powerful hepatic stimulant. It
also stimulates the intestine, but not nearly so powerfully as podo-
phylline.

12. “ Iridin,” an impure resinous matter prepared from the root
of Iris versicolor , is a powerful hepatic stimulant. It also stimu-
lates the intestine, but not so powerfully as podophylline.

13. Leptandria is a hepatic stimulant of moderate power. It is
a feeble intestinal irritant.

14. Ipecacuan is a powerful hepatic stimulant. It increases
slightly the secretion of intestinal mucus ; but has no other appa-
rent stimulant effect on the intestine. The bile secreted under
the influence of ipecacuan has the normal composition.

15. Colocynth is a powerful hepatic as well as intestinal stimu-
lant. It renders the bile more watery, but increases the secretion
of biliary matter.

16. Jalap is a powerful hepatic as well as intestinal stimulant.

17. Sodium sulphate is a hepatic stimulant of considerable
power. It also stimulates the intestinal glands.

18. Magnesium sulphate is an intestinal but not a hepatic stimu-
lant.

19. Potassium sulphate is a hepatic and intestinal stimulant of
considerable power. Its action on the liver is, however, uncertain,
probably owing to its sparing solubility.

20. Sodium phosphate is a powerful hepatic, and a moderately
powerful intestinal stimulant.

21. Eochelle salt is a feeble hepatic, but a powerful intestinal
stimulant.

22. Sodium chloride is a very feeble hepatic stimulant.

23. Sodium bicarbonate has scarcely any appreciable effect as a
hepatic stimulant.

24. Potassium bicarbonate has scarcely any appreciable effect as
a hepatic stimulant.

337

of Edinburgh, Session 1876-77.

25. Mercuric chloride is a powerful hepatic stimulant. Its
stimulant effect on the intestinal glands is feeble.

26. Calomel is a powerful stimulant of the intestinal glands,
but does not increase the secretion of bile.

27. Ammonium chloride has no stimulating effect on the liver of
the dog.

28. Castor oil stimulates the intestinal glands, hut not the liver.

29. Gamboge stimulates the intestinal glands, but not the liver.

The foregoing results, although adding greatly to our know-
ledge, are in complete harmony with observations on man in every
case, save those of calomel and ammonium chloride ; but the
want of harmony is probably more apparent than real, for there is
no evidence that in man these substances really do excite the
hepatic cells. They may possibly occasion merely expulsion of
bile already secreted, or may act on the liver in other ways. The
general conclusions of the research are as follows

1. That, as the liver of the dog is affected by medicinal agents
in the same sense as the human liver, this animal is suitable for
observations that cannot be made on man.

2. The attention of medical men is hereby directed to a number
of valuable cholagogues, such as euonymin, sanguinarin, iridin,
ipecacuan, sodium phosphate, sodium sulphate, &c., hitherto but
little or not at all employed as such, owing to the absence of
positive information regarding their actions.

3. As regards the whole question of hepatic pharmacology,
definite is hereby substituted for indefinite knowledge ; for it is not
only shown what substances really do act as cholagogues, but it is
proved that they all, excepting calomel and ammonium chloride,
really do stimulate the liver to secrete more bile.

4. It is shown that, as such substances as magnesium sulphate,
gamboge, and castor oil do not increase the secretion of bile,
although they irritate the mucous membrane of the duodenum and
the remainder of the intestine, the action of stimulants on the
secreting apparatus of the liver is probably not reflex from the
intestinal mucous membrane, but a direct action either upon the
hepatic cells or upon their nerves.

5. It is shown that when a purgative substance is not a chola-
gogue it diminishes the biliary secretion. The importance of a
knowledge of this fact is indicated.

338

Proceedings of the Royal Society

2. Specimen of Auriferous Quartz. By Patrick Dudgeon.

The specimen was found near Wanlockhead, Dumfriesshire, in
1872, by Andrew Gfemmell, miner, who unfortunately broke up the
piece, and disposed of the fragments to different parties in the
locality. Mr Dudgeon was enabled to get possession of all the
fragments, and has restored the mass to its original form. The
specimen is a very interesting one, being the largest known piece
of auriferous quartz found in Scotland ; and Mr Dudgeon thought
it would interest the fellows of the Society to exhibit it at the
meeting before placing it in the Museum of Science and Art, which
has now been done with the consent of the different owners.

The following Gentlemen were elected Fellows of the
Society : —

George Broadrick, C.E., Claremont Cottage, Leith.

John Napier, Engineer, Lancefield House, Glasgow.

James King, of Campsie, 12 Claremont Terrace, Glasgow.

George Cunningham, C.E., 2 Ainslie Place.

Monday , Vdth March 1877.

Sir WILLIAM THOMSON, President, in the Chair.

The following Communications were read : —

1. On a Problem of Arrangements. By Professor Cayley.

It is a well-known problem to find for n letters the number of
the arrangements in which no letter occupies its original place;
and the solution of it is given by the following general theorem : —
viz., the number of the arrangements which satisfy any r condi-
tions is

(1 - 1)(1 - 2) .... (1 - 0 ,

= 1-2(1) + 2(12) . . . ±(12 . . .r),

where 1 denotes the whole number of arrangements; (1) the
number of them which fail in regard to the first condition ; (2)
the number which fail in regard to the second condition ; (12) the
number which fail in regard to the first condition, and also in

339

of Edinburgh, Session 1876-77.

regard to the second condition ; and so on : 2(1) means (1) + (2)
... +(r): 2(12) means (12) + (13) + (2 r) ... + (r - 1, r) ; and so
on, up to (12 .... r), which denotes the number failing in regard
to each of the r conditions.

Thus, in the special problem, the first condition is that the
letter in the first place shall not be a; the second condition is
that the letter in the second place shall not be b ; and so on ;
and taking r = n , we have the known result, No. =

_ 71 , „ s n.n —

Tin — jll(?2 - 1) + — y~2 — ^ (w - 2). + . . =t=

01 . n — 1 ..2.1

“iTF.TTtT' ’

= 1.2.3... » I 1-- + A- - ± — I — ]

1 1 1.2 1.2.3 1. 2. 3. . .» J

giving for the several cases

w = 2,3,4, 5, 6, 7, . .

No. = 1,2,9,44, 265, 1851 . .

I proceed to consider the following problem, suggested to me by
Professor Tait, in connexion with his theory of knots : to find the
number of the arrangements of n letters a b c . . j h , when the
letter in the first place is not a or b , the letter in the second place
not b or c, . . . the letter in the last place not h or a.

Numbering the conditions 1,2,3 . . n , according to the places
to which they relate, a single condition is called [1] ; two condi-
tions are called [2] or [1 , 1], according as the numbers are conse-
cutive or non-consecutive : three conditions are called [3], [2 , 1] or
[1,1,1], according as the numbers are all three consecutive, two
consecutive and one not consecutive, or all non-consecutive; and
so on : the numbers which refer to the conditions being always
written in their natural order, and it being understood that they
follow each other cyclically, so that 1 is consecutive to on. Thus,
n = 6, the set 126 of conditions is [3], as consisting of 3 consecu-
tive conditions ; and similarly 1346 is [2,2].

Consider a single condition [1], say this is 1 ; the arrangements
which fail in regard to this condition are those which contain in
the first place a or b ; whichever it be, the other n- 1 letters may
be arranged in any order whatever; and there are thus 2 II (n— 1)
failing arrangements.

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Proceedings of the Boyal Society

Next for two conditions ; these may be [2], say the conditions
are 1 and 2, or else [1 , 1] say they are 1 and 3. In the former
case the arrangements which fail are those which contain in the
first and second places ab, ac , or be, and for each of these the other
n — 2 letters may be arranged in any order whatever; there are
thus 3 II (n- 2) failing arrangements. In the latter case the
failing arrangements have in the first place a. or b, and in the third
place c or d , — viz., the letters in these two places are a. c, a.d,
b.c, or b.d, and in each case the other n- 2 letters may be
arranged in any order whatever : the number of failing arrange-
ments is thus = 2 . 2 . II (n - 2) . And so in general when the con-
ditions are [a, p, y . .], the number of failing arrangements is
= ('0,4- l)(p + l)(y + 1) . . n(n - a - j3 - y . .) . But for [n], that is for
the entire system of the n conditions, the number of failing
arrangements is (not as by the rule it should be = n + 1 , but) = 2,
— viz., the only arrangements which fail in regard to each of the
n conditions are (as is at once seen), abc . .jk, and be. ..jka.

Changing now the notation so that [1], [2], [1,1], &c., shall
denote the number of the conditions [1], [2], [1,1], &c., respec-
tively, it is easy to see the form of the general result : if, for
greater clearness, we write n = 6, we have

1 -S(l) +2(12) -2(123)

No. = 720 - {([1] = 6)2} 120 + / ([2] =6)3 124-

( ((3]

= 6)4 \

\ + ([1,1] = 9)2.2/

+ ([2,1]

= 12)3.2 (

1 j / |

( + ([1,1,1]= 2.2.2)

+ 2(1234) -2(12345) +(123456)

+ ( ([4 )-6)5 n2 - {([5] = 6)6} 1 +{([6] = 1)2}

] +([3,1] = 6)4.2 1
(+([2,2] = 3)3.3)

or, reducing into numbers, this is
No. = 720 - 1440 + 1296 - 672 + 210 - 36 + 2 , = 80 .

The formula for the next succeeding case, n= 7, gives
No. = 5040 - 10080 + 9240 - 5040 + 1764 - 392 + 49 - 2 , = 579 .

of Edinburgh, Session 1876-77.

341

Those for the preceding cases, n- 3, 4, 5, respectively are

No. = 6-12+ 9- 2

No. = 24- 48+ 40- 16 + 2
No. = 120 - 240 + 210 - 100 + 25 -2

1

2

13 .

We have in general [1 J = n , [2] = n , [1, 1] = \n(n - 3) ; and in the
several columns of the formulas the sums of the numbers thus
represented are equal to the coefficients of (1 + 1)2, thus, n = 6 as
above, the sums are 6, 15, 20, 15, 6, 1. As regards the calculation
of the numbers in question, any symbol [a, /?, y] is a sum of sym-
bols [a -a +/3- jS' + y-y'. .], where a' + /3' + y'. . is any partition
of w — (a + /? + y . .) ; read, of the series of numbers 1, 2, 3 ... ti,
taken in cyclical order beginning with any number, retain a, omit
a', retain J3, omit /3 ', retain y, omit y', . . Thus in particular,
n = 6, [1, 1] is a sum of symbols [1 - 3 + 1 - 1] and [1 — 2 + 1 — 2] ;
it is clear that any such symbol [a - d + j3 - /3'. .] is —n or a sub-
multiple of n (in particular if n be prime, the symbol is always
= n): and we thus in every case obtain the value of [a, /?, y . .]
by taking for the negative numbers the several partitions of
n — (a + /3 + y . .) and for each symbol [a - a +/? - J3' + y - y'. .],
writing its value, ~n or a given submultiple of n, as just men-
tioned. There would, I think, be no use in pursuing the matter
further, by seeking to obtain an analytical expression for the
symbols [a, /?, y . .] .

For the actual formation of the required arrangements, it is of
course easy, when all the arrangements are written down, to strike
out those which do not satisfy the prescribed conditions, and
so obtain the system in question. Or introducing the notion of
substitutions,* and accordingly considering each arrangement as de-
rived by a substitution from the primitive arrangement abccl . . . jk,
we can write down the substitutions which give the system of
arrangements in which no letter occupies its original place : viz.,
we must for this purpose partition the n letters into parts, no part
less than 2, and then in each set taking one letter (say the first
in alphabetical order) as fixed, permute in every possible way the

* In explanation of the notation of substitutions, observe that (abode) means
that a is to be changed into b, b into c, c into d, d into e, e into a ; and simi-
larly ( ab)(cde ) means that a is to be changed into b , b into a , c into d , d into e,
e into c.

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Proceedings of the Royal Society

other letters of the set; we thus obtain all the substitutions which
move every letter. Thus n = 5, we obtain the 44 substitutions for
the letters abode , viz., these are

(abode), &c., 24 symbols obtained by permuting in every way

the four letters b , c, d , e.

(< ab)(cde ), &c., 20 symbols corresponding to the 10 partitions

ab, cde, and for each of them 2 arrangements
such as cde, ced.

And then if we reject those symbols which contain in any ( ) two
consecutive letters, we have the substitutions which give the ar-
rangements wherein the letter in the first place is not a or b, that
in the second place not b or c, and so on. In particular n = 5,
rejecting the substitutions which contain in any ( ), ab, be, cd, de,
or ea , we have 13 substitutions, which may be thus arranged : —

( acbed ) , (ac)(bed) , ( acebd ) , (adbec) , ( aedbc ) ,

( aedbc ) , ( bd)(aec ) ,

( acedb ) , (ce)(adb) ,

( aecbd ) , ( ad)(bec ) ,

( adeeb ) , ( be)(adc ) .

Here in the first column performing on the symbol (acbed) the sub-
stitution (abode'), we obtain ( bdeae ), = (aebdc), the second symbol ;
and so again and again operating with ( abode ) we obtain the re-
maining symbols of the column ; these are for this reason said to
be of the same type. In like manner symbols of the second column
are of the same type ; but the symbols in the remaining three
columns are each of them a type by itself; viz., operating with
(abode) upon (acebd) we obtain (bdace), = (acebd) ; and the like as
regards (adbec) and (aedbc) respectively. The’ 13 substitutions are
thus of 5 different types, or say the arrangements to which they
belong, viz.,

cebad , ceabd , edeab , deabc, eabed ,

edacb , edabc ,

caebd , daebc ,

edbac , debac ,

daecb , deacb .

are of 5 different types. The question to determine for any value
of n, the number of the different types, is, it would appear, a diffi-
cult one, and I do not at present enter upon it.

of Edinburgh , Session 1876-77-

343

2. On the Construction of the Canon of Sines, for the Decimal
Division of the Quadrant. Edward Sang, Esq.

The convenience of having only one system of numeration is
so well recognised, that there is no need for any discussion.
Already the numerical nomenclatures of all nations having any
culture have been converted to one, namely, the decimal system,
and traces of the ancient use of dozens, scores, fifteens, or sixties,
can be found in only a very few of them. Although we count our
hours in sixty minutes, we do not date the present as the year
thirty-one sixties and seventeen . Yet, in the matters of measure,
weight, and value, the old and irksome divisions continue to be
used ; nay, even in those departments of science which most need
laborious calculation, we continue to employ the ancient scale of
division.

It is, indeed, remarkable that, while men of business are striving
for uniformity in the modes of counting and of measuring, trigo-
nometers and astronomers should remain unconcerned as to the
subdivision of arcs and of time. We are rapidly approaching the
anomalous position of using the decimal division of the earth’s
quadrant as the source of our standards of weights and measures,
and of yet rejecting that division in our notation of angles.

The want of trigonometrical tables suitable to the new division
is the real cause of this backwardness; the construction of these
tables is essentially the first step to the universal employment of
the decimal system. This has been long and well recognised. In
the end of the last century, Borda computed the decimal canon ;
this computation was superseded by that which the French G-overn-
ment caused to be made under the superintendence of Prony ;
but neither of these has been put to press. The only centesimal
table available to the trigonometer is that given for each minute
of the quadrant, in Callet’s “Tables Portatives;” it was collated
with the manuscripts of Borda and of Prony, but is presented in
a most inconvenient form.

The eminent astronomer, Laplace, adopted the decimal divi-
sion of arcs, of distance and of time, in his “ M6canique Celeste,”
published in the last year of the century. The force of this illus-
trious example might long since have gained universal accept-

2 z

VOL. IX.

344

Proceedings of the Royal Society

ance for the system, had not the non-publication of the requisite
canon prevented all progress in this direction.

Notwithstanding many solicitations, and even the offer by
the English Gfovernment to defray a share of the expense, the
tables computed in the Bureau du Cadastre remain unpublished;
and the fact of their existence remains a discouragement to other
computers.

Now, fifty years ago, having fallen upon a method of approxi-
mating very rapidly to the roots of numerical equations, published
in 1829 under the title, “Solution of Algebraic Equations of all
Orders,” I applied it to the quinquisection of an arc, and thus
obtained directly the sine of any proposed decimal division of the
quadrant. After proceeding a short way in the construction of the
canon by this method, I laid it aside, from the conviction that the
labour could, at best, only produce a repetition of what had already
been accomplished.

Many years ago, after having felt for long the want of a table
of logarithms more extensive than any existing, I designed a
nine-place table up to one million ; and having carried the manu-
script fifteen-place table up to 300 000, laid it before this Society,
whose Council did me the exceedingly great favour of presenting to
Government a memorial soliciting aid in the completion and publi-
cation.

One of our scientific periodicals, in noticing this memorial,
supplied to Government a most potent reason for not acceding to
the request, in this, that the labours of Prony in the Bureau du
Cadastre had already anticipated and surpassed all that can be
done in future in this department of calculation.

Forced thus into a critical examination of the Cadastre Tables,
so far as that could be accomplished by help of published docu-
ments, I arrived at most unexpected conclusions.

In the first place, the fundamental table, that of the Logarithms
of the Prime Numbers, as given by Legendre in his work on
Elliptic Functions, was found to be correct up to 2000; that is, as far
as Abraham Sharp and other ancient computers had gone. But of
the primes between 2000 and 10 000 computed in the Bureau, only
five have their logarithms correctly given, while almost all of the
other logarthims err on one side.

345

of Edinburgh, Session 1876-77.

In the second place, Henry Brigg’s original table had been col-
lated by Prony’s assistants, and errors in the tenth and higher
places had been found ; yet no notice had been taken of the very
many errors in the fourteenth and even in the thirteenth place.

Thirdly, the system of computation adopted was so imperfect
that, although differences of the sixth order were extended to the
thirty-sixth place, the results were liable to errors up to the
twentieth figure.

Lastly ; the Cadastre calculations were used by M. Lefort for
correcting Adrian Vlacq’s ten-place table (that table of which all
the subsequently published seven-place tables are abridgments);
with the result of sometimes putting Vlacq in the wrong when he
is right. That is to say, the Cadastre calculations cannot be trusted
for the compilation of a ten-place logarithmic table.

Such being the case with that part of Prony’s great work which
was comparable with previously published tables, we are unable to
place confidence in the trigonometrical portion, which necessarily
is almost entirely new ; and we are forced, when contemplating the
compilation of the Canon of Sines, to hold the Cadastre Tables as
non-existent, or at best, as useful for controlling palpable errors of
the press.

In actual trigonometrical calculations we very seldom use the
sines and tangents themselves, but employ their logarithms instead;
wherefore, both the Canon of Sines and the Logarithmic Canon are
needed as the joint foundation of our working tables. Having car-
ried the table of logarithms as far as to 370 000, and being satisfied
of the insufficiency of the work done in the Bureau du Cadastre, I
resumed the computation of the sines, and have now proceeded to
such a length as to be able to submit the methods employed to
the Society, and through it to the mathematical public.

The decimal division of the quadrant is effected by bisections
and quinquisections, and the first thing to be determined is the order
in which these operations should be taken. Now, we obtain the
sine of the half arc, not from the sine of the whole arc, but from
its cosine, or rather from its co-versed-sine ; when the arc is small
the co-versed-sine, or defect of the cosine from the radius, is repre-
sented by a very small decimal fraction, the number of whose

346

Proceedings of the Royal Society

effective figures is less than the total number of figures in the cal-
culations; we have to extract the square root of its half, which
square root, can only be true to as many effective figures, and thus
cannot be extended to the full number. If, then, we desire to
obtain accuracy to a specified number of decimal places, we must
extend our first calculations far beyond. Whereas the sine of an
odd sub-multiple is deduced directly from the sine of the whole
arc, and the computation is such as to retain the full number of
effective figures. Hence we must proceed by first making all the
requisite bisections, and thereafter the quinquisections.

There is, however, an obvious exception. The sines of 20c, 40c,
60c and 80c are obtained by the solution of quadratic equations, so
that this quinquisection naturally comes first; the bisections after-
wards, and then the remaining quinquisections.

Having prescribed unit in the thirtieth decimal place as the
limit of inexactitude, and taken three figures more to obviate the
accumulation of the minute errors inevitable in all approximate
work, I computed the sines of these four arcs to thirty-three
places.

The bisection of the quadrant gave the sine of 50c; that of
60c gave for 30c and for its complement 70c; that of 20c gave for
10c and 90c, thus completing the table for each tenth part of the
quadrant.

In the same way the bisections of 10c, 30°, 50c, 70°, and 90c gave
the sines of the intermediate fifth degrees.

The bisections were continued in this way until the quadrant
was divided into 80 equal parts.

In performing this work, each of the roots

sina= cos 2a} , cosa= \Z{1 + J cos 2a}

was extracted twice, and sin a was also found from the division

sina =

sin 2a
2 cos ay

by which means the values of sin a and cos a were securely got,
and the previous computations of sin 2a, cos 2 a again verified.
There were, as a matter of course, small errors in the last places,
but the results, to the thirtieth place, were made sure.

of Edinburgh, Session 1876-77. 347

The quinquisections were obtained by help of the equation

16 sin a5 - 20 sin a3 + 5 sin a - sin 5a = 0 = E .

Regarding E as a function of sin a, its successive derivatives
are

XE = 80. sin a4 - 60. sin a2 + 5

aE = 320. sin a3 -120. sin a
3E = 960. sin a2 — 120
4E = 1920. sin a
5E = 1920

now, while resolving the equation, we get the values of all the
derivatives ; so, taking advantage of these, we have

cos a2 = ^ — -i- ..E
8 960 3

cos 2a = ? - 4— 3E
4 480 3

sin 3a - ~ sin a - 2E
2 80

cos 4a = —

1

4 480

E 4- — E •
3 + 101 ’

the first of these gives us, by extracting the square root, cos a.

Applying this method to the arc lc 25', the eightieth part of the
quadrant, I obtained the sine and cosine of 25', and proceeded to
compute the functions of its multiples by help of second differences,
according to the well-known formula.

sin (w + 1) a - 2 sin na + sin (a— 1) a = sin n a. 2 vera;

and, because the multiplier 2 vera is to be repeatedly used, a table
of its multiples was constructed, in the case of a = 25', up to the
hundredth, in the cases of a =5' and a = 1', up to the thousandth
multiple.

The sines of these multiples being computed continuously, an
error in any part of the work, propagated subsequent errors, which
could not possibly be overlooked in comparing the results at each

348 Proceedings of the Royal Society

fifth step with the previously computed test values. In this way
immunity from error was obtained, excepting in the last places,
where small errors are inevitable.

In performing the multiplication sinwa.2 vera stopping at the
thirty-third place, the last figure of each partial product may err in
excess or in defect by J; now it is possible, though not likely, that
all of these errors maybe on one side, and therefore there is a 'possible
error in the last place of the total product, of half as many units
as there are lines in the multiplication. By using the table of
multiples up to one thousand, we reduce the number of lines to one
third, and therefore the possible amount of residual error in the
same ratio ; so that the auxiliary table both saves labour and
augments the exactitude of the result.

These final-place errors were corrected at each fifth step by
altering the last figures of the second differences, and thus the
accumulation of those errors was prevented. In the whole calcu-
lation of the sines of the quarter degrees, it was not found necessary
to alter any one second difference to so much as the limit of possible
error, and therefore we may hold that the manuscript table of the
sines of these arcs is absolutely correct to within the prescribed
degree of precision, namely, unit in the thirtieth decimal place.

The next quinquisection, conducted in the same way, gave the
sine and cosine of 5'; the functions of whose multiples were ob-
tained as before, and compared, at each fifth step, with the previous
work. The table of sines to every fifth minute is already well
advanced.

The third quinquisection gave the sine and cosine of the single
minute of the decimal division. A table of the multiples of 2 ver 1'
has been constructed up to 1000, and has been used in forming a
good beginning of the canon of sines to each single minute.

For the purpose of preventing all error in the record of these

from the

duplicate scroll calculations, and the successive first differences
and sines were thence recomputed on the record sheet. Since any
error in copying, or even in the original computation, was neces-
sarily continued and extended into the after part of the record, its
detection was rendered certain, so that the recorded results may be
implicitly relied on. To make the record more secure, each page

calculations, the second differences only were copied

349

of Edinburgh, Session 1876-77.

was copied on thin transfer paper, on which no alteration can be
made without being obvious.

The method of computing might have been extended to differ-
ences of the fourth order, in which case the common multiplier,
4 vera2, would have been much smaller, and the terms of the
products fewer. But, on the other hand, the entries in the record
would have been more, and the effects of the residual errors would
have been much greater and more troublesome in correction. For
the interpolation of each quarter degree, the saving obtained by the
use of fourth differences would have been unappreciable ; for those
of each fifth and of each single minute, it would have been hardly
such as to compensate for the inconveniences just mentioned; but
for the future interpolations of each tenth second and of each single
second, the fourth differences may be advantageously used.

When the canon of sines shall have been completed, the com-
putation of the working table, that of logarithmic sines, will be
easy, particularly by help of my fifteen-place table of logarithms.

Beginning, as John Nepair did, at the sine of the whole quad-
rant and proceeding downwards, the computed logarithmic sines
may be verified by their differences, which are small. When the
work has been brought down to the log sin of the half-quadrant,
the farther progress is easy and rapid, for the formula

2 sin a . cos a — sin 2 a

gives log sin a = log \ + log sin 2 a - log cos a, so that the dif-
ferences of any order may be got at once from the previously
tabulated differences of that order, and, what is most worthy of
remark, may be used without the fear of an accumulation of
residual error.

The table of logarithmic tangents follows as a matter of course.

3. On the Precautions to be taken in recording and using the
Records of Original Computations. Edward Sang, Esq.

The real utility of tables of numerical results is only secured by
making them accessible to those computers who may require them ;

350 Proceedings of the Royal Society

and the essence of their utility lies in this, that the labour of a
single computer saves that of many others.

It is indispensable that those who use the tables he able to rely
implicitly on the accuracy of the tabulated numbers, and that they
have a ready means of detecting any error should the existence of
one be suspected.

I do not mean, at present, to say a word on the mechanical
arrangements of setting up the types, of stereotyping, revising the
proofs, and printing; these have already often been discussed, but
I shall take the matter up at this critical point : — The investigator
has in his hands a set of printed or of manuscript tables, which he
means to use in his researches, and he wishes to know whether the
individual book be or be not to be trusted. His confidence must
necessarily be influenced by the history of the book and by its co-
relatives. Thus, if it be a stereotype copy of a work in extensive
circulation, he may accept the general opinion as to its accuracy ;
but if the table be one seldom used, such as those which serve as
the foundation of working tables, this source of confidence fails him.

The nature of the case may be most clearly seen from an
example : —

We propose to extend the logarithmic canon beyond the limits
to which it has been already printed ; this extension must be
founded on the logarithms of the prime numbers ; now Abraham
Sharp computed, to 61 places, the logarithm of every prime num-
ber up to 1097 ; these were printed in Sherwin’s collection, and
thence reprinted by Callet in his Tables Portatives ; shall we then
build our more extensive tables on the computation by Sharp ?
Sharp was known as a most zealous and careful computer ; both
Sherwin and Callet would take care that the numbers be correctly
copied ; yet for all that, we cannot venture to found on Sharp’s
work because there is an essential omission.

If we were to proceed to compute, by help of these, the logarithms
of larger primes, and if, after a lengthened series of operations, we
were to find a disagreement, we should be left in doubt as to
which of the many logarithms that had been used may be in fault ;
we should have to recompute such of Sharp’s logarithms as might
be implicated, while the labour and irksomeness of the search would
become intolerable.

351

of Edinburgh, Session 1876-77.

Id all such calculations we seek to arrive at the result by two
independent processes. All the use, therefore, that can be made
of Sharp’s tables, is to hold his work as constituting one of these
processes ; a great use certainly, yet, at best, only half of what it
might have been.

Now, in the computation, to twenty-eight places, of the logar-
ithms of the prime numbers, no error whatever was discovered
among those given by Callet ; so here we have an instance of
records, in themselves quite exact, and yet insufficient to obviate
subsequent recomputation.

The means of readily verifying the record are awanting ; these
means must necessarily vary with the nature of the tabulated func-
tions.

In the volumes containing the computation of the logarithms to
twenty-eight places of all primes below ten thousand, which was
laid before the Society, the articulate steps of every calculation are
recorded and indexed, so that if an error be suspected in any one
logarithm, we have the means of instantly verifying the table, or
of detecting the source of the error. Had such a record accom-
panied Sharp’s admirable table, the need for subsequent re-calcula-
tion would have been entirely obviated.

The vast majority of tables have their arguments arranged with
equal differences, consequently the functions progress gradually ;
and, for the most part, these tables have been constructed by help
of differences. It is then sufficient to record the differences along
with the values of the functions. For the canon of sines I have
found it convenient to place the first difference, with the sign + ,
and then the second difference, with the sign - , below the pre-
ceding sine, as shown below : —

Arc.

Sine.

lc 12'

.01759 20113 41099 72108 93607 04490
4- 15 70551 06706 95090 77046 38118
4 37940 65992 07711 07444

1.. .13 .01774 90664 47806 67199 70653 42608

+ 15 70546 68766 29098 69335 30674
4 41815 82853 79716 53726

1.. .14 .01790 61211 16572 96298 39988 73281

VOL. IX.

352 Proceedings of the Royal Society

This arrangement enables the computer to examine any sin
which he wishes to extract, so as to guard against any typographi-
cal error; and, if the table of the multiples of 2verT were
appended, to check readily the computation itself. When, how-
ever, the differences have only a few figures, the ordinary method,
of placing them in separate columns, is to be preferred ; it saves
room, while the practised calculator has no difficulty in performing
the requisite additions or subtractions. The utility of this arrange-
ment has been long recognised.

In the case of tables for common use, which are, in general,
abbreviations of original calculations to a greater number of places,
it is enough to give the first differences when these vary much.

When such means of verification have been provided, the user of
the table can make sure that the number which he extracts con-
tains no error ; and if all users were to habitually make this
examination, printed tables, and above all those printed from
stereotype, would be gradually freed from errors of press.

4. On an Unnamed Palaeozoic Annelid. By Professor Duns.

(Plate IY.)

Cyhaderma* (nov. gen.). — Generis Characters : — Corpus cylindricum,
elongatum, nudum, striatum ; striae tenues, in ordinem undi ilatae, et ubique
corpus cingentes, ita ut cutis subrugosa videatur ; linea doi sualis continua,
alternasque cavaturas ovatus et vertices ostendens ; nulla ^ erorum articul-
amentorum indicia ; vestigium tortuosum, bisulcum.

Cymaderma (new genus). — Generic Characters: — Body cylindrical,
elongated, naked, striated ; striae minute, waved symmetrically, encom-
passing the form in all parts, and giving to the skin a subrugose appear-
ance ; a continuous dorsal line, showing alternate oval depressions and
slight ridges ; no traces of true articulations ; track, tortuous bisulcate.

This annuloid fossil was obtained from upper Carboniferous strata,
in a cutting on the Midland Railway, valley of the Kibble, near
Settle, Yorkshire. Peculiarities characteristic of the striation and
the median dorsal line led me to conclude that the form was pro-
bably rare, or one that had not been described. It was thus of
importance to get the other part of the slab on which the impres-

* Etymol. Kv/xa, unda, B4p/xa, cutis.

353

of Edinburgh , Session 1876-77.

sion, or intaglio , corresponding to the rounded relief, might be
expected. The friend who had forwarded the fossil made diligent
search, but found the upper part of the slab had been destroyed.
In answer to a request for any animal tracks, or traces of organisms
that might be met with in the same, or closely related deposits, he
sent me several slabs of compact dark-coloured micaceous, sandy
shale, on which some markings occurred. On splitting these, they
were found crowded with tracks and casts of forms closely resem-
bling that first sent, though the matrix is lithologically different.
These shales intervene between bands of the so-called gritstone, in
which the form now noticed was found. Its position was about 16
feet from the surface, in a gritstone bed 4 feet thick, having above
a deposit of alternating shales and gritstones nearly 15 feet thick
and below a bed of limestone.

The dark-coloured slabs present features of much interest. They
contain traces of three species, the prevailing one being identical
with that now before us, though none of the characteristic marks
are so sharply outlined. They make it clear, however, that the
surface on which the median line occurs is dorsal, and they estab-
lish the bisulcate character of the track. On the reverse of one
slab, the intaglio I was anxious to obtain shows distinctly that the
dorsal line is ridged. This is also very well marked in another.
In both the slight dorsal ridge is represented by a corresponding
depression or furrow in the overlying shale. Even the outlines of
these tracks are suggestive to the ichnologist. Some of them are
comparatively deep, some shallow ; in some the bisulcate character
is well seen, while in others the lower surface of the track is flat.
The explanation of this is obvious. If, for example, we look at the
tracks, say, of our common whelks ( Littorince ), we see that those
formed in shallow shore-pools are flat ; those on very wet sand are
slightly hollow, their edges presenting a corrugated appearance;
while those made on fine sand beginning to dry, are marked at
regular intervals with distinct transverse lines. It is not unusual
to observe all these crossing one another, or seeming to form loops
with each other. The waved whelk ( Buccinum undatem ) makes a
bisulcate track on the sand when it is partially dry. Occasionally,
however, it trails the sharp edge of its operculum in such a way as
to give three sulci. Ichnologists may thus have the track of only

354 Proceedings of the Royal Society

one form before them, when they describe three or four apparently
different ones, and trace them to different species. Thus, such
terms as unisulcus , bisulcus , trisulcus , unisulcus corrugatus , and the
like, instead of indicating so many distinct species, may, in reality,
express the varying form of the track of one only. Perhaps, even
the Hitchcocks’ in their magnificent works on ichnology have not
given due weight to this consideration.*

The slabs laid on the table have been examined with great care,
in the hope of detecting traces of hairs, setae, or any other charac-
teristic marks of true recent annelids. But neither hairs nor bristles
have been found. On most of the slabs, however, markings occur,
which I am inclined to regard as the outlines of organs analogous
to the gill-leaves of such forms as Phyllodoce. These are worthy
the attention of naturalists. They are numerous, and have not, I
think, been observed before. While occurring on the same surface
as the outlines and tracks of the organisms, only in one instance
they seem attached to them, but even in this case the association
is doubtful. See Plate IV. fig. 2, for an outline of some of these
markings. In one case, in which a good duplicate was obtained,
distinct traces as of a fringe appear. An enlarged rough outline
of part of this fringe is shown on the Plate, IV. fig. 4. On the
same specimen a good many annulate pointed objects occur, two of
which are represented at a and b fig. 2.

There can be no doubt that both tube inhabiting and errant
Annelida existed in palaeozoic time — traces of some being found
even in the Laurentian rocks — though little is known of their true
nature and relations. The genera conchiolites , cornulites, serpulites ,
spirorbis , and trachyderma, may be said to complete the list of the
former, and the genera arenicolites, crossopodia , myrianites , and
nereitcs that of the latter. But even some of these generic designa-
tions are open to criticism, or cumbered with doubt, and it is
questionable if, in any of these cases, we have a true representation
of the animal itself. Such considerations add to the value of the
specimen now under notice. It has no resemblance to any of the
forms just named. The first examples on record having some

* <f Ichnology of Massachusetts.” By Edward Hitchcock, Boston, 1858.

“ Supplement to the Ichnology of New England.” Edited by C. H. Hitch-
cock, Boston, 1865.

Proc. Royc P>oc . E dinT Vol IX. Plate IV!

Peaoli, delt. j^TFarla-no fc EriTrine. Lith” ESinT

I

I

of Edinburgh , Session 1876-77.

355

likeness to it were discovered by Mr Dixon, of Unthank,* * * § Northum-
berland, in fine-grained micaceus carboniferous slabs, in 1838, and
sent by him to the Newcastle Museum. In 1844, Dr Emmons, f of
Albany, U.S., published an account of annelids found by him in
Lower Silurian strata, but none of his figures bear the least resem-
blance to this. An account is given in the first volume of “ The
Naturalist” of corresponding markings obtained by Mr Ed. Wood,
in 1850, from the Northumberland strata, specimens of which were
sent to the Museum, Jermyn Street, which Edward Eorbes marked
“Casts of Annelid Tracks.” M‘Coy, who gives in his “British
Palaeontology ” | careful descriptions of the genera already named»
does seem to have had his attention turned to these. In 1858, Mr
Albany Hancock contributed an able paper to the Annals of Natural
History, entitled “ Remarks on certain Vermiform Fossils found in
the Mountain Limestone Districts of the North of England.” § This
paper is illustrated by six well-executed plates, the last two of
which (xviii. and xix.) bear on the present inquiry. The other
figures are undoubtedly mere tracks, and Mr Hancock believes
them to be those of crustaceans, but the grounds for this belief are
far from clear or satisfactory. Referr’ng to a species of Amphio-
poda — Sulcator arenarius — he says,— “ While forming its track,
the animal is never seen ; it moves along a little below the surface
of the sand, which it pushes upwards with its back, and the arch
or tunnel thus formed partially subsides as the creature passes
forward, and breaking along the centre the median groove is pro-
duced.” Now all that this observation shows is, that a median
groove is formed in the line of this crustacean’s track, though
the probability of the realisation of a form like this in such a
tunnel cannot be admitted. It would imply that the tunnel

* Since this paper was written I have received from a Fellow of the Society,
P. Dudgeon, Esq. of Cargen, several annulose specimens, one of which, from
Upper Carboniferous strata, Haltwhistle, Northumberland, not far from this
locality, bears a close resemblance to the forms figured by Mr Hancock, and
referred to below.

t “ The Taconic System.” By Eb. Emmons, Abany, 1844.

I “ Contributions to British Palaeontology.” By Frederick M‘Coy, F.G.S.,
Cambridge : Macmillan & Co., 1854.

§ Annals and Magazine of Natural History, vol. ii. December 1858.
(Plates xviii. and xix.)

356

Proceedings of the Royal Society

in wet sand was kept open till, by gentle infiltration, the hollow
was filled, and ah exact likeness of the interior of the tunnel
realised on the infiltrated matter ! A very good example of
the forms figured by Mr Hancock occurs on one of the slabs on
the table.

At a meeting of the Dublin Geological Society in 1858, Professor
Haugbton, the president, read a paper “ On the Occurrence of some
New and Hare Forms of Annelidoid Tracks in the Coal Measures,
Lugacurren, Queen’s County.”* A year later, and again in 1860,
he returned to the subject, indicating his belief that the Lugacurren
tracks resembled those described by Mr Hancock, and ultimately
accepting his theory of their crustacean origin. As Professor
Haughton’s papers were illustrated by lithographic plates ad
naturam , they, like Mr Hancock’s, are available for comparison
with the specimen before us. The Lugacurren specimens differ
from the Northumberland forms in having at one part four, in one
case, and in another five circular depressions in the median line.
They differ from that on the table in having circular depressions
confined to a small part of the form, and a median groove, instead
of, as here, oval depressions running the whole length of the body,
and a median ridge. In neither the English nor the Irish speci-
mens is the characteristic striation so conspicuous as in this. These,
however, seem all to be specimens of closely related species. Both
Mr Hancock and Professor Haughton think that the depressions
in the median groove may have been made by the pygidium
of a carboniferous trilobite, the print of the tail being the only
trace the animal has left of its having had a place in this
deposit ! Now such marks as those on the Lugacurren specimens
could only have been made by the pygidium being set down ver-
tically, then lifted for a time, and so placed at regular intervals,
their being no evidence of dragging, — most unlikely, if not im-
possible conditions. Fortunately, a good representation of the
form figured by Professor Haughton occurs also on these slabs.
From this it is evident that the characteristic circular punctures
run the whole length of the body.

It seems to me that the reference to the track of Sulcator arena-
rius has been misleading. It can, indeed, have no bearing on any

* Journal of the Geological Society of Dublin, vol. viii. 1857-1860.

357

of Edinburgh, Session 1876-77.

of these closely related forms, being unisulcus, destitute of striae,
and not more than three-eighths of an inch wide, while all these are
striated and seven-eighths of an inch wide ; that under notice being
moreover distinctly bisulcate. It is acknowledged that the relations
of this to recent forms are obscure. The features which chiefly
claim attention are—

First, The outline of the animal. — A glance at the specimen
is sufficient to convince us that we have here not a track merely,
but the representation of an annulose form. (See Plate IY. fig. 1.)
On one of the slabs this is associated with several inches of
the track over which it has passed. The median dorsal line
is fully exposed above, while the median ridge, which makes
the track bisulcate, is precisely what would be formed by the
ventral groove of a nereis — Alitta virens (Sars), for example.
The striae which pass round the body leave no traces of their
outline in this track ; but in another, from which the repre-
sentation of the animal was removed, these striae are well marked.
Again, on the bulged sides of the tortuous outline, the striae
are wider than on the opposite side, while in the comparatively
straight parts they are symmetrical. So far as I know, similar
markings do not occur on any recent annelid. They are, however,
represented, though not so distinctly as here, on a small annelid — •
Epitrachys rugosis- — figured by Ehler of Erlangen in his paper on
the “ Fossil Worms of the Lithographic States of Bavaria.1”*

Second , The tracks.— They differ widely from the tracks both of
mollusca and Crustacea— those of the former being, for the most part,
sharp in their turns, and those of the latter consist generally of
lines more or less straight, not tortuous. In addition, they have
two furrows divided by a distinct median ridge. I am sure that
had the able observers named above seen such specimens of the
tracks, and also of the intaglios of the rounded dorsal surface as are
now on the table, they would not have questioned the true annulose
character of this organism.

Third , The median dorsal line.— This is exceedingly well repre-
sented, not only on the outline of the animal itself, but also in one
of the intaglios referred to. It consists of small, shallow, oval

* Ueber fossile Wurmer aus dem lithographischen Schiefer in Bayern
Cassel, 1869.

358 Proceedings of the Royal Society

depressions, deepest in the centre, and narrowing at each end,
where they meet a slight ridge which stretches between the depres-
sions, giving to the line, looked at from a short distance, a chain-
like appearance. Were the branchial tufts of some recent annelids
plucked out, we would have a somewhat similar appearance.

Fourth , The characteristic striation. — This is most distinctly
and even sharply marked on the form in the gritstone slab. It is
also, though less definitely, marked on some of the softer micaceous
slabs. Mr Hancock says, with reference to his specimen which has
most resemblance to this — “ The transverse striae on the surface
of the grooved form certainly gives it much the appearance of some
organism but the value of this acknowledgment is lost by the
supposition that the striae might have been “ produced by the in-
termitting progress of the animal.” Now it is simply impossible
that such striation as is seen here could have been produced in this
manner.

The expression 11 ondeleusement et symmetriquementf used by
Cuvier in describing the striae on the shell of a cephalopode, very
well indicates a leading feature of this striation. Indeed, the
symmetry of these beautifully regular undulating striae may be best
understood by comparing them with the striae on the shells both of
recent and fossil nautilidse. Fig 3 is intended for a representation,
ad naturam , of the characteristic striation, but the striae are sharper
and better defined than shown on the figure.

In conclusion, it will be seen that the distinctive features of the
specimen now brought under the notice of the Society are the
median dorsal line and the waved striation. In the generic features
set down at the head of this paper, I have described the former
thus, — linea dorsualis continua, alternasque cavaturas ovatas et
vertices ortendens. As, however, uncertainty attaches to the
nature of this line, the latter — the striation — may be taken as the
outstanding generic feature, — striae tenues, in ordinem undulatae,
et ubique corpus cingentes, ita ut cutis subrugosa videatur. The
term Cymaderma, or wave-skin, is proposed for a genus, whose true
zoological position is as yet uncertain. Should the examination of
other specimens show that the oval depressions in the median dorsal
line are only specific marks, not points of insertion of organs, and
the striae mere lines formed by the contraction of the cutis — a most

of Edinburgh, Session 1876-77.

359

unlikely circumstance — the organism would have closer nemertean
than annelid relations. But, if proof be ultimately obtained that
the branchise-like organs referred to above were connected with the
oval depressions, and that the transverse markings are really not
strke but annuli, the zoological position of the animal will be
among true annelids, characterised, however, by structural features
widely divergent from recent forms.

5. On Eisenstein’s Continued Fraction. By Thomas Muir,

M.A.

6. Note on an Infinitude of Operations. By Thomas Muir,

M.A.

The assumption that there is a limit in Professor Tait’s problem
regarding the interpretation of Limn =co(cosna;) means that if we
start with an angle x, and find the number which is its cosine, then
the number which is the cosine of this number, and so on, we shall
at last come to a limiting result w, such that cos w = w. The
problem is thus transformed into the solution of the equation
to = cos to, which may be accomplished as follows

to = COS to,

whence o>>/3-1,

> * 73205 ....

Taking therefore ’733 as a first approximation, we find that with
it

to — cos to- - *01

and taking *75 or j as another approximation, which is readily
seen to differ from the former by erring in excess, we find that
with it

VOL. IX.

to — to = cos-1- "019 . . . .

360

Proceedings of the Boy at Society

from which two results by the regula falsi we derive a better
approximation, viz.,

.733 '75 -?33

iA •019 + -01 Ui

i.e

-7388....

Continuing in this way, it is found that

Limn=oo(cosna?) = -7390852,

a result correct to at least the fifth place.

This peculiar constant we should expect to find connected in
some way with tt, and that such a connection exists is easily seen
from the formula —

cos

4a?2\

svv ’

from which we have

(x)

-(*-5) (>-£)(»-

4<o2\

5W

An explicit expression of the same relation is obtained from the
identity

7 r la?3 1 ‘ 3 xb

cos — ^ = 2 “ * “ 2 “3 ~~ 2T4'5

,-i

which gives

7r 1 to3 1 • 3 CO5

w=:2 _t0“2*'3~2T4’5“

whence

, 0>3 3 CO5

’r = 4" + 3 + I' 5" +

the result of the u reversion ” of which is

cos00# ~~ -

7 r

1 (

-

7 r

4 3 . 4\4/ .3.4. 5\4

5

361

of Edinburgh, Session 1876-77.

The corresponding limit in the case of other functions may be
similarly interpreted; that is to say, the limit of if such be

possible, when n is indefinitely increased, is a root of the equation
<£(#) = #. We may view such limits as implying an infinitude of
operations ; and we have seen that when this infinitude of operations
is carried out upon any value (within certain limits) of the inde-
pendent variable, the result is always the same; in other words,
we have seen that those functions, in the case of which the limit is
possible, are levelling functions, having the property of bringing
everything they act on to the same dead level. In this respect
they may be compared with Euler’s expression

1 . 1 . 0 1
2 # + sin x + 2 sin Ax + ^ sin 3# + ....

7T

which for all values of x within certain limits equals ^ ; and this
suggests the possibility of finding a similar expression for cos00#
by means of Lagrange’s or Fourier’s theorem.

7. Note on Determinant Expressions for the Sam of a
Harmonical Progression. By Thomas Muir, M.A.

(Received February 27 — Reau. March 1877.)

Taking the harmonical progression

a a + b a + 2b a + 3b

and denoting the sum of n terms of it by Sn we have by means of
Euler’s transformation,

S

n —

1

-g— + 6)2

2a + b~ '2^+36. > + 26)2

2 a + 5b —

{a + {n - 2 )6}2
2a -f (2n — 3)6

a -

362

Proceedings of the Royal Society

and therefore from the theory of continuants,

2a + 6 (a + 6)2 0 0

1 2a + 36 (a + 2 6)2 0

0 1 2 a + 5b (a + 3b)2

0 0 1 2a + 76 ....

0 0 0 1

sw = J.._

a a? 0

1 2a + b (a + 6)2

0 1 2a + 3b

0 0 1

0 0 0

• • • * i • > • «

where the denominator is of the nih order and the numerator of the
( n - l)th, being formed from the denominator by the omission of
the first row and first column.

There is, however, another such expression for S« of more interest
and less likely to occur to one, viz.,

0 ....
0

(■ a + 2b )2 ....
2 a + 5b ....
1

1 -b - b - b - b - b

1 na -2b -3b - 46 — (n - 1)6

1 [n — 1 )a a — 26 - 36 — (n — 1)6

1 (n - 2 )a a a - 26 — (n — 1)6

1 (n - 3 )a a a a — (n - 1)6

1 2 a a a a a

a(a + b)(a + 26) |<3! + (n — 1)6}

This is easily verified for the cases where n — 2 and n- 3 . When
n = 4 we have

1 -6-6 - 6

1 -b - b 2b

1 4a -26 -36

1 4a — 2b 0

1 3 a a — 36

o

e

e

CO

rH

12 a a a

,

1 2a a a + 36

a(a + b)(a + 26)(a + 36)S4 =

of Edinburgh, Session 1 870-77.

363

— (a + 36,

1

-6

- 6

1

4a -

26

= (a + 36)

1

4 a

-26

-26

1

3 a

a

1

3 a

a

1

2 a

a

1

-6

- 6

1

0

- 6

l

An -

26

1

3 a

-26

+ (a 4- 36)

1

a

-26

-26

1

3 a

a

1

2 a

a

1

a

a

1

2 a

a.

— (cl + 36,

1 -6 -6
1 3a -
1 2 a a

-f (a + 6)a(a + 26) ,

for the last two determinants in the preceding line are each equal
to a(a + 26) . Thus we have

S, =

1 -b -b
1 3 a -2b

12 a a

+

1

ci(ci + 6)(a 4* 26)

a + 36

S,

+

1

a + 36

as it should be. And this method of showing that the validity of
the fourth case is dependent on that of the third is applicable in
other case.

8. Sevenfold Knottiness. By Prof. Tait.

(Abstract.)

From the point of view of the Hypothesis of Vortex Atoms, it
becomes a question of great importance to find how many distinct
forms there are of knots with a given amount of knottiness. The
enormous numbers of lines in the spectra of certain elementary
substances show that the form of the corresponding Vortex Atoms
cannot be regarded as very simple. But this is no objection against,
it is rather an argument in favour of the truth of, the Hypothesis.

364 Proceedings of the Royal Society

For not only are the great majority of possible knots not stable forms
for vortices ; but altogether independently of the question of kinetic
stability, the number of distinct forms with each degree of knotti-
ness is exceedingly small, — very much smaller than I was prepared
to find it. I have already stated that for three, four, five, and sixfold
knottiness, the numbers are only 1, 1, 2, 4. For a reason given
in my first paper, knots whose number of crossings is a multiple of 6
form an exceptional class : so I thought it might be useful to dis-
cover and to figure all the distinct forms with seven -fold knottiness.
Eight and higher numbers are not likely to be attacked by a
rigorous process until the methods are immensely simplified. The
method of partitions, supplemented by the graphic formulse of my
last paper, is to some extent tentative. I have verified the present
results by means of it, and have extended it to 8-fold knottiness,
but I am not certain that I have got all the possible forms of the
latter.

As I did not see how to abridge the process, I wrote out all the
admissible permutations of the seven letters in the even places of
the scheme. These I found to be 579, five of which were, of course,
unique. The others (as 7 is a prime number) were divisible into
82 groups-— those of each group being mutually equivalent. On
examination, it was found that only 22 of the 87 selected arrange-
ments satisfied the criterion for possible knots (see I §(£>) of my paper,
ante p. 238), and several even of these were repetitions. These
repetitions were of two kinds — 1st, the mere inversion of the order
of the scheme ; 2d, the relative positions of a 3-fold and a 4-fold knot
which in certain cases wero found combined as a 7-fold form.
Clearing off these repetitions, and along with them a form really
belonging to 6-fold knots (because consisting of two trefoil knots
and one nugatory intersection), there remain only eleven distinct
forms of the 7th order. These are as follows : —

1.

3

This has a great many forms, with correspondingly different

of Edinburgh, Session 1876-77. 365

symbols, being a mere compound of a 3-fold and a 4-fold knot,
which may have any relative positions on the string.

This is one of Listing’s knots.

3.

4.

\ /\/

2 2

Listing has shown that this is deformable into 2 above.
5-

/ \ / \

5 “ 4 or 3 —4-— 3

1/

2

I find that this can be deformed into 3 above. It is figured in
my paper on Links , ante , p. 325, first woodcut.

4

i

or

6.

366

Proceedings of the Royal Society

7.

5

4

or

4 — 4

3 _ 2

This can be deformed into 6 above

8.

2

/ \

6 EEE 6

This species of knot occurs for all numbers of intersections
greater than 2.

9.

2 — 2

This is the 7 knot which Listing does not sketch. Ante, p. 311.

10.

11.

7=7

This is the simple twist, which occurs for every odd number of
intersections.

As 2 and 4, 3 and 5, 6 and 7 are capable of being deformed into
one another, three of them are not independent forms, and thus
the number of distinct forms of seven -fold knots is only eight.

Drawings of various forms of each of these knots were given, as
well as indications of the modes in which they can be formed from
knottinesses of lower orders.

367

of Edinburgh, Session 1876-7 A

Monday , 2 d April 1877.

Ski WILLIAM THOMSON, President, in the Chair.
The following Communications were read : —

1. Professor Geikie exhibited a large Map showing the
progress of the Geological Survey of Scotland.

2. Notice of a Saline Water from the Volcanic Rocks of
Linlithgow. By Professor Geikie, F.R.S.

From a boring which has recently been made about a mile west
from the town of Linlithgow, water has been obtained differing so
much in character from that of the usual wells and springs of the
district that some notice of it deserves to be placed on record.
When the fact was communicated to me I was asked to explain by
what means sea-water could obtain access to underground rocks in
an inland district. On visiting the ground 1 found the site of the
bore to be among some hollows of the gravel and sand which
cover the country between Falkirk and Linlithgow, its height
being about 165 feet above the sea, from which it was distant
about three miles. The ordinary wells of the district are situated
in the superficial deposits, and supply good potable water, though
the supply is necessarily limited. A more copious flow being desired
the bore was sunk through the sands, gravels, and clays (here
rather more than 100 feet thick), and then entered upon a succes-
sion of green, brown, blue, and red “ wbinstone.” After a depth
of 317 feet had been passed through, consisting entirely of these
alternations of “ whinstone,’; a sample of the tolerably copious
supply of water which had now appeared was drawn up and sent
for analysis to Dr Stevenson Macadam, whose results were as
follow : —

Chloride of sodium,
Sulphate of lime,
Chloride of calcium,
Chloride of magnesium,
Chloride of potassium,

1 18*7 6 grains per imperial gallon.

7-94

6- 78

7- 83
1-46

33

33

33

33

33

33

33

33

3 c

VOL. IX.

368 Proceedings of the Royal Society

Carbonate of lime,

20-23 grains

per

imperial gallon.

Carbonate of magnesia,

3-48

55

5»

Oxide of iron,

0-34

55

55

Phosphates,

0-71

55

55

Soluble silica,

0*64

55

55

Organic and volatile matters.

, 2-37

55

55

170-54

This large admixture of saline ingredients rendered the boring
unavailable for the increase of the water-supply; but the boring-
rods were driven 30 feet further in the hope that possibly this
mineral water might find some other subterranean means of
escape. The hope was of course disappointed, and the operation ter-
minated at a depth of 451 feet from the surface, the lower 348 feet
of the boring having been found to pass wholly through “ whin-
stone ” in numerous bands of varying hardness and colour. Two
samples of the water, taken when the ultimate depth had been
reached, were submitted for analysis to different chemists, and gave
nearly similar results. The proportions of salts obtained by Mr
Robert M‘Alley, Falkirk, were the

Carbonate of lime,

Carbonate of magnesia,

Sulphate of lime,

Chloride of calcium,

Common salt,

Alumina,

Siliceous matter,

Volatile and organic matter,

One character of the water not noticed in the analyses, but dis-
tinctly perceptible to me in a freshly drawn sample, was the odour
of sulphuretted hydrogen. I may add that the bore was begun
from the bottom of a previously made well 18 feet from the sur-
face, and that I found the water flowing out abundantly from the
top of the bore-tube into the well from which it wras temporarily
pumped away.

It was evident that the idea of any subterranean communication

following

7 grains per gallon.

•60

55

55

•92

55

55

1-22

55

55

134*76

55

55

•20

55

5

1-20

55

55

1-60

55

55

147-50

369

of Edinburgh, Session 1876-77.

with the sea was quite inadmissible. In the first place, the
locality is three miles from the nearest part of the sea-coast, with
a ridge of high ground intervening. In the second place, between it
and the sea-margin lie the numerous deep pits of the Borrowstoun-
ness and Kinneil coal-fields, which, it may be supposed, must pre-
vent at least any superficial wrater-communication. And in the third
place, the proportions of the various salts contained in the water
are quite different from those which would have resulted from the
mere access of ordinary sea- water. The salts can only have been
derived from the subterranean rocks traversed by the water.

An acquaintance with the geology of the district enables me to
recognise the various kinds of “ whinstone ” found in the bore.
They are successive beds of the dull green and brown, usually more
or less decomposed, dolerites (diabases) forming the long volcanic
range between Bathgate and the sea, and which were poured out
partly as submarine and partly as, subaerial lavas during the de-
position of the Carboniferous Limestone, or Lower Coal series of
Linlithgowshire. Occasional bands <jf green and red tuff mark in-
tervals between the lava-flows. Since the water from the superfi-
cial gravels was of the usual potable quality there can be no doubt
that the saline impregnation comes from the underlying rocks.

So far as I am aware, the first detection of soda as a chemical
constituent of rocks was made by Dr Kobert Kennedy, and an-
nounced to this Society as far back as December 1798. He
analysed the specimens of whinstone employed by Sir James Hall
in his classical experiments upon the fusibility of whinstone and
lava, and found the constant presence of soda to the extent of four
or five per cent., with one per cent, of muriatic acid. He further
examined pieces of sandstone from the neighbourhood of Edinburgh
and elsewhere, with the invariable result of detecting an appreciable
quantity of common salt in them. Since the early date of his
researches chloride of sodium has been found very widely diffused
among the minerals and rocks of the earth’s crust.

There seems to be three chief sources from which rocks derive
their chloride of sodium: — 1. Bain; 2. The evaporated water of old
salt lakes and inland seas; 3. Volcanic sublimations.

1, Rain. — The researches of Dr Angus Smith * into the compo-

* See his Air and Rain .

370

Proceedings of the Royal Society

sition of rain in different parts of the country have shown the very
general prevalence of chlorides, and particularly of chloride of
sodium, in the air. As might be expected, the proportion of
chlorides is greatest nearest to the sea, though abnormally large
quantities are found in the air of manufacturing towns as the
result of the combustion of coal, &c. On the west side of Britain
the proportion of hydrochloric acid in rain was found sometimes to
amount to nearly four grains per gallon, or 56 parts in a million.
On the east side of Scotland the proportion sinks to *9 grain per
gallon, or 12 parts in the million. There can be little doubt that
most of this is chloride of sodium. Dr Smith has pointed out the
curious fact that this salt cannot be conveyed into the atmosphere
merely in spray driven from the surface of the sea by high winds,
for if that were the case the composition of the rain should be
approximately like that of sea-water. But the saline ingredients
do not occur at all in similar proportions. It seems reasonable to
suppose that the superficial parts of rocks liable to be saturated with
rain-water must thereby receive an appreciable amount of chloride
of sodium. In this case it is evident that much care should be
exercised in procuring for analysis portions of rock which lie
beyond the reach of this surface saturation. Possibly in some of
the instances cited by Kennedy, in the paper already referred to,
the common salt may have been introduced by the action of rain.

2. The Deposit of Salts on the Floor of Old Lakes and Inland Seas.
— This mode of origin is doubtless by much the most important
source of the chloride of sodium in rocks. When we consider the
large proportion of marine strata in the stratified part of the earth’s
crust it is surprising, as De la Beche remarked long ago,* that
saline waters are not more abundant than they really are. Dr
Sterry Hunt has pointed to the mineral waters of Canada and the
North-Eastern States as probably deriving their salts from the
original sea-water of palaeozoic times still imprisoned within the
pores of the rocks. f I need not refer to the abundant deposits of
rock-salt and gypsum, as well as of saliferous and gypsiferous
clays, which occur in so many districts of the world.

3. Volcanic Sublimations. — The occurrence of incrustations and

* Researches in Theoretical Geology,
t “Essays in Chemical Geology, 1875. :

371

of Edinburgh, Session 1876-77.

stalactites of common salt upon the walls and slopes of a volcanic
crater after eruption, and the appearance of the same substance
upon the surface or within the chinks of recently-consolidated lava
streams, have long been observed. On Yesuvius vast quantities of
salt have been gathered again and again, and have been used by
the inhabitants at the foot of the mountain. Among the Icelandic
volcanoes the same fact has occurred. But besides this outward
and conspicuous manifestation, chemical analysis has revealed the
presence of chloride of sodium in many volcanic rocks, either
diffused through their crystalline matrix or entangled within their
individual constituent minerals. In such volcanic minerals as
Hauyne, Nosean and Sodalite it has been found to be noticeably
present. It has been extracted even by pure water from clink-
stones, basalts, and from various plutonic rocks.

There can be little doubt that it is to this volcanic origin that
the large admixture of salt in the Linlithgow water is to be traced.
The bore may have reached a stratum of ancient lava or tuff,
originally permeated or incrusted with salt, which may have been
dissolved by percolating water, and yet have remained in solution
below for want of any ready means by which the water could
escape to the surface. This escape is now provided by the bore, and
the water is consequently now removing the salt from the rock.

It may be mentioned that some of the best known saline waters
of Scotland rise from volcanic rocks. At the Bridge of Allan, water
containing 95 grains of chloride of sodium in the gallon takes its
rise from near the top of the enormous mass of lavas and tuffs
erupted during the Lower Old Bed Sandstone period, and forming
now the chain of the Ochil Hills. At Pitcaithley, Bridge of Earn,
water containing 114 grains of the same salt in the gallon rises
from the same volcanic band, while at Dunblane, water with 48
grains of common salt in the gallon comes through the lower parts
of the red sandstones of that district, which lie upon the same
great volcanic series. In most of these cases the rise of the saline
water appears to have been determined by an accident, such as the
sinking of a bore for water, or, as at Bridge of Allan, during the
search for minerals.

372

Proceedings of the Royal Society

3. On the Arrangement and Relations of the Great Nerve-
Cords in the Marine Annelids. By W. C. MTntosh, M.D.,
F.R.S.E., F.L.S.

(Abstract.')

Fam. Eupiirosynid^:. — In Euphrosyne foliosa , Aud. and Ed., the
separate nerve-cords are comparatively large, and lie quite within
the body-wall, the oblique muscles, which generally bound the
longitudinal ventral muscles, decussating beneath them.

Ampiiinomidas. — The cords are somewhat small and flattened
in Chloeia , and occupy an area bounded internally by a trans-
verse band of fibres, and externally by the circular muscular layer
and the hypodermic basement-tissue. The oblique muscles
are attached at the outer border of each trunk.

ApiiRODiTiDjE. — The nerve-cords in Aphrodita aculeata , L., occur
in a transversely elongated space between the ventral attachments
of the oblique muscles, and bounded externally by the hypodermic
basement-tissue and the cuticle. In Hermione Jiystrix , Sav., again,
they lie — as distinct trunks — in a well-defined hypodermic area
within the dense cuticle, and separated by an interval from the
attachment of the oblique muscle on each side.

Polynoidje. — In Lepidonotus squamatus , L., the cords occupy a
hypodermic area between the ventral longitudinal muscles. The
oblique muscles pierce the vertical at the upper and outer angle of
the space, and are attached to the hypodermic basement-tissue,
external and superior to the cords. A belt of hypoderm intervenes
between the latter and the cuticle. In Polynoe scolopendrina , Sav.,
the interval between the ventral attachments of the oblique muscles
is less, and the cords are bounded superiorly by a special longitu-
dinal muscle.

Accetid.e. — In Panthalis (Erstedi , Kbg., the trunks are situated
in the hypodermic region between the ventral longitudinal muscles,
a thin layer of the former tissue occurring between them and
the cuticle. The great oblique muscles pass down to their
upper and outer border. The space between the ventral longitu-
dinal muscles is less than in the Polynoidae.

SiGALiONiDiE. — The space between the ventral longitudinal
muscles anteriorly in Sthenelais boa , Johnst., is still more narrowed

373

of Edinburgh, Session 1876-77.

than in Panthalis, and the hypodermic area for the nerve is thus
increased in depth. Superiorly the arch is completely covered by
the insertions of the vertical and oblique muscles ; and it is inte-
resting that the latter do not pierce the former (which occupy the
middle line), but are attached to the basement -tissue below them,
on each side of the nerve-area. The cords are almond-shaped in
transverse section, whereas in S. Mathilda e, Aud. and Ed., they are
round, and the hypodermic area enclosing them is much more
expanded inferiorly.

Nephthydjdje. — In Nephtliys coeca , Fabr., the combined oblique
and vertical are attached along the entire arch of basement-
tissue, above the nerve-area. A broad hypodermic belt exists
above the nerve trunks, and a narrower between them and the
cuticle.

Phyllodocid^:. — The nerves in Phyllodoce groenlandica, (Erst.,
are situated within the circular muscular coat, and above
the insertions of the oblique muscles (which decussate in the
middle line), as well as such fibres of the vertical muscles as are
inserted into the basement-tissue of the ventral hypoderm. In
Eteone picta , De Quatref., and Eulalia viridis , 0. F. Miiller, certain
fibres of the oblique pass at intervals right over the cords, so as to
form a continuous band from side to side, and in the former an
interval between the oblique muscles is indicated.

In Alciope the cords also lie within the circular muscular layer —
in the interval between the longitudinal ventral. The oblique pass
below the cords, but do not appear to meet in the middle line- The
sole specimen, however, is indifferently preserved for microscopic
work.

HEsiONiDiE. — The trunks in Ophiodromus vittatus , Sars., have
in the anterior region passed below the ventral attachment of
the oblique muscles to the basement-tissue. A thin stratum of
longitudinal fibres occurs superiorly, while externally is a thickened
hypoderm. The nerves seem to be proportionally large.

Syllidjs. — In Syllis armillaris, 0. F. Muller, the nerve-cords
are also comparatively large. A considerable depth of the closely
approximated ventral longitudinal muscles shuts them from
the very thin hypodermic elements within the thickened cuticle,
except in the intervals between the ganglia, where there is a

374

Proceedings of the Hoy at Society

slender pedicle. The oblique muscles bend below the cords to be
attached to the raphe in the same intervals. Fibres from the
walls of the alimentary canal also descend to the raphe on each
side of the trunks.

Nereids. — In Nereis pelagica , L., the nerve-cords lie rather
above the attachments of the oblique muscles to the hypodermic
basement-tissue, the area being continued to the hypoderm by a
central pedicle. Nereis ( Alitta ) virens , Sars., an epitocous form,
likewise has the oblique muscles attached on each side of the
pedicle of the nerve-area, while the vertical are inserted in a
chitinous arch at the upper and lateral regions. Two well-marked
longitudinal muscles lie over the cords. Several neural canals
exist, — viz., two large infero-lateral, a single superior median, and
a smaller, a little below the latter, on each side. In Nereis diversi-
color , 0. F. Muller, each cord has a neural canal of considerable
size towards its inferior border.

Staurocephalid^e. — The cords are large in Staurocephalus
rubrovittatus , G-rube, and occur in the somewhat wide interval
between the ventral attachments of the oblique muscles. Exter-
nally are the basement-tissue, hypoderm, and cuticle.

LumbrinereiDjE. — In a Lumbviconereis from Herm, a large
neural canal exists above the cords, which are carried inward by
the approximation of the great longitudinal ventral muscles. The
oblique meet over the neural canal. Externally are basement-
tissue, hypoderm, and cuticle. The nerves are pressed further
inward in Notocirrus tricolor , Johnst., the oblique muscles being
attached to the summit of the nerve-area (laterally), outside the
fibres forming the special chamber for the vessel. Some fibres
pass down each side, and cross below the nerve-area.

The neural canal in the posterior third of Lysidice ninetta, Aud.
and Ed., is situated toward the ventral border of the ganglia, but
between the cords in the intervals. The oblique muscles pass
below the cords. The latter takes place likewise in Palolo viridis ,
Gray.

EoNiciDiE. — The cords in Marphysa sanguined, Mont., lie be-
tween the greatly developed longitudinal vential muscles, and
present the aspect of a margin to the large median neural canal.
The fibres of the oblique muscles are attached to the upper and

375

of Edinburgh , Session 1876-77.

outer border of the region, — a few fibres passing downward to
curve outward at the circular coat of the body-wall. Externally,
between the latter coat (and a layer of somewhat isolated longitu-
dinal fibres within it), are the hypoderm and cuticle. In Eunice
norvegica , L., a similar arrangement occurs in the anterior third,
and a large median neural canal lies below the cords. The strong
oblique muscles pass down to the ventral hypoderm. Distinct
muscular bands also enclose the ventral blood-vessel and nerve
trunk in a tunnel. A little behind the middle of Eunice Harassii ,
Aud. and Ed., the cords present the same external coverings, only,
from the great size of the oblique and vertical muscles, they are
somewhat supported by the latter inferiorly. The same arrange-
ment occurs in a large male Eunice from the “ Porcupine.” The
constancy of the muscular tunnel for the nerve-cords and ventral
blood-vessel is interesting.

Onupbidid^. — The oblique muscles in both Notliria con-
chylega, Sars., and Hyalinoecia tubicola , 0. F. Muller, are well
developed, and not only meet, but slightly cross, in the middle
line. The nerve-cords lie in the angle of decussation superiorly,
and have a single neural canal of considerable size towards the
lower border. Besides the oblique are externally the circular
muscular coat (which, in H . tubicola , is specially developed in the
median line), a narrow band of hypoderm, and the dense cuticle.

Goniadxd^.— -In the anterior region of Goniada maculata,
(Erst., the powerful oblique muscles sweep from below the bristle-
bundles on each side, with a slight inclination downward and
inward, and meet for insertion on each side of the hypodermic
wedge above the nerves. The latter occupy a somewhat triangular
area of the hypoderm, and each has a small neural canal toward
the upper and narrow part. In Eone Nordmanniy Mgrn., the
nerves are proportionally smaller, and the hypodermic area less.

Glyceride. — The cords at the anterior third of Glycera
capitata , (Erst., are large, and occur in a hypodermic region, wedged
between the great longitudinal ventral muscles, which touch in
the middle line, so as to form an arch over the nerves. The great
external circular muscular layer ceases before reaching the nerve-
area, so that externally the latter has only the hypoderm and the
specially thickened cuticle. The oblique muscles are very slightly

VOL. ix. g d

376 Proceedings of the Royal Society

developed in this species, and their terminations over the cords
can only be seen occasionally. Each cord has a neural canal at
its upper third, near the middle line. Glycera Goesi, Mgrn., shows
nearly the same arrangements ; while G. setosa , (Erst., exhibits
more evident separation of the cords. The insertions of the oblique
muscles over the nerve-area are best seen in G. alia , Rathke, a
large species, in which the cords are proportionally less.

Ariciid.®. — In the anterior region of Aricia latreillii , Aud.
and Ed., the cords are situated at the upper part of a somewhat
triangular hypodermic area, bounded laterally by that part of the
circular coat clasping the ventral longitudinal muscles. Powerful
oblique muscles meet for insertion over each cord. In the same
region of Scolopos armiger , 0. F. Muller, the cords also lie beneath
the point of union of the greatly developed and nearly horizontal
oblique muscles, and supported laterally by the massive edges of
the ventral longitudinal. A single neural canal exists superiorly.
Between the cords and the hypoderm is the thick circular muscular
coat. In the middle of the body the nerves are thrust upward by
the great ventral muscles, which are only separated by the narrow
pedicle of the area.

OpheliiDjE. — Throughout the greater part of Ammotrypane
aulogaster , H. R., a peculiar modification of the body-wall exists,
in the form of a constriction between the dorsal and ventral longi-
tudinal muscles. The intermediate pedicle is formed apparently
by the metamorphosed vertical muscles, which have coalesced over
the nerve cords. The oblique muscles pass from the outer edge of
the ventral longitudinal to the middle line below the nerve-area.
A small and indistinct neural canal appears toward the upper part
of the latter. In Ophelia limacina , H. R., the cords in the smoothly
rounded anterior third lie in the middle of the long interval
between the ventral longitudinal muscles. The oblique are in-
serted far outside the cords. Externally are a granular area, a
series of transverse fibres, and the cuticle. Toward the posterior
part of the body, where the ventral ridges are well-developed, the
cords, by an intricate change in the relationships of the muscles,
get above the median (ventral) insertion of the vertical, the fibres
of which extend outward and somewhat downward into each pedicle.
The true oblique is with difficulty seen ; but it appears to be a

377

of Edinburgh, Session 1876-77.

slender muscle passing from the outer border of the ventral longi-
tudinal. In many sections a neural canal is seen somewhat above
the middle of the area. A muscle passes from the bristle-tuft up-
ward in a slanting direction through each pedicle to the raphe be-
low the nerve. In Travisia Forbesii , Johnst., the nerve-trunks are
situated between, and somewhat above, the insertions of the
oblique muscle. Externally are the circular coat, a translucent
basement-tissue, a granular hypoderm, and a very thin cuticle.

ScALiBREGMiDiE. — In Eumenia Jeffrey sii the cords in the anterior
region occur toward the inner aspect of the thick layer of trans-
lucent basement-tissue, below and between the insertions of the
two long oblique muscles. Toward the middle of the body the
trunks still indent the basement-tissue, the circular muscular coat
forming their inner boundary. A series of strong transverse fibres
occurs at intervals as an arch over the cords. In Scalibregma in-
flatum, H. B., the cords (in the posterior region) lie below the cir-
cular muscular fibres, which occur beneath the commissure of the
oblique in the middle line. Externally are the hypoderm and
cuticle.

TELETHUSiE. — In the anterior third of Arenicola marina , L., the
cords form a comparatively small ovoid mass— clasped by the great
longitudinal muscles, and connected with the circular coat by a
narrow granular pedicle.

Si’H/ERODORiDyE. —While there is a very thick cuticle in Ephesia
gracilis , H. R., the hypoderm is slightly developed below the
nerves. The oblique muscles pass from the inferior border of the
bristle-tufts to the outer margin of the nerve-trunks.

Chlor,emid,e. — In Trophonia plumosa, 0. F. Muller, the nerves
lie above the median decussation of the oblique muscles, the cords
being distinct in the intervals between the ganglia. Externally
are also the circular coat, a narrow hypoderm and a roughly
papillose cuticle.*

CmETOPTERiDiE. — In Chcetopterus norvegicus , Sars., the cords are
placed wide apart in front, in consonance with the peculiarly
modified muscular arrangements of the body- wall. They are hypo-
dermic. By the great increase of the median system of muscles

* Next the Chlorsemidse Dr Malmgren places the Sternaspididse, but in
structure Sfcernaspis is Gephyrean.

378 Proceedings of the Royal Society

the homologues of the ventral longitudinal are pushed outward.
The oblique preserve their usual relations with the latter and the
nerve-cords, over which their ventral termination occurs. Another
muscle, probably the homologue of the transverse, passes from the
termination of the oblique inward to the middle line on each side.
As the late M. Claparede has shown, the cords approach each other
in the posterior region in Chcetoyterus , while in Telepsavus they re-
main separate throughout.*

SpioniDjE. — As pointed out last session,! the cords in this family
are hypodermic in position. Their relation to the ventral inser-
tions of the oblique muscles are also well shown, since they follow
the latter in their gradual progress inward from the sides of the
body in front until the cords touch and the muscles meet over
them. The neural canals are largely developed.

CirrattjliD-ZE. — In Cirratulus cirratus , 0. F. Muller, the cords in
the anterior region lie in the median line ventrally within a thick
hypodermic area. The oblique muscles are inserted at the summit
of the area, and the sides of the ventral longitudinal muscles over-
lap its upper arch. The circular muscular coat is continuous over
(internal to) the cords. In Dodecaceria concharum , (Erst., a thick
median mass of blackish hypoderm protects the cords, and the
relations of the oblique and longitudinal ventral muscles are
similar.

Halelminthid^;. — This family approaches the Lumbricidse in hav-
ing the nerve-cords placed within the great and nearly continuous
longitudinal muscles of the body-wall. Externally (in the ventral
region of Gayitella capitata , Fahr.) are in addition a dense circular
muscular coat, a thin layer of longitudinal fibres, basement-tissue,
hypoderm, and cuticle. Anteriorly there are two divisions of the
ventral longitudinal muscular fibres under the nerves, but in the
middle region of the body they have coalesced into a single mass.
A neural canal occurs superiorly in the ovoid nervous area. Two
vertical muscles bound those above which the nerves lie, but the
oblique are not recognisable.

Maldaidn^;. — In the anterior region of Praxilla yrcetermissa ,
Mgrn., the nerve-cords lie beneath (outside) the circular muscular

*Annelides Sedent. p. 127, &c.
t Proceed. R.S.E., vol. ix. No. 94, p. 124, &c.

379

of Edinburgh, Session 1875-76.

coat, at the gap between the ventral longitudinal muscles. The
area is small and flattened, and has a large neural canal in the
centre superiorly. The oblique muscles are attached above the
area. A similar arrangement occurs in Nicomache lumbricalis,
Fabr., and in a large Canadian species of the same genus.

AmmociiaridjE. —About a quarter of an inch behind the snout
the nerve-area in Owenia filiformis , D. Ch., forms an ovoid mass
outside the tough basement-tissue bounding the great longitudinal
muscular layer. The area is entirely hypodermic, and as very little
of this tissue remains in the majority of the preparations, the
cords are often bare. The oblique muscles are not visible, and the
longitudinal are only separated in the median line dorsally and
ventrally.

HERMELLimE. — In Sabellaria spinulosa , R. Leuckart, the cords
remain quite separate throughout their entire length. Anteriorly
each is placed in the substance of the great ventral muscle, near
its upper and inner border. No distinct oblique muscles appear in
this form. Posteriorly the nerves occupy the same relative position
in the. diminished muscles, and each has a large neural canal at its
inner border.

Amphictenid^e. — In Cystenides hyperborea, Mgrn., the united
cords in the anterior region occur as an ovoid mass over the trans-
verse muscular fibres in the ventral median line. The large oblique
muscles are widely separated from the nerve-trunks.

Ampharetid^e. — In Amphideis Gunneri , from Canada, the nerves
(in transverse section of the body-wall) appear as two minute sepa-
rate bodies enveloped in a common neurilemma lying in the thick
hypoderm of the median ventral region. Internally are the fibres
of the circular coat and the insertions of the oblique and vertical
muscles.

Terebellid^e. — Anteriorly in Terebella nebulosa , Mont., the nerve-
cords are placed outside the transverse band of fibres (part of the
circular coat) between the oblique muscles, and therefore are hypo-
dermic. The same arrangement occurs posteriorly. In Polycirrus
aurantiacus, G-r., the cords have the same relative position, only
they are considerably larger— a feature of interest in connection
with the phosphorescent properties of the species. Within the
circular coat is a small median longitudinal muscle. In Terebel-

380

Proceedings of the Royal Society

j

tides strcemi, Sars., the cords are small, and lie within the hypoderm
and strong circular coat in a line between the ventral longitudinal
muscles. The slender oblique are attached on each side of the
trunks, and must be carefully distinguished from the much larger
muscles which cut off the great lateral longitudinal muscle
externally.

Sabellid^e. — In Sabella pavonina, Sav., the nerves occur in front
as widely separated cords — each situated at the inner border of the
ventral longitudinal muscle. A large neural canal lies above each.
Externally are the circular muscular coat, the greatly thickened
hypoderm and the cuticle. The feeble oblique muscles are partly
inserted above the neural canal and partly into the basement-
layer below and internal to the nerve. Proceeding backward, the
neural canal increases very much in size, so that it occupies the
whole area on each side of the central region, and presses the ovoid
nerve-cord to the exterior. The canals appear to be filled with a
slightly yellowish substance — consolidated in the preparations. The
same relative position is maintained posteriorly, though the neural
canal is smaller, and, as in front, placed superiorly. The arrange-
ment in Dasychone bombyx , Dalyell, agrees in most respects with
the foregoing.

Chone and JEuchme seem to approach the next family in the
arrangement of the nerve-cords and in the remarkable structure of
the great longitudinal muscles. In Chone infundibvlum , Mont.,
the nerve-trunks occur between the ventral longitudinal muscles,
and placed much more closely together than in Sabella. A large
neural canal lies over each nerve. Externally are the strong
circular coat, the thick hypoderm, and the cuticle. The oblique
muscles are attached to the sides of the median vessel above the
neural canals, and to the summit of the latter on each side. While
the cords are lost in the ganglia, the neural canals remain distinct.
In Euchone a similar condition exists, for though the cords are
distinct anteriorly they are closely approximated posteriorly.

Eriographidid^e. — In the anterior third of Myxicola infundi-
bulum, Renier, the cords are approximated in the interval between
the great longitudinal ventral muscles, and beneath the large
blood-vessel. A neural canal appears to exist toward the superior
border. The slender oblique muscles are inserted into the summit

381

o f Edinburgh , Session 1876-77.

of the nerve-area. Externally are circular coat, hypoderm, and
cuticle. Posteriorly the cords are connate, and a single neural
canal of considerable size exists superiorly.

Serpulule. — In Protula protensa the cords anteriorly are situated
under the great longitudinal dorsal muscles as widely separated
trunks. They then fall into position and approach the increasing
longitudinal ventral muscles — a large neural canal being at the
inner border. Posteriorly the neural canal is proportionally larger
than in front, but the relations of the nerves are similar. At their
commencement in front the nerve-cords are internal, and have
beneath them all the tissues under the dorsal muscles. After
reaching the inner border of the ventral longitudinal muscles they
have externally ( i.e ., interiorly) a thin layer of longitudinal mus-
cular fibres, the circular coat, hypoderm, and cuticle. A transverse
band bounds them superiorly. Posteriorly the first-mentioned
(longitudinal) layer is absent externally. In Serpula vermicular is,
L., a similar arrangement occurs, but the neural canal is external,
that is, next the ventral longitudinal muscle, and the thin longi-
tudinal stratum is internal.

4. On the Application of Graphic Methods to the Deter-
mination of the Efficiency of Machinery. By Professor
Eleeming Jenkin.

{Abstract.)

The general scope of the paper was to show how by graphic
methods we might find the relation between effort exerted at one
part of a machine and the resistance overcome at another part.
It was shown that for a given machine at any instant a linear
frame might be substituted, such that the stresses in the links
corresponded to the pressures at the joints between the elements
of the machine, including the pressures due to driving effort and
resistance. Numerous examples were given of the application
of this frame, called the dynamic frame, to the solution of the
above problem, the friction, inertia, and weight of all the parts
being taken rigidly into account.

382

Proceedings of the Royal Society

5. On Professor Tait’s Problem of Arrangement. By

Thomas Muir, M.A.

The problem in question is — To find the number of possible
arrangements of a set of n things, subject to the conditions that
the first is not to be in the last or first place, the second not in the
first or second place, the third not in the second or third place,
and so on.

A little consideration serves to show that we may with advan-
tage shift the ground of the problem to the theory of determinants.
For the sake of definiteness take the case of five things, A, B, C,
D, E. Here A may be in the second, third, or fourth places only ;
B in the third, fourth, or fifth places only ; and similarly of the
others — a result which we may tabulate thus : —

AAA.

. . B B B

c . . c c

D D . . J)

E E E . .

an A being written in the places which it is possible for A to
occupy, and a dot signifying that the letter found in the same
line with it may not occupy its place. Hence, to obtain the
various arrangements, we see that for the first place we may have
any letter that is in the first column ; for the second place any
letter that is in the second column, provided it be not in the same
line with the letter taken from the first column ; for the third
place, any letter that is in the third column, provided it be not in
the same line with either of the letters previously taken, and so
on. This law of formation, however, is identical with that in
accordance with which the terms of a determinant are got from
the elements of the matrix ; so that the problem we are concerned
with is transformed into this : Find the number of terms of the

determinant of the wth order of the form, —

of Edinburgh, Session 1876-77.

383

• *• * *

• • * * ■*

#■ * *■

where the dots and asterisks denote zero elements and non-zero
elements respectively.

In the solution of this, determinants of a set of other forms
require to be considered, viz., —

•

*

*

%

*

•

*

*

*

*

•

*

*

*

*

•

•

*

*

*

*•

•

*

*

%

•

•

*

*

•

•

*

*

*

•

•

*

*

*

*

•

*

*•

*

*

•

•

*

*

%

•

•

*

*

*

•

•

*

*

*

*

•

•

*

%

*

•

•

5

*

*

*

•

•

in all of which the elements of the main diagonal are zero ; the
elements of the adjacent minor diagonal being in the first also all
zero, in the second all zero except the first element, in the third
all zero except the second element, and so on. Let us denote the
number of terms in these when they are of the nth order by

XoO) , XiO) , xM ,

and let the number of terms sought be

Further, let any determinant-form with dots and asterisks stand
for the number of terms in such a determinant; the four forms
above, for example, being thus symbols equivalent to ^(5) , Xo(5) ,
Xi(5) , Xa(5) , respectively.

3 E

VOL, IX.

384

Proceedings of the Royal Society

Beginning with the first of the x forms we see it to be trans-
formable into

* * *•

* * *

*■ *

* *•

* *• *

+

* *

*

* #•

* * *

and the second term of this may in like manner be changed into
• • * *

*■ *■

* *

+

* *

and the second term of this again into

+

the second term of which is zero. Hence we have the result,
Xo (w) = ^(n) + V(n - 1) + - 2) + . . . + tf(3), ... (a)

Of the other x forms it is clear to begin with that

Xl Xn— i > X2 Xn— 2 5 • • • •

and treating the distinct cases as we have treated x0 > we equally
readily see that

XiO) = XoM + X<kn - !) + XoO - 2)

X*(n) = XoO) + Xo(n - !) + XiO - 2)

XsO) = XoO) + XoO - !) + X2O - 2)

X»-aO) = XoO) + XoO - !) + XiO - 2)
X«-lO) = XoO) + XoO “ !) + XoO - 2)

385

of Edinburgh , Session 1876-77.

which, on eliminating Xd X2) ••• fr°m the right-hand members,
become

XiO) = XoO) + Xo(n - !) + Xo(^ “ 2)

XaO) = XoOO + Xo(n - !) + XoO - 2) + Xo(n - 3) + XoO - 4)

Xs(n) = XoO) + XoO - !) + XoO - 2) + XoO - 3) + XoO - 4) + XoO ”5)

'+XoO“6)

X«-aO) = XoO) + XoO - 1) + XoO - 2) + XoO “ 3) + XoO - 4)
x«-i O) = XoO) + XoO - 1 ) + x<>0 - 2) •

Here the second of the series of right-hand members has two terms
more than the first, the third two terms more than the second, and
60 on until we approach the middle of the series, when, if n be odd,
the two middle right-hand members are found to be the same as
the one preceding or the one following them, the whole four ending
thus —

• • • -+Xo(5)+Xo(4)+Xo(3) >

and if n be even, the one middle right-hand member is found to be
greater by unity than the one preceding or the one following it,
and to end thus — -

. . . . + Xo(5) + Xo(4) + Xo(3) + 4 >

the 1 arising from the fact that the above process of reduction, in
the case of x* n(n), leads us finally, not to

• * *

• * *

* *

• *

• • *

+

, but to

• • *

+

• •

#

*

*

*•«•, t0 Xo(3)"h !•

Eeturning now to the ^ form, and taking

386

Proceedings of the Royal Society

we transform it into

•

*

*

*

•

•

*

*

•

•

*

*

*

•

*

*■

-+•

*

•

*

*•

+

*

•

•

*

#

•

•

*

*

*

•

*

*

*

•

*

*

*

•

•

*

*

•

•

*

*

*

•

the middle term of which*becomes by transposition of the first two
rows, and the subsequent transposition of the first two columns,

• * # #

• • * *

* *

Consequently we have

*(5) = X,(4)+x/4) + XsW.

and it is easily seen that a similar transformation is possible in
every case, giving

*0) = XiO - !) + xln “ !) + X*(w - 1) + . . . . + x«- a(w - 1) .

Expressing x2> Xa> — terms of x0 by means of wbat precedes, we
have

y(n) = Xo(n ~1) + Xo(n - 2) + Xu(n - 3)

+ XoO “ !) + XoO “ 2) + XoO “ 3) + XoO “ 4) + XoO - 5)

+ XoO - 1) + XoO - 2) + XoO - 3) + XoO - 4) + XoO - 5)
+ XoO - 1) +XoO - 2) + XoO “ 3) »

of Edinburgh, Session 1876-77. 387

and now using (a), to express x0 in terms of 4>, we find

'I' (w) = ty(n- l)424>(ft- 2)4- 3 {444 - 3)4- 4 4/(3)}

4 (w -1)4 2 *(w - 2) 4- 3 ty(n -3)4 4#(ft - 4)

+ 5{f(n - 5)4- 4 4/(3)}

4^(n - l)4 24(n - 2) 4 3^(ft - 3) + 4 *(n - 4)

4 5{4/(ft - 5) 4 4^(3)}

4 V(n - 1) 4 2&(n - 2) 4 3 {^(ft - 3) 4 4 ^(3j)

where, on the first line the coefficient of the third and all the fol-
lowing terms is 3, on the second line the coefficient of the fifth and
all the following terms is 5, on the third line the coefficient of the
seventh and all the following terms is 7, and so on, the middle term
(when such occurs) having a 1 superadded.

Hence, for the determination of 4/(ft) when 4>(ft - 1), - 2), ...

are known, we have

^(ft) = (n-2)^(w-l)4(2w- 4)*(w-2)4(3ft- 6)*(n-3)

4 (4n - 10)^(ft — 4)4 (5ft — 14)\k(ft — 6)

4 (6ft - 20)^(ft - 6) 4 (7ft - 26>k(ft - 7 )

+ 2

where the coefficients proceed for two terms with the common dif-
ference ft -2, for the next two terms with the common difference
ft - 4, for the next two terms with the common difference n - 6, and
so on.

And as it is self-evident that 4/(2) = 0, we obtain

*(3) = 14/(2)41 - 1

4/(4) = 24/(3) = 2

4/(5) = 3^(4) 4 64/(3) 4 1 =13

4/(6) = 44/(5) 4 8^(4)412^3) = 80

^(7) = 5'vff(6) 4 10¥(5) 4 15^(4) 4 1 8^(3) + 1 =579

4/(8) = 64/(7) 4 12^(6) 4 18¥(5) 4 22^(4) 4 26^(3) = 4738
and so forth.

388

Proceedings of the Royal Society

To the foregoing Professor Cayley has kindly made the follow-
ing additions : —

The investigation may he carried further : writing for shortness
u3> u±> &c-> in place of ^(3), 'VP(4), &c., the equations are

— 1

u. 4 — 2% ,

% — 3% + 6% + 1 ,

uQ = ^ub + + 1 2%

% = 5% + 10% + 1 5% + 18%+ 1 ,

and hence assuming

U = % + UjX + ubx2 + u5x3 + u7x* .

we have

u = YZ^+u3(2x + 6x2 + 12x3 + 18*4 +

+ %(3a;2 + 8a;3 + 15a?4 + 22a;5 +
+ %(4a;3 + 10a;4 + 1 8a?5 + 26a;6 +
+ %( 5x4+ 12a?5 + 21a;6 + 30% +

and hence forming the equation

u

a?"

(f- x)2 = X 2 + ^ + ^ + ^ xb +

+ %(2a?3+ 4a:4 + 6a;5 + 8a:6 +
+ %( 3a;4 + 6a;4 + 9a?6 + 1 2a;7 +

• ••)

...)

...);

du

whore u denotes ^ , we have

x

u-u (T -T)2 ~ l ~ x2 ^3 + U*X U[>x 2 ‘ ‘ )(^a? + + ^ + 1 8a?4 . . )

1

j-— ^ + w(2a; + 6a;2 + 12a;3 + 18a;4 + . . . ) ;

or, what is the same thing,

1

xA

1 f 2a? 2a:* )

f~i-x2+u\ (i-*)3_a -*)3( \+x) / ’

2x*

U-U

(l-x

of Edinburgh, Session 1876-77.

389

that is,

1-

2x 2x^ | x2 , 1

(1 - x)3 + (1 - #)3(1 + x) J (1 — x)2U 1 - X2 '

This equation may be simplified : write

then

and the equation is

!

1 - x2 2 1 +x 2

x 4 Jrx3(l-x)2 - x)2

A 1 2

X3 (1 - x)2 #(1 - x)2

+

1 + x ry — 1

(i -x)x2H -r=^2 ;

that is,

{

I 1 _ 2 2

X4 + x2 x3(l — x)2 x2(l - x)2

2 _

x(l — x)2

1 + X

( 1 - x)x2

2

( 1 — x)2

Q

i

viz., this is

J ( 1-x)2 (1-x)2 2 2 2 n} j-x2 !-x

( X 4 X2 X3 X2 X J ^ X2 1 + X ’

that is

giving

390

Proceedings of the Royal Society

and thence

u =

s2"1 --(■*+£)/* ^
a* J(x+ 1)2

dx ,

which is the value of the generating function

u — u3 + u4x + ubx 2 + &c.

But for the purpose of calculation it is best to integrate by a
series the differential equation for Q : assume

Q= - - q4xb - qbx 6 - . . .

then we find

q± = 4?3 - 2>

qb = 5g4 +q3 +3,

?6=625 + ?4 "4>

q7 = 7qQ +qb + 5,

Qn = W«- 1 +^»-a + ( -DW_1(w ~ 2) •

We have thus for g3, g4, q5 . . . the values 1, 2, 14, 82, 593, 4820,
and thence

u = (1 — a?2)(l + 2x+ 14a?2 + 82a?3 + 593a;4 + 4820a?5 + . . .) ,
viz., writing

1 2 14 82 593 4820...

-1-2-14 -82

the values of u3, u4 . . . are 1 , 2 , 13 , 80 , 579 , 4738 .. .
agreeing with the results found above.

In the more simple problem, where the arrangements of the n
things are such that no one of them occupies its original place, if
un he the number of arrangements, we have

u2 = 1 =1

u2 = 2u2 , = 2

u4 = 3(u3 + u2) , = 9

ub = 4K + %) > = 44

1 n(yin + un_i) ,

of Edinburgh, Session 1876-77.

391

and writing

u = u2 + u.pc + up? + . . .

we find

u = 1 + (2# + 3 x2)u + ( x 2 + x2)ii ;

that is

( - 1 + 2x + 3 x2)u + ( x 2 + x2)u' = - 1 ;

or, what is the same thing,

x2( 1 + x) ’

1

whence

-3

u — x e

but the calculation is most easily performed by means of the fore-
going equation of differences, itself obtained from the differential
equation written in the foregoing form,

( - 1 + 2x + 3 x2)u + ( x 2 + xs)u' = - 1 .

6. On Amphielieiral Forms and their Relations.

If a cord be knotted, any number of times, according to the
pattern below

it is obviously perverted by simple inversion. Hence, when the

is that of 4-fold knottiness. All its forms have knottiness expres-
sible as 4 n.

By Professor Tait.

{A bstract.)

free ends are joined it is an amphielieiral knot. Its simplest form

392 Proceedings of the Royal Society

The following pattern gives amphicheiral knots of knottiness
2 + 6n.

And on the following pattern may be formed amphicheiral knots
of all the orders included in 6n and 4 + 6w.

Among them these forms contain all the even numbers, so that
there is at least one amphicheiral form of every even order.

Many more complex forms are given in the paper, several of
which are closely connected with knitting, &c.

In one of my former papers I gave examples of type-symbol
which individually represent two perfectly different knots.

I now give examples of the same knot represented by type-
symbols which have neither right nor left-handed parts in com-
mon. One of the most remarkable of these is

which can be analysed (but not separated) into a combination of
the two forms of the 4-fold amphicheiral knot.

The following Gentlemen were elected Fellows of the
Society

William Jolly, H.M. Inspector of Schools, Inverness.

Rob. Milner Morrison, 21 Manor Place.

John Gibson, Ph.D., 12 Greenhill Gardens.

Chas. E. Underhill, B.A., M.B., 8 Coates Crescent.

Charles Edward Wilson, M.A., LL.D., 19 Palmerston Place.
George Carr Robinson, East Preston Street.

of Edinburgh, Session 1876-77.

393

Monday , 1 $th April 1877.

Professor KELL AND, Vice-President, in the Cliair.

The following Communications were read: —

1. On the Toothing of Un-round Discs which are intended
to roll upon each other. By Edward Sang.

(Abstract.)

This paper contained an extension to discs of any shape what-
ever of the principles explained in the “New General Theory of
the Teeth of Wheels,” as applicable to circular discs.

2. On the Mineralogy of Scotland. — Chapter II.

By Professor Heddle.

In this chapter Professor Heddle submitted the results of the
analyses of Orthoclase from fifteen localities ; of Albite from four;
of Oligoclase from eight ; of Labradorite from eleven ; of Andesiel
from five ; of Anorthite from three ; and of Latrobite from two.

The three last minerals being now, for the first time, recognised
as British species.

Dr Heddle also described a peculiar association of Orthoclase
with Oligoclase, in crystals nearly of the form of the former, from
certain localities ; he drew the conclusion from his researches that
the above felspars are all well individualised, if not by physical,
at least by chemical characters ; while they are probably more or
less special to certain rocks.

3. Least Hoots of Equations. By J. D. Hamilton Dickson.

394

Proceedings of the Royal Society

Monday , 7 th May 1877.

DAVID STE VENISON, Esq., Vice-President, in the

Chair.

The following Communications were read:—

1. On new and little-known Fossil Fishes from the Edin-
burgh District. No. III. By Dr B. H. Traquair.

2. On Ocean Circulation. By John Aitken.

It is with extreme reluctance that I venture to disturb the pre-
sent repose of the much-contested field of ocean circulation. My
object is not, however, to provoke discussion on the general theory
of ocean circulation, as I am sure all will agree in thinking that
the subject has already been discussed far beyond the point at
which it is likely to be benefited by discussion. My object is
simply to call attention to certain influences at work in the ocean,
the effects of which seem to have been totally overlooked.

The first of them to which I wish to refer is the influence of the
winds on the ocean. The extreme holders of the wind theory of ocean
circulation consider that the action of the wind is quite sufficient to
account for all the currents which we find in the ocean. That the
wind is a cause of ocean currents no one can doubt. If we
examine a lake when the wind is blowing over it, we shall find
that the plants growing in the shallow water near the surface are
all bending in the direction of the wind, indicating that there is a
current at the surface flowing in the direction of the wind, — the
appearance of the bending plants in the lake reminding one of a
slow-running river. To supply the water for this surface current
there must, of course, be another current, flowing in the opposite
direction underneath. The lake and the ocean are not, however,
parallel cases. In the case of the lake, the wind is blowing in the
same direction all over it, so that the return current is forced to
flow underneath the surface, as it cannot get back any other way;
whereas, in the ocean, the wind blows in one direction at one part,

395

of Edinburgh, Session 1876-77.

and in a different direction at another part, and the question now
comes to be : What is the effect of the difference in the two cases ?
If the wind does not blow in the same direction at all parts over
the surface of the water, will the return current flow underneath
the surface current, or will it return by some other route?

It is extremely difficult to get a satisfactory experimental
answer to this question. The following attempts were, however,
made : — A trough with glass sides was filled with water, the water
being well stirred just before the experiment was made, to prevent
difference of density due to temperature having any effect on the
result. When all was again at rest, a solution of colouring matter
was dropped into the water at different points. Each drop of
colouring matter, as it sunk to the bottom, left a vertical coloured
streak in the water. A jet of air urged by a pair of bellows was
now directed along the surface of the water, so as to act on only a
small part of the surface, near the middle of the breadth of the
trough. The upper part of the coloured streaks, situated underneath
the air-jet, at once indicated a current in the surface water in the
direction of the air-jet. The return current did not, however, flow
underneath the air-driven current, as in the case of the lake, but
the air-driven current divided in two at the far end of the trough,
and flowed back on the surface , one current on each side of the
air-driven current.*

When the air current was first started, the water currents were
confined to the surface; but after the motion had been kept up
some time, the depth of the currents gradually increased, till all
the water in the trough was in motion, — the direction of the
motion of the water at any part of the bottom being the same as
at the surface vertically over it. The water showed not the smallest
tendency to take up a vertical ” circulation, similar to the circula-
tion produced by difference of density. The surface water simply
circulated to different parts of the surface, and the bottom water to
different parts of the bottom, almost the whole of the motion taking

* The trough in which the experiment is made must have sloping and
not vertical ends, because if the wind-driven current strikes against a
vertical surface, it raises a “ head,” which causes a vertical current to
descend at the end of the trough, in addition to the two return surface
currents.

396

Proceedings of the Royal Society

place in a horizontal direction. In order to get quit, as much as
possible, of the effects of friction on the sides and bottom of the
vessel, the experiment was repeated in a pond, with a like result.

From these experiments we may conclude that, save under very
exceptional circumstances, the wind can only give rise to a hori-
zontal circulation of the oceanic waters, — the exceptional cases
being, when the wind-driven current is deflected by the irregulari-
ties in the outline of the bed of the ocean, or strikes against a
deep and nearly vertical coast; or when the north wind drives the
waters of the Antarctic Sea against the great barrier of ice-cliffs
which surround the south pole. The depth to which the vertical
currents will descend in these cases will depend much on the rela-
tive densities of the water in the currents and of the water sur-
rounding them.

It may possibly be objected that we are not entitled to come to
any conclusion, from experiments made on so small a scale, as to
what takes place in the ocean. Such objections would be perfectly
valid, if there was not some evidence, in the conditions we find in
the ocean, to support these conclusions. If the return currents in
the ocean flowed underneath the wind-driven surface currents,
then we should be perfectly justified in expecting some evidence
of their presence. For instance, we would expect that the water
near the bottom, underneath the wind-driven currents near the
equator, would be hotter than the water at corresponding depths
at other parts of the ocean. An examination, however, of the tem-
perature sections of the Atlantic Ocean, taken by the “ Challenger,”
shows no evidence whatever of the return current by this route;
we are therefore compelled to conclude that the water must return
by the surface, and that the wind does only produce horizontal
currents , and therefore cannot account for the presence of the cold
water which we find all over the bottom of the ocean, from the
poles to the equator.

The second point I wish to refer to, is the effect of these wind-
driven surface currents on the cold water underneath them. I;
have said that almost the whole of the motion of the wind-driven
currents takes place in a horizontal direction. Such was the
general result given by the experiment. But, in addition to this,
there is another point to which I must refer. The wind driven

397

of Edinburgh , Session 1876-77.

horizontal currents have an influence on the water underneath
them which, for the sake of clearness, I have reserved for separate
consideration here. Let us draw an imaginary section across a
wind-driven current, at a point near its source, that is, near where
the wind begins to act on it. And let us imagine another section
of this same current, at a point some distance farther “ down” the
stream. As the current is acted upon by the wind between these two
sections, it will be much deeper at the second section than at the
first, and will also be going at a greater velocity. There will, there-
fore, be much more water passing the second section than passed the
first, and the water necessary to supply this growing stream must
be supplied to it between the two imaginary sections. The result
is, part of the necessary supply rushes in at the sides', but part of it
rises from the still water underneath the surface stream. This
lifting of the deeper water by the surface current was very evident
in the experiment already referred to, so long as the surface current
was shallow, and gradually became less, as might be expected,
when the current deepened.

From these considerations, we are naturally led to expect that
the hot surface water at’ those parts of the ocean over which winds
are constantly blowing, will be much reduced in depth, and that
the cold bottom water will be found at a less depth underneath
these surface currents than at any other part of the ocean. Part
of this cold water will, in all probability, get mixed up with the
bottom water of the surface current. And further, we would expect
that this wind-driven hot surface water, after it passes beyond the
windy regions, will gradually lose its motion and increase in
depth.

These expectations are in a remarkable manner supported by the
evidence of the temperature sections of the Atlantic taken by the
(c Challenger,” and given in Dr Carpenter’s paper in the u Pro-
ceedings of the Royal Geographical Society,” vol. xviii. No. iv.,
1874. Take, for instance, the section between Tenerife and St
Thomas. In the first part of the journey there is not much altera-
tion in the relative position of the isotherms, but after crossing
the Tropic of Cancer and getting into the region of the north-east
trade winds, the hot surface isotherms gradually approach each
other, and the isotherm of 40°, which off the coast of Tenerife was

398

Proceedings of the Royal Society

at a depth of nearly 1000 fathoms, rises to about 700 fathoms be-
fore it arrives at St Thomas. Again, in the passage north from St
Thomas to Bermuda, and on to Halifax and New York, the tem-
perature sections show that after getting out of the region of the
trade winds, the drifted hot surface water has gradully lost its
motion and increased in depth. This refers to the great mass of
ocean water, and not to the comparatively shallow Gulf-Stream.
For instance, the isotherm of 60°, which at St Thomas was found
at a depth of only 200 fathoms, was found at a depth of 330
fathoms for hundreds of miles all round Bermuda, notwithstanding
a considerable reduction in the temperature of the surface water.

The temperature sections of the South Atlantic do not illustrate
these points so well as the temperature sections of the North
Atlantic, partly because a very large part of the hot surface water
of the south equatorial current does not return to the South Atlan-
tic, but is driven into the North Atlantic, and partly on account of
the great amount of cold surface water of the Antarctic drift, which
gets mixed up with the return current; and further, the temperature
sections are not taken at the best places for our present purpose.
The only two available sections, however, point to the same con-
clusion as the North Atlantic sections. There is no section of the
south equatorial current, but we may suppose it to be somewhat
similar to the section taken between St Paul’s Rocks and Per-
nambuco, which gives the isotherms of the branch of the south
equatorial current which passes into the North Atlantic. If we
compare this section with the part of the stream which has flowed
southwards, as given in the section taken between Abrolhos Island
and Tristan d’Acunha, we find that the hot surface water, in flowing
southwards beyond the region of the south-east trade winds, has
deepened, notwithstanding a considerable fall in the temperature of
the surface water. The isotherm of 40° which was found at a depth
of 300 fathoms off Pernambuco, sunk to a depth of between 400
and 500 fathoms between Abrolhos Island and Tristan d’Acunha.
We might have expected that this hot surface water would have
kept its depth all the way to the Cape of Good Hope. It, however,
does not do so, probably on account of the cold surface water of the
Antarctic drift.

I am aware Dr Carpenter has offered a different explanation of the

399

of Edinburgh, Session 1876-7 7.

rising of the glacial water under the equator. He considers that
the rising of the glacial water under the Line is due to the meeting
of the Arctic and Antarctic underflows. That part of the effect is due
to this cause is very probable, but when we consider the very great
area of section of the under glacial currents, and the small amount
of water that can be carried by them, it is evident that their rate
of motion must be very slow, and it is very doubtful how far the
whole phenomena can be explained in this way. Our doubts on
this subject are somewhat confirmed by the consideration of the
fact that the Arctic underflow is warmer than the Antarctic under-
flow, and would therefore — other things being equal — tend simply
to overflow the Antarctic underflow, and not to rise vertically as
Dr Carpenter supposes. That the wind-driven currents, so long
as they are increasing in volume, have the power of drawing the
bottom water upwards cannot be doubted, and I have already said
was most marked in the experimental illustration. We should not,
however, expect to find this lifting power so marked in the ocean,
as the ocean currents are so much deeper and do not so rapidly
increase in volume as in the experiment. And further, the bottom
water in the ocean is denser than the surface water, and does not
rise so easily as the bottom water in the experiment.

If we take the evidence of the temperature sections of the At-
lantic on the subject, we shall find that they also point to the wind
as one of the causes of the rising of the cold bottom water. If we
take the section between Madeira and lat. 3° N. and long. 15° W,
we find that the isotherm of 40°, which at Madeira lies at a depth
of about 900 fathoms, rises to a depth of only 300 fathoms at the
equatorial position, and further, neither this section nor the section
between lat. 3° N. and long. 15° W. and Pernambuco, show the
least evidence of the presence of Antarctic water so far north as
the equator, in the eastern basin of the Atlantic. This rising ,
then , of the glacial water on the eastern side of the Atlantic cannot
therefore be due to the meeting of the glacial streams , and in the
absence of further evidence we may suppose it to be due to the
wind-driven currents. We thus see, that though the great bulk of
the wind-driven circulation is a horizontal one, yet there is also
produced in a comparatively very small degree a modified vertical
circulation.

3 g

VOL. IX.

400

Proceedings of the Eoyal Society

It may here be asked, Is this lifting power of the surface currents
sufficient to account for the vertical circulation which we find in
the ocean ? In all probability it is not. There seems to be no
reason why this vertically rising current under the equator should
draw its supplies from the furthest limits of the ocean, which it
would require to do to explain the conditions we find existing.
Yet there can be no doubt but that these horizontal surface cur-
rents really do assist in producing a vertical circulation.

3. On a New Investigation of the Series for the Sine and
Cosine of an Arc. By Edward Sang.

The sines of the successive equidifferent arcs form a progression
having for its general character the relation

<f>n-l — 2 <f)7l + (f>n+ 1 — 4>n • V ,

and the properties of sines may be deduced from this general for-
mula. Viewed in this light, the angular functions become cases
only of more general ones.

If we suppose A, B, C to be three consecutive terms of such a
progression we must have

A - 2B + C = vB,

from which, when three of the four quantities, A, B, C, v are given,
the fourth may be found. Let then A and B, the first and second
terms of the progression, and v the common coefficient, be given ;
the succeeding terms may be computed thus : —

<f> 0 = A

- A +B

+ Bu

<f> 1 =

B

-A

+ B(l+v)

— Av

+ B( +2v + v2)

rf> 2 = — A

+ B(2 + v)

-A(l+v)

+ B(1 + 3u + u2)

— A( + 2v + v 2)

+ B( + 3v + 4u2 -l- vs)

401

of Edinburgh, Session 1876-77.

</> 3= — A(2 + u) +B(3 + 4w + i>2)

- A(1 + 3v + v2) + B(1 + 6v5v2 + v3)

$4 = — A(3 + 4v + v 2) + B(4 + 10v 4- 6u2 4- v3) ,

from which it is obvious that the coefficient of - A in the expres-
sion for (f>n , is a transcript of that of B in the preceding expression
for tf)(n - 1 ). Hence, for the present, we may confine our attention
to the latter.

The coefficients of B form the following progression : —

in cf> 0 0

in (f> 1 1

in <£2 2 + v

in <£3 3 + 4v 4- v2

in <£4 4 + 1 Ou + 6u2 + v3

in (f)5 5 + 20w 4- 2 Id2 + 8n3 4- v4

in <£6 6 + 35v + 56v2 4- 36n3 + KM + v5

in <j>7 7 + 56v+ 126v2 + 120v3 4- 55v4 + 1 2v5 4- n6

in cfjS 8 4- 84n + 25 2 v2 x 330v3 4- 220id 4- 78u5 + I4v3 + v7

in p 9 4- 120v4- 462u2 4- 792id 4- 715v4 4- 364v5 4- 105v6 4- 16u7 4- &c.

and in general

in <cf>n

n t n - 1 n n 4- 1

I + _jT ¥ “3“

n — 2n - l n n 4- 1 n 4- 2
“1 2~ 3 ~1 5”

v2 4- &c.

When v is positive the formula belong to the class of catenarian
functions ; when v is negative, to the circular ones.

If we put sin pa for <j> 0, sin p 4- 1 a for <£l, and - chord a for v,
we obtain

in _ i

sin (p 4- n)a = - mi pa j— |—

n-2 n-1 n , 9 , P

— _ cho a2 4- Ac.

A 2 6

, • / , 1\ fW »“l?l»+l , 9,0 )

4- sin {p+l)at j — - — — cho a2 4- &c. i

and in thus putting p = 0

sin na — n sin a

1<-*T

n2 — 1 cho a 2 n2 - 1 n* - 4 cho a 3

3

4-

1.2 3.4

- &c. |

402

Proceedings of the Royal Society

A

And again writing na — A, a = — , this takes the form

n

• a . A / n2 - 1 1 / , A\2 n2 - 1 n2 - 4 1 / , A\2 )

sm A = n sin — J 1 - i ( cho - ) + 7-7- -5-7- *( cho ) - &c.f
n\ 1.2 3 \ n ) 1.2 3.4 5\ n ) >

Now when n becomes indefinitely great, n sin - becomes A, so also

n

cho - , wherefore sin A = ^ = — 3 + — —
n 1 1.23^1.2.3./

&c.

1 1.2.3 1.2.3. 4.5

7J*

In order to obtain the series for the cosine we must put pa = ^
and therefore sin (p + l)a = cos a , which gives

cos na = - 1

( n - 1 n -

(T“l

2 n 1 n -i p n
— — - cho a- + &c.
A o

+ cos a

f n w-llw+1, 9,£> )

It — r 1 ~r ch0<l + &a [

and if, in this, we substitute for cos a , its value 1 - \ cho a2,

-1 71 n- 2 , 5ln-l?i» + lfl-4 , 4 „

cos = 1 - _ — - — cho a2 + • — - — - — — cho a4 &c.

i A 1 A O 4

whence, proceeding as before,
cos A = 1 - +

A4

A6

i-2 1 .... 4 r

6

+ &c.

4. Note on the Bifilar Magnetometer. By J. A. Broun,
F.B.S. Communicated by Professor Tait.

5. Addition to the paper “ On the establishment of the
Elementary Principles of Quaternions,” by G. Plarr, —
published in Vol. XXVII. of the Transactions of the
Society. Communicated by Professor Tait.

6. Note on Mr Muir’s Solution of a “ Problem of Arrange-

ment.” By Professor Cayley.

This note has been printed along with Mr Muir’s paper, ante ,
p. 382.

of Edinburgh, Session 1876-77.

403

7. Preliminary Note on a New Method of Investigating the
Properties of Knots. By Professor Tait.

As we cannot have knots in two dimensions, and as Prof. Klein
has proved that they cannot exist in space of four dimensions, it
would appear that the investigation of their properties belongs to
that class of problems for which the methods of quaternions were
specially devised. The equation

p = «Ks) »

where is a periodic function, of course represents any endless
curve whatever. Now the only condition to which variations of
this function (looked on as corresponding to deformations of the
knot) is subject, is that no two values of p shall ever be equal even at
a stage of the deformation. Subject to this proviso, <£ may suffer
any changes whatever-— retaining of course its periodicity. Some
of the simpler results of a study of this novel problem in the
theory of equations were given, — among others the complete repre-
sentation of any knot whatever by three closed plane curves, non-
autotom ic and (if required) non-intersecting.

The following Gentlemen were elected Ordinary Fellows
of the Society : —

XIobebt A. Macfie, Dreghorn, Colinton.

William Stirling, Sc.D., M.D.

Monday, 21 st May 1877.

Professor KELLAND, Vice-President, in the Chair.

The following Communications were read : —

1. On the Cranial Osteology of Rhizodopsis, and on some
points in the Structure of Ehizodus. By Dr E. H. Traquair.

2. Notice of Eecent Earthquake Shocks in Argyleshire
in 1877. By David Stevenson, Civil Engineer.

Two earthquake shocks have lately occurred in Argyleshire of
so decided a character that a description of their effects, as observed

404 Proceedings of the Royal Society

at four of the Lighthouse stations on the west coas: of Scotland,
will, it is thought, be interesting to the Society.

The first shock occurred on the 11th March, and was observed
at the Lighthouse station of Hynish in the island of Tyree, and
at Sound of Mull, near Tobermory, the distance between the two
places being about 34 statute miles.

The report from Tyree states: — u On the 11th current (March),
at half-past 11 o’clock a.m., a smart shock of earthquake was felt
all along the island ; a great many people both heard the noise
and at the same time felt the earth to tremble. It was heard and
felt very distinctly at the station.” Bar. 3018 at 9 a.m.

That from the Sound of Mull says: — “ On the 11th, at 11.30
a.m., this district was visited by a smart shock of earthquake. It
began by a rumbling noise like distant thunder. When the noise
was at its height the houses, and everything about them, shook,
and the slates on the roof rattled. The shaking was not of long
duration, but the noise was heard a considerable time before and
after the trembling of the earth.” Bar. 29*92 at 9 a.m.

The second shock, which seems to have been more severe, took
place on the 23d April, and was observed at the island of Phladda,
off Easdale, and at Lismore, at the eastern entrance to the Sound
of Mull, the distance between the two stations being about 73
statute miles.

The report from Phladda states : — “ At 3.40 a.m. the Principal
Keeper on the watch felt a severe shock of earthquake. The tower
and dwelling-houses shook very much. All the neighbouring
islands felt it at the same time.” Bar. 29*74 at 9 a.m.

At Lismore the lightkeeper describes the effect as follows
(the lighthouse clock had been under repair) : — “ I beg leave
to report that on the morning of the 23d, at 3.30 a.m., while
I was standing on the grating inside the lightroom I felt a
heavy shock on the tower, with a strange rumbling sound of noise
which lasted some seconds, and made everything in the lightroom
shake at an alarming rate. It awoke all the inmates of the dwell-
ing-houses. Mr M‘Leod jumped out of bed, thinking the tower
had fallen, but afterwards thought it was a peal of thunder. I do
not think it was thunder. I saw no lightning, and the wind was

405

of Edinburgh, Session 1876-77.

light at the time. There is do damage done to anything about
the station so far as I can see.” Bar. 29-43 at 9 a.m.

These observations are valuable because of their trustwortniness
as coming from wholly independent observers, and because few
more sensible earthquake shocks have, so far as X know, been ob-
served in Scotland. It is also remarkable that they do not appear
to have been felt at any other lighthouse stations, although there
are several others in the immediate vicinity. A record of them
may therefore be useful to those engaged in seismic investi-
gations.

3. Additional Remarks on Knots. By Professor Tait.

The author, in laying before the Society a revised and condensed
version of the various papers recently communicated by him, took
occasion to make some additional remarks. Of these only one
need be given here. He pointed out that another fundamental
term is requisite besides those already used viz., Knots and Links.
For three endless cords may be inseparably entangled with one
another, or locked together, even if no one of them be knotted and
no two interlinked.

Monday, 4 tli June 1877.

DAVID STEVENSON, Esq., C.E., Vice-President,

in the Chair.

The following Communications were read : —

1. On the Structure and Relations of the Genus Holopus.

By Sir C. Wyviile Thomson, F.R.S.

(Abstract.)

The “ Challenger ” Expedition had no opportunity of visiting
Barbadoes, and this I regretted greatly, as Sir Rawson Rawson,
who was at that time governor of the island, had paid great atten-
tion to the marine fauna, and was anxious to introduce us to his
fine collection, which included many specimens of the rare and

406

Proceedings of the Royal Society

remarkable forms for which the sea of the Antilles is famous.
However, although the “ Challenger ” was not there in person, on
her return Sir Rawson Rawson most kindly and liberally placed
the finest of his specimens at my disposal for examination and
description ; and it is through his liberality that I now have it in
my power to exhibit the very singular creature which is the sub-
ject of these notes. In 1837 M. Alcide d’Orbigny described and
figured in the “ Magasin de Zoologie,” under the name of Holopus ,
a new recent genus of fixed Crinoids ; and as the description of this
distinguished palaeontologist indicated an undescribed form of great
interest, it was speedily reproduced in the “ Annales des Sciences
Naturelles” and in Wiegmann’s “Archiv.”

The specimen described by D’Orbigny, which was for a long time
unique, was brought from Martinique by M. Sander-Rang. It sub-
sequently passed into the possession of M. D’Orbigny, who described
it under the name of H. rangii. D’Orbigny’s account was very
clear and intelligible, and his determination was fully borne out
by his figures ; and in Bronn’s “ Classen und Ordnungen des Thier-
Reichs,” published somewhere about 1861, the description and
figures are repeated, and a distinct family, Holopidae, is adopted
for the reception of the single species. It is very singular that
in the “ Historie Naturelle des Zoophytes Echinodermes,” by
Dujardin and Hupe, published as a volume of the “Suites k Buffon”
in 1862, the authors express their opinion that Holopus is not a
Crinoid, but some totally different thing, probably a Cirriped, and
they profess to have been unable to find D’Orbigny’s specimen.

At M. D’Orbigny’s death his whole museum was bought by the
Jardin des Plantes, and in the year 1867, through the courtesy of
M. Fischer, I had an opportunity of examining the original speci-
men there; and although it was in a very dilapidated condition,
I had no difficulty in satisfying myself that it was a true Crinoid
of a very peculiar type.

Professor Louis Agassiz called at Barbadoes in the “ Hassler ”
in 1873, and he there saw a second specimen of Holopus in Sir
Rawson Rawson’s collection. Professor Agassiz intended to have
published a full description of the specimen, which was lent to him
for that purpose by Sir Rawson Rawson, but he was prevented from
doing so by failing health, and after his death the figures which

407

of Edinburgh, Session 1876-77.

he had prepared were published by Alexander Agassiz, with a short
note by Count Pourtales, in the “ Zoological Results of the ‘ Hassler ’
Expedition.”

During the last few years three specimens of Holopus rangii
have fallen into Sir Rawson Rawson’s hands, and from these we
will be able to give a pretty good account of the hind parts. All
were brought up on fishermen’s lines from deep water off Barbadoes.
One is very complete in all important points, wanting only the
two “bivial” arms, but retaining the mouth-valves. The second is a
little larger; it wants the mouth- valves, and again the bivial arms ;
and with Sir Rawson Rawson’s sanction I boiled this specimen
down, to figure and describe the separate parts. The third speci-
men is quite perfect, the arms closely curled in, in their normal
position when contracted; but it is very young, only about 8 m.m.
in height. Besides the four examples mentioned I am aware of
only another, which I have not yet seen ; it was shown at the Phila-
delphia Exhibition, and was afterwards bought by the Museum of
Comparative Zoology at Cambridge, Mass.

Holopus is distinguished from all other recent Crinoids by hav-
ing the basal plates, and the first and probably also the second
radials fused together, forming the wall of a tube-like body-cham-
ber, which is cemented beneath to the foreign body to which the
Crinoid is attached, by an irregularly expanded calcareous base.
This mode of attachment also occurs in the fossil genus Apiocvinus ,
and in many other forms of the Apiocrinidae and Cyathocrinidae,
but in these, of course, the cement matter is thrown out at the
base of a jointed stem.

The upper portion of this hollow column expands slightly, and
its thickened upper border is divided into five strongly-marked
facets for the articulation of five arms. Each facet is traversed
by a transverse articulating ridge, a little in front of which there
is the mouth of the tube which lodges the sarcode axis of the
joints, and a little behind its centre there is a somewhat longer
aperture which appears to lead into the cancellated structure of the
outer part of the wall. There are two large shallow muscular im-
pressions on the surface of the facet on the proximal aspect of
the transverse ridge. These facets, I conclude, represent the upper
surfaces of second radial's, but if so, they differ from the second

3 H

VOL. IX.

408 Proceedings of the Royal Society

radials of all other recent Crinoids in being connected with the
radial axillaries by a true muscular joint instead of by a syzygy.
The alternative is that they may be the upper articulating surfaces
of the first radials, in which case the next joints may be formed
of the second and third radials coalesced, and the syzygy between
them obliterated ; or, finally, there may be only two radials. There
is no trace of any further division of the wall of the column, and
the cavity is continued contracting gradually to the bottom. A
vertical mark, sometimes a groove and sometimes a ridge, runs
from the centre of each articulating facet down the inside of the
wall for about two-thirds of the depth of the cavity, when it is lost.
The upper border of the cup, bearing the facets, is very irregular
in thickness ; and in all the specimens which I have seen, including
D’Orbigny’s, one side of the border is much thicker and consider-
ably higher than the other side, and the three arms articulated to
it are much larger than those articulated to the opposite side.
There is thus a very marked division into “ bivium ” and “ trivium,”
and consequently a bilateral symmetry underliestheradiated arrange-
ment of the antimeres. Singularly enough, the specimen described
by D’Orbigny was abnormal, only four arms being developed, a
circumstance which no doubt greatly conduced to the doubt with
which its determination as an echinoderm was received.

Five “ radial-axillary ” plates, three larger and two smaller,
articulate by corresponding ridges and muscular impressions with
the facets of the border of the cup, and each of these bears dis-
tally two facets, sloping outwards and downwards, for the insertion
of the first brachials. The outer surfaces of the radial axillaries are
very gibbous, thrown out into almost hemispherical projections,
studded with low tubercles ; a deep groove runs up the centre of
the inner aspect of the joint, and the two sides send inwards very
strong projecting processes, which abut against the corresponding
processes of the contiguous joints on either side, and lock into them
by a system of corresponding ridges and grooves, so that there
appears to be little or no motion between these joints.

The radial-axillaries are each succeeded by two series of about
eight similar, thick, wedge-shaped brachial joints, very convex
externally, and giving off laterally on each side of the arm alter-
nating, very flat broad pinnules each consisting of about six plate-

of Edinburgh, Session 1876-77.

409

like joints. The brachials are also provided with strong lateral
processes forming a wall on either side of the radial groove, and
the sides of adjacent series of these first eight arm-joints are
marked with corresponding grooves and ridges, so that, although
from the presence of articulating ridges of varying degrees of ob-
liquity, and of muscular impressions; the proximal portions of the
arms must be capable of some motion, that motion would appear
to be slight. After about the eighth the joints suddenly contract
in size and become greatly compressed, and this narrow teries
extends to about sixteen in number, gradually tapering to the end
of the arm.

At the bases of the arms, just above the edge of the cup, five
thick calcareous bosses, each composed of the contiguous lateral
processes of two radial-axillary joints, project interradialiy into the
cup ; and opposite these five rather large triangular plates, meeting
in the centre of the disk, form a low pyramid covering the mouth.
The oral plates are interrad ial, and the spaces between them radial
corresponding with the arm-grooves.

D'Orbigny described the animal as possessing no anal opening,
and this is probably the case, but the material is still too scanty
to admit of the full examination of a complete specimen of the
skeleton, and the soft parts are unknown.

All the specimens of Holopus which have been hitherto pro-
cured are in a very peculiar condition ; the thick-walled foot, and
massive, somewhat rudely shaped cup and arm-joints are formed
of a loose spongy calcified areolar tissue deeply stained with a
black-green pigment. There is no appearance of any separate
organic matter, either on the outer surface of the skeleton, which
is very delicately sculptured like shagreen, or on the articulating
surfaces of separated plates ; indeed, the whole body is so perfectly
hard and rigid that at first sight I thought it might be semi-fossil.
It is without doubt recent, but I suspect that the tissues are very
imperfectly differentiated, almost protoplasmic. When an arm is
put into boiling water it falls into pieces at once, the joints simply
coming asunder, and showing no trace of muscular or other or-
ganic connection except the axial cords of the joints, which some-
times keep two joints hanging in connection for a little.

Holopus is thus specially characterised among living Crinoids

410

Proceedings of the Royal Society

by the absence of an articulated stem or its representative the
centro-dorsal plate ; by its viscera being lodged in a hollow
peduncle with a continuously calcified wall ; and by the absence
of an anal opening.

In 1846 Professor Steenstrup described under the name of Gya-
thidium, a genus of fossil Crinoid from the chalk of Faxoe, which
occupies a debatable position between the base of the Eocene Ter-
tiaries and the top of the Cretaceous series. The only portion yet
described of Gyathidiuru is a deep cup or tube with a spreading
base of attachment and a thickened rim with articulating facets
for five arms. The cup of Cyathidium is somewhat more sym-
metrical and coralloid than that of the recent West Indian form ;
but I see no distinction between them of generic value, and I think
we must accept Holopus as another of the links which recent in-
vestigations have made so numerous between the faunae of later
geological periods and that of the present time.

2. On the Diurnal Oscillations of the Barometer. — Part II.

By Alex. Buchan, M.A.

In this communication the author stated that he limited his
remarks on the present occasion to some of the more prominent
results he has arrived at in the course of this investigation. The
paper itself, with the tables, will be submitted when the computa-
tions have been finished and thoroughly revised, — a work which
must necessarily yet take some considerable time.

It is proposed that Part II. consist chiefly of tables showing the
arithmetic mean values of the hourly variations of the different
months of the year, with remarks on the more evident conclusions
which may be drawn from them. The number of places for which
data of more or less completeness have now been obtained exceed
130, situated in different parts of the globe. To these it is proposed
to add the results of observations made at sea, chiefly those made
by the “ Challenger ” and “ Novara ” expeditions.

As regards temperate regions, such as Great Britain, periods of
no more than three years’ observations give only the broadest
characteristics of the diurnal barometric curve. From 20 to
25 years will probably be found to be required to show the

i 1

i

411

of Edinburgh, Session 1876-77.

peculiarities of the curve with such completeness as to exhibit
the variations impressed on the curve by season and by geo-
graphical position, particularly as regards masses of land and
extended sheets of water. In lowrer latitudes a comparatively
short time is required ; but even here, where a general regularity
in the phenomena is perhaps the most striking fact in the meteor-
ology of equatorial regions, the variations which do occur from
year to year ought to be carefully observed from their important
bearing on the whole theory of the movements of the atmosphere.
The summer months of the northern hemisphere, as regards the
diurnal oscillations of the barometer, that is the period when
the influence of the sun is at the maximum as regards its effects
on these phenomena, are May, June, and July, and the winter
months, November, December, and January, both corresponding
with the sun’s declination ; that is, the effects are not cumulative,
as in the case of the temperature of the air or that of the sea, by
which the critical periods are retarded from one to two months.

Among the many interesting features of the curves which were
pointed out may be noted the enormous influence of latitude and
of land and sea respectively in determining the amount and time
of occurrence of the different phases of the oscillations, and a
diagram was exhibited showing the curves of a large number of
places, from which it appeared that as regards the summer the a.ri.
maximum occurs at any time from 6-7 a.m. to 2 p.m., and the p.m.
minimum from 3 to 8 p.m. — the stations selected showing a regular
gradation between these extremes, a gradation dependent on geo-
graphical position. The tendency of assimilation of the curves for
certain elevated stations and those for strictly sea-side stations was
pointed out, and attention was drawn to the striking fact that the
summer curves of inland stations within lat. 30° N. and S. essen-
tially differed from those of higher latitudes — a difference which
the varying declination of the sun with season failed to obliterate.

An examination of the different theories yet propounded shows
that none of them are in accordance with the facts which have
been collected. It would not be difficult by a proper selection of
stations to bring proof in support of any of these theories. The
truth is, however, that as more facts are obtained the difficulty of
framing a satisfactory theory can scarcely be said to be materially

412

Proceedings of the Royal Society

lessened, even though it becomes easy to arrive at a close approxi-
mation to the curves of a place from its geographical position
alone, before determining the curves by working them out numeri-
cally.

An examination of these curves by the harmonic analysis and a
similar examination of the temperature, hygrometric, wind, mag-
netic, and electric curves, will in all likelihood be required before
the true theory of the diurnal barometric oscillations can be stated.

3. On the Air dissolved in Sea-Water. By J. Y. Buchanan.

4. Why the Barometer does not always indicate real
Vertical Pressure: A continuation of the Paper laid before
the Koyal Society of Edinburgh in July 1875, in which,
in addition to several other points, this was attempted i
to be shown. It is now more fully written out. By
Robert Tennent.

The barometer only indicates real pressure when the atmosphere
is in a state of perfect rest. It may then be represented a
existing in vertical columns, but when it moves over a resisting
surface its lower surface currents will be greatly retarded, while
those aloft will move comparatively free and unimpeded. In this
state it may be represented as moving in columns inclined in the
direction towards which it moves. The atmosphere may thus be
conceived as being divided into a number of spheroidal concentric
layers, each of which is possessed of a different rate of speed, and
moves more rapidly than the one beneath it : an increasing
amount of friction will take place betwixt the layers as they
approach the surface where its influence is greatest. What takes
place may be represented in this way. Let R S be the resisting
surface, and let

B a

b r

B'

r ^ c

b

C'

—

^ T>

l> ^ c

D'

— -

jS

A A', B B', C O', and D 13' represent different layers of air moving

413

of Edinburgh, Session 1876-77.

at different rates of speed. Those being most rapid where the
arrow heads are most numerous. Let these layers also exhibit
equal masses of air, but of different volumes, which increase in
size from the ground upwards, accompanied also by much greater
mobility, as shown by Tyndall in his experiments at Chamouni and
the summit of Mount Blanc. An important point is this. The surface
current D D' has only a horizontal source of supply from the
direction D' from which it is fed, while the upper current A A'
has not only a horizontal source of supply from A', but it also
derives supply from the slower moving current B B' beneath it,
which will be drawn upwards, or “ lifted,” in the direction of the
small inclined arrows abed. To enable this upper current to
supply itself in this way, while it possesses the same amount of
mass as that beneath it, it must have a greater velocity, and
therefore greater momentum than that of the current beneath it,
from which it draws its supply. Each of the lower currents, as
they approach the surface, are also supplied in the same manner,
but in a decreasing ratio, from those beneath them, until the lowest
layer is reached, which is that which is most retarded, not only
owing to its proximity to a resisting surface, but also to the
scarcity of supply, which can now only be derived from a horizontal
source, and not from beneath, as was the case with those above it.
A tendency in the air to accumulate aloft will now take place, by
“ lifting,” in the direction of the small inclined arrows abed.
Pressure is thus diminished at the surface, while it is abnormally
increased higher up.

The effect of this will be that the surface barometer will exhibit
diminished or fictitious pressure, while the real weight of the
atmosphere remains unaltered. A partial vacuum is found on the
lee-side of a wall, over the top of which a strong wind blow's : it with-
draws the air there to such an extent, that it causes removal to
exceed restoration, but it does not affect the real vertical mass of
the column overhead except to an infinitesimal degree. In this,
as in the former case, real pressure cannot be ascertained by the
surface barometer. It is only to be obtained from the result of an
observation of a series of barometers placed vertically above each
other, and not very far apart. From the results thus obtained, it
would be found that the normal upward diminution of pressure

414

Proceedings of the Royal Society

which takes place when the atmosphere is at rest would be greatly
altered when its upper portion is in rapid motion.

Ketarded surface currents and rapid upper currents which move
in inclined columns and produce these effects, can only be found
with an imperfect fluid, and on a resisting surface, into which the
element of friction enters. On a frictionless surface this could
not take place. The atmosphere would there move in vertical, not
in inclined columns, no “ lifting” would take place, pressure would
be real or statical ; its upward diminution would be normal, as
when it is at rest, and horizontal movement would not take off
vertical pressure.

Barometric pressure must hence be regarded in two points of
view — 1st as being a cause ; and 2d, as being an effect. When, as
in the first case, it is real or statical, it operates as a cause due to
gravitation, which is unresisted. When, as in the second instance,
there is an introduction of the dynamical element, surface gravita-
tion is diminished by “ lifting,” and it must then to a certain
extent be regarded as an effect. The practical conclusion from
this is obvious. On weather charts the constant rise and fall of
the barometer, which is there reported, is to a large extent simply
due to the passage of air over a resisting surface. Over a surface
devoid of friction these mechanical effects would be entirely
removed : its rise and fall would be greatly reduced, and might
be considered as being solely dependent on the effects of heat and
vapour. The gradients and isobars which are represented by these
movements of the barometer would consequently require also to be
similarly corrected.

The barometer does not indicate the real weight of the atmo-
sphere, it only exhibits the amount of its elasticity, from which its
real weight can only be deduced when the dynamical element of
motion does not enter into its currents. The two cases above
mentioned may illustrate this point. The surface barometer there
indicates fictitious pressure, or in other words, the amount of
pressure due to the elasticity of the air , hut not to that of its real
weight , which is there diminished by “lifting,” and as lifting can
increase or diminish in amount, so also can the elasticity of the air,
while its real weight remains unaltered.

As a general rule, in the British Isles, equatorial winds are

I

415

of Edinburgh, Session 1876-77.

accompanied by these rapid upper movements, while polar winds
move with a greater uniformity in the velocity of their various
layers, and sometimes even those on the surface move more rapidly
when copiously supplied from a vertical source. There is thus a
remarkable diference in their mode of inflow. Equatorial winds,
as they increase in force, are hence accompanied by “ lilting” and
a fall of the barometer. Polar winds are not attended by “ lifting,”
and if their supply is copious and partly from a vertical source,
their increase in force is accompanied by a rise of the barometer.

The range of the thermometer is equally great, both above and
below its mean ; but with the barometer the extent of its range
above the mean is not more than one-half of that which takes
place when it is below it. When it is below the mean, equatorial winds
generally prevail, which are accompanied by lifting and extensive
range. When above the mean, polar winds prevail, which are not
attended by lifting or such extensive fluctuations. Hence, as a
general rule, equatorial winds exhibit fictitious or dynamical
pressure, while polar wincjs possess more nearly, real or statical
pressure, being less accompanied by rapid upper currents, and by
the mechanical oscillations due to the passage of air over a resisting
surface.

Observations of a general description and illustrations will pro-
bably be afterwards introduced to exemplify the above conclusions.

It is to this diference in the mode of inflow that an attempt has
been made to explain the causes why depressions move in an
easterly direction.

5. Laboratory Notes. By Professor Tait.

(«) On an Effect of Heat on Electro-Static Action.

By means of a very delicate galvanometer, transient currents
were detected when one of two plates of the same, or of different,
metals, separated by a sheet of mica or glass, was suddenly
heated.

( b ) On Dr Blair’s Scientific Aphorisms in connection with the
Ultra-Mundane Particles of Le Sage.

Accident has recently called my attention to a work entitled
Essays on Scientific Subjects , by Kobert Blair, Regius Professor of

VOL. IX. 3 x

416

Proceedings of the lioyal Society

Practical Astronomy in the University of Edin. (Edin. 1818). In
the University Library there is a second edition of a part of the same
work with the title Scientific Aphorisms (Edin. 1827), I bring them
before the notice of the Society, as they contain an explanation of
gravitation, &c., almost identical with that of Le Sage, to which
our attention was lately recalled by our President. Professor Blair
seems to have invented this explanation for himself — because,
though he gives frequent references to other authors, whose results
he quotes, he makes, so far as I have seen, no reference to Le Sage.

On a future occasion I may enter on a discussion of the points
of resemblance and difference of these two theories.

5.

Note on an Identity. By

Professor Tait.

Whatever be p and q it

is obvious that

1 1

+

1

p q

q

V

Hence

1 _ 1

+

P-C +

02 -P

!)

P 0i

0i

\02

02

pj

and so on.

Finally we

see that

i =1 +

<h~P 1 , <h~P

• 4 •

02 ~P

1

— + .

P 0i

01 02

0i

02

03

... +?i“

P %-v

qa-l-p

. 1

rP 02^
•

P qn -p 1

0!

.02

071-1

0» 01 02

071 P

absolutely without any restriction on the values of the quantities
involved.

It is obvious that an immense number of curious results in the
form of sums of series, &c. can be derived with great ease from this
expression and from various modifications of it. I give, therefore,
only a few very simple examples.

Take qv q2} &c., as the first n of the natural numbers, and the
series becomes

1 1 p - \ p - \ p — 2

p ~ + ~2~ ‘

, .n-ip-l p-2 p-n-l, p-l p-2 p~nl

2 * 3 n K } 1 * 2 * ’ * n p’

417

of Edinburgh, Session 1876-77.

whence at once the sum of the first n + 1 terms of the expansion of
(1 - 1)^ is seen to be

/ _ w P~ 1 P~ 2 P~n

y ' 1*2 71

We obtain merely the same result if we take qv q.2} &c., as any
set of consecutive whole numbers ; but from the theorem itself it is
easy to obtain the equality,

p f , p + r p + r. p + r + 1 p -f r

r ( r+l r+l r + 2 r+l

p + s-

5=M

p + r p + r + 1 p + s

r ' r + 1 s

Next, write the general identity as follows : —

If in this we write each letter for its reciprocal we have

P = <h + ~(P ~ 2i) + J|.(p-$i) {p ~ q2) + &c.,
of which a particular case is the curious formula

Another is

1 = cos 0 + cos 26(1 - cos 6) + cos 30{1 - cos 0)(1 - cos 26)+ ...
+ cos n6( 1 - cos #)...(! - cos (n - 1)(9)

+ (1 - cos 6)( 1 - cos 26)... (\ - cos n6) ,

of which a very interesting case is given by n6 = 2i r .

418 Proceedings of the Royal Society

As a final example we have the singular for mula,

1

x-y

y

x(x + i )

+

y(y+i)

x(x + !)(# + 2)

+ &c.

whence it follows that, subject to the introduction of the remain-
ders as above (which vanish if the series are extended to infinity,
and if x > y ),

1 , v . y(y+ 1) . V1 y , >Av-v) .

x x(x+\) x(x+ l)(a?-f- 2) x(x+\) x(x+l)(x + 2)

1 . y 2 y2(y2+^) .

x2 x2(x2 + 1 ) x\x2 + 1 ){x2 + 2)

By another application of the formula we may easily obtain finite
expressions for the sum of the series of which two successive terms
are

y(y+ 1) • • • ♦ (y + r- 1) , y(y+ 1) .... ( y + r )

x(x+ 1) . . . . (x + s - 1) * ‘ x(x+ 1) .... (x + s) *

I obtained the first expression above by integrating by parts a
power such as xP~l, but the following mode of obtaining it shows at
once its nature.

Let there be a number of independent events, A, B, . . . . N,
whose separate probabilities are a, (3 , ... v. Then the chance that
one at least of them occurs is

1 — (1 — a)(l — /?) . . . . (1 — v) .

But we may obtain another expression for the same result by writ-
ing the chance that any one (say A) occurs, adding to that the
chance that another (say B) occurs while A does not occur, then
that C occurs and neither A nor B, &c. This gives

a + — a) + y(l — a)( 1

Equating these two expressions we get an identity which is easily
transformed into that first given.

But its truth is much more easily - seen if we write a for (1 - a),
&c., when the last given form becomes

1 - a/3'y'. . . . = 1 - a' + (1 - /3')a + (1 - yV/T + . . . .

of Edinburgh, Session 1876-77. 419

which is an obvious truism. The method seems well worth the
attention of any one with leisure and some analytical skill.

July 24. — Mr Muir has kindly given me a reference to Crelle,
vol. xii. p. 354, where it is stated that the above identity in one of
its forms is in Schweins’ “ Analyse,” p. 237. This work I have not
seen. Mr Muir adds that no developments or applications of the
theorem are made.

The following Gentlemen were duly elected Fellows of
the Society : —

1. James Stevenson, 4 Woodside Crescent, Glasgow.

2. James Roberton, LL.D., Professor of Conveyancing, 1 Park-

Terrace East, Glasgow.

3. George A. Panton, 24 Rennet’s Hill, Birmingham.

4. Isaac Baylf.y Balfour, Sc.D., 27 Inverleith Row.

5. Sir Daniel Macnee, 6 Learmonth Terrace.

6. William Pole, Mus.Doc., Memb. Inst. Civil Engineers, 31 Parlia-

ment Street, Westminster.

'

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

vol. ix. 1876-77. No. 99.

APPENDIX.

(The MSS. of the following papers were unfortunately mislaid , so that
the titles only were printed in last years “ Proceedings

3. The Thermo-Electric Properties of Cobalt, By Messrs
C. G. Knott, J. Gordon MacGregor, and C. Michie
Smith.

(Read 5th June 1876.)

As we could not find pure cobalt for sale in the state of foil
or wire suitable for thermo-electric experiments, we resolved to
prepare it by electrolysis of chloride of cobalt in the way recom-
mended by Mr Gr. W. Beardslee of Brooklyn, N.Y.* For this
there is required pure chloride of cobalt of a certain strength
to form the electrolyte, and spongy metallic cobalt to form the
positive electrode. By the kindness of Dr Crum Brown these
were prepared with very great care in the chemical laboratory by
Mr Robinson, to whom we are much indebted. The following
note of the method of preparation employed has been supplied by
Mr Robinson : —

“Oxide of cobalt was dissolved by heat in hydrochloric acid;
the acid solution was treated with ammonia in great excess, the pre-
cipitate at first formed being then dissolved ; the ammoniacal
solution of chloride of cobalt was then oxidised by passing clean,
dry air through it till the colour was no longer altered, i.e., till the
purple colour was succeeded by a reddish-brown, and till it
admitted of precipitation by hydrochloric acid. This was done,

* Les MondeSy vol. xxxv. p. 206.

3 K

VOL. IX.

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The precipitate purpureo-cobaltic chloride was collected on a filter,
well washed with very dilute hydrochloric acid, and dried carefully,
great care being taken to avoid contamination by iron. The dried
purpureo-cobaltic chloride was then reduced in a current of hydro-
gen in small reducing crucibles, and fine skeletons of spongy
cobalt were obtained. 26 gms. of cobalt were made in this way ;
the remainder of the purpureo-cobaltic chloride was heated to
expel chloride of ammonium, dissolved in hydrochloric acid and
water, and when evaporated to dryness, yielded 32 gms. of chloride
of cobalt. This was made up to 900 c.c. with distilled 'water.”
Having obtained these, some experiments were then made as to
the substitution of aluminium for the carbon-electrode used by
Mr Beardslee, and as to the strength of current required. The
aluminium was found to answer admirably. These preliminary ex-
periments over, we set about preparing such a bar as would serve us
instead of a wire in our thermo-electric work. For this end
we took a strip of aluminium about 100 mm. long, and 8 mm,
broad, carefully covered it with wax on one side, and used it as
the negative electrode. To form the positive electrode a piece of
glass tube, 10 mm. wide, and 20 mm. long, was taken and closed
at one end, through which a platinum wire was passed ; the one
end of this was connected with the positive pole of the battery,
while the other end was coiled into a spiral inside the tube,
into which some of the spongy cobalt was tightly packed so as to
make good contact with the wire. These electrodes were placed
in a porcelain bath containing some of the chloride of cobalt solu-
tion, rendered very slightly alkaline by the addition of ammonia.
The battery found most suitable consisted of two large Bunsen
cells ; when less was used the deposition went on too slowly,
while pieces prepared with a stronger battery-power were inco-
herent. The action was usually allowed to go on for two or three
days, at the end of which time the metal had a considerable thick-
ness. The cobalt was separated from the aluminium by boiling it
in a strong solution of caustic soda. The pieces of cobalt thus
prepared were of very great hardness and compactness, being with
difficulty filed.

It was with these pieces of cobalt that the thermo-electric obser-
vations were made. The firsi observations showed that the cobalt

of Edinburgh , Session 1876-77.

423

line lay very far down on the thermo-electric diagram, while subse-
quent observations showed that it lay below all the lines formerly
obtained. Hence it lies in a region in which it is very difficult
accurately to determine its position. This difficulty is increased
by the circumstance that the line which lies nearest it, namely,
that of nickel, is not a straight line. Another difficulty in carry-
ing out the experiments arose from the shortness of the cobalt bars,
but this was in a great measure overcome by the use of a slight
modification of the apparatus devised for the determination of the
thermo-electric properties of sodium and potassium, formerly de-

s

scribed to this Society.* The following is a brief account of the
experiments and their results : —

In the beginning of March one of the bars was ready for use.
Preliminary observations carried on with hot oil having shown that
no marked peculiarities existed within the temperature of boiling
oil, a quadruple junction of M, N,f nickel and cobalt was formed
and heated by means of a red-hot iron cylinder. The nickel-
cobalt deflections obtained from this experiment, when plotted in
terms of the M-N deflections, gave a line showing clearly the nickel
peculiarities, and supplied us with an approximate position for
cobalt.

On the opening of the laboratory for the summer session experi-
ments with the hot cylinder were resumed, and a quadruple junction
of M, N, palladium, cobalt, was used. This was connected with
the galvanometer in such a way that the deflections due to the
thermo-electric pairs Pd-Co, M-N, M-Pd, could be read separately,
and in rapid succession. The M-N junction supplied us with a
temperature scale as in former experiments, and the lines got by
plotting the other deflections in terms of this gave an easy method
of fixing the relative positions of cobalt, palladium and M, and hence
of fixing the position of cobalt on the thermo-electric diagram.”
Owing to the much greater electro-motive force in the Pd-Co and
M-Pd circuits than in the M-N circuit, a resistance of 192 ohms
had to be inserted between the palladium wire and the galvano-
meter. The M-Pd curve presented the usual well-known parabolic

* Proc. Key. Soc. Edin. 1873-4, p. 350.

t Trans. R. S. E. 1872-73, p. 138.

424

Proceedings of the Royal Society

appearance without any marked peculiarity, but the Pd-Co curve,
though parabolic at comparatively low temperatures, showed at the
higher temperatures an apparent tendency to straighten, thus
indicating a possible point of contrary-flexure, i.e., a bend in the
cobalt line at a temperature somewhere about or above a bright red
heat. The approximate position of the cobalt line may be gathered
from these facts : that the line of 15° C is divided by the points of
intersection of the cohalt, palladium and M lines in the ratio of
11 : 8, and that the cobalt line is inclined to the horizontal at an
angle not quite double of the angle of inclination of palladium.

In experiments made to-day with a double circuit of Co-Pd
against nickel, with some resistance thrown into the cobalt arm, a
neutral point has been got at a temperature of about 500° F. This
shows us that by the aid of cobalt we shall be able to investigate the
peculiarities of nickel more accurately, while from the parts of the
nickel line which are already known we shall be able to fix definitely
the position of the cobalt. It is worthy of notice that even at the
high temperatures of the red-hot or even white-hot cylinder the
cobalt shows no tendency to oxidise.

Electric Conductivity. — During the last few days we have been
carrying on a scries of experiments on the change of the electric
conductivity of cobalt with change of temperature. For this we
prepared a very narrow strip of cobalt by depositing it on the edge
of a piece of aluminium. To the ends of the strip so prepared
stout copper wires were soldered, and the experiments were then
carried on as in the case of nickel (Proc. Roy. Soc. Edin., 1875-6,
p, 120). The line obtained was not straight but slightly curved,
showing apparently a gradual alteration in the rate of change of
conductivity. Within the temperature of boiling oil, however,
there is no indication of a sudden change, and the curve in the
line may be due to several disturbing causes which we have not as
yet been able to eliminate.

of Edmburyli, Session 1876-77. 425

5. Notice of some Decent Atmospheric Phenomena.

By Professor Tait.

(Read 5th June 1876.)

On March 25th, at 8.15 p.m., very few clouds being visible,
there appeared a luminous arch in a vertical plane, passing true
E. and W. nearly through the zenith. This arch, to my surprise,
gave everywhere a continuous spectrum. I had, in company with
Professor Dewar, observed a phenomenon similar in all respects
(continuous spectrum included) some seven years before, and was
then inclined to fancy the arch a mere low-lying cloud, and its
light due to the town lamps. But on the present occasion, after
about forty minutes, when the arch bad disappeared, an aurora,
showing unmistakably in the spectroscope the characteristic green
band, appeared near the magnetic north. And a few days after-
wards there appeared in the Edinburgh newspapers several descrip-
tions of a similar arch seen at almost exactly the same time at
Colinton, &c., and even so far off as Dunfermline. Most of the
observers remarked the entire absence of coruscations as a proof
that the phenomenon could not be auroral. The facts stated seem,
however, to leave no doubt that it was connected with the aurora,
and the peculiarity of its spectrum remains to be explained.

On May 10th, the sky cloudless but hazy, from 11 a.m. till
nearly 3 p.m., I observed a magnificent halo of 22°, with its
tangent arcs forming almost a complete external oval. Various
observers in different parts of Scotland seem to have noticed the
halo itself from 2 p.m. till sunset, but none have mentioned the
external oval, which at midday was brighter than the halo.

As showing that the ice-crystals in the air were very widely
spread about this period, I append an extract from a letter I have
just received from Mr Aitken of Darroch.

“ I have sent you a sketch I made of an atmospheric pheno-
menon which I saw at Cadenabbia, Lago di Como^ on Sunday the
30th April, and hope it may be useful to you to-night.

“ The weather during the previous day was very bad ; it rained
heavily all day. The wind was northerly, and the temperature
low. In the evening there was a thunderstorm, accompanied by a
good deal of lightning. Sunday morning broke clear and tine ;

426

Proceedings of the Royal Society

without a cloud in the sky, almost no wind, and barometer high.
At 10.45 a.m., when I first noticed the phenomenon, the sky was
covered with a very thin uniform white haze, and no clouds visible.

“ When first observed, the large circle which passed through the
sun was complete, but only the upper half of the small circle
which surrounded the sun was visible. There was no colour in
the large circle, but the small circle was fringed with colour, the
outside being of a bluish-violet tint, the inside reddish. In the
centre of the band, between the two colours, no colour could be
distinguished ; it looked pure white. On each side of the small
circle there was a short strip of colour, cutting the large circle at
an acute angle. This short band was visible on the white band
of the large circle, and only extended to a short distance on each
side of it. The small coloured circle was never very perfect, only
the top part remained steadily brilliant, and at this part the colours
were more brilliant than at any other part. The sides were par-
ticularly always rather undefined. ,

“ For part of the time, while the phenomenon lasted, there was an
extraordinary change in its appearance. There appeared to be
two circles of nearly the same diameter surrounding the sun,
neither of which was concentric with the sun, and were separated
from each other horizontally, as shown in the lower of the two
sketches. While this was the case the circles were never com-
plete, only little more than the upper halves of them being visible.
Another curious point was that the coloured circle did not seem a
perfect circle. The horizontal axis seemed longer than the ver-
tical; but of this I am not certain, as I had no instruments to take
any measurements. The only means of observation I had was a
circular piece of paper I hurriedly cut, and held between my eye
and the sun, in such a position that the sun shone through a small
hole in the centre. Wiien this disc was held at such a distance
from the eye that the upper part of the coloured circle was just
seen past the edge, the lower part and the sides were seen to pro-
ject some distance beyond it.

“ About 11.5 a.m. the haze began to collect into clouds, and the
phenomenon ended at 11.20. As the day advanced, clouds con
tinned to form, and rain began to descend at 2 p.m. Towards
evening it became very wet, and it continued to rain every day for
more than a week.”

of Edinburgh, Session 1876-77.

427

1. On New and Little-known Fossil Fishes from the Edinburgh
District. No. III. By B. H. Traquair, M.D., F.G.S.

(Read 7th May 1877.)

Elonichthys ovatus, sp. nov. Traquair.

Of this I have only seen one specimen, from the limestone of
Burdiehouse, and preserved in the Edinburgh Museum of Science
and Art.

Description. — Allowing for the anterior part of the head, which
is deficient, the entire length of the specimen to the extreme point
of the upper lobe of the caudal fin would be about 5-| inches ; the
greatest depth of the body in front of the dorsal fin is li inch.
The distance from the origin of the pectoral fin to that of the
ventral is a little over 1 inch, to opposite the commencement of the
dorsal 1J inch, to opposite that of the anal 1-| inch, and to opposite
that of the lower lobe of the caudal nearly 3 inches. The general
form of the fish is thus remarkably short, deep, and ovoid, and its
general appearance does not indicate that its peculiar form is due to
post mortem distortion or change.

Nothing can be said regarding the osteology of the head, which is
hopelessly crushed, and its anterior part cut off by the edge of the
stone. The scales are of moderate size, and ornamented externally,
like those of E. striolatus , with delicate punctures and oblique
furrows, the latter mostly observable towards the anterior margins.
The paired fins are small, the pectorals only equalling f inch in
length, the ventrals being a little shorter ; the median fins, on the
other hand, are very largely developed. The dorsal and anal fins
contain about 35 rays each, as nearly as can be ascertained. The
former fin is the larger, and is very high and acuminate in front, the
length of its longest ray being l£ inch, while its base equals 1 inch in
extent. The anal fin commences opposite the posterior third of the
dorsal ; it is not so acutely pointed, for while the length of its base
is, as in the dorsal, 1 inch, that of its longest rays is the
same ; its posterior margin is also a little more concave. The prin-
cipal rays of these two fins have their transverse joints rather longer
than they are broad. As usual, they begin to dichotomise towards
their extremities ; this process, however, occurs proportionally
sooner in the shorter rays behind. The caudal is very powerful ;

428

Proceedings of the Royal Society

inequilobate. The anterior rays of the lower lobe have, for a con-
siderable extent of their length, their transverse articulations more
distant than those of its other rays and of the whole upper lobe, in
which the joints are very short.

Remarks. — This species closely resembles E. striolatus , but is
distinguishable from it by the very short and deep form of the body,
and the more largely developed median fins, of which the dorsal is
especially striking, from its great size. Although fully aware of
the danger, in dealing with Palaeozoic fishes, of defining or founding
species upon proportional measurements, yet, seeing that, as already
observed, there seems to be no evidence that the present specimen
has undergone any material change of form by post mortem
processes, I have, after due consideration, thought it best to bestow
upon it a new specific designation.

Geological Position and Locality. — From Burdiehouse, in lime-
stone of the calciferous sandstone series.

Elonichthys Bucklandi , Agass. sp.

Pygopterus Bucklandi, Agassiz, “Poissons Fossiles,” vol ii. pt. !2, p. 77 (1835).

,, ,, Hibbert (Agassiz), Trans. Roy. Soc. Ed., vol. xiii,

pp. 216-217, pi. vii. fig. 2 (1834-35).

I have not seen the original type of this species, figured by Dr
Hibbert in his celebrated memoir on the Burdiehouse limestone, and
stated by Agassiz to be in the collection of the Koyal Society of
Edinburgh. This may, indeed, have been a mistake, and the
specimen may possibly have been in the private collection of Dr
Hibbert, now unfortunately dispersed. From Hibbert’s figure,
however, and the very brief notice of this species in the “ Poissons
Fossiles,” I feel pretty confident in referring to it a number of
mostly fragmentary remains of a large Palseoniscoid fish from Burdie-
house contained in the Edinburgh Museum of Science and Art.

The only entire specimen I have seen is 11-|- inches in length. It
is, most unfortunately, crushed on its back. It displays, however,
the right pectoral and ventral fins. The former has its principal
rays articulated throughout ; the ventral is of moderate size. The
median fins are large. The dorsal is not shown in any of the
specimens belonging to the Edinburgh Museum, but in Dr Hibbert’s
figure it is seen to resemble the anal, and is evidently placed nearly

of Edinburgh, Session 1876-77.

429

opposite the interval between that fin and the ventrals, although the
latter are not shown in the figure. The anal is, however, well
shown in one specimen ; it is large, triangular, and acuminate, and
is closely followed by the caudal, which is very powerful. The fin
rays are externally ganoid and finely striated ; their transverse
articulations are very close ; the fulcra are closely set, and minute
for the size of the fish. The scales of the body are proportionally
small. Those of the front part of the body are apparently nearly
equilateral, but posteriorly, and more especially towards the ventral
margin, their form is low and narrow. Their anterior covered area
is very narrow ; the posterior margin is very finely denticulated.
The exposed area is covered with a delicate yet sharply-defined
ornamentation, consisting of fine sub-parallel ridges which pass from
before backwards across the scale in a gently sigmoid direction,
tending to become intermixed with punctures posteriorly, especially
above the diagonal between the two acute angles of the scale.
Towards the tail the ridges become less marked on the posterior part
of the scale, giving way to the thickly dotted punctures, till, on the
caudal body-prolongation, the former, after lingering at the anterior
margin, altogether disappear, and punctures alone remain.

Very little can be made out concerning the bones of the head ;
however, in the above mentioned entire specimen the lower jaw is
seen to be very stout, and ornamented externally with fine, sharp,
closely set, wavy, branching, and anastomosing and interrupted
ridges running in a longitudinal direction. The laniary teeth are
very strong, incurved, and smooth, with apical enamel cap ; similar
teeth are seen on the maxilla, the dental margin of which is finely
tuberculated.

Remarks. — The structure of the pectoral fin, the relative position
of the dorsal and anal fins, and the form of the latter, show clearly
that this species is not a “ Pygopterus,” to which genus it was
referred by Agassiz. On the other hand, its affinities to Elonichthys
striolatus are unmistakable, though it attains a larger size. In this
and in some other respects it resembles considerably the three large
species from the Coal-measures of North Staffordshire, which I have
recently described as Elonichthys semistriatus , caudalis , and oblongus *

*Memoirs of -the Palaeontographical Society for 1877, “Carboniferous
Ganoids,” pp. 49-57.

3 L

VOL. IX.

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Proceedings of the Royal Society

Elonichthys (?) pedinatus, sp. nov. Traquair.

Description. — Flank scales about ^ incb broad, and usually a
little higher, exclusive of the articular spine ; moderately thick.
Upper margin with prominent articular spine ; anterior covered
area narrow ; exposed surface brilliantly ganoid, sculptured with
oblique, sub-parallel, prominent ridges, occasionally branching,
anastomising, and intercalated, and terminating behind in delicate
denticulations of the posterior margin; about 7 or 8 of these ridges in
the space of inch. Under surface of scale with feebly marked
keel ; a narrow area along the posterior margin is obliquely grooved,
the short grooves terminating between the denticulations of the
margin, so as to produce a pectinated appearance. Scales from
apparently the ventral aspect are lower than broad, and with more
produced anterior-superior angles ; others, from their more regularly
rhomboidal shape, and scanty development or absence of the
articular spine, and more prominent keel of the attached surface,
were probably situated more towards the caudal extremity. In all
cases the external sculpture is similar, and the under surface dis-
plays the same peculiar pectinated appearance at the posterior
margin.

Associated with these scales there is on a specimen from Carluke
in the collection of Mr Grossart, of Salsburgh, a small fragment of
the edge of what must have been a pretty large jaw. This frag-
ment is nearly 1J inch in length, and displays the stumps of 5 stout
conical teeth, with traces of smaller ones external to them ; the
external surface of the bone is beautifully tuberculated.

Remarks. — Though as yet I only know this species from detached
and dislocated scales, often occurring together in masses, and, from
the small jaw fragment described above, there can be no doubt as
to its distinctness and novelty as a species. In external sculpture
these scales bear a considerable resemblance to those of Acrolepis
Rankinei (Gyrolepis Rankinei , Ag.), with which, on superficial
examination, they might perhaps be confounded, but from the latter
they may be at once distinguished by the narrowness of the anterior
covered marginal area, and the grooved pectination of the posterior
margin of the internal aspect. Of course, until further information
regarding its fins and head be obtained there must be some uncer-

of Edinburgh , Session 1S7C—77 . 43 1

tainty as to the genus to which it belongs. Meanwhile, I have
assigned this species to Elonichthys on account of the general con-
figuration of the scales. Should this opinion prove correct, it is
certainly the largest species of the genus hitherto described.

Geological Position and Localities. — In the hlackband ironstone
of Gilmerton belonging to the Lower Carboniferous Limestone
series ; in bituminous shale from a similar horizon at Carluke, in
the collections of Dr Rankin of Carluke, and Mr Grossart of Sals-
burgh ; in calcareous shale accompanying the limestone of Levenseat
in the Upper Carboniferous Limestone group. I am indebted to
Mr Grossart for specimens from the last-named locality.

Rhadinichthys, gen. nov. Traquair.

Palceoniscus (pars), Agassiz.

Body more or less elongated ; scales moderate, sometimes rather
large, variously ornamented or nearly smooth, their posterior margins
serrated. Caudal body prolongation slender. Dorsal fin placed
rather far back, commencing only very slightly in front of the anal ;
the principal rays of the pectoral unarticulated till towards their
terminations. Suspensorium very oblique ; gape very wide ; jaws
armed with a row of incurved conical laniaries, outside which there
is a series of smaller teeth.

I propose to institute the genus Rhadinichthys (paotvo?, slender, and
for the Palceoniscus ornatissimus of Agassiz, and a number of
other species from carboniferous rocks, many of which have hitherto
been undescribed. These fishes differ markedly from Palceoniscus
in the structure of the pectoral and in the position of the dorsal fin,
in these respects approaching Pygopterus, from which they are,
however, distinguished by their scales being proportionally larger
and thicker, the anal n not being prolonged backwards in a fringe-
like manner, and the caudal body prolongation being much less
powerful. Rone of the species of Rhadinichthys attain large dimen-
sions ; most of them are, indeed, fishes of very small size.

This genus is, so far as is yet known, confined to the carboni-
ferous formation, and is abundantly represented in rocks of that age
in Great Britain. Judging from the figures given, Palceoniscus
Oairnsii of Jackson, and some of the other small Pakeoniscidae from

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Proceedings of the Royal Society

New Brunswick figured but not named by him,* seem to be referable
to Phadinichthys , as is possibly also the case with his Palceoniscus
Albertii , though I regret that I have not seen any specimens of the
latter sufficiently perfect to enable me to come to a definite conclu-
sion as to whether or not it may belong to still another genus —
most certainly, however, it is not a “ Palceoniscus ” in the sense in
which that term ought now to be restricted.

Rliadinichthys ornatissimus, Agass. sp.

Palceoniscus ornatissimus (pars), Agassiz, “Poissons Foss.” vol. ii. pt. ii.

pp. 92-93 (1835); “Atlas,” vol. ii. pi. 10a, fig. 6, but not figs. 5 and 7.

“ Palceoniscus ” ornatissimus was described by Agassiz from three
specimens, all of which are figured in the “Poissons Fossiles.”
Two of these from Burdiehouse are in the collection of the Boyal
Society of Edinburgh ; they are in a very bad state of preserva-
tion, nevertheless enough is seen of their structure to convince
me that they belong to two different species. The original of fig.
5, tab. 10a (“ Atlas,” vol. ii.), seems to me to be only a peculiarly
crushed specimen of Elonichthys Robisoni. The other, represented
in fig. 6, is of larger dimensions, and though the fins are very
imperfectly shown, yet, from the general form of the body, and
from the sculpture of the scales and cranial bones, I have no hesita-
tion in identifying with it a number of specimens of a fish, which is
not uncommon in the rocks of the calciferous sandstone series of
the neighbourhood of Edinburgh. The specimen represented in
fig. 7 of the same plate of Agassiz’s work does not seem to me to
belong to the same species, and, unfortunately, there seems now to
be little hope of tracing the original to its present possessor, as it
belonged to the late Mr Jamieson Torrie, whose collection was,
after his death many years ago, sold by public auction and dispersed.
As type of “ ornatissimus ” we are therefore justified in taking the
original of fig. 6 of the plate referred to.

Description. — The length of the type specimen, which is so bent
round that the tip of the tail nearly touches the snout, is 5 inches ;
doubtless, its original length was greater, previous to the strange
contortion which has thus affected its form. It is, nevertheless,
small, the most perfect specimen in the Hugh Miller Collection

* Report on the Albert Coal* Mine, New Brunswick.

433

of Edinburgh, Session 1876-77.

attaining a length of 8 inches, while another, unfortunately wanting
the head, would probably have measured no less than 10 inches had
it been entire. The head seems rather large, and would probably
be contained about in the total ; the greatest depth of the
body is at the shoulder, whence it gradually tapers to the tail
pedicle, which is rather narrow. The suspensorium is very oblique,
the gape extensive ; the lower jaw is of a tapering form. Traces of
sharp conical teeth are seen in many specimens, and are, as usual,
arranged in two sets — internal larger and external smaller. The
operculum is large and oblong, with acute anterior-superior and
posterior-inferior angles ; the interoperculum is of the usual quadrate
shape. A specimen from Wardie, obliquely compressed upon its
back, shows on the right side a beautiful series of 15 branchiostegal
rays, along with the anterior 7 of those of the other side, besides
which there is a small median lozenge-shaped plate behind the
symphysis of the jaw, the anterior plate of each lateral series being
also much broader than the others. All the bones of the head are
finely and closely striated.

The scales are rather large on the front of the flank. In a
Burdiehouse specimen, which probably measured originally about
10 inches in length, one of these scales measures •§ inch in
height by in breadth ; they get much smaller posteriorly, and
those situated on the belly are rather low and narrow. Their
external ornament consists of sharp yet delicate slightly sigmoidally
curved ridges, mostly parallel with the superior and inferior
margins. In the furrows between these, numerous punctures may
be observed, and very often about the centre of the scale the ridges
are over a small space nearly obsolete, so that the punctures come
more prominently into view. Proceeding towards the tail, the
ridges become less and less prominent, especially in the middle of
the scale, so that the ornament ultimately appears to consist only of
short furrows and punctures, which are most marked towards the
anterior and posterior margins. The posterior margin of the scale
is finely denticulated ; the keel of the under surface is feebly
marked in the scales of the front of the body, but posteriorly
it becomes more apparent.

The paired fins are rather small, the pectoral attaining only about
one-half the length of the head. It consists of about 30 rays, of

434

Proceedings of the Royal Society

which the principal ones are, as in Pygojoterus and Oxygnathus,
unarticulated till towards their terminations. The ventrals are not
well exhibited in any of the specimens, though in two cases portions
of them are seen ; they seem to have been small, with delicate rays,
whose transverse articulations are rather distant. The dorsal and
anal fins are moderate, the former being placed far hack, and arising
only slightly in front of the anal. Both are acuminate, triangular,
with considerable concave posterior margins. The base of the anal
is slightly more extended than that of the dorsal, and a well-marked
interval occurs between its termination and the commencement of
the caudal, It is not possible to ascertain the number of rays in
those fins. They are rather delicate, and with their transverse
joints about twice as long as broad — at least, in the longer rays
before bifurcation. When the rays are in situ their articulations
appear proportionally still more distant, owing to the usual imbrica-
tion of the demi-rays. The anterior rays of the lower lobe of the
caudal are stouter than those of the rest of the fin, and have their
transverse articulations closer, the joints appearing nearly square as
seen from the outside; as the lower lobe passes into the upper one
the rays become more delicate, and their articulations more distant.
The outer surfaces of the rays of the pectoral are nowhere seen, but
in the other fins the rays are ganoid externally, and mostly smooth,
though showing here and there, especially towards their proximal

.... c* i • . i* rrri p i „

1

extremities, traces of longitudinal striation. The fulcra are small,
though very distinctly visible under an ordinary lens.

Geological Position and Localities. — The specimens which I have
included under the foregoing description are all from the Calciferous
Sandstone series of Midlothian, in which the species seems to be
widely distributed, though not very abundant as regards number of
specimens. It occurs in the Wardie shales, at Wardie (Museum of
Science and Art and collection of the author) ; near Slateford (col-
lection of the Geological Survey of Scotland) ; near Juniper Green
(Mr John Henderson) ; in the horizon of the Burdiehouse lime-
stone, at Burdiehouse and at South Queensferry. Its occurrence
in strata of similar age in Fifeshire is extremely probable, though
the specimen from Burntisland, figured as Palceoniscus ornatissimus
by Agassiz, seems now to be unfortunately lost.

435

of Edinburgh , Session 1876-77.

Rhadinichthys ferox , sp. nov. Traquair.

Of this new species there is one tolerably entire example from
Wardie in the Hugh Miller Collection in the Edinburgh Museum
of Science and Art. A short time ago also the Museum acquired a
fragment of the head and anterior part of the body, collected by Mr C.
W. Peach, and quite recently another fragment, a portion of the body,
was presented by Mr David Grieve. In the following description
these specimens will be referred to as Nos. 1, 2, and 3 respectively.

Description. — The specimen in the Hugh Miller Collection has
undergone a twist about the middle of the body, and shows, more-
over, only a portion of the caudal fin, so that it is difficult to
estimate its original length. As it is, it measures 5f inches in
length, but it is quite evident that when alive it must have been
considerably longer.

The head equals If inch in length, and shows superiorly a cast
of the greater part of the inner surface of the cranial buckler, with
the lines of demarcation between the parietal, frontal, squamosal,
and post-frontal bones. The opercular bones are not seen, but a
portion of the maxilla, and the greater part of the mandible are
exhibited, the latter bearing sharp conical teeth of different sizes,
those externally placed being very small, while one large laniary,
Jq inch in length, is conspicuous. In specimen No. 2 the impres-
sions are seen of the parietal, squamosal, opercular, prseopercular,
post-temporal, and supra-clavicular bones, and of the posterior part
of the maxilla, these impressions clearly showing that the external
sculpture of the bones in question was of a highly ornate character,
consisting of sharply defined, flexuous, branching, anastomising, and
interrupted ridges, tending to pass into tubercles at the inner margin
of each parietal.

The scales are of moderate size on the flanks, becoming rather
small posteriorly, while on the belly they are low and narrow.
Over the whole body their outer surfaces are highly ornate, the
ornamentation consisting of fine sharply defined ridges, forming a
pattern which is usually, as it were, divided by a diagonal passing
from the anterior-superior to the posterior-inferior angle of the scale.
On the anterior-inferior half of the scale the ridges run parallel with
the anterior and inferior margins, impinging posteriorly on the
diagonal, while on the posterior-superior half they pass obliquely
downwards and backwards, mostly parallel with the diagonal,

436

Proceedings of the Royal Society

ending in the dc-nticulations of the posterior margin ; in many cases
they are interrupted before reaching that margin, and are replaced
by other shorter ones springing np between them. In some cases,
also, a few of the ridges of the upper half, near the anterior-
superior angle of the scale, likewise impinge upon the diagonal,
consequently meeting those of the lower half at acute angles.

The pectoral fin is well displayed in specimen Ho. 1, in which it
measures rather more than 1 inch in length. It is of considerable
expanse, and consists of at least 30 rays, of which the stronger ones,
the first 15 counting from the lateral margin, are unarticulated till
towards their terminations, where bifurcation sets in. The ventrals
are not shown. Portion of the dorsal is seen in Ho. 1, in which it
seems to arise opposite the anterior part of the anal, and its entire
contour is exhibited in Ho. 3. It is triangular and acuminate, very
high in front ; its rays, which cannot be counted, are rather deli-
cate, and their transverse articulations considerably distant. In
Ho. 1 the anal is seen to be of large size, and of the same triangular
acuminate form as the dorsal. Its base is l-^ inch in extent, and
its longer anterior rays seem to have exceeded that measurement,
though they are cut off at the apex ; the fin is, moreover, badly pre-
served, and its anterior margin somewhat distorted and injured. In
the same specimen the origin of the lower lobe of the caudal is also
shown, consisting of exceedingly closely set deeply imbricating rays,
of which I count at least 40 up to where they begin to pass into those
of the upper lobe, but here the tail is unfortunately truncated by
the edge of the nodule. Interspinous bones of great strength are
seen supporting this part of the caudal fin.

Remarks. — This is a most distinctly-marked species, differing
obviously from R. ornatissimus in the proportions and sculpture of
the scales, and in the large size of the fins. I know of no other
species with which it can at all be confounded. The first time I
saw the most perfect of the three specimens described above, I was
struck with the general resemblance which it bore to the Permian
genus Pygopterus, but the larger proportional size of the scales, and
the anal fin not being prolonged backwards, indicate that its place
is in Rhadiniclitliys.

Geological Position and Locality. — In ironstone nodules from the
shales of Wardie, near Edinburgh, belonging to the Calciferous
Sandstone series.

437

of Edinburgh^ Session 1876-77.

Rhadinichtliys lepturus, sp. nov. Traquair.

I* am indebted to Dr Paterson, of Leith, and to Mr R. Etheridge,
jun., for the loan of two specimens of a small Rhadinichtliys from
Grange Quarry, Burntisland, which appears to belong to a new
species. With these I can identify a detached tail recently found
by myself in the same locality.

Description. — The length of Dr Paterson’s specimen is 3 \ inches,
allowing for the extremity of the snout, which is deficient. The
depth of the body, midway between the head and the dorsal fin, is
inch ; that of the tail pedicle at the commencement of the lower
lobe of the caudal is ~ inch. It is, however, just possible that the
anterior part of the fish may be a little shortened up by one of the
common forms of distortion, as, on the other hand, the whole shape
of the other specimen belonging to Mr Etheridge certainly is unnatur-
ally attenuated by a similar cause. Nevertheless, we have before us
a small fish of a fusiform shape, elegantly tapering posteriorly to a very
narrow tail pedicle, the dorsal and anal fins being nearly opposite each
other, and a well-marked interval occurring between the latter and the
commencement of the caudal, which is rather small and of a delicate
appearance. Nothing can be said regarding the head, which is
hopelessly crushed. The scales are of medium size, becoming
rapidly smaller posteriorly. Those of the anterior part .of the body
have their outer surfaces entirely covered by a delicate sculpture
consisting of fine furrows and ridges passing across the scale, and
ending in the denticulations of the posterior margin, those of the
upper and posterior part of the area being more oblique than those
of the lower and anterior. On the posterior part of the fish the
scales are seen only from their inner or attached surfaces. The
origin of the pectoral fin is seen in the second specimen referred to,
but it is in very bad preservation. Returning to Dr Paterson’s
specimen, a few rays of the ventral are seen, but the real size and
shape of the fin are not shown. The dorsal and anal fins are
moderate, and of the same form, triangular, concavely cut out
behind, with delicate rays, whose transverse joints are considerably
longer than they are broad. The dorsal commences only very
slightly in front of the origin of the anal, and an interval, equal to
■§ the length of the base of the anal, occurs between its posterior
termination and the commencement of tne lower lobe of the caudal.

3 M

VOL. IX.

438

Proceedings of the Royal Society

The last-named fin is unusually delicate in appearance, the upper
lobe only very slightly exceeding the lower in length, with a slender
body prolongation. In the lower lobe the transverse joints of the
principal rays are longer than they are broad, except just towards
their terminations.

Remarks. — In the contour at least of the hinder part of the body
this species strongly resembles R. carinatus, save that the caudal fin
is more delicate — the greater apparent depth of the body in front of
the dorsal fin may be, as already indicated, perhaps accounted for
by post mortem distortion. The sculpture of the scales, which is
very different from what we find in R. carinatus , reminds us of R.
ornatissimus, from which, however, the present species is obviously
distinguished by the greater delicacy of the rays of the lower lobe of
the caudal, with their more distant transverse articulations, as well
as the entire aspect of the fin. It is, however, very possible that
the imperfect specimen from Burntisland referred by Agassiz to
il Palceoniscus ” ornatissimus (Poisson’s “Fossiles Atlas,” vol.ii.pl. 10a,
fig. 7), and in which the tail is deficient, may belong to R. lepturus ,
but his figure being by no means good, it is impossible to decide, in
the absence of the original specimen.

Geological Position and Locality. — In calcareous shale overlying
the “ Burdiehouse ” limestone exposed in Grange Quarry, Burntis-
land (Calciferous Sandstone series).

Rhadinichthys Geikiei , sp. nov. Traquair.

Through the kindness of Professors Bamsay and Geikie I have
enjoyed the opportunity of examining a number of small specimens
of Palseoniscidse collected by the Geological Survey from the horizon
of the Wardie shales near Redhall, among which there is at least
one beautiful little species of Rhadinichthys hitherto* undescribed.
This I have much pleasure in dedicating to Professor Geikie, to
whom I am much indebted for cordial assistance in prosecuting
the study of Scottish Palaeozoic ichthyology.

Description. — The specimens are rather fragmentary, except two
in which the entire fish is shown. Of these the larger has undergone
an unfortunate twist, but its length may be estimated at 3J inches ;
the other, measuring only 2J- inches, seems to me to be a younger
example of the same species. The body is fusiform, the head

439

of Edinburgh, Session 1876-77.

rather large, being contained about 4 times in the total. The
cranial bones are beautifully ornamented with delicate wavy ridges,
running mostly in a longitudinal direction. The jaws are armed
with sharp conical teeth of different sizes. The scales are of mode-
rate size, gradually diminishing posteriorly, though those on the
flanks are not of specially large dimensions. The flank scales are
nearly equilateral in shape ; the free surface of each is ornamented
with 5 or 6 pretty well-marked oblique ridges, running downwards
and backwards, and terminating in the denticulations of the pos-
terior margin. Eelow there are a few more delicate striae parallel
with the lower margin. Along the back, between the head and the
dorsal fin, the scales are smaller, and the ornamentation takes the
form of a few sharply-marked striae passing diagonally across the
scale between the two acute angles. Posteriorly, as the scales
become smaller, the ridges are fewer, and the ornamentation becomes
more and more feebly marked, till on the tail pedicle the scales are
nearly smooth, and entirely so on the caudal body prolongation,
which is delicate. Some amount of individual variation occurs in
the scales of different specimens, which I see no good reason for
referring to different species. In two fragments representing
portions of rather larger fishes than the rest, the scales of the back,
between the head and the dorsal fin, are rather smoother, while
those of the flank show a greater number of ridges and denticula-
tions of the hinder margin ; on the other hand, in the smallest
specimen of the series, the ridging on the dorsal scales is very well
marked, and rather feeble in those of the flanks.

The pectoral fin is shown in one specimen, but not well, being a
little obscured by a thin film of the matrix ; the ventrals are visible
in none. The dorsal and anal fins are situated nearly opposite each
other, the anal commencing only a little further back. The entire
contour of these fins is not clearly exhibited, but their rays are
smooth, delicate, and slender, with distant transverse articulations,
The caudal is inequilobate, its rays are likewise delicate and smooth,
and with distant articulations; the caudal body prolongation is
slender.

Remarks. — In its general proportions R. Geikiei is not so slender
as most species of the genus, and there is not the usual interval
between the anal and caudal fins ; in these respects it agrees with

440 Proceedings of the Royal Society

R brevis , from which it may, however, be distinguished by the
nature of the ornamentation on the scales and cranial roof bones.

Geological Position cmd Locality. From the Wardie shales in
the Calciferous Sandstone series. The specimens were collected by
Mr James Bennie, of the Geological Survey of Scotland, in a very
fissile shale exposed near Bedhall, to the west of Edinburgh, in a
cutting made for the Caledonian Kailway loop line to J uniper Green
and Midcalder.

Rkadinichthys brevis , sp. nov. Traquair.

Description. — The length of the most perfect specimen in my
collection is 3 J inches ; the extremity of the caudal fin is not,
however, preserved. Another specimen, more badly preserved
posteriorly, must have been a little longer, judging from the size of
the head and body. The head is elegantly shaped, with bluntly
pointed muzzle. The opercular bones are rather small ; the jaws
pretty stout ; the dentition is not visible. The bones of the cranial
roof are sculptured, with contorted and rather flattened rugae ; those
of the face are ornamented with sharp and closely set wavy ridges,
which, on the operculum, pass obliquely downwards and backwards
over its surface. The scales are of moderate, indeed, rather small
size, and though, of course, diminishing gradually towards the tail,
those in the flanks U,re not marked by any very special excess in
size. The flank scales are nearly equilateral ; the posterior margin
of each shows 5 or 6 prominent oblique denticulations ; the outer
surface shows a few feebly marked, nearly obsolete ridges, pass-
ing obliquely backwards and a little downwards, and not very
regularly placed. Immediately behind the clavicle, and above the
origin of the pectoral tin, the sculpture is, however, more strongly'
pronounced, the ridges being finer, sharper, and closer together, but
posteriorly the scales soon become nearly quite smooth. The paired
fins are rather small, the principal rays of the pectoral are clearly
seen to be unarticulated till towards their terminations; the ven-
trals are situated midway between the pectorals and the origin of
the anal, their rays are delicate, and their transverse joints appear
at least three times as long as broad. The dorsal and anal fins are
large, and situated nearly opposite each other, the former commen-
cing, as usual in this genus, slightly in front of the latter. Both

441

of Edinburgh, Session 1876-77.

have the same form, being high and acuminate in front, and con-
cavely cut out behind; their rays are rather coarser than those of
the yentrals, and their transverse joints are considerably longer than
broad. In no case is the caudal tin well preserved, its rays being
more or less disjointed and broken up, but it is clear that the pro-
longation of the body in the upper lobe was delicate, the rays slender,
and with distant articulations.

Remarks. — As already indicated, this species agrees with
R. Geikiei in the general form of the body, and, along with
it, differs from all the other species of the genus with which I am
acquainted in the closer approximation of the anal fin to the caudal ;
in both, also, the flank scales are comparatively small. But the
action of the scale sculpture is essentially different. In R. brevis
such ridges as are seen on the flank scales have not the same short,
sharp, straight, and parallel character which distinguishes those
which in R. Geikiei pass to the denticulations of the posterior mar-
gin ; the rugae ornamenting the cranial roof bones are also coarser,
more flattened, and less capable of being described as “ striae.”
Geological Position and Localities .. — From the Calciferous Sand-
stone series. Five specimens are in my possession, four of which
are in ironstone nodules from Wardie beach ; the fifth I found in a
detached block of slaty carbonaceous ironstone, on the shore near
the mouth o f the Kenly Burn, between St Andrews and
Kingsbarns.

Rhadinichthys car hiatus, Agassiz sp.

Paloeoniscus carincitus, Agassiz ; ‘‘Poissons Fossiles,” vol. ii. pt. i. p. 104
(1835); “Atlas,” vol. ii. tab. 4 b, figs. 1 and 2.

The form of the body is slender, the length of the head being
contained about 4f- times in the total up to the bifurcation of the
caudal fin, and equalling the greatest depth of the body at the origin
of the ventral fins. The head is very elegantly shaped, rather
depressed above, but pointed when seen in profile. The bones
of the cranial shield are ornamented with sharp, delicate, wavy
ridges or “ striae.” A specimen from Wardie in my collection shows
most clearly the presence of extensive ossification in the periotic
and alisphenoid regions of the cranium, and, moreover, a cast of
the posterior semi-circular canal of the ear is most distinctly and

442

Proceedings of the Royal Society

beautifully preserved. The opercular bones are rather small ; the
jaws remarkably slender and delicate ; the external ornament of the
facial bones consists, like that of the cranial shield, of delicate wavy
ridges. No specimen I have as yet seen affords, however, the
smallest trace of teeth. The paired fins are rather small. The
pectoral is in no case well preserved, but there is sufficient evidence
that its longer rays were not articulated till towards their termina-
tions. The ventrals are still smaller, and are equidistant in position
between the pectorals and the commencement of the anal. The
median fins are, on the contrary, rather large in proportion to the
size of the fish. The anal commences rather in front of a point
equidistant between the origin of the ventrals and that of the lower
lobe of the caudal ; it is high and acuminate in front, and pretty
deeply cut out behind ; the length of its base is equal to that of its
longest rays. The dorsal is similar in shape to the anal, and com-
mences only slightly in front of the origin of the latter. The caudal
is pretty large, and deeply cleft, the body prolongation along the
upper lobe being, however, comparatively delicate. The rays of all
th ese fins are slender, ganoid, and smooth externally ; their
articulations tolerably distant ; the fulcra on their anterior margins
obvious, though minute.

The scales are remarkable for their large size on the flanks, while
on the belly they suddenly became very low and narrow ; they
diminish rapidly in size posteriorly, and on the tail pedicle are
rather small. Externally they are brilliantly polished and nearly
smooth ; on the flank scales, however, a few shallow furrows extend
a little way forwards from the posterior margin, which is, as usual,
sharply denticulated.

Remarks. — The original specimen, collected by Lord Greenock
at Wardie, and figured by Agassiz, is in the collection of the Royal
Society of Edinburgh. It is very imperfect, showing no fins save
the mere origins of the anal and caudal, the former of which seems
to have been overlooked by Agassiz. On the other hand, I cannot,
by the most careful examination, verify his statement regarding the
presence of small teeth, “ en brosse ” upon the jaw. I am indebted
to Professor Turner for the loan of a specimen from Cornceres, in
Fifeshire, which belonged to the late Professor Goodsir ; it is pos-
sible that this may be the “ Gat opt eras fusiformis v which Mr

443

of Edinburgh, Session 1876-77.

Robert Walker states was described by Professor Goodsir in 1838
before a meeting of the Literary and Philosophical Society of St
Andrews, and which, according to Mr Walker, he characterised as
closely allied to Palceoniscus , but differing from it “ in wanting the
scaling or false rays along the anterior ray of the fins, and also in
the dorsal fin being opposite the anal.”* In this specimen the
dorsal is, indeed, nearly opposite the anal (as in others of the same
genus as well as species), but, on close examination, fulcra are dis-
tinctly observable. I have not been able to obtain Professor
Goodsir’s description, or even to ascertain exactly where it is to be
found, but as it appears to have been published only in a provincial
newspaper, the generic name Catopterus must remain with the
Triassic semi-heterocercal Lepidosteids, to which it has been applied
by the Messrs Redfield.

Geological Position and Localities. — From the Calciferous Sand-
stone series. In ironstone nodules from the shore at Wardie, near
Edinburgh ; on the shore near Pittenweem, in Fifeshire, in the col-
lection of Mr J. W. Ivirkby ; in a compact grey limestone at Corn-
ceres near Kilrenny, collected by the late Professor Goodsir.

Rhadinichthys tenuicauda, sp. nov. Traquair.

Length, about 2J to 3 inches ; form slender, narrowly tapering
posteriorly. Head bones sculptured externally, with closely set
flexuous ridges ; dentition not visible. Scales rather large for the
small size of the fish, and especially large on the sides of the abdo-
men, becoming smaller on the back and towards the tail. The
posterior margins of the scales are denticulated, their external sur-
faces nearly smooth along the sides of the body and on the tail
pedicle, but along the back, especially between the dorsal fin and
the head, they are marked by a few rather prominent oblique ridges ;
a similar ornamentation, though rather finer and closer in character,
makes its appearance also on the scales along the ventral margin.
The pectoral fin is small ; the non-articulation of its stouter rays
seems to prevail over a less extent of the fin than is usual in this
genus. The ventral is still smaller. The dorsal and anal are of
medium size, and nearly opposite each other ; their rays are fine

* Trans. Geol. Soc. of Edinburgh, vol. ii. pt 1. (1872), p. 124.

444

Proceedings of the Poyal Society

and distantly jointed. Between the anal and caudal fins there is a
considerable interval. The caudal is inequilobate, with attenuated
body prolongation ; its rays are slender, smooth, and with distantly
placed articulations. The fulcra are very obvious in all the fins,
notwithstanding the small size of the fish.

Remarks. — This species is allied to R. carinatus in general form,
and in the large size of the scales of the flank, but differs obviously
from it in the general larger proportional size of the scales, in the
ornate character of those along the dorsal and ventral margins, and
in the greater delicacy of the fins, and smaller number of their rays.
The head seems also to be larger in proportion to the size of the fish.

Geological Position and Localities. — A fish of the middle or
“ Edge Coal ” group of the Carboniferous Limestone series, the speci-
mens above described being from Wallyford, near Tranent, in the
collections of Mr D. J. Brown ; and from Possil, near Glasgow, in
the collection of Messrs James Thomson and John Young, F.G.S.
To the kindness of these gentlemen I am indebted for the oppor-
tunity of describing this most distinct and interesting little form.

On the Cranial Osteology of Rhizodopsis, and on some points
in the Structure of Rhizodus. By Dr B, H. Traquair.

[Abstract.)

Read May 21, 1877.

This paper contains an account of the cranial structure of Rhizo-
dopsis as far as this can be elucidated by an examination of a suite
of specimens from the Coal Measures of Eenton, Staffordshire, in
the collection of Mr "Ward of Longton, supplemented by additional

specimens from various other localities.

.

The cranial shield of Rhizodopsis resembles in general form and
structure that of the Saurodipterini, though the surface of the bone
is elaborately sculptured instead of presenting the smooth glistening
aspect characteristic of the external plates and scales of the last
named group. The posterior part of the shield is composed of two
elongated parietals, and having on its outer margin two smaller
plates, anterior and posterior, which may be considered as the post-
frontal and squamosal respectively. The anterior or fronto-ethmoidal

of Edinburgh, Session 1876-77.

445

portion forms the depressed rounded snout, the front margin of which
above the mouth, is formed by two small dentigerous praemaxillary
bones entirely differing in form from the bones described as such by
Messrs Hancock and Atthey. The gape is wide, the kyomandibular
bone being slightly inclined backwards; there is apparently no
symplectic. The form of the maxilla is well known ; the structure
of the mandible is exceedingly complex. Its dentary element is
found to correspond with the bone interpreted by Messrs Hancock
and Atthey as “ prcemaxillaf but turned in a contrary direction,
i.e., with its toothed margin upwards instead of downwards as
supposed by them ; it bears the anterior laniary tooth and the
outer row of small teeth. The laniaries posterior to the front one
are borne on separate internal dentary ossicles, the presence of which
is clearly proved by a portion of a jaw of a large specimen of
Rhizodopsis in the Edinburgh Museum. The external aspect of the
lower jaw is completed by at least two infra-dentary plates situated
below the inferior margin of the dentary, behind which there is
another covering externally the articular and angular region of the
jaw, and which is probably the equivalent of the angular of other
ganoids. On the internal aspect of the mandible there is, besides
the internal dentary or laniary ossicles, a well-marked splenial.
The orbit is very anteriorly placed ; as in Megalichthys , three plates
cover the cheek behind the suborbitals, corresponding to the single
large one in Osteolepis. The author does not find Professor Young’s
statements that the jugular plates of Rhizodopsis are “ in two pairs,
principal and posterior,” and that there is “ no trace of median or
of lateral plates,” corroborated by the specimens under examination.
On the other hand, he finds one pair of large principal jugulars
with at least four lateral ones on each side, as well as very distinct
evidence of the presence of a median plate behind the symphysis of
the jaw. The shoulder girdle is provided with well-developed
infraclavicular plates.

The lower jaw of Rhizodus Hibberti is found to have essentially
the same structure as that of Rhizodopsis. The dentary element
is of the same form, and bears the anterior large laniary tooth and
the outer range of small teeth, the posterior laniaries being borne
on separate ossicles, which are sometimes found entirely detached.

3 N

VOL. IX.

Donations to the Eoyal Society Library during Session

1876-1877 : —

I. From Authors.

Acquoy (J. G. K.). Het Klooster te Windesheim en zijn Invloed.

2de Deel. 8vo. Utrecht, 1876. — From the Author.

Alston (E. E.), Gray (R), Cameron (P.). Rotes on the Fauna of
the West of Scotland. 12mo. Glasgow, 1876. — From the
British Association for the Advancement of Science .

Armstrong (James), Young (Professor John), and Eobertson
(David). Catalogue of the Western Scottish Fossils ; with
Introduction on the Geology and Palaeontology of the District.
By Professor Young, M.D. 12mo. Glasgow, 1876. — From
the British Association for the Advancement of Science.
Bechmann (F.). Kaiserschnitt wegen Carcinoma Uteri. Inaug.

Dissert. 8vo. Erlangen, 1877. — From the Author.

Bergbohm (Carl). Staatsvertrage und Gesetze als Quellen des
Volkerrechts. 8vo. Dorpat, 1876. — From the Author.

Bernet (H.). Arterienverletzungen des Hohlhand. Inaug. Dissert.

Erlangen. 8vo. Jena, 1876. — From the Author.

Blix (E.). De vigtigste Udtryk for Begreberne Herre og
Fyrste i de Semitiske Sprog. 8vo. Kristiania, 1876. — From
the Author.

Blom (Hans). Eussisk Sproglaere til praktisk Behov. 8vo.

Kristiania, 1876. — From the Author.

Bowditch (Nathaniel). The New American Practical Navigator ;
being an Epitome of Navigation, containing all the Tables.
8 vo. Washington, 1868. — From the Author.

Brauninger (W.). Beitrage zur Kenntniss des Buchenholztheer-
kreosots. Inaug. Dissert. 8vo. Erlangen, 1876. — From the
Author.

Broch (Dr 0. J.). Le Eoyaume de Norv4ge, et le peuple Norv4gien,
ses rapports sociaux, hygiene, moyens d’existence, &c. 8vo.
Christiania, 1876. — From the Author.

Burck (E.). Verhaltniss zwischen Intermittens und Leukamie.
Inaug. Dissert. 8vo. Erlangen, 1876. — From the Author.

of Edinburgh, Session 1876-77. 447

Caspari (Dr C. P.). Quellen zur Geschichte des Taufsymbols und
der Glaubensregel, herausgegeben und erlautert. Band III.
8 vo. Christiania, 1875. — From the Author.

Christenn (G.). Methoden der Analyse der Frauenmilch und
Kuhmilch. Inaug, Dissert. 8vo. Erlangen. — From the
Author.

Craig (Sir William Gibson-). See Scotland.

Christiansen (C.). Magnetiske Undersogelser. 4to. Kjobenh,
1876. — From the Author.

Colding (A.). Fremstilling af Besultaterne af nogle Undersogelser
over de ved Yindens Kraft fremkaldte Strominger i Havet,
4to. Kjobenh. 1876. — From the Author.

Collett (Robert). Norges Fiske med Bemaerkninger om deres
Udbredelse. 8vo. Christiania, 1875. — From the Author.

Cartes Zoo-Geographiques. Nos. 1-4, Folio. Chris-
tiania, 1875. — From the Author.

Crevet (B.). Ueber Hypertrophie des Cervix Uteri. Inaug,
Dissert. 8vo. Erlangen, 1874. — From the Author.

Davidoff (P.). Ueber Hemiatrophia facialis progressiva. Inaig,
Dissert. 8vo. Erlangen, 1875. — From the Author.

Davidson (Th.). Notice sur la Yie de Sir Charles Lyell. 8/o.
Paris, 1876. — From the Author.

Day (St John Y.), C.E., Ferguson (Professor John), Mayer (John),
F.C.S., Paton (James). Notices of the Principal Manufac-
tures of the West of Scotland. 12mo. Glasgow, 1876. —
From the British Association for Advancement of Science.

Dehio (Karl). Beitrage zur patliologisclien Anatomie der Lepra,
8 vo. Dorpat, 1877. — From the Author.

Dietlen (H.). Siphilidologie des Auges. Inaug. Dissert, Erlangen.
8vo. Rostock, 1876. — From the Author.

Dohnberg (Hermann). Die Temperatur am Auge unter physiolo-
gischen u. pathologischen Yerhaltnissen. 8vo. Dorpat, 1876.
— From the Author.

Dollen (W.) and Abbe (C.). The Portable Transit Instrument in
the Yertical of the Pole Star. 8vo. Washington, 1870. — From
the Authors.

Esenbeck (0.). Das Kindbettfieber. Inaug. Dissert. 8vo.
Erlangen, 1876. — From the Author.

448

Proceedings of the Royal Society

Ferguson (Professor John). Notices of the Principal Manufactures
of the West of Scotland : Chemical Manufactures. 12 mo.
Glasgow, 1876. — From the British Association for the Advance-
ment of Science.

Fleming (P.). Die Haufigkeit der Combination yon Pleuritis und
Tuberculose, und das Abhangigkeitsverhaltniss beider Krank-
heiten von Einander. Inaug. Dissert. 8vo. Weimar, 1876.
— From the Author.

Geriach (Dr L.). Ueber das Yerhalten des Indigschwefelsauren im
Knorpelgewebe lebeuder Thiere. Habilitationschrift. 8vo.
Erlangen, 1876. — From the Author.

Ueber die Nervenendigungen in der Musculatur des

Froschherzens. Inaug. Dissert. Erlangen. 8vo. Berlin,
1876. — From the Author.

Giulini (P.) Experimentelle Untersuchungen iiber die Wirkung
des Aconitins. 8vo. Erlangen, 1876. — From the Author.

Gorringe (H. H.). The Coast of Brazil. Yol. I. From the
Orange to Rio Janeiro. 8vo. Washington, 1873. — From the
Author.

Coasts of the Mediterranean Sea. Part I. 8vo. Wash-
ington, 1875.

Greene (B. F.). Finding the Error of the Marine Compass on
Board Ship. 8vo. Washington, 1875. — From the Author.

Guldberg (C. M.) et Mohn (H.). Etudes sur les Mouvements de
l’Atmosphere. lre partie. 4to. Christiania. — From the
Authors.

Handyside (Dr P. D.). “ Shall I study Medicine?” Aspects and

Probabilities. 8vo. Edin., 1877. — From the Author.

Heerdegen (F.). De Fide Tulliana. 8vo. Erlangen, 1876.

Heinlein (H.). Mackroscopische Anatomie der Thranenrorchen.
Inaug. Dissert. 8vo. 1875. — From the Author.

Hertzberg (M.). Sensibilitats-Storungen bei Tabes Dorsalis.
Inaug. Dissert. 8vo. Jena, 1875.

Hirsch (Arthur). Ueber die Diffusibilitat der Peptone, und den
Einfluss der loslichen Salze auf die Eiweissverdauung durch
Magensaft. 8vo. Dorpat, 1876. — From the Author.

Hoerschelmann (Guilielmus). Observationes Lucretianae alterae.
4 to. Lipsiae, 1877. — From the Author.

449

of Edinburgh, Session 1876-77.

Hoffmann (Ed.). Das Hesperidin. Inaug. Dissert. 8vo. Erlangen.
— From the Author.

Hrehorowicz (Thaddaeus). Das Yerbrechen der Abtreibung der
Leibesfrucht. 8vo. Dorpat. 1876. — From the Author.

Hudleston (W. H.) and Walker (J. E.). On the Distribution of
the Brachiopoda in the Oolitic Strata of Yorkshire. 8vo. — •
From the Authors.

Ihering (H. von). Die Gehdrwerkzeuge der Mollusken. Habili
tationschrift. 8vo. Erlangen, 1876. — From the Author.

Jiidell (G.). Die Yergiftung mit Blausaure und Nitrobenzol. Ha-
bilitationschrift. 8vo. Erlangen, 1876. — From the Author.

Kalb (0.). Ein Fall von letalen Mercurialismus. Inaug. Dissert.
8vo. Erlangen, 1876. — From the Author.

Kalning (Julius). Zur Casuistik und Kenntniss der Dermoidcyster
des Hodens. 8vo. Dorpat, 1876. — From the Author.

Keussler (J. von). Zur Geschichte und Kritik des bauerlichen
Gemeindebesitzes in Russland. 8vo. Dorpat, 1876. — From
the Author.

Kiaer (A. N.). et Salvesen (T.). Navigation maritime. 4to.

Christiania, 1876. — From the Authors.

Kohler (A.) XJeber Irombose und Transfusion, Eiter-und septische
Infection. 8vo. Dorpat, 1877. — From the Author.

Konig (F.). Ueber paralytische Seelenstorung. Inaug. Dissert.
8vo. Erlangen. — From the Author.

Konigshofer (0.). Distinctionsvermogen der peripheren Theile der
Netzhaut. Inaug. Dissert. 8vo. Erlangen, 1876.

Koppe (Oscar). Ophthalmoscopisch - ophthalmologische IJnter-
suchungen. 8vo. Dorpat, 1876.-— From the Author.

Kreissmann (R.). Zur Casuistik der Meningitis basilaris tuber-
culosa der Erwachsenen. Inaug. Dissert. Erlangen. 8vo.
Jena, 1876.

Kropp (Capt. W.) and Knorr (E. R.). The Red Sea, 8vo.
Washington, 1872.

Lagorio (Alexander). Microscopische Analyse Ostbaltischer Ge-
birgsarten. 8vo. Dorpat, 1876. — From the Author.

Le Gras (A.). The Mediterranean Sea : Its Winds, Currents, and
Navigation. Translated by R. H. Wyman. 8vo. Washington,
1870. — From the Translator.

450

Proceedings of the Royal Society

Lehmann (Th.). Ein Fall von hochgradiger Asphyxie. Inaug.
Dissert. Erlangen. 8vo. Leipzig, 1876. — From the
Author.

Lindsay (The Lord). See Struve (F. G. W.).

Long (Rev. J.). The Eastern Question in its Anglo-Indian Aspect.
8yo. London, 1877. — From the Author.

Lymas (G. A.). Wirkung des Salicylsauren Natrons auf den
thierischen Organismus. Inaug. Dissert. 8vo. Erlangen,
1876. — From the Author.

Macfie (R. A.). The Patent Bill. 8vo. Dreghorn, 1877. — From
the Author.

Marie (Maximilien). Les periodes cycliques ou logarithmiques de
la quadratrice d’une courbe algebrique du degr4 m sont les
products par 2tt J - 1 des racines d’une equation de degre m.
4to. Paris, 1877. — From the Author.

Sur les relations entre les p4riodes de la quadratrice de la

courbe la plus gen^rale de degre m et d’une courbe particuliere.
4to. Paris, 1877.

Sur les deux theorkmes de M. Clebsch relatifs aux courbes

quarrables par les fonctions elliptiques ou par les fonctions cir-
culaires. 4to. Paris, 1877. — From the Author.

Mehlis (T.). Ueber Heptylsaure aus Oenanthol und einige ihrer
Derivate. 8vo. Erlangen, 1876. — From the Author.

Mueller (Baron Ferd. von). Select Plants eligible for Culture or
Naturalisation in Victoria. 8vo. Melbourne, 1876. — From
the Author.

Muller (Albert). British Gall-Insects. 8vo. Basle, 1876.

■ On the manner in which the Ravages of the Larvae of a

Nematus on Salix Cinerea are checked by Picromerus Bidens
8vo. London, 1872.

■ — — On the Dispersal of Non-migratory Insects by Atmospheric
Agencies. 8vo. Basle, 1877. — From the Author.

Muller (Professor J. W.). Transfusion und Plethora : eine physi-
ologische Studie. 8vo. Christiania. — From the Author .

Mutschler (L.). Ueber Cyclamin, Primulin, u. Primula Camphor.
Inaug. Dissert. 8vo. Erlangen. — From the Author.

Otten (Ferdinand). Vergleichend histiologische Untersuchung der
Sarsaparillen. 8vo. Dorpat, 1876. — From the Author.

451

of Edinburgh , Session 1876-77.

Pavesus (Fr.). Hollandia : Carmen ornatum praemio aureo in Acad.
Reg. Amstel. 8vo. Amstelodami, 1876. — From the
Author.

Pieverling (L. von). Melissyl- Alcohol. 8vo. Erlangen, 1876. —
From the Author.

Pihlemann (R.). Untersuchungen iiber die angeblich praformirten
Yerbindungswege zwiscben den Blut u. Lymphgefassen des
Froscbes. 8vo. Dorpat, 1876. — From the Author.

Plantamour (E.) et Wolf (R.). Determination teDgraphique de la
difference de longitude entre 1’Observatoire de Zurich et les
Stations du Pfander et du Gabris. 4to. Geneve — Bale — Lyon,
1877. — From the Authors.

Pleyte (W.). Construction de l’Eglise Paroissiale de St Jacques k
Utrecht. Folio. Leide, 1877. — From the Author.

Powell (Baden H.). Handbook of the Economic Products of the
Punjab. Yol. I. — Economic Raw Produce. Yol. II. — Manu-
factures and Arts of the Punjab. 8vo. 1868—7 2.- — From the

Author.

Ramsay (J.), Stirton (J.). Notes on the Flora of the West of Scot-
land. 12mo. Glasgow, 1876. — From the British Association
for the Advancement of Science.

Reade (T. Mellard). On Geological Time. 8vo. Liverpool, 1877.
- — From the Author.

Redeker (P.). Die Elektricitat als Heilmittel bei Riickenmarks-
krankheiten. Inaug. Dissert. 8vo. Erlangen, 1876. — From
the Author.

Reynaud (Leonce) and Jenkins (Adm. T. A.). Memoir upon the
Lighthouse Illumination of the Coasts of France. 8vo.
Washington, 1871. — From Admiral Jenkins.

Rohrig (A.). Ueber Achsendrehung der Ovarien. Inaug. Dissert.
Erlangen. 8vo. Leipzig, 1876. — From the Author.

Roth (M.). Die Seekrankheit. Inaug. Dissert. Erlangen. 8vo.
Miinchen, 1875. — From the Author.

Sander (Alexander). Casuistik der Psychosen. 8vo. Dorpat,
1876. — From the Author.

Sars (G. Ossian). On some remarkable forms of animal life from
the great deeps off the Norwegian coast. No. 2. — The Genus
Brisinga. 4to. Christiania. —From the Author.

452

Proceedings of the Royal Society

Saubert (H.). Die Massage ; ein wichtiges chirurgisches Hilfs-
mittel. Inaug. Dissert. Erlangen. 8vo. Ansb., 1876. — From
the Author.

Scheiding (M.) Untersuchungs-Resultate der Angen der Schuler.
Inaug. Dissert. 8vo. Erlangen, 1876. — From the Author.

Schneider (G.). Die metaphysischen Grundlagen der Herbart’schen
Psychologie. Inaug. Dissert. 8vo. Erlangen, 1876. — From
the Author.

Schneider (H.) Zwei Falle von geheilter Lungengangrain. Inaug.
Dissert. 8vo. Erlangen, 1876. — From the Author.

Schiibeler (Professor F. C.). Die Pflanzenwelt Norwegens. 4to.
Christiania. — From the Author.

Scotland. The National Manuscripts of Scotland, selected by the
Lord Clerk Register, photographed by Sir H. James. Vols. II.,
III. Folio. Southampton, 1872. — From the Lord Clerk-
Register (Sir William Gibson-Craig , Bart.).

Seve (C. de). Windrosen des Siidlicher Norwegens. 4to. Chris-
tiania.— From the Norwegian Meteorological Institute.

Sorgenfrev (Alexander). Ueber Wiederbelebung und Nachkran-
kheiten nach Scheintod. 8vo. Dorpat, 1876. — From the
Author.

Steiner (J.). Das Amerikanische Pfeilgift Curare: Habilitation-
schrift, — Erlangen. 8vo. Leipzig, 1877. — From the Author.

Stroehmberg (Christian). Casuistik der amyloiden Degeneration
an den Augenliedern. 8vo. Dorpat, 1877. — From the Author.

Struve (F. G. W.) and Lord Lindsay. A summary or index of the
measurements in the “ Stellarum duplicium et multiplicium
mensurae micrometricae,” the “Synopsis observationum de stellis
duplicibus,” &c., rearranged and brought up to 1875. (Dunecht
Observatory Publications, No. 1.) 4to. Dunecht, 1876. — From
the Lord Lindsay.

Suss (J.). Catulliana, Th. 1. 8vo. Erlangen, 1876. — From the
Author.

Teichmiiller (Gustav). Festrede zur jahresfeier der Stiftung der
Universitat Dorpat. Dec, 1876. 4to. Dorpat, 1877. — From
the Author.

Teutlehen (E. von). Die Tuben-Tonsille des Menschen : Inaugural
Abhandlung. 8vo. Leipzig, 1876. — From i the Author.

453

of Edinburgh , Session 1876-77.

Theremin (Emil). Ueber congenitale Occlusionem des Diinndarms.
Inaug. Dissert. Dorpat. 8vo. Leipzig, 1877. — From the
A uthor.

Todaro (Augustino). Hortns Botanicus Panormitanus. Tom. I,
Ease. 1-6. Eolio. Panormi. — From the Author.

Van Dessel (Camille). L’Etablissement Belgo-Bomain de Rumpst,
8vo. 1876. — From the Author.

Vanselow (H.). Scrotal Verletzungen. Inaug. Dissert. Erlangen.

8vo. Bamb., 1876. — From the Author.

Voitlenlaitner (H.). Ueber Uterusfibroide. Inaug. Dissert. 8vo.

Erlangen, 1875. — From the Author.

Wagner (A.). Die deutschen Namen der altesten Friesingex Ur-
kunden. 8vo. Erlangen, 1876. — From the Author.

Walton (Haynes). A practical treatise on diseases of the eye.

3d edit. 8vo. Loudon, 1875. — From the Author .

Wein (E.). Ueber die in Butterfett enthaltenen Fettsauren. Inaug.

Dissert. 8vo. Erlangen, 1876. — From the Author.
Wiedemann (Carl). Ueber die Wirkung des Camphors auf den
Thierorganismus, und seine Ausscheidung aus demselben. 8vo.
Dorpat, 1877.— From the Author.

Wilson (Joseph) and Gorgas (A. C.). Naval Hygiene. 8vo.

Washington, 1870. — From the Authors.

Wittelshofer (M.). Das Pfandrecht an einer Forderung (pignus
nominis). Inaug. Abbandlung. 8vo. Erlangen, 1876. —
From the Author.

Wolf (R.). See Plantamour (E.).

Young (Professor John). See Armstrong (James).

II. Transactions and Proceedings of Learned Societies,

Academies, etc.

Amsterdam. — Jaarboek van de Koninklijke Akademie van Wetens-
chappen gevestigd te Amsterdam, voor 1875. 8vo. —

From the Academy.

Processen-verbaal van de Gewone Yergaderingen der
Koninklijke Akademie van Wetenscbappen. 1875-76”
8vo. — From the Academy.

3 o

VOL. IX.

454

Proceedings of the Royal Society

Amsterdam. — Verhandelingen der Koninklijke Akademie van We-
tenschappen. Natuurkunde, Deel XYI. Letterkunde,
Deel X. 4to, — From the Academy.

Yerslagen en Mededeelingen der Koninklijke Akademie van
Wetenschappen. Afdeeling Letterkunde, Deel Y. ; Afdeel-
ing Natuurkunde, Deel X. 8vo. — From the Academy.

Flora Batava, Afbeelding en Beschrijving van Nederlandsche
Gewassen. Aangevangen door wijlen Ian Kops, hooglee-
raar te Utrecht, voortgezet door F. W. van Eeden te
Haarlem. Nos. 232-236. 4to. — From the King of
Holland.

Catalogus van de Boekerij der Koninklijke Akademie van
Wetenschappen gevestigd te Amsterdam. Eersten Deels
tweede Stuk ; tweede Deel ; derden Deels eerste Stuk.
8 vo. 1860-76. — From the Academy.

Appalachia. See Boston.

Baltimore. — Tenth Annual Beport of the Provost to the Trustees
of the Peabody Institute. 8vo. 1877. — From the In-
stitute.

Berlin. — Monatsbericht der Koniglich Preussischen Akademie der
Wissenschaften zu Berlin. Juni-Dec. 1876, Jan. -Mai,
1877. — From the Academy.

Berne. — Beitrage zur Geologischen Karte der Schweiz herausgege*
ben von der Geologischen Commission der Schweiz.
Naturforsch. Gesellschaft auf Kosten der Eidgenossen-
schaft. Lief. 14te. 4to. 1877. — From the Commis-

sion.

Bologna. — Memorie della Accademia delle Scienze dell’ Istituto
di Bologna. Serie III. Tomi Y., YI. 4to. — From the
Academy

Eendiconti delle Sessioni dell’ Accademia delle Scienze dell’
Istituto di Bologna, Anni Accademici 1874-75, 1875-76.
8vo. — From the Academy.

Bombay.— ^ The Indian Antiquary. Yol. Y. Parts 61-69. 4to. —

From Bombay Education Society.

Bonn. — Yerhandlungen des Naturhistorischen Yereines der Preus-
sischen Bheinlande und Westfalens. Jahrgang XXXII.
1875-76. 8vo. — From the Society,

of Edinburgh , Session 18 76-7 7.

455

Bordeaux. — Memoires de la Soci6te des Sciences Physiques et
Naturelles de Bordeaux. Tome I., Seconde Serie, No. 3 ;
Tome II. No. 1. 8vo. — From the Society.

Boston. — Appalachia. Yol. I. Nos. 2, 3. 8vo. — From the Appar
lad dan Mountain Club.

Brussels. — Observations Met^orologiques faites aux Stations interna-
tionales de la Belgique et des Pays-Bas. Premiere annee,
1877. 4to. Bruxelles.

Bulletin de l’Academie Boyale des Sciences, des Lettres et
des Beaux-Arts de Belgique. Tome XLIL, Seconde S6rie,
Nos. 9-12. Tome XLII. Nos. 1-5. — From the Academy.
Calcutta. — Journal of the Asiatic Society of Bengal for 1876. Parts
I., II. — From the Society.

Proceedings of the Asiatic Society of Bengal for 1876. Nos.

8-10. 8 vo. — From the Society.

Records of the Geological Survey of India. Yol. IX. Nos.

2-4. 8 vo. — From the Survey.

Memoirs of the Geological Survey of India, Palaeontologia.
Ser. X. No. 2 ; Ser. XI. No, 1. 4to. — From the

Survey.

Memoirs of the Geological Survey of India. Yol. XII. Nos.
1, 2. 8vo. — From the Survey.

Cambridge ( U.S .) — Bulletin of the Museum of Comparative Zoology
at Harvard College, Mass. Yol. III. Nos. 11-16. 8vo. —

From the College ,

Annual Report of the Trustees of the Museum of Com-
parative Zoology at Harvard College, Cambridge, for
the year 1876. 8vo. — From the College.

Canada.- — Report of the Progress of the Geological Survey of
Canada for 1875-76. 8vo. — From the Geological Survey.
Che7'bourg. — Societe Nationale des Sciences Naturelles de Cher-
bourg. Compte Rendu de la Seance, 30th Pecember
1876. 8vo. — From the Society.

Christiania. — Criminalstatistiske Tabeller for Kongeriget Norge for
Aarene 1871-73. — From the Government of No?' way.
Oversigt over det Nordlandske Kirke og Skolefonds Ind-
tmgter og Udgifter, i Aaret 1874. 4to. — From the

Government of Norway.

456

Proceedings of the Royal Society

Christiania. — Tabeller vedkommende Skiftevsesenet i Norge, i Aaret
1871-73. 4to. — From the Government of Norway.
Beretninger om Norges Fiskerier, i Aarene 1873-74. Chris-
tiana, 1876. 4to. — From the Government of Norway.

Det Kongelige Norske Frederiks-Universitets Aarsberetning
for 1874-75. 8vo. — From the University.

Enumeratio Insectorum Norvegicorum. Auctore, H. Siebke.
Edidit J. Sparre' Schneider. Fasc. III., IV. 1876-77.
8vo. — From the Royal University of Norway.

Norske Historiske Forening. — Paul Christian Holst :
Optegnelser om sit Liv og sin Samtid. Hefte 1, 2.
1875-76. 8vo. — From the Society.

Nyt Magazin for Naturvidenskaberne. Bind XXI. Hefte
1-4 ; Bind XXII. Hefte 1-4. 8vo. — From the Physio-
graphical Society of Christiania.

Brandanus Saga: fragment. — From the University of Chris-
tiania.

Oversigt over Oplysningsvaesnets Fonds Indtsegter og
Udgifter i Aaret 1874. 4to. — From the Government of
Norway.

Uddrag af Consulatberetninger vedkommende Norges Handel
og Skibsfart, Aaret 1874. 4to. — From the Government
of Norway.

Fordhandlinger i Videnskabs-Selskabet i Christiania, Aar

1874, og Aar 1875. 8vo. — From the Society.

Norske Universitets- og Skole-Annaler. XIII. Heft 1-4,

1875. 8 vo. — From the University.

Driftsberetninger af de offentlige Jernbaner, i Aaret 1874.

4to. — From the Government of Norway.

Kommunale Forholde i Norges Land og Bykommuner,
Aarene 1869-71. 4to. — From the Government of Norway.
Oversigt over Kongeriget Norges Indtsegter og Udgifter,
Aaret 1873. 4to. — From the Government of Norway.
Tabeller vedkommende Norges Handel og Skibsfart, i Aaret
1874. 4to. — From the Government of Norway,
Copenhagen. — Oversigt over det Kongelige Danske Videnskabernes
Selskabs Forhandlinger, i Aaret 1876, Nos. 1-3; 1877,
No. 1. 8 vo. — From the Society.

457

of Edinburgh, Session 1876-77.

Copenhagen. — Tyge Brahe’s Meteorologiske Dagbog holdt paa Urani-
borg for Aarene 1582-1597. Udgiven som Appendix til
Collect. Meteorologica af Danske Yidenskabarnes Selskab.
8 vo. Kjob., 1876. — From the Society.

Davenport , Iowa. — Proceedings of the Davenport Academy of
Natural Sciences. Yol. I. 1867-1876. 8vo. — From

the Academy.

Dehra Dun. — General Report on the Operation of the Great Trigo-
nometrical Survey of India, during 1875-76. Folio. —

From the Survey.

Dorpat. — Meteorologische Beobachtungen im Jahre 1876. 8vo. —
From the University of Dorpat.

Yerzeichniss der Yorlesungen an der Universitat zu Dorpat.

8 vo. 1876. — From the University of Dorpat.

Personal der Kaiserlichen Universitat zu Dorpat. 8vo.
1876. — From the University of Dorpat.

Dresden. — Nova Acta Academhe Caesarese Leopoldino-Carolinse
Germanicae Naturae Curiosorum. Yols. XXXYIL,
XXXYIII. 4to. — From the Academy.

Leopoldina : Amtliches Organ der Kaiserlichen Leopold-
inisch-Carolinishen Deutschen Akademie der Natur-
forscher. Hefte 10, 11. 4to. — From the Academy.
Dublin. — Transactions of the Royal Irish Academy (Science). Vol.

XX Y. Parts 19, 20; Yol. XXVI. Parts 1-5. 4to.—

From the Academy.

Proceedings of the Royal Irish Academy (Polite Litera-
ture). Series II. Vol. I. No. 11 ; (Science) Vol. II.
Nos. 4-6. 8vo. — From the Academy.

Edinburgh. — Annual Reports of the Council of the Royal Scottish
Academy of Painting, Sculpture, and Architecture.
8vo. 1876. — From the Academy.

Catalogue of the Printed Books in the Library of the
Faculty of Advocates. Vol. Y. 4to. Edinburgh, 1877.
— From the Library.

Transactions of the Highland and Agricultural Society of
Scotland. Yob IX. 8vo. 1877. — From the Society.

Transactions of the Scottish Arboricultural Society. Yol.
VIII. Part 2. 1877, — From the Society.

458

Proceedings of the Royal Society

Edinburgh. — Transactions of the Royal Scottish Society of Arts.
Yol. IX. Part 4. 1876. 8vo. — From the Society.

Journal of the Scottish Meteorological Society. Uos. 49,
50. 8vo. — From the Society.

Quarterly Returns of the Births, Deaths, and Marriages,
registered in the Divisions, Counties, and Districts of
Scotland. 1877, Jan. to March. 8vo. — From the Regis-
trar General.

Monthly Returns of the Births, Deaths, and Marriages,
registered in the Eight Principal Towns of Scotland.
1877, Jan. to June. (Supplement for 1876.) 8vo. —

From the Registrar General.

Report on the Royal Botanic Garden for 1876. 8vo. — From
the Regius Keeper.

Guide to the Royal Botanic Garden, Edinburgh. — From the

Regius Keeper.

Essex. — Essex Institute, Mass. U.S. See Salem, U.S.

Frankfort. — Abhandlungen herausgegeben von der Senckenber-
gischen Uaturforschenden Gesellschaft. Band XI. Heft
1. 4to. 1877. — From the Society.

Bericht tiber die Senckenbergische Uaturforschende Gesell-
schaft. 8vo. 1875-76. — From the Society.

Geneva. — Memoires de la Societe de Physique et d’Histoire Uaturelle
de Geneve. Tome XXIY. Part 2. 4to. — From the
Society.

Glasgoic. — Proceedings of the Philosophical Society of Glasgow.
Yol. X. Xo. 2. 8vo. — From the Society.

Glasgow University Calendar for 1877-78. — From the Uni-
versity.

Gottingen. — Abhandlungen der Koniglichen Gesellschaft der Wissen-
schaften zu Gottingen. Band XXI. 4 to. — From the
Society.

Uachrichten von der K. Gessellschaft derWissenschaften und
der Georg- Augusts-Universitat, aus dem Jahre 1876-77,
1-4. 12mo. — From the University.

Gratz. — Mittheilungen des Haturwissenchaffclichen Yereines fiir
Steiermark. 8vo. 1876. — From the Society.

459

of Edinburgh, Session 1876-77.

Greenwich. — Astronomical and Magnetical Observations made at
the Royal Observatory in the year 1874. 4to. — From the
Observatory.

Haarlem. — Archives Neerlandaises des Sciences Exacte3 Naturelles
publics par la Societe Hollandaise a Harlem. Tome XI
Liv. 4, 5 ; XII. Liv. 1. — From the Society.

Archives dn Musde Teyler. Yob I. Ease. 1. 8vo. — From
the Museum. i.

Jena. — Jenaische Zeitschrift fiir Naturwissenschaft herausgegeben
von der Medicinisch - Naturwissenschaftlichen Gessell-
schaft zu Jena. Band X. Heft 2-4 ; Band XL Heft 2.
8 vo. — From the Society.

Kasan. — Reports of the University of Kasan. Nos. 1-6. Svo,

1876. — From the University.

Leiden. — Annalen der Sternwarte in Leiden herausgegeben von Dr
F. Kaiser. Yierter Band. 4to. Haag, 1875. — From the
Observatory.

Leipzig. — Sitzungsberichte der Naturforschenden Gesellsehaft.

Jahrg. L, II., III., IY., No. 1. 8vo. 1874-77. — From the
Society.

Liverpool. — Transactions of Historic Society of Lancashire and
Cheshire. Third Series. Yols. III., IV. Sessions
1874-75, 1875-76. 8vo. — From the Society.

London. —Proceedings of the Society of Antiquaries. Yol. VI.
Index. 8vo. — From the Society.

A Catalogue of the Books in the Admiralty Library. By R.
Thorburn, Librarian. 4to. London, 1875. — From the
Lords Commissioners of Admiralty.

Transactions of the Society of Antiquaries. Yol. XLIV.

Part 2 ; Vol. XLY. Part 1. 4to. — From the Society.
Journal of the Society of Arts for 1872-73, 1873-74,
1874-75. 8vo. — From the Society.

Monthly Notices of the Royal Astronomical Society for
1876-77. Yol. XXXVII. 8vo. — From the Society.
Journal of the Chemical Society. 1876, July to December;

1877, January to July. 8vo. — From the Society.

Journal of the East India Association. Yol. X. Nos. 2, 3.

8 vo. — From the Association.

460

Proceedings of the Royal Society

London. — Proceedings of the Eoyal Geographical Society. Yol.
XXL Xos. 1-5. 8 vo. — From the Society.

Journal of the Eoyal Geographical Society. Yol. XLYI. —
From the Royal Society.

Quarterly Journal of the Geological Society. — Yol.
XXXIII. Parts 1, 2. List of .. Members. — From the
Society.

Abstracts of Proceedings of the Geological Society. Session
1876-77. Xos. 326-339. Yol. IX. Parts 1-3, 4to.
— From the Society.

Proceedings of the Geologists’ Association. Yol. Y. No.

12. 8 vo. — From the Association.

Journal of the Eoyal Horticultural Society. Yol. IY.

Part 16. 8vo. — From the Society.

Proceedings of the Institution of Civil Engineers. Yols.

XLIY.-XLYIII. 8vo. — From the Society.

Journal of the Linnean Society. Yol. XIII. (Zoology),
Nos. 67-69 ; Yol. XY. (Botany), No. 88; Yol. XYI.
Nos. 89, 90. 8vo. — From the Society.

Transactions of the Linnean Society. Second Series
(Botany), Yol. I. Part 4 ; Second Series (Zoology), Yol.
I. Part 4. 4to. 1876. — From the Society.

Proceedings of the London Mathematical Society. Nos.

93-111. 8vo. — From the Society.

Proceedings of the Eoyal Medical and Chirurgical Society.

Yol. YIII. Nos. 3, 4. 8vo.- — From the Society.

Quarterly Weather Eeport of the Meteorological Office.
October-December. 4to. — From the Meteorological Com-
mittee of the Royal Society.

Quarterly Journal of the Meteorological Society. New
Series. Yol. III. Nos. 21, 22. 8vo. — From the Society.
Eeport of the Kew Committee for the year ending 1876.
8vo. — From the Committee.

Charts of Meteorological Data for nine ten-degree squares be-
tween 20° N. and 10° S. Lat., and 10° to 40° W. Long.;
and Eemarks. 2 Vols. 4to. 1876. — From the Meteoro-
logical Office.

461

of Edinburgh, Session 1876-77.

London. — Report of the Permanent Committee of the International
Meteorological Congress at Vienna for the year. Supple-
ment, 1877. — From the Meteorological Committee of the
Royal Society.

Mineralogical Magazine and Journal of the Mineralogical
Society, 1877. Nos. 1-4. 8vo. — From the Society.
Palaeontological Society. Vol. XXX. 1876. 4to. — From
the Society.

Proceedings of the Royal Institution of Great Britain. Vol.

VIII. Parts 1, 2. 8vo. — From the Royal Institution.
Proceedings of the Royal Society. Nos. 171-181. 8vo. —
From the Society.

Transactions of the Royal Society. Vol. CLXVI. Part 2.

List of Bellows, 1876. 4to. — From the Society.

Journal of the Statistical Society. General Index. Vol.
XXXIX. Part 4 ; Vol. XL. Parts, 1, 2. — From the
Society.

Calendar of the Royal College of Surgeons of England.

1876. 8 vo. — From the College.

Calendar of the University of London for 1877, 8vo.

— From the University.

Catalogue of the Library of the University of London, in-
cluding the Libraries of George Grote and Augustus de
Morgan. 8vo. London, 1876. — From the University.
Catalogue of Books in the Admiralty Library, by R. Thor-
burn. 4to. 1875. — From the Lords of the Admiralty.
Proceedings of the Zoological Society. 1876, 1877. 8vo.
— From the Society.

Transactions of the Zoological Society. Vol. IX. Parts 10
11 ; Vol. X. Part 1. 4to. — From the Society.

“ Nature ” for 1876-77. 4to. — From the Editor.

Madrid. — Memorias de la Comision del Mapa Geologico de Espaha.
8 vo. From the Commission.

Boletin de la Comision del Mapa Geologico de Espana,
Tomo III. — From the Commission.

Memoria Geologico-Minera de la Provincia de C&ceres par
D, J. Egozque y D. L. Mallada. 8vo. Madrid, 1876. —

From the Geological Commission.

8 v

VOL. IX.

462

Proceedings of the Pioyal Society

Manchester. — Transactions of the Manchester Geological Society.

Yol. XIV. Parts 6-10. Catalogue of Library, 1876.
8vo. — From the Society.

Milan. — Memorie del Eeale Istituto Lombardo di Scienze e Lettere.

Classe di Lettere e Scienze Morali e Politiclie. Vol. XIII.
Fasc. 2. Classe di Scienze Matematiche e Natural!

Vol. XIII. Fasc. 2. 8vo.— From the Institute.

Pendiconti del Eeale Tstituto Lombardo di Scienze e Lettere.
Serie II. Vol. VII. Nos. 17-20; Vol. VIII. 8vo.

— From the Institute.

Modena. — Annuario della Societa dei Naturalisti in Modena. Serie
II. Anno X. Fasc. 2, 3. 8vo.

Montpellier. — Memoires de l’Academie des Sciences et Lettres de
Montpellier. Section des Sciences. — Tome VIII. Fasc.
3, 4. Section des Lettres. — Tome VI. Fasc. 1. 4to.

— From the Academy.

Moscow. — Bulletin de la Societe Imperiale des Naturalistes de Mos-
cou. 1876, Nos. 1-4. 8vo. — From the Society.
Nouveaux Memoires de la Sodbtb Imperiale des Naturalistes
de Moscou. Tome XIII. liv. 5. 4to. — From the
Society.

Munich. — Abhandlungen der Koniglich Bayerischen Akademie der
Wissenschaften. Historische Classe. Band XIII. 2.
Mathematisch-Physikalische Classe. Band XII. 2, 3.
Philosophisch-Philologische Classe. Band XLIX. 1. 4to.

— From the Society .

Nanak, der Stifter der Sikh-Beligion. Festrede gehalten in
der Sitzung der K. B. Akad. der Wissenschaften zu Miin-
chen von Dr E. Trumpp. 4to. 1876. — From the

Academy.

Inhalt der allgemeinen Bildung in der Zeit der Scholastik.
Festrede in der Sitzung der K. B. Akademie der Wis-
sensch. zu Mimdien, von Dr E. v. Liliencron. 4to.
Miinchen, 1876. — From the Academy.

Sitzungsberichte der Konigl. Bayer. Akademie der Wissens-
chaften.— Philologische und Historische Classe. 1876-77,
Heft 1. Mathematisch-Physikalische Classe. 1876, Heft
2,3; 1877, Heft 1. 8vo.

of Edinburgh, Session 1876-77. 463

Munich. — Verstehen und Beurtlieilen. Im Auftrage der Philos. -
Philol. Classe, verfasst von Carl von Prantl. 4to. Miin-
chen, 1877. — From the Academy.

Die Geognostische Durchforschung Bayerns. Rede in der
Sitzung der K. Akademie, von Dr C. W. Giimbel.
4to. Mimchen, 1877. — From the Academy.

New Haven (U.S.). — Journal (American) of Science and Art, con-
ducted by Benjamin Silliman. Yols. XIII., XIV. Nos,
79, 80. 8vo . — From the Editors.

New Zealand. — -Eleventh Report on the Colonial Museum and
Laboratory, by Dr James Hector, 8vo. 1876. — From
the Geological Survey.

Nijmegen. — Nederlandsch Kruidkundig Archief. Serie II. Deel.
ii. Stuk 3. — From the Editors.

Oxford. — Astronomical and Meteorological Observations made at
the Radcliffe Observatory, Oxford, in the year 1874. Yol.
XXXIY. — From the Observatory.

Palermo. — Bulletino della Societa di Scienze Nat ed Econo-
miche. No. 2, 1877. — From the Society.

Paris. — Bulletin de la Society Mathematique de France. Tome V.
Nos. 1-5. 8vo. — From the Society.

Publications du Depot de la Marine (avec Cartes). 8vo. — -
From the Depot.

Recherches sur les Chronometres et les Instruments nautiques,
par E. Caspari. 11® Cahier. 8vo. Paris, 1876. — From
the Depot de la Marine.

Mer du Nord. 3e partie. Cotes d’Angleterre. 8vo. Paris,
1876. — From the Depot de la Marine.

Annuaire des Marees de Cochin Chine. 12 mo. 1877. — •

From the Depot de la Marine.

Annales de Mines. Tome X. Liv. 4-6. — From the Ecole des
Mines .

M4moires de lJAcad6mie des Sciences de lTnstitut de France.
Tomes XXIX. (1867) ; XXXII. (1864) ; XXXIY. (1864) ;
XXXY. (1866); XXXYI. (1870); XXXVII. Part 1
(1868), Part 2 (1870) ; XL. (1876) ; XLI. Part 2 (Recueil
des M6moires du Passage de V4nus), 1876.

464

Proceedings of the Royal Society

Paris. — M^moires pr4sent^s a l’Acad6mie des Sciences de lTnstitut
de France. Tomes XYIII. (1868); XIX. (1865) ; XX.
(1872); XXI. (1875); XXII. From the Institute.

Annales Hydrographiques. 1876. Xos. 2, 3. 8vo. — From

the Depot de la Marine.

Bulletin de la Soci4t6 G^ographique. December, 1876
Jan.-Juin, 1877. 8vo. — From the Society.
Comptes-Rendus Hebdomadaires des Stances de l’Acad^mie
des Sciences. 1876, Jan.- Juillet, 1877. 4to. — From the

Academy.

Philadelphia. — Journal of the Academy of Natural Sciences. New
Series. Yol. VIII. Part 2. 8vo. — From the Academy.
Proceedings of the Academy of Natural Sciences. 4to.
1876. — From the Academy.

Proceedings of the American Philosophical Society. Yol.

XY. No. 96 ; XYI. No. 98. 8vo. — From the Society.
Pourth and Pifth Annual Reports of the Zoological Society
of Philadelphia. 8vo. 1876, 1877. — From the Society.
Pulkoiva. — See St Petersburg.

Rome. — Bollettino del Comitato Geologico d’ltalia. Nos 11, 12.
Nov. e Dec. 1876.— From the Society.

Atti della R. Accademia dei Lincei 1876-77. Serie 2da.
Yol. I., II., III., Pti. 1, 2, 3. Serie 3za. Yol. I. Trans-
unti, Fas 1-6. — From the Academy.

Salem (U.S.) — Bulletin of the Essex Institute. Yols. VII., VIII.

8 vo. 1876. — From the Institute.

Steiermark. — See under Gratz.

Stockholm. — Meteorologiska Jakttagelser i Sverige utgifna af Kongl.

Svenska Vetenskaps-Akademiens anstallda och bearbetade
af Ei-Edlund. Bandet 1873. 4to. — From the Academy.
Voyage autour du Monde sur la Frigate Su^doise l’Eug^nie
pendant 1851-53. Observations scientifiques publics par
l’Academie Royale des Sciences a Stockholm, Physique,
III. 4to. 1874. — From the Swedish Government.

St Petersburg. — Annalen des Physikalischen Central-Observatoriums.
8 vo. 1875. — From the Russian Government .

Memoires de l’Academie Imphriale des Sciences de St-P4ters-
bourg. Shrie vii. Tomes XXII. 11, 12 ; XXIII., XXIV.
— From the Academy.

465

of Edinburgh, Session 1876-77.

St Petersburg. — Bulletin de l’Academie Imp^riale des Sciences de
St-Petersbourg. Tomes XXII., XXIII. 4to. — From the

Academy.

Jahresbericht der Nicolai-Hauptsternwarte, Pulkowa, filr
1875, 1876. 8 vo. — From the Observatory.
Comptes-Rendus de la Commission Imperiale Arcbeologique
pour les ann6es 1872, 1873, 1874, avec un Atlas pour
chaque ann^e. Folio. — From the Commission.
Supplement. D&dinaisons moyennes corrigdes des Etoiles
principals pour 1845, 0 ; et Recherches sur les erreurs de
division du cercle, par M. Nyren. 4to. 1875.- — From
the Observatory.

Hilfstafeln zur Berechnung der Polarisazimuthe, von Eugen
Block. 4to. St Petersb. 1875. — From the Observatory.
Turin. — Memorie della Reale Accademia delle Scienze di Torino.

Serie Seconda. Tomo XXVIII. 4to. 1876. — From the
Academy.

Upsala. — Bulletin M6t6orologique Mensuel de l’Observatoire de
1’Universite. Vol. VII. 4to. — From the University.
Xftva Acta Regise Societatis Scientiarum Upsaliensis. Vol.
X. Fasc. 1. 4 to. — From the Society.

Utrecht. — Aanteekeningen van bet Verhandelde in de Sectie-
Vergaderingen van bet Provinciaal Utrechtscb Genoot-
scbap van Kunsten en Wetenschappen, 1875, 1876. 8vo.
— From the Society of Science and Art.

Verslag van bet Verbandelde in de algemeene Vergadering
van bet Provinciaal Utreclitscb Genootschap van Kunsten
en Wetenscbappen, 1875, 1876. 8vo. — From\the

Society.

Construction de 1’Sglise Paroissiale de St Jacques a Utrecbt
par W. Pleyte, publi4e par bet Provinc. Utretscb Genoots-
cbap van Kunsten en Wetenscb. Folio. 1877. — From the
Prov. Society of Utrecht.

Xederlandscb Meteorologiscb Jaarboek, 1875. 4to. — From
the Meteorological Institute.

Venice. — Atti del Reale Istituto Veneto di SV«nze, Lettere ed Aiti.
Serie v. Tom. I., II., III. 1, 2, 3. 1874-75, 1875-76.

From the Institute.

466

Proceedings of the Royal Society

Victoria (Australia). — Victorian Yearbook for 1875, by H. H.
Hay ter. — From the Australian Government.

Statistics of the Colony, 1873-77. Agricultural Statistics,
1877. Vital Statistics, &c. — Part 8. Patents and
Patentees — Vol. VIII., 1873. Statistical Pegister of the
Colony of Victoria for 1875. Polio. Abstracts of Specifi-
cations of Patents — Part 2, Sect. 1 : Metals. 4to. Statis-
tics of Priendly Societies, 1875. — From the Registrar-
General,

Transactions and Proceedings of tlie Royal Society of Vic-
toria. Vols. XI., XII. 8vo. 1876. — From the Society.

Vienna. — Geologie der Kaiser Franz Josefs Hochquellen-Wasser-
leitung. Pine Studie in den Tertiar-Bildungen am West-
rande des Alpinen Theiles der Niederung von Wien, von
Felix Karrer. 4to. Wien, 1877. — Abhundlungen der k.
k. Geologischen Reichsanstalt. Band IX. 4to. — From
the Society.

Denkschriften der kaiserlichen Academie der Wissencbaften.
Math.-Natur. Classe — Band XXXVI. Phil.- Hist. Classe
— Bande XXIV., XXV. 4to. 187 6. — From the Academy.
Sitzungsberichte der kaiserlichen Academie der Wissen-
schaften. Min.-Bot.-Zooh Geo.-Pal.-Classe — BandLXXII.
Physiol.-Anat. Classe — Band LXXI. Hefte 3, 4, 5 ;
LXXII. Hefte 1-5. Phil.-Hist. Classe— Band LXXX.
Heft 4; LXXXI ; LXXXII. Hefte 1, 2. Math.-Nat.
Classe — Band LXXII. Hefte 1-5. 8vo. — From tlie
Academy.

Almanach der kaiserlidien Academie der Wissenschaften.

1876. 8vo. — From the Academy.

Jahrbuch der kaiserlich-koniglichen Geologischen Reichsan-
stalt. Band XXVI. Xos. 3, 4 ; XXVII. No. 1. 8vo.

1877. — From the Society.

Verhandlungen der kaiserlich-koniglichen Geologischen
Reichsanstalt. Nos. 1-4, 1876, 1877. 8vo. — From the
Society.

Verhandlungen der kaiserlich-koniglichen zoologish-botan-
ischen Gesellschaft in Wien. Band XXVI. 8vo. — From
the Society.

467

of Edinburgh, Session 1876-77.

Warwick. — Proceedings of the Warwickshire Naturalists’ and
Archaeologists’ Field Club. 8vo. 1877. — From the Society.

Washington. — Annual Report of the Board of Regents of the Smith-
sonian Institution for 1875. 8vo. — From the Institution.

Smithsonian Contributions to Knowledge. Yols. XX.,
XXI. 4to. — From the Institution.

.Smithsonian Reports for 1875. 8vo. — From the Institution.

Astronomical and Meteorological Observations made during
the year 1874. 4to. —From the U.S. Naval Observatory.

The Vertebrata of the Cretaceous Formations of the West,
by E. D. Cope. Yol. II. 4to. Washington, 1875. — -
From the U.S. Geological Survey.

Invertebrate Cretaceous and Tertiary Fossils of the Upper
Missouri Country, by F. B. Meek. Yol. IX. 4to.
Washington, 1876. — -From the U.S. Geological Survey.

A Monograph of the Geometrid Moths or Phalaenidae of the
United States, by A. S. Packard, jr., M.D. Yol. X.
4to. Washington, 1876. — From the United States Govern-
ment.

Bulletin of the Entomological Commission. Nos. 1, 2. 8vo.
1877. — From the United States Government.

Preliminary Report of the U.S. Geological Survey of Wyo-
ming and contiguous Territories. Conducted by F. V.
Hayden, 1870. 8vo. Washington, 1871. — From the
United States Geological Survey.

Report of the U.S. Coast Survey, showing progress during
1869, 1870, 1871, 1872, 1873. — From the United States
Government.

Polaris. — Narrative of the North Polar Expedition, U.S. ship
Polaris, Captain Charles F. Hall, commanding. Edited
by Rear-Admiral C. H. Davies. 8vo. Washington, 1876.
— From the United States Government.

Reports of Explorations and Surveys for a Ship Canal,
Isthmus of Darien, by T. 0. Selfridge. 4to. 1874. —
From the United States Government.

Explorations and Surveys for a Ship Canal between the
Atlantic and Pacific Oceans, through Nicaragua, 1872-73.
4to. 1874. — From the United States Government .

468

Proceedings of the Eoyal Society

Washington. — Ninth Census of the United States. Statistics of the
Population.— Statistics of Wealth and Industry. 3 vols.
4to. 1872. — From the United States Government.

Medical Essays compiled from Reports to the Bureau of Medi-
cine and Surgery, by Medical Officers of the U.S. Navy.
8vo. 1872. — From the United States Government.

The Practical Use of Meteorological Reports and Weather
Maps. 8 vo. 1871. — From the United States Government.

Tables and Formulae useful in Surveying, Geodesy, and
Practical Astronomy, including Projection of Maps. 8vo.
1873. — From the United States Government.

Directions for Water Level and Meteorological Observations,
and the Registry of Periodical Phenomena. 8vo. 1871.
— From the United States Government.

Reports of Explorations in 1869-72 of Colorado River of the
West and its Tributaries, by Professor J. W. Powell.
8vo. — From the United States Government.

Reports of Explorations and Surveys to ascertain the Prac-
ticability of a Ship Canal between the Atlantic and Pacific
Oceans by the way of Tehuantepec. 4to. 1872. — From

Sir Charles Hartley.

Report on the Difference of Longitude between Washington
and Ogden, Utah, by J. R. Eastman. 4to. 1876. — From
the U.S. Observatory.

Papers relating to the Transit of Venus in 1874, prepared
under the direction of the Commission authorised by Con-
gress. Part 2. 4to. — From the U.S. Naval Observatory.

Investigation of Corrections to Hansen’s Tables of the Moon ;
with Tables of their application. 4to. 1876. — From the
U.S. Observatory.

Besides the donations above mentioned, the Society has
received from the United States Government many im-
portant works, comprising Journals and Reports of Con-
gress and its Committees, Reports issued by the various
Departments of the State, and miscellaneous Papers re-
lating to the civil, military, and naval administration of
the United States. These works, though too numerous
to specify here, are duly entered in the General Catalogue
of the Library.

of Edinburgh , Session 1876-77. 469

Wellington. — Statistics of New Zealand. 1874, 1875. Folio. —
From the New Zealand Government.

Meteorological Report for 1875, including Returns for
1873-74, and Abstracts for previous years. 8vo. — From
the Geological Survey Department.

Ninth, Teuth, and Eleventh Annual Reports of the Colonial
Museum of New Zealand. 8vo. — From the Geological

Survey Department.

Transactions and Proceedings of the New Zealand Institute.
Vols. L-IX., 1868-76. 8vo. — From the Institute .

Whitby. — The Fifty-Fourth Report of the Whitby Literary and
Philosophical Society. 8vo. — From the Society.

Zurich. — Neue Denkschriften der allgemeinen schweizerischen
Gessellschaft fur die gesammten Naturwissenschaften
(Nouveaux Memoires de la Society Helvetique des Sciences
Naturelles). Band XXVII. Abth. 1. 4 to. — From the

Society.

Vierteljahrsschrift der Naturforschenden Gessellschaft zu
Zurich. Jahrg. XIX., XX. 8vo. — From the Society.

Schweizerische Meteorologische Beobachtungen herausge-
geben von der Meteorologischen Centralanstalt der
Schweizerischen Naturforschenden Gessellschaft. Lief.
2-5. Jahrg. XIII., 1855; Jahrg. XVI., 1858. 4to.
1876. — From the Society.

3 Q

VOL. IX.

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH,

vol. ix. 1877-78. No. 100.

Ninety-Fifth Session.

Monday, 2 Qth November 1877.

Sir WILLIAM THOMSON, President, in the Chair.

The following Council were elected

President.

Sir WILLIAM THOMSON, Knt., LL.D.

Honorary Vice-Presidents, having passed the Chair.
His Grace the DUKE of ARGYLL.

Sir ROBERT CHRISTISON, Bart., M.D.

Vice-Presidents.

Rev.W. Lindsay Alexander, D.D.
David Stevenson, Memb. In. C.E.
The Right Rev. Bishop Cottkrill.

Principal Sir Alex. Grant, Bart.
David Milne Home, LL.D.

Sir C. Wyville Thomson, LL.D.

General Secretary— Dr John Hutton Balfour.

Secretaries to Ordinary Meetings.
Professor Tait.

Professor Turner.

Treasurer— J) avib Smith, W.S.

Curator of Library and Museum — Dr Maclaoan.

Councillors.

Dr Ramsay H. Traquair.
Thomas Harvey, LL.D.
Professor John G. M‘Kendrick.
Professor Crum Brown.

Professor Kelland.

Professor Fleeming Jenkin.

Rev. R. Boog Watson.
Dr Hugh Cleghorn.
Professor T. R. Fraser.
Professor Rutherford.
Dr R. M. Ferguson.
Sheriff Hallard.

a r

VOL. IX.

472

Proceedings of the Royal Society

Monday , 3 d December 1877.

Principal Sir Alexander Grant, Bart., one of the Vice-Pre-
sidents of the Society, read the following Opening Address : —

Gentlemen, — I find it recorded* that in the year 1662, which was
the first year of the incorporation of the Royal Society of London,
the celebrated mathematician, Robert Hooke, drew up “ Proposals
for the good of the Royal Society,” the third article of which was as
follows : — “ That every member of the Society shall be equally
obliged to promote the ends thereof by paying 52s. yearly, and by
doing some one duty that shall be charged on him by the Council
once a year, or, if his occasions will not permit, to pay 52s. more
per annum.” This proposed salutary rule does not seem ever to
have been enacted by the Royal Society of London, nor do I believe
that any analogous article forms part of the statutes of this Society,
and yet it is in accordance with the spirit of such a rule that I
appear before you this evening.

When the Council of this Society requested me, only four weeks
ago, to open the ensuing session by addressing you, I at once, though
perhaps imprudently, resolved to obey them, and to do “ the one
duty charged upon me by the Council.” But in the meantime I
have become more and more conscious of the fact, that probably no
length of preparation would have enabled me to offer you an address
worthy of this occasion and of my predecessors in this chair, and that
it would be a simple impossibility to accomplish this within a few
weeks at a period of the year when the distractions are so manifold
that I can scarcely get a clear morning, not to speak of a clear day.
I must therefore ask you to accept for the nonce some discourse on
matters which are a very old story now. I know that the Royal
Society is like those Athenians of whom it was said that they “ spent
their time in nothing else, but either to tell or to hear some new
thing.” Therefore, an idea to be suitable for the Royal Society
ought to be brand new. But I shelter myself under the reflection,
that the topic which has suggested itself to my mind for this evening
is one which might perhaps always claim a certain welcome in this
room. For I thought of whiling away the opening half-hour of our

* In Weld's History of the Royal Society , vol. i. p. 139. To this excellent
history the following paper is much indebted.

of Edinburgh, Session 1877-78.

473

new session with some remarks upon our connection with him whom
I cannot but regard as our lineal progenitor and virtual founder,
Francis Bacon of Verulam. In the Harveian Society, I believe that
there is an annual eulogy of the great discoverer of the circulation of
the blood ; and how often in medical societies has the opening address
been given up to a panegyric of Hippocrates, the ancient father of
medicine h In societies like this, whose main function is the promo-
tion of experimental research, it can never be out of place to do
honour to Lord Bacon, the august herald and prophet of modern
science. I trust that you will concede me this proposition, and that
you will excuse the introduction of a trite subject on the present
occasion, and that you will bear with me if I repeat many things
which are quite familiar to you.

Principal Forbes, in an excellent address which he delivered in
this place fifteen years ago, traces the origin of the Royal Society of
London to the example of similar societies which sprang up in Italy
during the 16th and 17th centuries, especially the Society of Lincei ,
or Lynx-eyed Ones, founded in 1604, of which Galileo was a mem-
ber, and the Florentine Academy of Experiment (‘ del cimento ’),
founded in 1657. This view was, broadly speaking, correct ; but I
think that it ignores too much the forces working within England
itself. During the 15th and 16th centuries there was carried out
the most important revolution (except the introduction of Christi-
anity) that ever occurred among the human race — namely, the over-
throw of scholasticism, and the introduction into all departments of
knowledge of the modern spirit of inquiry. This revolution was far
greater and more important in its consequences than the downfall of
any dynasty, or the destruction of any empire : greater and more
important than the Renaissance and the Reformation which jointly
led to it ; far greater in its scope and results than the much- vaunted
French Revolution, of which, to the present day, it seems so hard
for France to reap the fruits. In contributing to this greatest of all
changes, in ushering in the new era, Italy may claim to have played
a glorious part. But the new spirit pervaded all Europe. Men of
the new era seemed to spring up everywhere. Columbus in Spain,
Copernicus and Kepler in Germany, Lionardo da Vinci and Galileo
in Italy, Tycho Brahe in Denmark, Gassendi and Descartes in
France, Harvey and Gilbert in England, — these and many more, as

474 Proceedings of the Royal Society

if inspired by some special impulse, had each started on a separate
road of discovery. They each shone like separate lights, and their
united effulgence created the new day. Countries, I think, as well
as individuals, moved independently of one another. At all events,
I think that England moved independently of Italy in respect of
the formation of scientific societies. In the eighth volume of your
“ Transactions ” there is a learned paper contributed by Professor
Macvey Napier fifty-nine years ago, in which he collects from writers
of the 17th century, evidences of the influence exercised hy Lord
Bacon’s works, and of the high esteem in which they were held.
Professor Napiers case is fully made out, and he not only establishes
the general fact that Bacon made a deep impression on his own age
and the succeeding times, but also he proves, in particular, the imme-
diate and direct connection between Lord Bacon’s writings and the
foundation of the Boyal Society. The original founders of the
Royal Society had those writings continually in their thoughts.
Bacon’s splendid aspirations, clothed in some of the stateliest prose
that the world has ever seen, had struck upon men’s minds and
filled them with enthusiasm. Bacon was not content with setting
forth his views in the abstract, but in his New Atlantis he exhi-
bited in concrete, but imaginary, form, the benefits which would
result, and the state of things which would arise, when the new
philosophy had been thoroughly welcomed, and experimental science
had been thoroughly established among men. The chief feature in
Bacon’s undiscovered island of the fancy was “ Solomon’s House,”
in which the employments of the Fellows are described as follows: —
“We have twelve that sail into foreign countries, who bring in the
books and patterns of experiments of all other parts. These we call
Merchants of Light. We have three that collect the experiments
which are in all books. These we call Depredators. We have three
that collect experiments of all mechanical arts, and also of liberal
sciences, and also of practices which are not brought into arts.
These we call Mystery-men. We have three that try new experi-
ments, such as themselves think good. These we call Pioneers or
Miners. We have three that draw the experiments of the former
four into titles and tablets, to give the better light for the drawing
of observations and axioms out of them. These we call Compilers.
We have three that bind themselves to looking into the experiments

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of their fellows, and cast about how to draw out of them things of
use and practice for man’s life and knowledge. These we call Dowry-
men, or Benefactors. Then, after divers meetings and consults of
our whole number, to consider of the former labours and collections,
we have three that take care, out of them, to direct new experi-
ments, of a higher light, more penetrating into nature than the former.
These we call Lamps. W e have three others that do execute the ex-
periments so directed, and report them. These we call Inoculators.
Lastly, we have three that raise the former discoveries by experi-
ments into greater observations, axioms, and aphorisms. These we
call Interpreters of Nature.”

Rawley, Lord Bacon’s chaplain and literary executor, says in his
preface to the New Atlantis , which was published in 1627, soon
after Bacon’s death — “ This fable my lord devised, to the end that
hee might exhibite therein a modell or description of a college, in-
stituted for the interpreting of nature, and the producing of great
and marvellous works for the benefit of men, under the name of
4 Solomon’s House, or the College of the Six Dayes’ Works.’”

Bacon’s imaginative conception, being so consonant as it was to
the spirit of the age, took root and fructified in the minds of many
of his countrymen, both those who were passing through the trying
scenes of the civil war in England, and those who had accompanied
Charles II. into his exile. The first attempt to realize the concep-
tion seems to have been made about nineteen years after Bacon’s
death, in the year 1645, by the formation in London of a scientific
society called the “ Philosophical College,” which was also called the
“ Invisible College.” Dr Wallis, in his autobiography, speaks of this
society as consisting of “divers worthy persons, inquisitive into natural
philosophy and other parts of human learning, and particularly of what
hath been called the New Philosophy, or Experimental Philosophy.”

Several eminent Oxford men who were in London in 1645,
owing to the interruption of university work caused by the civil
wars, became members of the “ Invisible College;” and in 1649,
returning to their Alma Mater , they founded the Philosophical
Society of Oxford, which used to meet in the house of Dr Wilkins,
then Warden of Wadham College, and afterwards Bishop of Chester,
or in the apartments of the Hon. Robert Boyle, who was then re-
siding in Oxford.

476 Proceedings of the Royal Society

Ten years later, in 1659, the accomplished and philanthropic
Evelyn addressed to Robert Boyle a letter containing his pro-
posal for the erection of “ a Philosophic-Mathematic College,5’ which
letter is full of Baconian inspiration. In it he says that, “ since we
are not to hope for a Solomon’s house in this sad catalysis (or dissolu-
tion of things), and inter los armorum strepitus , a period so uncharit-
able and perverse, why not might some gentlemen, whose geniuses
are greatly suitable, and who desire nothing more than to give a
good example, preserve science, and cultivate themselves, join
together in society, and resolve upon some orders and economy to
he mutually observed, such as shall best become the end of their
union1?” He then offers cheerfully to devote his fortune to the
carrying out of this scheme ; and he proceeds to say, in the Baconian
manner : — “ I propose the purchasing of thirty or forty acres of
land in some healthy place not above twenty-five miles from Lon-
don, of which a good part should be tall wood, and the rest upland
pastures or downs, sweetly irrigated. We would erect upon the
most convenient site of this, near the wood, our building, viz., one
handsome pavilion, containing a refectory, library, and withdrawing-
room;” this is the first storey. The second storey was to contain
“a fair lodging-chamber, a pallet-room ( i.e . a second-class bed-
room), and gallery, all of which should be well and very nobly
furnished, for any worthy person that might desire to stay any
time, and for the reputation of the college.” There were to be six
members of the college, each of whom was to have his cell and a
private garden, te somewhat after the manner of the Carthusians.”
Many details followed as to the mode of life to be pursued in this
institution, “ the principal end ” of which was to be the “ promotion
of experimental knowledge.” Of course, this dream of Evelyn’s was
never carried out; it is only mentioned as showing the sort of ideas
which the study of Bacon had engendered in men’s minds, and
which finally resulted in the establishment of the Royal Society.

A somewhat similar scheme was published about the same time
when Evelyn’s letter was being written, by the poet Cowley,
under the title of a Proposition for the Advancement of Experimental
Philosophy. This was to be effected by the creation of a Philoso-
phical College, with a revenue of <£4000 a year, and a staff of 64
persons, among whom are included 20 philosophers or professors ;

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1 6 young scholars, servants to the professors ; a chaplain ; a
chirurgeon ; “ 2 lungs, or chymical servants,”* and 4 old women to
tend the chambers. This college was to examine all existing theories
of nature, and to separate the true coins from those “ false moneys
with which the world has been paid and cheated so long.” Secondly,
it was to recover the lost inventions of the ancients. Thirdly, it
was to improve all arts which we now have, and discover others
which we yet have not.

These Baconian imaginings never obtained a literal fulfilment.
But in the next year, in 1660, immediately after the restoration of
Charles II., they received a modified realisation in the establishment
of the Royal Society. It is a point of some little interest that the
chief agent in effecting this result was a Scotsman. This was the
good Sir Robert Moray, who had accompanied the king in exile, and
who, at the Restoration, was made a Privy Councillor, and much
consulted on affairs of State. He was an ardent naturalist, and on
the king’s return to London in June 1660, he appears to have joined
the meetings of the “ Invisible College,” at one of which, in Novem-
ber of the same year, the schemes for a Physico-Mathematical Col-
lege were discussed, and it was resolved by the members present to
give themselves a more definite and regular constitution, “ according
to the manner in other countries, where there were voluntary asso-
ciations of men in academies for the advancement of various parts
of learning, so they might do something answerable here for the
promoting of experimental philosophy.” Sir Robert Moray was
present at this meeting, and in his intercourse with the king he took
occasion to communicate the proposal to His Majesty. At their
next meeting, a week later, he was able to state to his friends that
the king “ did well approve of their design, and would be ready to
give encouragement to it.” The members at once constituted them-
selves the “ Royal Society,” and Sir Robert Moray became their
first president ad interim. About a year and a half later, in July
1662, the Society received its charter of incorporation. Lord
Brouncker, who was a discoverer in mathematics, — “being the first
to introduce continual fractions, and to give a series for the quadra-
ture of a portion of the equilateral hyperbola,” — was named president
in the Royal Charter. The king continued to take an interest in
* The “ lung” was so called because he blew the fire for his master.

47 8 Proceedings of the Royal Society

the Society, and was often present at their experiments in his
gardens, his parks, or on the Thames ; and he even condescended
to chide them “ on the slowness of their proceedings.”

In 1663 he presented them with their mace. The charter and
the mace are the only substantial favours which Charles II. appears
to have conferred upon the Royal Society, and for a long period
they worked on, by means of the genuine enthusiasm of the
fellows, with no funds at their disposal for scientific purposes. I
think it is amusing to observe that Sir Robert Moray so far con-
trived to give a Scottish character to the Society, that their mace
was decorated all over with the thistle, and that St Andrew was
chosen as their patron saint.

As soon as the Royal Society was established, its members con-
nected it with the name of Bacon. Bishop Sprat, who published a
history of the Society in 1667, writes : — “The Royal Society was a
work well becoming the largeness of Bacon’s wit to devise, and the
greatness of Clarendon’s prudence to establish.” Oldenburg, the
first secretary of the Society, says : — “ The enrichment of the store-
house of natural philosophy was a work begun by the single care and
conduct of the excellent Lord Verulam, and now prosecuted by the
joint undertakings of the Royal Society.” Glanvil, in his work
called Plus Ultra , or the Advancement of Knowledge since the
days of Aristotle , after alluding to the New Atlantis , says : —
“ This the great man desired, and formed a society of experimenters
in a romantic model ; but he could do no more — his time was not
ripe for such performances. These things, therefore, were considered
by later virtuosi, who several of them combined together, and set
themselves to work upon his grand design.” Professor Napier
quotes several other more obscure authorities, to show the .same
opinion of Lord Bacon entertained in the minds of Englishmen.
One Dr Power, in 1664, in a work on the discoveries of Galileo,
Torricelli, and Pascal, calls Bacon “the patriarch of experimental
philosophy.” Another writer, of the same year, with the unfortunate
name of Mr Havers, says that “ Lord Bacon’& way of experiment, as
now prosecuted by sundry English gentlemen, affords more proba-
bilities of glorious and profitable fruits than the attempts of any age
or nation whatsoever and Dr Childrey entitled his work on the
Natural Rarities of England , “ Britannia Baconicaf in order to

of Edinburgh, Session 1877-78. 479

indicate its connection with those studies which Bacon had
originated. Lastly, I may perhaps be allowed to quote the well-
known lines from the Ode to the Royal Society , by Cowley,
himself one of the earliest fellows, in which, after detailing the
futility of the early philosophy, he says : —

“ From these and all long errors of the way,

In which our wandering predecessors went,

And, like th’ old Hebrews, many years did stray
In deserts but of small extent,

Bacon, like Moses, led us forth at last,

The barren wilderness he past,

Bid on the very border stand
Of the blest promised land,

And from the mountain-top of his exalted wit,

Saw it himself, and showed us it.”

Runo Fischer says that Bacon was an “ epoch-making ” thinker,
who put men into a new attitude towards things, and opened a new
world of possibilities. I think that it would be more strictly true
to say that Bacon was an “ epoch-marking ” man, a herald and fugle-
man, created and sent forward by his epoch. He was himself
unconscious of that ; he thought of himself as a solitary worker ; he
fancied that he derived nothing from others. He mentions his own
case as a source of encouragement, and says: — “ Some hope might, I
think, be afforded by my own example ; and I do not say this for
the sake of boasting, but because it may be useful. If any feel a
want of confidence, let them look at me, who of all my contem-
poraries have been most engaged in public affairs, who am of
somewhat infirm health (which of itself occasions great loss of time),
and who in this matter have assuredly been the first explorer,
neither following' in the steps of another, nor communicating with a
single individual, but who, nevertheless, by entering firmly on the
right way, and in submitting my mind to things , have, methinks, to
Some extent advanced these matters.” It is true that Bacon, in
solitary meditation, during the intervals of the law courts and State
affairs, built up the fabric of his philosophy, as a poet builds up an
epic poem or a drama. In 1605 he published his Advancement of
Learning , which was meant to be a map of the existing state of
human knowledge in all its various provinces, with a note of the
facts in which knowledge was deficient, and an exhortation to supply

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these deficiencies. The whole was to he a prelude to his Instauratio
Magna , or entire remodelling of the sciences, and was intended
especially to catch the mind of James I., who was, however, of too
pedantic an intellect, and too much absorbed in theology, to rise to
the level of Bacon’s great argument. In 1620, when Lord Chancellor
of England and Baron Yerulam, he brought out his Novum
Organum , or new method of the sciences, in two divisions, of which
the first was destructive of scholasticism, and the second constructive
of a better way. The Novum Organum contained the chief pith
of Bacon’s philosophy, but of this only the first or destructive part
was complete. No praise can be too high for the manner in which
scholasticism is for ever annihilated in this treatise. The trenchant
criticism, the large and luminous good sense, the grand and true
conceptions of man’s relation to nature, the striking metaphors — now
as familiar as household words — which pervade the first part of
Bacon’s Organum , have rendered it an immortal work, from the
point of view of literature as well as of philosophy. But it would
be ludicrous to maintain that, in writing it, Bacon followed the
footsteps of no one. There had been a host of attacks upon Aristotle
and the Aristotelians. Bamus, in Paris, as a young man, had
sustained the thesis, that “ everything which Aristotle had said was
false.” Patrizzi, in Venice, had published an assault upon Aristotle
characterised by the utmost malignity. Galileo, at Pisa, had roused
the anger of the Aristotelians by demonstrating that Aristotle was in
error when he said that heavy bodies fall faster than light ones. The
air in Europe was full of revolt against scholasticism, and yet Bacon
thought that when he laid down, in his brilliant way, that “ Truth
is the daughter of Time, and not of authority that the “ ancients
were the children of the world and that “ the syllogism is unequal
to the subtlety of things,” be was stating something original, and not
following in the footsteps of any one. Bacon, having imbibed, with
the quick apprehension of genius, numberless suggestions from his
contemporaries and predecessors, at once kicked down the ladders
on which his mind had risen : he spoke with the greatest disdain of
Ramus and Patrizzi : and he so little appreciated Galileo that, when
informed of some of the labours upon which Galileo was engaged, he
said to his informant : — “ I wish you would persuade those Italian
astronomers to give up amusing us with their idle stories, and stick

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a little closer to the experience of the senses.” It is a most curious
circumstance that Bacon, with all his great intellect, could not stomach
the Copernican theory. Indeed, in some things he was even behind
his age. He spoke slightingly of Gilbert as a mere specialist —
Gilbert, whose discoveries in magnetism have, I believe, been
scarcely superseded at the present day. He accords no just tribute
to Harvey, who had been his own physician. Harvey, on the
other hand, appears to have set no great store by Bacon. Harvey
is reported to have said : — “ He writes on philosophy like a Lord
Chancellor.” Now' that I have begun with Bacon’s intellectual
defects, I may as well finish with them. Bacon was strikingly
deficient in the power of looking at things historically ; indeed, it
never seems to have occurred to him to do so. He treated Aristotle
and Plato as if they were men of his own time, who differed from
him in opinion. In his work called the Wisdom of the Ancients ,
he undertakes to show that under each of the fables of the Greek
mythology there was wrapped up and concealed some piece of
physical, metaphysical, or political philosophy. His interpretations
of the myths are rich in ingenuity, but at the same time they are
perfectly arbitrary and reckless ; and they ignore the primary ques-
tion of all, which is, How are we to conceive myths originally to
have been formed and established in the minds of a people 1 To
this question the quite recent science of comparative mythology
offers some sort of solution. Bacon’s view of the myths was very
prosaic ; he regarded them as didactic stories for the improvement
of child-like minds. His view of poetry itself is of the same
character. He describes it as “ a part of learning,” and evidently
values it only so far as it is useful — that is to say, didactic. It is
with a covert sneer that he says : — “ Poesy was ever thought to have
some participation of divineness, because it doth raise and erect the
mind, by submitting the shows of things to the desires of the mind ;
whereas reason doth buckle and bow the mind unto the nature of
things.” He divides poetry into Narrative, Representative, and
Allusive. In speaking of Representative poetry — that is, the
drama — he makes no mention of Shakespeare, whom indeed he did
not appreciate. He cares most for Allusive poetry, which conveys
truth under the form of allegory. He excluded Lyrical poetry from
the category of poetry altogether. He says : — “We exclude satires,

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elegies, epigrams, odes, and the like, from our discourse, and class
them with philosophy and the arts of oratory.” In short, Bacon,
though he had himself many of the characteristics of a poet, utterly
misconceived the true nature of poetry, and in his theory reduced it
to the level of prose.

It is perhaps more excusable in Bacon that his outlook on the
future of human knowledge was, after all, quite limited. He
admitted that the instauration of the sciences would require some
ages for its completion ; but he thought that, within the compass
of no very long period, that completion would be effected. Bacon
would not have realized what was implied by Goethe’s phrase,
unendliche Natur. If you had asked him, he would probably have
prophesied that, before the year 1877, all the mysteries of nature
would have been cut and dried and garnered. He had some dim
notion of the science of chemistry; of the sciences of geology,
palaeontology, comparative philology, and political economy, which
have done so much to change modern ways of thinking, he had not
ftn inkling. Of the theory of evolution or of spectrum analysis, it
is needless to speak. Bacon had not even heard of gravitation,
and he held to the Ptolemaic system of the universe. After all,
men’s imagination is restricted to what they have had experience of,
or to some short flights of analogy beyond it, and we cannot in the
least anticipate or set bounds to what our successors may be think-
ing of some few centuries hence.

Bacon has been charged with having led the way, by his philo-
sophy, to empiricism, materialism, positivism, and sundry other
amiable “ isms.” But this charge is rather unfair ; for though, in his
physical philosophy, he seems to have tended more and more to an
atomistic theory, and though in the interval between his Advance-
ment of Learning and his Novum Organum he seems to have
abandoned the idea of metaphysics as a useful science, still he
himself always maintained a great respect for revealed religion.
Though he, very properly, enjoined that ethics should be studied,
like other sciences, inductively, he considered that mind itself is an
emanation from God, and not subject to the laws of science. He
thus, as Kuno Fischer remarks, entertained a dualism not dissimilar
to that of Descartes. He held that faith should go side by side
with science, and that we should “ render to Ceesar the things that

of Edinburgh, Session 1877-78. 483

are Csesar’s, and to God the things that are God’s.” Therefore, if
subsequent philosophers have taken a different attitude, the responsi-
bility surely rests with themselves.

The last reproach against Bacon is, that he made no discoveries
himself, and that he directly led the way to none. Both of these
allegations are, in fact, undeniable. Bacon sometimes showed
brilliant intuitions into the nature of things ; for example, in illus-
trating his method of discovery by “ prerogative instances,” he
says : — “The phenomenon of colour is discovered most readily, and
with the least heterogeneous admixture, in prisms, crystals, and
dew-drops ; for these have little or nothing in common with other
coloured bodies, such as flowers, stones, metals, varieties of wood,
&c. They are, in this respect, single instances, and from observing
them we easily arrive at the result that colour is nothing but a
modification of the image of the incident and absorbed light ; in
the former case by the different degrees of incidence, in the latter
by the textures and various forms of bodies.” This paragraph has
been said to contain an anticipation of Goethe’s theory of
colours. But such intuitions were only, like those of Aristotle,
the happy thoughts of a powerful intellect. Discovery, properly
so called, remains as the prerogative of the specialist ; and Bacon,
though he killed himself by the experiment of stuffing a fowl with
snow, cannot claim any discovery as his own.

Nor have discoveries been made by following the precepts of the
Baconian method of induction. Some attribute this to the incom-
pleteness of the second part of the Novum Organum ; others
say that it is because Bacon’s method is based on an erroneous
view of causation. Twenty years ago, Dr Whewell brought out a
Novum Organum Renovatum, to supply Bacon’s deficiencies ;
but we may safely venture to assert, that WhewelFs book will not'
he a hit more fertile in producing discoveries than Bacon’s has
been. Logic is a useful part of education, and is necessary as a
part of philosophy ; but every real worker in the world seems to
have an unconscious logic of his own, based on innumerable
analogies of the class of facts with which he is in the habit of
dealing. The study of deductive logic will never of itself create
powerful reasoning in the law courts or the senate ; and let the
logic of inductive method he laid down never so perfectly, still dis-

484 Proceedings of the Royal Society

covery and the advancement of science will go on independently of it.
The true method of studying nature had come into the world before
Bacon wrote ; it had been distinctly described, though in general
terms, by Lionardo da Vinci, Tycho Brahe, and Galileo ; and, quite
independently of Bacon, its adoption had been signalised by several
of the greatest discoveries ever made by the human race, — some of
which Bacon even refused to admit. Probably no direct connection
can be established between the influence of Bacon and the achieve-
ments of any separate science. But, as De Jouffroy says, “Is it
nothing to have seized, at the critical moment, the idea which would
open a new era to the sciences 1 Is it nothing, in the early dawn
of an immense revolution, to have predicted almost in detail its career?
Before Bacon’s time no one seems to have had a true sentiment of
the grandeur of nature ; this sentiment, conjointly with enthusiasm
for science, he preached and spread abroad. As soon as he had
written, the genius of observation raised its head, and marched on an
equality with the genius of thought.”

I have already given evidence of Bacon’s general influence upon
the minds of men, and it was by this general influence, on the
universities, on separate scholars, and on the reading world through-
out Europe, that Bacon assisted the birth of the new era. His
perceptive mind brought into one focus, beams of light which would
otherwise have remained scattered; like an eagle he soared till he
caught sight of the unrisen sun; he told the world what was going
on and what was in store for it; he made the new era conscious of
itself. In doing this, he employed the most splendid literary faculty.
Ho architecture is, after its kind, finer than the English prose of
Bacon’s Advancement of Learning. Kemusat justly^ recognises in
Bacon’s writing that quality which is termed “the great manner,” and
he envies him that balance of imagination with good sense, which
he considers to be a specially English characteristic. Bacon, in an
interval of short-sightedness, distrusted the permanence of the
English language; like Dante, and others of the great moderns, he
undervalued the worth and inherent vitality of his vernacular
tongue; he said “these modern languages will one day play the
bankrupt with books.” Therefore, after his first great treatise, he
preferred to write upon philosophy in Latin. This we may now
regret from a literary point of view, but it doubtless * extended the

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circle of his contemporary readers, and his Latin writings, not being
in classical style, and being full of pregnant thoughts, wise and
witty sayings, and the happiest metaphors, are easily translated into
any language, and are a treasure for all the world. In conclusion,
it is as an inspired seer, one of the greatest of men of letters, and
the prose-poet of modern science, that I reverence Lord Bacon, and
have ventured to make him the first topic of the evening.

Our own Royal Society doubtless borrowed its title and partly its
idea from the Royal Society of London. I am proud to think that
this Society is an emanation from the University of Edinburgh,
from which it sprang, on the suggestion of Principal Robertson, in
the latter part of 1782. Thus, in the same year when the University
will celebrate its tercentenary, this Society will be able, perhaps
conjointly, to celebrate its hundredth birthday. But in one essential
particular we differ from the Royal Society of London, whose
function was thus defined in 1663 : — “ To improve the knowledge of
natural things, and all useful arts, manufactures, mechanic practices,
engines, and inventions, by experiments (not meddling with divinity,
metaphysics, morals, politics, grammar, rhetoric, or logic).” These
exclusions form no part in our constitution. On the contrary, from
the first, the promotion of literature as well as science was the object
of the Royal Society of Edinburgh. I may say, then, that the name
of Bacon, as one of the greatest stars of literature, has a double
claim upon our regard. But it has been observed that the literary
element in our proceedings has been gradually dwindling away.
Principal Forbes, fifteen years ago, spoke of the difficulties under
which we laboured owing to a change in the manners of society, and
to our having become less “clubable,” or less intellectually sociable,
than our ancestors used to be a hundred years ago. And he exhorted
the then fellows to bestir themselves in the production of papers.
I have inquired the number of papers, not connected with physical
science, which have been contributed during the last fifteen years, and
it appears to be considerably less than forty, or little more than two per
annum. And of these, seven were contributed by Professor Blackie
on classical or philosophical subjects, four by Lord Neaves chiefly on
philology, three by Dr John Muir on Indian antiquities, three by
Mr Wyld on metaphysical topics, two by Sir James Simpson
on archaeological questions, two by Mr Skene on Celtic topography

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and philology, and the remaining twelve or fourten by separate
individuals. Thus, in the last fifteen years, out of about 37 0 Ordinary
Fellows of the Society, only about twenty have come forward to con-
tribute papers other than physical or mathematical. During the last
session not a single paper on any literary subject was read before us.
No doubt, there is much excuse for this, in the fact that the time of
literary men is often much occupied, and that they can obtain a high
remuneration elsewhere for the produce of their labour. It was
doubtless owing to this that Sir Walter Scott, who was for twelve
years President of this Society, never appears to have contributed a
single paper to it, though he was so full of history and archaeology
and lore of all sorts.

The day may even come when the general public is sufficiently
instructed to receive with interest, in ordinary periodicals, the
physico-mathematical papers, which form the staple commodity of
this Society, and then we shall have done our work. In the mean-
time I would venture, like Principal Forbes, to advocate “ intellectual
clubability.,, All tentative essays, which are not yet ripe to form a
book or an article, may fitly be contributed to this Society and
embodied in its Transactions, and I should have thought that
not a single professor of any department in the University could go
through the teaching of a session, without coming across at least
some one novel point, which it would be worth while to bring
forward.

In the course of last session, one of the three prizes in the gift of
this Society — the Macdougall-Brisbane prize, consisting of a Gold
Medal and £15, 14s. 7d., was awarded to Mr Buchan, for his paper,
“ On the Diurnal Oscillation of the Barometer.” This important
contribution to meteorological science has been published in the
Transactions of the Society, and I note here with pleasure the
words used in regard to it by our President, on presenting the prize :
— “ That it paves the way for discovering the complete thermo-
dynamic theory of its subject, and that Mr Buchan has well
followed up his laborious and most useful investigations of the
meteorology of Scotland by so valuable a discussion of barometric
observations from all parts of the world, collected and arranged
in the very best manner for the immediate application of the
harmonic analysis.”

of Edinburgh) Session 1877-78.

487

The following statement, in regard to the number of the present
Fellows of the Society, has been drawn up by the Secretary : —

1. Honorary Fellows : —

Royal Personage —

His Royal Highness the Prince of Wales, . . 1

British Subjects —

John Couch Adams, Esq., Cambridge ; Sir George
Biddell Airy, Greenwich ; Thomas Andrews, M.D.,

Belfast (Queen’s College) ; Thomas Carlyle, Esq.,

London; Arthur Cayley, Esq., Cambridge; Charles
Darwin, Esq., Down, Bromley, Kent ; John An-
thony Froude, Esq., London ; Thomas Henry
Huxley, LL.D., London ; James Prescott Joule,

LL.D., Cliffpoint, Higher Broughton, Manchester;

William Lassell, Esq., Liverpool ; Rev. Dr Humphrey
Lloyd, Dublin ; William Hallo wes Miller, LL.D.,

Cambridge; Richard Owen, Esq., London; Thomas
Romney Robinson, D.B., Armagh ; Lieut. -General
Edward Sabine, R.A., London ; Henry John
Stephen Smith, Esq., Oxford ; George Gabriel
Stokes, Esq., Cambridge ; James Joseph Sylvester,

LL.D., London ; Alfred Tennyson, Esq., Fresh-
water, Isle of Wight, ...... 19

F oreign —

Claude Bernard, Paris ; Robert Wilhelm Bunsen,

Heidelberg ; Michael Eugene Chevreul, Paris ;

James D. Dana, LL.D., Newhaven, Connecticut ;

Alphonse de Candolle, Geneva; Heinrich Wilhelm
Dove, Berlin; Jean Baptiste Dumas, Paris; Charles
Dupin, Paris ; Elias Fries, Upsala ; Professor Carl
Gegenbaur, Heidelberg ; Herman Helmholtz, Ber-
lin ; August Kekule, Bonn ; Gustav Robert Kirch-
hoff, Heidelberg ; Herman Kolbe, Leipzig ; Albert
Kolliker, Wurzburg; Ernst Eduard Rummer, Ber-
lin ; J obann von Lamont, Munich ; Richard Lep-
sius, Berlin; Ferdinand de Lesseps, Paris; Rudolph
Leuckart, Leipzig ; Joseph Liouville, Paris ; Carl
Ludwig, Leipzig ; Henry Milne-Edwards, Paris ;

Theodore Mommsen, Berlin ; Louis Pasteur, Paris ;

Prof. Benjamin Peirce, United States Survey ;

Henry Victor Regnault, Paris ; Angelo Secchi,

Carry forward, 20

VOL. IX.

488 Proceedings of the Royal Society

Brought forward, 20

Koine ; Karl Theodor von Siebold, Munich ; Ber-
nard Studer, Berne ; Otto Torell, Lund ; Rudolph
Virchow, Berlin ; Wilhelm Eduard Weber, Gottin-
gen ; Friedrich Wohler, Gottingen, ... 34

2. Non-Resident Fellow under the Old Statutes : —

Sir Richard Griffiths, 1

Total number of Honorary and Non-Resident Fel-
lows at November 1877, 55

The following are the Honorary Fellows deceased
during the year : —

Foreign — Urbain Jean Joseph Leverrier, John
Lothrop Motley, 2

British — William Henry Fox Talbot, ... 1

3

3. Ordinary Fellows : —

Ordinary Fellows at November 1876, 363

New Fellows , 1876-77. — Dr Isaac Bayley Balfour ; George
Broadrick, Esq. ; George Cunningham, Esq. ; Dr John
Gibson; Walter Noel Hartley, Esq.; William Jolly, Esq.;

James King, Esq.; Robert A. Macfie, Esq.; Sir Daniel
Macnee ; Dr Robert Milner Morrison ; John Murray,

Esq. ; John Napier, Esq. ; George A. Panton, Esq. ; Dr
William Pole; Prof. James Roberton ; George Carr
Robinson, Esq.; James Stevenson, Esq.; Prof. William
Stirling ; Charles E. Underhill, Esq. ; Walter Weldon,

Esq.; Charles Edward Wilson, LL.D., .... 21

384

Deduct Deceased. — Dr James Bryce ; Andrew Coventry,

Esq. ; Rev. D. T. K. Drummond ; Sir David Dundas,

Bart. ; William Keddie, Esq. ; The Hon. Lord Neaves ;

James Thomson, Esq., C.E., who died in August 1870,
but whose death was only intimated in August 1877, 7

Resigned — Dr Alexander Hunter ; Captain T. P. White, 2

Carry forward, 9 384

of Edinburgh, Session 1877-78. 489

Brought forward, 9 384

Cancelled— Prof. Arthur Gamgee, M.D. ; Ernest Bonar,

Esq., cancelled in 1856, and whose name has been

inserted by mistake in subsequent Lists, . . 2

_ 11

Total number of Ordinary Fellows at November 1877, . 373

Add Honorary Fellows and Non-Resident Fellows, . 55

Total Ordinary and Honorary Fellows at commencement

of Session 1877-78, 428

The following Obituary Address was read by Professor
Piazzi Smyth, Astronomer-Royal for Scotland

Le Yerrier — Urbain, Jean, Joseph — one of our most respected
HonoraryMembers for thirty years, died on the 23d of last Septem-
ber, aged sixty-six.

On the 23d of that same month, but in the year 1846, an astro-
nomical discovery was made on the Continent, which almost took
men's breath away for the moment in astonishment and admiration ;
and which in bringing the name of Le Yerrier for the first time
prominently before the general public, taught them that the age of
intellectual giants after the manner of Newton and La Place, was
not yet closed. And thirty-one years afterwards, or on that very
identical day of September in the present year 1877, the electric
telegraph flashed this other mournful news over an attentive world,
that the same Le Yerrier (without compare the greatest gravita-
tional astronomer of our time) had ceased to exist !

Death has been indeed too complete, for within a few days of Le
Yerrier’ s own demise, his adored Wife followed him to the tomb,
where one of his sons was already laid ; and we thus have the whole
life-lesson of this most eminent scientist ready for impartial historical
treatment, if at all.

But who shall prove equal to the task of writing the life of such
a man. Biographical notices of him innumerable have been pub-
lished, but not the one, full, history which posterity will require ;
nor is this the place to attempt anything of the kind. But what
has appeared in print already, swr-abundantly relieves your Council
of the necessity of any attempt on their part at formally justifying
their advice of thirty years ago, to the Society, to enrol the name of

490

Proceedings of the Royal Society

Le Verrier amongst its Honorary Members; and they cannot perhaps
do better in the few minutes now accorded to them, than simply
to describe something of the general character of, as well as progress
of alteration with time in, the public career of the departed.

The first period of Le Verrier’s virile existence may be considered to
extend from his leaving the Polytechnic School in 1831, to receiv-
ing the appointment of Director of the Observatory of Paris in
1853 ; a joyous, a rising and expanding existence to him the whole
of the time. Born in 1811 at St Lo, in the Department of Manche,
(which courts the west wind of the Atlantic along the whole extent
of its coast), and son of a Government official there, the young Le
Verrier had received his education first in provincial, then in Parisian,
schools, always manifesting a taste for, and superior power in, pure
mathematics; but with a further determination also to hold his own
course, and to prosecute his own excelsior ideals therein. Hence, on
ceasing to be a college student in 1831, and beginning his career
as a man, as the architect too of his own fortunes to be, he seems to
have chosen, not a poorly paid, over worked, hard scientific post,
but the more easily executed, and better paid employment of the
ordinary civil service of his country ; selecting such a branch therein
as should leave him most spare time for the prosecution of his pri-
vate reading; and only when, after some years, the further continua-
tion of that official employment, the Administration des Tabacs ,
would have obliged him to leave the neighbourhood of metropolitan
libraries, — did he seek to support himself by teaching mathematics,
of which he then became one of the assistant professors in his old
Polytechnic School.

But those pedagogic labours by day, the still youthful Le Verrier
never allowed to interfere with his own private studies at night.
He had already comprehended and fervently accepted his destiny ;
viz., to succeed La Place in those applications of the higher mathe-
matical analysis to celestial mechanics, which demand as much of
continued labour, and power of abstraction, as of penetration,
genius, and analytical resources. Hence his earliest paper presented
to the Academy of Sciences in 1839, attacked no less than the secular
inequalities in the movements of the principal planets. His second
paper took up the orbit of Mercury, and the most exact calculation

491

of Edinburgh, Session 1877-78.

of the numerical amounts of the perturbations it is subject to from
other planets. His third paper, presented in 1844, investigated in
the most masterly style the perturbations which the strangely
deflected Comet of 1770 must have experienced both before and
after that epoch, from the attraction of the planet Jupiter. And
his fourth paper, applied similar mathematical calculations to the
more modern discovered Comet of 1843.

But those Comet papers, though they gained Le Yerrier a seat
and a pension in the Academy of Sciences, were not altogether in
his destined line. In more immediate resumption of which, it was,
that in the beginning of 1846, he brought before the Academy his
fine investigation into the orbit of the planet Uranus, his computa-
tions of every perturbation it could suffer from every known mem-
ber of the solar system, and his finding them all insufficient to
account for the difference between theory and observation. And
then, after that essential clearing of the ground, he produced his
further and most remarkable of all his mathematical calculations,
confessedly and by its very title, on “ the hitherto unseen, outside
planet, which, acting from without, is producing the apparent
irregularities in the movement of Uranus, from a distance of 1500
millions of miles beyond, and is now in such and such a position in
our sky, and must have such and such an apparent diameter.” A note
of that position and size Le Yerrier sent to a German observer
on the 17th of September in that year, 1846. That observer, Dr
Galie by name, looked for it on the evening of the 23d of that
month, and within a few minutes, with the powerful and accurately
mounted equatorial telescope of the Berlin Observatory, he actually
succeeded in finding Le Yerrier’s theoretical planet, since called
Neptune, in the given direction, at the enormous distance and of
the indicated size, nearly.

This was the discovery, sensational it has been called, but most
worthy to make a sensation throughout the whole human race,
which immediately brought in honours of every kind, and from many
nations to Le Yerrier. Which presently too, wafted him in political
safety across the abyss which proved fatal to the then king and all
the royal family of France ; but gave the astronomer-mathematician
an eminent place under the subsequent republic, and a still more
eminent one under the Empire which followed. But none of those

492 Proceedings of the Royal Society

things, however flatttering personally, not even the powers invested
in him to reform the Polytechnic School, and to inspect all the uni-
versities of France, nor all the immense astronomical correspondence
of which he became the European centre, did he allow to interfere
with his continued private research in his own appointed task.
Wherefore the Academy was electrified again and again by further
of his magnificent planetary papers, in 1849, 1850, and 1853 — as,
on new methods of constructing the numerical tables required for
practically computing the places of the planets as subjected to all
perturbations of Newtonian gravitation origin; next, on improved
tables of the Sun, as representing the movements of the earth ; and
then on still more refined theoretical considerations touching the
whole group of planetoids, between Mars and Jupiter, whatever their
teeming numbers might eventually be found with the telescope.

All this time, too, Le Verrier was the most cheerful of beings, the
most admired of ail in scientific life, and envied by no one ; for he
had gained his successes by genius and force which were all his
own, which no one else could attempt to claim or compete with.
And he could be so smiling, so gracious, sweet as summer air, and
full of happy remarks to all he met. Occasionally even rather too
much so ; for we have seen him at that period of his life at a meet-
ing of the Academy, and while the very Perpetual Secretary was
reading out the papers of others , there was M. Le Yerrier joyously
walking in, and about, and through all the ranks of seated savants,
nodding to one, discussing with another, laughing with a third, pro-
posing problems to a fourth, and without the slightest idea he
could be doing anything wrong. While his personal appearance
was in those days a tall figure, with fine upright carriage, sparkling
eyes unconscious of offence, an immense dome of a head and abun-
dant flaxen hair. The French called it “blond:” and how that
man could have escaped being born an Anglo-Saxon, was more than
we could then understand.

So closed the first period of Le Verrier’s career : for the second
and very contrasted part of it began when Louis Napoleon appointed
him to the charge of the Imperial Observatory at Paris.

And why should it have been such a contrast1? Was not the
“ Observatoire” just the place for such a man 1 Not a bit of it !

of Edinburgh, Session 1877-78.

493

In our own Mrs Somerville’s autobiography, unfortunately not then
published, she pointedly records that when all the world was paying
her honour, immediately after the publication of her most unex-
ampled lady’s book on astronomy, entitled “ The Mechanism of the
Heavens,” elucidated there by her able expositions of the algebraical
analysis of La Place and other great French mathematicians —
one of her lady friends in Burntisland remarked so confidently,
“ Oh ! Mrs Somerville, what a happy life you must lead, for of
course you are always gazing at the stars through a telescope ! ”
Whereupon Mrs Somerville answered to the effect, “ that she had
never looked through a telescope in her life, except once ; and then
it was not at a star.” And of course ! For if she had been spend-
ing her nights in instrumental star-gazing, how could she have been
also getting up by midnight oil the totally different subject of
algebraical equations 1

Very similar too, mutatis mutandis , was the case of Le Verrier.
Bom to excel in astronomical mathematics on paper, what had he
to do with telescopes ! Why, the very, and most particular, praise
which all the world had given him in 1846, was, — “ Other astrono-
mers have occasionally discovered a little planet, by finding in the
sky with their telescopes a diminutive star, which varies its place
slightly from night to night : but here, in M. Le Verrier, is a man
who has discovered a planet without looking through a telescope at
all; without even casting a single glance at the sky; he saw his
grand planet at the end of his pen ! ” If that praise, then given so
freely, was genuine and honest, why take that man away from his
glorious pen work, and make him begin mechanical operations
which he has no taste for : which he has shown he can transcend
in their occasional results by totally different methods ?

But the imperial will had ordained it; and forthwith, from 1853
to 1870, Le Verrier was known as Director of the Observatory of Paris:
showing too, there, in many brilliant respects, how much a rigid
sense of mere duty may enable a man to perform in almost any
line. Though the world at large will be thankful chiefly, that in
all this second portion of his career, Le Verrier never allowed him-
self to be entirely absorbed in the continually increasing circle of
his official employments ; but held as closely as ever to his soul’s
private task, viz., the mathematical investigations, and then the

494 Proceedings of the Royal Society

practical computations, of every perturbation which the Solar planets
can suffer.

In this manner, with an energy, a constancy and an intellectual
power never combined before in any one individual, Le Yerrier had,
by the year 1868, produced new tables of all the inner planets
from Mercury to Mars and in the course of them had demonstrated
most unexpectedly, that the hitherto universally received quan-
tity for 70 years past, of 8-56" for the Solar Parallax, was
much too small. The effect on the astronomical world was magical.
For years there had been a languid idea that the Solar Parallax
value derived from the then last previous Yenus Transit, should
be improved upon by observations of Mars at opposition ; and the
Nautical Almanac had for half a century gone on publishing the
appropriate ephemerides of Mars and stars near him for Opposition
after Opposition. But few persons ever observed them ; or if they
did, and also, like Henderson at the Cape and Taylor at Madras,
computed the results as well, — they were not attended to. But the
moment it was announced that Le Yerrier had found from his cal-
culations in Physical Astronomy, that the mean Solar Parallax was
so far from 8*56" as to be nearer to 8*95", all Astronomical Associa-
tions were shaken to their very bases. Greenwich ran to court the
new quantity. The Nautical Almanac adopted it with fervour : and
half a dozen nations were presently competing with each other in
observing and re-observing Mars’ oppositions, and always finding
now that they gave out a quantity very like the Parallax announced
by the great Gravitational Astronomer of France,

But how went on things in general at the Observatoire, all this

time 1

For a while, wonderfully well ! If Le Yerrier had no practical
experience himself, he knew where he could obtain it in others. So,
the Emperor always aiding and abetting, the favoured savant had
only to propose schemes of improvement, and the means in both
men and money were always forthcoming to carry them out. First,
the whole Greenwich system was imported bodily, its instruments
imitated, its routine copied, and observing astronomers and com-
puters of a like order procured. Then came the concentration of
Meteorological Observations by electric telegraph from all quarters
of Europe, and the issue of a daily Bulletin, post free to all the

of Edinburgh , Session 1877-78.

495

world, by another corps of practical scientists newly incorporated
into the establishment. Then came the rise of the “ Association
Scientifique de France,” a voluntary popular institution after the
British model, but where all the sciences were taken up, and Le
Yerrier was President of everything.

He took care verbally and with semi-military hauteur , to appoint
his Observatory subalterns their tasks to perform ; but when these
were performed, largely by the native and peculiar, and often most
exalted, skill of the workers, they were pushed into obscurity on
every great occasion, and Le Verrier took sole ostensible authorship
of all their doings. Long had they borne, but how much longer were
they to continue to bear, this peculiarly affronting tyranny? To
perform the most exquisite work in their own lines, but to remain
unknown, trodden on, and see another, who in his heart despised
such things, gain all the advantage and all the credit? Feelings,
though silent, were growing more bitter and dangerously exasperated
day by day at the Observatoire. Something must come of it. At
length, not there, but at the Academy, the malcontents found a
leader in M. Delaunay : a younger man, but rising to be a still
greater mathematician in gravitational astronomy, than Le Yerrier
himself : and yet at the same time, was this most unique and
estimable Delaunay as much distinguished by natural amiability,
by the sympathetic tendencies of his disposition, and his earnest
regard for others, as the Director of the Observatoire, Imperial Lord
of the Ascendant, was daily becoming more and more antipathic,
as well as impatient of every one in the world but himself.

Now Delaunay’s grand mathematically scientific work at that
period was the theory of the Moon ; and he too had come therein
on certain equations whence he drew a new value for the Solar
parallax ; making it however more nearly 8,85//, and proving
Le Yerrier’s 8' 95" quite inadmissible. So thereupon the two great
mathematicians crossed swords. Their discussions, meeting after
meeting of the Academy, attained a vigour and an intensity which
drew half Paris to assist at these re-unions ; but chiefly to hear Le
Yerrier ! He was indeed rather in the wrong scientifically ; and
had, long afterwards, to modify his 8*95" to something very close to
Delaunay’s numbers. But what did the crowd care for minute
exactitudes ! They went to see how a hero fights, how he gains his

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496 Proceedings of the Royal Society

successes ; and Le Verrier gave them plenty of that. Though not
exactly an orator, he was clear in expression, fluent in words,
and ready, aye ready, at a moment’s notice. Kich too in cutting
sarcasm and scarifying irony, he taunted the slowness of his oppo-
nents who had to go home and think over their replies and
promise to give them at the next meeting of the Academy, — while
he stood there having answered, or at all events confounded, them
on every point yet produced ; he, the man of peace, who desired
nothing so much as to finish the war then and there.

On such occasions Le Verrier seemed to float in positive pleasure
through the combat, cutting down his enemies with ease on every
side. A smile was still on his countenance ; hut it was now the
smile which opens not the lips ; a distorting, disdainful smile,
betraying however within, both the consuming fires of egotism, the
love of conquering, and the voluptuous rapture of triumph become
a necessary accompaniment of his existence. Yet there was this
untoward feature about it all the time, that with every successive
conquest, Le Verrier was making a wider and wider void around
himself; until, with one dazzling victory more, — there came the
deadening news, that every one had left him, and the Director of
the Observatory reigned over telescopes alone !

The Minister of the Interior then had to step in and give
such a disorganizing Director his dismissal. Le Verrier answered
by a passionate appeal for an interpellation by the Senate : but
that body supported the Minister, and the tyrant-mathematician
had to go. He fell ; and never had there been such a catastrophe
known before throughout the scientific world. But Delaunay was
immediately appointed to the vacant place ; the observers, com-
puters and artisans all returned, and the public service flowed on
Once again.

Time passed ; and how heavy a time for France, after that aflair
of the Observatoire in the beginning of 1870. The terrific Franco-
German war began soon afterwards ; the Germans invaded France
with a larger army than the world had ever heard of since the days
of Xerxes, and, though professing to be “ Christians,” and calling
their country “ Holy,” yet armed with infinitely more terrible means
for the destruction of human life than his, or Mahomet’s either.

of Edinburgh, Session 1877-78. 497

Every battle went against the French ; their smaller armies were
annihilated, their fairest provinces rent away : their revenues
sacked, their people (even innocent and peaceable men, women,
and children) starved to the very bone, their capital city taken.
And then, after all these destructions from without, poor Paris
fell into the hands of her own revolutionary Communists ; who,
when at length attacked in their turn, by the recovered forces of
the nation, — most provokingly insisted on making the very Obser-
vatoire of Astronomical Science, one of their chief strategic points
of defence; drawing down thereby on the grand old building,
from loyal French guns too, an amount of cannon shot that rid-
dled the Equatorial Domes through and through, and ruined much
of the substantial masonry below.

But the chief part of the daily service of the Observatory was not
impeded thereby. For, with remarkable prevision of coming events,
Delaunay had removed a division of the working staff, long before
the siege of Paris began, to a Southern Department. There they
gathered up the telegraphic communications again, there they
carried on their collections of all European, with a few Asiatic and
some African Meteorological observations, and there also, without
the cessation of a day, they issued their daily lithographed Bulletin ;
contriving still to give to all nations, and by a free book-post, the
earliest information of every scientific event and Natural change
and thus to keep up their beloved France (though bleeding from
unnumbered wounds) an intellectual centre, a heralder of the way,
for all the learned world.

That grand result, however, came about mainly because it was
Delaunay who directed, or rather bound together with cords of
love, all the broken and scattered elements of the scientific service
of France. Under his sympathetic lead, every one put forth his
utmost powers, and with a will and a devotion which, in immediate
presence of death, wras almost sublime. And when at length peace
returned, and the reorganisation of the Observatory of Paris had to
be undertaken, every report which M. Delaunay addressed to the
Minister of the Interior was as surprising for its pellucid clearness,
as for its ably comprehensive character : alike too for including
every department of science, as for insuring the distinct recognition
of every good worker therein. A true and happy model Republic

498

Proceedings of the Royal Society

was the Observatoire thus becoming under this rare Savaut’s en-
lightened rule, tending to the American perhaps in its almost over
abundance of personal liberty, but to the Athenian in its perfection
of work and glorious ideals of still higher things to come, — when,
on a day, — alack the day ! — one most gusty, stormy, tempestuous
day ; when poor Delaunay, who had gone down to the sea-side
merely for a short visit, essaying to cross the harbour of Cherbourg
in an open boat, a squall came on, the boat capsized in deep water,
and France’s first, best, rising, genius was lost for ever.

All political and scientific society stood aghast. There was no
second Delaunay to be had anywhere ; and even those persons who
had been most active in bringing him forward only two years
before, — could do nothing now but tacitly consent, in their utter
dismay, to Le Yerrier returning to power again.

Le Yerrier returned accordingly to the Observatoire in 1&72, and
then began a third distinctly featured period of his career.

No longer the cheerful-looking Anglo-Saxon man of his earlier
days ; nor the tall, stern, conquering figure of his middle career ;
but now, bent and feeble, with a dark, jaundiced hue overspreading
his countenance (symptomatic of the disorder of the liver under
which he finally sank), and with the muscles of his face half
withered and shrunk down to the bone, so as to show the real osseous
foundation of the countenance and prove him a born Gaul, after
all, — Le Yerrier in his third stage pleased both friends and foes less
than ever.

With the latter he did not attempt any actual open war, but there
was underground work going on all the time ; mining and counter-
mining ; torpedo fighting of a very bad kind. He chafed in spirit
that he was returned to power only by the accidental death of his
grand, faultless, adversary ; and they were vexed that their whole
ranks contained not another man capable of openly meeting Le
Verrier. He , dominating at the Parisian Centre, obtained from the
Minister (who was now frightened to interfere with him) power to
revise and curtail as he chose almost all the other scientific Obser-
vatories of the country ; and their Directors were furious, that when
France was, as then, a Bepublic, they, the scientist portion thereof,
should have to live under the sway of a more than Emperor, a Czar )

499

of Edinburgh, Session 1877-78.

of one, moreover, wlio, while indulging himself in extending his
Observatory even by profuse public expenditure, — sought to gain a
character before the country for economy, by starving, or even
abolishing, their’s.

If too, the claims of some of those other astronomers to patriotic
recognition and govermental regard were occasionally too great to be
altogether and immediately overborne even by Le Yerrier, — he
undermined, and laid plans which must eventually lead to their
collapse and removal. Thus, was there a new Observatory lately
established in the south of Paris, where the Savant, who had car-
ried on the Meteorological bulletins during the German war, should
in future devote himself to a new kind of utilitarian meteorology
for the special benefit of agriculture and the service of the public
health ; — or was there another new Observatory allowed to be built
in the north of Paris at Meudon, near Montmartre, for the Savant
who so nobly risked life and limb by sailing forth in a balloon over
the heads of the truculent Germans then besieging Paris, — in order
that France, even in her agony for very existence, should still be
present among the nations at the observation of a total Solar Eclipse
on the Northern coast of Africa, — and where, in that new Observa-
tory, that patriot and fearless astronomer should, with no other con-
trol over him than the Minister of the Interior, seek to carry out his
own very original inquiries into the Physics of Astronomy, — -then
Le Yerrier insisted on having additions of new instruments and
young subaltern observers added to his own Observatory, to accom-
plish the very same ends, but on a far grander scale. Or was there a
new reflecting Equatorial ordered for the Observatory of Toulouse,
— whereto M. Delaunay, in his short but brilliant career, had sent
a young astronomer, of genius after his own heart, as Director, — Le
Yerrier did not actually interfere with its going there, but imme-
diately ordered, at his country’s expense, for his own Observatory,
a similar reflecting telescope, one-half larger, and with all the
economical fittings of the other in modest wood, replaced in his own
with ne-plus-ultra work in fine metals.

And then his mere manner was sometimes so intentionally pro-
voking.

When President Marshal Macmahon, — striving to entertain nation-
ally, and mentally impress the Shah of Persia, then on his gorgeous

500 Proceedings of the Royal Society

visit to Paris, — applied to Le Yerrier to arrange for a recep-
tion of the Eastern potentate and his bejewelled and glittering suite
at the grandly restored Observatoire, he only received the follow-
ing short note from the State’s chief paid Astronomer : —

Marechal, — La Science, n’illumine pas, les sauvages.

Le Yerrier.

Even in ordinary conversation it was almost terrible to see how
the old-man-misanthrope, in merely describing the course of an
argument with another scientist, could egregiously clench his fist
and act to the very life as though delivering a regular knock-down
blow right between the eyes. Or when the other’s equations were
faultless, and no other complaint could he found, he would be stig-
matised in society as “ that man with the big ugly mouth.”

All this would soon have become unbearable, but that it was
accompanied by two things, even three, which induced wise men to
be exceptionally tolerant.

First, for instance, they knew that there was still a truly heroic
spirit in that querulous disposition and decrepit frame. When all
the rest of educated society in Paris was utterly frightened at the
sudden rise of the Red Republic, and sought only to strike their
colours, and disappear by putting on the aspect of being more
canaille than the Red men themselves, — Le Yerrier stood out firm
in his appreciation of hereditary order, historic experience, accumu-
lated wisdom, and preservative rule. Red-republicans indeed claim
to be equal to, and on the same level with, him ! Let any Red-
republican of them all essay on the grandest test of man’s intel-
lectuality, to tread with him, if they could, the mathematical founda-
tions of the stability of the Solar system ! And they couldn’t: —
so were they to inscribe their wretched shibboleth of “ Liberte,
Egalite, Fraternite” over his door? No ! he would have none of
that sort of thing. And hence, when visitors from distant parts of
the world, even from the very antipodes, came to pay their homage
to the first physical Astronomer of France, and had been disgusted
on passing through Paris, to see its grandest public buildings, and
even the most sacred of its churches, scribbled all over, in fright, to
pacify the Red men, with those three most falsifying, misleading
words of their political creed and pretences,— such visitors read over

of Edinburgh, Session 1877-78. 501

the portal of the palace wherein Le Verrier resided, only this one
word — £i Observatoire.”

Second, within that respected building, in its private dwelling
portion, there reigned the gentle radiance, and mild dignity of
Madame Le Yerrier.

In those early days of the now passed away French Emperor,
when lie made no mistakes, and had to pay his visit of state to
London during the Crimean war, he not only took the Empress
Eug&nie with him ; but, while M. Le Yerrier was one of his suite,
Madame Le Yerrier was one of the ladies of honour in waiting on
the Empress. One of the most mentally distinguished of them too ;
for, after the grandest West-end reception on that occasion, this
saying worthily ran through the £lite of London society, “ Other
ladies present were expensively dressed, but Madame Le Yerrier
was well dressed.” And if there is any grim philosopher who
doubts whether there is much in that, let him refer to the printed
discussions on this very matter which took place at the Social Science
Association’s brilliant meeting at Aberdeen only two months ago.

But M. Le Yerrier himself, amid all his wielding the forces of
science, could appreciate the beautiful in art, and even assist at the
development of some of its forms ; for he fed his soul on music.
But it was with a change, as his career progressed. When he visited
England first, in 1847, and was asked to write something
in a lady’s album at Oxford, and not only composed a chanson then
and there, but set it to original music, took a ruler, ruled the ortho-
dox number of lines, and then wrote therein the musical notes with
the precision of a copper-plate engraving, — the whole thing had
the pleasant aspect of spring flowers ; primroses and cowslips,
daisies and buttercups in the opening months of the year. But.
when, as he felt impelled occasionally to do, in the long after
years of 1875 or 1876, he armed himself with his violin and pro-
ceeded to draw therefrom, as it seemed almost in spite of itself, the
most agonizingly beautiful strains, thrilling tones of dying grace, —
tones which a Paganini might have envied, and ordinary men almost
have wept that they could do nothing of the kind, — it reminded
one more of the dark autumn’s one, last, grand, garden flower, the
Tiger-lily, bowing over its prospective grave in the earth beneath.

Lastly, in still further mitigation of much of Le Yerrier’s manner

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during the final years of his official career and life itself, — all good
men were aware that his indefatigable, most original, and innate,
unapproachable genius was again toilsomely engaged on the grand,
self-imposed task of his life ; and was even then rapidly and mag-
nificently preparing as full mathematical theories and accurate
practically-computing numerical tables of the larger, outer planets
of the Solar System, as he had already done for the smaller,
inner members thereof. His analytical methods too were the
most comprehensive that had ever been attempted ; and were
specially distinguished by their capacity to take in and utilise all
good observations ever made in practical astronomy on the bodies
concerned, through all time, whether ancient or modern. The
work was immense, and it killed him in the end, though not before
he had satisfactorily finished it, even to the last page.

He had even the peculiar satisfaction before his death of seeing
his most difficult researches, almost in mathematical darkness, as to
the mass of the planet Mars— up to that time supposed by all the
world to be “ moonless Mars” — suddenly lighted up and confirmed
by the splendid and most unexpected American discovery of this
last summer, with their latest erected and largest equatorial telescope
at Washington, of two moons circulating around that planet, and
at rates of motion which admirably bore out his, Le Yerrier’s,
intellectually concluded number for its mass and consequent power
of gravitational attraction. But so truly immense, as well as
idtra difficult, was the whole planetary research, that not only
(as has been well said elsewhere) would it have been considered
mpossible for one man to have achieved the whole, if Le Yerrier
had not performed it in our own times, — but, only one man has
been found fully able even to describe the w’ork to others ; and that
one man is, — who 1

Le Yerrier’s early, unconscious, but unexceptionable, and equally
successful rival, in his greatest astronomical calculation, prediction,
and discovery, with regard to the once unknown planet, which
we all now so glibly call Neptune, — viz., the then young J. C.
Adams, of St John’s College, Cambridge.

Professor Adams has indeed not only described, in a late Presi-
dential address to the Koyal Astronomical Society of London, Le
Yerrier’s life long problems of the planetary orbits, — with an

of Edinburgh , Session 1877-78.

503

ability, clearness, and method which leave nothing to be desired for
scientific instruction’s sake, — but he has thrown into the execution
of his task such a plenitude of impartiality, such generosity of
feeling and goodness of heart, that his account has been enthusiasti-
cally reproduced in Paris, within the last few weeks, under the title
of “ The genius of Le Yerrier appreciated in England.”

Such then, so far as this imperfect account can go, was Urbain,
Jean , Joseph , Le Yerrier. That grand existency, who was lost
to the ranks of the Honorary Members of this Society, on the
23d of last September ; when his spirit returned to God who
gave it.

In recording the lamented decease of the Hon. Lord Heaves, we
have to record almost the greatest loss which the “ Literary class ”
of the Royal Society of Edinburgh could have sustained. When
this sad emit was announced in December of -last year, a universal
note of lamentation was raised throughout the city. It was felt
that a great figure had been taken away from our ranks ; that we
had lost not only a learned and weighty Judge, but an accomplished
scholar, a distinguished man of letters, a wit and a conversationist
who contributed salt to all social gatherings, a racy Scottish char-
acter, and “ one of the last links which connected the Edinburgh
of to-day with the greater Edinburgh of the past.” But the loss
which the Royal Society has sustained in Lord Heaves is special
and peculiar, for he was rarely qualified for a literary Fellow of
this Society, and as such he bravely played his part and contributed
his share to our Proceedings, and he has left very few behind who can
be at all compared with him. Lord Heaves possessed not only great in-
tellectual activity and a predilection for scientific research, especially
into questions of philology, but he was^also largely endowed with
that quality which has been, on a former occasion, referred to as
necessary for the maintenance of vitality in a Society like this —
the quality of “ intellectual sociability.” He loved to communicate
with others, to tell and to hear, upon topics of literature and science.
We can all call to mind his genial manner, when presiding at
meetings of the Royal Society, and the dry humour with which his
scholarlike papers were interspersed. An exhibition of the same
manner at one of the meetings of the Social Science Congress

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caused the late Sir John Bowring to give Lord Neaves the nick-
name of “ Wit and Wisdom.”

Lord Neaves, who was of Forfarshire extraction, was born in
Edinburgh in the year 1800. He was educated at the Edinburgh
High School, where he exhibited precocious scholarship, marked
intellectual tastes, and that quick, capacious, and retentive memory,
“ wax to receive and marble to retain,” by which he was dis-
tinguished to the very end of his life. He was dux of the High
School in 1814 ; and then passed through the Edinburgh Univer-
sity with distinction, though it does not appear that he graduated
— graduation not being the custom in those days. In 1822 he
was called to the bar, which then included among its numbers a
brilliant band of wits and scholars ; — the walls of Parliament House
then resounded with the talk and the laughter of Lockhart, Pro-
fessor Wilson, Professor Cheape, Sir William Hamilton, George
Moir, Patrick Fraser Tytler, and Patrick Robertson : while among
the older generation on the Bench were Cranstoun, Jeffrey,
Murray, and Cockburn. Of the spirit of those times Lord
Neaves was the last representative. In 1841 he was made Advo-
cate-Depute in 1845, Sheriff of Orkney ; in 1852, Solicitor
General; in 1853, on the death of Lord Cockburn, he was ap-
pointed a Judge in the Court of Session; and in 1858 he became a
Lord of Justiciary. The verdict of Lord leaves’ professional
brethren upon his legal qualifications appears to be that he was a
great “ case lawyer ” — his vast and accurate memory giving him
peculiar facilities in referring to precedents, and that he was highly
distinguished as a criminal Judge.

Side by side with the faithful discharge of his professional duties,
Lord leaves always maintained the part of the man of letters.
From the year 1830 onwards he was a constant contributor, both
of prose and verse, to “Blackwood’s Magazine.” He was the
author of a series of articles, in that periodical, on Grimm’s
“ Teutonic Grammar ” and Grimm’s “ Philological Magazine,”
which excited much interest at the time, and the republication of
which has often been urged. But his most lasting literary pro-
duction will probably be his volume of “ Songs and Verses, social
and scientific, by an old contributor to ‘ Maga,’ ” which was first
published in 1868. The motto of this volume might be “ Riden-

of Edinburgh, Session 1877-78.

505

tem dicere verum, Quid vetat ? ” In it playful and kindly satire
appears in its best form, directed against the exaggerations, false
sentiments, or fallacies of the day. And the songs themselves are
so well written and so full of sparkling life that they may well
continue to please many a future generation. His last published
work was the “ Greek Anthology for English Headers,” and the
preparation of this was with him indeed a labour of love. In it he
was able to combine his scholarlike fondness for classical antiquity
with his taste for the witty and the epigrammatic, and it afforded
him infinite pleasure to labour at reproducing in the most terse and
elegant English form the best flowers out of that garden of happy
conceits and concinnities bequeathed to us by the Grecian muse.
This work, though undertaken very late in life, was highly success-
ful ; the renderings were spirited, and they were accompanied with
annotations, in which was much curious learning, very creditable to
one with whom scholarship was not a business but a recreation.

Lord Heaves became a Fellow of the Eoyal Society of Edinburgh
in 1856. In 1859 he delivered the opening Address of the Session,
with a biographical notice of the venerable Principal Lee. Ten
years later he gave another opening Address for the Session 1869-70.
In the same session he read a paper on the “ Primitive Affinity
between the Classical and Low German Languages.” In this paper
he argued that the affinities between old English and Latin must
have arisen from prehistoric identity or connection, and he pointed
out certain limitations to which Grimm’s law of affinities must
be subjected. In 1871 he read a communication “On the Penta-
tonic and other Scales employed in Scottish Music,” when airs
illustrating his views were played by Mr Bridgman. In 1872 he
read a paper on “ Some Helps to the Study of Scoto-Celtic
Philology,” in which he pointed out the disguises which words
belonging to the Aryan family of languages assume in passing into
Gaelic, and showed the laws regulating those changes. Among
other points of interest, the paper contained a discussion upon so
and da, the Gaelic representatives of the Sanskrit prefixes su and
du, which appear in Greek as cv and Svs — “ well ” and “ ill.”

In 1874 Lord Heaves furnished biographical notices of Lord
Colonsay, Professor Cosmo Innes, and Mr Francis Deas ; and in
1875 he read a paper “On some remarkable changes, additions,

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and omissions of letters in certain cognate European words.”
This paper dealt in a most interesting manner with the transfor-
mations of words, and showed the identity between many pairs of
words in cognate languages, where the words themselves had grown
to be widely dissimilar.

In this place we may surely say, “ Quis desiderio sit pudor aut
modus Tam cari capitis?” What he brought to us here from time
to time was part of the stores which he was for ever gathering in
his library, where during all leisure hours he would sit, with heaps
of volumes about him, plunged and absorbed in books. In his
house many of us have enjoyed his genial hospitality, where, sur-
rounded by a bright and intellectual family, he was himself “ a
central warmth diffusing bliss,” ever gay and radiant, a downright
opponent indeed of all shams and false pretences, but yet with a
large-hearted charity for all. Beneath a laughing exterior Lord
leaves concealed steadfast internal principles ; the writer of this
paper remembers the “ sseva indignatio ” with which, on one
occasion, he turned upon a foreign gentleman who had uttered a
flippant and infidel remark. In all the relations of life he was
blameless, and by his example he has shown that it is possible to
combine piety, learning, wisdom, and hard and successful work
with kindliness, brightness, laughter and joy.

By the death of Mr Andrew Coventry, this Society, of which he
had been for more than thirty-four years a Eellow, has lost one of the
most amiable and accomplished of its members. Both Mr Coventry’s
father and his grandfather were men of mark. His grandfather was
a Congregationalist minister of some eminence near Kelso; his father
was the first Professor of Agriculture in the University of Edinburgh,
and is spoken of in terms of admiration in the letters of Kiebuhr,
the great German scholar and historian, who at the beginning of
this century was attending classes here. Mr Andrew Coventry was
educated at the High School of Edinburgh, of which, when he left
it, he was “ second dux.” He went through a course of study at the
University, and seems to have paid particular attention to chemistry.
In 1823 he was called to the bar, at which he made a good start,
and was apparently rising, when, in 1840, he succeeded to the fortune
of his uncle General Cuninghame, and relinquished professional

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pursuits. From this time forward he led the life of a dilettante , in
the best sense of the word, for he really delighted both in science
and in the fine arts, and exhibited no mean information in both
these provinces. The first product of Mr Coventry’s leisure, which
has been preserved, consists in “ A Letter to the Landed Interest of
Scotland,” advocating “ the merits of the Association for employing
an agricultural chemist.” This pamphlet, which appeared in 1843,
went through two editions. Mr Coventry travelled yearly on the
Continent, taking great interest both in scenery and works of art ;
he collected, to a certain extent, both books and pictures, and in
1851 he had the good fortune to purchase in Westmoreland a very
beautiful marble bust, which proved to be a genuine antique, and
was pronounced by Mr Burgon of the British Museum to be the
bust of Antonia Augusta, daughter of Mark Antony and Octavia,
and mother of Germanicus and of Claudius. On this discovery
Mr Coventry read a paper in 1852, being his first contribution to
this Society. It may be mentioned that the bust itself is now the
property of his nephew, Colonel Crighton. In 1854 he published
anonymously a little treatise entitled “The Certainty of Christianity,”
which he maintained chiefly on historical grounds. In 1856 he
delivered the “Ulbster Hall Lecture,” on “ Some of the most curious
Inventions and Discoveries of Decent Times.” This lecture gave
evidence of very extensive reading and great fulness of knowledge
as to the results of science, and the facts which it contained were
set forth in a lively and striking manner. In 1857 Mr Coventry
delivered the annual address to the students of the School of Design
under the Board of Manufactures, and in so doing displayed the
feeling and taste of a connoisseur. He always took a great interest
in the Association for the Promotion of the Fine Arts ; he was for
many years a member of their managing committee, and more than
once presided at their annual meeting. In later life, becoming a
director of the Commercial Bank of Scotland, he began to devote
himself to questions of finance, and in 1870 he read before us his
second paper, which was entitled “A Method for Economizing our
Currency.” The idea was, that by demonetizing the sovereign and
substituting for it notes, which should represent gold hoarded in the
cellars of the Bank of England, a considerable saving might be
effected in the wear and tear of gold. This idea, though ingeniously

508 Proceedings of the Royal Society

advocated, can hardly be said to have recommended itself to practical
financiers. Of late, for many months before his death, Mr Coventry
suffered from a painful and excruciating disorder, which he bore
with manly fortitude and pious resignation. To the end he continued
to solace himself as far as possible with his old pursuits. He was
one of those who take a pride in always having read and being able
to talk about the last new book. His conversation was always genial
and interesting, and his loss has been felt in many circles, as it
must also be in the Royal Society.

The next name in the obituary for this year is that of Sir David
Dundas, Baronet, a gentleman of that class who, without what has
been called a “ professional” acquaintance with science, art, or
literature, are still acceptable members of a Society like this, if
they show (as they must do by applying for admission) a sympathy
for and interest in our pursuits. By their admission to be Fellows,
a mutual compliment is at all events implied. Sir David Dundas
was born in 1803. He was admitted an advocate at the Scottish
bar in 1824, but never practised. He was a Deputy-Lieutenant for
Perthshire, and lived the life of an active country gentleman, chiefly
engaged in managing and improving his beautiful estate of Dunira.
And he was respected by those who knew him as a most kind and
honourable man.

By the death of Mr John Lothrop Motley the Society has lost
one of the most celebrated of its Honorary Fellows.

Mr Motley was born at Dorchester, Massachusetts, on the 15 th of
April 1814. He was educated at Harvard Unversity, where he
graduated in 1831, at a very early age; after which he spent two
years in Germany, residing successively in Gottingen and Berlin, and
some additional time in travel in Italy and other parts of Southern
Europe. On his return to America, he studied for the profession of
the law ; but, though he was called to the bar in 1837, he does not
seem to have sought for practice. He had resolved rather that
literature was his vocation. In 1839, at the age of five and twenty,
he published a novel, called “ Morton’s Hope, or the Memoirs of a
Provincial,” which had little or no success, and is remembered now
but slightly. In 1840 he was appointed Secretary to the American

of Edinburgh , Session 1877-78.

509

Embassy in Russia; but, after having been for some time in St
Petersburg, he resigned the appointment. Thenceforward, for nearly
ten years, American biographical authorities represent him as living
privately at home, engaged in miscellaneous studies and contributing
miscellaneously to American periodicals. A second novel, which he
published in 1849, under the title of “ Merry Mount, a Romance of
the Massachusetts Colony,” had no better fortune than the first.
Meanwhile he had been finding his true vein. The passion for
history, apparent in the title and conception of this novel, had
been manifesting itself more seriously and effectively in occasional
historical essays. A review of Tocqueville’s work on American
Democracy and a paper on Peter the Great of Russia are mentioned
as having attracted especial notice. By this time, indeed, it had
became known among Mr Motley’s friends that he had fastened on
a great subject for elaborate historical treatment by himself. No
one had adequately written the History of the Dutch People and
their Commonwealth; there were affinities and attractions recom-
mending this subject in a peculiar manner to an American of the
United States ; Mr Motley had been meditating these, and had
determined to make the subject his own. To qualify himself by the
necessary researches, he came to Europe again in 1850, and lived
for several years at the Hague, and in Dresden and Berlin, im-
mersed in documents. The result was the appearance, in 1856,
when Mr Motley was forty-two years of age, of his “ Rise of the
Dutch Republic : A History,” in three volumes. The work, published
simultaneously in London and New York, was eagerly hailed by
readers and reviewers on both sides of the Atlantic ; translations of
it into several European languages were at once begun ; and the
author at once took his place among the most eminent writers of his
generation. Undisturbed by applauses and honours, Mr Motley
persevered in his task. The volumes he had published, extending
from the accession of Philip II. of Spain in 1555 to the death of
William the Silent in 1584, had told only the story of the heroic
revolt of the Dutch from the Spanish tyranny and of the triumphant
foundation and beginnings of their little Republic of the Seven
United Provinces. But, in 1860, there appeared the first two
volumes, and in 1867, the last two, of what was virtually a sequel
in four volumes, though it bore the independent title of “ History of

510 Proceedings of the Royal Society

the United Netherlands from the Death of William the Silent to the
Twelve Years’ Truce, 1609.” If of less riveting interest than the
former work, these volumes were welcomed as of high historical
value, and fully sustained the author’s reputation. At the date of
the publication of the first two volumes, and also at that of the
publication of the last two, he was domiciled in London, — whence
his two prefaces are dated ; but, through nearly six of the inter-
mediate years, he had been ambassador for the United States at the
Court of Vienna, having been appointed to that important post in
November 1861, and removed from it in 1867. On the accession of
General Grant to the American presidency in 1869, Mr Motley was
again in request for diplomatic service, and was made American
minister in London. In consequence of some differences between
him and the American Secretary of State, he retained the office only
till November 1870. The rest of his life, which was passed mainly
in England, though with visits to Holland, was devoted entirely to
literary labour. In 187 4, under the title of “ The Life and Death of
John of Barneveld, Advocate of Holland, with a View of the
Primary Causes and Movements of the Thirty Years’ War,” he added
two volumes more of Dutch history to his former seven, and brought
his narrative down to the year 1623, when the farther fate of his
beloved Dutch had became involved in the vast struggle between
the opposed forces of Protestantism and Roman Catholic Absolutism
all over Europe. It had been his intention to overtake this vast
struggle too, and, in the form of an express history of the Thirty
Years’ War, to bring the Dutch safely through that great European
entanglement, on to the Treaty of Westphalia in 1648, when, in the
general pacification and winding up, the independence of the United
Provinces was at last formally declared and guaranteed. This
portion of his projected work he did not live to accomplish. He
died, in an English country-house, on the 29th of May in the
present year, at the age of sixty- three. Friendships and family con-
nections, as well as tastes, had attached him much to England in his
later years.

Mr Motley was a man of fine and stately presence, and of gravely
courteous manners. Of his private life, as well as of his services as
an American public man and diplomatist, accounts will probably be
forthcoming in time. For the world at large, he lives, and will

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live, as the historian of the Dutch Bepublic. It was his distinction
to have seized the great subject in the prime of his manhood, to
have clung to it tenaciously through five and twenty years, and to
have laboured assiduously all that while among archives and original
authorities for the attainment of the adequate knowledge. It was
no less his distinction to have infused into his treatment of the
subject the glow and energy of his own personal convictions, the
passionate and eloquent expression of his sympathies with the men
and the principles that he believed to be in the right, and his
detestation of those that he believed to be in the wrong, on a noted
theatre of human action eight or ten generations ago. So far as
there are differences of critical opinion about his writings, they
chiefly depend indeed on the views that may be taken as to the
limits of a historian’s right to interweave his own moral and poli-
tical approbations and censures with his narratives of the past. M.
Guizot, who was an admirer of Mr Motley, thought that he went
beyond bounds in this respect, and that his “ alternations of extreme
aversion and strong predilection ” were irritating. The criticism has
been repeated in England since Mr Motley’s death. He had pro-
bably his own theory on the matter, and could have defended it
well. It seems to have been an axiom with him that a historian,
of competent knowledge and power of imagination, may trust him-
self to feel as accurately about the persons and transactions of three
hundred years back as about those immediately around him, inas-
much as there are certain principles and tendencies of things that
ought to be dear to all humanity, while their opposites are into-
lerable,— inasmuch as everywhere and in all times a Philip II. and
all his belongings must be execrable, while a William of Orange or
a Barneveld is to be honoured and revered. By acting on this view
of a historian’s duty, Mr Motley certainly increased the effect and
popularity of his writings, and it does not appear that he subtracted
from their permanent worth.

Shortly after the appearance of his first historical work, Mr Motley
was elected a corresponding member of the Institute of France. He
was also D.C.L. of Oxford, and LL.D. of Cambridge, Leyden, Harvard,
and other Universities, Continental and American. He was elected
an Honorary Fellow of the Boyal Society of Edinburgh on the 1st
of March 1875. We have lost him after a too biief connection.

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The Society has this year to deplore the loss of one of the most
eminent of its Honorary Members in the death of Mr Talbot. It
is very rare indeed to find a man who attains to anything beyond
mediocrity in more than one or two departments of knowledge. Mr
Talbot is a remarkable exception to the general rule. Seldom has
the world seen so many-sided a man. He attained to distinction in
pure mathematics, in physics, in chemistry, in astronomy, in archae-
ology, and in literature; nor is his name altogether absent from the
records of botanical research. After studying at Harrow, Mr Talbot
graduated in Cambridge in 1821 ; and although his name appears
on the honour list in mathematics, it does not occupy so high a
position as his subsequent career would have warranted us in ex-
pecting. In fact, his early promise was eminence in classical litera-
ture, especially in Greek. As an undergraduate he obtained the
Porson prize for translation into Greek verse of a selected passage
from an English dramatic poet. This was followed at his gradua-
tion by his obtaining one of the two Chancellor’s medals, awarded
“ to the graduates who show themselves the greatest proficients in
classical learning.” Linguistic studies, though he never abandoned
them, had not that prominence in his after life which might have
been expected from this beginning. The year after taking his
degree we find him contributing to “Gergonne’s Annales” a paper
on a mathematical subject, which was followed up by others in the
same serial ; and from that time, for upwards of fifty years, there
emanated from him an uninterrupted stream of original papers on
mathematics, physics, astronomy, chemistry, and archaeology, as
valuable as they were varied. To take even a hasty glance at his
most important researches would vastly exceed the limits of this
necessarily brief sketch. We must not, however, pass by without
a few words his great discovery in photography. So early as 1826
he had turned his attention to the chemical action of light. The
results were communicated to the “ Edinburgh Journal of Science ”
and other periodicals. In 1833, when sketching on the shores of
Lake Como, he availed himself of the camera lucida , and it oc-
curred to him that images might be fixed on the paper by chemical
action. The idea was not altogether novel, but it had not as yet
led to any definite result. On Mr Talbot’s return to England, he
commenced a series of experiments on the decomposition of nitrate

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of silver by light, which he continued for many years. In 1835 he
had reached the length of producing images on paper by the camera
obscura ; but being anxious to perfect his discovery, he contented
himself with issuing brief notices of the results in the “ Philoso-
phical Magazine ” and the newspapers. It was not until the 31st
of January 1839 that he communicated to the Royal Society the
first of the papers on a process which will always be associated with
his name. The paper is entitled “ Some Account of the Art of
Photogenic Drawing, &c.” This paper was followed up, three
weeks later, by a memoir, describing the process for preparing the
paper, fixing the image, &c. The following year saw Mr Talbot’s
crowning discovery — that which virtually established the art as it
now exists — the development of an invisible image.

Daguerre in France had been at work at the same subject, using
metal instead of paper, and his discoveries were given to the world
almost simultaneously with those of Mr Talbot, It is not necessary
here to refer to the subsequent history of calotype. It was beautiful
at its very birth, and its beauty was recognised nowhere more fully
than in Scotland. Many members of the Society will remember how,
soon after the discovery was made known, the process was employed
by Dr Adamson and Mr D. 0. Hill to the production of life-like
portraits in a style which has never been excelled. The simultaneous
inventions of the daguerreotype and the calotype naturally created
jealousies on both sides the Channel. Mr Talbot found a warm
and able advocate in Sir David Brewster. These controversies may
now be consigned to oblivion. If the French did injustice to Mr
Talbot in the early days of photography, they made amends at a
later period. At the Paris Exhibition of 1867, the Commissioners
awarded him the great gold medal for his contributions to photo-
graphy, although he was not an exhibitor.

It must not be inferred from the prominence given to Mr Talbot’s
connection with photography, that his other contributions to
literature and science were unimportant. It is far otherwise. In
the most recent large treatise on the differential and integral calculus,
that of M. Bertrand, the reader will find the name of Mr Talbot
associated with those of James Bernoulli, Fagnani, and Chasles.
Mr Talbot was one of the early promoters of the Society of
Biblical Archaeology, and contributed largely to their Transactions.
Some thirty years ago, Mr Talbot, Sir Henry Rawlinson, Dr Hinks,

514 Proceedings of the Royal Society

and M. Appert agreed to decipher independently certain cuneiform
inscriptions brought from Nineveh, and to compare the results. The
comparison showed a general harmony amongst the four interpreta-
tions, hut by no means an identity. Mr Talbot’s genius was too
original and of too high an order to fail of recognition. The Eoyal
Society of London conferred on him both their Eoyal and their
Eumford medal. It also assigned to him the Bakerian Lecture for
1856, the subject being “Further observations on the optical
phenomena of crystals.” Mr Talbot’s contributions to our own
Transactions consist for the most part of historical sketches or short
papers on subjects lying on the borders of his early investigations ;
such are the papers on “Fermat’s Theorem,” on “Fagnani’s Theorem,”
<fec. Perhaps an exception to this remark may be found in the paper
“ On a new mode of observing certain spectra,” based on experiments
made in Professor Tait’s laboratory. In his brief note on “Ano-
malous Spectra” he shows that he long ago anticipated the wonderful
discovery of Le Eoux and Christiansen, but was prevented from pub-
lishing his observations by the advice of Sir D. Brewster. In private
life Mr Talbot was shy and reserved to strangers, but a lively and ani-
mated talker when in the congenial society of old friends, such as Sir
David Brewster, and indeed of some younger men whom he honoured
with his friendship. He sat for two years in the first Eeformed
Parliament. Of this he was reminded by Lord Palmerston, when in
1863 the University of Edinburgh conferred on these two men,
so very unlike each other, the honorary degree of LL.D. Many
honours from foreign societies were conferred on Mr Talbot, but it is
not easy to record them, from the fact that, with the accustomed
modesty of true genius, he shunned to display them.

He died September 17, 1877, in his 78th year.

Dr James Bryce was born at Killaig, near Coleraine, in the
north of Ireland, on October 22, 1806. He was the third son of
a Scottish Presbyterian minister, who had settled there three years
before, and obtained the earlier part of his education from his
parents, who were both, in somewhat different ways, persons of re-
markable intellectual gifts and cultivation. At the age of fourteen he
was sent to the University of Glasgow, where his father and his eldest
brother had been before him, and where he graduated M.A., receiv-
ing from it in after life the honorary degree of LL.D. There he

o f Edinburgh , Session 1877-78,

515

threw himself, with characteristic ardour, into the studies of the
classes, winning, among other distinctions, the Greek Blackstone
prize, which was then, and appears to he still considered, the most
considerable honour awarded in the linguistic classes. Although
he had been from childhood fond of nature and all natural objects,
the bent of his mind towards science did not definitely express
itself till he accepted, at the age of twenty, the post of head of the
mathematical department in the Belfast Academy, then one of the
chief foundation schools in Ireland, and of which his eldest
brother, the Bev. Dr Bryce of Belfast (who is still living) was then
Principal. Finding the teaching of geography to belong to his
department, he at once saw what hardly any one had then seen,
how important a branch of that subject physical geography
constitutes, and perceived that to deal adequately with it a know-
ledge of geology and mineralogy was necessary. From these he was
led on to zoology and botany, and not only threw himself into these
topics himself with • characteristic ardour, but formed large classes
for their study, which were attended as well by his own pupils as
by other young people in the town. At the same time he had
begun to connect the teaching of natural philosophy with that of
mathematics, explaining and illustrating by experiments the lead-
ing principles of mechanics, pneumatics, hydrostatics, electricity,
chemistry, and other cognate branches of inquiry. We have
listened to so many discussions during the last few years respecting
the necessity of giving to natural science a regular and important
place in schools and colleges, and now see so much actually done to
effect that object, that it is hard to realize the state of opinion and
practice in these matters fifty years ago, when such educational
reforms were unheard of, and little beyond Latin and Greek was
taught in all the best schools of the United Kingdom. It needed a
very warm love for science, and a very elevated view of the func-
tions of education, to lead a young man in those days to introduce, on
his own idea, so great a change in the established method of instruc-
tion. An able teacher perpetuates himself through his disciples,
and many eminent scientific workers trace back to Dr Bryce the
first impulse towards, the first guidance in, the study of nature
which they received. His services in promoting, by example and
by argument, both in Belfast and afterwards in Glasgow, the intro-

f> 1 0 Proceedings of the Royal Society

duction of these subjects into a school course can hardly be over-
estimated. While inspiring others with his own tastes, he had also
begun to do valuable scientific work on his own account, partly in
botany and mineralogy, but chiefly in geology. He investigated
and described certain interesting fossil plant beds (similar to the
leaf beds of Mull) occurring on the shores of Lough Neagh, and con-
tributed to the ‘‘Philosophical Magazine ” an account of the important
discovery which he had made of the remains of the Plesiosaurus in
the lias of Antrim, which conclusively established its identity with
the lias series of England. Pursuing his researches into the geology
of the northern counties of Ireland, he was the first accurately to
examine and describe the structure of the remarkable basaltic
formations on the coasts, and particularly of the Giant’s Causeway.
A series of papers contributed to the Journals of the Geological
Societies of London and Dublin, of which he had become a Eellow
in 1834, attest his activity in observation; while in Belfast itself he
was one of the most active members of a local scientific society,
which numbered many men of eminence among its members, and
exerted a powerful influence on the culture of the town, now the
most prosperous in Ireland.

He removed in 1846 to Glasgow, on being appointed head of the
mathematical and geographical department in the High School of
that city. Here, in a larger field, he continued the same enlightened
system of science teaching which he had started in Belfast. He
joined the Philosophical Society, was soon placed on its Council,
and was for three years its president, delivering in that capacity
addresses in which he reviewed the progress of scientific inquiry, and
discussed some of the main problems now lying before it with a
completeness and accuracy which supplies remarkable evidence of
the width of his cultivation, as well as the keenness of his observing
and reflective powers. There was scarcely a department of science
of whose leading principles and method he did not show himself
master, a remarkable achievement in an age when every study has
become so much sub-divided. His geological work during this
period lay chiefly but not exclusively in the Clyde basin and its
surrounding mountain groups. Papers on the “ Parallel Roads of
Lochaber ” and the “ Glacial Phenomena of the Lake District of
the North of England ” were followed by a systematic treatise on

517

of Edinburgh, Session 1877-78.

“ The Geology and other Natural Phenomena of Arran,” which has
reached a fourth edition, and constitutes the most complete and
satisfactory account of that interesting island.

Latterly he had devoted himself chiefly to the geology of the
North-West Highlands — first to that of Skye and Raasay, after-
wards to the determination of the age of those rocks in Ross and
Sutherland which have excited so much discussion among our
leading geologists. In several expeditions he had visited and
examined the sandstones of Loch Torridon and the remarkable
limestones of Assynt and Durness. It was while on his way north-
ward to complete these investigations that he met, at Inverfarigaig,
on the shores of Loch Ness, with the accident which closed his life,
by the fall of a pile of loose rocks which he was trying with his
hammer.

He was then (July 11, 1877) seventy-one years of age, but still
in full strength of body and mind, with his interests in science
unabated. He had come in 1874, on resigning his post at Glasgow,
to live among us in Edinburgh, had been elected to this Society, and
seemed likely to prove one of its most zealous and useful members,
when he fell by a heroic death in the service of the science to
which his energies and talents had been so long consecrated.

As an observer Dr Bryce was unwearied and careful, as a
describer and lecturer eminently lucid and graphic. He had also
the gift of being able to communicate to others his own enthusiasm,
and it was in great measure this, joined to a warm and genial
manner, that made him so successful as a teacher. His love for
nature and her beauties rose to a passion rare even among men of
science ; a ramble among woods and mountains was always to him a
pleasure far more intense than any which ambition could promise or
wealth purchase. His intellect was indeed an imaginative one, as
appeared both in the vivid descriptions of scenery which occur here
and there in his scientific papers, and in liis own love for poetry and
the dramatic aspects of history, branches of literature to which he
had been devoted from boyhood.

Although it is as a man of science that he was chiefly known, Dr
Bryce took an active part in current questions, especially those
relating to education. He was one of the first — perhaps the very
first — in Scotland to insist on the necessity for a reform in the con-

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Proceedings of the Royal Society

stitution of the Scottish Universities, and on the recognition of the
right of the graduates to a share in their government, and he
organised the first association formed for that purpose. He held
strongly that the educational system of Scotland ought to preserve
its distinctive character, instead of being administered from London
and assimilated to that of England. Among minor reforms which
he advocated was that of the introduction of a decimal system of
coinage, weights, and measures, on which he wrote a short hut
weighty treatise.

Besides the geological writings already mentioned, he was the
author of several educational hooks, such as treatises on algebra,
geometry, and the elements of astronomy, and a cyclopaedia of geo-
graphy. Most of these have gone through several editions.

It only remains to add that Dr Bryce’s gifts as a scientific writer
and teacher were not more remarkable than the simplicity and charm
of his character. He retained into old age not only the fire and
freshness of youth, but a perfect sweetness of temper, and an
ungrudging readiness to plate his time and knowledge at the service
of others, which advancing years seldom spare.

His memory as that of one of the most lovable of men will be
long cherished by hundreds of former pupils, with many of whom,
scattered through India and the Colonies, he kept up intimate rela
tions, and by the large circle - of scientific friends whom he was
accustomed to meet year after year at the meetings of the British
Association and of our own learned societies.

The Bev. David Thomas Her Drummond, descended from a
very old Highland family of that name, was the youngest son of
James Drummond of Strageath, and was bom at Edinburgh on
25th August 1805. He was educated at the High School and the
University of Edinburgh, with the view of entering the legal
profession; but he subsequently proceeded to Worcester College,
Oxford, where he took his bachelor’s degree in 1830. He was
ordained a deacon the same year by the Bishop of Llandaff, and
a priest in 1831 by the Bishop of Gloucester and Bristol. Eor
the first two years of his ministry he occupied the office of
curate at Henbury and Compton, and then came to Edinburgh,
where he entered into the incumbency of St Paul’s Episcopal

of Edinburgh, Session 1877-78.

519

Episcopal Chapel, Carrubber’s Close. Having remained here for
six years, he became joint-minister of Trinity Chapel, Dean Bridge,
along with the late Mr Coventry, where he laboured with much
acceptability, until his connection with the Scottish Episcopal
Church was severed in 1842. He then became incumbent of St
Thomas’s English Episcopal Chapel, and remained in the spiritual
oversight of the congregation there for upwards of thirty years.
During the long period of his ministry in Edinburgh, Mr Drum-
mond endeared himself to his congregation, both by his public and
private ministrations. With the ministers of other denominations
he was always on the most cordial and friendly terms, and no good
work, having for its object the religious or moral improvement of
the people, ever failed to elicit his co-operation and sympathy. By
the general public he was long known at once as the zealous advo-
cate and upholder of English Episcopalianism in Scotland, and as
an active and valued friend of evangelical movements. His writings,
also, although not extensive, served to bring his name before a
considerable section of the community. The most noteworthy of
these were, a series of Lectures on the 17th Chapter of St John’s
Gospel, a Life of Montague Stanley, and Scenes and Impressions in
Switzerland and the North of Italy.

Mr Drummond became a Fellow of the Royal Society in 1868.
He was fond of intercourse with the lovers of literature and science,
and took much pleasure in the study of natural science, especially
during his residence in the country, and his visits to the Continent
of Europe. He was also an excellent photographer, and executed
some fine views of Scottish scenery.

Mr Drummond, who was not a man of a strong constitution,
resigned his charge with advancing years, in the autumn of 1875,
and only a short time ago he changed his residence from Edinburgh
to Pitlochry. He was in his usual spirits on Friday, 8th June,
and went to bed in apparently good health. Early on the morning
of the 9th, he was seized with sudden illness, and died in a few
minutes, leaving a widow and a widowed only daughter to mourn
his loss.

He was buried in the churchyard overlooking the picturesque
loch at Duddingstone, in the grave where he had laid his only son
forty years before. The service was read by Bishop Beckles, assisted

3 z

VOL. IX.

520

Proceedings of the Royal Society

by the Rev. W. Scott Moncrieff, vicar of Bishop-Wearmouth, who
was for some years Mr Drummond’s colleague in St Thomas’, and a
large concourse of friends testified to the affection and respect in
which he had been held. His funeral sermon was preached in St
Thomas’ and St Yincent English Episcopal Chapels, by the Rev. C.
T. Astley, vicar of Gillingham, Chatham, who had formerly assisted
him at St Thomas’.

William Keddie became a Fellow of the Royal Society of Edin-
burgh in 1867, and died suddenly at Oban on 26th July 1877.
He was born at Peebles on 2 2d March 1809, and with the
exception of the first seven years, all his life-time was spent in
Glasgow. At the age of thirteen he entered a printing establish-
ment, and continued in it till he was twenty years of age. In 1832
he became sub-editor of the “ Scottish Guardian,” and contributed
many valuable scientific articles to that newspaper. He attended
also scientific classes at the University of Glasgow and the Ander-
sonian College. He was a pupil of the Botanical class in the former,
during the year 1843 when Dr Balfour was Professor. He
ultimately became principal editor of the “ Guardian.” He was
connected with the paper for twenty-seven years. Mr Keddie
afterwards lecturerd on Natural History in the Free Church
College. He made an excellent collection of geological and
zoological specimens, which were handed over to the College. He
was elected Secretary of the Glasgow Philosophical Society and
editor of its Transactions. He published accounts of his visits to
various Botanic Gardens in Britain, as well as to the Bass Rock and
the Highlands of Scotland. His kind and genial manner and his
fine flow of spirits made him a most pleasant companion in scientific
excursions. His loss is much felt by the followers of science in
Glasgow.

The following Communications were read : —

of Edinburgh, Session 1876-77.

521

2. Report of the Deputation to Upsala.

By Alexander Buchan, M.A.

The Deputation appointed by the Council to represent the Society
on the occasion of the 400th anniversary of the founding of the
University of Upsala consisted of Mr Sprague and myself.
Professor Balfour and Professor Sir Wyville Thomson, who re-
presented the Edinburgh University, also joined the Deputation.

The Latin Address from the Society for presentation by the
Deputation having been prepared, was signed in the absence of the
President by the Secretary. The Address, a copy of which accom-
panies the Report, is in its conception and execution, a characteristic
specimen of quaint and exact Latinity. It is wholly the work of
Mr Gordon, the Society’s Assistant Librarian.

The Deputies assembled by previous arrangement at the Grand
Central Railway Station, Stockholm, on the afternoon of Tuesday,
September 4, to be conveyed by royal express train to Upsala.
At 4.15 p.m. the train left the station amid the cheers and con-
gratulations of an immense assemblage of the inhabitants. About
seven o’clock Upsala was reached, and the whole of the inhabitants
appeared to have assembled at the station to do honour to their
guests. Of this great assemblage, the white caps of the students
filled the whole central space. Young Count Hamilton, in name
of the students, welcomed the Deputies, and thereafter the renowned
choir of this University sang one of the Swedish national airs.

In the evening a meeting of all the Deputies was held for the
purpose of deciding on the order of procedure to be observed in
presenting the Addresses on the Wednesday. Since the number of
learned bodies represented amounted to about seventy, it was re-
solved that, to save time, the different bodies be grouped into
nationalities, the Deputies choosing their own representative speaker,
while the Addresses would be presented without remark. The
British Deputies chose Professor Balfour as their representative
speaker. The British Deputies were, in addition to those already
named, Professor Humphry for Cambridge University, and they
were joined by Dr Curling of London, Fellow of the Royal Society,

522

Proceedings of the Royal Society

the Kev. Ch. H. H. Wright, Belfast, Bampton Lecturer elect ; and
the Key. Mr Metcalfe, Senior Fellow, Lincoln College, Oxford.

The festivities of the 5 th were opened with salvos of cannon
from the castle and peals of bells from the cathedral, and the streets
were early astir with crowds already in evening costume. By nine
o’clock the side aisles and tribunes of the transept of the cathedral
were filled to overflowing with gaily dressed ladies. The procession
formed in the upper hall of the Carolina Bediviva — the University
Hall — which is a handsome structure built on a fine site overlooking
the city. It then wound its way slowly down th3 beautiful avenue
of limes called Odin’s Grove to the cathedral, headed appropriately
by the students with their guests from the other Scandinavian
Universities, with the appropriate banners of the thirteen nations
into which the Upsala students are divided; followed in order by
representatives of the Universities and learned Societies of Sweden,
Iceland, Copenhagen, Helsinfors, and Christiania; representatives of
the Parliaments, the officials of the University of Upsala, the
Charter of its foundation being carried by the Secretary of the
Academy; State Councillors and Knights of the order of the
Seraphim; and other civil, military, and Court functionaries,
members of Parliament, and the Honorary Doctors, the rear being
brought up by the municipal and other authorities of the city, and
by all the other not included in the above. When all were seated,
Professor Sahlin, the rector, went out to receive the King, Crown
Prince, and their suite. The cantata composed for the occasion by
Mr Charles D. de Wirsen was a striking feature of the day’s
festivities. A Latin service having been performed by Archbishop
Sundberg, the Lector welcomed the Deputies in a Latin oration,
and thereafter the Deputies presented the Addresses in the inverse
order in which they had joined the procession. A speech from the
Eector and the concluding part of the cantata brought the ceremony
to an end about 2.30 p.m.

At 3 p.m. a dinner was given by the University in a large hand-
some hall, specially built for the festivities in the Botanic Garden.
The King presided, and covers were laid for 450 guests. By far the
best speech on the occasion was the King’s, in reply to the toast of
his health, proposed by the Hector. He urged the advantages of a
scientific and classical education to even the poorest of his subjects ;

523

of Edinburgh , Session 1877-78.

sketched with a rapid but firm hand the condition of Sweden when
the University was founded, and the salient points of its subse-
quent history; and the important part played by the University, as
seen in its brilliant history during these 400 years ; gave expression
to a fervent prayer that it would continue to maintain and extend
its renown; and concluded a most animated and eloquent speech by
announcing the gift of 40,000 kronors (2000 guineas) from the Crown
to the University for the encouragement of scientific research.

The town was illuminated during the evening, and what may be
called the club-houses of the various “ nations were thrown open
by the students, with the view of giving the guests some idea of this
characteristic phase of student life at Upsala.

The ceremonial of the Thursday was the conferring of degrees,
which statedly takes place in June, at the close of the spring session,
but which was appropriately deferred this year so as to form part
of the quater-centenary commemoration. The festivities of this
day were ushered in with the same formalities, and fortunately with
the same brilliant weather as favoured those of the previous day.
The doors of the cathedral were thrown open at 8.30 a.m., and the
seats set apart for the ladies were rapidly filled, the best places this
day being reserved, not as on the Wednesday in accordance with
social position, but for the friends of those who were to be mode
doctors in the four faculties.

The procession set out from the Carolina Kediviva at 9.15 a.m.,
differing from the procession of the day before in the chief place
being assigned to the four Faculties and the doctors elect; and all
were in due time seated in their places in the cathedral in the same
admirable order that marked the whole proceedings. The King,
Crown Prince, and their suite were again present, being received in
the porch by the Chancellor of the University, the Archbishop, the
Hector, and the four Promoters. The cantata for the promotion was
the work of Mr Victor Kydberg, a popular poet, and one of the
eighteen of the Swedish Academy. This cantata, with the music
set to it, was, like the cantata of the previous day, of a very high
order of merit, and was admirably rendered by the choir.

The ceremony of promotion occupied about three hours, the
degrees so conferred being strictly limited to persons resident in
Sweden, Norway, Denmark, and Finland, the universities of these

524 Proceedings of the Royal Society

countries being in peculiarly close relationship with that of Upsala.
The new doctors of medicine, law, and philosophy are nominated
by these respective Faculties of the University ; but the doctors of
theology are nominated by the King from a list submitted to him
by the Theological Faculty.

Among the many quaint traditional forms with which the cere-
monial was conducted may be mentioned the firing off of a piece
of ordnance instantly on the crowning of each doctor; a gold ring
put on the finger of each doctor in law, medicine, and philosophy ;
the crowning of the doctors of philosophy with wreaths of real
laurel; and the recrowning of doctors of fifty years’ standing, a con-
siderable number of such jubilee doctorates being conferred. At
3 p.m. the promotion dinner was given in the large hall in the Botanic
Garden, covers being laid for 1600. At dinner and during the rest
of the evening the doctors of philosophy still wore their laurel
wreaths.

In the meantime the gates of the Botanic Garden had been thrown
open to the dense throng of the public which had been waiting out-
side. Shortly thereafter the King and rest of the company repaired
to the open portico of the Hall, where speeches in all languages were
delivered to the assembled crowds, first in front of the fine statue of
Linnaeus, which was crowned with laurel on the occasion, and after-
wards from the broad staircase of the building, commanding a fine
view of the dense crowd which filled the broad avenue leading to
the Castle. Among the speakers were Chancellor Count Hamilton,
Donders of Utrecht, Topelius the popular Scandinavian poet, and
Professor Balfour. The speeches were varied with songs from the
students, whose white caps filled the middle space of the avenue,
and whose wild but well-ordered enthusiasm forms one of the
pleasantest reminiscences of the festivities. As darkness set in the
gardens were illuminated, and a little later there was a display of
fireworks, some of the pieces being very fine, particularly one
representing the new buildings of the University which are in con-
templation. The festivities of the day ended with a torchlight
procession of about 1000 students, who marched with their banners
to the stirring music of the choir that led the procession on to the
Castle, to pay their respects to the King.

On the Friday the large hall of the Carolina Rediviva was

of Edinburgh , Session 1876-77. 52 £>

crowded by twelve o’clock with an audience of about 4000, for the
concert given by the celebrated choir of the students. The mem-
bership of the choir is limited to 500, and as all in Sweden are taught
music in the elementary and secondary schools, and as it is re-
garded an object of ambition to be admitted a member, there is
no difficulty in maintaining the choir in a state of the highest
efficiency. On this, as on other high occasions, old members
wearing the little rosette of membership were permitted to join the
choir. It is enough to say that the concert was a very fine one, and
it may be added that a degree of excellence was achieved which no
existing university choir could rival. The pieces selected for the
concert were essentially Scandinavian, and were remarkable for the
strong patriotism and inextinguishable love of freedom which
breathed through them, and for a desire for union among the three
Scandinavian nations. In the evening the town gave a ball, at
which the King, Crown Prince, and suite, and about 7000 guests
were present in the hall in the Botanic Garden — a hall, by the way,
which was levelled with the ground on the following day.

By mid-afternoon of Saturday the guests had returned to Stock-
holm, and at 6.30 p.m. they met at the pier to be conveyed by six
steamers, specially engaged for the purpose, to Drottningholm Palace.
Invitations to supper were issued by His Majesty to 700 guests. The
magnificent rooms of this the stateliest of the summer palaces about
Stockholm were thrown open to the guests, the King freely and
cordially mingling with the company, as he did during the whole of
the festivities. After supper the foreign deputies were invited to
meet His Majesty in one of the larger rooms, where, after a graceful
speech, to which one of the deputies replied, the King touched
glasses, and shook hands with many of the deputies, and bade a
cordial good-bye to all. The grounds of the palace were finely
illuminated.

Thus worthily terminated the commemoration solemnities of the
400th anniversary of the founding of Upsala University, the cele-
bration and festivities being conducted in a manner and with a
munificence of which Upsala and Sweden may well be proud.

The Latin Address above referred to, which was presented by the
Deputation, is as follows : —

526

Proceedings of the Royal Society

Amplissimis Curatorihus , Rectori Magnified, Dodissimoque Senatui

TJniversitatis Upsaliensis.

Societas Regia Edinensis nos jussit, viri illustrissimi, vobis hoc
sollemni die gratulari, quo nihil exoptatius nobis evenire potest.
Itaque nobis animo perpendentibus quam excultus studiorum status
hodie sit, et quantopere vos in his augendis et amplificandis excel-
lueritis, grato animo laudanda est ilia fructuosissima opera quam vos
et Academia vestra in finibus scientiarum dilatandis posuistis ; et
admirationem observantiamque nostram in viros prseclaros qui tem-
poribus prseteritis exornaverunt et in suceessores eorum qui nunc
exornant Academiam vestram libenter enuntiamus. Ab Upsala
Societas nostra Regia semper lumen exspectavit et accepit ; in
Astronomia, Meteorologia, rebus Botanicis et Physicis, Historia Na-
turali, reliquisque studiis Academicis, in quae Socii nostri continuo
incumbunt, problemata difficillima solvistis, naturae recondita extri-
cavistis, patefecistis et illustravistis ; et vestro proventu secundo
Socii nostri in difficultatibus superandis valde profecerunt. In
regionibus Septentrionalibus juventutem disciplinis humanis et sub-
tilioribus instituendo Universitas Upsaliensis de republica literaria
optime meruit, et laboribus suis philosophicis de rerum natura orbi
terrarum notissimis tons et origo luminis fuit, imo quidem aurora
borealis, vel potius sol meridianus, Sueciae et aliarum nationum.

Ut gloria vestra per omnia saecula permaneat ex imo pectore opta-
mus et precation ibus ominamur.

Joannes Hutton Balfour, M.D.,
Societatis Regiae Edinensis Secretarius.

Nonis Sextilibus ,

ANNO CHRISTI MDCCCLXXVII.

3. On a Method of Determining the Cohesion of Liquids.

By J. B. Hannay, F.C.S.

(Abstract.

In this paper the author concludes that the measurement of the
breaking-strain of liquids is the only universally applicable method
of measuring their cohesion ; and as dropping is the phenomenon in
which the breaking-strain can be most easily measured, he examines
the work already done in this direction. Dr Guthrie’s theory that*

of Edinburgh , Session 1877-78.

527

the increase in the size of drop, with the increase in the rate of
dropping, is due to the attraction of the solid tearing more of the
root of the drop in low than in high rates is put to a crucial test by
an experiment in which mercury drops from a wide glass tube so
arranged that the tube only acts as a support for a column of liquid
from the end of which the drops fall. In this case there is no solid
to reclaim by adhesion any of the drop, and yet there is the same
increase in size as the rate increases. The author accounts for the
increase as follows : — 1. The rupture of the neck of a drop is not
an instantaneous process, but lasts for a short time, and during that
time liquid is flowing into the drop through the neck, and the faster
the flow the greater is the increment of the drop during rupture.
2. When the rate is high the breaking neck has a longer life-time,
as the stump follows after the full drop as in the beginning of the
formation of a stream. Briefly stated, the quicker the rate the larger
the drop, because more liquid flows into the drop after the rupture
has commenced, and the longer does that flow continue. The
author calls a drop when it begins to break a “normal ” drop ;
and to find its weight he determines the decrease of weight with
decrease of rate, and reduces the latter to zero when the weight of a
normal drop is found. Apparatus is shown by which experiments
were carried out, and inaccuracies eliminated. The normal drop is
found to weigh 0 4130 grm., and as the width of the neck is found
to be 3*395 mm., this gives a breaking strain of 0*0456 grm. per
square millimeter for mercury at 1 6° C.

4. Note on Vector Conditions of Integrability. By

Professor Tait.

(1.) The relation

dtr = uqdpq ~1

ensures that the tensor of d<r shall always be u times that of dp
Hence, if p be the common vector of three series of surfaces which
together cut space into cubes, <r possesses the same property. (See
§ 6 of my paper On Orthogonal Isothermal Surfaces, Trans. B.S.E.,
1873-4. In what follows this paper will be referred to as O.)

We may suppose the tensor of q to be any constant, unity suppose.
Then, from

4 A

VOL. IX.

T?2=l,

528

Proceedings of the Hoy at Society

we have

= S .dqq~l — 0 .

Thus, it appears that

q~l . dq and its equal — dq~x . q

are vectors.

(2.) From the given equation we have

da~ • _ i i d<r • i

jte - um and irr um

From these

9

, d?<r- .du , 0 Tr .dq 1 . du , 0 ,7 . dq~x

l - - * — -f 2 uV.i ~ — o=i — -b 2 uV. i «

J dx dx

q — i
dxdy dy

dy

From the three equations of this form we obtain by the operations
Si , S.j , S.&, nine scalar equations, of which the following are
three : —

— = 2«S.i %-q ,
dx dy

*- -2vS.kdJC!q,
dy dx

S.f%2q =

dy M dx

The last of these, with its two similar equations, shows that

Si

.dq

— i

q = S.j = 8.k-q-r q = <>

1

dx * v dy a dz

which express Dupin' s theorem for this particular case.
(3.) If we put for simplicity

du

dv

2 u

the equations of last section give at once three like

— q — V.iVv ,
dx

so that
and

dq . q~x = Y.dpVv , .

(® (33).)

Vq-X . q = 2 . iViVv = - 2V?; = -

or

V . uq~l =» 0

(o (13).)

of Edinburgh, Session 1877-78. 529

(4.) But we have, by differentiation, from the second equations
of § (3),

dxdy

dAl . dJL=A\.iVv
dx dy dy

1

*£?q + *LL .<k-±VJVv

dydx dy dx dx

Subtracting, and noticing that

dq 1 dq= _ {dq dq
dx' dy ^ dx ^ dy ’

we have

SV. q-^fldi = Y.(jd- i4-\vv = V. V IkV) Vv ,
1 dx * dy \Jdx dy) x ;

or

2S(&Vv) . Vv = Y.V (&V) Vv .

Three like this give at once

(Vvf= -V2v
or

0 = 2uV2u-(Vu)2 = 4u%V2(uh) . . . (O (21).)

(5.) But if, instead of combining the last set of three we equate
to zero the scalar coefficients of i, j, k separately in each, we have
three equations of each of the following forms : —

2

dv dv _ d2v d2v
dx dy dxdy * dx2

+

d2v

dy2

Transformed to u , they become

The integrals of the first three are obviously

\ du _ r, 1 du _ v, 1 du
u 2 dx ’ u2 dy 5 u2 dz

where the right hand members are functions of x, y , z respectively.
Thus

- = - X-Y-Z

a

530

Proceedings of the Royal Society

and the first of the second set of three equations becomes

or

Thus

and

u*(X" + Y" + 2uX'2 + 2uY'2) = u\X!2 + Y'2 - Z'2) ,
X" + Y" = - u(X’2 + Y’2 + 712) .

X" = Y" = Z" = C ,

1 = - 1 [(* - af + (y - by + (z - c)s] + C,

or, as we may take the origin where we please,

u oc

1

CTp2 + D ’

This is, therefore, the only value of u which satisfies the conditions
of the problem, and the last equation in § 4 above shows that
either C or D must vanish. If C vanish, u and q are both
constant.

(6.) If D vanish, we have by § 3 above

dq . <r' = Y.dp I? = - y = - dUo

This gives

q — aJJp

where a is any constant versor.
Also

d<r —

c2

fp2

all pdp(V p)~'a~

so that cr is the Electric Image of p rotated through any angle
about any axis through the centre of the reflecting sphere. (H § 12.)

(7.) If the equations of any three systems of orthogonal sur-
faces be

^\ = C2 , F2 = C2, F3 = C3,

we may obviously write for the flux of heat through each the ex-
pressions

VF VF2 = u2qiq~l , VF3 = u^qkq~x ;
so that we have three equations of the form

V (ufliq-1) = aY ,

531

of Edinburgh, Session 1877-78.

where aY , a2 , a3 are scalars , which separately vanish when the
systems are isothermal.

Expanding the last equation we have

— 1 qig~l -f Vq . q~l . qiq~l + qiq~lVq . q~l - 2S (. qiq~lV ) q . q~J = -1

ui

or, writing

qiq-i = % ,

i' + 2 Si'V? ?-> - 2 S(i'V) q.q-^'h.

We obtain Dupin’s Theorem in its most general form by operat-
ing by Si', S .j'f S.&' on this and the two similar equations respec-
tively. It is thus expressed as three equations, of which one is

Si'S(rv)2.?_1 = 0.

Again, by multiplication by i' , and by adding the other two
equations multiplied by / and k’ respectively, we obtain also

2 — + 22«'S*'— 1 - 2 Y.Vqq-1 + 2 Vq . q~l = 2

n ux

or

2^ + 2 V.Vqq-' + 2V?.o->= -2^li

M UY

whence

S.V? q-' = 0 ,

and

S — + 4 V? . q-1 = - .

u U1

When the systems are isothermal as well as orthogonal, this
equation may be put in the singular form —

The results given in this section were laid before the Society in
May 1876, but were mislaid, with other papers then read.

1(8.) The great desideratum in the application of quaternions to
problems such as those just treated, seems to lie in the discovery of
the general solution of the equation

Vr = 0,

I

where r is a quaternion. Unfortunately this seems to depend
ultimately upon Laplace’s equation, treat it how we may. It is

532

Proceedings of the Royal Society.

easily seen to be equivalent to the kiuematical problem of finding
a displacement which shall produce no compression, but shall
produce a rotation whose vector axis itself corresponds to a dis-
placement without compression.

The nature of the difficulty is also easily seen in another way ;
for, when we try to find the conditions of integrability of such an
equation as

V . Xdp. = dv ,

we may, of course, make the assumption

d/x =

where the coefficients of <f> are functions of p. This gives at once

S adp. — S. <j)'adp ,

so that

V.V<£'a = 0

whatever constant vector be a.

Suppose this satisfied, we have the farther condition

dp = dv ,

or

S.<f>'Y (aX) dp = S adv ,
so that, whatever be a ,

V.V<£' (YaX) = 0

Taken in conjunction with the former condition, this shows that
V may here be considered as operating on X only.

In this very particular case, however, we find at once that X must
be constant, and that

dp. = <f>dp = idu -f jdv + kdw .

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH

yol. ix. 1877-78. No. 101.

Ninety-Fifth Session.

Monday, 1th January 1878.

The Eight Eev. Bishop COTTERILL, Vice-President,

in the Chair.

The following Communications were read :• —

1. On Gladstone’s Theory of Colour-Sense in Homer. By

Professor Blackie.

2. Note on a Geometrical Theorem. By Prof. Tait.

In “Trans. R.S.E.” (1864-5) Fox Talbot proved very simply, by
means of a species of co-ordinates depending on confocal conics, the
following theorem, at the same time asking for a simple geometrical
proof.

If two sets of three concentric circles , with the same common differ-
ence of radii , intersect one another — the chords of the arcs intercepted
on the mean circle of each series by the extremes of the other are
equal.

A properly geometrical proof may possibly be obtained by show-
ing that the middle points of these arcs are equidistant from the
line joining the centres. It is, of course, quite easy to build up a
quasi-geometrical proof, but Talbot’s would be much better.

The following investigation shows the nature of the theorem, and
gives some elegant constructions.

Let d be the common difference, b and c the mean radii, and a
the distance between the centres. Then the square of one of the
chords is easily seen to be

y>2 = 2c2 (l - cos (O' ± $)),

4 B

VOL. IX.

534

Proceedings of the Royal Society

where & and 6 are given by

(b - d)2 = a2-\- c2- 2 ac cos 0 ,
(b + d)2 = a2 + c2 - 2ac cos O'.

The expressions for the other chords differ only by the inter-
change of b and c. Elimination gives at once

P

» o_-.fl q2 + c2-(6-rf)2 a2 + c2-(6 + cQ

2ac

2 ac

^ | i (a2 + c2-(b-d)2y |*| 1 _(a* + <*-(b + d)*y

= J_ { 4 (a? + d2)(b2 + <?) - 2(62 - c2)2 - 2(a2 - <Pf
4 a2 {

T 2(4a2c2 - (a2 + c2 - (b - rf)2)2)i(4a2c2 - (a2 + c2 - (b + d)2)2) i l
= ^ ^A2 + A'2 t 2AA'^

where A and A' are the areas of the “ inscribahle” quadrilaterals,
crossed and uncrossed, whose sides are a, b, c} d. This, of course,
proves Talbot’s theorem.

Hence

a remarkably simple expression. The two values of p are given at
once by Talbot’s diagram, and the rectangles under their quarter
sum, and difference, respectively, with the distance between the
centres, give the areas of the quadrilaterals above mentioned. Or,
better, the triangles whose angular points are the middles of the
arcs respectively, and the centres, have areas equal to half the sum
and half the difference of the quadrilaterals.

The symmetry of these expressions shows that in Talbot’s theorem
any two of the four quantities employed may be interchanged — the
lengths of the corresponding pairs of equal chords being always
inversely as the quantity chosen for the distance between the centres
of the two series of circles.

of Edinburgh, Session 1877-78. 535

Again, it is easy to see tliat we have by the above equations

A' = ac sin ~ cos - ,

A A

» ff . o

A =ac cos — sm - ,

so that, construct the figure how we will with four given lines, the
ratio of the tangents of the halves of the pair of angles correspond-
ing to 6 , &, is constant. This is the relation between True and
Excentric Anomaly. And we have also the very simple expression

A A' = ^ sin 0 sin 0',

4

so that the product of the areas of the crossed and uncrossed quad-
rilaterals is equal to the product of the areas of the (construction)
triangles whose sides are

a, c, b — d ,

and a, c, b + d ,

respectively. Here again the letters may be interchanged at will ;
which, in itself, is a curious theorem.

While seeking a quaternion proof of the above theorem, I hit
upon the following result. Given two opposite sides of a gauche
quadrilateral in magnitude and direction. If one of these be fixed,
and if the diagonals are to be of equal lengths, the locus of either
end of the other is a plane.

Professor Tait, in consequence of the lateness of the hour, post-
poned his paper u On the Strength of the Currents required to work
a Telephone.” He said that the title given in the billet did not
fully describe the contents. These referred not only to various
measurements of the actual currents employed, whether produced
from a cell or a Holtz machine, or by induction, but also to the mode
in which the sounds are reproduced. He stated that he believed it
would soon be possible to employ the instrument for the study of
internal changes of form in all bodies, and also that in its construc-
tion magnets might be entirely dispensed with. He also stated that
Mr James Blyth had with success substituted a copper plate for the

536

Proceedings of the Royal Society

iron disc in the receiving telephone, and had found that even wood,
vulcanised india-rubber, tinfoil, and paper, might be employed for
the same purpose — though not with very good results. In the
transmitting instrument Mr Blyth had managed to employ a block
of iron 8 inches thick.

Professor Tait also exhibited a double mouthpiece, by means of
which it is easy for two players to produce chords from a French
horn.

The following Gentlemen were elected Honorary Fellows
of the Society : —

Otto Struve, St Petersburg.

Professor J. N. Madvig, Copenhagen.

Professor Balfour Stewart, Manchester.

The following Gentlemen were duly elected Fellows of the
Society : —

W. H. Allchin, M.B. (Bond,), M.B.C.P., Wimpole Street, London.

Richard Norris, M.D., Professor of Physiology, Queen’s College, Bir-
mingham.

Daniel John Cunningham, M.D., 9 Gladstone Terrace.

Alan Macdougall, Memb. Inst. C.E., North British Railway, Miliburn
Tower, Corstorphine.

John Frederick Bateman, F.R.S., V.P. Institution C.E., 16 Great
George Street, Westminster.

William King, M.A., Stewart Villa, Dean.

P. R. Scott Lang, B. Sc., St Ronan’s, Viewforth.

Monday , 21 st January 1878.

Sir WILLIAM THOMSON, President, in the Chair.

The Canon of Sines for each 2000th part of the quadrant,
to 33 places, and true throughout to the thirtieth figure, by
Edward Sang, was laid on the table.

The following Communications were read : —

1. On the Tabulation of all Fractions whose values are
between two prescribed limits. By Edward Sang.

2. Can the Law of Multiple Proportions be demonstrated
from Analytical Data ? By W. Dittmar.

537

of Edinburgh , Session 1877-78.

3. On the Solid Fatty Acids of Coco-Nut Oil By
G. Carr Bobinson.

4. Suspension, Solution, and Chemical Combinations. By

William Durham.

Some time ago I made some experiments on “ Suspension of Clay
in Water, and in Acid and Saline Solutions.” These formed the
subject of several communications to the Royal Physical Society of
Edinburgh, and were afterwards published in the “Chemical News.”
I shall describe some of these experiments as an introduction to this
paper.

1st. Clay in Water. — A few grains of fine white clay were stirred
up with about a pint of pure water in a glass jar. The time which
the water took to clear and the clay to deposit itself in the jar was
noted, and found to be about 30 to 36 hours.

2d. Clay , Water , and Acid. — To a similar quantity of clay and
water were added a few drops of acid (various acids were tried, with
the same result in each case), and the time the liquid took to clear
again noted. In this case, the time was from half an hour to one
hour, according to the quantity of acid used. So sensitive was this
action, that when the water was just touched with a glass rod dipped
in sulphuric acid, the time of clearing was greatly shortened.

3d. Clay, Water , and Salt. — In place of acid, salts of various
kinds (including common salt (NaCl) ) were added to the clay and
water, and the effect in every case was to shorten the time of pre-
cipitation of the clay and clearing of the water, according to the
kind and quantity of salt used. As bearing on the precipitation of
salt at the mouths of rivers, I may mention that the water taken
from the end of Leith pier was about the best mixture for precipi-
tating the clay quickly.

4th. Clay, Water, and Alkali. — The alkalis (potash, soda, and
ammonia) were next tried with the clay and water, and when added
in very small quantities instead of hastening the precipitation of the
clay, like the acids and salts, they retarded it so that in some cases
it was 90 hours before the liquid was clear. In larger quantities
they acted like the acids and salts.

In endeavouring to ascertain the cause of these phenomena, I was
led to experiment on various solutions, and obtained results which

538 Proceedings of the Royal Society

appear to me very interesting, and to open up a line of research
likely to lead to important results as to the laws of solution and
chemical affinity. The following are the more important facts as
yet determined : —

1. NaCl and HCl. — To a saturated solution of common salt
(HaCI) was added some strong hydrochloric acid (HCl). Salt was
rapidly precipitated on each addition of acid. This action of HCl
is usually described by saying that salt is insoluble in hydrochloric
acid, but the mode of action does not seem to have attracted atten-
tion. The following experiments throw some light on the matter.

2. Na2SO± + I0H20 and HCl. — To a saturated solution in
water of sodium sulphate was added strong solution of hydrochloric
acid. Anhydrous sodium sulphate was quickly precipitated. This
precipitate was quickly dissolved on the addition of a further
quantity of HCl. In this case it cannot be said that anhydrous
sodium sulphate is insoluble in hydrochloric acid, because it is
dissolved by it when added after its precipitation. The action is
exactly analogous to what occurs when ammonia is added to a salt
of zinc ; the ammonia first combines with the acid of the zinc salt
throwing down a precipitate of zinc oxide, then, on a further
quantity of ammonia being added, the zinc oxide is dissolved. In
like manner, in the case of solution of sodium sulphate the HCl
first combines with the water and precipitates the anhydrous salt,
and then, by a further addition of acid, the salt is again dissolved.
This is made more clear by the next experiment.

3. Crystals of Na2SO± + 10 H20 and HCl. — Strong hydro-
chloric acid was poured over some undissolved crystals of sodium
sulphate. Rapidly the crystals were broken up, the water uniting
with the acid, and the anhydrous salt left, which, as in the former
case, was dissolved by the addition of more acid.

4. CaCl2 and HCl. — To a saturated solution in water of calcium
chloride was added some strong hydrochloric acid. Ho action was
apparent. As calcium chloride has a strong affinity for water, I
concluded that the affinities were balanced in the two solutions, and
therefore there was no action. To upset this balance, if it existed,
I added to the hydrochloric acid solution some fragments of solid
calcium chloride, which, as anticipated, rapidly dissolved with
effervescence, expelling hydrochloric acid gas copiously. Further,

539

of Edinburgh, Session 1877-78.

5. A weighed quantity of solid calcium chloride was dissolved in
a measured quantity of water, and the rise in temperature noted.
This was 15° Fahr.

6. The same quantity of calcium chloride was dissolved in strong
hydrochloric acid and the rise in temperature also noted. This was
6° Fahr., being a difference of 9°, accounted for, no doubt, by the
vapourising of the hydrochloric acid gas expelled in the latter case.

7. NaCl and CaCl2. — Calcium chloride, both in solution and
solid, was added to saturated solution of common salt, and in both
cases the sodium salt was precipitated, the calcium chloride taking
its place in the solution.

8. HCl and FT2$04. — Strong sulphuric acid was added to strong
hydrochloric acid, when the latter as gas was expelled with effer-
vescence.

9. CaSOfICl and H2SOr — Strong sulphuric acid was added
to a saturated solution of calcium sulphate in hydrochloric acid,
when calcium sulphate was precipitated, and hydrochloric acid gas
expelled.

I next looked about for two solvents which would dissolve the
same substance, and yet precipitate it when mixed. These results
I found with sulphuric acid, water, and calcium sulphate.

10. CaSO 4, Water , and H2SOr — To a saturated solution of

calcium sulphate in water was added some strong sulphuric acid.
On cooling, the calcium sulphate was precipitated.

11. CaSO±, H2SO± and Water .. — To a saturated solution of

calcium sulphate in sulphuric acid was added water. As before, on
cooling, calcium sulphate was precipitated.

12. Two solutions (saturated) of calcium sulphate, one in water
and one in sulphuric acid, were mixed when calcium sulphate was
precipitated on cooling.

Three experiments similar to Nos. 10, 11, and 12 were per-
formed, only substituting clay in suspension for calcium sulphate in
solution, and the results were similar. Clay, in sulphuric acid

(strong), was suspended nearly as long as in pure water, but on

mixing the liquid, or on adding sulphuric acid to the water, or water
to the sulphuric acid, the precipitation of the clay was greatly
accelerated.

I hope to extend these experiments to other substances than those

540 Proceedings of the Royal Society

already operated upon; to enter more minutely into the various
phenomena ; and to determine the law of what I may call
“ Solution Equivalents.” To know, for instance, the relation
between the quantity of calcium chloride dissolved and the
quantity of common salt precipitated or hydrochloric acid gas
expelled from solution, and various other points which suggest
themselves for investigation.

The experiments, however, so far as they go, seem to point to
certain conclusions which are interesting and suggestive.

1st. There seems to he a regular gradation of chemical attraction
from that exhibited in the suspension of clay in water up to that
exhibited in the attraction of sulphuric acid for water which we call
chemical affinity. The attraction of clay for water is not so strong
as the attraction of salts which are dissolved in water. Then again,
the attraction of salts is not so strong as that of hydrochloric acid,
which almost forms a definite chemical compound with water.
Then, finally, we reach sulphuric acid with the strongest attraction of
all, and forming more than one definite chemical compound with
water, and easily displacing from their combinations with water
hydrochloric acid ; salts it does not decompose and clay in sus-
pension.

2d. That chemical combination , solution , and suspension diffie
only in degree , and are manifestations of the same force. The few
drops of sulphuric acid added to the water with clay in suspension
attracts and holds the water with the same force as a salt in solution
and precipitates the clay in the same manner, and as the water
is evaporated increases its hold gradually on what remains until it is
strong enough to form definite chemical compounds.

3d. The attraction of chemical affinity is not , in all cases at any
rate , exhausted when a definite compound, is formed , but has sufficient
power left to form solution or suspension compounds. Thus calcium
sulphate is a definite chemical compound, but it still possesses
sufficient affinity for sulphuric acid to enter into solution with it.
This view would explain the researches of M. Stus on atomic
weighs He proved that Prout’s law, that the atomic weights of the
elements are simple multiples of that of hydrogen, is not correct,
though very nearly so ; the differences being very small fractional.
If it be true that the attraction of affinity is not entirely exhausted

of Edinburgh , Session 1877-78.

541

in a definite compound, but that there is a fraction of it, so to speak,
to spare, we should only find Prout’s law to hold good if we could
analyse only one molecule of any compound, but, as in any analysis
we can make, there must be many molecules, such atom of the
molecules having a fraction of its affinity for the other to spare,
these fractions would unite and hold in combination an extra
number of the other atoms, not so firmly, perhaps, but still firmly
enough to make the whole appear a definite compound on analysis,
and this would affect the calculation for atomic weight. Thus,
suppose two atoms of Cl = 71 combine with one atom of Ca = 40
and still have part of affinity to spare, then 200 atoms of Cl
would take up 101 atoms of Ca, and from this analysis we should
make the atomic weight of Ca not 40 but 40 ’4.

4th. If chemical combination and solution are due to the same
force, then solution will loosen the combination by spreading the
affinity, and possibly there may be a re-arrangement of the soluble
and solvent analogous to what is known to take place when two
salts are mixed having different acids and bases. Hence the power-
ful effects of solution in promoting chemical reaction and electric
conductivity.

5th. A point of practical importance may be noted regarding
analysis. Many substances are added indefinitely to solution to
render insoluble some body held in solution, which quantity is to be
estimated. How, if the way in which one substance renders another
insoluble is by combination with the solvent, it is quite clear that if
either too much or too little be added to the solvent, an error may
be made in the analysis, as the whole of the precipitated body may
not be thrown down.

6th. A further investigation of this subject may throw some
light on the manner in which the solubility of a solid in a liquid is
related to the chemical composition of the two.

5. Hote on the Surface of a Body in terms of a
Volume-Integral. By Professor Tait.

In § 25 of my paper on Green’s and other Allied Theorems

(“Trans. R. S. E.” 1869-70) I gave the following relation between a
VOL. ix. 4 o

542

Proceedings of the Royal Society

volume and a surface integral, the limits being determined by any
simply continuous closed space : —

fff^Tds=ff Uj/ rds.

If in this equation we assume r (which is arbitrary) to be equal to
Uv at every point of the surface, we have

r = Uv = UVP

where P = C is the (scalar) equation of the surface. The equation
then becomes

^7'VU(VP)(fs= -ffds.

Applied to the ellipsoid —

x 2 y2 z2 _

— v— -i — = 1

a2 h2 e2 ’

this gives for the whole surface the expression-

x2( 1

7-0 +

fffdxdydz

a4\62

2/7 1 , 1

+ fr4\ c2 a 2

dKa2 h2

(x2 y2 z2\ f

U+fs+?)

the limits being given by the equation of the surface.

6. On a White Sunbow. By Sir Bobert Christison, Bart.

As the phenomenon of a colourless rainbow, which was seen here
in the forenoon of Thursday the 10th January, seems to be very
rare, never having been witnessed before either by myself or by
any of my friends to whom I have mentioned the subject, I beg to
offer the Society the following description : —

On my way that forenoon to the Botanic Garden, and arriving
about a quarter-past eleven at the open view of the north at the
bottom of Pitt Street, my attention was arrested by the appearance
of a magnificent white bow, visible in its entire arch from end to
end in the northern sky.

The air was frosty, very dry, uncommonly still, and in most quarters
moderately clear. The smoke of the Old Town, however, rising
high in the stillness above the ridge of the High Street to the south,
obscured greatly the sun, which shone through the upper region of

543

of Edinburgh) Session 1877-78.

the smoky veil without the slightest definition of its disc, white
nevertheless, hut so shorn of its brightness that I could easily look
it in the face. I was unable to detect anywhere the slightest
appearance of a shower or rain-cloud. The sun, my place of obser-
vation, and the summit of the arch, were in the same vertical plane.
The summit of the arch reached about half-way to the zenith.
The northern sky on which it was formed was somewhat hazy and
grey in its lower region, but blue-grey, and tolerably clear in the
region of the upper two-thirds of the arch.

In form the arch was identical with that of an ordinary rainbow,
except that I thought it considerably broader ; and its edges were
in many places somewhat broken, so that it had exactly the appear-
ance as if the sun had gathered in an arch a number of little woolly
cloudlets. On minute search I could not detect any trace of colour
from end to end. I asked the opinion on this point of two gentle-
men whom I met at the lowest part of the road, at the wall between
the road and the river, and one of them thought he could detect a
very faint trace of colour over a small space at the extremity of the
western limb. As the absence of colour, however, was the main
phenomenon, I scanned the whole curve again and again with great
attention, but could see no coloration anywhere.

At this lowest point of the road the edges of the bow were seen
much more defined and sharp than when I first noticed it. As I
advanced up the gentle slope from Warriston bridge towards the
Botanic Garden, the summit of the arch began to break up, and to
present the appearance of irregular flimsy cloudlets ascending in the
sky above it. But before reaching the Garden gate the whole arch
again formed an unbroken bow, and with both edges sharply defined
like those of a common rainbow. At the same time a similar
secondary arch had begun to form below the principal one, only
half its width, and much closer to its neighbour than I remember

to have seen in a double rainbow of the ordinarv kind.

«/

On returning homeward, about fifteen minutes later, I still
observed, on issuing from the Garden, a sharply-defined colourless
principal bow, and now a complete secondary one under every part
of the bow visible from the roadway. As I proceeded southward
every now and then the upper region of the bow seemed to be
breaking up, and this appearance was very marked when I reached

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Heriot Row, at the head of Dundas Street, the highest station in
my walk. As I went westward along Heriot Row the breaking-up
appeared greater and greater at every interruption of the street,
which gave me a view of the northern sky ; and when I reached
the landing-place of my house, in Moray Place, from which, however,
only the western half of the region of the bow could he seen, the
whole appearances had vanished, and the sky was everywhere
mottled with thin grey fleecy clouds, small and of irregular ill-
defined outline. I did not again look for it, hut I understand it
was partly seen by others so late as two p.m.

Various particulars, which it is unnecessary to mention, led me
to suppose at the time that this colourless how had some connection
with the smoky column of air through which the sun’s rays pene-
trated. But this supposition was put an end to by learning from
my son that, when at Craigiehall, five miles west from town, in a
smokeless atmosphere, he observed the how distinctly about one
o’clock. Its edges were never sharply defined so long as he noticed
it. But it had no colour. Another gentleman present thought
there was a limited blueness at one place. But my son satisfied
himself that this was owing to a patch of blue sky behind, and he
is sure that there was no colour at any part of the how visible to
him.

A better explanation has been suggested to me by Professor Tait,
to whose theory I subscribe. But I leave it to himself to explain
his views.

By Professor Tait.

I was unfortunate in not seeing the phenomenon till nearly 2 p.m.,
when I was on my way from College to the Observatory. It was
then very faint, hut I saw at once that it differed in a marked
manner from an ordinary rainbow. Prom what I could see, I attri-
buted its apparent whiteness to the greatly increased effective surface
from which tho light came. This was probably due to reflection
from ice-crystals mixed with the drops of water in the thin strata of
cloud which covered the whole sky. The sun’s light was much
dimmed, and the edge of its disc was very indistinct, as the clouds
immediately round it, to the distance of at least a diameter, appeared
nearly as bright as the disc itself. Hence this rainbow was probably
very much less pure, while also much less bright, than the usual one.

of Edinburgh, Session 1877-78.

545

This suggestion seems fully to explain all the appearances which I
saw. It will he observed that both Sir R. Christison and Mr Buchan
noticed the peculiar brightness of the clouds near the sun, so that it
is probable that this explanation applies to the phenomenon as seen
by them also. The peculiarities noticed in the position of the spuri-
ous bows (when seen) are of course dependent on the actual size, as
well as the greater or less uniformity of size, of the drops which pro-
duced the rainbow ; and these may well have been exceedingly vari-
able as regards both time, locality, and height in the atmosphere.

[Added, April 8.]

I find that this nearly colourless rainbow is very easily reproduced
in my class-room, when the sunlight employed to form a rainbow
in fine spray is made to pass first through a large vessel with parallel
glass sides, containing water and a little milk. This arrangement
imitates very closely the circumstances of the 10th January.

By J. Christison , Esq.

I saw it first at Craigie Hall, five miles west of Edinburgh, about
11.30 or thereby. At first it did not make much impression, as the
house front runs east and west, and I was standing at the front
door, and consequently only saw half of the bow, and took it to be
an accidental arrangement of the light clouds that covered most of
the sky. By and by the idea of its being a rainbow struck me, and
a move out from the house showed the full bow. I noticed it off
and on for about an hour. Sometimes it was indistinct, but gene-
rally it was evident enough to attract attention at once. I did not,
however, at any time see anything like clear definition of outline.
There was always a sort of wavy indistinctness.

As to colour, I tried hard to convince myself I made it out, but
without effect, and am quite satisfied there was none at any of the
periods I looked at the bow. One of the party at Craigie Hall
thought he made out colour, but on his pointing out the part where
he thought it was visible I was satisfied that it was only a break in
the bow, with a bit of very light blue sky showing through. I did
not notice it after 12.30 or 12.45, as I was indoors.

It was pretty hard frost all the time. The only effect the sun
had was to disperse a little of the hoar-frost, which was thick and
heavy out there, and to make a few of the flat stones among the

546 Proceedings of the Royal Society

gravel show damp. I noticed a thermometer in the garden standing
at 32. It was well placed for shelter from the sun; hut it was within
a few feet of two brick walls, one of them the end wall of a forcing-
house. Could that affect the thermometer? The ground — grass,
gravel, and earth — remained hard all day. I noticed neither rain
nor snow.

The only local peculiarity on the occasion that I can remember
was that the gardener was burning rubbish, off and on, all the fore-
noon between us and the bow. There was no smoke that I noticed
after eleven, but there must have been a good deal of heat rising
from the red ashes. This was close to the house, say 100 yards at
most. The bow had all the appearance of being distant ; but had it
not been seen here (and no doubt elsewhere) there might have been
room for suspicion of this appearance being a deception perhaps.

By Mr Buchan.

The rainbow described by Sir Eobert Christison at meeting of the
Eoyal Society was observed by us from the north windows of the

Scottish Meteorological Society. The above is a rough sketch of it
made at the time.

The eastern limb of it rested on the tops of the houses of Leith
Street, against what appeared to be a smoke-like cloud, precisely
similar to what often accompanies the aurora. It was on this
portion only of the phenomenon that the following points were
noticed : —

1. Spurious Bows. — Two such bows, very distinctly marked, were
seen within the primary bow. The first spurious bow was separated
from the primary by an intensely black band the width of the
spurious bow itself, while this spurious bow and its black band were
together equal in breadth to the primary bow. The second spurious

547

of Edinburgh, Session 1877-78.

bow was separated from the first spurious bow by an intensely black
band the width of the second spurious bow, and both second spurious
bow with its black band were together the width of the first spurious

bow.

2. Colour. — Colours were seen on the portion of the limb
described abo^e as standing out against the black smoke-like cloud.
The colours, though far from being well pronounced, were distinct.
Miss Buchan stated she saw the colours as we looked at the bow
through the window, which at the time stood in need of the window-
cleaner ; but I was unable to detect the colours till the window was
thrown up, when they were distinctly visible.

In no other part of the bow was any development of colour
visible, either when I first observed it in St Andrew Square, or
afterwards at various times in the office.

The frost was keen at the time, but it is probable that a S.W.
wind with thaw had then set in aloft. I understand from Mr J.
Gibson-Thomson, of York Place, who called at this office shortly
thereafter, that while driving out to the country in the afternoon
the wind had shifted into S.W., and the tops of the mud-ridges on
the road had become soft with the thaw which had set in.

The width of the primary, or its visible portion, appeared to be
about a third narrower than the ordinary coloured rainbow.

The arrangement of the colours was that of the ordinary rainbow,
the yellows and yellow-reds being best marked.

The appearance of the sun, as seen in St Andrew Square, was
hazy, with light wisps of clouds and large patches or blurs of mist
in that part of the sky, giving rise to ill-defined shadows, so that I
looked about to see if there were any appearance of halos or mock-
suns visible, but none were seen.

By Dr Ferguson.

Dr Ferguson stated that he had read in the Inverness Advertiser
that a similar phenomenon had been seen at Naim and neighbour-
hood on the same day from eight in the morning till midday. It
is described as a pale blue arch on a white ground, having the out-
line and position of a rainbow, but differing from it in its remarkable
fixity.

I saw the rainbow at Edinburgh from the middle of the east

548 Proceedings of the Royal Society

division of Queen Street. I think it was at eleven, but the friend in
whose company I was at the time says it was twelve. I looked at
the bow attentively, but not critically, as I was not aware of the
exceptional character of the phenomenon. The day was fine, but
there was a haze in the sky, which gave an indistinct outline to the
masses of cloud which occupied the northern heaven. It looked to
me like a cloud rainbow, as its continuity seemed to correspond to
that of the cloudy mass on which it was seen. I remember particu-
larly one spot to the west of the middle, where there was a partial
break in the clouds and a similar defect in the bow. As regards
colour, it wore the appearance of a bleached rainbow, with an in-
definite stratification of tints. I did not specially mark each grada-
tion of colour from the red to the blue, but I had a distinct impres-
sion of such. The colours were faint, and the perception of the
coloured rainbow effect was as much, or more, due to contrast, than
to the colours taken individually.

7. Extract of Letter to the President from H. E. Eosevelt, Esq.,
dated New York, Dec. 23, 1877.

“ I saw the ‘ Phonograph’ the other day, and though it is very
crude I was much interested. I would briefly describe the idea as
follows : —

“ To the centre of an iron diaphragm is attached a metallic point
resting against a strip of paper or tinfoil. You speak against dia-
phragm through a mouthpiece, at same time the paper being drawn
under the points. The vibration of diaphragm and point indent the
paper to various depths, making an undulating (as it were) mark,
&c. Now, if said paper is afterwards drawn under the point, the
diaphragm vibrates exactly as your voice made it vibrate, and all
the sounds are reproduced exactly as you said them, making a most
astonishing effect — singing, laughing, and articulate words were all
reproduced. Of course it is by no means perfect, but it is very
interesting. By attaching a point to one of our strong telephones
we could record any messages sent. Though the phonograph is
purely mechanical in its ordinary use, I mention all this to you, as
you will probably soon hear of it, and naturally would not believe
it a possible thing. The above is the invention of Mr Eddison,
who showed it to me himself.”

of Edinburgh, Session 1877-78.

549

Monday , 4 th February 1878.

Sir C. WYYILLE THOMSON, Vice-President,

in the Chair.

In delivering the Neill Medal to Dr Traquair, the Chairman
made the following remarks : —

Dr Ramsay Traquair, — The Neill prize for the triennial period
1874-77 has been awarded to you by the Council of this Society,
nominally for your paper on the structures and affinities of Tristi-
chojpterus alatus (Egerton), communicated to this Society within
the required period, and published in the 27th volume of the Trans-
actions of the Society. The Council have, however, also taken
into account, as they are entitled to do by the conditions of the
prize, the many contributions which you have made during some
years past to the knowledge of the structure of recent and fossil
fishes.

I may mention as among the more important of these a memoir
“ On the Asymmetry of the Pleuronectkhe, as elucidated by an
examination of the skeleton in the Turbot, Halibut, and Plaiee,”
published in the Transactions of the Linnean Society of London
for the year 1865; a paper “On the Cranial Osteology of Polypterus,”
in the Journal of Anatomy and Physiology for the year 1870 : and
a work on “ The Ganoid Pishes of the British Carboniferous For-
mations,” now in course of publication by the Paloeontographical
Society.

You have been fortunately placed during the last few years in a
locality remarkably rich in the group of fossils to which you have
paid special attention, and already three parts of a valuable series
of papers “ On new and little-known Fossil Fishes from the Edin-
burgh District” have appeared in the Proceedings of this Society.

I have much pleasure in presenting to you the Neill medal in the
name of the Council of the Society.

The following Communications were read : —

VOL. ix. 4 D

550

Proceedings of the Royal Society

1. Chapters on the Mineralogy of Scotland. Chapter III.
The Garnets. By Professor Heddle.

In this third chapter Dr Heddle submits the results of his
analyses of garnets from thirteen localities.

Notwithstanding the great frequency of the occurrence of the
mineral, it is generally so largely contaminated with quartz that
he was unable to procure, from many localities, specimens fit for
examination.

Three varieties of garnet new to Scotland — one of these being
altogether new — have, however, been the reward of the present
investigation.

On a hill lying north of Balmoral, — Creag Mohr, — two of the new
varieties were found, both in limestone.

The first, the rarer, was the water garnet , or colourless garnet ;
he second was the grossular, or gooseberry garnet, hitherto found
only in perfection on the Wilni river in Siberia.

The dnnamonstone of Glen Gairn has next been analysed. This is
finer in colour than the Ceylon mineral, but so flawed as to be use-
less for purposes of jewellery.

Not so the pyrope of Elie — the “ Elie rubies,” as they used to be
termed. Dr Heddle regards these as, weight for weight, the most
valuable of Scottish gems.

Analyses of common garnet from Yell in Shetland, Killiecrankie
and Meall Luaidh in Perthshire, Knockhill in Banff, and Clach-an-
Eoin in Sutherland follow.

There are, lastly, analyses of a new garnet from five localities —
four of these in Eoss-shire ; the other, Ben Eesipol, in Argyll.

This is a precious garnet , containing about fifteen per cent, of
oxide of manganese. Its formula places it intermediate between
the ordinary precious garnet of Bohemia and the manganesian garnet
of America.

This garnet, in all the localities where it is found, is of a fine
currant-red colour, due probably to the manganese. From Eesipol
and the Eaven’s Eock. near Strathpeffer, pieces large enough for
cutting might probably be obtained.

The lime garnets occur in certain of the limestone beds, at the
upper waters of the Don and Dee, and not in others; and Dr

551

of Edinburgh, Session 1877-78.

Heddle thinks it probable that this fact will aid in the tracing out
of the individual beds — far from an easy matter in that troubled
district.

The conclusion of the chapter is devoted to a speculation upon
the metamorphism of these limestones.

2. On the Strength of the Currents required to Work a
Telephone. By Professor Tait.

(Deferred from January 7th.)

Perhaps the most singular fact connected with the telephone is
the excessive feebleness of the currents which suffice to work it. I
have had no opportunity of testing any but rough arrangements set
up by present or former students of my own, so that I cannot judge
how far my results may apply to the instrument as sold.

1. A striking illustration of the feebleness of the currents re-
quired is furnished by using a Holtz machine driven very slowly,
without condenser, and with its terminals so close that the discharge
is bareiy audible, and certainly invisible except in the dark. When
insulated wires were led from these terminals to the telephone
(placed in a distant room) the effect was very curious. The instru-
ment gave a hissing sound, quite comparable in intensity with that
which was produced directly when the terminals of the machine
were widely separated, one connected with the ground and the other
with a large conductor discharging by brushes into the air, the
machine being turned rapidly. The telephone continued to give
audible sounds with slow turning, even when the terminals of the
machine (somewhat tarnished) were pressed into contact.

2. To measure roughly the intensity of the current, I placed
one prong of an unmagnetised tuning-fork about half an inch in
front of the sending telephone, and measured by a microscope and
scale the extent of its vibrations when the note just ceased to be
audible to a listener at the receiving telephone. Next I substituted
for the receiving telephone an exceedingly delicate astatic galvano-
meter, with very small moment of inertia, and measured the swing
produced by one definitely assigned motion of the prong of the
tuning-fork. By means of a known thermo-electric couple, I deter-
mined the strength of the current corresponding to the observed

552

Proceedings of the Royal Society

swing. The result is, of course, only a very rough approximation.
It is that a single Grove’s cell would produce, in a circuit of some-
where about a billion B.A. units resistance, a current sufficient, if
reversed 500 times per second, to produce an audible sound in the
telephone I employed.

3. Several attempts at explanation of the action of the telephone
have been given here and elsewhere, and others are promised for
to-night. For my own part,' I think there are at least three separate
causes at work in the telephones I have used.

There can he no doubt that the inventor’s own explanation is, at
least to a certain extent, correct. For we can easily dispense with
the magnet in the receiving telephone, using merely a thin iron disc
in front of a coil.’ And Mr Blyth has, I believe, found that we may
make the disc, even in this case, of copper, and yet have transmission
(though very feeble) of intelligible sounds.

But this cannot be the full explanation. For it does not attempt
to account for the peculiar nasality of the transmitted speech.
Without going more closely into the matter, the difference of quality
between an open and a closed pipe suggests a certain amount of
constraint as the cause. And we know that the sounds in the
original telephone of Reiss were produced by molecular motions due
to magnetism in soft iron. Mr Blyth has shown conclusively that
molecular motion in the magnet itself has a large share in the results,
because he has successfully substituted other metals than iron, and
even non-conductors, for the disc, and in certain cases finds that he
can dispense with the disc altogether.

Besides this, however, it seems to me that there is a third cause,
which in certain cases is more effective than either of the others.
This is suggested by the fact that (at least with the instruments I
have tried) high notes, even of comparatively small intensity, are
much more clearly transmitted than low notes, — indicating that the
rapidity of the molecular change has a great deal to do with the
result. In fact, in this respect, the telephone is really a variety of
the so-called curb-key, giving very sudden reversals.

These considerations have led me to fancy that rapid change of
form in matter, whether paramagnetic or not, may probably be
capable of detection by the telephone, for the associated electric
currents may be in certain cases powerful enough to produce audible

553

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sounds. I am at present engaged in a series of preliminary experi-
ments on this subject.

3. Experiments with the Telephone. By James Blyth.
Communicated by Professor Tait.

In the telephones used in these experiments the permanent mag-
nets were of the ordinary horse-shoe form, about 4 inches long. No
cores of soft iron were attached to the poles, the insulated wire, No.
26, being wound directly round both, in such a way that a current
circulating through it followed the direction of Ampere’s currents.
The vibrating disc was the bottom of a shallow can of thin tinned
iron, 2J inches in diameter, supported directly above the poles of
the magnet, and almost touching them. The receiving instrument
was so arranged that any kind of disc could be easily substituted
for the ordinary vibrating plate, and tested by sound from the same
transmitting instrument, so as to allow of a comparison being made
between discs of various materials. Having first ascertained that
no sound was audible when no vibrating plate was used, I tried
discs of the following substances, and have arranged them approxi-
mately in the order of distinctness with which the sound was
heard : —

Ferrotype plate.

Thin steel.

Thin iron.

Wire gauze (fine).

Do. (a little coarser).

Cast-iron plate, f inch thick.

Sheet copper.

Sheet brass.

Sheet zine.

With the view of testing what effect would be produced by varying
the position of the wire coil on the leg of the magnet, I constructed
a telephone, so that the coil could be easily slipped up and down
the leg, while the sound was being sent from the transmitting
instrument. Very little difference in the sound was observable till
the wire coil was brought near the neutral point of the magnet. It

Tinfoil.

Vulcanite.

Thin fir wood.

Paper.

Vulcanised India-rubber.
Cast-iron, 6 inches thick.
Slice of raw potato.

Slice of fresh butter.

554 Proceedings of the Royal Society

then became very faint. I next slipped the wire coil entirely off
the magnet, and simply held it touching the pole side-ways. The
sounds were still quite audible, and continued to be so when the
coil was removed an inch or more away from the magnet. This led
me to try the effect of dispensing altogether with the steel magnet,
and merely holding the helix of insulated wire opposite the centre
of the vibrating plate. With an iron disc a very faint sound was
heard, but it became more distinct when a disc of copper was used.
From this it would seem, that the vibrations producing the sound
are caused by the attraction between the currents in the helix
and the induced currents in the copper disc.

Still using the same transmitting instrument, I next employed a
receiver, in which a soft iron core, carrying the insulated wire, was
rigidly attached to the vibrating plate. This was accomplished by
rivetting the head end of a screw-nail into its centre, and winding
the wire round it. The pole of a steel magnet was then fixed, just
clear of actual contact, opposite the head of the nail, and, with this
arrangement, sounds were distinctly audible, though not so loud as
when the wire coil surrounded the magnet.

With the view of rendering the telephone an instrument for
detecting the existence of very feeble currents, I constructed a pair
with magnets similar to those already described, but with ferrotype
discs. These were joined together by a strong semicircular spring
in such a way that they could be put on, after the manner of
spectacles, and stick close to the sides of the head, inclosing both
ears. India-rubber rings were provided for the double purpose of
excluding all extraneous sound, aud avoiding any disagreeable pres-
sure on the ear.

With this arrangement, I proceeded to test for the existence of
thermo-electric currents. A copper and iron junction was inserted
in the circuit of the telephone, and attached to a spring in such a
way that it could be made to vibrate rapidly out and into a gas
flame. A distinct grating noise was heard in the telephone. A
very peculiar rasping sound was produced when the ends of a copper
and iron wire were rubbed together while hot, and also when one
of the wires was attached to a file, and the hot end of the other
drawn rapidly along it.

of Edinburgh , Session 1877-78.

555

4. On the Theory of the Telephone. By
Prof. George Forbes.

The Telephone, invented by Mr Graham Bell, is an instrument
by means of which any sounds, musical notes or spoken sentences,
sounded into an instrument at the sending end of a telegraphic wire
may he reproduced at the receiving end. The theory of the Telephone
is two-fold. First, the mechanical theory of the nature of sounds
and of speech ; and secondly, the theory of the action of the instru-
ment. The first part is well known. All sounds consist of a
succession of waves propagated through the air, the rate and
intensity of their succession determining the nature of the sound, in
pitch, loudness, and tone. If the same succession of waves as a
speaker makes in using his voice can be reproduced in the air in
contact with the ear of any other person, by any means whatever,
the latter person will hear a fac-simile of the sound uttered by the
former. A theory of the action of the Telephone is distinctly given
by the inventor in the specification of his patent. The receiving
and sending instruments are identical. Pound the end of a bar
magnet a coil of fine wire is wound, connected with a telegraph
wire on the one hand and the earth on the other. In front of these
a thin iron plate is caused to vibrate by the sounds uttered in its
neighbourhood. Consequently, it approaches and recedes from the
pole of the magnet. This alters the magnetism in the neighbour-
hood. In Faraday’s language, 4 the lines of force are altered in
position, so as to go across the coil of wire. ’ In consequence of this,
by the well-known laws of electromagnetic action, a current of
electricity is sent in one direction with each approach of the vibrating
plate, and in the opposite direction with each recession. This suc-
cession of currents reaches the receiving end with a strength pro-
portioned to the extent of vibration of the iron plate. Here they
circulate through the coil, and so intensify or diminish the magnetism
of the bar. Thus, the vibrating plate at the receiving end is more
or less attracted, according to the direction of the current. Hence,
the plate at the receiving end vibrates to and fro in vibrations which
are synchro nus and proportionate to those at the sending end ; and
so the sounds are reproduced.

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Proceedings of the Royal Society

This theory gives a vera causa for the action of the instrument in
its normal form, and probably explains in part the true action
which takes place, but the author believes that this is not the whole
of the action. The fact that the inventor was working upon this
theory when he designed the instrument, does not prove the theory
to be correct, as is shown by his having at first employed a powerful
battery with the instrument, believing it to be necessary, and it was
only after diminishing the number of cells without impairing the
action of the Telephone that it occurred to him to try it without
a battery at all, when he found the action to be equally good.

The author’s mistrust of the theory commenced when he learnt
that a thick iron plate might be used, whose vibrations must be
extremely minute. And when he learnt that the instrument might be
used with plates of glass, wood, tinfoil, or vulcanite, or even with-
out any plate at all, he was convinced that the theory was imperfect,
and resolved to propose another theory which seemed more consis-
tent with facts.

This theory is divided into two parts — the action at the sending
end, and that at the receiving end. It is very simple, and is founded
upon two well-known experiments.

The theory of the action at the sending end is founded upon an
experiment by Sir William Thomson, who finds that iron subject
to magnetic induction has its magnetism increased when slightly
stretched in the direction of its magnetization, and we may assume
that it is diminished when compressed. How, what happens in the
Telephone ? Take the simplest case which has been tried, i.e.} where
there is no vibrating plate. S ound waves (which are capable of
passing through solid bodies as they do through the air) strike the
end of the bar magnet, and are propagated through it. Waves of
alternate compression and extension pass through the length of the
magnet. Consequently, the magnet is alternately increased and
diminished in intensity. Hence, currents are generated in the coil
of wire, and transmitted through the telegraph wire alternately, in
opposite directions, as in the theory hitherto adopted. The presence
of a vibrating plate of any kind may help this action, by increasing
the intensity of the waves transmitted through the bar magnet ;
and if the plate be of iron it will undoubtedly help to propagate
these currents.

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of Edinburgh, Session 1877-78

According to the author’s theory, the action at the receiving end
is explained by an experiment ascribed to Page. If a bar of iron be
surrounded by a coil of wire connected with a battery, a chink is
heard when the connection is broken, and a feebler one when the
connection is re-made. If the connection be made, and broken
rapidly by attaching one end of the wire to a file and drawing the
other along the file, a series of chinks are heard succeeding each
other at the same intervals as the contacts are made and broken.
It is due to the lengthening of the bar on magnetisation and the
rearrangement of the molecules of the iron. It takes place also
when the iron remains partially magnetised. In this case successive
contacts increase the magnetism of the bar. In the Telephone suc-
cessive currents pass in opposite directions through the coil. Hence
the bar is lengthened and shortened alternately, and chinks are
made at intervals corresponding to the intervals between successive
waves at the sending end. Hence the sound waves at the sending
end are reproduced at the receiving end alike in rapidity and in
intensity. When a vibrating plate of any kind is used it increases
the intensity of the sound, and if it be of iron the attraction will
increase the effect.

Since a chink is given off both when the magnetism is increased
and diminished it might be expected that the note should be heard
an octave higher. But since the one is more intense than the other,
the combined effect should be to give two notes, a loud one in the
tone of the speaker, and a feeble one an octave higher. This might
account for the common remark that a piano sounds wiry through a
Telephone, and that a clear lady’s voice is squeaky. But it is not
certain that this effect is produced, for the chink is produced at
least in part by the lengthening and shortening of the magnet.
Either of these alone will give a chink, but when following each
other in rapid succession they compress and rarefy the air in con-
tact, in periods exactly agreeing with the compressions and rarefac-
tions originated at the sending end.

In confirmation of the supposition that the sound is produced by
successive chinks of the material of the magnet, it was stated that
in a very large and massive pair of Telephones made by Mr Wm.
Bottomley, jun., when any one is speaking through one of them the

sound is distinctly (though not articulately) heard by every one in the

vol. ix. 4 E

558

Proceedings of the Boyal Society

room where the other is placed, and there is no doubt that the sound
seems to come from the magnet itself. The same is done in the case
of a compound Telephone with 25 bar magnets to one iron plate
exhibited by the author,

In conclusion, the author considers that the theory now explained
must be taken to supplement that of Mr Graham Bell (1), because
the phenomena alluded to undoubtedly take place, and (2), because
it is the only theory which explains the action when the vibrating
plate is not made of iron, or when there is no vibrating plate at all.

5. Some Experiments with the Telephone.

By John G. M‘Kendrick, M.D.

During the past two months my attention has been directed to
the telephone, chiefly as an instrument which illustrates in a
remarkable way the delicacy of hearing. As some of these experi-
ments are novel, and may possibly assist those who are investigating
the physical phenomena of the instrument, I beg to give a short
account of them to the Society. To save circumlocution in descrip-
tion, the term “ proximal ” will be applied to the telephone
receiving the stimulus, and the term “ distal ” to the one at the
other end of the arrangement. Thus, if A talks to B, A will use
the proximal, and B the distal telephone.

1 . Transmission of the Sounds o f Tuning-Forks. — At an early stage
of my investigations, finding it convenient to have a constant
source of sound at the proximal telephone, I placed a telephone
opposite one of the limbs of a tuning-fork, kept in vibration by an
electro-magnet, the current being interrupted automatically by the
fork itself. At the distal telephone the sound could be distinctly
heard. Then I removed the disk from the proximal telephone,
and allowed the limb of the fork to play in front of the naked end
of the core. The distal telephone then sounded more distinctly
than before. The next step was to remove the metal disk from the
distal telephone, and apply disks made of vulcanite, porcelain,
glass, paper, wood, a large piece of iron 1 J inches thick, a thick rod
of iron, 8 inches in length by 1 inch in diameter. Still the sound
of the proximal telephone could be heard, though faintly. There
could be no doubt of the fact. To ascertain whether the effect
might not be due to the communication of mechanical vibrations

of Edinburgh, Session 1877-78.

559

from the tuning-fork beside the proximal telephone, I found, that
moving the latter away 3 or 4 inches from the vibrating fork, was
followed by silence of the distal telephone ; indeed, to cause the
latter to sound, the proximal telephone has to be placed as near the
fork as possible.

The following experiment is of interest, as showing the effect of a
thin metallic disk in connection with the distal telephone : — Remove
the disk, and apply in its place a plate of glass ; listen, and the
sound of the proximal telephone will be heard faintly. Then put
one of the metal disks on the glass, and on listening again, the
sound will be found much intensified. It may be still further
intensified by placing a second disk on the surface of the first,
taking care to have a few morsels of paper interposed so as to pre-
vent them from touching.

The next step was to ascertain whether or not sounds could be
heard at the distal telephone without the use of a disk there.
There can be no doubt that sounds may be heard in these cir-
cumstances. They are very faint, however, and have not the same
quality as those heard with a disk.

The arrangements at the distal telephone were further modified
in the following experiment : — The disk was removed from the
distal telephone ; and the base of a glass cylinder, 8 inches in
length by 2J in diameter, filled with water, and closed at each end
by a ground glass cover, was placed against the core. Very feeble
sounds from the proximal telephone were heard, when the ear was
placed at the other end of the glass cylinder. These sounds were
slightly intensified by slipping in a thin metal plate between the
base of the cylinder and the core ; but when a second disk was
placed between the ear and the other end of the cylinder, the
sounds were nearly as loud as with the ordinary telephone. In this
experiment, the two disks were separated by a distance of 8 inches,
and it is difficult to explain the phenomena as depending merely on
conduction of sound.

At this stage it occurred to me to place opposite to the core of
the distal telephone a tuning-fork of the same pitch as that oppo-
site the proximal telephone. The result was, that the one tuning-
fork set the other in movement, so that the sound of the distal
tuning-fork could be heard throughout the room. As is now known,

560

Proceedings of the Royal Society

the same observation was made by Dr Rontgen, and recorded by
him in “Nature. It was interesting as being a proof of the
actual vibration of the metallic substance at the distal tuning
fork.

2. Transmission of the Sounds of Organ Pipes. — If an organ pipe
sounding loudly be brought into close proximity with a proximal
telephone, its sound is heard distinctly at the distal telephone. If
then a pipe of the same pitch be placed opposite the distal telephone,
and it be sounded feebly, the sound is reinforced when the pipe
at the proximal telephone is also sounding ; but I have never
succeeded in causing one pipe actually to initiate sound in the
other. Mr Aiken of Falkirk, however, has informed me by letter
that he has observed this phenomenon. I found also that there
was no intensifying effect when either of the disks was removed.

3. Transmission of the Sounds of Vibrating Strings. — I succeeded
in causing a string to vibrate by means of the telephone as follows : —
Two catgut strings, each having a telephonic disk cemented to the
centre of the string, were tuned as accurately as possible to a pitch
of about C ; one disk was placed opposite a large and powerful
telephone (the proximal), made by Mr William Bottomely, and the
other (the distal), opposite a similar instrument ; on plucking the
string at the proximal telephone, the string opposite the distal also
sounded, though feebly. This experiment holds out the hope, that
by suitable arrangements the sounds of strings might be transmitted
for musical purposes.

4. Optical Observations of the Movements of the Disk. — There can
be no doubt (1) that sounds may be heard even when the disk is
firmly pressed against the ear, so as to prevent its vibrations to a
great degree ; and (2) that sounds may be heard even without any
disk on the distal telephone. A disk, or moving metallic body
capable of magnetic action, is always necessary at the proximal
telephone. On the other hand, the existence of a disk, free to
vibrate, at the distal telephone always intensifies the sound, and,
in particular, it appears to be almost essential for distinct articula-
tion of language. One would therefore infer that the disk must
move as a whole. These movements I have studied in various ways,
and they will still be under observation.

ls£ method. — A strongly vibrating tuning fork was kept going

561

of Edinburgh , Session 1877-78.

opposite the proximal telephone ; a fine glass rod or filament, 3
inches in length, was cemented to the centre of the disk of the
distal telephone ; to the other end of this rod two common micro-
scopical covering glasses, having between them a drop of blood,
were also cemented so as to be in a horizontal position. The drop
of blood thus fixed to the telephone disk was then brought under a
Hartnack’s ^th inch, magnifying about 300 diameters, and the
coloured blood corpuscles were brought into accurate focus. A key
was placed near the distal telephone, by which the current might
be transmitted or interrupted at pleasure. On opening the key,
the circular-coloured corpuscles at once assumed an oval form, and
were put somewhat out of focus, plainly the result of lateral move-
ment. Thus, by an application of Lissajoux’s method of observing
vibrations optically, the movements of the disk could be seen. I
found that the amplitude of the movements of the vibrating fork
(moving 60 vibrations per second), near the proximal telephone,
was about -g-th of an inch ; the movements of the corpuscles were
about half their diameter, or about g^gth of an inch. On stopping
the current by means of the key, the movements almost immedi-
ately ceased. Again, on taking away the glass rod from the disk,
and applying the ear to the disk, the low booming sound of the
fork could be heard. It is, therefore, evident that these sounds
were produced by movements of the disk, the amplitudes of
which were about the -6 oVoth of an inch, an interesting example of
the sensitiveness of the ear. The minimum limit of excitation of
the ear has been thus stated : — The faintest sound perceptible is that
caused by a ball of pith, 1 milligramme in weight, falling 1 milli-
metre in height upon a glass plate, may be heard at a distance of
91 millimetres from the ear ( Schafhdutl ).

The telephone appears to be an instrument which illustrates the
extreme sensitiveness of the ear, even better than the method of
Schafhautl just alluded to. The length of the hair cells in the
cochlea (which are stated to be tolerably stiff and rigid) is about
the -g^nr^th of an inch. One of them could therefore perform
an excursion of the growth of an inch. If, as Helmholtz
states, the mechanical arrangements of the bones of the ear
are such as to diminish to one-third the excursion of the mem-
brana tympani, and if no further reduction took place in the internal

562

Proceedings of the Royal Society

ear itself, the oscillations of the plate I observed, and which were
capable of causing a sensation of sound, would only amount, when
they reached the hair cells, to about the y-giro o' °f an inch, and thus
cause a movement of the auditory hair through about Jth of its
possible amplitude of excursion.

2 d Method — The movements may also be observed by throwing
obliquely a beam of light on a reflecting surface on the disk, and
catching the reflected ray on a screen. I did not find this method
so satisfactory as the one just described.

3 d Method. — I cemented the disk of the distal telephone to the
thin membrane of one of Koenig’s manometric capsules, then there
was no difficulty in observing the oscillations of the flame in a
rapidly revolving mirror, when a strongly vibrating tuning-fork was
placed opposite the proximal telephone. I failed, however, in
seeing any movements produced by speech. The method, how-
ever, is capable of more refined application than the means at
present at my disposal will allow.

4 th Method. — I have attempted to record the movements of the
disk graphically by attaching to it a lever bent at right angles at
one end, bringing the point on a rapidly moving surface. Ko
oscillations could be detected. Such oscillations were, however,
recorded when, instead of a disk, I used forks at the proximal and
distal ends, as already described. The movements of the distal
fork were then recorded, but it was observed that the sound of the
fork was audible long after all oscillations could be recorded, show-
ing that the movements of the fork were too delicate to be recorded
by this method.

5. A Mode of Intensifying the Sound of the Telephone. — In study-
ing the transmission of sounds of various kinds, I had occasion to
use a rapidly revolving wheel opposite the proximal telephone.
The wheel in my possession, which moves with greatest velocity is one
about 4 inches in diameter, having placed transversely on its circum-
ference twenty-four rectangular bars of iron. The wheel is driven by
two electro-magnets, and the current employed was obtained from
twenty of Sir William Thomson’s tray cells. With this power it
performs about eighty revolutions per second. When the proximal
telephone was brought near the circumference of the wheel, the
distal telephone sounded so loudly that a rattling sound like that

563

of Edinburgh , Session 1877-78.

caused by the wheel could be heard quite distinctly all over the
room. Evidently the effect of bringing the horizontal iron bars on
the circumference of the wheel rapidly in front of the core of the
proximal telephone was to intensify the currents of the telephones.
The currents were so strong that a disk held in front of the core of
the distal telephone could be felt vibrating by the hand.

The following Gentlemen were duly elected Fellows of the
Society : —

James Alfred Ewing, 22 India Street.

Rev. John Wilson, M.A., Bannockburn Academy.

Robert Macfie Thorburn, Uddevalla, Sweden.

Andrew Peebles Aitken, Sc.D., 16 Gillespie Crescent.

John Milne, Mechanician, Trinity Grove, Edinburgh.

Monday , 18 th February 1878.

Sir WILLIAM THOMSON, President, in the Chair.

The following communications were read : —

1. The application of the Graphic Method to the determina-

tion of the efficiency of a direct-acting Steam-Engine.
By Professor Fleeming Jenkin.

2. On the Disruptive Discharge of Electricity. By Alex-

ander Macfarlane, M.A., B.Sc. Communicated by Pro-
fessor Tait.

(Abstract.)

Last summer session, with the assistance of Messrs Salvesen,
Connor, and Stewart, I applied the method of measuring great
differences of potential, described in a paper by Mr Patou and my-
self (Proc. Feb. 19, 1877), to investigate the laws of passage of the
electric spark. The method essentially consists in connecting the
prime conductor of the Holtz machine, not with the electrometer
directly, but with an insulated spherical ball. This ball acts

564

Proceedings of the Royal Society

inductively upon another insulated spherical ball which is in con-
nection with the electrometer.

Before proceeding with the investigation proper, I tested the
accuracy of the method by applying it to determine how the in-
duced potential of the ball in connection with the electrometer
depends on the distance between the centres of the balls. I found
that the equation

V = 6081 r"1- 42-26,

where Y denotes the induced potential, and r the distance, between
the centres of the balls, satisfies all the observed values of Y for
values of r greater than twenty-four centimetres, but for smaller
values of r the function requires to be corrected by being multiplied

by

/(?•) = • 524 + -02 r.

Our method, when applied to measure the difference of potential
required to pass a spark through air at the atmospheric pressure
between parallel metal plates at different distances, gave a result
agreeing well with that which Sir William Thomson discovered to
be true for small distances. The function for V, the difference of
potential in terms of s, the length of the spark is

Y = 66*94 J{s2 + '205 s}

the equation of an hyperbole, whose semi-transverse axis is *1025
centimetres, and semi-conjugate axis 6*8623 centimetre-gramme-
second units. We observed, for lengths of spark, up to 1*2 centi-
metre.

From the above equation we infer that —

R = 66*94 + -205

where R denotes the electrostatic force ; from which it is evident
that as s becomes smaller, R becomes greater. But when the discs
were heated well, immediately before the taking of the observations,
the curve obtained satisfies the equation —

Y = 87*04 s- 19*56 s2
a parabola ; from which we deduce

R = 87*04- 19*56 5.

565

of Edinburgh , Session 1877-78.

This result, in my opinion, establishes the truth of Clark-Maxwell’s
hypothesis, that the greater electromotive force required at the
smaller distances is due to the existence of condensed gas on the
surface of the discs. Precisely similar results were obtained when
hydrogen was substituted for air.

The method, when applied to measure the difference of potential
required to produce a *5 centimetre spark at different pressures of
the air, shows that for the range between the atmospheric pressure
and twenty mm.,

V = ’0458 + 203 p)

where p denotes the pressure in millimetres of mercury.

The electric strengths of several gases were determined by com-
paring the differences of potential required to pass a *5 centimetre
spark through the gas at 746 mm. pressure.

Dielectric.

Electric Strength.

Air,

. 1

Carbonic acid, .

. *95

Oxygen,

. *93

Hydrogen,

. *63

Coal gas,

. *93

Several series of observations of the difference of potential re-
quired to produce a spark between spherical surfaces for distances up
to 15 centimetres confirm the result published in the paper already
referred to, that the difference of potential is proportional to the
square root of the length of the spark.

3. On the Compressibility of Water, Sea- Water, a four per-
cent. Chloride of Sodium Solution, Mercury, and Glass.
By J. Y. Buchanan, M.A., F.B.S.E.

4. On the Action of Heat on some Salts of Trimethyl-Sulphine.
By Professor Crum Brown and J. Adrian Blaikie, Esq.

(Abstract.)

The authors describe the preparation, properties, and action of

heat upon the following compounds of trimethyl-sulphine : —

VOL. ix. 4 F

566

Proceedings of the Royal Society

1st, The sulphide [(CH3)3S]2S ;

2d, The hyposulphite (thiosulphate) [(CH3)3S]2S202, H20;

3d, The oxalate [(CH3)3S]2C204, H20.

1st, The sulphide was prepared by dividing a strong solution of
trimethyl sulphine hydrate ([(CH3)3S]HO) into two equal parts,
saturating one with sulphuretted hydrogen, and then adding the
other. The strong aqueous solution thus obtained was placed
under a hell jar filled with coal-gas over anhydrous phosphoric acid.
After a certain concentration had been attained, sulphide of methyl
began to evaporate along with the water. When a solution pre-
pared in this way was sealed up in a glass tube, a very slight rise of
temperature caused the liquid to separate into two layers, the upper
consisting of sulphide of methyl and the lower of aqueous solution —

[(CH3)3S]2S = 3(CH3)2S.

This aqueous solution has all the characters of an alkaline sul-
phide. It dissolves sulphur, forming an orange-coloured polysul-
phide, it dissolves sulphide of antimony, gives the characteristic
reaction with nitro-prusside, and, when treated with an acid, gives
off sulphuretted hydrogen, a salt of trimethyl-sulphine being left in
solution. When exposed to the air, the sulphide is rapidly oxidised,
hyposulphite being produced.*

2d, The hyposulphite is best obtained by oxidation of the poly-
sulphide, by exposure to the air.

It crystallises in clear four-sided prisms with one molecule of
water of crystallisation. Analysis gave the following results : —

I.

II.

III.

Calculated.

C,

. 24*85

24*64

• • •

25*35

H,

6*94

7*06

• • •

7*04

s,

.

...

44*65

45*07

The salt

is very hygroscopic,

sparingly soluble

in alcohol.

gives all the reactions of an alkaline hyposulphite. Over anhydrous
phosphoric acid it loses 6*37 per cent, of water — the formula re-
quires 6*33 per cent.

The anhydrous hyposulphite, when carefully heated to about 135°
C., gives off sulphide of methyl — 5 545 grammes, heated in this
way, lost T308 grammes of sulphide of methyl, equal to 23*58

* See ante , pp. 320, 321.

of Edinburgh, Session 1877-78.

567

per cent., and left a white crystalline substance, soluble in water,
alcohol, and ether. The authors are at present engaged in the
investigation of this product.

3d, The oxalate is obtained by treating the iodide with oxalate
of silver. It crystallises, with one molecule of water, in clear
hygroscopic plates.

Analysis gave the following results : —

I. II. Calculated.

C, 36-95 36-78 36-93

H, 7-87 7-89 7-69

On carefully heating the salt to 110° C., the water of crystal-
lisation is given off. At 146° C. the anhydrous salt decomposes
into sulphide of methyl and pure oxalate of methyl —

[(CH3)3S]2C204 = 2(CH3)2S + (CH3)2C204.

The chromate and the iodate of trimethyl-sulphine were also pre-
pared. Heated to about 140° C. they both fuse, and almost
immediately explode.

5. Extracts from two Letters by Professor Quincke on the
Eefractive Indexes of Glass and Quartz, as tested by
Reflection from the Surface. Communicated by Sir
William Thomson.

In answer to your question about the alteration of surface in
quartz crystals, I place the glass or quartz
plate whose refractive index y is to be
determined between two right-angled flint-
glass prisms, with oil of cassia, and measure
the angle 0, at which total reflection begins
from the hypothenuse of the first flint-glass
prism ; the angle 0 can easily be calculated
from i , /x the refractive index of the flint-
glass, and P the angle of the prism. Sunlight
falls from a collimator with a slit upon the
system of flint-glass prisms, and after passing
through the second prism is examined by a direct vision set of

568

Proceedings of the Royal Society

prisms, I turn the system of flint-glass prisms until the spectrum
appears to he broken off at a definite Fraunhofer line, measure
the angle z, and thus obtain —

Sint,-—', 6 = V-i, x = /usin0.

Of course one can use flint-glass prisms other than right-angled ones,
and, in fact, for measures of quartz, I have had flint-glass prisms
made by Steinheil in Munich, in which i was only a few degrees.
In a plate of quartz cut perpendicularly to the optic axis, one can
easily determine in this way the refractive indices of the ordinary
and extraordinary ray by interposing in front of the eye a Nichol’s
prism in the proper position. In fresh quartz plates I obtained
almost exactly the same values as Rudberg : —

Rudberg.

B

C

D

E

F

G

1-54090

1-54181

1-54418

1-54711

1-54965

1-55425

1-54990

1-55085

1-55328

1-55631

1-55894

1-56365

Quincke ^

zur Axe.

1-54108

1-54207

1-54412

1-54710

1-54966

1-55365

1-54987

1-55065

1-55338

1-55622

1-55892

1-57166

Quincke Quartz _L zur Axe

c

1-54022

1-54092

1-54318

1-54575

1-54845

1-55246

1-54880

1-54955

1-55245

1-55533

1-55801

1-56163

Quincke Quartz _L zur Axe

;>

1-53958

1-54087

1-54335

1-54649

1-54868

1-55243

1-54789

1-54933

1-55199

1-55508

1-55758

1-56192

The differences of the individual measurements in different speci-
mens I attribute to difference in the properties of the specimens of
quartz themselves.

In old quartz surfaces which have already been about twenty
years in my possession, and in others which I have found in the

of Edinburgh , Session 1877-78

569

physical collections in Wurtzburg and Heidelberg, the refractive
index for the Fraunhofer line D varied between 1*5141 and 1*5374
for the ordinary ray, and between 1*5216 and 1*5470 for the extra-
ordinary.

I allow the first surface of the quartz to adhere by capillary
attraction, and my large horizontal circle, by which /x and i are
measured, reads to two seconds.

Crown glass plates from Steinheil, which had lain ten or twelve
years in a press, and whose refractive index for D was 1*5245, gave,
by total reflection at the surface, the refractive index 1*4903.

The alteration of the surface appears to me to be due, in quartz as
in glass, to a chemical change of surface, perhaps to the vapour in
the air forming a hydrate of silicic acid, or a hydrate of silic.

The above measures and arrangements have not yet been pub-
lished, but they are entirely at your service if you can use them in
your article on Elasticity.

I hoped to have sent you with the former ones some measures of
the refractive indices of natural quartz surfaces, but then the obser-
vations have to be made with reflected light, which impairs their
accuracy; besides, in spite of great trouble, I have not been able to
procure any quartz whose surfaces were flat enough and complete
enough for this inquiry. The only crystalline surface which I
could examine seemed to have the same refractive indices as fresh
polished surfaces. Besides, I am not astonished to find different
refractive indices in different quartz crystals, since I have invariably
found slight variations in the optical constants even for light trans-
mitted through different specimens of crystals, for instance, in the
amount of rotation of the plane of polarisation. Even if one had
kept the crystal for thousands of years under the same physical
conditions, for instance, at the same temperature, &c., still, accord-
ing to my opinion, the mode in which it was originally formed
would affect its final stationary condition. Crystals, like human
beings, and like films of liquid upon heterogeneous solid or liquid
surfaces, carry with them during their whole existence the mark of
their origin or birth. Two bodies can only show properties ex-
tremely alike, never exactly the same.

570

Proceedings of the Royal Society

Professor Jenkin called attention to experiments made by Mr
Gott in St Pierre, and published in the Journal of the Society of
Telegraph Engineers. Mr Gott converted two siphon recorders
into a telephonic system by mechanically connecting the suspended
coils with diaphragms. In this experiment the only conceivable
mode of action was analogous to that suggested by Professor
Graham Bell as the explanation of his telephone. This explana-
tion, if not complete, was not, in Professor Jenkin’s opinion,
erroneous. Professor Jenkin announced that he had, with Mr J.
A. Ewing’s assistance, constructed one of Mr Edison’s phonographs,
and that this instrument, like the telephone, gave a nasal intonation
to the words spoken by it.

Monday, 4 th March 1878.

D. MILNE HOME, LL.D., Vice-President, in the Chair.

The following Communications were read : —

1. Proposed Theory of the Progressive Movement of Baro-
metric Depressions or Storms ; being in continuation of
the Paper read before the Society on July 5, 1875.
By Mr Robert Tennent.

In this paper it is not proposed to discuss in their relations to
storms the effects of rain, of the earth’s rotation, of areas of high
and low pressure external to the storm-area, and of the prevail-
ing westerly winds, which are doubtless occasional factors in the
progressive movement of storms. What it is intended to show
here is that storms possess in themselves a self-motive power,
by which their onward movement over the earth’s surface is deter-
mined.

It will tend to clearness if attention be pointed at the outset to
two very different kinds of barometric depressions. The one which
accompanies the true cyclones of the tropics is, on comparison
with the height of the disturbance, of very limited extent, while

571

of Edinburgh, Session 1877-78.

the other, of which our European storms are examples, and which
alone are dealt with in this paper, is of very great extent as com-
pared with the height. The modes in which these two distinct
kinds of barometric depressions tend to fill up are widely different
from each other, owing particularly to the degree in which the
element of friction is introduced by the forces set in motion within
the storm itself.

Mode in which a Barometrical Depression of a Narrow Diameter
fills up. — In this case, since the diameter of the depression is small
as compared with the vertical height of the storm, it follows that
the inflow of the air-currents towards the area of lower pressure
will take place over a surface of comparatively small extent, and will
consequently meet with but little retardation from friction. Hence
the process of inflow toward the centre of the barometrical depression
will take place with comparative facility in true tropical cyclones of
small extent, and be therefore characterised by steep barometrical
gradients.

A C

Fig. 1.

Let ABC (fig. 1) represent a vertical section of such a depression,
and let the small arrows a , b, c, show the direction in which it will
tend to fill up over a surface of comparatively small extent,
accompanied by a steepening of the gradients B A and B C.

Mode in which a Barometrical Depression of Wide Diameter fills
up and in the process tends to open out. — In European and American
storms, the barometer at their centres falls about as low as in tropi-
cal cyclones, but the barometric gradients are much less steep, and
the disturbances cover a much more extensive region. Bedfield has
pointed out that their vertical height is often not more than the two-
hundredth part of their horizontal breadth. It follows from this
essential difference between these storms and true cyclones that
the mode of inflow of the air-currents towards the central low
pressure can neither take place in the same manner nor with a

572 Proceedings of the Royal Society

similar facility, but, on the contrary, much friction must now be
called into play, owing to the extensive resisting surface over which
the air-currents are drawn.* Since friction is much greater near
the earth’s surface than it is aloft, it follows that such storms are
characterised by greatly retarded surface currents, and rapid upper
currents. Looking at the mass of the atmosphere on the outskirts
and outside the area of the storm as the source whence the incurring
air-currents draw their supply, it is obvious that as regards the true
cyclone the source of supply is easy and copious, whereas in the
case of our widespread European storms, supply is comparatively
scarce, and therefore defective. In truth, as the lower and denser
air-currents are, owing to the enormous extent of surface they cover,
much retarded by friction, the main source of supply for the inflow-
ing currents is chiefly to be found in the rarer, more mobile, and
more rapid upper currents which flow comparatively free and unim-
peded. This essential difference in the mode of inflow of the air-
currents of these two types of storms is considered to be due to
differences in the amount of friction, accompanied also by a great
difference in the introduction of the important element of Time.
The difference in velocity between the surface and upper currents
is often very great. Thus Glaisher has shown from his balloon
ascents that the upper currents are sometimes five or six times more
rapid than the surface currents, while from observations made at
the top and base of Mount Washington, it was shown that on one
occasion the wind on the summit was blowing with a velocity of
ninety miles an hour at the time that a calm prevailed at the base
of the mountain.

The following illustration will show what is meant in this paper
by the expression opening out all round. Let a barometric de-
pression be formed several hundred miles in diameter, and let the
stratum of air resting on the surface be calm, whilst aloft upper
currents flow in upon the centre at the rate of ninety miles an hour.
In this case the central inflow will be carried out entirely by the
upper currents, and consequently there will result from this mode of
inflow an outward extension or an opening outwards of the area of
diminished pressure.

In fig. 2, A B C may be supposed to represent the vertical section
* “ Proceedings of R.S.E.” vol. viii. p. 613 and p. 614.

of Edinburgh, Session 1877-78.

573

of the barometric minimum of a true tropical cyclone as in tig. 1.
Let now DBF represent a vertical section of a barometric minimum
of a very much larger diameter. When it opens up all round in the
way described by means of rapid upper currents, it will be accompanied
by a lowering of the surrounding gradients from the upper part
of which the main source of supply is derived. The result is

Fig. 2.

that the depression originally embracing a circular space whose
diameter was D F will widen out, and the diameter extend to G H.
The inflow which in this way takes place along the gradients
bounded by the circle whose diameter is D F, as shown by the
arrows a and /, will now have the effect of lowering the gradients
B F and B D to B H and B G. The result of this may be repre-
sented by the removal of the air comprised in the spaces G B D
and H B F.

When the air moves more rapidly aloft than it does near the sur-
face, it may be conceived as moving onwards, not in vertical, but
in inclined columns ; and we have endeavoured to show* that this
mode of inflow is attended by “lifting,” and to some extent by
fictitious pressure, by which is meant that although the barometer
indicates correctly the elasticity of the air, still it no longer
represents its real mass overhead, but a pressure more or less
diminished owing to the mechanical movement of the air and to
friction. The opening out or extension of the area of barometric
minimum, with D F for its diameter, to a wider area, having G H
for its diameter, is effected by the upper currents, indicated by a and
/ of fig. 2. These upper currents, which flow in upon the low
central depression from a great distance all round, have their source
of supply in the upper still atmosphere around and outside the cir-
cular space over which they blow. It is here where outward exten-
sion and shallowing out commences, viz., along the curve which

4 G

VOL. IX.

* “ Proceedings,” vol. ix.p. 412.

574

Proceedings of the Royal Society

indicates the points where removal of air first begins to exceed
restoration. This line is what has been previously designated as
“ the curve of outward propagation.”*

This point, which is considered to be of great importance, may be
better understood by an illustration. If a river flowing down an
incline does so uniformly, and at an equal rate of speed, removal
will equal restoration ; but if in the lower part of its course a more
rapid removal is inaugurated, while restoration or supply above
remains as before, the curve representing the point at which the
increased removal begins to travel upwards will represent the forward
movement of this curve of outward propagation or extension.! Let
ABC (fig. 3) represent the inclined surface of a river, A B the

D

Fig. 3.

lower part of its course, in which a more rapid flow, and conse-
quently a more rapid removal, has commenced, and D B the
curved line which represents increased removal beginning to travel
upward. Let us suppose that A is the low centre of a large sheet of
water, towards which currents set in all round, and are there carried
off. If now the inflow towards this centre there begins to increase
in speed, the curve which extends all round will be propagated out-
wards, or in a direction opposite to that in which the currents flow.
A depression may thus practically fill up by shallowing out, extending
all round, and thereby lowering the gradients. When a depression
fills up rapidly, it is, of course, attended by a correspondingly rapid
rise of the barometer ; but when it shallows out by a process of lateral
extension the barometric rise is much slower. It is only in the
case of an imperfect fluid, such as air, flowing over a resisting surface
that the more special modes of inflow here insisted on can occur.
On a frictionless surface they could not take place. When we
consider the differences in the high pressures surrounding the
depression on its different sides, and the different qualities of the
air, as regards moisture and temperature, in different parts of the

* “ Proceedings,” vol. viii. p. 613. t Ibid. vol. viii. p. 614.

575

of Edinburgh, Session 1877-78.

depression, it is evident that the mode of inflow cannot be uniform
all round, and that horizontal extension will take place in some
one particular direction. This direction will be determined by the
curve of outward propagation, which thus marks the direction of
the onward course of the depression or storm.

The Mode in which Opening Out takes place , accompanied by a
transference of the Depression from West to East . — If a vessel be
lowered into the sea a corresponding amount of water will be dis-
placed. Let it then be supposed to move forward to the extent
of its own length, an opening out ahead will take place, and a
filling up astern. The original displacement will thus be closed
up, but a similar displacement will be found in the new
position to which the vessel has moved. Owing to its rigidity the
vessel moves forward unaltered, but as the surrounding water is
mobile, it cannot do so, hence it opens out and fills up. The currents
which run aft on each side of the vessel represent its forward move-
ment, while there is no real movement of the surrounding water,
except its gradual transference to the rear, in the direction opposite
to that in which the vessel moves. When an area of low pressure
moves in an easterly direction over the British islands, and to a dis-
tance equal to that of its own diameter, it will do so in a somewhat
similar manner, viz., by opening out and filling up. There is, how-
ever, an important difference to be noted ; for while the tranference
of the water, which enables the vessel to move forward, takes place
on each side in the direction of the stern, the transference of the
air, when the depression moves eastwards, takes place on the north
segment from the front, where it opens out to the rear where it fills
up, as all observation shows. It may be pointed out here that
while depressions move forward, the aerial particles, or the mass of
air, does not move forward, and viewed in this light the curve of
outward propagation may be regarded as being a purely ideal curve.

The severe N.E. storms, which are of so frequent occurrence as
to form a marked feature of the climate of the New England States,
were long ago pointed out to advance on this region in an opposite
direction from that in which they blow. Let the area of the storm be
represented by the circle A B C E (fig. 4), then the front part ABC
is the curve of outward propagation, which moves toward the N.E. in
the direction of the arrow I) E, this being the contrary direction to

576

Proceedings of the Royal Society

that in which in the segment A B the N.E. wind blows. Clouds
apparently moving from the S.W. are often observed in this part
of the storm, where N.E. wind first begins to exhibit itself. No

general movement of the air, however, takes place, because it is
here that it first commences and continues to be generated from the
still atmosphere ahead, where the curve of outward propagation
advances upon it. This continued generation also represents what
takes place in the clouds. Their apparent movement, which is due
solely to their additional formation, is the result of atmospheric
changes which must here take place. Hence occasionally they do
not represent the force and direction of the wind. Similarly sea-
men often observe a gale approaching from some point to leeward.

It has been supposed by some writers that the progress of storms
is due to the area of low pressure being impelled forward by the
high pressure usually found near their rear, aided by the diminished
pressure in front, which is due to heat and vapour. If this were
the case, it is evident that a derangement would take place as
regards the circular symmetry of the storm and the direction of the
spirally inblowing winds, owing to the enormous friction which
these widespread storms would encounter in being pushed forward
over the earth’s surface. The more evident of these derangements
would be the steepening of the barometic gradients in front of the
storm, a result the reverse of what observation shows to take place.
The Rev. Clement Ley has shown that the isobars are widest, and
gradient consequently lowest in the front of the storm.* Further,
if this were the cause of the progress of storms, areas of depression
would move more rapidly over the ocean than over the land. Pro-
fessor Loomis has shown, however, that while the average rate of
* See “ Journal of Scottish Meteorological Society,” vol. iv. p. 149.

577

of Edinburgh, Session 1877-78.

progress of depressions over the ocean is 19 miles an hour, over
the land the rate is 26 miles an hour. It is also evident that
if a depression moves forward accompanied by spirally inflowing
winds, — considered simply as inflowing air-currents, and not as
representing an efficient motive force capable of generating forward
movement, — a derangement as regards their force and direction
would take place, especially on those occasions when the onward
march of the storm attains a speed of 70 miles an hour. But in no
case has such a derangement been observed.

Proposed Theory as to the Progress of Storms. — When, however,
the depression is not being impelled forward in the mode above
described, but in virtue of an opening out in front, and when
the air-currents, inflowing spirally upon the centre, are regarded
as an effective motive force capable of causing progressive motion,
no derangement can be supposed to take place as regards the
force and direction of the air-currents ; and no steepening of the
gradients in front will take place, since the change in the position
of the depression is effected with facility by the transference of the
air from the front to the rear along the north segment of the depres-
sion.

A depression advances by means of these spirally inflowing currents,
owing to the difference which exists in their mode of inflow, and conse-
quently in their force and direction ; and it is in this way that outward
extension in one direction is carried out. This difference in the mode
of inflow is mainly due to the introduction in a much higher degree
of the element of friction into the currents of the front segment ; in
this way scarcity of supply is produced in this part of the depres-
sion, and the effect is intensified by the ascending tendency of the
air in this segment of the depression. On the other hand, the
currents which enter in at the rear are much less retarded by fric-
tion, because there is a descending tendency of the air in this
segment, and, consequently, supply is copious.* The low central
pressure, by travelling onwards towards the region in front, where
supply is scarce, and where opening out takes place, practically
overcomes this scarcity of supply, and thus uniformity of inflow is
practically restored by progressive movement. If there was no
progress, and if the depression was accompanied by this want of
* “Proceedings,” vol. viii. p. 613-615.

578 Proceedings of the Royal Society

uniformity in the mode of inflow, it would then tend to fill up.
Progress is therefore the means by which a depression is maintained.

Since the difference in the mode of inflow is due to a difference in
the amount of friction called into play, we have here, probably, the
reason why storms advance more rapidly over the land than over
the ocean. The deflection of the winds produced by the earth’s
rotation, and the irregularity in the amount of pressure at different
points immediately outside the area of the depression itself, have
doubtless important bearings on this whole question.

It is very generally supposed that the spiral inflow to the centre
is supposed to be there carried off by means of a vast ascending
current from the centre. This opinion is, however, open to serious
objections, but which it would be out of place here to discuss.

The general result is, that progress is regarded as being due to an
irregularity in the direction and force of the spirally inflowing currents,
arising from the different degrees in which the element of friction
is called into play in the different segments of the storm, accom-
panied or aided by high pressure on the right of the direction in
which the depression moves.

Summary. — When a depression is formed with a narrow diameter,
it fills up rapidly if it has a copious supply from the surrounding
atmosphere, and the filling up is of course attended by a rapid
rise of the low central barometer. But if the depression has a
very large diameter, the element of friction must enter largely
into the problem. The retarding influence due to this cause will
necessarily be greatest in the denser currents near the earth’s
surface ; while the light, rarefied, and mobile upper currents
will move with great facility. Hence the main source of supply
will be thrown on these freely flowing upper currents. The
rapidity and facility with which they inflow give rise to horizontal
extension or shallowing out aloft, and this extension would take
place equally all round if the inflow were uniform in all the seg-
ments of the depression. If, however, this uniformity of inflow
does not exist, but is more copious in one segment and scarce in
another, then extension and shallowing out will take place towards
that particular direction where supply is scarce. Hence progressive
movement takes place in this direction, and is attended by filling
up in the rear. When supply is equally copious in all directions,

579

of Edinburgh, Session 1877-78.

the low central barometer rises rapidly ; but when the supply is not
copious and uniform all round, the barometer does not rise, because,
though the depression fills up in the rear, there is a corresponding
opening out in the front, and the central barometer remains low
— thus producing the central spiral inflow which generates the
motive force to which the progressive movement is due.

2. On the Thermo-electric Properties of Charcoal and certain

Alloys, with a supplementary Thermo-electric Diagram.
By C. G. Knott, B.Sc., and J. G. MacGregor, D.Sc. Com-
municated by Professor Tait.

3. On the Auriferous Quartz of Wanlockhead. By Dr Lauder

Lindsay.

4. On the Discharge of Electricity through Turpentine. By

A. Macfarlane, B.Sc., and Mr B. J. S. Simpson. Com-
municated by Professor Tait.

5. Remarks on the Phonograph. By Professor Fleeming

Jenkin and Mr J. A. Ewing.

Professor Pleeming Jenkin and Mr J. A. Ewing exhibited a
phonograph which they had constructed, and also some curves
drawn on paper representing the indentions produced in the tinfoil
of the instrument by vowel sounds.

The phonograph exhibited had been constructed from a description
of the instrument invented by Mr Edison, and consisted of a barrel
about four inches diameter and four inches long, mounted on a
spindle on which a square-threaded screw had been cut. One
bearing of the spindle was cylindrical, and the other was a nut in
which the screw worked. A fly-wheel handle turned the spindle
and barrel, which advanced during each turn by a distance equal to
the pitch of the screw. A helical groove, about — in. in breadth,
was cut on the surface of the barrel, having the same axial pitch
as the screw on the spindle.

A smooth strip of tinfoil was gummed round the barrel, and in-

580

Proceedings of the Royal Society

dentations produced in this strip by a point attached to a vibrating
disc stretched across a short brass cylinder 2|- in. diameter.

The same vibrating disc was used to produce the indentations
and to reproduce the sounds.

The usual ferrotype plate had not been tried as a vibrator, for
hard metal discs were found to give a disagreeable resonance to the
voice and its reproduction. A slack tinfoil disc had been used with
good results ; the marker was attached firmly to a small disc of
stiff paper \ in. diameter, gummed to the tinfoil ; a short piece of
watch spring was also attached to the marker, so as to give the disc
a rapid period of vibration.

A sentence reproduced by this disc was loud enough to be heard
by many people standing round, and sentences had been heard by
several persons who understood them without any previous idea of
what they were. This result could not, however, always be secured.
When the sentence was known to the hearers, it appeared to he
given back with startling accuracy. The vowel sounds were more
distinct than the consonants, hut the consonants also were dis-
tinctly to be heard. The tinfoil vibrator gave more articulate
sounds when slack and irregular than when it was neatly strained
over the end of the tube.

An oil-silk disc had also been tried with no spring, and a simple
marker attached to a disc of mica, gummed to the oil-silk. This
disc gave purer sounds than the tinfoil, but they were not nearly so
loud. The indentations on the tinfoil were excellent to the eye,
and quite as large as with the tinfoil.

The oil-silk answered best when irregularly stretched.

An india-rubber film, with a similar mica disc and rigidly attached
marker, had also been tried, and gave beautiful records on the tin-
foil strip, but this disc failed to reproduce the sounds accurately,
having a note of its own.

This latter disc was used to produce records which were subse-
quently enlarged and shown on paper in the form of curves. The
india-rubber was preferred for this purpose, because the gentle and
uniform pressure which it gave did not tend to obliterate the records.
The curves exhibited showed the form of the indentations magnified
about five hundred times. This magnification was effected by two
compound levers, of which the second was a glass siphon like that

of Edinburgh, Session 1877-78.

581

of Sir William Thomson’s recorder. This siphon deposited the
trace of the curves on a paper strip rolled on the periphery of the
large disc used by us for the experiments on friction published in
the “Transactions of the Royal Society of London” for 1877.

The authors had not yet had time to analyse these curves and
compare them with Helmholtz’s theory of vowel sounds.

The advantage of recording the curves corresponding to the
several sounds indirectly by means of the tinfoil, instead of directly,
as in the case of the phonautograph, consists in the fact that with
this arrangement the amplitude of the oscillations may he greatly
magnified without introducing any sensible error due to the inertia
of the moving parts. The paper band and tinfoil record were
moved at a very slow speed, and their relative advance was
rendered quite definite by a mechanical connection between the two
barrels on which they were wound.

The following Gentlemen were duly elected Fellows of the
Society : —

Charles Davidson Bell, Retired Surveyor-General, Cape of Good Hope,
19 Dean Terrace.

James Blyth, M.A., 8 Middleby Street.

R. K. Galloway, M.A., Jesus’ College, Cambridge, 10 West Claremont
Street.

Monday, 18 th March 1878.

Sir WILLIAM THOMSON, President, in the Chair.

The following communications were read : —

1. On Thermal Conductivity. By Professor Tait.

(Abstract.)

This paper contains the results of a laborious series of experi-
ments and calculations carried out during the last ten years, the
object being the repetition and extension to other metals than iron
of Forbes’ experiments, described to the Society in 1862 and 1865.

As a check upon his work, the author first experimented upon the

VOL. ix. 4 H

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Proceedings of the Royal Society

iron bar employed by Forbes, and reproduced, almost exactly,
Forbes’ results for that metal — the most notable feature of which,
besides the first really trustworthy determination of absolute con-
ductivity, was the discovery that the thermal conductivity of iron
is diminished by heating, and is very nearly proportional to the
reciprocal of the absolute temperature.

None of the other metals tried by the author, viz., copper (two
specimens, selected as being specially good and specially bad con-
ductors of electricity), lead, and German silver, gave at all analogous
results. Their absolute conductivities have been determined ; and
the changes produced by heat in these conductivities were, where
any, very slight, and uniformly in the direction of improved con-
ductivity at higher temperatures.

A second part of the paper is promised, to contain comparisons
of thermal and electric conductivity in the same substance, with an
investigation of the “ Thomson effect.”

2. On the Wave Forms of Articulate Sounds. By Professor
Fleeming Jenkin and Mr J. A. Ewing.

In this paper the authors gave a preliminary account of experiments
made with the help of the phonograph exhibited at the last meeting.
The following results have been obtained : —

1. The vowel sounds can be produced by maintaining the relative
pitch of the simple tones of which they are composed constant,
although the absolute pitch of those simple tones may vary greatly.
The authors found that whether they turned the barrel of the
phonograph at a greater speed or at a less speed than that which
had been maintained while the human voice produced the indenta-
tions, the several vowels were given back writh equal distinctness.

This experiment proves that within certain limits a given wave
form in the tinfoil produces a given vowel independently of the
rapidity with which it passes the pricker of the vibrating disc.
It proves therefore that within these limits a given group of partials
is competent to produce a given vowel effect, whatever be the
absolute pitch of the prime tone, and of the relative partials. This
result is of much importance, since Willis, Wheatstone, Donders,

583

of Edinburgh, Session 1877-78.

and Helmholtz seem all to consider that a certain absolute pitch is
characteristic of each vowel.

[Note. — May 24. — Since the above communication was made to
the Society, the authors have improved their phonograph, and also
their apparatus for enlarging the record embossed on the tinfoil.
For this reason they have substituted in the figures shown better
curves than those which were originally presented to the Society.
Subsequent experiments with the improved instrument also render
it desirable to add a few words to the statement made in the text as
to the effect of altered speed in the quality of the sounds given by
the phonograph. The original experiment consisted in speaking
the set of vowel sounds, A, E, I, 0, U (pronounced in Italian
fashion), to the phonograph, and then listening to the sound given
when the instrument was run at various rates. The vowels were
observed to maintain their relative places, so as to form the complete
series in which each individual sound was by contrast at least
recognisable as the vowel which had been spoken. This experiment
has since been frequently repeated with perfect success. Again, if
a single vowel sound, such as “ oh,” be sung to the phonograph at
an ordinarily high pitch, it will be found to remain oh through a
considerable range of speeds ; but the oh whose pitch has been
raised by quickening the phonograph seems to the authors brighter
than the oh sung by the human voice at a correspondingly high
pitch; that is to say, it resembles “awe” to some extent. Similarly
the spoken “ aive ,” when accelerated, passes into a sound like ah.
The change appears to be greater with some vowels than with others,
and also to depend partly on the pitch at which the vowel has been
originally sung. The instrument is, however, even in its present
improved form, not well adapted for testing any fine gradation of
the quality of sound. Although the authors now feel unable to
speak with any confidence as to change of quality produced by a
change of speed, they consider it proved that the vowels, A, E, I,
0, U, remain distinguishable by contrast when all their constituents
are simultaneously raised or lowered to a considerable extent, but
they do not consider that the phonograph is as yet sufficiently perfect
to enable them to judge how far the definition of constant quality
suggested in § 3 below would or could be accepted by the ear.]

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Proceedings of the Royal Society

The authors’ experiments do not prove that a given vowel always
produces a definite wave form.

2. A given person pronouncing or singing a vowel sound at a
constant pitch produces a wave form of remarkable constancy.
This proves that the relative phases of the simple tones, of which
the compound tone is built up, do not alter, while a single vowel is
being sung or intoned on one note. The same person or different
persons pronouncing the same vowel on different occasions, will
frequently reproduce wave forms closely similar, but the experiments
are not yet sufficiently extended to determine whether a given voice
speaking the same vowel at a given pitch will always produce the
same wave form.

3. A given person singing the same vowel throughout an octave,
often produces wave forms of different appearance on different, notes,
although he may be endeavouring to keep the quality of his vowel
constant. It must on this be remarked that up to the present time
there has been no standard or criterion as to constancy of quality at
different pitches. This has been a mere matter of appreciation by
different ears. A standard wave might, indeed, be taken and declared
to be the form which gives a constant quality at all pitches. The
phonograph is sufficiently distinct in its utterance to allow it to be
said that such a standard a or o will be accepted within a consider-
able range as the same vowel, but it cannot be affirmed that all
hearers would say that the quality of the vowel was constant in
their judgment at all pitches. It is, however, possible that hence-
forth constancy of quality may be defined as that given by constancy
of wave form.

4. The vowels are heard equally well, or nearly so, whether the
machine is run backwards or forwards. The authors put in the
saving clause “nearly” everywhere, because the sounds obtained
from the phonograph are not sufficiently clear to warrant more
absolute conclusions. This reversibility is a necessary consequence
of Helmholtz’s theory that the ear decomposes the compound tones
into their harmonic constituents, and is indifferent to the phase
relation of these.

5. Hot only the vowels but the consonants are substantially the
same when produced backwards. This result is novel to the authors,
and is, they believe, quite unforeseen. There is little to wonder at

of Edinburgh , Session 1877-78.

585

in the fact that r, or s, or 0, which are continuous, should sound
alike backwards and forwards, hut it is very remarkable that sounds
like p or k at the end of the syllable should, when produced back-
wards, give the same effect asj? and k at the beginning of a word.

The authors tested this singular fact in the following way : — They
first arranged that a simple combination, such as “abafa” or
“ afaba,” should be said to the instrument while one observer was
out of the room. He then came in, and heard the word backwards.
If the original word had been “ abafa,” he was in all cases able to
say that he heard “ afaba ”; if the original word had been “ adaka,”
he heard “ akada.” Inasmuch as he was quite uncertain whether
the word spoken to the instrument was “ adaka ” or “ akada,” this
experiment was in itself almost decisive. All the letters of the
alphabet were tried in this way. Tearing, however, that when the
alternative lay between two consonants, these might be recognised
by some other quality than their true sound, the authors next
proceeded to test the fact by speaking short words, such as “ amma,”
“ abba,” and so forth, to the instrument. These were recognised by
an observer from outside when spoken backwards. “ Alla ” was
recognised at once; “appa” was called “abba”; “amma” was re-
cognised at once; “ atta ” was called “adda.”

The greatest difficulty was met with in distinguishing s from /,
but the difficulty was not greater backwards than forwards. It
seems due to the fact that the instrument used will not record the
high tones which are obviously present in these sounds.

When the fact had been established that a consonantcould be
sounded backwards between two vowels, monosyllables were next
tested : “ ba” was reversed and heard as “ab ;” “ ka ” was reversed,
and heard as “ ak.”

This is even more remarkable than the previous results, inasmuch
as the mode of pronouncing b or k at the end of a word is different
from that employed when it begins a word.

Finally, by pronouncing any word backwards, such as
“ noshaeesossa,” and then reversing the instrument, the original
word (association) was clearly heard. With a little practice, a sen-
tence might be spoken backwards, and then heard intelligibly
forwards.

The letter li was not in the phonograph to be distinguished from

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Proceedings of the Royal Society

ch, and gave a single reversible sound. “ Ho,” when turned back,
sounded distinctly “ och.”

Since both vowels and consonants sound alike backwards and
forwards, it appears that articulate speech may be divided into a
series of successive parts, each having a character of its own, and
each reversible so far as sensation is concerned.

The separate reversible sensations correspond in the main to the
letters of our alphabet, but our letter i represents at least two rever-
sible elements, and ch , ?^y, or th , on the contrary, are single sounds.
Clear, clean sounds, as spoken by educated people in all countries,
seem remarkable for the small number of the elements that enter
into each word. An uneducated man, speaking a dialect or patois ,
will make each nominal vowel consist of a large group of simple
reversible sounds running into one another.

6. The wave form for the letter r has been recorded. It agrees
with that obtained by Donders on the phonautograph, and consists
of a series of simple curves, similar to harmonic curves, which gradu-
ally increase to a maximum, and then gradually decrease to a
minimum. The number of waves separating the maximum from the
minimum intensity of the sound was in the examples observed 7 or
8. The length of the whole period was therefore 14 or 16.

7. The wave forms obtained from the letter o in figs. 4 and 5
illustrate the difficulty which the ear, even of trained musicians,
feels in determining the octave in which a given note is sung. It
will be seen that each period consists of two very nearly equal parts,
and that the amplitude of the second partial has obviously been
large as compared with that of the prime tone. To one ear it might
seem natural to call the pitch that of the second partial, since this
was the loudest tone ; to another the pitch would be that of the
prime, because this tone was lowest in pitch. Naming a given note
by the lowest of its component tones, irrespective of the relative
intensity of the partials, seems to be a convenient but conventional
rule.

8. The instrument as at present made does not record all sounds.
This is shown by the fact that its reproduction of the French u is
very imperfect, and ee is only sometimes well heard from it.

The curves laid before the Society were obtained by multiplying
the traces on the tinfoil some 300 times by means of a system of

of Edinburgh, Session 1877-78.

587

levers. The lines were drawn on the paper by the plan of friction-
less marking invented by Sir William Thomson, and used in his
Siphon Recorder. A rise in the curve (on the page) corresponds to
a hollow in the tinfoil. The arrow pointing from right to left,
indicates the direction in which the tinfoil passed under the vibrat-
ing pointer when the sounds were uttered.

The authors hope soon to be able to communicate to the Society
the results obtained by subjecting the experimentally drawn wave
forms to harmonic analysis.

Fig. 1 gives the curve made by the sound of oo, as in “ food/’ on

Tig. 1.

the note b ; fig. 2 is oo on f by the same voice ; and fig. 3 is a still

Fig. 2.

Fig. 3.

higher oo by another voice. As the speed at which the phonograph
was turned was very nearly the same in all the examples, the relative

Fig. 4.

pitches are approximately given by the lengths of the periods.

588 Proceedings of the Royal Society

Figs. 4, 5, and 6 show the waves given by the sound “ oh f spoken at

Fig. 6.

various pitches by the same voice (that of Dr Crum Brown). Figs.

Fig. 7.

Fig. 8.

7 and 8 are given by the sound a in “ father,” the first on c by Sir
B. Christison, the second on c' by Professor Jenkin.

3. On the Action of the Chlorides of Iodine upon Acetylene
and Ethylene. By George M‘Gowan.

Before giving the action of ethylene on the chlorides of iodine, I
may shortly describe the method of preparing the latter, which I
found to he the most advantageous : —

A weighed quantity of perfectly dry iodine being introduced into

589

of Edinburgh, Session 1877-78.

bulb A of flask 1, perfectly dry chlorine gas is passed over it,
A being at the same time heated over a water-bath to about
60° to 80° C. The IC13, as it is formed, volatilises and condenses
almost entirely in B, only a small portion escaping into flask 2.
Chlorine is passed until no more iodine remains in bulb A. If the
heating be omitted, only the outermost layers of iodine are converted
into the trichloride, a kernel remaining unacted on. (Compare
Christomanos , Berl. Ber. X. Xo. 5, p. 434.)

The tubes connecting the two flasks are ground into one another
at D, so that no cork or caoutchouc fittings are required. This is
absolutely necessary.

By attaching a small CaCl2 tube to E, no moisture can enter the
apparatus. The flasks can be weighed either together or separately.
When passing ethylene or acetylene over either of the iodine
chlorides, I found it best to cleanse and dry flask 2, leaving the gas
to act on the chloride in 1. In that way any volatilised matter
from 1 was condensed in 2, and the loss of weight was very trifling.

By adding the required weight of iodine to the IC13, and heating
gently over a water-bath (the vessel being corked), IC1 is easily
prepared. I invariably got it in the state of long needles.*

Action of Ethylene (C2H4) on IC13.

By passing pure dry C2H4 over pure dry IC13 at 0° C., the two
compounds chloride and chloriodide of ethylene are formed.

This reaction takes place quantitatively, thus : —

(C2H4)2 + IC13 = C2H4C12 + C2H4C1L

grms. grms.

Weight of flasks, 169*2

„ +IC13, .... 202*5 = 33*3 IC13

„ after saturation with C2H4 . 210*1= 7*6 C2H4

Theory requires 7*98 grms. C2H4.

* It is generally stated that IC1 dissolves in alcohol and ether, forming
yellow solution. (See Watts’s Did. of Chem. vol. iii. p. 293, new ed.) The
fact is, that if ether (perfectly free from water and alcohol) be dropped into
I Cl, a most violent reaction ensues. If, on the other hand, IC1 be dropped
into a large excess of ether (or alcohol) at 0°, it dissolves, at first forming a pale
yellow-brown solution ; but, in the course of a few minutes, the ether becomes
darker and darker from separation of iodine. The chlorine probably acts on
the ether to form dichlor-ether (C4H8C120) for the most part. This requires to
be investigated.

VOL. IX. 4 I

590

Proceedings of ike Royal Society

After saturation, the fluid was almost colourless, having only a
pink tinge of iodine. The two above fluids can (after washing
with dilute KOH and drying) with some difficulty be fractionated.

C2H4C12 boils at 85° (Fittig).

C2H4C1I „ 147° (Maxwell Simpson).

Preparation of Acetylene (C2H2) from Ethylene Dibromide

(C2H4Br2).

Having prepared about a kilo, of C2H4Br2, 1 decomposed it accord-
ing to the method described by Sabanjeff (Annalen, Band 178).
Briefly described, this method is as follows : — Into a thick flask of

about one litre capacity, more than half filled with a concentrated
alcoholic solution of KOH, and heated over a water-bath to 100° or
thereabouts, C2H4Br2, pure or diluted with alcohol, is slowly and
regularly dropped from a separating funnel. The C2H2 disengaged,
passes off through an upright Liebig’s condenser, also affixed to the
flask, by which means most of the monobrom-ethylene (C2H3Br)
formed at first, and carried away along with the C2H2, is returned to
the flask. Some of it, however, escapes undecomposed from this flask
into a second one, also containing alcoholic KOH, and fitted with

of Edinburgh, Session 1877-78.

591

an upright condenser, precisely in the same manner as the first. In
this second flask it is practically entirely decomposed. The C2H2
is then passed through alcohol at 0° (to absorb traces of C2H3Br),
then through two Wollf’s bottles filled with water, and lastly through
two CaCl2 tubes. The gas may then be considered practically pure.
To test this, I passed it for about half an hour through the two
weighed flasks, surrounded by a mixture of ice and salt, but at the
end of that time they had not gained in weight to speak of.

To prepare first cuproso vinyl oxide-—

C4Cu4H20 ( Berthelot .)

and then decompose this by dilute hydrochloric acid, is an extremely
tedious and troublesome operation, and offers very little corre-
sponding advantage. Sabanjeff discusses the other known methods
for the preparation of C2H2 very fully in his paper. I also tried
some of them, but found the above by far the best of all.

Action of Acetylene (C2H2) on IC13.

On passing C2H2 over pure dry IC13 at 0°, combination takes
place with great evolution of heat. I always found more or less
iodine separated out. My chief object being to try to prepare the
compound, C2II2C1I, I did not investigate farther the products
formed. Probably, if the IC13 were kept cold in a mixture of ice
and salt, and the C2H2 diluted with air and passed over it very
slowly, one might get the compound C2H2C13I.

Action of C2H2 on IC1.

(a.) On pure IC1 at 0°.

The evolution of heat produced by the combination was so great
that more or less iodine always separated out.

( b .) On IC1 dissolved in excess of ether at 0°.

The ether used must be perfectly free from alcohol and water.
The C2H2 was passed as quickly as possible through this ethereal
solution, to reduce as much as might be the secondary reaction of
the IC1 on the ether. It was absorbed greedily.

After saturation the ethereal solution was diluted with water,
when a heavy liquid settled to the bottom. This was washed with
dilute NaOH solution, and then with water, and dried over CaCl2.

592

Proceedings of the Royal Society

What ether remained in the above liquid;was distilled off at 35° to 40°
in a current of C2H2. Even at this temperature a slight decomposi-
tion occurred (iodine separating), so I stopped heating. It was
found practicable, however, to fractionate the liquid (with very slight
decomposition) in a current of steam. Eepeated fractionating
yielded

(1.) Ether + C2H2C12, &c. (not examined).

(2.) C2H2C11 4- .

(3.) Solid C2H2I2.

To ascertain the composition of the above liquid I analysed it.

+ 0*6687 grm. ignited with pure CaO gave —

Tube . . . 22*9350 grms.

„ + (AgCl + Agl) 24*2482 „

„ + (AgCl + AgCl) 22*9207 „

(after converting Agl into AgCl by current of Cl).

AgCl (on filter) . . 0*0127 grm.

Calculated, this gives —

Found. Theory for C2H2C1I.
I 67*38 . . 68*77

Cl ... 18*83 . . 17*59

The above figures do not agree very exactly, but I had too
small a quantity of the compound to be able to fractionate it
perfectly. It was found impossible to determine its boiling point,
as it decomposed very rapidly on heating, with separation of iodine.*

Spec. Grav. . . . 2*41 at 13*5° C.

Acetylene chlor-iodide is an ethereal liquid with much the same
odour as the corresponding ethylene compound. Its vapour attacks
the eyes. It does not decompose to any extent if kept in the dark.

Remarks on Acetylene Iodide (C2H2I2).

I prepared from 50 to 60 grms. of the above compound bypassing
the gas through a saturated alcoholic solution of iodine. As the two

* It seemed to boil at first, on heating very rapidly, between 180° and 190° C.,
but this is not reliable.

593

of Edinburgh , Session 1877-78.

combine very slowly, tbe iodine must be distributed in numerous
small flasks, which ought to be hung on a glass rod, horizontally
placed, to admit of their being shaken from time to time. (See
Sabanjeff, Annalen, Band 178 ; also Semenoff (for C2H4I2),
Zeitschrift fiir Chemie, 1864.)

Sabanjeff states that he, while preparing the iodide in this
manner, got at the same time a large quantity of a liquid
iodide (also of the formula C2H2I2). He supposes the one to
CHI CH2.

be 1 1 and the other 1 1 Curiously enough, I only obtained a
CHI CI2.

few drops of a liquid which could at all correspond to this second
iodide. Whether it was the iodide, or a product of the action of
the iodine in the alcohol, &c., I cannot say. The quantity got was
too small.

The chief object which I had in view in preparing the preceding
acetylene compounds (chlor-iodide, iodide, also tetrabromide, &c.),
was that from them I might be able to obtain the corresponding
cyanogen ones, which, if got and treated with an alkali, would
probably have yielded chloro- (or iodo-) acrylic, and fumaric or
maleic acids. I have not, however, as yet succeeded in obtaining
them.

Whether C2H2 combines with iodide of cyanogen when the latter
is dissolved in alcohol, I cannot yet say. It does not with dry

ICK

All attempts to obtain the cyanogen compounds of C2H2 by
heating in sealed tubes (at temperatures ranging from 120° to 0°25)
chlor-iodide or iodide of acetylene with the various cyanides {KCN,
AgCN, (AgCH + KChT), H2(CN2),} or with ICN and a metal, were
fruitless.

When H2(CN)2 was used, generally no reaction occurred, and in
nearly all the other cases ammonium salts were formed in large
quantity. I had unfortunately only a small quantity of the chlor-
iodide at my disposal.

Acetylene does not seem to be absorbed if passed into a hot
solution of “ nascent” formic acid, i.e.} a solution containing KCN
and KOH.

594

Proceedings of the Royal Society

4. On some Definite Integrals. By Professor Tait.

The integrals referred to occur in connection with applications of
the Method of Electric Images. A curious special case was given
to the Society in July 1875, hut was not inserted in the “Pro-
ceedings.” It depended on the fact that the image of a sphere,
whose surface density is inversely as the cube of the distance from
a point, is another sphere with a similar law of distribution. But
any desired number of integrals, whose values can be at once
assigned, may be obtained by various applications of the following
process. Take any centrobaric distribution of electricity, and calcu-
late directly the density induced by it at any point of an uninsulated
sphere. This must be inversely as the cube of the distance from
the centre of gravity of the given distribution.

Take, as a simple example, a uniformly charged sphere of non-
conducting matter with unit charge, radius a, at a distance p from the
centre of an uninsulated sphere of radius r. Suppose r >a+p , so
that the inducing sphere is wholly internal. We see by the method
above that the density of the induced charge at points defined by
radii making an angle a with the line of centres is represented by

1

either of the following expressions, multiplied by

87r2r

rr

(r2 -a2-p2-\- 2 ap cos 0) sin 6d6d(p

2tt (r2 —p2)

[r2 + a2 +p2 - 2 ap cos 0 - 2 rp cos a + 2 ar (cos a cos 0 - sin a sin 0 cos <f>) ]f (r2 + _ 2 rp

cos

i.e ., the double integral is independent of a.

Again, if the unit charge on the small sphere be distributed
inversely as the cube of the distance from the centre of the large
one, we have obviously for the induced density on the large sphere
the expression —

87r2r.

yr,

(a2 - p2) (r2 - a2 -p2 + 2 ap cos 0) sin Oddd<p

0 0

[a2 + p2 - 2ap cos 0]i[r2 + a2 +p2 - 2ap cos 0 - 2 rp cos a + 2 ar (cos a cos 0 - sin a sin 0 cos

But if the small sphere include the centre of the large one, f.e., if
a>p, the induced density is uniform; so that the value of the
integral is

5j7T

ar

595

of Edinburgh, Session 1877-78.

If a<p, similar reasoning shows that the value is

fr2 ~(p~ jT)

a(r 2 + (p - jJ - 2 r[p - ^)cos a)
These values agree, as they should do, when a —p.

Monday, ls£ April 1878.

Sir WILLIAM THOMSON, President, in the Chair.

The following communications were read

1. Chapters on the Mineralogy of Scotland. Chapter IY.
Augite, Hornblende, and Serpentineous Change. By

Professor Heddle.

(Abstract.)

A. couple of months ago I had the honour of submitting to the
Society a speculation upon the metamorphism of a particular rock
mass. To-night I again return to metamorphism, submitting, how-
ever, not a speculation, but the closely elaborated process of the
change which has affected another rock.

It is perhaps natural that the attention of one who approaches
geology from the chemical and mineralogical sides should be imme-
diately directed to those rocks which are either aggregates of simple
minerals, or which are the products of changes effected upon. simple
minerals ; natural also that consideration should be first given to
those in which that change has been more immediately chemical
than physical.

To no rock mass does this apply more directly than to serpentine.
In my wanderings I have visited and closely observed the relation-
ship of — with a single exception — every bit of this rock which is to
be found between Unst and Tyree on the one hand, — Harris and
the Black Dog Pock on the other.

In my analyses of a number of ill-defined minerals, generally
believed to be products of the alteration of augite and hornblende,

596 Proceedings of the Royal Society

the subject recurred to me. In order to bring as much light to
bear upon it as possible, I greatly extended the number of analyses
which I undertook ; and, as hearing upon it, I have now analysed

20 specimens of augite and its allomorphs, 15 of hornblende, and

21 of the products of the alteration of these two substances.

Founding upon the information gained thereby, I work out

chemically the various steps and stages of the transmutation, — which
transmutation will be shown and seen to be the formation of
serpentine.

2. On the Old Red Sandstone of Western Europe. By
Professor Geikie, F.R.S.

In a historical introduction the author gives an outline of the

progress of research into the history of the Old Red Sandstone of the
British area. This system is at present regarded as composed of three
sub-divisions, Lower, Middle, and Upper, each characterised by a dis-
tinct suite of organic remains. From the absence of unequivocally
marine fossils, and from lithological characters, it has been inferred
by Mr Godwin Austin, Professor Ramsay, Professor Rupert Jones,
as well as other observers, and is now very generally admitted,
that the Old Red Sandstone, as distinguished from the “Devonian”
rocks, probably originated in inland sheets of water. The object of
the present memoir was to endeavour to trace out in that geological
system of deposits the changes of physical geography which took
place over Western Europe during the interval between the close
of the Upper Silurian and the beginning of the Carboniferous
period.

After a sketch of the probable conditions of the region previous
to the commencement of the Old Red Sandstone, the author pro-
ceeds to show how the shallowing Silurian sea was converted here
and there into salinas or inland seas, by a series of subterranean
movements, which have left their indelible traces upon the upturned
Silurian rocks. He divides his memoir into two parts, the first
dealing with the Lower and the second with the Upper Old Red
Sandstone. The present paper deals only with a portion of the first
of these sections. It traces out the limits of the different basins in
which the Old Red Sandstone of the British islands were deposited,

of Edinburgh, Session 1877-78.

597

and for the sake of convenience, as well as briefness of reference,
proposes short geographical names for these basins, which are arranged
as follows : —

Short reference names
proposed to be applied
to them.

Area of the Basins.

]■ Lake Orcadie.

Lake Caledonia.

1. The Old Red Sandstone tracts of the north

of Scotland, embracing the region of the
Moray Firth, Caithness, the Orkney
Islands, the mainland of Shetland, and
perhaps part of the south-western coast j
of Norway. J

2. The central valley of Scotland between

the Highlands on the north and the
Silurian uplands on the south, including
the basin of the Firth of Clyde, and
ranging across the north of Ireland to the
high grounds of Donegal.

3. A portion of the south-east of Scotland and '

north of England, extending from near
St Abb’s Head to the Head of Liddes- Lake Cheviot,
dale, and including the area of the
Cheviot Hills. J

4. A district in the north of Argyllshire, '

extending from the mouth of the Sound
of Mull to Loch Awe, and perhaps up
into the southern part of the Great
Glen.

- Lake Lome.

The Old Red Sandstone region of Wales
and the border counties of England,
bounded on the north and west by the
older palaeozoic hills, the eastern and
southern limits being unknown.

The Welsh Lake.

Lake Orcadie. — After describing the limits of this basin, and
giving a sketch of the labours of previous observers in the Old Red
Sandstone tracts of the north of Scotland, the author proceeds to
examine the evidence for the threefold arrangement of the Old Red
Sandstone proposed by Murchison. He shows that nowhere are the

4 K

VOL. IX.

598

Proceedings of the Pioyal Society

three groups, Lower, Middle, and Upper, found in consecutive
order; that this so-called “Middle” division occurs only in the
north of Scotland, where it lies unconformably upon the older
palaeozoic rocks, and is itself unconformably overlaid by the Upper
Old Eed Sandstone, thus occupying a position exactly similar to
that of the Lower Old Eed Sandstone on the southern side of the High-
lands. He further points out that while some species of fishes are
common to the Old Eed Sandstone on the two sides of the High-
land barrier, the lithological differences between the deposits of the
two areas are so great as to make it evident that the rocks were laid
down in distinct basins, and consequently that the fauna of each
basin, might be expected to be more or less peculiar, as in many
analogous cases at the present day. As evidence that adjacent
areas in the time of the Lower Old Eed Sandstone were strongly
marked off from each other in their faunas, reference is made to
the contrast between the fishes and crustaceans of the Welsh region
and those of Lanarkshire and Eorfarshire, not a single species being
common to the two countries, though some of the genera are.
Eeasons are then given why the argument used by Murchison from
the occurrence of many of the Scottish ichthyolites in Eussia could
not be regarded as establishing the existence of a “ Middle ” divi-
sion of the Old Eed Sandstone.

The conclusion arrived at by the author is that the Caithness flags
or “ Middle Old Eed Sandstone” are probably the general equiva-
lents of the Lower Old Eed Sandstone of other regions, and that
this system consists in Britain of two well-marked divisions only — a
Lower, which graduates in some places into the Upper Silurian
rocks, and is separated by an unconformability from an Upper,
which in many districts passes up into the base of the Carboniferous
system.

The various districts into which the area embraced under the
term Lake Orcadie may be divided are then described seriatim.
The detailed structure of Caithness has been worked out by the
author (partly with the co-operation of his colleagues in the Geological
Survey, Mr B. H. Peach and Mr John Horne) as affording the most
complete sections of the Old Eed Sandstone in the north of Scot-
land. Arranged in descending order, the various stratigraphical
zones stand as in the subjoined table : —

of Edinburgh^ Session 1877-78.

599

Thickness
in feet.

9. John o’ Groats red sandstones, flagstones, and

impure limestones and shales, . . . 2000

8. Huna flagstones, shales, and limestones, . . 1000

7. Gill’s Bay red sandstones, .... 400

6. Thurso or northern group of flagstones, shales,

and limestones, ...... 5000

5. Wick or eastern group of flagstones, shales, and
limestones passing down into red shales and
sandstones, ....... 5000

4. Dull red sandstones, red shales, and fine con-
glomerates, . . . . . . .2000

3. Brecciated conglomerates, .... 300

3. Badbea red sandstones and shales or clays, . 450

1. Coarse basement conglomerates, ... 50

-

16,200 ft.

From the four lowest sub-divisions no fossils have yet been
obtained. The flagstones have yielded to Mr C. W. Peach and
other observers many land plants (some of which resemble forms
described by Dawson from the Gaspe sandstones) as well &$Estheria
membranacea , Pterygotus, sp., and many ichtliyolites. Availing
himself of the list of localities furnished to him by Mr Peach (to
whom he cordially acknowledges his obligations), with the species of
fish found at each, the author has constructed a table of the vertical
distribution of the fossil fishes in Caithness. Some of the species
range through almost the entire succession of beds. Some, how-
ever, are either peculiar to or very characteristic of one sub-division.
Thus Osteolepis arencdus and Dipterus Valenciennesi are not noted
except from the group No. 5. In the Thurso and the higher
flagstones (Nos. 6, 8, and 9), Acanthodes, Parexus, Clieir acanthus,
Diplacanthus, Ptericlithys, and Tristicliopterus — genera absent from
the Wick beds — are found in greater or less abundance. These
strata are further marked by peculiar species of genera which occur
among the older flagstones, as Coccosteus pusillus and Ostaolepis
microlepidotus.

The Orkney Islands are assigned to the higher sub-divisions of

600 Proceedings of the Royal Society

the flagstone series, the protruding ridge of granite and gneiss
which rises at Stromness and Gremsa being merely an indication
of the irregular surface on which the deposits of Lake Orcadie
were accumulated, and of the slow progressive subsidence of the
area. The fossils, for which these islands have long been famous,
include most of those of the upper groups of Caithness, with the
addition of others which have been regarded as distinct. In the
determination of these fossils, much skill is required to discriminate
between the accidental differences of aspect resulting from the con-
dition of fossilisation. The Orkney fishes, for instance, are pre-
served as black jet-like impressions which, often very perfect when
first removed from the quarry, are apt to scale off, leaving in each
case only an amorphous layer which, though it retains the contour
of the fish, shows little or no trace of structure. On the shores of
the Moray Firth, on the other hand, the organisms have been
inclosed within calcareous nodules ; their colours are sometimes
brilliant, and their scales, plates, fins, and bones are often admirably
preserved and remain unchanged in the Museum. Want of
experience in these different modes of preservation may have led to
a reduplication of species, especially in the case of the Orkney
and Moray Firth fishes. Among the most interesting Orkney fossils
is a portion of a Pterygotus (recognised by Dr H. Woodward), now
in the British Museum. The occurrence there of this characteristi-
cally Upper Silurian and Lower Old Bed Sandstone genus supports
the view contended for in this paper as to the true horizon of the
Orkney and Caithness flagstones.

The Shetland Islands contain a portion of the shore-line of Lake
Orcadie, with its conglomerates and sandstones and the flagstones
and shales of deeper water. Among these strata the Caithness
Estheria occurs, with abundant stems and roots of large calamite-like
plants with well-marked flutings, but without observable joints.
Some ichthyolites of the Caithness type are said to have been found
in Bressay. The general lithological characters are quite those of
the sandy parts of the Orkney and Caithness groups. On the west
side of the mainland of Shetland interesting evidence occurs to show
the existence of volcanic action contemporaneous with the accumu-
lation of the Old Bed Sandstone. Beds of amygdaloidal lavas and
bands of tuff occur among the sandstones, the whole being pierced
by masses of pink felsite.

601

of Edinburgh, Session 1877-78.

The south-western and southern margin of this great northern
basin of the Old Red Sandstone can still he traced nearly continu-
ously from the confines of Caithness to the borders of Aberdeen-
shire, its position being marked by a zone of littoral conglomerates.
Beyond the edge of that zone, however, there occur some interesting
outliers, which in some cases may represent long fjord-like indenta-
tions of the coast-line ; in others may mark what were really inde-
pendent basins lying at the base of the Grampian mountains. The
author points out that probably most of the difficulty which has
hitherto been experienced in understanding the sequence of beds
along the southern shores of the Moray Firth, and their parallelism
with those of Caithness and Orkney, is not to be attributed to the
amount of detritus covering the country, but rather to the fact which
has not heretofore been observed, that the Upper Old Red Sand-
stone, with Holopty chius and Pterichthys major , really overlaps
unconformably upon the older nodular clays and conglomerates with
Coccosteus, Cheirolepis , &c. This relation can be satisfactorily
determined in Morayshire, and is now being worked out by Mr
John Horne in the course of the Geological Survey. The author
traces in great detail, from the Spey into Sutherlandshire, the
development of the lower sandstones, conglomerates, and clays, which
have been regarded as equivalents of the Caithness flagstones. He
thinks that in no sense can this comparatively thin group of rocks
(seldom 1400 feet in depth) be regarded as a mere southward
attenuation of the great Caithness series, as suggested by Murchison,
for that neither lithologically nor palseontologically can that view be
sustained. He has been led to the conclusion that the whole of these
rocks from the borders of Sutherlandshire to those of Aberdeenshire
represent only the higher portions of the great Caithness series, and
that they were formed during a gradual depression of the ancient
high grounds whereby the waters of Lake Orcadie were allowed to
creep southward over the descending land. This movement is indi-
cated by the character of the strata, and that it took place about the
time of deposit of the later flagstones of Caithness is shown by the
occurrence of the fossils of that division in the nodules, flags, and
clays of the Moray Firth region, while those of the Lower division
are absent.

Allusion is likewise made to the discovery of two localities where

602

Proceedings of the Royal Society

contemporaneous volcanic action has recently been observed in the
Moray Firth area, the whole of the basin of Lake Orcadie being
otherwise remarkably free from any trace of such action except
on the northern margin in Shetland. The history of the area
embraced by Lake Caledonia will form the subject of the next
paper.

3. On Beats of Imperfect Harmonies. By Sir
William Thomson.

According to a usage which has been adopted from the German
of Helmholtz by the best English scientific writers on sound, a sound
is called a “simple tone,”* or without qualification a “tone,” when
the variation of pressure of the air in the neighbourhood of the ear
which is the immediate excitant of the sense is according to a simple
harmonic function of the time ; that is to say, when the whole
pressure of the air varies in simple proportion to the distance, from
a fixed plane, of a point moving uniformly in a circle. Consider-
ing the actual sensibility of the human ear to musical sounds, we
must introduce farther as a practical restriction that the period of
the variation of the pressure must he less then ~ of a second, and
greater than jo- J-yo- or t 0 cro"o °f a second. The vibrations of the air
produced by a simple harmonic vibrator are either simple harmonic,
or are in circular or elliptic orbits, resulting from the composition
of two simple harmonic motions ; and the consequent change
of air-pressure in the neighbourhood of the ear follows the simple
harmonic law, provided the maximum velocity of the vibrator and
of the air in its neighbourhood be infinitely small in comparison
with the velocity of sound. Hence the more nearly this condition
is fulfilled the more nearly a simple tone is the sound heard ; but
it is far from being fulfilled when the vibrator, though itself per-
forming simple harmonic motion, has sharp edges round which the

* The old musical usage, according to which the word tone denotes an interval
(the major tone or minor tone, or the mean tone of the tempered scale), though
it unfortunately clashes with this recent scientific use of the word tone, can
scarcely be abandoned.

of Edinburgh , Session 1877-78.

603

air is forced to rush with great velocity, or when, as in the case of
free-reed organ pipes or the reeds of a harmonium, the vibrator is
an elastic solid moving to and fro in a very narrow aperture. (In
the case of a slapping reed, as of trumpet stops in an organ, the
motion of the vibrator itself is not simple harmonic, and the sound
is excessively rich in overtones, giving it its peculiarly rich or harsh
character.)

A harmony is any sound of which the excitant change of air-
pressure is strictly periodic, and is not a simple tone. According
to Fourier’s beautiful analysis* of periodic variations, to which the
name of the harmonic analysis has been given, any periodically
varying quantity may be regarded as the sum of quantities varying
separately according to the simple harmonic law, in periods respect-
ively equal to the main period, half the main period, a third of the
main period, and so on. According to this analysis we see that
the variation of air-pressure constituting a harmony may be regarded
as the sum of variations constituting simple tones, one having its
period equal to the period of the harmony; a second, half that of the
harmony; a third, one-third that of the harmony, and so on ; in other
words, we may regard the harmony as compounded of these simple
tones.

Practically, in musical language the term harmony is not applied
when the tone of the main period predominates in the sensory im-
pression, and in this case the sound is simply called a note ; its
pitch is reckoned according to the main period ; and the effect of
the other tones, now called overtones, which enter into its composi-
tion, are merely felt as giving it its character or quality of sound.
Thus the name harmony is in musical practice restricted to cases in
which there is either no tone of the main or fundamental period, or
not enough to produce a predominating impression, and a sound
compounded of two, three, four, or more simple tones, having com-
mensurable periods, is heard. In ordinary musical language a
harmony is not regarded as having any one pitch, but is thought
of as compounded of its known constituents. The true period of

* Compare “Trans. R.S.E.” April 30th, 1860, “Reduction of Observations
of Underground Temperature,” where a short description of Fourier’s analysis
is to be found.

604 Proceedings of the Royal Society

the harmony is, however, in every case the least common multiple
of the period of its constituent tones. The number of times that
the period of the harmony contains the period of any one of its con-
stituent tones is called the harmonic number of that tone. This
expression is only applicable to any particular tone when viewed as
one constituent of a harmony. Following the usage of Lord Rayleigh
and Professor Everett, I shall employ the word “ frequency ” to
denote the number of periods per unit of time, — per second, let us
say, generally in acoustical reckonings. Thus the “ frequency ” of
a tone or of a harmony means the number of its periods per second.
Similarly the frequency of any set of beats, according to the defini-
tions and descriptions below, will mean the number of the beats
per second, and in this application of the term it will designate some-
times a proper fraction, and sometimes a small whole number with
fraction.

The quality of a harmony, when the periods of its several con-
stituent tones are given, depends upon the amplitudes of the dif-
ferent constituents, and on the relation of their phases. Thus, for
example, consider a harmony of two tones. They may be so related
in phase that at one of the instants of maximum pressure of one of
the constituents there is also maximum pressure of the other con-
stituent. The same phase-relation, if the harmonic numbers of the
constituent tones be both odd, will give also coincident minimums.
But when one of the harmonic numbers is even and the other odd
the phase-relation of coincident maximums will also be such that
there is a coincidence of minimum pressure due to one tone with
maximum pressure due to the other ; and again there will be an
opposite phase in which there will be coincidence of minimums,
and in this opposite phase there will also be a coincidence of maxi-
mum and minimum. (To avoid circumlocutions a harmony of two
odd numbers will be called an odd binary harmony ; a harmony of
even and odd numbers will be called an even binary harmony.)
Thus we see that in an odd binary harmony there is a phase-rela-
tion of coincident maximums and coincident minimums, and again
an opposite phase-relation of coincident maximum minimum and
minimum maximum. The former will be called the phase-relation
of coincidences, the latter the phase-relation of oppositions. In an
even binary harmony there is a phase-relation of coincident maxi-

T

J

~

■

. n

l- t

Proc. Roy. Soc. Edin* VoL K Plate V

of Edinburgh, Session 1877-78.

605

mums and coincident maximum minimum ; and again an opposite
phase-relation of coincident maximum minimum and coincident mini-
mums. The former will be called the phase -relation Gf coincident
maximums, the latter the phase-relation of coincident minimums.
The annexed diagrams illustrate and prove these assertions. The
horizontal line in each may be either regarded as representing space
at any one instant in the direction of propagation of the sound, or
it may represent times at which successive phases of the motion are
perceived by an ear in a fixed position. The long vertical cross-
bar in each case denotes maximum of air-pressure ; the short vertical
cross-bar, minimum.

For lecture illustrations it is convenient to use long slips of wood
with paper pasted on one side, and the short and long cross-bars
marked upon it, and to support these slips of wood on a board with
nails to guide them so that they may be placed in groups of two,
three, or four, one over the other, and any of them moved in the
direction of its length to illustrate the different phase-relations of a
harmony.

Suppose now, one note of a perfect binary harmony to be very
slightly sharpened or flattened : so slightly that during a large
number of the periods of the perfect harmony, the phase-relation in
the imperfect harmony experiences but little change. Let the two
notes of the imperfect harmony be sustained long enough with
perfect uniformity as to pitch and intensity : — the effect will be that
of perfect harmony, modified by a slow change of its phase-relation
through a cycle ; which in the case of an even binary harmony is
from coincident maximums gradually to coincident minimums, and
thence gradually round again to coincident minimums ; and in the
case of an odd binary harmony is from oppositions to coincidences,
and round to oppositions again ; and so on in cycles. In favourable
circumstances, and with careful attention, a variation of the quality
of the sound recurring periodically in these successive cycles is dis-
tinctly heard, even by an unpractised ear, unless the duration of the
cycle be too long or too short to suit its sensibility. It is this
variation which is called the “beat” on the imperfect harmony.

The period of the beat — that is to say, the duration of the cycle
described above — is most easily found by taking the reciprocal of its
frequency, calculated by the following rule : — The frequency of the

4 L

VOL. IX.

606 Proceedings of the Eoyal Society

beat is equal to the error of frequency of one note multiplied by the
harmonic number of the other. When in a harmony of three or
four notes all are perfect except one, the heats due to the imperfec-
tion of the false one are to he reckoned just as if the harmony were
binary, according to the following rule : —

For the two or more notes which are in perfect harmony imagine
one whose period is the period of their harmony. Take this as if
it were one tone of an approximate binary harmony, the false note
of the given harmony being the other. Example : Let the
frequencies of the three notes be 257, 320, and 384 : the common
period of the two last-mentioned is of a second, and we have to
calculate the beats on two notes whose frequencies are 64 and 257.
The harmonic numbers of the harmonies to which these notes
approximate are 1 and 4, and the error in frequency of the higher
note is 1 per second ; hence the beats are at the rate of 1 per
second. When there is error in two or more notes of a multiple
harmony, two or more sets of beats in periods not commensurable
with one another are heard ; but the general effect is apt to be too
confused to allow any one of the sets to be distinctly counted. On
a multiple harmony with only one note false the beats are in
general exceedingly distinct, more so in general than in binary
harmonies.

Sometimes, as for distance in reckoning the beats in the imperfect
harmonies of a tempered musical scale, it is convenient to regard
the two notes of an imperfect harmony as in error from two notes
of a perfect harmony differing but little from them ; then the rule
for calculating the frequency of the beats is to take the difference of
the products of the errors of the two notes, each multiplied into the
harmonic number of the other. Thus, let n and n' be the harmonic
numbers of the perfect harmony to which the given notes approxi-
mate, and let e and e be the excesses of the vibrational frequencies
of the two actual notes above two in perfect harmony nearly agree-
ing with them. The frequency of the beat of the actual notes is
ne - ne\

For example, take the following table of numbers of vibrations in
a perfect diatonic scale, with 256 vibrations per second for C, and in
the corresponding scale of equal temperament (founded on 12 equal
semitones, in each of which the interval ratio is 2tIj) : —

of Edinburgh, Session 1877-78.

607

Frequencies of
True.

Frequencies of
Tempered.

Error of
Tempered.

C 256

256 C

o-o

D 286-75

287-35 p

+ 0-60

E 320

322-54 (S?

+ 2-54

F 341-33

341-72 f

+ 0-39

G 384

383-57 6

-0-43

A 426-67

430-54

+ 3-87

B 480

483-26 $

+ 3-26

C' 512

512 G'

o-o

D' 573-50

574-70 P'

+ 1-20

E' 640

645-08 <&'

+ 5-08

From these numbers we find the following table of beats : —

Perfect

Harmonies.

Harmonic

Numbers.

Imperfect

Harmonies.

Qualities of
Falseness
of the
Intervals.

Frequencies
of Beats.

is

{!

Errors.

j <& - 0-43

1 c o-o

| Too small

0-86

{S

/ 7# + 3-26
( <& + 2-54

| Too small

1-10

( C'

1 E

{S

f C' 0 0

\ f + 0-39

| Too small

1-17

f E'
(A

IS

j (l F + 5-08
+ 3-87

| Too small

1-45

{S

{1

If + 0-39
i C 00

| Too large

1-17

{e

{S

/& + 3-87
( © + 2-54

|> Too large

1-45

{b

{{

/ <!F + 5-08
\ + 3-26

| Too large

2-20

!c

{5

/ € + 2-54
\ C 0-0

| Too large

10-16

{!

/$, + 3-87
+ 0-39

| Too large

13-53

608 Proceedings of the Royal Society

Qualities of

m

<D

‘o

Perfect

Harmonic

Imperfect

Falseness

a c3

(X) <x>

Harmonies.

Numbers.

Harmonies.

of the

Intervals.

O 'H
fH O

Ph

Errors.

{S

{i

( ® - 043

| (2f + 2-54

| Too small

17-39

/ G 0-0

( ffi + 2-54

| Too small

15-24

(C

l a

{!

/ C' o-o

+ 3-87

| Too small

23-22

{c

{3

/$, + 3-87

\ c o-o

| Too large

11-61

/ E'

»G

{S

/ & + 5-08
t <S - 0-43

| Too large

17-39

( E

f5

( <£ + 2-54

)

12

} j G 0-0

f Too large

5-08

( |c

r

( \ c o-o

It is of course to be understood that the degree of falseness is the
same in all the tempered harmonies of the same name (or having the
same harmonic numbers) ; and that the different numbers shown for
the frequencies of the beats are (except for the case of the (0? with
the untempered G) in simple proportion to the vibrational frequencies
of one or other of the constituent notes. The slightness of the
imperfectness in the tempered fifth (approximately 2 : 3) is indicated
by the slowness of the beats, not so much as one per second on the
C The imperfectness of the fourth (approximately 3 : 4) is even
less than that of the tempered fifth, so that, notwithstanding the
greater harmonic numbers, the beats are scarcely more rapid (1*17)
for the C Jf than (*86) for the C But when we go to major and
minor thirds of the tempered scale, we take leave of mathematical har-
mony entirely. The beats on the C ($ (ten per second) are too rapid to
be counted, and it is only in virtue of their not being perceived, or
not being disagreeably perceived, that the combination is agreeable.
The same may be said still more unqualifiedly of the minor thirds,
the number of beats on (0? being more than seventeen per second.
It does not seem easy to explain on any physical or physiological

609

of Edinburgh, Session 1877-78.

principles the decidedly agreeable effect produced on the ear by a
succession of major and minor thirds of pianoforte notes. It is, no
doubt, to the slowing of the heats by the superposition of a third
note upon either of the binaries C (0f or (& in the ternary com-
bination C (0? (!i>, because of its comparatively close approximation to

C G 0 (for which the heats are only five per second), that the com-
paratively smooth harmoniousness of the common chord in the
tempered scale is due.

It is not generally known how easily beats on approximations to
other harmonies than unison are heard, even when the constituent
notes are simple tones. Through the kindness of Professor
M‘Kendrick I have been allowed the means of testing them in very
varied combinations, by aid of a series of excellent tuning-forks of
Koenig’s, each mounted on a wooden box resonator, after the
manner of Marloye. For such experiments Koenig’s tuning-forks
are much superior to Marloye’s, because of the greater quantity of
metal in each fork, in virtue of which it gives a louder and more
enduring sound. The sound proceeding from such a source is
essentially a simple tone, or very nearly so. I have tested that in
every case the number of beats counted is the smallest that could
be according to the preceding theory ; for it is to be remarked that
the theory only gives the whole period of the phenomenon, but
does not answer the question — Does the ear perceive a gradual varia-
tion of quality through the whole period, or does it fail to distin-
guish the difference of quality between two halves of the period,
or between three-thirds of it, and so on 1 My experiments demon-
strate that in every case the ear does distinguish the two halves of
the period of each beat. Thus, for example, in the beat on an
approximation to the harmony (1:2) in which the variation of air-
pressure on the ear is represented by the preceding curves for four
instants of the period noted, I find that the ear distinguishes the
quality of the sound represented by the sharp-topped and flat-
hollowed curve from that represented by the flat-topped and sharp-
hollowed curve. In the one case the pressure of air close to the ear
rises very suddenly to, and falls very suddenly from, its maximum,
and (as in cases of tides in which there is a long hanging on low
water) there is a comparatively slow variation of pressure for a few
ten- thousandths of a second on each side of the instant of minimum

610

Proceedings of the Royal Society

pressure; in the opposite phase-relation there is a slow change before
and after the time of maximum pressure, and a rapid change before
and after the time of minimum pressure. In the former case the
difference of maximum from mean exceeds the difference of mini-
mum from mean ; in the latter the difference of the minimum from
mean exceeds the difference of maximum from mean. If the ear
could not distinguish between two such sounds, but could distinguish
between either of them and the sounds represented by the first and
third quarter-period curves, the number of beats would be twice the
error of frequency of the higher note. But I find that the number
of beats is quite distinctly equal to the error of frequency of the
higher note. I have found that the beats on the 1 : 2 harmony are
most easily perceived when the intensity of the higher note is com-
paratively faint, as would be the case if they were explained by
Helmholtz’s theory that they are the beats on the approximation to
unison which there is between the higher note and the first overtone
of the lower note. But the simple-harmonic character of the two
constituent tones at the entrance of the ear precludes the acceptance
of this theory unless extended, as it has actually been by its author,
to the interior mechanism of the ear.

Whatever may be the physiological theory by which the beats
are to be explained, it is an interesting fact that the ear does dis-
tinguish, as it were, between push and pull on the tympanum in
the manner illustrated by the preceding curves, not only for the
case of approximation to the harmony 1 : 2, but for every other even
binary harmony. I have heard distinctly the beats on approxima-
tions to each of the harmonies 2:3, 3:4, 4:5, 5:6, 6:7, 7:8,
1 : 3, and 3 : 5. The two last mentioned, though sometimes less
easily heard than the beats on most of the others, are unmistakably
distinct ; and by counting the numbers of them in ten seconds or in
twenty seconds, I have ascertained that they, as do all the others,
fulfil the condition of having the whole period of the imperfection,
and not any sub-multiple of it for their period of audible beat.
They are interesting as being cases of odd binary harmonies. Before
making the experiments, I thought it possible that what is heard in
the beat might not make distinction between the configuration II.
and IV. (first quarter phase and third quarter phase) : but a revolving
character which I perceive in the beat seems to me distinct enough
to prove that the ear does distinguish between these configurations,

of Edinburgh , Session 1877-78. 611

which are one of them the same as the other taken in the reverse
order of time.

In every instance except the octave, the beat on the approximation
to a binary harmony is less distinct than the beat on an approximation to
a ternary or higher multiple harmony with only one note false. It is
not because of the comparative slowness of the beat on the multiple
harmony ; for by taking alternately beats with one note slightly
false in a binary harmony, and the same note made more false in a
ternary or multiple harmony to such a degree as to give the same
number of beats, I have always found the beats in the latter case
much more prominent than in the former. Thus by taking first the
perfect harmony C E G (4, 5, 6), and the three binary harmonies
C G (2 : 3), C E (4 : 5), E G (5 : 6), and flattening slightly any one
of the three notes by screwing on a small mass of brass to either or
to each prong of the tuning-fork producing it, it is easy after a little
practice to count the beats on each of the binary harmonies. Thus,
for example (supposing E to designate a note of a slightly lower
pitch than E), after a little practice it is easy to count the beats on
C E and on the E, G, and to verify that their frequencies are, the
first of them four times, and the second of them six times the error
of frequency of the E, , and then to verify that the much louder
beats on the ternary harmony C E, G, are of half the frequency of the
former, and of one-third of the frequency of the latter, and to verify
absolutely that they are of twice the frequency of the error of E .

If when the approximate harmony C E, is being sounded, the
faintest sound of G is produced by a very gentle excitation of
the fork by the bow, instantly a loud beat at half speed is heard.
The phenomenon is rendered very striking by alternately touching
the top of the G fork by the bow so as to stop its vibrations,
and then drawing the bow very gently for a fraction of a second*
along one side to re-excite them. It is marvellous how small
an intensity of the sound G is required to give a smooth unbroken
loud beat in the double period. I have found it difficult to excite

* In every case, to obtain regular beats, eacb tuning-fork, after being set
in vibration by the bow, must be left to itself. The sound is sensibly graver
as long as the bow is applied to augment or sustain the vibration than when
the fork is left free. Thus, if two tuning-forks nearly, but not quite, in uni-
son, are alternately acted on by the bow and left free, the beats are less rapid
during the time the bow is applied to the higher fork, and more rapid while to
the lower, than when both forks are vibrating freely.

612

Proceedings of the Royal Society

the G gently enough to give the gradual transition from, let us
say for example, four uniform heats per second, through the case of
four heats per second with every alternate beat somewhat louder, to
the case of only every second beat perceptible, or, in all, two beats
per second ; but it can be done, and the result is an interesting and
instructive illustration of the slowing down from the quick beat of
the binary harmony to half speed, or to one-third speed, or to one-
fifth speed, as the case may be, by the introduction of a third
note. In the several cases I have foundthat I can, by making
the added note faint enough, produce a succession of beats of
which every second, or every third, or every fifth, as the case may
be, is louder than the others, and that, as the intensity of the added
note is gradually increased, the fainter beats become imperceptible,
and a regular unbroken slow beat is heard distinctly alone, always
in the theoretical time of the whole imperfection of the harmony.
I have verified this distinctly in the cases of 1, 2, 3; 2, 3, 4 ; 3, 4, 5;
4, 5, 6 (as stated above) ; 5, 6, 7 ; and 6, 7, 8. I have not succeeded
in hearing the beats on the approximations to the harmonies 8 : 9
and 9 : 10. But the slow beat on the 8, 9, 10 (with vibrational
frequencies 256, 288, 320), with any one of the three notes slightly
flattened, is very remarkable. The sound is like that of a wheel
going round with decided roughness of motion in every part of its
revolution, but much rougher in one part than another, with a loudly
perceptible periodic return of the roughness in the theoretical period
of the approximate harmony.

The beats on the harmony C E G (vibrational frequencies 256,
320, 384), with any one of the three notes slightly flattened, are
very perceptible : untrained ears hear them instantly the first time
without any education, and the beat is heard almost to the very
end of the sound if three of Koenig’s forks, one of them, the
C, for example, being slightly flattened by a brass sliding piece
screwed to it, be caused to sound. The sound dies beating, the
beats being distinctly heard all through a large room as long as the
faintest breath of the sound is perceptible. The smooth melodious
periodic moaning of the beat is particularly beautiful when the beat
is slow (at the rate, for instance, of one beat in two seconds or
thereabouts), being, in fact, sometimes the very last sound heard
when the intensities of the three notes chance at the end to be
suitably proportioned.

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH,

vol. ix. 1877-78. No. 102.

Ninety-Fifth Session.

Monday , 1 5th April 1878.

Sir WILLIAM THOMSON, President, in the Chair.

The following Communications were read : —

1. On Vortex Vibrations, and on Instability of Vortex
Motions. By Sir William Thomson.

2. On the Theory of Vowel Sounds. By Professor

M‘Kendrick.

3. Preliminary Note on a Method of Detecting Fire-Damp in
Coal Mines. By Professor George Forbes.

The author exhibited two instruments, both founded upon the
same principles, for measuring the quantity of fire-damp present in a
coal mine. The first instrument consists of a tuning-fork fixed above
the open end of a resonating tube, whose other end is closed by a
piston whose position (read off on a scale) regulates the length of
the resonating tube. The length of the tube, which resounds to the
definite pitch of the tuning-fork, depends upon the nature of the
gas with which it is filledc The more fire-damp, the longer is the
tube. Barometric pressure has no effect upon this instrument.
The correction for temperature is made by reading off, not a fixed
mark upon the piston, but the top of the mercury of a thermo
VOL. ix. 4 M

614

Proceedings of the Royal Society

meter attached thereto, of dimensions determined by actual experi-
ment. The only source of error to which the instrument seems
liable is the counteracting influence of dense carbonic acid gas in
choke-damp. But it is found that the presence of choke-damp
destroys the explosive character of fire-damp ; and, so far as experi-
ments go, it seems certain that, in all cases when the presence of
choke-damp prevents the instrument from indicating the presence of
fire-damp, the fire-damp is denuded of its explosive character.

The second instrument is a combination of a harmonium reed
and an organ pipe, through which the air is driven. They are
arranged so as to sound the same note when pure air is used, so
that when there is a lighter gas present the organ pipe sounds a
higher note, thus producing beats.

So far as the experiments have gone hitherto, the first form is by
far the most accurate, being capable of detecting the presence of 1
or 2 per cent, of fire-damp.

4. Note on Electrolytic Conduction. By Professor Tait.

It is commonly said that there is a resistance to a current at the
surface of contact of a solid conductor and an electrolyte. Some
good authorities, however, say that we have as yet no proof of this,
as the effects observed may be due to polarisation. It is obvious
that, if the reverse electromotive force due to polarisation contain
a term directly proportional to the strength of the current, the
ordinary methods of measurement would not enable us to distin-
guish this from the surface resistance above mentioned. For, in the
expression

2(E)

2(B)’

if the numerator contain a term of the form - el, it may be ex-
punged, provided e be added to the denominator.

To clear up this point I have recently made a number of experi-
ments. These have led me to some curious results bearing on the
theory of electrolysis, which I propose to bring before the Society on
a future occasion. At present I refer to them merely so far as to
say that they establish fully the existence of the surface resistance
above mentioned. Thus I was led to see that if a slip of platinum

of Edinburgh, Session 1877-78. 615

be inserted between the electrodes of a decomposing cell it ought,
except in extreme cases, to produce almost precisely the same
result as a similar and equal slip of glass or mica. This was easily
verified. Here we have the singular result of a marked diminu-
tion of the current by the insertion into the electrolyte of a sub-
stance which is in itself a much superior conductor. Even when
the platinum completely closes the path from one electrode to the
other, so as to form two decomposing cells instead of one, a compara-
tively small hole made in it at once changes its function from
that of common electrode to each of two decomposing cells into that
of a mere obstruction in one cell. It is an interesting experimental
inquiry to trace the intermediate stages between these two states, as
a pinhole in the platinum is gradually enlarged. Whatever, then,
be the behaviour of the particles of an electrolyte, they do 7iot
behave like little pieces of platinum.

5. Note on Thermal Conduction. By Professor Tait.

Monday , 6th May 1878.

Sir C. WYVILLE THOMSON, Vice-President, in the Chair.
The following Communications were read : —

1. On the Indications of Molecular Action in the Telephone.
By II. M. Ferguson, Ph.D.

The accepted theory of the telephone represents that the vibra-
tions of the sending plate to and from the pole of the magnet before
which it is fixed is the origin of the currents generated in the pole
bobbin of wire, and that these currents transmitted to the receiving
telephone produce corresponding to-and-fro excursions of its plate.
This theory, which is that of the inventor, may be shortly desig-
nated, in the happy words of Sir William Thomson for a kindred
action, the push-and-pull theory. We have had in this session of
the Society two communications of a practical nature, which seem
directly confirmatory of this view. I refer to the lucid exposi-
tion of Gott’s telephone experiment in the island of St Pierre, and

616

Proceedings of the Royal Society

the beautiful and successful demonstration of the action of the
phonograph, both by Professor Fleeming Jenkin. In the former of
these, as we learned, one end of a thread was attached to the one
side of the light suspended coil of a Thomson ink recorder, and the
other to the paper disc of an ordinary mechanical telephone. This
was done at the two communicating stations. When the sending
disc was agitated by the voice, the coil to which it was attached
twisted round in the powerful and uniform magnetic field in which
it was placed, and dispatched corresponding electric current waves
to the receiving instrument, the coil of which was thereby moved
similarly in its field, and transferred its motion to its paper disc.
A more beautiful manipulation of an exquisitely designed and
executed apparatus it is not easy to conceive. In the phonograph
we have as it were a mechanical telephone, with the string connect-
ing the discs cut, and nothing left of it but the two ends stiffened
into pricking pins. Instead of the sending disc dealing directly
with the receiving one, its energy is employed in imprinting, by
means of the pricker, its vibrations on the tinfoil, and this imprint,
when again vivified by the energy of the rotating drum, reproduces
the vibrations which originally stamped it.

After two such demonstrations, it may be held as proved that the
electric telephone is equivalent to a mechanical telephone with an
electro-magnetic intervening action instead of a mechanical one. It
seems therefore a hopeless task to seek for indications of molecular
action where mechanical action declares itself so manifestly. The
mechanical action of the voice and of the membrane of the tympanum
of the ear is above question, and that mechanical vibrations are dealt
to the sending instrument, and emitted by the receiving one, is equally
undoubted; but the intervening electric agency, how generated in
the one and how transformed in the other, is a fair field for discus-
sion. The action is novel, and it is surely a likely inquiry to inves-
tigate whether its explanation by the first principle that comes to
hand, viz., the push-and-pull of the discs, fully covers the case.
The question may be raised, for instance, whether the mere impact
of the waves of air on the iron disc may not affect its magnetic
condition by internal change or vibration,* so as to excite currents
without vibrations of the push-and-pull kind, or whether in
* Something like this was suggested hy Professor Forbes.

of Edinburgh, Sessio?i 1877-78.

617

the receiving disc the particles may not set up an action on
their own account, independently of the displacement caused by
the poles of the adjoining magnet. In a mechanical telephone,
we do not find that it is made to sound only by the normal
push or pull of the thread, the faintest rubbing on the irregu-
larities of its surface, either on the disc or the tube to which it is
attached, makes a sound loud enough to be heard, and we can easily
admit that if an internal vibratory disturbance be set up in any
direction in it, the same would be audible enough. In a discussion
as to mechanical and molecular sounds, it may be safely admitted,
where electricity or magnetism is concerned, that any action that is
clearly traceable to disturbance within a body is molecular in its
origin. It will, moreover, be granted that the mere smallness of any
vibration does not necessarily give any clue to its origin. Infini-
tesimal vibrations are not necessarily molecular, nor are vibrations of
molecular source free from external motion ; and we can only say
that a vibration comes from molecules if we can assign to it no out-
side cause. It may, however, be to the point that a vibration may
be assumed to be molecular because of the difficulty in suppressing
it, a vibration springing from within being more independent of
direction than one produced from without from one quarter.

I propose in this communication to raise such questions in regard
to the telephone, and though the results obtained may not be de-
cisive, they may be some little contribution to the discussion.

I would begin with a case where internal action seems wholly
absent. I refer to the action of a tuning-fork on the telephone.
It has been mentioned in more than one communication to the
Society, that a tuning-fork acts best without the disc. We find that
the loudest sounds are sent to the listener at the receiving telephone,
when one prong is brought with its flat vibrating end in front of
the core or pole pin, and next to that when the prongs, if they are
not too far apart, are laid with their flat sides vertical at an equal
distance on each side of the pin. When the handle of the fork is
laid on the core, and held upright, the resonance of the wooden
frame of the telephone and the table on which it rests becomes loud,
but only a faint trace of this is sent to the distant hearer. If we
magnetise two like forks, one which we may call A, to be like a bar
magnet having the end of the handle as one pole, and the other

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Proceedings of the Royal Society

pole split in two in the two prongs ; and another fork B, the two
prongs of which are made like the poles of a horse-shoe magnet,
with the handle an excrescence between, we find that while the
fork A produces sounds alike with both prongs when held near the
core, the two prongs of the fork B show a marked difference. The
like pole to that of the core sounds much weaker than the other.
All this is indicative of the ordinary magneto-electric induction at
work.

If we detach the coil from the magnet, we have still further
illustrations of the same. Both forks, A and B, sound loudest when
placed with one prong on its flat side over the hollow at the centre
(fig. 1), and both continue to sound, but with diminished force, as
they are withdrawn in the same position from the middle to the
margin of the coil. When laid with the plane of the prongs hori-
zontal (fig. 2), they act differently. The A fork has its best sound-
ing position when each prong lies symmetrically to the hollow axis,
and it has a position of silence at a point between the middle and

the outside, whilst the B fork in these positions acts in the opposite
way. There are two positions that the forks may occupy at the
side of the coils, where their similar and dissimilar actions are
again shown. The first is when the plane of the fork is perpendi-
cular to the axis (fig. 3), where both forks transmit no sound when
held in the middle of the coil, but are heard when vibrating on
either side. The second is when the plane is parallel to the

of Edinburgh t Session 187 7—7 8.

619

axis (fig. 4), where A is silent when its prongs are equidistant
from the middle of the coil, and the fork B loudest. All this
is, as we have said, simply an illustration of a well-known
action, and at the same time a beautiful demonstration of the
way in which a tuning-fork vibrates. The coils I used were of
fine copper wire, 1^ inch diameter and J thick, but smaller coils
would do equally well, and the forks were the ordinary small A
and C forks sold by the musicsellers. It is perhaps worthy of
note that a coil, a magnetised fork, and a telephone form a handy
combination for testing the completeness of a circuit, as the sound
of the fork coming directly to the ear is immensely below that
heard in the telephone in the operator’s hand. When the telephone
does not sound, there is a break in the circuit. In these various
performances of the fork, we have evidence enough to prove that
the cause assigned by Bell for the sending action of the telephone
covers at least the greater part of that action. At the same time, it
must be borne in mind that the vibrations of the fork, and the
sounds produced by them, are immensely greater than any connected
with the telephonic effect of the voice, and that it is possible that
the conditions of iron vibrating under the energy treasured up in
it may be different from what they may be when the iron is beaten
by the air.

But even this tuning-fork performance is not quite free from
ambiguity. To find whether there might not be some change of
magnetic condition due to internal
vibration, able to generate currents,

I cemented two coils (fig. 5.) to the
vibrating ends of a large tuning-fork.

It was a C (256 vibrations), with
prongs upwards of 6 inches long,

broad, and more in average than
5 thick. The distance between the
prongs at the end inside was inch.

The coils weighed \ oz. ; they were
f inch diameter, 1 inch long, and
were of *007 inch copper wire.

They reduced the pitch from C to
A. The cement was the hard and tough black tarry compound

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Proceedings of the Eoyal Society

used by electricians. On connecting one of the coils with a
telephone and making the fork vibrate, I was astonished to hear
the sound in the telephone astonishingly loud. I found, how-
ever, that this arose from the connecting wires, which though
loose were able mechanically to transmit the vibrations of the fork.
This was shown by leaving only one wire in the connection, when
the sound of the fork was still heard. It is well known that the
thread of a mechanical telephone delivers its message to the first
fixed obstacle it meets and no further, and in this case, when the
lines were held in the fingers, a mere residuum of sound was heard,
which could only be properly estimated in a distant room away from
the direct sound of the fork. In this, as in all subsequent experi-
ments, I took the utmost care that no mechanical transmission was
possible, and the telephone used at the operating station was put out
of circuit each time a sound was made for investigation. Loud
tapping was made in every conceivable place to ascertain if such
could be transmitted in a mechanical way. The circuit was about
150 ft. of wire with a gas pipe return, and the two stations were in
different buildings. The results obtained from this fork were not
of any value other than illustrating the difficulty of insulating for
transmission what may be looked upon as an internal and not an
external vibration. They were these. The sound of the fork was
heard much less loud than if the prong had been vibrating in front
of the coils, but was louder than what was got when it vibrated at
a distance equal to that of the prong on which the coil was not fixed.
When the two coils were joined up consecutively, one way of joining
gave a maximum, the other a minimum sound. In another arrange-
ment the coil was attached to a hollow prism of thin brass § inch
inside, which in its turn was attached to the prong. The sound
given by this coil was less than when it was attached immediately
to the prong, but was louder than when the other prong vibrated
freely at the same distance. When I mounted the fork in this
way, one prong was feebly magnetised, and the other scarcely if
at all.

A perfect maze of reasons may turn up to account for the currents
dispatched by these fixed coils. One might be their motion in the
magnetic field of the earth, which is not likely, for earth-induced
currents proceed from the rotation of a coil, and the faint approach

621

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to rotation in this case can hardly he looked upon as such. To
exclude this cause, I put the coils in the best position for
generating such currents, and connected them with a moderately
sensitive reflecting galvanometer. I inserted a piece of wood
between the prongs, and wedge-like drove them suddenly out,
and allowed them to return, keeping time with the known
pendulum-like oscillation of the mirror so as to accumulate effect,
but no result was got. Again it might be that the coils, tightly
as they were wound, were yielding, and we had only a case of
shaking a coil in front of a magnet, instead of a magnet in front of
it. That this was not the case was proved by cementing the coils to
the sides of the prongs at right angles to the direction of motion, and
though the forks vibrated almost unmusically with such protube-
rances, yet what sound they emitted was telegraphed to the listener.
The most likely cause was that the coils were fixed as regarded the
prongs on which they were stuck, but were affected by the distant
prong which vibrated in front of them. The sounds of the vibrat-
ing coils were louder than when the coils were fixed, and the other
prongs vibrated at the same distance ; but that might be accounted
for by the fact that the prong to which the coil was fixed was an
active agent in propagating the vibrations of its companion prong
to its own coil. The only chance of anything like internal action
being heard here rests on the possibility that this last is not
sufficient, and that is certainly a slender enough basis to bufld a
theory upon.

In pursuit of the same internal sending action, I cemented two
coils, one to the end, the other to the middle of a bar magnet.
Both transmitted telephonic currents when the magnet was struck,
the end one much louder than the other. Again, an unmagnetised
tuning-fork was made to vibrate above a coil, and its note was feebly
yet distinctly heard at the listening end. To test wdiether it and
the other objects afterwards mentioned were magnetised, I brought
them near a small active magnet about an inch in length, and
before another much heavier, 9 inches in length, and watched to see
if repulsion or even indifference was shown to any part of them ;
and lastly, I made them vibrate in front of the coil connected with
the reflecting galvanometer in the position in which their sending
action was afterwards tested. These tests cannot be alleged to prove

VOL. ix. 4 N

622 Proceedings of the Royal Society

complete absence of magnetism, but they go far beyond the practical
application of the word unmagnetic. The fork in question answered
perfectly all these tests. I next tried to get sounds out of soft
iron plates kept fixed above the coil, and found no difficulty
in getting them to sound when laid on a table in a horizontal
position and beaten with a small hard wooden mallet, or with
something that would produce with them a sharp tap. When the
plates were held approximately in the plane of the magnetic
meridian there was more difficulty in getting the distant listener
to hear, but even in it they did not cease to sound under blows
sharp and hard enough. They also sounded when the coils were
cemented to them, but the hearer had his powers taxed to catch
the effect. Soft iron pins placed in the hollow axis of the coil
also sounded under similar treatment. I could not succeed, how-
ever, in getting a soft iron pin perfectly to answer the galvano-
meter test, ordinary nails and similar iron pins always caused a
slight deflection, which became more marked by pendulum accumu-
lation. Even a soft iron pin, as pure as I could get, after being ex-
posed for half an hour to a white heat, on being made to move at
right angles to the dipping needle, at least so nearly as this position
could be given to it by the hand, indicated through its coil faint
traces of magnetism. I had some difficulty in getting taps out of it
for the listening station, but I succeeded at last by using another
similar pin held in the same line as a mallet. Iron thus softened
seems to lose its telephonic power more by absence of elasticity
than by being less magnetic, for the said pin seldom failed in any
position before being annealed, and so far as tests went it was not a
bit more magnetic. A somewhat curious result was got by cementing
a small coil to a strip of ferrotype plate quite near to the edge, and
making that edge strike on the teeth of a syren wheel, made to
revolve on a turning table, when the screeching note thus produced
was distinctly telephoned. When there was any slight indication
of magnetism, such as was given by the spot of light shifting even
a millimetre for one quick motion, the taps were rendered with
great certainty. The soft iron pins just mentioned, when put on
the pole of a magnet, and very gently tapped with a common
pencil, made themselves distinctly heard. This can be done in
the case of any telephone on removing the disc.

of Edinburgh, Session 1877-78.

623

Now, it may be asked, are all such sound-exciting currents to

be traced to the shifting of magnetic matter in a magnetic field 1

or is there not ground for believing that a blow for the instant

disturbs the magnetic condition of a magnet, and magnetises soft

iron, in consequence of a disturbance of the molecules, enough to

excite telephonic currents ? And may not such magnetic changes

act without the displacement in the field that generally or

2

perhaps necessarily accompanies them, and heightens their effect •
Wiedemann has shown that blows alone given at right angles to
the magnetic needle, and consequently apart from the earth’s
magnetism, produce permanent magnetic changes, and that torsion
and change of external conformation may do the same. The
permanent effect also of blows in lessening the powers of a magnet,
or of giving to iron under induction a magnetic set, has long
been known. Now, may not the telephone reveal to us that they
in every case produce a momentary effect of an intensity in some
degree proportionate to the magnetisation of the iron %

The following telephonic arrangement, which is different from that
of Bell’s, may possibly have some bearing in the view just suggested ;
but knowing, from the instances discussed, the ambiguity that
attends a departure from the pusli-and-pull theory, I quote it more
as a problem for push-and-pull solution, than as a proof of blow-

induced effects. The apparatus (fig. 6), consists of a horse-shoe
magnet rather more than 5 inches long, with a pin on each pole
standing at right angles to the plane of the magnet. The pins are
provided each with a coil of fine copper wire, the two being joined
up as in an electro-magnet. The pole pins are inch apart, and
a stiff disc (No. 28), 3 inches diameter of untempered steel, is
screwed to them by large-headed screws. Such a disc, when aided by
a wooden or non-metallic resonating box, can both convey and receive
an articulate message, indistinctly certainly, but still it does it.
When it is joined up with the galvanometer, and tapped with a
pencil on any part, taking care of course not to combine the

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Proceedings of the Royal Society

striking and lifting motions, no visible deflection is got, though
the same taps on the disc of a Bell telephone make deflections of
from 5 to 10 mm. of the scale. When the disc is taken off, we
may ascertain the efficacy of vibrations in the line of the plate to
generate currents. Taking a small thin iron rod and giving it small
vertical excursions, I found that when these were made in the line
of the plate no effect whatever was got when the rod was held
equatorially to the line of poles, but that as the rod was brought to
either pole an increasingly slight effect was seen. This might be
due in part or perhaps wholly to the want of parallelism of the
motion to the pins, for the slightest side or horizontal motion pro-
duced a marked effect. That even this stiff plate vibrates when
spoken to there can be little doubt, but the vibrations cannot, on the
ordinary push-and-pull principle, push and pull at right angles to
themselves. The action of the disc may be due to the blow it gives
to the pole pins as an ordinary resonator, and possibly also the action
of blows just hinted at may be present. The aerial blows may
directly induce currents, or they may do so in altering the shape of
the plate by vibration. However this may be, the problem may
safely crave a solution from the push-and-pull theorists. When
the plate is not screwed down, but laid or gently pressed on the pins,
and more especially if it be made the bottom of a shallow tin box
with a hole on the top, its performance almost rivals that of Bell’s
telephone. The improved effect is no doubt due to facility of vibra-
tion which is as necessary to the sounding power of vibrations of
molecular origin as to those produced mechanically.

I made an attempt also to see whether the coil itself had any
sounding action. If a blow can make soft iron induce a current,
possibly a closed coil, the electric analogue of soft iron, may do so
under the same treatment. I first tried this by hitting the side of
a coil by a small wooden hammer, then as the frame of it gave way
under this usage, I cemented it to a piece of board and hit the board ;
but as again the whole coil split up under the blow's, I lastly tied
it to a strip of wood, and used it as the head of a hammer against
the end of a wooden rod. In each case I succeeded once or twice
in telephoning the taps, but most unaccountably, for I might tap
ever so hard and so often afterwards without being again so fortunate.
How the sounds were sent in these cases I cannot say. The coils

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used, which were the same as those employed with the tuning-fork,
could send with a brisk turn of the hand a current induced by the
earth, may have been so excited, but there was next to nothing
rotational in the blow they got or gave.

It may be well believed that many of the sounds thus produced
in the telephone were very faint, and required a sharp ear and
undivided attention. I have mentioned only these results which
have been repeatedly got. Possibly some of them may be wrong as
regards comparative loudness, but I had in almost every case the
impression of different listeners. The listener was provided with
two telephones of the following kind. One pole of a horse-shoe
magnet (fig. 7), carried the bobbin pin and a brass arm for an
adjusting screw. To the other
an iron stage was fixed, to which
was screwed a box 3J inches in
diameter and J inch deep, with a
hole in the top J inch wide, pro-
vided with a short tube for inser-
tion into the ear. The bottom
of this box was of untempered
steel plate (No. 28), and its distance from the pin could be adjusted
by the screw. Such an instrument told faint tuning-fork sounds,
which the ordinary one pole ferrotype plate telephone I had passed
over.

Leaving now the sending station, we proceed in our search
for molecular action to the receiving instrument, and we examine
the sounds emitted by its electric and magnetic parts. Instead
of having a person performing the irksome task of talking or
singing at the sending end, let us lay aside the distant telephone,
and put in its place and that of the speaker a Bunsen cell
charged with water and a mercury break. Such a cell would have
no effect on the telephone without the break, for it is only momen-
tary currents that affect the instrument. The break thus furnishes
us with an intermittent or discontinuous current, and is in fact an
untiring and uniform speaker, uttering a series of ticks or taps which
are very audible to the distant telephone hearer. Now let us begin
with the coil which is the “ fountain and source ” of all action in
the receiver. Let us detach it from the core, and hold it up to the

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Proceedings of the Royal Society

ear. By attentive listening a faint ticking is heard, and if we wish
to hear it without strain we must add another cell or two to the
battery. The sounds emitted by the coil are very faint, and cannot
be excited by the voice or even a tuning-fork. With small battery
power the coil may be made to sound, but with a strong battery it
may be heard at some distance from the ear. Thus the coil which
we thrashed almost to death to send a message receives one without
demur. W e now insert in the coil a piece of soft iron, and we have
a duet of two undistinguishable ticks, the principal part being per-
formed by the iron. Here again the receiving action is immensely
better than the sending, and leads us to suspect that our rough efforts
to send were mere bungling, due to our ignorance of the right way
to do it. If now we bring a magnet and place the soft iron pin on
its pole, or screw it into the pole, a sudden bound is made in the
loudness of the sound, and with the one cell water current we can
hear a few inches off. Whatever vibrations were effected in the
pin by itself now grow immensely more pronounced when it is made
magnetic. We may now replace the coil in its core in the
telephone, for our arrangement is nothing else than a telephone with-
out a disc. The sending and receiving powers are now more nearly
on a par, for we found that the gentle tap of a pencil can now be
sent. Let us now, in imitation of Professor Tait and Mr Blyth’s
experiments, put a piece of glass or pasteboard, or wood or other
non-conducting substance, on the core. The sound waxes thereby
louder, as was explained by the plate acting as an ordinary resonator.
Lift any one of these the smallest thing from the core, and it acts as
a dead wall to stop the sound of the core. In place of these, let us
take a series of conducting metal plates of lead, German silver,
copper, and silver, all equally thick and as nearly as possible of
the same temper. When we place one of these on the core we hear
the same resonance as in the non-conductor, but we also perceive
what appears to be a new and separate action set up by the plate on
its own account, and as we change from disc to disc we find that
the sound grows with the conductivity of the plate till we reach
silver, which is very audible. When now we put an iron disc of
similar size and temper, a sound is heard which completely eclipses
the loudest of the others. All these discs when held slightly away
from the core sound louder than when touching it, and the cul-

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minating receiving action, where sending and receiving are on a par,
is the disc of iron in front of the pole, almost hut not quite touching
it — in fact, the disc of Bells telephone.

Let us now retrace our steps, and go over the ground more
minutely, beginning again with the coil. The coils I used consisted
of from 30 to 100 ohms of copper wire '007 inches, and were of
various sizes and shapes. For such fine wire coils, as already stated,
one cell will suffice if the listener be sharp and attentive, but two or
three must be used for easy hearing. The intermittent current
given off by an ordinary medical electro-magnetic machine produces
very audible sounds in such coils. The electric wave of such a
machine is peculiarly adapted to excite telephonic sounds. It is a
double wave of opposite name, with a sharp beginning and an equally
sharp termination. For thick wire coils a more powerful electro-
motor is required. With five fully charged Bunsen cells, I managed
to get every coil I could lay hands on to render the ticking of the
break, whether they had iron cores or not. The sounds were per-
fect telephonic performances ; for it mattered not whether the wire
was thick or thin, covered with silk or wool or cotton, the tick was
not at all musical, but simply the reproduction of the sound of the
break. We should be inclined at once to call such a rendering
molecular, did we not know that in this era of mechanical telephones
and phonographs, discs of tinfoil, oiled silk, paper, potato, butter,
and other unlikely substances, can reproduce the tones of the human
voice without peculiar accent. Coil ticking or tapping is familiar
to any one who has dealt with a powerful induction coil. The sole
of the instrument resounds with the primary coil rendering of the
break outside the instrument.

Now, whence comes this sound in a coil? Wiedemann, who
gives De la Rive the credit of first noting the sound, attributes
it to the clashing of the various convolutions against each other,
due to the known action that wires conveying currents in the
same direction attract each other. With a view to answer
this question, I wound up 15 feet of '04 copper wire into
a spiral f of an inch in diameter, and sent the intermittent
current of a five-celled fully charged Bunsen battery through
it. On holding the end of the spiral to the ear, I heard the
tapping distinctly. On drawing out the spiral, so that no two

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Proceedings of the Royal Society

convolutions were in contact, I failed to hear any sound ; but when
I put two or three convolutions together and held them to the ear,
the sound was again heard. I now isolated one convolution, and
tied the thread of a paper telephone to it, and, although there
was no neighbouring convolution in contact, I heard, by means
of the telephone, the ticking distinctly, and, when the spiral was
drawn out into a plain wire, the same sound continued. The cur-
rent, as indicated by a tangent galvanometer of a single hoop of
stout copper rod, produced a deflection of 54° for the unbroken cur-
rent, and of 41° for the intermittent one. The cell resistance was
under two ohms, and the exterior resistance under one ohm. The
nitric acid was old, and had been frequently used. Removing the
’04 wire from the circuit, and substituting a short length of *024
copper wire, the current interruptions were heard still better in the
paper telephone. I suspected mechanical transmission of the sound,
but that could scarcely be, the wires being led from the open air by
a fixed course under the floor. When all mechanical connection
was broken through mercury troughs, there was no alteration ; and
when a loop of 2 inches of *024 wire was held firmly in a vice it
did not cease to sound. I need not, however, have been so scepti-
cal, for sounds of a similar origin had been got as early as 1845 by
Beatson, De la Rive, and other observers. They may not, without
the aid of the mechanical telephone, have got in the wires the same
clearly rendered series of ticks that we hear by its aid. De la
Rive’s description of them, however, is both definite and graphic.*

* His words are : — “Quant au son lui-meme, je ne peux pas mieux en donner
une idee, qu’en le comparant a celui qu’on produit avec la roue de Savart.
C’est une suite de bruits resultants du choc des particules metalliques les unes
contre les autres, beaucoup plus qu’un son musical. On entend aussi, il est
vrai, des sons musicaux. Ce sont les harmoniques du son que rendrait la tige
ou le fil par l’effet des vibrations transversales; ils proviennent du mouvement
vibratoire qu’eprouve le metal, mais ne sont pas un effet direct de l’influence
electrique a laquelle il est soumis. On peut en effet, les faire dispar&itre en
touchant avec la main le corps vibrant, sansque pour cela disparaisse le bruit
f ondamental. ” — “Le son que rend un fil de fer bien recuit quand il transmet
le courant est un son tres fort, qui ressemble beaucoup au son des cloches
d’eglise dans le lointain. On pourrait peut-etre l’employer avec avantage dans
les telegraphes electriques. ” — “ Le ton du son varie avec la vitesse avec laquelle
les courants discontinus se succedent ; quand cette succession est tres rapide, le
son ressemble beaucoup au bruit que fait le vent lorsqu’il souffle fortement.” —
Covip. Rend. , 1845.

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629

He details liis experiments, and, unlike other observers, extended
his researches to other metals besides iron. He stretched wires of
various metals on a sonometer with a helix of wire round them, so
that he could excite sounds by the simple passage of the current in
the wire, or by the magnetising action on it of the helix. He used an
electromotor of five Grove’s cells. He tells us that the sounds emitted
from iron and other metals, by the direct passage through them of
a discontinuous current, were in no way different from those
obtained by magnetisation when the same current was made to
pass through the helix surrounding the wire. This was especially
observable in the case of iron. He states also loosely that the
loudness of the sounds emitted with the same strength of current
was in proportion to the resistances offered by the wires, and that
possibly this sounding action had the same conditions as heat in the
galvanic circuit, so far at least as resistance was concerned. He,
moreover, states that iron stood quite exceptionally among the metals
in its power to give out such sounds.

The exact way in which De la Rive obtained these sounds appears
to have been lost, for no subsequent observer accords with him.
Wiedemann, for instance, in his “Electro-Magnetismus,” in keeping
with the investigations of Wertheim, states that iron alone emits
sounds under the above conditions, and he quotes De la Rive’s
remarks on other metals within parentheses. How, the simple
device of attaching the string of a mechanical telephone to the
wires when the intermittent current circulates, enables us to observe
these sounding effects with perfect ease and certainty. When
attached to a copper wire ("007 inches diameter) the sound is very
marked; and when to an iron wire (”008) the telephone sounds
many feet off, the current being that from the five-cell Bunsen
battery.* Indeed, for the iron wire a telephone is not necessary,
for the ticking can be heard when the wire is held in the teeth,
or when it is doubled on the finger and inserted in the passage
of the ear. There is only one objection to the last mode of pro-
cedure, viz., that the wire is almost too hot to be comfortable. It is
not, however, necessary to insert the wire itself into the ear, for a
cotton thread, tied to the wire and placed in the ear, sounds nearly

* This was distinctly heard in the auditorium of the Society when the paper
was read.

4 o

VOL. IX.

630

Proceedings of the Royal Society

as loud. A thin iron wire is therefore the most rudimentary form
of a telephone. G-ott’s telephone has thus another explanation in
addition to that of the mere twisting round in a magnetic field;
for if only the coil he left without a field, or even if only one con-
volution of it he left, and held in the chaps of a vice, its power of
moving the paper disc would not wholly disappear.

When the paper telephone was attached to the thin iron wire, and
the distant break worked by the hand of an operator, a loud sound was
heard when the dipper of the break entered the mercury, and another
equally loud, hut not louder, when it was lifted out. In this case
the break was two rooms off from the listener, at a distance of from
30 to 40 feet, and when the operator was made to say “in,” “out,” at
each motion, short as the distance was, the wire sounded before the
voice. The sounds thus given had a clear metallic ring about them.
This, however, disappeared when the wire was coiled tightly round
the finger. The mechanical telephone enables us to hear such sounds
in all portions of the wire without any interruption. We can hear,
for instance, the half musical sound in a straight wire, the dull un-
musical sound when the wire is tightly coiled, and the increase of
this when several convolutions of a covered wire are kept tightly
together. In the single wire, although the sound is loudest when it
is tense, yet it is distinctly heard when perfectly loose. De la Eive
tells ns that the resistance in the sounding wire must he greater
than that of the remaining circuit, battery included. I have found
that this is not necessary, for I can hear distinctly the sound of a
thin iron wire when the current is the weak one furnished by a
single Bunsen cell charged with water. The Bunsen cells mentioned
here have an active medium surface of 40 square inches. Again,
with a small magneto-electric machine for medical purposes, almost
any experiment can he demonstrated.

With reference to the strengths of current necessary to excite the
wires, the characteristic of the telephone mentioned by Professor
Tait, in his communication on the “ Strength of a Telephonic
Current,” must he borne in mind, viz., that the telephonic effect
does not depend so much on the actual strength of the sounding
current as on the rapidity with which changes in the strength
are effected. The break used in these experiments made from
five to six interruptions in the second, that certainly was not very

of Edinburgh, Session 1877-7 8.

631

sudden. Then, in a mercury break, the spark that ensues on the
separation of the dipper from the surface of the mercury is con-
ducting, and it may only be the break of the attenuated current
when the spark ceases that has telephonic power. This would
bring us down to a low scale of effective action, when working
with a water cell interrupted six times per second. It cannot,
however, be with certainty alleged that this kind of interruption
is strictly single, as there may be pulses in it preceding the final
stoppage.

The relation of resistance to sound can be shown by an experi-
ment like the following : — I measured off a yard of iron, German

silver, copper, and silver wire, of diameters respectively of *008, '0086,
*007, and ’006 of an inch. The resistance of each yard was re-
spectively 3, 8 '7, *7, and 1*4 ohms (the silver alloy was exceptionally
hard). From these again I cut off a foot and soldered them end to
end in a successive chain, and stretched them out (fig. 8) in a line,
with their junctions firmly clumped to prevent the sound of the one
running into the other. I then attached four similar mechanical
telephones to them, and found, at least so far as the ear could judge,
that the sounds emitted by each, when the same broken current
passed through all, were proportionate to the resistance such offered,
in the case of the last three metals, whilst the sound given out by
the iron distanced all the others. The German silver here was much
louder than the silver, which again was, one could fancy, twice as
loud as the copper. This seems to clash with what we have stated
with reference to the conducting discs on or near the core of the
magnet of the telephone. It may be somewhat hazardous to venture
an explanation, but there is one that turns up so readily at the first
consideration of the matter that I may mention it. In the case of
the wires the same current passed through all, but in the discs the
currents induced would be, as is generally received, relatively in pro*

632 Proceedings of the Hoy at Society

portion to the conductivity of each. If it now he accepted that the
sounding action be like heat proportionate to the square of the
current strength, the apparent discrepancy is accounted for. Suppose
the conductivity of silver to be ten times greater than that of German
silver, then in the silver plate a tenfold greater current would be
induced, and would have in consequence one hundredfold greater
sounding power than that of the German silver in the same resistance :
but as the resistance of the German silver is ten times greater than
that of the silver, there would still be a tenfold louder sound in the
silver than in the German silver, quite a sufficient margin to remove
the discrepancy. In addition to the action within the plates here
discussed, there may of course also be the external push-and-pull,
as with the iron disc. In wires the length involved has little
effect on the sound ; for though a long stretch of wire does
sound louder than a short one, the difference is by no means in
keeping with the respective lengths. In thick wires no sound is
got. I tried in vain with the strongest current I could conveniently
use to get a sound out of a No. 14 copper wire.

Now here at least it will be admitted that we have a molecular
action. It may be replied that the earth’s magnetism has something
to do with it. To show that it has not, we may try the somewhat
inelegant feat of holding the end of the thin iron wire in the teeth,
and turning it in every possible direction, when we shall find that
the loudness of the ticking has no relation to direction. Again,
when the string of the telephone is tied to the wire and made to go
round it in a circle, we shall find no maximum or minimum points.
This then is a telephonic action absolutely free from external push
and pull, proceeding undoubtedly from molecular disturbance in the
wire. That the action is magnetic in some way is evident from the
exceptional position of iron in the series of metals. De la Eive held
that the sounding action of an iron wire, when the seat of a dis-
continuous current was almost identical with, and must be traceable
to the same ultimate cause as, that it displays when placed in a
magnetising helix excited by a similar current. The parallelism
between the wire telephone and the ordinary electric telephone
is so striking that no theory of the latter can be held to be
complete without it includes the former. It seems to suggest that
the sounds we hear in plates and rods under sudden electric or

of Edinburgh , Session 1877-78.

633

magnetic changes is partially at least due to the molecular distur-
bances set up by induced momentary currents. Be that as it may,
surely no one would be inclined to say that the ticking of a Bell
telephone under a series of momentary currents is wholly mechanical,
and that of a wire telephone under the same conditions wholly
molecular.

After observing these sounds, my next inquiry was to ascertain
how they comported themselves in a helix capable of motion.
With this view I coiled about ten feet of fine iron wire (-0173 inch
diameter) into a spiral about •£ inch in diameter. I suspended it
(tig. 9) by a thick wire held on a stand, and
arranged that its lower end should dip into a
vessel of mercury. Such a spiral is exceed-
ingly delicate, and the up and down motion
of its slender convolutions is most easily ex-
cited. When left free to itself, and there is
no interruption in the mercury below, that
is, no spark reaction, the motion produced by
a discontinuous current of five Bunsen cells
is very slight; but if a §-inch soft iron rod
be introduced so as to be clear of the sides of
the spiral, the mechanical excitement of the
spiral is more marked, but still not much.

But if I hold down the lower end, and
it so happen that the tension and number
of convolutions be sufficient, the helix
divides itself into two very active ventral segments with a node
in the middle. The motion, especially at the middle of each
segment, is now very considerable. But if it does not vibrate
thus symmetrically, by shifting the fingers a little, a point is
easily found by which at least one very active ventral segment is
secured. If now to a point of maximum motion I solder a very fine
copper wire, to serve as the thread of a mechanical telephone and
make it come out at right angles to the motion of the spiral, it does
not interfere with it. By this contrivance I secure the advantage of
listening to what goes on in the wire without interfering with any
mechanical magnetic effect. Profiting by the experience of the fork, I
found that a fine wire could hang loosely, and yet convey vibrations to

¥

634 Proceedings of the Royal /Society

the telephone. Fine iron wire answers very well, but in this case it is
inapplicable, as it sets up a clearly audible action on its own account.
When the ear is now applied to the telephone the ticking that you
would hear in the wire, if it were straight, is heard distinctly, and
is the only distinct sound, for the up and down motion of the
convolution only produces a slight jingling in the connecting
wire, and possibly also in the coil. When the convolution is held
tight in the fingers the ticking goes on if anything more distinctly
than before. Whether the mechanical motion by the increased
fixity of the helix is converted into louder ticking, could not be
decided by the difference. Here we have two vibrations quite
distinct from one another, the ticking in the wire and the me-
chanical motion due to the mutual electro-magnetic action between
the rod and the coil. If this last were quick enough it would
also be telephoned, but the rate of vibration being below that of
musical frequency it is nothing but inaudible motion. In this
helix action I would submit we have a dissected view of all
receiving telephonic action — a vibration in the body clearly of
molecular origin, and another of the body of a push-and-pull kind.
The latter may be stopped or nearly so, but not the former. From
its internal origin it is bound to make itself good, and when the
body is held in the grasp of the most rigid substance it only propa-
gates in it the minute vibrations which no elastic matter can stop.
In the vibrations of coils, cores, or plates, the same thing holds.
Molecular vibration is present in them all, and how far mechanical
vibration chimes in in unison depends entirely on the ease with
which such can be produced.

There is apparently a marked difference between these two vibra-
tions. The one can make itself good acoustically by one impulse,
the other not. I have tried in vain, while holding taut the
thread of a mechanical telephone without letting the fingers slip, to
produce, by a sudden pull or let go, the tick that resounds in iron
or a conductor when a current suddenly begin or ends, and I could
only do so by letting the string slip the slightest degree, so as to set
up a short series of vibrations. Each galvanic or magnetic tick or
tap may not, in the first instance, be more than a simple shock ;
but so sudden is it that the particles concerned do not recover at
once, but continue vibrating for an infinitesimal time, and hence

635

of Edinburgh, Session 1877-78.

the pitch or musical sound that generally accompanies it. When,
however, a prolonged vibration is difficult, and the impulses brace
each other up by frequent repetition, we have possibly in the first
case a very short series, and in the other only one vibration. Such
vibrations are as capable of rendering all complex acoustic combina-
tions as vibrations of the push-and-pull kind.

It would be a matter of mere speculation to guess how the condi-
tions of the vibrating helix are transferred to vibrating rods or discs
of iron in an intermittent magnetic field. I would only say that
the same double vibration is clearly traceable in them. To illus-
trate this in the case of rods, I took a small coil of ISTo. 20 wire, 2
inches in diameter and about an inch high with a hollow axis of
| inch, and sent the interrupted current of a five Bunsen cell bat-
tery through it. Inside the axis I put a soft iron pin 2 inches long
and \ inch square (fig. 10). To the upper end a fine copper wire
was soldered to act as the thread of a telephone. When rightly
placed the pin supported itself in the hollow, and kept dancing up
and down symmetrically without much friction against the inside
of the bobbin hollow. Here the mechanical motion was not so
clearly eliminated as in the case of the helix ; yet the ticking was
heard, and it alone, when the motion of the pin was stopped by the
hand. The impossibility of stopping the ticking of the pin was

Fig. 10. F

shown by securing its ends between the jaws of a vice and making it
as tight as possible, when the vice itself took up the tale of electric
interruption, and made itself heard all round. A curious change
was observed in long iron rods when this coil was placed round the
middle of them and when shifted to the end. In the former posi-
tion the sound was a stuccato rendering of the longitudinal note of
the rod, and in the latter this sound was lost in a dull tapping. In

636 Proceedings of the Royal Society

the latter position there was a pronounced tendency to push and
pull.

I adopted a similar arrangement with the vibrating disc of the
telephone. To the middle of one T cemented an india-rubber tube
to act as a yielding handle, and the paper telephone wire was sol-
dered near the middle. The disc wTas made to move in front of a
telephone core excited by the coil just named. The movements of
the disc were very violent, and made in all directions, making the
conuecting string jingle loudly, so that the isolation of the ticking
sound was not so satisfactory as in the two previous cases. Still it
was heard, and when the motions of the disc were kept in one direc-
tion its loudness did not grow with the extent of the motion. With
a fine coil and a water cell the ticks were distinct enough ; but the
mechanical displacement was too small to yield the required com-
parison. The impossibility of stopping this ticking was illustrated
in the following way : — A ferrotype plate was held tightly between
two thin pieces of plate glass, the space between being filled up
with sealing wax so that the whole was a solid mass of glass and
wax. This was brought near a core excited by a water cell, when
the sound was loudly rendered. Another illustration to the same
effect was that of cementing by sealing wax the ferrotype plate of a
telephone to a disc of thick microscopic glass, and putting this in
the telephone with the glass side to the ear or mouth. Its articulate
functions, though much impaired, still continued.

Lastly, to test whether the tick in a coil was due to electric con-
duction, I screwed a pin into the core of the telephone so as to act as
a prolongation of the core ; round this I placed a coil of fine wire,
to which the string of a paper telephone was attached. There was
no ticking heard so long as the circuit of the coil was broken; but
the moment it was closed the ticking began. The coil was, of
course, clear of the core. At the same time, however, there was
mechanical action between the coil and core, illustrating the dif-
ficulty in such cases of determining by direct observation whether
the single mechanical pull may not also make itself heard.

In conclusion, I would say, by way of summing up the evidence
of this paper, that at the sending station the evidence of molecular
action, though suggestive, is by no means conclusive ; while at the
receiving station the existence of molecular as well as mechanical

of Edinburgh , Session 1877-78.

637

action amounts to demonstration. How the actual performance of
the receiving instrument is to be apportioned between these, it is,
of course, difficult to say. Taking into account Professor Tait’s
calculations as to the infinitesimal strength of a current that can
make a telephone tick, and assuming that that tick is purely mole-
cular, as we have done, molecular action must he there not the less
considerable.

2. Sketch of the Arrangement of Tables of Ballistic Curves in
a medium resisting as the Square of the Velocity, and of
the Application of these Tables to Gunnery. By Edward
Sang.

The motion of a body in a medium whose resistance is propor-
tional to the square of the velocity, has been the subject of many
inquiries. Its intimate connection with the theory and practice of
gunnery has produced for it the attention of almost every cultivator
of the higher analysis ; but, like several other seemingly elementary
problems in mechanics, it has hitherto received no complete solution.

If nothing else than the fluid’s resistance influence the motion
the investigation is comparatively easy ; thus, taking the time as
the primary variable, the
speed has its own square
for its derivative, and so
must be proportional to
the first inverse power of
the time, and consequently
the distance passed over
must be proportional to
the logarithm of that time.

Hence, if the present posi-
tion, the velocity and the

coefficient of resistance be

, , O B P A F

given, we can compute, for-
wards, the position and

velocity at any future time; or backwards, what those had been
at previous times. But since the velocities are inversely propor-
tional to the times elapsed from some fixed epoch, it follows that,

VOL. ix. 4 p

638

Proceedings of the Royal Society

at that epoch, the velocity must have been infinite, so that although
the body may have come from an infinite distance, setting out
therefrom with an infinite velocity, it must have begun that motion
a finite time ago.

If we represent time by distances measured along OF, one of the
asymptotes of a hyperbola, the ordinates, such as P p, drawn parallel
to the other asymptote, are proportional to the corresponding
velocities. Thus the present velocity being P 'p, that at the future-
time OA will be A a, while that at the former date OB had been
B b ; and the areas B5pP, PpaA represent the distances passed
over during the intervals of time BP and PA. The distance
corresponding to the finite previous time OP is thus infinite, and
so also must have been the velocity of projection at the date 0.

When the motion is affected by some influence other than the
resistance, the investigation becomes more intricate. The case of a
constant gravitation in a fixed direction is the simplest of these
complications, and the simplest case of this is when the directions
of the motion and of gravitation coincide.

If a stone be thrown straight upwards, its motion is impeded both
by its weight and by the air’s resistance ; in the subsequent descent
the motion is accelerated by gravity, but retarded by the air ; so
that, for the ascent, the soliciting influence takes the form g + cv2,
and for the descent becomes g - cv1. Now the change in the sign of
the velocity from + v in the ascent to -v in the descent, is not
accompanied by any change in the. sign of v2, and therefore both
parts of the motion cannot be represented by any one algebraic
formula. Accordingly we find the upward motion to be repre-
sented by circular functions ; the downward motion by the corre-
sponding catenarian ones.

In fig. 2, the left hand row of dots represents the upward
motion graduated to equal intervals of time. The stone is first
shown at A as having come from some indefinite distance below ;
its speed, rapidly diminished, is altogether extinguished at N. In
order to avoid confusion, the descent is shown on the adjoining right
hand column of dots.

In descending, the acceleration due to gravity becomes less and
less ; it would cease altogether if the velocity could become so great
as to cause a resistance equal to the weight; the tendency, there-

of Edinburgh, Session 1877-78.

639

Fig. 2.

N

i

9

,5

1,0

1,0

fore, is to reach a definite terminal velocity, and the stone ultimately
moves almost uniformly. If it had been
thrown downwards at a rate greater than this
terminal velocity, its motion would have been
retarded, but less and less so as it approximated
to the same limit of uniform motion.

We may study the ascent by tracing it back-
wards from the highest point, fancying the air
to have then the quality of hastening the
motion. In this case the velocity would in-
crease to become infinite ; but this infinite
velocity would be acquired in a finite time.

In fact, the time being represented by a cir-
cular arc, the velocity would be proportional
to the tangent of that arc, so that in the time
corresponding to a whole quadrant, the velocity
would become infinite. Thus it seems that,
however rapidly a stone may be thrown up-
wards, its motion is extinguished within a
finite time determined by the coefficient of
resistance.

Each particular body has its own terminal
velocity depending on the weight and on the
extent and peculiarities of the surface exposed
to resistance ; but the motions of all follow
exactly the same law, so that one diagram may
serve for all, the units of comparison alone
needing to be changed.

Also, one table of the positions and velocities
may be made to do for all cases. In the
arrangement of such a table we have to seek
for the most convenient system of units; now,
on contemplating the motion of a projectile
independently of our measures of time and
distance, we perceive that the terminal speed
is the only standard with which we can com-
pare the velocities at the various parts of the path, wherefore we
adopt this terminal velocity as the tabular unit of speed.

1,5

A

2,0

Z

640

Proceedings of the Royal Society

This terminal velocity has to he considered along with the inten-
sity ot gravitation, which intensity, if acting alone, would generate
velocities proportional to the times ; wherefore the time in which
the heavy body, falling freely, would acquire the terminal velocity,
presents itself as the proper tabular unit of time, and, as a necessary
accompaniment, the tabular unit of distance must he that over
which the body would pass with its uniform terminal velocity in
the time during which that terminal velocity was acquired ; or, in
other words, must he double the height of the free fall needed for
the acquisition of the final velocity.

The accompanying table has been constructed for these assumed
units ; the details of the rise are given on the left hand, those of
the fall on the right hand side, the times being reckoned before and
after the instant of culmination : —

Time.

Velocity.

Rise.

Fall.

Velocity.

Time.

Time of
Free Fall.

Time of
Actual
Fall.

-0*0

•00000

•ooooo

•ooooo

•ooooo

+ 0-0

1-00000

T

T0033

•00501

•00499

•09967

•1

•99918

•2

•20271

•02013

•01987

T9738

•2

•99669

•3

•30934

•04569

•04434

•29131

•3

•99265

•4

•42279

•08223

•07795

•37995

•4

•98714

-0*5

•54630

T3058

T2011

•46212

+ 0-5

•98026

•6

•68414

T9197

•17014

•53705

•6

•97221

*7

•84209

•26809

•22727

•60437

•7

•96313

•8

1-02964

•36139

•29075

•66404

•8

•95321

•9

1-26016

•47544

•35983

•71630

•9

•94260

-1*0

1-55741

•61573

•43378

•76159

+ 1-0

•93143

•1

1-96476

•79055

•51194

•80050

•1

•91988

•2

2-57215

1-01512

•59369

•83365

•2

•90806

•3

3-60210

1-31864

•67850

•86172

•3

•89608

•4

5-79789

1-77215

•76570

•88552

•4

•88393

-1-5

14T0143

2-64878

•85544

•90515

+ 1-5

•87204

•94681

•92167

•6

86005

1-03968

•93541

•7

•84824

1T3381

•94681

•8

•83637

1-22898

•95624

•9

-82516

1-32500

•96403

+ 2-0

•81394

Opposite the time 1*3 in the first column, we find the velocity
3-60210, this means that if the stone he thrown upwards with the

of Edinburgh, Session 1877-78.

641

velocity 3 -60210, as at A in fig. 2, it will reach its highest point
in the time 1*3, the height to which it will rise being 1 ‘31864, as
shown in the third column. The subsequent fall is shown in the
fourth column, and there we find that the same level is reached just
before the time 2*0; the whole time of flight being somewhat less
than 3 3.

To translate this into ordinary measures, let us suppose a body
whose terminal velocity is 320 feet per second ; the time in which
this velocity is acquired in free fall is 10 seconds, and therefore all
the tabular times must be multiplied by 10, the tabular velocities
by 320, and the linear distances by 3200. Hence if such a body
were thrown upwards with a velocity of 1152 feet per second, it
would rise in 13 seconds to a height of 4230 feet, and would thence
descend in 19 ‘9 3 seconds, striking the ground with the velocity of
308 feet per second.

This table enables us to interpret easily the results of experiments
made on falling bodies. Thus, if the height and the time of descent
be accurately observed, we may thence deduce the terminal velocity;
from which, again, knowing the weight and the extent of surface,
we may discover the constant of the coefficient of resistance. In
order to facilitate the computations for this class of experiments, we
may annex another column to our table, namely, one containing the
ratio of the time of free fall to the actual time of fall. Thus the
fall through the distance 1*32500, which is done in the time 2*0
with resistance, would be accomplished in 1*62788 if there were no
resistance due to velocity, and the ratio, as shown in the annexed
column, is *81394.

Suppose now that a body has been dropped from a height of 400
feet, and that the observed time of the fall is 6 seconds ; the time
of falling freely from this height is known to be 5 seconds, and
therefore the ratio is *83333. The table shows that this ratio be-
longs to the tabular time 1*8271, and that, consequently, 3*284
seconds is the time in which the terminal velocity is acquired in
falling freely ; that terminal velocity, therefore, must be 105 feet
per second.

In experiments of this kind, the disengagement at the beginning
and the stroke at the end of the fall may be made, by help of the

642

Proceedings of the Royal Society

electro-magnet, to record themselves alongside of the records of the
beats of a clock, and thus very great precision may be obtained.

When the stone is thrown obliquely, its path is curved ; were
there no air, that path would be the well-known parabola, which
forms the first ideal approximation. With speeds very small in
comparison with the terminal velocity, the deviation from the para-
bolic curve is slight ; but the deviation becomes excessive in the
ordinary practice of gunnery.

Beginning with the case of a body thrown obliquely upwards,
we observe that its upward motion is resisted both by the air and
by gravity ; when it has reached its highest point and is descend-
ing, the downward motion is less rapidly accelerated than the up-
ward motion had been retarded, so that the culminating point is
reached earlier than the half-time of flight. On the other hand, the
horizontal transference is retarded all along, wherefore the vertex of
the curve is beyond the middle of the horizontal range, as is seen
in fig. 3, which shows the positions of a projectile at equal inter-
vals of time.

Fig. 3 .

After having passed the highest point at V, the projectile bends
its motion more and more downwards, until ultimately the path
almost coincides with the plumb-line ; the speed, at the same time,
gradually approximates to the terminal velocity, and thus the curve
in that direction is limited by a vertical asymptote.

Beckoning backwards on the other side of the culminating point,
the speed is rapidly augmented, and would become infinite within a
definite time ; the inclination of the curve also tends to a definite
limit, wherefore this branch, too, has a rectilineal asymptote ; so that
the whole curve is continued in the angle formed by the two asymp-
totes as represented in fig. 4. Thus the branch VB, unlimited in

643

of Edinburgh, Session 1877-78.

length, is limited in the time of its description ; while the branch
VC, also unlimited in length, is unlimited as to time, but is limited
as to the extent of its horizontal range.

A

The intensity of gravitation being known ; if the terminal velo-
city, the direction, and the velocity at any point be given, we can
compute the position, the velocity, and the direction at any pro-
posed instant. These three data serve to determine the curve, and
in general any three data are sufficient, as, say, the inclination, the
range, and the time of flight. The direct computation from the first-
named three arguments is very operose; in the other cases it is
much more so, because we can only proceed by the method of suc-
cessive trials, or, what comes to the same thing, we must have
recourse to tabulated results.

My object at present is to describe the arrangement of tables of
this kind, and to explain their uses.

If we launch two masses at the same angle with speeds pro-
portional to the terminal velocities, the paths are similar in shape
though on different scales and performed in different times. This
circumstance is the first and principal guide in the arrangement of
the tables, because the computations for the one trajectory are easily
made to serve for the other. We naturally select for tabulation that
one in which the terminal velocity is unit.

These ballistic curves differ in character as well as in size. The
characteristic of the shape may be taken as the angle A (fig. 4),
made by the two asymptotes, or we may adopt the velocity at some
definite direction, say the velocity at the summit Y. The former is
general in its application, it includes the cases of projection obliquely

644

Proceedings of the Royal Society

downwards, even to the limit of projection in the direction of gravity;
but the latter has the advantage of more ready reference to practice,
and lies more to hand in the calculations.

In the subjoined example of a table, the velocity at the summit
is assumed to be just equal to the terminal velocity, and the details
are given for intervals of one-tenth part of the tabular unit of time.
For actual use these intervals must be made much smaller, and the
tables should be arranged for values of the characteristic velocity,
differing slightly from each other ; the former table may be regarded
as the beginning of the series with the title V = 0.

Since the curves extend indefinitely both ways, such tables must
always be incomplete ; we can do no more than carry them to the
limits of probable utility.

The first part of the table contains the details of the rise ; thus a
body shot off at the instant - *50, with the velocity 2T8, and at an

Velocity at Summit,

V = 1-00000.

Time.

Elevation.

Velocity.

Rise.

Hor. Distance.

•00

o°-oo/

1-00000

•ooooo

•ooooo

-•10

+ 5 ”25

1-11630

•00518

-•10537

-•20

+ 10 ”12

1-27188

•02158

- -22323

-•30

+ 14 ”17

1-48161

•05092

-•35716

-•40

+ 17 -42

1-77176

•09580

-•51262

-•50

+ 20 ”27

2-18190

•16041

- *69840

Time.

Depression.

Velocity.

Fall.

Hor. Distance.

•00

0°"00'

1-00000

•ooooo

•ooooo

+ •10

- 6 ”00

•91394

•00484

+ -09521

+ •20

-12 ”25

•85219

•01883

+ •18217

+ •30

-19 ”03

•81041

•04127

+ -26201

+ •40

-25 ”42

•78508

•07157

+ •33561

+ •50

- 37 ”08

•77348

•10921

+ -40362

+ •60

-38 ”38

•77521

•15481

+ *46631

+ •70

- 44 ”48

•79801

•20628

+ -52326

elevation of 20°"27', gradually loses speed, as shown in the third
column, and reaches the summit at the instant -00, having there a
velocity of FOO, and being now T60 above its original level. The
details of the descent are given in the second part of the table. On

645

of Edinburgh, Session 1877-78.

consulting the column marked Fall, we find that the original level
is reached between the instants + ’60 and + *70, by interpolation at
•611, so that the whole time of its flight has been 1*111. Also, in
the columns marked Hor. Distance, we find *6984 for that covered
during the rise, and -4726 for that passed over during the fall,
making the total horizontal range 1*1710. The velocity with which
the ball strikes the ground is seen to be -7777, while the impact is
at an angle of 39° ‘TO'. The squares of the initial and final velo-
cities are nearly in the ratio of 55 to 7 ; that is to say, of the work
done by the gunpowder in putting the ball in motion, 48 parts are
spent on the air, and 7 parts only remain to represent the destruc-
tive effort.

Thus we can readily compute the range, the time of flight, and
the incidence of the ball. A table of these, such as the following,
forms a convenient adjunct to the fundamental table

Velocity at Summit = L00000.

Elev.

Velocity.

Range.

Time.

Velocity.

Depr.

5°”26'

1-11630

•20372

•20347

•91142

6°”13/

10 ”12

1-27188

•41740

•41452

•84497

13 ”22

14 ”17

1-48161

•64538

•63470

•79993

21 ”26

17 ”42

1-77176

*89405

•86649

•77594

30 ”01

20 ”27

2-18190

1-17100

1-11087

•77768

39 ”19

In order to apply these results to business, we must ascertain the
values of the tabular units in terms of the actual units of time and
distance. This is easily done if the terminal velocity be known.
As an example, let us take a bullet whose terminal velocity is 800
feet per second, in which case the tabular velocities must all be
multiplied by 800. A heavy body falling freely acquires velocity
at the rate of 32 feet per second for each second of time, and would
acquire this velocity of 800 in 25 seconds, wherefore all the tabular
times must be multiplied by 25. Lastly, the unit of distance
is described with the unit velocity in the unit of time, where-
fore 800 x 25 = 20000 feet is the actual linear unit of the
tables as applied to this particular projectile. The above ex-
ample, therefore, expressed in English feet and in seconds of
time, becomes

VOL. ix. 4 Q

646

Proceedings of the Royal Society

Angle of elevation,
Initial velocity,
Time of ascent,
Rise,

Time of descent,
Horizontal range,
Final velocity,
Angle of incidence,

20°"27/.

1745*5 feet per sec.

12*5 sec.

3208 feet.

15*6 sec.

23420 feet.

622 feet per sec.
39°-19'.

If the same ball be shot from the same gun, but at another inclina-
tion, the shape of the path is changed and the details thereof must
be sought for in another table. We search among the various
tables for that one in which the given initial velocity is found op-
posite the proposed angle of elevation ; if the tables be constructed
for values of V sufficiently close, we shall find this either directly
or by an easy interpolation ; and then, proceeding as above, we can
get all the desired information.

Similarly, if the initial velocity and the horizontal range be given,
we convert these into the corresponding tabular numbers, and search
among the various tables for that one in which these two are found
together; the angle of inclination, the time of flight, and all the
other qusesita of the problem are then to hand.

It has been stated that three data suffice to determine the path.
When the terminal velocity is one of these, the solution is obtained
by simple inspection ; but when that velocity is one of the qusesita,
the operation becomes indirect.

Suppose that the velocity communicated to a given shot by a
specific charge of gunpowder has been ascertained, say, by help of the
ballistic pendulum, we may discover the terminal velocity of that
shot by observing the angle of elevation and the horizontal range.
For this purpose we assume some terminal velocity, thence compute
the corresponding tabular initial velocity, and thereby obtain the
corresponding horizontal range. If this come out too much, we
must reduce the assumed terminal velocity, and continue our trials
until the computed agree with the measured distance. If the time
of flight have also been carefully noted, we get a corroboration of
the accuracy of the result.

Hot only so, we may dispense altogether with the ballistic pen-

of Edinburgh, Session 1877—78..

647

dulum, and determine both the initial velocity and the resistance by
accurate observations of the angle, the range, and the time of flight.
For the purpose of facilitating the solutions of the various problems
which may arise in practice, auxiliary tables may be derived from
the fundamental ones.

When a shot is fired in a steady breeze, the direction in which
the ball meets the air is not the apparent direction of the gun, it is
that of the resultant of the two motions, and the computations have
to be made as for that resultant.

Thus if AZ (fig. 5) represent the horizontal direction of the
gun, and AB the initial velocity of the ball projected on the hori-
zontal plane, while £>B represents the velocity of the wind, A b will
be the horizontal direction in which the ball meets the air. Since
the vertical motion is not affected, the tangent of the elevation of
the gun must be changed in the ratio of A b to AB in order to get
the tangent of the true angle of elevation in relation to the air, and
A b multiplied by the secant of that elevation is the true initial
velocity.

If we now, using these corrected arguments, compu te the hori
zontal distances corresponding to equal intervals of time, measure
those along the prolongation of Ah and from the successive points
draw parallels cC, dl. ), &c., multiples of 6B, we shall have the

648

Proceedings of the Royal Society

horizontal projection of the ball's path, that path being a line of
double curvature.

As an example of the variety and completeness of the information
conveyed by such tables, we may cite the path detailed in the pre-
ceding table and represented by fig. 3.

The ball is projected from A with the velocity of 2T8, and at
once encounters a resistance 4§ times greater than its weight. Ths
speed is rapidly lessened, and the path is deflected to become hori-
zontal at Y, where, in the present instance, the resistance is just
equal to the weight. On account of this resistance the speed is
still slackened, but gravity now comes to accelerate the motion
downwards, and, at about the fifth interval from V, has overcome
the retardation, thereafter the velocity slowly increases, and tends
ultimately to reach the limit l'OO.

Those cases in which the characteristic angle A of fig. 4 is
obtuse have little or no application to gunnery ; in them the path
is never horizontal, but is inclined downwards all along.

The analysis of these motions is complex, and the calculations
thereon following are tedious, but the results, when tabulated, are
of easy application. The theory would be uninteresting to those
engaged in the actual business, just as the mode of construction of
trigonometric and logarithmic tables is scarcely ever thought of by
the navigator or surveyor. What we have at present to consider is
the advantage to be gained by the compilation of a series of tables
such as those sketched out.

3. On some Physical Experiments relating to the Function of
the Kidney. By David Kewman, Glasgow. Communi-
cated by Professor M'Kendrick.

[Abstract.)

This paper treats of the physical influences which promote the
secretion of urine, as far as can be demonstrated by experiments
upon animal membranes and the kidneys of animals recently killed.
Before going on to consider the subject I may be permitted simply
to mention the theory held regarding the means by which the

of Edinburgh, Session 1877-78. 649

kidney performs its function, and also say a word or two in connec-
tion with the structure of that organ. As regards its histology the
kidney may he said to he composed of two elements — (1) the blood-
vessels. and (2) the tubuli uriniferi. (This is leaving out of account
the lymphatic arrangement.) The kidney receives its supply of
blood from the renal artery, which, as it passes into the substance
of the kidney, penetrates the cortical portion and gives off
branches. The uriniferous tubules, in this part of the kidney
end in globular dilatations called the capsules, or Malpighian
bodies ; it is into these that the branches of the renal artery
pass to form convoluted coils, the glomeruli. The branches
of the renal artery which pass into the glomeruli are called the
afferent vessels, and the vessels that are formed by the reunion of
the branches of the glomeruli are called the efferent vessels. After
the efferent vessels emerge from the capsule of the Malpighian body
they again subdivide to form true capillaries, most of which go to
form a closely meshed network round the tubuli uriniferi. They
finally unite to form the radicals of the renal vein.

To make use of the description of Mr Bowman, “ it would be dif-
ficult to conceive a disposition of parts more calculated to favour
the escape of water from the blood than that of the Malpighian
body. A large artery breaks up in a very direct manner into a
number of minute branches, each of which suddenly opens up into
an assemblage of vessels of far greater aggregate capacity than itself,
and from which there is one narrow exit. Hence must arise a very
abrupt retardation to the velocity of the current of blood.” But
besides this arrangement, by which a large volume of blood is
exposed to circumstances the most conducive to free filtration of its
fluid constituents, we have a condition, namely, the secondary capil-
lary system on the distal side of the glomerulus, which, by its resist-
ance to the onward flow of the blood, subjects the blood inside the
Malpighian body to considerable pressure. It is now generally sup-
posed that the excretion of urine takes place by filtration of a dilute
solution of the soluble constituents of the urine through the glome-
rulus into the capsule of the Malpighian body. This weak solution
then passes along the tubuli uriniferi, where it comes into close con-
tact with the blood it has just left. It is then supposed that an inter-
change takes place between the blood in the capillaries surrounding

650

Proceedings of the Boyal Society

the tubules and the fluid inside by which a certain amount of the
water passes again into the blood, and so leaves the urine in a more
concentrated state than it was when it first passed from the glome-
rulus into the dilated end of the urine tubes (Ludwig). It is believed,
however, that the epithelium, which lines the convoluted tubes, per-
forms certain functions in connection with the secretion of the solid
constituents.

The rapidity of the secretion of urine may be said to depend upon
the following factors: — (1) The relationship which exists between
the pressure of the blood in the glomerulus of vessels and the urine
in the capsule of the Malpighian body and in the tubuli uriniferi ;
(2) the state of the blood pressure in the venous system of the kid-
ney; (3) the pressure upon the lymphatics; (4) the quality of the blood
in the artery of the Malpighian tuft ; (5) the state of the walls of the
artery constituting the Malpighian tuft, and of the capsule itself,
these being regarded as the filter through which the fluids and soluble
constituents of the blood have to pass. The influence of vaso-motor
nerves upon secretion must not, however, be forgotten; not only do
they exert an influence upon the quantity and quality of the secre-
tion by dilating or contracting the arterioles, but their influence
upon the chemical processes, by reason of their communications
with the secreting cells (Pfliiger), must be remembered ; (6) activity
of tubular epithelium.

In the experiments I have endeavoured to imitate the conditions
found in the Malpighian body of the kidney. I have not been
able, however, to represent the lymphatic arrangement.

The apparatus, a drawing of which, kindly executed for me by
my friend Dr Robert Moffatt, is shown in the following woodcut. It
consists of a piece of rabbit’s bowel A2 enclosed in a glass tube B2.
To each end of the bowel a small glass T -tube is attached. One of
those tubes is connected with a pressure-bottle A, and a mano-
meter A1. The pressure exercised upon the fluid inside the bowel
by the pressure-bottle and indicated by the manometer A1 will be
designated the afferent pressure. The tube attached to the other
side of the bowel conveys the fluid that passes along the bowel to
the vessel B, and the pressure exercised upon the fluid which it
contains, called the efferent resistance, is indicated by the manometer
B1. Through a cork at the right hand side of the large tube, another

651

of Edinburgh, Session 1877-78.

T -tube communicates, on tlie one band, with the inside of the large
glass tube containing the bowel, and, on the other, the vessel E and
manometer C1. The vessel E will therefore contain the fluid that
filters through the membrane A2.

The index in the manometer A1 will therefore represent the
afferent pressure , and correspond to the arterial tension of the renal
artery; B1 will indicate the efferent resistance (when applied to the
kidney,, the venous resistance), while the manometer C1 will show
the resistance offered by the fluid in the tube B2 to the transuda-
tion of the fluid inside the bowel, and therefore correspond to the
tension of the urine in the capsule of the Malpighian body.

In the first series of experiments water w7as passed into the
bowel under an afferent pressure of from 10 to 50 mm. of mercury,
the efferent resistance being the same in each experiment as the
afferent pressure, so that no water passed along the bowel to B.
The amount of fluid which transuded through the bowel was found
to increase in accordance with the pressure used. It was shewn
that for every 10 mm. increase in the pressure, there was -533 c.c.
more water filtered through the bowel per minute. Thus under a
pressure of 10 mm. 2T33c.c. transuded in a minute, and when a
pressure of 50 mm. was applied 4°266 c.c. passed in the same time.
From these results we would therefore conclude that the amount of
fluid which transudes through an animal membrane is increased ac-
cording to the tension of the fluid inside. In relation to this ex-
periment, take the following : — Instead of an animal membrane the
kidney of a recently killed horse was employed ; in this case a
three-quarters per cent, salt solution was used instead of water, as it

652 Proceedings of the Poyal Society

was found that when water is passed into the vessels it almost
immediately passes through the walls and causes oedema of the
tissue, arid the onward flow of the fluid is prevented. The salt
solution seems, however, not to pass through the walls of the
vessels into the lymphatic spaces so readily if the kidney is quite
fresh, hut still it passes from the glomeruli into the dilated end of
the tubuli uriniferi. I found it very difficult to get this experi-
ment to work satisfactorily, as the kidney requires to be used imme-
diately after the death of the animal, and a number of precautions
need to be taken which it is not necessary to mention here.

In the experiments alluded to the salt solution was passed into
the artery under various pressures, the venous resistance being
equal to 20 mm. in all except the first, in which case no resistance
was offered to the exit of the fluid by the vein. In the first ex-
periment the solution seemed simply to pass from the arterial into
the venous system, very little being pressed into the urine tubules.
When, however, the efferent resistance is raised to 20 mm., and at
the same time the afferent pressure advanced to 40 mm., the increase
in the amount of fluid pressed into the ureter is obvious. In the
other experiments upon the kidneys of animals, the results of which
I will not give in detail, a somewhat similar plan was adopted. The
following are the results : — (1.) When the fluid contained in the
ureter is subjected to pressure, the quantity of fluid that passes
from the vein is diminished in relation to the pressure employed,
and so also is the amount of fluid that transudes from the glome-
rulus into the capsule of the Malpighian body. (2.) The quantity
of fluid that passes from the vein depends upon the amount of
afferent pressure ; the greatest increase takes place between 40 and
50 mm. (3.) The temperature of the fluid affects the rapidity of
the flow through the vessels and the quantity that transudes into
the tubuli uriniferi. The higher the temperature the greater is the
amount of fluid passed from the ureter, and the more rapid the cir-
culation through the vessels. (4.) When the fluid is pressed into
the artery, it finds its way readily into the vein, but when injected
into the vein, it does not escape by the artery. There must, there-
fore, be some arrangement in the kidney, probably in the Mal-
pighian body, by which regurgitation of the fluid is prevented.

The results of the experiments with the bowel show (1.) that

of Edinburgh, Session 1877-78. 653

the amount of fluid that transudes is in accordance with the pres-
sure upon the fluid inside. (2.) For every 10 mm. increase in the
aflerent pressure *275 c.c. more fluid transudes per minute, and the
flow along the bowel is increased ; whereas, when the efferent resist-
ance is increased, the amount of fluid that transudes is augmented
by ’31 c.c. in the same time, and the flow along the bowel is
diminished. Therefore the afferent pressure may be said to be
expended in two ways — increasing the amount of fluid that tran-
sudes, and the quantity that passes along the bowel — but the efferent
resistance exerts its whole force in pressing the fluid through the
membrane, therefore, 10 mm. increase in the efferent resistance has
more effect than the same increase in the afferent pressure, and for
the same reason we would suppose that a given increase in the
venous resistance would conduce more to rapid secretion of urine
than the same increase in the arterial pressure, unless when the
venous resistance is extreme when other factors come into play.
(3.) The addition of urea slightly retards the transudation of water
through the membrane. The filtrate contains the same percentage,
whatever pressure maybe employed, as the original solution. (4.)
Albumen also retards the transudation of water, but it differs from
urea in this respect, that the percentage of albumen in the filtrate
is in relation to the pressure. The higher the pressure the larger
the quantity of albumen in a given amount of the filtrate. (5.) The
presence of urea in a solution of albumen assists the filtration of
the albumen at the expense of the urea. The following table shows
the results : —

Pressure
in mm.

Albumen.

Urea.

Quantity of
Solution.

With Urea.

Without

Urea.

With

Albumen.

Without

Albumen.

10

0 73 grms.

T 31 grms.

6*5 C.grms

7T C.grms

14’2 c.c.

20

•460 „

•332 „

10-8 „

13-5 „

27* „

30

•750 „

•600 „

16-8 „

19-5 „

39-5 „

40

1-306 „

•900 „

22-3 „

26- „

52- „

(6.) The higher the temperature of the solution the more rapid
the transudation of the fluid. Thus, when water was passed into
the bowel at a temperature of 15 ‘9° Cl, and under a pressure of 45
min., 142 5 c.c. filtered through in thirty minutes; whilst, when

4 R

VOL. IX.

654 Proceedings of the Royal Society

the temperature alone was raised to 34‘20 C,, 197 c.c. transuded in
the same time.

At tlie beginning of this paper I referred to Ludwig’s theory regard-
ing the secretion of urine, namely, that the blood is subjected to a high
pressure inside the glomeruli, a free filtration into the dilated end of
the tubuli uriniferi takes place, and this filtrate, which is at first very
dilute, gradually parts with a portion of the water that holds it in solu-
tion. This is believed to take place by a process of diffusion between
the fluid in the tubuli uriniferi and the blood in the veins surrounding
them on all sides. Now, if it were not that albumen retards to a
certain extent the passage of crystalloids (salts and urea) through an
animal membrane, then the fluid in the inside of the urine tubules
would be of the same concentration (in crystalloids) as the blood.
But it has been shown that when a solution of albumen and urea
are filtered through an animal membrane under pressure, the filtrate
is less concentrated than the original solution, particularly as regards
the amount of albumen, but also to a slight extent the urea. This
is more especially the case when the pressure is not great. If the
blood contained nothing but crystalloids (urea and salts) then the
fluid inside the tubuli uriniferi would be the same as the fluid cir-
culating in the vessels, and no diffusion would take place during the
passage of the urine from the glomerulus to the pelvis of the kidney.
This is, however, not the case ; the blood circulating in the vessels
contains a large quantity of albumen, and, if the theory above stated
be correct, more urea than the fluid in the tubules, so that, putting
aside any special function the epithelium may have, diffusion must
result, and a portion of the water in the tubules pass back again into
the blood. This diffusion will take place as the urine passes along
the tubuli uriniferi either till it becomes of the same concentration
as the blood outside, or makes its escape into the common ducts that
convey it to the pelvis of the kidney. Therefore, the longer the
urine remains in the tubuli uriniferi, other things being equal, the
more concentrated will it be.

4. Note of a Method of Studying the Binocular Vision
of Colour. By John G-. MTCendrick, M. I).

There are several well-known methods of mixing colours, such as
the superposition of two spectra or of different parts of the same

of Edinburgh, Session 1877-78.

655

spectrum — the method of reflection, Czermak’s modification of
Schemer's experiment, the use of rotating disks having coloured
sectors, and the direct mixture of coloured powders or coloured
liquids. In all of these cases the effect may be seen with one eye,
and is due to the action of light on a definite portion of one retina.
But may sensations of mixed colours be produced by binocular
vision of the components ] Regarding this question various well-
known observers have arrived at completely opposite results. Thus,
as mentioned by Helmholtz in his “ Optique Physiologique,” p. 976,
H. Meyer, Volkmann, Meissner, Funke, and he himself fail in ob-
taining the sensation of the resulting colour, whilst Dove, Regnault,
Briicke, Ludwig, Panum, and Hering state the reverse. In his
great work, Helmholtz describes various methods by which he
investigated the question, and his opinion amounts to this, that we
have no true binocular perception of colour. According to him we
may have a resultant sensation of a particular kind, different from
that of the two components, but also unlike the sensation of the
mixed colour obtained by methods appealing to one eye only.

In studying this subject I lately devised the following simple
arrangement : — Take two No. 3 eye-pieces of Hartnack’s microscope,
or any similar eye-pieces of considerable focal length, and place one
before each eye. If they be somewhat diverged, two luminous fields
will be seen, and by adjustment, the edge of the one luminous field
may be caused to touch the edge of the other. In these circum-
stances a definite area of each retina is illuminated. By converg-
ing the eye-pieces, the two fields may then be partially overlapped,
and when the axes of the two eye-pieces are parallel, both fields
coincide. It will then be found that the overlapped portion is in-
tensely luminous, whilst the other portions become less luminous,
as if cast into shadow. By increasing or diminishing the amount of
convergence of the eye-pieces, the extent of the luminous field may
be varied at pleasure, and the two fields coincide when the two
images fall on the two yellow spots. If, then, a small piece of
coloured glass be inserted into each eye-piece, say red into one and
blue into the other, on repeating the experiment as above mentioned,
I find that the overlapping portion of the two fields gives a sensa-
tion of the resultant colour. I have repeated the experiment with
various coloured media, such as coloured gelatine paper, coloured

656

Proceedings of the Royal Society

paper rendered translucent by oil, &c. In showing the experiment
to others, I have found that certain people do not see the resultant
colour, whilst others do so readily. The cause of this and of the
opposite statements of the observers above alluded to, I believe to
be this : The sensation resulting from the fusion in the brain of the
two impressions, one coming from each eye, appears to be capable
of decomposition by a mental effort. Thus, the purple produced
by red and blue appears as such to my eye so long as I simply look
at it without any conscious effort ; but if I wish to analyse it, I
then find that the two colours, red and blue, seem to be superposed
on each other, and the one appears to shine through the other. On
ceasing to make any effort, they again fuse together as before.
Again, by thinking of the colour opposite the right eye, say red, the
field ceases to be purple and has a decided tinge of red, and on
thinking of the colour before the left eye, say blue, the prevailing
tone of the field is blue. Apparently, then, if corresponding points
of two retinae be simultaneously stimulated by two different colours,
the impressions are fused in consciousness into the resultant colour ;
but the resulting sensation may be decomposed by an act of atten-
tion. The decomposition is effected partly by strongly directing
the attention to one eye, and less strongly to the other, and the
result is a sensation corresponding to the colour placed before the
eye to which the attention is most strongly directed. Some of the
same facts may be studied with the aid of the stereoscope.

The following Gentlemen were duly elected Fellows of the
Society : —

Alex. Macfarlane, M.A. , B.Sc., 2 Roseneath Terrace.

Samuel Drew, M.D., D.Sc., Chapelton, near Sheffield.

George M ‘Go wan, 24 Argyll Place.

James Brunlees, Yice-Pres., Inst. C. E., 5 Victoria Street, Westminster.

John Grahame Dalziel, 95 South Street, St Andrews.

of Edinburgh, Session 1877-78.

G57

Monday, 20 tli May 1878.

DAVID STEVENSON, Esq., C.E., Vice-President,

in the Chair.

The following Communications were read : —

1. On the Genus Rhizodus. By Dr R. H. Traquair.

(Abstract.)

In this paper the author first sketches the history of Rhizodus,
from its discovery by Ure of Rutherglen to the most recent papers
on the subject.

Placed by Agassiz among the “ Coelacanthi ” (i.e., cycliferous
Crossopterygia of modem nomenclature) it was classified by Professor
Huxley in the cycliferous division of his family Glyptodipterini,
along with Holoptychius , Glyptolepis, Dendrodus. The discovery
by the author, in 1875, of its subacutely lobate pectoral fin revealed
the fact that it was much more closely allied to Rliizodopsis than to
Holoptychius, and that it ought, along with the former genus, to be
classed in a family (Cyclodipterini) distinct from the acutely lobate
Holoptychiidae. The author does not consider the identity of
Leidy’s genus Apepodus with Rhizodus as proved.

M‘Coy admitted two species of Rhizodus — R. Hibberti , Agassiz,
and R. gracilis , M‘Coy, merging with the former of these the Holop-
tychius Portlockii of Agassiz. An examination of the types of
Holoptychius Portlockii, preserved in the Museum of Practical
Geology, shows, however, that this species is not only specifically
but also generically distinct from Rhizodus Hibberti , as the teeth are
devoid of the cutting edges characteristic of Rhizodus, and in this
particular, as well as in the minute striation of the surface, they
closely resemble those of Hancock and Atthey’s genus Archichthys ,
to which the author proposes to transfer it, at least provisionally.

An investigation of the large store of Rhizodus remains from the
Gilmerton ironstone, belonging to the Edinburgh Museum of Science
and Art, shows the presence of two well-marked species of Rhizodus,
differing in the bulk to which they attained respectively, as well as
in the relative thickness of the scales, the shape of many of the

658

Proceedings of the Royal Society

bones, and the external sculpture as well of the bones as of the
scales. For the larger of these two species, there can be no doubt
of the propriety of retaining the specific name Hibberti , as it is
clear that its enormous laniary teeth, as occurring in the limestone
of Burdiehouse, and at first considered by Hibbert to be reptilian,
originally suggested the name Megalichthys Hibberti to Agassiz,
which he afterwards altered to Holopty chins Hibberti, after elimi-
nating the Saurodipterine remains previously confounded with them,
and to which latter he then limited the term Megalichthys, rather
unfortunately, as “ Megalichthys ” is the smaller fish ! M‘Coy’s
R. gracilis is certainly a synonym of R. Hibberti, the apparent
greater slenderness of the dentary bone being due to the infra-
dentary plates (not known to M‘Coy) being, as is often the case,
awanting in the specimen ; and as regards the greater slenderness of
the anterior laniary, a large series of teeth from Gilmerton shows
every possible amount of gradation in that respect. For the smaller
species, whose remains have hitherto been confounded with R.
Hibberti, the author proposes the name of R. ornatns.

1. Rhizodus Hibberti , Ag. sp.

This species must have attained a gigantic size, a detached den-
tary bone in the Edinburgh Museum measuring no less than. 25
inches in length. Externally the cranial bones are ornamented by
a rather fine tuberculation, the tubercles more or less confluent with
tortuous ridges. The mandible displays the same structure as in
Rhizodupsis , the dentary element being narrow, pointed behind,
thick in front, where it carries the anterior or symphyseal laniary
tooth, the three other laniaries behind being borne upon separate
internal dentary pieces. Below the dentary, and forming the lower
margin of the jaw, are three infra-dent ary plates, while posteriorly
the articular region is covered by a large plate representing the
angular element. Other determinable bones described in this paper
are the maxilla, which, as in Rliizodojpsis, only bears small teeth,
the principal jugular, the opercidum , the clavicle, the infra-clavi-
cular ; there are others also whose place in the skeleton is not easily
determinable. The clavicle and infra-clavicular are not tuberculated
like the cranial bones, but ornamented with delicate reticulating
ridges and pits ; the posterior superior angle of the infra-clavicular

of Edinburgh , Session 1877-78.

659

is produced upwards and backwards in a long slender process. The
scales are comparatively thin and very large, sometimes, as noticed
by Hibbert, attaining a diameter of 5 inches ; usually they occur in
a broken condition. Their attached surface is marked by a central
boss and concentric lines of growth. The outer surface, very rarely
seen, is ornamented by closely set granules, which towards the
posterior border of the exposed area are confluent into wavy ridges
terminating in the margin. These seem certainly to be the scales
attributed to R. Hibberti by M‘Coy, but not by Young ; they are
probably also the same as the undescribed ‘ Phyllolepsis tenuissimus '
of Agassiz.

R. Hibberti occurs throughout the Cementstone and Carboniferous
Limestone series of Scotland, the most noted locality being Gilmerton,
near Edinburgh.

2. R. ornatus , sp. nov. Traquair.

To this species, which seems never to have attained anything like
the dimensions of R. Hibberti , belong the specimen showing the
pectoral fin described by the author in 1 87 5, the head described by
Mr L. C. Miall, and in fact nearly all the specimens in which any
portion of a fish with bones or scales in situ is shown. The orna-
ment of the cranial bones is somewhat similar in character to that
in R. Hibberti , but very much coarser ; the same is the case with
the bones of the shoulder. Of the bones the following have been
recognised by the author — dentary , operculum , principal jugular ,
clavicle , infra-davicular ; there are also others whose determination
is still somewhat doubtful. The clavicle differs somewhat in form
from that of R. Hibberti, its lower portion being narrower from
before backwards. The expanded portion of the infra-clavicular is
also shorter than in the larger species, but the same slender process
is sent backwards and upwards from its posterior superior angle.
The pectoral fin is subacutely lobate. The scales are thicker than
those of R. Hibberti. The exposed area of the external surface is
marked with short, interrupted, wavy, reticulating ridges, whose
direction is mainly parallel with the posterior border of the scale ;
in the interval between these, more delicate ridges are seen radiating
from the centre. It is apparently on a scale of this species that Dr
Young has founded his description of those of R. Hibberti.

660 Proceedings of the Royal Society

R. ornatus occurs in the Calciferous Sandstone series of Scotland,
as at Burdiehouse in Mid-Lothian, and Pittenweem in Fifeshire ; but
it is especially abundant in the blackband ironstone of the Lower Car-
boniferous Limestone group at Gilmerton, above which horizon it has
not yet been discovered.

2. On the Anatomy of a recent species of Polyodon, the
Polyodon gladius (Martens), taken from the river Yang-
tsze-Kiang, 450 miles above Woosung. Part III., being
its Viscera of Organic Life. By P. D. Handyside, M.D.

The author proceeded with his anatomical description of the
respiratory, circulatory, and pneumatic systems in this remarkable
hsh ; referring to the differences that exist in the male, the female,
the young, and the adult specimens. He also shortly noticed the
alimentary and other viscera of Organic life.

Dr Handyside illustrated his paper by 24 additional drawings
— including 7 microscopic views — of structure in this fish.

The fourth and last part of Dr Handy side’s paper will consist of
a description of the articular system and the endo-skeleton of the
Polyodon gladius.

3. A Mechanical Illustration of the Vibrations of a Triad of

Columnar Vortices. By Sir William Thomson.

4. Fourth Report of Boulder Committee, with Remarks.

By D. Milne Home, Esq.

Since the last Report was drawn out and laid before the Society,
the Convener has had an opportunity of inspecting a considerable
number of boulders not mentioned in previous Reports. Some
of these are interesting, on account not only of size, but also of
shape, marks on them, and position. The Committee consider
that advantage will result from a special description of these,
and from woodcuts of a few.

The cases have been arranged, as in previous Reports, according
to counties, to indicate the geographical position of the boulders,
and enable persons desirous of inspecting them, to know where to
find them.

661

of Edinburgh, Session 1877-78.

His Grace the Duke of Argyll, at the meeting of the British As-
sociation in Glasgow in 1876, was pleased to allude in complimentary
terms to the researches of the Committee, and to express a hope that
a condensed abstract of all the boulders reported on, might ultimately
he framed. The suggestion will receive the consideration of the
Committee.

ARGYLLSHIRE.

1. Glenelg. — Blocks of grey and red granite occur in the drift-
beds through which the river Elg has cut. The rocks of this dis-
trict are not granite, but clay schists.

On the right side of the valley of the Elg, immediately above the
road, about 2J miles east of Glenelg, there is a grey granite
boulder, 21x18x10 feet, as shown on figs. 1 and 2, Plate I.
The sharp end points hT.ET.W. Its height above the road is 1020
feet, above the sea 1120 feet.

It goes by the name of the Macrae Boulder, in consequence of a
prophecy by a Mackenzie of Kintail, that some day, when one of
the clan Macrae is travelling on the road below, it will fall and
crush him.

The boulder is on the very edge of a shelf of the hill, and pro-
jects beyond it about 6 feet, as shown in figs. 1 and 2, Plate I.

The rocks on which it lies are clay-stone schists. The boulder
must therefore have been brought to its present position. It is
said that on a hill some distance to the west there is a granite rock
similar to that of the boulder. By what means, and how the
boulder was deposited in its present precarious position, it is difficult
to explain. Possibly, when deposited, there was no steep cliff, at the
edge of which it now projects. The whole valley may have been
filled with detritus up to the level of 1100 feet, and thereafter
scooped out by the river, as the sea, in falling from one level to
another, gave to the river more cutting power. This process of
scooping might have continued for such length of time, that the
cliff thereby formed at length reached the boulder.

2. In Glen Rossdale (about 8 miles from Glenelg), at a height of
about 900 feet above the sea, there is a boulder of coarse red
granite, 5 x 4J x 3 feet, on the top of a narrow ridge of hypersthene
rock, as shown on fig. 3, Plate II., on the left side of valley.

VOL. ix. 4 s

662

Proceedings of the Royal Society

Its position also is precarious, and suggests a doubt whether,
when brought here, it could have been deposited on the precise
point where it now stands. There was nothing to indicate the
direction from which the boulder had come.

3. There is another boulder on the right side of the valley, about
820 feet above the sea, 12x15x7 feet, fig. 4, Plate I.

It lies on a shelf near the ridge of a hill, and close to a slope
of the hill which rises up from the boulder, and facing the
H.W. The spot suggested the idea that the boulder had been
brought from the H.W., and that this hill stopped its further
progress. There is towards the H.W. an opening among the hills
through which it might have been floated towards its present site.

4. A little lower down the valley (Rossdale), and on the same
side, at a height of about 630 feet above the sea, there is a rocky
knoll somewhat flat on the top, and presenting an area of about
8 or 9 yards in diameter, on which are five or six boulders lying
pretty close together, as shown on fig. 5, Plate I. The boulders are
granite, the knoll is mica schist.

5. At a still lower part of the glen there is a steep hill sloping
down to the river. Hear the top of this hill, and on the very edge
overhanging the river, a boulder rests at a height of 300 feet
above the river. The boulder is of granite, about 20 feet in
diameter. It rests on mica slate rocks, which form a smooth surface
sloping down towards the river at an angle of about 30°. Its posi-
tion indicates transport from the north, as the land there is low
enough to have allowed it to be floated over, whilst high hills to
the south exclude that direction.

In the valleys where these boulders lie, there are some remark-
able terraces. They were made known to the Convener by
Captain Burke, RE., two years ago, when he was still at the
head of the Scotch Ordnance Survey. The surveyors employed in
drawing the contour lines for the maps were struck by the hori-
zontality and continuity of the terraces. Captain Burke was
so obliging as to draw on the Convener’s map lines to indicate
their position. As these terraces suggest important views bearing
on the position of the boulders, and their mode of transport, it
seems not irrelevant to record the notes supplied by Captain Burke
and give a copy of the map, to show where the terraces are.

of Edinburgh, Sessioii 1877-78.

663

Before, however, describing these higher terraces, it may be right to
refer to certain flats at the mouths of the valleys near the sea.

The town and village of Glenelg are situated on a flat which
prevails all along the Scotch coasts, about 11 or 12 feet above high-
water mark. Between Glenelg and Glenbeg the base of some
high rocky cliffs is at the same level.

Mr Fraser, schoolmaster at Glenelg, having learned that the
Convener was desirous of seeing examples of flat land, conducted
him to the following spots : —

(1.) At Glenbernera, about half a mile to the north of Glenelg,
there is a well-defined flat, about 44 or 45 feet above high water.
A corresponding flat occurs at many other parts of the coast.

(2.) Behind and above the new schoolhouse at Glenelg, there is a
considerable extent of flat land, at a height of 72 feet above high
water. On the opposite, i.e., the south side of the valley, which is
half a mile distant, there is a flat at exactly the same height,
judging by the spirit-level. The river has cut through this flat.
Its original formation cannot be ascribed to river action.

Beyond the manse and church, there is another extensive flat,
88 feet above the sea.

In a higher part of the valley, there are terraces on a smaller
scale. If they slope with the river, as they seem to do, they pro-
bably had been formed by the river, when it ran at a higher level,
that is, when the sea also stood at a higher level than now.

Near the mouth of Glenbeg, about a mile from the sea, there
is a great mass of detritus, through which the river Beg has cut
its channel. There is a flat here also on each side of the river, the
level of which is about 120 feet above high water.

Fig. 6, Plate I. is (from memory) a plan of this valley. The parts
marked a , a, &c., are patches of detritus, the tops of which are all
on the same level, or very nearly so, viz., 50 feet above the sea.

The whole valley apparently had been filled with detritus, when
the sea stood at least 150 or 200 feet above its present level. As
the sea retired, channels were cut in the detritus, not only by the
main stream now occupying the valley, but by the numerous and
rapid side streams from the steep mountains which enclose the valley
on both sides.

At about 3 miles from the sea, the place in Glen Beg is reached,

664 Proceedings of the Royal Society

where Captain Burke states he noticed a horizontal terrace on both
sides of the river, at a height of 330 feet above the sea. It is
marked (A) on plan, fig. 7, Plate II.

The Convener recognised a terrace on the right bank at 338 feet, but
he could see none on the opposite or left bank. At a little distance
farther up, there are on the left bank gravel knolls at a somewhat
higher level. At this place, the channel of the river is about 40 feet
below the terrace, and is of rock, which has of course prevented
any deeper cutting of the drift beds.

At the junction between Glen Beg and Glen Rossdale (B) in the
plan, there are very large knolls of detritus with flattened tops.

From the highest of these knolls, the Convener, on looking across
the valley in a direction by compass E. by N., descried a terrace, con-
tinuous for about 80 yards, and apparently horizontal. Its position
is indicated on the plan by five small vertical strokes. When the spirit-
level was turned in a direction about E. by S., it struck on another
horizontal terrace, about half a mile distant. All these flats are at
one height, viz., 528 feet above the sea.

Higher up Glen Rossdale on the left bank, and at a spot about
1 J mile from (B), there is an extensive flat, which had been marked
by Captain Burke. He states it at 750 feet above the sea. The
Convener made it 760 feet. When a person is on the terrace, it is
not distinctly traceable for more than 300 or 400 yards ; but when
viewed from the opposite side of the valley, at a distance of about
a quarter of mile, it can be distinctly traced for more than a mile
continuously ; and at its east end it is seen to cross the ridge which
divides Glen Beg from Glen Rossdale.

In a higher part of Glen Rossdale, and still on the left side of
the glen, the Convener observed traces of a shelf at 853 feet, with a
steep slope or bank below it of about 30 feet in height. The Ord-
nance surveyors observed traces of a horizontal terrace still higher,
viz., at 1500 feet above the sea. The Convener, looking in that
direction, observed, at a distance of about 3 miles, something like a
horizontal line running for nearly a mile continuously at what might
be about that height.

On the plan, Captain Burke indicates as existing in adjoining
glens, traces of the 330 feet terrace by the cypher 0. These glens
the Convener had not time to visit.

665

of Edinburgh , Session 1877-78.

He has also put a X at the head of three several glens to indicate
that at these places, and at a height of 750 feet, there are gravel heaps.

Some quotations may he made from Captain Burke’s letter, dated
25th August 1876 : —

“ I was up Glenelg yesterday. There is evidence of the sea having
stood at more than one height, considerably above its present level.

“ The only terrace of any consequence is in Glen Rossdale. It is
about 300 yards in length. It has nothing in the least resembling
Glen Boy.

“ I will now answer your questions : —

1. — Height above the sea —

(1) Principal terrace, about 750 feet.

(2) Another, very doubtful, . . 520 ,,

(3) Some rather more apparent, . 330 ,,

“ This terrace, at the head of Glen Beg, affords strong evidence of a
beach, such as now exists in all sea lochs hereabouts. Beds of
gravel at 330 feet are cut through by the stream running through
the valley.

“ On crossing the high neck, 450 feet above the sea, and
descending into Glenmore, similar beds were found at the head of
that valley, at the same altitude.

“ The spot marked in my sketch mu at 530 feet is very doubtful.

“The 750 feet terrace is visible in patches in Glenbeg and Glen
Bossdale. I tried to trace it down Glenmore, for I have no doubt
the land between these glens was once an island. But, although I
fancied I found a mound sometimes, it can’t be traced.

“ The longest vestige of a terrace which I saw, is in Glen Bossdale,
viz., about 300 yards ; for the rest, there is only a mound here and
there on the hill side.

“ As to the width of the terraces, the greatest I saw is about 30
yards.

“ You ask how high up these hills is sand and gravel found ? I
saw appearance of gravel at over 1200 feet. There are gravel heaps
at 750 feet at the heads of the valleys marked X, at the spots one
would expect to find them, and also at ®, apparently washed when
the country was under water, and since cut through by the streams
in the valleys. In fact, all the appearance is as if these valleys

666 Proceedings of the Royal Society

were once sea lochs, just as are Lochs Nevis and Hourn at the
present day. These marks are frequent throughout the Highlands.
I have seen similar gravel-heds along streams in several other glens.

“ Whether it will he decided to survey the shelf, I cannot say.
But there is nothing definite except the hit in Glen Rossdale; and
a surveyor would not find it easy, when on the hillside, to know
what mounds he should show, unless he had previously run a
contour at the required height.

“ I have made two sketches, one of Glenheg looking east, another
of Glen Rossdale looking west, which I shall he happy to show
you.”

With reference to these last remarks by Captain Burke, it occurs
to the Committee to express an opinion that, when the Ordnance
surveyors discover on the hill sides terraces of the kind referred to,
there should he some record given of them on the maps, accom-
panied by a contour line at the same level along the adjoining hills,
so that it might he seen whether there are separate patches of
gravel elsewhere at the same height. It is also desirable that when
the officer at the head of the Survey verifies what the surveyors have
found, and makes sketches of the terraces, these sketches should he
given with the maps when published.

In walking down Glen Bossdale valley, on the right bank, the
Convener fell in with a large mass of detritus, cut up into a series
of knolls by the action of streams and rain. The height of these knolls
above the sea was on an average 858 feet — agreeing pretty nearly
with the level of the shelf already noticed as existing on the oppo-
site side of the valley.

These remains of gravel in Glen Rossdale and the adjoining glens,
looking to the height and the form in which they occur, seem
conclusive as to the occupation of these valleys by the sea ; and they
confirm the inference derived from the position of the boulders, that
the boulders were probably floated into these positions.

The Convener was at first puzzled to account for the circumstance
that most of the large boulders which he saw in these valleys were
not upon drift, but upon bare rock ; and in many other parts of the
country, the same thing occurs. If these boulders were floated by
ice and thrown down, they must most generally have fallen upon the
detrital beds then forming the sea-bottom, and not upon bare

667

of Edinburgh, Session 1877-78.

rocks. When the sea retired, the boulders would then be on the
drift, or buried in it. But when the streams from the hill sides
began to flow and to remove the drift, the boulders would sink until
rock was reached by them, where, of course, they would remain.
The denudation of the old sea-bottoms has been everywhere so exten-
sive, that very probably most of the boulders now existing are not
in precisely the exact positions which they occupied when originally
deposited.

6. In the Pass of Brander , where the Biver Awe flows out of
the lake of the same name, there are several boulders deserving
notice.

On the right bank of the river, near the spot where there is a
pier for the small lake steamer, there are two terraces on drift.
Both terraces have boulders on them. The boulders are of reddish
granite. The rocks in the Pass are a slaty schistose rock like
greywacke. The boulders have apparently come from some distant
region, as the granite of the Loch Etive hills is not red, but almost
entirely grey in colour.

The height of Loch Awe above the sea is (by Ordnance Survey)
110 feet. The lowest terrace is 68 feet, the higher terrace about
120 feet above the loch.

Both terraces appear to be horizontal. They can be traced for
nearly a mile continuously.

On the opposite or left bank of the river no corresponding
terraces are distinguishable. That side of the valley consists of
nearly bare rock, and is almost vertical, so that there cannot be
expected to be on it any trace of a beach line.

Have these terraces in the Pass of Brander been formed by a lake
or by the sea1? In a lower part of the valley there is a large amount
of detritus, and it reaches at some places to a higher level than the
terraces. The valley in that lower part is narrow, so that there
might have been a blockage for a lake. On the other hand,
how can the granite boulders be accounted for which are on the
terraces 1 If, as seems most probable, they have come from the
north, they must have been floated by ice on a current flowing
from the N.N.W.

7. Inveraray. — His Grace the Duke of Argyll (Nov. 1876) con-
ducted the Convener to a small hill, about 1000 feet above the sea,

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Proceedings of the Uoyal Society

at a place called “ Brae Leckanf 7 miles west of Inveraray, well
covered with angular boulders. The boulders were of the same
nature as the rocks of the hill — a dark grey porphyry. But the
boulders had evidently been transported to the hill from some other
place, there being no cliff from which they could have fallen.
The Duke thought they had been floated from the eastward, and in
that direction certainly the land was lower than in any other
direction. But the Convener observed that towards the west there
was an opening among the hills low enough and wide enough for
a current to have flowed to and over the hill on which the boulders
rested.

8. A few miles to the north of Inveraray there are some huge
boulders of a coarse conglomerate, quite distinct from any of the
rocks in the immediate neighbourhood. The rock of these boulders
is a greenish or grey coloured Silurian rock full of quartz pebbles.
One of these conglomerate boulders, weighing about 60 tons, is on
flat ground about 800 feet above the sea, and resting on gravel.
Another, 10 x 9J x 7\ feet (weighing about 48 tons), is on the
left bank of the River Arey, and about 180 feet above the sea.

The gamekeeper, who pointed out these boulders, said that there
was no rock of the kind composing them, except at a place about 6
miles due west. Between that spot and the sites of the boulders
there were several ranges of hills and valleys.

When the subject was mentioned to the Duke of Argyll, he corro-
borated the gamekeeper’s statement. He informed the Convener,
that there is conglomerate rock, of the same character as that of
the boulders, on the summit or ridge between Loch Awe and
Loch Fine, which lies to the north-west of the boulders.

On the tops of several of the hills to the north-west of Inveraray,
about 700 feet above the sea, boulders were noticed where it was
manifest, from their peculiar position, that they could have got into
it only by coming from the west. Sketches of these were taken.

9. Oban and Neighbourhood. — (1.) At Dunolly, close to the sea
shore, there is a grey granite boulder 12x8x6 feet. It is about
20 feet above high water, and rests on an old sea beach. Its *
longer diameter points W. by N.

The nearest rocks of grey granite are in Loch Etive, situated to
the eastward. There are ranges of hills between Loch Etive and the

;etidin(?S Hoy. Soc. EdjJ

Plate .VI.

Jiooeedmgs Hoy Soc.Edin?

Plate .'Vii

Fig. 3

Glen Rossdale

Hi
m

’ ^

Fig. 13

F ig . 14-

F 4*. 15

~ ^

__a —

■4

— .

■mm3***

mmmm

Plan of G I e r, e I g
,-wKy«Wf^W\,

'5s

Hi

5 ; TV -s 1 ^ 5^1 bout 330 Feet.

HHHuii” ® Gravel Heaps.

^'X Gravel Heaps about 750 f
Blark (vnitoui' lines- of 750 It drawn by O Surveyor

W t A. K. JOHNSTON, E OtNBUP

W. 8c AX. JohnstoZL . 1

669

of Edinburgh, Session 1877-78.

site of the boulder. Moreover, the boulder is close to the foot
of a high rocky cliff, which being on the east side of the boulder,
must have prevented the boulder reaching its site, except by trans-
port from the westward, — probably the north-west, as the island
of Kerrera is situated to the west and south-west, and would pre-
vent the boulder coming from that direction.

The Convener was accompanied by a gentleman resident in the
neighbourhood (Mr Clerk), well acquainted with the Loch Etive
granite, who expressed doubts whether the granite of this boulder
was of a similar composition.

(2.) The north part of Kerrera Island is strewed with numerous
grey granite boulders, all well rounded. Most of them are on the
beach, and on the old terraces adjoining the beach. There are some
also, on Baltimore Earm, at heights of from 357 to 437 feet above the
sea, on short terraces or flats of detritus facing the east and north-east.

In these cases there would be less obstruction to a transport from
Loch Etive than in the case of the Dunolly boulder, but the range
of hills near Glenlonan, reaching heights of from 500 to 1500 feet,
still presents a difficulty.

If the Dunolly boulder came from a northern source, the Kerrera
boulders probably came from the same quarter.

(3.) On the hills to the east and north-east of Oban, there are
numerous boulders, chiefly of granite, whose position does not
suggest one direction more than any other.

The rocks of these hills being clay slate, the boulders on them
must have been transported from some distant quarter.

The granite is grey of different varieties, and very like the Loch
Etive granite. But there are others, with large crystals of quartz
and felspar, which betoken some other source.

One of this kind is on a hill to the south of the old public road
between Oban and Loch Etive, at a height of 530 feet above the
sea. It is extremely angular, and rests on a bare rock of the hill.
This position would most easily have been obtained by floating ice.

Besides these granite boulders there are some of dark porphyry
and of quartzite, which most probably come from the north.

This conclusion is somewhat strengthened by the circumstance
that in this district, where the rocks are smoothed and striated, the
surface of the rocks slopes down towards and faces the north, and

VOL. IX. 4 T

670

Proceedings of the Royal Society

the striae run north and south. Examples occur on the old public
road before-mentioned.

(4.) An angular boulder of grey granite, 11 J x 7J x 7 feet, occurs
at Inverlievern, on Loch Etive, above Bonawe Ferry. This boulder
rosts on three or four smaller granite boulders, and these again on
bare granite rock. There is no hill from which it could have
fallen. It must have been transported. A sketch was taken.

It rests on the 40 feet old sea-margin, which is visible round
the greater part of Loch Etive.

(5.) The Convener was informed of two very large boulders in the
district between Loch Etive and Glen Lonan, at places called Auch-
nacoshen and Duntarnichan. But he was unable to reach them.

10. Fasnacloich on Loch Creran. — Captain Bedford, B.H., wrote
to the Convener, calling his attention to a large boulder which he
had seen when surveying for the Admiralty. He sent a description
of it, and mentioned that its average girth was 30 feet.

The Convener discovered the boulder. It had recently been
blown up into four or five fragments, with a view to being used
for building a bridge. But they were found unsuited for the
purpose, being too hard for masons’ tools. The rock consisted of a
dark porphyry, with which the Convener was unacquainted.

Mr Hall, the tenant of the farm of Easnacloich, on which Captain
Bedford’s boulder was situated, conducted the Convener to a spot,
about a mile higher up the glen, where there were multitudes of much
larger boulders of the same species of rock. The spot proved to be a
mass of detritus, consisting of water-borne gravel, forming a sort of
terrace abutting against the hill, which forms the north-east side of
Glen Creran. This terrace is covered by numerous boulders, some of
very large size. A view of one of them is given in fig. 8, Plate I.

This boulder has the Celtic name of “ Fas-na-cloich” or “ Fas-
na-clachf which means “ stone with growth,” — referring to three
trees growing on it, two on the top being firs (each about 15 feet
high), — one at the side, a stunted oak. The name of the farm
occupied by Mr Hall, and of the residence of the proprietor, Captain
Stewart, is Easnacloich, so-called, most probably, after the boulder.

The boulder with the three trees on it is about 25 yards in girth ;
its length is 23 feet, its width 15, and its height, in so far as visible
above ground, is 15 feet.

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Another boulder, a few hundred yards to the south, measured
(above ground) 18x18x12 feet.

It deserves notice that the sharpest end of each boulder points in
the same direction — viz., about S.W. (magn.) — i.e., towards the
mouth of Loch Creran.

The terrace on which these boulders lie, is about 290 feet above
the sea.

Hall mantioned that, in a higher part of Glen Creran, the
boulders are more numerous, and some of them larger than the two
examined.

All the boulders appeared to be of the same species of rock. Hall,
who evidently had some practical knowledge of rocks, called it a
black granite, and affirmed that there was no granite like it in all
that district. The rocks of the mountain on the opposite, or south
side, of Loch Creran, rising steeply to a height of above 2000 feet, he
knew were a grey granite. The Loch Etive granite, about four miles
to the south, and the Durra granite, about eight miles to the east,
being of a light grey colour, he had always wondered where these
dark coloured boulders could have come from.

The rocks in Loch Creran, and in the hills immediately adjoining,
are a blue schistose clay slate, with a rapid dip.

One or two other points may here be noted, communicated by
Hall ; —

A small river runs into Loch Creran, at its head, flowing out of a
small fresh-water lake, which is separated from the sea by a spit of
gravel and sand, crossing the valley, and cut through by the river.
The sand, Hall stated, is full of sea-shells, and so is the bed of the
lake, and even the channel of the river before reaching the lake. In
this last-mentioned river, the shells are in a bed of fine clay — whitish
in colour, which is used as a manure for arable land. In fact, it is
this bed of shell clay which originated the name “ Crer-an,” i.e.,
“ Clay," or “ Chalk River."

These facts indicate, of course, a period when the sea stood at
a higher level — to the extent of at least 20 feet, which is about the
height of the shelly bed above mentioned. When the sea fell to
its present level, a blockage of drift, now between the sea and
the lake, caused the lake to be formed, with an overflow by the
river, which runs out of the lake into the sea. There are several

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other places in the West Highlands where there are fresh-water
lakes close to the sea, formed in like manner.

With regard to the boulders, it occurred to the Convener, judging
from their locality and their position, that they had probably been
floated up Loch Creran, and been then stopped in their further pro-
gress by the contraction of the valley and the higher level of the land.

But if they were floated up Loch Creran, from what quarter did
they come ? It was natural to look to places facing the mouth of
Loch Creran, if in these places there were mountains composed of
rocks similar in composition to the boulders. The island of Mull,
situated to the W.S.W. of Loch Creran, seemed therefore to he one
locality which might have supplied the boulders, as from Mr Judd’s
instructive paper on Mull,* describing numerous varieties of granite
in the mountains of that island, it appeared likely that rocks of
the same character as the Fasnacloich boulders existed there. With
the view of testing this idea, the Convener sent specimens of
the boulders to Professor Judd, who he heard had, during the
past autumn, spent three months among the Mull mountains,
and asked him to state whether he recognised the rock composing
these boulders as being identical with, or at all events similar to,
any of the Mull rocks ? Professor J udd was so obliging as to respond
to the application.

With the Fasnacloich specimens, there went to Professor Judd
specimens of the rock composing two very large boulders on the
shore at Appin, which rock the Convener found on examination
to he the same as that of the Fasnacloich boulders. These Appin
boulders lie on upturned blue clay slate rocks. Their shape indi-
cated that they had undergone great friction, in consequence pro-
bably of being rolled over the sea-bottom by icebergs floating through
what was then a sea strait, but now the Linnhe Loch, and the
chain of lakes forming the Caledonian Canal. Sketches of these
Appin boulders were taken. The largest is!5xllxl0 feet. Both
boulders are well rounded at the angles.

Professor Judd’s Beport is in the following terms : —

“Appin Boulder s, No. 1. — This rock is not a granite, but a rock of
basic composition. It appears to be a gabbro with some black mica.
It is very similar in character to the gabbro of Skye, Bum, Ardna-
* See 1 ‘ Geolog. Society’s Trans. ”

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murchan, and Mull, which are described in my paper. I think
there is no room to doubt it was derived from one of these localities
— the rock is so peculiar and well characterised.

“ Fast lacloich Boulders , Nos. 2, 3, 4, are very ordinary gabbros,
such as form great mountain masses in Skye, Ardnamurchan, and
Mull. These rocks are of a striking character, and differ from any
which I know of on the mainland. I think it is certain, they were
derived from the Western Isles.”

Professor Judd, in his paper on the ancient volcanoes of Mull,
Skye, and Ardnamurchan, refers to proofs that these volcanoes
reached a greater height above the sea-level than any of the
existing Scotch mountains, perhaps even to the height of 14,500
feet,* and that “ denudation” had acted to an enormous extent in
breaking up the old volcanic rocks and lowering their height.
Professor Judd does not particularly specify the nature of the
denuding agent which he supposed produced this effect. But if the
sea with ice floating in it, at a height of say 2000 or 3000 feet above
the present level, be allowed to be a denuding agent, it is easy to
see how the boulders of Appin and Fasnacloich, if derived from Mull
or Ardnamurchan, might have reached their present positions.

The distance of Appin and Fasnacloich from Mull and Ardna-
murchan is about 30 miles. The intervening sea has in some
places a depth of 100 fathoms. The island of Lismore, which is
in this part of the Linnhe Loch, at one spot only reaches a height
of 420 feet. A sea current flowing across Mull and Ardnamurchan,
towards and through what is now known as “ Glen na Albin,” with
mountains on each side of the Glen reaching to 2000 feet above the
present sea-level, might, by floating ice, have carried boulders and
lodged them in lateral valleys, such as Loch Creran.

11. Crinan Canal. — At the summit level, about half-way between
the two extremes, there is a large accumulation of boulders, chiefly
angular in shape. On the west side of the canal at the “ locks” a
body of rock stands up, whose surfaces facing the north present
marks of abrasion as if caused by some body or bodies passing over
from the north. On the south side of this rocky knoll, lie a num-
ber of boulders which, if they came from the north on floating ice,
may have been projected over the knoll by its intercepting the ice

* Quarterly Journal of the Geological Society for August 1874, page 259.

674 Proceedings of the Poyal Society

in its farther progress through this kyle or sea channel. One of
the largest of the boulders is lying with its longer axis N. and S.,
or parallel with the general axis of the 'valley at this point.
These conditions would be met by the sea standing at a height of
from 140 to 150 feet above the present level. On both sides of
the valley here there are horizontal lines traceable at that height,
as if made by the sea.

12. Island of Islay. — The Convener, in August 1877, paid a visit
to this island, for the purpose chiefly of examining the famed raised
sea beaches on the adjoining island of Jura, and also of inspecting
some boulders of which notice had been sent to him.

(1.) On the farm of Lossit, about three miles south of Port Askaig,
there are four or five boulders of large size. Only two were seen.

One of these, 13x8x8 feet) is a composite rock containing
crystals of quartz, augite, and hornblende. The stone is ex-
tremely hard ; it was with much difficulty that a small specimen
was detached. The boulder was resting on a bed of bright yellow
clay, apparently a sediment of deep water. The rocks of the district
are a slaty schist. On inquiry, it was surmised that rock of a
similar' kind existed near Kildalton, about 20 miles to the S.E.
But doubt exists on this point.

The other boulder, scarcely so large as the foregoing, resembled a
compact Silurian rock, containing numerous crystals of a whitish
felspar.

There was nothing to indicate how or from what quarter these
boulders came. Their height above the sea was about 300 feet.

(2.) On the farm of Arnahoo, about three miles north of Port
Askaig, and 228 feet above the sea, a boulder stands conspicuously
on the summit of a hill in a position most precarious (fig. 8,
Plate III.). The rock composing the boulder is a hard porphyry,
quite different from the rocks of the hill on which it rests. Its
height above the sea is 228 feet, and the hill itself is about 300
yards from the sea, towards which it slopes very steeply.

The boulder is not absolutely on the highest peak of the hill,
but a few feet below the peak, and on the slope which faces north
by east (magn.). The only way in which the boulder could
have stuck on this slope was by its coming right against it, and
being let down on it gently, i.e., without falling from a height. It

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must have come in a direction from N. by E. If floating ice
brought it — -and no other way is here conceivable— from the south,
the boulder could not have reached its present position. It would
have stuck on the south side of the hill. It could not have reached
its position by a somersault over the hill top, for the impetus
acquired by its fall would have projected it down the hill altogether.

As bearing on the direction from which this boulder may have come,
it is proper to add that towards the north-west there is a range of hills,
apparently much higher than 300 feet, whilst towards the north and
north-east it is open sea, and the island of Mull is in that direction.

(3.) On the farm of Persibus (occupied by Mr Rounsfell), about
three miles S.W. of Port Askaig, four or five boulders, well rounded,
occur, and were seen. They are all of a hard porphyritic rock,
differing from any of the Islay rocks. Their height above the sea
was found to be about 228 feet.

With regard to the probable line of transport to their positions,
it may be noticed that towards 1ST. by E. there is an opening or
depressed part of the country, through which the boulders might
have been floated to their sites.

Mr Rounsfell pointed out a very large boulder situated on a hill
slope to the north, about two miles distant, which, however, the
Convener was unable to visit. But Mr Ballingall, factor on the
Islay estate, has had the kindness to examine the boulder, at the
request of the Convener, and he reports as follows : — “Girth, 33-| feet;
height, 11 feet ; length, 12 feet ; breadth, 18 feet. It lies on clay slate
rocks, and is all exposed to view. Its thickest end faces S.W. Its
height above the sea is 410 feet.” Mr Ballingall has sent with his
letter a small chip of the boulder. It proves to be an igneous rock,
with much hornblende. It has probably come from some northern
region. The weight of the boulder Mr Ballingal estimates at 25 tons.

(4.) On the south side of the high road between Bridgend and
Port Helen a boulder rests at the foot of a low hill which faces
about due north. The boulder is tolerably well rounded, and about
7 feet in diameter. It is a stranger to this district. Most probably
it came from the north like the rest, and was in its farther progress
intercepted by the hill at the base of which it lies. Its height above
the sea is about 50 feet. (See fig. 10, Plate III.)

(5.) On the west coast of Islay, in the parish of Kilcheran,

676 Proceedings of the Poyal Society

there are porphyritic boulders lying on the blue slate rocks, and so
situated as to make it clear, that they have been brought and lodged
there by some agency from the N.W,

Below the old parish church of Kilcheran a small stream joins
the sea through a valley in a direction W.1ST.W. (magn.). The
rocks on the south bank of the stream are ground down and
striated in such a way as to show that some force has passed
obliquely across the valley from N.W.

In regard to these Islay boulders, it is very apparent that they
have all come from the north — some of them very probably from
Mull. It is also rather remarkable that the largest should occupy
sites very nearly on the same level, viz., 228 feet above the sea,
a circumstance suggesting the same means of transport. As bearing
on this last point, it may be observed, that on various parts of the
Scotch coasts there are traces of old sea-beaches, at heights between
250 and 500 feet above the present sea-level.

13. On the Peninsula situated between the Firth of Clyde (on the .
east side), and Loch Striven (on the west side), there are several
boulders of some interest.

(1.) At Dunoon and Kirn there are boulders of a micaceous
sandstone rock, all well rounded, lying on the edges of the blue
slate rocks which form the beach. One has had painted on it
the .words “ Jim Crow ,” being 15 x 8 x 6 feet; another, the words
uJohn Bull,” 15x12x6 feet.

It was stated to the Convener by a local correspondent, that rock
of the same nature as in these boulders occurs in the Holy Loch,
situated about a mile to the north-west.

Two of the boulders on this part of the beach are so fixed as to
indicate from what quarter they must have come into their present
position, viz., from the North. Sketches of these were taken.

(2.) Along the shore towards Innellan there are numerous boulders
differing from the rocks on which they lie. Some of these rocks
show surfaces smoothed and striated, the striae running north-east
and south-west — a direction parallel with the general line of coast.
Some local agency has, therefore, probably been at work here.

(3.) On the east shore of Loch Striven lies the large, well-rounded
boulder, called “ Craig na Calleachf or u Stone of the Witch ” — the
legend being that in former times, the witches inhabiting both

of Edinburgh, Session 1877-78.

677

banks of the loch, threw these great stones at one another. It is
said that on the west bank of the loch, near Strome Point, and
almost immediately opposite to “ Craig na Calleach,” there is a
boulder of about the same size — -which, however, the Convener was
unable to go in search of. “ Craig na Calleach ” is a compact schist
of a light grey colour, with thick nodules of quartz in it. The
rocks of the beach on which the boulder lies are a slaty schist of a
greenish blue colour. A sketch was taken.

(4.) On the farm of Acli-na-foud , situated about a mile from
“ Craig na Calleach/’ there is on the slope of a hill an angular
boulder. It is at a height of 222 feet above the sea, and on the
edge or verge of a precipitous bank. It rests partly on rock,
and is in a very critical position. If the bank be now in the same
condition as when the boulder was deposited, it must have been let
down very gently or gradually, to avoid receiving an impetus which
would have caused it to roll down the bank. A sketch was taken.

BERWICKSHIRE.

In the parish of Dunse the boulder clay has lately been cut through
for some hundred yards to make a new road, and to a depth of 8 or
10 feet below the surface of the boulder clay. Beds of gravel and
sand lie over the boulder clay, in some places to the thickness of 1 2
feet. On an inspection by the Convener (November 1877), in com-
pany with Mr Stevenson, Dunse, boulders in the clay were recog-
nised as having all come from the west, chiefly W. by N. The
Kyles Hill and Dirrington Hills porphyries were among these ; the
former is three miles W. by N., the latter six miles W.N.W.
There were also sandstones with fossils, which Mr Stevenson
knew to have come from a sandstone rock a few hundred yards to
the westward, and which he pointed out to the Convener. The
fossils were the ordinary plants of the coal formation, and an
annelid.

DUMBARTONSHIRE.

1. Loch Lomond. — The large Mica schist boulder reported to the
Committee by Mr Jack, and mentioned in the Committee’s Second
Report (Roy. Soc. Proc. for 1872-73, p. 152), was visited by the
Convener, in company with Mr Smollett of Cameron House. Its
VOL. ix. 4 u

678 Proceedings of the Royal Society

provincial name is “ Ker stone Galloch” it is situated on the farm of
Callendoon, and is about 150 feet above the sea. Its length is 28
feet; width 19 feet; depth 12 feet.

It is shown on fig. 11, Plate III., with Mr M‘ Arthur, tenant of
the farm, standing on it.

Originally, the boulder had been in a somewhat higher position.
A small stream running past the boulder at its east side had washed
away part of the gravel bed on which it had been resting, — so allow-
ing it to sink.

With reference to the quarter from which this boulder was trans-
ported, Mr Jack suggested that if it came from the west, it must have
come over hills from 1000 to 1200 feet high ; and therefore he thought
it more probable that it had been floated south down the valley now
occupied by Loch Lomond, and then floated west up Glen Fruin.

It appeared to the Convener, that the line of transport was more
likely from the westward. The land towards W. by N. (true), is
on about the same level as the land to the north-east, as shown by
the contour lines on the Ordnance maps of the district. If the
boulder came from the westward, there would he no obstruction to
its progress in a direct line ; whereas, if it came from the north
end of Loch Lomond valley, as suggested by Mr Jack, it must have
changed its course to reach Callendoon.

2. On a moor, about half a mile to the north east of the above
boulder, there are several smaller boulders of mica schist, of the
shapes and sizes shown on fig. 12, Plate III.

It will he observed that they all occupy similar positions in respect
of their longer axis, and their sharpest end. Their height above the
sea is about 250 feet. The rocks of this district are Old Eed Sand-
stone. There is much probability that these boulders had been left
here by floating ice, in a current flowing from the westward; and
that they acquired their hearings from the action of the current.

3. On the west side of Loch Lomond there is at Arden a low
valley, which runs up from the Loch in a westerly direction. The
summit level of this valley towards the west is about 150 feet above
the sea.

Along the south side of this valley a number of bouldeis, chiefly
of primitive rocks, have been deposited. They are at a height
of about 94 feet above the sea. As usual, the most frequent position

of Edinburgh, Session 1877-78. 679

is here, as elsewhere, N.W. and S.E. for the longer axis, and the
sharpest end towards the west.

4. In the policy of Cameron House a boulder of gneiss, 6 J x 5 x 5
feet, is lying on gravel, and at a height of about 55 feet above the
lake, or 80 feet above the sea. Its longer axis is N.W. and S.E.

5. There is a hill called “ Caer-man,” about 3 miles to the S. W.
of the south end of Loch Lomond. Its height above the sea is 720
feet. From its top, a good view is obtained of Helensburgh and
Greenock towards the S.W.

The rocks on the top of this hill are a coarse porphyry. Huge
fragments have been strewed in great abundance down the side of
the hill sloping eastward, and especially S.E. The unmoved rocks
present their west surfaces rounded and smooth, their east surfaces
angular and rough.

On examining the separate blocks where heaped upon one another,
it was apparent that the uppermost blocks, to obtain their positions,
must have been projected on the others from the westward.

EAST LOTHIAN.

Linton. — On the farm of Drylaw, a greenstone boulder, 5| x 3J
x 3 feet, was found in cutting a deep trench through the boulder clay.
The jST.W. end was the most rounded. The longer diameter was
N.N.W. (magn). There were i|0 s trice on the top, but there were
horizontal striae on the two sides fronting the H.E. and the S.W.
These two sides met in an angle towards the N.W. If a current had
flowed from W. by N. the current would divide at the angle; and if
ice floated in the current, the striae on the two sides might have been
produced by hard pebbles from the westward pushed against them.
The smoothing and striation on the north were greater than on the
south side. Close to the boulder there were pebbles of limestone
shale, sandstone, and coal, which most probably came from the west-
ward. The nearest greenstone rocks are on the Garlton hills, situated
about 6 miles to W. by N. The boulder, therefore, most probably
came from these hills.

About half a mile to south, there are rocks (viz., in Linton vil-
lage, and in a railway cutting to the west), presenting smoothings
and stria tions, made by some agent moving over them from W.
by N.

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Proceedings of the Royal Society

FIFE.

1. Isle of May. — There are small Sienitic boulders on west side,
at sea-level. On the west side there are also smoothed rocks.
Direction of smoothing agent has been from W. J N. No boulders
or smoothings are on east side.

2. In Bogward Den (Mr White Melville’s property), 3 miles west
of St Andrews, there is a boulder of conglomerate rock. Probably
it came from Drum Carro Craig, which is said to be same species of
rock, and situated some miles to N.W. The legend is, that the
devil threw it from that hill, when the first Protestant church
was being erected at St Andrews.

3. At Kincraig , Fife , there is on the beach a granite boulder,
with girth of 23 feet and height of 4 feet. The lower half is
angular, the upper half rounded. Has this boulder been floated
from westward, and been stranded on the rocks at Kincraig?
Stirling Castle, which is visible, bears W. J N. But it probably
came from a more north-westerly direction. Fragments of this
Kincraig rock (a trap tuff), have been carried eastward, and were
found in the cuttings made for the railway 2 miles distant from
Kincraig point.

4. At Elie. — Whinstone boulder on beach, 8 x 4 x 2J feet.
Its longer axis N.W. Striae on boulder run N.W.

INVERNESS.

The Convener having been informed by the officers of the Ord-
nance Survey that some remarkable horizontal terraces had been
discovered by them in Glendoe, a valley branching off from Glen
Morriston, on the north side of the Caledonian Canal, he took the
opportunity, when paying a visit to Mr Ellice of Invergarry, of going
to Glendoe.

Under the guidance of two gamekeepers on the property of Mr
Grant of Invermorrison, who reside at the foot of Glendoe, the
Convener proceeded to the head of Glendoe, the place indicated in
his map by the Ordnance Surveyors.

Unfortunately, a heavy fall of snow had (17th October 1877)
occurred during the night preceding this visit, and it continued
during the expedition.

of Edinburgh , Session 1877-78.

681

There was at first some difficulty in making the gamekeepers com-
prehend the spot wished to he reached; and it was not till the
party had gone some miles up the valley of the Doe, that the
gamekeepers began to see what was sought for at the head of
the glen. This was brought about by the Convener drawing atten-
tion, as he proceeded up the valley, to two lines of a terrace or flat
noticed by him on a hill on the opposite side of the river. On his
asking the keepers, whether there were similar lines at the head of
the glen, — still about 6 miles distant, as they alleged, — the answer
was, that there were such terraces, and so remarkable, that on one
occasion, when accompanying a shooting party, some of the gentle-
men remarked, that marks were there of Noah’s flood !

The Convener was encouraged by this information, and in spite of
snow and wind continued his progress up the glen.

The keepers stated that the marks to which they referred were on
“ English Hill; ” and that though this hill was rocky on some parts,
there was a great deal of sand and gravel near the top.

Following up the river Doe, a point was reached where the river
divided into two branches, and called by a Celtic word meaning
“Tongue of the Burns.” The portion of the stream towards the right
has the name of “ Carriscreuch,” or “ Middle Corry ; ” and it was
along that stream, flowing through what the keepers called “ The
Long Glen,” that “ English Hill ” could best be reached. But the
snow was here so deep, that no track was visible, and walking be-
came dangerous, at least to a stranger.

At this point a consultation was held. The height above the sea
reached was only about 850 feet, whereas the highest terrace marked
by the Ordnance Surveyors was 1280 feet, and apparently still about
2 miles further up the glen.

The gamekeepers’ advice was to abandon any hope of reaching the
terrace, and to be satisfied with a distant view of the place, which
could be obtained from a low hill in front.

This low hill accordingly was ascended, and with satisfactory re-
sults. The hill itself was found to consist, as shown by numerous
scaurs, of fine gravel and sand ; and on its flat top, the aneroid
showed a height above the sea of 1190 feet.

This gravel knoll was as it were in an amphitheatre of hills, on
several of which, towards the west, horizontal terraces were observed,

682 Proceedings of the Royal Society

at a somewhat lower level. These appeared to run continuously for
about a mile. On the opposite side, the hill hearing about east
showed a short line at the same level. Looking towards “ English
Hill ” on the N.E. no terraces were discernible ; the snow, owing to
the direction of the wind (which was west), was so thick on the slope
of the hill facing the knoll, that inequalities, if any existed, were
undisc overahle. But one of the keepers pointed in the direction of
the part of the hill for the terraces he. had before spoken of. The
part so pointed out seemed to he about 2 miles distant, and at an
elevation of about 100 feet above the knoll on which the party were
then standing.

The Ordnance Surveyors had marked on the Convener’s map two
lines of terrace, one at 1280 and the other at 1140, as existing on a
hill on the left side of the Doe water. Though, from the circum-
tances above stated, it was impossible to make out these terraces,
there was enough discovered to show a line at the lowest of these
levels on the other hills adjoining — and the existence of detritus
quite capable of being formed into a terrace at a much higher level.
One of the keepers stated that on a hill towards the N.W. there
were beds of gravel and sand to the very top, and without any
covering of turf. He pointed in the direction of Ben Doe, which
has an elevation of 2000 feet above the sea.

The Convener having on his way up Glen Doe observed several
large boulders on the slope of a hill above him on the left hand,
resolved to visit them on his way hack. So, accompanied by one
of the keepers, he ascended the hill, and in looking across the valley,
he discovered four horizontal terraces on the opposite hill, and con-
tinuous for about half a mile. They were apparently on detritus,
for at one spot, where a rock projected, there was an interruption.

The uppermost terrace the aneroid showed to he about 985 feet
above the sea, the lowest about 895.

The first of the boulders visited was 919 feet above the sea. Its
dimensions, roughly measured, were 14 J x 11 J x 7 feet. It was
a coarse reddish granite, and very angular. It could not have been
rolled or pushed. It seemed to have been carried from its parent
rock, wherever that was, without undergoing any change of form.
It was resting on gravel and sand.

The next boulder reached was at a height of 1204 feet above the

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683

sea. It also was a coarse red granite. It was about 30 yards in girth,
and 14 or 15 feet in height. It is known as “ The Glen Morrison
Stone,” probably because of being the largest boulder in the glen.

This boulder is on a flat, and in looking across the valley, a
terrace is seen which corresponds in level with the boulder.

In several parts of the hill the boulders were in clusters or groups,
piled over one another.

It deserves notice that all these boulders were resting on gravel
and sand ; and that the hills on both sides of the valley were thickly
covered with detritus.

The gamekeepers spoke of a very large boulder at Clachnaharry,
about 16 feet high, on the south side of Loch Clunie, which is two
or three miles to the west of Glen Doe. The Convener saw it
through his glass.

It may be added here, that Mr Ellice of Invergarry informed
the Convener of a large bed of pure white sand, which he could not
distinguish from sea sand, existing on a property belonging to him
in that district, at a height of about 1000 feet above the sea.

MID-LOTHIAN.

1. In September 1877 the Convener visited excavations on the
north side of Craiglochhart Hill , about two miles S. W. of Edinburgh.
His attention was drawn to them by Mr Hutchison of Carlowrie.

These excavations were in the boulder clay. A number of
boulders had been exposed, and were still undisturbed in their
original positions.

The largest was angular, the smaller boulders wrere comparatively
round. The greatest number were of blue whinstone rock. Among the
smaller boulders, there were some of sandstone. The contractor for
a large new building about to be erected being present, had his
attention drawn to the sandstone boulders, and was asked if he
knew any rock of the same kind which was in sufficient quantity to
be quarried 1 He said that the sandstone of Hailes Quarry and Red-
hall Quarry was the same rock as that of the boulders. On being
asked to point out the direction of these quarries from where the
boulder lay, he pointed in a direction which was N.W. (by com-
pass) A

* These quarries are about a mile distant from the site of the boulders.

684 Proceedings of the Royal Society

The height of these boulders above the sea is about 340 feet.

2. At Granton Harbour (on west side) a very large blue whin-
stone boulder lies on the beach at high-water mark, part of which
only is visible, the rest being covered and concealed by the sea wall
which protects the road. On the upper surface of this boulder,
there are innumerable striae, the direction of which is W. 3° S.
(magn).

About 100 yards to the eastward, there is another whinstone
boulder having an iron ring in it, by which boats or vessels may be
moored. There are striae on it running in the same direction.

Between these two boulders there are some strata of hard sand-
stone rock, portions of which have been ground down and show
striations running also as above.

3. In the New DocJcs, situated to the eastward of Leith , there is
an immense bed of boulder clay, which continues along the coast
eastwards for some miles.

This boulder clay at the Docks is covered by a muddy sand in
horizontal beds about 8 or 10 feet thick. On the surface of the
boulder clay there is a bed of oyster shells, of large size. There is
as usual on the surface of the boulder clay a great accumulation of
boulders, these having remained when the upper portion of the
boulder clay bed was washed away by the sea. Most of the
boulders are well rounded. The largest I saw, a light coloured blue
whinstone, measured 10x8x6 feet, and was estimated to weigh 18
tons. About nine-tenths of the boulders are whinstones, but there
are also some of quartz, limestone, sandstone, silurian, granite, and
black ironstone concretions from beds of shale. These boulders
have evidently come from the westward. On a great many, there
are ruts or striae all maintaining the same direction, viz., W. by H.
(magn.) Those which are longer than they are broad, have their
longer axis in the same direction.

Among the boulders, there were two metallic in composition,
which deserve special notice.*

One, nearly spherical, measures 7J inches in circumference, and

* The Committee have to thank Mr Hugh Campbell, who is professionally
engaged in the formation of these new docks, for bringing to them the two
remarkable balls here referred to, as well as for affording to the Convener
opportunities for seeing the excavations.

of Edinburgh, Session 1877-78.

685

weighs 24 oz. It was found about 4J feet down in the boulder
clay, among the large boulders.

The other ball was even more spherical, its least girth being 30
inches, and its greatest 31 inches. Its weight was 54 lbs. It was
found 10 feet below the top of the boulder clay.

Professor Crum Brown (Edinburgh University) was so obliging
as to examine both of these balls for specific gravity and composi-
tion. He reports that the smallest ball is marcasite or white iron
pyrites, and that its specific gravity is 4’63. It is entirely of pure
ore, being apparently unmixed with any other substance.

With regard to the larger ball, the Professor has sent the follow-
ing report : —

“ The fragment of the large round stone which I took for exami-
nation had a specific gravity of 3 '36. It consisted of a mixture of
silica (not obviously crystalline) and iron pyrites, in the following
proportions : —

“Silica, 52 '3 )

__ . , . _ > per cent.

“Pyrites, 47*7 /

“ Calculating from these numbers and the sp. gr., it is plain that
the pyrites must be in the 1 marcasite ’ form, as ‘ pyrite ’ would give
a considerably higher sp. gr.

“ The sp. gr. of the whole stone, i.e., the mean sp. gr., was found
to be 3 ‘28. It cannot, therefore, be a uniform mixture.”

Mr Murray having kindly offered to examine, microscopically,
this large stone ball, has sent the following report : —

“ Challenger Office, Teviot Row ,
May 1878.

“ Dear Sir, — The microscopic section of the boulder is made up
of crystalline particles of quartz and marcasite. The marcasite fills
the interstices between the grains of quartz ; and among the quartz
there are pieces of mica. (Signed) John Murray.”

The Convener paid two visits to the excavations in the boulder
clay at Leith to examine the spot where these two remarkable balls
were found. He saw the superintendent, who was directing the
excavations, and also the “ navvy ” who found the larger ball. The
latter pointed to a whinstone boulder, and said the “ big bullet ”
was close to this boulder.

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There can be no doubt that both balls had come with the
boulders, and had been deposited with them in the great bed of
clay which covers the rocks in this district. This bed extends for
fully half a mile on each side of the Water of Leith at its mouth,
and reaches to a depth in some places of nearly 100 feet.

The black ironstone concretions found in this boulder clay bed
show marks of friction. There are strata of shale containing such
concretions, two or three miles to the westward. These concretions,
as well as the boulders of granite and quartz, clearly indicate
transport on a large scale from the westward.

The Convener learns from Mr Robertson, C.E., Albany Street,
Edinburgh (who planned both the Albert Docks at Leith, exe-
cuted some years ago, and the new docks now being constructed),
that similar metallic balls were found in the Albert Docks excava-
tions. But he has no specimens of them.*

* Since the foregoing was written, the Convener has received from Mr Charles
W. Peach, of 30 Haddington Place, Edinburgh, a letter regarding marcasite
nodules, from which letter, with Mr Peach’s permission, the following
extracts are made : —

“In the Falkirk and Slamannan district a band of these nodules, known as
‘ Speckled Ball Ironstones occurs. It occupies a horizon a few fathoms above
that of the ‘ Slaty Band Ironstone ,’ the base of the Coal measures.

“ The direction of the stride on the rocks and the carry of the boulders and
boulder clay is towards the east, and varies from E. 10° N. to E. 15° N.

“ Near Kilsyth, and about 2 miles to the west of that place, the tributaries
of the Corrie burn cross an area of blue shales, with several courses of
ironstone nodules. Some of these are of iron pyrites (marcasite), and aie
known among the mining population as ‘ brassy balls. ’ They occupy a
horizon between the Hosie and Hurlet limestones, near the base of the
carboniferous limestone series.

“The direction of the strice and carry of the boulders in this district is
E. or E. 5° H.

“Either of these sources could supply balls at Leith, as they are right in
the direction of the ice-flow.

“ As to concretionary balls in sandstone, — there is on the coast of East Lothian
near Cockburnspath, to the north of Cove, a cliff of calciferous sandstone
full of spheroidal concretions, which weather out on the wasting of the cliff by
the sea, and being harder than the matrix, they lie piled up in great numbers
at the base of the cliff. Many of them are of very large size.

“Similar concretionary balls occur in sandstone rocks at Grange Quarry
near Burntisland, from whence, no doubt, the ball found lately at Leith was
carried. (Signed) “ C. W. Peach.”

This information in regard to marcasite brassy balls, the Committee
deems highly interesting. If the marcasite ball found in the boulder clay
at Leith, was transported from any part of the district situated to the north

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of Edinburgh , Session 1877-78.

4. At Almoick Hill , near Liberton Church , at an elevation of about
350 feet above the sea, extensive excavations have been made in
the boulder clay for the new Edinburgh water-works. The boulders
consist chiefly of fragments of rocks, which are known to be in situ
situated in districts of the country to the west and north-west. The
great majority of the boulders are of hard red sandstone rock, such
as occurs at Grange and Merchiston, to the west of Edinburgh,
though these places are at a lower level. There are boulders of
marine limestone, similar to rocks of that description in Linlith-
gowshire. There is an immense quantity of blue-coloured green-
stones and dark-coloured basalts, and also buff-coloured felspathic
rocks. There are some small boulders of pure quartz, which pro-
bably hail from the Silurian rocks to the north-west of Callendar
and Doune.

Many of the boulders occupy positions, present shapes, and bear
marks of some interest.

The largest seen by the Convener were about 7 feet long by 4
feet wide, and 2 ^ thick or deep.

The boulders were all well rounded and smooth, but more par-
ticularly so on what had been the upper and the under sides.

Mr Black, the superintendent of the excavations, being aware of
the interest attaching to the position of the boulders and the strice
on them, had, with a compass, ascertained that the long-shaped
boulders, before being moved, generally were lying in directions
varying between W.IST.W. and 1ST.W. ; that the strise, when such
existed, were almost always parallel with the longer axis of the
boulder ; and that there were striae, sometimes only on the upper
side, sometimes only on the lower side, sometimes on both sides.
In one of the boulders, well rutted on the under side, he had re-
marked that the ruts were deepest at the east end of the boulder,
and that they gradually diminished in depth and numbers towards
the west. This feature might be accounted for on the supposition
that the boulder, whilst being pushed forward, encountered hard
obstacles which produced deep ruts on the boulder when the first

of Glasgow, as suggested by Mr Peach, what was the transporting agent to
suit those localities ? A glacier moving from west to east by the action of
gravity would be hardly conceivable. The levels preclude that agent. A sea
current, loaded with floating ice, seems a more probable conjecture.

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Proceedings of the Poyal Society

contact took place, afterwards the boulder would rise over these
obstacles, and in consequence the striae produced by them would
diminish in depth.

5. Tynecastle, near Edinburgh. — A basalt boulder, x 4 x 2 feet,

was discovered, striated on both upper and under side, but the ruts
were much deeper on the under side. The under side ruts had
begun to be formed at the east end of boulder, — the striae on the
upper side begun at the west end. This might be accounted
for by supposing that the boulder had been pushed towards the
east over hard rocks, and that floating ice from the westward
had pushed stones over the upper surface. The smallest end of
boulder pointed towards west. The sides of the boulder were well
rounded.

This boulder lay in a hill of muddy sand containing many pebbles
of all kinds, hard and soft, such as quartz, shale, and coal. Height
above sea, 200 feet. — Ed. Geol. Soc. Tr ., vol. ii. p. 347.

PEEBLESSHIRE.

At the east end of the town of Peebles there is a boulder of white
quartz, about 3 feet long, 2 J feet broad, and with a girth of about 7
feet. It is now built into a wall. Previously to its being thus dis-
posed of, the stone stood from time immemorial in an adjoining low
hill, which in consequence had obtained the popular name of the
“ White Stone Knowe.” It is alluded to as a boundary stone in a
title deed dated in 1436. Mr Eichardson, the Secretary of the Edin-
burgh Geological Society, who was the first to take public notice of
this boulder, says that “ the nearest beds of quartz are about 80 miles
to the ]ST.W.” The boulder on its surface is smoothed and polished.
It is, like many other boulders, rudely pointed at one end, whilst the
other extremity is more broad and heavy. The height above the
sea is 550 feet. — Ed. Geol. Soc. Trans ., vol. ii. p. 397.

PERTHSHIRE.

1. Loch Tay. — On the farm of Morenish, situated on the north
bank of the lake, and about 2 miles from the village of Killin, there
are several boulders worthy of notice.

Figs. 13, 14, 15, Plate II., are intended to show the positions and
specialties of these boulders. They were at a height of about 1400
feet above the sea, assuming Loch Tay to be 30.0 feet.

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These boulders had all come from the westward, viz., down the
valley, as shown by the way in which they were fixed.

If the question be, whether they were brought by glacier or
by floating ice, the answer is, that there is not much evidence
either way. It may however be remarked, that if they were pushed
forward by a heavy glacier, it is odd that the boulders should not
have been carried further down the valley, and that the obstructions
on their east side, against which they have stuck, should not have
yielded under the pressure of a ponderous glacier. The boulders
in figs. 13 and 14 were resting on detritus, and pressing against
detritus only on their east sides. The boulders in fig. 15 was
pressing against a hard rocky stratum of clay slate on its east side.

In several parts of the hill, smoothed rocks of mica schist occur,
with knobs of quartz standing up above the general surface. Being
harder than the mass of rock, they had resisted the friction better ;
these knobs were smoothed, the smooth parts being always on the
west sides.

Fig. 16, Plate III., shows a rock with joints. The projecting
angles facing the west have been smoothed by some abrading and
grinding force.

2. Glen Dochart. — There are many boulders of considerable size,
resting on detritus, and chiefly on the south side of the valley.

One near an old toll-bar measured, in so far as above the ground,
13x12x8 feet, at a height of 630 feet above the sea.

At the small farmdiouse of Wester Lix, at a height of 660 feet
above the sea, there is a flat or terrace, partly rock, partly detritus,
on which there are several large well-rounded boulders, two of
them a coarse granite, probably from Ben Cruachan.

On ascending the hill towards the south, a boulder, 12x9x5
feet, was met with, at a height of 1116 feet above the sea. Its
longer axis bore E. \ S., which is also the direction of the axis
of the valley in this place. There being no rocky hill near, from
which this boulder could have come, it has certainly been brought
to the spot where it now lies, by some transporting agent.

At the height of 1250 feet there is a mass of rock on the same side
of the valley, and nearer the top of the ridge, which has on it some
noteworthy marks. The rock stands out prominently, and forms a
nearly vertical cliff, as shown in fig. 17, Plate III. On the side

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Proceedings of the Royal Society

facing the west, there are horizontal groovings, apparently formed
by some force, which, acting on the whole mass, has worn down
certain portions more than others, these portions being less com-
pact, and so more capable of abrasion.

Such abrasion might have been effected by a body of water passing
from the westward ; and more readily, than by the solid ice of a
great glacier.

On the top of the ridge forming the south bank of this valley
(GlenDochart), a cairn stands at a height of 1500 feet above the
sea. A boulder of considerable size lies on the top of this ridge, on
the east side of a projecting knoll. Has the boulder been stranded
on what was the lee side of the knoll ?

ROSS-SHIRE.

At Auclinaslieen (Dingwall and Strome Ferry Railway,) there is a
boulder about 15 feet in girth, which stands on a flat of detritus
about 610 feet above the sea.

In this district, there are several other detrital flats, in sight of
this one, all nearly on the same level. There can be no doubt that
these flats have been originally one continuous plateau, which formed
a sea-bottom. It has been cut through by several streams, the banks
of which, about 18 feet high, show an enormous accumulation of
gravel and sand; — sand, below (deposited probably when the water
was deep) ; gravel, above (deposited when the water was shallower
and more subject to currents).

The annexed diagram represents a portion of these remarkable flats,
— cut through by several streams, the principal of which flows from
Loch Rosque, — situated to the north of the boulder. The knobs,
on the woodcut are intended to represent knolls of gravel or sand —
remnants of a greater mass of these materials. The boulder is
well rounded, and it has evidently come from a distant quarter.

Professor Nicol of Aberdeen has expressed an opinion * that the
formation of these Auchnasheen terraces is due to the action of a
oreat river flowing from the west. I regret to differ on this point
from a geological friend; but I can see no grounds for that opinion.

To the east of Auchnasheen, close to the railway, there are several
spots of rock evidently rounded by friction — whether by ice or by
* Nicol’s Geology of Scotland, p. 69.

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water, or by both, it is difficult to say. Their height above the sea
is about 780 feet. On the hills, on each side of the railway, there
are traces of horizontal lines on the detritus, which deserve better
observation than could be given from the railway carriage.

STIRLINGSHIRE.

1. On Sheriffmuir, 3 miles from Bridge of Allan, near Blackford,
there is said to be a large boulder, called Wallace’s Putting Stone.

NORTHUMBERLAND.

It was intended that only Scotch boulders should be inquired
after by the Committee ; but it is not irrelevant to notice a
boulder which, though now in England, was probably transported
from a Scotch mountain.

In Chillingham Park, the seat of the Earl of Tankerville, near
Alnwick, there are several small boulders of granite. The rocks of
the immediate neighbourhood are carboniferous sandstones and lime-
stones. The nearest point for granite is the “ Big Cheviot,” eight
miles to the W.KW., and reaching a height of about 1800 feet
above the sea, The largest boulder is 3 feet 2 in length, 2 feet

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Proceedings of the Royal Society

4 in width, and 2 feet high. It is round in shape, and about 400
feet above the sea.

Several valleys and ridges of hills lie between Chillingham and
the Big Cheviot, across which the boulder must have been trans-
ported to reach its present site.

Remarks by David Milne Home, LL.D., Convener of the
Society’s Boulder Committee, on presenting the Commit-
tee’s Fourth Beport at a Meeting of the Society, 20th
May 1878.

1. In presenting a Fourth Report from the Society’s Committee on
Boulders, I may he allowed, first, to refer to the main object for
which the Committee was appointed.

It was to collect data which might help towards a solution of the
problem, by what agency boulders in Scotland had been transported
from the parent rocks to the positions they now occupy.

The Transactions of the Society contain numerous papers by
eminent geologists on this question.

At a very early period, Sir James Hall, when he drew atten-
tion to many large boulders, and also to the remarkable appear-
ances called “crag and tail ” in the midland districts of Scotland,
ascribed both sets of phenomena to the agency of great bodies of
water, which had passed over the country from west to east.

At a later period (about the year 1842), Agassiz and Dr
Buckland started the idea, that as in Switzerland, glaciers had
been the means of carrying masses of rock from the Alps across the
valley of Geneva to the Jura mountains, so there might in former
days have been glaciers in Scotland producing similar effects.

More recently a third theory was started, — that if the sea stood
several hundred feet above its present level, floating ice might have
been the means of transporting the boulders, and carrying them
great distances.

2. There being thus three different theories of transport, each
supported by eminent geologists, the Committee has endeavoured to
gather facts to ascertain which theory is the most probable, or
whether any better can be suggested.

I do not presume to say that the information contained in this and

693

of Edinburgh, Session 1877-78.

the previous Reports will yet allow the problem to be solved.
But at all events it may be conceded that some new facts have been
ascertained, which throw considerable light on the question.

I venture to indicate what appear to me to be several con-
clusions warranted, though in doing so I offer only my own
opinion. Perhaps the Committee, after more information has
been obtained, may be induced to consider whether they will pro-
nounce on the various questions of interest which the subject
presents.

I confine myself this evening to only a few points, and chiefly
to illustrate what occurs in our last Report.

3. The boulders referred to in the Report may be divided into two
classes.

First, There are boulders which, from the nature of the rock com-
posing them, are so soft and friable, that they could have been trans-
ported only short distances — such as sandstone, coal, and shale.
In the Report, examples are given of such boulders, from Berwick-
shire and Mid- Lothian.

The second class of boulders, namely, such as are ascertained
to have come from remote quarters, are composed of rocks, hard,
compact, and homogeneous in composition; such as basalt, green-
stone, granite, felspar, quartz, greywacke, and old conglomerate.

Boulders of these rocks have been found even as far as 80 or 100
miles from the parent rocks; and, generally speaking, they are well
rounded, presenting evidence of enormous friction undergone whilst in
transitu; and even in some cases acquiring almost a spherical shape.

Specimens of small sjiherical boulders are now on the Society’s
table.

There are, however, exceptions to the rule that boulders of hard
compact rocks are generally well rounded. Cases of boulders of
these hard rocks occur extremely angular in shape. Examples are
shown in this Report, by the lithographs appended to it, and in
previous Reports. These angular boulders are almost invariably at
high levels, on the sides of mountains or near their tops. The well
rounded boulders are generally at loiv levels, and most frequently
imbedded in boulder clay.

4. It will be asked, whether the Committee has in any case ascer-
tained the parent rock from which a boulder has come.

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The answer is, that the Committee can in no case point out the
particular rock from which a boulder had originally been broken off.
All they can affirm is, that in several cases they have ascertained
the district or quarter from which the boulder must have come.

(1.) For example, in Berwickshire, as will be seen from this last
Report and the second Report, particular hills are specified from
which boulders must have come. The direction in which they
came, and the number of miles traversed, are therefore in these cases
matter of certainty. In every case over the whole county of Berwick,
from its lowest to its highest level, the direction of transport is
from points between W. and Iff W. (magn.)

The same is the case in Mid-Lothian. The sandstone boulders at
Craiglockhart are shown to have most probably come from rocks
situated a few miles to the Iff W. The quartz and other hard rock
boulders at the same place, as also at Liberton and at Leith, in like
manner probably came from points between W. and IffW.

(2.) The two remarkable spherical balls of marcasite, found in the
boulder clay at Leith and mentioned in this Report, must in like
manner have come from the westward. A presumption to that
effect arises, from the mere fact that they are in the same bed of
clay which contains granite and other Highland rocks. But there
is more than presumption. Mr Peach having indicated where
pyrites balls might be found in situ , viz., at Campsie and Kilsyth,
I went to Campsie last week, and on inquiry was shown some thin
strata of coal, abounding in nodules of pyrites, several of the nodules
so large as to weigh half a cwt. The coal is worked for burning
limestone. It is too full of sulphur for domestic use. Specimens of
this coal, with the pyrites nodules which I obtained on the spot,
are now on the table of the Society.

Kilsyth I did not visit, because the overseer at Campsie
told me that he had worked at Kilsyth, and that there were pyrites
nodules in the coal strata there, similar to those at Campsie, but
of rather smaller size.

Some of the nodules which I obtained at Campsie I submitted to
Professor Crum Brown, that he might examine them to see whether
they contained “ marcasite.” He has reported to me as follows : —
“ These nodules have a specific gravity of 4T2, and consist of
iron, sulphur, and coaly matter in the following proportions : — -

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695

“ Iron, . . 44 ‘5 6 per cent.

“Sulphur,. . .52-14 „

“ Coaly matter, . . 3*30 ,,

Deducting the coaly matter, the iron and sulphur would he in the
proportions in which they are generally found in ‘marcasite,’ viz.,

“ Iron, 45*61; and Sulphur, 54 •29.”

As regards chemical compositions, therefore, the small metallic
boulder may be considered as exactly agreeing with the nodules
found in the Campsie coal strata. This agreement in composition
affords a strong ground for inferring that the boulder had been
transported from Campsie, or from Kilsyth, as suggested by Mr
Peach.

With regard to the larger spherical ball found in the same bed of
boulder clay at Leith, I am now able also to indicate the part of the
country from which it was probably transported. Mr Hutchison
of Carlo wrie, happening to see this stone ball, informed me of two
quarries in Linlithgowshire where concretions resembling it were
in abundance. These quarries are near Humbie and Dalmeny,
situated from nine to ten miles due west from Edinburgh. Mr
Hutchison having sent to me several of these concretions, I was
induced to visit Dalmeny Quarry. I found in the sandstone rock
there, numerous concretions of all sizes up to nearly 4 feet in
diameter. Humbie Quarry I did not visit, as the working of it had
been given up, and it was full of water. A concretion from
this last mentioned quarry, sent to me by Mr Hutchison, Professor
Crum Brown has examined, with the following result : — “ It
weighs 17J lbs. It consists externally of a thin shell of sandstone,
and internally of a mixture of quartz and marcasite, closely re-
sembling the substance of the large ball from Leith. The mean
specific gravity of the ball was 3 -49.”

There is thus a sufficient similarity of composition in regard to the
stone ball and the Humbie concretions, to make it exceedingly pro-
bable that these Humbie sandstone rocks supplied the stone ball.
I do not say that Humbie Quarry was the exact spot from which
the stone ball found at Leith actually came. The sandstone strata
which occur at Humbie and Dalmeny of course crop out elsewhere
in the district near South Queensferry ; all that can be said is, that

696 Proceedings of the Roycd Society

the stone ball may have come, and most probably came, from some
part of that district. Mr Peach mentions in his letters, quoted in
the Report of the Committee, that similar concretionary balls occur
in sandstone rocks near Burntisland, and suggests that the ball in
question came from that quarter. In that case, the direction of
transport would be from about due N. If the stone came from near
South Queensferry, the direction would be from W.H.W., which
last would be more in accordance with the evidence of direction in-
dicated by many other data.

Assuming, then, as most probable, that the large stone ball, as
well as the small metallic ball found in the Leith boulder clay, came
from parent rocks, situated to the westward, the next question will
be, by what agency were they transported 1

Mr Peach, in his letter, apparently assumes, as matter of course,
that these balls were transported by the agency of ice. But “ ice ”
in what form1? — land-ice, or sea-ice?

If the metallic boulder came from Campsie, the distance over
which it travelled to Leith could not have been less than 30 miles ;
and as the Campsie coal strata are only about 150 feet above the
present sea-level, there would not be gradient sufficient for a glacier
either to carry on its surface, or to push before it, debris of rocks
from Campsie to Leith. Moreover, Leith is not at or near the
mouth of any valley which could create or guide a glacier from the
west of Scotland.

But there are in the Campsie and Kilsyth districts marks of
various kinds, indicating the action of a deep-sea current. These
marks it is proper to notice, as having an important bearing on
the general question of boulder transport.

Mr John Young of Glasgow, in the year 1868, wrote an in-
structive paper in the “Transactions of the Glasgow Geological
Society,” on the geology of Campsie. He says (page 14) — “There
are few localities in the central district of Scotland, where such an
extent of polished and striated rock surface is to be seen, as along
the flat summits of the south hill of Campsie. The striae vary in
their direction from a few points north of west to south of west,
according to the deflection of the ground ; — many tracts of the sand-
stone rock, still showing the channelled markings in great perfec-
tion,” at about 600 feet above the sea.

697

of Edinburgh, Session 1877-78.

Mr Young then refers to the Strathblane Valley, which lies
between the north and south hills of Campsie, and to the appearances
indicating that it had been “ swept by powerful currents of water ,
which have helped to produce those inequalities of surface seen
along the outer margin of the tracts now occupied by the rivers
Kelvin and Glazert. It was during the period when Scotland sat
several hundred feet lower in the sea than it does at present, and
when the valley of the Kelvin existed as a deep sound connecting the
German and Atlantic Oceans , that those great beds of stratified
sand and gravel were deposited which we now see filling up the
Strath (as near the village of Torrance) to more than 100 feet above
the level of the river. At other points along its course, similar
deposits exist to more than 100 feet beloiv the present sea-level.
This shows that a very deep sound or valley must have originally
extended across Scotland, previous to the glacial period, in this parti-
cular direction. A depression of the land to the extent of 350 feet
would produce the following results : — The German and Atlantic
Oceans would be united by the valley of the Kelvin, also by the
valley of the Leven, Loch Lomond, and onwards by the low ground
near Ivippen to the Forth at Stirling. A narrow sound through the
Campsie valley would connect the two seas, as the water-shed at
Ballagan Bridge is only 330 feet. The Campsie and, Kilpatrick
hills would then form two islands, and the valleys of the Carron and
the Endrick would be estuaries or arms of the sea. It is only by
assuming conditions such as these, that we can hope to explain the
superficial sedimentary deposits” (page 16).

In the year 1871, in company with Mr Young, I had an oppor-
tunity of visiting the Campsie district, and from my note-book I
make the following extracts : —

a. On Craigend moor, at about 450 feet above the sea, situated
two miles west of Strathblane, I found the sandstone rock present-
ing extensive sheets of smoothed horizontal surface, evidently ground
down by friction, and presenting occasional striae, running in a
direction S.E. by S. The rock had in some places imbedded in it
quartz pebbles, standing up above the general surface. Being
harder than the sandstone rock, these pebbles had been able to
withstand the friction ; but some of them showed marks of rubbing
on their north-west sides.

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b. At this place, looking towards the N.W. — viz., in the
direction of Loch Lomond — an opening between the hills, which
are apparently about 1000 feet high, was discernible; this opening-
being about 1J mile wide.

c. At four other places on Craigend moor, from 500 to 600
feet above the sea, two to three miles apart, there were striations on
the rocks, pointing repectively S.E. by S., S.E. J S., S.E. by S.,
and S.S.E.

At all these places the direction was seen to pass through the
opening between the hills above referred to, indicating that the
agent, whatever it was, which produced the striations might have
come, and probably came, by that opening.

d. On this same moor (forming an extensive plateau of about 6
miles long by about 3 miles wide) I had pointed out to me by Mr
Young several boulders in different places.

Two were of trap, from the Kilpatrick hills, situated some miles
to the W.K.W., and at a height of 570 feet above the sea. In cir-
cumference, each boulder measured 27 feet, and, so far as not
buried in the drift on which they were lying, the height of one was

feet, of the other 6- feet.

Another boulder, well rounded, 500 feet above the sea, was of
grey granite, weighing about 2 cwt., which Mr Young considered,
from the size of its felspar crystals, to have come from Ben Awe,
a mountain situated to the N.W., and distant about 50 miles.

There were several smaller boulders of old conglomerate —
transported, no doubt, from the well-known hand of that rock
which, running from Dumbarton, crosses Loch Lomond in a K.E.
direction towards Aberfoyle.

e. In the valley of the Blane there are deep beds of sand
formed, most probably, whilst the sea occupied the valley, and
numerous well-rounded boulders of all descriptions. At Strathblane
Bailway Station there was a deep cutting of a sandbank, with several
boulders in the sand, and one in such a position as to indicate that
it had fallen from some raft which had been conveying it, as it was
sticking with its narrowest point downmost.*-

/. It was remarked to me by Mr Young, that whilst boulders,

* See a diagram of this sandbank and boulder in a little book, published
by Edmonston & Douglas in 1871, called “ Estuary of the Forth.”

of Edinburgh . Session 1877-78.

699

gravel, and beds of sand are abundant in the valleys of Strathblane
and Campsie, he had never found any marks of grinding or striation
on the rocks in these valleys. These effects seemed to have been
produced at levels higher than 400 feet above the sea.

On another occasion, when geologising on the Campsie hills,
above Glorat, situated 3 miles to the east of Campsie, and at a
height of 800 feet above the sea, I found the sandstone rock
striated, in a direction due E. and W. On the Kilsyth hills, a few
miles still farther east, and at a height of 1200 feet above the sea,
the striations on the rocks were seen to be E. and W.

g. One other fact observed was the immense accumulation of
boulders of all kinds at Croyliill, a knoll of trap, at the summit
level betweeen the firths of- Clyde and Forth — viz., about 1G0 feet
above sea-level. As some of these boulders were of u old co?i-
glomeratef they afford additional evidence of an agency which
brought them from the westward.*

h. In addition to these facts, notice may be taken of two
boulders reported to the Committee by Mr Jack of the Geological
Survey. One is of mica slate, weighing about 6 tons, on the
Kilsyth hills, at 1260 feet above the sea, the parent rock of
which Mr Jack supposes to be situated about 15 miles to the
north. The other is of conglomerate, weighing about 7 tons,
on the north hill of Campsie, at 1803 feet above the sea, with its
longer axis W. 20° JST. Its parent rock is supposed by Mr Jack to
be to K.W. (First Keport of Committee, p. 51.)

Kow what do all these facts prove ? They prove that an agent
of some kind or other moved over this district, having a depth of
at least 1800 feet, and covering a great breadth of country; and
that, whilst this agent was moving, the rocks over which it passed
were ground down and rutted and striated ; large boulders, at a
high level, were carried forward, and boulders at a low level
were pushed in a similar direction.

There is an additional fact deserving notice. The valley at
Lennoxtown, where the pyrites coal strata are worked, seems to
have at one time been filled up by these strata. These strata now,
however, exist only on each side of the valley. Some agent has scooped
them away, whereby the present valley was excavated ; and it is

* “Estuary of the Forth,” p. 95.

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Proceedings of the Royal Society

possible that the balls found in the Leith boulder clay form a
portion of the debris of these pyrites strata so broken up.

What agent can fit into all these conditions so well, as a sea
current loaded with ice ?

On this theory, it is intelligible why the rocks along the moors
of Craigend and Craigmaddie, stretching for 5 or 6 miles in a
direction S.E. and S.S.E., at a level of from 500 to 700 feet above
the sea, should show more effects of grinding and striation than the
rocks at a lower level. Had a glacier been the agent, the grinding
would have been chiefly at the lowest, not at the highest levels.

The subjoined plan and section of Campsie hills and valley will
make the foregoing explanations more intelligible. The plan is
copied from a published map by Johnston. The section has been

Ground Plan of Campsie Yalley.

A, Pyrites coal strata, out-crop of.

B, Craigend Moor, 450 feet.

C, Craigmaddie Moor, 700 feet.

D, Boulder and striated rocks at Croyhill.

K, Kilsyth coal strata.

Boulders shown by black dotts.

Striae on rocks by arrows.

FAE, Line of section across Campsie Valley.

kindly drawn for me by Mr John Young of Glasgow, who is
thoroughly well acquainted with the geology of the district. In his
letter sending the section, Mr Young says — “ The Campsie coal and
limestone is at present worked on the flank of the north hill, as well
as in the mine which you saw in the south hill. The valley

o f Ed i n b in yh, Session 1877-78. 7 0 L

between these hills is one of denudation. Several hundred feet of
strata, belonging to the Lower Carboniferous Limestone series, have
been removed, or scooped out by currents of the ocean.

“If you examine Sheet 8 of the horizontal section of the
Geological Survey (by Professor Geikie) you will find on the south
hill of Campsie the outcrop of the coal and limestone. This sheet
shows, quite as distinctly as my sketch, the valley running between
the south and north hills, and the great denudation of the coal
strata containing the marcasite balls.”

laoo fi

Section across Campsie Valley ; coal and limestone strata overlaid by gravel

and earth.

These explanations go far to show how the small marcasite ball
found in the Leith boulder clay probably came from Campsie. A
geological study of that district indicates the agency of deep-sea
currents loaded with ice, which flowed upon the Campsie hills from
the W.hT.W., scooping out the valley which now occurs there, and
breaking up to a large extent the coal strata in that valley. The
debris of these strata would be swept along to the eastward; and
some of the nodules forming part of these strata would be buried in
the boulder clay now existing at Leith.

4. The cases which I have just been describing are of boulders,
large and small, which have come from remote places, now separated
by an intervening tract of dry land from the present sites of these
boulders.

(1.) But there are cases of boulders which to reach their present
sites must have crossed arms of the sea , even now of considerable
depth and extent. In such cases, the theory of local glaciers is,
of course, scarcely conceivable.

Thus on the Island of Islay, the Committee’s last Report refers to
several large boulders of rock, differing from any rock known in

4 z

VOL. IX.

702

Proceedings of the Royal Society

the island. At least, such was the opinion I formed after a
week’s ramble, and after inquiring among intelligent persons well
acquainted with the rocks of the island.

So also in the Island of Kerrera, opposite to Oban, there are
numerous blocks of grey granite, though no rocks of any kind of
granite occur in the island.

On the small island of Staffa, consisting entirely of basalt and
greenstone, I found boulders of red granite and gneiss, which
probably came from the Mull mountains, situated to the N.E.
(Committee’s 2d Rep., p. 157).

(2.) In Nairnshire there are many conglomerate boulders of huge
size, and angular in form, which must have been transported across
what is now the Cromarty Firth from Ross-shire. They are at a
height of from 400 to 600 feet above the sea. (First Rep. of Com-
mittee, p. 42.)

Other examples are afforded by the black granite boulders at
Appin and in Loch Creran. Specimens of these are now on the
table. As the present Report gives a full explanation regarding
these boulders, I do not require to repeat how, when these speci-
mens were submitted to Professor Judd of London, who has made
the igneous rocks of the West Highlands a special study, he
gave his opinion that there was no rock of the same description on
the mainland, and that it was to be found only in Mull. From
that island, therefore, these boulders must have been transported, and
across a sea, which even now has at one place a depth of 100
fathoms, but which transportation probably took place at a period
when the sea stood hundreds or even thousands of feet above
its present level, or when the land sat that much lower in the
ocean.

(3.) If Professor Judd’s opinion of the Loch Creran and Appin
boulders be correct, it goes far beyond an explanation of the boulders
in these localities. For example, the Island of Lismore, whose rocks
are entirely limestone, has on it many boulders of granite, which
probably also came from Mull, inasmuch as Lismore lies between
Mull and Appin (Com. 2d Rep., p. 157). In Lochaber, there is the
hill called Craig Dhu, about 2000 feet in heig'ht, so called, I believe,
from the great number of black granite boulders resting on and near
its top. These boulders, on account of their peculiar colour as well

of Edinburgh , Session 1877-78.

703

as position, attracted the notice of Professor Hicol and Mr Jamieson;
and they are mentioned in both of my recent papers “ On the
Parallel Roads.” (See also Committee’s First Report, p. 39.)

In these papers I had occasion to point out how the position of
the boulders both in Glen Roy and Glen Spean indicated that they
had come — not down these glens, but up the glens. If the boulders
at Loch Creran were rafted on ice from Mull by a sea current
flowing eastward, the position of the boulders in Glen Roy and
Glen Spean could be explained in the same way.

(4.) There is another fact connected with the position of boulders
in the West Highlands, and indeed over Scotland generally, which
receives explanation from Professor Judd’s paper “ On the Ancient
Volcanoes of the Hebrides,” I mean the high position of many large
boulders.

In the Committee’s Second Report notice is taken of a remark by
the Ordnance Surveyors (p. 157), that in the Stratherrick district,
where the highest hills are about 2900 feet above the sea, the
boulders on the sides of these hills extend down to a level of
about 2250 feet, bid not lower.

In Fortingall parish (Perthshire) a gneiss boulder, weighing above
400 tons, is lying on clay slate rocks at a height of 2500 feet, being
very near the ridge of clay slate hills. The gneiss hills form a
range about 20 miles to the north and north-west. (Committee’s
First Report, p. 49.)

On the Fannoch Mountains (Ross-shire) a gneiss boulder of about
130 tons weight lies on a water-shed at a height of 2000 feet above
the sea. (Committee’s First Report, p. 49.)

On Schehallion (Perthshire) blocks of grey granite are seen at a
height of 3000 feet. (Committee’s Second Report, p. 173.)

On the top of a hill in Lochaber, exceeding 3000 feet above the
sea, there are granite boulders. (Paper on Parallel Roads, Tr. of
Soc. vol. xxvii. p. 740.)

How where are there at present in Scotland ranges of mountains
from which fragments could have been transported to such heights as
those above named 'l There are now none such. Isolated peaks there
are, but none exceeding 4300 feet ; and of these there is but one, in
the West Highlands (Ben He vis), though it is from the westward
that the great bulk of the boulders which overspread Scotland have

704

Proceedings of the Royctl Society

come. Professor Judd’s paper, giving reasons for believing that there
were in Pliocene times mountains in Skye, Mull, Ardnamurchan,
and even in Rum, some of which reached to a height of at least
14,000 feet, solves the difficulty, and explains many other curious
facts besides.

For example, there is a series of granite boulders containing
unusually large crystals of quartz, felspar, and mica, which occupy
the straths between Fort- William and Kingussie. A boulder near
Fort-William is 1500 feet above the sea, and from its position
appears to have necessarily alighted on the hill from the westward
(Committee’s 2d Report, p. 161-2). If the sea stood at 2000 feet
or more above the present level, the valleys of Lochaber and the
Spey would be occupied by sea, and through them a current could
flow from the ocean on the west to the ocean on the east. The
summit level now between Lochaber and Strathspey is 850 feet
above the sea, so that if the climate at that time was such as to
allow of glaciers among the mountains and of floating ice on the
sea, there would be means of transporting boulders from Mull to
Lochaber and Strathspey.

5. There are several other instructive features connected with
boulders brought out in this as well as in previous Reports.

(1.) The different shapes of boulders.

The Appin boulders are round shaped, whilst the Loch Creran
boulders are angular, though the rock composing them is the same.
The former are known in the district as “ the round stones of Appin.”

These Appin boulders are on the shore of the Linnhe Loch,
through which in former times there must always have been
a rapid current flowing, between the high mountains, forming the
Glen-na-Albin or Great Glen of Scotland.

If icebergs then floated on the sea, these boulders must have
undergone much pushing and rolling ; whereas the Loch Creran
boulders, being in what would then be only an arm or inlet from
the main channel, would be exposed to no such friction.

In reference to the Kyle or sea strait, in what is now the line
of the Caledonian Canal, the grinding to which the rocks on the
sides of the valley have been subjected, is well seen at Cullochy
on the north side, and at Inverfarrignig on the south side of the
canal.

of Edinburgh, Session 1877-78.

705

(2.) Another common feature presented by boulders in Scot-
land is, that when they are longer than they are broad, the
longer axis is parallel with the direction in which the boulder had
been transported. Very frequently also, when one end is sharp
and the other end broad, the former points towards the direction
from which the boulder has come. On the theory of icebergs and
floating ice this feature is intelligible ; on any glacier or ice sheet
theory it is not.

(3.) The existence of striae on boulders, and the circumstance
that these striae are sometimes deeper at one edge than on the rest
of the surface, is a new fact brought out in this last Report (page
688).

6. In several parts of the Report allusion is made to the evidence
which boulders seem to afford, of the enormous denudation which
there must have been in the district where these boulders are
situated (pp. 662-667).

7. Notice is also taken in two districts of the West Highlands
of horizontal terraces on the sides of hills, up to a height of 1800
feet above the sea.

If these are to be ascribed to sea action, as suggested in the
Report, they would only show that Scotland possesses the same
features in this respect as Norway, Sweden, and America, where
there are horizontal terraces to even greater heights. It is only
reasonable to expect that in the north of Scotland such records
of the ocean should be discernible, considering the enormous beds
of sand and gravel found at great heights in many of the moun-
tains. On Schehallion (Com. 2d Rep., p. 173) there is gravel up
to a height of at least 3000 feet.

In reference to the suggestion, that these terraces on the sides of
mountains in the Highlands are marine, it is not unimportant to
observe, that similar horizontal terraces at high levels occur also in
lowland districts. Mr James Geikie, in his “ Great Ice Age,”
refers to a series of “high level terraces of gravel and sand at
Eaglesham,” about 12 miles S.W. of Glasgow, the highest being 800
feet above the sea. “ I have also traced them,” he adds (page 248),
“on the Moorfoots, up to 1050 or 1100 feet; and these, like the
Eaglesham beds, seem equally to require the agency of the sea.
Still farther south, high level shelves of gravel and sand have been

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Proceedings of the Royal Soeiety

detected by my colleague, Mr Skae, in Mthsdale, at a height of 1250
feet above the sea.”

8. Lastly, may I be permitted, as there is still a wide field for
farther investigation, to express a hope that the Boulder Committee
may be re-appointed, and with additional labourers to carry on the
work. I will he happy to he allowed to remain on the Committee,
hut I wish to resign the honour of being Convener. I begin to find
that I am now not able for the hill-climbing and trudging across
Highland moors and morasses, which boulder-hunting requires.

Edinburgh , 24 th May 1878.

At a Meeting held this day, the Council re-appointed the Boulder
Committee, with the addition of Dr Andrew Fleming, M.D. ;
William Jolly, Inspector of Schools, Inverness ; and Balph Bichard-
son, Secretary of the Edinburgh Geological Society ; and agreed to
express a hope, that Mr Milne Home would continue Convener of
the Committee.

The Council further agreed, that the “ Kemarks ” by Mr Milne
Home, at the Society’s meeting on the 20th inst., when he presented
the Committee’s Fourth Beport, appear in the Society’s Proceedings,
along with the Beport.

J. H. Balfour, Secretary.

The Boulder Committee now consists of the following Fellows : —

Sir Bobert Christison, Bart.

Sir Charles Wyville Thomson.

Bev. Thomas Brown, Edinburgh.

Dr Andrew Fleming, M.D., Edinburgh.

Professor Archibald Geikie, Edinburgh.

William Jolly, Inverness.

Dr Arthur Mitchell, M.D., Edinburgh.

Professor Nicol, Aberdeen.

Balph Bichardson, Edinburgh.

Thomas Stevenson, C.E., Edinburgh.

David Milne Home, LL.D. {Convener).

of Edinburgh, Session 1877-78.

707

Monday, 3 d June 1878.

Sir C. WYVILLE THOMSON, Vice-President, in the Chair.
The following Communications were read : —

1. On the Splitting up of Electric Currents, as detected by
the Telephone, and the founding thereon of a Sounder to
call attention from one Telephone to another. By R. H.
Bow, C.E.

The telephone is of no use as a “ far-speaker,” without some
means of calling the attention of the attendant at the distant
station. Nothing could well he better than the “ electric-hell call,”
and the sounder which I am about to describe makes no preten-
sions of competing with the bell, except on the points of simplicity,
cheapness, and facility of use ; and although its employment is
limited to short length lines, it may be assumed that it is upon
short length lines that the telephone will be most frequently used.
I have had this sounder in experimental use for more than three
months, and have shown it to many persons as a very obvious
expedient. However, as it does not appear to have been referred
to in any publication, I venture to bring it as a Note before the
Society; it is of too trilling a nature to he made the subject of a
formal paper.

In any of the sounders I have seen described, the battery, or
other source of electrical excitement, has been placed in simple
circuit with the pair of telephones, or put into circuit with the
distant one. In the proposed method of sounding, by means of a
galvanic battery, the battery is kept separate, and, when used, the
short wire from the one electrode is rested against one of the wires
of the telephone, while the wire from the other electrode is slid
with a very gentle vibrating touch upon the other wire leading from
the telephone. On the well-known principle of derived currents ,
we know that the greater portion of the electricity will pass through
the shorter or less resisting circuit of the nearer telephone, and yet
that there will be a not inconsiderable portion diverted to travel round
by the distant one ; and this, if the distance be not very great, and

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Proceedings of the Royal Society

the telephones be of suitable construction, will suffice to elicit
sufficient noise at the distant station to call the attention of any one
in the same or even an adjoining apartment ; the noise given out
by the distant telephone will not be altogether due to this diverted
current, but will owe part of its volume of sound to telephonic
sympathy with the great agitation produced in the one near the
operator.

Before entering into any details as to the construction of tele-
phones best suited for this mode of sounding a “ call,” and for short
distances, permit me to describe two experiments upon the detec-
tion of derived currents by means of the telephone.

Fig.

1.

Fig. 1 represents a wire of about 320 feet in length, bent so as to
bring the middle of its length near to the telephone T, to which its
extremities are attached ; G is a battery of one cell, and A and B
the wires from its electrodes ; one of these, A, is fixed to the long
wire at a ; the other, B, is movable at b , the point b being taken at
different distances from a. When the length of a-b is taken equal
to from 3 to 4 feet, the noise emitted by the telephone might
be sufficient to act as a call, although only about 1 per cent, of the
current from the battery can then pass through the telephone ;
when the length of a-b is reduced to 1 foot, the sound from the
telephone may yet be heard several feet away, and as the distance
of a-b is decreased, the telephone must be brought nearer and
nearer to the ear in order to hear the crepitating sound ; with a-b
equal to 3 inches, it may be heard 3 inches off ; and when the
telephone is held against the ear the distance of a-b may usually be
reduced to less than a quarter of an inch before the sound is lost.
Now, when the length of a-b is one quarter of an inch, the strength
of the diverted current passing through the telephone used would
only amount to the one twenty-thousandth (-2-^w) of that circulat-
ing through the battery. But I have now to note a very puzzling
circumstance. Sometimes-, under conditions I have not been able

of Edinburgh, Session 1877-78.

709

to determine, the crepitating sound was found not to cease even
when b and a were brought together, but continued to be heard
when the one wire, B, was moved upon the other A, at e. Here
there can be no dynamic current produced in the long wire. I
shall not detain you with my speculations on the subject ; but I
should mention that the wire was very imperfectly insulated.

The second experiment gives an interesting practical example of
the interference of one pair of telephones with another pair, due to
the splitting up of currents. The rough diagram, fig. 2, will serve
to explain the arrangement. A and A' constitute one pair of tele-

phones, the single connecting wire measuring 60 feet ; B and B' are
another pair of telephones — these are connected by a copper wire
270 feet long; for the return currents the gas pipes and earth are
employed. The gas pipes are indicated by dotted lines ; M and M'
are gas metres belonging to different houses ; and P and P' are the
gas mains in different streets, and at a direct distance apart of about
400 feet. It will be observed that the gas pipe from C to M is
common to the two circuits. Now, it was soon noticed that when
the battery-sounder was made use of at A, it caused a sounding not
only in A', as intended, but also in B, sufficiently loud to be heard
several yards off if attentively listened for. This noise was, of
course, due to a derived current splitting off at C, and making the
long circuit round by B, B', M', possibly to the gas main P', and
thence to P and back by M, where it rejoins the principal current
on its way to A. And using the battery at any one of the tele-
phones causes more or less noise in all the four. But the small
amount of sound produced by such straying currents is not likely
to cause confusion.

The Telephones used with the Battery- Sounder. — If it were
attempted to use the sounder in combination with telephones con-
structed in accordance with Professor Bell’s instructions — that is,

VOL. ix. 5 A

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Proceedings of the Royal Society

having coils so long as 180 feet of wire so thin as No. 36 — com-
parative failure would result from the very great resistance offered
to the current. We must try to do with coils offering an insignifi-
cant amount of resistance.

I find that the mode of arranging the parts of the telephone has
a great influence on the efficiency, and the construction I have
found up to the present time to he the best is as follows : — Taking
a 3-inch horse-shoe magnet, I break off about half an inch from one
leg ; the nick made to indicate the north end is usually at about
this distance from the extremity, and the breaking of it there is an
easy operation. I then round the unbroken end on a grindstone,
and next gum a strip of thin paper round that leg, and upon the
paper coil the desired length of silk-covered wire. Taking next a
piece of wood 4x4 inches or 4 x 5 inches, and half an inch thick, a
hole 2 inches in diameter is cut cleanly through it, and crossing the
hole is fixed, in letter T fashion, another piece of wood 4x3 inches ;
on this latter piece the magnet is laid with its south or coil-covered
eud projecting centrally into the hole, and it is fixed down by one
screw passing through a small cross piece of wood placed above it.
This admits of after-adjustments being very readily made. The
ferrotype plate, 2J inches in diameter, is laid as a cover over the
outer aspect of the 2-inch hole, and secured there by the usual ring
of wood which constitutes the ear or mouth piece.

With such an instrument placed at A, fig. 2, and another tele-
phone at A', I have experimented on the length of coil needed.
Four or five feet of wire gave very satisfactory results, speaking
being heard distinctly, and with sufficient loudness. I then tried
shorter and shorter lengths, and found the volume of sound to
become reduced certainly, but in a surprisingly small degree ; and
at last I carried the shortening so far, that only 4J inches remained
as a coil, and though the sound with this fragment was much
reduced, giving the voice a far-away character, conversation could
still be carried on. I did not think it necessary to push the reduc-
tion further, having become convinced that no very great length of
wire was needed for the coil to secure distinct hearing, at least for
short lines, say of quarter of a mile or less. And for the present I
have adopted a length of 9 feet of No. 28 wire (weighing 6 grains
per foot length) as a satisfactory coil, presenting a resistance of only

of Edinburgh, Session 1877-78.

711

one-third of an ohm, in place of the twenty or thirty ohms when the
coil is made up of 180 feet of the much finer wire.

I have had no opportunity of satisfactorily testing the limits to
which the sounder is restricted, but it would probably work well
enough when the resistance did not exceed ten or fifteen ohms per
Daniell cell. A marked advantage is usually found to attend the
sending of the currrent in that direction, which increased the power
of the magnets of the telephones. And in using the sounder a little
skill will elicit a considerably augmented effect.

The principle of split currents may be applied to other purposes ;
it might offer a ready method of communicating with two adjoining
stations on a railway from any intermediate point — that is to say,
at any point between the two extreme telephones we could attach a
battery or a telephone for sounding to, or communicating with, the
attendants at the extreme telephones ; or, if a battery be permanently
included anywhere in the circuit, a wire alone, at any point on the
line, offers the means of sounding the telephones at both stations,
the wire being so used as to form an intermittent connection
between the earth and the telephone line ; and this might perhaps
be practicable even from a train in motion, the engine and rails
taking part in the earth connection.

2. An Account of some Experiments on the Telephone and
Microphone. By James Blyth, M.A.

Dr M£Kendrick stated, that by applying the microphone or
carbon-interrupter of Hughes to the membrane of a phonograph, he
had succeeded in using the latter as a transmitting instrument.
With such an arrangement, speech could be heard in the distant
telephone even after it had become inaudible near the phonograph.
He also mentioned that a tambour of Marey, used in physiological
experiments, spoke distinctly when the fine point at the end of the
lever was applied to the marks on the tinfoil of the phonograph.
When a tube was carried from the tambour to the ear, distinct
speech could be obtained from phonographic tracings on copper foil,
which were scarcely perceptible to the eye. This method also got
rid of the difficulty of having the tinfoil impressions quickly rubbed
out, as happened when the stillette of the phonographic membrane

712

Proceedings of the Royal Society

was employed. He also introduced to the Society a phonograph
made by Messrs Macgillivray and Scohie of Glasgow, which, for
loudness, was superior to any one he had yet heard.

3. Note on a Variation of the Microphone. By
R. M. Morrison, D.Sc.

Following out a suggestion made by Mr Seabrook in Nature of
May 30th, I mounted the three carbon blocks of Professor Hughes’
microphone on, not as Mr Seabrook recommends, a plate of 3 inches
diameter, but on a ferrotype plate about 6 inches by 4. This plate
formed part of the top of a box, thus —

Plate

This form I found to be extremely sensitive, as a piece of cotton
wool \ inch in diameter falling through 1 inch made a loud sound
in the telephone. When the plate was lightly brushed by a camel’s
hair brush the sound produced in the telephone could be heard a
yard away. A small clock placed on any part of the table on which
the microphone stood could be heard distinctly ; also a tap on the
table, or even walking on the floor, each step producing a clang in
the telephone. On speaking into the open part of the box the
words spoken were distinctly and loudly heard in the telephone,
notwithstanding the difficulty of hearing words spoken by one’s self
at the same time.

4. On the Action of Heat on some Salts of Trimethyl-Sulphine.

Part II. By Prof. Crum Brown and J. Adrian Blaikie, B.Sc.

{Abstract.)

In the former paper on this subject, the authors stated that
when hyposulphite (thiosulphate) of trimethyl-sulphine is heated
to about 135° C., it loses sulphide of methyl to the extent of 23*58
per cent., the salt at the same time fusing to a clear colourless
liquid. On cooling, this solidifies to a hard, very hygroscopic crys-
talline mass.

of Edinburgh, Session 1877-78.

713

Analysis agrees with the formula

The solution of the substance does not decolourise iodine solution.
These results point to

as the probable rational formula of the substance.

Sulphite of Trimethyl- Sulphine. — This salt was obtained by the
action of sulphurous acid on the hydrate. It crystallises well, but
there is some difficulty in preparing a perfectly normal salt. The
salt, as nearly normal as possible, does not, like the hyposulphite, give
up its water of crystallisation in the cold over anhydrous phosphoric
acid; at 140° C., however, it becomes anhydrous. Heated to 175°
C. it gives off sulphide of methyl — 8-3 grammes lost 2-32 grammes,
or 27 '95 per cent. On cooling, the clear liquid residue solidifies,
forming a hard, very hygroscopic crystalline mass. This substance
was so deliquescent that no analysis of it was made. The mode of
formation leads to

as its most probable formula.

Note received on July 24, 1872. — In order to ascertain the nature
of the crystalline substance obtained by the action of heat on the
sulphite of trimethyl-sulphine, the authors converted it, by double
decomposition with iodide of potassium, into the corresponding
potash salt, which was purified from the iodide of trimethyl sulphine
by crystallisation. This potash salt was found to agree in pro-
perties and composition with the “ sulpho-metholate,” or “ methyl-
sulphonate ” of potash —

The bearing of this fact on the constitution of the sulphites is
obvious.

0

K— 0— S— CII3

0

714

Proceedings of the Pogal Society

5. On a Class of Determinants. By Mr J. D. H. Dickson,
Tutor of St Peter’s College, Cambridge.

6. On the Wave-Forms of Articulate Sounds. By Professor
Fleeming Jenkin, F.E.S., and J. A. Ewing, B.Sc.

{Abstract.)

By the help of the phonograph we have continued the investiga-
tion described in a previous Communication (Proc. R.S.E., p. 582),
and have now obtained about two hundred magnified traces of the
phonographic records of vowel sounds spoken and sung by various
voices, and of these sixty-five have been already subjected to har-
monic analysis, extending as far as the sixth partial tone. In each
case the results have been accepted as satisfactory only when, after
the magnified trace had been obtained, the record on the tinfoil of
the phonograph still gave the vowel sound satisfactorily. Our
attention has hitherto been almost exclusively directed to the vowels
u (the vowel sound in “ food,”) and o (as in “ oh,”) both of which
are well spoken by the phonograph. The results, which are still
incomplete, are briefly as follow : —

When a vowel sound is continuously sung without change of
pitch or quality, the wave-form produced is of remarkable constancy,
showing that the compound sound does not contain any, or at least
any important, constituent which is inharmonic to the prime tone.

A naturally high man’s voice, with the comparatively small range
/ to f saying u at any pitch throughout its range, produced a wave-
form which was substantially a simple harmonic curve of length
corresponding to the pitch. The upper partials, when present at all,
were present only very feebly. Thus u sung on iS gave a prime
whose amplitude was 25 (in the unit of measurement used), the second
partial was only 0*8, the third IT, and the others inappreciably
small.

When the same voice spoke o anywhere throughout the same
range, it produced a trace which in every case consisted of a strong
prime and a strong second partial (that is to say, the octave of the
prime), the higher partials being feeble or absent. Experiments on
this part of the scale with various voices proved that the proportion
which the amplitude of the prime bore to the amplitude of the

of Edinburgh, Session 1877-78.

715

second partial might vary greatly at any one pitch, although the sounds
were all sung or spoken as o, and received by the ear as (generically)
that vowel. For example, on b one voice gave the ratio of prime
to second as 1 to 0’87, while another voice on the same note gave
the ratio 1 to 1*8. In any one voice there is not very much change in
the ratio in passing from note to note. When the pitch is as high
as d' or higher, the ratio of prime to second is decidedly greater
than on the lower notes of this range. It is probable that the ratio
is a minimum for any one voice about the pitch 5b, but this is a
point requiring further investigation. We have not yet got any
satisfactory o’s above /'.

When, however, the investigation was carried lower in the scale
by help of voices of a wider range, several much less simple pheno-
mena presented themselves. Voices capable of singing bass, when
singing u down the scale gave the usual simple harmonic from above
a ; but, at or near that note a remarkable change suddenly took
place in the wave-form given by the vowel sound u. At that point
it became a duplex wave, with a very small prime, which corre-
sponded to the pitch, and an immensely strong second partial, the
ratio of amplitudes being somewhere about 1 to 4. This form
continued as the voice went down the scale ; but in addition to the
very strong second partial a weak third appeared, which became
pretty strong on c. We cannot say that we have got true and
articulate w’s at any lower pitch.

The voice of small range mentioned at the beginning of this paper
continued to give the single simple harmonic form for u down to
/, below which it could not go. Two other voices experimented
with agreed in making the change at or near a.

The excessive weakness of the prime in the lower, or what we
call the duplex, form of u shows how weak a prime tone may be
as compared with its upper partials, and yet fix the musical pitch.
It also shows how small even the prime may be when not reinforced
by oral resonance. The primes of the duplex ?As, even when
loudly uttered, were absolutely as well as relatively much weaker
than those of the o’s already described.

The experiments with u seem to point to the conclusion that so
long as the simple form is given the mouth cavity is adjusted so as
to reinforce the prime exclusively, whatever be the pitch. When

716

Proceedings of the Royal Society

the duplex form is reached the cavity must he suddenly changed so
as to he approximately if not exactly in unison with the second
partial. A voice singing u up the scale may sometimes carry the
duplex form as high as feb, hut the vowel quality of an u so spoken
is apt to approach o . When attempts were made to slur either up
or down, past the place at which the change occurred, one or other
of two things took place — either the sound died away almost
completely while the critical point was being passed, or the vowel
quality changed form u to o for an instant. This has been observed
both directly and by examination of the magnified phonographic
record, in which either an almost blank space or the well known
wave-form of o might he seen.

An examination of the sound o through the lower regions of the
scale, and by the help of several bass voices, did not show any such
sudden change as took place in u , hut the number of partials con-
spicuously present became more and more numerous as the pitch fell.
The third partial began to appear about /, and on d and e the
prime second and third were all strongly present, the prime being
the weakest of the three, and the second the strongest. On c the
fourth partial was moderately strong, the third stronger, the second
stronger still, and the prime weaker than any. The first four par-
tials were all conspicuous on B. On Bh the fourth was much
stronger than any of the others, and the prime was the weakest of
the lower ones. The same description applies to A. On G the
fourth was still much the strongest, and the fifth appeared weakly.
The lower ones were weak. On F the fifth was much the strongest,
but the prime, second, third, and fourth were all distinctly present.
We have not got any trace good enough for analysis below F. We
reserve the numerical result for more detailed publication.

The hearing of our experiments on the theory of vowel
sounds is very important. For a considerable range it will he
seen that the constituents of o and u might he simply described,
with no reference whatever to absolute pitch — the u always being
a simple tone, and the o a compound of two simple tones an
octave apart.

When, however, certain limits are passed, phenomena appear
which are evidently connected in some way with an absolute pitch.
It seems, however, that this connection is rather due to the neces-

of Edinburgh, Session 1877-78.

717

sities of the mouth than to the requirements of the ear ; for, as stated
above, one voice will give a simple harmonic curve for u, while
another gives (at the same pitch) a double curve for a sound which is
intended for the same letter in the same language, and which is at least
generically the same vowel. This fact suggests that the mouth,
being unable to shape itself so as to continue the simple form of the
letter, adapts itself in some way so as to produce what may perhaps
be termed an imitation. It is by no means impossible that this
imitation may in some cases be produced by a recurrence to the
form used for the same letter at a higher pitch. If this be so, then
the hypothesis of a constant cavity for a given vowel sound would
be true for the letter u when pronounced on notes an octave or a
twelfth apart, although not for intermediate notes.

When we examine the sound o we find less necessity for insisting
on recurrence or any tuning of the mouth cavity. A fair approach
to the phenomena observed might be obtained by assuming a constant
mouth cavity, having a pitch of maximum resonance near 6'b, as
stated by Helmholtz, and reinforcing tones over a large range of
nearly two octaves — from f" to /, or thereabouts. There are, how-
ever, some peculiarities in the constituents which suggest that the o
cavity may also be adjustable. Our results are not inconsistent
with the assumption that the cavity is slightly altered or tuned so
as to bring the maximum resonance approximately into unison with
that upper partial of the prime sung which lies nearest to &'{?. This
hypothesis would allow us to diminish the very large range of rein-
forcement which the constant cavity theory requires, although even
an adjustable cavity must still reinforce tones over a considerable
range. Further experiments are required to determine how the
mouth actually produces the results obtained, but is clear that the
idea of relation between the constituents must be combined
with that of absolute pitch in any complete vowel theory. The
relation may, however, depend for some vowels, though hardly
for u, on the simple range over which the reinforcement
acts. The pitch of maximum resonance in the o cavity given
by Helmholtz is V b, and this, on either hypothesis, agrees well
with our results. It is either the pitch of maximum resonance of
the constant cavity, or the pitch near which the upper and strongest
resonance is to be found, where the cavity is tuned. It may be

VOL. ix. 5 B

718

Proceedings of the Royal Society

observed that, in the case of this letter, possibly the idea of a
tuned cavity may be true for singing, and that of a constant cavity
for speech.

7. On the Electric Conductivity of the Bars employed in his
Measurements of Thermal Conductivity. By Prof. Tait.

The following Gentleman was duly elected a Fellow of the
Society : —

Dr J. J. Kirk Duncanson, 8 Torphichen Street.

Monday , Vlth June 1878.

Sir WYYILLE THOMSON, Vice-President, in the Chair.

The following Communications were read : —

1. On the Biliary Secretion, with Reference to the Action
of Cholagogues. Part II. By Professor Rutherford,
F.R.S.S, L. and E., and M. Vignal.

(Abstract.)

The method of experiment hy which the following results have
been obtained has been described in the abstract of Part I., pub-
lished in the “Proceedings” February 1877. All the experiments
were performed on dogs. In the previous abstract the effects of 29
different substances were briefly stated : —

30. Dilute nitro-hydrochloric acid is a hepatic stimulant of consi-
derable power.

31. Jaborandi is a very feeble hepatic stimulant.

32. Calabar bean stimulates the liver, but not powerfully, unless
it be given in very large doses.

33. Atropia sulphate antagonises the effect of Calabar bean on
the liver, and thus reduces the hypersecretion of bile produced by
that substance. It does not, however, arrest the biliary secretion ;
and when given alone, does not notably affect it.

34. “ Menispermin,” a resinous matter obtained from the Yellow

of Edinburgh, Session 1877-78. 71 9

Parilla, does not stimulate the liver. It slightly stimulates the
intestinal glands.

35. “ Baptism,” a resinous matter derived from the Baptisia
tinctoria, is a hepatic and also an intestinal stimulant of consider-
able power.

36. “ Phytolaccin,” a resinous matter prepared from the Phyto-
lacca decandra, is a hepatic stimulant of considerable power. It
also slightly stimulates the intestinal glands.

37. Sodium Benzoate is a powerful stimulant of the liver. It
does not stimulate the intestinal glands.

38. Ammonium Benzoate stimulates the liver, but not quite so
powerfully as the sodium salt of benzoic acid. It does not stimulate
the intestinal glands.

39. Benzoic acid stimulates the liver, but owing to its insolu-
bility, its action is less rapid and much less powerful than that of
its salts.

40. Sodium’ Salicylate is a powerful hepatic stimulant. It does
not notably stimulate the intestinal glands.

41. Ammonium Phosphate is a moderately powerful stimulant of
the liver. It is not an intestinal stimulant.

42. Tannic acid does not affect the biliary secretion.

43. Hyosciamus does not notably affect the biliary secretion, and
does not prevent such a stimulant as sodium salicylate from aug-
menting it.

44. Morphia does not affect the biliary secretion, and does not
prevent the stimulating effect of such a substance as sodium sali-
cylate.

45. Pure diluted alcohol does not affect the biliary secretion.

46. Potassium iodide does not affect the biliary secretion.

47. Yeratrum viride has no notable effect on the biliary secretion.

48. Manganesium sulphate is not a hepatic stimulant. It power-
fully stimulates the intestinal glands, and like other purely purga-
tive agents, such as magnesium sulphate and gamboge, it indirectly
lowers the biliary secretion.

49. Ailanthus glandulosus is an intestinal but not an hepatic
stimulant.

50. Acetate of lead somewhat diminishes the biliary secretion,
probably by a direct action on the liver.

720

Proceedings of the Eoyal Society

51. “ Hydrastin,” a resinous matter, prepared from tlie root of
the Hydrastis canadensis , is a hepatic stimulant of considerable
power. It also slightly stimulates the intestinal glands.

52. “ Juglandin,” a resinous matter, prepared from the root of
the Juglans cinerea , is a hepatic stimulant of considerable power.
It also slightly stimulates the intestinal glands.

Thus, by means of a new and precise experimental method, the
physiological pharmacology of one of the most important organs of
the body has been in this research worked out as far as at present it
ajepears desirable to proceed, and knowledge that is definite and
reliable, because obtained by a method of accurate measurement,
after the elimination of disturbing factors, has by this research been
substituted for the vague traditions of the past.

The effects of fifty-two medicinal agents upon the liver have been
investigated, and the vast majority of the conclusions are in complete
harmony with the results of clinical observation. Very many new
facts are, however, given to the physician, and even as regards well-
known substances, our knowledge of their effects on the liver is
now of a character very different from that which previously ob-
tained.

All the experiments relate to the bile-secreting and not to the bile-
expelling mechanism. The authors do not intend to investigate the
effects of medicinal agents on the latter, as this point appears to
them one of very minor importance compared with the subject of
the above research.

The following remarks indicate the position in pharmacology of
the above results. Of necessity, the influence of a drug upon a
diseased state is the ultimatum of pharmacology, and every experiment
upon a healthy bodily system, whether of man or animal, is merely
ancillary to experiments with the drug in disease. Having discovered
that this or that drug stimulates the healthy liver of a dog, we do
not infer that it must also stimulate the human liver in health, and
still less do we conclude that it must also have this action in disease.
The experiments on the healthy liver of the dog, on the normal and
on the abnormal human liver, are three sets of experiments closely
related, but still distinct. The facts derived from any one of the
three sets cannot be substituted for those of the other two. Each
set of facts has its own proper place. The above research, therefore,

721

of Edinburgh, Session 1877-78.

leaves it to the clinical observer to experiment on man with such
substances as sodium benzoate, sodium salicylate, baptism, euonymin,
sanguinarin, &c., and thereby to ascertain whether or not these
substances also stimulate the human liver; and of necessity it is also
left to him to ascertain in what diseased state the employment of
this or of that substance is most advantageous.

Other general conclusions have been already stated at the close of
Part I.

2. On a New General Method of Preparing the Primary
Monamines. Bv E. Milner Morrison, D.Sc.

3. On the Preparation and Properties of Pure Graphitoid and
Adamantine Boron. By E. M. Morrison, D.Sc., and E.
Sydney Marsden, B.Sc.

4. On Colour in Practical Astronomy, spectroscopically
examined. By Professor Piazzi Smyth.

Monday , 1st July 1878.

Sir WYVILLE THOMSON, Vice-President, in the Chair.
The following Communications were read : —

1. On the Disruptive Discharge of Electricity. By Alexander
Macfarlane, D.Sc., and P. M. Playfair, M.A.

[Abstract.)

During the months of May and J une of this session, we have
endeavoured to investigate certain questions suggested by our
experience of the discharge of electricity through the gases and
through oil of turpentine.

Ordinary paraffin- oil, when used as a dielectric, exhibits the same
phenomena as oil of turpentine. Gas is liberated by the passage
of the spark, and at the same time carbon is deposited. Once
produced, the gas bubbles make the passage of the spark more easy
through bringing the electrified surfaces nearer to one another; hence,

722

Proceedings of the Poycd Society

in taking a series of observations, it is necessary to get rid of the
bubbles after the passage of each spark. They were attracted gene-
rally to the positive surface, but sometimes to the negative. The
attraction was more marked when no jars were attached to the
Holtz ; it was not so powerful as in oil of turpentine, and was gene-
rally in the opposite direction.

The electrostatic force required to pass a spark through a layer
of paraffin oil or of turpentine is constant, whereas it is variable in
the case of air and other gases. For the observed differences of
potential plotted with respect to the thickness of layer give a
straight line through the origin, while in the case of the gases the
curve is concave.

The electric strength of the paraffin oil used was found to be 4,
of the turpentine 3 m7 ; air being unity.

To investigate the effect upon the electric spark of heating the
electrodes, we constructed electrodes of thick platinum wires placed
at right angles to one another — a suggestion we owe to Professor
Clerk Maxwell. When one of the wires was heated by a current
from a battery of four Bunsen elements, the electrometer deflection
was diminished by about one-fourth of its amount, and that
whether the wire heated was positive or negative. A similar
diminution was observed when the deflection for continued sparks
was taken. This diminution of the difference of potential must be
due to change at the surface of the wire ; for the air between the
wires (the shortest distance between the wires being 4 millimetres)
cannot be so much rarefied by the heating of the wire as to produce
the effect.

We have also investigated the effect upon the electric spark of
heating the air round the discs, the pressure being kept constant.
We have observed the deflections of the electrometer for a
constant spark for temperatures from 20° C. to 280° C., and find
that they indicate a curve, which slopes down gradually as the
temperature is increased, while the deflections during cooling give a
curve which is somewhat lower at the lower temperatures.

It appeared an important matter to ascertain whether the
electrometer used in all these observations gives deflections strictly
proportional to the inducing charge. To calibrate it by means of
cells would have required a very large number ; hence the following

723

of Edinburgh, Session 1877-78.

method suggested by Professor Tait was adopted. A charge was
put upon the inducing ball of the pair on the stand, and the
deflection read ; the charge was then divided by bringing an equal
ball into contact with the inducing ball, the deflection read, and so
on. The deflections were so nearly halved each time, that we may
infer that they are strictly proportional to the charge on the inducing
ball. We had arranged to verify our former observations in this
matter last Thursday forenoon (27th June) ; but as the deflection
on the scale always fell in the negative direction, and went to a
great distance beyond the proper zero when the dividing ball was
brought into contact, we gave it up. This effect was, doubtless, due
to a strong negative electrification of the air ; for the thunderstorm
came on immediately.

2. On the Wave Forms of the Vowel Sounds produced by the
Apparatus exhibited by Professor Crum Brown. By
Professor Fleeming Jenkin, F.Pt.S., and J. A. Ewing, B.Sc.

At a recent meeting of the Society, Dr Crum Brown exhibited a
gutta percha bottle of irregular form, which, when applied as a
resonance cavity to reeds of various pitches, gave very good imita-
tions of certain vowel sounds. By closing certain apertures in the
side of the bottle it could be made to say A (“father”), A (“ awe”),
0 (“oh”), and I (“machme”). When the cavity was kept con-
stant, and the pitch of the reed was altered, the same vowel con-
tinued to be given. Dr Crum Brown was good enough to lend us
the apparatus, in order that we might investigate the sounds given
by the bottle in the same way as we have been investigating certain
human vowel sounds, by obtaining and magnifying phonographic
traces, and then subjecting them to harmonic analysis as far as the
sixth partial tone. Of the vowels which the bottle speaks, 0 is the
only one which we have fully examined in this way when spoken
by the human voice, and we have confined our attention to it among
the artificial vowels also.

By using reeds of various pitches we have obtained curves or traces
of the artificial O’s sufficiently good for harmonic analysis on the
following pitches : — e, /jj, g, b , c', e'b, and e'. The pitch was in
each case determined by measuring the length of the traces. The

724

Proceedings of the Royal Society

vowel quality of the sounds, as repeated by the phonograph, was
exceedingly good, even better that the original sound, as the jarring
noise of the reed was lost. The sounds were thoroughly recognis-
able as 0, of perhaps a somewhat bright species. The table below
shows the amplitude of the successive partial tones, along with their
absolute pitch to the nearest semitone.

L

2

3

i

.

7

'"3

V

On e.

On fl

On g.

On b.

On d.

On

eb'.

On d.

dn

i

rd

o

4-3

r— 3 Q}

S 3
<■*

r-j

o

4-3

i

rP

o

4J

P

S s

rd

CJ

4-3

i

rP

rd

a

4-3

i

^ aj

O-i Td

S 3

rd

O

4-3

\

rd

o

E

E

C4

P P
<-*

£

E

H d

E

I.

3-8

e

4-3

4

9-8

9

91

b

4-2

d

2-9

eb'

21

d

II.

7’3

d

6-8

4

*9-0

9'

5’2

V

4*5

c"

2-3

eb"

31

e"

III.

3-9

V

2-8

4 ‘

4-8

d"

0-8

4"

0-5

9"

0-2

b b"

01

b"

IY.

21

e"

1-0

4"

1-6

9"

0-3

b"

0-4

c'"

0-3

eb

01

d"

Y.

0-6

4

0-3

bb"

0-8

b"

0-3

eb'"

0-3

d"

0-3

9"'

01

4"

YI.

0-2

V

0-2

4"

01

dm

0

4"

0-2

g"'

01

bbm

0-2

V"

It cannot be said that these figures show any specially strong
resonance on or close to tyf, which Helmholtz gives as the proper
tone of 0, but they do show a wide range of resonance, extending a
long way above and below that pitch. There is distinct reinforce-
ment as high as g", or even gjj\ and as low as e, if not lower, and
partial tones falling anywhere between these limits are more or less
reinforced.

The above analysis appears to show that a strong resonance on or
near b\>' is not essential to 0, and that this vowel effect may be satis-
factorily produced by other joint resonances above and below that
pitch.

In a previous communication we pointed out that if the view be
adopted that the constituents of the O’s, sung at various pitches by a
human voice, are due to the reinforcement caused by a constant oral
cavity, the results of our analyses showed that this cavity not only
has the property of strongly reinforcing tones close to bV , but must
also be capable of strengthening, more or less, tones widely distant
from that pitch, and extending over a large range. The analysis of
the artificial O’s now shows that a constant cavity may possess the
latter property in quite a sufficient degree.

of Edinburgh, Session 1877-78.

725

In order, however, to test this still further, we made the following
experiment. A tube consisting of a piece of cane of the same size
as one of the reeds was put into the neck of the bottle in place of
the reed, and the side apertures of the bottle were closed so as to
arrange the cavity for the vowel sound 0. The end of the tube was
then inserted in the ear, so that the whole apparatus acted as a
resonator to sounds from outside. Then, striking the keys of a
piano in succession, we observed what notes gave the peculiar
humming effect due to reinforcement by the resonator. On working
down the scale the resonance first became appreciable on gjfc'. It
then got stronger and stronger down to f" and e ", which were both
intensely and nearly equally strong. e\>" and d" were a little weaker,
but still very strong, and on cty' the resonance again became very
intense, c" was a little weaker, but also very strong. The reson-
ance continued as the pitch fell, being sometimes stronger and
sometimes weaker, g and /$' were both strong, — decidedly stronger
than could be accounted for by the reinforcement of their second
partials g" and /J". f was weaker, — so much so that the resonance
observed on it might be due to the second partial.

The presence of the upper partials in the notes struck made this
method of testing the resonant qualities of the cavity inapplicable
to pitches below those named. But the above cases, in which the
reinforcement was distinctly of the prime, sufficed to show that the
cavity would strengthen any tones between gfy" and fjf/, at least,
some more and some less strongly, while they left it an open ques-
tion whether there was not resonance down to a lower limit of abso-
lute pitch. Of course, it is to be observed that the bottle, when
applied to the ear in the manner described, might differ in its
resonant peculiarities from the same bottle applied to a reed, but its
range is probably as great in the former case.

When the bottle was arranged for the vowel sound A, and tested
in the same way, the resonance was perceptible as high as e'", and
the highest maximum occurred on c'". In this case also there was
reinforcement over a range of at least an octave.

Traces of the wave forms of the artificial O’s spoken of in this
paper will be given along with those of other O’s when the full
account of our work is printed.

5 c

VOL. IX.

726 Proceedings of the Royal Society

3. Notes on the Fungus Disease affecting Salmon. By A. B.
Stirling, Assistant Conservator of the Anatomical Museum
in the University of Edinburgh. Communicated by Pro-
fessor Turner.

It is widely known that a destructive epidemic has this spring
appeared among the salmon of the rivers Eden, Esk, and Nith.
The mortality among the fish has been so great as to cause consider-
able alarm among proprietors, salmon commissioners, taxmen,
anglers, and the general public.

The newspapers inform us that within three days the watchers
have taken out of the Esk as many as 350 dead salmon. All who
have examined the fish carefully, agree in referring the disease to
the presence of a fungoid growth.

The other fish in those rivers, as the smolts, trout, eels, lampreys,
minnows, pike, and flounders, are also said to be attacked in a
similar way to the salmon, aud fears are entertained that the disease
may become thoroughly established in the district.

In these circumstances, I have thought it might be interesting to
describe the condition of some of the fish which have come under
my observation. In March last my friend Dr Philip Hair of Car-
lisle sent me the fin of a salmon which had been affected by the
disease, and requested me to state if possible its nature. Unfor-
tunately, the fin was in a putrid condition when it reached me, and
as a result of the examination, I could only state to Dr Hair that
the disease was probably a fungoid one. A few days later I received
from Dr Hair a fine specimen of a trout, but it was not stated
whether the fish was taken alive or picked up dead. It was, how-
ever, quite fresh, and the effects of the disease were painfully
exhibited on the carcase. A hurried examination of this specimen
enabled me to inform Dr Hair that the disease was due to what I
had previously suspected, namely, a fungoid growth.

While examining this specimen, I observed entangled among the
fronds of the fungus foreign matter of various kinds, namely, torulse
or yeast fungus, triple phosphates, fecula, human hairs, hairs of the
cat and the mouse, also desmids, diatoms, shreds of dyed wool and
cotton, with other fragments of matter unknown to me. Respecting
the torulse, I, in my letter to Dr Hair, asked if their presence could

of Edinburgh , Session 1877-78.

727

be accounted for by bakeries or breweries in Carlisle, whose refuse
might have got into the river.

My letter was published by Dr Hair in the Carlisle Journal of
March 29th, and in the Field newspaper of March 30th, and as
worded it might have been inferred that I regarded the presence of
bakeries and breweries as the cause of the disease. This was of
course not intended. On 12th April I received two salmon and a
trout from J. Dunne, Esq., chief constable of Cumberland and West-
moreland, all of them in a diseased condition. Mr Dunne requested
me to make an examination of those fish, and hoped, on public
grounds, that I might be able to discover the true nature and cause
of the disease.

As a result of my examination of those fish I sent a preliminary
report to Mr Dunne. This report was forwarded to the Fishery
Inspectors, and was considered of so much importance that it was
published in the Times and many of the provincial and local
newspapers. Sir Robert Christison had also very kindly supplied
me with a number of specimens from the river Nith, all of them
affected with this disease. An examination of these has confirmed
me in the opinion expressed in the report above referred to. All
these fish had the disease in an advanced stage, being more or less
affected about the head, chin, branchiostegal rays, and fins in every
instance. One salmon had rubbed the chin till the lower jaw had
nearly separated at the symphysis, the skin was rubbed off the
branchiostegal rays, and the rays broken ; a trout had the upper
left jaw bare of skin, the bone worn and hanging loosely attached
to the cheek, the pectoral fin of the left side in rags, and the rays
worn to stumps.

Another salmon had the skin rubbed off the nose and crown, and
the matted fungus covered the bare parts; the dorsal fin was quite
destroyed, the strong anterior rays being reduced to stumps of half
an inch in length, and the remains of the fin bare, bleached, and
without membrane. Beneath the dorsal fin on each side were
spaces extending 3 inches forward towards the head, and 2J inches
backwards toward the tail, thickly covered with the fungus.
Besides these there were other spaces on the sides of the fish from 1
inch to 2 inches in diameter, all covered by the fungus, which gave
the fish a spotted appearance.

728

Proceedings of the Royal Society

This fish appears to have been alive when taken, as the skull and
brain had been punctured by the fisherman. The greater part
of this fish was cooked ; it was very firm and fat, and the three
persons who made a meal of it pronounced it capital. I tasted a
portion of the flesh from a part where the fungus covered the skin,
and could not detect anything different in the flavour from an
ordinary fishmonger’s salmon.

The fungus appears, in the first instance, to attack those parts of
the fish that are not covered with scales, as the crown, nose, sides
of the head, chin, throat, and the membranous parts of the fins.
From those parts the fungus extends by vegetative growth (which
seems very vigorous), to those portions of the surface of the body
which are covered with scales. On the sides of the fish where
small patches of the fungus were situated on the scales (and no
rubbing had taken place) no sore could be detected, and the fungus
was easily wiped off with the finger.

I may also mention that all the fish which I received from the
Eden river, both trout and salmon, were infested with tape- worms
of a large size, the worms being about 2 yards in length and ^-ths
of an inch in breadth. One of the salmon had from 60 to 80 yards of
those worms in the pyloric portion of the gut. Another salmon had
three varieties of worms in various parts of its alimentary canal.
ls£. In the stomach were many round worms, about 4 inches in
length, tapering to each end, and as thick as ordinary whip- cord in
the thickest part of the body ; many of those worms were entangled
among the gill rays, it being their habit to crawl there when the
fish dies, and from their presence in this situation they are called
gill worms by the fishermen. 2 d. A small spiral worm, which
attaches itself, by burrowing in the outer walls of the intestine, in
the fat and pyloric appendages. 3d. Tape-worms seated within the
pylorus and intestine.

On 30th May, I received from Sir Eobert Christison a large
salmon from the Mth. This fish was believed to have been to the
sea, after being attacked with fungus, and was captured on
its return. The specimen was a female, and had the roe about
one-fourth grown ; the viscera were very healthy, and no entozoa
were found in it. The head of this female is peculiar in having a
kip on the under jaw, and a cavity in the upper jaw to receive it,

729

of Edinburgh, Session 1877-78.

as in the male fish of the species. The right side of the head,
including the eye and nose, was very deeply rubbed and the bones
injured, but no fungus adhered to the injured part. The pectoral
fin on the same side had no membrane, the rays being hare, broken,
and separate from the muscles at their roots. There were several
patches on both sides of the fish, from which the scales were rubbed
off, but no fungus adhered to the rubbed parts. In several of those
rubbed parts, although the skin was unbroken, a portion of the
muscle, corresponding in breadth to the external injury, and half an
inch in depth, was in a pulpy condition ; beneath other rubbed spots
the muscle was quite sound. The dorsal, ventral, caudal, and anal
fins were all more or less injured by rubbing. No fungus adhered
to any of the fins except the anal, the rays here being reduced to
stumps of an inch or half an inch in length, on which a thickly
matted covering of fungus is seated. The branchiostegal rays are
very slightly rubbed, and are the only other part of the fish on
which the fungus remains. In my report to the Fishery Commis-
sioners in April last, I stated that the fish did not die of the fungus,
but of the injuries they inflict by rubbing in trying to rid them-
selves of the pest. As some objection was taken in regard to
this statement, I quote, in corroboration of my views, from a letter
published in the Field of 25th May last. The letter was written by
Commander Duncan Stewart, B.N. He says : — “ In regard to the
disease from which salmon are suffering in some of our rivers, it may
be of advantage that I should mention what I observed in a small
river at the head of Oastrie’s Bay in Siberia. I found the river
rather low, but with plenty of clear running water. But what
astonished me was to see thousands of salmon in all stages of disease
and death, some darting away, but soon stopping to rub the side on
the bottom or on a rock ; others were constantly rubbing, others
unable to rub. In those last cases large sores, from the size
of a shilling to that of a half crown, of a most filthy appearance,
were always present. Fish in which the scales had been rubbed off
would try to get out of my way, but I could kill them with a
stick ; those with the skin gone would rub themselves against
my trousers.”

Supposing this salmon from the Nith had been to the sea, and
had while there got rid of the greater part of the fungus with

730

Proceedings of the Royal Society

which it was affected, it had returned to the river in such a
mutilated condition, and with unhealed sores of such a nature, as in
all likelihood would have ultimately proved fatal. Besides, the fact
that the fungus was not killed by the salt water, but was found in
a highly vigorous condition on the parts to which it still adhered,
gives but small hope of any permanent benefit to diseased fish from
a visit to the sea.

The fungus belongs to Saprolegnieae, a natural order of doubtful
affinity — said to have the habits of moulds and fructification
algae. This order consists of the genera saprolegnia and achlya,
which are great enemies of fish and other animals preserved in
aquaria.

The filaments of the fungus arise free from the outer surface of the
epidermic layers of the fish, having neither branches nor articulations.
They are tubes, the walls of which are perfectly translucent, and in
their interior at irregular intervals are small groups of fine granular
matter.

The majority of the filaments are spear-shaped at their upper
terminations, and appear to be barren.

The prolific filaments, on the contrary, enlarge at their upper
extremities, and form elongated club-shaped chambers, in which
granular matter gathers. In the midst of this granular matter small
round bodies appear, and those enlarging, gradually develop into
spores. The prolific filaments apparently contain more granular
matter, and are of greater calibre than the other filaments. They are
evidently destined from the first to be the propagating media.

The spores escape by an opening in the summit of the chamber.
This aperture is not an original opening. It is produced in a some-
what remarkable manner — so long as the spores are unripe and unfit
for expulsion, a slender continuation of the filament projects from
the apex of the chamber in manner similar to the neck of a bottle.
At the point at which this joins the spore-sac, there is a slight
contraction, which goes on gradually increasing in depth. Ultimately,
when the spores are fully matured it drops off, and the aperture is
formed. The filaments forming the mycelium of the plant are
tortuous and branched ; they ramify in the mucous and epidermic
layers of the fish ; they do not penetrate the corium where there
are no scales. In other situations they never reach a greater

731

of Edinburgh, Session 1877-78.

depth than the outer surface of the scales ; they are tubular, the
whole plant being without septa forms a single individual of
apparently indefinite extent. The spores are variously shaped at
different stages, ovate and kidney being the commonest forms. They
are very minute, and require a power of 450 to observe them well.
The cilia are two in number, a longer and a shorter one, and are
situated at the long axis of the spore. They are difficult to observe,
and always disappear in permanently mounted preparations, although
the spores themselves remain unaltered in all other respects. When
the fungus is stained with logwood or picric acid, excellent
permanent preparations can be got. It has been stated that the
fungus dies with the fish. I have not found this to be the case; on
the contrary, all my observations have been made from dead fish.
Some of the specimens sent me from Carlisle by Mr Dunne were
mis-sent to Aberdeen, and returned to me on the seventh day after
the death of the fish, and yet I have scores of permanent prepara-
tions from these specimens, which show distinctly the characteristic
form of saprolegnia ferax.

I have also found the fungus perfectly identical in ail the
specimens I have examined, which consist of salmon, sea trout, and
river trout from the Eden, and salmon and grayling from the
Mth.

It has also been said that a salt solution destroys the fungus,
“which, melts in the solution like sugar in ivater .” On the contrary,
salt and water is an excellent preservative of saprolegnia ; masses of
it before me as I write have been in a salt solution for two months,
and it remains unaltered. Further, the salmon captured in
the Nith, which is believed to have gone to the sea in order to
get rid of the fungus, had the fungus growing vigorously on several
parts of its body. The fungus must either have instantly attacked
the fish on its return to the river, or not have been destroyed during
its stay in the salt water.

Regarding the cause of the disease, I can offer no opinion further
than that some functional condition of the fish seems necessary for
the propagation of the fungus. The germs of saprolegnia ferax
must exist at all times, and in many places; and if so, there must
be a reason why fish are not constantly affected with the fungus and
in every river. I am persuaded that the condition of the fish

732

Proceedings of the Royal Society

is in some way either suitable or unsuitable for the propagation
and growth of the fungus. Whether this arises from too high
or too low condition, I am quite unable to say ; hut I may remark
that while some of the fish examined were in the kelt stage, others
were in a condition perfectly fit for food.

Saprolegnia ferax parasitic on the Salmon.

a. Barren filament, b. Prolific filament, c. Prolific filament, more highly

magnified.

4. On some New Bases of the Leucoline Series, Part I.
By Gr. Carr Bobinson.

5. On the Crystallisation of Isomorphous Salts.

By G-. Carr Bobinson.

It is generally stated that isomorphous salts are capable of crys-
tallizing together in any proportions, or that the isomorphous
elements which enter into them are capable of replacing one another
in any proportion; e.g., potash alumina alum and potash iron
alum can crystallise together in all proportions.

of Edinburgh, Session 1877-78. 733

Hauer * states that mixed crystals of alumina and chrome alum
grow in a solution of ammonia iron alum ; and, again, he states f
that the more soluble isomorphous salt completely hinders the solu-
tion of the less soluble, so that if solutions of common alum, chrome
alum, and iron alum be mixed, precipitation of the less soluble
alums will occur.

The present paper is the result of some experiments made with
the four alums — potash alumina, ammonia alumina, potash chrome,
and ammonia iron.

The solutions of the two first, potash alumina and ammonia
alumina, were obtained by saturating water at 100° C. with the
salts, and pouring off the mother-liquor from the crystals that de-
posited on cooling.

The chrome alum solution was obtained by saturating water with
the alum at a temperature carefully kept below that at which the
green modification of chrome alum is produced.

Whilst the solution of iron alum was made by saturating water,
acidulated with sulphuric acid, with the alum, at about 50° C.

The following experiments were then made and observed : —

a. When a crystal of potash chrome alum is placed in a solution
of potash alumina alum exposed to the air, the chromium is turned
out by the alumina, the interior of the crystal becomes granular,
whilst a clear shell of alumina alum grows over it, the faces of
which are finely striated.

b. When potash chrome alum meal is added to a solution of
potash alumina alum in a well-closed bottle, and kept at very nearly
a constant temperature, the chrome alum dissolves, but no replace-
ment takes place.

c. When a crystal of potash chrome alum is placed in a solution
of ammonia alumina alum exposed to the air, the ammonia alumina
alum grows on it, there being only very slight replacement.

d. Potash chrome alum meal added to solution of ammonia
alumina alum in well-closed bottle, and kept at very nearly a con-
stant temperature, no change takes place.

e. Ammonia iron alum grows on crystals of potash alumina alum.

/. Ammonia iron alum grows on crystals of potash chrome alum.

* “ Sitzungsberichte,” Imperial Academy of Sciences, Vienna, 1860, xxxix.

+ “ Sitzungsberichte,” Imperial Academy of Sciences, Vienna, 1866, liii.

VOL. IX.

0 !>

734

Proceedings of the Royal Society

g. When a crystal of ammonia iron alum is placed in a solution of
ammonia alumina alum, replacement goes on very slowly, rust at
the same time being thrown down.

h. Potash chrome alum grows on crystals of potash alumina alum.

i. If a crystal of ammonia iron alum he placed in a solution of
potash chrome alum, the iron alum is turned out, whilst a skeleton
in chrome alum of the original crystal is left ; if this skeleton be
placed in a solution of ammonia alumina alum, the latter alum
grows on it, completing the form of the original crystal of ammonia
iron alum.

6. On a New Method for the Separation of Yttrium and Erbium
from Cerium, Lanthanum, and Didymium. Part I. By
J. Gibson, Ph.D., and R. M. Morrison, D.Sc.

The method for the separation of these two groups hitherto in use
was first proposed by Berzelius, and has been followed by almost
all chemists who have investigated these earths. For the details of
this method we must refer to his “Handbuch;” but we may briefly
state that it depends on the relative solubilities of the double sul-
phates of these metals with potassium in a saturated solution of
potassic sulphate. The yttrium and erbium double sulphates are
said to be easily and completely soluble, while the double sulphates
of cerium, lanthanum, and didymium are said to be perfectly
insoluble. Wishing to prepare pure salts of yttrium and erbium,
in order if possible to obtain the metals and to determine their
specific heats, we tried this method, and found that, although it is
a good rough method, the separation is by no means complete.
We repeated the separation six times, but never obtained the
earths pure, the spectroscope always showing the characteristic
absorption-spectrum of didymium, provided we examined a suffi-
ciently thick layer of a saturated nitric acid solution. The incom-
pleteness of this method is indeed acknowledged by Bahr and
Bunsen in their well-known paper on these metals.* The test
given for the presence or absence of these two groups by these
chemists was the presence or absence of the absorption-spectra of
didymium and erbium respectively. We found, however, that

* Ann. d. Chem. u. Pliar. cxxxvii.

of Edinburgh, Session 1877-78.

735

not only are the double sulphates of the didymium group some-
what soluble in a saturated solution of potassic sulphate, but that
some erbium, if not also some yttrium, is precipitated. Repetition
of this process fails to remove the last traces of the didymium
group.

After trying various modifications of this method, some of which
gave better results, notably boiling the double sulphates with the
saturated potassic-sulpliate solution and filtering hot, we determined
to look for another method, none of these variations being suffi-
ciently good.

We have obtained better results by the following method.
After having extracted as much as possible of the didymium
group by the old method, the earths are dissolved in nitric acid,
and to this solution a large excess of a solution of carbonate of
ammonia is added, and the whole allowed to digest for a day in a
closed flask, the precipitate being frequently shaken up. The
liquid is then filtered and the undissolved residue washed. On
acidifying the filtrate with hydrochloric acid, and adding oxalic
acid, a precipitate is obtained which, on ignition, yields the oxides
of yttrium and erbium, free from, or only containing the merest
trace of, lanthanum or didymium, which may be removed by a
repetition of the process. Any cerium originally present goes
into solution, and must be removed by boiling a solution of the
sulphates with carbonate of magnesia. The undissolved residue of
the carbonate of ammonia solution still contains yttrium and
erbium carbonates, but is much richer in didymium, and must be
treated with a fresh portion of carbonate of ammonia solution.

It is essential that the ammonium carbonate solution be neither
too concentrated or too dilute, as in the first case some lanthanum
and didymium dissolves, and in the latter the carbonates of yttrium
and erbium, after dissolving, crystallize out as double salts, leaving
almost nothing in solution. The strength we found most suitable
was about half saturated.

736

Proceedings of the Royal Society

7. On certain Effects of Periodic Variation of Intensity of a
Musical Note. By Professor Crum Brown and Pro-
fessor Tait.

Recent discussions as to the nature of vowel-sounds have led us
to make experiments (partly with an apparatus constructed some
years ago for the same purpose) upon the effect of a periodic varia-
tion of intensity of a simple tone.

It is obviously impossible to secure a simple harmonic variation,
so we endeavoured to produce a displacement varying as

1 - cos mt.

An organ-pipe, giving a tone very free from harmonics, was
sounded on one side of a partition in which were cut a series of
large holes. These were opened and shut periodically by a revolving
disc cut into separate sectors. The form of the holes was calculated
on the rough assumption that the intensity of the sound passing
through them was at each instant proportional to the uncovered area
of the openings. This may be approximated to in many ways, most
simply by making the holes approximately square or of rhombus
form, with one diagonal radial, and the corners at the ends of that
diagonal somewhat rounded off.

Supposing the adj ustment perfect, the result should have been the
disturbance

(1 - cos mt) cos nt,
or

cos nt cos (m + n)t - J cos (in - n)t.

Thus, in addition to the tone given by the pipe, there should be two
others of the order of summation and difference tones. The result
was tested very easily by the help of resonators. Standing in
front of the openings in the partition, the observer applied a
resonator to each ear, and the pipe giving the tone whose number
of vibrations was the arithmetical mean of those of the tones of the
resonators wras sounded on a small organ, and the disc made to
rotate with gradually increasing velocity. The resonators were
found to be affected simultaneously.

The experiments, as we made them, succeed much better with

of Edinburgh, Session 1877-78.

737

low notes than with high — because, though the rotating apparatus
always produces a siren effect, the intensity of this effect is very
small at low speeds. A very curious case occurs when m = n (i.e.,
the siren giving the same note as the pipe), for then the first har-
monic comes in very marked.

8. Note on a Mode of Producing Sounds of very great
intensity. By Professor Tait.

Two years ago I had an opportunity of making from the deck of the
steamer “ Pharos” some observations on the performance of the fog-
siren at Sanda, off the Mull of Cantire. The instrument is worked
by air at about 1| atmospheres pressure; and, though driven by a
powerful air-engine, sounds for 7 seconds only per minute. One
obvious defect of such an arrangement I saw to be the waste of
energy in producing a current of air through the trumpet of the
siren along with the oscillations. It then occurred to me that a
regular alternation of puffing and sucking — exactly analogous to the
air-disturbance produced by a drum — must be a much less costly
source of sound. I have since constructed a siren on this double
action principle, the air in the trumpet, which acts as a resonator,
being put alternately in connection with reservoirs of compressed
and rarefied air. The small model has given very good results, and
a larger one is in progress. The only defect which my model
showed was a waste of energy in the form of pulsations in the
tubes leading to the exhausted receiver and to that containing
compressed air. This can be very greatly reduced, but I do not
yet see how to get rid of it entirely, unless it be possible to make
both receivers so exactly as to act as additional resonators to the
siren. If this can be carried out in practice there will be no
energy spent except in sound. It is obvious that the principle just
described is approximated to in practice whenever steam is employed
in a siren : — the vacuum being produced by the condensation of the
steam.

Another device of a somewhat different character was suggested
to me by the experiments described in the preceding paper. After
trying, without much success, to reduce the intensity of the siren
notes by filing the edges of the apertures, it occurred to me that I

738 Proceedings of the lloyal Society of Edinburgh.

might usefully intensify them. I therefore had copper plates
soldered perpendicularly to the revolving disc, so as to increase
instead of diminishing the virtual thickness of the edges of the
apertures. The result was very striking. Such a siren gives a
sound whose intensity is not sensibly increased by a powerful blast
from an organ bellows. It produces strong currents of air through
the holes in the fixed disc, whose direction in general depends upon
the direction in which the rotating disc is made to revolve; and
especially does so when the copper plates are inclined to the surface
of that disc. When the discs are both furnished with these plates,
turned in opposite directions, the result is still more striking.
Various other modifications have occurred to me, and are now
under trial, especially one for producing currents alternately in
opposite directions through the holes.

By bringing up a flat plate towards the instrument, the quality
of the sound is altered in a remarkable manner, and to such an
extent that it seems well adapted for rapid Morse-signalling. As
this instrument requires no work to be spent except in turning it,
a very large number may be kept continuously at work at once by the
same expenditure of power as is required for the intermittent roaring
of a single fog-siren.

The following Gentlemen were duly elected Fellows of the
Society : —

James R. Stewart, M.A. Oxon., 10 Minto Street.

John Archibald Campbell, M.D., Garland’s Asylum, Carlisle.

Donations to the Library of the Loyal Society during

Session 1877-78.

I. Transactions and Proceedings of Learned Societies,

Academies, etc.

American Association. See United States.

Amsterdam. — Flora Batava. Afbeelding en Beschrijving van Neder-
landsche Gewassen, aangevangen door wijlen Jan Kops
hoogleeraar te Utrecht, voortgezet door P. W. van Eeden.
Afleveringen 237, 238, 239, 240. Leyden. 4to. — From
the King of Holland.

Linnaeana, in Nederland aanwezig. Tentoongesteld, op. 10,
Jan. 1878, in het Kon. Zool. Genootschap “Natura Artis
Magistra.” 8vo.

Bede ter Herdenking van den Sterfdag van Carolus Linnaeus
uitgesproken door C. A. J, A. Oudemans. 1878. 8vo.-—

From the Society.

Elementary and Middle-Class Instruction in the Nether-
lands. 1876. 8vo. — From the Royal Commission of the
Netherlands.

Baltimore — Peabody Institute. Eleventh Annual Beport. June
1, 1878. — From the Institute.

Basel. — Yerhandlungen der Schweizerischen Naturforschenden
Gesellschaft. 59 Jahresversaminlung. Jahresbericht,
1875-76. 8vo. — From the Society.

Berlin. — Monatsberichte der konigl. Preussischen Akademie der
Wissenschaften zu Berlin. Jun. 1877-Jun. 1878. —
From the Academy.

Abhandlungen der koniglichen Akademie der Wissenschaften
aus dem Jahre 1876. 4to.

Die Eortschritte der Physik in Jahren 1872, 1873, darges-
tellt von der physikalischen Gesellschaft zu Berlin.
XXVIII., XXIX. Jahrgangen. Berlin, 1876-78.—

From the Society.

VOL. IX. 5 E

740 Proceedings of the Royal Society

Bern. — Mittheilungen der Naturforsclienden Gesellschaft, a us dem
Jalirel876. Nrs. 906-922. 1877. 8vo.~ From the Society.
Beitrage zur Geologischen Karte der Schweiz. Die Sentis-
Gruppe, von A. E. v.d. Linth. 1878. 4to. — From the
Swiss Government.

Bombay. — The Journal of the Bombay Branch of the Royal Asiatic
Society, 1876, and extra Number, 1877. 8vo. — From the
Society.

The Meteorology of the Bombay Presidency. By Charles
Chambers. Bond., 1878. 4to. — From the Indian Govern-
ment.

Bonn. — Yerhandlungen des Naturhistorischen Yereines der Preus-
sischen Rheinlande u. Westfalens. Jahrg. XXXIII. und
XXXIY. 1877. 8vo. — From the Association.

Bordeaux. — Memoires de la Societe des Sciences Physiques et
Naturelles. 2de Serie. Tome II. cahier 2. 1878. 4to.

— From the Society.

Boston. — Memoirs of the Boston Society of Natural History. Yol.
II. Part IY. No. 5. Boston, 1877. 4to.

Memoirs of the Boston Society of Natural Society. Yol. II.
Part IY, Nos. 5, 6. 1877-78. 4to. Proceedings.

Yol. XYIII., Parts 3 and 4 ; XIX., 1, 2. 1876-77.—

From the Society.

Proceedings of the American Academy of Arts and Sciences.
New Series, Yol. IY. From May 1876 to November
1876. Boston, 1877. 8vo. — From the Academy.

Brer a. — Osservatorio di. See Milano.

British Association. — Report of the Forty-sixth Meeting of the
British Association for the Advancement of Science, held
at Glasgow in September 1876. London 1877. 8vo. —

From the Association.

Brussels. — Bulletins de l’Academie Royale des Sciences, des Lettres
et des Beaux- Arts. Tomes XLII., XLIII., XLIY.,

XLY. 1877-78. — From the Academy.

Notices Extraites de l’Annuaire de TOhservatoire Royal de
Bruxelles, pour 1875 et 1876. 2 vols. 12 mo.

Annuaire de TOhservatoire Royal de Bruxelles, 1877.
44me Annee. Brux. 1876. 12mo.

of Edinburgh, Session 1877-78.

741

Bnissels. — Annales de I’Observatoire Royal de Bruxelles, publiees
par lAstronome, E. Quetelet. Tomes XXIII., XXIV.,
XXV. — From the Observatory.

Essai sur la Vie et les Ouvrages de L. A. J. Quetelet, par
Ed. Mailly. Bruxelles 1875. 8vo. — From the Observatory

Les Perseides en 1874. Aurores Boreales du mois d’Octobre
1874. 8yo. — From the Observatory.

Annales de la Societe Scientifique de Bruxelles. Annies I.,
II. , et III., fasc. 1. 1875-78. 8vo. — From the Society.

Buenos Ayres. — Anales de la Oficina Meteorologica Argentina.

Tomo I. Clima de Buenos Ayres. 1878. 4to. — From
the Argentine Government.

Calcutta. — General Beport on the Great Trigonometrical Survey of
India during 1876-77. By Colonel J. T. Walker. Cal-
cutta, 1878. Fol.

Memoirs of Geological Survey of India : —

Ser. II. 2. Pala^ontologia Indica.

Ser. II. 3. Jurassic (Liassic) Flora of the Rajmohal
Group. By 0. Feistmantel. 1877. 4to.

Ser. IV. 2. Ganoid Fishes from the Deccan. By Sir
P. de M. Grey Egerton. 1877.

On the genus Ceratodus. By L. C. Miall.
1878. 4to.

On the Kota-Maledi Deposits. By W.
T. Blanford. 1878. 4to.

Ser. X. 3. Indian Tertiary and Post-
Tertiary Vertebrata. Vol. I. 3.

Crania of Ruminants. By R. Lyddekker.
1878. 4to.

Ser. XI. 2. Flora of the Jabalpur Group. By 0. Feist-
mantel. 1877 4to.

Records of the Geological Survey of India. Vol. X., Parts
1-4. 1877. 8vo.

Memoirs of the Geological Survey of India. Vol. XIII,
Parts 1, 2.

General Report on the Operations of the Great Trigonometri-
cal Survey of India during 1876-77. By Colonel J. T.
Walker. Calcutta, 1878. Fol. — From the Survey Office.

742 Proceedings of the Hoyal Society

Calcutta. — Catalogue of Mollusca in the Indian Museum, Calcutta.

By Geoffrey Xevill. — Fasc. E. Calcutta, 1877. 8vo. —
From the Trustees of the Museum.

Journal of the Asiatic Society of Bengal. Yol. XLY. Part
2, Ho. 4, 1876; Part 2, No. 1, 1877. Edited by Nat.
Hist. Secretary. Yol. XLYI. Part 2, Xo. 2, 1877.
8vo.

Proceedings of the Asiatic Society of Bengal, Xo. YI.
January to June 1877. 8vo. — From the Society.
Cambridge. — Proceedings of the Cambridge Philosophical Society.
Yol. III. Parts 1, 2. 1876-77. 8vo.

Transactions of the Cambridge Philosophical Society. Yol.
XI. Part 3; Yol. XII. Parts 1, 2. — From the Society.
Cambridge (U.S.). — Harvard College. Memoirs of the Museum of
Comparative Zoology at Harvard College. — Yol. Y. Xo. 1.,
American Starfishes, by Alexander Agassiz. — Yol. Y. Xo.
2, Eeport on the Hydroida of the Gulf-Stream, by Geo.
J. Allman, M.D., &c. 1877. 4to.— Yol. YI. Xo. 2,

Eeport on the Fossil Plants of the Auriferous Gravel of
the Sierra Xevada, by Leo Lesquereux. Camb., 1878.
4to.

Bulletin of the Museum of Comparative Zoology at Harvard
College, Cambridge. Yol. Y. Xo. 1. 1878.

Annual Eeports of the President and Treasurer and Library
Committee of Harvard College. 1876-77. 8vo.

Harvard College Observatory. Annual Eeport of the
Director of Harvard College Observatory. Xovember
1877. 8vo.

Annals of the Astronomical Observatory of Harvard College.
Yol. I. Parts 1, 2 ; Yol. II. Parts 1, 2; Yol. III. ; Yol.
IY. Part 1 ; Yols. V., YI., YU, YIII.

Yol. IX. Photometric Eesearches.

Yol. X. Observations made with the Meridian Circle during
1871 and 1872, by Professors J. Winlock and William
A. Eogers. 4to. Cambridge, 1877. — From Harvard
College.

743

of Edinburgh, Session 1877-78.

Cape Town. — Results of Astronomical Observations made at the
Royal Observatory, Cape of Good Hope, during the
year 1874, under the direction of E. J. Stone, F.R.S.,
H.M. Astronomer at the Cape. 8vo. 1877. — From the

Observatory.

Cherbourg. — Memoires de la Societe Nationale des Sciences
Naturelles. Tome XX. 8vo. 1876-77. — From the

Society.

Davenport , Iowa. — Proceedings of the Davenport Academy of
Natural Sciences. Yol. II. Part 2. January-June 1877.
— From the Academy.

Dunecht. — Dunecht Observatory Publications, No. I. Summary of
Measurements in Struve’s “ Stellarum duplicium et multi-
plicium Mensurae,” and “ Synopsis Observationum de
Stellis Duplicibus,” brought up to 1875.

Dunecht Observatory Publications, No. II. Mauritius
Expedition, 1874. Determination of the Solar Parallax
by Observations of Juno, with Description of Heliometer.
4to. Dunecht, 1877. — From the Lord Lindsay.

Dorpat. — Blumberg (Theodor). Zur Kenntniss der Mutterkorn-
Alkaloide, (Inaug. Dissert., Dorpat Univ.) 1878. 8vo.

Bonwetsch (G, Nathanael). Die Schriften Tertullians nach
der Zeit Hirer Abfassung. (Inaug. Dissert., Dorpat Univ.)
1878. 8vo.

Buch (Max). Zur Kenntniss der peripheren Temperatur des
Menschen. (Inaug. Dissert., Dorpat Univ.) 1877. 8vo.

Dybowski (Wlad). Die Chaetetiden der Ostbaltischen Silur-
Eormation. (Inaug. Dissert., Dorpat Univ.) 1878. 8vo.

Eichelmann (Otto). Ueber die Kriegsgefangenschaft : eine
vdlkerrechtliche Studie. (Inaug. Dissert., Dorpat Univ.)
1878. 8vo.

Gordon (Ludwig). Ueber die Messung der Inspiratorischen
Ausdehnungsfahigkeit der Lungenspitzen. (Inaug. Dis-
sert., Dorpat Univ.) 1877. 8vo.

Grube (Oscar). Anthropologische Untersuchungen an Esten.
(Inaug. Dissert., Dorpat Univ.) 1878. 8vo.

Hach (Fr.) Ueber Lage und Form der Gebarmutter.
(Inaug. Dissert., Dorpat Univ.) 1877. 8vo.

744 Proceedings of the Royal Society

Dory at. — Hirschsohn (Eduard). Chemie der wichtigeren Harze
Gummiharze und Balsame. (Inaug. Dissert., Dorpat
Univ.) 1877. 8vo.

Kessler (Kenatus). Yersucli ueber die Wirkung einiger
Diuretica. (Inaug. Dissert., Dorpat Univ.) 1877. 8vo.

Knieriem (W.) Ueber das Verhalten der im Saugethier-
korper als Yorstufen des HarnstofFes erkannten Yerbin-
dungen zum Organ ismus der Hiihner. (Inaug. Dissert.,
Dorpat Univ.) 1877. 8vo.

Lemberg (J.) Ueber Silicatumwandlungen. (Inaug. Dis-
sert., Dorpat Univ.) 1877. 8vo.

Messing (Wlad.) Ueber den Testikel der Saugethiere mit
Beriicksichtigung des Corpus Higbmori. (Inaug. Dissert.,
Dorpat Univ.) 1877. 8vo.

Meyke (Wilhelm). Beitrage zur Ermittelung einiger Hop-
fen-Surrogate im Biere. (Inaug. Dissert., Dorpat Univ.)
1878. 8vo.

Miram (Joh. Ed.) Zur Casuistik der spontanen Amputa-
tionen und ihrer Eolgezustande. (Inaug. Dissert , Dorpat
Univ.) 1877. 8vo.

Ostwald (Wilhelm). Yolumchemische Studien iiber Affini-
tat. (Inaug. Dissert., Dorpat Univ.) 1877. 8vo.

Petersenius (E.) Atreus u. Thyestes nach Sophocles. 1877.

Schroeder (Leop.) Die Accentgesetze der Homerischen
Nominalcomposita dargestellt, und mit denen des Yeda
verglichen. (Inaug. Dissert., Dorpat Univ.) 1877.

Stieda (Wilh.) Die Eheschliessungen in Elsass-Lothringen,
1872-76. (Inaug. Dissert., Dorpat Univ.) 1878.

Tiling (G.) Ueber 124 im Serbisch-Tiirkischen Kriege im
Baracken-Lazareth des Dorpater Sanitats-Trains zu Swilai-
natz behandelte Schussverletzungen. (Inaug. Dissert.,

Dorpat Univ.) 1877. 8vo.

Tobien (Alex.) Yeratrum-Alkaloide. (Inaug. Dissert.,

Dorpat Univ.) 1877. 8vo.

Walter (Fried.) Ueber die Wirkung der Sauren auf den
thierischen Organismus. (Dissert. Inaug., Dorpat Univ.)
1877. 8vo.

The preceding Dissertations from the University of Dorpat.

745

oj Edinburgh , Session 1877-78.

Edinburgh. — Fiftieth Annual Report of the Council of the Royal
Scottish Academy of Painting, Sculpture, and Archi-
tecture. Edinburgh, 1877, 8vo.- — From the Aca-

demy.

Transactions and Proceedings of the Botanical Society. Yol.
XIII. Part 1. 8 vo. — From the Society.

Transactions of the Edinburgh Geological Society. Yol.
III. Part 1. — From the Society.

Transactions of the Highland and Agricultural^ ociety of
Scotland. Fourth Series, Yol. X. 1878. — From the

Society.

Journal of the Scottish Meteorological Society. Hew Series,
Nos. LI.-LIY. — From the Society.

Monthly and Quarterly Returns of the Births, Deaths, and
Marriages registered in the Eight Principal Towns of Scot-
land. July 187 7- July 1878. 8vo. — From the Registrar-
General.

Royal Observatory.' — Edinburgh Astronomical Observations,
Yol. XIY. for 1870-77. By Piazzi Smyth, Astronomer-
Royal for Scotland. — From the Observatory.

Edinburgh University Calendar for Session 1878-9. — From
the University.

Erlangen University. — Beetz (Dr Felix). Ueber Faradisation bei
Polyarthritis Rheumatica. (Inaug. Dissert., Erlang. Univ.)
Leipz. 1876. 8vo.

Bestmann (H. J.). Qua ratione Augustinus notiones Philo-
sophise Grsecse ad Dogmata Anthropologica describenda
adhibuerit. (Dissert. Inaug,, Erlangen Univ.), 1877.
8vo.

Bischoff (Otto). Ueber das Yerhalten des Epithelkrebses zu
den quergestreiften Muskeln. (Inaug. Dissert., Erlangen
Univ.). 1877. 8vo.

Blay (Yito). Experimentelle Untersuchung iiber die
Wirkung des Gallensauren Natrons auf die Herztthatigkeit.
(Inaug. Dissert., Erlangen Univ.) 1877. 8vo.

Drumm (Dr Aug.). Ueber das Auftreten der Aethyldiacet-
saure beim Diabetes mellitus. (Inaug. Dissert., Erlangen
Univ.) 1877. 8vo.

746

Proceedings of the Royal Society

Erlangen University . — Eckstein (Dr Max). Zur Frage der Handels-
gerichte. (Inang. Dissert., Erlangen Univ.). 1877. 8vo.

Erhard (Dr Jul.). Ueber Ernahrung der Ueugeborenen.
(Inaug. Dissert., Erlangen Univ.) 1877. 8vo.

Federschmidt (Hermann). Zur Wirkung des Pilocarpiuni
mur. (Inaug. Dissert., Erlangen Univ.) 8vo. 1877.

Fikentscher (Georg.). Ueber die Wirkung von Adstrin-
gentien auf die Gefasse der Zungenschleimbaut des
Frosches. (Inaug. Dissert., Erlangen Uni ver.) 8vo. 1877.

Finn (Dr Benjamin). Experimented Beirtage zur Glycogen-
und Zuckerbildung in der Leber. (Inaug. Diss., Erlang.
Univ.) 8vo. 1877.

Fleischer (Dr B.). Untersuchungen iiber das Resorptions-
vermogen der menschlichen Haut. (Inaug. Dissert.,
Erlangen Univ.). 1877. 8vo.

Geiger (Wilhelm). Die Pehlevi-version des ersten Capitels
desVendidad. (Inaug. Dissert., Erlangen Univ.). 1877.
8 vo.

Hellmuth (Hermannus). De Sermonis Proprietatibus quae
in prioribus Ciceronis Orationibus inveniuntur. (Dissert.
Inaug., Erlangen Univ.). 1877. 8vo.

Helmreich (Georg). Observationes criticae in Galeni de
Elementis secundum Hippocratem libros. (Dissert. Inaug.,
Erlangen Univ.). 1877. 8vo.

Keiper (Philipp). Die Perser des Aeschylos als Quelle fur
altpersisch Altertumskunde, nebst Erklarung der darin vor-
kommenden altpersischen Eigennamen. (Inaug. Dissert.,
Erlangen Univ.). 1877. 8vo.

Keller (Valentin). Die Volumverminderung des kindlichen
Schadels, bei seinem Durchtritte durch das Becken,
Inaug. Dissert., Erlangen Univ.). 1877. 8vo.

Kellermann (Christoph). Die Kartoffelpflanze. (Inaug.

Dissert., Erlangen Univ.), 1877. 8vo.

Kopp (Hermann). Untersuchungen iiber die Sauren im
romisch Camillenol. (Inaug. Dissert., Erlang. Univ.)
Erlangen, 1877. 8vo.

Krueger (Otto), Ein Beitrag zur Kenntniss des Laserpitins.
(Inaug. Dissert., Erlangen Univ.). 1877. 8vo.

of Edinburgh, Session 1877-78.

747

Erlangen University. — Lehner (Fr.). Beitrage zur Kenntniss der
Citraconsaure und ihrer Salze. (Inaug. Dissert., Er-
langen Univ.) 1877. 8vo.

Oberst (Max). Bericlit liber die cliirurgische Abtheilung des
Krankenliauses Augsburg. (Inaug. Dissert., Erlangen
Univ.) 1877. 8vo.

Papilsky (Dr Julius). Ueber die Einwirkung der Blausaure
auf Kreislauf und Blut. (Inaug. Dissert.) Wiirzb. 1877.
8 vo.

Pause (Carl Hermann). Ueber die Kerven der Iris. (Inaug.

Dissert., Erlangen Univ.) 1877. 8vo.

Eebs (Heinrich). Ein Fall von Katatonie. (Inaug. Dissert.)
Erlangen, 1877. 8vo.

Bembe (Dr Johannes). Beitrag zur Lehre von der Wirbel-
spalte. Erlangen, 1877. 8vo.

Roesch (Ludwig). Beitrage zur Kenntniss des Glycyrrhizins.

(Inaug. Dissert.) Erlangen, 1877. 8vo.

Schmidtlein (Dr Carl). Ein Fall von Anus Praeter-
naturalis mit Inversion des Darms. (Inaug. Dissert).
1877. 8 vo.

Seifert Otto). Beitrag zur Pathologie und Therapie der
Chorea minor. (Inaug. Dissert., Erlangen Univ.) 1877.
8vo.

Sendtner (Rudolf). Ueber einige Yerbindungen des Urans.

(Inaug. Dissert., Erlangen Univ.) 1877. 8vo.

Siegel (Alb.). Ueber das einfache chronische Duodenal-
geschwiir, mit Perforation in den Ductus choledochus.
(Inaug. Dissert., Erlangen Univ.) 1877. 8vo.
Spruner-Merz (Edmund v.). Ueber traumatische Aneurys-
men. (Inaug. Dissert., Erlangen Univ.) 1877. 8vo.
Stein (E.). Ueber die sogenannte Psychische Contagion.

(Inaug. Dissert., Erlangen Univ.) 1877. 8vo.

Stover (Karl). Ueber die Entstehung lokaler Tuberkulose
durch Infection aus kasigen Herden. (Inaug. Dissert.,
Erlangen Univ.) 1877. 8vo.

Surminski (Bernhard). Ueber die Wirkungsweise des
Uicotin und Atropin auf das Gefassnerven-System und die
Pupille. (Inaug. Dissert., Erlangen Univ.) 1877. 8vo.

5 F

VOL. IX.

748

Proceedings of the Royal Society

Erlangen. — Waller (Dr Max). Beitrage zur Behandlung der
Crouposen Pneumonie. (Inaug. Dissert., Erlangen Univ.)

1877. 8vo.

Wunderlicli (Dr Georg). Heilung der Briiche Schenkel-
halses. (Inaug. Dissert., Erlangen Univ.) 8vo.

The preceding Dissertations presented by the University of
Erlangen.

Geneva. — Nivellement de Precision de la Suisse, execute par la
Commission Geodesique F4d4rale, sous la direction de
A. Hirsch et E. Plantamour. 1877. Liv. 6me. 4to. —

From the Commission.

Memoires de la Soci6t4 de Physique et d’Histoire Naturelle
de Gen&ve. Tome XXY. Partie 1. 4to.

Rapport du President de la Soci4t4 de Physique et d’Histoire
Naturelle de Geneve, Mai 1876-Juin 1877. — From
the Society.

Glasgoiv. — Proceedings of the Philosophical Society of Glasgow.

Yol. X. Nos. 1, 2. 1875-1877. 8vo .—From the

Society.

The Glasgow University Calendar for 1878-79. Glasgow

1878. 8vo. — From the University.

Gottingen. — Nachrichten von der K. Gesellschaft der Wissen-
schaften u. der Georg- Augusts-Universitat aus dem Jahre
1877-78. 8vo.

Abhandlungen der koniglichen Gesellschaft der Wissenschaf-
ten. Band XXII. vom Jahre 1877. 4to. — From the Society.
Graz. — Mittheilungen des naturwissenschaftliches Yereines fur
Steiermark. 1877-1878. 8vo. — From the Association.
Greenwich. — The Nautical Almanac and Astronomical Ephemeris
for the year 1881 for the Meridian of Greenwich. Bond.
8vo. — From the Lords of the Admiralty.

Transit of Yenus. Copy of the Report by the Astronomer
Royal, Sir G. B. Airy, on the Telescopic observations of
the Transit of Yenus, 1874. 1877. Eol. — From the

Observatory.

Haarlem. — Archives NAerlandaises des Sciences Exactes etNaturelles.

Tome XII. Liv. 1-5, 1877; XIII. Liv. 1-3, 1878.—

From the Society.

of Edinburgh, Session 1877-78. 749

Haarlem. — Naturkundige Yerhandelingen der Hollandsche Maats-
chapij, 3d. Yersameling. Deel II. Nos. 6. 4to.

Memoire sur les Chroniides marins on Pomacentroides de
lTnde Archipelagique, par P. Bleeker. 1877. 4to. — From
the Society.

Halle. — Mittheil ungen des Vereins fur Erdkunde zu Halle. 1877.
8vo. — From the Society.

Innsbruck. — Berichte des Naturwissenschaftlich-Medizinischen

Yereines. Jalirg. YU. 1876, Hefte 1. — From the
Association.

Jena. — Jenaische Zeitsclirift fiir Naturwissenschaft der Medicinisch-
Naturwissenschaftlichen Gesellschaft zu Jena. Bd. XI.
Hefte 3, 4; Bd. XII., 1, 2. 1877-78. 8vo. — From the

Society.

Kasan. — Reports of the University of Kasan. Nos. 1-6. 1877.

8 vo. — From the University.

Kiel. — Jahresbericht der Commission zur wissenschaftlichen Unter-
suchung der deutschen Meere in Kiel. Jahrg., IY., Y.,
YI. Hefte 1, 2. 1874-76. Pol. — From the Commis-

sion.

Schriften der Universitat zu Kiel aus dem Jahre, 1876.

Band XXII. Keil, 1877. 4to.

Die Einweihungsfeier des neuen Universities- Gebaudes zu
Kiel, von Dr F. Yohlbehr. October 1876. 8vo. —

From the University.

Leeds. — Fifty-seventh Report of the Council of the Leeds Philoso-
phical and Literary Society, Session 1876-77. Leeds,
1877. 8 vo. — From the Society.

The Worth of Life : an Address delivered at the Opening of
the 58th Session of the Leeds Philosophical and Literary
Society by the Archbishop of York. Lond. 1877. 8vo.
— From the Society.

Leipzig. — Annalen der Physik und Chernie, 1877-78. Beiblatter,
1877-78. — From the Editor in exchange for the Society’s
Publications.

Leyton , Essex. — Astronomical Observations to the end of 1877, at
the Observatory of J. G. Barclay, Esq. Yol. III., IY.
4 to. — From J. G. Barclay , Esq.

750 Proceedings of the Royal Society

Lisbon . — Memorias da Academia Eeal das Sciencias de Lisboa,
Classe de Scien. Moraes Politicas e Bellas-Lettras. Tom.
IY. Pt. 2, 1877. Classe de Sciencias Math., Phys. e Nat.

Tom. Y. Pt. 1, 1875. Jornal de Sciencias Math.

Tom Y. Eelatorios das Sessoes. 1875-77. Historia

dos Estabelecimentos Scientificos, &c. Tom. I. a YII.
Curso de Meteorologia, 1869. Tratado de Optica, 1874.
Chemica Agricola per Yidal, 1875. Descobrimentos dos
Portugueses na Africa, 1877. — From the Academy.
Liverpool. — Transactions of the Historic Society of Lancashire and
Cheshire. Third Series. Yol. Y. Session 1876-77. —

From the Society.

Proceedings of the Literary and Philosophical Society of
Liverpool. Yol. XXXI. Session 1876-77. 8vo. — From
the Society.

London. — Proceedings of the Society of Antiquaries of London.
Yol. YII. Nos. 2, 3. 1876-77. — From the Society.

The Indian Antiquary : a Journal of Oriental Eesearch in
Archaeology, History, Literature, Languages, &c. Parts
LXX.-LXXXII. 1877-78. 4to. — From the India Office.
Memoirs of the Eoyal Astronomical Society. Yol. XLIII.
1875-77. Lond. 1877. 4to.

Monthly Notices of the Eoyal Astronomical Society. Yol.

XXXYIII. Nov. 1877 to June 1878. — From the Society.
Journal of the Society of Arts. 1877-78. 8vo. — From the
Society.

Journal of the Chemical Society. Aug. 1877-78. — From
the Society.

Transactions of the Clinical Society of London. Yol. X.

1877. 8vo. — From the Society.

Minutes of Proceedings of the Institution of Civil Engineers.
Yols. XLIX., L., LI., LII. 1877-78. 8vo. — From the
Institution.

Proceedings of the Geologists’ Association. YoL Y. Nos.
3, 4. 1877. 8 vo.

Proceedings of the Geologists’ Association. Yol. Y. Nos.
5, 6. Nos. 4, 5, 6. Oct. 1877 to April 1878. — From the
Association.

751

of Edinburgh, Session 1877-78.

London. — The Quarterly Journal of the Geological Society. Yol.

XXXIII. Pts. 3, 4, 1873 ; Yol. XXXIV. Pts. 1, 2,
1878. — From the Society.

Abstracts of the Proceedings of the Geological Society of
London. Xos. 340-356. 1877-78. 8vo. — From the

Society.

Proceedings of the Royal Geographical Society. Yol. XXII.
Xos. 1-5. 1878. 8vo.

Journal of the East India Association. Yol. X. No. 4 ;

Yol. XI. Xos. 1, 2. 1877-78. 8vo. — From the Association.
Report of the Kew Committee for the year ending 31st
October 1877. — From the Committee.

Transactions of the Linnean Society of London. Second
Series — Botany, Yol. I. Part 5, 1877 ; Second Series —
Zoology, Yol. I. Parts 5, 6. Lond. 1877. 4to.

Journal of the Linnean Society. — Botany, Yol. XYI. Xos.

91-97; Zoology, Yol. XIII. Xos. 70-74. — From the Society.
Proceedings of the London Mathematical Society. Yol.
VIII. Xos. 112-123; Yol. IX. Xos. 124-129.— From
the Society.

Proceedings of the Royal Medical and Chirurgical Society
of London. Yol. VIII. Xos. 5, 6.

Medico-Chirurgical Transactions, published by the Royal
Medical and Chirurgical Society of London. Second
Series. Yol. XLII. 1877. 8vo. — From the Society.
Quarterly Journal of the Meteorological Society. Xos. 23,
24, 26, 27. 1877-78. — From the Society.

Quarterly Weather Reports of the Meteorological Office.
Part 1, Jan. to March; Part 2, April to June; Part 3,
July to Sept. 1875. 4to. — From the Meteorological Office.
Catalogue of the Chiroptera in the Collection of the British
Museum. By G. Edward Dobson, M.A. — Guide to the
Department of Natural History and Antiquities, 1878, in
British Museum. — From the Museum.

Transactions of the Pathological Society of London. Yol.

XXVIII. Lond. 1877. 8vo. — From the Society.
Proceedings of the Royal Institution of Great Britain. Yol.
VIIT. Parts 3, 4. 1877-78. — From the Roy cd Institution.

754

Proceedings of the Royal Society

Napoli. — Atti della R. Accademia delle Scienze Fisiclie e Matema-
tiche. Yol. YI. Napoli, 1875. 4to.

Rendiconti dell’ Accademia delle Scienze Fisiche e Matema-
tiche. (Sezione della Societa Reale di Napoli.) Anni
XII., XIII., XIY. — From the Academy.

Neuchatel. — Bulletin de la Society des Sciences Naturelles. Tome
XI. lerCatiier. Neuchatel, 1877. 8vo. — From the Society.

New Haven. — Transactions of the Connecticut Academy of Arts
and Sciences. Yol. III. Part 2; Yol. IY. Part 1. 1877-
78. — From the Academy.

Oxford. — Astronomical and Meteorological Observations made at
the Radcliffe Observatory in the year 1875. Yol. XXXY.
Oxford, 1877. 8vo. — From the Observatory.

Astronomical Observations made at the University Observa-
tory, Oxford, under the direction of C. Pritchard, Savilian
Professor. 1878. — From the Observatory.

Palermo. — Bulletino della Society di Scienze Naturali ed Econo-
miche. Nos. 2-8. 1877. 8vo.

Giornale della Societa di Scienze Naturali ed Economiche.
Anno 1876-77. Yol. XII. 4to. — From the Society.

Memorie della Societa degli Spettroscopisti Italiani. Dis-
pense 1-7. 1878. — From the Society.

Paris. — Comptes Rend us Hebdomadaires des Stances de l’Academie
des Sciences. Aoftt 1877 ; Aout 1878. 4to. — From the
Academy.

Bulletin de la Societe de Geographic. Juillet 1877 — Juillet
1878. 8vo. — From the Society.

Bulletin de la Societe MatlUmatique de France. Tomes Y.,
YI. 1877-78. 8 vo. — From the Society.

Annales des Mines. Tomes XI.-XIII. Liv. 1. Paris,
1877-78. 8vo. — From the Pcole des Mines.

Revue Politique et Litteraire, 1877-78. 4to. Revue Scien-
tifique, 1877-78. 4to. — From the Editor in exchange for
the Society’s Publications.

Pavia. — Onoranze di Alessandro Yolta. 1878. 8vo. — From the
University of Pavia.

Philadelphia. — Proceedings of the Academy of Natural Sciences
for 1877. Parts 1, 2, 3. 8vo. — From the Academy.

of Edinburgh, Session 1877-78.

755

Philadelphia. — Journal of the Academy of Natural Sciences of
Philadelphia. New Series. Yol. VIII. Part III. 1877.
4to. — From the Academy.

Proceedings of the American Philosophical Society held at
Philadelphia, for Promoting Useful Knowledge. January
to May 1877. Yol. XYI. No. 99 ; Yol. XYII. No. 100.
1877. 8vo. — From the Society.

Pray. — Astronomische, Magnetische und Meteorologische Beobach-
tungen an den K. K. Stern warte im Jahre 1877. 4to. —

From the Observatory.

Rome. — Atti della E. Accademia dei Lincei. — Transunti. Serie
Seconda — Yol. I., 1873-4; Yol. II., 1874-5 ; Yol. III.
Parte 1™, 1875-76. Serie Terza— Yol. I., 1877-78.
Memorie della E. Accademia dei Lincei. Serie Prim a — To mi
L-XXYL, 1847-73 — Memorie e Communication! Serie
Seconda — Yol. I., Yol. II., Yol. III., Parte Prima. Parte
Seconda : Memorie della Classe di Scienze Pis. Mat. e Na-
turali, 1875-76 ; 4to. Parte Terza : Memorie della Classe
di Scienze Morali, Storiche e Filologiche, 1875-76. Serie
Terza — Yol. I. ; Memorie della Classe di Scienze Fisiche,
Math, e Nat., Yol. I. Disp. lma, 2da, 1877. Memorie della
Classe di Scienze Morali, Storiche e Filol. Yol. I., 1877.
Nuovo Statuto della E. Accademia dei Lincei. Eoma, 1875.
4 to. — From the Academy.

St Petersburg. — Bulletin de TAcad4mie Imperiale des Sciences de
St-P4tersbourg. Tomes XXIY., XXY. 1, 1877.

Memoires de l’Acad4mie Imperiale des Sciences de St-
Petersbourg. YIIe Serie — Tome XXIY. Nos. 4-11 ;
Tome XXY. Nos. 1-4. — From the Academy.

Annalen des physikalischen Central-Observatoriums. Jahr-
gang 1876. — From the Observatory.

Compte-Bendu de la Commission Imperiale Archeologique
pour l’ann4e 1875. Fol. — From the Commission.
Jahresbericht der Comit6 der Nicolai-Hauptstern warte.

1876. 8yo. — From the Observatory.

Bepertorium fiir Meteorologie, berausgegeben von der kaiser-
lichen Akademie der Wissenschaften, redigirt von Dr
Heinrich Wild. Band Y. Heft. 2. 1877. Supplement
Band, lte Halfte. 1877. 4to.

5 G

VOL. IX.

756 Proceedings of the Royal Society

St Petersburg. — Observations de Poulkova. Yol. VII. 1877. —
From the Observatory.

Salem , U. S. — Bulletin of the Essex Institute. Yol. IX. Nos. 1-12.
1877. 8 vo — From the Institute.

Shanghai. — Journal of the North-China Branch of the Royal Asiatic
Society. New Series, Nos. X., XI. 1876,1877. 8vo. —
From the Society.

Stockholm. — Kongliga svenska Yetenskaps-Akademiens Handlingar.
Ny Eoljd. 13de 14de Band. 1874. 4to.

Bihang till Kongl. svenska Yeten.-Akad. Handlingar. Bd.
III. Hafte. 2.

Ofversigt af Kong. Yetensk.-Akad. Forhandlingar. 33dJ’e
Argangen. 1876-77. 8vo.

Minnesteckning ofver Augustin Ehrensvard foredragen pa
K. Yetensk.-Akademiens Hogtidsdag, Mars 1876, af Fr.
Waern. 8vo. Stockholm, 1876.

Iconographia Crinoideorum in Stratis Sueciae Siluricis
Fossilium. Auctore N. P. Angelin. Holmiae, 1878. Fol.
— From the Royal Swedish Academy.

Meteorologiska Jakttagelser i Sverige, utgifnaaf K. Svenska
Yetenskaps-Akademien. Band XYI. 1874. 4to.—

From the Academy.

Sydney. — Journal and Proceedings of the Royal Society of New
South Wales, 1876. Yol. X.

Climate of New South Wales, Descriptive, Historical, and
Tabular, by H. C. Russell, Government Astronomer.
Sydney, 1877. 8vo. — From the Society.

Railways of New South Wales, Report on their Construction
and Working, 1872-1875, by John Rae. A.M. Fol.
— From the Government of New South Wales.

Annual Report of the Department of Mines, New South
Wales, for the year 1876. Sydney. 4to. — From the
Society of New South Wales.

Turin. — Atti della R. Accademia delle Scienze di Torino. Yol. XII.
Disp. 1-5. 1876-77. 8vo.

Annuario del! Accademia Reale delle Scienze di Torino
per l’anno 1877-78. Anno I. 8vo. — From the Aca-

demy.

of Edinburgh, Session 1877-78. 757

Turin. — Bolletino del! Osservatorio della Regia Universita di 1'orino.

Anno XI. (1876). 4to. — From the Observatory.

Toronto. — The Canadian Journal of Science, Literature, and History.
Yol. XV., No. VII. Oct. 1877.

United States. — Proceedings of the American Association for
the Advancement of Science, 26th Meeting, held at
Buffalo, X. Y., August 1876. 8vo. — From the Association.
Upsala. — Xova Acta Regiae Societatis Scientiarum Upsaliensis.

Volumen extra ordinem editum ad celebranda sollemnia
quadringenaria Universitatis Upsaliensis. 1877. Upsaliae
4to. — From the Society.

Venice. — Atti del Reale Istituto Yeneto di Scienze, Lettere ed Arti
Serie 5ta, Tom. 3Z0, Dispense 4ta, 5ta, 6ta, 7ma. Yenezia
1876-77. 8vo. — From the Institute.

Victoria. — Statistical Register of the Colony of Victoria for the
year 1876. Pts. 1-6. Victoria, 1877. Fol.

Agricultural Statistics, 1876-77. Part VII. — Interchange.
Part VIII. — Law, Crime, &c. Part IX. — Religious, Moral,
and Intellectual Progress. 1876. Pol.

Statistics of Friendly Societies for 1876. Folio. — From
the Government of Victoria.

Vienna. — Denkschriften der K. Akademie der Wissenschaften.

Philos. -Histor. Classe, Bd. XXVI., 1877c Math.-Xatur-
wissensch. Classe, Bd. XXXVII. 1877.

Sitzungsberichte der K. Akademie Math.-Xaturwissensch.
Classe III. Abtheil. Physiologie, &c., Bd. LXXIIL,
Hefte 1-5; Bd. LXXIV., Jahrg. 1876; LXXV., Jahrg.
1877 ; Abtheil. I. Mineralogie, &c., Bd. LXXIV., Hefte
3-5, Bd. XXXV. 1877. Philos. -Hist. Classe, Bde.

LXXXII., Heft 3, Jahrg. 1876 ; Bd. LXXXIII.,
LXXXIV., LXXXV., LXXXVI., LXXXVIL, 1877;
Mathematisch-Xaturw. (Mathematik), Bd. LXXIII.,
Hefte 4-5; Bd. LXXIV., LXXV., LXXVI., Heft 1.
— From the Academy.

Jahrbuch der Kaiserl.-Konig. Geologischen Reichanstalt.

Jahrg. 1877, Bd. XXVII., Xos. 2, 3, 4 8vo.
Verhandlungen der K, K. Geologischen Reichanstalt. Xos.
5-10. 1877. 8 vo.

758

Proceedings of the Royal Society

Vienna. — Abhandlungen der K K. Geologischen Reichanstalt.

Band VII., Heft. 4. Ueber Oesterreicliiscbe Mastodonten.
Wien 1877. 4to.

K. K. Geologische Reichanstalt. Beitrage zn Kenntniss der
Flora der Yorwelt. Heft. II. Die Culm-Flora der
Ostrauer und Waldenburger Schichten, von D. Stur.
Wien. 1877. Fol. — From the Institute.

Verhandlungen der K. K. Zoologiscb-botanischen Gesell-
cbaft. Jabrg. 1877. Bd. XXVII. — From the Society.
Zeitscbrift der Oesterreichischen Gesellschaft fur Meteoro-
logie. Bde. VI-XII. 1871-77. 8vo.

Jahrbiicher der K.-K. Central Anstalt fur Meteorologie
und Erdmagnetismus, Bd. III. 1852, Bd. V. 1853. Neue
Folgen, Bd. I. 1864, Bd. II. 1865, Bd. III. 1866 ;
Bd. IV. 1867, Bd. V. 1868, Bd. VI. 1869, Bd. VII.
1870, Bd. VIII. 1871, Bd. IX. 1872, Bd. X. 1873,
Bd. XI. 1874, Bd. XII. 1875.— From the Society.
Warwick. — Proceedings of the Warwickshire Naturalists’ and
Archaeologists’ Field Club. 1877. 8vo. — From the Field
Club.

Warwickshire Natural History and Archaeological Survey.
Forty-first Annual Report, 1877. 8vo.- — From the Survey.

Washington. — Washington Astronomical and Meteorological Observa-
tions for 1874. Wash., 1877. 4to.

Continuation of De Damoiseau’s Tables of the Satellites of
Jupiter to the year 1900. By D. P. Todd. 1876. 4to.
Investigation of Corrections to Hansen’s Tables of the Moon.

By Simon Newcomb. Wash., 1876. 4to.

Telegraphic Determination of the Differences of Longitude
in the W. Indies and Central America. By F. N. Green.
Wash., 1877. 4 to.

American Ephemeris and Nautical Almanac for 1878 and
1880.

A New System of Binary Arithmetic. By Benj. Peirce.
1876. 4 to.

The Elements of the Differential Calculus founded on the
Method of Fluxions. Part Third. By J. M. Rice and
W. Woolsey Johnson. Wash., 1876. 8vo.

759

of Edinburgh, Session 1877-78.

Washington. — Daily Bulletin of Weather- Beports, with the Synopses,
Probabilities, and Pacts, from May to December 1873,
and from January 1873 to September 1874.

Contributions to North American Ethnology. Vol. I.
Washington, 1877. 4to.

United States Geological Survey of the Territories. Miscellan.
Pub., No. 8. Fur-bearing Animals: A Monograph of the
American Mustelidae. Contributed to the History of
North American Mammals, by Elliott Coues. Washington,
1877. 8vo.

Ninth Annual Report of the United States Geological
and Geographical Survey of the Territories, embracing
Colorado and adjacent Territories, being a Report of
Progress for 1875. 1877. Svo.

Report of the United States Geological Survey of the Terri-
tories. By F. V. Hayden, U.S. Geologist in charge.
Vol. IX. — Invertebrate Palaeontology, by F. B. Meek.
Washington, 1876. 4to. Yol. XL — Monograph of
North American Rodentia, by Elliott Coues and Joel
Asaph Allen. Wash., 1877. 4to.

Bulletins of the U.S. Geological and Geographical Survey of
the Territories. — Yol. II. No. 2, 1876 ; Yol. III. Nos.
1-4, 1877 ; Yol. IY., No. 1, 1878. Wash. 8vo.

U.S. Geographical and Geological Survey of the Rocky
Mountain Region. — Palaeontology of the Black Hills
(Preliminary). By R. P. Whitfield. Wash., 1877. 8vo.

Geological Survey ; Miscellaneous Publications, No. 9,
Descriptive Catalogue of Photographs of N. American
Indians. By W. H. Jackson. Wash., 1877. 8vo.

Microscopical Petrography. By Ferdinand Zirkel. Wash.,
1876. 4to.

Report of the U.S. Geographical Surveys, west of 100th
Meridian. Yol. IY. — Palaeontology. Parti. — Report upon
the Invertebrate Fossils in Nevada, ] Utah, Colorado,
N. Mexico, and Arizona, by Charles A. White, M.D.
Part II. — Report upon the Extinct Yertebrata in New
Mexico, by Professor E. D. Cope.

Barometric Hypsometry : Instructions. 1876.

760 Proceedings of the Royal Society

Washington. — Catalogue of Publications of the U.S. Geological
and Geographical Survey of the Territories. 1877.
8vo.

Report of the Physics and Hydraulics of the Mississippi
River ; upon the Protection against Overflow, and upon
Deepening the Mouths. By Captain A. A. Humphreys
and Lieut. H. L. Abbot. Wash., 1876. 4to.

Report of a Reconnaissance from Carroll (Montana Territory)
to the Y ellowstone National Park, in 1 8 7 5. By W. Ludlow.

1876. 4 to.

Narrative of the North Polar Expedition, U.S. ship Polaris,
Capt. C. E. Hall, commanding. Wash., 1876. 8vo.
United States Coast Survey. Methods, Discussions, and
Results. Field-work of the Triangulation. Wash., 1877.
4to.

United States Coast Survey. Methods, Discussions, and
Results. Measurements of Terrestrial Magnetism. Second
Edition. Wash., 1877. 4to.

United States Hydrographic Office. Navigation of the
Caribbean Sea and Gulf of Mexico. Yol. I. The
West India Islands. Compiled by F. M. Green. Wash.,

1877. 8vo.

The Coasts of Chili, Bolivia, and Peru. Wash., 1876. 8vo.
Coasts and Ports of the Gulf of Lyons and Gulf of Genoa.

By H. H. Gorringe and S. Schroeder. Wash., 1877. 8vo.
List of Lights on West Coast of Africa and the Mediterranean
Sea. Wash., 1877. 8vo.

West Coast of Africa. Part III. Wash., 1877. 8vo.
Bureau of Navigation. List of Charts of North and South
Atlantic Stations (1877), of Pacific Stations (1877).

List of Charts of the European Stations, 1877.

Coast of South Australia ; Hydrographic Notice. 8vo.

List of Lights of English Channel and of British Islands.
1877. 8vo.

Sailing Directions for the English Channel. Part II.
Wash., 1877. 8vo.

Discussion of Tides in New York Harbour. By William
Eerrel. 1875. 4to.

of Edinburgh , Session 1877-78.

761

Washington. — List of Lights of the Atlantic Coast of Europe, the
English Channel, and North Sea. Wash., 1877. 8vo.
Catalogue of Charts, Plans, and Views, published by the
U.S. Hydrographic Office. Wash., 1876. 8vo.

Bureau of Navigation. List of Charts for the Asiatic Station.
1877. Fob

Historical Sketch of the U.S. Naval Academy. By Professor
J. R. Soley. Wash., 1876. 8vo.

Catalogue of Minerals of the U.S. Naval Academy. 1877. 8vo.
A History of the Rock Island Arsenal (1863-1876), and of
Rock Island (1804-1863). By D. F. Flagler. Wash.,
1877. 4to.

Contributions to the History of Medical Education and
Medical Institutions of the U.S. By N. S. Davis, M.D.
Wash., 1877. 8vo.

Reports of the Board of Indian Commissioner, 1875, and of
Indian Inspector, 1876. 8vo.

Bulletins of the U.S. National Museum. No. 4 — Birds of
S.W. Mexico. No. 5 — Catalogue of Fishes of the Ber-
mudas. No. 6 — Animal Resources of U.S. No. 7 —
Natural History of Hawaiian and Fanning Islands and
Lower California. No. 8 — Subdivisions of the Class
Brachiopoda. No. 9 — N. American Ichthyology.

A Manual of the Common Native Trees of the Northern U.S.
Wash., 1877. 8vo.

Report upon the Yellowstone National Park. By P. W.
Norris. Wash., 1877. 8vo. — From the Government.

The Royal Society has also received many other publi-
cations from Washington, chiefly relating to the
proceedings of Congress and the Civil Service of the
United States.

Wellington. — Transactions and Proceedings of the New Zealand
Institute. Vol. IX. Part 2, 1876 ; VoL X., 1877.
Index to Vols. I. -III. — From the Institute.

Maps of the Buller Coal-Field, New Zealand. By W. M.
Cooper and James Hector, M.D. Geological Survey of
New Zealand. 1877. FoL — From the Geological Survey
Office.

762 Proceedings of the Royal Society

Wellington. — Twelfth Annual Report of the Colonial Museum and
Laboratory. 1877. 8vo.

Statistics of the Colony of New Zealand for the years 1875,
1876, compiled from official abstracts in the Registrar
General’s Office. Wellington. Fol.

Wurzburg. — Die Medicinische Fakultat in Wurzburg. Ueber die
Jacobson’schen Organe des Menschen, von A. Kolliker.
Leipz., 1877. 4to.

Ein neuer Wellenzeichner, von A. Fick. Leipz., 1877.
4to.

Die Bosartigkeit der Carcinome dargestellt als eine Folge
ihrer ortlichen Destructivitat, von Dr Georg Eduard
Rindfleisch. Leipzig, 1877. 4to. — From the Medical

Facidty.

York. — Yorkshire Philosophical Society. Annual Report for 1877.
York. 8vo.

Communications of the Monthly Meetings of the York-
shire Philosophical Society. 1876. 8vo. — From the
Society.

Zurich. — Nouveaux M^moires de la Socffite des Sciences Naturelles.

Band XXVII. Abth. II. 1877. 4to. — From the Society.
Schweizerische Meteorologische Beobachtungen. 12er Jahrg.
1875, Lief. 6; 14er Jahrg., Lief. 1, 2. Supplementband,
Lief. 3.

Schweizerische Meteorologische Beobachtungen. Jahrgang
XII., 7e Lief., Titel u. Beilagen ; XIII., 5e Lief.; XIV.,
3e Lief. — From the Meteor olog. Central-Anstcdt.

II. From Authors.

Ardissone (Franc.). Enumerazione delle Alghe della Marca di
Ancona. Fano, 1866. Fob

Le Alghe; Sunto di alcune Lezioni di Botanica Crittogamica.
Milano, 1875. 8vo.

— La Vie des Cellules et Y Individuality dans le Regne Vegetal,

Traduit par Andre Champseix. Milano, 1877. 8vo.

Blacker (Rev. Beaver H.). Monumental Inscriptions in the Parish
Church of Cheltenham, Gloucester. London, 1877. 4to.

of Edinburgh, Session 1877-78.

763

Buchan (Alexander, Sek. Skot. Meteorolog. Sallsk.) Meteorologiens
Forsta Grunder : Ofversattning och delvis Bearbetning af H.
H. Hildebrandsson, Adj. vid Upsala Universitet. Upsala,
1874. 8vo. — From, Professor H. H Hildebrandsson.
Burmeister (H.) Description Physique de la Republique Argentine.
Traduite de I’AHemand, avec le concours d’ E. Daireaux,
Tome II. Paris, 1876. 8vo.

Cheseaux (T. Ph. L.) Remarques astronomiques sur le Livre de
Daniel. Lausanne, 1777. MS. 4to. — From Dr Handy side,
F.R.S.E.

Davidson (G.) and Schott (C. A.). Comparison of the Methods of
determining Heights by means of Levelling, Vertical Angles,
and Barometric Measures. Washington, 1871. 4to.

Du Breuil (Guillaume). Style du Parlement de Paris. Paris,

1877. Fol. — From the Editor , Paris.

Fayrer (Sir Joseph). The Bael Fruit and its Medicinal Properties. 1878.
Gamgee (Sampson). On the Treatment of W ounds ; Clinical Lectures.

1878. 8vo.

Gairdner (Prof. W. T.). Two Introductory Addresses — I. Lec-
tures, Books, and Practical Teaching; II. Clinical Teaching.
Glasgow, 1877. 8vo.

Gray (Robert). The Birds of the West of Scotland, including the
Outer Hebrides, with occasional Records of the occurrence of
the rarer species throughout Scotland generally. 1871. 8vo.
Holmgren (Prof. F.). De la Cecite des Couleurs dans ses rapports
avec les Chemins de Fer et la Marine.

Lancaster (A.). Quelques Remarques it propos de l’Hiver, 1876-77.
Periodicite des Hivers doux et des Et4s chauds. Brux.
1877. 8vo.

Listing (Johann B.). Heue Geometrische und Dynamische Constan-
ten des Erdkorpers; Eine Fortsetzung der Untersuchung : —
iiber unsere jetzige Kenntniss der Gestalt und Grbsse der Erde.
Gottingen, 1878. 8vo.

Lloyd (Humphrey). Miscellaneous Papers connected with Physical
Science. Lond. 1877. 8vo.

Main waring (Colonel G. B.). A Grammar of the R6ng (Lepcha)
Language, as it exists in the Dorjelling and Sikim Hills.
Calcutta, 1876. 4to. — From the Author.

5 H

VOL. ix.

764 Proceedings of the Royal Society

Martius (C. F. P. von). Memoir of C. F. P. von Martius, by
Charles Eau. Washington, 1871. 8vo.

Meldrum (C.). Sunspots and Kainfall. Mauritius, 1878. Fol.
Melsens (M.). De 1’ Application du Ehe-electrometre aux Paraton-
nerres des Telegraphes. Brux. 1877. 8vo.

Millar (W. J.). On the Transmission of Yocal and other Sounds by
Wires. 1878. 8vo.

Miller (John). Metaphysics ; or the Science of Perception. New
York, 1875. 8vo.

Milne Edwards (M.). Beckons sur la Physiologie ct l’Anatomie Com-
pare de l’Homme et des Animaux faites k la Faculty des
Sciences de Paris. Tome XII. 2me Partie. Paris, 1876-77.
8vo.

Mueller (Baron Ferdinand von), M.D. Fragmenta Phytographiae
Australiae. Yol. X. Melbourne, 1876-77. 8vo.

See Wittstein (Dr G. C.).

Muir (Dr John). Original Sanskrit Texts on the Origin and His-
tory of the People of India. 2d Edition. Yols. I. -III.
1872.

Fourth Set of Metrical Translations from the Sanskrit.

Edin. 1878. 8vo.

Neumeyer (M.). La Tempete du 12 Mars 1876. Brux. 1876.
8vo.

Plantamour (E.). Eecherches Experimental sur le Mouvement
Simultane d’ un Pendule et de ses Supports. Geneve, 1878.
4to.

Quetelet (E.). Memoire de la Temperature de l’Air k Bruxelles
1833-1872 (Supplement). 4to. — From the Author.

Quelques Nombres Characteristiques Eelatifs a la Tempera-
ture de Bruxelles. Brux. 1875. 8vo.

Sur la Periode de Eroid du Mois de Decembre 1875. Brux.

1875. 8vo.

— Note sur la Temperature de l’Hiver de 1874-75. Brux.
1875. 8vo.

La Tempete du 12 Mars 1876. Brux. 1876. 8vo. — From

M. E. Quetelet.

Eobinson (Charles). The Progress and Eesources of New South
Wales. Sydney, 1877. 8vo.

765

of Edinburgh, Session 1877-78.

Rossetti (Prof. Francesco). Sui Telefoni senza Lamine. 1878. 8vo.

— — Relazione su alcune Esperienze Telefoniche. Venezia, 1878.

8vo.

Sulla Temperatura delle Fiamme. Venezia, 1878. 8vo.

Sulla Temperatura del Sole. Padova, 1878. 4to.

Scheffler (Hermann). Die Naturgesetze und ihr Zusammenhang
mit den Prinzipien der Abstrakten Wissenschaften. Theil. I.
Lief. 1, 2; Theil. II. Lief. 1, 2. Leipzig, 1876-77. 8vo.

Snow (Edwin M.), M.D. Report upon the Births, Marriages, and
Deaths in the City of Providence for 1872. 8vo. — From Dr
E. M. Snow.

Stevenson (David). Lectures: Canal and River Engineering, de-
livered at the School of Military Engineering, Chatham.
Chatham, 1877. Fol.

Stevenson (Thomas). Die Illumination der Leuchtthiirme : Eine
Beschreibung des Holophotal-Sy stems u. anderer Leuchtthurm-
Apparaten. Bearbeitet von Chr. Nehls. Hannover, 1878.
8vo. — From the Author.

Tennant (Colonel J. F.). Report of the Preparations for, and Ob-
servations of the Transit of Venus as seen at Roorkee and
Lahore on December 8, 1874. Calcutta, 1877. 4to.

Terby (F.) et Quetelet (E.). Ar^ographie ; ou Etude sur 1’ Aspect
de la Planete Mars. 1874. 8vo.

Tommasi (Donato). Riduzione dei Clorati in Cloruri senza l’inter-
vento del preteso Stato ISTascente dell’ Idrogeno. 1877. 8vo.

Sull’ azione della cosi detta Forza Catalitica spiegata secondo

la Teoria Termodinamica. 1878. 8vo.

Toner (J. M.), M.D. On the Natural History and Distribution of
Yellow Fever in the United States from 1668 to 1874. Wash-
ington, 1874. 8vo.

Dictionary of Elevations and Climatic Register of the

United States. New York, 1874. 8vo.

Wittstein (Dr G. C.) and Mueller (Baron Ferd. von). The Organic
Constituents of Plants and Vegetable Substances, and their
Chemical Analysis. 8vo. Melbourne, 1878. — From the Baron
Ferd. v. Mueller.

Wright (C. R. A.). Metals and their chief Industrial Applications.
Loud. 1875. 1 2 mo.

INDEX

Absorption of Light by Magnetism,
by Professor Tait, 118.

Acetylene, Action of Chlorides of
Iodine upon, 588.

— Preparation of, 590.

Adamantine Boron, 721.

Aitken (David), D.D., Obituary Notice
of, 14.

Aitken (John), Experiments illustrat-
ing Rigidity produced by Centri-
fugal Force, 73.

— on Ocean Circulation, 394.

Albert (Prince), Remarks by, 31.

Albite, 393.

Alexander (Rev. Dr W. Lindsay)
delivers Opening Address for Ses-
sion 1876-77, 204.

■ contributes Obituary Notices

of Sir George Harvey, Dr J. War-
burton Begbie, Mr David Bryce,
Mr George Stirling Home Drum-
mond, Mr Alexander Russel, Pro-
fessor Laycock, George Marquis of
Tweeddale, M. Adolphe Pictet, M.
A. T. Brongniart, and M. C. G.
Ehrenberg, 205-231.

Ammonia-Cupric Zinc Chloride, by
Dr E. W. Prevost, 302.

Amphicheiral Forms and their Rela-
tions, 391.

Annelids, Great Nerve Cords in
Marine, by W. C. MTntosh, M.D..
372.

— An unnamed Palaeozoic Anne-

lid, by Professor Duns, 352.

Arch. — On a Stable and Flexible Arch,
by Professor Fleeming Jenkin, 151.

Arrangements, On a Problem of, by
Professor Cayley, 338, 402.

Professor Tait’s Problem of,

by Mr T. Muir and Professor Cayley,
382, 388, 402.

Asia, Physical Observations in Nor-
thern, by Professor George Forbes,

161.

Atmosphere. — On the Percentages of
the Atmosphere and the Ocean,
which would flow into a Rent on
the Earth’s Surface, by Professor
Tait, 333.

Atmospheric Phenomena, by Profes-
sor Tait, 170, 425.

Augite, by Professor Heddle, 595.

AuriferousQuartzofWanlockhead,579.

Bacon (Lord), his New Atlantis, 474,
475.

liis Influence in promoting

Experimental Philosophy, by Sir
Alex. Grant, 484, 485.

Appreciation of his Literary

and Scientific Writings, by Sir
Alex. Grant, 485.

Balance. — On a NewFormof Precision
Balance, by William Dittmar, 144.

Balfuur (Professor) contributes Obitu-
ary Notice of the Rev. D. T. K.
Drummond, 518 ; also, Obituary
Notice of William Keddie, 518.

Ballistic Curves, Tables of, and their
application to Gunnery, by E. Lang,
637.

Barometer, its Diurnal Oscillations,
by Alex. Buchan, M.A., 410.

Why the Barometer does not

always indicate real Vertical Pres-
sure, byR. Tennent, 412.

Barometric Depressions (or Storms),
Progressive Movement of, by Mr
Robert Tennent, 570.

Beats of Imperfect Harmonies, by Sir
William Thomson, 602.

Begbie (Dr James Warburton), Obitu-
ary Notice of, 209.

V68

Index.

Beknottedness. See Knots.

Bennett (Professor John Hughes),
Obituary Notice of, 15.

Bifilar Magnetometer, 402.

Biliary Secretion, The, with refer-
ence to the Action of Cholagogues,
by Professor Rutherford and M.
Vignal, 334, 718.

Binocular Vision of Colour, 654.

Blackie (Professor) on the Origin of
Language, 98.

Is the Gaelic Ossian a Trans-
lation from the English ? 151.

on Gladstone’s Theory of

Colour-Sense in Homer, 533.

Blaikie (J. Adrian), Action of Heat on
some Salts of Trimethyl-Sulphine,
565, 712.

Blair (Dr), his “Scientific Aphorisms ”
in connection with the Ultra-
Mundane particles of Le Sage, 415.

Blyth (James) substitutes Copper-
Plate, Wood, India-rubber, &c.,
for the Iron Disc of Telephone,
535.

his experiments with the

Telephone, 553.

An Account of some Experi-
ments on the Telephone and Micro-
phone, 711.

Boron, Adamantine, 721.

Boulder Committee, Third Report of,
by D. Milne Home, Esq., 170.

Fourth Report of, by D. Milne

Home, Esq., 660.

Bow (R. H.) on the Splitting up of
Electric Currents and the founding
thereon of a Sounder to call atten-
tion from one Telephone to another,
707.

Brongniart (Adolphe Theodore), Obit-
uary Notice of, 229.

Broun (J. A.) on the Decennial Period
in Diurnal Oscillation of Magnetic
Needles, and of the Sun Spot Area,
155.

on the Bifilar Magnetometer,

402.

Brown (Professor Crum) awarded
the Keith Prize for the biennial
period 1873-75, for “ Researches on
the Sense of Rotation and on the
Semi-Circular Canals of the Inter-
nal Ear,” 153, 231.

on the Action of Sulphuretted

Hydrogen on the Hydrate and
Carbonate of Trimethyl-Sulphine,
319.

Brown (Professor Crum) on the Action
of Heat on some Salts of Trimethyl-
Sulphine, 565.

— on the Action of Heat on some

Salts of Trimethyl-Sulphine, 712.

his Apparatus for producing

Vowel Sounds, 723.

on Certain Effects of Periodic

Variation of Intensity of a Musical
Note, 736.

Bryce (David), ObituaryNoticeof,216.
Bryce (Dr James), Obituary Notice of,
by his son, Professor Bryce, Oxford,
514.

Bryce (Professor) contributes Obitu-
ary Notice of his Father, Dr James
Bryce, 514.

Buchan (Alexander), M.A., on the
Annual Periods of Thunder (with
Lightning), Lightning (only), Hail
and Snow, at Oxford, 135.

on a Peculiarity of the Diurnal

Hygrometric Curve at Geneva, 304.

Presentation of the Makdou-

gall-Brisbane Prize to, 319, 486.

on the Diurnal Oscillations of

the Barometer, 410.

Report of the Deputation to

Upsala, 521.

Note on a White Sunbow, 546.

Buchanan (J. Y.) on the Specific
Gravity of Ocean Water, 283.

on the Manganese Nodules

found on the Bed of the Ocean, 287.

on the Air Dissolved in Sea-

Water, 412.

Burton (Captain), Volcanic Eruptions
of Iceland in 1874 and 1875.
Calculus of Operations, Certain For-
mulae in, by Professor Stokes, 101.
Canon of Sines for each 2000th part
of the Quadrant to 33 places, and
true to the 30th Figure, by E. Sang,
536.

Cayley (Professor) on a Problem of
Arrangements, 338, 402.

— on Mr Muir’s Solution of a

“ Problem of Arrangement,” 402.
Centrifugal Force as producing Rigi-
dity, 73.

Cetacea, On the Placentation of, by
Professor Turner, 103.

Charcoal, Thermo-Electric Properties
of, 579.

Chemical Combinations, 537.
Cholagogues. See Biliary Secretion.
Christison (J.), Note on a White
Sunbow, 545.

Index.

769

Christison (Sir Robert). Note on a
White Sunbow, 542.

Circles, — Properties of two sets of three
Concentric Circles, intersecting one
another, by Professor Tait, 533.

Clapeyron’s Formula, Note on, by Pro-
fessor Dewar, 283.

Closed Plane Curves. See Curves.

Cobalt, Note on the Thermo-Electric
Position of, by Professor Tait, 138.

Note on the Thermo-Electric

Properties of, by Messrs Knott,
MacGregor, and C. M. Smith, 170.

Cocoa-Nut Oil, On the Solid Fatty
Acids of, by G. Carr Robinson, 537.

Cohesion. — On the connection between
Cohesion, Elasticity, Dilatation,
and Temperature, by Professor
George Forbes, 141.

of Liquids, by J. B. Hannay,

526.

Colour. — Method of Studying the
Binocular Vision of Colour, by
Professor M‘Kendrick, 654.

in Practical Astronomy, by

Professor Piazzi Smyth, 721.

Columnar Vortices, Vibrations of a
Triad of, by Sir William Thomson,
660.

Combinations (Chemical), 537.

Conductivity of Stretched Silver
Wires, by J . G. MacGregor, M. A., 79.

Coniferae, On the Defoliation of the,
by Dr Stark, 85.

Constant (Cyclic) of a Vortex, p. 70.

Continued Fractions, Transformation
of Infinite Series into, by Thomas
Muir, M.A., 117.

Cook (J.) on an Improved Form of
Galvanic Battery, 148.

Corals, On New Forms of Palaeozoic,
by Professor Alleyne Nicholson
and James Thomson, 149.

Core, or Vortex Core, by Sir W.
Thomson, 69.

Coventry (Andrew), Obituary Notice
of, by Sir Alex. Grant, 506.

Crawford (Dr Thomas Jackson), Obit-
uary Notice of, 17.

Crystals, Note on Circular, by E. W.
Dallas, 129.

Curves. — Applications of Theorem
that Two Closed Plane Curves
intersect an even number of times,
by Professor Tait, 237.

• On the Curves produced by Re-

flection from a Polished Revolving
Wire, by Edward Sang, 302.

Curves. — Tables of Ballistic Curves
applied to Gunnery, by E. Sang, 637.

On a Peculiarity of the Diur-
nal Hygrometric Curves at Geneva,
by Alexander Buchan, 304.

Cyclic Constant of a Vortex, 69.

Dallas (E. W.), Note on Circular
Crystals, 129.

Danube, Works for the Improvement
of the, designed by Sir Charles A.
Hartley, by David Stevenson, 142.

De Candolle (Alphonse) elected an
Honorary Fellow, 287.

De la Rive (M.) on Sounds emitted
by Induction Coils, 627, 628.

Determinants. — On Determinant Ex-
pressions for the Sum of aHarmoni-
cal Progression, by T. Muir, 361.

On a Class of Determinants,

by J. D. H. Dickson, 714.

Dewar (Professor) on Clapeyron’s
Formula, 283.

Diamagnetic Rotation, by Prof.
George Forbes, M.A., 85.

Dickson (J. D. Hamilton) on the
Least Roots of Equations, 393.

on a Class of Determinants, 714.

Differential Equation of Second Order.
See Equation.

Digester. — On a Glass Digester in
which to heat Substances under
Pressure, by Dr E. A. Letts, 139.

Dilatation. — On the Connection be-
tween Cohesion, Elasticity, Dilata-
tion, and Temperature, by Professor
George Forbes, 141.

Disruptive Discharge of Electricity,
by Alex. Macfarlane, M.A., and P.
M. Playfair, M.A., 563, 721.

Dittmar (William) on New Forms of
Precision Balance and Gas governor,
145.

Can the Law of Multiple

Proportions be demonstrated from
Analytical Data ? 536.

Diurnal Oscillations of the Barometer,
Part II., by Alex. Buchan, M.A.,
410.

Donations to the Library, 739-765.

Dove (Heinrich Wilh.) elected an
Honorary Fellow, 43.

Drummond (Rev. David Thomas Ker),
Obituary Notice of, by Professor
Balfour, 518.

Drummond (George Stirling Home),
Obituary Notice of, by Dr W. L.
Alexander, 218.

770

Index.

Dudgeon (Patrick) on a New Fossil
Foot- print from Permian Sandstone,
154.

exhibits Specimen of Auri-
ferous Quartz, 333.

Dundas (Sir David), Obituary Notice
of, by Sir Alex. Grant, 508.

Duns (Professor) on the Ruff ( Machetes
pugnaz), 272.

on an Unnamed Palaeozoic

Annelid, 352.

Durham (William) on Suspension,
Solution, and Chemical Combina-
tions, 537.

Earthquake Shocks in Argyleshire in
1877, by D. Stevenson, 403.

Ehrenberg (Christian Gottfried), Obit-
uary Notice of, 230.

Eisenstein’s Continued Fraction, by
Thomas Muir, 359.

Elasticity. On the Connection be-
tween Cohesion, Elasticity, Dilata-
tion, and Temperature, by Prof.
George Forbes, 141.

Electric Conductivity of Bars, by
Prof. Tait, 718.

• of Nickel, by C. Michie Smith

and J. Gordon MacGregor,

of Stretched Silver Wires, by

J. G. MacGregor, M.A., 79.

Electric Current, On the Passage of
the, from Amalgamated Zinc Sul-
phate Solution, by J.G. MacGregor,
170.

Electric Currents produced by Con-
tact of Wires, 333.

On the Splitting up of Electric

Currents, as detected by the Tele-
phone, 707.

Electricity, Disruptive Discharge of,
563.

Electrolytic Conduction, by Prof.
Tait, 614.

Electrostatic Attraction, On Some
Effects of Heat on, by Professor
Tait, 302.

Equations, Linear Differential, of
Second Order, by Professor Tait,
93, 118.

Equation V p<pp = 0, by Gustav Plarr,
237.

• Least Roots of, by J. D.

Hamilton Dickson, 393

Ethylene, Action of Chlorides of
Iodine upon, 588.

Ewing (Mr J. A.), Remarks on the
Phonograph, 579.

Ewing (Mr J. A.) on the Wave
Forms of Articulate Sounds, 582
714.

on the Wave Sounds pro-
duced by the Apparatus exhibited
by Professor Crum Brown, 723.

Faraday (Professor), Rotation of Plane
of Polarization of Light, 85, 118

Ferguson (Dr R. M.), Note on a White
Sunbow, 548.

on Indications of Molecular

Action in the Telephone, 615.

Fire-Damp, On a Method of Detecting,
613.

Fishes, New and Little-Known Fossil,
from the Edinburgh District, by Dr
R. H. Traquair, No. 1, 262; No. 2,
275 ; No. 3, 394, 427.

Footprint, On a New Fossil, from
Permian Sandstone, by Patrick
Dudgeon, 154.

Forbes (Professor George) on Diag-
magnetic Rotation, 85.

on the Connection between

Cohesion, Elasticity, Dilatation, and
Temperature, 141.

Physical Observations in

Northern Asia, 161.

on the Theory of the Tele-
phone, 555.

Preliminary Note on a Method

of Detecting Fire-Damp in Coal
Mines, 613.

Fossil Fishes. See Fishes.

Fractions.— Transformation of Infinite
Series into Continued Fractions, by
Thomas Muir, M.A., 117.

Tabulation of all Fractions

whose Values are between two pre-
scribed limits, by E. Sang, 536.

French Horn, Mouthpiece for Produc-
ing Chords from, 536.

Fungus Disease affecting Salmon, by
A. B. Stirling, 726.

Galvanic Battery, On an Improved
Form of, by J. Cook, 148.

Garnets, by Professor Heddle, 550.

Gas-Coke, Thermal Conductivity of,
333.

Gases, Vortex Theory of, Condensa-
tion of Gases on Solids, and Con-
tinuity between the Gaseous and
Liquid State of Matter, by Sir
William Thomson, 144.

Gas-governor, On a New Form of, by
William Dittmar, 147.

Index.

771

Gegeubaur (Professor Carl) elected an
Honorary Fellow, 287.

Geikie (Professor) exhibits Map show-
ing Progress of Geological Survey
of Scotland, 367.

on Saline Water from Vol-
canic Rocks of Linlithgow, 367.

Geological Survey of Scotland, 367.

Gibson (Dr J.) on a New Method for
the Separation of Yttrium and Er-
bium from Cerium, Lanthanum, and
Didymium, 734.

Gladstone (Mr), Remarks by, 40.

his Theory of Colour-Sense in

Homer, 533.

Glass Digester. See Digester.

Glass, Refractive Index of, 567.

Gordon (James) writes Latin Ad-
dress Presented by the Society’s
Deputation to the University of
Upsala, 521, 526.

Gordon (Lewis D. B.), Obituary
Notice of, 212.

Gott (M.) converts two Siphon Re-
corders into a Telegraphic System,
570.

Government Fund of £4000, 275.

Grant (Sir Alexander), V.P., contri-
butes Opening Address for Session
1877-78, 472.

contributes Obituary Notice

of the Hon. Lord Neaves, 503.

contributes Obituary Notice

of Andrew Coventry, Advocate, 506.

• contributes Obituary Notice

of Sir David Dundas, Bart., 508.

Graphic Methods of Determining the
Efficiency of Machinery, by Prof.
F. Jenkin, 381, 563.

Graphic Method applied to the De-
termination of the Efficiency of a
Direct-acting Steam Engine, by
Professor Fleeming Jenkin, 563.

Graphitoid, The Preparation and Pro-
perties of, by R. M. Morrison, 721.

Grieve (G. J. P.) on the Properties of
the Perigon Versor, 149.

Guthrie (Colonel Seton), Notice of
Death of, 4.

Harmonica! Progression, Sum of a,
361.

Harmonies (Imperfect), by Sir Wm.
Thomson, 602.

Hartley (Sir Charles A.), Works for
the Improvement of the Danube,
142.

Harvey (Sir George), Obituary Notice
of, 205.

Hawaiian Islands, Volcanoes of, by J.
W. Nichol, 113.

Heat. — On the Effect of Heat on In-
fusible Palpable Powders, by Pro-
fessor Tait, 298.

On some Effects of Heat on

Electrostatic Attraction, by Profes-
sor Tait, 302.

On an Effect of Heat in Elec-
trostatic Action, by Prof. Tait, 415.

On the Action of Heat on Some

Salts of Trimethyl-Sulphine, by
Professor Crum Brown and J.
Adrian Blaikie, 565, 712.

Heddle (Professor), The Mineralogy
of Scotland, Chap. I., Rhombohedral
Carbonates, 144; Chap. II., Ortho-
clase, Albite, &c., 393 ; Chap. III.,
The Garnets, 550 ; Chap. IV.,
Augite, Hornblende, and Serpen-
tinous Change, 595.

Helmholtz (H.), His Simple Circular
Ring, 68.

Holopus, The Structure and Relations
of the genus Holopus, by Sir C.
Wyville Thomson, 405.

Home (David Milne) delivers Opening
Address for Session 1875-76, 2.

on the Parallel Roads of

Lochaber, 159.

Third Report of the Society’s

Boulder Committee, 170.

Fourth Report of Boulder

Committee, 660.

Remarks by, on Presenting

the Boulder Committee’s Fourth
Report, 692.

Homer, Colour-Sense in, 533.

Horn. See French Horn.

Hornblende, by Professor Heddle, 595.

Hail and Snow at Oxford, by Alex.

Buchan, M.A., 135.

Hannay (J. B.) on a Method of De-
termining the Cohesion of Liquids,
526.

Handyside (Dr P. D.) on the Ana-
tomy of a Recent Species of Polyo-
don, the Polyodon gladius (Martens) ,
660.

VOL. IX.

Iceland, Volcanic Eruptions of, in
1874 and 1875, by Captain Burton,
44.

Identity. — Note on an Identity, by
Prof. Tait, 416.

Infinitude of Operations, by T. Muir,
359.

Infusible Palpable Powders. See
Powders.

5 i

77-2

Index.

Integrals. — On Some Definite In-
tegrals, by Professor Tait, 594.

Integrability, Vector Conditions of,
by Professor Tait, 527.

Integrating by Mechanism the General
Linear Differential Equation of
Second Order, by Prof. Tait, 118.

Integrator, Prof. James Thomson’s, 138.

Iodine, Action of Chlorides of, upon
Acetylene and Ethylene, 588.

Isomorphous Salts, The Crystallisa-
tion of, 732.

Isothermal Surfaces, by Prof. Tait, 170.

Jardine (Sir William), Obituary No-
tice of, 20.

Jenkin (Professor Fleeming) on a
Stable and Flexible Arch, 151.

on Graphic Methods of deter-
mining Efficiency of Machinery, 381.

Application of the Graphic

Method to the determination of the
Efficiency of a Direct-Acting Steam-
Engine, 563.

Considers M. Gott’s and Pro-
fessor Bell’s Explanation of the
Action of Telephone to be not
Erroneous, 570.

Remarks on the Phonograph,

579.

on the Wave Forms of Articu-
late Sounds, 582, 714.

on the Wave Forms of the

Vowel Sounds produced by Pro-
fessor Crum Brown’s Apparatus, 723.

Keddie (William), Obituary Notice
of, by Professor Balfour, 520.

Kelland (Professor) contributes Obit-
uary Notice of W. H. Fox Talbot,
512.

Kekule (August) elected an Honorary
Fellow, 43

Kidney, On some Physical Experi-
ments relating to the Function of
the, byDavidNewman, Glasgow, 648.

Knots. Theorem of Intersection of
Two Plane Curves, by Prof. Tait, 237.

— On the Measure of Beknot-

tedness, by Professor Tait, 289.

On Links, by Prof. Tait, 321.

Professor Tait’s Problem of

Arrangement, 382.

On Amphicheiral Forms and

their Relations, by Prof. Tait, 391.

On a New Method of Investi-
gating the Properties of, 403.

— Additional Remarks on, 405.

Knott (C. G.) on the Thermo-Electric
Properties of Cobalt, &c., 170, 421.

on the Thermo-Electric Pro-
perties of Charcoal, 579.

— on Thermal Conductivity of

Gas Coke, 333.

on Currents produced by Con-
tact of Wires, 333.

Kolbe (Herman) elected an Honorary
Fellow, 43.

Kummer (Ernst Eduard) elected an
Honorary Fellow, 43.

Laboratory Notes, by Professor Tait,
118.

Language, On the Origin of, by Pro-
fessor Blackie, 98.

Latin Address presented by the So-
ciety’s Deputation to the Univer-
sity of Upsala, 526.

Laycock (Professor Thomas), Obit-
uary Notice of, 223.

Leopold (Prince), Remarks by, 30.

Le Sage, Ultra-Mundane Particles of,
415.

Letts (Dr E. A.) on a Glass Digester
in which to heat Substances under
Pressure, 139.

Leucoline Series, New Bases of, by
G. Carr Robinson, 732.

Le Verrier (Urbain Jean Joseph),
Obituary Notice of, 489.

Lightning, Hail, and Snow at Oxford,
by Alex. Buchan, M.A., 135.

Lindsay (Dr Lauder) on the Auri-
ferous Quartz of Wanlockhead, 579.

Linear Differential Equation of
Second Order, by Professor Tait,
93, 118.

Links, by Professor Tait, 321.

Linlithgow, Saline Water from Vol-
canic Rocks of, 367.

Liouville (Joseph) elected an Honorary
Fellow, 43.

Liquid. — On Two-Dimensional Ap-
proximately Circular Motion of a
Liquid, by Sir William Thomson,
98.

Liquids, Method of Determining the
Cohesion of, by J. B. Hannay, 526.

Lochaber, On the Parallel Roads of,
by David Milne Home, LL.D., 159.

Logan (Sir William Edmund), Obitu-
ary Notice of, 9.

Login (Thomas), Obituary Notice of,
205.

Lyell (Sir Charles), Obituary Notice
of, 6.

Index.

773

Macdonald (Professor William), Obit-
uary Notice of, 22.

Macfarlane (Alex.), Potentials required
for Sparks of a Holtz Machine, 170,
332.

on Thermal Conductivity of

Gas-Coke, 333.

on Currents produced by Con-
tact of Wires, 333.

on the Disruptive Discharge

of Electricity, 563. 721.

on the Discharge of Electricity

through Turpentine, 579.

M‘Gowan (George), Action of Chlo-
rides of Iodine upon Acetylene and
Ethylene, 688.

MacGregor (J. Gordon) on the Electric
Conductivity of Nickel, 120.

on the Thermo-Electric Pro-
perties of Cobalt, &c., 170, 421.

on the Passage of the Electric

Current from Amalgamated Zinc
Sulphate Solution, 170.

— - — — on the Thermo-Electric Pro-
perties of Charcoal, 579.

Machetes pugnax , by Professor Duns,
272.

Machinery, Graphic Methods of Deter-
mination of Efficiency of, by Prof.
F. Jenkin, 381.

MTntosh (Dr W. C.) on the Structure
of the Body- Wall in the Spionidae,
123.

on Arrangement of Great

Nerve Cords in the Marine Anne-
lids, 372.

M'Kendrick (Professor), Some Experi-
ments with the Telephone, 558.

On a Method of Studying the

Binocular Vision of Colour, 654.

Mackenzie (Donald, Lord), Obituary
Notice of, 23.

Madeira, On Dredging in, by Rev. R.
B. Watson, 153.

Madvig (Professor J. N.) elected an
Honorary Fellow, 536.

Magnetic Needle, On Decennial
Period in Oscillation and Disturb-
ance of, by J. A. Broun, 155.

Magnetism. — On a Possible Influence
of Magnetism on the Absorption of
Light, by Professor Tait, 118.

Magnetometer (Bifilar), 402.

Makdougall-Brisbane Prize presented
to Alex. Buchan, M.A., 319.

Marsden (R. Sydney) on Pure
Graphitoid and Adamantine Boron,
721.

Masson (Prof.) contributes Obituary
Notice of John Lothrop Motley, 508.

Max Muller (Professor) on Origin of
Language, 98.

Microphone. — An account of some Ex-
periments on the Telephone and
Microphone, by James Blyth, M.A.,
711.

Note on a Variation of the, by

R. M. Morrison, D.Sc., 712.

Mineralogy of Scotland, by Professor
Heddle — Chap. I., Rhombohedral
Carbonates, 144 ; Chap. II., Ortho-
ciase, Oligoclase, &c., 393; Chap.
III., the Garnets, 550 ; Chap. IV.,
Augite, Hornblende, and Serpen-
tinous Change, 595.

Molecular Action in the Telephone,
by Dr R. M. Ferguson, 615.

Monamines. — On a new General
Method of Preparing the Primary
Monamines, by R. Milner Morrison,
D.Sc., 721.

Monodon Monoceros , On the Placen-
tation of, by Professor Turner, 103.

Morrison (Dr R. M ), Note on a Vari-
ation of the Microphone, 712.

on a new General Method of

Preparing the Primary Monamines,
721.

on Pure Graphitoid and Ada-
mantine Boron, 721.

Motion. — Extended definition of

“ Steady ” Motion, 59.

On Two-Dimensional Approxi-
mately Circular Motion of a Liquid,
by Sir William Thomson, 98.

Motions, On Parallel, by Rev. John
Wilson, M.A., 161.

Motivity, On Thermo-Dynamic, by Sir
William Thomson, 144.

Motley (John Lothrop) elected an
Honorary Fellow, 43.

Obituary Notice of, by Profes-
sor Masson, 508.

Muir (Thomas), Transformation of
Infinite Series into Continued
Fractions, 117.

on Eisenstein’s Continued

Fraction, 359.

on an Infinitude of Opera-
tions, 359.

on Determinant Expressions

for Sum of a Harmonical Progres-
sion, 361.

on Professor Tait’s Problem

of Arrangement, 382, 402.

Multiple Proportions, 536,

774

Index.

Murray (John) on the Distribution of
Volcanic Debris over the Floor of
the Ocean, 247.

Musical Note, Periodic Variation of
Intensity of, 736.

Neaves (The Hon. Lord), Obituary
Notice of, by Sir Alexander Grant,
603.

Neill Prize for the triennial period
1874-77 awarded to Dr Traquair,
549.

Nerve Cords in Marine Annelids, 372,

Newman (David) on some Physical
Experiments relating to the Func-
tion of the Kidney, 648.

Nichol (J. W.) on the Volcanoes of
the Hawaiian Islands, 110.

Nicholson (Professor Alleyne) on
New Forms of Palaeozoic Corals,
149.

Nickel, The Electric Conductivity of,
by C. Michie Smith and J. Gordon
MacGregor, 120.

Note. — Periodic Variation of Intensity
of Musical Note, 736.

Obituary Notices : —

Aitken (David), D.D., 14.

Auld (John), 4.

Begbie (Dr James Warburton),
209.

Bennett(Professor John Hughes),
15.

Brongniart (Adolphe Theodore),

229.

Bryce (David), Architect, 216.

Bryce (Dr James), 514.

Coventry (Andrew), Advocate,
506.

Crawford (Dr Thomas Jackson),

17.

Drummond (Rev. David Thomas
Ker), 518.

Drummond (George Stirling
Home), 218.

Dundas (Sir David), of Dunira,
508.

Ehrenberg (Christian Gottfried),

230.

Gordon (Lewis D. B.), 212.

Harvey (Sir George), 205.

Jardine (Sir William), 20.

Keddie (William), 520.

Laycock (Professor Thomas),
223.

Le Verrier (Urbain Jean Joseph,
489.

Obituary Notices — continued —

Logan (Sir Wm. Drummond), 9.

Login (Thomas), 205.

Lyell (Sir Charles), 6.

Macdonald (Professor William),

22.

Mackenzie (Donald, Lord), 23.

Meldrum (Edward), 4.

Motley (John Lothrop), 508.

Neaves (The Hon. Lord), 503.

Pictet (Adolphe), 227.

Remusat (Charles, Comte de), 4.

Russel (Alexander), 219.

Sinclair (Archdeacon John), 24.

Talbot (W. H. Fox), 512.

Tweeddale (George, Marquis of),
225.

Wheatstone (Sir Charles), 11.

Ocean. — Distribution of Volcanic De-
bris over the Floor of the Ocean, by
John Murray, 247.

On the Manganese Nodules

found in the bed of the, by J Y.
Buchanan, 287.

On Relative Percentages of the

Atmosphere and the Ocean, which
would flow into a given Rent in
Earth’s Surface, 333.

Ocean Circulation, by John Aitken,
394.

Ocean Water, Note on the Specific
Gravity of, by J. Y. Buchanan,
283.

See Sea-Water.

Oligoclase, 393.

Operations, Note on an Infinitude of,
by Thomas Muir, 359.

Orthoclase, 393.

Orthogonal Isothermal Surfaces, by
Professor Tait, 170.

Ossian. — Is the Gaelic Ossian a Trans-
lation from the English ? by Pro-
fessor Blackie, 151.

Palseozoic Corals. See Corals.

Paton (Mr), Potentials required for
Sparks of a Holtz Machine, 170,
332.

Perigon Versor, On the Properties of
the, by G. J. P. Grieve, 149.

Phonograph. — Letter from H. E.
Rosevelt, Esq., to the President,
describing the Phonograph, 548.

Remarks on the Phonograph,

by Professor Fleeming Jenkin and
Mr J. A. Ewing, 579, 582, 714.

Pictet (Adolphe), Obituary Notice of,
227.

Index. 775

Placentation of the Cetacea (Monodon
Monoceros), by Prof. Turner, 103.

Plarr (Gustav) on the Roots of the
Equation V pcpp, 237.

Addition to Paper on Princi-
ples of Quaternions, 402.

Playfair (P. M.) on the Disruptive
Discharge of Electricity, 721.

Polyodon Gladius, Anatomy of, by Dr
P. D. Handyside, 660.

Potentials required for Sparks of a
Holtz Machine, by Alex. Macfarlane,
170, 332.

Powders — On the Effect of Heat on
Infusible Palpable Powders, by Pro-
fessor Tait, 298.

Precautions in using and recording
Original Computations, by E. Sang,
349.

Prevost (Dr E. W.) on Ammonia-
Cupric Zinc Chloride, 302.

Prizes. — Makdougall-Brisbane Prize,
presented to Alexander Buchan,
M.A., 319.

Neill Prize, presented to Dr

Traquair.

Progressive Movement of Barometric
Depressions or Storms, by Mr
Robert Tennent, 570.

Proportions. — Can the Law of Mul-
tiple Proportions be Demonstrated
from Analytical Data? by W.
Dittmar, 536.

Quartz, Specimen of Auriferous, 338.

— — — Refractive Index of, 567.

Auriferous, of Wanlockhead,

579.

Quaternions, addition to Paper “ On
the Establishment of the Element-
ary Principles of,” by G. Plarr, 402.

Quincke (Professor) on the Refractive
Indexes of Glass and Quartz, as
tested by Reflection from the Sur-
face, 567.

Remusat (Charles, Comte de), Obitu-
ary Notice of, 4.

Rhizodopsis, The Cranial Osteology
of, by Dr R. H. Traquair, 403, 444,
658.

Rhizodus, The Structure of, by Dr R.
H. Traquair, 403, 444, 657.

On the genus Rhizodus, 657.

Hibberti, 658.

■ Ornatus, 659.

Rhombohedral Carbonates, by Pro-
fessor Heddle, 144.

Rigidity produced by Centrifugal
Force, 73.

Robinson (G. Carr) on the Solid
Fatty Acids of Cocoa-nut Oil, 537.

on the Crystallisation of Iso-

morphous Salts, 732.

New Method for Separation of

Yttrium and Erbium from Cerium,
Lanthanum, and Didymium, 734.

on Some New Bases of the

Leucoline Series, 732.

Rosevelt (H. E.), Letter as to the
Phonograph, 548.

Rotation (Diamagnetic), by Professor
George Forbes, M.A., 85.

Ruff (Machetes Pugnax), by Professor
Duns, 272.

Russel (Alex.), Obituary Notice of, 219.

Rutherford (Professor) on the Biliary
Secretion, with Reference to the
Action of Cholagogues, 334, 718.

Salmon, Fungus Disease affecting, 726.

Salt, Note on the Flame produced by
putting Common Salt into a Fire,
by C. Michie Smith, 133.

Salts (Isomorphous), The Crystallisa-
tion of, 732.

Sang (Edward) on the Curves pro-
duced by Reflection from a Polished
Revolving Wire, 302.

on the Construction of a

Canon of Sines for Decimal Divi-
sion of Quadrant, 343.

on Precautions in Recording

and Using Records of Original
Computations, 349.

Toothing of Unround Disks

intended torollupon each other, 393.

Canon of Sines for each

2000th Part of the Quadrant to 33
Places, and True to the 30th
Figure, 536.

on the Tabulation of All

Fractions whose Values are be-
tween Two Prescribed Limits, 536.

on Arrangement of Tables of

Ballistic Curves, and their Applica-
tion to Gunnery, 637.

Saprolegnia, affecting Salmon, 730.

Sea-Water, The Air Dissolved in, by
J. Y. Buchanan, 412.

Compressibility of, by J. Y.

Buchanan, 565.

See Ocean -Water.

Series. — Transformation of Infinite
Series into Continued Fractions, by
Thomas Muir, M.A., 117.

776

Index.

Serpentinous Change, by Professor
Heddle, 595.

Silver Wires, Electrical Conductivity
of, by J. G. M'Gregor, M A., 79.

Simpson (R. J. S.) on the Discharge
of Electricity through Turpentine,
579.

Sinclair (Archdeacon John), Obituary
Notice of, 24.

Sines. — On the Construction of a
Canon of Sines for Decimal Division
of Quadrant, by Edward Sang, 343.

Canon of, for each 2000th

Part of the Quadrant to 33 Places,
by Edward Sang, 536.

Smith (C. Michie), on the Zodiacal
Light, 110.

on the Flame Produced by

Putting Common Salt into a Fire,
133.

on the Electric Conductivity

of Nickel, 120.

on the Thermo-Electric Pro-
perties of Cobalt, &c., 170, 421.

Smyth (Professor Piazzi) contributes
Obituary Notice of Urbain Jean
Joseph Le Verrier, 489.

on Colour in Practical Astro-
nomy, 721.

Sounder to Call Attention from one
Telephone to another, by R. H.
Bow, C.E., 707.

Sounds, Wave-Forms of Articulate, by
Professor Fleeming Jenkin, 582,
714, 723.

Sounds of very great Intensity, by
Professor Tait, 737.

Specific Gravity. See Gravity.

Spionidse, On the Structure of the
Body-wall in the, by Dr W. C.
MTntosh, 123.

Stark (Dr), on the Defoliation of the
Coniferae, 85.

Steam Engine, The Efficiency of,
Determined by the Graphic Me-
thod, by Professor Fleeming Jen-
kin, 563.

Stevenson (David), V.P., On Works
for the Improvement of the Danube,
Designed by Sir Charles A. Hartley,
142.

on Earthquake Shocks in

Argyllshire, 403.

Contributes Obituary Notices

of Mr Thomas Login, 205 ; and
Professor Lewis D. B. Gordon, 212.

Stewart (Professor Balfour) elected an
Honorary Fellow, 536,

Stirling (A. B.) on the Fungus
Disease Atfecting Salmon, 726.

Stokes (Professor) on Certain For-
mulse in the Calculus of Operations,
101.

Storms. See Barometric Depressions.

Struve (Otto), Elected an Honorary
Fellow, 536.

Sunbow, Notes on a White, by Sir
Robert Christison, Bart., Professor
Tait, Mr J. Christison, Mr Buchan,
and Dr Ferguson, 542-48.

Sunspots. — On the Decennial Period in
Sunspot Frequencv, by J. A. Broun,
155.

Surface of a Body in Terms of a
Volume-Integral, by Prof. Tait, 415.

Suspension, Solution and Chemical
Combinations, by William Dickson,
537.

Tabulation of Fractions. See Frac-
tions.

Talbot (W. H. Fox), Obituary Notice
of, by Professor Kelland, 512.

His Proof of Theorem, as to

Properties of Two Sets of Three
Concentric Circles, which have the
Same Common Difference of Radii,
and which Intersect one another,
533.

Tait (Professor) on the Linear Dif-
ferential Equation of the Second
Order, 93.

Mechanism for Integrating

the General Linear Differential
Equation of the Second Order, 118.

on Orthogonal Isothermal Sur-
faces, 170.

on Vector Conditions of In-

tegrability, 527.

Note on a Geometrical Theo-
rem, as to Properties of Two Sets
of Three Concentric Circles, which
have the same Common Difference
of Radii, and which Intersect one
another, 533.

Note on the Surface of a Body

in Terms of a Volume-Integral,
541.

on some Definite Integrals,

594.

on Applications of Theorem

that Two Closed Plane Curves In-
tersect an Even Number of Times,
237.

Mr Muir on Professor Tait’s

Problem of Arrangement, 382.

Index.

Ill

Tait (Professor) on the Measure of
Beknottedness, 289.

on Knots, 306.

on Links, 321.

on Sevenfold Knottiness, 363.

on a New Method of Investi-
gating the Properties of Knots, 403.

Additional Remarks on Knots,

405.

on a Possible Influence of

Magnetism on the Absorption of
Light, 118.

on the Origin of Thunder-
storms, 136.

on some Recent Atmospheric

Phenomena (5th June 1876), 170,
425.

on the Relative Percentages

of the Atmosphere and of the Ocean
which would Flow into a Rent in
the Earth’s Surface, 333.

Note on a White Sunbow, 544.

Note on the Thermo-Electric

Position of Cobalt, 138.

on Effect of Heat on Infusible

Impalpable Powders, 298.

on Some Effects of Heat on

Electrostatic Attraction, 302.

on Thermal Conductivity, 581.

Note on Electrolytic Conduc-
tion, 614.

Note on Thermal Conduction,

615.

on the Electric Conductivity

of the Bars Employed in his
Measurements of Thermal Con-
ductivity, 718.

on the Strength of the Cur-
rents Required to Work a Tele-
phone, 535, 551.

exhibits a Double Mouth-
piece, by means of which Two
Players can Produce Chords from a
French Horn, 536.

on Certain Effects of Periodic

Variation of Intensity of a Musical
Note, 736.

Note on a Mode of Producing

Sounds of very great Intensity, 737.
Telephone. — On the Strength of the
Currents required to work a Tele-
phone, by Professor Tait, 535, 551.
Mr Blyth substitutes Copper-
plate, Wood, India-rubber, &c., for
the Iron Disk of Receiving Tele-
phone, 535.

— — Experiments with the Tele-
phone, by James Blyth, 653.

Telephone. — An Account of Some Ex-
periments on the Telephone and
Microphone, by James Blyth, 711.

On the Theory of the Tele-
phone, by Prof. George Forbes, 555.

Some Experiments with the

Telephone, by Professor John G.
M‘Kendrick, 558.

— Indications of Molecular

Action in the Telephone, by Dr R.
M. Ferguson, 615.

On the Splitting up of Electric

Currents, as detected by the Tele-
phone, and the Founding thereon of
a Sounder to call attention from one
Telephone to another, by R. H. Bow,
C.E., 707.

Tennent (Robert), Why the Baro-
meter does not always indicate real
Vertical Pressure, 412.

on Progressive Movement of

Barometric Depressions or Storms,
570.

Thermal Conductivity of Gas Coke,
by Messrs Knott and Macfarlane,
333.

Thermal Conduction, by Prof.Tait, 615.

Thermal Conductivity, Measurements
of, by Professor Tait, 581, 718.

Thermo-Dynamic Motivity, by Sir
William Thomson, 144.

Thomson (Sir C. Wyville) on the
Structure and Relations of the
genus Holopus, 405.

His Address on delivering the

Neil Prize to Dr Traquair, 549.

Thomson (James, F.G.S.) on New
Forms of Palaeozoic Corals, 149.

Thomson (James, C.E.), Notice of
death of, 488.

Thomson (Professor James), Applica-
tion of his Integrator to Harmonic
Analyses of Meteorological, Tidal,
and other Phenomena, and to the
Integration of Differential Equa-
tions, by Sir Wm. Thomson, 138.

Thomson (Sir William) on Vortex
Statics, 59.

— on Two-Dimensional Motion

of Mutually Influencing Vortex
Columns, and on Two-Dimensional
Approximately Circular Motion of
a Liquid, 98.

on Vortex Theory of Gases,

Condensation of Gases, and the
Continuity between the Gaseous
and Liquid State, 144.

— on Vortex Vibrations, and

Index.

778

on Instability of Vortex Motions,
613.

Thomson (Sir William), Mechanical
Illustration of the Vibrations of a
Triad of Columnar Vortices, 660.

Application of Prof. Jas. Thom-
son’s Integrator to Harmonic Analy-
ses of Phenomena, and to the Integ-
ration of Differential Equations, 138.

His Address on Presenting

the Makdougall- Brisbane Prize to
Mr Alex. Buchan, M.A., 319.

on Thermo-Dynamic Motivity,

144.

on Beats of Imperfect Har-
monies, 602.

Thunder (with Lightning), Lightning
(only), Hail and Snow at Oxford,
by Alex. Buchan, M.A., 135.

Thunderstorms, On the Origin of, by
Professor Tait, 136.

Toothing of Unround Disks intended
to roll upon each other, by E. Sang,
393.

Transformation of Infinite Series into
Continued Fractions, by Thomas
Muir, M.A., 117.

Traquair (Dr It. H.) on New and
Little-Known Fossil Fishes from
the Edinburgh District, No. 1, 262;
No. 2, 275 ; No. 3, 394, 427.

on the Cranial Osteology of

Rhizodopsis, and Structure of
Rhizodus, 403, 444.

on the genus Rhizodus, 657.

Awarded the Neill Prize for

the Triennial Period 1874-77, 549.

Trimethyl-Sulphine, On the Action
of Sulphuretted Hydrogen on the
Hydrate and on the Carbonate of,
by Professor Crum-Brown, 319.

On the Action of Heat on

some Salts of Trimethyl-Sulphine,
by Professor Crum-Brown and J.
Adrian Blaikie. B.Sc., 565, 712.

Turpentine, Discharge of Electricity
through, 579.

Turner (Professor) on the Placenta-
tion of the Cetacea ( Monodon Mo-
noceros), 103.

Tweeddale (George, Marquis of),
Obituary Notice of, 225.

Two-Dimensional Motion of mutually
influencing Vortex Columns, and
Two - Dimensional approximately

Circular Motion of a Liquid, by Sir
William Thomson, 98.

Upsala, Report of the Deputation to,
by Alex. Buchan, M.A., 521.

Vector Conditions of Integrability, by
Professor Tait, 527.

Vignal (M.) on the Biliary Secretion
and Cliolagogues, 334, 718.

Volcanoes of the Hawaiian Islands, by
J. W. Nicol, 113.

Volcanic Debris, Distribution of, over
the Floor of the Ocean, by John
Murray, 247.

Volcanic Eruptions of Iceland in 1874
and 1875, by Captain Burton, 44.

Volume-Integral. — Note on the Sur-
face of a Body in terms of a Volume-
Integral, by Professor Tait, 541.

Vortex - Columns. — On Two - Dimen-
sional Motion of mutually influ-
encing Vortex-Columns, by SirWm.
Thomson, 98.

Vortex Core, by Sir Wm. Thomson, 69.

Vortex Filament, by Sir William
Thomson, 70.

Vortex Motions, Instability of, by Sir
William Thomson, 613.

Vortex Statics, by SirWm. Thomson, 59.

Vortex Theory of Gases, by Sir
William Thomson, 144.

Vortex Vibrations, by Sir William
Thomson, 613.

Vortices (Columnar), Illustration of
the Vibrations of a Triad of, by
Sir William Thomson, 660.

Water, Compressibility of, by J. Y.
Buchanan, 565.

Watson (Rev. R. B.) on Dredging in
Madeira, 153.

Wave-Forms of Articulate Sounds, by
Professor Fleeming Jenkin and Mr
J. A. Ewing, 582, 714.

W edgwood(Mr) on Origin of Language,

100.

Wheatstone (Sir Charles) Obituary
Notice of, 11.

Whitney (Professor) on Origin of
Language, 100.

Wilson (Rev. John) on Parallel
Motions, 161.

Wires. See Electric Currents.

Zodiacal Light, Observations on the,
by C. Michie Smith, 110.

PKINTED BY NEILL AND COMPANY, EDINBUliGH.

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