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PROCEEDINGS

OF

THE ROYAL SOCIETY

EDINBURGH.

VOL. VII.

NOVEMBER 1869 xo JUNE 1872.

EDINBURGH:

PRINTED BY NEILL AND COMPANY.

MDCCCLXXir.

CONTENTS.

Opening Address, Session 1869-70. By the Hon. Lord Neaves, Vice-
President, . . ...... 2

On the Geological Structure of some Alpine lake- Basins. By Archi-
bald Geikie, Esq., F.R.S., . . . . . .33

J Preliminary Notice of the Great Fin Whale, recently stranded at

Longniddry. By Professor Turner, . . . .34

Note on Aggregation in the Dublin Lying-in Hospital. By Dr
Matthews Duncan, . . . . . .38

On a Method of Economising our Currency. By Andrew Coventry,

Esq., . . . . . . . .39

On the Old River Terraces of the Earn and Teith, viewed in connec-
tion with certain Geological Arguments for the Antiquity of Man.

By the Rev. Thomas Brown, Edinburgh, . . . .41

Experiments on the Colorific Properties of Lichens. By W. Lauder

Lindsay, M.D., F.R.S.E., F.L.S., 43

On the Principles of Scientific Interpretation in Myths, with Special
Reference to Greek Mythology. By Professor Blackie, . . 44

On Reciprocal Figures, Frames, and Diagrams of Forces. By J.

Clerk Maxwell, Esq,, F.R.SS. L. & E., . . . .53

On the Extension of Brouncker’s Method. By Edward Sang, Esq., . 56

On the Forces experienced by Solids immersed in a Moving Liquid.

By Sir William Thomson, . . . . . .60

On the Equilibrium of Vapour at a Curved Surface of Liquid. By
Sir William Thomson, . . . . . .63

On a Bow seen on the Surface of Ice. By J. Clerk Maxwell, Esq. ,

F.R.SS. L. & E., 69

Note on the Atomic Volume of Solid Substances. By James Dewar,

Esq., Lecturer on Chemistry, Veterinary College, Edinburgh, . 70

Note on Inverted Sugar. By James Dewar, Esq., Lecturer on Che-
mistry, Veterinary College, Edinburgh, , , . .77

On the Flow of Electricity in Conducting Surfaces. By W. R. Smith,
M.A., Assistant to the Professor of Natural Philosophy in the
University of Edinburgh. Communicated by Professor Tait. (With
a Plate.) . . . , . . . .79

On the Kombi Arrow-poison ( Strophanthus hispidus, DC.) of the
Manganja district of Africa. By Dr Thomas R. Fraser, . .99

On Thebo-lactic Acid. By J, Y. Buchanan, M.A., . . . 103

On the Bones of a Seal found in Red Clay near Grangemouth, with
Remarks on the Species. By Professor Turner, . . .105

On the Rate of Mortality of Assured Lives as experienced by Ten
Assurance Companies in Scotland from 1815 to 1863. By James
Meikle, Esq. Communicated by Professor Tait, . . .115

Notes on Indian Society and Life in the Age when the Hymns of the
Rigveda were composed. By John Muir, D.C.L., LL.D., Ph.D., . 119
On the Lake Basins of Eastern Africa. By Keith Johnston, Jun.,

Esq., F.R.G.S., . . . . . . .122

On the Steady Motion of an Incompressible Perfect Fluid in Two
Dimensions. By Professor Tait, . , , . .142

iv CONTENTS.

On the most general Motion of an Incompressible Perfect Fluid. By
Professor Tait, . . . . . . .143

Address by Professor Wyville Thomson on the “Condition of the
Depths of the Sea,” . . . . . . 144

Facts as to Brain- Work ; in Illustration of the New and Old Methods
of Philosophical Inquiry in Scotland. By Thomas Laycock, M.D., 145
On Change of Apparent Colour by Obliquity of Vision. By Robert
H. Bow, C.E., F.R.S.E., ...... 155

Remarks on the Theories of Capillary Action. By Edward .Sang,

Esq., F.R.S.E., . . . . . . .160

Theory of Construction of the Great Pyramid. By John Christie,

Esq. Communicated by the Rev. W. Lindsay Alexander, D.D., 162

On the Structure of Tubifex. By W. C. MTntosh, M.D., . . 166

Primitive Affinity between the Classical and the Low German Lan-
guages. By the Hon. Lord Neaves, . . . .167

On the Genetic Succession of Zooids in the Hydroida. By Professor
Allman, ........ 168

On Green’s and other Allied Theorems. By Professor Tait, . .168

Proposed Method of ascertaining the Temperature of Falling Rain.

By Thomas Stevenson, F.R.S.E., Civil Engineer, . . . 170

Letter from Professor W. J. Macquorn Rankine as to Diagrams of
Forces in Framework, . . . . . .171

On Spectra formed by Doubly Refracting Crystals in Polarised Light.

By Francis Deas, LL.B., F.R.S.E., .... 172

On the Heat Disengaged in the Combination of Acids and Bases.

Second Memoir. By Thomas Andrews, M.D., F.R.S., Hon. F.R.S.E., 174
Note on Professor Bain’s Theory of Euclid I. 4. By Wm. Robertson
Smith, M.A., Assistant to the Professor of Natural Philosophy.
Communicated by Professor Tait, . . . . .176

A Simple Mode of Approximating to the Wave-Length of Light. By
W. Leitch, Assistant to the Professor of Natural Philosophy in the
University of Glasgow. Communicated by Professor Tait, . 179

Note on Linear Partial Differential Equations. By Professor Tait, . 190
On the Oxidation Products of Picoline. By James Dewar, F.R.S.E.,
Lecturer on Chemistry, Veterinary College, Edinburgh, . .192

Notes of some Experiments on the Rate of Flow of Blood and some
other Liquids through tubes of narrow diameter. By J. Matthews
Duncan, M.D., F.R.S.E., and Arthur Gamgee, M.D., F.R.S.E., . 193

On Cystine (C3H7N02S). By James Dewar, F.R.S.E., Lecturer on
Chemistry, Veterinary College, Edinburgh, and Arthur Gamgee,
M.D., F.R.S.E., Lecturer on Physiology, at Surgeon’s Hall, Edin-
burgh, ........ 201

Notes from the Physical Laboratory of the University. By Professor
Tait. (With a Plate), ...... 206

Donations to the Society, ...... 209

Opening Address, Session 1870-71. By David Milne Home, Esq., . 232
Additional Remarks on the Theory of Capillary Attraction. By
Edward Sang, Esq., ...... 308

Laboratory Notes : On Thermo-Electricity. By Professor Tait, . 308
Note on Linear Differential Equations in Quaternions. By Professor
Tait, . . . . . . . .311

On some Quaternion Integrals. By Professor Tait, . . .318

Note on an Ice Calorimeter. By Dr A. Crum Brown, . . 321

Address “ On the Educational System of Prussia.” By Principal Sir
Alex. Grant, Bart., ....... 309

CONTENTS.

V

On the Physiology of Wings : being an Analysis of the Movements
by which Flight is produced in the Insect, Bat, and Bird. By
James Bell Pettigrew, M.D., F.R.S. Communicated by Professor
Turner, ........ 336

Address on “ The Results of the More Recent Excavations on the
Line of the Roman Wall in the North of England.” By Dr J.
Collingwood Bruce, ....... 350

Note on two Species of Foraminifera, and on some Objects from the
Nicobar Islands of great Ethnological interest. By T. C. Archer,

Esq., ........ 353

Certain Phenomena applied in Solution of Difficulties connected with
the Theory of Vision. By R. S. Wyld, Esq,, . . , 355

Additional Note on the Motion of a Heavy Body along the Circum-
ference of a Circle. By E. Sang, Esq., . 361

On the Capture of a Sperm Whale on the Coast of Argyleshire, with
a Notice of other Specimens caught on the Coast of Scotland. By
Professor Turner, ....... 365

On the Efficient Powers of Parturition. By Dr J. Matthews Duncan, 370
On the Pentatonic and other Scales employed in Scottish Music. By
the Hon. Lord Neaves, . . . . . .382

On the Motion of Free Solids through a Liquid. By Sir William
Thomson, ........ 384

Laboratory Notes. By Professor Tait —

1. On Thermo-electricity, ..... 390

2. On Phyllotaxis, . . . . . .391

Account of the Extension of the Seven-Place Logarithmic Tables,

from 100,000 to 200,000. By Edward Sang, Esq., . . 395

On the Place and Power of Accent in Language. By Professor
Blackie, ........ 395

Notice of Exhibition of Vegetable Spirals. By Professor Alexander
Dickson, ........ 397

On the Old River Terraces of the Spey, viewed in connection with
certain proofs of the Antiquity of Man. By the Rev. Thomas
Brown, F.R.S.E., ....... 399

On the Gravid Uterus and Arrangement of the Foetal Membranes in
the Cetacea. By Professor Turner, . . . .407

Note on some Anomalous Spectra. By H. F. Talbot, Hon. F.R.S.E., 408
Laboratory Notes. By Professor Tait —

1. On Anomalous Spectra, and on a simple Direct- vision Spec-

troscope, ....... 410

2. On a method of illustrating to a large Audience the com-

position of simple Harmonic Motions under various con-
ditions, . . . . . . .412

3. On a simple Mode of explaining the Optical Effects of

Mirrors and Lenses, . . . . .412

On the Structure of the Palceozoic Crinoids, By Professor Wyville
Thomson, ........ 415

On the Formation and Decomposition of some Chlorinated Acids. By
J. Y. Buchanan, A.M., . . . . . 419

Notes on the Antechamber of the Great Pyramid. Based on the
Measures contained in vol. ii. “Life and Work at the Pyramid,” by
C. Piazzi Smyth. By Captain Tracey, R.A. Communicated by
St John Vincent Day, C.E., F.R.S.E., .... 422

Experiments and Observations on Binocular Vision. By Edward
Sang, Esq., ........ 433

Vi CONTENTS.

On the Eall of Rain at Carlisle and the neighbourhood. By Thomas
Barnes, M.D., ....... 434

Mathematical Notes. By Professor Tait —

1. On a Quaternion Integration, .... 434

2. On the Ovals of Descartes, . . . . . 436

On the Remarkable Annelida of the Channel Islands, &e. By W. C.

MTntosh, M.D., ....... 438

Note. On the Use of the Scholastic Terms Vetus Logica and Nova
Logica, with a Remark upon the corresponding Terms Antiqui
and Moderni. By Thomas M. Lindsay, M.A., Examiner in Phi-
losophy to the University of Edinburgh, .... 441

On some Abnormal Cones of Pinus Pinaster. By Professor Alex-
ander Dickson, ....... 449

Address on Spectrum Analysis. By Professor Tait, . . . 455

Note on the Early History of Spectrum Analysis. By H. Fox Talbot,

Hon. F.R.S.E., . . . . . . .461

On some Optical Experiments. By H. F. Talbot, Hon. F.R.S.E. —

1. On a New Mode of observing certain Spectra, . . 466

2. On the Nicol Prism, ...... 468

Note on a New Scottish Acidulous Chalybeate Mineral Water. By

James Dewar, F.R.S.E., ...... 470

On the Homologies of the Vertebral Skeleton in the Osseous Fishes
and in Man. By Professor Macdonald, . . . . 472

Scheme for the Conservation of Remarkable Boulders in Scotland,
and for the Indication of their Positions on Maps. By D. Milne
Home, Esq., ....... 475

Note of a New Form of Armature and Break for a Magneto-Electric
Machine. By R. M. Ferguson, Ph.D., .... 488

Mathematical Notes. By Professor Tait —

1. On a Property of Self-Conjugate Linear and Vector Func-

tions, ....... 498

2. Relation between corresponding Ordinates of two Parabolas, . 499

3. On some Quaternion Transformations, . . . 501

4. On an Expression for the Potential of a Surface-distribu-

tion, &c., ... ... 503

An Experimental Research on the Antagonism, between the Actions
of Physostigma and Atropia. By Dr Thomas R. Fraser. (With a
Diagram), ........ 506

On the Homological Relations of the Coelenterata. By Professor

Allman, F.R.S.E., 512

Donations to the Society, ...... 514

Opening Address, Session 1871-72. By Sir Robert Christison, Bart. 531
On the Computation of the Strengths of the Parts of Skeleton or
Open Structures. By Edward Sang, . . . .575

On Vortex Motion. By Professor Sir William Thomson, . .576

On the Ultramundane Corpuscules of Le Sage. By Professor Sir W.
Thomson, ........ 577

Note on Spherical Harmonics. By Professor Tait, . . . 589

Laboratory Notes : On Thermo-Electricity. By Professor Tait, . 597
On the Relation of Magnetism to Temperature. By D. H. Marshall,
Esq,, M.A., Assistant to the Professor of Natural Philosophy.
Communicated by Professor Tait. (With a Plate), . . 603

Note on a Singular Property of the Retina. By Professor Tait, . 605
On the Operator <p(v). By Professor Tait, .... 607

Note on Pendulum Motion. By Professor Tait, . . . 608

CONTENTS.

vii

On the Decomposition of Forces externally applied to an Elastic Solid.

By W. J. Macquorn Rankine, O.E., LL.D., F.R.SS. Lond. & Edin., 611
On Geometric Mean Distance. By Professor Clerk Maxwell, . 613

On a Singular Case of Rectification in Lines of the Fourth Order. By
Edward Sang, Esq., . . . . . .613

On the Wheeling of Birds. By Professor Fleeming Jenkin, . 615

Notice of a New Family of the Echinodermata. By Professor Wyville
Thomson, LL.D., F.R.SS. L. & E., F.L.S., F.G.S., . . 615

On the Principles which regulate the Incidence of Taxes. By Pro-
fessor Fleeming Jenkin, ...... 618

Additional Notes on the Occurrence of the Sperm Whale in the Scot-
tish Seas. By Professor Turner, ..... 632

Address on Thermo-Electricity. By Professor Tait, . . . 644

Note on Cystine. By James Dewar, F.R.S.E., . . . 644

Remarks on Contact-Electricity. By Sir William Thomson, . 648

On the Curves of the Genital Passage as regulating the movements of
the Foetus under the influence of the Resultant of the Forces of
Parturition. By Dr J. Matthews Duncan, . . . 648

On a Method of Determining the Explosive Power of Gaseous Com-
binations. By James Dewat, Esq., .... 662

Note on Sprengel’s Mercurial Air-Pump. By James Dewar, Esq., . 662
Exhibition of a large series of abnormal cones of Pinus Pinaster.

By Professor Alexander Dickson, ..... 663

On the Connection between Chemical Constitution and Physiological
Action — Continued. On the Physiological Action of the Salts of
Trimethylsulphin. By Professor Crum Brown and Dr Thomas R.
Fraser, ........ 663

On the Mean Monthly Rainfall of Scotland. By Alexander Buchan, 665
Note on the Strain Function, By Professor Tait, . . .667

On the Motion of Rigid Solids in a Liquid circulating Irrotationally
through Perforations in them or in any Fixed Solid. By Sir Wil-
liam Thomson, . . . . . . 668

On the Extraction of the Square Root of a Matrix of a Third Order.

By Professor Cayley, . . . . . .675

Second Note on the Strain Function. By Professor Tait, . . 682

Note on the Rate of Cooling at High Temperatures. By Professor
Tait, . . . . . . . .682

Notice of a Large Boulder in the Parish of Rattray, and County of
Perth, having on one of its sides Cups and Grooves, apparently
artificial. By D. Milne Home, ..... 682

On the Fruiting of the Ipecacuan Plant (Cephaelis Ipecacuanha, Rich.)

in the Royal Botanic Garden. By Professor Balfour, . . 688

On Cardiocarpon. By Professor Duns, D.D., F.R.S.E., New College, 692
On the Composition of the Flesh of the Salmon in the “ Clean” and
“ Foul” condition. By Sir Robert Christison, Bart., . . 694

On Recent Estimates of Solar Temperature. By James Dewar, Esq., 697
On the Temperature of the Electric Spark. By James Dewar. Esq., 699
On the Action of Water on Lead. By Sir Robert Christison, Bart., . 699
On the Preservation of Iron Ships. By James Young, Esq. of Kellie, 702
First Report by the Committee on Boulders appointed by the Society, 703
On the Chemical Efficiency of Sunlight. By James Dewar, Esq. . 751
On the Rainfall of the Continents of the Globe. By Alexander
Buchan, Secretary of the Scottish Meteorological Society, A.M., . 755

On the Lunar Diurnal Variation of Magnetic Delineation at Tre van-
drum, near the Magnetic Equator. By J. A. Broun, F.R.S., . 756

Vlll

CONTENTS.

Some Helps to the Study of Scoto-Celtic Philology. By the Hon.

Lord Neaves, . . . . . . 758

Some Observations on the Dentition of the Narwhal (. Monodon
monoceros). By Professor Turner, . . . . .759

On the Occurrence of Ziphius cavirostris in the Shetland Seas, and a
comparison of its Skull with that of Sowerby’s Whale ( Mesoplodon
Sowerbyi). . By Professor Turner, . . . . . 760

On the Maternal Sinus Vascular System of the Human Placenta.

By Professor Turner, . . . . . .760

On Dimorphic Flowers of Cephaelis Ipecacuanha, the Ipecacuan Plant.

By Professor Balfour, . . . . . .763

On the Crinoids of the “Porcupine” Deep-Sea Dredging Expedition.

By Professor Wyville Thomson, . . . . .764

Laboratory Notes. By Professor Tait —

On Thermo-electricity: Circuits with more than one Neutral
point. (With a Plate). ..... 773

On a Method of Exhibiting the Sympathy of Pendulums, . 779
On some Quaternion Integrals. Part II. By Professor Tait, . 784

On the Currents produced by Contact of Wires of the same Metal at
Different Temperatures. By W. Durham, Esq. Communicated by
Professor Tait, . . . . . . .788

Remarks on the Deep;Water Temperature of Lochs Lomond, Katrine,
and Tay. By Alexander Buchan, A.M., .... 791

Donations to the Society, ...... 796

Index, ......... 821

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

vol. vii. 1869-70. No. 80.

Eighty-Seventh Session.

Monday, 22d November 1869.

Professor KELLAND, Vice-President, in the Chair.
The following Council were elected :■ —

President.

Professor CHRISTISON, M.D.

Honorary Vice-President.

His Grace the DUKE of ARGYLL.

Vice-Presidents.

Dr Lyon Playfair, C.B.
David Milne Home, Esq.
Professor Kelland.

The Hon. Lord Neaves.

Professor Sir William Thomson.
William Forbes Skene, Esq., LL.D.

General Secretary — Dr John Hutton Balfour.

Secretaries to the Ordinary Meetings.
Professor Tait.

Professor Turner.

Treasurer — David Smith, Esq.

Curator of Library and Museum — Dr Maclagan.

Councillors.

George Robertson, Esq., C.E.
Professor Piazzi Smyth.

Patrick Dudgeon, Esq.of Cargen.
Dr Hugh Cleghorn.

Dr James M‘Bain, Surgeon, R.N.
Dr William Robertson.

Thomas Stevenson, Esq., C.E.

Dr Handyside.

Archibald Geikie, Esq.

Professor A. Crum Brown.
Principal Sir A. Grant, Bart.
Rev. L>r W. Lindsay Alexander.

vol. vii,

2

Proceedings of the Royal Society

Monday , §th December 1869.

The Hon. Lord Neaves, Vice-President, read the
following Address : —

I have been deputed by your President to address you to-night
from this chair, and so to attempt a task which would have been
much better performed by one who possesses all the requisite
scientific acquirements which I want, and without which, I fear,
justice can only be imperfectly done to the work which I have
undertaken.

It is usual at this meeting to give some notice of those of our
Members who have died during the preceding year, and the list on
this occasion contains so many, and some of them such distin-
guished names, that it will leave me no space for touching on other
topics.

I cannot mention the name of Dr James Begbie to an audience
like the present without feeling that it recalls to them pleasing
remembrances and painful regrets connected with one who was so
highly esteemed among us as an eminent physician and an excel-
lent man, and who, but a little while ago, seemed likely for some
years to continue his course of usefulness and success.

To myself the subject is specially calculated to communicate
such feelings. Dr Begbie was my early school-fellow and friend,
and in that relation, and also in my resort to him as a medical
attendant in whose anxiety and skill I had the utmost confidence,
there were many years, more than half a century, of cordial inter-
course between us.

Dr Begbie was born in Edinburgh in October 1789. He was
educated at the High School and at the University of Edinburgh,
and early betook himself to medical studies. According to the
system then established, but now I understand wholly or almost
wholly discontinued, he became an apprentice with Dr Abercrombie,
and was afterwards his assistant; in which capacity he had excellent
opportunities of learning his profession, and of practically applying

of Edinburgh, Session 1869-70.

3

his natural talents and theoretical studies. At this period, too, he
showed those kindly and amiable qualities for which he was after-
wards distinguished, and which gained him the affection both of
his principal and of the pupils of Dr Abercrombie, with whom he
was brought in contact, and who in a great measure were placed
under his guidance and professional instruction. Dr Begbie in his
turn became, under the system already noticed, the master of ap-
prentices of his own, who regarded him with the same feelings,
and among whom were some of the most esteemed medical men
now among us.

Dr Begbie, on relinquishing his connection with Dr Abercrombie,
became engaged in an extensive practice as a family medical
attendant, and continued in that branch of the profession till about
twenty years ago, when he confined himself entirely to the func-
tions of a consulting physician, in which he was eminently suc-
cessful, his assistance being extensively resorted to both by his
brethren in Edinburgh and by practitioners throughout the country,
who had confidence in his skill, and in his solicitude to do his duty
to the utmost.

It is perhaps a remarkable circumstance that Dr Begbie, although
he had hospital experience during his studies, never acted as an
Hospital Physician. It is not a little creditable to him that he
should have been able otherwise to supply the want of those
opportunities from which he was thus excluded, and we should by
no means be tempted to recommend a similar experiment in the
ordinary case. Dr Begbie, however, was specially enabled to
supply any deficiency in this part of his professional career by
the very extensive means of observation which were within his
reach as the assistant of Dr Abercrombie, for whom, to a great
extent, he conducted those post-mortem examinations and patho-
logical inquiries which were so intimately connected with Dr Aber-
crombie’s reputation and success, particularly in certain classes of
diseases.

We are inclined to think that in some respects Dr Begbie did not
do himself full justice. He worked too hard and perhaps too ex-
clusively at his own profession; he allowed himself scarcely any
time for relaxation, although he thoroughly enjoyed the too short
intervals which he occasionally employed in this manner. He was

4

Proceedings of the Royal Society

fond of natural scenery, and particularly attached to the English
Lake country, and it would have been better if he bad indulged
his taste more in that direction. We think, too, that in another
respect he denied himself some enjoyments which might have
done him good. A certain quietness, if not shyness, of disposition
seemed to indispose him to much social intercourse, and he
seems not to have betaken himself with any degree of interest to
extra professional pursuits. We hold that every hard-working
man is the better for a considerable amount of social recreation, and
for that relaxation which arises from the prosecution of collateral
pursuits.

Though not much known as a scientific man beyond the limits
of his profession, Dr Begbie distinguished himself, we believe, by
several excellent essays, both of a pathological and of a thera-
peutical kind. We must, of course, on this subject speak entirely
from hearsay; but we understand it is generally considered that
his volume of “ Contributions to Practical Medicine ” contains
much that is valuable and original. His essays on Fatty Degen-
eration of the Heart, and on Anaemia and its consequences, have
been specially mentioned to me as having excited great attention,
and obtained much praise.

In one position which he occupied Dr Begbie was very promi-
nently useful, and deserves to be specially pointed out for general
imitation. I refer to the office which for nearly forty years he held
as medical adviser to the Scottish Widows’ Fund Assurance Office.
In saying this, I do not wish to give him any preference over his
brethren who, among ourselves, bold similar situations. That
would not only be invidious, but utterly unjust; for I know that
all the Edinburgh offices, and I have no doubt the Scottish offices
generally, are in this respect aided by advisers of the greatest
skill, assiduity, and conscientiousness. But the Scottish Widows’
Fund is, I believe, our oldest Edinburgh office, and certainly one
of our most prosperous, and I cannot resist this opportunity of
saying, without disparaging the merits and services of officers of
another class in such institutions, that the character and conduct
of their medical adviser must always be of the utmost importance
to their prosperity. Some recent occurrences have opened our eyes
to a danger that we were apt to forget, that those who profess to

of Edinburgh, Session 1869-70. 5

give security to others, may not be themselves secure. As the
epigram says,

“ Payment of premiums will but make you poorer,

Unless you’re very sure of your insurer.”

And certainly there can be no disappointment more cruel, no
injustice more culpable, than that which takes from hard-working
men of business a share of their annual earnings on the faith of
providing for their families, and then at the end leaves those
families unprovided for.

Now, one of the best guarantees for the success and solvency of an
insurance office is to be found in the skill and fidelity of the medical
officer. It is by testing carefully the value of the lives proposed
for insurance that the office is enabled to meet its engagements
and realise its profits ; for one great source of profit must he that
the lives insured are in one sense picked lives, so that they shall
not be more hazardous, but rather less so, than the average rate
of life on which the tables are framed; and that if any extra
hazard is run, it shall be compensated by a corresponding extra
payment. The medical duty thus to be discharged is not an easy
one, and is beset by many difficulties and snares. It is not always
easy to detect the seeds of latent disease, even when the person
insured is presented to the medical officer ; and it is still more
difficult when the judgment is to be formed at second-hand from
information that may be careless, inaccurate, or even treacherous,
and where the utmost vigilance and acuteness are required in
order to detect any concealed flaw. On the other hand, it is not
right that lives, even of a doubtful kind, should altogether be
excluded from the benefit of insurance, and still less that the
medical officer should reject any from ignorance or rash-
ness.

The task thus devolving on Dr Begbie for the important Society
to which he was attached was discharged by him in a manner
highly satisfactory to his constituents, and tending, there is no
doubt, to aid in achieving for that society the great and growing
success which has attended it. Dr Begbie’s septennial papers on
the causes of death in the records of that society were extremely
interesting, and, I believe, very instructive. It is a great satis-
faction to his friends, and to those interested in that institution,

6 Proceedings of the Royal Society

that his place is now filled by a son who is every way worthy to
succeed him.

I shall note here some dates of the principal incidents of Dr
Begbie’s professional life, and add also from the “ Edinburgh
Medical Journal ” some account of his last illness.

Dr Begbie graduated in medicine in 1821 in the University of
Edinburgh. In 1822 he was elected Fellow of the College of
Surgeons, and at this time entered on the duties of private medical
practice. In 1847, having become much engaged in consulting
practice, he joined the College of Physicians as a Fellow. Of that
College he was President in 1854-56, and discharged the duties of
the office with ability, dignity, and grace. For a few years after
the institution of the office, he acted as one of the Examiners in
Medicine in the University. During 1850-52 he was President
of the Medico-Chirurgical Soeiety. For several years he was
Physician in Ordinary to the Queen in Scotland.

The illness which led to his death began in the end of 1868
from exposure to cold, which gave rise to an attack of pneumonia.
This was got under, but he returned too soon to his duties, and
again became ill from some long journeys which he made. It
was then seen that his health was seriously impaired. He suffered
much from breathlessness, and the action of the heart became em-
barrassed. A change of air and scene was tried without success, and
on his returning home his symptoms became more violent, and his
strength declined. The immediate cause of his death was pulmon-
ary congestion. But he remained conscious and collected to the
last, enduring much suffering with great patience, and looking for-
ward to his end without fear and with a well-founded religious
confidence. He died on the 26th of August 1869.

William Brand, another of our departed members, was born
in 1807, in the parish of Peterhead, and received his early educa-
tion in that parish. After serving an apprenticeship in Peterhead
with the respectable gentlemen who were factors for the Merchant
Maiden Hospital of Edinburgh in that place, he came to this city,
about the year 1829, and served a second apprenticeship with
Messrs Scott, Findlay, and Balderston, W.S., of which firm, after
himself entering as a Writer to the Signet, he became a partner.

of Edinburgh, Session 1869-70.

7

He was an excellent man of business, of great intelligence, accu-
racy, and integrity ; and his high character in this respect led
to his appointment, in 1846, to the secretaryship of the Union
Bank of Scotland, a situation which he filled with great useful-
ness and universal approbation until his death. His knowledge
of financial affairs, his readiness to oblige and assist wherever
his services were desired, and his great courtesy and frankness,
made him most acceptable to his constituents and their customers,
as well as to all who came in contact with him.

Mr Brand’s love of science early took the direction of a decided
taste for botany, and he was one of the original members who
founded the Botanical Society of Edinburgh. Of that Society he
continued all along to be a most valuable member, contributing
many excellent communications to it, and enriching its herbarium
with many thousand specimens of interesting plants, collected by
him and by his friends in the course of their numerous botanical
excursions, on which he always entered with great enthusiasm,
and for which he was admirably adapted by his active habits and
buoyant spirits, and by his readiness to bear, and even enjoy,
the little hardships and inconveniences which such excursions
sometimes involve. The spoils with which these excursionists
returned were given to the Society, partly for distribution, partly
for preservation, and were of no small importance in fostering
and diffusing a taste for botany and a knowledge of the Scottish
flora.

Some months before his death Mr Brand’s health began to fail;
and although at first no serious alarm was felt as to his case, he
at last sank rapidly and unexpectedly, and died on the 18th
October last, having completed his sixty-second year.

Mr Brand was well known as an active member of the Episcopal
Church of Scotland. He died deeply lamented by his relatives
and friends, and amidst the general respect and regret of the
community, for his excellent qualities and exemplary character.

Dr Allen Dalzell, an able and amiable member of our Society,
was born in 1821 at Madras, where his father held the position of
Postmaster- General. Like most children of European parents, he
early came to this country and resided with his mother in Bum-

8

Proceedings of the Royal Society

fries, where his preliminary education was mainly carried on. He
served for some years, first in the navy and then in the army, and
saw a good deal of actual warfare ; but in 1846 he resolved to
change his profession, and, having commenced with great ardour
the study of medicine, he took the degree of Doctor of Medicine
at the University here with high distinction. While yet a student
he had rendered great assistance to Professor William G-regory in
his researches as to creatine and the products obtained from uric
acid, and he received from that eminent chemist a special certificate
of having exhibited much original research, while he obtained at
the same time from the Senatus a remission of one Annus Medicus
of the usual medical curriculum. In 1853, at the time of his
graduation, he obtained the gold medal of the University of Edin-
burgh for a series of extended researches on physiology, and in
December of that year he was appointed by Professor Gregory his
class and laboratory assistant, with the duty of teaching the class
of Practical Chemistry. During the winter preceding the Pro-
fessor’s death, when he was laid aside by illness, Dr Dalzell
supplied his place in the chemical class, and was afterwards
appointed by Dr Lyon Playfair, Dr Gregory’s successor, to the
same duties of conducting the practical laboratory which he had
formerly discharged. His connection with the University con-
tinued to the last, with these additional labours, that in 1859 he
delivered in the New College, Edinburgh, a six months’ course on
Natural Science, and succeeded the late Dr G-eorge Wilson in the
Chair of Chemistry and Materia Medica in the Royal Veterinary
College, which office he filled for many years with credit to
himself and benefit to his pupils. He was also in much request,
and much esteemed as a popular lecturer on scientific subjects in
various institutions in England as well as in Scotland. He was
possessed of decided talents, and, with much professional infor-
mation, he had great refinement and elevation of character ; and
his frank, affectionate, and generous disposition secured the attach-
ment of all who knew him. With his quick feelings and impulsive
disposition, it is possible that his health, already affected by over-
work, may have been further injured by an unpleasant lawsuit in
connection with his official position in the Veterinary College.
An erroneous verdict was returned against him, but which, on

9

of Edinburgh, Session 1869-70.

an appeal to the Court, was set aside, and a verdict in his favour
unanimously given by a second jury.

His health was for some time delicate, and it was found that he
had severe disease of the heart. He died on the 29th July 1869,
after an illness of much suffering, borne with pious and exemplary
patience. His removal, thus occurring in the prime of life, was felt
as a great loss and a severe affliction by his relatives and friends.

Dr Robert Dyce was the eldest son of the late Dr William D) ce,
an eminent physician in Aberdeen. He was born in November
1798, and was the eldest of a family of sixteen, of whom the late
eminent artist, Mr William Dyce, was one. He took his degree of
M.A. at Marischal College in 1816, and afterwards studied medicine
at Aberdeen, Edinburgh, and London. After being for some time
attached to the Military Hospital at Chatham, he went out, in 1821,
on a staff appointment to the Mauritius. There he became
extremely popular with the English residents, from whom he
declined to take fees for medical attendance, but who eagerly
showed their gratitude by valuable presents. He was afterwards
transferred to the Cape, where he remained for five years, and
married the daughter of a gentleman holding a high official posi-
tion there. He returned to England in 1833, and spent a
winter in Aberdeen, after which he accepted a staff appointment
at Maidstone ; but in 1836, on the death of his father, he was
induced to settle in his native town, where he succeeded to an
extensive practice and to valuable appointments. In 1860, on the
union of the two Colleges at Aberdeen into one University, he was
appointed to the Professorship of Midwifery, then established,
having previously held a college lectureship on that branch of
science for nearly twenty years.

Both as a lecturer and as a practitioner in his special depart-
ment he was looked up to as a high authority ; and to his students,
as well as to all who came in contact with him, he recommended
himself by his kind and courteous manners, and his high principles
and honourable feelings, which were in every respect those of a
thorough gentleman. His medical assistance to the poor was given
gratuitously, with unremitting and unostentatious liberality. He
was an accomplished man, well acquainted with several import-

VOL. VII.

10

Proceedings of the Royal Society

ant branches of natural history, which he had had peculiar oppor-
tunities of studying at the Mauritius and at the Cape ; and he had
made extensive collections of specimens, some of which were of
great value. Though not an artist, like his distinguished brother,
he had a great love of art, and a fine and critical taste in painting.

He had been ailing for some little time before his death, but had
not felt any serious alarm about his case. At last, however, he came
to Edinburgh for medical advice, when it was found that he had
acute inflammation of the lungs. It was hoped that it might easily
be subdued; but the disease suddenly took an unfavourable turn, and
he died in Edinburgh, 11th January 1869, in his seventy-first year.

Among our Honorary Members whom we have lost I have to
notice the eminent physiologist M. Flourens, lately deceased. He
is well known among us, both by his reputation and by his works ;
and notices of the principal events of his life are to be found in
the usual books of contemporary biography. I am sorry that I
have been unable to ascertain any particulars as to the cause or
circumstances of his death, a matter which, in his case, and in con-
nection with his own speculations, might be thought to possess a
special interest.

He was born in the district of Herault, in France, in 1794, and
early devoted himself to medical science, and particularly to phy-
siology and biology. He made various researches and experiments
on the nervous system, and on the several functions of the great
sources of nervous power ; and his countrymen consider that the
disclosures thus made by him, preceding, as they did, the pro-
mulgation of the discoveries of Sir Charles Bell, entitle him to high
praise, and form the best foundation of his scientific reputation.
He published a variety of works on other cognate subjects from
time to time, one of the most remarkable of these being upon
u Longevity, and the amount of life diffused over the globe,” in which
he vindicated for man the period of 100 years as the normal
duration of his existence under favourable circumstances. He
was elected a member of the Academy of Sciences, of which he
afterwards became one of the secretaries. He was also after-
wards elected a member of the Academie Fran^aise, and had
numerous other honours conferred upon him, both scientific and

11

of Edinburgh, Session 1869-70.

political. But he seems to have valued his scientific position
above all adventitious dignities. At his death he had attained
his seventy-fifth year, which might be generally thought a pretty
fair allowance of life; but from our ignorance of facts above
alluded to, we are unable to say whether this, in his view, & prema-
ture termination of his existence, is or is not a confirmation of
his own theory on the subject.

There is no member of the Roj^al Society of whom we have
occasion to lament the death, and to cherish the memory, more
than Principal Forbes, who was for so long a period our faithful
and efficient Secretary. It will not be easy to do justice to the
merits of one who had so many claims upon our gratitude and
regard, and who reflected so much honour on every public institu-
tion with which he was connected.

James David Forbes was born at Edinburgh, on the 20th of
April 1809, and was the son of Sir William Forbes, of Pitsligo,
Bart. The death of his mother in the year after his birth, and the
delicacy of constitution which proved fatal to her, made his father
feel anxious about the boy’s health ; and as he grew up, his slender
frame, and almost premature intellectual development, seemed to
indicate that his education should be conducted with caution,
and limited, in the first instance, to the simplest and most essential
subjects. It is remarkable, that it was thought necessary, on this
ground, to prohibit strictly his study of mathematics ; and it was
only at spare moments, and almost by stealth, that he acquired a
branch of knowledge so intimately connected with the pursuits in
which he was afterwards destined to excel. His preliminary edu-
cation was chiefly domestic, but in due time he attended several of
the classes of the Edinburgh University. On leaving it, he has
told us that geology, meteorology, and physics were his favourite
pursuits; and he then began those excursions at home and abroad
which were to him all his life so great a source of pleasure and
scientific improvement. While he was still a youth his father had
occasion to spend two successive winters in Italy, whither he took
his son with him; and young Forbes’s natural taste for investiga-
tion led him to make frequent visits to Vesuvius and the celebrated
Pillars of Serapis. His mind was strongly moved by what he

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Proceedings of the Royal Society

there saw ; and in 1827, when eighteen years of age, his first
scientific papers appeared in Dr Brewster’s Journal, but without
his name. Two other papers from him, on the natural features of
the same region, appeared in the same journal, also anonymously,
but with the signature “Delta;” and from that time forward he
continued to be a regular contributor to that publication in com-
munications which were avowed.

In 1830, in compliance with his father’s wishes, Mr Forbes
passed advocate at the Scottish bar, and walked the boards for a
short time; but his heart was not there, and it would have been
vain to confine his buoyant spirit and active frame to the close
discipline of that profession, when it was in his power to indulge
his tastes and faculties in the pursuit of physical science and
geological exploration. He soon afterwards resolved to quit the
law, and rejoiced in the change he had thus made. At this time
he visited Switzerland, and imbibed that interest in the subject of
the glacier formations which afterwards stimulated so much of his
exertions, both as an explorer and as a scientific author.

In 1833, on returning from the Continent, he found that the Chair
of Natural Philosophy had become vacant by the death of Professor
Leslie, and that Forbes’s friends had put him in nomination as a candi-
date. It was a painful position for him to occupy when his competitor
was Sir David, then Dr Brewster, who had been among his earliest
scientific friends, and who had fostered and encouraged his talents
by the kindest sympathy and assistance. It was a keen contest,
and the friends of Brewster might naturally feel indignant that so
young a man should be preferred to one of such high eminence
and long standing as Brewster had attained to. This preference
was imputed entirely to political feeling or local influence, and
these undoubtedly entered largely into the question. But the
supporters of Forbes were no false prophets when they predicted
for their candidate a long career of ardent exertion and eminent
success, not only as a scientific inquirer, but as a lecturer and
teacher ; and as to his youth, it was pointed out that Maclaurin,
Dugald Stewart, and other eminent professors, were appointed at
as early an age, or earlier. The appointment, ultimately, had all
the justification which the event could supply. Professor Forbes
occupied the Chair of Natural Philosophy for more than a quarter

13

of Edinburgh, Session 1869-70.

of a century, with the utmost honour to himself and the University
to which he belonged. It is creditable to both parties, and more
especially so to Sir David Brewster, that the contest which thus
terminated did not dissolve their friendship, or prevent their
cordial co-operation in everything that could promote the interests
of science.

For a long series of summers Professor Forbes resorted to Swit-
zerland and to other districts of alpine scenery in Europe, and thus
matured those profound and important views which he promulgated
on geological and other questions — in particular, on the subject of
glaciers. It is quite unnecessary, and would he very presumptuous
on my part, to attempt any account or criticism of his works or
researches, and indeed everything that could be desired has in this
respect, so far as geology is concerned, been excellently done by our
friend Mr G-eikie, in the minute and kindly memoir of Principal
Forbes which he lately read to the (Geological Society. Appended to
that memoir will be found a correct and complete list, as I believe, of
Principal Forbes’ scientific writings, and the catalogue of our own
library will supply similar information. I may shortly say, that
Principal Forbes was an ardent geologist — that from an early period
he had been imbued with the enthusiasm for that branch of science
which prevailed among scientific men in Edinburgh in the first
quarter of the present century, and that he earnestly desired
to see a school of geology fully revived and established among us.

Principal Forbes, it is somewhat singular to observe, had on the
motion of Dr Brewster been admitted a member of the Boyal
Society before he had attained his twenty-first year. The Keith
Prize was twice awarded to him by the Council. In 1846, on the
death of Sir John Bobison, he was appointed to the office of
Secretary of this Society, and for about twenty years thereafter he
discharged the duties of the appointment with the most efficient
assiduity and the most conscientious diligence. His desire to
maintain the usefulness and the dignity of the Society, and to
preserve its ranks and its discussions free from anything that was
unworthy of a scientific body, and the pains that he took in pro-
curing and preparing for publication the compositions which con-
stitute its “ Transactions,” and on which its character and reputa-
tion will in a great measure permanently depend, were beyond all

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Proceedings of the Royal Society

praise, and were both proved and rewarded by the condition in
which he maintained the Society while he was Secretary, and in
which he left it when he resigned that office

On occasion of his giving up the office of Secretary, the Eoyal
Society recorded the expression of their sense of his valuable
services in the following resolution : — “ That the Eoyal Society
deeply laments that a necessity has arisen for the retirement of
Principal Forbes from office as General Secretary. That it desires
now to record in its minutes its grateful sense of the obligation
under which it lies to Principal Forbes for the zeal and ability with
which he has acted as its Secretary for the last twenty years, for
the many important discoveries and inquiries in science which he
has brought before its meetings, and for the eminent degree in
which his exertions and example have contributed to its present
prosperity ; and that, as a mark of the regard in which he has been
long held, alike as an office-bearer and as a cultivator of physical
science, he be requested to sit to an eminent artist for his portrait,
to be hung in the Society’s apartments.”

On the removal of Sir David Brewster to the headship of the
University of Edinburgh, Professor Forbes was chosen Principal
of the United College of St Salvator and St Leonard in the Univer-
sity of St Andrews. His failing health, which, there can be little
doubt, had suffered much from excessive exertions in his mountain
excursions, and perhaps also from overstrained labour in some of
his scientific researches, made the retreat thus offered to him a
welcome refuge from the task of daily lectures to which he had be-
come quite unequal. For a time after his removal to the retirement
of St Andrews, he seemed to be rallying in strength, with the
assistance of his annual residence in the pure air and amidst the
interesting scenery of Perthshire, but the improvement did not
continue, and his old ailment of hemorrhage from the lungs returned
with alarming violence. He left St Andrews and removed to a
milder climate, stopping ultimately at Clifton, where he died on
the 31st of December 1868. We are told that “ whilst his body
was reduced to the last stage of weakness, his mind remained self-
controlled, unclouded, and peaceful to the end.” His activity and
usefulness in his office of Principal of St Andrews University have
been borne witness to, and a truthful and touching tribute paid to

15

of Edinburgh, Session 1869-70.

his memory* in the address lately delivered by his excellent and
accomplished successor Principal Shairp.

Principal Forbes had a certain reserve and apparent dryness of
manner, but he had a kind and noble heart, an unremitting zeal for
the promotion of science, a conscientious desire to discharge every
duty, an ardent love of truth, and a strong detestation of injustice.
He was not unmindful of what he felt to be his own claims, but he
also fought many a battle in vindication of what he considered to
be due to others.

The late Master of the Mint will be readily enrolled by all who
knew him, or who know what he has done, as another among the
great names that Scotland can boast of in chemical science.

Thomas Graham was born at Glasgow, on the 21st December 1805,
and after passing through the usual course of preliminary study in
that city, he entered the University of Glasgow in 1819. He early
showed a strong taste for science, and a decided bias for chemistry
as a pursuit. His father, it is believed, wished him to enter the
Scotch Church; but Graham felt that his true vocation lay in
another direction, and his desire of penetrating the secrets of
natural knowledge was too strong to be repressed. Thomas Thom-
son was then Professor of Chemistry in Glasgow University, and it
cannot be doubted that from his instruction Graham derived great
benefit, and received a strong confirmation of his natural tastes in
that direction. After graduating at Glasgow, he repaired to
Edinburgh, and studied for two years under Dr Hope, who, if not
distinguished by powers of original discovery, was an able and ele-
gant expositor of the discoveries of others, and most successful in
conducting the experiments by which his lectures were illustrated.
Graham at this time also made the acquaintance of Professor
Leslie, a man of undoubted originality and of most diversified
knowledge, and with whom it was impossible to associate without
being stimulated to intellectual exertion and scientific inquiry.

It is probable that, during the time when he was engaged in his
University studies, both in Glasgow and Edinburgh, he was sub-
jected to much anxiety as to his prospects, and as to the proba-
bility of his being able to justify, by success, the choice which he
had made of a position in life, which could scarcely be said to

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Proceedings of the Royal Society

amount to a profession, and which, at that time in particular, pro-
mised few and scanty rewards for the efforts and sacrifices which it
involved. In these trials it would appear that Graham was com-
forted and supported by the sympathy and affection of an excellent
mother, with whom, when he was absent, he regularly corresponded,
and to whom he confided his most intimate and anxious feelings.

In such circumstances, it must have been a source of pride and
satisfaction to him that, in 1829, when scarcely twenty-four years of
age, he was appointed Lecturer on Chemistry at the Mechanics’
Institution, Glasgow, and in 1830 Professor of Chemistry at the
Andersonian Institution, an event of which his mother just sur-
vived to hear.

In 1837 he was appointed Professor of Chemistry in the London
University, and remained in that appointment till the year 1855.
During the five and twenty years for which he thus occupied a
professorial chair, first in Glasgow and then in London, Graham
found himself in that position which was the one he would himself
probably have selected as the best for carrying on his favourite
plans of scientific investigation; and that long period was accord-
ingly devoted to the assiduous prosecution of his great object, in
the course of which his enthusiastic researches were rewarded by
numerous important discoveries, which are not only in themselves
valuable, hut which must ever deserve the attention of chemical
students, as examples of that assiduous application and persevering
inquiry by which alone the hidden truths of nature can be
brought to light.

It is quite beyond my power to give any detailed account of Mr
Graham’s discoveries, or to make a just estimate of their value in a
science with which, in its rapidly advancing and ever expanding
state, I am so imperfectly acquainted ; but I believe the statements
on the subject which lately appeared in the new periodical,
“ Nature,” may be relied on as accurate and just; and I have been
furnished from a high authority with some materials as to these
points, which I shall endeavour here to embody to the best of
my ability.

Graham’s tendency to the prosecution of scientific discovery
showed itself while he was yet a pupil of Professor Thomson
in Glasgow. He made some suggestions to that Professor as to

17

of Edinburgh, Session 1869-70.

the possibility of water playing an important part in the con-
stitution of acids and salts. The Professor was struck by the
ideas of his young pupil, and encouraged him to continue his in-
vestigations on the subject. This ultimately led to his splendid
researches in phosphoric acid, as to which he shows that its three
varieties — common phosphoric acid, pyrophosphoric acid, and meta-
phosphoric acid — differed only by containing a different number
of atoms of water, chemically combined with the an-hydride. He
followed this inquiry up by researches on water in salts, and
showed that in a salt the different numbers are held with dif-
ferent degrees of tenacity. His attention was early attracted to
the diffusion of gases. The manner in which gases mix with each
other, and the permanence with which the intermixture is main-
tained, are remarkably different from what is experienced in the
case of liquids ; and it is probably to this fact that we owe the
stability of the proportions in which the ingredients of the atmo-
sphere are maintained, a uniformity which is so essential to organic
life. The laws also according to which gaseous diffusion takes
place were found by Graham to be based upon mathematical rela-
tions between their density and their velocity of diffusion, which
were at once interesting and unexpected. The laws as to the
effusion of gases into a vacuum, and their transpiration through
narrow tubes, were also traced by him with indefatigable diligence
and complete success ; and it is a fact of which wre may be proud,
that his first paper on that subject was read before this Society.
The importance of these investigations, particularly in connec-
tion with the phenomena of osmosis, will probably be seen, in
its full extent, in the clue which they seem to give to some of
the most remarkable facts in physiology. The discoveries of
Hr Graham were due mainly, it may be said, to his close
adherence to any subject on which he once entered. He never
quitted it until, by steadfast attention, deliberate consideration,
and varied experiment, he had extracted out of it every atom
of scientific truth which it was capable of yielding. The secret of
his success in this respect was probably not different from what
may be seen in other eminent discoverers. Newton ascribed his
achievements not to genius, but to earnest and unremitting atten-
tion; and it must be manifest how much more likely it is that a

VOL. VII.

18 Proceedings of the Royal Society

new truth should dawn upon the mind which has been long and
intently occupied with a subject than that it should be the fruit
of a casual and transient consideration. It was by this habit and
faculty of perseverance that Graham was enabled to do what he
did ; it was to this that we owe all that he has taught us as to the
diffusion of gases and liquids, as well as his last and crowning
discovery as to the nature of hydrogen, of which, perhaps, the full
effect is not yet fully seen or recognised.

At an early stage of his inquiries as to hydrogen, he had seen
that it was isomeric with some of the metals, but his later experi-
ments went further still towards establishing the metallic character
of that gas. He showed that certain metals — palladium, platinum,
and iron — can, under certain circumstances, absorb considerable
quantities of hydrogen gas. This he termed the “ Occlusion of
Hydrogen Gas.” Latterly, his investigations were made almost
exclusively with palladium, which absorbs a much larger propor-
tion of hydrogen than any other metal. The method he pursued
was to decompose water by a galvanic battery, the negative elec-
trode, at which the hydrogen is liberated, being formed of a plate or
wire of palladium. In this arrangement, when the decomposition
takes place, oxygen is given off copiously at the positive electrode,
but no hydrogen, or very little, appears at the negative in the first
instance, the avidity of the palladium for oxygen requiring that it
should first be saturated with that substance, after which the
hydrogen begins to he given off. In this way Graham succeeded
in charging palladium with a quantity of hydrogen, which, in the
form of gas, would occupy 900 times the volume of palladium.
The palladium so charged retains its metallic appearance, and
differs from pure palladium, very much as a metal containing a
small quantity of metallic alloy differs from the pure metal. From
these facts, Graham inferred that hydrogen in its solid state was
truly metallic, and to this substance, according to the usual ana-
lysis of chemical nomenclature, the name of hydrogenium was
given, and a medal of palladium and hydrogenium in the alloyed
state was struck in honour of the discovery. Another of his recent
discoveries is said to have been that, while the gas shut up in
terrestrial iron is carbonic oxide, the gas contained in meteoric
iron is hydrogen.

of Edinburgh, Session 1869-70.

19

Prior, I believe, to the year 1850 the Mastership of the Mint had
for a long time been a political office, the occupant of which was
removable with the ministry with whom he was associated. The
individual who held it was, in this way, not a man of science, but
a statesman of general intelligence and business habits, whose
duty it was to superintend and keep to their tasks the permanent
officials by whom the work was understood and performed. In
1850 a change was made in this respect, and apparently a change
for the better. It was determined that the office should be held
by a man of science, not connected or removable with the ministry
of the day, but who should give his talents and time to the actual
working of the department. The office, as thus remodelled, was
conferred upon Sir John Herschel, in acknowledgment of the high
eminence which he had attained in so many branches of science.
He held the office till 1855, when he resigned it from bad health,
and Dr Graham was then appointed. He continued to hold the
office and discharge its duties till his death with the utmost dili-
gence and efficiency.*

All who knew Graham concur in bearing testimony to the purity
and simplicity of his nature, and to the justice, generosity, and
kindness of his conduct. He was physically too weak, and perhaps
too much engrossed with scientific objects, to enter much into
society; and he had no ambition for display, but was solely bent
upon the discovery of scientific truth for its own sake, and for the
advancement of scientific objects. He has been cut off in the
midst of a noble and useful career, when it might have been
hoped that some years of active investigation would still be allowed
him, and from which it is not easy to estimate what results might
have followed. The loss which science has thus sustained can only
be repaired by similar exertions made in a similar spirit by those
who possess the natural qualifications that are essential to scientific
inquiry.

Dr Graham, for some time previous to his last illness, had
occasionally gone to Malvern for a day or two at the end of a
week, and derived much benefit from the change. On the last

* If any further change be contemplated in this department, it is to be
hoped that it will not tend to deprive men of science of what is at once a
fair reward and a fitting sphere of usefulness.

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Proceedings of the Royal Society

occasion, however, of his being there, he had over-fatigued himself
by walking, and caught a chill from falling asleep near an open
window. The result was an attack of inflammation in one of the
lungs. He returned immediately to London, where his medical
advisers from the first took an unfavourable view of his case, either
in its immediate or ulterior consequences. He died on 16th Septem-
ber, after ten days’ illness, having been assiduously attended by his
sister and one of his nieces. His remains were brought to Glas-
gow, and interred in the family burying-ground attached to the
Cathedral, where two months before he had erected a tombstone to
the memory of his parents and other members of the family, space
being left merely for his own name and that of his only surviving
sister.

Charles Frederick Philip von Martitjs, the greatest, perhaps,
and most celebrated botanist of the present day, was born at Erlan-
gen, in Bavaria, in the year 1794. His family are said to have
been of Italian origin, but they had been for some time settled in
Bavaria, where his father had a medical appointment in connection
with the court. Young Martius received, in the first instance, the
usual medical education, but when about eighteen years of age
resolved to devote himself to botany, and shortly afterwards was
appointed to a subordinate position in the Botanic G-arden at Munich.
His diligence in that situation, and the merit of some treatises
which he then published, attracted the notice of Maximilian Joseph
I., who was an ardent lover of plants, and a frequent visitor to
the garden. In 1816, when the joint expedition was concerted by
Austria and Bavaria to explore the natural history of Brazil, Martius
was named by the king as the Bavarian botanist, though then little
more than twenty-two years of age. He immediately set out on
this enterprise, and was absent for a period of four years, having
returned to Munich on the 8th of December 1820. The explora-
tions made by the two Bavarian travellers, Spix and Martius, who
proceeded in a separate direction, and over a wider field than their
Austrian associates, were on a scale much larger and more compre-
hensive than any that had previously been attempted. The expe-
dition, we are told, irrespective of the sea voyage, extended over
nearly 1400 geographical miles, and for months led through the

21

of Edinburgh, Session 1869-70.

most inhospitable and dangerous regions of the New World. Both
explorers, however, escaped without any important disaster on the
road, and they had the rare good fortune to preserve and bring
home their collections, complete and uninjured, through all the
perils to which they were exposed. These collections, finer and
richer than all previous and most subsequent ones from Brazil,
were made over to the Academy.

The task thus successfully achieved established Martius’s reputa-
tion, and settled for life the special destination of his studies. He
received from his sovereign distinguished honours, and was recog-
nised by men of science as worthy of a high place among them.
The publication of the narrative of this Brazilian journey, which
appeared in 1823-31, and which, in consequence of the early death
of Spix, was chiefly prepared by Martius, carried the admiration
of his talents to a very high pitch. There was here seen a worthy
rival of Alexander Humboldt ; and readers were at a loss whether
to admire most the copiousness of the information furnished, or
the beauty of the diction, and the poetical and yet truthful power of
the colouring, in which were presented all the characteristic features
of those wonderful regions, with their productions and their inha-
bitants. A relative work at the same time was commenced, and
continued in a magnificent series of volumes, exhibiting to scientific
eyes the minute representation and description of the natural ob-
jects, whether plants or animals, with which the expedition had made
the travellers familiar. The esteem in which these works were
held procured for Martius the distinguished honour of being elected
a member of the Trench Institute. He was enrolled in nearly all
the other learned bodies in Europe ; he was appointed an Honorary
Member of our own Society in the year 1855.

After the accession of Louis I. to the Bavarian throne, Martius
was appointed Professor of Botany in the University of Munich,
and subsequently was promoted to be Chief Conservator of the
Botanic Garden.

In 1823, Martius began his celebrated Monograph upon Palms,
which was completed in three folio volumes in 1845. It is con-
sidered one of the finest monuments of modern botany, and is said
to contain a description of 582 different species of Palm, while
Linnaeus had only given 15, and Humboldt 99. It was to

22 Proceedings of the Poyal Society

this work that his friends specially alluded when, in 1864, on
the jubilee of his graduation at the Academy, a medal was struck
in his honour, dedicated “ Palmarum Patri,” with the motto “ Tu
Palmis Resurges and the same idea was followed when, four years
afterwards, on 13tli December 1868, his bier was bedecked with
palm leaves, and a similar motto inscribed on his tomb.

The last great work in which Martius was engaged is the “ Flora
Brasiliensis,” which was continued, from time to time, upon a scale
worthy of the subject, and at his death had reached its forty-sixth
part. It is to be hoped that it will be continued in the same spirit
in which it was begun.

Martius was a most popular lecturer, and in every way a superior
man. His general intellectual powers were very great, and his
readiness to communicate his knowledge was unfailing. His
hospitality was liberal, and his best recreation, after the labours of
each day, was the reception in his house of scholars, travellers, and
men of science, and more especially of young inquirers after know-
ledge, whose projects and aspirations he delighted to encourage and
direct. He died in his seventy-fifth year ; but I regret that I am
unable to state any particulars as to that event, or his last illness.

Among those members whom we have this year lost by death is
the late venerable and excellent pastor of St Stephen’s Church, in
this city. He took no prominent part as a man of science, but he
felt an interest in its progress, and watched its rapid advance ; and
though not mixing actively in the proceedings or debates of this
Society, he strongly approved of its objects and recognised its
benefits. It is an honour to have such men enrolled among us,
and when they are removed in the course of nature, they should not
be deprived of the just tribute to which their virtues and talents
are entitled.

Dr William Muir was a native of Glasgow, the son of a Glasgow
merchant. He was a distinguished student at Glasgow University,
and having chosen the Church for his profession, he was ordained in
the year 1812. It is said that his own predilection originally was for
the Church of England, and that he entered the Scotch Church in
deference to his father’s wish. However this may be, the choice
then made by him was fully ratified by his ultimate convictions.

of Edinburgh, Session 1869-70.

23

He was first assistant, and afterwards minister, of St G-eorge’s,
Glasgow, and was about the year 1822 removed to the New G-rey-
friars’ Church, Edinburgh. On the erection of the parish of St
Stephen’s in 1828, he was appointed to that charge, which he
continued to hold till his death on 23d June last.

In every situation in which Dr Muir was placed as a minister
he discharged his parochial duties in the most exemplary and effi-
cient manner; in particular in St Stephen’s parish, of which he
was the pastor for forty years, not only his ministrations in the
pulpit, but his diligence in personal attention to his flock, his care
of the young, his kindness to the sick and suffering, and his
organisation for the promotion of education, and the diffusion of
sound Christian faith and active Christian practice, were such as
to call forth the strongest feelings of gratitude and admiration in
his congregation and parishioners. His elders, embracing among
them some of the most eminent and respectable of our citizens,
concurred in looking upon his pastoral services as invaluable, and
omitted no opportunity of testifying their confidence in his char-
acter and their sense of his worth. Documents have been placed
in my hands, by some of their number, which enable me to make
these statements with a perfect conviction that they are in no
respect exaggerated, and that Dr Muir was, in all his parochial
relations, the model of a Christian minister. I have read with
peculiar interest the proceedings of his congregation in 1862, when,
on occasion of his completing the fiftieth year of his ministry, they
placed at his disposal the fruits of a liberal subscription among
them, but which he declined to receive personally, and insisted on
forming into a sinking fund, of which the proceeds were to be
annually applied to pious and charitable uses, parochial or congre-
gational. I have also read, with a perfect persuasion of its sincerity
and truth, the address which the late excellent Dr Hunter delivered
in 1864, on occasion of Dr Muir being compelled to withdraw from
active duty in consequence of a failure of eye-sight, with which
he was visited. That address was obviously from the heart of the
speaker, as it must have gone to the hearts of those who heard
him, and bears unequivocal testimony to the high character of the
man who was the subject of it.

This is not the place to speak of Dr Muir’s career or opinions,

24 Proceedings of the Royal Society

either on religious or on ecclesiastical questions. I may venture,
however, to make one or two observations in connection with these
matters.

1. Dr Muir, from an early period of his ministrations, came to
occupy a somewhat peculiar position as a minister. He belonged
to what was called the Moderate party in the Church, having no
sympathy with the strong views either of popular rights or of
spiritual independence, which characterised the High Church Pres-
byterians. But the Moderate party had also the reputation, whether
well or ill founded, of being rather too moderate in their doctrinal
views; and, in this respect, Dr Muir’s opinions and style of
preaching were more decidedly and prominently evangelical, as it
was called, than was generally the case with his political friends.

2. Dr Muir’s opinions were always listened to in the Church
Courts with respect and deference; but he was not altogether
adapted to the position of a party leader, which, in other respects,
he might have well attained. He had a fault, or what will be con-
sidered such by some men ; but it was that fault which a delightful
poet has ascribed to the greatest man of his own age — he was

“ Too fond of the right to pursue the expedient

It has been well observed to me, by one who knew him well,
that it is a rare thing, and anything but a disparagement, when
all that can be said against a man is, that he followed conscience
exclusively, and valued integrity and independence too high for
any price to tempt him even to the semblance of a surrender.

Perhaps his most marked characteristic was this high-minded
conscientiousness of disposition. His habit of making conscience
of everything made him appear stiff and unbending to those from
whom he differed in opinion, and many may think that he took
the alarm too soon and too sensitively when he thought that even
the outworks of principle were in danger. His steadfastness cer-
tainly to what he held the truth never quailed ; his independence
was unshaken by what to others might even seem legitimate feel-
ings. His superiority to all selfish motives had in it the essence
of chivalry. Though to strangers his manner was reserved, those
who had the privilege of familiar intercourse with him knew that
beneath the surface there lay a native geniality of temper which

25

of Edinburgh, Session 1869-70.

could break forth and sparkle into its natural gleams, and a heart
as warm as ever beat in human bosom.

Dr Muir was an accomplished scholar, and all along kept himself
abreast of the literature and science of the day. He was well read
in the classics, and had a more than usual acquaintance with the
literature of his own profession. Suffering for a year or two before
his death under nearly total blindness, he had a reader always with
him, to read to him his favourite authors, not in English merely?
but in Latin and Greek, and even Hebrew.

Dr Frederick Penney, Professor of Chemistry in Anderson’s
Institution, Glasgow, was born in London in 1817. He was
brought up as a professional chemist, having early shown a predi-
lection for that branch of science. He studied under Mr Hennel of
London ; and it has been stated that he was present when his
instructor was killed, while conducting some experiments, by an
explosion of fulminating powder. Dr Penney recommended him-
self very early by important experiments and communications on
chemical subjects; and in 1839, while only twenty-two years of
age, when the Chair of Chemistry, which he ultimately held,
became vacant, he was recommended for the office by the late
Professor Graham, and unanimously appointed by the patrons. Dr
Penney was a man of great talent, quickness, and intelligence, and
an excellent chemist, both theoretical and practical. As a chemical
analyst, he enjoyed a high reputation for his fidelity and accuracy,
and, I should suppose, must have derived a considerable income
from that source. In one department, that of a scientific witness,
I can bear personal testimony to his ability and excellence. His
evidence in the witness-box was always clear, ready, explicit, and
consistent ; and he had one qualification essential to every good
scientific witness, but which is certainly not possessed by all who
place. themselves in that position, — he underwent the operation of
cross-examination with perfect composure and good temper, and
showed himself as ready to speak to any fact that seemed to bear
against the side adducing him as he had been to give evidence
in its favour. This demeanour, which every scientific witness
should at least assume, made his testimony very influential and
valuable. In his private relations, Dr Penney appears to have

VOL. VII.

26

Proceedings of the Poyal Society

been an amiable and agreeable man, with strong feelings of affec-
tion to his friends, and much kindly consideration for the feelings
of others. He was well informed and highly accomplished. He
was fond of travelling when he could command a holiday, and
his skill as an amateur artist enabled him the better to enjoy and
perpetuate the beauties of the scenery which he visited.

His frame was never robust, and for some time past he suffered
from a complication of ailments, which terminated his life on the
2d November 1869, at the age of fifty- two.

His funeral was attended by many scientific friends and respect-
able citizens of Glasgow, as well as by the chief office-bearers of
Anderson’s Institution, and the students of that seminary joined
the procession and proceeded with it to the burying-ground.

Dr William Seller, an eminent member of the medical pro-
fession, and long an esteemed Fellow of this Society, was born
in Peterhead, Aberdeenshire, in 1798, the son of a respectable
merchant, who died while his family were children, leaving them
under the charge of a widow, who was herself still young, and
who found that, in consequence of losses arising from misplaced
confidence in others, she must depend on her own exertions
for the family’s support. She came to Edinburgh as a better
field, both for earning a livelihood and educating her children, and
here her son William had the advantage of the excellent educa-
tion which the High School and the University afforded. He was
distinguished at both of these seminaries, and latterly was enabled
to assist his mother by his creditable exertions in private tuition.

He became at the University a member of the Dialectic Society,
where he formed many pleasing and permanent friendships with
several of his contemporaries, including, among others, Lord Deas,
Dr Aitken, for many years the Minister of Minto, and Dr Cumming,
Government Inspector of Free Church schools. With these gentle-
men he maintained a life-long friendship, as well as with many of
those whom he had attended as private tutor, and who had learned
to respect his learning and his virtues. Ultimately he made choice
of medicine as his profession, and took the degree of M.D. in August
1821.

Prudential considerations led him soon afterwards to make his

of Edinburgh, Session 1869-70.

27

knowledge and abilities available in a form which generally brings
to those who adopt it less honour than its usefulness and its in-
trinsic merit truly deserve. He opened a house for the reception
of medical students as boarders during the College session, and
instituted classes for preparing such students for their examina-
tion. It is not impossible that the department thus chosen by him
formed some impediment to his success as a medical practitioner ;
but no one who knew Dr Seller, or watched his conduct, could fail
to see, both in his choice and in the manner in which he followed
it out, proofs of his manly independence, and of his earnest desire
to promote medical science and maintain the dignity of his pro-
fession. His lectures and lessons, we believe, were admirably
adapted for that purpose, delivered in the most kindly and con-
ciliatory tone, and skilfully framed to lead his pupils by easy
gradients to the most commanding views of medical knowledge.
His general learning and accomplishments were at the same time
suited in an eminent degree to illustrate and adorn medical
studies. He was an excellent classical scholar; he was profoundly
acquainted with the intellectual and moral sciences, for which he
had early shown a strong predilection ; and he was a proficient in
those physical sciences which were most closely connected with his
own professional subjects. The extent and accuracy of his infor-
mation were only equalled by his readiness in communicating it
and his modest estimate of his own acquirements.

His last book, which he published in conjunction with Mr Henry
Stephens, on u Physiology at the Farm,” will illustrate at once, to
those who are capable of appreciating it, the extent and variety of
his scientific knowledge, and some defects at the same time which
attended his mode of conveying instruction in this form.

In that volume there is a marvellous exposition of all the most
important facts and principles connected with the subject of animal
growth and nutrition, particularly as applicable to the rearing and
feeding of stock; and the ground there travelled over in physiology,
anatomy, chemistry, and botany is so extensive, that no one who
was not thoroughly master of all these subjects could do them the
justice which has there been dealt to them. The only fault in his
dissertations is that they are too profound, and that it may be
necessary to find an interpreter to stand between the man of science

28

Proceedings of the Boyal Society

and the practical farmer. From this fountain, however, all in-
structors desirous of communicating to those concerned a familiar
and available view of the truth on these subjects will be able to
draw the most important and reliable materials. In the prepara-
tion of this book, Mr Stephens, in a pleasing letter addressed to
me, bears testimony to the assiduity, readiness, and disinterested
zeal of Dr Seller, who declined all remuneration for his labours,
though offered from a high quarter, and was with difficulty per-
suaded to let his own name stand first on the title-page before
that of his excellent associate, who in the scientific department of
the book felt how great a claim Dr Seller had to the commenda-
tions due to the work.

I am not personally acquainted with his other productions, and
should be ill qualified to form an estimate of their worth; but a full
account of these will be found in the notice of Dr Seller contained
in the “ Edinburgh Medical Journal” for May 1869. That memoir
is, I believe, from the pen of Dr Alexander Wood, who was on
the most intimate terms with him, and who has shown his ability
both to appreciate and to record the talents and virtues of his friend.

Mention is there made of the great merit of the lectures on Mental
Diseases which he annually delivered, under the Morrison Endow-
ment, in the College of Physicians. “We have called them
wonderful,” Dr Wood says ; “ they were truly so, whether we have
respect to the learning they displayed, to the acuteness and
originality of the views which they enforced, or to the power of
mental analysis which they exhibited. But,” he adds, “ if ever
published, they will require some gifted and loving hand to
popularise the style, and let the whole matter down to the compre-
hension of the busy workers of our every-day world.”

The same memoir contains a full account of the professional
honours which he attained. Among the most distinguished of
these was his appointment as President of the Eoyal College of
Physicians from 1848 to 1850. He was also the librarian of that
College and a councillor for twenty years. A few years ago they
did him the honour to request him to sit for his portrait, to be hung
in the new hall, and the picture thus painted was among the last
works of the late Sir John Watson Grordon. Dr Wood thus speaks
of his personal character with equal kindness and truth : —

of Edinburgh, Session 1869-70. 29

“ His moral qualities reached almost higher than his intellectual,
aud were the secret of the influence he possessed, and of the affec-
tion with which he was regarded. His courtesy of manner and
delicacy of feeling marked him as a true gentleman in all that he
did. In him sterling integrity, firmness of principle, unswerving
rectitude, and thorough persuasion in his own mind, were combined
with a breadth of view, and a tolerance for the opinions, ay, even
for the weaknesses, of others, as pleasing as it is rare. Guileless as
a child, he was yet sagacious beyond most men ; while the delicate
susceptibilities of his kind heart prevented him from saying or
doing anything that could by possibility wound the feelings of
another.”

In society Dr Seller’s manners were most genial and agreeable,
and he had the power of attaching to himself all who made his
acquaintance. Mr Stephens, his “collaborates” in the “Physiology
of the Farm,” and who came to know him only through their union
in that work, writes to me of him — “ I never made so dear a friend
on so short a notice.”

Until about the year 1865 Dr Seller enjoyed a fair amount of
good health, and retained his active habits; but shortly after that
time his constitution gave way ; and when, after some interval, he
sought medical advice, a complication of disorders was discovered
to exist, including disease of the heart.

Under the care of Mr Archibald W. Dickson, assisted by
other eminent medical friends, the worst symptoms were kept in
check for a time, but at last resisted the remedies applied to them,
and made it apparent that his end was approaching. He bore the
sufferings incident to his illness with the fortitude of a philosopher
and the resignation of a Christian. He discussed with his medical
attendants every symptom of his malady, and its probable termina-
tion, with the same calmness as if the patient had been a stranger.
He retained his courtesy and kindness to all around him to the
very last. His death occurred on the 11th April 1869, at the age
of seventy-one. The great respect with which he was regarded was
shown by the number of those who, unbidden, were present at his
funeral. The College of Physicians, who had long considered him
an honour to their body, attended in their official robes, preceding
the coffin to the grave, and surrounding it while the last rites were

30 Proceedings of the Royal Society

performed. It will be long before we see supplied the place of
one who had so many high attainments and so amiable a character
— so many solid and so many agreeable qualities.

James Wardrop, one of our oldest members, and long known as
a very eminent surgeon, was born, in August 1782, at Torbanehill,
a small property which had been long in his family, and which has
since earned a marked reputation in a mineral and chemical as well,
as a forensic point of view. He commenced the study of medicine
under the care of his uncle, Dr Andrew Wardrop, an eminent surgeon
in Edinburgh. He became assistant to Dr Barclay, the celebrated
anatomist, and was for some time house-surgeon in the Boyal Infir-
mary here. He afterwards went to London, to prosecute his studies
in the lecture-rooms and hospitals of the metropolis ; and afterwards
passed over to Paris, though by this time the peace of Amiens had
been broken off, and war had recommenced between France and
England. Had he been known as an Englishman, he would have
been detained as a prisoner ; but he contrived to elude the vigil-
ance of the police whilst he remained in Paris, and ultimately suc-
ceeded in effecting his transit from France into Germany. He
attended various lectures at Vienna, and had there his attention
specially directed to the diseases of the eye, for the treatment of
which he afterwards attained so high a reputation. On returning
to Edinburgh, he commenced the practice of his profession, and
very soon selected surgery as his department. After practising
here for four or five years, Mr Wardrop left Edinburgh, and settled
in London as a surgeon. Instead of attending, however, the public
hospitals there established, he preferred to institute a surgical
hospital of his own, the wards of which were thrown open to the
profession gratuitously, and where he had a weekly concourse of
visitors, when medical topics were made the subject of conversation.
This hospital he continued to superintend for about eight years,
when he found the labour that it involved was more than he could
undertake consistently with his other avocations. In this manner,
and from surgical lectures which he delivered in London, Mr
Wardrop’s reputation became well established. In 1818, he was
appointed Surgeon Extraordinary to the Prince Begent ; and when
the Prince, after his accession to the throne, visited Scotland, Mr

31

of Edinburgh, Session 1869-70.

Wardrop attended him. He is understood to have been a great
favourite with the king ; but, towards the last days of that monarch,
a misunderstanding at Court arose which excluded Mr Wardrop
from attendance, in consequence, it was thought, of his having
complied too frankly with the king’s urgent inquiry as to the
nature and probable termination of his disease. There can be no
doubt that Wardrop was right in the opinion he formed, though
whether the communication he made was consistent with the rules
of courtly etiquette is not easy to determine. It is, however, be-
lieved that, from some of those who had been instrumental in
excluding him from the royal death-bed, Mr Wardrop ultimately
received an ample apology. Mr Wardrop, though an excellent
surgeon in all respects, soon showed a special familiarity with
ophthalmic surgery, and attained the highest reputation in that
department, both by his writings and his practice. In 1813, Mr
Wardrop published the well-known case of James Mitchell, the boy
born blind and deaf, who, I believe, only died in the present year.
The case excited a great deal of interest both among metaphysicians
and physiologists. Mr Wardrop’s account of it is extremely in -
teresting and curious. He had partially succeeded in admitting
light to the boy’s eye by operating for cataract, and the sight was
thereby improved, so as to afford the patient the delight that
colours could convey, and which he keenly enjoyed, though his
vision still remained too imperfect to become a source by which
practical information of external objects could be introduced. Mr
Wardrop was a man of very varied tastes and talents. He had a
great love and appreciation of art. He was very fond of horses,
and frequented the hunting-field till a comparatively late age ;
and it was with great satisfaction that he wrote his essay on
the diseases of the eye of that animal, which obtained a prize from
the Board of Agriculture. It has been said that he operated with
success on several valuable race-horses and hunters by couching
them for cataract, to the great gratification of their owners ; but
whether the animals when so treated required a pair of spectacles
or an artificial lens to supply the place of the extirpated humour, I
am unable to tell.

I shall not here attempt any account of Mr Wardrop’s works,
which must be well known to medical men, who are most likely to

32

Proceedings of the Royal Society

feel an interest in the subject. An enumeration of them is given
in Pettigrew's “ Medical Portrait Gallery,” where also the inci-
dents of his life are fully narrated. I believe that he enjoyed a
peaceful and cheerful old age, and attained his eighty-seventh year,
without much suffering. I have heard that he latterly discontinued
the use of wine, and attributed to that circumstance mainly his
continued enjoyment of health. He had always been a temperate
man, his favourite beverage being tea. Not very long before his
death he had the misfortune to lose his wife, who also attained a
great age, and latterly his eyesight failed him completely. This
he felt as a great privation, but he bore it with patience, and
never murmured. He sank into a state of great weakness, which
gradually led to his death without any struggle. He was much
loved and respected by all who knew him, and his reputation as
a good man and as an excellent surgeon, and especially as a dis-
tinguished and scientific oculist, ought not soon to be forgotten in
his profession.

It is said that he has left behind him a manuscript record of his
recollections, which, if published, would in all probability, coming
from a man of his ability, observation, humour, and experience, be
highly interesting, not only to the profession, hut to the public.

The following statement respecting the Members of the Society

was read by the Chairman : —

I. Honorary Fellows —

Royal Personage, ....... 1

British subjects, 19

Foreign „ 33

Total Honorary Fellows, 53

II. Non-Resident Member under the Old Laws, . . 1

III. Ordinary Fellows : —

Ordinary Fellows at November 1868, . . . 289

New Fellows, 1868-69. — Robert Henry Bow, Alexander
Buchan, Rev. H. Calderwood, James Dewar, Professor A.
Dickson, William Dickson, George Elder, Principal Sir
Alexander Grant, Bart., Sir Charles Hartley, Isaac Ander-

son-Henry, Alexander Howe, Professor Fleeming Jenkin,

Carry forward,

289

33

of Edinburgh , Session 1869-70.

Brought forward, 289

Dr John W. Johnston, Maurice Lothian, David Mac-
Gibbon, Dr R. Craig Maclagan, Dr W. C. MTntosh, John
Maclaren, Dr Henry Marshall, 0. G. Miller, John Pender,

Rev. T. M. Raven, Dr W. Rutherford, J. L. Douglas
Stewart, Yiscount Walden, Capt. T. P. White, . 26

Deduct Deceased. — Dr Begbie, William Brand, Dr Dalzell,
Professor Dyce, Principal Forbes, Rev. Dr Muir, Dr

Penney, Dr Seller, James Wardrop, ... 9

James Anstruther (formerly noticed), ... 1

Resigned. — Dr A. E. Mackay, Bishop Morel), . . 2

12

Total Number of Ordinary Fellows at November 1869, 303

Add Honorary and Non-Resident Fellows, . . 54

Total, 357

Monday , 20 th December 1869.

Professor KELLAND, Vice-President, in the Chair.

The Keith Prize for the Biennial Period ending May 1869,
having been awarded by the Council to Professor P. G. Tait, for
his paper “on the Rotation of a Rigid Body about a fixed point, ”
which has been published in the Transactions, the Medal was
delivered to him by the President at the commencement of the
Meeting*

The following Communications were read : —

1. On the Geological Structure of some Alpine Lake-Basins.

By Archibald Geikie, Esq., F.R.S.

In this paper the author reviewed the arguments by which the
geologists of Switzerland endeavour to prove that the so-called
“orographic” lakes are essential parts of the architecture of the
Alps. He showed from detailed sections of one or two lakes, parti-
cularly of the Lake of the Four Cantons, that the amount of denuda-
tion, which the surrounding rocks had suffered, demonstrated that

VOL. VII

34 Proceedings of the Royal Society

the lakes must be greatly younger than the plication of the strata
of the Alpine chain ; that from the known effects of subaerial denu-
datoni, the lakes must be, in a geological sense, quite modern ; and
that the Alpine lakes possessed no distinctive features which en-
titled them to be considered apart from the numerous lakes which
are scattered over northern Europe and America. He regarded the
enormous development of lakes at the present period in northern
latitudes as a fact which could not be explained by reference to
subterranean movements. Such movements must have taken place
in a late geological period, otherwise the lakes would have been
filled up with sediment, as is going on every day. He could not
but think that the formation of such lake-basins was connected in
some way with the action of the denuding forces, and he believed
that the theory proposed by Professor Ramsay — that the rock-
basins had been hollowed out by the ice of the glacial period — ful-
filled all the geological conditions of the problem, and would
eventually come to be accepted even by the geologists of Switzer-
land.

2. Preliminary Notice of the Great Fin Whale, recently
stranded at Longniddry. By Professor Turner.

This communication was preliminary to a more extended memoir
which the author hopes to lay before the Society during the Session.

The colour, general form, and dimensions of the animal, wrere
taken when the whale was lying on the shore at Longniddry. The
observations on its internal structure were made whilst it was
undergoing the operation of flensing at Kirkcaldy, or on specimens
which were brought over to the Anatomical Museum of the Uni-
versity. These specimens it was his intention to preserve in the
Museum. In conducting the examination he had been ably and
willingly seconded by the thoroughly cordial and enthusiastic
co-operation of his assistant Mr Stirling, and his pupils Mr Millen
Coughtrey, and Mr James Foulis.

Most of the Fin Whales which had been subjected to examina-
tion by British and Continental anatomists had been found floating
dead on the surface of the sea, and had then been towed ashore ;
but the Longniddry whale had got entangled, whilst living, amongst

35

of Edinburgh, Session 1869-70.

the rocks and shoals, where it was left as the tide receded. The
length of the animal, measured from the tip of the lower jaw to
the end of the tail, 78 feet 9 inches. The girth of the body imme-
diately behind the flipper was 45 feet. Its girth in line with the
anal orifice was 28 feet, whilst around the root of the tail it was
only 7 feet 6 inches. The inner surface of the lower jaw, close to
its upper and outer border, was concave, and sloped inwards so as
to admit the edge of the upper jaw within it. The lower jaw
projected at the tip l-£ foot beyond the upper. The length from
the angle of the mouth to the tip of the lower jaw, along the
upper curved border, was 21 feet 8 inches. The dorsum of the
upper jaw was not arched in the antero-posterior direction. It
sloped gently upwards and backwards to the blow holes, from
which a low but readily recognised median ridge passed forwards
on the beak, gradually subsiding some distance behind its tip.
On each side of this ridge was a shallow concavity. Immediately
in front of the blow holes the ridge bifurcated, and the forks passed
backwards, enclosing the nostrils, and then subsided. The outer
borders of the upper jaw were not straight, but extended forward
from the angle of the mouth for some distance in a gentle curve,
and then rapidly converging in front, formed a somewhat pointed
tip. Their rounded palatal edge fitted within the arch of the
lower jaw. The transverse diameter of the upper jaw over its
dorsum, between the angles of the mouth, was 13 feet 3 inches.
From the blow holes the outline of the back, curved upwards and
backwards, was uniformly smooth and rounded, and for a consider-
able distance presented no dorsal mesial ridge. From the tip of
the lower jaw to the anterior border of the dorsal fin the measure-
ment was 59 feet 3 inches. This fin had a falcate posterior border.
Behind the dorsal fin the sides of the animal sloped rapidly down-
wards to the ventral surface, so that the dorsal and ventral mesial
lines were clearly marked, and the sides tapered off to the tail.
The ventral surface of the throat, and the sides and ventral surface
of the chest and belly, were marked by numerous longitudinal
ridges and furrows. When he first saw the animal, the furrows
separating the ridges were not more than from J to f- inch broad,
whilst the ridges themselves were in many places 4 inches in
breadth, but as the body began to swell by the formation of gas

36 Proceedings of the Royal Society

from decomposition, the furrows were opened up, became wider
and shallower, and the ridges underwent a corresponding diminu-
tion in breadth. At the same time a considerable change took
place in the contour of the body in the thoracic and abdominal
regions, which presented a huge lateral bulging, giving a greater
girth than when it first came ashore.

The flipper, which measured 12 feet 3 inches from root to tip
along its anterior convex border, projected from the side of the
body 31 feet 4 inches behind the tip of the lower jaw, and 14 feet
behind the angle of the mouth. It curved outwards and back-
wards, terminating in a free pointed end. The distance between
the two flippers, measured over the back between the anterior
borders of their roots, was 18 feet 6 inches.

On the dorsum of the beak and of the cranium, on the back of
the body, and for some distance dowm its sides, the colour was
dark steel grey, amounting in some lights almost to black. On a
line with the pectoral flipper the sides were mottled with white,
and on the ventral surface irregular, and in some cases large patches
of a silvery grey or whitish colour were seen. An experienced
whaling seaman, Mr Walter Roddam, who had repeatedly seen
this kind of whale in the northern seas, told him that it was known
to the whalers by the name of “ silver bottom.” The dorsal fin
was steel grey or black, except near its posterior border, where it
was a shade lighter and streaked with black lines. The anterior
margin of the lobes of the tail, its upper surface near the root and
for the anterior two-thirds, were black, whilst the posterior third of
the same surface and the interlobular notch were lighter in tint.
The upper surface of the flipper was steel grey, mottled with white
at the root, at the tip, along its posterior or internal border, and on
the under surface ; white patches were seen on the upper surface
near the tip, and here they were streaked with black lines running
in the long axis of the flipper. White patches also extended from
the root of the flipper to the adjacent parts of the sides of the
animal. The outside of the lower jaw was black, whilst the in-
side was streaked with grey. The tongue of the whale was of
enormous size. The dorsum was comparatively smooth in front,
but at the posterior part it was elevated into hillocks which were
separated by deep furrows. The baleen had a deep black colour,

of Edinburgh, Session 1869-70.

37

and consisted on each side of plates which projected from the
palate into the cavity of the mouth. The plates were arranged in
rows— 370 were counted on each side — which lay somewhat
obliquely across the palate, extending from near the base of the
great mesial palatal ridge to the outer edge of the palate. The
plates diminished in size so much, that at the tip, where the two
sets of baleen became continuous, they were merely stiff bristles*
The blubber varied much in thickness. Mr Tait, by whom the
whale was purchased, and to whom the author was indebted for the
opportunity of examining the animal during the flensing operation,
stated that he had obtained from the blubber, and from the inside
fat, 19 tons 12 cwt. of oil ; whilst the skeleton, including the lower
jaw, weighed 9 tons 12 cwt., and the baleen, including the gum,
about one ton ; the weight of flesh, intestines, and other refuse,
was estimated at about 50 tons.

The author believed the whale to be an example of the whale
called Steypireybr by the Icelanders, a description of which by
Professor Reinhardt has recently appeared in the Annals of Natural
History (Nov. 1868). The Steypireybr has been identified with
the Baloenoptera Sibbaldii or Physalus Sibbaldii of Grray. The
Longniddry whale differed from the Baloenoptera musculus ( Physalus
antiquorum , Grray), or common Razor-back, in having a broader and
more rounded beak, in the flipper being longer in proportion to the
length of the body, in the baleen plates, fringes, and palatal mucous
membrane, being deep black, in the plates being longer and broader,
in the belly possessing a more silvery grey colour, and in the blubber
being thicker, so that the animal is commercially more valuable.

The whale was with calf, but the foetus, a male, had been dis-
placed, and thrown out of the abdominal cavity into a space
between the outer surface of the right ribs and the blubber. The
displacement had probably occurred whilst she was being towed by
the tail across the firth from Longniddry to Kirkcaldy. The
whale may have entered the firth in order to give birth to her calf,
as there seems reason to think that whales do frequent arms of the
sea for that purpose. Although nothing definite seemed to be
known of the period of gestation of the Fin whales, yet, from the
length of the calf — amounting to nearly 20 feet, or about one
fourth the length of the mother — he thought it was probable that

38

Proceedings of the Royal Society

the whale was at or about her full time. Several square feet of the
foetal membranes were examined. The outer surface of the chorion
was thickly studded with villi, which over large areas had no
special mode of arrangement ; but in some localities they formed
an irregular network, in others they were seated on long ridge -like
elevations of the chorion, and in other cases conical folds of that
membrane, 5 or 6 inches long, were closely covered with villi. The
placenta was diffused, but with a tendency to aggregation of the
villi where the chorion was raised into ridge-like and conical folds.

The paper contained an account of the vessels, the pharynx,
laryngeal pouch, the omentum, the intervertebral discs, the cylin-
driform fibrous mass which supports the lower jaw, and a description
of the atlas, axis, hyoid bone, sternum and pelvis. The sternum
was shown to be not a rudimentary bone, but of considerable size,
consisting of three large lobes with a posterior pointed process.
The dissection of the foetus proved that the opinion entertained by
anatomists, that in the baleen whales the sternum is a single
bone developed from one ossific centre, is not correct for all the
species. For in this Balanoytera the foetal sternum consisted of two
distinct masses of cartilage, one of which corresponded to the
posterior pointed process, the other to the larger 3-lobed anterior
portion. The pelvic bones were also described. In the foetus they
were still cartilaginous, but had the same general form as in the
adult, which proved that in the process of ossification no important
change took place in their external configuration, and that the
pelvis of the male differs in no essential feature from that of the
female. From the appearance presented by the skeleton generally,
the large whale was obviously in the stage of growth which Mr
Flower has termed C£ adolescent.”

The paper w^as illustrated by photographs, drawings, and speci-
mens.

3. Note on Aggregation in the Dublin Lying-in Hospital.
By Dr Matthews Duncan.

In this paper it is pointed out that deliveries are a better means
of arriving at an estimate of the healthiness of an hospital than
amputations ; that the deliveries in the Dublin Hospital are re-
markably valuable because of their great number (nearly 200,000),

39

of Edinburgh, Session 1869-70.

and of the length of time of the hospital’s operation (above 100
years) ; and that the evidence derivable from them relative to the
danger of confinement, as regulated by the amount of aggregation,
or number brought together at the same time, has never been
properly taken.

It has been asserted by Dr Evory Kennedy and others, that the
mortality is in direct proportion to the aggregation. But an
analysis of the whole data indisputably shows that in the Dublin
Hospital the mortality does not increase with the increased number
of the inmates, and does not rise with the aggregation. The mor-
tality of this hospital is neither in the direct nor in the inverse
ratio of the aggregation.

The data, indeed, seem to favour the view that the mortality
diminishes when the aggregation is increased. Certainly a smaller
proportional number die when there were many in the hospital than
when there were fewer.

The following Gentlemen were elected Fellows of the
Society : —

St John Vincent Day, Esq., C.E.

David Munn, Esq.

Robert R. Tatlock, Esq.

Monday , 3 d January , 1870.

Dr CHRISTISON, President, in the Chair.

The following Communications were read: —

1. On a Method of Economising our Currency. By

Andrew Coventry, Esq.

In the outset, it was stated that the currency consisted mainty
of a large mass of paper, whose convertibility had been provided
for by Sir Robert Peel’s Bank Bill of 1844-45, with which paper,
and the gold set aside for it, the author did not propose to meddle.
But alongside of the paper there circulated a large quantity of gold,
and the object of his paper was to economise it. Row, gold having
only three uses — as currency, in the arts, and to discharge debts
abroad — it was desirable that some arrangement should be thought

40

Proceedings of the Royal Society

of which might relieve it of the first mentioned service, in which
it suffers much waste, and set it free for the two others.

The plan proposed was to disqualify gold, under legal penalties,
for currency or barter within the island, upon which it would flow
into the Bank, to be kept there for the security of the notes which
would take its place, and for the arts and foreign trade. The gold
currency being shown to amount to 80 millions, it was next
explained that, agreeably to an article in the “Economist” of 3d
July last, the saving thereby effected (in tear and wear, coining
and recoining) to the country would be fully L. 56, 000 a year, or
rather L. 60, 000 a year, as L.4000 might be added for loss by fire
and shipwreck. As to the expense, again, of the paper which
would be needed to represent the 80 millions of gold brought in by
the disqualification, the author proposed to provide for it in the
following way : — Let the Bank have to itself two of the 80 millions
of gold, and yet be allowed to issue paper to the full amount of 80.
The uncovered part of the issue would be a slight extension of the
14 or 15 millions already privileged by statute, and such an ex-
tension has been often proposed, and by able men. In return for
the two millions of gold, the Bank might very fairly be expected to
provide the paper currency and pay the State L. 25, 700 a year.
These figures are arrived at by the terms of the arrangement
between the Bank and Government as to the 14 millions being
adopted for the two millions now. Farther, a return to the use of
small notes in England was recommended, as the experience of
Scotland showed that certain improvements in engraving were
complete preventives against forgery ; and he advocated also gold
bars, a suggestion of the late Mr Ricardo, instead of coins.

The result of gain on the whole would be, to the State L. 60, 000
and L. 25, 700, besides L. 18, 000 of profit to the Bank after defraying
the paper currency — or, in all, L. 103, 700 a year, which, capitalised,
would be three millions.

Such was Mr Coventry’s proposal. But he added that some
might reasonably be inclined to go further, and to take the whole
or part of the remaining eight of the 78 millions, making some
compensation to the Bank, of course, seeing that a reserve of 78 of
gold against 80 of paper, large at any time, would be extravagant
when gold fell to be disused for currency. Even if we were to

41

of Edinburgh, Session 1869-70.

assume the cost of 80 millions of paper to be not far short of the
cost of maintaining a gold currency of like amount, the scheme
proposed would have this merit, that it would bring 80 millions of
gold into the bank, of which 70 millions would be an ample reserve
against 80 of paper — thus effecting a gain of Ten Millions. Mr
Coventry showed, too, that bullion was seldom required to be sent
abroad to any very great amount by the exchanges, and instanced
the year 1864, when the trade of the country amounted to nearly
500 millions, and the balance only to 4J millions, or a trifle more.

2. On the old River Terraces of the Earn and Teith, viewed
in connection with certain Geological Arguments for
the Antiquity of Man. By the Rev. Thomas Brown,
Edinburgh.

The author described the circumstances which led him, in 1863,
to begin the investigation of these terraces, and showed he had traced
their course along the Earn from Loch Earn to where they meet
the tide. He had also examined the valley of the Teith, and had
found the same deposits from the head of Loch Lubnaig to near
Stirling. There are three different levels on which the terraces
lie at different heights above the river bed. The lowest consists of
the present banks of the stream and haughs or meadows ; above
this there is an intermediate terrace, which, in its turn, is sur-
mounted by the highest. Owing to the effects of denudation, one
or other of these levels is frequently interrupted or obstructed, but
they are ever again found recurring, and the whole three present
themselves so frequently as to show that this threefold terrace
system is the true key to these valley deposits. It was shown that
they were neither sea-beaches, as some geologists have held, nor
lake-margins, as has been maintained by others, but must have
been formed by the river itself, at some former age, when its
floods had the power of rising to the requisite height. All the
three terraces are found varying in height at different points
according to the width of the valley, the strength of the current,
and other circumstances. The lowest, which consists of the pre-
sent banks, &c., varies from 3 to 10 feet, according to the locality ;
the second, from 15 to 24; while the third is from 35 to 60, or

VOL. VII.

42

Proceedings of the Royal Society

even more above the river bed. Numerous examples were given
of their outward form and inward structure to illustrate these views.

The author next proceeded to describe the exact geological
position of these deposits. As the time of the kames or escars
belonged to the close of the glacial epoch, so the formation of these
terraces followed the time of the kames, and they were constructed
by river floods out of the pre-existing collections of gravel, &c.
The fossil remains of the flora of Strathearn, which they enclose,
show that the climate of the period must have been as mild as the
present.

Certain geological arguments for the antiquity of man were
referred to, especially these deduced from the gravel deposits of
the Somme in France and the Brixham cave in England. From
the height at which these deposits with flint weapons had been
found above the present river courses, it had been held that the
human period must be extended so as to leave time for the erosion
of the valleys. The author adduced evidence to show conclusively
that the Scottish valleys had been eroded down to their present
depth previously to the formation of these old gravel deposits,
which are found at so great a height above the rivers. If, there-
fore, the analogy of the Scottish valleys and streams could apply
to those of France and England, the time needed for the erosion
of the valleys must be thrown out of the account. It was vain to
attempt to dissociate the formation of the valley system of France
and England from that of Scotland, as if they were not analogous.
He had no doubt that these views would be established ; but, in
the meantime, it was at least right that men should suspend their
judgment till the question thus raised bad been thoroughly in-
vestigated.

The following Gentlemen were elected Fellows of the
Society : —

Alexander Russel, Esq.

James Crichton Browne. M.D.

John Duncan, M.D., F.R.C.S.E.

W. Burns Thomson, F.R.C.S.E.

Dr W. R. Sanders, Professor of Pathology.

Rev. Andrew Thomson, D.D.

Joseph Lister, Professor of Clinical Surgery.

William Anderson, LL.D.

of Edinburgh, Session 1869-70.

43

Monday , \lth January 1870.

GEORGE ROBERTSON, Esq., Councillor, in the Chair.

The following Communications were read: —

1. Experiments on the Colorific Properties of Lichens. By
W. Lauder Lindsay, M.D., F.R.S.E., F.L.S.

The author’s paper consists mainly of a Table exhibiting certain
of the positive results of many hundred experiments on the colour-
ing matters contained in or educible from Lichens. The experi-
ments in question are partly a repetition, and partly an extension
on a more systematic and complete scale, of a series of researches
made by the author between 1852 and 1855, the results of which
were originally submitted to the Botanical Society of Edinburgh.
The present series of experiments includes the whole family of the
Lichens. The Table represents mainly the effects of chemical re-
agents on solutions of the lichen colouring-matters, or colorific
principles, in boiling alcohol or water. The nomenclature of the
Colour-reactions is that of Werner and Syme. As the subjects of
his experiments, the author confined himself in great measure to
the lichens contained in published Fasciculi; so that comparative
experiments may hereafter be made on authentic specimens of the
same species and varieties by other observers in other countries. The
author’s results are submitted as a mere pioneer contribution to a
subject, which has been as yet most imperfectly worked out, viz.,
the Chemistry of the lichen colouring-matters ; but he trusts they
may furnish a partial basis for a future more exhaustive series of
researches to be undertaken conjointly by Chemists and Lichenologists.

The present Table illustrates pro tanto —

I. The kinds of colour producible from lichens : those, viz. —

(а) Which exist ready formed in the thallus — for the most

part green, yellow, or brown, — and which are of little
practical utility ; and

(б) The colourless colorific principles, which, under the action

of ammonia and atmospheric oxygen, yield red or purple

44 Proceedings of the Royal Society

dyes of the class of which Orchil, Cudbear, and Litmus
are the familiar types.

II. The families, genera, or species that possess practical colorific

value; as well as the relative values of colorific species or
varieties.

III. The irregularities or uncertainties of colour-development,

according to

(a) The condition of the lichen operated on ;

( b ) The condition of the reagent ; or

(c) The circumstances of experiment.

There is thus a rough indication, on the one hand, of the so-called
Dye-lichens ; and, on the other, of species and genera that are practi-
cally useless to the colour-maker.

The present series of experiments, moreover, has a direct prac-
tical bearing on

I. The recent introduction of Colour-tests as Specific Characters in
Lichens ;

II. The modern manufacture from Lichens (e.y., in France) of
fast dyes , capable of competing successfully with the brilliant
coal-tar colours and other dyes of recent introduction ; and

III. The use, which still lingers in certain parts of Scotland, and
probably also of W ales and Ireland, of lichens as Domestic
dye-stuffs.

2. On the Principles of Scientific Interpretation in Myths,
with Special Beference to Greek Mythology. By Pro-
fessor Blackie.

Professor Blackie commenced by saying that, of all the branches
of interesting and curious learning, there was none which had been
so systematically neglected in this country by English scholars as
mythology — a subject closely connected both with theology and
philosophy, and on which those grand intellectual pioneers and
architects, the Germans, had expended a vast amount of profitable
and unprofitable labour. The consequence of this neglect was,
that of the few British books we had on the subject, the most
noticeable were not free from the dear seduction of favourite ideas
which possessed the minds of the writers as by a juggling witch-

of Edinburgh, Session 1869-70.

45

craft, and prevented them from looking on a rich and various
subject with that many-sided sympathy and catholic receptiveness
which it required. In fact, some of our most recent writers on
this subject have not advanced a single step, in respect of scientific
method, beyond Jacob Bryant, unquestionably the most learned
and original speculator on mythology of the last century; but
whose great work, nevertheless, can only be compared to a grand
chase in the dark, with a few bright flashes of discovery, and
happy gleams of suggestion by the way. For these reasons, and
to make a necessary protest against certain ingenious aberrations of
Max Muller, Gladstone, Inman, and Cox in the method of mytho-
logical interpretation, he had undertaken to read the present paper;
which, if it possessed only the negative virtue of warning people
to be sober-minded and cautious when entering on a path of in-
quiry, full of bogs below and clouds above, could not be deemed
impertinent at the present moment.

One great fact as to the origin of Polytheism may be considered
as firmly established, and by general consent admitted — viz., that
the great physical shows and forces by which man finds himself
surrounded and conditioned, assuming, under the influence of
reverence and imagination, various anthropomorphic disguises,
constituted the original council of the great gods. When we say
physical, however, we do not mean physical in the material and
mechanical modern sense of the word; but we mean physical in a
sort of pantheistic sense, in which nature is regarded as everywhere
interpenetrated, inspired, and fashioned by spirit. This being so
and ascertained, be it noted, by an overwhelming array of strictly
inductive evidence, there can be no difficulty in predicating, a
; priori , what the great gods of the Greeks, to whom I shall confine
myself in this paper, must have been originally in their elemental
significance. They must have been those powers of Nature and of
the human soul, or of Nature considered as animated by a human
soul, whose display was most striking, and whose influence was
most felt by primeval man. Those powers are — The sky, the
earth, the sun, the moon, the stars, the sea and rivers, the atmo-
sphere and winds, the subterranean forces, the underground world,
and the unseen powers of darkness beyond the grave, the vege-
tative or generative principle, the fervid domain of moral emotions,

46 Proceedings of the Pioyal Society

and the sovereign sway of intellect. For I do not believe in any
period when man was merely a brute, or a nondescript creature,
half emergent from the primeval man-monkey or monkey-man.
Individual tribes of a low type, such as those whom my ingenious,
acute, and learned friend, Mr M‘Lennan, calls by the undignified
name of Totems , may always have existed ; but in a general Totem -
state of an embryo and embruted humanity I do not believe.
Hypotheses of this kind are the conceit of speculative scicence,
not historical fact. Starting from this base of operations, our first
business is to look our gods fairly in the face, and by a reverential
and poetic study of their forms, attitude, dress, badges, and symbols,
to recreate the anthropomorphised power in its original elemental
significance. And this must be done in an extremely cautious and
careful way, so as to make legitimate our inductive conclusions,
after the method of which such admirable examples are given by
Ottfried Muller in his “Prolegomena” — a small book in respect
of bulk, but a truly great book in respect of significance ; and to
the principles laid down in which it would be well if some of our
recent mythological speculators would seriously recur. Mr Ruskin’s
method of interpreting tbe G-reek gods without such a careful
scholarly preparation, is mere brilliant trifling ; and all excursions
into the realms of comparative mythology and philology, after the
fashion of Creuzer and Bryant, without first taking sober counsel
from home materials, can result only in floating conjecture, not in
stable knowledge. Now, to give an example of what I mean : if
we take three of the principal gods of the Hellenic Olympus —
Zeus, Poseidon, and Apollo — and peruse them carefully, I defy any
man who has a common amount of classical reading, and who, like
Wordsworth, can put himself into the position of the original
creators of mythology, to form any other conclusion than that these
personages are mere anthropomorphic disguises of the heavens, the
ocean, and the sun ; and towards forming this conclusion, with a
man who is entitled to have a judgment on such subjects, not a
single shred of Hebrew or Sanscrit, or any foreign organon of
interpretation, is required. It may be interesting to know that
Zevs in its Sanscrit form means bright or shining; but it is not
necessary towards a well-grounded scientific induction of the ori-
ginal significance of the god.

47

of Edinburgh, Session 1869-70.

But there are other persons in the Pantheon whose significance is
anything but plain ; and in their case, unquestionably, recourse may
be had with advantage to etymology, first, in the native language,
of course, and then in the kindred languages, in some one of
which the original form of the sacred title may have been pre-
served. A striking example of the utility of native etymology in
fixing the significance of the Greek mythological personages is pre-
sented in the familiar case of the Harpies, whose whole character
and actions, taken along with the open evidence of their Greek names
in Hesiod, prove, beyond all doubt, that they are the impersonated
forms of such sudden gusts and squalls of wind as come down
fuequently on the Black Sea or the Highland lochs. But etymo-
logy, though a safe guide in such instances, is, in less obvious
cases, of all guides the most fallacious. And this is what my
distinguished friend Max Muller, and some who follow in his train,
seem at the present moment somewhat apt to forget. An etymo-
logy, though not caught up in the arbitrary fashion of Bryant and
Inman, but traced with the most cautious application of Grimm’s
laws, is, after all, only a conjecture. It is a conjecture not in the
teeth of all philological analogy. It implies a possible, or, as the
case may be, a probable identity. But alone, and without extrinsic
and real, as opposed to verbal indications, it affords no ground for a
legitimate induction. Nothing is more common than accidental
coincidences in mythological names — such as the Latin Hercules
and the Greek Heracles — which, as scholars know, have not the
most remote connection. Besides, even if the true etymology of
any Greek god could be found in Sanscrit or any other language,
the signification of the original name affords no sure clue to the
character of the accomplished god. Our dictionaries are full of
words whose ultimate signification has travelled so far away from
its original, that the original meaning could supply no key to the
modern usage, n op<£vpeos, for instance, means dark in Homer, but
in Horace brilliant or shining. Usage alone can inform us of this
perversion or inversion of the original meaning of words. But
if this be true with regard to mere philology, it is much more true
with regard to mythology. The root of a word, like the stock of
a tree, may remain stiff enough for centuries; but the human
imagination, when employed in the forming of myths, is a kaleido-

48 Proceedings of the Royal Society

scope whose changes are incalculable, and whose results are so
transmuted from the original type as to he unrecognisable. On
these grounds, I feel myself bound to protest in the strongest
manner against the fashion recently introduced by Max Muller
and Mr Cox, of giving a new interpretation of Hellenic gods,
founded on no firmer basis than slippery Sanscrit etymologies, and
a few ingenious conjectures. After reading the distinguished
German’s lucubrations on Hermes, and Athena, and Erinnys, I
stand as unconvinced as before the portentous array of Protean
u Radicals, ” in the first volume of Rryant; it is only another turn
of the mythological kaleidoscope from the hand of a man who
combines the erudition, the speculation, and the subtlety of his
people, with an eloquence and a taste seldom surpassed by the best
Englishmen writing their own language in the best way — a man
whose character I respect, and whose instructive intercourse I have
enjoyed now for a long series of years ; but, with regard to whose
speculations on curious points of Greek mythology, I can only say,
Amicus Plato sect magis arnica veritas. And etymology is not the
only point on which I am forced to dissent from Max Muller and
that large school of Herman thinkers of whom he is the spokesman
in this century. A long familiarity with the writings of German
scholars has convinced me that there is a particular idiosyncrasy
in their minds which, when applied without qualification in mytho-
logical research, is peculiarly apt to mislead. This idiosyncrasy
leads them to believe in no facts that they are not able to construct
from certain favourite presupposed ideas. Now, I believe in facts
as having an independent value, and a right to he recognised alto-
gether independent of any favourite ideas which an interpreter of
facts may bring to explain them. I believe that one domain ot
myths is to be explained by ideas ; but I believe also in a class of
myths, of which the main root and stem are historical, and only
the outer limbs and flourishes mythical. I see no presumption
whatsoever that the Trojan War represents a conflict between the
powers of light and darkness ; that Achilles is a degraded solar
god, as Muller would indicate, or a water god, as is the fashionable
idea of most Germans. The most improbable thing in the world
is that a nation should have drawn a brush over all its human
memories, and left nothing but myths of the Dawn and the Dark

of Edinburgh, Session 1869-70.

49

in the shape of European peeis and Asiatic princes. I refuse,
therefore, on the faith of a few specious etymologies, to see any-
thing mythical in the main action of the “ Iliad ; ” and I deem it
a waste of brain to seek the interpretation of a stout old Thessalian
thane, from a Sanscrit epithet of the sun. But India is not the
only country to which adventurous scholars have travelled in
search of a key to unlock the mysteries of the Hellenic Pantheon.
Mr Gladstone, as it is well known, has reverted to the expedient —
a favourite one with our old theological giants — of explaining
Greek gods through the medium of a primitive sacred tradition.
There might he no objection to this if the Hebrews had possessed
any original quarry of theologic material from which an Apollo or
an Athena could be built up ; but the only idea that the Hebrews
could have supplied to the Greeks was that of the one Supreme
God, whom no doubt we have in Zeus, but unaccompanied with
any special Hebrew character by which he might be identified.
The same distinguished scholar’s most recent excursion into far
Eastern lands has not brought back, in my opinion, any more
valuable booty. That Aphrodite and Hercules were of Phoenician
extraction, at least contained a strong admixture of Phoenician
elements, was known long ago ; and few facts in early Hellenic
history can be considered more certain ; but beyond this, all pro-
positions with regard to early Phoenician influence on the persons
of the Greek Pantheon, seem to me to stand on too slight a basis
of ingenious conjecture to possess any scientific value.

Having made these protests against the brilliant, but, so far as
Greece is concerned, in my opinion barren excursions of recent
writers into the regions of comparative mythology, I have only to
say in conclusion, that the only safe method in the present state of
the science of mythology, is to confine our attention to the actual
forms and attitudes and symbols of the gods as they present them-
selves before us in their accomplished impersonation. By tracing
Hermes, for instance, to the breeze of the early Dawn, nothing is
gained, even it be true; it were only a pretty fancy of the infant
Aryan mind on the banks of the Indus, with which a pastoral
Greek on Mount Cyllene had nothing to do. The Hermes of the
Greeks, is plainly, in the first place, a pastoral god of increase,
then a god of gain, when the shepherd became a merchant, and

VOL. VII.

5 0 Proceedings of the Royal Society

then generally a god of commerce, and the adroitness which com-
merce demands. Athena, in the same way, the daughter of the
dark-clouded Jove, is the flashing-eyed maiden, because she repre-
sents the feminine aspect of the sky, of which her sire represents
the masculine. Juno, again, by many manifest signs, is certainly
the earth anthropomorphised out of the physical yrj, just as Zetis
was out of ovpavos. Then, again, if Apollo be the sun, Artemis,
his sister, without going further, must be the moon ; and Dionysus,
the wine god, whose Oriental origin and late introduction is certified,
stands by virtue of the phallic symbol manifestly an Oriental god
of the generative virtue, just as Hermes was in Arcadia by the same
symbol proclaimed the patron of breeding to the sheep-farmers
of the Pelasgic peninsula. Then, by the same process of look-
ing at what is before me, apart from Herman theories and Sanscrit
etymologies, I reserve a considerable domain in the mythological
land for exaggerated and met amorphic history; not at all con-
cerned that I may be looked on by the winged Hermans as a
dull, prosaic fellow, or a disciple of the atheistic Euhemerus — for
Euhemerus also was not altogether wrong, and the worship of
human ideals as, at least, one element in many mythologies, is one
of the most accredited facts in the history of the human race. And
if I seem to have achieved a very small thing when I keep myself
within these bounds, I have at least kept myself clear of nonsense,
which in mythological science is as common as sunk rocks in the
Shetland seas. To Max Mtiller, and other Sanscrit scholars,
I hope I shall always be grateful for any happy illustrations which
they may supply of the general character of Aryan myths, and of
occasional coincidences of the Hellenic mode of imagining with the
Indian ; and I think the somewhat cold and unimaginative race of
English scholars are under no small obligations to him for having
taught them to recognise poetical significance and religious value
in some legends, which passed in their nomenclature for silly
fables or worthless facts ; but I profess to have been unable to
derive any sure clue from the far East to the most difficult questions
of Hreek mythology; nor do I expect that, when every obsolete word
in the Rig Veda shall have been thoroughly sifted and shaken, a
single ray of intelligible light will thence flow on the Athena of
the Parthenon or the Hermes of the Cyllenian slopes. I believe

ERRATUM.

Index, vol. vi. p. 608, Professor Tail’s Paper, line 4 from bottom, second
column, for Parts read Roots.

51

of Edinburgh, Session 1869-70.

that in the region of mythology they will ultimately he found to
be the wisest, who are at present content to know the least ; that
while some mythological fables are too trifling to deserve interpre-
tation, others are too tangled to admit of it; and that the man
who, at the present day, shall attempt to interpret the Greek gods
from the transliteration of Sanscrit or Hebrew words, will be found,
like Ixion, to have embraced a cloud for a goddess, and to have
fathered a magnificent lie from the fruitful womb of his own con-
ceit. There is no more dangerous passion than that which an
ingenious mind conceives for the fine fancies which it begets.

The following Gentlemen were admitted Fellows of the
Society : —

Dr G. H. B. Macleod, Professor of Surgery in the University of Glasgow .

Dr Thomas A. G. Balfour, F.R.O.P.E.

The following Gentlemen were admitted Honorary Fellows
of the Society : —

1. Foreign.

Hugo von Mohl, M.D., Ph.D., Member of the Imperial Academy Naturae
Curiosorum, and Professor of Botany in the University of Tubingen.
Claude Bernard, Member of the Institute of France, Professor of Physio-
logy in the College of France.

2. British.

Thomas Andrews, M.D., F.R.S., M.R.I.A., Vice-President and Professor of
Chemistry in Queen’s College, Belfast.

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

yol. yii. 1869-70. No. 81.

Eighty-Seventh Session.

Monday, 7 th February 1870.

Dr CHEISTISON, President, in the Chair.

The following Communications were read : —

1. On Eeciprocal Figures, Frames, and Diagrams of Forces.
By J. Clerk Maxwell, Esq., F.E.SS. L. & E.

The reciprocal figures treated of in this paper are plane recti-
linear figures, such that every line in one figure is perpendicular
to the corresponding line in the other, and lines which meet in a
point in one figure correspond to lines which form a closed polygon
in the other.

By turning one of the figures round 90°, the corresponding lines
become parallel, and are more easily recognised. The practical
use of these figures depends on the proposition known as the
“ Polygon of Forces.” If we suppose one of the reciprocal figures
to represent a system of points acted on by tensions or pressures
along the lines of the figure, then, if the forces which act along
these lines are represented in magnitude, as they are in direction,
by the corresponding lines of the other reciprocal figure, every
point of the first figure will be in equilibrium. For the forces
which act at that point are parallel and proportional to the sides of
a polygon formed by the corresponding lines in the other figure.

In all cases, therefore, in which one of the figures represents a
frame, or the skeleton of a structure which is in equilibrium under

YOL. VII. II

54

Proceedings of the Royal Society

the action of pressures and tensions in its several pieces, the other
figure represents a system of forces which would keep the frame in
equilibrium ; and, if the known data are sufficient to determine
these forces, the reciprocal figure may be drawn so as to represent,
on a selected scale, the actual values of all these forces.

In this way a practical method of determining the tensions and
pressures in structures has been developed. The “polygon of
forces ’’has been long known. The application to polygonal frames,
with a system of forces acting on the angles, and to several other
cases, was made by Professor Rankine in his Applied Mechanics.
Mr W. P. Taylor, a practical draughtsman, has independently
worked out more extensive applications of the method. Starting
from Professor Rankine’s examples, I taught the method to the
class of Applied Mechanics in King’s College, London, and published
a short account of it in the “Philosophical Magazine” for April
1864. Professor Pleeming Jenkin, in a paper recently presented
to the Society, has fully explained the application of the method to
the most important cases occurring in practice, and I believe that
it has been found to have three important practical advantages.
It is easily taught to any person who can use a ruler and scale.
It is quite sufficiently accurate for all ordinary calculations, and is
much more rapid than the trigonometrical method. When the
figure is drawn the whole process remains visible, so that the
accuracy of the drawing of any single line can be afterwards tested ;
and if any mistake has been made, the figure cannot be completed.
Hence the verification of the process is much easier than that ol‘
a long series of arithmetical operations, including the use of
trigonometric tables.

In the present paper I have endeavoured to develope the idea of
reciprocal figures, to show its connection with the idea of reciprocal
polars as given in pure mathematics, and to extend it to figures in
three dimensions, and to cases in which the stresses, instead of
being along certain lines only, are distributed continuously through-
out the interior of a solid body. In making this extension of the
theory of reciprocal figures, I have been led to see the connection
of this theory with that of the very important function introduced
into the theory of stress in two dimensions by Mr Airy, in his paper
“On the Strains in the Interior of Beams” (Phil. Trans. 1863).

55

of Edinburgh, Session 1869-70.

If a plane sheet is in equilibrium under the action of internal stress
of any kind, then a quantity, which we shall call Airy’s Function
of Stress, can always be found, which has the following properties.

At each point of the sheet let a perpendicular be erected pro-
portional to the function of stress at that point, so that the
extremities of such perpendiculars lie in a certain surface, which
we may call the surface of stress. In the case of a plane frame the
surface of stress is a plane-faced polyhedron, of which the frame is
the projection. On another plane, parallel to the sheet, let a per-
pendicular be erected of height unity, and from the extremity of
this perpendicular let a line be drawn normal to the tangent
plane at a point of the surface of stress, and meeting the plane at
a certain point.

Thus, if points be taken in the plane sheet, corresponding points
may be found by this process in the other plane, and if both points
are supposed to move, two corresponding lines will be drawn, which
have the following property: — The resultant of the whole stress
exerted by the part of the sheet on the right hand side of the line
on the left hand side, is represented in direction and magnitude
by the line joining the extremities of the corresponding line in
the other figure. In the case of a plane frame, the corresponding
figure is the reciprocal diagram described above.

From this property the whole theory of the distribution of stress
in equilibrium in two dimensions may be deduced.

In the most general case of three dimensions, we must use three
such functions, and the method becomes cumbrous. I have, however,
used these functions in forming equations of equilibrium of elastic
solids, in which the stresses are considered as the quantities to be
determined, instead of the displacements, as in the ordinary form.

These equations are especially useful in the cases in which we
wish to determine the stresses in uniform beams. The distribution
of stress in such cases is determined, as in all other cases, by the
elastic yielding of the material ; but if this yielding is small and
the beam uniform, the stress at any point will be the same, what-
ever be the actual value of the elasticity of the substance.

Hence the coefficients of elasticity disappear from the ultimate
values of the stresses.

In this way I have obtained values for the stresses in a beam

56 Proceedings of the Royal Society

supported in a specified way, which differ only by small quantities
from the values obtained by Mr Airy, by a method involving cer-
tain assumptions, which were introduced in order to avoid the con-
sideration of elastic yielding.

2. On the Extension of Brouncker’s Method.

By Edward Sang, Esq.

The operation in use by the ancient geometers for finding the
numerical expression for the ratio of two quantities, was to repeat
each of them until some multiple of the one agreed with a multiple
of the other; the numbers of the repetitions being inversely pro-
portional to the magnitudes.

The modern process, introduced by Lord Brouncker, under the
name of continued fractions, is to seek for that submultiple of the
one which may be contained exactly in the other; the numbers
being then directly proportional to the quantities compared.

On applying this method to the roots of quadratic equations, the
integer parts of the denominators were found to recur in periods ;
and Lagrange showed that, while all irrational roots of quadratics
give recurring chain-fractions, every recurring chain-fraction ex-
presses the root of a quadratic ; and hence it was argued that this
phenomenon of recurrence is exhibited by quadratic equations alone.

The author of this paper had supplemented Lagrange’s proposi-
tion, by showing that when the progression of fractions converging
to one root of a quadratic is continued backwards, the convergence
is toward the other root. The singularity of this exclusive property
of quadratic equations led him to consider whether some analogous
property may not be possessed by equations of higher degrees.
Putting aside the idea of the chain-fraction as being merely acci-
dental to the subject, and attending to the series of converging
fractions, he came upon a kind of recurrence which extends to
equations of all orders ; and which proceeds by operating on two,
three, or more contiguous terms according to the rank of the equa-
tion. In this way a ready means of approximating tp the greatest
and to the least root of any equation was obtained.

The following cases were cited : —

If we begin with the terms ^ , and form a progression by

of Edinburgh, Session 1869-70. 57

adding the respective members of the preceding term to the doubles
of those of the last, thus —

1 1 3 7 17 i1 ^ &

0’ 1’ 2’ 5’ 12’ 29’ 70’ 169’

we form the well-known series converging to the ratio of the
diagonal of a square to the side.

Beginning with the terms 0, 1, if we add together the last two,
thus —

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, &c.,
each term bears to the succeeding one a ratio approaching to that
of the side of a regular pentagon to the diagonal thereof.

If we assume the three terms 0, 0, 1, and continue the progres-
sion by adding to the double of the last term, the difference of the
two preceding ones, thus —

0, 0, 1, 2, 5, 11, 25, 56, 126, 283, 636, 1429, &c.,
the ratio of each term to the following approaches to that of the
side to the greater diagonal of a regular heptagon.

Or again, beginning with the same three terms, if we form a
progression by deducting the antepenult from the triple of the last
term, thus —

0, 0, 1, 3, 9, 26, 75, 216, 622, 1791, 5157, &c.,
we obtain an approximation to the ratio of the side to the longest
diagonal of a regular enneagon .

From these examples it would appear that important results may
be expected from the study of this branch of Logistics. Now, the
roots of quadratics were reached by the comparison of two magni-
tudes, wherefore those of cubics may result from the comparison of
three incommensurables ; and analogously for equations of higher
degrees. The comparison of several magnitudes thus forms the
subject of tbe paper.

Assuming three homogeneous quantities, A, B, C, arranged in
the order of their magnitudes, we take the second B as often as
possible from the greatest A, and obtain a remainder less than B ;
this remainder may or may not be greater than C. If it be greater,
we take C as often as possible from it, and obtain a remainder I)
less than C, the least of the three quantities. B, C, D may now be

58 Proceedings of the Royal Society

treated in the same way, and thus we form a series of equations —

A = 4- 4- D

B = p.2 G 4- q.2J) 4- E
C = p.f> -f 23E 4- F, &c.,
in which p can never he zero, while q may be so.

In order to compute, by help of these quotients, the approximate
ratios of A, B, C, we may put Av A2, A3, &c. ; Bw B2, B3, &c. ; C1}
C2, C3, &c., for the corresponding successive values, and then we
obtain the equations —

An -j- 1 = pn-\-l An 4" qn An _i + An _ 2 ,

B n 4-1 = Pn -f i Fft 4- qn B^ — i 4~ B« — 2 j

Qn -f- 1 ~ pn 4- 1 Qn 4* qn Qn — 1 4~ Qn — 2 >

which indicate a very simple arrangement, best studied from an
example. Thus, if the successive equations were —

A = 2.B 4- 1.0 4- D

B = 3.C 4- 2.D 4- E

C = 2.D 4- O.E 4- F

D = 3.E 4- l.F 4- G

E = 2.F 4- 2.G- 4- H

F = 3.G- 4- O.H 4- I

G = 2.H + 1.1 4- K

H = 3.1 4- 2.K 4- L, &c.

we should write the values of p, q , 1 in horizontal lines as in the
accompanying scheme ; and the successive approximate values of
A, B, 0 in lines below them. Unit being written as the first value
of A under pv which in this case is 2, we multiply this by 2, and

1

1

1

1

1

1

1

1

1

2

1

2

0

1

2

0

1

2

0

P

2

3

2

3

2

3

2

3

2

A

1

2

7

19

59

144

569

1197

4304

11571

B

1

3

8

25

61

241

507

1823

4901

C

1

2

6

15

59

124

446

1199

D

1

3

7

28

59

212

570

E

1

2

8

17

61

164

F

1

3

6

22

59

G

1

2

7

19

II

1

3

8

I

1

2

K

1

59

of Edinburgh, Session 1869-70.

write the product in the column containing p2, q2. We then
multiply the newly found A by the p above it; the preceding A
by its q, that is in this case 3.2 and 1.1, and write the sum 7 as
the third value of A. Again, taking the sum of the products
jp3A3, q,2 A2, and, as we may call it for generality’s sake, r1A1, we
have 2.7 + 2.2 + 1.1 = 19 for A4. In this way we obtain the
successive values of A.

The values of B are found in the same way, observing that
Bx = 0, Ba = 1. So also are the values of C, and if it be wished,
those of D, E, F, &c., obtained, the first effective term being de-
layed a step, as shown in the scheme.

This method was applied to the three irrational quantities, log 5,
log 3, and log 2 ; and the results were used in explaining the doc-
trine of musical temperaments.

When two quantities only are compared, it is well known that
the cross products of the adjoining fractions differ by unit, or that,
taking three contiguous terms, such as —

^-3, ^5, we have the equation,

^3 B4 Bg

A3B4 - A4B3 = - A4B5 + A5B4,

which may be expressed, according to Cayley’s notation of deter-
minants—

| A3 a., I

I A4 Ag 1

1 B, B4 1 -

1 B, Bg |

In the very same way, when three magnitudes are compared,
we have the equation —

A3 A4 Ag

K Ag A,

b3 b4 b3

== 4-

B4“ Bg Bg

03 C4 Cg

C4 Cg Cg

that is to say, this determinant is unit throughout.

The extension of this method to more than three quantities is
easy. In conclusion, an opinion was expressed, that as the Brounc-
kerian process applied to two magnitudes has already thrown great
light on the doctrine of squares, this extension of it may be
expected to do as much for the still higher departments of the
theory of numbers.

60

Proceedings of the Royal Society

3. On the Forces experienced by Solids immersed in a
Moving Liquid. By Sir William Thomson.

Cyclic irrotational motion,* [§ 60 (z) ] once established through an
aperture or apertures, in a movable solid immersed in a liquid,
continues for ever after with circulation or circulations unchanged,
[ § 60 (a)] however the solid he moved, or bent, and whatever influ-
ences experienced from other bodies. The solid, if rigid and left
at rest, must clearly continue at rest relatively to the fluid sur-
rounding it to an infinite distance, provided there be no other solid
within an infinite distance from it. But if there he any other solid or
solids at rest within any finite distance from the first, there will he
mutual forces between them, which, if not balanced by proper
application of force, will cause them to move. The theory of the
equilibrium of rigid bodies in these circumstances might be called
Kinetico- statics ; but it is in reality a branch of physical statics
simply. For we know of no case of true statics in which some if
not all of the forces are not due to motion ; whether as in the case
of the hydrostatics of gases, thanks to Clausius and Maxwell, we
perfectly understand the character of the motion, or, as in the statics
of liquids and elastic solids, we only know that some kind of mole-
cular motion is essentially concerned. The theorems which I now
propose to bring before the Boyal Society regarding the forces ex-
perienced by bodies mutually influencing one another through the
mediation of a moving liquid, though they are but theorems of ab-
stract hydrokinetics, are of some interest in physics as illustrating
the great question of the 18th and 19th centuries : — Is action at a dis-
tance a reality, or is gravitation to be explained, as we now believe
magnetic and electric forces must be, by action of intervening matter?

I. (Proposition.) Consider first a single fixed body with one or
more apertures through it ; as a particular example, a piece of
straight tube open at each end. Let there be irrotational circula-
tion of the fluid through one or more such apertures. It is readily

* The references §§ without farther title are to the author’s paper on
Vortex Motion, recently published in the Transactions (1869), which contains
definitions of all the new terms used in the present article. Proofs of such
of the propositions now enunciated as require proof are to be found in a con-
tinuation of that paper.

61

of Edinburgh, Session 1869-70.

proved [from § 63 Exam. (2.) ]* that the velocity of the fluid at any
point in the neighbourhood agrees in magnitude and direction with
the resultant electro-magnetic force, at the corresponding point, in
the neighbourhood of an electro -magnet replacing the solid, con-
structed according to the following specification. The “ core,” on
which the u wire ” is wound, is to be of any material having infinite
diamagnetic inductive capacity, f and is to be of the same size and
shape as the solid immersed in the fluid. The wire is to form an
infinitely thin layer or layers, with one circuit going round each
aperture. The whole strength of current in each circuit, reckoned
in absolute electro-magnetic measure, is to be equal to the circulation
of the fluid through that aperture divided by The resultant

electro-magnetic force at any point will be numerically equal to
the resultant fluid velocity at the corresponding point in the
hydrokinetic system, multiplied by \Z4?r.

Thus, considering, for example, the particular case of a straight
tube open at each end, let the diameter be infinitely small in com-
parison with the length. The u circulation ” will exceed by but an
infinitely small quantity the product of the velocity within the
tube into the length. In the neighbourhood of each end, at dis-
tances from it great in comparison with the diameter of the tube and
short in comparison with the length, the stream lines will be straight
lines radiating from the end. The velocity, outwards from one end
and inwards towards the other, will therefore be inversely as the
square of the distance from the end. Generally at all considerable
distances from the ends, the distribution of fluid velocity will be the
same as that of the magnetic force in the neighbourhood of an infi-
nitely thin bar longitudinally magnetised uniformly from end to end.

Merely as regards the comparison between fluid velocity and re-
sultant magnetic forces, Euler’s fanciful theory of magnetism is thus
curiously illustrated. This comparison, which has been long known
as part of the correlation between the mathematical theories of elec-

* Or from Helmlioltz’s original integration of the hydrokinetic equations.

t Real diamagnetic substances are, according to Faraday’s very expressive
language, relatively to lines of magnetic force, worse conductors than air.

The ideal substance of infinite diamagnetic inductive capacity is a substance
which completely sheds off lines of magnetic force, or which is perfectly im-
pervious to magnetic force.

VOL. VIT.

62

Proceedings of the Royal Society

tricity, magnetism, conduction of heat, and hydrokinetics, is merely
kinematical, not dynamical. When we pass, as we presently shall,
to a strictly dynamical comparison relatively to the mutual force
between two hard steel magnets, we shall find the same law of
mutual action between two tubes, with liquid flowing through each,
hut with this remarkable difference, that the forces are opposite in
the two cases ; unlike poles attracting and like poles repelling in
the magnetic system, while in the hydrokinetic there is attraction
between like ends and repulsion between unlike ends.

II. (Proposition.) Consider two or more fixed bodies, such as the
one described in Prop. I. The mutual actions of two of these
bodies are equal, but in opposite directions, to those between the
corresponding electro-magnets. The particular instance referred to
above shows us the remarkable result, that through fluid pressure
we can have a system of mutual action, in which like attracts like
with force varying inversely as the square of the distance. Thus,
if the exit ends of tubes, open at each end with fluid flowing through
them, be placed in the neighbourhood of one another, and the enter-
ing ends be at infinite distances, the mutual forces resulting will be
simply attractions according to this law. The lengths of the tubes on
this supposition are infinitely great, and therefore, as is easily proved
from the conservation of energy, the quantities flowing out per unit
of time are but infinitesimally affected by the mutual influence.

III. Proposition II. holds, even if one of the bodies considered
be merely a solid, with or without apertures ; if with apertures,
having no circulation through them. In such a case as this the
corresponding magnetic system consists of a magnet or electro-
magnet, and a merely diamagnetic body, not itself a magnet, but
disturbing the distribution of magnetic force around it by its dia-
magnetic influence. Thus, for example, a spherical solid at rest
in the field of motion surrounding a fixed body, through apertures
in which there is cyclic irrotational motion, will experience from
fluid pressure a resultant force through its centre equal and op-
posite to that experienced by a sphere of infinite diamagnetic capa-
city, similarly situated in the neighbourhood of the corresponding
electro-magnet. Therefore, according to Faraday’s law for the lat-
ter, and the comparison asserted in Prop. I., it would experience a
force from places of less towards places of greater fluid velocity,

63

of Edinburgh, Session 1869-70.

irrespectively of the direction of the stream lines in its neighbour-
hood ; a result easily deduced from the elementary formula for fluid
pressure in hydrokinetics.

I have long ago shown that an elongated diamagnetic body in a
uniform magnetic field tends, as tends an elongated ferromagnetic
body, to place its length along the lines of force. Hence a long
solid, pivoted on a fixed axis through its middle in a uniform stream
of liquid, tends to place its length perpendicularly across the direc-
tion of motion ; a known result (Thomson & Tait’s “ Natural Philo-
sophy,” § 335). Again, two globes held in a uniform stream with
the lines joining their centres, require force to prevent them from
mutually approaching one another. In the magnetic analogue, two
spheres of diamagnetic or ferromagnetic inductive capacity repel
one another when held in a line at right angles to the lines of
force. A hydrokin etic result similar to this for the case of two
equal globes, is to be found in Thomson and Tait’s “ Natural Philo-
sophy,” § 332.

IY. (Proposition.) If the second body considered in § III., that is
to say, a body either having no apertures, or, if perforated, having
no circulation through the apertures, he acted on by one system of
forces applied so as always to balance the resultant of the fluid
pressure, calculated for it according to II. and III. for whatever
position it may come to at any time, and if it be influenced, besides,
by any other system of applied forces, superimposed on the former,
it will move just as it would move, under the influence of the latter
system of forces alone, were the fluid at rest, except in so far as
compelled to move by the body’s own motion through it. A parti-
cular case of this proposition was first published many years ago, by
Professor James Thomson, on account of which he gave the name
of “ vortex of free mobility ” to the cyclic irrotational motion sym-
metrical round a straight axis.

4. On the Equilibrium of Vapour at a Curved Surface of
Liquid. By Sir William Thomson.

In a closed vessel containing only a liquid and its vapour, all at
one temperature, the liquid rests, with its free surface raised or
depressed in capillary tubes and in the neighbourhood of the solid
boundary, in permanent equilibrium according to the same law of

64 Proceedings of the Royal Society

relation between curvature and pressure as in vessels open to the
air. The permanence of this equilibrium implies physical equi-
librium between the liquid and the vapour in contact with it at all
parts of its surface. But the pressure of the vapour at different
levels differs according to hydrostatic law. Hence the pressure of
saturated vapour in contact with a liquid differs according to the
curvature of the bounding surface, being less when the liquid is
concave, and greater when it is convex. And detached portions of
the liquid in separate vessels all enclosed in one containing vessel,
cannot remain permanently with their free surfaces in any other
relative positions than those they would occupy if there were hydro-
static communication of pressure between the portions of liquid
in the several vessels. There must be evaporation from those
surfaces which are too high, and condensation into the liquid at
those surfaces which are too low — a process which goes on until
hydrostatic equilibrium, as if with free communication of pressure
from vessel to vessel, is attained. Thus, for example, if there are
two large open vessels of water, one considerably above the other
in level, and if the temperature of the surrounding matter is kept
rigorously constant, the liquid in the higher vessel will gradually
evaporate until it is all gone and condensed into the lower vessel.
Or if, as illustrated by the annexed diagram, a capillary tube, with
a small quantity of liquid occupying it from its bottom up to a
certain level, be placed in the neighbourhood of a quantity of the
same liquid with a wide free surface, vapour will gradually become
condensed into the liquid in the capillary tube until the level of
the liquid in it is the same as it would be were the lower end of
the tube in hydrostatic communication with the large mass of
liquid. Whether air be present above the free surface of the
liquid in the several vessels or not, the condition of ultimate
equilibrium is the same; but the processes of evaporation and
condensation through which equilibrium is approached will be
very much retarded by the presence of air. The experiments of
G-raham, and the kinetic theory of Clausius and Maxwell, scarcely
yet afford us sufficient data for estimating the rapidity with which
the vapour proceeding from one of the liquids will diffuse itself
through the air and reach the surface of another liquid at a lower
level. With air at anything approaching to ordinary atmospheric

65

of Edinburgh, Session 1869-70.

density to resist the process, it is probable it would be too slow to
show any results unless in very long continued experiments. But
if the air be removed as perfectly as can be done by well-known
practical methods, it is probable that the process will be very
rapid: it would, indeed, be instantaneous, were it not for the cold
of evaporation in one vessel and the beat of condensation in the
other. Practically, then, the rapidity of the process towards
hydrostatic equilibrium through vapour between detached liquids,
depends on the rate of the conduction of beat between the several
surfaces through intervening solids and liquids. Without having-

made either the experiment, or any calculations on the rate of con-
duction of beat in the circumstances, I feel convinced that in a
very short time water would visibly rise in the capillary tube indi-
cated in the diagram, and that, provided care is taken to maintain
equality of temperature all over the surface of the hermetically
sealed vessel, the liquid in the capillary tube would soon take very
nearly the same level as it would have were its lower end open ;
sinking to this level if the capillary tube were in the beginning filled
too full, or rising to it if (as indicated in the diagram) there is not
enough of liquid in it at first to fulfil the condition of equilibrium.

66

Proceedings of the Boyal Society

The following formula show precisely the relations between
curvatures, differences of level, and differences of pressure, with
which we are concerned.

Let p be the density of the liquid, and <r that of the vapour; and
let T be the cohesive tension of the free surface, per unit of breadth,
in terms of weight of unit mass, as unit of force. Let h denote
the height of any point, P, of the free surface above a certain plane
of reference, which I shall call for brevity the plane level of the
free surface. This will be sensibly the actual level of the free
surface in regions, if there are any, with no part of the edge (or
bounding line of the free surface where liquid ends and solid
begins) at a less distance than several centimetres. Lastly, let
r and r' be the principal radii of curvature of the surface at P.
By Laplace’s well-known law, we have, as the equation of equi-
Hhrium,

(p-a)7t = T(-+±) . . . (1).

Now, in the space occupied by vapour, the pressure is less at the
higher than at the lower of two points whose difference of levels is h ,
by a difference equal to crh. And there is permanent equilibrium
between vapour and liquid at all points of the free surface. Hence
the pressure of vapour in equilibrium is less at a concave than at a
plane surface of liquid, and less at a plane surface than at a con-

T<x

vex surface, by differences amounting to - per unit difference

of curvature. That is to say, if « denote the pressure of vapour in
equilibrium at a plane surface of liquid, and p the pressure of
vapour of the same liquid at the same temperature presenting a
curved surface to the vapour, we have

p — z?

p-(T\r r J

(2),

- and being the curvatures in the principal sections of the sur-
face bounding liquid and vapour, reckoned positive when concave
towards the vapour.

In strictness, the value of o- to be used in these equations, (1)
and (2), ought to be the mean density of a vertical column of
vapour, extending through the height h from the plane of reference.

67

of Edinburgh, Session 1869-70.

But in all cases to which we can practically apply the formulas,
according to present knowledge of the properties of matter, the
difference of densities in this column is very small, and may be
neglected. Hence, if H denote the height of an imaginary homo-
geneous fluid above the plane of reference, which, if of the same
density as the vapour at that plane, would produce by its weight
the actual pressure w, we have

■zat

°* = H '

Hence by (1) and (2)

p“*(1“h) ■ • • (3)-

For vapour of water at ordinary atmospheric temperatures, H is
about 1,300,000 centimetres. Hence, in a capillary tube which
would keep water up to a height of 13 metres above the plane
level, the curved surface of the water is in equilibrium with the
vapour in contact with it, when the pressure of the vapour is less
by about j-oVoth of its own amount than the pressure of vapour in
equilibrium at a plane surface of water at the same temperature.

For water the value of T at ordinary temperatures is about -08 of
a gramme weight per centimetre; and p, being the mean of a
cubic centimetre, in grammes, is unity. The value of a for vapour
of water, at any atmospheric temperature, is so small that we may
neglect it altogether in equation (1). In a capillary tube thoroughly
wet with water, the free surface is sensibly hemispherical, and
therefore r and r' are each equal to the radius of the inner surface
of the liquid film lining the tube above the free liquid surface; we
have, therefore,

h = -08 x - .

r

Hence, if h - 1300 centimetres, r = -00012 centimetres. There can
be no doubt but that Laplace’s theory is applicable without serious
modification even to a case in which the curvature is so great (or
radius of curvature so small) as this. But in the present state of
our knowledge we are not entitled to push it much further. The
molecular forces assumed in Laplace’s theory to be “ insensible at
sensible distances,” are certainly but little, if at all, sensible at
distances equal to or exceeding the wave lengths of ordinary light.
This is directly proved by the most cursory observation of soap

68 Proceedings of the Royal Society

bubbles. But the appearances presented by the black spot which
abruptly ends the series of colours at places where the bubble
is thinnest before it breaks, make it quite certain that the action
of those forces becomes sensible at distances not much less than a
half wave length, or 3-5-0 -gr of a centimetre. There is, indeed,
much and multifarious evidence that in ordinary solids and liquids,
not merely the distances of sensible inter-molecular action, but the
linear dimensions of the molecules themselves, and the average
distance from centre to nearest centre,* are but very moderately
small in comparison with the wave lengths of light. Some
approach to a definite estimate of the dimensions of molecules
is deducible from Clausius’ theory of the average spaces travelled
without collision by molecules of gases, and Maxwell’s theory
and experiments regarding the viscosity of gases. Having
perfect confidence in the substantial reality of the views which
these grand investigations have opened to us, I find it scarcely
possible to admit that there can be as many as 1027 molecules in
a cubic centimetre of liquid carbonic acid or of water. This makes
the average distance from centre to nearest centre in the liquids
exceed a thousand-millionth of a centimetre !

We cannot, then, admit that the formulae which I have given
above are applicable to express the law of equilibrium between the
moisture retained by vegetable substances, such as cotton cloth or
oatmeal, or wheat-flour biscuits, at temperatures far above the
dew point of the surrounding atmosphere. But although the
energy of the attraction of some of these substances for vapour
of water (when, for example, oatmeal, previously dried at a high
temperature, has been used, as in the original experiment of Sir J.
Leslie, to produce the freezing of water under the receiver of an air-
pump), is so great that it might almost claim recognition from
chemists as due to a “ chemical affinity,” and resulting in a “ chemi-
cal combination,” I believe that the absorption of vapour into
fibrous and cellular organic structures is a property of matter
continuous with the absorption of vapour into a capillary tube
demonstrated above.

* By “ average distance from centre to nearest centre,” I mean the side of
the cube in a cubic arrangement of a number of points equal to the number
of real molecules in any space.

of Edinburgh, Session 1869-70.

69

5. On a Bow seen on the Surface of Ice. By J. Clerk
Maxwell, Esq., E.E.SS. L. & E.

On the 26th of January, about noon, I observed the appearance
of a coloured bow on the frozen surface of the ditch which sur-
rounds S. John’s College, Cambridge. Its appearance and position
seemed to correspond with those of an ordinary primary rainbow.
I at once made a rough measurement of the angle on the board of
a book which I had with me, and then borrowed from Dr Parkin-
son, President of S. John’s College, a sextant, with which I found
that the angle between the bright red and the shadow of the large
mirror was 41° 50', and that for bright blue 40° 30'. The angle
for the extreme red of the primary bow, as given in Parkinson’s
Optics, is 42° 20', and that for violet 40° 327 The bows formed by
ice crystals are seen on the same side as the sun, and not on the
opposite side. I suppose the bow which I saw to be formed by
small drops of water lying on the ice. If the lower part of
each drop were flattened, so as to bring the point at which the
reflexion takes place nearer to the points of incidence and emer-
gence, the effect would be of the same kind as that of a diminution
of the index of refraction — that is, the angle of the bow would be
increased. How a drop of water can lie upon ice without wetting
it, and losing its shape altogether, I do not profess to explain.

Only a small part of the ice presented this appearance. It was
best seen when the incident and emergent rays were nearly equally
inclined to the horizontal. The ice was very thin, and I was not
able to get near enough to the place where the bow appeared to
see if the supposed water drops really existed.

The following Gentlemen were admitted Fellows of the
Society : —

W. E. Heathfield, Esq., F.R.G.S., F.C.S.

Edward James Shearman, M.D., F.K.C.S.L.

Patrick D. Swan, Esq.

Dr H. Alleyne Nicholson.

A ballot also took place for the Rev. Dr Hodson, who resigned
the Fellowship of the Society in 1867. Dr Hodson was re-
admitted.

VOL. VII.

70

Proceedings of the Royal Society

Monday , 21 st February 1870.

Professor KELL AND, Vice-President, in the Chair.

The following Communications were read : —

1. Note on the Atomic Volume of Solid Substances. By
James Dewar, Lecturer on Chemistry, Veterinary Col-
lege, Edinburgh.

The investigation of the volume retained by different elementary
substances, when combined in the solid condition, has attracted
the attention of many chemists. We have only to look at the
laborious memoirs of Schroter, Kopp, Playfair and Joule, Boullay,
Pilhol, and others, to be convinced of the great amount of labour
expended on the subject. Nor is it at all remarkable that so many
workers should take to this field of research, when we remember
the simplicity of the laws regulating the combining volumes of
gaseous substances, and the probable extension of some such similar
law to the solid condition of matter. Emboldened by analogy, tfie
forementioned workers endeavoured to find some constant to which
volumes of elements and compounds held the relation of some
simple multiple, and thus extend the apparent simplicity of Prout’s
law of combining weights to combining volumes. The great object
in view wras evidently to extend the speculations and laws of Dalton
and G-ay Lussac to the volumes of solid substances, and thus to
arrive at some general explanation of the results. However credit-
able the desire to reveal simplicity from out of the apparent chaos,
no one, in examining the subject, can help arriving at the conclusion
that the means employed to extract the seeming harmony from the
results were purely arbitrary. It does not follow, however, that
the results were fruitless, although no great generalisation was
discovered. The solid state of matter is relatively far more com-
plicated than either the liquid or gaseous conditions. The uni-
formity of expansion of gaseous matter, and the easy comparison
of liquid substances under similar conditions, enable us to arrive
at some satisfactory conclusions regarding the volume in these
states : but, in examining solid matter, we have no guarantee

71

of Edinburgh , Session 1869-70.

that the substances are under similar physical conditions. We
cannot, therefore, expect the same uniformity in the results ; hut
although, strictly speaking, we may entertain grave doubt on the
real value of the results, yet, in some cases, we cannot help recog-
nising some curious analogies, especially on comparing similar
classes of compounds. It is not the object of this note either to
criticise or discuss the labours and speculations of others, no
originality being claimed in the subject matter itself, all that is
original being merely the addition of a few new analogies.

The first important discovery in the subject of atomic volumes
was made by Schroter. He observed that the equivalent volume
of oxygen, obtained by subtracting the volume of metal in the free
istate from the volume of the oxide, gave, approximately, the same
value of 5-2 in the oxides of copper, zinc, cadmium, lead, mercury,
iron, cobalt, and titanium. In other words, the oxygen occupied the
same volume in each combination. Other classes of oxides gave a
volume of twice, or half the above number. In order to arrive at
the volume of the oxygen, Schroter started with the premises that
the metal in the combined state occupied the same volume as the
uncombined metal. Granting, for the present, that oxygen has
a definite volume in combination in the oxides, it is clear that the
volume obtained by difference will vary with the volume of the
combined metal. The same method applied to the oxides of the
less dense metals would give a negative volume to the oxygen ;
and in these cases we must admit condensation to have taken
place in the metal itself. We may have three cases, therefore,
according as the volume of the combined metal differs from
that of the uncombined. If it remains the same in combina-
tion, we obtain the real volume; if it condenses, the volume
is a minimum ; if it expands, a maximum. Seeing that the
oxygen in the dense metals has the volume 5-2, we may regard
the greater and smaller volume obtained from some oxides as the
result of condensation or expansion of the metal. Supposing the
above volume (5*2) to exist generally in the oxides, we would
have a condensation in the less dense metals in combination,
approaching very nearly, in the case of potassium, sodium, and
aluminium, to one-third, and in calcium, magnesium, and strontium
to nearly one-half, of the volume in the free state. Thus far,

72

Proceedings of the Royal Society

then, this number would give a rough explanation in admitting
condensation in many of the metals.

I have thought that it would be interesting to compare this
volume with the volume of oxygen when it is combined with solid
substances other than metallic, and to take a series of analogous
combinations. For this purpose the chlorine family is well fitted
in their respective combinations with potassium, and these with
oxygen. The following table contains the best known density
determinations and volumes of chloride, bromide, and iodide of
potassium, compared with the densities of chlorate, bromate, and
iodate.

The total volume of the oxygen in chlorate of potash, on the sup-
position the chloride of potassium retains its original volume in
combination, is 15 ; whereas it is only 7 in bromate of potash, if
we allow that the bromide of potassium retains its original volume ;
and it appears to occupy no volume in iodate of potash, assuming
that iodide of potassium maintains its original volume. The
apparent disappearance of the volume of the oxygen, in changing
iodide of potassium into iodate, is analogous to the apparent loss
of volume of many salts in their water of hydration, the salt occu-
pying the volume of the crystal water taken as ice, as pointed out
many years ago by Playfair and Joule. It is clear that, in assum-
ing the halogen compounds of potassium as retaining their primi-
tive volume in their oxidised derivatives, we place these compound
substances in the same position as the metals in the simple oxides.
Now, we saw that in many oxides the volume of the oxygen
varied, and that, in all probability, from metallic condensation
taking place during the act of combination. The metals having
the lowest density and the greatest atomic volume condense the
most in combining. Generally speaking, if we examine the

of Edinburgh , Session 1869-70. 73

volumes of the halogen salts in the above table, it is clear that
the equivalent volumes increase, chloride of potassium being 37,
bromide 44, and iodide 55' 3, and their relative stability diminishes.
The equivalent volumes of chlorine, bromine, and iodine are iden-
tical in the liquid state ; and thus the formation of the respective
potassium compounds is one of the results of unequal condensa-
tion, the co-efficient of contraction in the formation of chloride of
potassium being 046, bromide 0*29, iodide 0*23 per unit volume.
Their formation is attended with the evolution of very different
amounts of heat. The following table contains some of the con-
stants found with reference to combination and solution : —

Constants of Group.

Contrac-
tion per
Unit
Volume.

Total heat.

Heat of
solution.

Diffusion

times

(relative).

Co-efficient of
expansion per
equivalent
volume.

Specific heat
per atom.

KC1

046

97086

3874

74-5

0-001429

12-88

KBr

0-29

85666

4522

119

0-001848

13*47

KI

0-23

72721

4847

166

0*002358

13-60

Generally speaking, the number found for bromide of potassium
is nearly the mean of those attached to chloride and iodide. A
similar observation has recently been made by M. Yalsen in exa-
mining the equivalent capillary constants of these bodies. Look-
ing at the atomic thermal number, there is a far greater likelihood
of condensation taking place in the bromide and iodide of potassium
in the combined state, than in case of chloride, seeing that it
would be relatively far more difficult to condense. But neither the
chlorate, bromate, nor iodate can be produced through the direct
addition of oxygen to the respective halogen salt. And the
chlorate, it is well known, evolves heat on giving off its oxygen,
and thus necessitates an absorption of heat during combination.
It is just possible that the heat produced during the decomposition
is the result of the necessary expansion of volume in the chloride
of potassium in combining with oxygen, and its return to its
normal volume on losing it. It makes no change in volume to
suppose that, in the one case, the oxygen is added as a whole to
the chloride of potassium, or, in the other, that it is between the

74

Proceedings of the Royal Society

potassium and chlorine, each occupying its individual volume
unchanged, hut it would alter greatly the heat evolved in so doing.
If oxygen combined with chloride of potassium as a whole, with-
out any condensation taking place, the natural result would be an
evolution of heat. But if the addition of the oxygen diminishes
the co-efficient of contraction, as compared with that of the free
compound, then we have a physical explanation of the evolution
of heat on decomposition. In this case the actual work performed
by the condensation of oxygen is retained in a potential form, and,
therefore, reappears as heat on its decomposition. If, now, we
examine the mode in which the oxygen is attached to the respec-
tive halogen compounds, we can trace, as a necessary consequence,
the retention of varying amounts of energy. Chlorate, bromate,
and iodate of potash are formed by a similar chemical reaction,
according to the following formula of exchange, given in equiva-
lents, the whole reaction supposed to take place in the presence of
water : —

We have appended the thermal equivalents attending the for-
mation of these bodies in a large volume of water. It will be
obvious on comparing the formation of chlorate of potash, through
the above reaction, that it may be the result of absorption of heat ;
whereas it is certain that the formation of iodate of potash must
be attended with an evolution of heat, or else cold must be the
result of their action. In special experiments, made with the
object of determining the thermal action, neither absorption nor
evolution of heat could he detected. Thus the formation of iodate
of potash is attended with an evolution of heat. This would, then,
accord with the easy transformation of the chlorates into iodates, or
of chloric acid into iodic acid, and the easy transformation of the
iodide of potassium into the iodate, through the action of perman-
ganate of potash, seeing that we must have an evolution of heat.

6KO + 6 Cl

6(76238)

6KO + 6Br
6(76238)

6KO + 61

6(76238)

5KC1 + KC106

5(97086)

5KBr + KBr06
5(85666)

5KI + KI06
5(72721)

75

of Edinburgh, Session 1869-70.

The oxygen, therefore, may he assumed to he in a very different
condition relatively to the other elements, or else we must suppose
that it has not affected the co-efficient of contraction, certainly not
to have diminished it. The author throws out this simply as a
possible explanation ; he is also well aware that many other ex-
planations might be given, all, possibly, equally satisfactory. "But
a physical explanation, however far it may lie from the truth,
seems to convey to us the clearest ideas of what may possibly take
place.

There is one point connected with the subject of volumes that
requires very careful attention. All bodies in combining do not
unite with condensation ; that is, the volume of the compound
might exceed the volumes of the isolated constituents, and yet a
large evolution of heat might take place during its formation. A
well-known example is that of iodide of silver. Now, M. Fizeau
has shown that iodide of silver contracts regularly with increase of
temperature, and M. St Claire Deville has given an explanation of
this anomaly. Deville believes that bodies combine at such a
temperature as would be required to transform the volume of the
compound to that of the sum of the volumes of its constituents in
the free state. Applying this to iodide of silver, it is clear that
contraction must take place, and in all similar cases where we have
an increase of volume. One cannot help associating this increase
of volume to a purely physical change of state, such as the change
of water with expansion into ice. Now, as Sir William Thomson
has proven that pressure lowers the freezing point of water, and
Mousson has actually liquefied ice by enormous pressure, if the
formation of a chemical compound is analogous to a physical
change of state, we ought to be able by mere pressure to decom-
pose a chemical compound, if the formation of that compound is
attended with an increase of volume. No doubt, in order to get
experimental proof of this fact, we must use a relatively weak
chemical compound, one attended with the evolution of no great
amount of heat; and the well-known experiments of Joule on the
effect of pressure on amalgams, seems to confirm my anticipation.
Joule has shown that the amalgams of zinc, lead, and tin are de-
composed by pressure alone, and these are the amalgams produced
with the least contraction of any. In order to get definite proof of

7(5 Proceedings of the Royal Society

the expansion, it is, of course, necessary to use the specific gravity
of mercury in the solid state. Now, Joule states, as the mean of
his experiments, that mercury in the solid form has the specific
gravity 15-19, whereas in the above amalgams it would have the
density of only 14*1. The observations of Matthiessen on the
specific gravity of alloys enables us to confirm Joule’s results : —

Lead Series (A. Matthiessen).

Sp. Or.

Calculated
Sp. Gr.

V + V'

V

Pb2Hg, . . .

11-979

12-008

1-0024

PbHg, . . .

12-484

12-358

0-9899

PbHg,, . . .

12-815

12-734

0-9937

The specific gravity of the mercury used in calculating the mean
density was 13-573. Now, seeing that there is little or no con-
traction, and even in one case a slight expansion, in taking the
above specific gravity of mercury, the higher density of mercury
given by Joule as the result of his experiments would necessarily
lead to an expansion in their formation. To illustrate the effect
of pressure on the composition of an amalgam, let us take Joule’s
experiments on the tin amalgam. The composition of this
amalgam was 100 of mercury to 51-01 of tin, and the specific
gravity 10-518. The effect of 5400 lbs. pressure for thirty days,
changed the amalgam, so that it had ultimately the composition
100 of mercury to 384 of tin. It is natural to believe, therefore,
that the effect of pressure in this case is quite analogous to the
inverse change of state, when a body that has expanded in chang-
ing its state has been subjected to its influence.

In the early part of this paper we saw that the volume of oxygen
in some oxides, instead of being 52, was sometimes double this
amount, or even more. It has also been remarked, that if the
metal in combining was to expand, the volume of the oxygen
would appear as a maximum. This apparently large volume of
the oxygen seems to belong to suh-oxides, such as sub-oxides of
mercury and copper, and oxide of silver. If we suppose, now, that
this large increase of volume in the oxygen is the result of an
expansion in the metal in combining with the normal oxide, it is

77

of Edinburgh, Session 1869-70.

possible that mere pressure would decompose these oxides, at least
in part, into metal and the higher oxide. The instability of a
body of this type, such as sub-oxide of mercury, is well known,
mere titration effecting the liberation of metal with formation of
the higher oxide. In this way, therefore, it seems to support the
argument adduced.

2. Note on Inverted Sugar. By James Dewar, Lecturer on
Chemistry, Veterinary College, Edinburgh.

For some time past an animated discussion has been going on in
the columns of the “ Comptes Bendus de l’Academie des Sciences”
between MM. Dubranfaut and Maumene regarding the nature of in-
verted sugar. M. Dubranfaut, many years ago, made many valuable
additions to our knowledge concerning the composition and reac-
tions of various sugars, especially in explaining the result of the
action of dilute acids on cane sugar. He explained the levo-rotatory
action of inverted sugar, and its rapidly varying power with the
temperature, as the result of a molecule of water in reacting with
a molecule of cane sugar, generating one molecule of glucose and
one of laevulose. Dubranfaut believed that inverted sugar consisted
of a mixture of glucose and laevulose in equal weights; and although
he did not make a direct analysis of the product, yet he was justly
entitled to assume that it was so constituted, seeing that, generally,
it agreed with a mean of the properties of inulin sugar and dex-
trose.

In order to support the above view, he separated levo-glucose
from the inverted sugar, through the insolubility of the lime com-
pound, and compared its properties with pure lsevulose. The de-
composition would, according to Dubranfaut, be as follows : —

Wa + H.,0 = C6Hl30„ + C.IT.A
+ 73-8 +56 -106

(-25)

So thoroughly had his facts and explanations been accepted by
chemists generally, that, up till a recent date, no one discovered
any flaw in his researches, and therefore no doubt was thrown on
the validity of this theory. Recehtly, Maumene has reinvestigated

VOL. VIT.

78

Proceedings of the Royal Society

the composition of inverted sugar by analysis. He has attempted
to separate the two sugars through the action of chloride of sodium.
The dextro-glucose forms a well-defined crystalline compound with
chloride of sodium, whereas the lasvulose does not form any com-
pound. The results obtained by this method differ greatly from
theory. Instead of finding 50 per cent, of leevulose, he found 88 per
cent. In repeating the experiments of Dobranfaut on the separation
of levo-glucose by hydrate of lime, he has not met with any better-
results ; in fact, his results are quite opposed to those of Dubranfaut.

Apart altogether from expressing an opinion on the merits of
the views entertained by the different parties to this discussion,
the author has thought some observations of the same subject
might not be unworthy of notice at the present time.

Linneman, many years ago, applied the process of hydrogenation
to the sugars that he had found so successful in treating the simple
organic substances. In the way named he obtained marmite from
inverted sugar, the following reaction taking place : —

W, + h2 = c6h14o8.

Mannite had long been known to be the product of certain kinds
of fermentation, and occurring as a secondary product in the vinous
fermentation; but it was this elegant synthesis of Linneman that
first clearly showed the connection. But although inverted sugar
can be changed into mannite, the next point that demands a solu-
tion is the proving the inverted sugar to be composed of equal
quantities of dextrose and lmvulose. Are they both transformed by
hydrogenation into mannite? or is only one of them, and which?
Linneman seems to have directed his attention to the solution
of this question. He states that it is only the Levulose that is
so affected. The reasons why he entertains the above views are
not given. In all likelihood he thought that, just as Berthelot
had changed mannite by a peculiar fermentation into levo-glucose,
so would the levo-glucose in inverted sugar be hydrogenised into
mannite.

In repeating the action of sodium amalgam on inverted sugar, I
have not seen any reason why the one sugar any more than the other
should be supposed to generate the mannite. The following is a
description of the mode by which- the sugar was inverted and hydro-

of Edinburgh, Session 1869-70.

79

genised : — Twenty grammes of cane sugar were dissolved in 150
grms. of water, and inverted through the action of 2 grms. of
sulphuric acid, keeping the solution at the temperature of 70° C.,
afterwards adding pure carbonate of barium, filtering, and then
adding one gramme of sodium in the form of a weak amalgam.
The action took place without any evolution of hydrogen. If
the amalgam was impure, from the presence of other metals, it
evolved hydrogen at once, and the solution became brown ; other-
wise it remained perfectly clear. After one month the solution
gave no trace of sugar with the alkaline copper solution. It was
then carefully neutralised with dilute sulphuric acid, evaporated
on the water bath, the greater part of the sulphate of sodium
separated by crystallisation, and the residue treated with boiling
70 per cent, alcohol, the solution filtered, and allowed to crys-
tallise. Sometimes the mannite did not crystallise until all the
alcohol had evaporated, leaving a syrup that slowly assumed the
crystalline form. The product had no rotatory power. In no
case was the sugar entirely changed into mannite — a gummy sub-
stance was invariably left, that would not crystallise after expo-
sure to the air for months. Mannitan, or some similar body,
may be one of the products.

Dextro-glucose made from honey gave mannite when treated
in the same way, having exactly the same melting point as ordi-
nary mannite. In treating milk sugar with dilute sulphuric acid,
changing into gallactose and hydrogen ising, dulcite was not iso-
lated ; but I have not specially studied the reaction.

3. On the Flow of Electricity in Conducting Surfaces. By
W. R. Smith, M.A., Assistant to the Professor of Natural
Philosophy in the University of Edinburgh. Communi-
cated by Professor Tait. (With a Plate.)

The conditions of a steady flow of electricity in a conducting sur-
face are completely determined, if we know either the nature of
the electrical distribution throughout the surface, or the direction
and intensity of the flow at every point. On the first of these ways
of considering the question, the problem is solved if we can express
the potential v at any point as a function of the co-ordinates, and

80

Proceedings of the Royal Society

the nature of the distribution will be indicated to the eye by form-
ing the equipotential curves

v ~ const (1).

From the second point of view, we should endeavour to deter-
mine the lines of flow by equations of the form

u — const (2).

The curves determined by equations (1) and (2) are obviously
orthogonal, and since

d2v d2v _ q
dx1 dy 2 5

we know, by a theorem of Lame and Stokes,* that

d2u d2u _ q
dx1 dy 2

Kirchhoff, in the year 1845, took up the problem for plane surfaces!
in the first of the two ways we have indicated. By an application
of Ohm’s law, he expressed analytically the conditions to be satis-
fied by v. When the electricity enters and issues by a number of
individual points, he found (apparently by trial) that an integral
of the form 5(a log r), where rx r2, &c., are the distances of the
point ( x , y) from the successive points of entrance and issue, satis-
fies these conditions when the plate is infinite. For a finite plate,
it is necessary that the boundary of the plate should he orthogonal
to the curves

2(a log r) = const. . . . (3).

He was thus led to form the orthogonal curves, whose equation

he gives in the form

2(a [r,B]) = const. . . . (4),

where [r, R] is the angle between r and a fixed line B. These

equations he applies to the case of a circular plate, completely
determining the curves when there is one exit and one entrance
point in the circumference, and showing that in any case a proper
number of subsidiary points would make the equipotential lines
determined by (3), cut the circumference at right augles. Kirch-

* Seo Thomson and Tait’s Natural Philosophy, i. 542.
t PoggendorfFs Annalen, Bd. lxiv.

A

Z/ines of flow when/ fhes sources forms ou rectangular parallelograms^ whose/ diagonals mnJces
am angles of -jr Thes unbroken/ times ares times of flow when sources of the; sanoc signs
ares Ifogonallp opposites . Ones times smlcs to as circles another to as rectangular hpper=

loins, four rest arc timrus castes . Whens at sources and smlcs are t Iransposeati the circlet

is stills parts of at streams' whoses other Iramchy is as straight tin es^ huts the le/oruseatcs
pass over in to that dotted curves.

Proceedings Roj Soc. sEeLitP Yol VII.

B

Ca^eS of tern sources and two sinks giving threes egwnls streams circles with/ two
points oh 7/ij'o flow. When/ oo source/ ansi svnJc/ ares' transposed/ they lower circlet
is stills a/ hnes of llow. The/ other lines assume/ thee dotted' tunny.

81

of Edinburgh , Session 1869-70.

hoffs paper is throughout properly busied with the function v, and
the stream lines are only dealt with incidentally. There is no
attempt to give a physical meaning to the equation (4).

In 1846, Thomson drew attention to the orthogonal systems (3)
and (4), as an example of Lame’s theorem.* He showed that the
rings and brushes of biaxal crystals are a special case of these curves.
They correspond, in fact, as we shall see, to the equipotential lines
and lines of flow in an infinite plate with two equal sources of
electricity.

Maxwell, in 1856, suggested the application to problems of
electric currents of his beautiful theory of the motion of an imma-
terial incompressible fluid in a resisting medium, but does not appear
to have developed the suggestion.!

The object of this paper is to show that, by regarding, in accor-
dance with Maxwell’s suggestion, every point of exit or issue as a
source or sink, spreading or absorbing electricity, independently of
all other sources, Kirchhoff’s general equations may be deduced by
easy geometrical processes, and extended to certain cases of flow
in curved surfaces. We shall, by this method, be naturally led to
look mainly at the function u , which in the analytical investigation
is subordinated to v. The equation u = 0 will receive an obvious
physical interpretation, and we shall then proceed to consider in
detail the nature of the flow in certain special cases apparently not
yet examined.

If a source P, in an infinite uniformly resisting plate, steadily
give forth a quantity of electricity E per unit of time, the flow per
second over the whole circumference of all circles with P as centre is
equal. Hence the rate of flow at each point of the circumference of

E

such a circle is inversely as the radius = - — . The potential due

to P satisfies the equation

dv

dr

A

2ttt ’

or,

v = 0 — - — log r .

2i7T

* Camb. and Dub. Math. Journ. vol. i. p. 124.
t Cambridge Phil. Trans, vol x.

82

Proceedings of the Royal Society

The potential due to any number of sources P1} P2, and sinks
P/ P2', &c., all of equal power, is got by simple superposition. If
E be equal for all points,

u = C - 2 A log r 4- 2 A log r' ,

where r corresponds to a source, and r' to a sink. Hence the equi-
potential lines are

= G . . . . (5).

ri r.2 r3 ...

The equation of the lines of flow follows at once from the equa-
tion of continuity. Across any element ds of a stream line sub-
tending angles d61 d0.2 , &c., at the sources, and d02 d0.2 , &c. at
sinks, no fluid must flow. But the quantity of fluid per second

reaching ds from P » is E. The quantity withdrawn by P'n

2i7T

dO'

is -—A E. Hence the differential equation of the stream-line is

2 dd - 2 dO’ = 0 .

Integrating, 2# - 20' = const.

where 6 and O' are the angles between radii vectores and any fixed
lines. If we agree to reckon 0 in opposite directions for sources
and sinks, the equation becomes

2# = a . . . . (6).

The following are elementary consequences of this equation : —
(a.) When we have one source P and one equal sink P', the
stream line through any point Q has for its equation

20 = QPP' + QP'P = X - PQP' - a.

Hence the locus of Q is a circle through P and P', which is Kirch-
hoff’s case. The orthogonals are circles whose centres (R) lie in
PP' produced, and whose radii = VPR.PTt.

( b .) If we have two equal sources and no sinks, or what is the

of Edinburgh, Session 1869-70. 83

same thing, sinks at an infinite distance, the stream lines are
rectangular hyperbolas. For in this case,

P Pr N x

QPN + QP'N = a = QNx, if we make P'QN = QPN. Also QN
touches the circle through PP'Q, therefore
QN2 = NP' . N P

- the equation of a rectangular hyperbola through P and P',
whose centre is the middle point ofPP', and which is referred
to conjugate diameters inclined at angle a. The orthogonal
system in this case consists of the lemniscates rrf - c. One of
the hyperbolas consists of the straight line PP', and the line equi-
distant from P and P'. Dividing the plate along the latter line,
we have the case of one source in a plate bounded in one direction
by an infinite straight line, but otherwise unlimited or bounded by
a lemniscate of infinite conductivity, having P and its image due
to the boundary line for poles.

(c.) To find the image of any point in a circular boundary, i.e, to
find the source which in combination with a source at the centre
of the circle, and an equal sink at any other point, will make the
circle a stream line.

Let A be the centre of the circle, and P the given sink. In AP
take P', so that AP.AP' = AQ2. Then PAQ and QAP' are
similar triangles, and QPA = AQP' .

Therefore QAP + QP'A 4- QPA = 2tt, or (6) is satisfied for any
point in the circle by assuming at P' a sink == P.

(rZ.) Hence if there be within a circle m sources and n sinks, we

84 Proceedings of the Royal Society

must assume the same number of sources and sinks without the
circle, and n — m sources at the centre.

(e.) The straight line equidistant from two equal sources of the
same sign is clearly a stream line for these points. Hence the
image of any point in a straight line is an equal point, which is its
optical image.

I have constructed the equation

29 = a

on the assumption that all the sources are equal, because the degree
of the stream line is equal to the number of equal sources (positive
and negative) to which the system can be reduced. For if h , h be
the co-ordinates of P, the equation becomes

2±tan^=C, . . . (7).

X—il

If f y — denote the sum of all the combinations of expres-
\h—xjm

sions dtz y~ — \ , taken m at a time, we may write this
x-li ’ J

1 - cY y-^\ - + A"f) -&c, =0 (8),

\x — hj i \x - hJ-2 \x-hj-s \x — lij 4

an equation of the nih degree if there be in all n sources.

The degree of the equipotential lines is also = n if there be an
equal number of sources and sinks. In general, if there be m
sources of one sign, and n — m of another, and m ]> n— m , 2 m is the
degree of the equipotential lines. This is one of many features
which make it more convenient to work with stream lines.

It is obvious from equation (8), that every stream line must pass
through all the sources. Thus, the circle in case (c), which passes
through no source, is not a complete stream line, the other branch
being the straight line APP', which passes through all the sources.
Distinct stream lines can intersect only at a source, for at no other
point can 2$ be indeterminate. Where two branches of the same
stream line intersect the velocity is necessarily zero, changing sign
in passing through the point. The physical meaning of a branch
is that two streams impinge, and are thrown off with an abrupt
change of direction.

of Edinburgh, Session 1869-70.

85

The same result is easily found from the analytical condition for

a singular point ^ ^ = 0.

ax ay

For - ^ ~ = velocity parallel to axis of y,

ClCC

= velocity parallel to axis of a?,

ay ax

or directly by differentiation.

du

dx

(Lib

dy

)

(»)■

The nature of the intersection of the branches of a stream line
at a multiple point is easily determined.

At an ra-point, the angles at which the branches cut the axis of
x are the roots of the equation —

(s + “ = 0

(10).

TirK * d u d u

Where, since — — = - — —

dx 1 dy 2

dmu

dxm

dmu

dmu

dm

dxm 2 dy1 dxm ~ *dy-

d 1

<fec.,

dxm~1dy dxm 3dyi

Whence (10) becomes

m . m — 1

&c.

dmu A

V

c&c”1 ldy

[ w tan <p

tan2 <p 4- &c,^ +

tan3 <p + &c.^ — 0.

1 . 2

m . m — 1 . m — 2

1.2.3

We can choose the axes so that —7 = 0, and reduce the equa-

dxm

tion to

, ^ m.m — l.m — 2, * ^

m tan p - - — g tan3 ? + ■•• = 0 . (11),

VOL. VII.

M

86

Proceedings of the Royal Society
or tan m<p = 0 . . . (12),

<p = — , where l is any integer from 1 to m.

m

Thus the branches make equal angles with each other. This
proposition depends solely on the relation = 0. It is therefore
true, also, for the equipotential lines, as is otherwise obvious.*

The general nature of the stream lines will be different, accord-
ing as the number of sinks is or is not equal to the number of
sources. In the former case, 2(0) = 0 is satisfied at all points
infinitely distant, the radii being all parallel, and the positive
and negative angles equal in number. Hence one stream line
has the straight line at infinity as a branch, or intersects the straight
line at infinity at right angles, and therefore has an asymptote.
This stream line will, in general, be of the n — 1th degree. In some
cases it may be of a lower degree ; as, for example, when the conic
at infinity is its other branch. A case of this sort will be given
below. The other stream lines of the system cannot meet the line
at infinity, and cannot have asymptotes. However far they run
out, they must therefore loop and return.

When there are more sources than sinks, 20 becomes indeter-
minate at an infinite distance, as might have been anticipated from
the fact, that in this case there is a constant flow of electricity out-
wards, implying a sink at an infinite distance. The line at infinity
is not in this case a stream line, and will be cut by all the stream
lines, which do not loop except at finite distances, and have all
asymptotes.

The asymptotes, in this case, may be easily constructed by the
aid of equations (6) and (8).

At the infinitely distant point of contact the velocities due to
all sources are in the same direction, or the asymptote must be
parallel to the radii.

If there are m sources and n — m sinks, the stream line whose
asymptote makes an angle a with the initial line is obviously

2 9 = (2m-w)a = tan 0 (13).

* I have since found that this result has been already proved for plane
curves by Professor Rankine and Professor Stokes (Proc. R.S., 1867), and for
spherical harmonics by Sir W. Thomson and Professor Tait, in their treatise
on Natural Philosophy.

87

of Edinburgh, Session 1869-70.

This equation has 2 m-n roots.

«i, eq +

2m- n ’

+

2tt

2m — n

&c.

So that each stream line has 2m - n asymptotes equally inclined
to one another.

Transforming to rectangular co-ordinates, and choosing the
asymptote as axis of x, (8) reduces to

_ (y- h\

x-hji \x ~ h Ji

+

When y = 0 , x lias two roots = co if

2(=fcfc) = 0

= 0.

. (H).

Hence the asymptote is such that the algebraic sum of the per-
pendiculars from the sources diminished by the sum of the perpen-
diculars from the sinks is zero. It is obvious without analysis
that this condition is necessary, that the velocity perpendicular to
the asymptote, at its point of contact with the curve, may be absolute
zero. If sinks weigh upward, all lines passing through the centre
of gravity of the system are asymptotes, and 2m — n of these lines,
equally inclined to each other, belong to one stream line. The
system must have a centre of gravity, for by pairing sources and
sinks we produce couples which will always give a single resultant
when compounded with the weights of the extra sources.

A complete system has no centre of gravity, but (14) is satisfied
for all lines perpendicular to the axis of the resultant couple. If
the axis of the couple formed by pairing a source and sink at dis-
tance pm makes an angle \J/m with the axis of the resultant couple

2 (p sin i//) = 0 . . . (15) ,

an equation with only one root to determine the direction of the
asymptote. In this case the asymptote meets the curve in a double
point, and has contact of the third order, or x has three roots = oo .

The condition for this is obviously —

2(=fcfcfc) = 0 . . . (16),

which since 2 (db k) — 0, does not depend on the point of the
asymptote from which h is reckoned.

If (15) is satisfied identically, the asymptote meets the curve in

88

Proceedings of the Royal Society

a triple point. Two of the branches belong to the line at infinity,
and the finite branch sinks to the n- 2 degree.

In this case not only 2(db k) — 0, but 2(d= h) = 0. Hence (16)
no longer gives a fixed point on the asymptote, but only fixes its
direction. A further analytical condition is easily found, but is
unnecessary. For in this case the centre of gravity of the sources
coincides with the centre of gravity of the sinks. The stream lines
due to the sources alone would have the same sets of asymptotes
as those due to sinks. One of these sets is necessarily asymptotic
in the complete system, which has always one line with real

asymptotes. The set will consist of ^ rays, all passing through

A

the common centre of gravity of the sources and sinks, and equally
inclined to one another.

Rectilineal Branches are asymptotes coinciding with their curves.
Hence, in an incomplete system, all straight lines pass through
the centre of gravity of the system, and belong to one stream line,
unless the centre of gravity be a source. In any case they are
equally inclined to one another, for if not branches of one stream
line, they would be so for the system got by removing the source
at their intersection.

In a complete system there can be only one rectilineal stream line,
unless sinks and sources have a common centre of gravity. In the
n

latter case, there can be at most ^ straight lines, forming equally

inclined rays through that point.

The condition for a rectilineal branch is in general that the
sources must be either on the line or be two by two, each other’s
images on the line. For if not, remove all the sources on the line
and all pairs of sources which are each other’s images in the line.
Next, remove all sources on one side of the line by placing equal
sources of opposite sign at the place of their images The straight
line is still a stream line, and on one side of it there are no
sources, and therefore constant potential, which is absurd. Simi-
larly it can be shown that a circle is a possible stream line only
when the sources are on the curve or image each other. From
this it follows that no finite number of sources can give parallel
rectilineal streams or non-intersecting circular streams.

of Edinburgh, Session 1869-70.

89

A similar investigation applies to equipotential lines. The image
of a point in a rectilineal eqnipotential line is the same in position
as the image in a stream line, but of opposite sign. No source
can lie on an equipotential line. Hence, to show that for right
equipotential line the points must image two by two, we have only
to remove all sources on one side of the line, placing equal sources
of the same sign at their images. The line is still equipotential,
therefore we may suppose it charged to constant potential, and all
sources removed. Hence all stream lines become rectilineal, which
is absurd. Similarly if a circle is equipotential, the sources must
balance about it two by two, i.e., must be in a straight line with
its centre, at distances to which the radius is mean proportional —
otherwise we can find a system reducible to a single point at the
centre of the circle, and in which all stream lines are rectilineal.
Hence, no incomplete system can have a rectilineal or circular
potential line.

Points of Inflexion occur at all points on the locus —

d2u g d?u dy + d2u dy\2 _ q

dx1 dxdy dx dy 2 dx\ v ' '

Remembering that
d?u
dx 2

we can readily bring (17) into the form-
^cos (0 + 0')^ _ 2 /cos 20^

g /sin 20\ 2 / cos (0 + 0/)\ _ 2 /cos 26\ ^ /sin (0 + 0Q\
( r2 J y rr' ) \ t*2 / \ rr' )

or,

2 sin (20 - O' - 6") _ Q

(18).

In this last expression 6' and 6" may assume the value 0.

The radius of curvature may be similarly expressed, but such
expressions can hardly have a practical application.

The cases of practical interest are mainly those where the number
of sources is small. We have already examined the cases of two

90 Proceedings of the Boy at Society

sources of the same or opposite signs. We will now proceed to
consider the cases that arise when there are three or four sources.

Three Sources. — In general the curves will be cubic passing
through the three sources, and having asymptotes determined as
above. The direction of flow at any point of the field may be
found by observing that if <p be the angle between the tangent
and a radius vector,

sin_£ =
r

It will sometimes be possible to find the direction of flow geometri-
cally by the following obvious theorem.

If a circle be described touching a stream line at any point, and
cutting off from the radii vectores of that point, fractions of their
lengths, /x p/, &c., where /x is negative if the point of intersection
is in the radius vector produced, and also negative if the radius
vector is drawn from a sink, then —

2 oo = ° •

When the number of sources is large this theorem is not in
general convenient, but it is often applicable where there are only
three points.

The lines of flow can, however, be readily described with any
degree of accuracy when there is one sink, by describing segments
of circles with constant difference of angle through the sink and
one source, and drawing through the other source straight lines
with the same difference of angle. The stream lines will be
diagonals of the quadrilaterals into which the field is thus divided.
The process may be extended to the case of two sources and two
sinks by taking the intersections of two sets of circles.

When there are two sources and one sink, the singular points
may be found by an easy geometrical method. Let A, B, be
sources, G the sink, and P a point of zero velocity. The resultant
velocity due to A and C is in the tangent to the circle PAG, and
also — since P is a singular point — in the line PB. Therefore —

BPO = PAG .

Similarly

APC = PBC .

Hence PCA, BCP are similar triangles, and there are two points

of Edinburgh , Session 1869-70.

91

of zero flow, P and P', lying in the line bisecting the angle C, and
such that PC is a mean proportional to BC and AC. The directions

of the orthogonal branches at P bisect the angle APB and its
supplement.

For the initial line is a tangent at the singular points if

d?u

dx1

, S(±I£«)

- 0

(19).

Let now APC = a, BPC = — - a = j3, and assume the bisector

u

of APB as initial line. Then

• C / 1 1 \

Sm 2 (pA2 PB2)

sin a - (3 _ 2 sin 26

which since

*) +

PC2

1

PC2 '

sin2 (3
2

1

PC2

sin2 a

' . 2 c

sm2 — .

2

becomes,

sin2 (3- - sin2 a - sin a — (3 . sin a + j3 = 0 ,

which satisfies (20).

The chief interest lies in the cases where the cubic breaks up
into a straight line and a conic. This takes place for one stream
line of the system when all the sources lie on a straight line, or
when they form an isosceles triangle with points of the same sign
at the base. The cases are —

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Proceedings of the Royal Society

1. Two Sources and a Sink. — The conic is always a circle with
the sink as centre. If the sink lies in the line of the sources pro-
duced, the radius of the circle is a mean proportional to the dis-
tances of the sink from the sources. If the sink lie between the
sources, the circle is impossible. If the sink is the vertex of an
isosceles triangle, the circle passes through both sources, and all
asymptotes meet in the point of zero flow furthest from the sources.
If the sink is half way between the sources, there are two straight
lines and a real and impossible circle.

2. Three Sources of the same Sign. — Every stream line has
three asymptotes, meeting in the centre of gravity, and inclined at

angles of . If one of these asymptotes becomes a branch, the

other branch is a hyperbola, with centre of gravity as centre, and
axes in ratio of fS to 1. If the points form an isosceles triangle,
the hyperbola passes through the extremities of the base. If the
triangle is equilateral, the hyperbola coincides with its asymptotes.

7T

If the vertical angle is less than -g , the rectilineal branch is the

77"

transverse axis ; if greater than -g- , it is the conjugate. If the

points are all in a line, the vertices of the hyperbola lie on that
line, and are the points of zero flow, which are easily found. If one
point is half way between the other two, we have two rectilineal
branches and two hyperbolas, the conjugate axis of the one being
equal to the transverse axis of1 the other. The hyperbolas are,
therefore, confocal.

Four Points. — Complete System .

Singular Points. — If A and B are sources, C and D sinks, there
is a singular point at P, if the circles APC, BPD, and also APD,
BPC touch at P. Hence, there are no real singular points if the
sides of the quadrilateral ACBD intersect, unless all the points be
on a circle, which in this case contains all the singular points.

Straight Lines. — The one stream line which has an asymptote is
of the third degree. If a straight line is one factor, the other
factor is a conic, which is always a circle. For if A, C are the
images of B, D respectively in the straight line, a circle can be

93

of Edinburgh, Session 1869-70.

drawn through them, which is obviously the branch sought. But if
A, B lie without the line, and 0, D on it, a circle through A, B hav-
ing its centre 0 in CD produced, so that OA is a mean proportional
between OC and OD is the circle required. If ABCD are all on a
straight line, the other branch is manifestly a circle with centre on
the line.

Conics. — The parabola is an impossible conic for any finite num-
ber of points. For the parabola has two asymptotes meeting at
infinity. Hence the centre of gravity of an incomplete system, or
of the sinks and sources separately in a complete system, must
heat an infinite distance, which is absurd. The conics are there-
fore central.

The hyperbola , which has two asymptotes, is only possible when
the cubic reduces to a conic. This demands that the centre of
gravity of sinks and sources shall coincide, i.e that AB, OD are
diagonals of a parallelogram. The asymptotes must meet at right
angles, and the hyperbola is equilateral. It is obvious, indeed,
that in this case the sources and sinks give separately sets of con-
centric rectangular hyperbolas, of which the one passing through
the four points belongs to both sets, and is the only asymptotic
curve of the complete system.

In this case the equipotential lines are lemniscates. Let the
origin be the centre of the system, 2 a and 2 b the diagonals of the
parallelogram, a and /3 their angles with the initial line. At any
point P

AP2. BP2 + A.CP2 . DP2 = 0.

That is,

r4 + a4 — 2 aV2 cos 2 6 - a + A(r4 + b* — 2&V2 cos 2 6 - |3) = 0
(1 + A)(r4 + a4) - 2 r2 cos 2 6 (a2 cos 2a + Xb2 cos 2/3)

+ 2r2 sin 2 0 (a2 sin 2a + Xb2 sin 2/3) = 0 .

TTT1 . a2 sin 2a , .

When A = — to • no , the curve becomes

bl sin 2p ’

( b 2 sin 2/3 - a2 sin 2a)(r4 + a4) — 2 a25V sin 2(/3 - a) cos 26 = 0 ,
a lemniscate, with foci on the initial line, and centre at the origin.
If the parallelogram is a rectangle a =■ b, and the curve is

r4 - 2aV ?0S ^ - cos 20 + ai = 0.

cos B + a

VOL. VII.

94

Proceedings of the Royal Society

It is easily shown that the stream lines orthogonal to these are
lemniscates with the same centre, passing through the four points,
one of which becomes a circle when the parallelogram is rectan-
gular.

The ellipse appears to be an impossible conic for four points,
for conics occur in pairs orthogonal to each other. The orthogonal
of the ellipse must be a confocal hyperbola, which is impossible,
the only hyperbola being that discussed above. Orthogonal circles,
however, are possible, and fall under two classes, according as all
the points are on one circle, or two on each.

If ABCD lie on a circle, that circle is obviously a stream line.
Let BA.DC produced meet in 0. Then OA.OB = 00. OD, and
the circle, with centre 0 and radius ^/OA.OB is the other branch
of the stream line. If 0 lies within the circle ABCD, the second
circle becomes impossible. If CA.BD produced meet B and
CB.AD in S, B and S are centres of equipotential circles, only
one of which is real, unless the second stream circle is imaginary.
We may take as an example the case of a rectangle, points of the
same sign lying on the same diagonal. Let the circle through the
four points be (2a and 2b being the sides of the rectangle)
x2+ y2 - a2 - b2 = 0 .

The other branch is the imaginary circle

x2 + y2 + a2 + b2 — 0 ;

and we know that another stream line is the hyperbola
y2 - x2 - a2 + b2 = 0 .

Hence the stream lines are

(x2 + yy - (a2 + b2)2 + \(y2 - x2 - a2 + b2) = 0 ,
lemniscates as above.

The equipotential circles degenerate into the straight lines
x — 0 and y = 0 .

If 0 be the point in OD produced which is equidistant from A
and B, and OC.OD = OA2 = OB2, the circle with 0 as centre
passing through A,B is a line of flow.

The circle having its centre P in AB produced, and passing
through CD, is obviously orthogonal ; and since PA.PB = PC2

of Edinburgh, Session 1869-70. 95

= PD2 is also a line of flow. In this case both circles are neces-
sarily real.

It is clearly impossible that the same system should have two
pairs of circular stream lines of either of the classes we have
analysed. Nor can two complete pairs of different classes occur,
since otherwise two stream lines would intersect. But three real
and an imaginary circle are possible, if ABCD lie on a circle,
and at the same time obey the condition for a pair of circles of
the second class, that is, if AB produced pass through the pole of
CD with respect to the circle ABCD. The three circles are mani-
festly orthogonal, and their radical centre is centre of the fourth
(imaginary) circle.

If the circle through ABCD is

S = x2 + y2 - a2 = 0 ,
the lines AB, CD respectively

u — hx + ky - a2 = 0

v = h'x + h'y — a2 = 0 ,

we have

hli -j- hk' — a? — 0 ,
and the second and third circles become
S - 2u = 0

S - Zv = 0 .

The fourth or imaginary circle is

S - 2w= 0,

where

w __ a*(V-k)x + af(h-hr)y _ ^
hk‘ — kh’ hk' — kh'

w = 0 representing the polar of the intersection of AB, CD.

Thus the equation to the stream lines may be written

(S - 2t*)(S - 2v) + AS(S - 2w) = 0 ,

or,

(1 + A)S2 - 2(m + v + \w) S + 4 uv = 0 ,

which degenerates into a cubic when A. = - 1.

The equations may, in general, be simplified by a proper choice
of co-ordinates.

96 Proceedings of the Royal Society

Take, for example, the case when S - 2u, S - 2v are equal circles.
Then ¥ + k 2 = li2 -f k* ,

and by proper choice of axes,

h = - h'
k = V
¥ - ¥ = a2.

Hence,

The lines become

( 1 + A)S2 - 2(2 ky - 2a2 + ^ + 4 (ley - a2)2 - ihV = 0.

If the three circles are equal, we have further,

¥ + ¥ = 2 a2

k —

V2

Accurate drawings of this case, and of the lemniscates in the
case of a rectangular parallelogram, have been prepared, to accom-
pany this paper, by Messrs Meik and Brebner, in the Physical
Laboratory of the University. The dotted lines in these diagrams
show the lines of flow, when the signs of a source and sink are
transposed.*

Verifications have been sought by determining equipotential
lines experimentally, and superposing them upon drawings of the
stream lines. The experiments were executed by students in the
Physical Laboratory. The process employed was essentially that of
Kirchhoff, but the use of Thomson’s galvanometers has made it
much more rapid, as well as more delicate.

Spherical Surfaces. — To extend the method above used to spheri-

* That a greater variety of curves might be given, without overcrowding
the figure, the two sides of one of the diagrams have been made unsym-
metrical, some of the curves being given (in half) on the one side, others on
the other.

97

of Edinburgh, Session 1869-70.

cal surfaces, we must take as starting point, not a single source,
but a source and sink at the extremities of a diameter. For
brevity, we shall speak only of the source, assuming the existence
of a corresponding sink.

When there is one source, the stream lines are manifestly great
circles through it, and the equipotential lines small circles, of which
it is the pole.

If the radius of the sphere is a , the circumference of the small
circle, whose angular radius is 0, is & ra sin 6. Hence if u be the
potential,

du

dd

u

For any number of sources the potential will be

-fs ± log l~cos ej,

2 \ ^l-s-cosfl/’

and the equation of the equipotential lines,

1 - cos 0X 1 - cos _ q 1 - cos 0\ 1 - cos

1 + cos 9l ’ 1 + cos 0% 1 + cos 9\ * 1 + cos Q'f" ;

the accented angles belonging to sinks.

For the lines of flow we have, precisely as in a plane, 2(=fc (p) = c,
where <p is the angle between the great circle through a source
and a point on the line, and a fixed great circle through the source.

Let us take, as an example, the case of one source and one sink.
Let the co-ordinates of these points be h, k, 0 ; h , - h} 0, and those
of any point on an equipotential line, x, y , z.

We have for the equation of this line,

1 - cos 0 + ^ 1 - cos $'

1 + cos 6 1 + cos &

where

hx + ky

cos 6 = , cos 6 =

a 2

Hence the projections of the equipotential lines on the plane of
xy have as equation,

(a1 -hx- Tcy) ( a 2 + hx — hy) + X (a3 - hx + ky) (a2 + hx + ky) = 0,

= o,

hx — ky

1 , 1 - cos 9

2 logr^T0

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Proceedings of the Royal Society

or —

a4 -f &2y2 — h2x2 — 2 ^ a2ky = 0

— a series of similar hyperbolas, whose centres lie on the axis of y,
whose axes are parallel to the co-ordinate axes, and inversely pro-
portional to the co-ordinates of the source, and which all cut the
a2

axis of x at points distant ± — from the origin. Obviously one

of the lines is the great circle perpendicular to the line joining the
sources.

For the stream lines we have in this case,

observing that

<p — <p' = c,
tan <p =
tan <p ' =

xk — hy
— az

xk + hy

This equation becomes

k2x2 - Wy2 - a2z 2 + \xz = 0 ,

a cone which intersects the tangent plane to the sphere at the
extremity of the axis of zc, in a series of similar ellipses, having
their centres on the intersection of the plane with the plane of xz,

and passing through the points a, ri= ^ , 0. Two of the stream

lines are manifestly great circles, whose equations are x = 0 and
2 = 0.

If we divide the sphere along the former of these circles, we cut
off the subsidiary source and sink, and get the case of a hemisphere,
in which the source and sink are equidistant from the pole. A
curious hemispherical case is got by dividing the sphere along the
equipotential hemisphere. In this case we have two sources of
the same sign within the hemisphere, one being the subsidiary
source of the removed sink. But in order that the distribution
may remain unchanged, we must have the potential maintained
constant at the edge of the hemisphere. This may be effected by
making the base a conductor with a sink at its centre, or, indeed,

99

of Edinburgh, Session 1869-70.

by placing the sink at the vertex of any conducting surface of
revolution which joins the hemisphere. From these hemisphere
cases, obvious cases of half and quarter hemispheres follow.

4. On the Kombi Arrow-Poison (Strophanthus hispidus , DC.)
of the Manganja district of Africa. By Dr Thomas E.
Fraser.

{Abstract.)

In nearly every narrative of exploration in uncivilised tropical
regions, accounts are given, often no doubt somewhat fanciful, of
poisonous substances which are said to possess the most remark-
able properties. Usually these poisons are of vegetable origin ; and
the great majority may be included in the two divisions of ordeal
and of arrow poisons, according as they are applied to one or other
of these purposes. Among the most remarkable of the ordeal-
poisons are the Tanghinia venifera of Madagascar, the Physostigma
venenosum of Old Calabar, and the Akazga poison of the Gaboon ;
and of the arrow-poisons , the famous Curara or Wourali of South
America, and the Antiaris toxicaria of Java.

The examination of these substances has not only proved of
great value to physiology, but practical medicine .has likewise been
benefited — one of them, at least, being now an important medicinal
agent.

In bringing before the Society a few of the results of a recent
examination of a new arrow-poison, the author has to express his
gratitude to the President, who very kindly gave him the specimens
of poison with which the experiments have been made. These
specimens, consisting of a number of ripe follicles, were sent to Dr
Christison by Mr Walker, and were collected in the expedition of
the late Bishop McKenzie.

Several specimens of the poison have likewise been sent to Pro-
fessor Sharpey by Dr Kirk, H.M. consul at Zanzibar. Dr Kirk
says “ that the plant is a woody climber, growing in the forest, both
of the valley and hills, and found at various places between the
coast and the centre of the continent, above the Victoria Falls of
the Zambesi. The stem is several inches in diameter, and rough
outside. The plant climbs up the highest trees, and hangs from

100

Proceedings of the Royal Society

one to the other like a bush vine. The flowers are of a pale yellow,
and last for but a short time during the months preceding the first
rains of the season (October and November). The fruit is ripe in
June, and collected by the natives, who separate the rough outer
coat before drying it, preserving the more leathery inner covering
and the seeds.”*

Dr Livingstone gives some interesting information regarding the
poison in his “ Narrative of an Expedition to the Zambesi and its
Tributaries.” He mentions that arrows poisoned with it are used
for killing wild animals only ; arrows destined for the more noble
object of killing men being poisoned with the entrails of a small
caterpillar. Dr Livingstone says that in hunting, the natives follow
the game with great perseverance and cunning : — “ The arrow, mak-
ing no noise, the herd is followed until the poison takes effect, and
the wounded animal falls out ; it is then patiently watched till it
drops ; a portion of meat round the wound is cut away, and all the
rest eaten” (p. 465).

Dr Livingstone also says that the poisoned arrows are made in
two pieces. “ An iron barb is firmly fastened to one end of a small
wand of wood, ten inches or a foot long, the other end of which,
fined down to a long point, is nicely fitted, though not otherwise
secured, in the hollow of the reed which forms the arrow-shaft.
The wood immediately below the iron head is smeared with the
poison. When the arrow is shot into an animal, the reed either
falls to the ground at once, or is very soon brushed off by the bushes ;
but the iron barb and poisoned upper part of the wood remain in
the wound. If made in one piece, the arrow would often be torn
out, head and all, by the long shaft catching in the underwood, and
striking against trees ” (p. 466).

The follicles examined by the author vary in length from about
nine and three-fourths, to about twelve and one-fourth inches, and
in greatest thickness from about one inch to three-fourths of an inch,
and they vary in weight from about 130 to 330 grains. They con-
tain from 100 to 200 seeds, each of which weighs about half a grain,
and has attached to it a beautiful comose appendix, placed on an
extremely brittle stalk. For the identification of the plant the
author is indebted to Professor Oliver of Kew, who writes, in a letter
* Extract from letter to Professor Sharpey, dated January 1, 18G4.

101

of Edinburgh, Session 1869-70.

dated 10th Dec. 1869, — “ I reopen your note to say that I have just
dissected a flower, and conclude to name the Kombi plant Strophan-
thus hispidus , DC.” This plant belongs to the natural order Apo-
cynacece.

When the seeds contained in these follicles are bruised and
treated in a percolator with rectified spirit, a greenish yellow tinc-
ture is obtained. By distilling off the greater part of the spirit, and
drying the residue on a water bath, and in the exhausted receiver of
an air-pump, an extract is procured which weighs about 25 per cent,
of the seeds employed, has an intensely bitter taste, and contains
about one half of its weight of an inert fixed oil. From this extract
the author has succeeded in separating a very powerful active
principle.

As, however, the greater number of the experiments have been
made with the extract, the results of these experiments only will be
described in the following brief account of the physiological action
of the Kombi arrow-poison, it being understood that the action of the
active principle is of the same character.

When a small dose (^-th °f a grain) of this extract is mixed with
a few minims of water, and injected under the skin of a frog, no
distinct symptom is seen until about half an hour, when the
animal’s movements become somewhat sluggish. Soon afterwards
the respirations cease, some stiffness occurs in the thoracic extremi-
ties, reflex sensibility diminishes, some stiffness appears in the
pelvic extremities, and in about two hours after the administration,
voluntary movements entirely cease, and strong galvanic irritation
produces no effect, even when applied to exposed muscles and
nerves. An examination of the heart shows that it is completely
paralysed, the ventricles being pale and contracted, while the
auricles are dark and distended.

It was obviously suggested by these phenomena that this sub-
stance acts as a cardiac poison; and, accordingly, some experiments
were made in which the heart was exposed before the administration,
of which the following is an example : —

One-tenth of a grain of extract was injected under the skin of a
frog. Five minutes thereafter, it was observed that the ventricular
systole was somewhat prolonged; in six minutes, the ventricular
diastole was imperfect, so that only portions of the ventricle dilated

VOL. vii. o

102 Proceedings of the Royal Society

to admit blood from the auricles ; in six minutes and thirty
seconds, the greater portion of the ventricle was continuously pale
and contracted, each auricular systole propelling merely a small
drop of blood into the ventricle, where it produced a dark, pouch-
like projection, which at times disappeared, and at other times
only changed its position during the imperfect systole of the ven-
tricle; in seven minutes, the ventricle altogether ceased to con-
tract, while the movements of the auricles continued at nearly
the normal rate; and in eighteen minutes, the auricles in their
turn became motionless, but, in place of being contracted and empty
like the ventricle, they were distended and full of dark blood.
Notwithstanding this absolute paralysis of the heart, respiratory
movements occurred for thirty-five minutes after the ventricle had
ceased to contract, and the frog jumped about actively for some
time after this.

The experiments that have been performed with birds and mam-
mals have likewise shown that this poison acts primarily on the
heart.

An endeavour was made to ascertain by what mode of action
these very peculiar cardiac effects are produced. With this object
experiments were made, in which the cerebro-spinal axis was com-
pletely destroyed, in which the vagi nerves were divided, and in
which the peripheral terminations of the vagi were paralysed by
atropia, previously to the exhibition of the Kombi poison ; but no
important modifications were thereby caused, and it is therefore
obvious that the action on the heart is not exerted through the
cerebro-spinal nerves. In other experiments, after complete cardiac
paralysis, the surface of the heart was irritated by galvanic and
other stimulants, but no effect was thereby caused.

Another very prominent action of this poison is that exerted on
the voluntary muscles, by which their activity is gradually impaired,
and finally completely destroyed, so that the muscles are quickly in
a condition of true rigor mortis.

Regarding the other physiological effects, it is sufficient briefly
to mention that the sensory and motor spinal nerves, the abdominal
and cervical sympathetics, and the muscular walls of the stomach,
intestines, bladder, and uterus, are paralysed at an early stage,
although not until the blood-heart has ceased to contract; while

oj Edinburgh , Session 1869-70.

103

the lymph-hearts of the frog maintain a normal rate long after
paralysis of the blood-heart.'*

From these results it is apparent, that the primary action of the
Kombi arrow-poison is isolated in the heart, and that it may there-
fore be included in the class of the cardiac poisons , — a class of
poisons whose action has been most accurately defined by the
researches of Kolliker, Yulpian, Pelikan, Hammond and Weir
Mitchell, Hilton Fagge and Stevenson, Holme, Dibkowsky, and
others.

5. On Thebo-lactic Acid. By J. Y. Buchanan, M.A.

Thebo-lactic acid was discovered in Turkey opium by Messrs T.
& H. Smith, the eminent morphia manufacturers of this city. It
was examined by Stenhouse, and found to have the same composition
as lactic acid, from which, however, it was supposed by the Messrs
Smith to differ in the crystalline form of its copper and morphia
salts. At present we are acquainted with three isomeric lactic acids,
two of them differing from each other chemically, whilst the third
is distinguished by its power of rotating the plane of polarisation
of light. The last named acid, having been but recently! discovered,
it is impossible to say whether it possesses any decidedly distinctive
chemical properties or not. The other two, namely, the ordinary
or ethyliden — and the ethylen-lactic acids, possess perfectly distinct
chemical properties, determined by the different relative position
in each of the alcoholic hydroxyl. The following rational formulae
express the different constitution of the two acids : —

They may be distinguished at once by replacing in each the
alcoholic hydroxyl by chlorine. We thus obtain from ordinary
lactic acid the so-called a-, from ethylen-lactic acid, the /3- chloro-

* The author is indebted to Professor Sharpey of London for an account
of some experiments made with this poison in 1862. The results mentioned
in the above abstract harmonise in the most satisfactory manner with those
obtained by Professor Sharpey.
t Berichte der Deutschen Chem. Ges. 1869, 620.

gh3

CHOH

COOH

CH2OH

ch2

COOH

Ordinary lactic acid.

Ethylen-lactic acid.

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Proceedings of the Royal Society

propionic acid. These two bodies possess such different properties,
that they may be at once and with certainty recognised.

The task, therefore, which I set myself, was, by the assistance of
the chlorinated acid, to determine the position in the molecule
of the alcoholic hydroxyl. Thebo-lactate of lime, dried at 150°, was
treated with perchloride of phosphorus in the proportion of two
molecules of the latter to one of the former. This mixture was
heated in a retort, attached to the lower end of a Liebig’s condenser,
until the disengagement of hydrochloric acid ceased, when the
condenser was reversed and the volatile products distilled off. By
this means the decomposition is so complete that the residue, con-
sisting of chloride of calcium, may be heated until the glass of the
retort softens without carbonising to any very sensible extent.
The distillate was separated by rectification up to 111° into a residue,
which did not distil without partial decomposition, and a distillate.
The latter was treated with the necessary precautions* with water,
to obtain the chlorinated acid, and the former with absolute alcohol,
to obtain its ether.

The acid thus obtained possessed all the properties of that formed
from ordinary lactic acid. A chlorine determination gave 32'95
per cent, chlorine. The theoretical amount calculated from the for-
mula CSH5C10.2 is 32-72. Its specific gravity is 1*27, against 1*28
found for the acid derived from ordinary lactic acid. It passed
entirely between 185° and 186°; the boiling point of a- chloropro-
pionic acid is 186°. The two acids have also the same outward
appearance, being colourless, uncrystallisable liquids, possessing the
same smell, and exercising the same corrosive action on the skin,
unaccompanied by pain or blisters.

The ether also possesses exactly the same properties as that pre-
pared from ordinary lactic acid. A chlorine determination gave
26-34 instead of 26,01 per cent, demanded by the formula C5Ii9C102.
They both boil at 144°, and have the same smell ; they are also
both formed with great ease by heating their acids with alcohol and
sulphuric acid.

It is thus evident that the chlorinated acids obtained by the same
means from the two acids under comparison are identical. The
chlorine, therefore, in both cases, is united to the same carbon atom,
* Compt. Rend. lxvi. 1157.

105

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and consequently the acids, in which this chlorine is replaced by
hydroxyl, have this last named group attached to the same carbon
atom, and are therefore identical.

It is proper to mention that all the above experiments on
thebo-lactic acid were repeated with ordinary lactic acid, and with
uniformly identical results.

The copper 6alts of thebo-lactic and of ordinary lactic acids were
prepared side by side, as nearly as possible under the same con-
ditions, and in similar vessels, and on comparing the two salts, it
was impossible to detect the slightest difference in their crystalline
form. The free acid in concentrated solution produced no effect on
the plane of polarisation of light.

I am engaged at present on the further comparison of the acids,
and hope to have the honour of communicating my results to the
Society on a future occasion.

In concluding, I take this opportunity of expressing my best
thanks to the Messrs Smith, who in the most liberal manner placed
at my disposal a large quantity of perfectly pure thebo-lactate of lime.

6. On the Bones of a Seal found in Red Clay near Grange-
mouth, with Remarks on the Species. By Professor
Turner.

Towards the end of last autumn, one of my pupils, Mr William
Stirling, B.Sc., requested me to determine some bones which had
been found whilst sinking a new shaft for a pit in the Grangemouth
coal-field. On examination, I found these bones to be the two
halves of the lower jaw, a fragment of the upper jaw with some loose
teeth, the right temporal bone, the atlas with fragments of other
vertebree, the glenoid part of the left scapula, the right astragalus
and femur, and small fragments of other bones of the skeleton of a
seal. The animal had not reached the adult state, for the epiphyses
of the femur were not united to the shaft. The bones were im-
bedded in a stiff red clay.

Early in the present year, I Was informed by Mr Stirling, the
manager of the Grangemouth collieries, that Mr Burns, of Glasgow,
had obtained some seal’s bones from the same locality, and had ex-
hibited them at a recent meeting of the Geological Society of Glas-

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Proceedings of the Royal Society

gow. Through the courtesy of Mr Geikie and Mr Croll of the
Geological Survey, I have had the opportunity of examining the
bones obtained by Mr Burns, which undoubtedly formed a part of
the skeleton of the animal, some of the bones of which Mr Stirling
had previously given to me, for I found amongst them the missing
condyloid epiphysis of the right femur. These consist of one of the
cervical, and of fragments of other vertebrm, of portions of the ribs,
of the left occipital condyle, of a portion of the innominate bone
and acetabulum, and of digital bones, more especially the terminal
phalanges.

On a visit to the locality a few weeks ago, Mr Stirling gave
me the following particulars : —

In the summer of last year a new shaft was sunk on Towncroft
Farm, Grangemouth, to reach the coal in that district.* In the
course of the operations the following strata were bored through : —

ft. in.

Surface soil,

4

0

Gravel sand, .

0

9

Blue mud and sand, ....

. 16

0

Channel bed, .....

4

0

Sand and water, ....

8

0

Bed clay mixed with sand,

. 11

0

Pure red clay, .....

. 36

0

Soft blue till,

. 38

0

Red sand, ......

1

0

Blue till,

5

0

Sand,

1

0

Hard blue till, .....

. 31

0

155 9

The hard blue till lies on the rock in which the coal occurs.

* In a paper read before the Geological Society of Edinburgh, May 1869,
and published in their Transactions, Mr Jas. Croll has given an account of
the geology of this district; and in a paper read before the Geological Society
of Glasgow, April 2, 1868 (Transactions, iii. p. 183), Mr Jas. Bennie has
recorded the results obtained in the course of “ boring” operations in the valley
of the Clyde near Bowling, the haugh of Balmore, the valley of the Kelvin,
and round by the south-eastern end of the Campsie Hills into the valley of
the Forth, near Grangemouth, which reveal that “ a great deep hollow
stretched from sea to sea, fairly splitting Scotland in twain.”

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Whilst removing the blue mud and sand, superficial to the channel
bed, the lower end of the left humerus of a large red deer was met
with.

The seal’s bones were found near the bottom of the pure red clay,
at a depth of nearly 80 feet from the present surface of the soil, and
nearly 68 feet below the present sea-level. The shaft of the pit is
530 yards distant from the Oarron river to the south, and 1680
yards from the estuary of the Forth on the east.

That bones of a species of seal have occasionally been found im-
bedded in clay, in the middle district of Scotland, is a fact well
known to naturalists. But the relations which these bones had to
the surface, and to the present sea-level, differ in some important
particulars from those of the Grangemouth seal.

In 1825, Dr Knox* directed attention to the bones of a seal found
near Camelon, in a bed of clay 90 feet above the present level of the
Forth. Dr David Page described! and presented to the Museum
of Natural History in this city the almost perfect “ skeleton of a
seal, found in the Pleistocene clays of Stratheden,” 150 feet above
the present sea-level, about 16 feet from the surface of the soil, and
about 5 miles inland from the influence of the tides.! Dr Allman
on two occasions § exhibited to this Society bones of a seal — in the
one instance, obtained from the Tyrie clay-field, Kirkcaldy, 30 feet
above the present sea-level, 18 or 19 feet from the surface of the
soil, and a quarter of a mile from the shore of the Forth ; in the
other instance, from the clay-field at Portobello, about 20 feet above
the present high-water level, and about 15 feet below the surface of

* Memoirs of Wernerian Society, v. 572.

t Proc. British Association, Sept. 1858.

i Since my paper was read to the Royal Society, Dr Page has informed me
that he obtained a second young seal’s skeleton from the Stratheden clay,
which is now in the Museum of Natural History, St Andrews. Nearly perfect
skeletons of the surf and eider ducks, Oidema and Somateria, were found in the
same clay. Dr Page also tells me that he has obtained seal’s bones from the
brick clays at Garbridge and Seafield, near St Andrews ; from a brick-field
at Dunbar ; and from brick clay at Invernetty, Aberdeenshire. These clays
are in the same horizon as the Stratheden clay. I find also that the skeleton
of the young seal, in the St Andrew’s Museum, has been carefully described
by Mr R. Walker [Annals and Magazine of Natural History , Npv. 1863). He
shows clearly that it is not Callocephalus vitulinus, and he considers it to be a
young individual of P. groenlandicus. I have not yet examined this specimen.

\ Proc. Roy. Soc. Edinburgh, April 19, 1858, and March 21, 1859.

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Proceedings of the Royal Society

the soil. The Rev. Thomas Brown showed to this Society* portions
of the skeleton of a seal, obtained from a brick-field at Errol, 45
feet above the present sea-level, and about 1 \ mile from the estuary
of the Tay. The bones were well imbedded in the brick clay, which
also contained shells such as are now found in the polar seas, and
which testify to the arctic rigour of the climate at the time when
the clay was deposited.

As to the character of the clay in which the bones of the Grange-
mouth seal were found, Mr Peach, who has surveyed the district, and
Mr Gfeikie, and Mr Croll, pronounce it to have been deposited
under decidedly arctic conditions. Mr Peach also tells me that the
Grangemouth clay is continuous with that at Camelon, near Falkirk,
where the seal’s bones which Dr Knox examined were found, and
that it possesses the same characters as the Stratheden clay, in
which lay the skeleton of the seal described by Dr Page.

Mr David Robertson of Glasgow has also examined the Grange-
mouth red clay with reference to the occurrence in it of minute
organisms. He reports that he has found two species of Fora-
minifera, Polymorphina compressa (D’Orb) and Nonionina asterizans
(F. & M.), and one species of Ostracoda, Cytlieroyteron montrosiensi.
This Ostracod Mr Robertson states to be common in the brick clays
of Annochie, Dryleys, Errol, Elie, and Bannie on the east of Scot-
land, which deposits contain arctic shells not now living on the
British coasts.

Mr Bennie also informs me that Mr Robertson has obtained from
the muddy sand and fine sandy clay which overlie the Grangemouth
pure red clay, fragments of shells, the Tellina balthica , a shell
which, Mr Jeffreys states, agrees exactly with similar fragments
found by Professor Lilljeborg at Upsala. No fragments of shells
have as yet been found in the red clay itself. The geological evi-
dence is in favour of the view that the Grangemouth clay is glacial,
and belongs to the same class as other undoubtedly glacial clays on
the east coast of Scotland. The difference in the relation to the
present sea-level between the Grangemouth clay and the other
clays presents no difficulty in placing them in the same category ;
for we have but to suppose that, during the period of submergence,
when these clays were formed, the water in the Grangemouth
* Trans. Roy. Soc. Edinburgh, xxiv. p. 629.

109

of Edinburgh, Session 1869-70.

locality was some 200 feet deeper than in the districts of Stratheden
or of Errol, so that the change in the relative position of land and
water which has taken place since that time has caused the Strath-
eden clays to be elevated 150 feet above the present sea-level,
whilst the Grangemouth clay is some 60 or 70 feet below it.

I shall now proceed to inquire into the characters of the bones
of the Grangemouth seal, with the view of determining — lssf. Whether
the animal was of the same species as the seals whose bones have
been found in beds of clay in Scotland by other naturalists ; and,

2 d, Whether the species is or is not the common seal, Callocejphalus
vitulinus , which now frequents our coasts.

With regard to the first part of the inquiry, I have compared
this Grangemouth seal with the Errol seal found by the Rev. Thomas
Brown, with the skeleton from Stratheden, and with the bones of
the Portobello seal, which form a part of the natural history
collection in the Museum of Science and Art. I may mention, that
the bones from Portobello have received some important additions
since Dr Allman drew attention to them at the meeting of this
Society ; for Dr Andrew Balfour, by whom they were discovered,
has added to the collection one-half of the lower jaw and several
teeth.

As regards the Errol seal, the bones recovered were vertebras and
ribs, of which two only, viz., the atlas and one of the lower cervical
vertebras, have representatives in the Grangemouth skeleton. The
Errol seal is an older animal, and the bones are larger and more
completely ossified than those of the Grangemouth seal ; but when
due allowance is made for the difference in age, their form and
general characters are so much alike that I believe them to be
animals of the same species. The materials for comparison with the
Portobello and Stratheden seals are, fortunately, more complete ; for
in them, as in the Grangemouth seal, the lower jaw and teeth are
almost perfect, and the femur, scapula, and other bones are repre-
sented in each skeleton. All three animals were immature, for the
epiphyses of the thigh bones are not yet anchylosed to the shafts.
The atlas of the Portobello seal is somewhat less in its antero-
posterior diameter than in the one from Grangemouth, and the
distance of the inferior dental foramen from the hinder end of the
lower jaw is greater in the Portobello and the Stratheden than in the

VOL. VII.

110 Proceedings of the Royal Society

Grangemouth specimens. These differences are, I believe, merely
individual and not specific. On the other hand, there is so close a
correspondence in the general form of the lower jaws, in the num-
ber and cuspidation of the teeth, and in the mode in which they
are implanted in their sockets, that I am of opinion these seals
were animals of the same species. This identity in the specific
characters of the seals found in the clay formations on the east
coast of Scotland furnishes an additional argument in favour of
the view, that they have been deposited at the same epoch and
under the same conditions. We may now inquire if this clay
seal corresponds with the present British species, the Gallocephalus
vitulinus.

Inner surface of the right half of the lower jaw of the Grangemouth seal,
the size of nature. The outline of the coronoid process is filled in from
the Portobello seal. The single tooth is one of the upper molar series.

Dr Knox stated that the Camelon seal was identical with the
species now inhabiting the Forth, and many other naturalists who
have written on this matter are inclined to the same view. At
the time when Dr Knox wrote, the specific differences between the
various northern seals had not been precisely made out, and the
determination is even yet one of much difficulty, unless the skulls
and teeth can be compared with each other. Dr Knox does not say
what the bones were which came under his observation, so that we
have now no means of knowing how far he had in his possession
the materials for making an exact comparison.

Ill

of Edinburgh, Session 1869-70.

Dr Page expresses himself with more reserve regarding the Strath-
eden seal. He looks upon it “ as a pretty widely divergent variety
of the common seal, if not a distinct species — a point, however, which
yet awaits the precise determination of the comparative anatomist.”

I have now carefully compared the jaws (more especially the
lower, which are best preserved), and the teeth of the Grangemouth,
Stratheden, and Portobello seals, not only with the adult skulls
and teeth of the common seal, but with a young skull of that species,
apparently about the same age as the fossil specimens, and I have
no hesitation in saying that they are not of the same species. The
number of teeth is indeed the same, but the character and mode of
implantation of the molars exhibit important differences. In the
clay seals, the number of cusps in the premolar and molar series
does not exceed four, and this number is distinctly marked in all but
the first and last. The second cusp in each tooth is the largest, hut
it does not preponderate very greatly over the first and third cusps,
and the bases of the crowns are not much swollen. The teeth are
set in the jaw in longitudinal series, one directly behind the
other.

In the young of the common seal the cuspidation of the lower
molars is not so uniform as in the clay seals ; the last molar has
four cusps, the penultimate has five, and the third and second only
three. One cusp preponderates largely over the others, and the
base of the crown is swollen. The molar teeth, also, are set obliquely
in the jaw, so that one tooth not only lies in front, but somewhat
to the outer side of the one behind it. This oblique setting of the
grinders is also seen in well grown specimens.

The upper molars in the clay seals are smaller and more delicately
formed than in the common seal. They are, as a rule, tricus-
pidate, and with, as a rule, the central cusp the largest. They are
not set obliquely, and the more anterior do not overlap those
which lie behind. In the common seal, again, the anterior cusp
is usually the biggest, and the upper, like the lower molars, are set
obliquely.

I have also compared the jaws and teeth of these clay seals with
the skulls of Phoca barbata, Halichoerus gryphus , and Pagopliilus
groenlandicus , northern seals, which possess the same general dental
formula. With barbata and gryphus there are so many points of

112 Proceedings of the Royal Society

difference that I cannot regard them as identical. With the Green-
land seal, again, the points of resemblance are, in some respects,
very striking. They agree in the number, mode of arrangement,
and relative size of the cusps, and in the mode in which the teeth
are implanted in the jaws, though the teeth are set closer together
in the fossil than in the Greenland species. Unfortunately, I have
not had access to a young skull of the Pagopliilus groenlandicus , or
to an adult clay seal, so that the materials for comparison have
not, in this respect, been as perfect as to enable me to identify the
species with accuracy. The examination, however, which I have
made, leads me to think that these young clay seals maybe either
immature specimens of the Pagophilus groenlandicus , or of a closely-
allied species. But it will be difficult to express a positive opinion
until adult skulls are compared with each other, and the skulls of the
clay seals be compared with the crania of Pagomys foetidus, crania
of which are not yet in my possession.

Addendum, March Vlth .

Since this paper was read to the Society, I have received some
additional material of considerable importance in connection with
the determination of the species of seal found in the glacial clay-
beds of Scotland. Ur Howden has kindly sent me the bones of an
adult seal, found in glacial marine clay at Puggiston, three miles
from Montrose.* Through Mr William Livesay and Dr MkBain,
I have had the opportunity of examining three crania of the small
arctic seal, Pagomys foetidus , Gray ( Phoca hispida , Cuvier). These
skulls were from two adult and one young specimen. f

The bones from Montrose included several vertebras and ribs,
pelvis, scapulas, and the long bones of the extremities, together
with the two halves of the lower jaw and the left upper jaw. They
were found thirty feet below the surface, about three quarters of a
mile from the tidal estuary of the South Esk, and about five feet

* The geology of this district has been carefully described by Dr Howden
in the Trans. Ed. Geolog. Soc. 1867-68.

t These skulls were procured in the Spitzbergen seas during the arctic
expedition conducted last summer by Mr Lamont.

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of Edinburgh, Session 1869-70.

above the present sea-level. I have compared these bones with the
corresponding bones in the skeleton of the common seal, and have
satisfied myself that they belong to animals of different species. I
have also compared them with the bones of the other clay seals
already referred to, and am of opinion that the Montrose seal is an
adult of the same species as the Stratheden, Portobello, and Grange-
mouth specimens. Comparing the lower jaw of the Montrose seal
with that from Grangemouth, depicted on page 110, we find that
they have the same general form, differing from each other only
slightly in size; that the teeth have the same characters, and are
implanted in the jaw after the same manner.

If we compare the lower jaw of the adult Montrose clay seal with
that of an adult Pagophilus groenlandicus, we find important dif-

ferences in size, which are expressed in the following
dimensions being taken in straight lines —

Clay seal.

Length from posterior border of condyle

table, the

P. groen.

to socket of canine tooth,

Vertical diameter of horizontal ramus

4-2

5-1

opposite last molar, ....
Antero-posterior diameter of ascending ra-

0-8

1-0

mus just above the tubercle, at the angle,

1-1

16

Vertical diameter of ascending ramus,

1-6

2-4

On the posterior border of the ascending ramus of the lower jaw
of P. groenlandicus, a large triangular tubercle projects obliquely
backwards and inward; in the clay seals, both adult and immature,
the corresponding tubercle is not triangular, and has the form of an
elongated almost vertical ridge. The teeth in the adult clay seal
are set more closely together than in P. groenlandicus , and though
the cusps in the fossil are considerably worn, yet there is not that
preponderance of the central cusp over the anterior and posterior
cusps in the fossil, as in the Greenland seal. The comparison of
the temporal bones, and of the upper jaw with its teeth, of the
adult fossil with the Greenland seal also showed important differ-
ences, so that I am constrained to give up the idea, at one time
thought probable, that these seals were of the same species.

I have now instituted a comparison between the lower jaws of the
adult clay seal and of the Pagomys foetidus , and find they correspond

114 Proceedings of the Royal Society

much more closely, not only in form, hut in dimensions. The corres-
ponding dimensions of the latter to those of the clay seal already
given in the table, being respectively 4 inches, 08 inches, T2 inches,
and 1-4 inches ; the differences, therefore, being so trifling as to be
merely individual. They both possess the elongated ridge-like
tubercle on the posterior border of the ascending ramus, and a deep
masseteric fossa on its outer surface, which is bounded posteriorly
by a ridge ascending to the outer end of the condyle, which ridge
becomes continuous with that on the posterior border already re-
ferred to ; in both the lower border of the horizontal ramus is in-
curved opposite the last molar tooth, behind which incurved portion
it sweeps backwards and outwards in a graceful curve; in both
the arrangement and cuspidation of the teeth are closely similar,
although the intervals between the anterior molars are somewhat
greater in P.foetidus , than in the fossil.

The upper jaws and temporal bones in the two seals closely
correspond in form.

The affinity, therefore, of the fossil seal to Pagomys foetidus is
very close, — so close, indeed, that I should not consider myself
justified in pronouncing them to he distinct species.

So far, then, as I have had access to materials for comparison, I
am inclined to think that the seal, the remains of which are found
in the brick-clays of Scotland, corresponded with the now existing
small arctic seal, P. foetidus .

I am not aware that there is any satisfactory evidence to show
that this northern seal ever visits our shores at the present day,
so that we may consider the determination of its bones in the brick-
clays to he an additional piece of evidence to those advanced from
other data, that at the time when these clays were deposited an
arctic climate prevailed over Scotland.

The following Gentleman was elected a Fellow of the
Society : —

Dr J. Warburton Begbie, F.R.C.P.E.

of Edinburgh, Session 1869-70,

115

Monday, 1th March 1870.

WILLIAM FORBES SKENE, Esq., Vice-President, in
the Chair.

The following Communications were read: — -

1. On the Rate of Mortality of Assured Lives as experienced
by Ten Assurance Companies in Scotland from 1815 to
1863. By James Meikle, Esq. Communicated by
Professor Tait.

The mortality of assured lives is introduced by a short statement
of the process followed in the obtainment of the rate of mortality
among the male population of England and Wales during seven
teen years, and in which the results are compared with the rate
obtained by following the same process with the male population of
Scotland during ten years. A statement is given of the method
employed for collecting the facts referring to assured lives, and of
tabulating the results with the view of extracting, not only the
total numbers entering upon and dying in each year of life, but of
exhibiting the experience of several highly interesting and impor-
tant sections of risks, and more especially with the view of show-
ing the nature and benefits accruing from the assurance of selected
healthy lives.

The subject generally is divided into the consideration of the
mortality on healthy lives — males — females — and diseased lives.

Assured Male Lives.

In treating of healthy lives — males — a comparison is made of the
actual number of deaths during each quinquennial period of life, with
the number which might have died according to the Carlisle table
and the Actuaries’ table of 1837. The rates of mortality at each
age, summed in periods of five years, are also compared. These
comparisons point out that the Carlisle table exhibits a greater rate
of mortality up to age fifty, and a lesser rate at higher ages than the
experience of the offices ; and that the Actuaries’ table, at nearly
all ages, is slightly greater than that of the Offices. A short com-

116

Proceedings of the Royal Society

parison is made of the rates of mortality of male lives according to
the three English life tables and that derived from the population
of Scotland, already referred to, with the mortality of the selected
healthy assured males of the ten Scottish offices. A very general
view of the benefits of selection is thus obtained. The assurances
on healthy male lives are divided into two classes — assurances with
profits, and assurances without profits ; the mortality of the u with
profit ” class exhibiting results in a highly favourable direction, and
of the “ without profit” class in an ^favourable direction — the one
being 10 per cent, and 7 per cent, less than the Carlisle and Actuaries’
tables respectively, and the other about 12 and 13 per cent, greater.

The foregoing comparisons of the actual and computed number
of deaths at each year of life are reclassified in another form, so as
to exhibit the actual and computed deaths out of the entrants at each
age , and thus show how far one aggregate table of mortality expresses
or represents the experience of its several parts or sections. These
comparisons are made with the Carlisle and Actuaries’ tables, from
which it will be seen that neither table accurately measures the
experience of sections of entrants. Young entrants exhibit a greater
mortality than estimated by either table. There is, at same time,
exhibited a similar comparison of the experience of the ten offices,
derived from the aggregate male lives, reapplied to the several
sections of entrants, which points out in a still more marked manner
the inappropriateness of one aggregate table of mortality to measure
the experience of its sections. There is also exhibited the extent
of the deviations, favourable as well as unfavourable, in each yean
of the assurances , from which it will be seen that the deviations
are highly favourable during the first four years, and that after the
fourth year they are almost always ^favourable.

Assured Female Lives.

In considering the mortality of females, there is, in the first place,
given a comparison of the difference between the mortality of males
and of females of the population, and of the Actuaries’ table of 1837,
pointing out that a nearly similar relation exists between the results
of these tables with that experienced between male and female
assured lives in the Scottish offices, viz., a greater mortality of
female life up to age forty-five. On the other hand, the male arul

117

of Edinburgh, Session 1869-70.

female Government annuitants of 1829 and of 1860 exhibit a greater
mortality of male life at all ages. An explanation of these dif-
ferences is offered. A comparison is then made between the actual
number of deaths and rate of mortality, of healthy assured females,
with the computations according to the Carlisle and Actuaries’
tables. There is, at same time, given a table, showing the favourable
and unfavourable deviations of the one aggregate table of mortality,
as a measure of the experience of sections of entrants. From this
table it will be seen that neither the Carlisle nor the Actuaries’ table
correctly measures the mortality of female assurants under age thirty -
five; and it will be inferred from the results given, that the table,
based upon the aggregate experience of assured female lives, cannot
measure the aggregate experience and at same time accurately re-
present the mortality of its sectional parts.

Total Lives — Males and Females.

After the usual comparisons of the actual and computed number
of deaths and of the rates of mortality, according to the Carlisle and
Actuaries’ tables, there is given a view of the rates of mortality expe-
rienced on assurances effected with participation in profits and with-
out participation, and an explanation is given of the reason of the
greater mortality of assurances without profits, by pointing out that
a very much greater mortality has been experienced on assurances
(without profits) effected for temporary periods, averaging about 40
per cent, on lives under age 50. The relation of the aggregate to
the sectional experience, as in the case of male and female lives
separately, is shown with similar results. A very full comparison is
thereafter effected between the mortality of assured lives with the
mortality of the population. After comparing these aggregate expe-
riences, a comparison is made between the rate of mortality expe-
rienced on assured lives, excluding the light mortality of the first
year, first two years, &c., of the assurances, and the general aggre-
gate rate of mortality of the population, wdth the view of pointing out,
in this form , the relation of the mortality of assured lives, after the
effects of selection have subsided, to the mortality of the population.
The effect of selection is thereafter considered in its proper manner,
and comparisons made between the mortality of persons in the
same quinquennial period of life, but arranged according to the

VOL. VII.

Q

118

Proceedings of the Royal Society

duration of the risks, showing that the light mortality during the
years while selection is in operation is balanced by a heavier mor-
tality thereafter, and showing further that that heavier mortality
is considerably greater than the general average mortality of a
single aggregate mortality table. These are exemplified in various
forms. The comparisons, however, are all based upon lives once
assured. There is, finally, given in one view the rate of mortality
experienced on all entrants of each age, during each year of assur-
ance, as the true exponent of the rate of mortality on assured lives,
along with five abridgments of the same, in the case of persons
assuring at each quinquennial age.

Causes of Death.

There is also given the intensity of the causes of death at each
age, and the relation of the deaths of assured lives, from various
causes, to the deaths of the male population of Scotland, pointing
out the several orders of disease in which the mortality of assured
lives is greater or less than the population. There is also given, in
a general form, the effects of selection upon the various causes of
death, pointing out those in which selection appears to have been
of greatest benefit.

Diseased Lives.

The usual comparisons are made of the actual with the computed
number of deaths, and also with the rates of mortality, pointing out
that the mortality on diseased lives is greater than on healthy lives
by about 20 per cent. The diseased lives were thereafter broken
up into sections, according to the nature of the imperfections for
which the extra charge was made, and showing the rate of mortality
experienced on four such classes. For two of these classes — un-
favourable personal history and gout — and also for the general class
of diseased lives, the law of mortality is given, as well as the
annual premium for assurance of L.100 at death, showing the extra
charge for such classes of lives.

Years of Life.

All the foregoing methods of comparing actual with computed
results have dealt with numbers of deaths. A method is pointed out

119

of Edinburgh, Session 1869-70.

for making comparisons of the actual years lived, with the computed
number according to any table. Examples are given in the case of
entrants at age 25, 30, 35, 40, 45, and 50.

Interpolation.

A description is given of the methods of deducing, and of practi-
cally applying, two processes of interpolation. One of them is based
upon the principle that the quantum of mortality in each decennial
period of life, in the adjusted and unadjusted results, shall agree.
The second principle is based upon a formula, which expresses the
number living in the law of mortality, at any age, in terms of con-
stants, and the complement of life at that age. The formulas for
several differences are given in both cases, and the results applied
to the total assured lives in the general mortality experience of
the English and Scottish Assurance Offices.

2. Notes on Indian Society and Life in the Age when the
Hymns of the Bigveda were composed. By John Mnir,
D.C.L., LLD., Ph.D.

(. Abstract .)

The paper began by stating, that although the hymns of the
Rigveda exhibit a simpler and less developed stage of religious be-
lief and conception than we find in the works of the earliest Greek
poets, and a system of ideas wildly diverse, both from the my-
thological forms and the theosophic opinions, of the later Indian
pantheon, and of subsequent speculation ; and although many of the
customs and practices of that early age are different from those of
later times, we are not to suppose that in the former period the
condition of society was of a very primitive description. On the
contrary, there are many signs of a considerable progress in civilisa-
tion and culture then existing. The opinion of the late Pro-
fessor H. H. Wilson on this head was then quoted ; and as one proof
in support of the position, the variety and occasional elaborateness of
the metres in which the hymns are composed was referred to.

1. Some account was then given of the country occupied by the
Indians of the Yedic era — of which a considerable portion is con-

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Proceedings of the Boyal Society

sidered to have been cultivated, though much was also covered by
forests — and of their villages and cities, or fortified places, and their
houses.

2. A sketch was then given of the manner in which a priest of
the Yedic age may be supposed to have spent the greater part of
the night watching for, and hailing, with hymns and offerings, the
appearance of the several deities, the Asvins — Ushas (the Dawn),
Agni (Fire), Surya (the Sun), &c., at the times when they were
supposed respectively to manifest themselves.

3. The discrepant opinions of two Sanscrit scholars, Professor Max
Muller and Dr Bollensen, on the question whether or not the
Indians made images of their gods during the Yedic age, are adduced,
but it was considered that the question is not ripe for decision.

4. It was next stated that this tract of country was divided into
numerous principalities, governed by their respective kings, who
appear to have lived in considerable state, and. to have been possessed
of a good deal of wealth, both in cattle and goods of different
descriptions.

5. Deference was made to the existence of both rich and poor in
the communities, and some verses, in praise of liberality to the latter,
translated from the original, were read.

6. Some particulars relating to domestic relations, and life and
manners, were then given. Polygamy appears to have existed, but
not of course as the rule. It was considered a misfortune for a woman
to grow old unmarried. Women appear, sometimes at least, to have
been allowed to choose their own husbands. According to a hymn
of the Atharva-veda, the remarriage of widows seems to have been
permitted ; and from a verse of the Eigveda, it appears probable that
a widow could marry the brother of her deceased husband, when the
latter had died childless. Allusions to conjugal infidelity and
sexual immorality occur.

7. It was stated that considerable attention seems to have been
paid to personal decoration, as reference is made, in various places,
to elegance of dress, and to the use of jewels. No mention is made
of cotton as a material for clothing; though, as the plant is con-
sidered to be indigenous in India, and the use of light cotton cloth
seems essential to comfort in so warm a climate, it is probable
that it was well known. Wool is mentioned in various places.

of Edinburgh, Session 1869-70.

121

The hair appears to have been occasionally worn wound or braided
upwards in a spiral form.

8. Barley, at least, if not wheat also, and no doubt other grains,
were used as food. The flesh of kine also seems to have been eaten.
Wine (from what material distilled does not appear) was drunk by
people of the upper classes, contrary to the usage of the later
Hindus.

9. A hymn, descriptive of the variety of men’s tastes and pursuits,
was given in a metrical translation, in which, various professions
are mentioned, viz., those of poet, priest, physician, carpenter : the
construction of chariots is often alluded to; and working in iron or
other metals, and in hides, must have been common, as the mention
of weapons of war and other metal implements, and of leather, is
constantly occurring. Weaving, too, was of course practised, and
boat building understood, as boats are frequently referred to. The
caste system does not seem to have been developed during the earlier
part of the Yedic era ; but in a few of the later hymns Brahmans are
mentioned; and in one text the names of the four castes Brahman,
Rajanya, Yaisya, and Sudra, occur in conjunction. A free translation
was given of a hymn in which the Brahmans and their observances
appear to be satirised. From what precedes under head 8, it will
be seen that agriculture was practised, and specific references to it,
and apparently to irrigation as auxiliary to it, occur.

10. Playing at dice was a favourite amusement of the Yedic
Indians, as appears from numerous texts. A hymn, in which the
miseries of a gambler’s life are strikingly described, was given in an
English metrical dress. G-aily dressed dancers or actors are referred
to as exhibiting their performances.

11. Theft and robbery are alluded to as common offences.

12. As animals, wild or tame, mentioned in the Rigveda, kine,
horses, sheep, goats, dogs, deer, boars, buffaloes, apes, wolves, and
lions, are adduced. Elephants, too, are alluded to in the Rigveda,
certainly as wild, but whether or not as tame also is not so clear.
Among birds, pigeons, falcons, vultures, ducks, swans, and quails
are referred to.

13. It need scarcely be said that wars were frequent in the Yedic
age. Parts of two hymns translated in prose were read — one of them
in celebration of Indra’s prowess, and supplicating victory, and the

122 Proceedings of the Royal Society

second in praise of armour and the bow, &c. ; and a portion of one of
them was also given in verse. War chariots were in use, and banners,
defensive armour, and various kinds of offensive weapons, bows and
arrows, spears, &c., are referred to.

14. Finally, allusion was again made to the number and elaborate-
ness of the metres in the Eigveda; and as regards the occasional
beauty and variety of the illustrative imagery, the moral depth of
many of the sentiments, and the power of observation exhibited in its
contents, reference is made to the hymns to the Dawn, and to seve-
ral of those adduced in the course of the paper. In a few hymns
we find the beginning of speculation on the origin of all things.
One of these was communicated, rendered into English verse.

The following Gentleman was elected a Fellow of the
Society : —

John Winzer, Esq., Assistant Surveyor, Civil Service, Ceylon.

Monday , 21st March 1870.

The Hon. Lord NEAVES, Vice-President, in the Chair.
The following Communications were read : — -

1. On the Lake Basins of Eastern Africa. By Keith
Johnston, Jun., Esq., F.R.G.S.

1. Livingstone’s Recent Discoveries.

In 1866 the indefatigable Dr Livingstone is again in Africa, with
the determination of filling up the great gaps in our knowledge of
the lake region from Nyassa to Tanganyika, beginning the great
journey from which he has not yet returned.

News arrived in England, in September 1866, that the traveller
had, for a third time, entered the Eovuma river, and had succeeded
in penetrating for 130 miles from its mouth, where he had found a
friendly chief, whose residence he intended to make the starting-
point of his expedition to the northern end of Nyassa, and the
south of Tanganyika. A long period of silence then intervened,
during which we were ignorant of the whereabouts of the traveller,
till a report was brought to the east coast by some lying Johanna

123

of Edinburgh, Sessionl869-70.

men who had deserted him, that Livingstone had been murdered
near the south end of the lake. This report, however, was dis-
credited by the bead of the Eoyal Geographical Society, and a boat
expedition sent out by the Society, under the leadership of Mr
Young, confirmed the opinion of its untruth.

From his more recent letters, we learn that Livingstone passed
round the southern end of Lake Nyassa, where he seems to have
struck into nearly the old route of Lacerda and Monteiro, along
the water parting between the tributaries of the Zambezi and the
Nyassa.

Passing at a distance of about twenty miles to westward of Chin-
yanga, the furthest point which he had reached in his excursion of
1863 from Nyassa, he got into the valley of the Loangwa or Arangoa.
The greater part of Livingstone’s subsequent route is contained in
his letter of date July 1868. In this he says — “ Leaving the valley
of the Loangwa, which enters the Zambezi at Zumbo, we climbed
up what seemed to be a great mountain mass, but it turned out to
be only the southern edge of an elevated region, which is from
3000 to 6000 feet above the sea. This upland may be roughly
stated to cover a space south of Tanganyika of some 350 miles
square. It slopes to north and west, but I have found no part of
it under 3000 feet of altitude. The country of Usango, situated
east of the space indicated, is also an upland. . . . Usango forms
the eastern side of a great but still elevated valley. The other, or
western side, is formed by what are called the Kone Mountains,
beyond the copper mountains of Katanga.”

Livingstone continues — “ The southern end of the great valley,
enclosed between Usango and the Kone Mountains, is between 11°
and 12° south. In 11° 6' south, ascending from the valley of the
Arangoa, we were fairly on the upland.” This was perhaps in
January 1867, or about the middle of the rainy season here. He
writes— “As we advanced, brooks, evidently perennial, became
numerous. Some of these brooks went eastward, to fall into the
Loangwa; others went north-west, to join the Chambeze.” The
Chambeze, with all its branches, flows from the eastern side into
the centre of the great upland valley, “ which,” says Livingstone,
“ is probably the valley of the Nile. It is an interesting river,
helping to form three lakes, and changing its name three times in

124 Proceedings of the Royal Society

the 500 or 600 miles of its course. I crossed the Chambeze in 10°
34' south, and several of its confluents, north and south, quite as
large as the Isis at Oxford, but running faster, and having hippo-
potami in them.”

Livingstone reached a place called Bemba, on the plateau, in
February 1867, and fixed its position in 10° 10' south, 31° 50' east.
Proceeding northwards, in April 1867, he discovered Lake Liemba.
It lies in a hollow, with precipitous sides 2000 feet down, on the
northern slope of the upland. “ It is extremely beautiful, sides,
top, and bottom being covered with trees and other vegetation.
Elephants, buffaloes, and antelopes feed on its steep slopes ; whilst
hippopotami, crocodiles, and fish swarm in the waters. It is as
perfect a natural paradise as Xenophon could have desired. On
two rocky islands men till the land, rear goats, and catch fish.
The villages ashore are embowered in the oil palms of the west of
Africa.”

“ Four considerable streams flow into Liemba, and a number of
brooks, from 12 to 15 feet broad, leap down the steep bright red
clay, such are the rocks, and form splendid cascades, that made the
dullest of my attendants pause and remark with wonder.”

Livingstone does not give any note of the direction of these four
rivers, which flow into the lake ; but it appears a necessary con-
clusion, from its position, that these should have their rise on
the higher side of the plateau, and flow to the lake from the
east.

u The lake is from 18 to 20 miles broad, and from 35 to 40 miles
long. It goes off to north-north-west, in a river-like prolongation,
two miles wide — it is said to Tanganyika.” Livingstone continues
— “ I would have set it down as an arm of Tanganyika, but that
its surface is 2800 feet above the level of the sea, while Speke
makes the lake Tanganyika 1844 feet only.” The observation of
Livingstone here confirms the opinion of Mr Findlay, given in an
able paper read before the G-eographical Society in 1867, in which,
by a recomputation of the thermometer heights measured by Captain
Speke, he came to the conclusion that Tanganyika Lake was at an
elevation of 2800 feet above the sea; and that, since its fresh
waters must have an outlet, this would most probably be found to
be to northward.

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of Edinburgh, Session 1869-70.

Livingstone continues — “ I tried to follow this river-like portion
of Liemba, but was prevented by a war which had broken out
between the chief of Itawa and a party of ivory traders from
Zanzibar. I then set off to go 150 miles south, then west till past the
disturbed district, and to explore the west of Tanganyika, hut, on
going 80 miles, I found an Arab party, showed them a letter from
the Sultan of Zanzibar, which I owe to the kind offices of his
Excellency Sir Bartle Frere, late governor of Bombay, and was at
once supplied with provisions, cloth, and beads. . . . After peace
was made, I visited Nisama, the chief of Itawa, and having left the
Arabs, went on to Lake Moero, which I reached on the 8th Sep-
tember 1867. In the northern part Moero is from 20 to 33 miles
broad. Further south it is at least 60 miles wide, and it is 50
miles long. Banges of tree-covered mountains flank it on both
sides, but at the broad part the western mountains dwindle out of
sight.”

Lake Moero is the central one of the three on the Chambeze
river. The river runs into Lake Bangweolo, at the head of the
valley, and on coming out of it assumes the name of Luapula.
The Luapula flows down north, past the town of the Cazembe, and
12 miles below it enters Lake Moero. Passing up the eastern side
of Moero, Livingstone came to the Oazembe’s town. It stands on
the north-east bank of the lakelet Mofwe. This is from 1 to 3
miles broad, and nearly 1 long. It has several low reedy islands,
and yields plenty of fish, a species of perch. It is not connected
with the Luapula or Moero.

“ I was forty days at Cazembe’s,” says Livingstone, “ and might
then have gone on to Lake Bangweolo, which is larger than either
of the other lakes, but the rains had set in, and this lake was
reported to be very unhealthy. I then went north for Ujiji, where
I have goods, and I hope for letters ; for I have heard nothing from
the world for more than two years ; but when I got within thirteen
days of Tanganyika, I was brought to a standstill by the abundance
of water in front. A native party came through and described the
country as inundated, so as to be waist deep, with sleeping places
difficult to find. This flood lasts till May or June. At last I
became so tired of inactivity that I doubled back on my course to
Cazembe.”

VOL. VII,

126 Proceedings of the Royal Society

In this attempt to reach Ujiji, Livingstone appears to have in-
tended to reach the west side of the Tanganyika by the road which
Captain Speke reported from Warruwa (evidently the Rua of
Livingstone) to the ferry by which he had crossed from Ujiji ; and
it was apparently during this attempt that Livingstone obtained,
by actual observation, the report which he gives of the lower course
of the Luapula. He says — “ On leaving Moero at its northern end,
by a rent in the mountains of Rua, the river takes the name of Lua-
laba, and passing on north-north-west forms Ulenge in the country
west of Tanganyika. I have only seen it where it leaves Moero,
and where it comes out of the crack in the mountains of Rua.”

The flat inundated country beyond this point seems to have been
his turning-point. He says — “ To give an idea of the inundation
which, in a small way, enacts the part of the Nile lower down, I
had to cross two rivulets, which flow into the north end of Moero —
one, the Luo, had covered a plain abreast of Moero, so that the
water on a great part reached from the knees to the upper part of
the chest. The plain was of black mud, with grass higher than
our heads. We had to follow the path which the feet of passengers
had worn into deep ruts. Into these places we every now and then
plunged, and fell over the ankles into soft mud, while hundreds
of bubbles rushed up, and bursting emitted a frightful odour.”

Having returned to Cazembe’s in about February or March of
1868, Livingstone seems to have gone south at the beginning of
the dry season, to Lake Bangweolo, from which his letter is dated
in July 1868.

The next news we have of the great traveller is in a letter from
Ujiji, on Lake Tanganyika, dated May 1869. He appears to have
reached this point by the eastern side of Tanganyika, not by the
western as before attempted ; since he writes in the above letter, u As
to the work to be done by me, it is only to connect the sources
which I discovered from 500 to 700 miles south of Speke and
Baker’s, with their Nile. The volume of water which flows north
from latitude 12° S., is so large, that I suspect I have been working
at the sources of the Congo as well as those of the Nile. I have
to go down the eastern line of drainage to Baker’s turning-point.
Tanganyika and Nyige Chowambe (Baker’s?) are one water, and the
head of it is 300 miles south of this. The western and central

127

of Edinburgh, Session 1869-70.

lines of drainage converge into an un visited lake west or south-west
of this. The outflow of this lake, whether to Nile or Congo, I
have to ascertain.” From the above it would appear that Living-
stone had made an excursion northward from Ujiji, either by land
or on the lake, to ascertain the union of the Tanganyika with the
Albert Nyanza.

News has since been received, which shows that Livingstone was
still at Ujiji in July 1869. In January of this year, a report arrived
from the west coast of the continent, describing the fearful end
which the traveller had come to, of his being quartered and burnt ;
but this report turns out to be an old story of date June 1868, with
its plot laid on the Zambezi, and at this time we know that Living-
stone was safe on the Chamheze lakes.

2. The Sources of the Nile.

The main point of interest in the latest travels of Livingstone,
and that which gives to them a distinctive importance over the
great accomplishments of his former journeys, is that in these
Livingstone has undoubtedly visited and beheld the long sought-
for sources of the Nile. It is true that there is considerable doubt
as to which of the basins that he has explored will ultimately be
acknowledged as the cradle of the Nile ; but this at least is certain,
that the real head streams have been visited by Livingstone, and
the long-vexed question has, by these last explorations, resolved
itself into a choice between two or perhaps three main streams.

Livingstone himself has apparently no bias in favour of one or
other, so that the discussion is a perfectly open one. The three
rival head streams are — first, the feeders of Lake Liemba; and,
second, the Chambeze and its lake chain, both of which rise near
the eastern edge of the great longitudinal plateau of the side of
Africa next the Indian Ocean ; the third is the source recently
claimed for the Nile by Dr Beke, in his “ Solution of the Nile
Problem,”* the Great Casai or Kassabi river, which rises nearer
the Atlantic side, in 12° S. Of the first of these, the feeders of
Lake Liemba, we may say, with almost absolute certainty, that
they are tributaries to the Nile, and it is most probable that they
are the sources of that river. Livingstone has found these rivers
* Athenaeum, February 1870.

128 Proceedings of the Royal Society

flowing into Lake Liemba; a river-like prolongation unites Liemba
and Tanganyika, these two appearing to be at the same level • then
Tanganyika and Nyige Chowambe, which is evidently the Albert
Nyanza, are one water, and that the last is a reservoir of the White
Nile is undoubted.

The union of the second presumptive head stream, the Cham-
beze, with the Nile, is less apparent ; indeed, the balance of evi-
dence seems to show that it must be the head of the other great
river of Africa, the Congo. If the Chambeze prove to join the
Nile, then the streams to the Lake Liemba become mere tributaries,
since the course of the Chambeze is by far the longer of the two.
The feeders of Liemba and the Chambeze rise, however, side by
side, on the eastern plateau. The Chambeze flows down into the
central valley through Lake Bangweolo, and then northward
through Lake Moero. Livingstone describes Lake Moero as begin-
ning 12 miles below the position of the town of Lunda, the capital
of the Cazembe (lat. 8° 40' S., long. 28° 20' E.), whose position
may be laid down with tolerable accuracy from the former journeys
of the Portuguese travellers. Since Livingstone proceeded north
from Cazembe’s town, along the eastern shore of Moero, in his
attempt to reach Ujiji in 1867, the great bulk of this lake must lie
to the westward of the meridian of Lunda, or about 120 miles to
westward of Tanganyika. Dr Livingstone has seen the river at its
outflow from the lake, and also at the point where it emerged
from the crack in the mountains of Bua, when, according to his
own observation, the river turned to north-north-west to form
Ulenge, a third lake or marsh in the country west of Tanganyika.
This north-westerly turn would carry the river quite out of the
direction of the Nile basin, and the higher side of the continent
being to the east, the probability is, that the river continues to
curve to the west.

Again, the valley of the Chambeze, in the plateau where Living-
stone crossed it, is, no doubt, one of the greatest hollows in the
high land, so that the height of the river bed here may be
taken at 3000 feet, the lowest level of the limits which Living-
stone gives to the undulation of the plateau, or only 200 feet
above the level of Tanganyika. Descending into the great
valley to Lake Bangweolo from the plateau, the Chambeze must

of Edinburgh, Session 1869-70.

129

have a considerable fall; from Bangweolo to Moero there must
be a second descent. The Cazembe’s country, which extends
round to the south of Tanganyika, is described as flat, and
its rivers are currentless and stagnant. If Moero were at a
higher level than Tanganyika, would not the river which leaves
it take a course over the level country instead of facing towards,
and making its way through a crack in the mountains northward?
Seeing that the river does force its way through these mountains,
the presumption is, that Moero is at a lower level than Tanganyika ;
and if this be the case, the river which descends from it through
the mountains can never again ascend to the level of the Nile lakes
to join them, but must find some other course.

With regard to the third advocated source, the Kassabi river, of
which Dr Beke affirms it to be his belief that it is the head stream
and upper course of the Nile of Egypt, the difficulties of its joining
the Nile appear to be even greater than the last. The upper course
of this river only has been explored. It springs in the Mossamba
Mountains, which are on the inner borders of Angola and Benguela,
its sources being close to those of the Quango river, a tributary of
the Congo. The Kassabi is known to flow northward as far as 8°
S. to westward of the capital of the Muata Yanvo,

Dr Livingstone crossed its head on his journey from the Zambezi
to Loanda ; and the reports which he collected from the subjects
of the Muata Yanvo’s kingdom, all tend to prove, that whatever
direction its middle course may take, in its lower course the Kassabi
flows round to westward, and is joined by the Quango. The trader,
G-raca, who penetrated to the Muata Yanvo capital in 1846, says,
that u the territory of this chief is shut in by the great rivers
Kassabi and Lurua (a tributary of the Kassabi).” “ These rivers,”
he continues, u flow into the river of Sena” (the Zambezi). The
latter part of this statement we now know to be incorrect ; but,
taken as a whole, it indicates an easterly bend in the lower course
of the river to enclose the kingdom of the Yanvo on the west and
north, and to flow as if to the Zambezi. The Hungarian traveller,
Ladislaus Magjmr, has penetrated furthest of the three who have
visited this region, and his information seems to agree well with this
last. He reports that the Kassabi, after forming the waterfall of
Muewe (in about 11° S. latitude), bends gently to northward ; but

130 Proceedings of the Royal Society

further on takes an easterly direction in its lower course, and
reaches a breadth of several miles at the place where it touches upon
the extensive lake Mouva or Uhanja.

Now, if we turn the Kassabi river eastward in latitude 8° S.,
in agreement with the above description, we find that it meets the
position which Livingstone’s letters give to Ulenge, the lake or
marsh to which the Chambeze river flows, and whose waters Living-
stone tells us by report, in his recent letters, are taken up by the
Lufira, a large river wThich, by many confluents, drains the western
side of the great valley.

Is not the Lufira , then, the lower course of the Kassabi, and the
Lake Ulenge of Livingstone, whose waters are taken up by the
Lufira — the Uhanja lake of Magyar, which the Lower Kassabi
touches upon ?

The same difficulties which appear in the way of the Chambeze
river and lake chain joining the Nile, hold also against the Kassabi,
which, from the above reports, would seem to join this river at Lake
Ulenge.

Next, the question arises, if these rivers do not form a part of
the Nile system, where then shall we find an outlet for them ?
The answer to this is plainly, in the Congo river.

The Congo was described by the Jesuit missionaries, who first
visited its mouth, as so u violent and so powerful from the quantity
of its waters, and the rapidity of its current, that it enters the sea
on the west side of Africa, forcing a broad and free passage (in
spite, of the ocean) with so much violence, that for the space of 20
leagues it preserves its fresh waters unbroken by the briny billows
which encompass it on each side.” In the introduction to his nar-
rative of his expedition to the Congo, Tuckey says, “ If the calcula-
tion he true that the Congo, at its lowest state, discharges into the
sea two millions of cubic feet of water in a second, the Nile, and
the Indus, and the Granges, are hut rivulets compared with it, as
the Granges, which is the largest of the three, discharges only about
one-fifth of that quantity at its highest flood.” This estimate is
greatly exaggerated, but Tuckey actually found that this vast river
has a width of two, three, or even four miles, whilst flowing with a
current of two or three miles an hour (p. 342), and this not at its
mouth, but inland beyond the mountainous coast regions. Such a

of Edinburgh, Session 1869-70. 131

vast river cannot be formed in a short course, but must have its
rise far in the interior of the continent.

If we take the Kassabi river and its drainage to the Nile, where
shall we find a sufficiently lengthened course for the Congo?
Tuckey’s unelaborated notes give the opinion that the “extraordi-
narily quiet rise of the river shows it to issue from some lake, which
had received almost the whole of its waters from the north of the
line;” and again, he says, “ I cannot help thinking that the Congo
will be found to issue from some large lake or chain of lakes, con-
siderably to northward of the equator.” The reason of Tuckey’s
supposition that the lakes, which evidently maintain the volume
of water in the Congo, would be found north of the equator, is
this, that he found the rising of the river beginning on the first
days of September. At the time of his journey little or nothing
was known of the times of the rainy seasons in Central Africa
from actual experience. Since then the traveller Burton has told
us (in his account of the expedition to Tanganyika, R. Gr. S.
Journal, vol. xxix.), that in the latitude of Tanganyika the rain
sets in at the end of August, lasting till May; and Livingstone
says, in his latest letter, that he did not proceed to Lake Bangweolo
from the Cazembe’s capital, where he arrived about the middle of
September, because the rains had set in. Lake Ulenge lies between
these latitudes, so that the rise of the waters of the Congo on the
first of September is perfectly explainable without the necessity of
taking its reservoir lakes to the north of the equator ; if the lakes
were there, the rise of the Congo would occur at a much earlier
period of the year, as we shall afterwards notice, and, indeed, the
space in which Lake Ulenge lies, seems to be the only one on the
continent whose rainy season would agree with the observed rise
of the Congo.

3. The Physical Features of the Lake Legion and the Lakes.

The great highlands of the world encircle and turn their steepest
verge towards the Pacific and Indian Oceans ; the slope is gentle
towards the great plains which surround the Atlantic and Arctic
Seas. Africa is no exception to this rule, since it presents to the
Indian Ocean the abrupt descent of the plateau which extends
along its eastern side from the Cape Colony to Abyssinia, north-

132 Proceedings of the Boycd Society

ward. It is true that the whole of South Africa is a plateau, with
a general elevation of about 3500 feet, and that the outer edges of
it rise steeply from both coasts ; but the eastern side is the higher
of the two, and the law of a general slope towards the Atlantic is
maintained on its surface. The Lake Eegion occupies the central
part of the eastern, or higher side, of the South African plateau,
and here the line of descent to the coast-land of the Indian Ocean
is marked continuously from north to south ; first by the south-
ward continuation of the outer slope of the Abyssinian table-land,
then near the equator by the edge on which the great mountain
peaks of Kenia and Kilima Ndjaro rise; farther south by the
Bubeho Mountains, up which Burton and Speke ascended to the
plateau; and then by the N’jesa Mountains, which wall in the
Lake Nyassa. Farther south the cataracts of the Shire river, 35
miles in extent, show where this river tumbles over the edge of
the plateau, and the Zambezi breaks through it at the narrows of
Lupata. Below this steep edge the coast-land slopes in gently to
the sea, and is diversified by wide plains or scattered hill ridges.

The high surface of the South African plateau inland is hollowed
out in the wide high valleys which contain its lakes and great
rivers. The most northerly of these depressions in the Lake Eegion
is that of the great lake reported by the ivory trader Piaggia, who
approached within 60 miles of its northern shore. This lake ap-
pears to lie in a high valley on the northern edge of the plateau
of South Africa, or rather in a recess of the northern lower land,
partly shut in by the slopes of the plateau southward, and the
mountain range which the traveller saw rising to south-westward
beyond the lake, is perhaps only the steep northern edge of the
southern plateau here.

The wide depression in which the Victoria Lake lies is shut in
eastward by the continuation of the Abyssinian highland into the
South African plateau. This valley appears to include the basin
of the Bahari N’go, which is believed to be a vast salt marsh, or
perhaps a sort of backwater of the Victoria Lake, and its slope is
to north-westward, towards the angle of the northern lower land
which is formed by the inner side of the Abyssinian highland run-
ning north and south, and the northern edge of the plateau of
South Africa, which has a direction from east to west.

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Between these two northern depressions lies the deeper and
narrower valley of the Nile, which contains the Tanganyika and
Albert Lakes. The beginning of this depression may be said to
be at Lake Liemba, which lies sunk 2000 feet down in the edge of
the plateau north of Lake Nyassa; then it opens out into a wider
valley to the east of Southern Tanganyika, but again closes in the
northern part of that lake, and is only a little wider where the
Albert Lake is sunk between the edge called the Blue Mountains
and the part of the plateau which separates this depression from
the higher one of the Victoria Nyanza. To south-west of Tan-
ganyika the narrow valley of the Upper Nile appears to have an
opening into that one which contains the Chambeze and its lakes,
made known by Livingstone, in the low-lying country of the
Cazembe.

This valley of Bangweolo and Moero Lakes seems to be most com
pletely surrounded on all other sides ; by the high plateau of Usango
eastward, by a narrower portion of it called the Muchinga Moun-
tains southward, and again by the Kone Mountains, and a broader
part of the plateau, the copper country of Katanga, on the west.
The only other opening or outlet into this valley is apparently the
rent in the mountains of Kua, through which the river makes its
escape to join Ulenge. Westward is another and wider depression
— the wide high plain which forms the kingdom of the great
Muata Yanvo, watered by the Kassabi Biver, and stretching out
between the Mossamba Mountains where the river rises, and the
plateau of Katanga, which separates the Yanvo’s from the Cazembe’s
valley.

The Zambezi valley closes the Lake Region southward. The
Zambezi is the exceptional river of Africa, since it breaks through
the higher side of the plateau to reach the Indian Ocean. Its
sources, however, seem to be on the inner side of the plateau,
springing on the western slopes of the Kone Mountains, and flow-
ing first to the south-westward. The vast basin of this river
(about 568,000 square miles) is comparable to that of the Volga,
and would make more than one hundred river basins such as that
of the Thames.

On the west, the waterparting of the Zambezi valley at Lake
Dilolo is apparently but little elevated above the plain of the Muata

vol. vii. s

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Proceedings of the Royal Society

Yanvo’s kingdom ; but as the valley descends eastward its northern
side appears to rise to the range of the Kone and Muehinga Moun-
tains, and the valley becomes deeper and narrower where it cuts
through the high edge of the plateau eastward, to reach the coast.

Lake Nyassa, a tributary lake of the Zambezi, lies in a deep
longitudinal hollow near the edge of the plateau, only retained
by the high barrier of the N’jesa Mountains. The narrow valley
of the Shire river, which flows from it, continues this hollow to
the Zambezi. Lake Shirwa is similarly situated, but has no outlet,
and in consequence its waters, in distinction to the fresh sweet
water of the other lakes, are brackish. The approximate area of
each of the eleven great lakes of this region, so far as their
extent is known, is as follows : —

Victoria Nyanza, .

Square Miles.

29,900

Albert Nyanza,

25,400

Piaggia’s Lake,

11,000?

Tanganyika,

10,400

Nyassa,

8,600

Bahari N’go,

6,000 ?

Bangweolo, .

3,700

Moero, .

2,000

Ulenge,

1,000?

Shirwa,

800

Liemba,

700

99,500

The whole extent of water surface in this Lake Region is then
nearly 100,000 square miles, an area not far short of that of the
British Isles. A more definite notion of the great extent of these
inland seas of fresh water may perhaps be obtained, if we observe
that a direct passage across the Victoria Lake, from shore to shore
(in its presently believed extent), corresponds in length to a voyage
across our North Sea from Hull to Rotterdam, or from the east-
most land of Scotland at Peterhead, to the Norway coast.

The more important of the rivers of the Lake Region have been
noticed in speaking of the routes taken by the travellers who have
discovered them. One of the main hindrances to the exploration

135

of Edinburgh, Session 1869-70.

of South Africa, is the difficulty of making use of these rivers as
highways into the continent. The coast rivers of the Lake Begion,
or, indeed, of the whole of Eastern Africa, are barred at their
mouths by the aggregated debris which they carry down, raised in
banks on the coast between the downward current of the river and
the opposing monsoon, or trade wind, blowing towards the coast.
If this bar is passed at the mouth, still the navigation even of the
largest rivers cannot cross the edge of the plateau where cataracts
and rapids form a new obstruction. The vast lakes of the interior,
and their great connecting rivers, however, present great lines of
navigable water, which in a higher civilisation would be utilised
for busy traffic, the line of the Nile basin in the Tanganyika and
Albert lakes alone affording an unbroken voyage of about 900
English miles.

Piaggia, the traveller who has been nearest to the great lake
which lies to the north-west of the Albert Nyanza, reports a great
river called the Buri, flowing to westward, at some days’ journey
from Kifa (his furthest point), and which issues out of his great
lake. The same river has been reached, at some distance from its
supposed outlet, by the brothers Poncet (French ivory traders), who
have long trafficked in this region, and they express the opinion
that this river unites the equatorial lakes with Lake Tchad, by
means of the Shari river. This they proposed to prove by an ex-
pedition on it in boats. The question, What becomes of this great
river? which, at its outlet from the lake, is so large as to be only
passable in boats, is an interesting one. It is certainly no tribu-
tary of the Nile, and the two most probable lower courses which
it may have are those of the Shari to Lake Tchad, or of the Benue
river to the Niger. If it ultimately proves to flow to Lake Tchad,
it will give a striking evidence of the vast amount of evaporation
which must exist in the region of that lake, since it has no outlet ;
but the Benue river seems to be its most probable course, for at its
confluence with the Niger, the Chadda, or Benue, is the larger river.
The Ogowai river is also a possible lower course for the Buri, but
if the lake reported by Piaggia be, as we suppose, on or beneath the
northern edge of the plateau of South Africa, it seems only natural
that the river from it should seek the lower land to northward,
than turn westward along the northern slope of the plateau.

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Proceedings of the Royal Society

4. The Nature of the Surface of the Lake Region — Its Great Fertility.

Africa, the only one of the continents which has a large extent
of land on each side of the equator, presents a series of zones, each
of which has a different nature of surface, and these belts correspond
very closely with one another on the opposite sides of the equator.
The central area of Africa, below the equator, in the zone of long
rainy seasons, or of almost constant rain, is a region characterised
by dense forests, and a most luxuriant overgrowth of vegetation,
comparable to that of the selvas of the Amazon River in South
America, which occupy the same equatorial position on the globe.
To north and south of this forest zone is a belt of less wooded
country, merging gradually into open cultivated or pasture lands.
Next, these grass lands pass into the two great almost rainless
deserts of the Sahara in the north, and of the Kalahari southward.
Beyond the deserts, at the extremities of the continent, the outer
slopes of the Cape Colony in the south, and of the plateau of
Barbary, the “ Tell ” country, in the north, present a second zone
of fertile and cultivated country.

The Lake Region extends from this central forest zone, in which
the equatorial lakes are formed, through the more open belt of less
wooded country southward, as far as the Zambezi valley, and this
area is almost everywhere adorned with the choicest natural
varieties of shady forest, with luxuriant underwood, or clumps of
trees with rich grassy plains between.

5. Climate of the Lake Region.

Nowhere more than in this central region of Africa are the sub-
jects of temperature, rain, and winds, more closely interwoven, or
mutually dependent, the one upon the other. In the passage of
this area beneath the sun, a low atmospheric pressure is produced
by an ascending heat column, and by the condensation of vapour in
this ; the winds flow into the ascending column, and bring with
them the moist air of the ocean, which, condensing in copious
floods of rain, reduces the temperature, whilst causing a further
opening, into which the winds blow with increased power. The
area of low pressure, with its attendant circumstance of winds and
rains, always tends towards that part of the continent which is

137

of Edinburgh, Session 1869-70.

vertically beneath the sun’s rays, and thus moving up and down
the face of the land within the tropics, gives the wet and dry, the
cold and hot, seasons of the year in this region. On the coast
the seasons are sharply defined : the continental and the oceanic
monsoons divide the year between either a single or a double
wet and dry season ; but in the high interior plateau in which the
lakes are situated, the winds are drawn into the pendulating area
of low pressure from the ocean, nearly throughout the year, and it
is only when extreme limits of the tropical zone come directly
under the sun, that a higher barometric pressure, an outflow of the
winds, and a consequent dry period, is experienced here.

In the coastland under the equator, the country explored by the
German traveller Brenner, the mean temperature of the year is
850,1 (mean of three daily observations), the highest observed tem-
perature (of 920,8) having occurred in January, and the lowest
(730,4) in May. The rainy season here sets in with the south-east
monsoon in April, and lasts till the end of June. The second
rainy season, which we shall notice, taking place farther south in
September and October, is almost lost at the equator. The north-
east monsoon brings a cloudless sky of clear blue, and begins to
blow here in November, lasting till March, and in this season rain
is never thought of.

At Zanzibar Island, six degrees south of the equator, the mean
temperature of the year is nearly 80° Fahr., rising in January to
an average of 83°, falling in July to 77°; and it has a double rainy
season, a stronger in March, April, and May, when the column of low
pressure has passed this latitude in moving northward ; and again
in a weaker in September and October, when the low pressure
passes in its southward course, at which times the monsoon winds
change from the north-east, blowing out of Asia towards South
Africa, to the south-west, blowing from Africa towards the Asiatic
continent. In the low countries, beneath the edge of the plateau,
about Zungomero, Burton tells us that the rain is constant, except
for a single fortnight in the month of January; at most times the
sun shines through a vale of mist with a sickly blaze and a blister-
ing heat, and the overcharge of electricity is evinced by frequent
and violent thunderstorms, so that the climate of Zanzibar is
equally ruled by these two great land masses. On the Mozambique

138 Proceedings of the Royal Society

coast the winds are again ruled by the African continent only, and
the year is divided into a dry and wet season. From April till
November the undeflected south-east trade wind blows upon this
coast, and either from the lowness of the land or the shelter it
obtains from the high island of Madagascar, this wind brings the
dry season. From November to March the north-east monsoon,
here at its furthest south limit, having passed over the warm
Indian Ocean, brings the rainy season.

On the plateau inland, the climate and seasons are different.
The mean annual temperature of the table-land in the neighbour-
hood of the Victoria Nyanza was found by Speke and Grant to be
only about 68° Fahr., a temperature not greater than that of the
south coasts of the Mediterranean, a climate not unsuitable to
Europeans, since a hot summer in England is far more oppressive.

The rainfall in this high region is also an exceptionally small
one for a tropical country, having been found to be only about 49
inches, or not so much as that of many parts of England, and this
may partly be accounted for by the fact that this part of Africa is
deprived of all rain from northerly winds, which come overland, and
the prevailing east winds lose much of their moisture on the high
eastern slopes of the plateau before reaching this region.

The traveller Burton gives an account of the very different
climate of the deeper valley of the Tanganyika Lake. Here the
rains divide the year into two unequal portions of eight and four-
months, — namely, the wet monsoon, which commences with violence
in the end of August, and lasts till May, and the dry hot weather
which completes the year. During the wet monsoon (1858) the
prevalent winds were constantly changing. The most violent
storms came up from the south-east or south-west of the plateau of
Umyamwesi, to westward of the lake. Here he says that there are
but two seasons, a summer and winter, and the rains begin in the
middle of November. u The moisture bearing wind in this part of
Africa is the fixed south-east trade, deflected into a periodical
south-west monsoon.” Further south in the Cazembe’s country,
the rainy season appears from Dr Livingstone’s letter to begin in
September, and he says that the floods in the country west of Tan-
ganyika last till May or June. In the northern part of the Zambezi
valley the traveller Silva Porto found the rains set in on the

of Edinburgh, Session 1869-70. 139

Arangoa river in February, and they ended with him on the
eastern side of the Nyassa in June.

On the Zambezi river in the Makololo district, Livingstone
observes that the rain follows the course of the sun, since it falls
first in October and November when the sun goes over this zone
southward. When the tropic of Capricorn is under the sun in
December, it is dry, and December and January are the months in
which the droughts are most severe in the countries between the
Zambezi and the Kalahari. When the sun turns again to north-
ward in February, March, and April, the great rains of this part
of the Zambezi valley are experienced.

6. Population.

The Lake Kegions of Africa are well peopled. Behm, in his
“ Geographical Year-book,” has estimated the population of that
part of Eastern Africa, which lies between the equator, the line of
Lake Tanganyika, the Cazembe’s country, and the Portuguese
colonies on the coast, at 3,500,000. This gives a density of popu-
lation of about six to a square mile, but is apparently rather under
than above the mark. It is true that the slave trade must reduce
and disturb the population of this part of Africa to a great extent,
since many thousands of slaves are annually brought down to and
exported from the harbours on the coast ; but, on the other hand,
travellers in this region report a continuous population. Captain
G-rant describes the part of the Lake Region which he traversed as
too thickly peopled to harbour many wild animals; the shores of
Lake Tanganyika are, according to Speke, “ thickly inhabited by
numerous tribes ;” and in his voyage on Lake Nyassa, Livingstone
says, “ Never before in Africa have we seen anything like the dense
population of the shores of Lake Nyassa, especially in the south.
In some parts there seemed to be an unbroken chain of villages.
On the beach of well-nigh every little sandy bay, black crowds
were standing gazing at the novel spectacle of a boat under sail.”

The inhabitants of the Lake Region appear to belong entirely to
the negro or negroid race, but are closed in to north and south by
peoples of a different stamp.

The Niam Niams who inhabit the country north of the lake
reported by Piaggia, and west of the Albert Lake, who had formerly

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Proceedings of the Royal Society

the reputation of being “ half men and half dogs, with a fan-like
tail,” and of having a disposition to eat their fellow-creatures,
prove, on nearer inspection by the traveller Piaggia, to he men of
powerful, regular, and fine figure, of stately carriage, with bronze-
coloured skin, long hair, and thick beard, barbarous indeed in their
customs, hut not cannibals. They are considered to be identical
with the interesting race of the Fellatah , the dominating people of
the western Soudan, or are perhaps a step between these and the
G-allas of the east.

Burton describes the peoples he met with between the east coast
and the Lake Begion : — u The Sawahili of the Zanzibar coast are
sprung from the intercourse of foreign traders and emigrants, Phoe-
nicians, Jews, Arabs, and Persians, with the African aborigines.
The Balonda people of the kingdom of the Muata Yanvo, to the
west of Lake Tanganyika, are almost pure negroes ; and between
these and the mixed east coast there is a tolerably regular grada-
tion of negroid races from east to west, brought about partly by
long intercourse with foreign settlers, and in part by intermixture
with the non-negro races of North Africa. The high road from
the coast to TJjiji runs through comparatively quiet and peaceful
races.” “ Cannibalism,” says Burton, “ is rare in Eastern Africa,
and results either from policy or necessity.”

The aspect of the great mass of this negroid race is not unpre-
possessing. They are tall and well-made mulattos, rather above
the European standard. A giant or a dwarf is never seen. The
people of the maritime regions have rough dirty skins of a dull
pale black, like that of diluted Indian ink ; from the central ele-
vation of the eastern plateau the complexion improves, and further
inland the yellow skin, so much prized in Eastern Africa, appears.
From the Unyam wesi plateau to Tanganyika Lake, in those lower
levels where heat and humidity are in excess, the people become
lamp black, without a shade of brown. The negroid races appear
to extend down the outer slope of the continent to near the Zam-
bezi valley southward.

Livingstone speaks of the negro peoples of the shores of Lake
Nyassa; and Silva Porto describes the natives he met with in the
northern watershed of the Zambezi valley as “ hospitable negroes.”

The Biver Zambezi is nearly the boundary between the negroes

of Edinburgh, Session 1869-70. 141

or negroids of the Lake Region, and the Kaffir races of South
Africa.

South of the Zambezi the kingdom of Mosilikatze has been
made up of the remains of a number of formerly independent
tribes conquered by the Matebele Kaffirs pushing northwards ; and
Sekeletu’s Makololo kingdom, in the Upper Zambezi valley, was
founded by a former ruler who led this conquering Kaffir tribe from
the head of the Orange river northward, and incorporated the van-
quished tribes with this one to form his kingdom.

The most important kingdom of South Africa is the empire of the
Muata Yanvo, whose subjects are purely negroes. The dominion
of this potentate seems to reach from the Mossamba Mountains, at
the head of the Kassabi river westward, to the town of Shinte, on
the Leeba river, and the Muchinga Mountains southward, and
thence round to the southern part of the Tanganyika Lake.

The northern extent of this kingdom is as yet unknown. The
Muata Yanvo’s empire includes that of the Cazembe, who is his
vassal, and who rules for his sovereign over that part of the king-
dom which is separated from the main portion by the desert or
mountainous country of Katanga. The fertile and thickly peopled
area, known to be under the sway of this great Central African
ruler, is far greater than any of the kingdoms of Western Europe,
and might be compared in extent to the united bulk of France and
Italy.

In conclusion, we may glance at the enormous labours of the
great traveller Livingstone, to whom the world is indebted for so
vast a portion of its knowledge of the African continent, and whose
recent travels have given a fresh interest to this part of the globe.
The area of South Africa, which Livingstone has already explored,
and not only explored, but in great part surveyed with accuracy,
has an extent of about one million of square miles. It is difficult to
form a correct notion of the space covered by such an area ; and it
may help to give an idea of the work which has been accomplished,
if we remember that the united areas of all the western kingdoms
of Europe — France, Austria, Germany, Italy, Spain — would scarcely
make up the extent of land which Livingstone has virtually added
to the known world.

VOL. VII.

142

Proceedings of the Royal Society

2. On the Steady Motion of an Incompressible Perfect
Fluid in Two Dimensions. By Professor Tait.

While discussing some of Mr Smith’s applications of Maxwell’s
ingenious idea of representing galvanic currents by the motions of
an imaginary fluid (ante, p. 79), I was led to the present investi-
gation. I have since found that, as was only to he expected, I
had been anticipated in a great many of the results I obtained —
especially by Stokes, in the Trans, of the Cambridge Phil. Soc.
1843. Still it appears to me that I have a few novel results to
communicate.

If if/ — const, be the equation of a current-line, Stokes has
shown that —

where /is an arbitrary function.

By the integration of this equation various singular results are
obtained, especially as to the nature of the families of curves which
can be lines of flow.

The equation of lines of equal pressure is then formed, and from
it corresponding results are derived. A curious result is obtained
when the motion is irrotational; in which case there is a velocity-
potential <£, and we have —

dx 2 dy 2 ~~

Here the elimination of gives us —

d2 log P d2 log P

cfa;2 + dtf = •

The method is also applied to certain cases of motion which, though
not steady, can be treated as if they were steady — viz., cases in
which a given state of motion is propagated in the fluid by transla-
tion or rotation ; so that to a spectator moving in a given manner
in a plane parallel to the fluid, the motion appears to be steady.
Thus, for instance, we can treat as steady motion the case of two

p = + c

p

d2(j>

+ P, = 0.

of Edinburgh, Session 1869-70. 143

equal parallel vortex-filaments rotating either in the same or in
contrary directions.

3. On the most general Motion of an Incompressible
Perfect Fluid. By Professor Tait.

This is a quaternion investigation into the circumstances of fluid
motion, especially with reference to the case of vortices. The
method employed is very similar to that which I gave to the
Society in 1862 ( Proc . R.S.E. April 28).

It is shown that if <n be the vector-velocity of a particle of fluid,
so that

cn = iu + jv + Jew ,

and if we introduce the operators IV and 8 ^ such that
d . d d d

A +

dt dx dy dz dt

IV = V + uf + v-~ +
dx dy

together with Hamilton’s operator —

<1 =

.d
% dx

x • d , 7 i

+ j-j- -f h -

dy ' ~ dz’

the equations of fluid motion and of continuity are-

<1P - Up = D,«r)

S<jcn = 0, )

where r is the density, and P the potential of the applied forces.

The principal transformation is effected by means of the
curious theorem in kinematics

- D <r<<r =

Thus, for instance, we have from the equation of motion

= o,

because <l2 (p-0 is obviously a scalar. The above theorem then

D»-<1 = 8,^,

gives

which proves that if <1 cr is ever zero for any particle of the fluid
it must remain so for that particle.

As an additional instance of the simplicity of the method
employed, the following may be given in this abstract:—

144 Proceedings of the Royal Society

If T be the instantaneous axis of the element of fluid, whose

velocity is <r-, we have —

<! cn = - 2 r .

But

S <J 2cj- = 0,

whence,

^ <] ’2cn = V <1 r

2

and

- ^ = <1 0 + <J

!V<r.

This contains the solution of the problem, treated by Helmholtz,
to determine the linear velocity of each fluid particle, when the
angular velocity is given.

4. Mathematical Notes. By Professor Tait.

The following self-evident propositions were employed for the
deduction of several curious consequences —

(a.) 4a? = (x + l)2 - (x — l)2 ,

or, x3 (x(x + 1) y _ (x(x - 1) J ;

or, “ Every cube is the difference of two squares, one at least of
which is divisible by 9.”

(b.) If

x3 + y3 = z3 ,

then

( 'x 3 + z3)3y3 -f- (a?3 - y3fz3 = (z3 + y3)3x3 .

This furnishes an easy proof of the impossibility of finding two
integers the sum of whose cubes is a cube.

Monday , 4 th April 1870.

The Hon. Lord NEAVES, Vice-President, in the Chair.

At the request of the Council Professor Wyville Thomson, Bel-
fast, delivered an address on “ The Condition of the Depths of the
Sea.”

of Edinburgh, Session 1869 -70.

145

Monday , 1 8th April 1870.

Professor KELLAND, Vice-President, in the Chair.

The following Communications were read : —

1. Facts as to Brain- Work ; in Illustration of the New and
Old Methods of Philosophical Inquiry in Scotland. By
Thomas Laycock, M.D.

A few words in explanation are needed. In my summer course
of lectures on Medical Psychology and Mental Diseases delivered
in the University, I have to investigate the human mind in its
practical relations to the body, and especially I have to teach how
each influences the other, so that the physician, or any intelligent
person, may be able to modify these relations beneficially. The
starting-point in these inquiries is the fundamental fact of ex-
perience, that no changes in the mind or the consciousness of what-
ever kind can or do arise, or continue, without a corresponding series
of changes somewhere in the brain-tissue. This fact being held as
certain as the fact of gravitation, the solutions of the problems to
be solved depend upon a knowledge of the relations which the
two series of phenomena bear to each other ; for which knowledge
it is necessary to analyse and classify the varying states of con-
sciousness on the one hand, and the changes in the brain-tissue
which correlate them on the other. As to the last mentioned, it
is certain that they are vital; they come, therefore, under the
sciences of Life collectively termed biology.

But all molecular changes in living tissues, of whatever kind
they may be, and consequently those of the brain, can be brought
also within the circle of molecular physics, for they can all be
resolved into motion of something, whether we designate that
something an atom, a molecule, a vortex, a ring, or a centre of
force. They are due, therefore, to energy; or, as distinct from
mind, to motor energy. The Bev. Professor Haughton, M.D., of
Dublin University, was led by experimental research to the con-
clusion, that as much motor energy is expended in brain-work in

146 Proceedings of the Royal Society

five hours as in muscle-work — say by a street-paviour — in ten hours.
Although all the changes going on in living tissues may be finally
resolved into chemical changes, — a fact well illustrated by Dr W. B.
Richardson, and by Professor Crum Brown’s and Dr Thomas R.
Fraser’s valuable researches into the connection between physio-
logical action and chemical composition, lately communicated to
the Society, — they are distinct from those induced in inorganic
matter by chemical affinity, and hence the need of connoting the
energy by the term vital. Now the distinguishing character of that
energy, whether manifested in plants or in animals, is adaptation
of all motion to ends. Evolved in the brain, this vital energy is
manifested as mind, and life is thus spiritualised. I would even
venture to say that matter is thus immaterialised, for since all
states of consciousness correlate motion of something, it is not the
connection of mind with mere ponderable or brute matter we have
to discuss, but of mind with adapted motions in infinite variety.
All external impressions received through the senses and exciting
states of consciousness can be resolved into motions that can be
exactly measured, in regard to impressions on the eye and ear, and
all internal impressions passing from one part of the brain or of
the body to another part, can be resolved also into an energy cor-
relative with motion, termed vis nervosa. So that psychology by
this method is, in one sense, a department of physics; in a wider
sense it is a science or philosophy of nature, and therefore differs
essentially from modern physiology, which is only a restricted de-
partment of physiology in the true and ancient sense of the word.
In fact, the method I adopt is an adaptation of the ancient Aristo-
telian method to modern philosophy, and in adopting it with me,
the Faculty of Arts of the University would only return to a for-
mer arrangement of work. Sir William Hamilton observes on this
point to the effect, that “ Aristotle’s treatise On the Soul being
(along with his lesser treatises on Memory and Reminiscence , on
Sense and its Objects , &c.) included in the Parva Naturalia , and
he having declared that the consideration of the soul was part of
the philosophy of nature, the science of mind was always treated
along with physics.”*

* Lectures on Metaphysics, vol. i. p. 127.

147

of Edinburgh, Session 1869-70.

The cause of this change in Faculty-work was, in fact, the rise
of different methods of philosophical inquiry named the reflective,
which discarded all observation and experimental research what-
ever. Sir William Hamilton explicitly taught that the only ex-
ternal condition needed for philosophical inquiry is a language
“capable of embodying the abstractions of philosophy without
figurative ambiguity,” — a condition not yet attained, however, nor
likely to be. “With this one condition,” Sir William declares,
“ all is given ; the philosopher requires for his discoveries no pre-
liminary preparations, no apparatus of instruments and materials
.... it is only necessary that the observer enter into his inner
self [and here is truly a figurative ambiguity of language] to find
there all he stands in need of.”* Hence the reading and writing
of books, and discussions of opinions, are the proper results of
reflective inquiry. It was to his extreme devotion to the literature
of philosophy that was due that lamentable palsy of the sign-
making organs, the right hand and speech-muscles, termed aphasia,
with which he was afflicted, for these were overworked in the acqui-
sition of that immense erudition which distinguished him. The
locality of the brain-disorder in these cases is in the anterior lobes,
more especially the posterior third of inferior frontal convolution.

Although the principles of the reflective method there laid down
by its greatest modern master exclude observation and experi-
mental research, Sir William Hamilton did not neglect physio-
logical inquiry. My own researches into the reflex and unconscious
functions of the brain, made twenty-five years ago, were>e warded by
his highly valued approval and friendship, because he saw in them
the physiological side of his doctrine of “latent” consciousness;
but the kind of inquiry he followed was physiological in the re-
stricted sense of a physiology of the human brain, and not in the
wider sense of a science of nature. But I do not advocate this
restricted method as the best or even a true method of philosophical
inquiry, nor do I wish to defend the errors to which it leads. I
speak only for my own method as just explained.

Matters being thus, it interested me to read the manifesto of
principles and methods which my reverend and respected colleague,

* Lectures on Metaphysics, vol. i. p. 383.

148 Proceedings of the Royal Society

the Professor of Moral Philosophy, gave forth when he took posses-
sion of his chair in November 1868, and which he published under
the title of “Moral Philosophy as a Science and a Discipline.”
In this essay he specially criticised the physiological method, and
in such a way that the Professor of Physiology thought it ex-
pedient to publicly controvert his views. The facts I have to place
before the Society having a reference to this criticism, I quote it.
Professor Calderwood said, “ There are evidences of great activity
on the part of upholders of a sensational philosophy, differing only
in its modifications from that which Scotland formerly rejected
under the leadership of Reid and Stewart. In conjunction with
this revival of sensationalism, there is eagerness not only to com-
bine physiological and mental science, hut even to question the
sufficiency of our investigations regarding the facts of consciousness
— to make nerves and muscles the only safe approach to a science
of mind, — and to proclaim the necessity of making physiology the
basis of psychology. The consequence of this is, not only that
mental philosophy is being encumbered with irrelevant investiga-
tions concerning such physical processes as mastication and respira-
tion, and such physical experiences as toothache and cramp in the
stomach, hut we are involved in all the hazard connected with the
use of a false method.” I gather from this sentence that my
reverend colleague, however opposed or misinformed he may he
as to the physiological method, certainly means not only to defend
and resolutely maintain the sufficiency of the reflective method as
laid down by his great master, hut to assert its superiority over the
Aristotelian method of observation and research. Now, it is upon
these points that I join issue with him. I shall select two prob-
lems for illustration, taken from my respected colleague’s own de-
partment, viz., the nature of belief and of personal identity, being
guided to the selection by his own declaration, viz., “ The supposi-
tion that physiology can lead us to philosophy of mind, is doomed
to rejection by all to whom it is clear that our personality is not
essentially connected with our body, which is only a temporary
dwelling,” &c. In this condemnation of physiology is included
the assertion of the psychological proposition that mind, considered
as an energy or principle, is separable from life, and that it only
occupies the living body as a temporary tenant. Now, the holders

149

of Edinburgh, Session 1869-70.

of this opinion have, in common with the physiologists, a belief in
a future life, and follow two methods of inquiry as to that truth of
religion, viz., the confirmatio veri and the inquisitio veri. The
spiritualists (so-called) have adopted the latter or scientific method,
the orthodox philosophers the former. To this end they state
certain propositions as unquestionable. Firstly, that every man
assuredly believes he is a mental unity, one, or Ego ; secondly, that
“ our thinking Ego . . . is essentially the same thing at every

period of its existence,’" — I quote Sir William Hamilton, vol. i.
p. 374; and, thirdly, that the evidence upon which these assumed
beliefs are founded is sufficient, being that of consciousness itself.
In other words, I feel assured that I am one and the same person
that I ever was, and therefore I am one and the same. Is this
evidence sufficient ? Can we rely absolutely and without need of
verification upon the veracity of consciousness manifested as belief?
To answer this question clearly, it is necessary to understand how
beliefs arise and are modified. Now, since according to the funda-
mental fact that every state of consciousness coincides with corres-
ponding molecular change in brain-tissue, we conclude that all
beliefs, being states of consciousness, must be coincident with such
changes. Is this conclusion true in fact ? First, as to the Ego. A
man, like other mammals, is one in body — a corporeal unity — in
accordance with the fundamental biological law of organisation ad
hoc. The belief that he is one, or Ego, bodily, is founded upon his
knowledge of this fact. The belief that he is a mental unity, or a
thinking Ego, correlates, as I shall shortly show, the unity of cere-
bral function manifested in the various states of consciousness of
the man at any given moment. But the belief that this Ego,
whether corporeal or mental, is essentially the same thing at every
successive period of a man’s existence, includes wholly different
phenomena, since it refers to past time, and consequently implies a
reminiscence of what it was at some moment of past time, or in
past time generally. Now, reminiscence is proveably dependent
upon a recording vital process, whereby we are enabled to know in
time present by virtue of the so-called association of ideas — what we
were, and thought and did in past time. If there be no record or
memory, or if there be a record, but no association of ideas so as to
induce reminiscence, then there is no knowledge of past mental
vol. vn. u

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states. What is essential, therefore, to belief in continuous personal
identity as a mental state, is that consecutive continuity of vital
processes which is necessary to reminiscence, and not a continuous
consciousness, as is the doctrine of reflective philosophy. Memory
in this sense may, and does extend in fact beyond the con-
sciousness, so that changes may and do take place in the conscious-
ness which are due to preceding records made without consciousness,
but which not being for that reason recognised as belonging to
past mental life, are believed to he intuitive. Memory in the in-
dividual from this point of view, and considered as a vital process,
has its exact counterpart in what may be termed memory of the
species of both plants and animals, in virtue of which consecutive
continuity of vital process through the seed or germ is maintained,
and ancestral qualities reproduced in offspring.

Such being the philosophy of belief, considered as the result of
brain-work, it is not difficult to understand why the philosophy of
morals, in so far as it is founded on identity of belief simply, or
orthodoxy, and not upon knowledge, is chaotic ; nor how it is that
all the efforts made to secure identity of mere belief, independently
of knowledge of the order of nature, whether by education or
otherwise, must fail.

I shall now illustrate these views by morbid or insane beliefs.
The reflective philosophy, as is well-known, discards all inquiry into
aberrant mental states ; with much the same propriety, however, as
an astronomer would discard the observation of planetary observa-
tion : in the inductive method these are of the greatest value as
experiments of nature. By examining every kind of result of the
molecular change as manifested by others, and comparing these
with our own, we are enabled in truth to study them as directly
manifested to our own consciousness. Hence all facta, all writing,
all art, and all conduct, however normal or abnormal, are the appro-
priate facts for inductive inquiry. To illustrate the method in this
direction, and at the same time to show the true relations of belief,
I place before the Society the portrait of a house-carpenter painted
by himself, with a descriptive legend describing himself as three
persons, viz. — 1. G-eorge Elliot, his true personality. 2. “ George
the Fifth, son of George the Fourth;” and, 3. “ The Emperor of
the world — the true and lawful God.” The reflective philosopher

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would think it a sufficient explanation to say that the man is a
lunatic. He should remember, however, that he owes this ex-
planation to the physiological method. Formerly, the explanation,
according to the reflective method was, and with many still is, that
the lunatic is either inspired or else possessed by a spiritual being.
The inductive philosophy, starting from the fundamental fact that
all states of consciousness of a man, however manifested, cannot be
manifested independently of vital processes, lays down the law that
in the living man Life and Mind are inseparable, and consequently
that the “ thinking Ego” is the man himself. Now, although
his person is double, whether as to limbs or brains, his corporeal
condition of unity is no more affected thereby in a healthy state
than the unity revealed in consciousness — the one being the reflex
of the other. His two brains act together so as to attain the unity
of consciousness, just as his two eyes act in unity of vision ; but
as he may see double when the two eyes act disjoin tly, so may he
have a double consciousness when the two brains act disjointly.
Whether he believes, or whether he doubts that he sees two objects,
or that he is one or two persons, depends upon those molecular
conditions upon which the belief and doubt of the moment depend.
Or, again, just as an object of vision may, from disorder of the
corresponding brain-tissue, appear to a man to be something wholly
different, as when his friend appears to be the devil, constituting
what is termed a hallucination, so his personality, from disorder of
the corresponding brain-tissue, may appear to be something wholly
different, and he may chance to have an hallucination that he is
the devil. It appears probable, therefore, that although a man may
have many and various delusions as to his state of mind and body,
he will rarely exceed three distinct and fixed delusions as to his
personality, viz., one resulting from disorder of each brain acting
disjointly, and one from disorder of both acting conjointly. Under
the restrictions stated, the result of numerous observations I have
made is in accordance with this view. So much for the break-up
of the unity of consciousness by brain disorder. It is obvious at a
glance that these diversities of belief as to personal identity are
associated with brain changes involving memory and reminiscence ;
otherwise, when Elliot came to a belief in his royal birth and
parentage, he would also remember, to the confusion of the belief,

152 Proceedings of the Royal Society

that he is and always has been George Elliot the house-carpenter ;
or, at least, a reminiscence, however vague, would induce doubt.
But no such results followed, and the belief is fixed and un-
wavering.

These considerations apply to belief only; but to understand the
questions at issue better, I shall inquire how a man comes to doubt,
and what is essential to as accurate knowledge as he can attain
under the circumstances. For this purpose I shall select the state
of consciousness known as dreaming. No well-informed inquirer
now holds the doctrine that in that state man is inspired, or that
the soul or mind acts independently of the body ; it is admitted
that every such change of consciousness as constitutes dreaming is
directly dependent upon molecular changes in the brain-tissue. In
accordance with the physiological law already laid down, the dreamer
believes in the reality of his dreams, however absurd they may
be, and however far removed from the normal conditions the mole-
cular changes. It is only when he awakes, and the normal condi-
tion is restored, that he doubts or disbelieves. Now, an analysis
of these purely physiological phenomena shows that those states
of consciousness which in the waking condition of the brain are
either reminiscences or anticipations, have in dreams no true
element of time, either past or to come ; they are either wholly of
the present, or have no true relation either to time or to space.
Memory, therefore, as the knowing reminiscence of past states of
existence, and judgment as the perception of the future, are
abolished. Memory of the past is abolished, on the one hand,
because the association of ideas upon which that faculty depends,
and which began at some past time, is abolished ; while, on the
other hand, there is no knowledge of any existing personal rela-
tions to time and space, because the senses being shut, there is no
perception possible of these relations. Hence the merest phan-
tasms of the imagination, admittedly due to molecular changes
induced under these conditions, are received as verities. Beid
relates how, on a certain occasion, when he slept with a blister on
his head, he believed he was being scalped by Indians. It is only
on awaking, when memory, and external perception, and normal
associations of ideas are restored, that a true knowledge of the
fallacious character of the beliefs can be attained. Hence it is

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clear that these conditions are necessary to a right belief in con-
tinuous personal identity. These conclusions are strictly applicable
to all hallucinations and beliefs of morbid origin. Many persons
have delusive beliefs during the waking state as transient as
dreams. This is very common in the brain-failure of old age.
Delusive beliefs, more strictly insane, may come and go in like
manner in the earlier stages of an insanity. I had a patient under
my care, in whom they came on only when he was in a heated
room, and who could recover from them by the cold douche applied
to the face. In cases like G-eorge Elliot, the morbid state is best
described as a fixed dream. When those molecular changes, which
coincide with the mnemonical records of his daily life, of things done,
succeed each other, he truly believes he is George Elliot, a house-
carpenter; but when the mnemonical records of his dream-life,
and which are wholly dissociated from the former, are presented to
the consciousness, then the associated personality is presented also,
and, for the time being, he believes as firmly he is another person
than George Elliot. These delusive states may have every degree
of duration. In certain kinds of waking somnambulism, the
individual lives an actual life, as two wholly dissociated persona-
lities, for hours or days alternately, the mnemonical records of
the two being quite as dissociated as dreaming and waking life ; or
they may occupy only a few moments, as in the artificial somnam-
bulism induced mesmerically, where the brain has been so acted
on that the patient is made to hold the most absurd beliefs, — to
believe, in short, whatever he is told is real. In this way Sir J.
Young Simpson changed the personal identity of two ladies in
regard to the husband of one of them, so that the unmarried
believed she was the married, and vice versa. From these facts,
and they might be multiplied to any extent, it is clear that the
notion or belief of personal identity is not due to mind in the
abstract, considered as an immaterial substance acting in entire
independence of life and organisation, but to mind in the concrete,
as inseparably associated, not with brute inert matter, but with
the motions and forces upon which life depends. This, I need
hardly say, is no new doctrine of philosophy, whether profane or
biblical. The earliest record of Scripture affirms that man only
became a living soul after the breath of life was breathed into his

154 Proceedings of the Royal Society

nostrils ; and St Paul, the philosophic apostle, adopting this view
to explain the resurrection, uses the biological analogy of the
continuous life of the species of plants through the germ, to indi-
cate how the individual or personal life of man may be continued
independently of consciousness, and how it may he evolved into
consciousness at some future time, plainly adopting thereby the
Aristotelian doctrine of the soul.

Many attempts have been made to verify the separate existence of
the soul, whether as a religious dogma or a philosophical doctrine,
and, of necessity, all have failed. I have placed before the Society
an illustration of these attempts, by the so-called spiritualists, to
prove the fact of an independent personal identity. It is a drawing,
by a member of an eminent literary family, of the spirit-emblem
of a distinguished and much esteemed fellow of this Society. Here
are published representations of like emblems, taken from Mrs
Newton Crossland’s “ Light in the Talley.” The seeress, we are
told, who beholds these mystical appearances, describes them as
appearing to her in colours of liquid light, with the utmost clear-
ness, more rich and radiant than earthly jewels. These emblems
are usually seen to be situate behind the persons to whom they
belong, the centre of the emblem rising just above the head, and
occupying a circumference of several feet. They are the badges
by which persons are recognised in the spirit-world, even while
they remain on earth. To the production of these emblems a
belief in the separate existence of “ spirits ” is essential — doubt,
like the waking from a dream, either prevents or dispels the
phantasies. Physiologically they differ in no respect from the
delusions of George Elliot, or of dreamers. The verification of
any belief means the investigation of the order of nature, so as to
determine whether the conclusions presented to the consciousness
as brain-work coincide with the natural order of events. To those
who are confident that they can assuredly believe in their own
eyes, the sun undoubtedly moves, and the observer is motionless,
but a verification of the conclusion shows that the motion is in the
observer, and the sun is motionless. Now, when a spiritualist
attempts to verify his belief in spirits, he ignores the fact that his
belief is due to molecular changes out of, at least, direct relation
to any spiritual influence, except that which constitutes his own

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spiritual nature, and is thus led to esteem the mere phantasms
of his own imagination as proof of external agencies which may
exist, hut which, by the terms of the hypothesis, cannot be veri-
fied. Resolved into their ultimate elements, all the so-called
proofs of spirit-life, when stated bona fide , are simply presentations
to the consciousness of the inquirer’s own brain- work, as delusive
as those of the lunatic or the dreamer. It has been commonly
said that this class of inquirers are, for the most part, either of
weak mind, or credulous, or ignorant. But this is not so. Here
are delineations of the od-force, as investigated by Baron von
Beichenbach, a skilled scientific inquirer. He never saw what is
here represented as the manifestations of the od-force, he simply
shows what was described to him as such by hysterical and
morbidly nervous women ; and if they he true as descriptions,
they are only representations to the consciousness of phantasmal
brain -work. Some of these so-called spirit operations are instruc-
tive illustrations of sesthetical automatic action of a cultivated
brain. The emblem of a fellow of this Society, drawn by a person
of high culture, is contrasted well with the uncouth mystical
emblems of an uneducated female lunatic before me. I was assured
by my late friend David Ramsay Hay, and no one was more com-
petent to judge, that it is exactly true to the geometrical principles
of form and colour.

In the delusions of Gfeorge Elliot we have an illustration of
another interesting result of brain-work, the ideational evolution
of the intuition of the infinite, a subject so much and so earnestly
discussed by reflective philosophers, and which is equally as capable
of biological illustration as the preceding.

2. On Change of Apparent Colour by Obliquity of Vision.
By Robert H. Bow, C.E., F.R.S.E,

I discovered the peculiarity of chromatic vision, which is the
subject of this paper, in the month of January, when conducting
some experiments upon the perfection of definition at different parts
of the retina ; and I may introduce the subject by first referring to
these experiments.

In the case of ordinary sensation seated in the skin, there are

156 Proceedings of the Royal Society

two offices performed by the nerves — first, that of informing the
mind of the fact of the contact or impression being made ; and,
second, that of giving more or less minute information as to the
locality of the sensation. Professor Weber experimented upon the
latter power, by testing the least distance apart at which two
objects touching the skin of any part of the body could be felt as
two distinct sensations ; and, as you are aware, this tactile power
bears no constant proportion to the mere power of feeling a sensa-
tion of contact. For instance, the back of the hand is perhaps
more sensitive to a simple contact than the tip of the finger, but
Weber found that the points of contact are required to be fourteen
times further apart at the back of the hand than at the tip of the
finger, before they can be distinguished as separated.

Now, a very strong analogy exists between these two functions
of ordinary sensation and corresponding offices of the retina.
Objects seen obliquely are not strikingly different in brightness
from the same seen in the direction of the optical axis, but the
power of definition (apart altogether from mere optical causes)
varies immensely. I attempted to investigate this defining power
for different parts of the retina by a method exactly analogous to
Weber’s — namely, by inspecting two white spots on a blackened
card, and determining, for different angles of obliquity and direc-
tion, the greatest distance from the eye at which these spots could
be detected to be double. But I soon found that, when the vision
is very oblique, there is a puzzling feeling of uncertainty as to the
result ; and it occurred to me to assist the judgment by substituting
for the white spots objects of contrasting colours.

On attempting to put this idea into practice, I made the im-
portant discovery, that when coloured objects are inspected under
oblique vision, the colours are at the same time reduced in inten-
sity, and changed in character : thus, scarlet becomes successively
orange, yellow, and whitish-yellow, according to the obliquity;
green , of a medium character, tends to become white, and violet to
become blue.

In experimenting upon the subject, it is best to place the coloured
object obliquely on the nasal side of one eye, the other eye being
closed ; much smaller angles of obliquity bring about the phenomena
when seen on this side of the eye, and we get rid of any complicity

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with the insensitive spot where the optic nerve joins the retina. I
may point out here, however, an experiment that shows the general
peculiarity, and also the excess of change that takes place when
the object is on the nasal side compared with the other. Against
a dark-coloured wall hold up, at arm’s-length, an orange-coloured
object of three or four inches in diameter. We suppose it held by
the right hand ; then turning the face rather towards it, look at a
point in the wall eighteen or twenty inches to the left of the object ;
and now closing the eyes alternately, it will be observed that, when
the right eye is open, the object will appear of nearly its full orange
colour, but when the right eye is closed and the left opened, the
object will assume a pale, sickly, yellow tint ; and if the point in
the wall be taken further from the object, the colour seen by the
left eye will approach nearer to white. To cause the same amount
of change to the right eye, the obliquity must be very much greater.
Another mode of conducting the experiment, as depending upon
the contrast of effect upon the two sides of the eye, is this : Choose
two objects of the same colour, place these two or three inches
above or below a mark on the wall, close one eye, and with the
hands withdraw the objects equally away on either side from the
central position, the eye being rivetted to the mark on the wall ;
it will then be noticed that, relatively, the object on the nasal side
of the observing eye undergoes a rapid change of tint or colour.
But, it may be repeated, the most satisfactory mode of examining
the changes is to use one eye and observe with the coloured object
on the nasal side of it, the eye being held steadily upon a mark,
which may or may not be of the same colour as the object. Observed
in this way, the following changes will be presented : —

First. The colours lose more or less their chromatic intensity,
and approach nearer to white or black, according as they are placed
upon a dark or light ground. But extreme red is especially marked
as losing illuminative power, as well as chromatic character. Ultra-
marine blue, on the contrary, appears to lose very little by oblique
vision ; it assumes a lighter blue hue.

Second. The colours undergo a change of chromatic character.
a. Brilliant scarlet , painted with biniodide of mercury and
gum arabic. — This, when placed on a dark ground, and
observed at an obliquity of about 30° on the nasal side,
VOL. VII. x

158 Proceedings of the Royal Society

appears orange ; at 40° to 50° it looks of a somewhat
meagre yellow, beyond this a pale yellow. As seen at
the outside of the eye, the orange only appears when the
obliquity reaches 80°, and the yellow at 90°.

b. Some orange colours show the change very markedly to

yellow, and to nearly white.

c. Emerald green. — This, at 40°, becomes nearly white, gene-

rally yellowish.

d. Ultramarine. — This is very persistent, visible at 40° as a

blue.

e. Pink , of a purplish cast. — This in day light, when placed

on a white ground, appears — even at a very moderate
obliquity — a purplish blue ; if placed on a black ground,
it assumes a lavender blue colour.

This change of purples and pinks to blue is one of the
most striking; perhaps the best way of witnessing it is to
use two thicknesses of cobalt blue glass, fortified with a
pink or purple one, so as to allow both extremities of the
spectrum to pass freely. This screen, held before a gas
light, appears by direct vision of a fine pink colour, but
by a moderate obliquity it is reduced to a bright blue.

/. A bluish-preerc glass, held in front of a gas light, appears
to become blue by oblique vision.

g. A yellowish-grrem glass becomes by oblique vision more
decidedly yellow.

Remarks and Speculations on the Phenomena.

Under oblique vision the purples or pinks become blue, and the
extreme red becomes dull. It would appear, therefore, that towards
the margins of the retina the sensation of blue is less reduced in in-
tensity than that of red , and a step in the explanation of the results
is this : the red in the purple or pink becomes a dull orange or
yellow under oblique vision ; this gives rise to the sensation of white
light when combined with a part of the blue, and reduces the re-
maining part of the blue to a paler cast. The same explanation
applies to a blue-green becoming blue — the green becomes white or
pale yellow under oblique vision, and so dilutes the blue ingredient
to a paler shade.

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The second observation that may be made upon the results is,
that by oblique vision the various colours are seen under the same
conditions as in the most common form of colour-blindness, wherein
there are really only two colour-sensations, the upper half of the
spectrum, from blue-green up to violet, and including pinks and
purples, appearing blue ; and the lower half, from yellow-green
down through yellow, orange, and scarlet, to bright red, appearing
yellow ; and in such colour-blindness the extreme red is frequently
very dull. We may, therefore, expect the discovery of some simi-
larity in the conditions of the central part of the retina of an eye
affected with this form of colour-blindness, and the marginal parts
of the retina of a normal eye.

Before concluding, I would venture to connect the discovery
with an existing theory of colour-sensation, as it may help to
establish that theory, should a prediction the connection leads to
be found to be correct.

The figure here given shows a section of part of the retina
(Kolliker). Now, it has been suggested that
each of the layers Y, Gf, and B, is receptive of the
sensation of light, — the layer Y being affected
by the more refrangible rays blue and violet, B
being affected by the less refrangible yellow,
orange, and red, while the central layer Gf is
affected by the central parts of the spectrum,
blue, green, yellow, and orange ; and this would
account for the approximate achromaticity of
the eye, for when the eye is arranged for the most acute vision,
the focus of blue rays will correspond with Y, of green rays with
Gf, and of scarlet rays with B.

But it is well known that the eye does not see any colour quite
purely; there is always white light present, or, in other words, one
of the layers, Y, Gf, or B, cannot be agitated or excited without the
others partaking to some extent in the excitation. Now, there is
a probability that the degree of freedom with which one layer may
transmit its special sensation without one or both of the others
participating, to an important degree, in the excitement, depends
in part upon the maintenance of a considerable interval between
the layers. Let us then imagine the interval between Gf and B to

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become more or less perfectly obliterated, and it is evident that no
simple sensation of red or green could be felt, but only a colour-
sensation, which corresponds with the excitement of both of these
layers, which is yellow. It may, therefore, be worth the attention
of anatomists, skilled in working with the microscope, to ascertain
if any decided reduction of the interval Gr to R takes place towards
the margins of the normal retina, or has place in the central part
in eyes that have shown, during life, the commonest form of de-
fective vision of colour ; we should also expect a reduction of the
interval Y to Gr, but to a less decided degree. In the case of an
eye completely colour-blind, we should look for the coalescence of
the three layers into one, unless the defect were accounted for by
the absence or paralysis of two of the layers.

The following motion by Mr Sang was considered : —

1. Every Communication intended for the Society shall be sub-
mitted to the Council, and passed by them as not containing anything
objectionable, before being mentioned in the Billet.

2. The Society shall not take up any matter which has not been
announced in the Programme, except in cases of extreme urgency.

The motion was not adopted, as the Society thought that
Mr Sang’s views were already embraced in the printed regu-
lations for the order of business.

Monday, 2 d May 1870.

DAVID MILNE HOME, Esq., Vice-President, in
the Chair.

The following Communications were read : —

1. Remarks on the Theories of Capillary Action. By
Edward Sang, Esq., F.R.S.E.

That theory of capillary action, which seems to have satisfied
the greater number of physicists, is founded on the assumption
that the particles of a fluid are separated by distances immensely

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great in comparison with their magnitudes, and that these particles
attract each other, — the sphere, however, of their attraction extend-
ing to a distance infinitesimally small in comparison with the
observed disturbances of the fluid-level.

The accommodation of this theory to the actual phenomena is
accomplished by long operations, comprehensible only by those
who are familiar with the higher calculus. The object of the pre-
sent paper is to examine this theory in the light afforded by a
general knowledge of the leading laws of mechanical science. For
this purpose, the author proceeds to analyse the ordinary pheno-
mena of the rise of water round a piece of clean glass which has
been plunged into it. Assuming a fluid particle situated upon the
inclined surface, he observes that, according to the hypothesis of
an infinitesimally small sphere of attraction, this particle is beyond
the direct influence of the glass ; the only other influences to which
it is subjected are gravitation and the attraction by the adjacent
fluid particles.

Now, according to this same hypothesis, the particle is attracted
by that part of the fluid which is within a small sphere described
around it ; but the curved surface, having its radius of curvature
infinitely greater than the radius of this sphere, may be regarded
as flat within the range of attraction, and therefore the solicita-
tion, to which the particle is exposed, must be exerted in a direc-
tion normal to the surface. By a more minute examination, the
author shows that, if the radius of the sphere of attraction be
reckoned as a differential of the first order, any deviation from nor-
mality must belong to the third order of differentials — that is,
must be of an order infinitesimally smaller than the infinitesimally
small sphere of attraction.

Thus the only two solicitations to which the particle can be
subjected are, the attraction of the fluid exerted in a direction
normal to the surface, and gravitation. Now, it is impossible that
the resultant of these two solicitations can be normal to the sur-
face ; but no fluid can be in repose if the attraction exerted upon a
particle at its surface be not normal to that surface, wherefore, the
author of the paper concludes, the infinitesimally-small-sphere-of-
attraction-hypothesis is untenable.

On considering the hypothesis of attraction generally, the author

162 Proceedings of the Royal Society

proceeded ro remark that, in order to prevent the condensation
which would result, we must suppose some resistance to the farther
approach of the particles, which we may typify by a repulsion ;
and that these tendencies — the attractive and the repulsive — must
he in equilibrium. A theory, then, which takes into account only
one of these equilibrated antagonists, must necessarily he defective.
And since, in all cases, the attraction supposed to exist between
two sets of particles must necessarily he resisted by actions between
them, there can be no tension like that which has been supposed to
he exhibited by the superficial films of fluids.

2. Theory of Construction of the Great Pyramid. By John
Christie, Esq. Communicated by the Bev. W. Lindsay
Alexander, D.D.

In his early investigations on the principles of construction of
the Great Pyramid, the author was forcibly struck with the follow-
ing fact — viz., that if a perpendicular be drawn through the
apex of the Pyramid to its base, and the unit angle with the hori-
zontal thrown up from the base on each side of this perpendicular,
the angle comes out on the faces of the Pyramid at the openings
of the north and south ventilating air-channels ; at the same time
he was led to the conclusion that one-tenth of the base line, and
the same tenths also applied to the faces of the Pyramid, ruled the
entire structure. Following this out, and having erected per-
pendiculars on each of these tenths, and horizontals from each
of the facial divisions, the first step procured a grand central
point — viz., in the centre of the grand gallery; the next step
was to account for the position of the King’s Chamber, by the
intersections of the first and second circles — used in the con-
struction of the Pyramid, as shown in Diagram No. 1. Having
thus obtained a central perpendicular for the King’s Chamber, he
then made use of the direction of the celestial equator, and where
it cut the last-named perpendicular, a third point was gained as a
centre for the third circle, which completes the Pyramid in its
external form. He next found, that by connecting the south out-
crop of the air-channel with the north corner of the base, a

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of Edinburgh, Session 1869-70.

parallel was gained for the angle of the grand gallery. By draw-
ing a horizontal line between the two air-channel months, and
dropping perpendiculars from these to the base, two oblongs are
formed, one on each side of the axis ; the diagonals of each of
these being the unit angle.

The astronomical hearing of the Pyramid seems manifestly to
he indicated in the sections of the King’s Chamber. In the sec-
tion of it in its breadth, the chamber is filled up by — first, a section
of the Pyramid itself, the base of which is the floor line of the
chamber; the space above, as regards height, being filled by an
equilateral triangle, its angles 60°, corresponding as they do with
the direction of the celestial equator, 60° seem to point with
threefold force to the fact that the Pyramid has a direct reference
to the sun.

The same is twice repeated in the section of the King’s
Chamber in its length, the length of the chamber being exactly
twice its breadth. Another very marked reference of the same
kind occurs in the position that the Queen’s Chamber hears to the
King’s Chamber. If an equilateral triangle, whose apex is in the
centre of the floor of the King’s Chamber, be constructed, having
its base in the base line of the Pyramid, the centre of the floor
of the Queen’s Chamber will he found to he exactly in the middle
of the north limb of this triangle, other instances are also shown
to he regulated by the equilateral triangle.

The unit angle regulates the length and height of the King’s
Chamber, the~space between it and the ante-chamber, the form of
the ante-chamber, and the distance to the great step, also the in-
terior length, breadth, and depth of the much- abused granite
coffer.

Coffer Unit Bloch.

Breadth, jg- part of interior length of coffer.

Height, i „ „ depth „

Thickness, £ „ ,, breadth „

90 of these cover one side of coffer.

90 „ bottom „

450 exactly fill coffer.

The shape of this block is regulated by the unit angle in its top
sides and face, and consequently conserves the Pyramid facial

164 Proceedings of the Royal Society

angle, which it would not do had its length, breadth, or thickness
been different, in which case the complement of these blocks would
have been too large or too small for the coffer content.

Record of Physical Facts — Water-Levels.

The King’s Chamber is a noted index of these. That this was
intended by the Pyramid builder seems to be demonstrated by
the fact of the rock on which the Pyramid stands having been
scarped down to the level of the Pyramid’s base, so as to procure
a horizontal line midway between the external physical fact to
be recorded, and the internal index of that fact contained in the
King’s Chamber, serving as it did, at the same time, astronomical
purposes, neither of which would have held good had the rock not
been so scarped down.

These water-levels have been previously indicated by other
modes than those by which they are now illustrated. It will be
observed that the circles used to indicate them have also peculiar
references to other parts of the Pyramid besides those they bear to
the King’s Chamber. One marked instance may be noted here.
The circle, which indicates the High Nile-level, touches the floor
of the King’s Chamber in the centre, and also indicates the angle
of the floor of the grand gallery. Reference may also be made
here to one of the circles used in the construction of the chambers
and passages, it being of a very marked and significant character.
This circle has its centre in the Pyramid’s base, in the point where
the “direction of the celestial equator” cuts the base, its radius is
the prime central point in the centre of the grand gallery, and in
its course it touches — ls£, The mouth of the entrance passage ; 2 d,
The step leading down to the Queen’s Chamber ; 3d, The “bottom
of well” in the lower part of descending passage; 4 th, Rounds
the Low Nile-level; and 5th, Where it cuts the lower portion of
the direction of the celestial equator, the High Nile-level. The
difference between the mean Nile-level and the mean sea-level is
indicated by an equilateral triangle, the apex of which is in the
mean sea-level, and the base the mean Nile-level, the length of
the latter being contained between two perpendiculars — the first
from the north corner of the Pyramid’s base, the second from the
first remarkable perpendicular joint in the entrance passage.

of Edinburgh, Session 1869-70.

165

Independent Methods of Constructing the Great Pyramid Externally.

1st. Grive a horizontal line. Bisect it, erect perpendiculars at
both ends and also from the centre, from one of the ends throw up
the unit angle with the vertical, and through the point where the
angle cuts the opposite perpendicular draw a horizontal line, an
oblong will thus be formed, the diagonal of which is the unit
angle, join the top of the central perpendicular with the lower
corners of the oblong, and the Pyramid is complete.

2d. Gi-iven a vertical line, the radius of a circle, at right angles,
through the centre of circle, draw a horizontal line, bisect the
vertical line, and throw down the unit angle with the vertical from
both sides of the vertical at its bisection, through the points where
these cut the horizontal line, join the extreme end of the radius,
and the Pyramid is complete.

The Diagrams submitted to the Society were as follow:-—

Diagram No. 1. — Construction of the Grreat Pyramid in its ex-
ternal angles, its chambers and passages by the unit angle, and
one-tenth of the base, on a given horizontal line.

Diagram No. 2, one-sixteenth of the full size. — Sections of the
King’s Chamber, in its length, and also in its breadth, showing-
how it is regulated by the unit angle, &c.

Diagram No. 3, one-half of the full size. — Sections of the
granite coffer in its length, and also in its breadth, showing how it
is regulated by the unit angle and conserves the Pyramid facial
angle.

Coffer unit block , in further illustration of Diagram No. 3.

Diagram No. 4, one-sixteenth of the full size. — Section of the
King’s Chamber in its breadth, the ante-chamber, great step, and
south end of grand gallery, showing that the space between the
King’s Chamber and ante-chamber, the form of the ante-chamber
itself, and the distance to the great step, are all regulated by the
unit angle; showing also the references between a portion of the

VOL. VII. y

166 Proceedings of the Royal Society

chambers of construction and the overlappings of the grand
gallery.

Diagram No. 5. — Independent method of constructing the G-reat
Pyramid in its external angles from a unit angle oblong.

Diagram No. 6. — John Taylor’s theory of the reference the
G-reat Pyramid bears to the circle, with Professor C. Piazzi Smyth’s
amplification of the same, and further amplification by the author.

3. On the Structure of Tubifex. By W. C. MTntosh, M.D.

The paper consisted of a detailed account of the external form ;
the arrangement of the body-cavity and its walls; the perivisceral
space and corpuscles ; the digestive, circulatory, and generative
systems.

It was specially mentioned, in regard to the perivisceral cor-
puscles, that the author was not at all inclined to think that they
originated from the glandular fatty coating of the digestive tract
and the dorsal blood-vessel. The corpuscles seem rather to he the
product of the perivisceral cavity itself and its special (free) con-
tents. This view requires no stretch of ordinary physiological
principles, and is quite in keeping with what is found in other
groups. In the Nemerteans, for instance, a complex corpusculated
fluid is produced within a closed chamber with smooth walls.

The following Gentlemen were elected Fellows of the
Society

James Sime, Esq.

Thomas Harvey, LL.D.

John Young Buchanan, M.A.

John Hunter, M.A., Belfast.

The Bight Hon. The Lord Justice-Clerk.

The Hon. Lord Gifford.

of Edinburgh, Session 1869-70.

167

Monday, 1 §th May 1870.

Dr CHMSTISON, President, in the Chair.

On taking the chair the President alluded to the loss
which the Society had sustained by the death of Sir James
Y. Simpson, Bart.

The following Communications were read : —

1 . Primitive Affinity between . the Classical and the Low
German Languages. By the Hon. Lord Neaves.

(Abstract. )

In this paper the author adverted to the limited attention that
was paid in this country to comparative philology, and noticed
the principles it had developed and the progress it had made else-
where of late years*

In illustration of the results thus attained in the Aryan or Indo-
Germanic languages, he took as familiar examples the affinities
that could be traced between the Latin and the Old English tongues,
viewing the Latin as a type of the earlier branches of the family,
including the Greek and Indian ; and the English as a type of a
later branch, consisting chiefly of the Low German dialects. The
affinities referred to were not those which connected Latin with
English through the romance languages, but those which subsisted
between Latin and vernacular English, and which must have arisen
from a prehistoric identity or connection.

The chief law regulating these affinities was what is commonly
called Grimm’s law, but which is subject to various limitations and
exceptions.

The affinities between words in cognate languages which have
had no historic connection are to be found out — 1st, by studying
the general law of letter-change prevailing between the primary
and secondary branches of the family ; and 2d, by finding out the
peculiarities or idiosyncrasies of the individual languages sought
to be compared ; for each language has a character of its own, and

168

Proceedings of the Royal Society

both Latin and English have strong peculiarities distinguishing
them from other languages, which help to conceal cognate words
from each other, and which must be mastered before the double
disguise can be seen through.

He exemplified these views by detailed instances, and concluded
by urging that all nations of the Aryan race ought to be regarded
as susceptible of the highest culture, and that the good hopes
might be entertained of their being all raised to as elevated a state
of Christian civilisation as the best of them had attained.

2. On the Genetic Succession of Zooids in the Hydroida.

By Professor Allman.

In this communication an attempt was made to express by
means of formulae the various modifications presented by the life
series of the Hydroida. It was also shown that there existed
among the Hydroida both centripetal and centrifugal forms of
development. These were compared with one another, and numer-
ous analogies between the hydroid gonosome and the inflorescence
of plants were demonstrated.

3. On Green’s and other Allied Theorems. By Prof. Tait.

(. Abstract .)

In this paper an attempt is made to supply, at least in part, what
the author has long felt as a want in the beautiful system of
quaternions, so far as it has yet been developed. To apply it to
general inquiries connected with electricity, fluid motion, &c., we
require to have means of comparing quaternion-integrals taken
over a closed surface with others extended through the enclosed
space — and of comparing integrals taken over a non-closed surface
with others extended round its boundary. The author recently
found that he had already, in the Quarterly Math. Journal , and in
the Proc. R. S. H., furnished the means of attacking the problem.

By very simple considerations it is established that

fff&V<rds = ff S. crUv ds,

of Edinburgh, Session 1869-70.

169

where v is Hamilton’s operator,

. d .d l7 d

ldx + % + kdz

o- is any vector-function of the position of a point, d<s an element
of volume, ds an element of surface, v the normal at ds ; and the
integrals are extended respectively through the content, and over
the bounding surface, of a closed space %

From this equation G-reen’s Theorem is deduced in the form

fff S.vPvP^v = -ff/PyVd, + j^S.vPlWs,

= -fffVv'Ufs +J^PS.vP1Uv«fo.

Some sections are devoted to the representation of

///&

(where q is any quaternion whatever) by a surface-integral, and
the arbitrary part of the solution in the equation

ff/rds=//ds S(U,V-1)t,
where r is any vector, is explained.

It is next shown that, if p be the vector of a point, a- and y as
before, we have the equation

f8 <T"dp = ff8.Vo-Uv.ds,

expressing an integral taken over a limited and non-closed surface
by another taken round its curvilinear boundary. That some such
representation is possible is obvious from the fundamental theorem
above, which shows that for a closed surface

^S-v cr-Ui/.c/s = fff Sv2<t" ds = 0,

and therefore the surface -integral must have the same value (with
a mere change of sign depending on the difference between outside
and inside ) for the two parts into which the surface is divided by
any closed curve drawn upon it.

Other theorems of a similar character are given, such as
fVcndp = - ffds V.(V.UvV)
and

fVdp = ffds V.UvvP,
which, in fact, contains the two preceding.

170

Proceedings of the Poyal Society

4. Proposed Method of ascertaining the Temperature of
Falling Bain. By Thomas Stevenson, F.B.S.E., Civil
Engineer.

A friend informed me some time ago that the late Principal J.
D. Forbes had often noticed that a long continuance of rain
resulted in a track of cold weather. Principal Forbes attributed
this fact to the rain having a lower temperature than the atmo-
sphere through which it fell. It does not appear, however, that he
made any observations to determine the truth of his hypothesis, and
as the subject is of considerable importance in other meteorological
questions, it occurred to me that a simple instrument could be
made for ascertaining the temperature of falling rain. This in-
strument, a rough model of the funnel of which 'was lately shown
at a meeting of the Scottish Meteorological Society, is repre-
sented in the accompanying diagram, in which A B C is a
conical funnel of thin glass, terminating in a small tube deep
enough to contain the bulb of a thermo-
meter, and recurved so as to form an off-let
or waster. ADDA represents a box
of wood into which the glass funnel is
inserted, the space between the glass and
the wood being carefully filled with saw-
dust or any other had conductor of heat.
The rim of the funnel should be bent over
the upper edges of the box, so as to prevent
the possibility of rain lodging itself among
the sawdust.* The rain-drops intercepted by the funnel will pass
off through the bottom of the box by the tube 0.

By this or some such simple arrangement the temperature of any
heavy fall of rain may be ascertained with tolerable accuracy. It
is, of course, necessary that a dry bulb thermometer, properly pro-
tected by a louvre boarded box, should be observed simultaneously
with the rain thermometer.

The difference of temperature between the air and rain could

* It may be found better to carry the tube, at the second curve, horizontally
through the side of the box instead of downwards.

171

of Edinburgh, Session 1869-70.

also be ascertained by means of an instrument on the principle of
Leslie’s differential thermometer, one bulb of which would be placed
at the bottom of the glass funnel, while the other would be pro-
tected from the rain. In this way the differences of temperature
would be constantly shown by means of a single instrument.

The following Gentlemen were elected Fellows of the
Society : —

James Watson, Esq.

The Hon. Lord Mackenzie.

Monday, 6th June 1870.

Dr CHBISTISON, President, in the Chair.

The Secretary read the following letter from Professor W.
J. Macquorn Bankine : —

Diagrams of Forces in Framework.

To the Secretary of the Royal Society , Edinburgh.

Sir, — As Mr Clerk Maxwell, in a paper lately published in the
Transactions of this Society, has done me the honour to refer to
me as having been the first to show how to combine in one diagram
a system of lines representing the directions and magnitudes of all
the forces acting in a given frame, I wish to put on record, in the
Proceedings of the Society, the time and manner of my first publi-
cation of the method in question. It was in the year 1856, in a
lithographed synopsis of lectures which I delivered in the Univer-
sity of Glasgow, entitled “ Mechanical Laws, Formulae, and
Tables.” Copies of that synopsis were distributed to the students
of my class, and to a few men of science.

I beg leave herewith to send for presentation to the Society a
copy of the first part of that synopsis, and regret that at present I
am unable to make up a complete copy. The construction of
diagrams of forces for unbraced frames is shown at p. 7, and for
braced frames at p. 8.

The next publication of the method took place in 1857, in the

172

Proceedings of the Royal Society

article “ Mechanics Applied,” of the “ Encyclopsedia Britannica,”
eighth edition ; and the next again in 1858, in a work of mine
entitled “ A Manual of Applied Mechanics.”

Mr Clerk Maxwell made a material improvement in the mode of
applying the method to braced frames, which he published in the
u Philosophical Magazine ” for 1866, and described to the Dundee
meeting of the British Association. — I am, Sir, your most obedient,
servant, W. J. Macquorn Rankine.

Glasgow, 2d June 1870.

The following Communications were read : —

1. On Spectra formed by Doubly Refracting Crystals in
Polarised Light. By Francis Deas, Esq., LL.B., F.R.S.E.

The instrument used in the experiments forming the subject of
this paper was a spectrum microscope, to which a polarising appara-
tus is attached, consisting of two NicoFs prisms, each of which is
capable of being turned through any required number of degrees.

The first part of the paper relates to the spectra obtained when
one or more thin films of mica or selenite are interposed between
the polariser and the dispersion prisms, the light being subse-
quently analysed.

The method employed was, having first determined the axes of
the films, to place them on the stage of the instrument which is
rotatory, and to adjust them at various angles to the plane of
polarisation.

The general appearance presented, may be described as being a
more or less continuous spectrum, interrupted by one or more well
defined black bands, not unlike the ordinary absorption bands pro-
duced by many chemical substances.

The bands have in many cases a curious movement along the
length of the spectrum as the analyser is turned. Sometimes a
band may be observed to split into two halves, which move in op-
posite directions, and unite with other bands which advance to
meet them.

In all cases a set of complementary bands is obtained when the
plane of analysation has been turned through 90° to that of polar-

173

of Edinburgh , Session 1869-70.

isation. The positions and relative movements of the bands de-
pend partly on the thickness of the films, partly on the inclination
of their axes to one another, and to the planes of polarisation as
detailed in the paper.

Curious varieties of the movements are obtained by circularly
polarising the light before or after its passage through the film.

Very beautiful results were further obtained by substituting a
double image prism as the analyser. When the spectra thus ob-
tained are superposed, the bands are no longer black, but coloured,
each band in the one spectrum being of the colour of that part of
the other spectrum on which it is superposed, while the adjacent
colours are those arising from the blending of the two spectra.

To obtain these effects in perfection, however, certain adjust-
ments of the apparatus must be attended to, which will be found
described in the paper.

The second part of the paper relates to the effects obtained
when a section of a doubly refracting crystal, cut perpendicular to
its axis, so as to give the well-known systems of coloured rings, is
substituted for the mica or selenite in the former experiments.

The crystal must in this case be placed, not upon the stage, but
immediately over the eye lens of the instrument, and between it
and the analyser. The entire length of the spectrum is now seen
intersected by a system of black arcs, accompanied by two or more
brushes, which are black or coloured according to the position of
the analyser.

Interesting effects are produced upon the rings by interposing
films of mica of different thicknesses, so as to polarise the light
either circularly or elliptically ; the mode in which the black and
coloured rings alternate and change places during the revolution of
the analyser depending on the thickness of the film used.

The effect of the rings, when viewed through a double image
prism, is strikingly beautiful. Exquisite patterns resembling tessa-
lated pavement, chain armour, &c., may thus, with a little inge-
nuity in the mode of arrangement, be produced by the interlacing
-systems of rings.

VOL. VII.

174

Proceedings of the Royal Society

2. On the Heat Disengaged in the Combination of Acids
and Bases. Second Memoir. By Thomas Andrews, M.D.,
F.R.S., Hon. F.RS.E.

(. Abstract .)

In the beginning of this paper the author recapitulates the five
fundamental laws of the heat of combination, which he had de-
duced from his previous researches, and which form the subject . of
several memoirs published in the Transactions of the Royal Irish
Academy and of the Royal Society of London, from 1841 to 1848.
They are as follows : —

Law 1. — The heat disengaged in the union of acids and bases is
determined by the base, and not by the acid ; the same base pro-
ducing, when combined with an equivalent of different acids, nearly
the same quantity of heat ; but different bases, different quantities.

Law 2. — When a neutral is converted into an acid salt by com-
bining with one or more atoms of acid, no change of temperature
occurs.

Law 3. — When a neutral is converted into a basic salt by com-
bining with an additional proportion of base, the combination is
accompanied with the evolution of heat.

Law 4. — When one base displaces another from any of its
neutral combinations, the heat evolved or abstracted is always the
same, whatever the acid element may be, provided the bases are the
same.

Law 5. — When an equivalent of one and the same metal re-
places another in a solution of any of its salts of the same order,
the heat disengaged is always the same, but a change in either of
the metals produces a different disengagement of heat.

The concluding part of the elaborate memoir of MM. Favre and
Silbermann, on the heat disengaged in chemical actions, which ap-
peared a few years later, is chiefly devoted to a repetition of the
experiments already published by the author. They state that
they consider the fourth law, which asserts the equality of thermal
effect in basic substitutions, to be fully established ; but they
dissent from what they consider to be the enunciation of the first
law, and infer from their own experiments that the organic acids —

175

of Edinburgh, Session 1869-70.

oxalic, acetic, &c. — disengage sensibly less heat in combining with
the bases than the nitric, hydrochloric, and other mineral acids.
In his first memoir (published in 1841) the author of this com-
munication had, on the contrary, found that the oxalic acid dis-
engages quite as much heat as the nitric and hydrochloric acids,
when it combines with the bases, and this property of oxalic acid
he always regarded as the key to his whole investigations on this
subject. He therefore considered it important to institute a new
set of experiments in order to settle the question. These experi-
ments, which were performed with great care, and with accurate
instruments, are fully described in the present communication.
The results confirm the general accuracy of his original experi-
ments of 1841. They show that oxalic acid, far from disengaging
sensibly less heat than the hydrochloric and nitric acids in com-
bining with the bases, actually disengages a little more heat than
either of those acids, when it combines with potash, soda, or
ammonia. The following extract from a table given in the pre-
sent communication will illustrate this point : —

Acid.

Potash.

Soda.

Ammonia.

Oxalic,

3o,058

3°;040

2°-648

Hydrochloric,

3°-021

2°-982

2°-623

Nitric,

2°-993

2°-929

2°-566

The original experiments of the author, according to which
oxalic acid stands, as regards thermal action, in the same rank as
the phosphoric, nitric, arsenic, hydrochloric, hydriodic, boracic, and
other mineral acids (with the exception of the sulphuric acid), are
thus completely confirmed. The new experiments also agree with
the former ones in showing that sulphuric acid disengages about
^th more heat, and a group of acids comprising the tartaric, citric,
and succinic acids, about ^th less heat than the mean of the other
acids. The results are fully discussed in the present memoir, and
the influence of extraneous circumstances considered, which in this,
as in other similar physical inquiries, disturb in all cases to a cer-
tain extent, and in some cases considerably, the experimental in-
dications, and render them only first approximations to the general
laws they are designed to illustrate.

176

Proceedings of the Royal Society

3. Note on Professor Bain’s Theory of Euclid 1. 4. By Wm.

Robertson Smith, M.A., Assistant to the Professor of
Natural Philosophy. Communicated by Professor Tait.

In a paper communicated to this Society last session, I pointed
out that the proof of Euc. I. 5, given by Mr Mill, is unsound;
endeavouring, at the same time, to show that this is no mere
accident, but that it is impossible to give a mathematically correct
analysis of the processes of Synthetic Geometry on any theory
that holds figures to be merely illustrative, and does not admit
that intuition in the Kantian sense — i.e., actual looking at a single
engraved or imaginary figure — may he a necessary and sufficient
step in a demonstration perfectly general. I now venture to draw
the attention of the Society to the confirmation which I conceive
that this argument derives from the way in which Euc. I. 4 is
treated by Professor Bain in his recent “ Logic ” — a book which,
on the whole, is based on Mr Mill’s principles, and which is mainly
original in an attempt, which I cannot regard as felicitous, to
bring these principles into closer contact with the special sciences,
especially with Physics and Mathematics.

It will he remembered that Mr Mill, undertaking to demonstrate
Euc. I. 5 from first principles, has to supply, in the course of his
proof, a demonstration of Euc. I. 4, and it is in the attempt to give
to this process the form of syllogistic inference from Euclid’s
axioms that he errs. Professor Bain does not attempt to defend
the blunder of his predecessor. He admits that Euclid’s proof
cannot be reduced to a chain of syllogisms. But, instead of sur-
rendering Mr Mill’s theory of mathematical reasoning, he concludes
that Euclid has not demonstrated his proposition — that the super-
position which he enjoins is only an experiment, and that “if his
readers had not made actual experiments of the kind indicated,
they could not be convinced by the reasoning in the demonstra-
tion.” *

Now I believe, and in my former paper expressly pointed out,
that the position that Euc. I. 4 is really an inductive truth, and
that the usual demonstration is not in itself convincing, is the only

* Logic, vol. ii. p. 217=

177

of Edinburgh, Session 1869-70.

ground that remains to Mr Mill and his adherents. So far, then, I
am confirmed by Professor Bain : it remains only to show that this
new position is mathematically as untenable as that from which
Mr Mill has been dislodged. If Professor Bain grants that the
proof of Euc. I. 4 is not by syllogism from axioms — if, again,
mathematically it is plain that there is none the less a real proof,
not merely an induction — we shall have gone far to establish the
validity of proof by intuition.

Professor Bain tells us that Euclid, while professedly going
through a process of pure deduction, requires us to conceive an
experimental proof. There is surely an ambiguity here. Does Mr
Bain mean that Euclid merely calls to our mind former concrete
experiments with triangles of card-board or paper, for these alone
are actual and concrete to our author? Does Euclid’s “ experi-
ment ” agree with the descriptions of experiments in books of
Physics, save only in this, that we have all njade Euclid’s experi-
ment before ? Clearly not. In picturing to myself an experi-
mental proof in the usual sense, I imagine mentally, or with the
help of a diagram, certain arrangements, and then I am told to
imagine a certain result following — or rather, I am told to believe
this result, for to picture it is quite superflous and often impossible.
Euclid, on the other hand, tells me to superpose ideally the point
A on C, the line AB on CD, and so forth, and then I do not require
to be told that the coincidence of the whole triangles follows. I
have no choice to imagine coincidence or non-coincidence. I see
that it follows, and that quite apart from previous experiment.

Professor Bain allows the possibility of ideal experiments on
mathematical forms.* I presume, therefore, that he will not deny
that the intelligent reader of our proposition does, as he reads,
make a valid experiment in favour of the proposition. But if this
be so, where is the deception in Euclid’s proof, and what is the
necessity of supplementing that proof by further “ideal” or
“actual experiments”? The course of Euclid’s argument shows
that the two triangles are not only equal, but equal in virtue of the
way in which they have been constructed, viz., the equality of the
two sides and the included angle. The fact that the. proof is not
syllogistic does not make it any the less a case of that parity of
* Logic, vol. i. p. 225.

178 Proceedings of the Hoy at Society

reasoning which Professor Bain, in another connection, admits to
be not induction but demonstration.*

Our author draws a broad line between the fourth proposition,
with its “ appeal to experiment or trial in the concrete,” and the
mass of geometrical proofs in which the figure is referred to for
verification only, “the effect of every construction and every step
of reasoning being judged of by actual inspection.” But if the in-
spection follows the construction, what is the construction itself?
A construction is not proved by syllogism from axioms. It is
necessarily drawn, and in the drawing (mental or other) looked at.
Every construction involves a figure and an intuition, which, while
it looks at the individual figure, sees in it the general truth. f Mr
Bain grants that of such consequences as that the diagonal of a
parallelogram divides it into two triangles, Euclid offers no other
proof than an appeal to the eye.J In fact, no other proof can be
offered. Yet surely it will not be asserted that this too is an
induction. In one word, if no proposition is fairly demonstrated
where it is essential to look at the figure, there is no sound de-
monstration in synthetic geometry.

Finally, Professor Bain himself seems not quite satisfied as to
the inductive nature of Euc. I. 4. “The proof,” he says, “rests
solely on definitions,” and hence “ the proposition cannot be real —
the subject and predicate must be identical.” Surely an identical
proposition is not an induction ! And surely, too, the proof rests
not on definitions merely, but on definitions and the use of the
figure ! But I do not think that Professor Bain means to speak
here in strict logical terms, for he straightway adds in explana-
tion, “ The proposition must, in fact, be a mere equivalent of the
notions of line, angle, surface, equality — a fact apparent in the
operation of understanding these notions. It is implicated in the
experience requisite for mastering the indefinable elements of
geometry, and should be rested purely on the basis of experience.”
We should have known better what this sentence means, if the
author had adopted here the distinction between synthetic and
analytic judgments. He cannot mean that a truth that is an in-

* Logic, vol. ii. p. 5.

t Cf. Kant, Krit. d. r. Yern. p. 478. Ed. Hartensiein, 1867.

I Logic, vol. ii. p. 218.

of Edinburgh, Session 1869-70.

179

duction, and rests on experience, is an analytic judgment, that it
can be reached by a purely formal dividing and compounding of
the definitions of terms. Such a proposition could be shown to he
true without any figure or any experiment. Yet the proposition
is, we are told, involved in the notions ; we cannot know what
lines, angles, &c., are without knowing this too. If this means
anything, it means that Euc. I. 4 is a synthetic judgment a ‘priori ;
and that, after all, Kant and the mathematicians are right, and Mr
Mill and the empirical logicians wrong.

4. A Simple Mode of Approximating to the Wave-Length
of Light. By W. Leitch, Assistant to the Professor of
Natural Philosophy in the University of Glasgow. Com-
municated by Professor Tait.

The fundamental phenomenon or fact of the science of optics is
vision, that is, the perception we have of distant objects through
the eye, or by the sense of sight. That vision is an effect trans-
mitted to the mind by the object seen, is a necessary truth, involved
in the definition of the term, and independent of all theoretical
views beyond the consciousness of that perception.

Common observation informs us that vision cannot take place
without that which we call light, and that light itself cannot exist
without the presence of a self-luminous body. Every one has a
distinct conception of the meaning of the' terms light and luminous;
their definition according to that conception would be a verbal
exercise of no utility at present.

Next may be placed the fact, first revealed by astronomical ob-
servations, and afterwards verified by other experiments, that light is
not transmitted instantaneously, — in other words, that some portion
of time elapses between the occurrence of a visible phenomenon
and our perception of it by the eye, such as, for simplicity, the
passage of an electric spark, or the occultation of a star by the dark
body of the moon or of a planet; and that the portion of time in
question is in direct proportion to the distance of the object seen
from the eye, the intervening medium being the same.

The progressive motion of light from the object seen to the eye
being established, and the supposition that it is a substance emanat-

180 Proceedings of the Royal Society

mg from the object with the velocity found, being seen to be in-
consistent with the phenomena of interference, we can scarcely be
said to make use of a hypothesis when we conclude that it is an
action transmitted through a medium bodily at rest, it may be, but
whose component molecules act upon one another in such a way as
to propagate the effect in question. By the term light we mean
this action considered as a physical fact, separate from our percep-
tion of it by the eye, and independent of its arrival or non-arrival
at our organs of vision.

The propagation of light from a luminous point with the same
velocity in all directions (in a homogeneous medium), implies that
the action originating at any instant in the source is diffused over
a spherical surface whose radius, measured from the luminous point
as centre, constantly increases at the rate of the velocity of light ;
and the constancy with which this propagation is kept up, implies
that there are an infinite number of such spherical surfaces, over
each of which is diffused an action which originated in the source at
a preceding instant. Next the question presents itself whether all
these actions originating in the source at successive instants, and
occupying successive spherical surfaces, are similar and equivalent.
The phenomena of interference answer, that if we imagine a series
of these spherical surfaces separated from each other by a very
small constant distance A, the action propagated upon each of these
surfaces is the same, and that midway between each pair of the
series is a surface propagating an action capable of destroying that
of its neighbour of the first series, from which it is separated by the

constant distance ^ . Now, that is equivalent to saying that each

thin spherical shell of the medium through which the action is
transmitted, vibrates between opposite phases, and as it is im-
possible for us to conceive or believe that any finite change can
take place in the material world that does not involve an infinite
number of intermediate infinitesimal changes, we are authorised to
say that light consists in periodic vibrations, propagated with very
great velocity, and decomposable in an infinite number of ways
into half vibrations exactly contrary to one another.

Thus far we have arrived without having recourse to any hypo-
thesis, having assumed nothing regarding the nature of these

181

of Edinburgh, Session 1869-70.

vibrations, the word vibration being understood in its most general
sense as meaning oscillation between opposite phases or conditions,
a fact revealed to us by the phenomena of interference. Even at
this point, however, the hypothesis which forms the basis of the
undulatory theory cannot fail to present itself to our minds, the
hypothetical part being not so much the existence of a medium, or
the propagation of vibrations, but the nature attributed to these
vibrations, viz., that they consist in mere mechanical action, in-
volving nothing but variations of pressure and displacement among
the particles of which the medium is composed, and propagated
according to the same laws as in ponderable media with which we
are more familiar. The suspension of interfering vibrations is
interpreted in the simplest manner as the result of the simultaneous
application of equal and opposite forces, or according to a fiction
easily understood, the superposition of equal and opposite motions,
and their reappearance after separation as the natural consequence
of the indestructibility of force. Moreover, our experience does
not enable us to conceive any other kind of vibrations decomposable
in the same manner, though the phenomenon of electrolysis seems
to indicate the propagation of a periodic oscillation between opposite
phases of decomposition and recomposition, involving something
more than variations of pressure and displacement among the
particles of water. Even the small degree of uncertainty that may
remain at this stage of the inquiry, is diminished by the pheno-
menon of diffraction, and by the physiological analogy between the
eye and the ear, both of them situated like feelers of the brain ; we
know the variety of perceptions that are communicated to the
mind by the effect of mechanical vibrations upon one of these
organs.

Adopting the hypothesis, we call these vibrations waves, from
their analogy to the vibrations so designated in the case of water,
and the distance A. above mentioned we call the length of a wave
of light. In order to effect its measurement, we produce the pheno-
menon of interference ; that is done most directly by deflecting two
pencils of light proceeding from the same source in such a way

that they may be superposed after traversing paths differing by

a

2 A

VOL. VII.

182

Proceedings of the Royal Society

°r -g, 2~, &c. ; but the most instructive method is to produce the

phenomenon of diffraction, which is usually accompanied by that
of interference.

Diffraction is the name given to the lateral deviation of light in
passing the edge of an obstacle, i.e., of an opaque body. Having
adopted the undulatory theory, we are ready to admit that such a
deviation ought to take place, both from our experience of similar
effects in air and water, and from our general ideas of the structure
and equilibrium of fluids, from which we conclude that no single
particle of a fluid can be disturbed without disturbing those sur-
rounding it on all sides, that is, propagating a disturbance in all
directions. When light, proceeding from a luminous source of
very small apparent diameter, passes the edge of a dark body and
is received upon a screen, instead of a sudden transition from light
to darkness at the line where the geometrical shadow commences,
we observe a gradually diminishing illumination for some distance
inside of that line, and outside of it we observe maxima and
minima of illumination arranged in bands parallel to it, if it is a
straight line. In order to effect the measurement of the length
A, and understand the principle of the process, it is not necessary
to follow the mathematical investigation of the position and in-
tensity of these maxima and minima. That investigation is based
upon the axiom that each point of a wave of light is a centre of
force, the molecule there situated tending to propagate the energy
with which it is animated in all directions around it, so that, if it
were at any instant the only molecule agitated, it would imme-
diately become the actual centre of a spherical wave. In the case
of the uninterrupted propagation of a spherical wave, it is the
envelope of all these elementary undulations to which is trans-
mitted the vibratory movement of each molecule, and which, by
reason of symmetry, is a spherical surface concentric with that
which it succeeds. Diffraction takes place when part of the wave
is intercepted by an obstacle, and the symmetry is destroyed
which kept the surface of the wave concentric with its first posi-
tion. The propagation of a spherical wave does not require that
contiguous molecules be allowed free play. If we look at a
luminous source through a fine grating, we see it in the same

of Edinburgh, Session 1869-70.

183

position as if the grating were removed, which proves that a con-
centric spherical wave is formed by the union of the fragmentary
parts of the incident wave which the grating has allowed to pass,
or at least the fragmentary parts distributed over the spherical
surface produce the same effect upon our sense of vision as if the
surface were occupied by an unbroken wave. If the grating be
sufficiently fine, and the luminous source not too near, we see not
only the source in its proper position, but also images of it on
both sides in the direction at right angles to the wires or dark
lines of the grating. If the light of the source be homogeneous,
that is, the same as we find at any point of a pure spectrum, these
lateral images are counterparts of the true image, of various in-
tensities. If the source emit white light, it is exhibited in each
of these images separated into its component colours, the image
being spread out so as to form a spectrum, with the violet extremity
nearest to the central image.

In order to understand the origin of these lateral images, first
suppose the transparent intervals to he of infinitely small width,
and separated by dark spaces of finite and equal breadth. Suppose
light coming from a distant source to be incident upon them in a
direction perpendicular to their plane. The space occupied by the
system of lines and spaces being very small, the surface of an
incident wave may be considered as coinciding with their plane,
so that a similar phase of vibration passes at all points of the
transparent lines at the same instant. Each of these lines thus
becomes the axis of a system of cylindrical waves behind the
grating, and at any instant the same phase of vibration is found in
each system at the same distance from the axis.

Suppose the dark lines in the figure to represent sections of
these cylindrical surfaces in the same phase of vibration. Upon
the surfaces which envelope a succession of these surfaces of similar
phase, in a direction parallel to AB, are formed a system of waves
by which we see the true image in its real position ; similarly, by
a system of waves which envelope surfaces of similar phase, in a
direction parallel to CD, we see the first lateral image to the right ;
by a system of waves parallel to EC, we see the second image, and
so on. If we denote by a the distance between the transparent
lines, and by D, the angular deviation of the first lateral image,

184

Proceedings of the Royal Society

we find, from the position of the surface CD, a sin D as the dis-
tance between successive surfaces of similar phase parallel to CD,
that is to say, as the length of the wave of the light propagated
in the direction normal to CD. Similarly, by drawing perpen-

A \

diculars upon the successive envelope surfaces through C from
the first opening to the right, we get for the same wave length

^ a sin D2 from the second image, ~ a sin D3 from the third, and so

LI O

on. In the case of white light, the separation into its component
colours exhibited in each lateral image enables us, by observing
the deviation of each colour of the spectrum, to measure the wave
length of light of that colour.

The lateral images are thus easily accounted for in the imaginary
case, in which the transparent intervals are of infinitely small
breadth. Gratings have been constructed by ruling sensibly dark
lines upon glass so closely that the breadth of the transparent
interval is only a small fraction of the length of wave. The
explanation of the images seen through these is the same as that
just given for the imaginary case.
Suppose, however, the width of the
spaces to be so much greater than the
length of wave, that the small inclined
surface AC which covers the opening,
as seen in the direction AP normal
to AC, stretches obliquely across the
exact length of a wave of the inci-
dent light, the surface AC, which
would be the locus of the same, or at least concordant phases
of vibration if light were propagated in the direction AP,

185

of Edinburgh, Session 1869-70.

will contain nothing but a series of equal and opposite phases,
which will he discordant and mutually destructive, as far as con-
cerns the propagation of light in the direction AP, and no image
will be seen in that direction, whatever may be the distance be-
tween the transparent spaces. The same will he the case if the
breadth of the spaces be such that the surface AC stretches across
exactly 2, 3, or any whole number of wave lengths. But if the

surface AC stretches across n -f ^ wave lengths, ^ being a proper
9 9

fraction, the vibratory movement transmitted along AP by the
fractional part of the wave length will not be destroyed by the
concurrence of its complete opposite, and light will he propagated
along AP. The other transparent spaces will send concordant
phases to the envelope wave, if AP be at the proper angle. In
this case, however, the breadth e of a transparent space must be
added to a in the formula a sin D, &c., a + e being the distance
between the successive effective remnants of the vibratory move-
ments which pass to the envelope surfaces. The breadth a -f e
occupied by a dark and a transparent space is called an element of

the grating. If the fractional part ^ of the wave length, which is

effective in forming any one of these envelope waves, be either a
very small or a very large fraction, its effect will be feeble, and
the corresponding image of small intensity ; but if it be exactly
one-half of the wave length, its effect will be the greatest possible,
and the envelope wave will receive from each opening the greatest
possible amount of concordant action. In this manner is explained
the difference of intensity of these lateral images, the one nearest
to the central image not being always the brightest. Proximity
to the central image is, however, also a cause of greater brightness,
it being evident that the less the surface AO in the last figure is
inclined to the incident waves, the greater is the absolute length
of that part of it which stretches over any given fraction of the
wave length, and the greater the amount of action of which it is
the locus.

In the above the incident waves have been supposed to be ex
actly parallel to the plane of the grating, so that the same phase
of vibration passes at the same instant through all the openings.

186 Proceedings of the Royal Society

The figure annexed shows that if the incident waves be inclined to
the grating at such an angle that the perpendicular from any open-
ing upon the wave surface
passing through the next
opening is equal to the wave
length, the same phase will
in this case also pass all the
openings at the same in-
stant, though derived from different incident waves, and the first
lateral image will be seen in a direction normal to the grating.
The same formula will give the wave length in this case, D being
always the angular deviation from the true image or from the
direction of the incident light. This is the condition approxi-
mately realised in the arrangements for measuring the wave length
about to he described, but as no provision is made for an exact
adjustment of the grating to the inclination just indicated, and
as a very minute error in such an adjustment would cause the
conditions of the experiment to be altogether different from those
indicated by the figure above, it is necessary to account for the
appearance of lateral images in the case of light incident at any
angle, and find a formula for the wave length applicable to that case.

If, as in the figure below, the incident waves be so inclined to
the grating that the perpendicular BC, together with the perpen-
dicular BD, make up the wave
length, the same phase of vi-
bration will be situated at A
and D ; for the same reason,
behind every two consecutive
openings, like phases will be
situated upon surfaces inclined
at the same angle as AD, that is to say, AD produced will en-
velope like phases, and the first lateral image will be seen in the
direction normal to AD. If we denote by I the angle of incidence
CAB, and as before by D, the angle of deviation CAD, we get
X = (a + e) {sin I + sin(D-I)}. So long as I and D are small,
the latter factor is approximately = I + D - I = D = sin D, the
same as before, so that in that case the error introduced by using
the formula first obtained with only an approximate adjustment of

of Edinburgh, Session 1869-70. 187

the grating is inconsiderable. The same is the case if either I
alone or D - I be very small.

By differentiating the formula we get

cos I + cos (D - I) ^5 -1^=0 . (2).

. dD _ cos (D - I) - cos I _ ^ _ cos I
' ' dl cos (I) - I) cos (D - I) ’

(and if D = 21) = 1 - cos 1 = 0,

COS I

that is, D is constant for small variations of the position of the
grating, or angle of incidence, while the variation of the latter
by condition (2) does not affect the value of A calculated from the
formula. There is, therefore, an advantage in observing with the
grating adjusted to bisect the angle between the directions of in-
cidence and diffraction, that being the position in which a small
error in the adjustment has the least effect upon the result given
by the formula, which becomes in this case,

A = 2 (a + e) sin 5 .

In the arrangements now to be described, in which we use two
sources of light, one on each side of the normal to the grating,
we make the angle (D - 1) approximately vanish, and use the mean
of the two angles of incidence in the formula
A — - (a + e) sin I.

By neglecting the part (a + e) sin (1) - I), which is positive for
the one light, and negative and of the same magnitude for the
other, as is plain from the method of observing, we introduce no
error into the result.

AC, BD, are sections of two rectangular pieces of tin bent into
a cylindrical form round the glass funnels of two paraffin lamps.
Their edges come short of meeting so as to leave a slit at A and B
of about 1 millimetre in breadth. These slits are partially covered
with tin as shown immediately below, where they are drawn as
they appear to the eye of the observer. A thread is stretched
round the two cylinders, partly shown between A and B. EF

n

Proceedings of the Royal Society

A

is a straight stick passing horizontally immediately under the
thread, and graduated in centimetres on its upper edge. A
_ grating constructed by drawing trans-

parent lines at the rate of 2000 to the
inch upon glass covered with a dark
ground, is held by the hand against the
end E of the stick, cut square with its
edges. The stick is then pushed in or
out in the direction of its length till the
red colour of the first spectrum to the
right of A is seen to be directly above
the same colour of the first spectrum to
the left of B. A pencil mark is then
made upon the stick directly below the
thread. The stick is then drawn further
out until the yellow colours of the two
spectra are seen in the same vertical
line, and another mark is made ; and so
with the remaining colours. The dis-
tance from centre to centre of the two
slits, in a horizontal line, being 10 centi-
metres, the distances marked off between
E and the thread were read 99-5 centi-
metres for the red, 107 for the yellow,
116 for the green, and 135 for the blue.
These numbers were taken for the dis-
tance to the light in each case, being
only about ^ per cent, less by calcula-

E

tion. The corresponding wave length
by the formula X = (a + e) sin I, are

Bed

5

i

^ of an

inch = -000638 millimetre.

99-5

* 2000

39800

Y ellow

5

107

1

* 2000

1

42800

- -000593

Green

5

1

X 2000

1

= -000547 „

116

46400

Blue .

5

1

1

= -000470 „

135

X 2000 '

54000

189

of Edinburgh, Session 1869-70.

Different measurements pay be got by the same observer at dif-
ferent times from his uncertainty as to the points in the spectrum
at which he should consider each colour to begin and end. This
uncertainty is usually considered to be obviated by using solar
light, and measuring the deviations of the dark lines in the spec-
trum ; but as these lines are the parts of the spectrum from which
no light comes, the process can scarcely be called the determina-
tion of the wave length of light.

Since the above measurements were made, an improvement was
made in the apparatus by which the gratings were constructed, and
finer gratings were made, which gave more brilliant spectra, by
reason of the greater number of apertures from which similar
phases of vibration came to the eye. With one of these, consisting
of transparent spaces drawn at the rate of 3000 to the inch, a new
set of measurements was taken in the following manner

EF represents a rectangular piece of
wood upon which is pinned a piece of
paste-board ABCD, whose edge AFB ^
is an arc of radius 20 inches and
centre at E. The chord AB is divided
into tenths of an inch by perpendicu-
lars to it meeting the arc. Touching
the arc are placed, but not fixed, two
pieces of tin bent as represented at Gr,
each having a narrow slit so situated
that the bottom of the one slit is on a
level with the top of the other, and
carrying a small piece of candle im-
mediately behind the slit. The grat-
ing is held at E, and the pieces of tin
are moved along the arc until the
colour observed in each spectrum is in
the same vertical line at F. The dis-
tance between the two slits is then
read upon the graduated chord, and
the half of that distance divided by
20 inches is the sine of the deviation. In this case the second
spectrum from each light was observed, and the observed dis-

2 b

VOL. VII.

190

Proceedings of the Royal Society

tances for the red, yellow, green, and blue, were 5’9, 5*5, 5*025,
and 4-25 inches respectively. The wave lengths calculated from
these data are in millimetres —

1

5*9

1

25*4 _

*000624 millimetre for the red.

2 *

2 ’

20

' 3000

1

2 *

55

2 *

1

20'

25*4 _
' 3000

*000582

,, yellow,

1

5*025

1

25*4

•000531

2'

2 *

20

' 3000 “

„ green,

1

4*25

1

25*4

•000449

„ blue.

2 *

2 ’

20'

3000

The apparatus contrived and constructed by the author to pro-
duce these tine gratings has not been described, because its con-
struction involves considerable trouble and expense, which the
experimenter may avoid by applying to an instrument-maker who
has a dividing machine. The difficulty of getting a sufficiently
fine dark ground upon the glass will also be avoided if the dividing
machine be fitted with a diamond point, which will scratch com-
paratively opaque lines on the transparent surface of the glass.
The finest gratings constructed are produced in that way.

5. Note on Linear Partial Differential Equations. By
Professor Tait.

The equation

^ du _ du du
P di + Q‘dy+ = 0

may be put in the very simple form

S(o- V)u — 0,

if we write

<t~ = $"P T^Q T' /rR,
and

. d . d d
^ ~ 1 dx 3 dy+ c dz

This gives, at once,

Vn = mV Ocn t

where m is a scalar and 6 a vector (in whose tensor m might have

of Edinburgh, Session 1869-70. 191

been included, but is kept separate for a special purpose.)
Hence

du — — S (dpV)u
= — ?7iS . 6<3~ dp

= - 8 .Odr,

if we put

dr = mV. cr dp

so that m is an integrating factor of Y. <r- dp. If a value of m can
be found, it is obvious, from the form of the above equation, that $
must be a function of r alone ; and the integral is therefore
u = F(r) = const.

where F is an arbitrary scalar function.

Thus the differential equation of Cylinders is
S(a V)u = 0 ,

where a is a constant vector. Here m = 1, and
u = F(Vap).

That of Cones referred to the vertex is

S (pV)u = 0.

Here the expression to be made integrable is

Y. pdp.

But Hamilton long ago showed that

dJJp dp Y. pdp

Of = v7 = (TpF5

which indicates the value of m, and gives
u — F(Up) = const.

It is obvious that the above is only one of a great number
of different processes which may be applied to integrate the
differential equation. It is quite easy, for instance, to pass from
it to the assumption of a vector integrating factor instead of the
scalar m, and to derive the usual criterion of integrability. There
is no difficulty in modifying the process to suit the case when the
right hand member is a multiple of u. In fact it seems to throw
a very clear light upon the whole subject of the integration of
partial differential equations. But I have not at present leisure to
pursue the subject farther than to notice that if, instead of 8(<r^ V),

192 Proceedings of the Royal Society

we employ other operators as S(V V) S(rV), S ,cr VrV, &c. (where V
may or may not operate on u alone), we can pass to linear partial
differential equations of the second and higher orders. Similar
theorems can be obtained from vector operations, as Y(<r* V).

6. On the Oxidation Products of Picoline. By James
Dewar, F.B.S.E., Lecturer on Chemistry, Veterinary
College, Edinburgh.

(Abstract.)

The author in this paper details the results of a series of experi-
ments, commenced three years ago, on the oxidation of the
pyridine series of bases. These bodies are readily attacked by
permanganate of potash ; and the oxidation products of picoline
thus obtained are ammonia, carbonic, nitric, oxalic, acetic, and
dicarbopyridenic acids, along with a very small quantity of some
solid base, possibly a condensed base.

CO H

Dicarbopyridenic acid, C5H3N

is bibasic, and bears the

same relation to the nucleus pyridine that phthalic acid and its
isomers bear to benzol. It crystallises from hot aqueous solutions
in plates resembling naphthaline; the majority of its salts are
soluble and crystallisable. The silver salt of the acid is very
characteristic, being insoluble and gelatinous, not decomposed by
boiling water, and not visibly affected by light. As this acid was
got in only small quantity, the author had not the opportunity
of producing its various derivatives.

The author observes that the two well-defined series of nitrile
bases found in coal tar, viz., the pyridine and chinoline series,
bear the same relation to each other that the benzol series
of hydrocarbons does to thehiaphthaline. Thus, pyridine is sup-
posed to he the nucleus in these bodies that benzol is in the
aromatic series. The following are some of the analogies pointed
out in the paper : —

Benzol. Naphthaline. Anthracine. Pyridine. Chinoline.

c2h2 c„h4 c„h4 c2h2 c,ii,n

c2h2 c2h2 c2h2 nch c2h2

Gft C2H2 C6H4 C2H2 C2H2

Chinoline and pyridine, therefore, ought to be readily obtainable

193

of Edinburgh^ Session 18G9-70.

from each other, and it is the intention of the author to work in
this direction. It is observed also that indol, the nucleus of
indigo, is benzol-pyrrol, being related thus,

Indol.

Pyrrol.

C6H4

CA

NH

NH

C>A

CA

It is therefore likely that indol may be met with along with pyrrol
among the products of the destructive distillation of nitrogenised
organic substances. While this paper is passing through the press,
Professor Baeyer of Berlin has pointed out, independently, a simi-
lar relation between pyrrol and indol, a note of which has just been
published.

7. Notes of some Experiments on the Eate of Flow of Blood
and some other Liquids through tubes of narrow diameter.
By J. Matthews Duncan, M.D., F.E.S.E, and Arthur
Gamgee, M.D., F.E.S.E.

The experiments, of which the results are recorded in the present
communication, were undertaken in order to determine the rate at
which blood flows through tubes of moderately small diameter, with a
view to the study of the mechanical theory of dysmenorrhoea ; they
were afterwards extended to blood-clot, serum, milk, and urine, &c.

In a memoir inserted in the ninth volume of the “ Memoires des
savants etrangers,” M. Poiseuille stated the results of an investiga-
tion on the flow of water and other fluids through capillary tubes,
showing how this is influenced by pressure, by the length and
diameter of the tube, and by temperature. A committee of the
French Academy, of which M. Begnault was the reporter, corrobo-
rated the results of M. Poiseuille’s researches.* Subsequently this
observer published a still more extended series of observations, in-
cluding the determination of the rate of flowT of serum and defi-
brinated blood.t

* Recherches experimentales sur le mouvement des liquides dans les tubes
de tres-petits diametres. Commissaires MM. Arago, Babinet, Piobert, Reg-
nault rapporteur. Academie des Sciences, seance du 26th Decembre 1842.

t Recherches experimentales sur le mouvement des liquides de nature dif-
ferente dans les tubes de tres petits diametres par M. le Dr Poiseuille. An-
nales de Chimie et de Physique. Troisieme serie t. xxi. 1847.

194

Proceedings of the Royal Society

The method employed by Poiseuille in his researches, and which
is described at length in his Memoir, consisted essentially in
causing air under a known pressure to force a known quantity of
the fluid to be experimented upon through tubes of known diameter
and length, and determining the time employed.

The following are the general results to which he arrived con-
cerning the influence of the length and diameter of tubes of smaller
diameter than a millimetre on the rate of flow of any liquid at a
constant pressure and temperature : —

1st. The volumes of liquid flowing in equal times through capil-
lary tubes of equal length, but of different diameters, are amongst
themselves as the fourth powers of the diameters.

2d. The volumes of liquids which flow in equal times through
capillary tubes of the same diameter, but of different lengths, vary
inversely as the length of the tubes.

With regard to the influence of pressure, it was found that the
rate of flow increased directly as the pressure ; and with regard to
the temperature, that, as a general rule , the rate of flow of solutions
increases as the temperature rises.

With regard to the influence of various substances held in solu-
tion by a fluid, on the rate of flow, no general law was arrived at,
connecting it either with chemical constitution, density, capillarity,
or viscosity.*

The following are some of the results, extracted from M. Poi-
seuille’s Memoir —

I. Tube employed (B) is 64 millimetres long; its diameter is
0mm,249 ; capacity of receiver, 6 0. 0.; pressure, 1 metre; tempera-
ture, 14°5 C.

* We may merely allude to the fact that M. Graham succeeded in showing
a decided connection between the rate of flow of the different hydrates of
sulphuric acid and their chemical constitution. His very interesting results
are to be found in a paper' “ On liquid transpiration in relation to chemical
composition.” ( Philosophical Transactions , 1861, p. 373).

Time of Flow.

s.

1. Distilled water,

2. Ether,

3. Alcohol, .

4. Serum of ox’s blood.

535-2

160-0

1184-5

1029-0

195

of Edinburgh, Session 1869-70.

M. Poiseuille made a single determination of the rate of flow of
blood serum ; of blood serum plus a small and unknown quantity of
corpuscles, and of defibrinated blood, the same animal’s blood (an
ox’s) having been used to furnish the three liquids. The following
are the results —

Temperature and pressure stated to have been kept constant
during all the experiments; length of tube, 110 millimetres; dia-
meter, 0mm,256 ; capacity of receiver, between 5 and 6 C. 0.

Time of Flow.
m. s.

Serum, ..... 20*33

Serum and a small and unknown quantity of

blood corpuscles, . . . 21T7

Defibrinated blood, .... 68*47

Poiseuille points out that the aggregation of blood-corpuscles,
which always takes place in defibrinated blood, leads to a choking
of the tubes employed, especially when these are of narrow diameter
(0mm,l), or to an irregular flow, and that consequently defibrinated
blood cannot readily be injected through the capillaries of the
lungs of animals which have been bled to death. The recent ex-
periments of Dr J. J. Muller,* carried on under the direction, and
according to the method, of Professor Ludwig, in the Physiological
Institute of Leipzig, are opposed to the statement of Poiseuille,
for he succeeded in keeping up for long periods a flow of defibrin-
ated blood through the lungs.

Method employed in the present research.

All experiments were conducted according to a method suggested
by, and under the direction of, Professor Tait, in the Physical
Laboratory of the University of Edinburgh. The liquids to be
experimented upon were allowed to flow through tubes of known
diameter and length, into a large air-pump receiver exhausted to a
partial and known extent, the fluid being thus subjected to the
pressure of the atmosphere, minus that of the air in the receiver.

Before enumerating our experiments, it may be well to point
out certain fundamental differences which exist between them and

* “ Ueber die Athmung in der Lnnge von Dr J. J. Muller.” Arbeiten aus
der Physiolog. Aust. zu Leipzig Mitgetheilt durcli C. Ludwig. Leipzig,
1870, p. 37-76.

196

Proceedings of the Royal Society

those of M. Poiseuille. ls£, Our tubes had a much wider diameter —
those used by the French observer varied in diameter from
0mmT949-0mm,256, whilst our tubes were from 0mm,845-lmra*259.
2 dly, By our tubes being much longer than those of Poiseuille ;
and, 3 dly, By the liquids being allowed to flow, not into water, but
into empty vessels placed in the partially exhausted receiver.

I. — Influence of the Shape of the Tubes employed on the Rate of Flow.

It was considered advisable to determine, in the first place,
whether bends in the tubes through which the liquids were made
to flow wrould exert any influence on the rate. Accordingly, a
tube 1129 millemetres long was bent twice at right angles; one
end was connected by means of a tightly fitting cork with the

Table I.

Time of

No. of

Diame-

Length

Temper-

ature.

Pres-

Flow of

Experi-

Fluid used.

ter of

of

lOOCubic

ments.

Tube.

Tube.

sure.

Cents, in
Seconds.

mm.

mm.

mm.

Tube bent

twice

1-5

Water, . .

0-845

1129-8

13?0 C

708-59

126-4

at right angles,

5-8

Common Sul-
phuric Acid,

!"

13-5

»

2978-0

thus,

f

8-9

Water, . .

”

”

13-5

588-5

158-0

10-11

Water, . .

0-845

1129-8

13-5

588-5

159-8

Tube bent four

times at right an-
gles in the same

plane, thu;

A

s,

11-12

Water, . .

0-845

1129-8

11-5

588.5

157-4

Tube bent

four

times at right an-
gles; at one point
bent at an angle
of about 135° to

its former plane.

13-14

Water, . .

0-845

1129-8

11-4

588-5

161

Tube again

. bent

as in experiments

15-17

Water, . .

0-845

1129-8

33-0 C

588-5

108

10 and 11.

of Edinburgh, Session 1869-70.

197

exhausted receiver, and the other was at a given instant immersed
in water. The rate of flow having been determined, the tube was
bent four times at right angles, and the experiment repeated ; then
it was not only bent four times at right angles in one plane, but
bent at one point at an angle of about 135° to its former plane.

The results of these various experiments are exhibited in
Table I., page 196.

It results from these experiments that the bends in the tubes
had no perceptible influence in modifying the flow — the quantity
of fluid flowing in the same time being directly as the pressure,
and very much influenced by rises of temperature.

II. — Hate of Flow of Defibrinated Blood of Sheep.

Having determined that the shape of the tubes exerted no
influence on the flow of fluids through them, we proceeded to
examine the comparative rate of flow of the defibrinated blood of
the sheep. The results are recorded in Table II.

The tube used in this experiment was 908-9 millimetres long,
and was twice bent at right angles. The diameter was 1-214
millimetres.

Table II.

No. of
Experi-
ments.

Fluid used.

Diameter
of Tube.

Length
of Tube.

Tempera-

ture.

Pressure.

Rate of
Flow of
100 Cubic
Cents
in Seconds.

18-21

Water,

mm.

1-214

mm.

908-9

10°-5

mm.

583-5

67-6

22-25

Defibrinated sheep’s
blood,

1 »

„

167

583-5

\

26-28

,,

,,

i 227-6

29-31

, ,

,

,,

)

32-35

-

”

”

31 "0

”

143.4

2 c

VOL. VII.

198

Proceedings of the Royal Society

Table III.

Comparative Rate of Flow of Water , Defibrinated Ox-Blood , Serum
of Blood ( obtained from same sample of Blood), and Defibrinated
Sheep's Blood.

No. of
Experi-
ments.

Fluid used.

Diameter
of Tube.

Length
of Tube.

Tempera-

ture.

Pressure.

Time
occupied
by Flow of
100 Cubic
Cents
in Seconds.

36

Water,

mm.

1-214

mm.

908-9

12°-0C

mm.

598-7

68-16

37*

Serum of ox-blood,

,,

,,

13-1

,,

9710

38

,,

,,

,,

,,

,,

9814

38

,,

,,

,,

16°"0

,,

94-50

40

Defibrinated ox- )
blood, . . \

>>

>>

365-7

41+

Defibrinated )

sheep’s blood, $

”

”

18°-0

”

260-2

III. — On the Rate of Flow of Pure (i.e., uncoagulated) Blood at the
Temperature of Body through Narrow Tubes.

Exp. 43. — In this experiment a calf, about a week old, was made
use of. The jugular vein on the left side having been exposed, an
opening was made into it as low in the neck as possible, and a
flexible catheter was passed into the right side of the heart ; the
venous blood used was thus obtained.

Thereafter the carotid artery was exposed on the same side,
and a ligature having been applied on the distal side of the
exposed portion, a tube was introduced into the cardiac end. From
this tube was obtained the arterial blood used in the experiment.
The temperature of the calf before the experiment was, 38°-8 C.
After the experiment, .... 380,7 0.

The blood was received directly into graduated tubes heated to
38-°8 0.

* Solids in 1000 parts of serum, 90-41

Water, 909-59

f Solids in 1000 parts of the blood, 212-21

Water, . 787-79

199

of Edinburgh, Session 1869-70.

Two tubes were used in these experiments. The length was 56
inches. The first (Tube C) had a diameter of T259 of a millimetre.
The second (Tube A) had a diameter of 09289 of a millimetre.

Table IY.

No. of
Experi-
ments.

Fluid used.

Diameter
of Tube.

Length
of Tube.

Tempera-

ture.

Pressure.

Time of
Flow of
100 Cubic
Cents
in Seconds.

43

Water,

Tube C.
mm.

1-259

mm.

914-

15°' C

mm.

601-7

42-10

44

Water,

,,

,,

39°-5 C

,,

39-43

45, 46

Venous blood of calf,

,,

,,

0°

OO

CO

589-0

54-9

46, 47

Venous blood of )
calf, defibrinated >
and arterial, . )

”

”

”

”

53-11

48, 49

Arterial blood of calf,

”

”

”

”

60-07

50

Water,

Tube A.

0.9289

914-

38° -5

601-7

69-4

15-53

Arterial blood of calf,

”

”

”

”

160-1

From this experiment it would appear that the rate of flow of
blood just drawn from the vessels of a living animal is very much
greater than the rate of flow of blood which, having been defibri-
nated, has been allowed to stand for some time, as was the case in
experiment 40. In defibrinated blood the corpuscles tend un-
doubtedly to run together, and the masses thus formed by their
coherence must necessarily account for the extreme slowness. The
pure and perfectly warm blood flowed, indeed, more rapidly than
did the serum obtained from ox-blood, which had been used in a
previous experiment. In experiments 36, 37, 38, and 39, it was
found that the time of flow of equal quantities of serum and water
were represented by the ratio of 1*4:1. In experiments 43-49,
it was found, on the other hand, that the rate of flow of equal
quantities of pure blood and water were represented by the ratio of
1-3:1.

In a former part of this paper we stated that the diameters of
the tubes used by us differed from those of Poiseuille in being
much wider.

200 Proceedings of the Royal Society

As was previously stated, the French author found that in capil-
lary tubes of different diameter, the quantity of fluid flowing in
equal times through equal lengths, varies not as the squares, but
as the fourth power of the diameters. In the tubes used by us,
in the experiment above described, the diameter was such that the
quantities of water flowing through equal lengths were, cceteris
paribus, as the squares of the diameters. It is interesting to
observe in connection with experiments 43-53 inclusive, that
whilst the amount of water flowing varied very much as the
squares of the diameters, the quantity of blood flowing through the
two tubes did not obey this law ; . the blood being retarded in its
flow more than water though by no means to such an extent as
to show that, for it, the tubes obeyed Poiseuille’s law.

IV. On the Pressure required to force Blood Clot through Tubes of

Narrow Diameter.

The clot used was obtained by allowing ox’s blood to coagulate,
and separating it from serum.

Exp. 54. — In this experiment a tube having a diameter of IT 62
millimetre was used. Although subjected to the whole atmo-
spheric pressure (700 M.) none of the clot would pass through the
tube.

Exp. 55 and 56. — In this experiment the same clot was used,
but a different tube. The clot was found freely to flow through
the tube, which had a diameter of 2'00 millimetres.

In experiment 55 the pressure of a column of mercury 24 inches
high was employed. In experiment 56 that of a column 29 inches
high was required.

V. On the Rate of Flow of Milk and Urine through Narrow Tubes.

The results of these experiments are shown in the annexed table.

It will he observed that two tubes were employed in the determi-
nation of the rate of flow of milk, whilst the two sets of experi-
ments with urine were performed with one tube. The rate of flow
of urine is shown to be almost identical with that of water, whilst
the rate of flow of milk is about the same as that of water when a
large tube is used, but much slower when a tube of narrow
diameter is employed.

of Edinburgh, Session 1869^70.
Tube A.

201

Fluid Used.

Diameter

of

Tube.

Length

of

Tube.

Tempera-

ture.

Pressure.

Time of Flow
of 100 Cubic Cents
in Seconds.

Water,

mm.

•928

mm.

914

17° C

mm.

601-97

69 "2

Urine, Sp. Gr. 1018

,,

,,

17-5

,,

71-3

Urine, Sp. Gr. 1007

,,

,,

,,

,,

70-3

Cow’s Milk,

”

”

24-6

594-3

90'3

Tube C.

Fluid Used.

Diameter

of

Tube.

Length

of

Tube.

Tempera-

ture.

Pressure.

Bate of Flow
of 100 Cubic Cents
in Seconds.

Water,

mm.

1-259

mm.

914

15

mm.

601-97

42-1

Cow’s Milk,

,,

,,

27

,,

38-1

Goat’s Milk,

”

22

”

36-09

8. On Cystine (C3H7N02S). By James Dewar, E.R.S.E.,
Lecturer on Chemistry, Veterinary College, Edinburgh ;
and Arthur Gamgee, M.D., E.R.S.E., Lecturer on Physio-
logy, at Surgeon’s Hall, Edinburgh.

Preliminary Notice.

With the exception of the physical characters of this rare chemi-
cal substance, which is only known as an abnormal constituent of
the human body, we know so very little, that even a few facts with
regard to its behaviour with reagents may not be altogether unin-
teresting.

Cystine has the composition C3H7N02S ; and crystallises in the
form of six-sided plates. It forms with hydrochloric, nitric, and
phosphoric acids, definite crystalline compounds.

Some of the most important facts with regard to the chemical
reactions of cystine have been recorded by Dr Bence Jones, who
for the first time showed that nitrous acid decomposes it with the
evolution of nitrogen, and that in this operation the sulphur which
it contained is oxidised to sulphuric acid, whilst a non -crystalline

202 Proceedings of the Royal Society

substance is left which is precipitable by nitrate of silver, mercuric
chloride, as well as by acetate of lead.

The cystine used in our experiments was obtained from two
portions of calculi, one of which was furnished to us by Professor
Maclagan, the other by the Eoyal College of Surgeons of Edin-
burgh. The cystine was obtained by treating the pounded calculi
with strong liquor ammoniee, which dissolved the greater part, and
allowing the solution to evaporate at a very gentle heat. The
cystine which separated was then again dissolved in ammonia and
recrystallised.

Preparation of Hydrochlorate of Cystine.

One gramme of cystine was dissolved in boiling hydrochloric acid;
on cooling beautiful needle-shaped crystals separated, which were
very soluble in water. When thoroughly dried in vacuo over quick-
lime the crystals were found not to be readily soluble in water. 0*05
grm. of crystalline hydrochlorate of cystine yielded 0*0452 grm. of
AgCl, corresponding to 22*2 per cent, of HC1 (Calcd. 22*5).

Action of Nitrate of Silver on Cystine.

Cystine was dissolved in strong solution of ammonia, and to the
solution was added a solution of silver nitrate in ammonia. No
precipitate-occurred, nor did the solution darken in the cold. When
slightly acidified with nitric acid, a canary-yellow precipitate was
thrown down, which was collected and dried in vacuo. The fil-
trate blackened when heated, and on filtering off the black preci-
pitate a clear colourless solution was obtained, which was not
further blackened when boiled with ammoniacal solution of oxide
of silver.

On analysis the substance precipitated proved to be a compound
of cystine with nitrate of silver.

In a subsequent experiment an ammoniacal solution of cystine
was boiled with an ammoniacal solution of nitrate of silver. A
black precipitate fell which consisted of sulphide of silver. The
filtrate from the precipitate of sulphide of silver was subsequently
treated with solution of chloride of ammonium to separate the
excess of silver. The solution was found not to be precipitated by
hydrochloric acid and chloride of barium, nor by sulphate of cal-

of Edinburgh, Session 1869-70. 203

cium. It is therefore evident that when an ammoniacal solution of
cystine is heated with ammoniacal solution of oxide of silver, the
sulphur is separated entirely as sulphide of silver, none being
oxidised ; it is also obvious that no oxalic acid is formed.

Action of Caustic Soda and Caustic Baryta on Cystine.

Cystine, when treated with pure solution of pure NaHO, and
evaporated in a silver basin, gives a reddish fluid ; sulphide of
sodium is then produced, blackening the basin, and ammonia is
copiously evolved. On treating the residue with water, neither
sulphuric nor oxalic acids can be detected. The liquid contains,
however, a large quantity of sulphide of sodium with a mere trace
of sulphite.

Cystine, when heated to 150° C. with solution of caustic baryta in
sealed tubes, gave off ammonia, a large quantity of sulphide of
barium, a smaller quantity of sulphite of barium, and a trace of
hyposulphite being formed. No trace of sulphocyanide could be
detected.

Action of Alcoholic Solution of Potash on Cystine.

Cystine was heated for several hours in a sealed tube at 130° C
with an alcoholic solution of potash. At the conclusion of the
experiment a small quantity of dark sticky matter was found
adhering to the tube, which contained a yellowish fluid. The latter
smelt strongly of ammonia, which was separated by distillation.
The residue was acidified with dilute sulphuric acid, and shaken
up with ether. Ether left a yellow non-crystalline substance,
possessed of an indefinite but disagreeable odour. This substance
had a strong acid reaction, and was found to contain no sulphur.

Action of Nascent Hydrogen on Cystine.

When cystine is added to a mixture of tin or zinc and dilute
hydrochloric acid, large quantities of sulphurated hydrogen are
given off ; the evolution of gas gradually slackens, till even after
the action has gone on for several days, traces of sulphuretted
hydrogen continue to be given off. When treated in the same
manner taurine does not evolve H^S.

It is to be noted that this evolution of H,S, when cystine is

204 Proceedings of the Royal Society

treated with tin or zinc and hydrochloric acid, might be used as a
test for the substance, care being previously taken to separate any
sulphide which might exist.

Action of Nitrous Acid on Cystine.

Cystine was placed in water and a stream of nitrous acid gas
passed through it. No action took place until the water was
heated ; it then commenced and proceeded briskly, with abundant
effervescence, until the whole of the substance was dissolved.

The clear solution contained a large quantity of sulphuric acid,
but not a trace of oxalic acid. When boiled with an ammoniacal
solution of nitrate of silver, considerable reduction took place, a
beautiful mirror of silver being deposited on the glass. The fluid
was again subjected to the action of nitrous acid ; still no oxalic
acid could be found, and the reduction of an ammoniacal solution
of oxide of silver continued. A portion of the fluid was treated
with carbonate of barium and heated; the clear filtrate had an
alkaline reaction, and was abundantly precipitated by nitrate of
silver and acetate of lead. The remainder of the fluid, after the
treatment with BaC03, was treated with solution of nitrate of silver.
An abundant canary-yellow precipitate was formed. This was
suspended in water and decomposed with H2S ; the filtrate was
evaporated to dryness, and presented the appearance of a sticky
solid. It was soluble in water. The aqueous solution was evapo-
rated and treated with absolute ether, which dissolved the greater
part. The ethereal solution left on evaporation an acid fluid.
This was dissolved in water, neutralised with ammonia, and pre-
cipitated with solution of nitrate of silver. The yellow precipitate
obtained was amorphous ; it was dried in vacuo. Two specimens of
the silver salt prepared at different times were analysed by us.
The following are the results of two analyses

Silver,

56-9

57-5

Carbon, .

19-43

21-32

Hydrogen,

5-29

4-64

In considering the discrepancies of these analyses, it must be
borne in mind that we were operating in excessively small quan-
tities of a substance prepared at different times by complicated
processes.

of Edinburgh, Session 1869-70.

205

L

Remarks.

Cramer believed that cystine was intimately related to the body
called Serin, C3H7N03, which is obtained as one of the products
of the action of alkalies on silk. Serin, when treated with nitrous
acid, yields glyceric acid, as alanine under the same circumstances
yields lactic acid, and therefore serin may be looked upon as
amido-glyceric acid.

Cramer further believed that cystine was a sulpho-amido-glyceric
acid, i.e., serin in which hydroxyl has been replaced by HS.

This supposed relation is exhibited below —

ch2oh

ch2nh2

ch2nh,

CHOH

CHOH

CHSH

co2h

co2h

co2h

Glyceric Acid.

Amido-glyceric Acid
or Serin.

Cystine.

Considering that this relation of cystine to serin really exists,
some have argued that on treatment with nitrous acid, cystine
should yield glyceric acid. We do not, however, admit that this
would really be the case. If we examine the case of sulpho-lactic
acid, an analogous body to the supposed sulphur derivative of
serin, we find that, on oxidation, it gives sulpho-propionic acid,
and therefore we should, in the case of cystine, expect that a
sulpho-acid would be formed on treatment with nitrous acid, were
it built up as Cramer supposed. We have uniformly observed,
during the course of our experiments, that, however carefully we
attempted to regulate the action of nitrous acid on cystine, or of a
nitrite on a salt of cystine, the sulphur separated as sulphuric acid
thus pointing to a material difference in its reactions from what
we should have expected from its supposed constitution. Although
we cannot consider our experiments as definitive, we can assert
that glyceric acid is not a product of the action of nitrous acid,
and we venture to predict that, in all probability, cystine will be
found to be related to pyruvic acid — to be an amido-sulpho-pyruvic
acid. We base this supposition on the near approach of the
analyses of the silver salt of the acid obtained by the action of
nitrous acid on cystine, to the composition of a pyruvate, and on
the general character of the oily acid produced.

We intend to pursue this subject further.

2 D

VOL. VII.

206

Proceedings of the Royal Society

9. Notes from the Physical Laboratory of the University
By Professor Tait. (With a Plate.)

After passing through the usual routine work of acquiring skill
in the fundamental operations, several of my students have re-
mained long enough in the laboratory to make investigations in
various branches of Physics. A great many of these inquiries
related to matters already thoroughly known ; but some have
claims to notice as dealing with subjects on which our information
is as yet incomplete. These I propose, from time to time, to lay
before the Society. Their value as scientific results must depend
on the skill and care of the experimenters. For the forms of
apparatus employed, and the mode of conducting the experiments,
I am, in most cases, responsible.

(1.) Mr J. P. Nichol has made a long series of experiments upon
the Radiation and Convection of Heat, mainly to determine the
amount of radiation in absolute measure, but incidentally with a
view to finding how convection varies with the density of the air.
The following is a preliminary notice of his work. The radiating
body was a thin spherical shell of copper, filled with hot water.
Its surface was sometimes bright, sometimes covered (by means of
photographic varnish) with lamp-black. It was suspended by fine
wires in a metallic vessel, which was blackened internally, fitted with
a pressure-gauge, surrounded by cold water, and connected with an
air-pump. An iron cup was let into the top of the shell, and con-
tained a little mercury surrounding the bulb of a thermometer
whose stem ascended in a glass tube which was inserted in the lid
of the closed vessel. Considerable trouble was caused at first by
the water leaking out of the shell when its temperature was high
and the vacuum good — but in the later experiments this was
entirely got over.

As it was suspected that a difference of thickness of the lamp-
black coating might influence the amount of radiation, the mode of
experimenting finally adopted was to alter the air pressure in the
vessel from time to time ; first, for instance, half an hour’s cooling
at 100mm, then half an hour at 200mm, then at 100mm, and so on.
But the portions of the curves of cooling thus found on separate
days fitted well together into a single continuous line, as is seen in

207

of Edinburgh, Session 1869-70.

the corner of the diagram, where the dotted lines belong to one
day’s experiments, and the double lines to those of another day.

The numbers (H) given in the following table, which is formed
from means of many experiments, and which is shown graphically in
the diagram, express in grains the quantity of water which would
be heated 1° Centigrade by the heat lost (by radiation and con-
vection jointly) by one square inch of surface in an hour, its
temperature being kept constant. With the apparatus employed,
it was not easy to keep the pressure lower than 10mm ; but the
curves for different pressures show that in this case the convection
must be small, so that (roughly) we may take the numbers given
for that pressure as representing the radiation alone.

Blackened. Bright.

Pressure.

Temperature C.

H.

Temperature C.

H.

760mm

61*2

6258

63*8

3537

50-2

4875

57T

3091

4T6

3867

50*5

2637

34*4

3082

44-8

2251

27-3

2294

40-5

2013

20 ’5

1629

34-2

1571

29*6

1353

23*3

996

18-6

751

102mm

62-5

4650

67-8

1763

57 -5

4150

61*1

1552

53-2

3760

55*

1371

47-5

3220

49-7

1220

43*

2835

44-9

1082

28-5

1755

40-8

960

10mm

62-5

4236

65-

1390

57-5

3847

60*

1273

54*2

3593

50-

1025

41*7

2600

40-

786

37*5

2292

30-

563

34*

2040

23-5

445

27-5

1600

24' 2

1400

208

Proceedings of the Royal Society

(2.) Mr A. Brebner made during last winter a number of careful
determinations of the polarisation of electrodes of various materials
in commercial sulphuric acid of various strengths and at various
temperatures. The process employed was essentially the same as
that described by me in the Proceedings B.S.E. for May 31, 1869.
The following are means of many experiments : —

The results of such experiments cannot be expected to be very
accordant, but, if the means above given may be trusted, the
polarisation is less for 1 acid to 20 water than for either stronger
or weaker acids ; and it also falls off more slowly with increase of
temperature.

(3.) Messrs P. W. Meik and J. Murray made many observations
with an electric balance, and resistance coils, to test the change of
electric resistance produced in a wire by extension. The wires
tested were of two specimens of copper — one of high, the other of
very low, conducting power. They were taken of equal gauge and
of such lengths as to have almost equal resistance ; one was associ-
ated with a 10 B.A. Unit coil as one side of the balance, the other
had associated with it a box of resistance coils initially set at 10
B.A.U. The value of the galvanometric scale was determined in
each experiment by increasing by a small known amount the
resistance of the coils in circuit. The results are not yet quite
reduced ; as we require to know the linear extension, and (if possible),
the cubical contraction, of each wire produced by the appended
weights. But, even in their present state, they appear to be of
some consequence, as they show changes of conducting power almost
exactly proportional to the weights appended, but singularly differ-
ing in absolute amount for these dissimilar specimens of copper.

Acid to
Water.

Tempera- Polarisa-
tnre C. tion.

Platinum Electrodes.

Polarisa- Acid to
tion. Water.

Tempera- Polarisa-

tnre C. tion.

o

of Edinburgh, Session 1869-70.

209

The following Donations to the Society were announced -

Agassiz (Louis). Address delivered on the Centennial Anniver-
sary of the Birth of Alexander von Iinmboldt, under the
auspices of the Boston Society of Natural History. Boston,

1869. 8 vo. — From the Author.

Contributions to the Fauna of the G-ulf Stream at G-reat

Depths. Cambridge, Mass. 8vo. — From the Author.

— Report upon Deep Sea Dredgings. Cambridge, Mass.

8vo. — From the Author.

Allen (J. A.). Mammalia of Massachusetts. Cambridge, Mass.
8vo. — From the Author.

Balfour (Professor). Description of Hieracium collinum of Fries ,
a new British Plant. 8vo. — From the Author.

Barclay (Joseph G-urney). Astronomical Observations taken
during the years 1865-69, at his Private Observatory. Yol.
II. London, 1870. 4to. — From the Author.

Botten-Hansen (Paul). La Norvege Litteraire. Christiania,

1868. 8vo. — From the Author.

Brink (B. Ten). Levensbeschrijving van Rijklof Michael van
G-oens. Utrecht, 1869. 8vo. — From the Author.

Bristow (H. W.) and Whitaker (Wm.). On the Formation of the
Chesil Bank, Dorset. 8vo. — From the Authors.

Caspari (Dr le P.). Ungedruckte unbeachtete und wenig beachtete
Quellen zur G-eschichte des Taufsymbols und der G-laubens-
regel. Christiania. 8vo. — From the Author.

Chatelier (M. L. Le). Railway Economy. Translated by Lewis
D. B. G-ordon. Edinburgh. 1869. 8vo. — From the Trans-
lator.

Day (St John Yincent). On Patents for Inventions. Glasgow,

1870. 8vo. — From the Author.

Dircks (Henry), C.E., LL.D. Patent Monopoly, as represented by
Patent Law Abolitionists, impartially examined. London,

1869. 8vo. — From the Author.

— Scientific Studies, two Popular Lectures. 1. Marquis of

Worcester. 2. Chimeras of Science. London, 1869. 8vo.
— From the Author.

210

Proceedings of the Royal Society

Dircks (Henry), C.E., LL.D. Nature Study. London, 1869. 8vo.
— From the Author.

The Policy of a Patent Law. London, 1869. 8vo. — From

the Author.

Fayrer (Dr J.) H.R.H. The Duke of Edinburgh in India. Cal-
cutta, 1870. 4to. — From the Author.

Gamgee (Dr Arthur). Researches on the Blood. — On the Action of
Nitrites on Blood. 4to. — From the Author.

On Force and Matter in Relation to Organisation. Edin-
burgh, 1869. 8 vo. — From the Author.

Ghirardini (Alessandro). Studj sulla Lingua Umana sopra alcune
Antiche Inscrizioni, e sulla Ortografia Italiana. Milano,
1869. 8vo. — From the Author.

Giltay (Dr K. M.). Gedachtenisviering von het honderdjarig
bestaan von het Bataafsch Genootschap der Proefondervinde-
lijke Wijsbegeerte te Rotterdam 1769 — 1869. Rotterdam,

1869. 4to. — - From the Author.

Gore (G.), F.R.S. On Hydrofluoric Acid. From the Transactions
of the Royal Society for 1868. 4to, — From the Author.

Gorresio (Gaspare). Sunti dei Lavori Scientifici letti e discussi
nella Classe di Scienze Morali, Storiche e Filologiche. Torino,

1868. 8vo. — From the Author.

Gould (Benjamin Apthorp). Investigations in the Military and
Anthropological Statistics of American Soldiers. New York,

1869. 8vo. — From the United States Sanitary Commis-
sion.

Haeckel (Dr Ernst). Entwickelungsgeschicbte der Siphonophoren.
Utrecht, 1869. 4to. — From the Author.

Harris (Thaddeus William), M.D., Entomological Correspondence
of. Edited by S. H. Scudder. Boston, 1869. 8vo. — From
the Boston Society of Natural History.

Hasskarl (Carolo). Commelinacese Indicae, imprimis Archipelagi
Indici. Yindobonae, 1870. 8vo. — From the Author.

Haswell (James). On Columnar Structure developed in Mica
Schist, from a Vitrified Fort in the Kyles of Bute. 8vo. —
From the Author.

~ Notice of Sandstone, now in the course of formation at

Elie, Fifeshire. 8vo. — From the Author.

211

of Edinburgh, Session 1869-70.

Henwood (William Tory), F.R.S. Address to the Royal Institu-
tion of Cornwall. Penzance, 1869. 8vo. — From the Author.

Hertzberg (Ebbe). En fremstilling af de norske Aristokratis bis-
torie. Christiania, 1869. 8vo. — From the Author.

Hoffman (Dr C. K.), und H. Weyenbergh (J.). Die osteologie nnd
myologie von Sciurus vulgaris L. Haarlem, 1870. 4to. —
From the Authors.

Lea (Isaac), LL.D. Observations on the G-enus Unio, together
with Descriptions of new Species in the Family Unionidse,
and Descriptions of new Species of the Melanidae and Palu-
dinse, with 26 Plates. Yol. XII. Philadelphia. 4to. — From
the Author.

Leveque (Gk). Recherches sur 1’Origine des G-aulois. Paris, 1869.
8 vo. — From the Author.

Lindstrom (G-.). Om Grotlands Nutida Mollusker. Wisby, 1868.
8vo. — From the Author.

Linnarsson (J. G-. 0.). On some Fossils found in the Eophyton
Sandstone at Lugnas in Sweden. Stockholm, 1869. 8vo. — -
From the Author.

Littrow (Carl von). Ueber das Zuriickbleiben der Alten in den
Naturwissenschaften. Wien, 1869. 8vo. — From the
Author.

Logan (Sir W. E.). G-eological Map of Canada. 1866.

Loven (Af. S.). Om en marklig i Nordsjdn lefvande art af Spongia.
Stockholm. 8vo. — From the Author.

Lowe (E. J.). Natural Phenomena and Chronology of the Sea-
sons. London, 1870. 8vo. — From the Author.

Martins (Ch.), et Chancel (G-.). Des Phenomenes Physiques qui
accompagnent la rupture par la Congelation de l’Eau des
Projectiles Creux de divers calibres. Montpellier, 1870. 4to.
■ — From the Authors.

Meissner (C. F.). Denkschrift auf Carl Friedr. von Martius.
Munich, 1869. 4to. — From the Author.

Mohn (H.). Temperature de la mer entre Flslande, l’Ecosse et
la Norvege. Christiania, 1870. 8vo .—From the Author.

Morris (John). Lead-bearing Districts of the North of England.
London, 1869. 8vo. — From the Geologists' Association.

212

Proceedings of the Royal Society

Mueller (Ferdinandus de). Fragmenta Phytograpliias Australise.
Yol. YI. Melbourne. 8vo. — From the Author.

Muir (J.), D.C.L., LL.D. Original Sanskrit Texts on the
Origin and History of the People of India. Yol. Y. Lon-
don, 1870. 8vo. — From the Author.

Mullins (J. D). Catalogue of the Keference Department of the
Birmingham Free Libraries. Birmingham, 1869. 8vo. —
From the Author.

Nordenskiold (A. E.). Sketch of the Geology of Spitzbergen.
Stockholm, 1867. 8vo. — From the Author.

Orlandini (0. 0.) Bivelazioni Astronomiclie aggiunte alia Decla-
mazione Filosofica. Bologna, 1869. 8vo. — From the Author .

Peters (Dr). Beport on the Longitude of the Western Boundary
Line of the State of New York. Albany, 1868. 8vo. — From
the Author.

Plantamour (E.). Resume Meteorologique de l’annee 1868, pour
Geneve et le Grand Saint Bernard. Geneve, 1869. 8vo. —
From the Author.

— Nivellement de Precision de la Suisse. Geneve, 1870.

8vo. — From the Author.

Plaseller (Dr J.). Compendium Stenographic Latinee. (Eniponte,
1868. 8 vo. — From the Author.

Pourtales (L. F. de). Contributions to the Fauna of the Gulf
Stream at Great Depths. (Second Series.) Cambridge, Mass.
1868. 8vo. — From the Author.

Prestel (Dr M. A. F.). Das Gesetz der Winde abgeleitet aus dem
Auftretenderselben iiber Nordwest-Europa. Emden, 1869.
4to. — From the Author.

Quetelet (Ad.). Note sur l’Aurore Boreale du 6ie Octobre et les
Orages de 1869. Brussels. 8vo. — From the Author.

■ Physique Sociale ou Essai sur le Developpement

des Facultes de l’Homme. Brussels, 1869. 8vo. — From the
Author .

Sur les Orages observes en Belgique pendant l’Annee

1868, et le premier Trimestre de 1869. Brussels. 8vo. —
From the Author.

Sur les l^toiles Filantes du mois d’Aout 1869, observees

a Bruxelles. 8vo. — From the Author.

213

of Edinburgh, Session 1869-70.

Quetelet (Ern.) Notices sur les Aurores Boreales des 15 Avril et
13 Mai 1869. Brussels, 1869. 8vo. — From the Author.

Realis, (M. S.). Note sur le Nombre. Paris, 1869. 8vo. — From
the Author.

Regnault (M. V.). Relation des Experiences pour determiner les
lois et les donnees Physiques necessaires au calcul des
Machines a Feu. Paris, 1870. 4to. — From the Author.

Rein (Dr J. J.). Bericht iiber die Senckenbergisch'e Naturfor-
schende G-esellschaft in Frankfurt om Main. 1869. 8vo. —
From the Author.

“ Research.” Earth, True Theory of the. Edinburgh, 1869. 8vo. —
From the Author.

Report on Measures adopted for Sanitary Improvements in India
during the year 1868, and up to the month of June 1869.
London, 1869. Fol. — From Dr Morehead.

Risfen (Hartvig). Stolevmfenets Ordnung i Massachusetts.
Christiania, 1868. 8vo. — From the Author.

Roy (Alphonse le). L’Universite de Liege depuis sa fondation.
Liege, 1869. 8vo. — From the Author.

Settimanni (Capt. Cesar). D’une seconde Nouvelle Methode
pour determiner la Parallaxe du Soleil. Florence, 1870.
8vo. — From the Author.

Sexe (S. A.). Le Glacier de Boium en Juillet 1868. Christiania,
1869. 4to — From the Author.

Smith (Dr John Alexander). Notice of Remains of the Rein-
deer (Cervus tarandus ), found in Ross-shire, &c., with Notes
of its occurrence throughout Scotland. Edinburgh, 1869.
8vo. — From the Author.

Snellaert (F. A.). Nederlandsche Gredichten uit de veertiende
eeuw van Jan Boendale, Hein van Aken, en anderen. Brussels,
1869. 8 vo. — From the Author.

Stal (Carolus). Hemiptera Africana. Tom. I.-IV. Holmise,
1864. 8vo. — From the Author.

Steen (Adolph). Om Integrationen af Differentialligninger, der
fore til Additionstheoremer for transcendente Funktioner.
Copenhagen, 1868. 4to.— From the Royal Academy of Sciences,
Copenhagen.

2 E

VOL. VII.

214

Proceedings of the Royal Society

Stevenson (David), F.R.S.E. Altered Regulations of British and
Foreign Industries and Manufactures ; the Cause and the
Cure. An Address to the Royal Scottish Society of Arts on 8th
November 1869. Edinburgh, 1869. 8vo. — From the Author.

Stirling-Maxwell (Sir Wm.), Bart. Address to the Students of
the School of Arts, Edinburgh, under charge of the Hon. the
Commissioners of the Board of Manufactures, at the delivery
of Prizes, January 13, 1870. 8vo. — From the Author.

Strecker (Adolph). Jahreshericht uber die Fortschritte der
Chemie, &c., fur 1868. Heft 2. Giessen. 8vo. — From the
Editor.

Struve (Otto). Jahreshericht am 5 Juni 1869 dem Comite der
Nicolai-Hauptsternwarte. St Petersburg, 1869. 8vo. — From
the Author.

— Tabulae Quantitatum Besselianarum pro annis 1850 ad

1810 computatae. Petropoli, 1869. 8vo. — From the
Author.

Studer (B.). Erlauterungen zur zweiten Ausgabe der Geologi-
schen Karte der Schweiz vonB. Studer und A. Escher. Win-
terthur, 1869. 8vo. — From the Authors.

Sundevall (Carl J.). Die Thierarten des Aristoteles von den
Klassen den Saugethiere, Vogel, Reptilien und Insekten.
Stockholm. 8vo. — From the Author.

Conspectus Avium Picinarum. Stockholm, 1866. 8vo.

— From the Author.

Suringar (W. F. R.). Algae Japonicae Musei Botanici Lugduno.
Batavi. 8vo. — From the Author.

Synnestvedt (A. S. D.). En Anatomisk Beskrivelse af de par
over-ag Underextremiteterne forekommende Bursae mucosae.
Christiania, 1869. 4to. — From the University of Christiania.

Toynbee (Capt. Henry). On the Meteorology of the North At-
lantic between the Parallels of 10° and 50° North. London,
1869. 8 vo. — From the Author.

On the Use of Isobaric Curves. London, 1869. 8vo. —

From the Author.

Turbiglio (Sebestien). L’Empire de la Logique, Essai d’un Nou-
veau Systeme de Philosophic. Turin, 1870. 8vo. — From the
Author.

215

of Edinburgh, Session 1869-70.

Unger (C. R.). Thomas Saga Erkibyskups-Fortselling om Thomas
Becket Erkebiskop af Canterbury to Bearbeidelser Saint frag-
menter af en Eredie. Christiania, 1869. 8vo. — ■ From the

Author.

Yignoles (C.B.). Address on his Election as President of the In-
stitution of Civil Engineers, Session 1869-70. London, 1870.
8 vo. — From the Author.

Yigorniensis. An Historical Keview of the Nature and Besults of
Yaccination as unfolded in Dr Baron’s Life of Jenner.
Cheltenham, 1869. 8vo. — From the Author.

Yogel (August). Uber die Entwicklung der Agrikulturchemie.
Munich, 1869. 4to. — From the Author.

Wallis (S. T.). Discourse on the Life and Character of George
Peabody* Baltimore, 1870. 8vo. — From the Peabody In-

stitute.

Waterhouse (Lieut. J.). Eeport on the Cartographic Applications
of Photography. Calcutta, 1870. 8vo. — From the Author.

Watson-Wemyss (Alexander), M.D. On the Construction of
Hospitals for the Sick and Hurt. Edinburgh, 1870. 8vo.
— From the Author.

Will (H.). Jahresberickt liber die Eortschritte der Chemie, etc.
fur 1867, Heft 2, 3; 1868, Heft 1, 2. Giessen. 8vo. — From
the Editor.

Wilson (Robert). The Screw Propeller, who Invented it? Glas-
gow, 1860. 8 vo. — From the Author.

Wiltshire (Rev. Thos.). On the Chief Groups of the Cephalopoda.
1869. 8vo. — From the Geologists’ Association , London.

Thansactigns and Peoceedings of Societies, Academies, &c.

Amsterdam. — Jaarboek van der Koninklijke Akademie van
Wettenschappen gevestigd te Amsterdam. 1868. 8vo.
— From the Academy.

Processen-verbaal van de Gewone vergadering der Xon-
inklijke Akademie van Wettenschappen; Afdeeling
Natuurkunde, van mei 1868, tot en met April, 1869. 8vo.
— From the Academy.

216

Proceedings of the Royal Society

Amsterdam . — Yerliandelingen der Koninklijke Akademie van
Wettenschappen. Deel IV. 4to. — From the Academy.

Yerslagen en Mededeelingen der Koninklijke Akademie
van Wettenschappen. Natuurkunde. Deel III. 8vo.-~
From the Academy.

Baltimore. — Address of the President to the Board of Trustees of
the Peabody Institute. 1870. 8vo. — From the Institute.

Third Annual Report of the Provost of the Peabody Insti-
tute to the Board of Trustees. 8vo. — From the Institute.

Basel. — Verhandlungen der NaturforschendenGesellschaft in Basel.
Fiinfter Theil, Zweites Heft. 8vo. — From the Society.

Berlin.— Abhandlungen der Koniglichen Akademie der Wissen-
schaften. 1868. 4to. — From the Academy.

Die Fortscliritte der Physik im Jahre 1866, dargestellt von
der Physikalischen Gesellschaft zu Berlin. Jahrgang
XXII. 8vo. — From the Society.

Monatsberieht der Koniglich Preussischen Akademie der
Wissenschaften, March, April, Mai, Juni, Juli, August,
September, October, November, December, 1869. Januar,
Februar, Marz, April, Mai, 1870. 8vo. — From the
Academy.

Bern. — Mittheilungen der Naturforschenden Gesellschaft in Bern,
aus dem Jahre 1868. Nos. 654-683. 8vo. — From the
Society.

Birmingham . — Report of the Free Libraries’ Committee, Birming-
ham, for 1869. 8vo. — From the Committee.

Bologna .- — Archivio per la Zoologia, l’Anatomia, e la Fisiologia.

Serie II. Yol. I. Yol. II., Fasc 1. 8vo. — From the
Editors.

Bordeaux. — Memoires de la Societe des Sciences Physiques et
Naturelles de Bordeaux. Tome Y. No. 4. Tome YII.
8 vo .—From the Society.

Boston. — Memoirs of the Society of Natural History. Yol. I. Part
4. 4to. — From the Society.

Proceedings of the Society of Natural History. Yol. XII.
Pages 1 to 272. 8vo. — From the Society.

Occasional Papers of the Society of Natural History. No.
1. 1869. 8 vo —From the Society.

of Edinburgh, Session 1869-70. 217

Boston . — Annual Eeport of the Trustees of the Museum of Com-
parative Zoology. 1868. 8vo. — From the Trustees .

Bulletin of the Public Library. Nos. 10-14. 8vo. — From
the Library.

Brussels. — Annuaire de FAcademie Royale des Sciences, des
Lettres et des Beaux- Arts de Belgique. 1870. 12mo. —

From the Academy.

Annuaire de FObservatoire Royal de Bruxelles, par A
Quetelet. 1870. 12mo. — From the Observatory.

Bulletin de FAcademie Royale des Sciences des Lettres et
des Beaux- Arts de Belgique. Tome XXVII. ; Tome
XXVIII. ; Tome XXIX. Nos. 1-6. 8vo .—From the
Academy.

Observations des Phenomenes Perio cliques pendant les
Annees 1867 et 1868. 4to. — From the Royal Academy.

Annales de FObservatoire Royale de Bruxelles publics
aux frais de FEtat, par le directeur A. Quetelet. Tome
XIX. 4to. — From the Observatory.

Memoires couronnes et Memoires des Savants Etrangers,
publics par FAcademie Royale des Sciences, des Lettres
et des Beaux-Arts de Belgique. 4to. — From the Aca-
demy.

Memoires couronnes et autres Memoires, publies par
FAcademie Royale des Sciences des Lettres et des Beaux-
Arts de Belgique. Tome XXI. 8vo. — From the

Academy.

Calcutta. — Journal of the Asiatic Society of Bengal. Part I.
Nos. 1-4; Part II. Nos. 2-4; 1869. Part I. No. 1;
Part II. No. 1 ; 1870. 8vo. — From the Society .

Proceedings of the Asiatic Society of Bengal. Nos. 2-11,
1869. Nos. 1-4, 1870. 8vo. — From the Society.

Annual Report of the Geological Survey of India, and of
the Museum of Geology for 1867. 8vo. — From the
Survey.

Memoirs of the Geological Survey of India. Vol. VI.
Part III. 8vo. — From the Survey.

Memoirs of the Geological Survey of India, Palmonto-
logia. Vol. V. Parts V.-X. 4to. — From the Survey.

218 Proceedings of the Royal Society

Calcutta. — Records of the Geological Survey of India. Vol. I.
Parts L-IIL 1868 ; Vol. II. Part I. 1869. 8vo. — From
the Survey.

Cambridge. — Proceedings of the Philosophical Society. Parts 3-6.
8 vo. — From the Society.

Transactions of the Philosophical Society. Vol. XI. Part
2. 4to. — From the Society.

Cambridge ( U . Si). — Proceedings of the American Academy of Arts
and Sciences. Vol. VII. 8vo. — From the Academy.

Proceedings of the American Association for the Advance-
ment of Science. Sixteenth Meeting. 1867. 8vo. —
From the Association.

Christiania. — Flateyjarbok en Samling af Norske Kongl. Sagaer,
&c. 1868. 8vo. — From the Society.

Forhandlinger i Videnskahs-Selskahet. Aar 1868. 8vo. —
From the Society.

Forhandlinger ved de Skandinaviske Naturforskeres, Tiende
mode, fra den 4de, til den 10de Juli 1868. 8vo. —
From the Sooiety.

Det Kongelige Norste Frederiks-Universitets Aarsberetning
for 1868. 8 vo. — From the University.

Norsk Meteorologisk Aarhog for 1868. Aargang. II.
4to. — From the Meterological Institute.

Norske Universitets-og-Skole, Annaler udgivne af Univer-
sitets Secretair, Mai 1869. 8vo. — From the University.

Nyt Magazin for Naturvidenskaberne. Bind XVI. Hefte
1-3. 1869. 8vo. — From the Royal University of Nor-

way.

Cincinnati. — Annual Address, delivered in 1845, before the As-
tronomical Society by E. D. Mansfield, Esq. 8vo. —

From the Society.

Annual Report of the Director of the Observatory. 1869.
8vo. — From the Observatory.

An Oration delivered before the Astronomical Society, by
J. Quincy Adams. 8vo. — From the Society.

Copenhagen. — Det Kongelige danske Videnskabernes Selskahs,
Skrifter, femte Rgekke. 1869-70. 4to. — From the Royal
Academy of Sciences.

219

of Edinburgh , Session 1869-70.

Copenhagen. — Oversigt over det Kongelige danske Yidenskabernes
Selskabs Forhandlinger og dets Medlemmers Arbeider i
Aaret, 1867, Nos. 6, 7; 1868, Nos. 1-4; 1869, Nos. 1, 2,
3, 5. Kjobenhavn. 8vo. — From the Royal Academy of
Sciences.

Dublin. — Journal of the Eoyal Geological Society of Ireland.
Yol. II., Parts 1, 2. 8vo. — From the Society.

Observations made at the Magnetical and Meteorological
Observatory at Trinity College. Yol. II. 1841-50.
Dublin, 1869. 4to. — From the College.

Proceedings of the Eoyal Irish Academy. Yol. X. Parts
1-3. 8 vo. — From the Academy.

Transactions of the Eoyal Irish Academy. Yol. XXI Y. ;
Science, Parts 9-15 ; Polite Literature, Part 4 ; Antiqui-
ties, Part 8. 4to. — From the Academy.

Edinburgh. — -Thirteenth Annual Eeport of the Eegistrar- General.
1869. 8 vo. — From the Registrar-General.

Quarterly Eeturn of the Births, Deaths, and Marriages
Eegistered in the Divisions, Counties, and Districts of
Scotland. Nos. 58 to 61. Monthly Eeturn s of the
same, July to December 1869, January to June 1870.
8vo. — From the Registrar-General.

Transactions and Proceedings of the Botanical Society.

Yol. X. Part 1. 8vo. — From the Society.

Transactions of the Geological Society. Yol. I. Part 3.
8vo. — From the Society.

Transactions of the Highland and Agricultural Society of
Scotland. No. 5. 8vo. — From the Society.

Forty-Second Annual Eeport of the Council of the
Eoyal Scottish Academy of Painting. 8vo.— From the
Academy.

Transactions of the Eoyal Scottish Society of Arts. Yol.
YIII. Part 1.

Journal of the Scottish Meteorological Society. Nos. 21-
26. 8vo. — From the Society.

Frankfort. — Abhandlungen herausgegeben von der Senckenbergi-
schen Naturforschenden Gesellschaft. Band YII. Heft
1,2. 4to. — From the Society.

220 Proceedings of the Royal Society

Geneva . — Memoires de la Societe de Physique et d’Histoire
Naturellede Geneve. Tome XX. Partie 1. 4to. — From
the Society.

Glasgow. — Transactions of the G-eological Society. Yol. III.
Part 2. 8 vo. — From the Society.

Gottingen. — Abhandlungen der Konigliclien Gesellschaft der
Wissenschaften. Band XI Y. 4to. — From the So-

ciety.

Astronomische Mittheilungen von der Konigl. Sternwarte
zu Gottingen. Erster Theil. 4to. — From the Society.

Nachrichten von der K. G-esellschaft der Wissenschaften
und der Georg- Augusts-Universitat, aus dem Jahre 1869.
— From the Society.

Greenwich. — Astronomical and Magnetical and Meteorological Ob-
servations made at the Eoyal Observatory in the year
1867. London, 1869. 4to. — From the Observatory.

Halifax , Nova Scotia. — Proceedings and Transactions of the Nova
Scotian Institute of Natural Science. Yol. II. Part 2.
8 vo. — From the Society.

Haarlem. — Archives du Musee Teyler. Yol. II. Ease. 1, 2, 3,
4. 8vo. — From the Museum.

Archives Neerlandaises des Sciences Exactes et Naturelles
publiees par la Societe Hollandaise a Haarlem. Tome
III. Liv. 3-5 ; Tome IY. ; Tome Y. Liv. 1, 2, 3. 8vo.
—From the Society.

Jena. — Jenaische Zeitschrift fur Medicin und Naturwissenschaft
herausgegeben von der Medicinisch Naturwissenschaft-
lichen Gesellschaft zu Jena. Bands I., II., III., IY.
Heft 3, 4 ; Band Y. Heft 1, 2. 8vo. — From the
Society.

Jerusalem. — Ordnance Survey of 1865. Maps. Eol. — From the
Secretary of State for War.

Kiel. — Schriften der Universitat zu Kiel, aus dem Jahre 1868.
Band XY. 4to. — From the University.

Lausanne. — Bulletin de la Societe Yaudoise des Sciences Naturelles.
Yol. X. No. 62. 8vo. — From the Society.

Eeuille Centrale de la Societe de Zofingue. Huitieme Annee,
No. 8. 8vo. — From the Society.

221

of Edinburgh, Session 1869-70.

Leeds. — Eeport of the Proceedings of the Geological and Poly-
technic Society of the West Eiding of Yorkshire, 1869.
8 vo. — From the Society.

Forty-Ninth Eeport of the. Philosophical and Literary
Society, 1868-69. 8vo. — From the Society.

Leipzig. — Berichte iiher die Yerhandlnngen der Koniglich Sachsi-
schen Gesellschaft der Wissenschaften zu Leipzig; Math.
Phys. Classe, 1867, Nos. 3, 4; 1868, Nos. 1-3; 1869,
No. 1. 8 vo. — From the Royal Saxon Academy.

Entwickelung eines nenen veranderten Yerfahrens znr
Ausgleichung eines Dreiecksnetzes mit besonderer Be-
trachtung des Falles in welchem Gewisse Winkel voraus
bestimmte Werthe bekommen sollen, von P. A. Hansen.
No. II. 8vo.' — From the Royal Saxon Academy.

Fortgesetzte geodatsche Untersuchungen bestehend in
zehn Supplementen znr Abhandlung von der Methode
der kleinsten Quadrate im Allgemeinen und in ihrer
Anwendung aaf die Geodasie. Yon P. A. Hansen. 8vo.
— -From the Royal Saxon Academy.

Supplement zu der Geodatische Untersuchungen benann-
ten Abhandlung die Eeduction der Winkel eines Spharoi-
dischen Dreiecks betreffend von P. A. Hansen. 8vo.
— From the Royal Saxon Academy.

Preisschriften gekront und herausgegeben von der fiirst-
lich Jablonowskischen Gesellschaft zu Leipzig. XIV.,
XV., XYI. 8vo. — From the Royal Saxon Aca-

demy.

XY. Tafeln zu H. Engelhard! Flora der Braunkohlen-
formation im Konigreich Sachsen. Preisschriften der
Fiirstl Jablonowskischen Gesellschaft XYI. 8vo. — From
the Royal Saxon Academy.

Tafeln der Pomona mit Berucksichtigung der Storungen
durch Jupiter, Saturn, und Mars berechnet von D.
Otto Lesser. No. 9. 4to. — From the Astronomical
Society.

Vierteljahrsschrift der Astronomischen Gesellschaft ;
J ahrgang IY. Heft 2, 3, 4; Jahrgang Y. Heft 1. 8vo.
— From the Society.

vol. vn, 2 f

222

Proceedings of the Royal Society

Liverpool . — Transactions of the Historic Society of Lancashire
and Cheshire, Vols. VIII., IX. 8vo. — From the

Society.

London, — Proceedings of the Society of Antiquaries. Yol. IY.
Nos. 3-6. 8vo. — From the Society.

Transactions of the Society of Antiquaries. Yol. XLII.

Part 1. 4to. — From the Society.

Journal of the Society of Arts for 1869-70. 8vo. — From
the Society.

Journal of the Eoyal Asiatic Society of G-reat Britain and
Ireland. Yol. IY. Parts 1, 2. 8vo. — From the Society.
Monthly Notices of the Eoyal Astronomical Society for
1869-70. 8vo. — From the Society.

Journal of the Chemical Society. May, June, July,
August, September, October, November, December, 1869;
January, February, March, April, May, June, July,
August 1870. 8 vo. — From the Society.

Journalof the Eoyal (Geographical Society. Vols. XXXVIII.,
XXXIX. 8vo. — From the Society.

Proceedings of the Eoyal (Geographical Society. Yol.
XIII. No. 5; Yol. XIY. Parts 1, 2. 8vo. — From the
Society.

Eeport of the (Geologists’ Association and Excursions for
1869. 8 vo. — From the Association.

Quarterly Journal of the (Geological Society. Yol. XXY
Parts 3, 4; Yol. XXYI. Parts 1, 2. 8vo. — From the.

Society.

Catalogue of the Published Maps, Sections, Memoirs, and
other Publications of the (Geological Survey of the
United Kingdom to March 31st, 1869. 8vo. — From the
Survey.

Memoirs of the (Geological Survey of (Great Britain. 4
Parts. London, 1869. 8vo. — From the Survey.

Journal of the East India Association. No. 2. 8vo. —

From the Association.

Proceedings of the Institution of Civil Engineers. Yols.
XXVIL, XXVIII. 8vo. — From the Institution.

223

of Edinburgh, Session 1869-70.

London. — Proceedings of the Royal Institution of Great Britain.
Yol. Y. Parts 5, 6. 8vo. — From the Society.

List of Members of the Royal Institution of Great Britain.
8 vo. — From the Society.

Journal of the Linnean Society. Yol. XI. (Botany) ;
Yol. XII. (Botany), Nos. 50, 51, 52, 53; Yol. X.
(Zoology), Nos. 46, 47, 48. 8vo. — From the So-
ciety.

Proceedings of the Linnean Society, [Session 1869-70.
8 vo. — From the Society.

Transactions of the Linnean Society. Yol. XX YI. Parts
3, 4; Yol. XXYIL Parts 1, 2. 4to .—From the

Society.

Proceedings of the Mathematical Society. Nos. 16-26.
8vo. — From the Society.

Proceedings of the Royal Medical and Chirurgical Society.
Yol. YI. Nos. 4-6.

Transactions of the Royal Medical and Chirurgical Society.

Yol. L1I. 8vo.' — From the Society.

Charts showing the Surface Temperature of the South
Atlantic Ocean in each Month of the Year. London,
1869. Fol. — From the Meteorological Office.

Quarterly Weather Report of the Meteorological Office,
with Pressure and Temperature Tables for the Year
1869. 4to. — From the Office.

Proceedings of the Meteorological Society. Nos. 42, 43,
44, 45, 46, 47, 48, 49. 8vo. — From the Society.

The President’s Address delivered before the Royal
Microscopical Society, February 10th 1869. 8vo. — From
the Society.

Transactions of the Pathological Society. Yol. XX. 8vo.
— From the Society.

Proceedings of the Royal Society. Nos. 112-121. 8vo, —

From the Society.

Royal Society Catalogue of Scientific Papers. Yol. III.
4to. 8vo. — -From the Society.

Transactions of the Royal Society of London. Yol
CLIX. Parts 1, 2. 4to. — From the Society.

224 Proceedings of the Royal Society

London . — List of the Royal Society of London. 1869. 4to. —
From the Society.

Report of the Meteorological Committee of the Royal
Society, for the Year ending 31st December 1868. 8vo.
— From the Society.

Journal of the Statistical Society. Yol. XXXII. Parts
2-4; Yol. XXXIII. Parts 1, 2. 8vo. — From the
Society.

Proceedings of the Zoological Society. 1868, Part 3 ;

1869, Parts 1-3. 8vo. — From the Society.

Transactions of the Zoological Society. Yol. VI. Part 8.
Yol. VII. Parts 1, 2. 4to. — From the Society.

Lyons. — Memoires de 1’Academie Imperiale des Sciences Belles-
Lettres et Arts de Lyon ; Classe des Sciences. Tome
XVII.

Annales des Sciences Physiques et Naturelles d ’Agriculture
et dTndustrie. Tome XI. 8vo. — From the Society.
Madrid.— Censo de la G-anaderia de Espana segun el recuento
verificado en 24 de Setiembre de 1865 por la Junta
General de Estadistica. 8vo. — From the Junta.

Maine. — Reports of the Commissioners of Fisheries of the State
of Maine for the year 1867 and 1868. 8vo. — From the
Commissioners .

Manchester.— Memoirs of the Literary and Philosophical Society.
Yol. III. 3d Series. 8vo. — From the Society.

Proceedings of the Literary and Philosophical Society.
Yols. V., VI., VII. 8vo. — From the Society.

Milan. — Annuario del Instituto Lombardo di Scienze e Lettere
1868. 12mo. — From the Institute.

Memorie del Reale Istitutb Lombardo di Scienze e Lettere —
Classe di Lettere e Scienze Morali e Politiche, Yol. XI.
Fasc. 1, 2. Classe di Scienze Matematiche e Naturali,
Yol. XI. Fasc. 1, 2. 4to. — From the Institute.

Rendiconti Reale Istituto Lombardo di Scienze e Lettere.
Serie 2, Yol. I. Fasc. 11-20 ; Yol. II. Fasc. 1-16. 8vo.
— From the Institute.

Solenni Adunanze del R. Istituto Lombardo di Scienze e
Lettere. Yol. I. Fasc. 5. 8vo.— From the Institute.

225

of Edinburgh, Session 1869-70.

Moscow. — Bulletin de la Societe Imperiale des Naturalistes. 1868,
Nos. 3, 4; 1869, Nos. 1-4. 8vo. — From the Society.

Munich. — Sitzungsberichte der konigl. bayer. Akademie der Wis-
senscbaften. 1869, Band I. Heft 1-4; Band II. Heft
1-4; 1870, Band I. Heft 1. 8vo. — From the Aca-

demy.

Abkandlungen der koniglich. bayeriscken Akademie der
Wissenschaften. — Historiscben Classe, Band XI. Abth. 1.
Matkematisch-Physikaliscken Classe, Band X. Abtb. 2.
Philosophisck-Philologischen Classe, Band XI. Abth. 3.
4to. — From the Academy.

Annalen der Koniglichen Sternwarte bei Miinchen. Band
XYII. 8 vo. — From the Eoyal Observatory.

Verzeichniss von telescopischen Sternen, Supp. Band VIII.
IX. 8vo. — From the Royal Observatory.

Naples. — Bendiconto delle Tornate e dei Lavori dell’ Accademia di
Scienze Morali e Politiche. 1869, Jan. to May, Septem-
ber to December ; 1870, Jan. to March. 8vo. — From the
Academy.

Neuchatel. — Bulletin de la Societe des Sciences Naturelles de
Neuchatel. Tome VIII. No. 2. 8vo. — From the

Society.

New Haven ( U.S .) — Journal (American) of Science and Art, con-
ducted by Benjamin Silliman. Nos. 141-147. New
Haven. 8vo. — From the Editor.

New York. — 20th Annual Report of the Regents of the University
of the State of New York, on the Condition of the State
Cabinet of Natural History. 8vo. — From the Univer- .
sity.

50tli and 51st Annual Reports of the Trustees of the New
York State Library. 8vo. — From the Library.

New Zealand. — Statistics of New Zealand for 1868. Wellington,
1869. Pol. — From the New Zealand Government.

Ohio. — Report (22d) of the State Board of Agriculture for 1867.
Columbus, 1868. 8vo. — From the Board.

Oxford. — Astronomical and Meteorological Observations made at
the Radcliffe Observatory, Oxford, in the year 1866. Vol.
XXYI., XXYII. 8vo. — From the Observatory.

226

Proceedings of the Poyal Society

Oxford. — Second Radcliffe Catalogue, containing 2386 Stars deduced
from Observations extending from 1854 to 1861 at the
Radcliffe Observatory, Oxford. 8vo. — From the Observa-
tory.

Palermo. — Griornale di Scienze Naturali ed Economiche. Yol. IV.

Fasc. 4; Yol. Y. Fasc. 1-4. 4to. — From the Insti-
tute.

Paris. — Publications of the Depot de la Marine with Charts. Nos.

448, 449, 452, 454, 455, 456, 458, 459, 461, 462, 463,
464, 465, 467, 468. — From the Depot de la Marine.
Annales Hydrographiques. No. 4, 1868; Nos. 1-3, 1869.

8 vo.- — From the Depot de la Marine.

Annales des Mines. Tome XY. Liv. 2e, 3e; XYI. Liv. 4e,
5e, 6e. 8vo. — From the Ecole des Mines.

Bulletin de la Societe de G-eographie ; Mai, Juin, Juillet,
Aout, Septembre, Octobre, Novembre, Decembre 1869 ;
Janvier, Fevrier, Mars, Avril, Mai 1870. 8vo. — From
the Society.

Comptes-Rendus Hebdomadaires des Seances de 1’Academie
des Sciences, 1869-70. 4to. — From the Academy.
Philadelphia. — Journal of the Academy of Natural Sciences. New
Series. Yol. YI. Parts 3, 4. Yol. YII. 4to. — From the
Academy.

Proceedings of the Academy of Natural Sciences. Nos. 1-
6, 1868; Nos. 1, 2, 1869. 8vo. — From the Academy.
Proceedings of the American Philosophical Society. Yol.
X. Nos. 78, 79. Yol. XI. No. 81. 8vo.— From the

Society.

Transactions of the American Philosophical Society. Yol.
XIII. Part 3. 4to. — From the Society.

Portland. — Proceedings of the Portland Society of Natural His-
tory. Yol. I. Part 2. 8vo. — From the Society.

Quebec. — Manuscripts relating to the Early History of Canada.
8vo. — From the Literary and Historical Society.

Report of the Council of the Literary and Historical Society,
1869. 8vo. — From the Society.

Transactions of the Literary and Historical Society. New
Series. Part 5. 8vo. — From the Society.

227

of Edinburgh, Session 1869-70.

St Andrews. — University Calendar for 1870-71. 12mo. — From the

University .

St Petersburg. — Jaliresbericht des Physikalischen Central- Obser-
vatoriums fur 1869. 4to.—~ From the Eoyal Aca-

demy.

Compte-Rendu de la Commission Imperiale Arcbeologique
pour 1’Annee 1867. 4to. (Atlas Fol.) — From the Com-
mission.

Ann ales de l’Observatoire Physique Central de Russie.

Annee 1865. 4to. — From the Russian Government.
Observations faites a la Lunette Meridienne. Yols. I., II.

1869. 4to. — From the PouTkowa Observatory .

Repertorium fur Meteorologie. Band I. Heft 1. 4to. —
From the Royal Academy.

Bulletin de l’Academie Imperiale des Sciences de St
Petersbourg. Tome XIII. Nos. 4, 5; Tome XIV. Nos.
1-6. 4to. — From the Academy.

Melanges Physiques et Chemiques tires du Bulletin de
l’Academie Imperiale des Sciences. Tome VIII. 8vo.
— From the Academy.

Memoires de 1’ Academie Imperiale des Sciences de St Peters-
bourg. YIIe Serie. Tome XII. Nos. 4, 5 ; Tome XIII.
Nos. 1-8; Tome XIY. Nos. 1-9 ; Tome XY. Nos. 1-4.
4to. — From the Academy.

Salem , Mass. — Memoirs of the Peabody Academy of Science. Yol.
I. No. 1. 4to. — From the Academy.

Proceedings of the Essex Institute. Yol. Y. Nos. 7 and
8. 8 vo. — From the Institute.

The American Naturalist. Yol. II. 1868-69. 8vo. — From
the Peabody Academy of Science.

Stockholm. — Kongliga Svenska Fregatten Eugenies Resa Omkring
Jorden under befal af C. A. Virgin Aren, 1851-53.
Haft 12. 4to, — From the Academy.

Kongliga Svenska Vetenskaps-Akademiens Handlingar.
Ny Foljd. Band Y. Heft 2, 1864; Band VI. Heft
1, 2, 1865-66; Band VII. Heft 1, 1867. 4to.~ From the
Academy.

228 Proceedings of the Eoycd Society

Stockholm. — Lefnadsteckningar ofver Kongl. Svenska Vetenskaps-
Akademiens efter ar 1854 aflidna Ledamoter. Band I.
Heft 1. 1869. 8vo. — From the Academy.

Meteorologiska lakttagelser i Sverige ntgifna af Kongl.
Svenska Vetenskaps-Akademien anstaallda och bearbe-
tade under Inseende af Er. Edlund. Band VI., 1864; Band.
VII., 1865; Band VIII., 1866. 4to. — From the Academy .

Ofversigbt af Kongl. Vetenskaps-Akademiens Forband-
lingar, 1865, 1866, 1867, 1868. Svo.-— From the Academy.

Switzerland. — Verkandlungen der Sckweizerischen Naturforscben-
den G-esellsckaft in Einsiedeln. 1868. 8vo. — From the
Society.

Throndhjem. — Det Kongelige Norske Videnskabers-Selskabs,
Skrifter i det 19de Aarhnndrede. Bind V. Heft 2. 8vo.—
From the Society.

Toronto. — Canadian Journal of Science, Literature, and History.

Vol. XII. Nos. 3-5. Svo .—From the Canadian Insti-
tute.

Turin. — Atti della Beale Accademia delle Scienze. Vol. IV.
Eisp. 1-7. 8vo. — From the Academy.

Bollettino Meteorologico dell’ Osservatorio Astronomico
dell’ Universita, 1868-69. 4to. — From the University.

Ulm. — Verkandlungen der Verein fur Kunst und Altertbum in
Him und Oberschwaben. Heft 1, 1869. 4to. — From the
Editor.

Utrecht. — Aanteekeningen van bet Verhandelde in de Sectiever-
gaderingen van liet Provinciaal Utrechtscb Genootscbap
van Kunsten en Wetenscliappen, 1868-69. Svo .—From
the Society.

Catalogus der Arclieologiscbe Verzameling van bet Pro-
vinciaal Utrecbtscb G-enootscbap van Kunsten en Weten-
schappen, 1868. Svo. — From the Society.

Nederlandscb Meteorologiscb Jaarboek 1867-68. Utrecbt,
1868. 4to. — From the Meteorological Institute of Utrecht.

Verslag van bet Verbandelde in de algemeene Vergadering
van het Provinciaal Utrecbtscb Genootscbap van Kuns-
ten en Wetenscbappen, 1868-69. Svo. — From the

Society.

229 '

of Edinburgh , Session 1869-70.

Venezia. — Atti del Reale Istituto Veneto di Scienze, Lettere ed
Arti. Tomo XII. Dispense* 10; Tomo XIII., X1Y. Dis-
pense 1-5. 8vo. — From the Institute.

Victoria. — Statistics of the Colony for 1868. Part 1. Population.
Fol. — From the Registrar -General.

Statistics of the Colony of Australia. Parts 2-8. Mel-
bourne, 1868. Pol. — From the Australian Government.

Vienna. — Almanack der kaiserlichen Akademie der Wissenschaf-
ten. 12mo. — From the Academy.

Denkschirften der kaiserlichen Akademie der Wissen-
schaften. Math. Nat. Classe, Band XXIX. Phil. Hist.
Classe, Bands XVI., XVIII. 4to. — From the Academy.

Jalirbuch der kaiserlich-koniglichen geologischen Reich-
sanstalt. Band XIX. Nos. 1, 3, 4; Band XX. No. 1.
8 vo. — From the Society.

Sitzungsherichte der kaiserlichen Akademie der Wissen-
schaften — Phil. Hist. Classe ; Band VIII. Heft 1, 2 >
Band IX. Heft 3, 4, 5 ; Band XXVII. Heft 2, 3 ; Band
XXX. Heft 1 ; Band XXXVI. Heft 2 ; Band LIX. Heft
1, 2, 3, 4 ; Band LX. Heft 1, 2, 3 ; Band LXI. Heft 1, 2,
3; Band LXII. Heft 1, 2, 3, 4. — Mat. Nat. Classe; Band
XXVII. Heft 2 ; Band XXX. Heft 16, 17; Band XXXV.
Heft 7, 8, 9; Band XXXIX. Heft 2; Band LVII.
Heft 4, 5 ; Band LVIII. Heft 1, 2, 3, 4, 5 ; Band LIX.
Heft 1, 2, 3, 4, 5. Band LX. Heft 1, 2. — Minera-
logie-Botanik, &c. Band LVII. Heft 4, 5 ; Band LVIII.
Heft 1, 2, 3, 4, 5; Band LIX. Heft 1, 2, 3, 4, 5 ; Band
LX. Heft 1, 2. 8vo. — From the Academy.

Register zu den Ban den 51 bis 60 der Sitzungsberichte der
Philos. -Ilistor. Classe. — From the Academy.

Verhandlungen der kaiserlich-koniglichen zoologisch-
botanischen Gresellscliaft in Wien. Band XIX. 8vo. —
From the Society.

Verhandlungen der kaiserlich-koniglichen geologischen
Reichsanstalt. 1869, Nos. 1-5, 10-18 ; 1870, Nos. 1-5.
8 vo. — From the Society.

Washington. — Annual Reports of the Commissioner of Patents for
1867. 8vo. — From the United States Patent Office.

VOL. VII. 2 G

230 Proceedings of the Royal Society.

Washington. — Astronomical and Meteorological Observations made
at the United States Naval Observatory during 1866.
Washington, 1868. 4to. — From the United States Govern-
ment.

Reports of the National Academy of Sciences for 1867 and

1868. 8vo. — From the Academy.

Smithsonian Miscellaneous Collections, Catalogue of Or-
thoptera of North America described previous to 1867.
8vo. — From the Institution.

Annual Report of the Board of Regents of the Smithsonian
Institution for 1867. 8vo. — From the Institution.
Wellington ( New Zealand). — Statistics of New Zealand for 1867.

1869. Fol. — From the New Zealand Government.
Zurich.^- Neue Denkschriften der allgemeinen schweizerischen

Gressellschaft fur die gesammten-Naturwissenschaften —
(Nouveaux Memoires de la Societe Helvetique des Sciences
Naturelles). Band XXIII. mit 26 Tafeln. 4to. — From
the Society.

PROCEEDINGS

ROYAL SOCIETY OF EDINBURGH.

VOL. VII.

1870-71.

No. 82.

Eighty-Eighth Session.

Monday, 2 8th November 1870.

Dr CHRISTISON, President, in the Chair.
The following Council were elected
President.

Professor CHRISTISON, M.D., D.C.L,

Honorary Vice-President.

HiS Grace the DUKE of ARGYLL,

Vice-Presidents.

David Milne Home, LL.D.
Professor Kelland.

The Hon. Lord Neayes.

Professor Sir William Thomson.
William Forbes Skene, LL.D.
Principal Sir Alex. Grant, Bart. -

General Secretary- — Dr John Hutton Balfour.

Secretaries to the Ordinary Meetings *
Professor Tait.

Professor Turner.

Treasurer — David Smith, Esq.

Ourator of Library avd Museum— Dr MacLagan,

Councillors

Dr James M‘Bain, R.N.

Dr William Robertson.
Thomas Stevenson, Esq., C.E.
Dr Handyside.

Archibald Geikie, Esq.
Professor A. Crum Brown.

Rev. Dr W. Lindsay Alexander.
Professor Fleeming Jenkin.

Prof. Wyville Thomson, LL.D.
James Donaldson, LL.D.

Dr Thomas R. FraseR.

Dr Arthur Gamgee.

2 A"

VOL. VII.

232

Proceedings of the Boycd Society

Monday, 5th December 1870.

David Milne Home, Esq., Vice-President, read the
following Address

Gentlemen, Fellows of the Eoyal Society of Edinburgh, —
In compliance with a special request of the Council, I come before
you this evening to deliver the Address usually given at the open-
ing of our Winter Session.

This practice of annually taking stock to ascertain what business
we are doing, and how we are doing it, seems to me very right and
expedient. The whole Society is thus made aware whether it is
retrograding or advancing, — whether it is or is not, carrying out
the objects of its institution.

I see that in some former Addresses, not only was the exist-
ing state of the Society reported on, but occasion was taken to
open up general views on science and literature, and sometimes
to point out important discoveries recently made in particular fields
of knowledge. An Address of that instructive character probably
would have been given to-night, had the place I now unworthily
hold, been occupied by the distinguished savant who stood above
me on the roll of Vice-Presidents, as he also stands immeasurably
above me in knowledge. That gentleman’s numerous engagements
elsewhere, and the expectation that he would be in Italy, pre-
vented his guaranteeing to the Council when they applied to him,
that he would be here to-night. My own usual avocations are not
such as fit me for executing the duty which Dr Lyon Playfair
would have so ably performed, — my time being chiefly occupied
with the duties incumbent on a landed proprietor resident in the
country, who has to attend justice of peace courts, road meetings,
cattle plague committees, and parochial boards. My address,
therefore, will not be literary or scientific, but of a practical
character as more congenial to my habits of life; — containing
nevertheless some information and suggestions which I hope mny
not be entirely useless.

"What I shall venture to submit, will be under the following
heads : —

of Edinburgh, Session 1870-71.

233

ls£. The work done by us as a Society, during the past year.

2d. The means we possess, of doing our work.

3 d. Suggestions for rendering our Society more efficient.

4 tli. The usefulness of Societies like ours.

5th. The best way of encouraging and assisting such Societies.

I. Work of tlie Society during the past Year.

The ordinary business of the Society, as we all know, is done
during the winter, at evening meetings, when papers are read.
These are abstracted into our printed Proceedings, and the most
valuable inserted verbatim in our Transactions.

The number of our meetings last winter was 13, being on an
average two, each month. The number of papers read at these
meetings, was 43. The authors of these, were 33 persons.

Of the 43 papers, 5 were literary ; the other 38 papers, on matters
of physical science.

In the previous year, the -total number of papers had been 44,
all on physical subjects.

The following epitome shows the number of the papers under
each branch of science : —

Mathematical papers, . . . .11

Chemical „ .... 7

Mechanical or Natural Philosophy papers, . 6

Medical .... „ .4

Geological .... „ .3

Zoological .... „ .3

Geographical 2

Botanical . . . . „ . 1

Meteorological . . . „ . 1

In a few instances, and I regret they were so few, discussion
occurred on the part of the Fellows present, after the papers were
read or described.

I have said that all these papers appear in an abstracted form
in our printed Proceedings. Last year’s printed Proceedings
extend to 209 octavo pages. Those of the year before, contained
200 pages.

Of the 43 papers presented last winter, 11 were selected as worth

234

Proceedings of the Poyal Society

of publication in our Transactions. The titles and authors of these
papers were as follows : —

1. Reciprocal Figures, Frames, and Diagrams of Forces. By J.

Clerk Maxwell, F.R.S.

2. Scientific Method in the Interpretation of Popular Myths,

with Special Reference to G-reek Mythology. By Professor
Blackie.

3. Extension of Brouncker’s Method to the Comparison of Several

Magnitudes. By Edward Sang, Esq.

4. Gfreen’s and other Allied Theorems. By Professor Tait,

5. Heat developed in the Combination of Acids and Bases. By

Dr Thos. Andrews, Hon. F.R.S.E.

6. The G-enetic Succession of Zooids in the Hydroida. By

Prof. Allman.

7. Influence of the Yagus upon the Yascular System. By Prof.

Rutherford, of King’s College, London.

8. Old River Terraces of the Earn and Teith, viewed in connec-

tion with certain proofs of the Antiquity of Man. By Rev.
Thos. Brown.

9. Spectra formed by the Passage of Polarised Light through

Double Refracting Crystals. By Francis Deas, LL.B.

10. Oxidation Products of Picoline. By James Dewar, Esq.

11. Account of the G-reat Finner Whale stranded at Longniddry.

By Professor Turner.

I may here add that our volumes of Transactions are rapidly
eihibiting an increase in the number, — I hope also in the value of
their contents. About ten or twelve years ago, one year’s Transac-
tions did not exceed 100 quarto pages. During the three years
which followed, their average size was measured by 250 pages ;
during the last three years by 310 pages.

The Society is aware that we have three prizes in our gift, created
by members of our body at different periods, — the Heill prize, the
Keith prize, and the Brisbane prize. A period of two years
elapses, in the case of the two latter, before bestowal. Last year
the Keith prize was awarded, consisting of a gold medal and £50,
11 for the best communication on a scientific subject.” It was
awarded to Professor Tait, for a paper, published in our Transac-
tions, on the “ Rotation of a Rigid Body about a fixed point.”

235

of Edinburgh, Session 1870-71.

In alluding to the award of this prize, it is only right to men-
tion the high estimation in which, as I have reason to know,
this paper and other mathematical papers by the same author
are held by men of science. These papers are examples of the
application and use of a new and wonderful instrument of ana-
lysis invented by the late Sir William Hamilton of Dublin, one
of the profoundest philosophers of his day, known by the name of
“ Quaternions .” I am told that there are as yet few mathematicians
who can work with it. But Professor Tait has been able, both to
work with it, and to improve upon it; and has applied it to the
solution of many important physical questions not easily solved
by ordinary analysis.

To show that these remarks rest on better testimony than my own,
I beg to refer to the high appreciation of Professor Tait’s applica-
tion of “Quaternions,” as expressed by the distinguished inventor
himself, in a work published shortly after his death. Sir William
Hamilton’s “ Elements of Quaternions” (page 755) contains the
following passage : —

“ Professor Tait, who has already published tracts on other applications of
Quaternions, mathematical and physical, including some on Electro-dynamics,
appears to the writer eminently fitted to carry on, happily and usefully, this
new branch of mathematical science, and likely to become in it, if the ex-
pression may be allowed, one of the chief successors to its inventor.”

To these gracious words of Hamilton, may be added the testimony
of Professor Sir William Thomson of Glasgow, himself a mathe-
matician and physicist second to none in Europe, contained in a
letter to our General Secretary, from which I am allowed to quote : — ■

“ My Dear Balfour, — The marked appreciation by Sir William Hamilton
of Tait’s work in quaternions, is about the highest possible testimonial to its
excellence. His book on the subject will constitute, I believe, a permanent
monument of the most marvellously ingenious generalisation ever made in
mathematical science. It has already done much to render the new instru-
ment available for researches in Natural Philosophy, and I can see signs
(witness the two most transcendent and practical naturalists of the age,
Helmholtz and Clerk Maxwell) of quaternions becoming, through its teach-
ing, a useful implement, though many years may pass before fruits resulting
from quaternionic husbandry can be gathered.”

Besides the ordinary business of the Society for the past year

236

Proceedings of the Royal Society

to which I have been adverting, there have been one or two other
matters taken np by the Council which it is proper to mention —

(1.) The Council agreed to co-operate with other public bodies
in this town, in giving to the British Association for the Advance-
ment of Science, an invitation to hold their next year’s meeting
in Edinburgh. That invitation was communicated through our
general secretary, Professor Balfour, at the Liverpool meeting.
We all know the result ; but perhaps all do not know how much
is due to the efforts of this Society. It must also be matter of
congratulation to ourselves to learn, that the President elect of
the Association is one of our own members — a member of whom
any Society may feel proud — Sir William Thomson of Glasgow ;
and, moreover, that the local secretaries and treasurer of the meet-
ing are all Fellows of out Society. May I therefore be allowed
to express a hope, that the members of this Society will do their
utmost to assist in promoting the success of the meeting, and
that the Society will be able to give a handsome subscription to
the fund for expenses.

(2.) Another matter out of the ordinary business of the Society,
is the application which the Council made to Her Majesty’s
Gfovernment, for the establishment of a Chair of Geology in the
University of Edinburgh, and for assistance to endow it.

The circumstance which led to this application was the resig-
nation of Professor Allman, and an intimation received about the
same time, from that eminent geologist and true-hearted Scotch-
man, Sir Koderick Impey Murchison, that he was willing to set
apart £6000 from his own funds, to yield a moiety of the endow-
ment.

The Council of the Society, feeling that they would go with
greater hope of success to Government if backed by other public
bodies, obtained the co-operation of the University, the Royal
Scottish Society of Arts, the Geological Society, and the Highland
and Agricultural Society.

We all know, in consequence of an intimation in the newspapers,
that the Premier has so far yielded to these applications, by
agreeing that Government should pay £200 yearly to this object *
so that, adding the dividends which will be obtained from Sir
Roderick Murchison’s more generous gift of £6000, there will be

237

of Edinburgh, Session 1870-71.

for tlie support of the chair, a fixed income of £450. I believe
there is in existence a separate yearly sum of £35, hitherto drawn
by the Professor of Natural History, and which, in the event of a
separate Professorship being established for geology and mineralogy,
was appointed to be transferred to the latter. This bequest was
made a number of years ago by a Scottish gentleman named
Thomson, who died at Palermo.

Before taking leave of this subject, I wish to draw attention to
the fact that in the other Universities of Scotland the same incon-
venience exists, which is about to be remedied in Edinburgh ; and
perhaps I maybe permitted to express from this chair a hope, that
in them also, means maybe found, for removing that inconvenience.
I was glad to observe, that the Lord Rector of Aberdeen University,
in an address delivered by him about ten days ago, took notice
of the multifarious branches of instruction which the Professor of
Natural History has there to teach, and is unable to overtake. Mr
Grant Duff is a member of the present Government, so that I trust
he will call the Premier’s attention to the subject. The chair of
Natural History at Aberdeen was established by the Crown, and its
occupant is appointed by the Crown. I presume the design and
intention of the Crown was, that geology, and the other recognised
branches of Natural History, should be taught in that University.
Therefore if, in consequence of the extension and growth of these
branches, it has become impossible for any one man to give in-
struction in all, there seems to be a sort of moral obligation on
the Crown to carry out its own intention and undertaking, by
appointing separate Professors for these branches.

These remarks apply equally to the two other Universities of
Glasgow and St Andrews ; the latter, however, viz., St Andrews,
presenting an additional evil of its own, viz., the anomaly, that the
Professor of Natural History has to lecture on Civil History besides.

It humbly appears to me that there should be no great diffi-
culty, both at St Andrews and at Glasgow, of providing means
for remedying the evils to which I have been adverting. The
Government gives aid to schools to an equal extent with funds
supplied locally for their support, even when these schools are
of an elementary character, and supply instruction only for a
parish. Much more must Government be disposed to assist when

238 Proceedings of the Royal Society

the institution wanting help, draws scholars from a wide area of
country, as is the case with a University. What persons are so
interested in establishing means of instruction in geology and
mining, as proprietors of coal, iron, shale, fire-clay, and building
stones ? or who more able than they, to provide the amount of funds
necessary to warrant an application to Gfovernment to assist in en-
dowing professorships for giving that instruction. The counties
of Fife and Forfar, near St Andrews ; — the counties of Lanark,
Renfrew, and Ayr, so intimately connected with Glasgow, are all
rich in mines and minerals. Surely the proprietors and manufac-
turers of both districts will have patriotism enough to raise, by a
conjoint effort, the sum which one single individual-— their own
countryman — though not resident among us, has so cheerfully given.

I have adverted to this subject so fully, because of the interest
which our Society, from a very early period, has taken in this
particular science. Indeed, it is to geology that our Society is
chiefly indebted for the reputation it first acquired in the scientific
world, in consequence of the animated and stirring speculations
and discussions instituted by its members, among whom were Sir
James Hall, Lord Webb Seymour, Col. Imrie, Hutton, Playfair,
and Jameson. I believe that little or nothing was known of
geology, in Great Britain, before the time to which I have
alluded ; and that even the Geological Society of London, founded
in the year 1808, owed its origin chiefly to Scotsmen resident
in England, who had imbibed their taste for the science by taking
part in the discussions, or studying the transactions of our Society.
When, from various causes, the science of geology at a later period
begun to flag in Scotland, our Society lamented and remonstrated,
and endeavoured to waken public sympathy on the subject. Thus
the late Principal Forbes, in his address from this chair in the
year 1862, says

“Of all the changes which have befallen Scottish science during
the last half century, that which I most deeply deplore, is the
progressive decay of our once illustrious geological school.”

In the year 1865, our Society presented a memorial to the
Government of which Earl Russell was then head, pointing out the
inconvenience of there being no separate Professorship of Geology,
and asking Government to institute one.

of Edinburgh, Session 1870-71.

289

Though our attempt to obtain redress was not then successful, it
may be presumed that good was done, by our having kept it before
the eye of the public; and that seeds then were sown, which have
now produced the results we had so long been desiring.

II. I come now to the next division of this address, which
refers to

The means we possess of carrying out the objects of the Society.

I allude to strength of membership, and to available funds.

With regard to funds, I am happy to say that, though not rich,
we have now rather more funds, than we have ever had before ;
thanks to our excellent treasurer, Mr Smith, who does what he
can to keep up income, and keep down unnecessary expendi-
ture.

Our income is derived from three main sources : —

(1.) Contributions of ordinary Fellows, about . £800

(2.) Dividends from capital invested, . . 280

(3.) Annual grant from Government, . . 300

Making a total revenue of £1380

Our expenditure may be classed under the following five
heads : —

(1.) Cost of printing and circulating Proceedings

and Transactions, about . . . £400

(2.) Rent of apartments, taxes, cleaning, &c., . 300

(3.) Books, periodicals, and newspapers, . . 150

(4.) Salaries of officers, .... 240

(5.) Expenses of evening meetings, . . 30

£1120

With regard to membership — the number of ordinary Fellows
— on whom of course we chiefly depend for papers, and for attend-
ance at our evening meetings, stands thus. This time last
year, the total number was 303. Since then, 30 new ordinary
members have been elected— making altogether 333. But from
this number must be deducted five who have died, and two

2 i

VOL. VII.

240 Proceedings of the Royal Society

who have resigned — leaving a balance at this date of 326 ; which
is a larger number of ordinary Fellows than we have had since
the institution of the Society. The number of our honorary
members is the same as formerly, 36 foreigners, and 20 British —
all men of known celebrity.

Before referring more particularly to the individual members
who, during the past year, have been taken from us by death,
allow me to say that I think the giving of obituary sketches of
deceased associates is a practice highly becoming. It should
be remembered that our Society is intended, not only to aid
science and literature, but also to promote good fellowship among
the votaries of both. One object of our association, is to en-
courage and assist one another by sympathy, and interchange
of views; for which purpose we not only listen to papers, and
discuss these at our evening meetings, but also hold personal
intercourse in our library and reading-room. When, therefore,
any of our comrades are removed from our midst by death, it is but
fitting we should offer a parting tribute of regret at the dissolution
of our connection, and endeavour to fix some traces of our departed
associates in our memory, by recounting the part they have taken
in helping to carry on the business of the Society, by recording
any services rendered to the country, and by noting the leading
events of their lives.

Whilst we have reason to be thankful that, during the past
year, the number of deceased associates is small — smaller, when
regard is had to the total number of members, than in any
former year, that circumstance is more than counterbalanced by
the worth and preciousness of the lives whose loss we deplore.

The following are the names of deceased Fellows, of each of
whom I proceed to give a short obituary notice: —

Adam Hunter.

Edward Francis Maitland.

Robert Nasmyth.

James Young Simpson.

James Syme.

Adam Hunter was born at Greenock on 20th June, 1791. He
»>btained his classical and mathematical education at Glasgow

241

of Edinburgh, Session 1870-71.

University, and afterwards came to Edinburgh for the medical
classes. He graduated in the year 1813. He died in Edinburgh,
24th June, 1870.

In the year 1815 he commenced practice in Edinburgh as a
family physician, and continued there in the same vocation all his
life. He was most attentive to his duties, very gentleman-like
in his bearing, and an agreeable, social companion. He possessed
the regard and esteem of the late Hr Abercrombie, whose family
he attended when any of its members were ailing. He was with
Hr Abercrombie himself, during his last illness ; and, after his
death, he wrote a short biographical memoir of his friend and
patient for the newspapers.

In the year 1839 Hr Hunter became a Fellow of this Society.
He was a member of the Medico-Chirurgical Society of Edinburgh,
and contributed a paper to its Transactions, on “ Hislocations of
tbe Shoulder and Hip-Joints.” He was a life member of the
British Association. In the year 1865, he published an in-
teresting pamphlet of forty-one pages on the subject of Life
Insurance ; contrasting the London and Edinburgh offices, and
showing the superiority of the latter, as regards honest adminis-
tration and principles. He had been a policy holder in a London
office, as well as in the Scottish Widows’ Fund, and found how
much more advantageous it was to be connected with the latter,
than with the former.

Hr Hunter was employed by the Hirectors of the Scottish
National Insurance Company to make a special report on the
lives of the assured in that Company. His report, which was
printed, received much commendation. He had been the medical
adviser of that Company since the year 1843; as also of the
English and Scottish Law Life Assurance Association, since the
year 1847. On the occasion of his death, tbe Hirectors of both
Companies passed minutes, expressing the very high regard
which they entertained for him. Whilst his health remained,
Hr Hunter’s practice was extensive ; and his patients had not
only full confidence in his professional skill, but derived great
comfort from his visits. One of them writes thus : “ On more than
one occasion he was the means, in the hand of Grod, of saving
my life, and many, many times he has lightened my anxieties?

242 Proceedings of the Royal Society

and cheered my heart, in a way no one but himself could do.
G-od was good to me, in giving me such a valuable adviser.”

In the year 1865, Dr Hunter underwent an operation for removal
of a tumour in the throat. But the disease was not eradicated.
The tumour re-appeared, and continued up to the period of his
death, which took place suddenly.

Dean Ramsay, to whose congregation Dr Hunter belonged, after
his funeral, alluded from the pulpit to him, in these terms :
“ He had for many years a very extensive medical practice in
the families of this city, and no man more conscientiously, more
carefully, and more sedulously performed the duties of his pro-
fession. From the presence of an impending and fatal malady,
death had for some time been familiarised to his mind. But I
know how he met that monition, as he met all the trials of life,
with a firm trust in the love of his Redeemer, and with unshaken
faith in the fulness of His atonement.”

Dr Hunter, in October 1820, married Elizabeth, the eldest
daughter of John Kircaldy, Esq., and by her had six children.

Edward Francis Maitland, known after his elevation to the
judicial bench under the title of Lord Barcaple, was born in Edin-
burgh, 10th April, 1808, and died there 23d February 1870. He
was the youngest son of Adam Maitland of Dundrennan, in the
county of Kirkcudbright — a property which a Dr Cairns of London
left to his niece, whom Mr Maitland married. Edward Maitland’s
elder brother was Thomas, who also was raised to the bench, under
the title of Lord Dundrennan.

He received his education at the High School, and at the
University of Edinburgh, and came to the bar in the year 1831.
lie was possessed of considerable ability, and also of much general
knowledge derived from reading. He was shy and reserved, and
had an awkward manner, so that his real merits were less known
than they deserved to be. For many years he had little or no
business as a lawyer, and at one time in consequence meditated a
change of profession. During this period of involuntary profes-
sional idleness, he became editor of the “North British Review,”
and contributed to it several papers, which were characterised by
vigour of thought, and correctness of composition. Being a

of Edinburgh, Session 1870-71.

243

Whig in politics, when his friends obtained office, he received
the appointment of Advocate-Depute. In the year 1851 he was
made Sheriff of Argyle. In the year 1855 he was appointed
Solicitor-General, which office he lost with the change of Govern-
ment; but in 1859 it was restored to him. These professional
appointments afforded an opportunity of showing his qualifica-
tions as a good lawyer, and an accomplished pleader; and busi-
ness at length flowed in, so as to afford a handsome income. He
was thoroughly conscientious in the fulfilment of his professional
engagements. When Solicitor-General, it was remarked that he
never missed being present in the Justiciary Court, and he was
always well prepared with the business of which he had charge.
There were several cases of public interest in which he was
counsel, — one of them the famous Yelverton case. He was senior
counsel for Miss Longworth, and evinced the utmost anxiety to
have her claims properly presented. Shortly before her case came
on for discussion in the Inner House, he received from the Crown
his commission to the bench. But he withheld it for a week, that
he might have it in his power to plead once more on Miss Long-
worth’s behalf; and it has been stated, that it took him three
days’ hard work to prepare for the pleading. He declined to
accept of any remuneration for his services in this case. His title
of Barcaple was derived from a property of that name which he
had purchased from his brother, David, a merchant in New York.
It is situated in Kirkcudbrightshire, and I believe not far from
the family estate of Dundrennan.

It was in 1862 that Mr Maitland was raised to the bench, and
it was in the same year that he became a Fellow of our Society.
But he did not contribute any papers, or often attend our meet-
ings. He was the first representative of the Edinburgh University
Council in the University Court. He was also the first Rector of
Aberdeen University, after the union of King’s and Marischal
Colleges in 1860. Not being able to understand how Mr Maitland
should have been thought of for this appointment, being in no
way connected with Aberdeen, I wrote to my friend Principal
Campbell for an explanation ; and I have much pleasure in
making the following extract from his answer: —

“ His appointment to the office of Rector was the result of a

244 Proceedings of the Royal Society

severe and bitter contest between the friends and the opponents of
the union of the Colleges, or rather a portion of the latter, for the
more sensible and disinterested opponents had by that time seen
the necessit}^ of acquiescing in the union, and of either facilitating
or not impeding the working of the University under the new
arrangements. The malcontents, whose object was to bring about
a dead-lock and embarrass the Universities’ Commissioners, in-
duced a party of the students to set up the late Sir Andrew Leith
Hay, who certainly would never have been thought of in other
circumstances. The friends of peace and order chose Mr Mait-
land, although — I perhaps ought to say, because — he was totally
unconnected with this locality and district, and yet well-known
as a man combining a cultivated mind with the aptitude for
academic business, as well as the firmness which our circum-
stances required.

“ The votes of the Nations stood two to two, and the casting
vote having fallen to me — the Chancellorship being vacant — I
gave it in favour of Mr Maitland, although, owing to local in-
fluence and intimidation, the aggregate majority of individual
votes was in favour of his opponent. I need not now say any-
thing of the abuse and threats with which my decision was received
by many in the town, of the childish and abortive application
to the Court of Session for an interdict, or of the violence with
which some of Sir A. Leith Hay’s supporters attempted to inter-
rupt the installation, and the Rector’s address. All was amply
repaid, to me, at least, by Lord Barcaple’s great services to the
University, in circumstances of difficulty which the authorities of
a Scotch University have rarely, if ever, encountered — services
which eventually gained for Lord JBarcaple the esteem of most of his
opponents, and the lasting gratitude of the friends of the Univer-
sity. He made the duties of his office a matter of conscience. Not-
withstanding the demands on his time, of such a practice at the
bar as his, he never hesitated to come to Aberdeen when required ;
and I can safely say that no Rector in Scotland, during his three
years’ tenure of office, has ever attended an equal number of meet-
ings of Court and Council. His inaugural address was in a high
degree sensible, elegant, and scholarly, but I do not remember that
it was remarkable for anything in the topics or mode of discussion.

of Edinburgh, Session 1870-71. 245

“ Lord Barcaple was a Whig and a Free Churchman. I am
neither. But there are few men whose memory I cherish with
greater veneration.”

Lord Barcaple’s inaugural address referred to by Principal
Campbell, I have, since receiving the Principal’s letter, had an
opportunity of reading. It contains an admirable summary of
the duties of University students, and also of the temptations to
which young men of their age are exposed. The language em-
ployed is correct and forcible — clearly indicating that Lord Bar-
caple was a person of high intellectual powers, and of cultivated
mind.

Lord Barcaple, though of decided political views, was too con-
scientious to be a party man. His friends had looked forward to
his holding the office of Lord Advocate, and going into Parlia-
ment. It was probably lucky for him that he did not undergo
this ordeal, as the exercise of patronage in a party spirit would
have been to him a perpetual misery. It is understood that,
soon after he became judge, he regretted his elevation, as it
not only greatly lessened his emoluments, but imposed on him
more onerous duties than he was able comfortably to discharge.
The death of Lord Manor, and the unaccountable delay on the
part of Government in filling up the vacancy, threw on Lord
Barcaple a very large amount of judicial work. The load proved
too much, and he broke down ; continuing, however, to the very
last the performance of duty. If, in consequence of his reserved
habits, Lord Barcaple had not many friends, he had no enemies.
His amiable dispositions, and strictly truthful character, ensured
to him a peaceful life, and the esteem of all who knew him.

Bobert Nasmyth was born in Edinburgh in the year 1792. He
died there, 12th May, 1870. He was educated first at the High
School, and when about fifteen years old went to the Univer-
sity of Edinburgh. Intending to belong to the medical pro-
fession, he first became a pupil of Dr Barclay, then an extra-
academical lecturer on anatomy. Ultimately he became his pro-
sector, and was always seated beside him during the lecture.
At first he seemed inclined to adopt surgery as his profession.
In the year 1823 he became a Fellow of the Koyal College of

246 Proceedings of the Royal Society

Surgeons — Syme also being elected about the same time. He
was intimate with Syme, Liston, Fergusson, and Wardrop, and
often assisted these eminent surgeons when they operated. He
afterwards went to London, and there was led to study den-
tistry. He probably foresaw, that there would be a favourable
opening in Edinburgh, when Dr Law, who had a large practice
as a dentist, died or retired.

Mr Nasmyth, when he began practice in Edinburgh, was the
first who united the profession of a dentist, with the education and
qualifications of a surgeon. He soon succeeded in obtaining public
confidence.

He wrote very few scientific papers. The subject of his in-
augural thesis had been “Tie Douleureux ; ” and, in the year
1843, he communicated to the London and Edinburgh Journal of
Medical Science a comprehensive paper on the “ Physiology and
Pathology of the Teeth.” I understand that most of the prepara-
tions in the Museum of the Royal College of Surgeons in this
town, to illustrate the development of the teeth, were made by Mr
Nasmyth.

The late Professor G-oodsir was for seven years assistant
to Mr Nasmyth, and has publicly acknowledged the valuable
instruction he received from him. In 1842 Mr Nasmyth was
elected a Fellow of the Royal Society of Edinburgh, but I do not
think he contributed any papers or notices to our transactions.
He was vice-president of the Odontological Society of London,
and had been so for thirteen years before his death. He had
held the offices of surgeon-dentist to King George IV., to King
William, and also to Queen Victoria. He was a person of affable
manners, and easy access. Dr Smith of Wemyss Place informs
me that he kindly gave him much assistance in preparing the
lectures which he delivered in Surgeon’s Hall, and also in estab-
lishing the Dental Dispensary of Edinburgh.

Mr Nasmyth had in all four sons and four daughters. Two
sons successively followed for a time their father’s profession ;
but both died of consumption, as well as a daughter and another
son. His third son was an officer in the artillery, and highly dis-
tinguished himself in the defence of Silistria.

Mr Nasmyth had a much larger and longer practice, in his

of Edinburgh, Session 1870-71.

247

peculiar vocation, than any one before in Edinburgh. He was an
agreeable companion, a fast friend, and possessed of much general
knowledge. He will long be remembered as a skilful dentist, and
a highly respected citizen of Edinburgh.

James Young Simpson was born 7th June 1811, and died 6th
May 1870, being at the time Professor of Midwifery in the Uni-
versity of Edinburgh. His birthplace was Bathgate. The house
in which he was born, is, I understand, still standing. It is a
two-storeyed slated house, part of which has been converted by his
brother Alexander into a hall used for meetings of various kinds.
His father kept a baker’s shop. His grandfather was a small
farmer. He was the youngest of seven sons ; and was sent by
his father to the parish school.

He was sent to Edinburgh University to study medicine, and
his expenses there were paid by his eldest and now only surviving
brother, Mr Alexander Simpson of Bathgate, to whose kindness
and brotherly care he was infinitely indebted. His parents both
died when he was young. Whilst studying in Edinburgh, he
lodged with his brother David, then in business as a baker in
Stockbridge.

His taste for books in his boyhood was remarkable. He was
constantly to be seen sitting at the corner of the fireplace devour-
ing any books he could get, and oblivious of the talking or noise
around him.

In the Humanity Class, he attracted the attention and patronage
of Professor Pillans, who, learning that he wished to study medi-
cine, but that he was scant of funds, recommended him to com-
pete for a bursary endowed for the support of boys of the name of
Stewart or Simpson. This advice he followed. An extended
study of Latin and Greek was however required. He succeeded in
gaining the bursary, thereby drawing £10 yearly for three years.

In the year 1832 he obtained his medical degree, and was imme
diately afterwards elected by his fellow-students — among whom he
had become a favourite — to be Senior President of the Roya
Medical Society of Edinburgh, — an institution which, for about
a century and a half, has been supported chiefly by the University
medical students.

2 K

VOL. VII.

24:8 Proceedings of the Hoy at Society

Young Simpson’s graduation thesis so pleased Professor John
Thomson, who held the Pathological Chair, that he made him
assistant in his house, and employed him in the arrangement of
his library; and in this new position he made rapid progress,
not only sucking in all the knowledge which the Professor pos-
sessed, but venturing on views and speculations of his own. He
was permitted occasionally to read the Professor’s lecture to the
class when the latter was unable from feeble health to do so — the
Professor himself, however, being generally present. It seems
that young Simpson did not always confine himself to the mere
reading of the lecture, but presumed occasionally to introduce
verbally an exposition of his own ideas, to the surprise of both
students and Professor. The latter, on one occasion, having heard
some new and startling propositions from the chair, after the
lecture was over, expressed his dissatisfaction in the retiring-room
by saying to his young assistant, “ I don’t believe one word of it,
sir.”

Simpson having acquired some confidence in his own powers,
thought of setting up for himself; and seeing in the newspapers
an advertisement that a doctor was wanted to attend the poor in
the parish of Innerkip on the Clyde, he offered himself. But he
was rejected. He used to say that he felt this disappointment more
keenly than any he ever met with in after life. I may add here
what I think Simpson once told me, that an old-established medi-
cal practitioner in a town not far from Edinburgh, wishing to get a
young licentiate as an assistant, and who might ultimately become
a partner, gave out a subject for an essay among the medical
students of the Midwifery Chair, intending to judge of their quali-
fications partly by their essays and partly by conversation.
Simpson gave in an essay, and was one of those sent for, but was
again doomed to disappointment; though from this village doctor
he received much friendly counsel and a promise of future patronage.

During the next two or three years, he continued to prosecute
his studies, chiefly in obstetrics, and read several papers in the
Royal Medical Society. He also visited France. He now began
to form a museum of preparations and objects bearing on anatomy,
and at length announced his intention of giving public lectures.
These he continued for three years, and they obtained so much

249

of Edinburgh, Session 1870-71.

success, that lie probably then conceived the idea, in the event of
a vacancy in the University Midwifery Chair, of offering himself
as a candidate.

In the year 1839 the venerable Dr Hamilton, who occupied that
chair, died, on which event Simpson became a candidate, support-
ing his claims by an octavo volume of 200 pages of testimonials,
and accompanied by a catalogue of the museum which, in the short
space of three years, he had formed, containing no less than 700
obstetric preparations. The assiduity with which he plied his can-
vass, and the steps he took to overcome objections, may be judged
of from the circumstance that one of the magistrates (the present
Lord Provost of this city) having stated it as a drawback, if not a
disqualification, that he was an unmarried man, Dr Simpson replied,
“ I admit it is a disqualification, but it may perhaps be removed.”
The next day he started for Liverpool, and contracted a mar-
riage there with the daughter of Mr Walter G-rindlay. In about
ten days thereafter, he returned to Edinburgh ; and having called
on Bailie Law, he informed him of the step he had taken in
deference to his opinion, and then claimed a promise of his vote —
which he at once received. It was by that vote he won the Pro-
fessorship.

After Simpson was elected, there were confident predictions that
the obstetrical class in the University would fall off, and that many
fewer patients would come to Edinburgh to be under the Pro-
fessor’s care. Animadversions fell freely on the magistrates, as
patrons of the chair, for electing a man without either experience or
reputation, instead of his opponent, who had both. These antici-
pations soon proved to be utterly unfounded. After Simpson’s
election the Midwifery Class was crowded. Not only did students
flock to it in greater numbers even than formerly, but medical
officers of the navy and army, when home on furlough, frequently
attended to hear the original views of the youthful Professor,
and were delighted by the aptness of his illustrations and the
earnestness of his style of lecturing.

He also carried on obstetric investigations and experiments on
various points of difficulty, accounts of which were given by him
from time to time in papers read at Societies, or inserted in
medical journals. He soon came to be- employed extensively

250 Proceedings of the Royal Society

as a practitioner, so that he had abundant opportunity of seeing
cases, both novel and instructive, and of trying improved methods.
At the same time, he was acquiring a complete knowledge of all
that had been written by others, not only in Europe and America,
but even by the G-reeks and Eomans, — his good classical knowledge
in this respect proving serviceable. He allowed himself very little
sleep ; and even in the houses of his patients, whilst waiting in an
adjoining room till his services were required, used to write out
papers, or arrange materials for them.

His mind was so exuberant and versatile, that it often flowed
over and beyond the pale of his own special department. Thus,
one of his papers read before the Medico-Chirurgical Society in
1841 was entitled, “ Antiquarian Notices of Leprosy and Leper
Hospitals in Scotland and England .” Another had this title,

“ Was the Roman Army provided with Medical Officers f”

His great delight, and therefore his incessant aim, was to search
out something new; and for this purpose, whilst he ransacked his
own brain, he did not disdain to rummage among the rubbish of
old authors, or to talk with any one who had anything to com-
municate on any topic whatever. One of the subjects, in his
special department, which interested him greatly, was the use of
anesthetics. He had read of the experiments performed in
America by several surgeons and dentists, to render their patients
insensible to pain by inhaling sulphuric ether. He did not see
why this substance should not be used in obstetric practice. Ac-
cordingly, he administered it to one of his patients for the purpose
of lessening the pains of parturition. This case occurred on the
19th January 1847. Before that time, no one had ventured on
such an experiment. It was entirely successful ; and he thought
it so important that, next day, he communicated the discovery
to his class, and gave a special report of it to the Obstetric Society.
The case got into the newspapers, and within ten days the process
was repeated successfully in the hospitals of London and Paris.
During the following six months, Dr Simpson continued the use
of sulphuric ether both in the Edinburgh hospitals and in private
practice, resorting to it, however, only in cases where nature had
to be assisted. Simpson found several drawbacks in the use of
sulphuric ether, and in consequence began to search for something

of Edinburgh, Session 1870-71.

251

better. One of the many substances he tried was chloroform, — a
liquid discovered in 1832 by two G-erman chemists, and first accu-
rately investigated and described in 1835 by Dumas of Paris. The
trials which Professor Simpson made with the vapour of this sub-
stance, and which led him to adopt it, took place in November
1847. But it is right to add that, though he discovered its
suitableness for the purpose wanted, and was the first to introduce
it into surgical practice, the idea of so using it, had occurred to
others previously, and trials had even been made with it. Thus
Bouchardat, in a book called u Nouveau Formulaire Magistral ,”
published in 1845, and a copy* of which Professor Simpson was
possessed of, under the head of “ Chloroforme,” observes —

“ Cependant on pent se croire autorise a regarder F effect du Chloroforme
comme antispasmodique, et a penser, que si une grande analogie de composi-
tion rapprochait cette substance des ethers , une grande analogie d' action etait
.■ egalement commune a chacune de ces substances

Another French physician, Flourens, read to the Paris Academy
in March 1847 a paper on the properties of chloroform, mentioning
a number of experiments he had made of its effects on animals,
and adding that 11 he did not think it could he used with safety in
medical practice.”

Besides the information or hints derived from these sources, it
must be added, that a Mr Waldie of Liverpool, who was chemist
to the Apothecaries’ Company there, being in Edinburgh during
the month of October 1847, called on Professor Simpson ; and
on the Professor telling him that he was seeking for some
better anaesthetic than sulphuric ether, Mr Waldie spoke to him of
chloric ether , and advised him to try pure chloroform unmixed with
alcohol. He asked Mr Waldie to submit to anaesthesation by
chloroform, but Mr Waldie was not willing to risk the experiment.

Acting on this hint, Professor Simpson procured — I believe
from Professor Gregory — a small quantity of pure chloroform,
which, however, he did not at the moment make use of. It was
put aside, to be tried with other substances at some more conve-
nient opportunity. Late one evening — it was the 4th November
1847 — to quote from Professor Miller’s pamphlet, Professor Simp-

* I state this, on the authority of the Editor of the Edinburgh Medical
Journal for Nov. 1870, p. 441,

252

Proceedings of the Royal Society

son resumed his experiments, aided by his two friends and assist-
ants, Drs Keith and Matthews Duncan —

“ Having inhaled several substances, but without much effect, it occurred
to the Professor to try a ponderous material, which he had formerly set aside
on a lumber table, and which, on account of its weight, he had hitherto re-
garded as of no likelihood whatever. That happened to be a small bottle of
chloroform. It was searched for and recovered from beneath a heap of waste
paper. With each tumbler newly charged, the inhalers resumed their voca-
tion. Immediately an unwonted hilarity seized the party. They became
bright-eyed, very happy, and very loquacious — expatiating on the delicious
aroma of the new fluid. The conversation was of unusual intelligence, and
quite charmed the listeners — some ladies of the family, and a naval officer,
brother-in-law of Dr Simpson. But suddenly there were sounds like those of
a cotton mill, louder and louder. A moment more, then all was quiet ; and
then — a crash. On awaking, Dr Simpson’s first perception was mental.
‘ This is far stronger and better than ether,’ said he to himself. His second
was, to note that he was prostrate on the floor, and that among the friends
about him there was confusion and alarm. Hearing a noise, he turned round
and saw Dr Duncan beneath a chair, his jaw dropped, his eyes staring, his
head bent half under him, — quite unconscious, and snoring in a most deter-
mined manner. More noise still, and much motion, caused by Dr Keith’s
legs making valorous efforts to overturn the supper-table. By and bye, Dr
Simpson having regained his seat, Dr Duncan having finished his uncom-
fortable slumber, and Dr Keith having come to an arrangement with the
table, the sederunt was resumed. Each expressed himself delighted with the
new agent, and its inhalation was repeated many times that night — one of
the ladies gallantly taking her place at the table — until the supply of chloro-
form was exhausted. In none of these subsequent inhalations, however, was
the experiment pushed to unconsciousness. The first event had quite satisfied
them of the agent’s full power in that way. The festivities on the occasion
did not terminate till three in the morning.”

Such is the graphic account given by the late Professor Miller of
the way in which Simpson discovered the properties of chloroform
vapour. The value of the discovery depends upon the superiority
of chloroform to sulphuric ether, the anaesthetic previously employed
in medical practice; and its superiority was manifested thus, viz. —
1st. That a much less quantity of chloroform answered ; — 2d. That
insensibility came on more rapidly ; — 3^. That no special instru-
ment for its administration was required ; — 4 th. That the odour
was more agreeable.

On the 8th November 1847, this new anaesthetic was employed
by Professor Simpson in a case of labour for the first time, and
with complete success. It soon became known in the profession,

253

of Edinburgh, Session 1870-71.

and it has in this country almost superseded every other anaesthetic,
both for aiding parturition and for numberless surgical operations.
In these operations, especially, it has been of incalculable service,
not only by relieving from suffering, but by saving life. I observe
a statement by an American army physician made lately at a public
meeting in Washington that — *

“ In the Crimea and Italian campaigns, chloroform was employed without
a single disaster. A similar result attended its use during the seven weeks’
Austro-Prussian war. In our own unhappy struggle [he alludes to the
American Civil War] chloroform was administered in more than 120,000
cases, and I am unable to learn of more than eight cases in which a fatal
result can be fairly traceable to its use.”

The immense quantity of chloroform manufactured, is a suffi-
cient proof of the trust universally placed in it, and of the
immense amount of human suffering relieved by it. In October
1869, when the freedom of this city was bestowed on Simpson,
he mentioned that the distinguished firm of apothecaries in Edin-
burgh, who manufacture chloroform, were making it in such quan-
tities as to yield about 8000 doses daily. On inquiry last week,
I learnt from Mr Flockhart, that the quantity of chloroform
now manufactured in this town is about double what it was a
year ago, partly in consequence of the sanguinary European war
which has raged for the last five months, but chiefly in con-
sequence of the rapidly increasing use of chloroform in general
practice. Mr Flockhart told me that just before Paris was
invested, he sent to the medical staff there 1000 bottles of 1 lb
each, — which he heard had reached their destination. He also sent
800 bottles to the Germans. These went chiefly to the army of
the Crown Prince.

Numerous were Simpson’s discoveries and improvements, even
in departments of medicine which lay outside of his own special
field. The stopping of haemorrhage from cut arteries is effected
by ligatures or torsion. He proposed pins or needles, by which to
close the artery.

With a view to arrest the spread of epidemics, he urged the
complete isolation of the patients affected ; maintaining that, as
rinderpest could be stamped out by the immediate slaughter of
cattle attacked by it, so scarlet fever, measles, hooping-cough, and
* Ed. Med. Journal for Nov. 1870, p. 473.

254

Proceedings of the Royal Society

even small-pox might be, if not extinguished, at all events
arrested, and so cease to be epidemic, by strict confinement and
complete isolation of the first individual attacked.

His views on the subject of large hospitals were founded on the
same principle. He insisted that, where large numbers of sick
persons were accommodated in one building, the atmosphere of
the building became tainted, so that the patients had less chance
of recovery ; and this position he attempted to prove, by contrast-
ing the proportion of recoveries in hospitals with those in private
dwellings."' On these grounds Simpson advocated the abolition of
large hospitals in towns, and the substitution of detached cottages
in the country ; but if hospitals were to be retained, then instead
of wards, with from fifty to one hundred beds in each, and reached
by lobbies and staircases inside of the house, he urged that the
wards should contain as few beds as possible, and that access should
be had to them by stairs outside of the hospital altogether.

That the principle on which these views are based, as to the
expediency of isolating persons afflicted with any complaint what-
ever, is a sound one, none can doubt, who has read the recent
discoveries of minute and invisible organic dust in the atmosphere,
consisting in many cases of germs — germs wrhich, inhaled, and
entering the blood, engender diseases in the body.

I see it stated in a well-informed medical paper that, among

* In the speech which he made on receiving tlie Freedom of the City, he
remarked that — “ When such a simple operation as amputation of the fore-
arm is performed upon a poor man in the country, and in his own cottage
home, only about one in 180 dies. But the statistics of our large metro-
politan hospitals disclose the stern and terrible truth, that if these men had
been inmates of their great wards, thirty of them, or about one in six, would
have perished ; a fact, among many others, which calls earnestly and strongly
for some great reform in our large hospitals, if these institutions are to main-
tain their ancient character as the homes of charity and beneficence.” These
statistics applied to the amputation of the arm. He gathered similar statistics
from the hospitals, and from country practitioners, in regard to amputations
of the leg, which showed that these amputations in like manner were always
more successful in the country than in town hospitals, notwithstanding the
greater skill of town surgeons ; and he deduced the following conclusions : —
“ Is?. That about three times as many patients die after limb amputations in
our large hospitals, as die from the same operations in private and country
practice. 2c?. That to reduce the death-rate from operations in our surgical
hospitals, we should strive to assimilate their form and arrangements to the
condition of patients in private and country practice.”

255

of Edinburgh, Session 1870-71.

Professor Simpson’s unpublished papers, some notes have been
found bearing on hospital reform. That he felt there was some-
thing more which he could have done on that subject, is evident
from a remark made during his last illness, when informed
that his recovery was doubtful. He said that his principal reason
for desiring a prolongation of life,, was that he might do a little
more service in the cause of hospital reform.

These suggestions for improved practice, in the various depart-
ments of the medical profession, exposed Professor Simpson to
much controversy. Naturally zealous and ardent, and knowing
that energy and perseverance were required for any reform which
was likely to disturb old customs, or existing interests, he fre-
quently drew down on himself opposition of a disagreeable and
personal character. Thus, with reference to his proposal to sub-
stitute acupressure for deligation, the Professor of Clinical Surgery,
in the same University, complained bitterly of his interference in
matters alien to the midwifery chair ; observing that he had not
interfered, as he might have done, to denounce certain useless
and often dangerous innovations introduced in the treatment of
diseases of women.

The amount of private practice which Professor Simpson
obtained, not only in his own special department, but even in
other cases, is probably greater than any one ever before pos-
sessed. No other result could be expected, as the discoveries
and improved practices which emanated from him, indicated not
only knowledge to an immense extent, but inventiveness in
meeting the most difficult cases. He had also an agreeable
expression of countenance, and a melodious voice, qualities
which, in a sick room, made his attendance doubly acceptable.
I have often seen in his house, after two o’clock, a levee of
patients of all classes, rich and poor, amounting sometimes to hun-
dreds, desirous of consulting him. Not only were the drawing-
room, dining-room, and library filled, but even the lobby and
passages. Frequently persons had to leave without being able to
see the Professor, after waiting two hours. A relative of my own,
having succeeded in catching him as he looked into the room
where she was waiting, told her case to him. He then, without
saying anything, left the room, but immediately returned with a

VOL. VII. 2 L

256 Proceedings of the Roycd Society

book, in which he pointed out to her the part where she would
find her ailment described. He asked her to read it whilst
he went to another patient, promising to come back in a few
minutes. Having read the passages, and waited patiently an
hour, she rang the bell to inquire for the Professor, and found he
had left the house, having forgotten his promise to return.

Professor Simpson was untidy in his dress, and on one occasion
much offended a lady of rank who called on him at his house, *by
coming to see her in his u stocking soles.” Frequent complaints
were made by patients, as to his want of punctuality in returning
to visit them. One lady, having been desired by him to remain in
bed till he returned again in a day or two, remained ten days in
bed, waiting for his return. He had been called to the country,
and had forgotten this town patient altogether.

It wras indeed not to be wondered at that, with such multitudes
of objects engrossing his thoughts, he should be occasionally dis-
tracted and diverted from his professional engagements. Never-
theless, so great was the confidence reposed in his skill, that these
breaches seldom caused patients to forsake him. Traps were
often laid to catch him for attendance, or a consultation. With
that view persons went to his house to breakfast though unin-
vited, and they were always graciously received. Sometimes when
they saw his carriage standing at a door, they used to get into it
and wait till the Professor came out from his visit.

It has been estimated, by those who had means of knowing the
extent of Simpson’s practice, that the number of strangers who
came to Edinburgh for his advice and treatment, must have caused
an expenditure of at least £80,000 a-year among the hotel and
lodging-house keepers.

It is obvious that, on account of Professor Simpson’s extensive
practice, the instruction which he was capable of giving must
have been most valuable. Nor was it only in the class-room and
to students, that instruction was given by him. He was ever
accessible to his professional brethren, and particularly to country
oractitioners, when they were at a loss in cases of difficulty. One
of this last class,* who frequently resorted to him, having been

* Dr Turnbull of Coldstream. He has allowed me to quote from his letter.

of Edinburgh, Session 1870-71. 257

asked by me for any notices of his deceased friend, wrote as
follows : —

“ My own success in practice has been far beyond anything I ever antici-
pated when I commenced it, now upwards of a quarter of a century since
and, beyond all question, I feel indebted to Simpson, more than to all my
other teachers put together. He was loveable and winning to an extent
which no words of mine can express. I spent the forenoon of the day on
which he returned from the Mordaunt trial with him. Then he performed
upon a patient of my own, a difficult operation, on which he showed great
resource and skill, probably the last operation of importance he did. He
gave me an account of the trial, and of Serjeant Ballantyne’s examination.
He inquired most anxiously about Dr Watson’s lecture given the previous
night at the Royal College of Surgeons,* at which I was present, and at his
absence from which he expressed great regret. A part of the day on which
he died, I spent with Dr Warburton Begbie; and when he told me that I
would never see Simpson again, adding ‘ I know full well how genuine has
been your mutual friendship for many long years,’ I could give no reply.
The tears stole down my cheeks, and I experienced then, and many a time
since, a genuine sorrow which I need not describe. To his faults I was not
blind, and for them he has assuredly been sufficiently abused by those who
think that he only was blameworthy. While I live, I shall never cease to
think of him, as I always found him, generous, attractive, and loveable, far
beyond any other man whom I ever met.”

Let me add, that he did not confine his teachings and coun-
sel to students and to medical practitioners. To all and sundry
who chose to consult him, and who could obtain access to
him, he was ever ready to open up the stores of his wonderful
memory and inventiveness. On the last occasion that I had a
lengthened conversation with him, he adverted to the future pros-
pects of medical discovery, and pointed out that these would
depend more on the chemists than on any other class of inves-
tigators. He remarked, how little we yet knew the reasons
why particular medicines were efficacious in arresting disease, and
said that he thought no medical student should receive a licence
who was not an expert chemist.

Whilst ready to teach verbally, whether in the University, or in
medical societies, or in his own house, he had little taste for writing
medical books, but it was a recreation to him to write on archaeologi-
cal subjects. The two large volumes on obstetrics, which bear his
name, were published, not by him, but by two medical friends, who
undertook the labour of collecting and arranging his papers and
* The subject of lecture was Hospital Reform.

258 Proceedings of the Royal Society

notices, published and unpublished. In the few words of preface to
the first volume, written to express his gratitude to Dr Priestley
and Dr Storer who edited the work, Professor Simpson states that
most of the communications, which appeared in it, “ were written
hurriedly, and amid the incessant distractions of practice.” He
adds, “If I had attempted to remodel, extend, and correct them,
they would never have been published in a collected form.” Why
not, he explains in his preface to volume second, in these words,
“ The life of a busy accoucheur, is not a life fitted for literary
work. Besides, I am quite deficient in some of the principal quali-
fications generally laid down as requisite for success in medical
authorship ; having no heart or habit for the daily written annota-
tion and collection of individual cases and observations — no suffi-
cient industry and endurance for the pursuit of any tedious and
protracted investigation, and no great love of lifting my pen, but
the very reverse.”

The reasons thus assigned by Professor Simpson why he would
never have published these two volumes, must, of course, be
accepted. But there was probably another and a stronger reason,
which it might have been thought ostentatious for him to mention,
—and that was his insatiable love of discovery — his constant desire
to be ever searching for new truths, and to occupy as much of
his time as possible on fields where these truths were likely to be
found. He would have considered it a waste of time to have gone
back on his own previous researches, in order to present them
again before the world in the form of a published work. That
was a mechanical labour which he willingly and wisely handed
over to the kind friends who voluntarily undertook it, and thus he
was left free to apply his time and talents to the nobler business
of advancing human knowledge by fresh discoveries.

His active and buojmnt mind, not finding enough to occupy it
within the circle of medicine, sought more work in other fields,
and hence he was led to become a member of various societies of
a scientific character. The first that he joined after becoming
Professor of Midwifery, was our own Society. He joined it in the
year 1841, and contributed the following papers, which were read
at our evening meetings, and afterwards printed in our Proceed-
ings:—

of Edinburgh, Session 1870-71. 259

On the 16th December 1850. Notice of a Roman Practitioner’s
Medicine Stamp, found near Tranent.

On the 6th March 1857. History of an Anencephalic Child.

On the 19th December 1859. On Acupressure, a New Method
of arresting Haemorrhage.

On the 6th April 1863. Note on the Anatomical Type in the
Funis Umbilicalis and Placenta. (Transactions, Yol. XXIII.)

On the same night. Note on a Pictish inscription in the Church-
yard of St Vigeans.

On the 2d January 1866. Notices of some Ancient Sculptures
on the walls of caves in Fife.

On the 26th January 1868. Pyramidal Structures in Egypt and
elsewhere ; and the objects of their erection.

With reference to this last paper, the chief purpose of which was
to refute Professor Piazzi Smyth’s theory about the origin and
object of the G-reat Pyramid of Egypt, it has been publicly
stated, by a person who alleges he knew the fact, that to enable
him to test the correctness of Professor Smyth’s calculations, and
to write the papers above referred to, he devoted three weeks to a
study of decimals and a perusal of astronomical works; — a pro-
ceeding which shows the zeal and energy with which, even at a late
period of life, he could take up a new subject.

Another Society, unconnected with the profession which he
joined, and in the business of which he took almost inconceivable
interest, was that of the Antiquaries of Scotland. Every volume
of the “ Transactions ” of that Society, after he joined it in the
year 1859, teems with notices from his pen ; and a very consider-
able number of the articles in the Society’s instructive museum
were donations from him. I have heard that he had formed a
kind of map or glossary applicable to both England and Scotland,
showing the sites of curious old buildings, camps, or stand-
ing stones; so that on the occasion of making any professional
visits to districts where these relics occurred, he might contrive to
see them.

When made a Vice-President of the Society of Antiquaries, he
delivered an address, which for archeological lore and acquaint-
ance with the early history of Scotland, astonished those who had
made this subject a special study all their lives. This address was

260 Proceedings of the Royal Society

published, and had a motto from Wordsworth prefixed to it, truly
expressive of the heartfelt pleasure which these researches gave to
him. The motto was —

“ I have owed to them
In hours of weariness, sensations sweet
Felt in the blood.”

I remember being so struck with this address, that after reading
it, I begged a common friend to ask Sir James, how and when he
had found time to compose it. His answer was, that he had
written it, after twelve o’clock at night, as he always felt refreshed
by writing papers of that kind. There is a paragraph at the con-
clusion of this address, which deserves to be quoted for its own
sake, and because it led to an occurrence which illustrates Pro-
fessor Simpson’s readiness to aid in any good object.

“ In the name of this Society, and in the name of my fellow-countrymen
generally, I here solemnly protest against the perpetration of any more acts
of useless and churlish Vandalism in the needless destruction and removal of
our Scotch antiquarian remains. The hearts of all leal Scotchmen, overflowing
as they do with a love of their native land, must ever deplore the unnecessary
demolition of all such early relics and monuments, as in any degree contri-
bute to the recovery and restoration of the past history of our country and of
our ancestors. These ancient relics and monuments are in one sense national
property, for historically they belong to Scotland and to Scotsmen in general,
more than they belong to the individual proprietors upon whose ground they
happen to stand.”

Shortly after this address was published, a visit was paid by
the Berwickshire Naturalists’ Club to a remarkable old fortress in
Berwickshire, called Edins Hald, situated among the Lammermuir
Hills. Those members of the Club who had known the building
in former years, were distressed to see how much it had been muti-
lated, and to hear, that it was about to be again used as a quarry,
for some stone dykes soon to be erected. The Club addressed the
proprietor on the subject, with the view of obtaining a promise
to prevent farther dilapidation. He, however, showed no dis-
position to grant our request. We resolved then to submit the
matter to Professor Simpson, on the faith of the admirable address
to which I have just adverted. It turned out fortunately for us,
that the wife of the proprietor, who resided near Edinburgh, was
then attended by Professor Simpson. He willingly undertook to
intercede with her on behalf of this old relic, and obtained from

261

of Edinburgh, Session 1870-71.

lier husband a letter containing a written promise to have the ruin
protected from further injury; which letter he handed over to the
secretary of the Society of Antiquaries.

Professor Simpson made several visits to Northumberland, to
examine the sculptured rocks at Old Bewick, Poddington,
and Roughting Linn, as well as to inspect the excavations of
the British forts, dwellings, and sepulchres on Yevering Bell,
among the Cheviot Hills. On one of these occasions, he joined a
meeting of the Berwickshire Naturalists’ Club — of which club he
was a member; but not being able to keep up with the party,
walking through long wet brackens, and over rough moorland, he
borrowed a horse. Not being a good rider, he soon came to grief,
in a bog which had to be crossed. The horse finding himself
sinking, reared, and tumbled the Professor into the mud, out of
which he was extricated, with some difficulty, and to the no small
detriment of garments. After getting through the bog, he valiantly
mounted again, glad to have that method of reaching the top of
one of the highest of the Cheviots.

One of the archaeological topics on which Professor Simpson wrote
an interesting paper, was a history of the Oratory on the island of
Inchcolm. I understand that he had collected materials for a simi-
lar account of all the islands of the Firth of Forth — on most of
which there are still traces of ancient ecclesiastical edifices. I
know also, that he had begun to write an account of the Roman
Wall, extending between the Firths of Forth and Clyde, as he once
spoke to me on the subject, wishing to know my opinion of Mr
G-eikie’s theory, that this district of Scotland had risen twenty
or thirty feet out of the sea, since the wall was erected. It is to
be hoped that if his MSS. on these subjects are found, they will
be put into a proper form for publication.

Animal Magnetism , Mesmerism , and Biology , were subjects,
which at an early period, he studied ; and for a time he was much
impressed with the phenomena : — so much so indeed, that he used
to hold “seances” in his own house, and show that he himself
possessed a certain strange power over others. I have heard of
his even performing in the houses of his friends, at evening
parties, — when selecting some one, whom by a mere glance he
discovered to be particularly nervous or sensitive, he would show

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Proceedings of the Royal Society

how completely a strong will could so influence the mind of another,
as to cause confusion of ideas almost amounting to imbecility.

This meddling with mesmerism brought the Professor into some
disrepute; and he was severely attacked in the Medical Journals,
for his supposed credulity. At first, he took no notice of these
attacks ; but in consequence of the solicitation of his friends he
in September 1851, published a letter in the •• Lancet ” explaining
the object of his miscalled u mesmerie soirees.” In that letter he

“ During the last ten or fifteen years, I have repeatedly seen experiments,
and also made them myself. In the course of them I have witnessed very
interesting physiological and psychological results, such as the production of
deep sleep, fixture and rigidity of muscles, &c. But I have no belief what-
ever, that these phenomena are the effects of any power, force, or agency
such as is understood by the term ‘ animal magnetism ,’ — passing from the so-
called ‘ mesmeriser ’ to the so-called ‘ mesmerised.’ They are merely the
effects produced by the mind of the ‘ mesmerised 5 upon his or her own eco-
nomy ; — self-mental acts so to speak. These may no doubt be produced by
the influence of the will of one individual acting on another. But they
are no proof of any magnetic, mesmeric, or other supposed agency. In proof
of my utter disbelief in clairvoyance , I may state that having sometime ago
been present at a lecture on the subject, I offered to place L.100 in the
hands of the President of the Medico-Chirurgical Society which he was to
give to the lecturer, if the latter would bring any clairvoyant, who could read
a line of Shakespeare, or two or three words out of a dictionary, which he
(Professor Simpson) would shut up in a box.”

Professor Simpson had no patience for tbe quackery and credulity
of spirit rapping ; and as Faraday condescended to expose “ table
turning ” by a written opinion which he sent to the “ Times ”
newspaper, so in like manner Professor Simpson took occasion, in
the course of his address to the Society of Antiquaries, to remark —

“ In our own days many sane persons profess to believe in the possibility of
summoning the spirits of the departed from the other world back to this sub-
lunary sphere. When they do so they have always hitherto, as far as I have
heard, encouraged these spirits to perform such silly, juggling tricks, or re-
quested them to answer such trivial and frivolous questions as would, to my
humble apprehension, seem to be almost insulting to the grim dignity and
solemn character of any respectable ghost. If, like Mr Home, I had the
power to call spirits from the vasty deep, and if the spirits answered the call,
I, being a practical man, would fain make a practical use of their presence.
Methinks, I should next ask them hosts of questions regarding the state
of society, religion, the arts, &c., at the time when they themselves were

263

of Edin burgli , Session 1870-71.

living denizens of this earth. Suppose that our Secretaries, in summon-
ing the next meeting of this Society, had the power of announcing in
their billets that a very select deputation of ancient Britons and Caledonians,
Piets, Celts, Scots, and perhaps of Scottish Juranians, were to be present in
our Museum for a short sederunt between midnight and cock-crowing to an-
swer any questions which the Fellows might choose to ply them with, what
an excitement would such an announcement create ! What a battery of quick
questions would be levelled at the members of this deputation on all the end-
less problems of Scotch archaeology.”

About the same time Professor Simpson took part in the
discussions which agitated the medical world on the subject of
Homoeopathy. At a meeting of the Edinburgh Medico-Chirurgical
Society, the following motion was made by Professor Syme, and
seconded by Professor Simpson : — ■ “ That the publie profession of
Homoeopathy shall be held to disqualify for being admitted, or re-
maining a member of the Society.” Professor Simpson sup-
ported this motion by a very able address, which he afterwards
expanded into a book. This, as well as the reply to it by Pro-
fessor Henderson, shows an immense extent of reading and in-
formation .

Another subject which deeply engaged Professor Simpson’s
attention was the so-called Bathgate coal , and also the shales of
the Scotch coal fields, on account of the petroleum which they
yielded by proper treatment. I have seen the outer lobby of his
house in Queen Street greatly obstructed with huge specimens
of the various kinds, and occasionally he spoke to me regarding
them ; not so much in their geological relations as in their
mercantile value and uses. It is matter of notoriety that Pro-
fessor Simpson joined one or more of the companies which
were formed for the purpose of extracting oil from these beds,
and it is understood that he suffered considerable losses in con-
sequence.

The number and variety of topics which thus engaged Simpson’s
attention — professional, scientific, literary, and speculative — im-
plied an activity of mind, a grasp of intellect, and a strength
of constitution truly marvellous. His inquisitiveness on almost
all subjects was incessant. “ Anything new turned up in Ber-
wickshire?” was the first question which he generally put to me
when on coming to Edinburgh I happened to meet him, — hoping
probably to hear of more Piets’ houses discovered, or more relics

vol. vn. 2 M

264

Proceedings of the Royal Society

found at the old Broch on Cockburn Law. His greatest delight
and recreation was to explore ancient mins, caves, and encamp-
ments ; to decipher inscriptions or sculptures on standing stones or
rocks ; and to explore the rubbish of antiquated chronicles or musty
parchments. Legends, superstitions, and charm stones were not
beneath his notice, and were carefully studied, in the hope of
extracting from them some gleam of historical truth. As a ray
of sunlight enters a prism colourless and comes out radiant with
beauty, — so these old inscriptions, sculpturings, and legends, after
passing through Simpson’s scrutiny, often appeared in a new light,
and gave out a meaning not before suspected.*

His memory was surprising. Notwithstanding the legions of
books which he read, — notwithstanding the numbers of places he
visited, and the multitudes of facts which he gathered up at these
visits, — he made no notes, and kept no diary, as most persons have
to do. Any information obtained, whether from his own obser-
vation or from other persons; or any new views expressed on sub-
jects which interested him, he seldom forgot ; and could at once
reproduce or refer to, when necessary.

Professor Simpson, engaged as he was in the teaching of youth,
and attentive to subjects of public interest, could scarcely avoid
taking some part in the educational discussions which have occurred
during the last ten or twelve years in Scotland. The points he
chiefly urged for improving public instruction were peculiar, and
gave surprise to many of his friends. As President of the Gfranton
Literary Association, he, in November 1867, delivered an address
or lecture, which was published, *•' on the necessity of some change
in the mode and object of education in schools, in reference to
modern and ancient languages .” In this lecture the following pithy
sentences occur : —

“ Should they teach the modern languages, that are throbbing with life and
activity ? or should they teach the old languages of Greece and Rome spoken
2000 years ago ?

“ Was it right that one-seventh of a man’s life should be spent in the
acquisition of these dead languages ? For the clerical profession, he admitted

* As examples, see Simpson’s paper on “ The Cat-stane ; Is it not the Tomb-
stone of the Grandfather of Hengist and Horsa ?" Also to his paper “ On
Ancient Sculpturings of Cups and Concentric Rings in Scotland."

of Edinburgh , Session 187 0-7 1 . 265

this was a necessary study. But it was no longer necessary for the mass of
the people.

“ It was said that Latin and Greek were the best training. This he thought
a great error ; for the faculty called into exercise was chiefly memory. The
power of observation required in science and art was called little into play,
and the reasoning power of the mind became stunted and deformed ; — to such
a degree, indeed, that the students were ignorant even of their own ignor-
ance.”

In like manner, in his address to the Society of Antiquaries, he
took the opportunity of undervaluing classical education, by such
declarations as these : —

“ Archaeology has gained for us a clearer and nearer insight into every-day
Roman life and habits, than all that classic literature supplies. Archaeology,
by its study of the old works of art belonging to Greece, has shown that a
livelier and more familiar knowledge of that classic land is to be derived
from the contemplation of its remaining statues, sculptures, gems, models,
and coins, than by any amount of school-grinding at Greek words and Greek
quantities!”

It is the more surprising that such views as these should have
been put forth, considering the frequent and good use to which
Professor Simpson put his own classical information. In his papers
on u Homan Medical Stamps ” and u Was the Homan Army pro-
vided with Medical Officers?” he was able to give information, not
only interesting, but instructive and useful, both papers displaying
an extensive and intimate acquaintance with Greek and Roman
authors. In his work on Anaesthetics, he devotes two chapters to
obviate the theological objections taken to their employment to
lessen the pains of child-bearing, and in these chapters discusses
the true meaning of the Hebrew text of certain scriptural passages.

I have hitherto spoken of Simpson chiefly as regards his
professional knowledge and his varied scientific and intellectual
attainments. But it would be wrong in me .to pass over unnoticed
other features of his life and character quite as remarkable. He
was a man of strong emotions. It of course depended on the ex-
citing cause, how these influenced him. When attacked pro-
fessionally or otherwise ; — or when, after he had set his heart and
hand to the attainment of some object, he found himself opposed,
he was like a war-horse in a battle-field. His impetuosity some-
times carried him too far, brought him upon dangerous ground
and caused him to resort to means for accomplishing his ends

266 Proceedings of the Royal Society

which he himself afterwards regretted. He hit his opponents
severely, and I think even in this room expressions dropped from
him which, in a scientific discussion, were out of place. But he
was not of an unforgiving temper. I myself know, that he could
offer the hand of reconcilement, after a contest was over. I saw
the other day in a medical newspaper* a statement that not long
before his death, he sent letters to some of his professional brethren
whom he thought he might have hurt in the heat of controversy,
expressing regret and asking forgiveness. Being curious to know
whether this was really the case, I applied to one of the medical
gentlemen who attended him during his last illness, and he in-
formed me that he did not know of any letters to that effect ; but
he knew of a message having been sent to one professional gentle-
man, then also unwell, with whom there had been bitter contro-
versy and long estrangement, — and the result was complete recon-
ciliation.

I have already alluded to the multitudes of patients who every
day thronged his house. The poor always could rely on getting
advice from him gratuitously. But he was never very exacting
from any class ; and when persons in a better rank of life, who had
come for advice, were discovered by him to be in greatly embar-
rassed circumstances, he is known to have generously helped
them.

Two examples of this generosity may be mentioned. A lady
whom he had attended was recommended by him, for the cure of
her ailment, to go to a certain watering-place. Tendering to him
such a fee as she was able to give, and for the smallness of which
she apologised, the lady mentioned that the expense of going
there would put it beyond her power. Simpson said nothing at the
time, but afterwards in the most delicate way returned the fee, and
enclosed £20 to enable her to obtain the means of cure which he
had recommended. The other case was the wife of a New York
merchant who had come to Scotland to be under his care. Whilst
here, her husband died, and in bankrupt circumstances. Shortly
after this, intelligence reached her that her only son, whom she had
left at New York, was ill with a dangerous fever. She resolved at
once to return home, though she was to have remained longer
* Medical Times and Gazette, 14th May 1870.

267

of Edinburgh, Session 1870-71.

under the Professor’s care. She was obliged to explain to him the
cause of her abrupt departure, and to ask him to wait for payment
of his services till she returned home. He not only intimated
to her that he would accept no fee, but gave her in a present
enough to pay her passage to New York.

His kindness was not confined to his patients. From persons
who were entire strangers to him, and who were merely passing
through Edinburgh, hospitality was never withheld. His breakfast
and luncheon table was often crowded by foreigners, who, knowing
the Professor no otherwise than by his world-wide reputation, and
being told that he was extremely accessible, used to send in their
cards, and received from him a cordial welcome.

Professor Simpson, in the spirit of true philanthropy, took much
interest in the welfare of that wretched part of the population of
Edinburgh occupying cellars, and frequenting haunts of vice in
the Old Town. Many a time did he visit them at night, after his
day duties were over. Moreover, he tried to interest others in
their behalf, forming for that purpose, at his own house, parties of
gentlemen and even ladies to accompany him. But the practice
gave offence, and was discontinued.

Professor Simpson was imbued with strong religious feelings.
Most persons here will probably remember how, in narrating the
conversation which he had with Sir David Brewster on his death-
bed, he was evidently pleased to be able to testify to the Christian
faith of the dying philosopher. Simpson both lived and died a
Christian ; not only holding fast his trust in the Saviour, but desir-
ing to impart the same comfort to others. His name may there-
fore well be added to those of Faraday and Brewster, who in our
own day have shown that the highest attainments in philosophy
and science, are not incompatible with strong religious feeling and
the sincere faith of a Christian.

Professor Simpson was so remarkable in his outward appearance
and expression, that any one, even happening to meet him in the
street, could not fail to take special notice of him. Though short
in stature, he had large features, and a shaggy head of unkempt
hair. His eye was piercing, and his lips expressive. The energy
of his physical constitution was wonderful, and he taxed it severely.
Thus, after going to Oxford, to receive a University distinction,

268 Proceedings of the Boyal Society

he started next morning with two friends for Devizes, from
whence he went on to Avebury to see “ the standing stones,” not
getting back till midnight. On the following morning at five
o’clock, he started for Stonehenge, and the same afternoon went
to Bath to visit the Boman remains in that neighbourhood. On
getting back at midnight, he found a telegram summoning him to
a patient in Northumberland. He lay down for a few hours to
sleep, and then went by the 4 a.m. train to London, and caught the
Scotch “ Express,” which took him to Northumberland, from
which place he went on to Edinburgh to resume his usual pro-
fessional work.

What constitution could stand such incessant wear and tear ?
A severe attack of rheumatism followed the fatiguing journeys
I have been describing, and this complaint continued frequently
to torture him during the last two years of his life. Eventually
the action of the heart became impaired, and angina pectoris super-
vened,— causing occasionally intense agony.

The fatigue and cold endured last February, in journeys made
to London on the occasion of Lady Mordaunt’s trial, brought
on the illness which proved fatal. For two months he was con-
fined to the house, and chiefly to bed, though even then he was
able to write a letter on the subject of chloroform for publication
in an American Medical Journal, the object of which was to
refute some one who, in the previous number, had been endeavour-
ing to dispute that he was the first to apply chloroform to anaes-
thetic purposes.

■ My sketch of Simpson’s life, imperfect as it is, would be still
more so, were I to omit notice of the distinctions which were
showered upon him from almost every quarter of the globe. I
cannot recount all the Academies, Universities, and Societies which
bestowed their honours upon him. There was not one nation in
Europe from which these honours did not come, and America joined
in the general acclaim. Simpson was created a baronet of the
United Kingdom. He received the knighthood of the Swedish
Koyal Order of St Olaf. He was made a laureate of the Imperial
Institute of France ; and the French Academy of Science bestowed
on him what is called the “ Mon thy on Prize ” of 2000 francs, given
for any great discovery beneficial to humanity.

269

of Edinburgh, Session 1870-71.

Gratifying to Simpson as these honours and distinctions no
doubt were, there was one fact which must have been even more
gratifying, and that was the introduction of chloroform, for medical
purposes, in every civilized country, coupled with the almost uni-
versal acknowledgment that he had been the first to suggest and
employ it for the relief of human suffering. He must also have felt
that the world generally accorded to him the highest eminence in
his profession, inasmuch as patients had come to him from every
quarter of the globe, and as his works had been translated into
every European language. Probably no man ever lived who, at the
close of life, had the satisfaction of looking back on the same amount
of work done for the benefit of his fellow creatures, and of possess-
ing so largely their approbation and confidence.

In these circumstances, it is not surprising that, at the sugges-
tion of the most eminent of the medical faculty in London, and
warmly seconded by men there of high social position, a proposal
was made, soon after Simpson’s death had been announced, that
his remains should be interred in Westminster Abbey, — that last
resting-place of Britain’s most illustrious sons. But the proposal
was modestly, and I think properly declined by the surviving mem-
bers of his family. Their decision was in this respect in accord
with the unostentatious character and habits of the deceased. It
was right and becoming that a man of his domestic dispositions
should not be separated, even after death, from the other members
of his own family, to whom he was deeply attached, but that he
should lie beside them in the spot which he himself had selected,
and where several had already been buried. Moreover, his inter-
ment at home allowed of an honour being conferred on him at his
funeral, which, to my mind, was far greater than entombment in
Westminster Abbey; — for his funeral was attended by all the
public bodies and corporations of Edinburgh, and was thronged by
thousands of sorrowing mourners, who, even from distant parts of
the country, came to pay the last tribute of respect to one who had
been so great a benefactor of the human race.

We have all to lament that our deceased friend and associate
should have been cut off in the meridian of his fame, and whilst
still running a career of usefulness. But we have reason to be
thankful that his life, shore if reckoned by years, was long, if

270 Proceedings of the Royal Society

reckoned by good deeds and great services, not the least of which
was the example he bequeathed of a man devoted to noble pur-
suits, characterised by incessant industry, imbued with benevolent
dispositions, animated by Christian faith. In the letter already
referred to, written on his death-bed, for the American Journal,
he concluded it by saying, that he regarded the friendship of his
medical brethren in America so highly, that he would not think
this last effort at professional writing, altogether useless, if it tended
to fix his memory in their love and esteem. It was to friends abroad,
that this appeal was made. To friends at home, no such appeal
was required. He knew that he had accomplished, what would for
ever fix his memory in their love and esteem. To that sentiment,
sure I am that his own countrymen and countrywomen cordially
respond ; and not less sure am I that the Fellows of this Society
will ever remember with respect the eminent and diversified talents,
as well as the signal services to science and humanity, of their
distinguished associate.

James Syme was born 7th November 1799, and died 26th June
1870. Up to within a year of bis death, he was Professor of Clinical
Surgery in the University of Edinburgh, which chair he had held
for thirty- six years. His father had originally followed the pro-
fession of a Writer to the Signet, but had retired at an early period
with his family to the estate of Gfartmore and Lochore in Fife.
It is understood that, in consequence of there being no public
school in the country which he could conveniently attend, Mr Syme
obtained a tutor for his son whilst resident in Fife, so that he had
in his early days no opportunity of associating with other boys, —
a circumstance which may perhaps account for his shy and re-
served manner in after life. Whilst a boy, it is said that he indi-
cated a taste for anatomy, by frequently resorting to a butcher’s
shop, where he watched with interest the cutting up of sheep
and oxen. His father at length seeing the necessity of giving
to his son a better education and training than he was receiving
in the country, sent him to Edinburgh to attend the High School.
Afterwards, at the age of sixteen, he passed to the College, and
became much interested in chemistry. When he returned during
the holidays to Fife, he generally brought with him a supply of

of Edinburgh, Session 1870-71.

271

apparatus — purchased with his own pocket-money — to enable him
to carry on chemical experiments for his amusement.

So early as the year 1818 he had discovered a solvent for
caoutchouc in the naphtha obtained by distillation from coal-tar,
and in March of that year addressed a letter describing his discovery
to Dr Thomson, then editor of the “Annals -of Philosophy,” which
appeared in that publication in August following. Mr Syme in this
letter states that “ he had, by means of the discovery, waterproofed
a silk cloak , so that it afforded complete protection from the heaviest
rain, and could be employed as a pitcher by turning up its skirt.”
He adds that he had “ constructed flexible tubes of the same sub-
stance.” It appears that he had worked at this subject for two
years before the discovery. The discovery was deemed so important,
that Dr Thomson and some of his friends recommended young
Syme to take out a patent, assuring him that it would make his
fortune. But by this time he had determined on following the
medical profession, which he thought more respectable than that of
a manufacturer. He therefore contented himself with publishing
his discovery, and receiving general commendation for his disin-
terestedness. Hot long afterwards the discovery was turned to
good account, as we all know; by Mr Macintosh of Glasgow, who
made a large fortune by means of it, and who gave his name to the
cloth, though in reality invented by Syme.

Syme became a pupil of Dr Barclay in order to study anatomy ;
and in 1818 he went into Liston’s dissecting-rooms, as his assistant.
He was a distant cousin of Liston’s.

In 1820 he obtained the appointment of Medical Superintendent
of the Fever Hospital, — an appointment entailing much personal
risk, as Mr Syme soon discovered ; for he caught the infection,
and nearly died.

In 1821 he became one of the dressers in the Edinburgh Koyal
Infirmary. As such, it was his duty to carry out the instructions
of the acting surgeon. In this position he showed the possession of
considerable courage and self-reliance, by disobeying some instruc-
tions which his judgment condemned. The system of blood-
letting was then in full operation, and every evening at a certain
hour, the dressers had to bleed the patients whose names were
entered in a book, and take from each the number of ounces of

VOL. VII.

272 Proceedings of the Royal Society

blood there specified. On one occasion Syme had to take from a
patient in one of his wards so much as 65 ounces, to he followed
next day by other 35 ounces. Another patient was a boy, one of
whose legs had a compound fracture, which gave rise to profuse
suppuration. About three weeks after the injury, the boy’s strength
being much exhausted, Syme took it upon him to order porter and
a beef-steak. Next day the acting surgeon, then one of the most
largely employed medical men in Edinburgh, expressed disapproval
of this regime, as he said it would feed the disease, and directed
Syme to take 14 ounces of blood from the boy’s arm. Syme obeyed
with reluctance, and not without remonstrating. Before the end
of forty-eight hours, the boy was dead.

In 1821 Syme was elected a member of the Royal College of
Surgeons of London, and in 1823 a Fellow of the Edinburgh
College of Surgeons. About the same time he went abroad to
Germany and France, visiting different hospitals, and forming-
useful acquaintances. He also entered into a sort of partnership
with Mr Liston, and occasionally took Liston’s place in the lecture-
room. This partnership, however, did not continue long. A quarrel
occurred, which caused an estrangement of many years’ duration.

But Syme, notwithstanding that he thereby lost an advantageous
position, was not discouraged. He entered into another partner-
ship with Dr Macintosh (who then lectured on midwifery and
the practice of medicine), for the purpose of establishing a new
medical school, with an anatomical theatre, dissecting-rooms, and
museums, — he himself intending to lecture on anatomy and sur-
gery. The very boldness of the undertaking arrested public
attention. The school, however, failed ; but Syme himself, fortu-
nately by zeal, talent, and complete knowledge of his subject,
coupled with an indication of views which were innovations on
established practice, soon attracted a large number of students.
His chief difficulty arose from the scarcity of subjects for dissec-
tion, except by dealing with the “Resurrection-men,” as they were
profanely called, — a course which Syme detested. In order to
pursue his anatomical researches, be took advantage of the holidays
to go over to Dublin. When there, he made acquaintance with
several eminent surgeons, and was so delighted with their modes
of operation — which he thought superior to those of Edinburgh —

o f Edinburgh, Session 1870-71. 273

that he resolved to abandon anatomy, and confine his teachings to
surgery.

In 1829 he had as many as 250 pupils attending his surgical
lectures, a success the more remarkable, considering that Liston,
Lizars, and Turner, were rival lecturers. This well-attended class
he kept up for several years.

Syme had been most anxious to get on the surgical staff of the
Eoyal Infirmary. But Liston was one of the surgeons ; and the
managers knowing the animosity which existed between him and
Mr Syme, felt that by admitting both into their institution, there
would be every probability of dispeace. They refused Syme’s ap-
plication. He therefore resolved to set up a rival institution, and
took Minto House, with 15 rooms in it. These he converted into
wards. He also formed an out-patient department. This was a
still bolder exploit than any before ventured on, but it was re-
warded with complete success. On the very fi^st day that the
new hospital was opened several patients sought admission, and in
the next two days as many as ten young medical men applied for
the house surgeoncy, though £100 was required as a fee. The
report for the first year tells of 265 in-door cases, 1900 out-door
cases, and 95 operations. For four years this new institution was
carried on, with unvarying success, vieing with the old established
Royal Infirmary in the number and importance of its operations,
and presenting a striking proof of what could be done by one
young man, not only unsupported by local influence, but overcom-
ing local and social influence arrayed against him, by dint of
indomitable zeal, natural talents, and great professional knowledge.

Syme’s seminary for instruction in Clinical Surgery, was re-
cognised by the College of Surgeons in London, as qualified to give
instruction for medical students. The Edinburgh College of Sur-
geons refused to recognise the new hospital, but agreed to recognise
a course of lectures on Clinical Surgery, if Syme chose to give
them, on the condition, however, that the pupils attending these
lectures did not exceed 40 in number, and that they paid the same
fees as were received by Mr Russell, the Professor of Clinical Sur-
gery in the University. To these terms Syme acceded; and by
his admirable lectures soon laid the foundation of subsequent
brilliant reputation as a clinical teacher.

274 Proceedings of the Royal Society

It was during this period, when he was an extra-academical
lecturer, that he published two hooks, one “ A Treatise on Excision
of Diseased Joints;" the other “The Principles of Surgery."
These books, which embraced numerous cases of successful opera-
tions by the author, — many of them indicating new and improved
practices, extended Syme’s fame over Europe, and paved the way
for another distinction. This was his appointment to the Chair of
Clinical Surgery in the University of Edinburgh, which Mr Eussell
(now in his 83d 3?,ear) resigned. It was obtained in spite of the
opposition of his former master and jealous rival, Liston, who
wished it for himself, hut would not accede to the conditions re-
quired by the Patron, the Crown, that Mr Russell should have from
his successor £300 a year of retiring pension. Mr Liston had, up
to this time, succeeded in shutting Syme out from access to the
Infirmary. That exclusion, however, the managers saw could
scarcely be continued after Syme had become Clinical Professor
in the University. It was a fortunate event for both parties that,
about this time, an invitation came to Liston to remove to London
to become Professor of Clinical Surgery in University College, an
invitation which lie gladly accepted. Shortly after this event
Liston wrote to Syme expressing a wish to be reconciled — a wish
to which the latter readily acceded.

Liston died in 1847, and Syme was then invited to succeed him
as Clinical Professor in University College, London. Syme felt
flattered by the proposal, and was pleased at the prospect of going
to a capital where private practice would be far greater and more
remunerative. He was, however, exchanging a certainty for an
uncertainty. He had L.700 a-year from his class in Edinburgh,
and full employment as consulting surgeon, whereas all that was
offered to be ensured to him in London was a fixed salary of L.150
independently of class fees. Nevertheless he resolved on throwing
up his position in Edinburgh, where he commanded both respect
and emoluments, and in February 1848 repaired to London. He
soon found that he had taken a wrong step. His class was less
numerous, and though his practice might eventually become great,
he felt that it would be long before that pecuniary advantage was
arrived at, and perhaps still longer before he could attain the social
position which he held in Edinburgh. His manner was also rather

of Edinburgh , Session 187 0-7 1 . 2 7 5

reserved for acceptance in London society. Hence, though he was
making rapid progress in surgical practice, he soon began to wish
he had never left Scotland. It was when in this mood that he
received a request from the council of the London University to
deliver lectures on systematic as well as on clinical surgery.
Thereupon he at once sent in his resignation. In fact, before
leaving Edinburgh he had stipulated that he should he exempted
from this additional duty. The month of July 1848 found him
back again in Edinburgh, after only a four months’ stay in London,
during which time, however, he had succeeded in acquiring the
entire confidence and esteem of the medical students ; insomuch
that, when they heard of his intention to leave them, a committee
of their number waited upon him, beseeching him to remain, and
saying that an address was about to be presented, signed by every
individual student. But he declined the entreaty, flattering though
it was. He felt he had made a mistake when he left Edinburgh,
and he was resolved to correct it before it was too late. Fortu-
nately for Syrne, the Chair of Clinical Surgery in the Edinburgh
University, vacated by his going to London, had not been filled up.
He was again appointed to it, and his return to the scene of his
former success was greeted by general acclamation alike from
students and old friends.

In subsequent years Professor Syme, besides teaching his class
and attending the Infirmary, took part in the proceedings of
various medical and scientific societies. He became President of
the Edinburgh Medico-Chirurgical Society in 1848. He had pre-
viously become a Fellow of our own Society, and communicated
to it a very important discovery, that the formation of bone is due
to the Periosteum — a discovery which was the subject of a paper
published in our Transactions. The importance of this discovery
is great, as it often renders amputation of a limb unnecessary,
in the case of diseased bones, if the disease be not in the perios-
teum.

At a later period, Mr Syme’s active mind led him to pay atten-
tion to subjects of more general interest connected with the medical
profession. In the year 1854 he took up the question of medical
reform, and addressed a letter to Lord Palmerston and Lord
Elcho, recommending the appointment of a General Council to

276 Proceedings of the Royal Society

pass regulations for the granting of medical licenses in the United
Kingdom. He continued for several years to take part in the
public discussion of this question. His views were very generally
approved of, and, I believe, formed the basis of much of the
Legislation which has since taken place.

Another subject of much local interest in Edinburgh, which
engaged Professor Syme’s attention, was the best site for a new
Infirmary. At first he advocated the old site ; but, on farther con-
sideration, he confessed he was in error, and ultimately ener-
getically assisted those who wished the new hospital to be built in
the suburbs of the town, where purer air for the patients would be
secured.

During the winter of 1868-9 Mr Syme’s health was not what it
had been. Fie was less able for the fatigues of lecturing. He
was also much harassed by the frequent meetings he had to attend
about the new Infirmary, and he was greatly annoyed and irritated
by a disagreeable professional controversy in which he was in-
volved. The spring of 1869 also brought heavj domestic afflic-
tion. On the 6th April, after performing an operation in the
Infirmary, he had a bad attack of paralysis, which, however, left
his mind unclouded. He so far recovered that he was able once
or twice to walk from his villa of Millbank to see patients in his
consulting rooms in Edinburgh, and even to give advice in the
Infirmary as a consulting surgeon. He resigned his chair in July
1869. In the spring of 1870 he still continued to see patients,
but another worse attack of paralysis occurred in May, and he died
on the 26th of June. He was interred in St John’s Episcopal
Church, of which he had long been a member, followed to the grave
by very many of his old friends and pupils.

I will of course not attempt any account of the services ren-
dered by Professor Syme to the special branch of the medical art
to which he attached himself. All authorities concur in saying
that, in virtue of the many important discoveries made by him, his
skill as an operator, his diagnostic sagacity, and his accurate
teaching, he was the greatest surgeon of his time. His services
were twofold. He abolished, or assisted to abolish, many bad
practices in surgery, and he was the means of introducing many
new practices which have been generally adopted. Among this

277

o f Edinburgh, Session 1870-71.

last class may be mentioned his diminishing the frequency of
amputations, and substituting excision instead, whereby many a
person now retains an arm or a leg, which surgeons previously
had been in the habit of cutting off. The like good effect followed
from his discovery, that the formation of bone was due to the perios-
teum, His treatment of aneurisms was very successful. He had
an almost instinctive faculty in discerning the true character of
tumours, of which one example, not generally known, may be
mentioned. A Scotch nobleman was suffering from polypus in the
nose. He had consulted the most eminent surgeons in Paris and
London. In both of these capitals he received the same opinion,
that the tumour being of the malignant type, it could not be ex-
tracted with any probability of saving life. Some of this nobleman’s
friends suggested a visit to Edinburgh, to obtain Professor Syme’s
opinion. He accordingly came here, and a consultation took place.
Mr Syme thought the tumour not malignant, and he gave an
opinion that it might be radically extirpated. The operation was
performed, and with complete success. The nobleman alluded to
is now alive, and in good health.

Syme’s manner was reserved and sometimes abrupt to his patients,
of which the following anecdote, related to me the other day by a
medical friend, is an illustration. A landed proprietor in Nor-
thumberland had been thrown out of his dog-cart, and was so
severely bruised that he feared his shoulder had been dislocated.
His medical attendant had a doubt about it. He therefore resolved
to go at once to Edinburgh that Syme might see it. At the hour
appointed he called on Syme, and was shown into a room where
the Professor was standing before the fire. As the gentleman
advanced, Syme bowed stiffly, but did not speak. The gentleman,
who was lame from gout, — as he hobbled into the room, by way of
beginning conversation, intimated that he was very gouty, on
which Syme said, “ If that ’s all that ’s the matter with you, you
need not come to me; I don’t cure gout.” The gentleman next
said, u But I think my shoulder is dislocated, and I want you to
examine it, if you will help me off with my coat.” Syme replied,
“I need do nothing of the kind; — your shoulder is not dislocated.
Take my word for that. I don’t need to see it.” The decided
tone in which S}^me spoke, so impressed the old gentleman that

278 Proceedings of the Royal Society

he obeyed, and bid Mr Syme good morning, but not before giving
him a double fee for bis welcome opinion. He told bis medical
man, when be returned borne, that be thought Mr Syme the most
self-possessed man be had met with, and would assuredly go back
to him if be ever had again to consult a surgeon.

Syme was remarkable not only for self-possession, but for the
more noble qualities of professional sincerity and honesty. When
he found himself in the wrong, he never hesitated to alter bis course,
nor was be ashamed to confess it. When the late Sir David Baird
of Newbyth was severely hurt by a kick from a horse in Berwick-
shire, Dr Turnbull of Coldstream, who attended him, becoming
somewhat anxious, brought Mr Syme out to see him. Mr Syme,
after inspecting the broken leg, and considering the case, gave a
decided opinion that there was no reasonable ground of apprehen-
sion, and returned to Edinburgh the same day. But that night
Sir David Baird became restless and feverish, and Dr Turnbull,
notwithstanding Syme’s opinion, on the following morning thought
of again sending for Syme. Early that forenoon he was surprised
to see a carriage drive up to the door, and to find that Syme was in
it. Dr Turnbull expressed his happiness at seeing him so soon
again, but asked what had brought him back ; on which Syme
said, “I never closed my eyes last night, because I began to fear
I had given you a wrong opinion, and I have come back to see
your patient again.” Syme, after another examination, satisfied
himself that there was too good reason for anxiety, and intimated
that he thought Sir David Baird would not recover. He died two
days afterwards.

Syme, though he published very many papers in the medical
journals, was not a voluminous writer. As in his operations he got
through his work quickly, never drawing from his patient an un-
necessary drop of blood, so in his publications he wrote concisely,
and seldom wasted a drop of ink on illustration. His most im-
portant work, “ The Principles of Surgery,” went through five
editions, the last edition being in bulk smaller than any of its pre-
decessors. His aim, both in his books and in his lectures, seemed
always to be, to give a maximum of instruction in a minimum of
words.

Syme was proud of his profession, and proud of his own posi-

279

of Edinburgh, Session 1870-71.

tion at the head of it. Perhaps it was from this cause that he
was charged with unwillingness to admit and adopt the improve-
ments suggested by others in surgical practice. On the other
hand, he was quite indifferent about pressing his claims to any
honorary distinction. Nevertheless, from various public bodies, he
did receive, unasked for, acknowledgments of his merit; as when
there was conferred the M.D. degree from the Universities of
Dublin and of Bonn, the D.C.L. degree from Oxford, and the
Knighthood of the Dannebrog from the King of Denmark, an
honour rarely granted to a foreigner. On a G-eneral Medical
Council for the United Kingdom being appointed, he was chosen
a member of it, to represent the Universities of Edinburgh and
Aberdeen. For ten years he took a lively interest in its proceed-
ings, and his opinion was always listened to with respect. It was
probable that Syme would have been elected President of the
G-eneral Medical Council on the retirement of Dr Burrows in 1869,
but Mr Syme about this time became unwell, and his friends saw
he would he unable to fulfil the duties of the office.

After Syme resigned his professorship in July 1869, a move-
ment among his professional brethren, who knew his merits as a
surgeon, was commenced, for the purpose of raising a testimonial
which might keep his name before future generations. It was all
the more striking and gratifying that this movement commenced
in London, and was warmly supported in America, because indi-
cating the judgment of those who could estimate his services free
from the influence of local feelings. The testimonial will embrace
a scholarship to bear Syme’s name of L.100 a year for students of
surgery in Edinburgh University, and a marble bust of Mr Syme
for the great hall of the library. The funds for the testimonial
have been nearly all subscribed. Should there be any deficiency,
I understand it will he made up by the University Endowment
Association.

Besides testimonies from abroad to his professional services, -
several from his countrymen in Scotland, of a very gratifying
kind, were not wanting. From many provincial associations of
medical men, there came addresses expressing regret that he should
have found it necessary to resign his professorship, and conveying
to him the respect and gratitude of those who had benefited by

VOL. VII.

280

Proceedings of the Royal Society

his advice, teaching, and example. One of those addresses, from
the Border Medical Association, dated at Kelso, on the 18th August
1 869, runs as follows : —

“At the twenty-third annual meeting of the Border Medical Association,
we, the undersigned members,, unanimously resolved to ask you to receive
from us a short address on the occasion of your resignation of the Professor-
ship of Clinical Surgery in the University of Edinburgh.

“We desire to convey to you our warmest thanks for the very kind manner
in which you have at all times discharged your duties towards our patients
and ourselves. We beg also to thank you sincerely for innumerable acts of
personal kindness and attention, for which we shall ever feel grateful. Al-
though the members of our profession generally have resolved to offer you
some testimonial in recognition of your inestimable services, and although
you have already received a most hearty expression of sympathy and regard
from the profession practising in far distant lands, we trust that it will not
he otherwise than agreeable to you to know that the medical and surgical
practitioners in your own Border-land are equally sensible of and grateful for
the great advantages they have derived from your precepts and example. It
was with unmingled feelings of sorrow and regret that we heard of your ill-
ness, and we now most heartily rejoice to know that you have so far recovered
as to he able, in some degree, to resume those professional duties which we
have all learned to value so highly. We desire to express the earnest hope
that you may yet be long spared to give us the benefit of that eminent wisdom,
vast knowledge, and matchless diagnostic tact and skill which have rendered
your name famous wherever the science and art of surgery are known. It is
to us a source of pleasure that, on the very day of our assembling here, it has
become known that you are to be succeeded in your chair by your son-in-law,
Mr Lister, believing as we do that his appointment will be peculiarly grati-
fying to yourself, in the highest degree acceptable to the profession at home
and abroad, and highly calculated to maintain the celebrity of the Edinburgh
surgical school, in which you have so long been the distinguished master.”

If there was any taste or pursuit beyond that of his own special
profession for which Mr Syme had a predilection, it was gardening.
He long cultivated with great success the rarest plants of distant
temperate and tropical countries, and annually carried off the
highest prizes at the exhibitions of the Horticultural Society of
Scotland. He was equally successful with tropical fruits, among
others the banana, which he was one of the first in this country to
ripen in perfection. In his later years, at his villa of Millbank, he
formed a large collection of Orchids. Among these he spent much
of his leisure hours. To his friends and former pupils, when they
came to see him, he was ever ready to show kindness and hospi-
tality ; and the friendships which he made were lasting, warm-
hearted, and disinterested.

281

of Edinburgh, Stssio7i 1870-71.

Perhaps the leading qualities of Syme’s character, and which
ensured his success in life, were clearness of perception, fearless
honesty of purpose, and strength of will. He was always able to
see clearly the point at which to aim, and by steadiness both of
eye and hand, to reach it, in spite of obstacles and difficulties
which would have made most other men flinch. Self-reliance
was liis chief stepping-stone to fame, — the honourable fame of
having greatly advanced the science which tends to save life and
limb, and also to assuage human suffering.

III. I come now to the third head, which is to offer . a few sug-
gestions for increasing the efficiency of our Society.

Under this head there are two points which demand attention.

ls£. Can our present arrangements he improved ?

2d. Are there any drawbacks which can be counteracted ?

(1.) In regard to our present arrangements for carrying on the
Society’s business, the most important is undoubtedly the publica-
tion of papers in our Proceedings and Transactions. Its import-
ance cannot well be over-estimated. Probably but for this mode of
recording discoveries, speculations, and inventions, and also of pub-
lishing them, half of these would never have become known to
the world. It is no disparagement to the papers which appear in
our Proceedings and Transactions to say of them, that to only one
person out of a thousand are they of any interest, and therefore
that they would not be read, and would not pay to be published by
the authors at their own expense. But next to the pleasure of
effecting discovery, is that of making known the discovery to others.
This last pleasure can therefore in many cases be obtained only
through means of societies like ours. But there is another and a
separate good done : not only are investigators stimulated, but
when the results of their investigations become widely known,
these often suggest new views to other inquirers, who make use
of these published results as stepping-stones for overcoming some
difficulty which had obstructed their own inquiries. In that
way, also, men of science and literature in different countries
become acquainted, so as to aid one another in their respective
labours.

I have surely said enough to show how useful these publications

282

Proceedings of the Royal Society

are, and it is no small proof of this when we find, as I have already
stated, that our Transactions are almost every year becoming more
bulky.

The only practical suggestion which it occurs to me to offer
under this head is, that means should be taken to ensure early
publication. I am sorry to find that the volume containing last
year’s papers has not yet been published, though the Society’s law
expressly states that “ the Transactions shall be published at the
close of each Session.”

(2.) Another part of our proceedings to which I respectfully
invite attention is the best mode of conducting our evening
meetings. What is the object and use of these meetings ? From
a paper published in the first volume of our Transactions, entitled,
“ History of the Society ,” drawn up, I believe, by the first secre-
tary, Dr Robison, it is stated that these meetings were held in
order that —

“ Essays and observations of members or their correspondents may be read
publicly, and become the subjects of conversation. The author is likewise to
furnish an abstract of his dissertation, to be read at the next meeting, when
the conversation is renewed with increased advantage.

“ Several papers have been communicated with the sole . view of furnishing
an occasional entertainment to members, which do not afterwards appear in
the Transactions. Essays and cases are often read at the meetings in order
to obtain the opinions of members on interesting or intricate subjects. Some
papers intended for future publication have been withdrawn for the present
by their authors, in order to profit by what has occurred in the conversations
which the reading of the papers has suggested.”

The original intention, therefore, of our evening meetings was
to encourage discussion among the members on the papers read,
and this object we have ever since kept in view, though on account
of the length and number of the papers put down to be read in one
evening, there has often been no time for any discussion of them.

I suppose it had been with the view of remedying this incon-
venience that in October 1836 the Council of the Society made a
remit to the three secretaries-—

“ To report as. to the possibility of economising time by some change in
the present order of the business of the general meetings, and by inducing
the authors of papers to give (when necessary) condensed abstracts of them,
leaving the details for being printed when their publication in the Transac-
tions may be determined on.”

of Edinburgh, Session 1870-71. 283

The three secretaries accordingly, in December 1836, reported
how this object might be brought about, viz., that

“ The members of Council to whom papers are referred for preliminary
examination shall, after perusal, advise with the authors in what manner they
may be shortened in reading them to the Society. The secretaries farther
submit, that some course of this kind is imperiously called for, by the increas-
ing number and value of the communications presented to the Society.
They farther express their conviction, that the change in question, if acted on
by authors, will add greatly to the spirit of the Society's meetings, and to the
interest of the members in its proceedings."

They add in their report, “ That the public business, if time
enough be left, should be concluded with verbal communications
of scientific news.”

This report was adopted and approved of by the Council, and
ordered to be printed, so that I have no doubt it was communi-
cated to the Society generally, and attempted to be carried out.

In now therefore bespeaking renewed attention to this subject,
I only desire to urge what seems to have been alike intended
by the founders of the Society, and aimed at by those who have
preceded us in the Society’s management.

The advantages of a good attendance of members at our meet-
ings, and also of a discussion of the papers read at them, are
obvious. It is for the credit of the Society, that its members
should take an interest in its objects, and show that interest by
attending its meetings. It is an encouragement to literary and
scientific authors to bring forward papers, when they know that
these will be read, not to dead benches, but to living associates,
and to associates who will listen, and some of whom will state, after
hearing the papers, whether they appreciate the views contained in
them. It is also an advantage to members to have an opportunity
of meeting one another, for the purpose of cultivating friendly
intercourse, and obtaining information.

In the G-eological Society of London — the only Society there,
whose meetings I have had an opportunity of attending — special
means are taken to induce a good attendance, and also to induce
verbal discussion at evening meetings. As papers are more intel-
ligible and attractive when illustrated by diagrams, authors of
papers are encouraged to exhibit diagrams whenever that is
possible, the Society paying the cost of them, subject to certain

284 Proceedings of the Royal Society

chocks. Discussion almost invariably takes place ; though whether
any previous arrangement to ensure this is made, I cannot tell.
After the public business is over, there is an adjournment to
an adjoining apartment for refreshments ; in which apartment
there are comfortable chairs and sofas, where members and their
friends can chat together if they like. There is also at these
meetings a greater variety of refreshments than we provide.

I trust I may be excused for referring to these common-place
details, but I attach so much importance to a good attendance at
our evening meetings, that I would desire to leave no means un-
tried to secure it.

What are the means wThich, for this purpose, I suggest?

ls£, I think that papers of so abstruse a nature as not to be
intelligible to three-fourths of the members, ought not to be read,
nor even an abstract of them, — but only a verbal account given of
the nature of the paper, and its bearings.

2 dj No paper, however intelligible, should be read verbatim ,
unless it occupy only a few minutes, say fifteen or twenty, but
only an abstract of it shall be read or verbally stated.

3d, The members of Council to whom the paper has been re-
ferred to report on its fitness for the Society should be prepared,
after the author has read his paper or stated its substance, to give
their opinion of the merits of the paper, the President for the night
also adding a few remarks.

4 th, Diagrams, where possible, ought to be exhibited, one-half
of the cost of which should be paid from the Society’s funds, sub-
ject to the check of a committee.

5th , It shall be competent for a Fellow at the commencement of
business, with the leave of the Secretary and President for the
night, to exhibit any article or object, organic or inorganic, or any
instrument of scientific interest recently discovered or invented,
and give a short verbal explanation, it being understood that such
verbal explanations shall be concluded before 8.15 p.m., so that the
written papers announced in the billet may then be proceeded with.

5th, There ought to be in the retiring-room something better
provided, in the way of refreshment, than a cup of tea, as also chairs
or sofas for the convenience of those who attend the meetings.

2. The next point to which I advert is the existence of certain

285

of Edinburgh, Session 1870-71.

drawbacks to fche efficiency and influence of our Society, and the
possibility of counteracting these.

When our Royal Society was established, now nearly ninety
years ago, no other society devoted to literature or to science
existed in Edinburgh. It was therefore natural and right that
the Society should embrace, among its objects, all the depart-
ments of knowledge which were then known, or were beginning to
be cultivated.

The rapid extension of different sciences soon rendered it im-
possible for one society to give due attention to all these, or to
assist investigators in each, to the full extent that they desired.

Hence separate societies came to be formed, devoted to parti-
cular sciences ; and these societies were naturally joined by many
persons who, but for them, would have probably become members
of our Royal Society.

What has been the consequence? We have in Edinburgh, and
our other large towns, very many institutions, both literary and
scientific, which are strong in membership; and even in our pro-
vinces, we have societies and clubs, devoted to botany, geology,
zoology, and archaeology, some of which also possess a large staff
of members.

Let me enumerate the membership of some of the Edinburgh
societies : —

The Medico- Chirurgical Society, instituted 1821,

has about 300 Members.

The Philosophical Institution, about . . 2000 „

The Geological Society, instituted in 1834, has 180 Ordinary Members.
The Royal Physical Society, .... 250 „ „

The Botanical Society, instituted 1836, . . 360 „ „

The Arboricultural Society, .... 500 „ „

The Society of Antiquaries, .... 300 „ „

The Royal Society of Arts, instituted 1821, has 420 „ ,,

The Meteorological Society, instituted 1856, . 600 „ „

With regard to provincial societies, I may mention that Sir
Walter Elliot* of Wolfelee has lately been making out a list
of Natural History Societies and Field Clubs, existing not

* The list here referred to will be found in an address delivered by Sir
Walter Elliot to the Botanical Society of Edinburgh on 10th November 1870 ;
and is to be printed in that Society’s Transactions for 1870-71.

286 Proceedings of the Royal Society

only in Scotland, but in England and Ireland. This list will
be exceedingly instructive, as I understand it specifies the ob-
jects of each Society or Club, the nature of its operations, and the
district of country with which it is connected. He has had the
kindness to send to me an account of twelve of these provincial
societies, the most northern being in Orkney and Shetland, the
most southern in Berwickshire, Dumfries, and G-alloway. About
one-lialf of these societies publish proceedings or reports in some
form or other, for circulation among their own members. To one
of these last-mentioned provincial societies, connected with the
Eastern Borders of England and Scotland, “ The Berwickshire
Naturalists’ Club,” Sir Walter Elliot and I belong. It has a
membership of 250 persons, and has published six octavo volumes
of reports on topics — Botanical, Geological, Zoological, Entomo-
logical, and Archaeological.

Though it is chiefly the Edinburgh societies which keep mem-
bers from our Boyal Society Roll, and papers from our Transac-
tions, there can be no doubt that the societies of other towns, and
of the provinces, act more or less in the same direction. But in
saying this of any of these separate societies, I mean no disparage-
ment of them ; nor, in spite of their interference with our useful-
ness and influence, do I regret their multiplication. On the prin-
ciple of the division of labour, the more societies the better, for
the sake of the stimulus they give to scientific investigations.
The late Principal Eorbes, in his address from this chair in the
year 1862, in alluding to the effect which these societies had on
us, thought that they “ fostered (to use his own words) a spirit of
rivalry towards the larger, more national, and more permanent
Institution, which the Royal Society of Edinburgh might fairly
claim to be.” I have never seen indications of a spirit of rivalry,
in the sense of hostility. All the length I can go is to admit —
as, indeed, I affirm — that the existence of so many separate scien-
tific societies in Scotland has the effect of curtailing our member-
ship and our operations, and that this effect will increase unless
means be devised to counteract it.

I think such means may be devised, and with advantage, not
only to our own and other societies, but to the cause of science.
There are many researches and inquiries which can be pro-

of Edinbw 'y li, Session 187 0-7 1 .

287

secuted successfully only by the co-operation of many persons
acting together, or acting in different districts. Opportunity for
such co-operation might be afforded by separate societies. Thus
the Committee of the British Association on Luminous Meteors
lately applied to the Scottish Meteorological Society to have a
certain number of their observers, situated in different parts of the
country, told off to watch on particular nights the occurrence of
meteors, and mark down on maps furnished to them their posi-
tions, the direction of their movements, and other particulars.
That is an example of two independent scientific bodies co-operat-
ing together. What I next mention shows the co-operation of six
or eight societies. In Switzerland, and in the South of France,
the various Natural History and Physical Societies have been
carrying on a joint investigation to record the exact position of
the most remarkable “ boulders” in the districts with which they
are severally connected. For this purpose one central society —
the Helvetic Society — has issued to the societies at Neufchatel,
Berne, Aargau, Geneva, Lyons, and Grenoble, suitable maps and
schedules. These societies have already made great advances in
ascertaining and marking down the exact position of numerous
boulders above 100 tons in weight. They have done more, for
they have succeeded in stopping the wholesale destruction of
boulders, which were being victimised to agricultural improve-
ments; and so much have their objects been appreciated by the
municipal and State authorities, that the latter pay the cost of the
necessary printing, and other expenses required for the investiga-
tion.*

Another case of co-operation nearer home may be mentioned.
Professor Roscoe of Manchester is forming what he calls a
“ National Science Union,” embracing not only scientific inves-
tigations, but also, and even more especially, action on the Legis-
lature and the Government. With reference to this last object,
he observes, that “ although those who are engaged in scientific
investigation or instruction, undoubtedly form one of the most
intelligent professions in the kingdom ; yet, for want of union,

* Professor Faure of Geneva has had the kindness to send to me several of
the Maps, Schedules, and Reports, showing the progress made by the different
societies aiding in this investigation.

2 P

VOL. VII.

288 Proceedings of the Royal Society

they have no commensurate influence on the Legislature. The
interests of commerce, manufactures, agriculture, railways, and
the clerical, legal, naval, and military professions are represented
by strong parties in Parliament, yet there are very few members
of either House who can be said to represent the high interests of
science. It is therefore urged that no time should be lost in
creating an organisation, which will enable those interested in the
progress of science to use their proper influence, and when the
time arrives, to press their legitimate claims upon the Legislature.”
A programme has been widely circulated for the purpose of ascer-
taining how far the proposals contained in it meet with the
support of men cultivating all branches of science, and living in
all parts of the country. Professor Eoscoe adds, that “the pre-
sent moment appears to be well suited for action in this matter,
as the establishment of a union amongst men of science must
strengthen the hands of the Eoyal Commission now considering
the whole subject of State aid to science.”

The movement thus commenced, and going on in various quar-
ters for co-operation and confederation, deserves our consideration.
We see the important purposes which may be thereby attained,
not only by facilitating important physical investigations, but also
by giving to scientific bodies a greater powTer and influence in the
country to which they are well entitled.

If it be asked how co-operation and confederation can best be
secured, I may perhaps be told that it will be enough to trust
to sympathy with each other, created by the pursuit of common
objects, and that no special or formal alliance is necessary. As
among all the branches of human knowledge relationship prevails,
so it is said there is naturally and unavoidably a similar connec-
tion among societies. Hut the well-known Roman aphorism
which speaks of this relationship, speaks also of a bond to cement
it, “ Omnes artes quae ad humanitatem pertinent, habent com-
mune vinculum, et quasi cognatione quadem inter se continentur.”
The “commune vinculum” here referred to, is, I think, desir-
able ; and that bond may fitly be constituted by a central society,
which, embracing in its own programme of operations various
sciences, holds out a hand of welcome and co-operation to other
societies, severally devoted to some one of these sciences. The

of Edinburgh, Session 1870-71.

289

late Principal Forbes strongly maintained the expediency of a
central society on a separate ground, which is explained in the
following paragraphs of his address. He urged that —

“ To maintain the character for energy and stability of one central society,
is in reality the common interest of all who cultivate science. Delightful
and instructive meetings may he held by a local body of geologists, or
chemists, or naturalists* But such local associations require immense vitality
to be permanent. Generally they fall into abeyance in twenty or thirty
years ; and if they attempt to record their labours by publications, these
publications having never attained more than a very limited circulation, be-
come inaccessible and forgotten. The matured written reports of these
labours in minor societies, are best consigned for preservation to the publica-
tions of a central and enduring association.”

All these views evidently point to our own Society, as being one
well qualified to undertake the duties and position Of a central
body in order to promote co-operation and confederation among
the various scientific bodies in Scotland ; and if it be objected
that my views could not be carried out without some considerable
change in our established customs, I have only to say, that as in
Grovernments, it is wise to make from time to time such reforms as
are called for, in order to retain public confidence, or promote
more efficient action ; so in other institutions, it is equally expedi-
ent to watch the progress of events, which may necessitate from
time to time some changes in their modes of operation.

The changes, however, which would benefit both our own Society
and others, are really not so important, as that the Council of its
own authority may not competently adopt them. They are as
follows : —

(ls£.) That should any society in Scotland having literary or
scientific objects, desire to be connected with the Eoyal Society of
Edinburgh, it shall, if our Council approves, be held to be affiliated
with us, and to be entitled to the privileges of an affiliated society.

(2d.) That any member of an affiliated society, on intimating
to our secretary his name and address, shall receive a billet, en-
titling him to free access to our meetings, as well as to our library
and reading-room.

(3d.) That an affiliated society shall have right to send to us,
through its office-bearers, reports or papers by any of its members,
on literary or scientific subjects, which if approved by the Council,

290 Proceedings of the Royal Society

maybe read at our evening meetings, and may be published in our
Transactions.

(fthi) That our Council, on the other hand, shall be entitled to
appeal to any affiliated society for co-operation in the ascertainment
of facts, or the investigation of phenomena, lying within the com-
pass of its objects, and also within the field of its operations ; and
if, in response to this appeal, a report is made, we may, if approved
by the Council, have it read or noticed at our meetings, and pub-
lished in our Transactions.

(fthi) That in the event of any important investigations or ex-
periments being wished to be made by the members of an affiliated
society, which however cannot be made by them on account of the
expense thereof, it shall be competent for the office-bearers of such
affiliated society to apply to the Council, of our Society to defray a
portion of the expense, out of the funds of our Society, or out of
an annual grant, should such be obtained from Government, to
aid scientific investigations in Scotland.

Some such arrangements as those I have now suggested, would
probably produce co-operation among most of the societies in Scot-
land devoted to science or literature, a co-operation which would
be attended by advantages, both to them and to the advancement
of their objects.

IY. In adverting, under the next head of this address, to the
usefulness of such societies as ours, it is only necessary to observe
that they have been established to aid philosophers in the peculiar
work to which they devote themselves. Whether we regard the
work they accomplish, or the motives which inspire them, these
philosophers deserve all the encouragement and aid which can
be given. They love knowledge for its own sake; — their chief
pleasure consists in searching for knowledge ; — and their highest
happiness is to discover some new truth. Fortunately for the
world, there have been in all ages, and among almost every people,
individuals who have cherished those noble aspirations. The old
Hebrew king has recorded, how he “ applied his heart to know
and seek out the reasons of things,” and avouched from experience,
how “ Happy is the man who findeth wisdom.” The enlightened
Roman expressed the same sentiment when he exclaimed, “ Felix

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of Edinburgh , Session 187 0-7 1 .

qui potuit rerum cognoscere causas.” The Greek mathematician,
on discovering that the square of the hypothenuse in aright-angled
triangle is equal to the sum of the squares of the other two sides,
in testimony of his happiness offered a hecatomb to the gods ;
whilst a Sicilian philosopher, when he found how to ascertain the
specific gravity of bodies, was so overjoyed, that he rushed out of
his bath naked into the streets, mad with delight. Our own Sir
Isaac Newton became so elated or agitated when approaching the
end of his calculations, which he saw would prove that the plane-
tary movements were all governed by the law of gravitation, — that
law which he was the first to discover, — that he was obliged to
hand over his calculations to a friend to complete them. These
men, and thousands more of the same stamp, were all animated
by a heaven-born instinct to pry into the mysteries of nature, to
study the mechanism of the universe, and deduce the rules or
principles which the Almighty had followed in the work of crea-
tion, and still follows in the equally great work of upholding the
universe. Their tastes were noble, because pure ; their researches
and labours also were noble, because disinterested. They worked
not for their own individual benefit, nor even for that of their own
kin or country, but for that of the human race. Men characterised
by such tastes, such motives, and such pursuits, surely deserve
encouragement, and if scientific societies afford it — their usefulness
is unquestionable.

How these societies afford this encouragement I have already
partly explained, when adverting to our own operations, and
in particular to the stimulus given to men of science, when
by means of our meetings, and our Transactions, they obtain
an opportunity of intimating their discoveries and publishing
them. It is probable that there are thousands of discoveries —
the groundwork of important inventions, — which never wrould
have become known, — nay, which never would have been made,
but for the existence of such societies as ours. For example, the
Principia of Newton would not have been given to the world at
the time they were given, had the Royal Society of London not
agreed to print them ; for Newton was so poor, that he could not
afford to continue his subscription as a member of the Society,
small as that was.

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Proceedings of the Royal Society

Whilst philosophers are encouraged by these societies to investi-
gate, by knowing that their discoveries will be recorded and pub-
lished by the societies of which they are members, others who
may or may not be members, when they see these discoveries
and study their bearings, are often able to turn them to account,
and in a way never anticipated by the authors. Hundreds of cases
can be stated, where papers published in scientific transactions, on
being perused and studied by other inquirers often in a distant
part of the world, have been to them as bridges, enabling them to
pass over difficulties which previously had obstructed progress, and
on the brink of which they had been sitting in despair.

That scientific societies contribute immensely to the advance-
ment of knowledge, may be farther inferred from this circum-
stance, that as it is during the last fifty years that discoveries
and inventions have been more plentiful than in any former age,
so it is during the last fifty years that these societies have multi-
plied, and a wide circulation given to their published transactions.

To these societies mainly, mankind is therefore indebted for the
marvellous contrivances and processes which distinguish the pre-
sent age above all that have preceded it. Most of these — such as
electro-magnetism, electro-plating, photography, artificial light,
improved telescopes and microscopes, steam machinery, ancesthe-
tical agents and medical disinfectants — sprung out of experiments,
observations, or speculations, were very unpromising as regarded
any practical utility when first announced, but ultimately became
sources of incalculable material wealth, as well as of vastly in-
creased comfort and enjoyment to man.

These triumphs of modern science, are also the chief elements of
our present civilisation, and for them the world is indebted chiefly
to scientific bodies such as ours.

Y. In adverting to the last head of this address, viz. : — on the
best way of encouraging and aiding such societies as ours, I have to
remark that it may be effected in two ways, viz , — directly, by
grants and accommodations from the State ; and indirectly, by
creating among all classes of the population a greater taste for
scientific pursuits.

1. Taking the indirect method first, it is hardly necessary to

293

of Edinburgh, Session 1870-71.

point out how, as this scientific taste increases, persons will be more
inclined to join societies of a scientific nature. The practical
question then arises how this taste can be increased ?

At a former period I had the faith which many others had in the
efficacy of mechanics’ institutes. But having had some experience
of the working of these institutions, I am now satisfied that popu-
lar lectures do very little else than afford amusement, — though in
that respect they are not altogether useless. But if they are to
give instruction, and promote habits of observation, or a taste for
scientific pursuits, they must inculcate and administer the hard
discipline of personal study. Accordingly, many mechanics’ insti-
tutes have established classes for different branches of study, and
with much advantage.

I confess, however, that I have more faith in the instruction which
begins at an earlier period of life than can be conveniently given
at mechanics’ institutes. I have seen that boys even under four-
teen or fifteen years of age may acquire a taste for scientific pursuits,
and habits of accurate observation — very serviceable, in whatever
field of useful industry they may afterwards engage. No interfer-
ence with essential branches of study would be necessary. In our
Scottish parish schools, the time now spent in teaching French
and German* to the children of the working classes, would perhaps
be more usefully spent in teaching the elements of physiology,
botany, chemistry, or geology ; and as it is now7 the general prac-
tice in all primary schools to have an entire holiday on Saturday,
that day of idleness or mischief would be more beneficially spent
in a walk along the sea coast, or up a hill side, or through a rocky
dell, or even along hedges and ditches, accompanied by a master
competent to point out objects of interest. Who can doubt that
in the course of such rambles, aided by a small amount of indoor
instruction, seed would be sown in many a boy’s mind and disposi-
tion, which would bear good fruit of a scientific kind in after years.
I am glad to be able to say, that I know of several parish schools in
East Lothian and in Perthshire, where the masters, having them-
selves a turn for science, have a class for instruction in the par-
ticular branch with which they are conversant. In one school,

* I see from this year’s Education Report, that in the parochial schools,
the number learning these languages is 2500.

294 Proceedings of the Royal Society

chemical experiments are made once or twice in the month. In
another school, the teacher has a telescope, through which he shows
to the older boys of his school the moon and larger planets. In
another school, a small collection of specimens has been formed to
illustrate the rocks and minerals of the neighbourhood. The chief
drawback in this matter, next to the want of teachers competent
and well-disposed, has been the want of suitable text-hooks. But
I am glad to find from the Secretary of, the Education Committee,
that this last drawback is being removed, as he has himself been
preparing Elementary Science School Books, with the assistance of
Professor Kelland, Professor Balfour, Mr Archer, Mr G-eikie, and
other eminent scientific men.

Whilst on the subject of scientific instruction in schools, I can-
not avoid referring to the very gratifying encouragement given by
the Gfovernment Department at South Kensington. That encourage-
ment is very considerable, consisting not only of money rewards to
pupils and teachers, but also of apparatus and books to schools.
It is already producing fruit ; for whilst last year, the number of
schools in Scotland which received these Grovernment grants
amounted to 24, this year they are 45, being an increase of nearly
100 per cent.

Therefore, as these science and art classes in schools are multi-
plying, a taste for science will no doubt quickly germinate among
the working and middle classes, thus supplying candidates in
greater numbers for scientific pursuits and scientific societies.*

2. The foregoing remarks apply to the aids given indirectly to
societies. I next notice the amount of aid given directly by the
State.

Here it is proper to distinguish the aid given to science classes
in schools, from the aid given to scientific societies. In the former

* Since this address was delivered, I see ( Nature , Dec. 22, 1870) that an
address has been presented by the President of the British Association for
the Advancement of Science, supported by the office-bearers and an influen-
tial deputation, comprehending Sir Charles Lyell, Sir John Lubbock, Dr
Lyon Playfair, and Mr Francis Galton, — to the Vice-President of the Privy
Council Committee on Education, pointing out the expediency of authorising,
in the new national elementary schools, systematic instruction in elementary
science, so as to create a taste among the pupils, whereby they may be in-
duced to follow out scientific studies in the more advanced schools.

295

of Edinburgh, Session 1870-71.

case, aid is given for instruction in facts and principles which are
already known. In the latter case, aid is given for searching new
facts and new principles. It is very evident that the latter object
is all important, if any advances in knowledge are to be made.
Moreover, it is an object which needs more help from external
sources. The student who obtains technical knowledge, or the know-
ledge which fits him for a profitable trade or profession, may not
unfairly he left to pay the expense of his instruction, in considera-
tion of the gains which that trade or profession will bring to him.
With an investigator of scientific phenomena, who hopes to dis-
cover some new principle, the case is widely different. As bis
impelling motive is not the prospect of gain, so in nine cases out
of ten the original discoverer of a new law, or a new principle, or a
new product, is not the man who ever benefits by it in a pecuniary
sense. Whilst he sows the seed, others reap the fruit, and yet, to
procure the seed, probably much capital had to be spent and years
of study endured, at the sacrifice of both health and fortune.
Therefore the man who devotes his time to the discovery of new
truths, and who bravely adheres to that pursuit in spite of diffi-
culties and embarrassments, is surely a man standing in more
need of help and encouragement than the engineer or artisan
or mechanic who is receiving instruction which will enable him
to follow a profitable profession. If the latter deserves assistance
from the State, much more should the former. These investiga-
tors of science are the men of whom a country, when it possesses
them, should be proud ; and it would be a bad sign of the age if
such men did not exist, or if no interest was felt about them.
When ancient Rome was becoming degenerate, the question was
significantly asked — “ Quis nunc virtutem amplectitur, proemia
si tollas?” So also it would be a sign of the degeneracy of a
people, were no one to embrace science, except from the hope
of profit ; and it would be equally a sign of a degenerate Govern-
ment, if it refused to encourage men of science and scientific
societies.

In all civilised countries such encouragement is given in a
greater or less degree, and in one form or another. Whether the
amount of the encouragement given by the British Government
is sufficient, is a point on which I at present offer no opinion.

VOL. VII. 2 Q

296 Proceedings of the Royal Society

Bat one thing is obvious, viz., that whatever were the difficulties
which, thirty or forty years ago, investigators of new facts and
new principles had to encounter, these difficulties are tenfold
greater now, and therefore help to overcome these difficulties
ought now to be more ample. The first discoveries in all the
sciences were made by methods and processes far more simple
than are now serviceable. The first steps in astronomy were
made by the human eye alone. After all the knowledge was
collected, which the unaided eye could supply, the next advances
in the science were made by telescopes — telescopes simple and
rude at first, but soon superseded by others of greater size and
more accurate construction, so as to admit of a farther pene-
tration into the depths of ethereal space, and a more minute
examination of the movements and forms of the planetary bodies.
When an eclipse of the sun has to be observed, the only way of
now proceeding is, besides employing highly improved telescopes,
to have also the spectroscope, the polariscope, and photographic
apparatus ; and, in order to use these instruments to the best
advantage, large parties of observers must co-operate, and, at
a great sacrifice of time and money, repair to favourable and
probably remote spots on the earth’s surface. So it is with all the
other sciences. To enable a chemist to make discoveries now in
his science, lie must have apparatus and instruments ten times
more numerous and expensive than those with which chemists
formerly worked. The botanical physiologist can make no farther
advances, except by means of powerful microscopes, which to his
predecessor were unknown. For progress in meteorology, obser-
vations by individuals, in a few districts once or twice a day, are
no longer of much avail. There must be a complete network of
observations made over large portions of the earth’s surface —
and at least three or four times in the twenty-four hours. There
must be self-recording instruments in particular districts, besides
occasional ascents in a balloon. In short, there is no one science
which can now be advanced by the same simple means which were
available formerly. Science would stand still if improved methods
were not resorted to. The difficulties, therefore, which men of
science and scientific societies have to encounter in their researches
are far greater than formerly, and what may have been a sufficient

297

of Edinburgh, Session 1870-71.

amount of aid and encouragement to them twenty or thirty years
ago is now manifestly quite inadequate.

Another obstacle in the way of farther discovery must not be
overlooked. A great proportion of the philosophers who search
after new truths and new principles are teachers, whose income as
such alone enables them to obtain the means, scanty and precarious
as it is, of prosecuting original investigations. But as know-
ledge advances, the labours of instruction increase; — and if the
teacher does his duty in that capacity very little time is left to
allow of extraneous investigations. Yet these persons are often
better qualified to be investigators of new truths, than teachers of
old truths. I have in my own experience met with professors in
our universities whose occupation in the work of teaching deprived
science of those who most probably would have been instrumental
in making great discoveries.

The circumstances to which I have been adverting, as obstacles
to the future advancement of science, were felt to be so serious,
that two years ago they engaged the attention of the British Asso-
ciation— an association whose chief object it is “to give a stronger
impulse and more systematic direction to scientific inquiry,” and
“to remove any disadvantages of a public kind which impede its
progress.” The view submitted to the Association by those who
brought the subject before it was, that as there are institutions for
teaching old truths, so there ought to be institutions for discovering
new truths, and that, as this last work had now become so difficult
and costly, that few individuals could enter on it from their own
resources, the State — which, on behalf of the great interests of the
country, is interested to encourage discoveries and investigations —
ought to come forward and establish institutions, in which men
with an aptitude for original investigations might have facilities for
carrying them on, without being distracted by any other vocation.

The British Association so far entered into these views as to
appoint a committee, consisting of some of its most eminent and
influential members, and the two following questions were put to
the committee for consideration : —

“(1.) Does there exist in the United Kingdom of G-reat Britain
and Ireland sufficient provision for the vigorous prosecution of
physical research ?

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Proceedings of the Royal Society

11 (2.) If not, what further provision is needed, and what measures
should be taken to secure it? ”

At the meeting of the Association in 1869 that committee
reported —

“(1.) That the provision now existing in the United Kingdom
of Great Britain and Ireland is far from sufficient for the vigorous
prosecution of physical research.

“(2.) That, whilst greatly increased facilities for extending and
systematising physical research are required, your committee do
not consider it expedient that they should attempt to define how
these facilities should be provided.”

In explanation of this last finding, the committee observed
that —

“ Any scheme of scientific extension should he based. on a full and accurate
knowledge of the amount of aid now given to science, of the sources from
which that aid is derived, and of the functions performed by individuals and
institutions receiving such aid. Your committee have found it impossible,
with the means and powers at their command, to acquire this knowledge.
Moreover, as the whole question of the relation of the State to science, at pre-
sent in a very unsettled and unsatisfactory position, is involved, they urge
that a Royal Commission alone is competent to deal with the subject.”

The Association approved of this report, and appointed applica-
tion to he made to her Majesty’s Government to appoint a Royal
Commission to consider the whole subject. This application was
successful; for, in May 1870, the Gazette announced the names of
nine Commissioners, with power “ to make inquiry with regard to
Scientific Instruction and the Advancement of Science, and to
inquire what aid thereto is derived from grants voted by Parlia-
ment, or from endowments belonging to the several Universities
in G-reat Britain and Ireland, and the Colleges thereof, and whether
such aid could be rendered in a manner more effectual for the pur-
pose.”

The importance of this measure I need not dwell upon. The
backwardness of the British Government to aid institutions and
individuals devoted to scientific investigations, and the miserable
amount of any pittances conceded to them, affect the credit and
prosperity of the country quite as much as the interests of science.
G-reat Britain, whose influence in the wrorld depends almost more
on moral than on physical power, ought not to be behind other

of Edinburgh, Session 1870-71.

299

nations in its patronage of science. Yet what has happened within
the last six weeks? A remarkable eclipse of the sun, to take place
on the 22d of this month, had been looked forward to by astro-
nomers as affording an excellent opportunity for solving many
important questions regarding the constitution of that great orb
on which all living things in our planet, and in other planets also,
depend ; but, for the proper observation of which eclipse, expedi-
tions were necessary, requiring much previous preparation and
great expense. The United States Urovernment, even eight
months ago, began preparations, a sum of L.6400 having been
unanimously voted by Congress,* and a Government officer
despatched to visit Spain and Sicily, to find proper places of
observation, and to make suitable arrangements for the recep-
tion of a party of astronomers. A ship of the United States
navy was appointed to convey them, accompanied by two eminent
engineer officers, representing the Government, to take a general
charge.

In England what were the arrangements for this interesting
astronomical phenomenon ? Early last spring, on the suggestion
of the Astronomer Royal, a committee was formed, consisting of
himself and the Presidents of the Royal Astronomical Society,
and of the Royal Society of London, to organise an expedition. A
party of astronomers soon volunteered, about sixty in number,
who were to be divided into two parties, one for Spain and another
for Sicily, each subdivided into sections, to make different kinds
of observations, with suitable instruments. As total obscuration
would last only two minutes, the more that the work could be

* The following appropriations, under the head of Astronomy and Meteoro-
logy, were made by Congress, as given in “ Nature ,” Jan. 26, 1871 : —
Observations of Eclipse, Dec. 1870, under Coast Survey, 29,000 dols.

U. S. Nautical Almanac, .... 20,000 „

National Observatory, ..... 19,800 ,.

New Telescope for do , . . . . . 50,000 ,,

Telegraphic Notices of Storms, . . . 50,000 „

In the same Congress there were additional appropriations to the amount of
no less than 1,877,766 dollars, for the support of Museums, Botanic Gardens,
Mining Statistics, Polar Explorations, Surveys, and other objects of a scien-
tific nature. These appropriations, be it observed, were by the Federal
Government. Similar appropriations, but larger altogether in amount, are
made by the different States in aid of their own societies.

300 Proceedings of the Royal Society

distributed among different observers the better. The Committee
bad entertained no doubt that her Majesty’s Government would
give ready, if not liberal, assistance. On the last occasion of a
solar eclipse — viz., in 1868 — several European Governments sent
expeditions to India, where it could best be viewed. Ours gave
the use of a ship, besides appointing officers, and paying expenses.
But when the committee, last summer, applied to the Admiralty
to ascertain if one of her Majesty’s ships would be allowed to
convey the English astronomers, the answer they received was that
Parliament had not placed either ships or funds at the disposal
of the Admiralty for any such purpose. This was a rebuff little
anticipated ; and, I may add, little deserved by those of our
countrymen, who, in a noble spirit of disinterestedness, had offered
to give up their time, and leave their homes, to undergo fatigue
and risk in the cause of science. In consequence of this answer
some delay arose, to consider what was to be done. An appeal
against the decision of the Admiralty, to the Premier and the
Chancellor of the Exchequer, was resolved on. Some farther
delay occurred in consequence of the absence of these high
functionaries from London. Meanwhile, the United States ship
arrived in England, bringing with them the American astronomers.
They soon learnt the unsatisfactory position of the negotiation
with our Government; and, in consequence of it, they sent a
formal invitation through their director, inviting the English
astronomers to accompany them in their ship to Spain and Sicily.
This letter was published in the London newspapers ; and severe
comments were made by the press on our executive, if they should
oblige the English party to avail themselves of the invitation, and
be beholden to a foreign Government for assistance. Fortunately
for the credit of the country, our Government at length yielded to
the pressure. A sum of L.3000 was agreed to be set apart to pay
expenses, and a .troop ship was appointed to convey the party and
their instruments. But no Government astronomer received
authority to accompany the expedition, and no engineer officer, or
other official representing the Government, was appointed to take
charge of the expedition, and give assistance. In all these
respects the British Government fell far short of what had been
done by the United States Government, to aid in the cause.

of Edinburgh, Session 1870-71.

301

I have related thus fully the circumstances connected with this
Solar Eclipse Expedition, because it has occurred recently, and
therefore shows too plainly the indifference to science, and to men
of science, which actuates those who manage the affairs of this
country. It is, however, a charge which unfortunately does not
lie at the door of the present executive alone. The same indif-
ference has been too clearly manifested by almost all preceding
Governments. Unmistakable evidence of this indifference is
afforded by the treatment of the societies and associations formed
for the advancement of science. What aid is given to any of
these? The only part of the United Kingdom in which such aid
is liberally given is in Ireland.* Except to the Academy of
Music in London, which receives annually a grant of L.500, I
know of no Society of a scientific character, either in England or
in Scotland, which receives any grant to carry out its special
objects. The only patronage to English scientific societies con-
sists in the free use of Government apartments in London to seven
of these societies, and the free use of Government apartments
in Edinburgh to two Scotch societies — viz., the Royal Society and
the Society of Antiquaries. j* There is another society which has
been very kindly allowed to occupy two small apartments in the
General Post-Office Buildings; but for the use of these a rent is
exacted ; and, moreover, from this society statistical information
is obtained by Government, for which, however, Government does
not pay, and declines to pay.

This illiberal feature of the British Government in not aiding
voluntary associations for scientific objects, is the more remark-
able considering the principle which our Government adopts for

* In Dublin there are six societies, two of which are for the encourage-
ment of the fine arts, particularly painting, which receive about L. 13. 000
yearly, to enable them to carry out their special objects and to keep their
buildings in repair. (See Report of Royal Commissioners on Aid given to
Irish Societies, presented to Parliament in 1869.)

t The Royal Society of Edinburgh has, since the year 1836, received from
the Exchequer a yearly sum of L.300 to enable them to pay rent, taxes, and
maintenance of the apartments they occupy. The rent charged by Govern-
ment for these apartments is L.260. The Society of Antiquaries receives
L.300, which is all applied to pay the officers who take charge of the Museum,
and the necessary repairs and cleaning. The Museum belongs to the
Government.

302 Proceedings of the Royal Society

other associations having objects not more beneficial to the public.
The principle is, that when funds are voluntarily supplied from
local sources, the State supplements these by an addition of as much
money from the Exchequer. The local subscriptions are justly
taken as evidence that the objects are praiseworthy, and that they
are appreciated by the community ; whilst any risk of misapplica-
tion or mismanagement is avoided by an annual report to Govern-
ment. This principle has been applied to schools and various
other educational institutions, to volunteer corps, to county con-
stabulary, &c.

Whilst pointing out the illiberal, short-sighted, and inconsistent
policy of the British Government in not assisting scientific socie-
ties with pecuniary grants to aid them, it would be wrong in me
not to take grateful notice of a parliamentary grant of L.1000 a
year given to encourage scientific investigations carried on any-
where in the United Kingdom or colonies of Great Britain. Of
this grant I could find no authentic account in any publication.
General rumour only was my authority for believing that such a
grant existed, and that it was at the disposal of the Koyal Society
of London. On my speaking to Professor Balfour on the subject, I
found that he could give me no information, but he kindly under-
took to apply to Dr Sharpey, the secretary of the Boyal Society of
London. Dr Sharpey at once responded, by sending a memoran-
dum explanatory of the grant — a memorandum which appears to
me of sufficient importance to be now laid before our Society

Memorandum as to the c Government Grant ’ placed annually at
the disposal of the Boyal Society. — Nov. 30, 1870.

u In 1849 the First Lord of the Treasury (Lord John Bussell)
offered , on the part of the Government, to place L.1000 at the dis-
posal of the Boyal Society, to be by them applied towards the
advancement of science.

“ This offer was accepted. The first payment was made in 1850,
and it has been repeated annually up to the present time. Up to
1855 the grant was paid from a special fund at the disposal of the
Treasury, but since then it has been annually voted by Parliament.

“ The Council of the Boyal Society consider the grant as a con-
tribution on the part of the nation towards the promotion of science

303

of Edinburgh, Session 1870-71.

generally in her Majesty’s dominions, regarding themselves as
trustees of the grant, and accountable to the public for its due
administration, as long as it shall be continued.

“ To aid the Council in the distribution of the fund, a committee
is annually appointed, consisting of the 21 members of the Coun-
cil and 21 Fellows of the Society not on the Council, selected on
account of their acquaintance with the different branches of science
which the Society cultivates. All applications for grants from the
fund are submitted to this committee, and the appropriations are
made by the Council on the committee’s recommendation.

“ The grants are commonly made to individuals engaged in
some definite scientific investigation, chiefly to meet the expense
of apparatus and materials, and not as remuneration for time or
labour bestowed by the inquirer. To a less extent appropriations
have been made for like purposes to scientific institutions, and,
more rarely, to aid in the publication of valuable scientific results.

“ The distribution of the fund is not restricted to Fellows of the
Eoyal Society, nor have they any privilege in regard to it ; men
of science, whether belonging to the Society or not, and where-
ever they may carry on their researches, in this country or the
colonies, have an equal title to participate, and their claims have
been in all cases equally recognised.

“No part of the fund is applied towards the expenses of the
Eoyal Society, and the Society neither asks nor would accept any
remuneration for its stewardship.

u It is to be noted that, in 1864, the Council, finding that the
unappropriated balance, together with other funds at their dis-
posal, would meet the probable demands for scientific objects,
repaid the grant of that year into the Exchequer.

“ A return was made to Parliament in 1855, stating the appli-
cation of the fund for the five years ending 5th April 1855. This
statement will be found printed in the ‘ Proceedings of the Eoyal
Society,’ vol. vii. page 512. A second return was made in 1862,
showing the distribution of the fund from 1855 to 1862. No
later return has been called for, although the Council would be
glad to make it if ordered.

“ It is proposed hereafter to publish an annual statement of
the disposal of the grant in the Proceedings. W. S.”

2 n

VOL. VII.

301 Proceedings of the Royal Society

Dr Sharpey, besides drawing out the foregoing memorandum,
explaining the origin and objects of this parliamentary grant, has
been so obliging as to send two printed returns, giving for the first
twelve years the names of the persons who have shared in the
grant, and the nature of the researches aided. Besides these re-
turns (to Parliament), he has sent a statement — apparently not yet
published — containing similar information for the years 1869 and
1870. For the years from 1862 to 1869, no information is given,
except that in the year 1864, as the memorandum mentions, the
remarkable circumstance occurred, of the Society having paid back
to Government the L.1000, in consequence of there being no claims
on it which could not be otherwise met.

Now, no one who looks at the returns showing how these annual
grants were expended, will question the judicious and impartial
manner in which they have been administered. I would, however,
venture to remark, that as the grant was intended to assist scien-
tific researches in all parts of her Majesty’s dominions, colonies
included, some means should have been taken to make the exist-
ence and the objects of the grant publicly known. The grant
would, of course, be known to the Fellows of the Royal Society of
London, but it has remained ever since its institution, now twenty
years ago, generally unknown to men of science, and especially to
persons resident in Scotland and Ireland. It is therefore not
surprising that, in the year 1864, there being no demands on the
grant, it had to be paid back to Government ; and that out of the
L. 14,000 embraced by the returns, no more than L.610 should have
been expended on researches in Scotland. The great part of these
researches was made by two individuals, both of them Fellows of
the Royal Society of London.

It appears to me that, so far as the interests of science in Scot-
land are concerned, these interests, if intended to be aided by a
pecuniary grant from the State, would be better promoted were
the grant administered by a suitable board in Scotland, instead
of by one in London. Any researches and experiments carried
on in Scotland, and the scientific character of the men who carry
them on, must surely be better known in Edinburgh than in Lon-
don. Limited as are my own opportunities of knowing of such
researches and experiments, I may refer to some on the difficult

305

of Edinburgh, Session 1870-71.

and important subject of ozone, which, after being carried on for
some time in the Edinburgh Botanic Garden last year,* had to
be discontinued on account of the want of apparatus and instru-
ments which those who instituted them had no means of paying
for.f

I certainly do not wish, however, that the grant of L.1000,
which is at the disposal of the Royal Society of London, should
he split up, so that a part of it may be administered to a Scotch
Society, if the London Royal Society think that they can apply
it all usefully in England. All that I contend for is, that when
parliamentary grants are voted for aiding scientific researches
throughout the United Kingdom, it is not a judicious arrangement
for the object in view to place these grants at the exclusive dis-
posal of a society in London, when there are societies in Scotland
and in Ireland competent to be intrusted with the duty. A com-
mittee of the Royal Society of London are also intrusted with
the administration of the still larger parliamentary grant of

L. 10, 000 a year for meteorological purposes, — a considerable part
of which grant is devoted to the obtaining of meteorological re-
turns from Scotland, and of establishing self-recording instru-
ments in Scotland, besides upholding other stations. Our own
Royal Society has from time to time done a good deal to pro-
mote meteorology in Scotland, — Sir David Brewster, Sir Thomas

M. Brisbane, and Principal Forbes, having been distinguished
meteorologists, and published largely in our Transactions. There
is also a society in Scotland specially devoted to that science,
which is allowed to be doing useful work. Yet neither society has
any voice in the administration of that large grant of L. 10, 000 a
year.

Whilst as regards the interests of science it seems more expe-

* See an account of these experiments in the “ Journal of the Scottish
Meterological Society ” for January 1869.

t The test papers for ozone indications are affected by the varying force of
wind, as also by the varying humidity of the atmosphere, insomuch that at
several Observatories ozone observations have been discontinued. When I
was at Rome last winter, Padre Secchi told me he had ceased to take notice
of ozone for these reasons, not having been able to devise any method for
eliminating the effects of wind and moisture. The object of the experiments
in the Edinburgh Botanic Garden was to construct an apparatus which should
allow only dry air to reach the test papers, and in certain quantities.

306

Proceedings of the Royal Society

dient that the board intrusted with the expenditure in Scotland
should be in Edinburgh rather than in London, is it not also a slur
on Scotch scientific societies that they should he altogether ignored,
and a London society selected, as if the former were unworthy,
or could not be trusted ?

I therefore regret this system of centralisation in London, and
cannot help thinking that our Society ought not so tacitly to
acquiesce in it. In one of his addresses from this chair, Sir
David Brewster, in alluding to the annual grant of L.1000, as well
as the two royal medals, placed at the disposal of the Boyal
Society of London, expressed his belief “ that an earnest repre-
sentation made to the G-overnment would obtain for us a similar,
though probably a smaller grant ; ” and it humbly appears to me
that such a representation ought to be made without farther delay.

The expediency of energetic action on our part is more manifest
because of a proposal made lately in an influential quarter to
enlarge the amount of the grant to the Boyal Society of London.
Professor Balfour Stewart a few weeks ago, at the inauguration of
Owen’s College, Manchester, in his opening address there, made
the following remarks : —

“ If Government be disposed to grant pecuniary aid to physical researches,
an extension of the allowance made annually to the Government Grant Com-
mittee of the Royal Society, would be a very legitimate way of accomplishing
this object. Ho one can doubt that the small sum of L.1000 annually intrusted
by Government to that Society for miscellaneous experiments is administered
in a praiseworthy manner ; and if the Government would be ready to grant,
and the Boyal Society willing to undertake, an extension of this trust, it would
be a great point gained.”*

This suggestion will no doubt obtain consideration from the
Boyal Commissioners appointed to report whether the State now
gives enough for the encouragement of science. All or most of
these commissioners are Fellows of the Boyal Society of London,
and two of them are office-bearers of the Society. A fairer selec-
tion of eminent men for the object in view could not have been
made ; and though none of them are Fellows of the Boyal Society
of Edinburgh, I am sure that they will not on that account be less

* Lieutenant-Colonel Strange, an influential member of the British Associa-
tion, sends a letter to 11 Nature," Nov. 3, 1870, in which he adverts to Pro-
fessor Balfour Stewart’s idea of enlarging the grant of L.1000 administered
by the Royal Society of London, and expresses cordial concurrence.

of Edinburgh, Session 1870-71. 307

disposed, perhaps the more disposed, to listen to any representa-
tion which we may lay before them.

But, apart from our own interest as a society in the deliberations
of these Royal Commissioners, I entertain a very sanguine hope
that much good will accrue from them. The very concession of a
Commission on the part of Grovernment seems to imply a convic-
tion and acknowledgment, that the patronage hitherto given in
this country to science is not what it should have been, and that
reform in this respect is quite as much needed as in other matters.
We have been lately confessing our shortcomings as regards
national schools, and are endeavouring to remedy these ; hut we
ought not to he satisfied with merely teaching old truths and well-
known facts. The investigation of new truths and new facts, and
the opening out of new pathways in the wide field of knowledge,
are also necessary if we are to help in extending civilisation, and
if we are to uphold our position in the family of nations. It
should no longer be left to the chance of individuals being found
to carry on, from their own resources, the great and noble work of
making fresh discoveries in science and art. That work is worthy
of State patronage, as it also more than ever needs State assist-
ance ; and unless that work is carried on energetically and success-
fully, we shall lose caste as an enlightened people, and see the
chief sources of our prosperity and power dried up.

Therefore I look forward, with no small anxiety, to the report
of these Royal Commissioners. But I confidently anticipate favour-
able results ; and in pointing out the best channels through which
aid to science from the State may flow, I have no doubt that our
own past services, and our present efficiency as a society, will not
be overlooked.

In these expectations I may possibly he over-sanguine, and
therefore allow me to add, in conclusion, a single remark as to our
own duty in this matter : — As a society, and so far as our scanty
funds enable us, we will continue to encourage scientific researches
in Scotland, not forgetting, however, that we have also literary
objects ; and as Fellows of the Society, — a Society which during its
time has done much in the cause of science, and something too
on behalf of literature, we will do what we can to uphold its repu-
tation, and extend its influence and usefulness.

308 Proceedings of the Royal Society

The following Gentleman was elected a Fellow of the
Society : —

John Auld, Esq., W.S.

Monday , 19 th December 1870.

Dr CHRISTISON, President, in the Chair.

The following Communications were read : —

1. Additional Remarks on the Theory of Capillary
Attraction. By Edward Sang, Esq.

2. Laboratory Notes : On Thermo-Electricity.

By Professor Tait.

In a paper presented to the Society in 1867-8 I deduced from
certain hypothetical considerations regarding Dissipation of Energy
results connected with the thermal and electric conductivity of
bodies, the electric convection of heat, &c. As these were all of a
confessedly somewhat speculative character, I printed at the time
only that connected with thermal conductivity, which I had the
means of comparing with experiment, and which seemed to accord
fairly with Forbes’ experimental results. But the assumption on
which this was based was essentially involved in all the other por-
tions of the paper.

With a view to the testing of my hypothetical result as to electric
convection of heat, several of my students, especially Messrs May
and Straker, last summer made a careful determination of the elec-
tromotive force in various thermo-electric circuits through wide
ranges of temperature. Their results for a standard iron-wire,
connected successively with two very different specimens of copper,
when plotted, showed curves so closely resembling parabolas that I
was led to look over my former investigations and determine what,
on my hypothetical reasoning, the curves should be. This I had
entirely omitted to do. I easily found that the parabola ought, on
my hypothesis, to be the curve in every case, and I made last
August a numerous and careful set of determinations with Kew
standard mercurial thermometers as an additional verification.

309

of Edinburgh, Session 1870-71.

My hypothetical result was to the effect that what Thomson
(Trans. R.S.E. 1854, Phil. Trans. 1856) calls the specific heat of
electricity, should be, like thermal and electric resistance, directly
proportional in pure metals to the absolute temperature, the coeffi-
cient of proportionality being, for some substances, negative.

Hence, using Thomson’s notation as in Trans. R.S.E., we have
for any two metals

JcTi = kj, , J cr\, = k.Jt ,

where \ and h 2 are constants, whose sign as well as value depends
on the properties of each metal, trq ; cn2 are the specific heats of
electricity, and J is Joule’s Equivalent.

Thus, introducing these values into Thomson’s formuke, we have

where n is the Peltier effect at a junction at absolute tempera-
ture t. Integrating, we have

or

where t0 is the constant of integration, obviously in this case the
temperature at which the two metals are thermo-electrically neutral
to one another. Hence the Peltier effect may be represented by
the ordinates of a parabola of which temperatures are the abscissae ;
the ordinates being parallel to the axis of the curve.

The electromotive force in a circuit whose junctions are at ab-
solute temperatures t and t' is then represented by

E = 3 Tdt = - 0 ~ O2 - f'2)]

= ft - *,)(< - o [<o - .

This, of course, is again the equation of a parabola. That t - t' is
a factor of E has long been known, and Thomson has given the

results of many experiments tending to show that t0 - — is also

310 Proceedings of the Royal Society

a factor. But it was not till the experiments in my Laboratory
had been carried on for some months that I was referred by
Thomson to a paper by Avenarius ( Pogg . Ann. 119), in which it is
experimentally proved (partly in contradiction of an assertion of
Becquerel) that in a series of five different thermo-electric circuits
the electro-motive force can be very accurately expressed by two
terms of the assumed series

E = b (t - t2) + c (t* - tf) + . . .

where ti and t2 are temperatures as shown by the ordinary mercurial
thermometer. It follows from this that (neglecting the difference
between absolute temperatures and those given by the mercurial
thermometer) E has no other variable factor than those above given.

Curiously enough, Avenarius, whose paper seems to have been
written mainly for the purpose of attempting to explain (by the
consideration merely of the effect of heat on electricity of contact
of two metals) the production of thermo-electric currents, does not
allude to the fact that the above equation represents a parabola.
In fact he gives several figures, in all of which it is represented
as a very accurately drawn semicircle. He makes no application of
his empirical formula to the determination of the amount of the
Peltier effect, nor does he seem to recognise the existence of what
Le Roux has called “ l’efifet Thomson,” which is indispensable to
the explanation of the observed phenomena.

All the curves plotted by Messrs May and Straker, which were
derived from iron, copper, and platinum alone, as well as my own,
which included cadmium, zinc, tin, lead, brass, silver, and various
other substances (sometimes arranged with a double arc of two dif-
ferent metals connecting the hot and cold junctions) were excellent
parabolas. When the temperatures were very high, the parabola
was slightly steeper on the hotter than on the colder side. This,
however, was a deviation of very small amount, and quite within
the limits of error introduced by the altered resistance of the cir-
cuit at the hotter parts, the deviations of the mercury thermometers
from absolute temperature, and the non-correction of the indication
of the thermometers for the long column of mercury not immersed
in the hot oil round the junction.

To settle the question rigorously, I have been for some time ex-

311

of Edinburgh, Session 1870-71.

perimenting with an arrangement sometimes of double metallic
arcs, sometimes of two separate thermo-electric circuits acting on a
differential galvanometer — a second object being to obtain, if it be
possible, an arrangement capable of replacing with sufficient accu-
racy the air-thermometer in the measurement of very high tempera-
tures, and where very exact results are not required.

In fact, if the formula above be correct, we have for two circuits
with their junctions immersed in the same vessels

E =«(<-<,) («„ - )

E' = a' (t -«,)(<'„ -

so that if the resistances in the circuits be made as a to a' their
resultant effect on the differential galvanometer will be proportional
to

(fa ~ t'o) (f ~ Q •

It is obvious that so far as these factors are concerned the most
sensitive arrangements will be such as have their neutral points
farthest apart. On a future occasion I hope to lay the results of
my new experiments before the Society. They appear to promise
to be of great use in furnishing an easily working and approxi-
mately accurate substitute for the air-thermometer in an inquiry on
which I am engaged respecting specific heats and melting points
of various igneous rocks, &c., while the comparison of the indica-
tions of two such arrangements at very high temperatures will
give the means of determining whether the quantities called h
above are really constants.

3. Note on Linear Differential Equations in Quaternions.
By Professor Tait.

The generally non-commutative character of quaternion multi-
plication introduces into the solution even of linear differential
equations with constant (quaternion) coefficients, difficulties of a
somewhat novel character. To some of these which have presented
themselves to me in many investigations, I wish to draw attention
in the following note, but want of leisure prevents my attempting
at present either to classify the numerous curious forms which may
be met with in physical inquiries, even when these lead to mere

VOL. vii. 2 s

312

Proceedings of the Eoyal Society

vector equations of an order no higher than the second, or to de-
velope the subject of the curious functional equations which are
incidentally involved.

1. The integration of an equation such as

where m is a scalar (usually a function of t, which is assumed
throughout as the independent variable), and q an unknown qua-
ternion, is obviously to be effected by the ordinary method, multi-
plication by efmdt •

2. But if a be a quaternion , the integration of

even when a is constant, requires a little care, unless we boldly
treat a as m was treated in the preceding section. This, no doubt,
gives the correct result, but the process requires to he defended.
Assume therefore r to be a factor which makes the left hand mem-
ber integrable. Then we must have

or, if r' be a proximate value of r,

r' = r + rSt = r (1 + aSt) .

Hence, dividing the finite interval t into a great number of equal
parts, and taking the limit

q -f mq = a ,

q -f aq = a' ,

r = ra ,

= U

where r0 is an arbitrary but constant quaternion.
Now we have

at t(Sa + TVa . TJVa) t{m + na)

£ = £ = > sum

’ suppose

2 nt

mt 7T

s a

Hence the solution of the given equation is

313

of Edinburgh, Session 1870-71.

the arbitrary quaternion constant r0 having disappeared, but a new
one being introduced by the integration on the right.

When a is variable, the tensor of r is easily seen to he % fSad*}
but its versor, s, is to be found from the equation
s = sY a

the fundamental relation between the instantaneous axis and the
versor of rotation of a rigid body (Trans. R.S.E., 1868).

When r is a vector, 0 suppose, we have
6 = Y 6a ,

whence, as above,

e = y e0sfadt .

3. In the succeeding examples we restrict ourselves to equations
for the determination of unknown vectors , as we thus avoid the in-
troduction of the quartic equation which has been shown by
Hamilton to be satisfied by a linear function of a quaternion ,
This would appear, for instance, in the solution of even the simple
equation

q + aqb = c

where a and b are constant quaternions ; though, of course, its use
may be avoided by employing a somewhat more cumbrous pro-
cess.

4. Suppose we have

p + <Pp ~ a

where <p is a self-conjugate linear and vector function with con-
stant constituents. Operate by S . S, and we have

SSp + S . p(pS = SSa .

The left hand side is a complete differential if
S = <pS .

The general integral of this equation may be written as

s=

where s $ is another linear and vector function ; but it is not neces-
sary to discuss here the validity of such a result, deduced as it
must be by a process of separation of symbols. [See Tait’s Quater-
nions, § 290.] For, on account of the properties of p, we may

314 Proceedings of the Royal Society

assume (since but three distinct and non-coplanar values of 8 are
required)

8 = x y

where y is a constant unit-vector, and x a scalar function of t.
This gives

x ~

- 1 = 9*! •

x

The values of y are therefore unit- vectors parallel to the axes of
the surface

S p(pp = 1 ,

and those of - are the roots of the auxiliary cubic in <p . Call

x

them rj1, y.2, yA and giy g,ly gs respectively, then the values of 8 (into
which no arbitrary constant need be introduced), are of the form

jt

g y.

Thus, finally,

p = — %y^yp

= - [fs^Syadt + C] .

5. If, in the equation of (4), we suppose a constant, we may
easily apply a process similar to that of (2).

For

p = p + pSt = (1 — St . <Q) p + a St .

Hence, as a is constant,

/ v (i ~ -T- 1

-T I 1 _ ) , x V nJ .

P n)Po + ■^00^1 _ _ 1 n

= *~t<P Po + @ a

where p0 (which is arbitrary) has been increased by <p-1a. It is
easy to showr that this agrees with the final result of (4), and the
coincidence is so far a justification of the use of the method of
separation of symbols.

The verification of the general result of (4), where a is variable,
can also be effected by this method, but not so readily.

6. Let us take the linear equation of the second order with

315

of Edinburgh, Session 1870-71.

constant coefficients (equivalent to three simultaneous linear
equations in scalars of a very general form)

P + <pp + = 0 ,

where <p and if/ may, or may not, be self-conjugate.

If they be self-conjugate, this represents oscillation under the
action of a force whose components, in each of three rectangular
directions, are made up of parts proportional to (though not neces-
sarily equimultiples of) the displacements in these directions. The
resistance parallel to each of three other rectangular directions
depends in a similar manner on the corresponding components of
the velocity.

The operator in the left hand member may be written

f-s + ’M*

It + x) (

dt

suppose, where x and 6 are two new linear and vector functions.
Hence, comparing, we must have

X + 0 = <p

xo =

or, eliminating 0 ,

X2 + t = x9

a curious and apparently novel species of equation from which to
determine the function

[We might have arrived at it, by a somewhat more perilous but
shorter route, by assuming as a particular integral of the given
equation the expression

P = •“**■]

If we take their conjugates in addition to the two equations
connecting 6 and y, we see at once that all four are satisfied by
assuming these two functions to be conjugate to one another, pro-
vided <p and kJ/ are self-conjugate. Hence in this special case we
may write

x = if + v-e 1
V.e/'

It only remains that we should find e, and the rest of the solution
is to be effected as in (4) or (5).

316

Proceedings of the Royal Society

We have

When <p is a constant scalar, i.e., when the resistance is in the
direction of motion (which is the case generally in physical appli-
cations) the middle term vanishes, and we have

In fact, in this case, <p and % are commutative in multiplication,
so that the equation in ^ may be solved as an ordinary quadratic.

Even this very particular case involves a singular question,
though not one of such difficulty as that of the general problem
above. We have, in fact, to solve an equation of the form

where w is a given, and nr a sought, linear and vector function.
This leads to an equation of the sixth degree in with pairs of
roots equal but of opposite signs. The coefficients of the cubic in
33- are formed by the solution of a biquadratic equation.*

* Suppose the cubic in -nr to be

-nr3 + g-zr2 + ggur + g» — 0 ,

the given equation enables us to write it in either of the (really identical) forms
(nr + g)u + gga + g2 = 0 ,
or *r(« + gi) + ga + g2 = 0 ;

or, as it may be written,

whence

(g<* + g *
V » +ff!

or

w3 + (2 gx — g2) «2 + {g\ - 2 ‘ggja - g\ — 0 .

If the cubic in a be

a3 -f mu2 + + m2 — 0 ,

we have by comparison of co-efficients

2 gl—g2 — m, g\ — 2ggt = mx , g\ — ~ m2
so that g2 is known and

of Edinburgh, Session 1870-71. 317

In fact, if we apply the members of the general equation above
to e, we have

V.«* = 2(,_ £)..

This leads to the two equations

S-e(V - f =

_t)€ = °’

which, belonging to two cones of the second degree, give in general
four values of e.

7. The interest of the general question before us, from the
analytical point of view, lies mainly in the determination of the two
unknown linear and vector functions x and 6 from the equations

X + 6 = <p,

xe = 4,

each of which is in general equivalent to nine or in certain cases
six (not, as in ordinary quaternion equations, /owr, or as in vector
equations three ) simultaneous scalar equations. They have also a

where

The values of g being found, -a is given by the expression above.

A similar process may easily be applied to the general equation of (6), but
it may be well to exhibit the present simple case in its Cartesian form.

Let

S iui -

-Pi >

s iaj = P2

Pz

Bjai -

= <h >

= q2

S <juk —

S kui -

= ri >

S kaj — r2

S kc*k =

*3

Also let

■or —

«s i + jssy

+

y$k ,

where

** 1 +

+

kx3 ,

i8 =

Wi + 3V%

+

%3-

y —

i?i + J\

+

kza ,

then the problem reduces itself to the determination of the nine scalars
cc, y, z, &c., from nine equations of the second degree, of which we write only
the first three : — viz.

aq2 + 2/i*2 + zix3 — Pi »

*2*1 + 2/2*2 + *2*3 ~ Pi »

*3*1 + 2/3*2 + % ~Pi ’

318 Proceedings of the Royal Society

physical interest, inasmuch as they include the problem of finding
two homogeneous strains, such that the vector-sum of their effects
on any vector shall represent the effect of one given strain on that
vector, while the effect of their successive performance in a given
order on any vector shall be equivalent to that of another given
strain. It is curious to compare this with the physical meaning of
the differential equation from which these forms are derived.

If g be one of the roots of the symbolical cubic in x (of which
two will in this case generally be imaginary) and rj the correspond-
ing unit vector, such that we have three conditions of the type

(x “ 9)v =

we have

(g2 - g<p + <10 rj = 0 .

The vectors, which satisfy this and the two similar equations, are
(all three) sides (real or imaginary) of the cone of the third order
S .p<pp$'p = 0 .

One curious result, which is easily derived from the equations
above, is that, if a solid experience a pure strain, the planes in which
any three, originally rectangular, vectors are displaced intersect in
one line,

4. On some Quaternion Integrals. By ProfessoPTait.
(Abstract.)

In my paper on “Green's and other allied theorems ” (Trans.
R. S. E. 1869-70), I showed that

f?dp =ffds V.UvVP,

where P is any scalar function of p, and the single integral is ex-
tended round any closed curve, while the double integral extends
over any surface bounded by the curve, v being its normal vector.
Writing

a" = i'P -f- jQ +

this gives at once

fcrdp = ffds (S . UvV<^ - Y . (Y . UvV) cr) ,
of which the scalar and vector parts respectively were, in the paper
referred to, shown to be equal.

319

of Edinburgh, Session 1870-71.

From these equations many very singular results may be de-
rived, some of which form the first part of the subject of the pre-
sent communication.

Let <rbe a vector which, having continuously varying values
over the surface in question, becomes U dp at its edge. Then

-fTdp = Jf ds S .UvVo-'j

there being no vector part on the left-hand side. This gives the
length of any closed curve in terms of an integral taken over any
surface bounded by it.

We have evidently

Tp dTp = — S pdp ,

whence

fPdTp = - /PS . Vpdp = - ffdsS . UvV(PUp) .

Hence

f cndTp = - ffds S . (UpUvV) <r ,
for

Now if Tp be constant over the boundary, *.e., if the bounding
curve lie on a sphere whose centre is the origin, we have for any
surface bounded by it

ffds S . (UpUvV)o- = 0 ,
whatever be the value of the vector <r .

Again, if cn be a function of Tp only, we have
/ cr dTp = 0

for all closed curves. Hence, whatever be the vector-function p,
and whatever the surface and its bounding curve, we have always

ffds 8 . (UpTJj/V) <p (Tp) = 0.

Another very simple but fundamental theorem, in addition to
those given in the paper above referred to, may be stated as fol-
lows : — Let P be the potential of masses external to a space 5.
Then throughout 2 we have

V2 P = 0 ,

so that

//V Ws = ff SUvVP . ds = 0 .

2 T

VOL VII.

320

Proceedings of the Royal Society

The double integral is therefore of constant value for all noil-closed
surfaces having, as common boundary, a closed curve and not
extending into space occupied by any part of the masses. To find
its value in terms of a single integral taken round this curve, let
V2r = VP .

As P is known, the constituents of r are perfectly definite, being
the potentials of given distributions of matter. And the substitution
of functions of r for those of P gives us, by means of the general
formula at the beginning of this paper,

j^SUi/VP . ds = S/V (dpV) r ,
with the condition

SVr - 0 .

Again, we have obviously, as V2o- is necessarily a vector,

JfS . TJvX/2o~'ds = /S . Y<r~dp.

Now, let cr = ^P, then

JfS . iJJv . V2P ds = /S(idpV)P .

From this

jfUvV^ds =/V(dPV) P .

A particular case of this, for a curve in the plane of xy and the
surface bounded by it, is

jr<$* $)**-/£* -s*)

which has obvious applications to fluid motion parallel to a plane.
But, generally, we have also

JfUvV2a-'ds = fY(dp V) . <r.

If we take the vector of this, or if we subtract from each side the
corresponding member of our first equation above, we have

Jfy.TJvY2(T'ds = fY .(Y.dp^)a~.

These results appear to be of considerable importance for physical
applications, and are particularly interesting, because they involve
the operator (indicated merely in my former paper).

V(dpV) .

The paper contains several applications and modifications of these
theorems.

of Edinburgh, Session 1870-71.

321

5. Note on an Ice Calorimeter. By Dr A. Crum Brown.

The principal upon which this calorimeter is founded is, that a
contraction of a definite amount takes place on the conversion of
ice at 0° C. into water at 0° C., and that a definite amount of heat
is required for this conversion. Early in the year 1866 I sent a
description and drawing of the instrument to Messrs Kemp & Co.,
instrument-makers here, with an order to have it constructed.
Some mechanical difficulties occurred which prevented its comple-
tion at the time. I should not have laid before the Society an
account of an unfinished instrument were it not that Professor
Bunsen has recently published * an account of a calorimeter
founded on the same principle. The two instruments are quite
different in detail, and are primarily intended for different pur-
poses— Professor Bunsen’s for the estimation of specific heat, and
mine for the estimation of the heat produced during chemical
changes.

While, of course, fully acknowledging Professor Bunsen’s priority,
I lay this note before the Society for the purpose of preserving to
myself the right to use my own instrument.

It consists of a cylindrical vessel A, the calorimeter , furnished
with a tightly-fighting flanged lid of a conical form. This is fixed
to the corresponding flange on the calorimeter by means of binding
screws, and has a small hole at its apex, which can be completely
closed by means of a screw D.

Within the calorimeter is contained a smaller cylindrical vessel
B, the laboratory , closed above by means of a flanged lid. Into it
open two tubes, EE and FE. One of these, EE, carries a small
plate, upon which apparatus may be placed. From the bottom of
the laboratory a tube, GGrGf, passes, spirally bent in its descending
part, and having a reservoir with a stop-cock between its descend-
ing and ascending parts. All these tubes pass tightly through the
lid of the calorimeter.

The whole apparatus is enclosed in an outer cylinder CO.

The doubly bent glass tube II connects the vessel K within the
calorimeter, and the vessel J without. It passes through a tight
stuffing-box in the wall of the calorimeter, and through a perforated
* Poggendorff’s AnnaleD, vol. cxli. p. 1. 1870.

322 Proceedings of the Royal Society of Edinburgh .

cork in the wall of the vessel 0 ; it is formed of two pieces, whicli
can be disconnected at L, so as to allow of the removal of the
calorimeter from the jacket. The calorimeter A is to be filled with
ice and water, both free from air; the tubes EE and EE supply
the gases (previously cooled to 0° 0.) necessary for the chemical

operation taking place in the laboratory B ; while GrGr removes the
products of combustion, those which condense collecting in H.
The vessels J and K contain mercury, and it is obvious that the
quantity of mercury transferred from the one to the other is the
measure of the thermal, change accompanying the chemical action.
The space between the calorimeter and the jacket C is filled with
melting ice.

The following Gentleman was elected a Fellow of the
Society : —

Rev. Thomas Lindsay, M.A.

* ! /

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

Eighty-Eighth Session.

Monday , 1 §th January 1871.

Dr CHRISTISON, President, in the Chair.

At the request of the Council, Principal Sir Alex. Grant,
Bart., delivered an address “ On the Educational System of
Prussia.”

Mr President and Gentlemen, — If I were addressing almost
any other assembly, I should probably begin by saying that the
subject of the educational system of Prussia possesses a peculiar
interest at the present moment for two reasons — ls£, Because the
wonderful successes of Prussia make one curious to know all the
methods which have- been applied to bring that nation to its pre-
sent state ; 2 dly, Because public instruction is just now one of the
chief questions of the day for the inhabitants of Great Britain and
Ireland.

But in this Society considerations of the temporary and the
contingent would be out of place. And therefore, omitting alto-
gether such allusions, I propose to submit some account and esti-
mate of the Prussian educational system merely as a sort of
contribution to human natural history.

Probably no human institution is perfect, and yet I think we
may see nature working in and by means of human societies
towards constant improvement — that is, towards the best. While
a large portion of mankind seem content to remai

VOL. VII.

1870-71.

No. 83.

VOL. VII.

310 Proceedings of the Royal Society

without any desire for progress, there have always been progressive
races who have respectively devoted themselves to working out
different problems of civilisation. Among these is the problem of
national education, for the working out of which Prussia has made
great, and, as it is generally thought, successful efforts. At all
events, she has accumulated so great a mass of experience on the sub-
ject, as to make the history of her efforts worthy of being studied.

It is a common, but erroneous, notion to suppose that education
in Prussia is the product of the arbitrary will of modern despotic
governments — that it was conceived as a whole by some Minister
of Instruction, drawn out on the foolscap paper of a bureau, and
then issued by the fiat of the State to be accepted by the people.
Such an account would be as far as possible from historical truth.
Put some notion of the kind has obtained currency, perhaps partly
under the authority of M. Cousin, who visited Prussia in 1831,
and made a report on the state of education there for the French
Government. His account of the primary educational system was
translated by Mrs Austin, and so became tolerably well known in
this country. M. Cousin got hold of a scheme for the organisation
of education throughout Prussia, which had been drawn up in
1819 by Yon Altenstein, then Minister of Instruction. Viewing
matters rather superficially, Cousin referred 'all he saw to this
scheme, as if it had been the cause and origin of the school system
which he found. But the fact is that Yon Altenstein’s document
was merely what we would call a a draft bill.” It was never
carried in the Chambers, and never became law, and it had no
more influence on education in Prussia than the several abortive
bills for education in Scotland have had on our parochial schools.
The curious thing is that Prussia, up to the present day, has never
had a substantive Educational Act. Several bills have been drawn
up, as for instance in 1819, in 1850, and in 1869, but they have
always been ultimately rejected. And the Liberals in Germany
are looking forward to the actual passing of an educational law,
after more than fifty years of unsuccessful attempts at legislation
in this department, as one of the first internal results which will
be achieved after- the conclusion of the present war.

It is true that the administration of public instruction in Prussia
is bureaucratic in the extreme ; but this is not the same as saying

311

of Edinburgh, Session 1870-71.

that the educational system has been created in a bureau. The
schools grew up in accordance with the ideas of the people ; the
character of the schools has been modified from time to time by
public opinion ; till within the last sixteen years the schools varied
according to the difference of the different provinces ; in short, the
central Government has only gradually and lately got its grasp on
that which it found, but did not create.

The Volksschulen , or people’s schools, in Prussia were in the
outset a product of the Reformation. The great characteristic of
Prussian popular education is universality of school attendance
under legal compulsion. Now, the legal compulsion is of com-
paratively late introduction. It was only brought in after the
sending of children to school had long been recognised as a religious
duty incumbent on all, and had thoroughly become a habit of the
people. Just as John Knox was the author of the parochial
school system of Scotland, so Martin Luther was the author of
the universal school attendance of Germany. The custom dates
from a circular letter which, in the year 1524, Luther addressed to
the burgomasters and councillors of all the towns in Germany. It
was a manly, earnest, powerful appeal, painting in strong colours
the neglected condition of the children, and urging that schools
should be provided for them. Luther pleaded that each child
should go to school for at least two hours a day, giving the rest of
its time, if absolutely necessary, to work. This letter had a striking
and permanent effect. The town councils, the landowners, and the
princes of Germany were stirred up to action ; new schools were
provided, and the old ones improved all over the country, and the
people gradually took up the idea and never dropt it, that to send
their children to school was a plain Christian duty.

At the beginning of the eighteenth century, in 1716, King
Frederick William, issuing certain ordinances for the regulation of
schools, assumes the universal attendance of unconfirmed persons ;
he merely gives his royal sanction to an existing practice. In
1763 an Allgememes Landschulreglement, or general regulation for
country schools, was issued, which for the first time defined the
age of school attendance, namely, from five to fourteen. Thus the
law was merely an expression, a ratification, and a definition of
the custom of the people.

312 Proceedings of the Royal Society

I will now mention the way in which the compulsion is carried
out. Compulsory school attendance may he of two kinds — either
(1) the parent may he obliged to show that the child is taught
somewhere ; or (2) the child may be compelled to attend a parti-
cular school for which it is registered. The second is, of course,
the harsher and more bureaucratic method, and it is distinctively
called Schuhwang , or school compulsion ; while the first and milder
obligation is Schulpflichtichkeit, or school duty. The second method,
while leaving less liberty to the parent, is more efficient from the
point of view of the State ; and as such it was adopted in Prussia
in 1857, and is now the law of the kingdom. The police-office of
each place makes out a list of children as they arrive at school age
—that is, five years old. It registers each child for the school
nearest its dwelling-place, and sends the list to the school board,
which now becomes responsible for the child not only joining the
school, hut also regularly attending for the next eight years — that
is, up to the time of its confirmation. The master keeps a register
of attendances, and in some places it is the custom, after the first
school hour, to send round a messenger to inquire after missing
children and the reason of their absence. Each case of absence is
marked by the master as “ excused ” or “ unexcused.” When un-
excused absences occur, it becomes the duty of the clergyman, as
chairman of the school board, or of some deputed member of the
hoard, to use moral suasion with the parent or guardian, with the
view of obtaining greater regularity. If these means fail, the
name of the parent or guardian is sent to the police-office, and he
is mulcted with a small fine for each unexcused absence, and, in
case of non-payment, is sent to gaol. Mr Mark Pattison (from
whose admirable report on the primary schools of G-ermany most
of my details for this part of the subject are taken) mentions that
in Berlin, in the year 1856, there were 1780 convictions for irre-
gular attendance, being rather more than three per cent, on the
whole number of children on the rolls of the schools. This was
thought a very large proportion, and was attributed to the growth
of pauperism, and consequent demoralisation in a large city. I
am sorry that I have not more recent statistics to offer, but the
system remains the same, and I think that we can see its general
working.

313

of Edinburgh, Session 1870-71.

In that same year, 1856, there were 2,943,251 children of school
age in all the Prussian provinces. Of these, 2,828,692 were in
attendance at elementary schools, public and private. Of the
remainder, 114,559, many were in attendance at the lower classes
of grammar schools and real schools, which are open to pupils of
nine years of age ; others were being educated at home ; a few
were doubtless invalids, or physically or mentally incapacitated ;
the residue, which must be small, represents the children of itine-
rating families who manage to escape getting upon any school
register. Even if we suppose that 100,000 children escaped school
attendance altogether, that would give less than three and a half
per cent, on the entire population of school-going age. But the
proportion for most of the provinces is nothing like so large. Out
of the recruits that joined the Prussian army during the past year,
it is true that exactly three and a-half per cent, of the troops had
never had any schooling. But the great bulk of the unfavourable
returns is made up of recruits from Posen, a Polish province which
has been called “ the Ireland of Prussia,” and from the natives of
East Prussia, whose vicinity to the frontier facilitates their evasion
of school attendance. From the province of Brandenburg, only
one-eighteenth per cent, of the recruits had not attended school.

On the whole, the law of compulsory attendance in Prussia may
be said to be perfectly efficacious in producing the result at which
it aims, and it appears to be very seldom complained of. Even in
the political disturbances of 1848" this law was not put forward as
one of the grievances against the Government. The law is
thoroughly in harmony with popular custom ; and just as in this
country it is a matter of course for the well-to-do classes to send
their children without any exception to school, so in Germany it is
equally a matter of course for the peasant and the labourer to send
off his children every morning to the school which the community
has provided. Day schools throughout Germany (as in Edinburgh)
are the rule for rich and poor alike, and there is an air of equality
given by the spectacle of rich children, as well as poor, goingroff
each day to their respective schools.

The Sclmlzwang, or compulsion to attend a particular school, is
of course relaxed in favour of the rich. The parent applies for
exemption, stating his reasons, and naming the school (generally a

314 Proceedings of the Royal Society

private one) to which his child is to be sent. In some places he
has to pay the school fee all the same to the school for which his
child was registered. In two parts of G-ermany there used to be
no law of compulsion, namely, in the free towns of Hamburg -and
Frankfort-on-the-Maine. Frankfort, however, has now become
Prussian. It was said that in these places the attendance of
children at school was quite as universal as in Prussia itself ; and
some persons argue that the custom of the people might be relied
on everywhere in Germany, and the law dispensed with. But we
have already seen that the growing pauperism of places like
Berlin tends to invalidate the custom. The law, at all events,
helps to keep the custom straight, else it might well he doubted
whether the ideas of the sixteenth century as to the duty of school
attendance could be kept alive in manufacturing centres, and in
very poor neighbourhoods. In the agricultural districts, it is said
that the farmers dislike schools because they raise wages ; in
manufacturing districts, the parents dislike schools because they
deprive them of a certain amount of wages which their children
might otherwise be earning. In the cotton manufacturing districts
of Saxony, the Government has made an equitable compromise
between the claims of industry and of school learning, by allowing
a system of half-time schools for children employed in the factories.
The children under this system appear to be ultimately as well
instructed as those under a whole time system. I think that this
experiment deserves particular attention. For I believe that chil-
dren up to nine or ten years’ old can learn as much in three hours
per diem as they could learn in six hours per diem, and that light
industrial tasks for the remainder of the day would rather tend to
develope the intelligence of the child. In Prussia the minimum
age for children being employed in a factory is twelve, and up to
fourteen no child must work more than six hours per diem. Thus
plenty of time is still left for attendance at a three hours’ school.

We have now to consider the funds by which the elementary
schools of Prussia are supported. There are very few endowments
available for them. The Government has at its disposal for educa-
tional purposes about L. 50, 000 per annum, derived from seques-
trated Church property, and from charitable bequests. But this is
almost entirely devoted to higher education. The elementary

of Edinburgh, Session 1870-71.

315

schools may be said, in a word, to be supported wholly by contri-
butions from the annual income of the community, in the shape of
— 1st, school fees ; 2d, local rate ; 3d, general taxation. The first
step towards providing for the maintenance of a Volksschule is,
that the proper authorities of the gemeinde, or commune, register
each family as assessed at a certain rate of school fees for any
children that may be of school-going age. In this country there
appears to he a sort of repugnance to the idea of a graded scale of
fees in proportion to the income of parents. But in Prussia
this is the first principle of public instruction. Fees are assessed
upon families not in relation to the cost of the school, but solely in
relation to the circumstances of those who are to pay the fees.
G-overnment, however, fixes a maximum and a minimum rate.
No child is to pay more than fifteen thalers, or about forty-four
shillings per annum ; and the lowest rate (from which there would
only he exemption in the case of extreme poverty) is one groschen,
that is about three halfpence, per week. Between these extremes
the assessment takes place.

The next source of revenue for the school consists in the collec-
tions made in the parish church during one Sunday in each year.
Then there is a small capitation tax on poor and rich alike, and,
finally, a rating on property, estimated by a loose valuation.

Grants from the general taxation of the country for elementary
schools are only made in cases where the commune can show real
inability, on account of the poverty of its inhabitants, to meet the
necessary cost. The Go vernm ent, however, has occasionally allowed
grants for increasing schoolmasters’ salaries. It is clear, then, that
as the fees are almost always extremely low, the burden of main-
taining the primary schools falls mainly upon the rate-payers.
This principle was introduced by the Allgemeines Landrecht , or
general code of Prussia of the year 1794, which lays down
that u where there are no endowments for the support of the
common schools, then the maintenance of the teacher falls upon
the collective householders, without distinction of religion. The
contributions requisite for this purpose, whether they he paid in
money or kind, must he equitably divided among the householders,
in the proportion of their property and holdings.”

To show the working of this system in a large city, it may be

316 Proceedings of the Poyal Society

mentioned that in Berlin (which has about three times the popu-
lation of Edinburgh) there were some time ago about 55,000
children in the elementary schools, and it was estimated that each
of these children, in addition to the school fees, cost the municipality
about L.l sterling per annum, — the total expenditure on this object
being about twelve per cent, on the municipal budget.

We have seen how the primary schools in Prussia are filled, and
how they are supported ; we have now to inquire how they are
managed. The Volksschule has never forgotten the tradition of
its origin, at the time of the Reformation, as an ecclesiastical
institution. The immediate and local management of all the
schools is practically in the hands of the clergy. The clergyman
of the parish is ex officio local inspector of the common school. He
is chairman of the school board, which consists of representatives
of the householders. He has really onerous duties in connection
with the school. He is expected to visit it constantly, in some
places as often as once a week. He is not merely the inspector of
the school in the sense of examiner and critic, but he is responsible
for its management and superintendence. He has to prepare the
children for confirmation by a religious lesson of at least an hour a
day for the two or three months preceding Easter.

The central power is said to regard the clergy as useful in
repressing the instinct of self-government in the commune. The
clergy are said generally to take a bureaucratic and centralising
point of view in the discharge of their functions as school inspectors.
But they have a difficult and thankless office. They have to
encounter the jealousy of the school board, and often the discontent
and mutiny of the schoolmaster, who has, perhaps, the chronic
grievance of an inadequate salary, and who, having been profes-
sionally prepared in a training college, finds himself controlled by
one who has no technical acquaintance with the details of school
management.

In the political disturbances of 1818-49 ^which were designated
as “ the schoolmasters’ rebellion ”), one of the great cries was for
the autonomy of schools, that is, for greater freedom from the
control of the Church. And this is one of the things which the
Prussian Liberals expect from the Educational Bill of the future.
They do not seem to ask for a secular system of instruction, but

317

of Edinburgh, Session 1870-71.

rather for emancipation from clerical management. The Govern-
ment depends much on the moral influence of the clergy in pro-
moting regular school attendance among the people, and generally
in playing a conciliatory part in relation both to the school board
and the master. In many cases the clergy appear to perform
these offices in a most Christian and self-denying spirit. But, on
the oth^r hand, they appear frequently to fall into a state of apathy
and indifference about the schools. Their labours, as school
inspectors, are an unremunerated addition to their proper functions,
and are such as often, individually, they have no taste for.

The present system is recommended by its cheapness, as under
it school inspection costs nothing to the Government. But, on the
whole, it can hardly be called successful, and it is probably doomed
to alteration. It is not only the clergy themselves, who in many
cases exhibit a want of interest in the schools, but the local com-
munities also have their sympathies chilled, in the first place, by
an over predominance of the clergy in school management, and,
secondly, by the excessive interference of bureaucratic action from
above. The nature of this bureaucratic action has now to be
described.

The kingdom of Prussia is divided into provinces, each province
into departments, each department into circles or districts, each
circle into parishes or communes. For the whole kingdom, the
central educational authority is, of course, the minister of public
worship, and medical and educational affairs. Beneath him there
is a gradually descending scale of officers, for the superintendence
of instruction on the system that a civil authority is always asso-
ciated with clerical or scholastic affairs. Thus for the province,
the president of the province is associated with a provincial school
council. For the department, the prefect of the department is
associated with a departmental school councillor. For the circle
or district, the landrath, or district councillor, is associated with
the superintendent, who is an ecclesiastic of about the same
dignity as an archdeacon in England, and who supervises the
inspection of schools in from twenty to forty parishes. In the
parish there is the school board associated with the local clergy-
man, who, as we have seen, is ex officio school inspector and school
manager.

2 x

VOL. VII.

318 Proceedings of the Royal Society

The provincial school council, in conjunction with the president
of the province, manages higher education alone.

All reports on primary instruction are sent up by the superin-
tendents of districts to the departmental school councillor, who, in
conjunction with the prefect of the department, forwards them
direct to the minister of instruction. The superintendent, though
an ecclesiastic, is said to act invariably in a bureaucratic, and not
a clerical spirit. It may easily be supposed that, with all this
network of reports radiating towards the centre, there is little
scope left for local action in the matter of the common schools.
Though the rate-payers furnish the funds, they have little to say
on their expenditure. The schoolmasters appear to be appointed,
not by the parish school boards, but in each case by the depart-
mental school councillor. For some time there was a certain
liberty left to individual masters and to local feeling in the kind
of teaching to be given in the schools ; but, in 1854, certain famous
Regulative , or Minutes of the Bureau of Public Instruction, were
issued, absolutely defining the subjects and manner of teaching.
Of these minutes I will speak presently. They gave final extinc-
tion to anything like local and characteristic life in connection
with the country schools.

In large towns they have another board called the Schul-depu-
tation, or school delegacy, for the collective management of the
city schools. These bodies were first created in 1808, when, under
Stein’s advice, every possible means was being adopted for calling
forth the energies of the nation, and, amongst other things, it was
thought desirable to awaken municipal life. In Berlin, the school
delegacy, consisting of chosen members of the town council, have
the management of all the schools, both higher and primary,
within the city, except a few which are of an exceptional character.
But the school delegacy has to report to the provincial council of
Brandenburg, and Mr Pattison mentions that on one occasion they
were reproved for too much independence, for having examined
some candidates as teachers in needle-work without having sought
the permission of the provincial government. In short, the central
power has of late evinced much jealousy of the school delegacies,
and has apparently wished to take back, or neutralise, the dangerous
concession of 1808.

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of Edinburgh^ Session 1870-71.

In Prussia the so-called “ religious difficulty ” has never existed.
The schools of every kind are religious and denominational. The
religious difficulty arises from a multiplicity of sects, and from
antagonism between established and non-established churches.
But in Prussia there are three leading confessions, all endowed
respectively in different localities, which cover almost the entire
population, — the Lutheran, the Keformed, and the Catholic. The
two first are conjoined for school purposes ; and thus we have the
denominational proportions of population stated some little time
ago, as follows : —

Protestant . . 64*64 per cent.

Catholic . . 32*71 „

Other creeds . . 2*65 „

Of these other creeds five-sixths were Jews, the remainder
Dissenters — such as Baptists, Mennonites, Irvingites, &c. This
phenomenon of more than ninety-seven per cent, of the population
belonging to established churches may remind us of the case of
Scotland, where, I believe, about eighty-eight per cent, of the
population belong, if not to one establishment, at all events to one
confession, without material doctrinal differences.

The Jews in Prussia, whenever congregated in sufficient numbers,
have schools of their own, with their own religious teaching. If
they exist in isolated families, their children attend the Christian
schools, and are generally not withdrawn even from the religious
teaching. They are said to look on instruction in Christianity as
a piece of useful or curious information, and. to be quite above the
fear of conversion. In this respect they are like a certain Brahmin
of Bengal, who, having attended a missionary school, reassured his
caste by telling them that.“ he had gone through the whole Bible,
and it had done him no harm.”

The Dissenters are obliged to attend the public schools, but they
are under the protection of a conscience clause. The authorities
require evidence that the children of Dissenters are taught religion
according to their own formulae by their respective clergy. The
Prussian constitution of 1851 contained the following article : —
“ In the ordering of public schools for the people, regard shall be
had to denominational relations. The religious instruction in the
people’s school is under the conduct of the respective religious

320 Proceedings of the Royal Society

bodies.” The conscience clause dates back from the Prussian
code of 1794, which lays down that “ admittance into the public
schools shall not be refused to any one on the ground of diversity
of religious confession. Children whom the laws of the State
allow to be brought up in any other religion than that which is
being taught in the public school, cannot be compelled to attend
the religious instruction given in the same.” This order, however,
except in the numerically insignificant case of the Dissenters, appears
seldom to have been put in force. Mixed schools, where teachers
of different confessions are associated together, have been tried
occasionally, but have not been found successful. It has long been
an established maxim in Prussia, that all schools must be denomi-
national, and, as a rule, every child appears to find him or herself
at a school belonging to his or her religious denomination.

The obstacles in the way of legislating for the instruction of the
people in this country arise in limine from differences of opinion
as to the questions of religious teaching, school management,
rating, and compulsory attendance. The obstacles in the way of
educational legislation in Prussia arise from differences of opinion
as to the relation of Church and State to local communities. But
in Prussia the difficulty is only about altering the character of a
system. The system is there, and is complete enough in itself.
The only question is, Could not a better and freer system be intro-
duced? We have seen how the Prussian people, following the
advice of Luther, adopted universal school attendance as a national
habit; how this habit was ratified and confirmed by law in the
eighteenth century ; how the support of people’s schools was thrown
on the householders by the code of 1794 ; and how, by common
consent, and by law, the schools have remained denominational,
with a conscience clause for the benefit of a very small section of
the population. Thus has Prussia, in the march of time, quietly
stepped over all those preliminary and merely parliamentary
difficulties, which in this country have so long prevented large
numbers of the people from getting any school education at all,
while Lords and Commons have been wrangling as to the exact
form under which the schools were to be started.

But all this touches merely the external politics of public
instruction. The question remains, What is the teaching in the

oj Edinburgh , Session 1870-71.

321

people's school when you have got it established? On this point
the experience of Prussia is not uninteresting. The elementary
school in Prussia was, in its origin, a catechetical instruction ; it
was a repetition by some subordinate ecclesiastic of the Sunday
catechising of the pastor. Gradually the teaching of reading and
singing was added, hut only as a means to a religious end, namely,
reading the Bible and singing in church. By the middle of the
eighteenth century more secular elements of instruction were grafted
on ; and Frederick II., in 1763, orders that “the people shall be
Christianly brought up in reading, praying, chanting, writing and
arithmetic, catechism, and Bible history. The Prussian code of
1794 lays down that schools and universities are “ institutions of
the State.” It prescribes the teaching of religion as a part of
useful knowledge, and as tending to make good and obedient
citizens. At the end of the last century the Prussian elementary
schools appear to have been easy-going mechanical institutions,
with nothing about them specially to call for remark. But an
immense ferment in relation to them was preparing, a passionate
upstirring of the whole question of popular education, endless
theory and counter theory, action and reaction, the history of
which constitutes a whole literature, and the effects of which have
all been felt upoir the character of the Prussian VoTksschulen ,
which now remain like the fossilised result and record of the
storms of the past.

All this commotion rose from the fervid brain and heart of one
man, Henry Pestalozzi, a Swiss, who was born at Zurich in 1746.
Pestalozzi was a loving enthusiast ; of a most unpractical turn of
mind ; always embarking in visionary schemes for the good of
others ; of a large and noble heart, living a life of poverty and
struggle himself, but always spending his whole strength in efforts
for the welfare of the poor. He lived to be eighty-one years old,
and long before his death he had been publicly visited and
honoured by emperors, kings, and statesmen, and had seen his
ideas warmly received and widely spread over the continent of
Europe. Pestalozzi was much influenced in early youth by reading
the “Emile” of Rousseau. In 1780 and subsequent years, after
many failures in life, he began to bring out books on education.
The chief of these were, “ The Evening Hour of a Hermit,” con-

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taming educational and religious aphorisms ; and “ Leonard and
Gertrude,” a story to illustrate what might be done by a particular
method of teaching children. These and other writings of his
excited great attention. lie had successively different schools
under his management, in which he developed his system by prac-
tical experiment. Finally, at Yverdun, in the year 1805, he had
obtained care of an institution which has now become a classical
name in the history of pedagogy.

Pestalozzi’s fundamental idea was that the children of the poor,
in a public school, should be taught as if by an affectionate mother,
who entered into all their feelings, and anticipated their difficulties.
His conception was that primary instruction should not consist in
giving knowledge verbally, mechanically, or by rote, but in drawing
out the powers of the child. He laid it down that no child should
be taught anything which it could not understand. The first
development of this idea resulted in lessons upon form, number,
and language. At Yverdun, Pestalozzi would carry his class
through a lesson of the following kind : — Pointing to the wall, he
would say, —

“ Boys, what do you see V*

(Answer) u A hole in the wainscot.”

“ Very good ; now repeat after me —

u I see a hole in the wainscot.

“ I see a long hole in the wainscot.

“ Through the hole I see the wall.

“ Through the long narrow hole I see the wall.

“ I see figures on the paperhangings.

■ “ I see black figures on the paperhangings.

“ I see round black figures on the paperhangings.

“ I see a square yellow figure on the paperhangings.

“ Beside the square yellow figure, I see a black round figure.

“ The square figure is joined to the round one by a thick black
stroke.” And so on.

It was said that Pestalozzi used to shout out sentences of this
kind without any explanation, and was echoed in chorus by the
class. It is true that words in this way became associated with
impressions of the sense. But if this were all, we should say that
Pestalozzi was incapable of developing his own theoretical idea.

323

of Edinburgh, Session 1870-71.

A trace of such teaching reached this country in the shape of the
so-called “object lessons,” which, without much fruit, were once in
vogue in England.

But the Pestalozzian method had in reality far greater results.
A swarm of enthusiastic assistants, perhaps more clear-headed
than their master, came to serve under him ; and by them there
was worked out —

(1.) All sorts of methods for conveying in an easy manner to the
child the arts of spelling, reading, ciphering, and so on.

(2.) The practice of a sort of Socratic dialogue, for developing
the intelligence of the class upon the subject of the lesson, what-
ever it might be.

(3.) The idea of pedagogy as a science, based upon psychological
data.

(4.) The idea that religion, which with Pestalozzi was made the
basis of all, must not be taught dogmatically and confessionally,
but rather universally ; in short, that the first teachings must be
of natural religion, and not of the religion of any Church.

All this was new, and it had a peculiar fascination for several
of the greatest minds of the age. When, in 1806, Prussia was
crushed by Napoleon, and went through afflictions strikingly
analogous to those that have now befallen France, Stein and
Fichte, the statesman and the philosopher, both earnestly pro-
claimed that the moral energies of the nation must be regenerated
by the universal adoption of the Pestalozzian ideas. Pestalozzian
schools were established over the country, and in subsequent years
the system was thoroughly exploited ; all its strength and weak-
ness were brought to the full light of trial and experience.

The result of fifty years’ exhibition and discussion of the Pesta-
lozzian system has been as follows : —

(1.) There is a considerable residuum in the shape of excellent
technical methods for teaching the elements of knowledge. Thus
each child is taught to read easily, alone, within twelve months.
The old plan of first learning the names of the letters, and then
spelling, is abandoned. In arithmetic, the child is taken through
the operations of the four rules, both in integers and fractions in
the tens, before he reaches the hundreds. The magnitudes to be
dealt with form the only distinction between the classes in arith-

324 Proceedings of the Royal Society

metic. These and other methods are the result of the immense
attention which has been bestowed on the question of primary
teaching.

(2.) Public opinion has pronounced against much that was char-
acteristic of the Pestalozzian system. From the principle that
children should be taught nothing that they could not understand,
there was deduced the practice of much abstract and formal
lecturing, totally unsuited to children from six to nine years of
age. Thus, lessons on the theory of number were made to precede
empirical teaching of arithmetic. While much stilted talk was
used both about the children and to the children, it was found that,
in many cases, they were suffered to go through school without
learning to read and write. A general reaction set in against the
idea of intellectual training in common schools.

(3.) This tendency of public opinion was taken up and ratified
by the G-overnment. In October 1854, Regulative , or Minutes from
the Office of Public Instruction in Berlin, were issued, which bear
a close analogy in some points to the revised code of Mr Lowe.
The object of these minutes was to restrict the teaching in elemen-
tary schools to a few humble and necessary subjects, and to ensure
these subjects being efficiently taught. In direct opposition to
Pestalozzi, the Regulative proceeded on the principle that, in an
elementary school, it is not the object to develope the child’s
reasoning faculties, or to give him knowledge, but only to give him
the power of doing certain things ; — Konnen, and not wissen, was
to be the result to be produced. The schools were to turn out the
children in possession of the actual capacities (fertigheiten) of reading,
writing, and ordinary ciphering, and everything outside of this range
was to be sternly excluded. Thus the children were on no account
to learn grammar, as this is an abstract, logical thing, suited to the
high school ; whereas, in an elementary school, children should
learn to use their own language correctly by practice, and not by
rules. Even mental arithmetic was to be excluded, as being a
needless fatigue of the brain. Of secular subjects, in addition to
the three B-s, only singing was as a general rule to be taught,
for the sake of practising the voice and ear. Only church tunes %
and national songs were to be permitted, the words being previ-
ously well studied and explained. History and geography were

325

of Edinburgh, Session 1870-71.

discouraged ; if taught at all, they must be limited to Heimaths-
kunde, or information about the child’s native land. Drawing, if in-
troduced, must be confined to linear freehand copying from the flat.

Religion remained an essential and prominent element for the
people’s schools, but the Regulative made a great change in regard
to the mode of imparting it. Under the Pestalozzian system,
religion had been taught not confessionally, but universally; not
as a matter of Church formulas, but in a free and spiritual way,
which, of course, depended for its characteristics very much on the
individual master. When the time for confirmation arrived, the
clergyman would find the children furnished with ideas, more or
less orthodox, of natural religion and of Christianity, but perhaps
never having seen the Church Catechism, and the labour would
devolve on him of making them learn this. It appeared to the
Government that the schools, though denominational in their
foundation, were too independent of the Church in their religious
teaching. The Regulative , by one stroke, altered all this. They
laid down exactly what was to be taught in the shape of religion,
namely, some fifty hymns were to be learnt by heart, the whole of
the gospel portions which are read in the Lutheran churches were
to be committed to memory, and the Catechism (either Luther’s or
the Heidelberg) was to be learned off by rote, without any explana-
tion. All explanation of the doctrine contained in it was to be
reserved for the pastor, when the time of confirmation drew nigh.
By these rules, the relative positions of the clergyman and the
schoolmaster were completely subverted. All the charm of teaching
religion to the children was taken away from the master, whose
task was, in this respect, made mechanical, while he himself was
made completely subordinate to the clergyman.

The minutes on religious teaching had, doubtless, a political and
ecclesiastical motive, and a reaction against them is possibly in
preparation. Those regulating the secular subjects in the people’s
schools are a specimen of the Prussian Government, as a powerful de-
cisive will, proposing to itself certain definite ends, and going straight
at these ends without compromise or collateral considerations.

In the case of the elementary schools, there can be no doubt
that the end aimed at is attained ; for the schools embrace the
entire population, and the result is, that the children of every

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326 Proceedings of the Royal Society

peasant and labourer have, as a matter of course, the arts of
reading, writing, and cyphering, know the Church formulae and a
good deal of the Bible, and can take part in singing a hymn or
national chorus.

But I think that one misses in these schools anything calculated
to raise the intelligence of the people, anything analogous to the
influence of the parochial schools of Scotland. The repression of
the high-flown Pestalozzian aspirations has been too absolute.
The definition of an elementary school has been too logical.
There is nothing to lead on towards the higher grades of education.
The people’s school seems sharply separated off, and to give the
children of the people no encouragement or opportunity to rise.
One proof of this may be found in the fact that pupils who, at
fourteen years of age, have passed eight years in the primary
school, and who then have two years further preparation under a
public schoolmaster or clergyman, are, at sixteen years of age,
commonly unfit to enter upon the very simple curriculum of the
training college.

It may be asked whether industrial or technical instruction does
not form part of the Prussian system ? But in the ordinary
people’s school nothing of this kind is attempted. The Prussian
Educational Department conceives that it has a particular function
to discharge for the people, and of this it acquits itself, and does
no more. It is argued that seven or eight years’ schooling, at the
rate of twenty-six hours per week, is not more than sufficient for
imparting to all with certainty the elements of common knowledge
and religion, and that any attempt at technical instruction would
only interfere with this ; and everything technical must be learnt
practically, or otherwise, after the age of fourteen. One means of
supplementing the meagre results of the people’s schools, consists
in the Fort-bildungsanstalten, or improvement schools.” These
exist generally in the shape of evening classes in mathematics,
French, &c., for youths and adults. They have not been organised
systematically, and even if they were, could hardly supply the
want of a more early awakening of the intellect.

But, of course, many children, and some even of the poor, quit
the elementary school at nine years of age, to enter on the course
of higher instruction.

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of Edinburgh, Session 1870-71.

In all the departments of higher instruction, Prussia seems to
me to be distinctly ahead of England, and still more so of Scotland.
But I have already take up so much of your time, that I mnst now
confine myself to a few aphorisms on this subject. In Prussia
education is considered to be so completely a matter of national
concern, as always to call for the supervision of the State. No man
may start a private school, whether primary, middle, or higher,
without a license from the educational office. And this license is
only given after the passing of prescribed examinations. The too
common charlatanry of private schoolmasters in England is thus
avoided. A useful censorship of schoolbooks is exercised by the
minister of instruction. By this the crotchets of schoolmasters in
the use of eccentric and useless hooks are checked.

The minister of instruction is not only a man of science or
learning himself, hut he has the advice of councillors of the highest
scientific and literary reputation. The opinions of such a central
board on questions of higher instruction are not merely bureau-
cratic edicts, but constitute a valuable intellectual guidance.

With regard to resources, the following distinction is to be
observed in Prussia. The elementary schools get very little money
from Government, only a small contribution from school fees, and
the great bulk of their expenses from parish and municipal rating.
The support of the higher schools of all kinds appear to be as
follows : —

From Fees, a proportion of

5A

From Municipal assignments,

2

From Grants by Government,

1-6

From Endowments,

1-

Thus the fees of scholars pay considerably more than half the
cost of the higher schools. Municipal contributions amount to
one-fifth, and grants from general taxation to nearly one-fifth,
endowments to one-tenth. Fees in the high schools are often
remitted wholly or partially on the ground of the circumstances of
the parents. Out of about 90,000 scholars attending the superior
schools of Prussia, about 20,000 appear to be wholly or partially
free scholars.

The higher education goes in Prussia, the more entirely does it

328 Proceedings of the Royal Society

become recognised as a proper object for State maintenance. Thus
the universities, so far as their own resources fall short, are fully-
supplied by the Government. The University of Berlin, in the year
1864, had an income of about L.30,000. Of this, L.24 only was
the interest of funded property of the University; L.1133 was the
amount of entrance and examination fees ; L. 28, 842 was the grant
from Government.

If we compare with this the University of Edinburgh, we find
the income for the current year to be L.20,351, of which L.4153
are fees of various kinds, L.9869 funds from private endowments
and other sources in the hands of the Senatus, L.6329 parliamen-
tary grants. This shows how comparatively small is the proportion
of State assistance to our University.

The higher schools of Prussia consist of two distinct branches. —
the Gymnasien, or grammar schools, with their Pro-Gymnasien , or
preparatory grammar schools, and the Real-scliulen , or scientific
schools, with the “ higher burgher schools ” in preparation for
them. The Gymnasien are, of course, the product of the Middle
Ages, the Renaissance, and the Reformation. The Real-schulen
sprang from the modern protest on behalf of science against the
predominant claims of classics. The Gymnasium is a first-rate
classical day school, with a time-table of 30 hours per week. It
has six classes, Prima being the highest. The 30 hours in Prima
are thus allotted : — Religion, 2 ; German, 3 ; Latin, 8 ; Greek, 6 ;
French, 2; History and Geography, 3; Mathematics, 4; Physics,
2. Besides these school hours there is extra-time instruction in
singing and gymnastics ; and those who propose subsequently to
study theology or philology in the University are required to learn
Hebrew, also in extra hours.

The time-table, though thus definitely prescribed, is not rigidly
adhered to ; for promising pupils in the first class are allowed a
good deal of liberty for private study in lieu of the stated lessons.

Many enter the Gymnasium irrespective of an intention to proceed
to the University, for the sake of the privileges which it holds out.
For, those who have gone through the classes and passed the leaving
examination, besides qualifying for the public service, are allowed
to serve for one year as volunteers in the army, instead of three
years according to the ordinary course.

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of Edinburgh, Session 1870-71.

But yet it is endeavoured to keep up a thoroughly intellectual
atmosphere in the Gymnasiens. The Prussian Government lays it
down that culture for its own sake, and not with any premature
regard to the practical exigencies of life, is to be the object of these
schools. And it expressly forbids that those who propose to enter
the army as a profession, should abate any of the higher classical
studies of the first class. This is certainly very different from the
principle adopted in English public schools.

The crowning result, and the most distinctive feature of the
Gymnasium is the abiturienten-examen , or leaving examination.
The certificate of having passed this examination is, of course,
ardently desired by the pupils, as it is the key to entry into any of
the learned professions, and gives important exemption in military
service. This being the case, it may be affirmed that in this
country an analogous examination would often lead to over-
strenuous preparation on the part of the pupils when the time of
the examination drew nigh.., But the Prussian Government takes
the greatest care to obviate a result which they would deem utterly
unsatisfactory. They lay down the strictest rules, both in general
terms and in 'detail, to prevent the examination being of a kind for
which any special preparation, spasmodic efforts, or cram would be
of any avail. It is by no means to turn upon the learning up of
names, dates, and isolated facts; but it is to exhibit (as the
educational minute says) “the slowly ripened fruit of a regular and
contant industry throughout the whole school course.”

With this object, one of the grounds for the certificate is made
to consist in a record of the pupil’s work throughout perhaps the
nine previous years in all the classes of the Gymnasium from sexta
to jorima. In addition to this, the examination is to show how
much of the school study has really been assimilated by the pupil,
and has become part of himself. The Prussians are much wiser
than some other countries in the matter of examinations. They
always keep in view the exact end they are aiming at. In the
abiturienten-examen they don’t want a paper, but a man ; and they
certainly adopt the best means of testing the man’s real acquire-
ments and deserts, when, on the one hand, the examiners have
before them a continuous record of his previous work for years,
and, on the other hand, submit him to such general exercises in

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languages and mathematics as show in each subject what amount
of proficiency he has really available. The examiners consist of
the upper masters of the school itself, with certain commissioners
from the G-overnment associated with then. Persons who have
been brought up in private high schools, and who wish to proceed
to the University, must present themselves at the examination of
the G-ymnasium, where they will be equitably examined. But on
the whole the public schools are most popular in Prussia, and the
scholars of private schools are quite in a minority. The paper
work of the examination occupies a week. The chief subjects are
— (1.) An essay in German, which is intended to exhibit general
culture, taste, and correct writing. It is analogous to the English
composition in the Indian Civil Service competition. (2.) A Latin
essay. (3.) A piece of simple G-reek prose to he written. (4.) A
translation of G-erman into French. (5.) Two geometrical and two
arithmetical problems to be solved. A viva voce examination
follows, consisting of translation from pieces, not prepared in class,
of the Latin and G-reek authors, questions in metre, mythology,
history combined with geography, and antiquities; conversation
in Latin ; examination in Bible history and the Church Cate-
chism ; and for future philologists and theologians, an examination
in Hebrew.

The certificate which each candidate receives is marked either
“ insufficient,” “sufficient,” “good,” or “excellent.” The mark
“ insufficient ” is meant to indicate unripeness for the University.
The pupil receiving it is recommended to prolong his attendance
at school, or to seek some other career in life for which University
study is not required. But if he and his parents wish it, he may
still enter the University, with his certificate of “unripeness.” In
that case he will be restricted to the faculty of philosophy, and not
allowed to enter any learned profession, unless he can, by subse-
quently presenting himself at the gymnasial examination, obtain
a certificate of being “ripe;” and in the meantime he will be
debarred from holding any University scholarships or stipends.
The holders of favourable certificates, with “good ” or “excellent”
for their examination, and a full record of previous conduct and
performances, carry with them an important testimonial for the
outset of life.

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331

In all these arrangements of the leaving examination of high
schools, we see, I think, that Prussia dares to be thorough in a
matter of this kind. She insists that high schools should do their
work, and by giving the universities, the public service, and the
learned professions an organic connection with these schools, she
makes it a very serious matter for all the pupils to take advantage
of their opportunities. Without any apparent strain upon the
pupils, she succeeds in obtaining a higher standard of results from
school boys than is implied in the ordinary M.A. degree of the
Scotch universities, or the ordinary B.A. degree of Oxford or
Cambridge.

Of the Eeal-schulen , or scientific schools, I have not much to say.
Started originally more than a hundred years ago, it is only within
the last fifty years that they have had a considerable development.
Of the 90,000 pupils attendant on secondary schools in Prussia,
about 30,000 appear to go to the Eeal-schulen or their preparatories.
These schools do not prepare for the universities, but for business,
certain departments of the public service (such as architecture or
mining), and for the Polytechnic College.

The time-table for Prima in a Eeal-schule consists of thirty-two
hours, made up as follows : — Religion, 2 ; German, 3 ; Latin, 3 ;
French, 4; English, 3; Geography and History, 3 ; Natural Sciences,
6 ; Mathematics, 5 ; Drawing, 3. Latin, however, is not insisted
on, and a liberty is left to the school delegacy of adjusting the
subjects in some degree to the necessities of the immediate neigh-
bourhood, with reference either to particular languages or parti-
cular industries, that may exist. A suitable leaving examination
is prescribed, qualifying the holders of certificates for military
exemption and for the public service.

An eminent authority, Dr Jager, told Dr Matthew Arnold that
the Eeal-schulen were not considered successful institutions. He
said that the boys in corresponding classes of the classical schools
beat the Eeal-schule boys in subjects which both do alike, such as
history, geography, German, and even French, on which the Eeal-
schule boys spend much more time. Dr Jager assigned as the
cause for this result that classical training strengthens a boy’s
mind more than modern or scientific teaching. I confess, how-
ever, that I think the comparison, as stated, not quite complete,

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as in matters not connected with language and history the JReal-
schule boys might be found to have faculties of observation and
deduction to which the classical boys would be strangers. I merely
state what has been said.

Turning now to the universities of Prussia, we find ourselves in
the region of pure unfettered science. The abiturienten-examen of
the classical schools gives the universities such a starting ground
in the thorough previous education of all the students who matri-
culate, that they are able to commence the treatment of all subjects
on a high scientific level, in confidence that such a mode of treat-
ment will be followed and understood.

The appointments of professors are invariably made, so far as I
can learn, on the grounds of greatest scientific eminence. The
appointments are all in the hands of the Crown — that is, of the
minister of instruction. When a vacancy occurs, the faculty to
which the chair belongs sends up a short leet of names to be recom-
mended to the minister, and from these he generally makes the
appointment. But I believe that the name chosen is always that
of the man whom previous public performances and general opinion
in the scientific world have designated for the place. I believe
that anything like political or theological bias in the appointment
of professors is unheard of. Other personal considerations (which
might be more plausibly entertained) are also omitted, such as
power of clear exposition and capacity for managing a class.
Hence it may happen that the professor, when appointed, is obscure
in style and unattractive as a lecturer ; but the students have, at
all events, the feeling that in him they have the greatest authority
that could be found on the particular subject. And there is in
G-erman universities a general consciousness that it is better to
have the last and most reliable results in science than to have a
popular exposition of what is old and perhaps exploded. The
professor has a fixed salary from Gfovernment, frequently amounting
to L.350 or L.400 a year, in addition to a share of examination fees
and the fees of his class. But* he is bound to lecture free of charge
twice a week. The fees in theology or philosophy are about 17s.
for the six months. In the medical classes they go as high as
L.l, 14s. 5d. for the course. Several professors have altogether an
income of from L.1000 to L.1500 a year, which, in proportion to

333

of Edinburgh, Session 1870-71.

ordinary rates of expenditure in (Germany, is something consider-
able. We all know that the headmasters of Eton and Rugby
realise L.4000 or L.5000 per annum, which is probably superior to
most university emoluments within the United Kingdom. But no-
thing of the kind occurs in Prussia ; the highest schoolmasterships
are below, both in rank and emolument, the ordinary run of professor-
ships. The best school appointment in Prussia appears to be the
rectorship of the Schul-Pforta , an endowed gymnasium in Prussian
Saxony; to this L.300 per annum and a house are attached. The
professors, being fairly endowed by (Government, are far from being
sheltered from competition by any kind of monopoly. The State
can always appoint any eminent man as full professor, even in a
faculty which has already its full complement. Then, secondly,
the State at its pleasure appoints extraordinary or assistant pro-
fessors, who have a small salary, their chief reliance being on fees.
Thirdly, the Faculties appoint as Privat-docenten persons who can
prove their fitness. . The Privat-docenten appear not to fulfil the
functions of what we should call tutors, but rather to be analogous
to our extra-academical lecturers in the Medical Faculty. The
Privat-docenten and the extraordinary professors form a reserve of
men, establishing their reputations, from whom the future full pro-
fessors will he chosen. Before the beginning of the session a
harmonious arrangement is made between the professors, extra-
ordinary professors, and Privat-docenten , in a Faculty, as to the
subjects on which each is to lecture, so as to cover the whole field
of instruction proper to the Faculty. The dean then publishes the
programme, and the only restriction is that the fees must be
uniform.

There is, in short, absolute liberty of teaching to those who can
prove their competent knowledge of any subject; and there is
equal liberty of learning, for no student is obliged to attend any
particular courses, or number of lectures, with a view to his degree.
All that general culture which we endeavour to ensure by our Arts
curriculum is provided in Prussia beforehand by the abiturienten -
examen , and the student is considered fit to choose absolutely for
himself his own University curriculum. In the professional Faculties
he, of course, cannot dispense with instruction in all the separate
branches; but in the Faculty of Philosophy, which answers to our

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VOL. VII.

334

Proceedings of the Poyal Society

Faculty of Arts, and embraces the humanities and the mathematical
and natural sciences, tlie student is allowed to choose any two sub-
jects he likes for his final examination; and if he passes in these,
he gets his degree as Doctor of Philosophy. To pass, however, in
any subject is supposed to imply, not a schoolboy preparation, but
a manly mastery of the whole subject. For instance, in order to
pass in G-reek and Latin philology a student would be called on to
revise the readings in some Greek or Latin book, with scholarly
reasons for all his opinions on each point, and, in addition, to show,
viva voce , a complete knowledge of classical literature, philology,
and antiquities. The liberty allowed to students is doubtless often
abused. In a recent life of the Count von Bismarck it is men-
tioned that, while attending the University of Berlin, he fought
innumerable duels, and only attended one lecture. That lecture
was by the eminent Professor Savigny; but Bismarck, thinking
that he did not gain within the hour as much information as would
suit his purposes, abandoned the course, and applied himself to a
repetitor or crammer, by whose assistance he succeeded in passing
the examination of the Law Faculty.

On the whole, there is probably not so much industry among the
students of a German as of a Scotch University; but there is far
more than at Oxford or Cambridge. And whenever industry exists,
being based on more complete previous preparation, and being in
relation to really scientific lectures, it is probably of a higher and
more fruitful kind than can be found among the students of Great
Britain.

Still, complaints are made against the Prussian university
system. One of these is, that the students are too exclusively
engaged in taking notes of lectures, and that they have too little
practice of their creative faculties. The prejudicial effects of this
may, perhaps, be traced in the want of the graces of style which
characterises to so great an extent most German books.

Another complaint is, that the students., though systematically
prepared up to entrance into the university, are afterwards left
without sufficient guidance as to the order in which they should
take up successive subjects.

It is quite possible that Prussia, which honestly and thoroughly
desires the best in education, may descend a little from the clouds

335

of Edinburgh, Session 1870-71.

in its university system, and deign to adopt something like the
Little-go or Moderations examination of the English universities,
though such an examination in Prussia would be, of course, on a
distinctly higher level. Prussia might, perhaps, with advantage
curtail a little the liberty of her universities, and increase a little
the liberty of her primary schools, in respect both of studies and
management. She might allow a more easy and natural connec-
tion than appears to exist between the primary school and higher
education. She would like also to see a gradual relaxing of the
leading strings of Government, and a greater development of cul-
tivated local energies. It would be a great misfortune for the new-
born German empire if military successes should be found to have
intensified the centralising forces in all the affairs of national life.
The Liberals appear sanguine that this will not be the case. But
a struggle on questions of internal policy may very likely succeed
the conflicts of the war. In the meanwhile, on the educational
question Germany and England hold positions the very opposite
of each other. In Germany there is the idea of what is wanted,
and a universal carrying out of that idea. But too much comes
from the central power. There is a deficiency of communal life
and independent individual action. The question with Germany
is how to shift, without losing, the motive power. In England
there is abundant local action and vitality, but a deficiency in cul-
tivated guidance for that action. There is with us an immense lee-
way to make up, both in overtaking, with primary instruction the
masses of the people, and also quite as much in regulating and
defining the aims and the method of secondary and university
education. The great question for England in this matter seems
to be, first, how to get over religious difficulties in the way of
primary instruction ; and, secondly, how to obtain a sufficiently
enlightened guidance for our higher education, without adopting,
which all ought to deprecate, anything like a bureaucratic system.

336

Proceedings of the Royal Society

On the Physiology of Wings : being an Analysis of the
Movements by which Flight is produced in the Insect, Bat,
and Bird. By James Bell Pettigrew, M.D., F.R.S. Com-
municated by Professor Turner.

(Abstract.)

(Received 2d August 1870.)

In the present memoir the author enters very fully into the
figure-of-8 wave movements , described by the wing in space, to which
he first directed attention in March 1867.* He has adduced the
experiments with natural and artificial wings, on which his descrip-
tion was originally based, and has shown, by the aid of original
models and a large number of diagrams and drawings, that artificial
wings can be made to approach indefinitely near to natural ones ,
not only in their structure, hut also in their movements. He
further points out that the fins and tail of the fish — the flippers
and caudal extremity of the whale, dugong, manatee, and porpoise,
and the flippers of the seal, sea bear, walrus, and turtle — hear a
close analogy to wings, and ought to be studied in connection with
them. As further proof that the wing describes a figure-of-8 wave-
track in flight, the author cites the results announced in February
1869 by Professor J. B. Marey, of Paris.f

* Vide “ The Various Modes of Flight in Relation to Aeronautics ; ” by the
Author in the “ Proceedings of the Royal Institution of Great Britain for
March 22, 1867 ; ” also his memoir “ On the Mechanical Appliances by which
Flight is attained in the Animal Kingdom,” read to the Linnean Society of
London on the 6th and 20th of June 1867, and published in extenso in the
26th volume of their Transactions, a large number of woodcuts and engrav-
ings being specially devoted to the elucidation of the figure-of-8 wave track
made by the wing as observed in the flight of the insect, bat, and bird.

t “ Revue des Cours Scientifiques de la France et de l’Etranger.” Professor
Marey, in a letter addressed to the French Academy, under date May 16, 1870,
fully acknowledges the author’s claim to priority (as regards himself) in the
discovery of the figure-of-8 wave movements made by the wing in flying. M. Marey,
in the letter referred to, states (“ Comptes Rendus,” page 1093, May 16,
1870), “ J’ai constate qu’ effectivement M. Pettigrew a vu avant moi, et
represente dans son Memoire, la forme en 8 du parcours d© l’aile de l’insecte:
que la methode optique a laquelle j’avais recours est a peu pres identique a

la sienne je m’ empresse de satisfaire a cette demande legitime,

et je laisse entierement la priorite sur moi, a M. Pettigrew relativement a la
question ainsi restreinte,”

of Edinburgh, Session 1870-71.

337

Professor Marey, by employing a sphygmograph similar to
that used for ascertaining the state of the pulse, succeeded in
causing the wings of insects and birds to register their own move-
ments. He says : — “ But if the frequency of the movements of
“ the wing vary, the form does not vary. It is invariably the same ;
“ it is always a double loop , a figure of 8. Whether this figure be
“ more or less apparent, whether its branches be more or less equal,
11 matters little; it exists, and an attentive examination will not fail
“ to reveal it.” *

The subjoined are a few of the results obtained by the author in
the course of his numerous observations and experiments: —

The wing is of a generally triangular form. It is finely gradu-
ated, and tapers from the root towards the tip, and from the anterior
margin towards the posterior margin. It is likewise slightly twisted
upon itself, and this remark holds true also of the primary or rowing
feathers of the wing of the bird. The wing is convex above and
concave below, this shape, and the fact that in flight the wing is
carried obliquely forward like a kite, enabling it to penetrate the
air with its dorsal surface during the up stroke, and to seize it with
its ventral one alike during the down and up strokes. The same re-
mark applies to the remiges or rowing feathers of the wing of the
bird.

The wing is moveable in all its parts; it is also elastic. Its
power of changing form enables it to be wielded intelligently, even
to its extremity ; its elasticity prevents shock, and contributes to
its continued play. The wing of the insect is usually in one
piece,f that of the bat and bird always in several. The curtain of
the wing is continuous in the bat, because of a delicate elastic
membrane which extends between the fingers of the hand and along
the arm ; that of the bird is non-continuous, owing to the presence
of feathers, which open and close like so many valves during the up
and down strokes.

The posterior margin of the wing of the insect, bat, and bird, is
rotated downwards and forwards during extension, and upwards

* Revue des Cours Scientifiques de la France et de l’Etranger, p. 252.
20th March 1869.

f The wings of the beetles are jointed, so that they can be folded up
beneath the elytra or wing cases,

338

Proceedings of the Royal Society

and backwards during flexion. The wing during its vibration
descends farther below the body than it rises above it. This is
necessary for elevating purposes.

The distal portion of the posterior margin of the wing of the
insect is twisted in a downward and forward direction at the end
of the down stroke, whereas, at the end of the up stroke it is
twisted downwards and backwards. The proximal portion of the
posterior margin always assumes a reverse position to that occupied
by the distal portion, so that the posterior and anterior margins of
the wing are not in the same plane, and in certain situations the
two margins appear to cross each other. What is here said of
the insect’s wing applies equally to the wings of the bat and
bird.

The wing during its vibrations twists and untwists , so that it acts
as a reversing reciprocating screw. The wing is consequently a
screw structurally and functionally .

The blur or impression produced on the eye by the rapidly
oscillating wing is twisted upon itself \ and resembles the blade of an
ordinary screw propeller.

The twisted configuration of the wing and its screwing action
are due to the presence of figure- of- 8 looped curves on its anterior and
posterior margins ; these curves, when the wing is vibrating, re-
versing and reciprocating in such a manner as to make the wing
change form in all its parts. The curves in question are produced to
a great extent by vital movements, independently alike of the elas-
ticity of the wing and the reaction of the air. They can, however,
be produced by the latter agencies likewise. The change and
reversal of the curves occurring on the anterior and posterior
margins cause the different portions of the wing to strike at various
angles during the down and up strokes.

The angles which the different parts of the wing make with the
horizon are greatest towards the root, and least towards the tip of
the wing. The angles are, in fact, adjusted to the speed at which
the different portions of the wing travel — a large angle with a low
speed giving the same amount of buoying and propelling power as
a small angle with a high speed.

The speed attained by the tip of the wing is always very much
higher than that attained by those portions nearer the root— the

of Edinburgh, Session 1870-71.

339

root corresponding to the short axis of rotation. (The long axis of
rotation runs along the anterior margin of the wing.)

The angles which the wing makes with the horizon are increased
during the down stroke, and decreased during the up stroke, the
posterior margin of the wing being screwed down upon the air
during the down stroke to increase the elevating and propelling
power of the wing, and unscrewed or withdrawn from the air during
the up stroke to afford support, and assist in propulsion.

The wing, in virtue of the variations of inclination of different
parts of its surface, acts as a true kite during both the down and up
strokes, i.e ., it flies down and up alternately in such a manner as to
keep its ventral concave or biting surface always closely applied
to the air. The wing is, therefore, effective during both the down
and up strokes , so that it is a mistake to regard the down stroke as
alone contributing to flight. In reality the down and up strokes
are parts of one movement, the wing describing first a looped and
then a wave track.

The tip of the wing in especial acts as a kite during the up
stroke, the kite being inclined upwards, forwards, and outwards.

The kite formed by the wing differs from the boy’s kite in
being capable of change of form in all its parts. The change of
form of the wing is rendered necessary by the fact, that the wing is
articulated or hinged at its root (short axis), its different parts, as a
consequence, travelling at various degrees of speed in proportion
as they are removed from the axis of rotation. It is also practi-
cally hinged along its anterior margin (long axis), so that the tip
travels at a higher speed than the root, and the posterior margin
than the anterior. The compound rotation and varying degree of
speed attained by the different parts of the wing has the effect
of twisting the wing upon its long axis, and producing a variety of
kite-like surfaces calculated to operate effectually upon the air,
whatever the position of the wing may be.

The wing, when the flying animal is fixed or hovering steadily
before an object, describes a figure-of-8 wave track in space, — the
figure-of-8, when the animal flies in a horizontal direction, being
opened out or unravelled to form first a looped and thqn a waved
track.

In horizontal flight the wing describes a series of large waves or

340 Proceedings of the Royal Society

curves, the body describing a series of smaller and opposite curves,
the wing always rising when the body falls, and vice versa. The
descent of the wing in this manner necessitates the elevation of the
body, and the descent of the body contributes to the elevation of
the wing.

The wing elevates the body when it descends, and the body,
when elevated, falls forwards in a curve, and so contributes to the
elevation of the wing. This arrangement draws the wing forward
upon the air during the up stroke, and opposes the direct down-
ward action of gravity by presenting the concave or biting surface
obliquely to the air in the direction of the travel of the body.
The under surface of the wing is thus made to act as a true kite
during the up stroke.

The wing is urged at different velocities, the power applied being
much greater during the down stroke than during the up one.
The power is also greater at the beginning of the down and up
strokes than towards the termination of those acts. The variation
in the intensity of the driving power is necessary to slow the wing
towards the termination of the down stroke, to prepare it for the
up stroke, and to afford the air an opportunity of reacting on the
under surface of the W'ing, to the elevation of which it contributes.
The wing is elevated more slowly than it is depressed, and allows
the body time to fall downwards, the fall of the body assisting in
elevating the wing relatively to the bird. The wing, the air, and the
weight of the body, are consequently active and passive by turns.

The wing is depressed by voluntary muscular efforts. It is
elevated by vital, and mechanical acts, viz., by the contraction of
the elevator muscles and elastic ligaments, by the reaction of tbe
air called into play by the fall and forward travel of the body.

If the wing is in one piece, it is made to vibrate figure-of-8
fashion in a more or less horizontal direction . It thus attacks the

air by a series of zig-zag movements, very similar to those per-
formed by an overloaded dray-horse when ascending a hill. If the
wing is in more than one piece, it is made to oscillate in a more
or less vertical direction ; the wing, under these circumstances, being
usually closed during the up stroke and opened out during the down
stroke. The wing is closed and its area diminished during the
up stroke, expressly to avoid the resistance of the air.

of Edinburgh, Session 1870-71.

141

The wing of the insect is, in some cases (the wasp, for instance),
folded upon itself during the back stroke to avoid the resistance of
the air ; in other cases, when two pairs of wings are present (the
butterfly, for example), the first pair of wings is made to overlap
the second pair for a similar purpose.

When the wing is in one piece, and made to vibrate in a more or
less horizontal direction, it is followed in its passage from right to left
by a current which the wing meets in its passage from left to right.
When the wing passes from left to right it is followed by a current
which the wing meets in its passage from right to left, and so on.
The wing has therefore the power of creating the current on which
it rises.

When the wing is in several pieces, and made to vibrate more or
less vertically, one portion of the pinion (during the acts of exten-
sion and flexion) makes a current which another portion utilises.
Thus the tip and root of the wing (hand and arm) make a current
during extension on which the middle part of the wing (fore-arm)
acts during flexion, and the reverse. This arrangement begets a
cross pulsation, and extends in the bird even to the primary and
secondary feathers. The wing may thus be said to rise upon a
whirlwind of its own forming.

The wing has the power of producing artificial currents, and of
utilising and avoiding natural currents, so that it is equally adapted
for flying in a calm and in a storm. As the wing (or parts of the
wing) strikes in opposite directions, it in this manner reciprocates,
the down stroke running into and contributing indirectly to the
efficacy of the up stroke, and the reverse. The down and up strokes
consequently form one continuous act, and neither is complete
without the other. The down stroke produces the current on
which the wing operates during the up stroke, and vice versa.

The reciprocation of the wing is most perfect when the animal
is fixed in one spot, and least perfect when it is flying at a high
horizontal speed. It is, however, a matter of indifference whether
the wing attacks the air or the air attacks the wing, so long as a
sufficient quantity of air is worked up under the wing in any given
time.

The wing of the bat and bird are drawn towards the body and
flexed at the termination of the down stroke to destroy the

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VOL. VII.

342

Proceedings of the Royal Society

momentum acquired by the pinion during its descent, and to
prepare it for making the up stroke. It is elevated as a short lever
to avoid the resistance of the air, and pushed away from the body or
extended towards the end of the up stroke to prepare it for making
the down stroke. It is depressed with great energy as a long
lever , and hence the greater elevating and propelling power of
the down as compared with the up stroke.

When the bat and bird are stationary, the tip of the wing, from
its alternately darting out and in, and forwards and backwards,
during extension and flexion, and during the down and up
strokes, describes an ellipse, the axis of which is inclined obliquely
upwards and forwards. When the bat and bird are progressing at
a high speed, the axis of the ellipse is inclined obliquely down-
wards and forwards, the ellipse itself being converted into a spiral
and then a wave line. The outward and forward (extension) and
inward and backward (flexion) play of the pinion contributes to the
balancing power of the bat and bird, as it augments the horizontal
area of support.

The wing of the insect is recovered or drawn towards the body,
and that of the bat and bird recovered, flexed, and slightly elevated
by the action of elastic ligaments. Those ligaments, by their con-
traction, conserve and interrupt muscular efforts without destroying
continuity of motion.

The elastic ligaments are in many cases furnished with muscular
fibres, and are most highly differentiated in those animals whose
wings vibrate the quickest.

The primary, secondary, and tertiary feathers of the wing of the
bird are geared to each other by fibrous structures in such a
manner that the feathers are made to rotate in one direction during
flexion, and in another and opposite direction during extension.
The double rotation of the feathers in question confers a distinctly
valvular action on the wing of the bird.

The under surface of the wing of the bat and bird is thrown into
a beautiful arch during extension and the down stroke, the arch
being so formed that its tension increases according to the pressure
applied.

The wing is inserted into the upper part of the thorax, and
balances the body by playing alternately above, beneath, and on a

of Edinburgh, Session 1870-71.

343

level with it. When above the body, the latter is suspended from
the wings as from a parachute. When beneath the body, it is
suspended from the top of a cone formed by the wings, and when
on a level with the body, the latter is placed in the centre of a
circle described by the rapidly oscillating wings. The body
is suspended from the wings very much as a compass set upon
gimbals is suspended.

The wing balances the body in consequence of its travelling at
such a speed as enables it to convert the area mapped out by its
vibrations into what is practically a solid basis of support.

The wing, whether in one piece or in many, rotates upon two
centres, the one centre corresponding to the root of the wing (short
axis), the other to the anterior margin (long axis). The rowing
feathers have a similar compound motion. This mode of action of the
wing is intimately associated with the power it enjoys of alter-
nately seizing and evading the air, of producing artificial currents,
and of utilising artificial and natural currents.

The wing is cranked slightly forwards, a small degree of rotation
of the anterior margin being followed by a very considerable sweep
of the posterior margin.

The wing area is greatly in excess of what is absolutely neces-
sary, and as much as four-sixths may be removed in certain
insects (the common blow-fly, e.g.f without destroying the power
of flight. The wing area may also be considerably reduced in
birds without in any way impairing flight. This shows that
elaborate calculations of wing area, in relation to weight of trunk,
must prove futile, unless the rapidity with which the wing
vibrates and the state of the air are also taken into account.

Weight is necessary to the flight of the insect, bat, and bird, as
at present constructed. If flying creatures were lighter than
the air, the wing would require to be twisted completely round as in
the auks and penguins, so that the under ventral or concave surface
wrould strike from below upwards, instead of from above downwards.

In aerial flight the under or concave surface of the wing is
applied from above , whereas in subaquatic flight it is applied from
below . The scull, like the subaquatic wing, is applied from below,
so that the analogy between the aerial wing and the oar as employed
in sculling is more apparent than real.

344 Proceedings of the Poyal Society

A diving bird which flies under the water is lighter than the
zuater, and flies downwards. A bird which flies in the air is
heavier than the air , and flies upwards. Relative levity and weight
are therefore necessary to the diving and flying bird as at pre-
sent constituted.

Weight, when associated with or operating upon wings, con-
tributes to horizontal flight. A flying animal, when it drops from
a height with expanded motionless wings, does not fall vertically
downwards, but downwards and forwards , the wings converting
what would otherwise be a vertical fall of the body partly into
forward travel. The weight of the body thus to a certain extent
relieves the muscular system from excessive exertion. If a suffi-
cient breeze be blowing, the weight of the trunk and the breeze
upon the wings operating conjointly are sufficient to keep the
body of the animal in the air for protracted periods. This is well
seen in the case of the albatross, which can sail about for an hour
at a time when there is wind without once flapping its wings.

The wing, as a rule, is more flattened in the insect than in the
bat and bird. It is, moreover, driven at a higher speed, those
animals which fly the quickest having for the most part the
flattest wings. The dragon fly furnishes a good example.

The greater the concavity of the wing, the greater the elevating
power ; the flatter the wing, the greater the propelling power.

The wings in living animals are thoroughly under control both
during the down and up strokes ; the wing, consequently, is not
simply an elastic apparatus, which derives the movements of its
separate parts from the air ; on the contrary, it directs and
controls the air in such a manner as to extract the maximum of
support and propulsion from it.

The wings of bats and birds are moved by direct muscular action
in combination with certain elastic ligaments, and the same holds
true of the dragon fly and some other insects. The elasticity of
the wing and the resiliency and reaction of the air, however, assist
the muscles and ligaments.

The great speed attained by the tip and body of the wing is due
to the fact that the wing is articulated or jointed at its root, any
movement communicated at the root being quickened in propor-
tion to the distance from the root. In other words, a compara-

145

of Edinburgh, Session 1870 -71 .

tively slow movement communicated to the root of the wing is at
once converted into a very rapid one at the tip.

If an artificial wing be constructed in strict accordance with
any of the natural wings (insect, bat, or bird), and applied by a
sculling figure-of-8 movement to the air, it will be found to supply
a steady buoying and propelling power, similar in all respects to
that supplied by the living wing.

In order to secure this result, the artificial wing should be
concavo-convex, and slightly twisted upon itself, i.e., it should be
finely arched in every direction. It should be mobile as well as
elastic,* and be applied to the air at different angles and at different
degrees of speed, in such a manner that the wing and air may be
active and passive by turns.

The artificial wing , like the natural one, must be more or less
triangular in shape. It must taper from the root towards the tip,
and from the anterior margin in the direction of the posterior
margin. It should be capable of change of form, and elastic
throughout, the flexibility being greatest at the tip and posterior
margin of the wing, and least at the root and along the anterior
margin. It must move in all its parts at different periods of
time, as in this way the air is alternately seized and dis-
missed, dead points avoided, and a continuous reciprocating
movement secured. In producing a continuous vibration of
the artificial wing, much assistance is obtained by employing a
ball-and-socket joint at its root, with a system of elastic springs
of different strengths. The principal springs should be ar-
ranged at right angles to each other, the superior and posterior
springs being stronger than the inferior and anterior ones.
Oblique springs may be added, and the whole, because of their
different strengths and their peculiar directions and insertions,
can be made to give the wing any amount of torsion in the direc-
tion of its length during every portion of either the up or down
stroke. The muscles and elastic ligaments of insects, bats, and
birds, perform a similar function. A ball-and-socket joint, or
what is equivalent thereto, is necessary at the root of the wing,

* Borelli (1668), Durkheim, and Marey state that an artificial wing should
be composed of a rigid rod in front and a flexible sail behind, but experiment
lias convinced the author that no part of the wing should be absolutely rigid.

346 Proceedings of the Royal Society

because the pinion should be free to move in an upward, downward,
forward, and backward direction. It should also be able to rotate
around its anterior margin to the extent of nearly a quarter of a
turn. All the movements referred to are derived in the author’s
models from a direct piston action , from the reaction of the air, the
elasticity of the wings and springs, and the weight of the machine
bearing the wings. They are restrained and directed by the
gearing apparatus extending between the piston and the wings, but
more especially by the different lengths, strengths, and directions
of the elastic springs themselves. The- piston is made to descend
with a very violent hammer-like motion at the beginning of the
down stroke, the movement being gradually slowed as the wing
descends to a certain point, at which the movement is re-
versed and the piston ascends more slowly, its ascent being
occasioned for the most part by the reaction of the air, the elas-
ticity of the wing and of the springs at its root, and by the descent
of the engine propelling the wings. The driving power, the
weight of the apparatus, the recoil of the air, and the elasticity of
the wings and springs are thus made to act in concert, the different
forces being active and passive at intervals, and no two forces
acting together at precisely the same instant of time.

If a longitudinal section of a bamboo cane, 10 feet in length and
half-an-inch in breadth, be taken by the extremity and made to
vibrate, it will be found that a wavy serpentine motion is produced
in it, the waves being greatest when the vibration is slow, and
least when it is rapid. It will further be found that, at the
extremity of the section where the impulse is communicated,
there is a steady reciprocating movement devoid of dead points.
The continuous movement in question is no doubt due to the fact
that the different portions of the reed reverse at different periods,
the undulations induced in the reed being to an interrupted or
vibratory movement very much what the continued play of a fly-
wheel is to a rotatory motion.

If a similar reed has added to it at its outer or distal half
tapering rods of whalebone radiating in an outward and backward
direction to the extent of a foot or so, and the whalebone and the
reed be covered with a thin sheet of india-rubber, an artificial wing
resembling the natural one in all its essential properties is at once

347

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produced.* Thus if the wing be made to vibrate at its root, a double
wave is produced , the one wave running in the direction of the length
of the wing, the other in the direction of its breadth. The wing
further twists and untwists figure-of-8 fashion during the down and
up strokes. There is, moreover, a continuous play of the wing,
the down stroke gliding into the up one, and vice versa , by a
system of continuous and opposite curves, which clearly shows
that the down and up strokes are parts of one whole, and that
neither is perfect without the other. This form of wing is endowed
with the very remarkable property that it will fly in any direc-
tion, demonstrating more or less conclusively that flight is essen-
tially a progressive wave movement. Thus if the anterior or thick
margin of the wing be directed upwards, and the angle which the
under surface of the wing makes with the horizon be something less
than 45 degrees, the wing will, when made to vibrate, fly with an un-
dulatory motion in an upward direction , like a pigeon to its dove-cot.
If the under surface of the wing make no angle, or a very small
angle with the horizon, it will dart forward in a series of curves in
a horizontal direction, like a crow in rapid horizontal flight. If the
angle made by the under surface of the wing be reversed, so that
the anterior or thick margin of the wing be directed downwards,
the wing will describe a wave track and fly downwards , as a
sparrow from the top of a house or tree. In all those move-
ments 'progression is a necessity ; the movements are continuous
gliding forward movements ; there is no halt or pause between the
strokes, and if the angle which the wing makes with the horizon
be sufficiently great, the amount of steady, tractile, and buoying
power developed, is truly astonishing. This form of wing elevates
and propels both during the down and up strokes, and its working is
accompanied with little or no slip. Its movements may be regarded
as the literal realisation of the figure-of-8 hypothesis of flight.

* The author has made a great variety of artificial wings. Of these some
are in one piece, with a continuous covering ; others in a single piece, with
the cover broken up into a large number of small valves ; others in several
pieces, with a continuous covering, and others jointed, with the cover broken
up into a number of valvular segments. In all cases the frames of the wings
are composed of elastic material, such as steel tubes, bamboo and other canes,
osier twigs, whalebone, gutta percha, &c., &c. ; the covers of the wings are
made of india-rubber cloth, tracing cloth, argentine, linen, silk, &c., &c. ; the
springs of the wings of steel, caoutchouc, &c., &c.

348 Proceedings of the Royal Society

If the artificial wing be in one piece, it ought to be made to vibrate
in a more or less horizontal direction ; if in several pieces, it should
be worked in a more or less vertical direction, as the wing in this
case acts alternately as a short and long lever, in virtue of its
closing and opening during the up and down strokes, the acting
area of the wing being greatly reduced during the up stroke, and
greatly increased during the down one.

If a properly constructed artificial wing be made to vibrate in a
vertical direction, it invariably darts downwards and forwards in a
curve during the down stroke, and upwards and forwards in a similar
but opposite curve during the up stroke, the two curves running
into each other to form a progressive, continuous, wave track.

If the wing be made to vibrate from side to side in a more
or less horizontal direction, it rises zig-zag fashion by a series of
looped curve movements, each pass of the wing being on a
higher level than that which preceded it. Whether the wing be
moved vertically or horizontally, it invariably twists and untwists
during its action. In twisting and untwisting, it developes figure-
of-8 curves, not only along its anterior and posterior margins, but
throughout its entire length and breadth.

The figure-of-8 vertical movement may be converted into the
figure-of-8 horizontal movement by a slight rotation of the wing
on its long axis, or by a tilt of the body or frame bearing the
wing. It is in this way that the wing may act either as an ele-
vator and propeller, or merely as an elevator. Thus it is not
uncommon to see an insect elevate itself by a horizontal screwing
figure-of-8 movement, and then, suddenly changing the direction
of the stroke of the wing and of the body, dart forward in a nearly
horizontal direction.

The artificial wing, like the true one, attacks the air at a great
variety of angles during the down and up strokes. Thus during
the down stroke the angles which the wing makes with the horizon
are increased, whereas during the up stroke they are diminished.

The angles made by the different portions of the artificial wing
vary as in the living wing, the angles made by the parts nearest
the root being greater than those nearer the tip. This is occa-
sioned by the manner in which the artificial wing twists and
untwists during its action, the torsion in question being due to the

of Edinburgh, Session 1870-71.

349

elastic properties of the wing and the resistance which it experi-
ences from the air, as well as to the fact that the tip and posterior
part of the wing travel at a much higher speed than the root and
anterior part. The small angle made by the tip, as compared with
the root of the wing, equalises its action, a large angle urged at a
low speed giving the same amount of buoyancy and propelling
power as a smaller angle urged at a higher speed.

The artificial wing, because of its elasticity and by the aid of
certain springs, can be made to slow and reverse of its own accord
at the end of the down and up strokes in precisely the same
manner as the natural wing. It can likewise be made to change
its course without halt or dead point, so as to give continuity of
motion and continued buoyancy.

If the artificial wing be moved figure-of-8 fashion in a more or
less horizontal direction, it can be made to create and utilise its
own currents, the stroke from right to left producing the currents
on which the wing rises in its passage from left to right, and the
reverse. It can also be made to utilise and evade natural currents.

If the tip of a properly constructed artificial aerial wing be
turned downwards, and the wing be made to move from side to side
figure-of-8 fashion like the tail of a fish, it forms a very excellent
aerial propeller.

The artificial wing, to be effective, must rotate about two separate
axes, the one corresponding to its root (short axis), the other to its
anterior margin (long axis).

If two artificial wings, similar to those described, be placed end
to end, inclined at a certain upward angle, and made to revolve,
they form a most powerful aerial screw. This form of screw is
propelled with comparatively little force, and its working is
attended with quite a nominal amount of slip.

The aerial screw here recommended is elastic and capable of change
of form in all its parts, and so constructed that its angles vary to
adapt themselves to the speed attained by the different portions of
the blades at any given time. Thus the angles made by the blades
are greatest when the speed at which the screw is driven is least, and
vice versa ; the angles made by those portions of the blades which
are nearest the axis of rotation being always greater than those
made by the portions nearer the tips of the blades. This form of

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350 Proceedings of the Royal Society

aerial screw differs widely from the aerial screws at present in use*
and from the screw propeller employed in navigation, inasmuch
as it is moveable in all its parts, and adjusts itself to its work in
such a manner as to secure the maximum of elevating and pro-
pelling power, with a minimum of slip. The screw propeller and
aerial screws as at present employed are, on the contrary, rigid
and unyielding , and possess no accommodating power. As a con-
sequence, much propulsive power is sacrificed in slip.

If the blades of the aerial screw referred to be greatly diminished
in size, and formed of carefully tapered, finely graduated steel
plate, it operates with remarkable efficiency in water, the elasticity
of the screw diminishing the slip, while it greatly augments the
propelling power.

The following Gentlemen were admitted Fellows of the
Society : —

Rev. Thomas M. Lindsay, M.A.

William Robertson Smith, M.A.

Stair Agnew, Esq.

Monday , 30 tli January 1871.

Professor KELLAND, Vice-President, in the Chair.

At the request of the Council, Dr J. Collingwood Bruce
delivered an Address on “ The Besults of the More Decent
Excavations on the Line of the Roman Wall in the North
of England.”

Nearly a century after Julius Caesar had landed in this island
the conquest of Britain was begun in earnest.

In the year 79 Agricola planted the Eagles of Rome on the banks
of the Tyne, and during the next campaign carried his conquests
as far as the Tay. Before he gave up his command, he had raised
the Roman standard in the Orkney Islands.

When Rome planted her foot she usually planted it firmly, and
thus she retained in her grasp all the best portions of the island
for more than 300 years. Some of the legions which landed in-tbe

of Edinburgh, Session 1870-71. 351

time of Claudius remained in the island until the close of the
Roman domination.

In the year 410, when Alaric and his Goths entered Rome,
Honorius renounced all claim upon the allegiance of Britain.

As to the origin of the wall, when Agricola advanced agains/
the Caledonians, he thought it necessary to use precautions against
a rising amongst the conquered tribes whom he left behind him.
lie made good roads contemporaneously with his advance. As he
moved along he drew the road with him. By this means his
retreat was always secure and his supplies comparatively certain. It
is believed that we owe to him the northern Watling Street and the
Maiden Way, which run northwards parallel to each other at about
twenty-five miles apart. For miles together both of these roads
remain to this hour as the Romans left them. Another precaution
adopted by Agricola was the planting of garrisons in well-selected
situations. There were two parts of the island where these
garrisons could he best placed, namely, where the influx of the sea
brings the eastern and western coasts into near contiguity — between
the Firths of Clyde and Forth, and between the Tyne and Solway.
Here walls were afterwards built. The southern wMl was not a
mere fence. It was a line of military operation. In erecting it
the Romans did not give up the country to the north of it, but by
its means made it more thoroughly their own. A transverse road
along it was a necessary adjunct. At the Northumberland Isthmus
Watling Street and the Maiden Way went north and south ;
another road, which has been called the Stanegate, went from east
to west.

Dr Bruce then enumerated some of the principal stations in the
wall as amplified and finally completed by Hadrian, who made
use of such of the pre-existing stations of Agricola as served his
purpose.

The stationary camps on the Roman wall usually have four-
gateways, one in each end, and one in each side rampart. Each
gateway consists of two portals divided by strong piers of masonry,
with its own arch overhead. There is uniformly a guard chamber
on each side of the gateway.

The wall, as erected by Hadrian, exists to this day in wonderful
completeness. Except in places where towns have sprung up on

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Proceedings of the Royal Society

its site, there is scarcely a yard of its course from Wallsend to
Bowness where traces of it are not to be found. Where the stone-
works have disappeared the fosse or earthen ramparts generally
show themselves.

The wall is really an important fortification, consisting of
several parts. There is first the stone wall, with a deep and
broad fosse on its northern margin ; next, the vallum or earth wall,
which at varying distances keeps to the south of the stone wall.
Then between these was a well-made road. Lastly, there was a
series of stationary camps, castles, and turrets, for the accommoda-
tion of the soldiery who garrisoned the structure.

The length of the great wall is said to be seventy-three and
a-half miles. It is usually about eight feet thick, and in two
places it now stands nine and a-half feet high. Its original eleva-
tion was much greater.

The stations were military cities, mostly attached to the wall.
The largest of them contain an area of six acres, some of them
only three. The stations are distant from one another at an
average of about four miles. Their form is that of a parallelogram
with the corners rounded. The first thing which the builders of
the wall did was to build the station, when they felt that they
could safely undertake the other parts of the fortification, running
the wall right and left. The masonry of the gateways is pecu-
liarly massive and strong. In some of them the joints are as
close as ever, and the courses as true as they were 1700 years ago.
As far as can be ascertained, every station had a double gateway
opening northwards, as well as in other directions. The north
gate of Borcovicus station (House-steads) must have been much
used, for its threshold is deeply worn by the feet of passengers.

That the Romans did not give up to the enemy the country on
the north side of the wall is shown by a circumstance that the
garrison at the station of Borcovicus had an amphitheatre provided
for their amusement on the north side of the wall, where the
ground outside the wall was best suited for its formation. It was
not unusual with the Romans to provide amusements for the
soldiery even upon a campaign.

In crossing from sea to sea, the wall, about the centre of its
course, comes near an upheaved mass of basalt. For about ten

353

of Edinburgh, Session 1870-71.

miles it takes advantage of this circumstance, and swerving out of
its direct course, seizes hill after hill, so as to present to the
enemy not only the obstacle of its own height, but that of the
ridge of which it is built. A similar and more striking one of the
natural ground is seen at Peel Crag.

When the wall runs over precipitous ledges like this, the fosse
on the north side of it is of course discontinued, but the moment
it again descends into the valley it is renewed.

Dr Bruce’s paper contained several other particulars illustrating
the present condition of the wall, and showing the powerful and
systematic organisation displayed in its construction as a means
of commanding and keeping in subjection the adjacent country.
It also contained references to the monuments and inscriptions
found in the line of the wall, indicating in particular the prevalent
religious feelings of the period, and in particular showing an
infusion of Eastern ideas into the native mythology of the Bomans.

The following Gentlemen were admitted Fellows of the
Society : —

Charles Hayes Higgins, M.D.

Angus Macdonald, M.D., F.R.C.P.

Monday , §th February 1871,

Dr CHBISTISON, President, in the Chair.

The following Communications were read : —

1. Note on two Species of Foraminifera, and on some
Objects from the Nicobar Islands of great Ethnological
interest. By T. C. Archer, Esq. Specimens were exhi-
bited.

Mr Archer exhibited two interesting Foraminifers, one being
Saccammina Carteri , which forms a large proportion of the Carbonif-
erous limestone at Elfhills, Northumberland; the other, a gigantic
species of the Arenaceous group brought from Persia by the late Mr
Loftus, and named after him, Loftusia persica. The latter specimen
was that to which Mr Archer especially called the attention of the

354 Proceedings of the Royal Society

Society, as it was similar to a class of fossils which had previously
been found in the Upper Greensand formation in England, and
believed to be sponges. However, the whole history of these
monsters of their Order has been so well worked out in the
admirable monograph of Dr Carpenter and Mr H. B. Brady, that
their proper character is now thoroughly known.

Mr Archer also exhibited some objects of great Ethnological
interest from the Nicobar Islands.

The following is the Memorandum accompanying the Wooden
Figures obtained by Captain Edge, R.N., commander of H. M. S.
“ Satellite,” from the Nicobars, in July 1867.

Reports having reached the authorities at Singapore that several
vessels had, from time to time, been attacked by the savages upon
these islands, and their crews barbarously murdered, it was deter-
mined to despatch an expedition to that spot ; and accordingly, in
July 1867, H. M. ship “ Wasp,” Captain Bedingfield, B.N., and
H. M. ship “ Satellite,” Captain Edge, R.N., proceeded thence.
The savages fled on the approach of the vessels of war, and upon
landing at Enounga, one of the largest of the villages, Captain
Edge discovered these figures in their huts, and upon his return to
Singapore he gave them to Major M‘Nair of the Royal Artillery
for presentation to a museum.

The photographs are those of three of the savages who were
captured, and of a little girl of seven years of age, who was rescued
from their hands and brought to Singapore.

List of Wooden Figures from the Nicobar Islands, procured by
Captain Edge, R.N., and presented to the Edinburgh Museum of
Science and Art, by James M‘Kenzie, master of the ship “ Shree
Singapora.”

1. Large figure of a woman.

2. Male idol.

3. Figure of a native male in European style.

4. Do. do. (smaller size).

5. Figurehead of a native female.

6 & 7. Two small figures.

8. Figure of an animal.

These specimens were exhibited to the Ethnological Society in
London at the beginning of last year.

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of Edinburgh, Session 1870-71.

After all that has been read of the complete absence of any kind
of Art amonst the savages of these islands and the neighbouring
Andamans, one is irresistibly led to think that these objects are
not the works of the natives, but have been produced by some
debased European or other captive.

2. Certain Phenomena applied in Solution of Difficulties con-
nected with the Theory of Vision. By R. S. Wyld, Esq.

The theory of vision has been the subject of much more scientific
study than that of any of our other senses, but notwithstanding
this, the subject is still encumbered with some difficulties and con-
tradictions, the solution of which is essential to our having a true
and complete theory. Such are the questions, — first, — regarding
single and double vision, as depending on the excitement of cor-
responding, or, as they are generally called, identical points of
the retinse ; second, — the question whether perception is in the
retinae or in the brain; and lastly, the question regarding the'
decussation and ultimate course of the fibres of the optic nerves.

Regarding the subject of single vision with two eyes, there has fre-
quently been exhibited a great amount of misunderstanding ; since
the discovery of the stereoscope, however, the nature of what has
commonly, though not with strict propriety, been called single
vision, has become much better understood. The truth is, there
is no such thing as single vision when two eyes are in use, and
a very little attention will make it clear how the case stands.
Take two shillings of like appearance, and place them correctly
and with the same sides up, in the different compartments of the
stereoscope, but so far apart that they do not appear to coalesce.
In this position they are distinctly seen by each eye as two
separate objects. Cause the coins next gradually to approach till
they seem to coalesce or unite into one — we say seem, for there is
no true visual union. Even when they seem to unite, there are
still two impressions made — one on each retina — and a correspond-
ing impulse is from each of these membranes sent to the brain and
to the mind, though from the close resemblance of the two im-
pressions it may be impossible to distinguish the one from the
other.

356 Proceedings of the Royal Society

To prove that there are two mental impressions, let us re-
verse one of the coins. When this is done, we have no longer
the impression of one coin, but of two coins occupying the same
place. Both are visible, and they appear as if the one were visible
through the other. While we steadily regard this anomalous
presentation, the eye and the judgment become alike puzzled by
it, and an effort is made to reduce the phenomenon to a normal and
intelligible object of vision ; a succession of transformations is the
result of the joint action of the mind, and of the disturbed nervous
centres which ensues; at one moment we see one coin, and then,
suddenly, it disappears, and the other takes its place ; then we see
both coins at once, or a part of each perhaps becomes alone visible.
In ordinary vision, then, we must conclude that objects make an
equal impression on the identical points of each retina, though we are
not intellectually conscious of the fact of duality ; and the question
thus arises, If there are two retinal impressions, how do we account
for the two appearing as if superimposed the one on the top of the
other? The eyes are set apart in the head, and the supposed
sensory ganglia at the base of the brain, the corpora geniculata, the
corpora quadrigemina , and the optic thalami, are all in duplicate :
and the cerebral hemispheres divide the head in two equal sections.
How, then, are we to account for the two visual images being
united? It has been very generally assumed that the mind com-
bines the two impressions, as it were, into one. This is the
opinion of Professor Wheatstone and Dr Carpenter, and it was for
many years my opinion ; but the phenomena about to be alluded
to convinced me that I was wrong, and that there exists a physical
cause for the union of the two images ; and to prove this is the
main purpose of the paper.

When we take two strips of white card-board about an inch
broad, and insert one at each side of the stereoscope, we find that
each strip is distinctly seen by each eye ; but when we cause them
gradually to approach till the two ends appear to overlap say an
inch or more, the effect is singular. Where the strips seem over-
lapping, the brightness is observed instantly to become very much
increased : so much so, indeed, that when we fix the attention on
the quadrangular part formed by the overlapping ends, all the rest
of the strips become invisible, and the overlapping parts alone

357

of Edinburgh, Session 1870-71.

remain distinct objects of vision. It may however be mentioned,
by the way, that either of the cards may be recalled to sight by
the simple act of moving it two or three times backwards and
forwards, and thus exciting the nerve and arousing the attention ;
hut this in no degree impairs the superior brightness of the over-
lapping parts.

Such are the facts, but what is the cause of the increased bright-
ness where the cards appear to overlap, and what is the cause of
the apparent overlapping where corresponding points of the retinae
are excited by objects in reality apart? I am not aware of any
writer having distinctly laid before us a specific physical cause
accounting for these several phenomena. It appears to me that
they clearly point to an anatomical cause.

A great many writers have attributed single vision to habit.
Dr Smith in his optics attributes single vision to this cause. Dr
Carpenter also seems to take this view. He says (“Physiology,” p.
705), “ A condition of single vision seems to be that the two
images of the object should fall on parts of the retinae accustomed
to act in concert, and habit appears to be the chief means by which
this conformity is produced.” Dr Reid, in his “ Inquiry into the
Human Mind,” states that he has devoted thirty years to the study
of the subject, and he accepts it as a mystery which cannot be
explained. Sir Wm. Hamilton attempts no explanation. Neither
does Sir D. Brewster in his famous controversy with Professor
Wheatstone attempt any explanation. Buffon thinks we first see
objects double and inverted, and that we correct this judgment by
experience. Blanville, Grassendus, Porta, Tacquet, and Grail, main-
tain that we see with only one eye at a time.

Perhaps the majority of writers have looked no deeper than
the surface of the retina, and have been content to state the
phenomena as depending on an inscrutable property of that
sensitive membrane, or simply as a law of our being : even as they,
with quite as little ingenuity, and with less excuse, attribute our
sense of visual direction to an inscrutable property of the retina.
Some anatomists have, however, supposed that the decussation of the
optic nerves might explain the phenomena. Dr Wollaston, from a
peculiar occasional disorder in his vision, suggested that there was
a crossing of the fibres from the inner parts of either retina to the

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358 Proceedings of the Royal Society

ganglion on the opposite side of the head, while the fibres on the
outer side of each eye went to the ganglion on their own side of
the head. This explanation evidently implies that the retinse are
optically divided in two halves, and that the images of objects
falling on the centres of the retinse are similarly divided, one half
of every object being represented on the right side of the head,
and the other half on the left ; and that objects whose images fall
on the one side of the retinae are represented only on the lobe on
that side of the head. This is surely extremely improbable.

Newton, in his optics, throws out a query (query 15th at the
end of Second Book), suggesting that the species or picture of the
objects seen with both eyes may be united in the commissure of
the optic nerves, the fibres of the right side of both nerves uniting
there, and, after union, going tfience into the brain on the right
side of the head, and the fibres on the left side of both nerves, after
union in the commissure, going into the brain on the left side of
the head, and the two meeting in the brain in such a way that the
fibres make but one entire species or picture. The writer had not
seen Newton’s query till after his paper was submitted to the
Council, but he considers that Newton’s is the most advanced
position which has up to the present times been taken on the
subject. It is evident, however, that Newton had never very
carefully reduced his idea to form, nor had he then the means
which we now possess of testing its correctness; and it was
doubtless owing to this circumstance that the idea, instead of being
followed up and corrected in its details, was allowed to fall out of
sight, and failed to gain the attention of optical writers.

Whether there is or is not a crossing of the true visual or optic
nerves in man and the higher mammalia seems yet to be an
unsettled point, though the opinion is gaining ground that there
is a crossing of the inner fibres. It is always asked if there is no
crossing of fibres, why are the optic nerves brought into connection ?
The question, as an argument in favour of the crossing, is, how-
ever, robbed of half its force, when we consider that the apparent
union of the commissure may not be for a transfer of the true
nerves of vision, but for effecting a union of the nerves essential
for the nutrition of the retinse, and of those nerves whose func-
tion it is to secure equality and unity of action in the reflex opera-

of Edinburgh , Session 187 0-7 1 . 359

lions which regulate the expansion and contraction of the iris of
the eyes.

I do not believe in any partial crossing of the true visual nerve-
fibres. The fact, however, of an entire crossing, or of no crossing
at all, in no ways affects my theory, which I shall now, after a few
necessary words of explanation regarding the functions of the
retina, proceed to explain.

The central point of the retina, the fovea centralis , is distin-
guished from the rest of the retina by its peculiar anatomical struc-
ture. It is also distinguished by its superior discriminating powers.
It is the only part of the retina which takes minute cognisance of
the forms of objects. We may satisfy ourselves of this by fixing
the eyes on any word in a printed book held at the usual reading
distance. While the eyes remain fixed on the middle of any
word of, say six or seven letters, most persons will find that they
are quite unable to perceive a single letter of the adjoining word.
This proves how limited is the area of distinct vision on the
retinas.

When we fix the eyes on any distinct object in an extended
landscape we turn the axis of each eye to the object especially
examined, and the images of it fall on the fovece centrales , and
appear single. All the other objects in the landscape are mapped at
the same time around these central points, on corresponding parts of
each retina, i.e., on parts which are correspondent in distance and
direction, from the foveoe centrales; and these objects also, so far as we
can see them, appear single. The remarkable circumstance, how-
ever, is, that the slightest shift or displacement of the axis of one
of the eyes, and of the image on it, disorders correct vision, and
produces the perception of a duplicate impression of the landscape.
This circumstance has led authors very generally to the con-
clusion, as I have said, that either habit, or some inscrutable law
of the retinas, causes single vision when corresponding parts of that
organ are impressed, and double vision when non-corresponding
parts of the two retinas are acted on. The writer maintains that
these phenomena, and also the phenomenon of increased brightness
obtained by the use of both eyes, can only be explained on the
assumption or theory, that the retinal impulses of both eyes are
united in a central cerebral sensor ium. He, therefore, suggests

360 Proceedings of the Poyal Society

that the true optic or visual nerve-fibres from the retinae cross at
the optic commissure, that they are continued through the optic
tracts, and sweep inwards to the corpus quadriyeminum; that those
from the left eye enter that cerebral lobe at the right side, and
spread across and forward in it in the form of an inverted cone ;
while the nerve-fibres of the right eye enter the same lobe at
the left side, and spread in a like manner across it from left to
right. The fibres from each eye thus cross each other in this
lobe, which, from being an important central ganglion, and most inti-
mately connected with the fibres from the optic nerves, the writer
suggests as the probable sensorium in vision. The effect of this
simple arrangement is, that the corresponding nerve-fibres from each
retina are brought into juxtaposition, fibre to fibre ; and in natural
vision the sensorium thus becomes the organ in which the nervous
impulses which come from the two eyes are united and grouped in
the form they occupy on the retinas.

When, then, in the experiment before-mentioned we advance
the two strips of card-board but a short way at each side of the
stereoscope, their images are found on the inner parts of each
retina, and the ends of the strips are seen as two separate objects,
because their images are thrown on non-identical portions of the
retinae, and different parts of the sensorium are accordingly im-
pressed. When, again, the strips are advanced a little further,
till the images begin to cross the centre of the retina of each eye,
the spectator immediately sees the ends to overlap, and at the same
time to acquire additional brightness. This evidently arises from
the corresponding parts of each retina being impressed, and the two
similar impulses being transmitted to that portion of the sensorium
with which these parts of the retinae are in connection, — each
nerve-fibre from the one eye bringingits impulse into juxtaposition
with the corresponding impulse from the other eye. And thus we
account at once, for the increased brightness, and the apparent
superposition of the images of external objects. A diagram at a
glance shows how these are the necessary results of the arrange-
ment of the nerve-fibres which we have suggested.

That the nerve-fibres coming from each eye are not united or
fused in the sensorium, but merely brought into juxtaposition, is a
fact also proved by the following experiment with coloured strips.

of Edinburgh, Session 1870-71. 361

When we introduce a blue strip at the one side of the stereo-
scope, and a red or yellow one at the other side, till they appear to
overlap or unite into one object, the result is increased brightness
where they overlap ; but there is no blending of the colours so as
to produce purple or green. The one coloured strip, as in the
experiment with the coins, shines through the other; or at one time
the colours are alternately visible, at another time one-half of each
coloured end only is visible, and occasionally spots of the one are
seen to shine through the ground colour of the other, thus estab-
lishing the important fact or law, that though the combination of
different colours, external to the living organism, produces the
effect of an intermediate colour, yet the impulse of different colours
on separate retinae can not be so combined by the mind, but the
impulse peculiar to each colour is conveyed by the nerve receiving
it to the sensorium unchanged, and excites in the mind its own
characteristic sensation. The increased intensity where the adjoin-
ing nerve-fibres in the sensorium are all in action I attribute to the
well-known law of irradiation, or lateral expansion of nervous
action, which exists among neighbouring nerve-fibres when power-
fully excited

The arrangement of the fibres above suggested explains —

ls£. The nature and cause of the peculiar action of the identical
retinal points.

2d. The physical cause of single and double vision.

3 d. The reason why we have increased brightness by the use of
both eyes, whether in ordinary vision or when using the stereoscope.

Ath. The several phenomena force us to the conclusion that visual
sensation is notin the retinas, but in a common cerebral sensorium.

3. Additional Note on the Motion of a Heavy Body along
the Circumference of a Circle. By E. Sang, Esq.

Abstract.

In the course of physical inquiries we meet with many problems
having the appearance of great simplicity, and yet presenting to
the analyst difficulties of the highest order. The law of the
motion of a heavy body along the circumference of a circle is one
of these.

362 Proceedings of the Royal Society

One particular case of this motion, viz., the case of the swing-
ing of a clock-pendulum, is of paramount importance, and has been
investigated with very great care. In this case our attention is
directed principally to the computation of the time of an entire
oscillation, since it is this which determines the heating of the
clock. In the paper to which this note is an addition (Yol. xxiv.
Trans.), a very rapid method of computing this total time is
given. My object is now to supply the deficiency in that paper,
and to show how the time of describing any given portion of the
whole arc may be computed.

The general question may be stated thus: — A heavy body is
projected with a known velocity along the circumference of a circle,
and we are required to compute the time in which it will reach
any indicated position, as also its place at any prescribed time.

No practicable solution of either of these problems has hitherto
been given, with the exception of the case already mentioned.
This note contains a simple and complete solution of both
problems.

If a heavy body be projected from the lowest point of a circle
along the circumference with a velocity less than that due to a fall
from the highest point, its motion becomes slower as it ascends,
and its speed is entirely exhausted at some point in the semi-
circumference; from that point it returns to the bottom of the
curve, passes to the other side, and so oscillates. But, if the
initial velocity he greater than what is due to a fall along the
diameter, the body passes the zenith point, and circulates round
and round the circumference with an unequable motion. And if the
velocity be just sufficient to carry the body to the zenith point, it
rests there, and the motion ceases. Now, while the investigation
of the oscillatory and of the continuous motion is difficult, that of
the limit between .the two is easy.

If the body move away from N with a velocity due to a fall
through the distance ZN, it will have, when it reaches the point
A, a velocity due to a fall through ZGr, But the distance through
which a weight falls freely is proportional to the square of its
acquired velocity, and ZGr is proportional to the square of ZA ;
wherefore the velocity at the point A must be proportional to the
chord ZA ; that is to say, the rate of increase of the angle NZA is

of Edinburgh, Session 1870-71. 363

proportional to its own cosine; or, writing A for this angle, we
have

d A oc cos A . dt , dt <x sec A . dA

and, therefore, the time occupied in passing over some fixed
minute portion of the arc at A is proportional to the secant of the
angle NZA.

In Mercator’s Projection of the Sphere, the differences of the
meridional parts are proportional to the secants of the latitudes,
wherefore the time of describing
the arc NA must he proportional
to the meridional part correspond-
ing to the angle NZA, that is,
must he proportional to the
logarithmic tangent of 45° + ^A.

Measure off then some distance
ZE horizontally to represent the
linear unit, and bisect the angle
AZE by the line ZT meeting the
plumb-line from E in T, the time
of passing along NA is propor-
tional to the logarithm of ET,
or rather to the logarithm of the
ratio of ET to EZ. Hence, when
the angle is given we can readily
compute the time, or when the time is given we can as readily
compute the angle; and thus for this particular case the problem
is completely resolved.

Fig. 1.

Making El equal to EZ, if we make a series of continued pro-
portionals El, EK, EL, ET, EU, &c., and, joining Z with the
several points, make angles doubles of EIK, EIL, &c., we shall
obtain the positions of the moving body after equal intervals of
time. The time of its reaching Z is thus infinite.

The relation of the continuous to the reciprocating motion may
be exhibited by a simple contrivance. Let two straight rods
AC, OB be jointed at the point C, and let the two ends A, B be con-
nected by a straight line, say an elastic thread.

If the rods be turned so as to lessen the angle ACB, the angles

364

Proceedings of the Royal Society

at A and B will increase. If the motion be sufficiently con-
tinued, the greater angle A will become a right angle, and then

B will have reached its maximum. Should the motion be still
further continued, A becomes obtuse and B decreases ; till, when
the rods have entirely closed, A becomes 180° and B becomes
zero. Continuing the angular motion, A becomes a reverse angle,
and B appears on the opposite side of AB. Thus the alternate
increase and decrease of the smaller angle B resembles the changes
of the angle NZA (fig. 1), when the motion is oscillatory. And

at the same time the continual development of the angle at B

Fig. 2.
C

A P B

E

C Q D

Fig. 3.

resembles the change of NZA when the heavy body over-passes
the zenith point. The resemblance is a close one, for if we suppose
CAB to increase with a velocity proportional to the distance PB,
intercepted by the perpendicular CP, its variations are then
exactly analogous to those of the angle NZA, when a heavy body
revolving in a circle whose diameter is proportional to AC, has its
velocity at the lower point equal to that obtained by falling
through a distance proportional to CB. And similarly the varia-
tions of the smaller angle B are analogous to the oscillations of a
heavy body in another circle, the greatest height being to the
whole diameter in the ratio of AC to CB.

When AC is very small in comparison with CB, the maximum
angle Bis also small; that is to say, the arrangementrepresents an
oscillation in a small arc ; but when the two rods are nearly of
equal lengths, as in the case of CE, ED (fig. 3), the maximum
value of D approaches to a right angle, and the arrangement
represents an oscillation extending to nearly the whole ciroum-

365

of Edinburgh, Session 1870-71.

ference. If the trigon were isosceles, the representation would be
that of the motion which we have already investigated.

If the angle A vary with a velocity proportional to PB, and B
with a velocity proportional to AP, the exterior angle at C must
have the rate of its variation proportional to AB. Now, if we
make DCE (fig. 3), equal to half the sum of CAB and ABC, CE
a mean proportional between AC and CB, and then inflect ED
equal to half the sum of the same lines, the perpendicular EQ
intercepts QD just half of AB. Thus QD is proportional to the
rate of increase of ECD, and consequently CQ to the rate of change
of CDE. Thus the synchronous variations of the trigons ACB
and OED would represent four connected cases, two of oscillation
and two of revolution in a circle.

Now, the ratio of CE to ED is much nearer to one of equality
than is the ratio of AC to CB ; and if we were to proceed again in
the same way, we should obtain a trigon still more nearly isosceles ;
and, after a very few operations of this kind, we shall obtain a trigon
sensibly isosceles. That is to say, we shall have referred the
oscillation in a given arc to the motion in just the whole circum-
ference. So, seeing that the motion in this last case has been
completely investigated, we have a complete solution of the general
problem ; the necessary calculations being of remarkable simplicity.

4. On the Capture of a Sperm Whale on the Coast of
Argyleshire, with a Notice of other Specimens caught on
the Coast of Scotland. By Professor Turner.

In the autumn of last year, whilst spending a few days in the
neighbourhood of Oban, I visited Dunstaffnage, and in the court-
yard of the Castle saw the two halves of the lower jaw-bone of a
sperm-whale. On inquiry, I learned that they were the relics of a
whale captured some years ago in the neighbouring sea. From
some of the older inhabitants of Oban I gleaned some particulars
respecting this animal; and as no record of its capture has as
yet found a place in zoological literature, I am induced, as the
sperm-whale so very seldom visits our shores, to communicate a brief
notice to the Society.

In the month of May 1829 a large whale was seen spouting in

3 n

VOL. VII.

366 Proceedings of the Royal Society

the Sound between Lismore, Mull, and the mainland. The fisher-
men were at first afraid to approach it, hut as, after a few days,
the animal became less active in its movements, they sallied forth
in boats, and inflicted severe wounds with harpoons and other
weapons. The animal was then secured, and towed ashore in
Dunstaffnage Bay, close to the ruins of the Castle. It was said to
have been about 60 feet long, and possessed a very bulky head, with
a square snout. It was at once seen to be very different in its form
and appearance from the large whales which usually visit our shores;
but it was not until an oily fluid, which flowed out of a wound near
the snout, and congealed on the surface of the water, was recognised
to be spermaceti, that the character and value of the animal was
determined. A considerable quantity of spermaceti was obtained
from the great cavity in the head, and the blubber yielded a large
amount of oil. I could learn nothing definite as to the sex.

The lower jaw was preserved as a relic in Dunstaffnage Castle,
and, in the garden of one of the hotels in Oban, I met with a caudal
vertebra, which was said to have belonged to this animal.

When I saw the jaw it was much injured. Not only were
all the teeth lost, but the symphysial ends of both halves were
broken off, and the expanded articular portion of the right half
sawn off and removed. It is to be feared, if some care be not taken
to preserve the fragments which remain, that in a few years all
trace of this rare and interesting specimen will have disappeared.

From the left mandible some measurements were obtained which
may give an approximation to the dimensions of the bone. The
length was 149 inches; but as the anterior end was absent — as,
indeed, only the sockets of sixteen teeth remained — this measure-
ment falls several inches short of the original length of the bone.
The articular end was expanded, and possessed a vertical diameter
of 22 inches. On its inner face was the very large opening of the
dental canal. Close to the junction of the articular and dentary
parts of the mandible was a well-marked constriction, where the
bone measured only 8 inches in breadth. The breadth of the
alveolar edge of the jaw, about its middle, was 4J inches. In its
general form the mandible was broad and thin at its articular
part, then constricted, beyond which it dilated, and then gradually
tapered away to the anterior extremity.

of Edinburgh, Session 1870-71.

367

The first instance on record of the stranding of a sperm-whale
on the Scottish coasts is the specimen described in the “ Phal-
ainologia Nova,” by Sir R. Sibbald, which came ashore at Lime
Kilns, on the north side of the Forth, in February 1689. It
was a male, 52 feet long, and had 42 teeth in the lower jaw.
Several portions of this animal were preserved by Sibbald in his
museum, and formed a part of the collection which was presented
by him* to the University of Edinburgh.

In the copy of the “ Phalainologia Nova,” in the library of the
Royal College of Physicians of this city, a manuscript letter has
been inserted, in which an account is given of the stranding of
another sperm whale in the Forth. The manuscript is entitled
“ Part of a Letter from Mr James Paterson, Keeper of the
Balfourean Museum at Edinburgh, to Mr Edward Lhwyd, Keeper
of the Ashmolean Museum at Oxford. Edinburgh, July 22, 1701.”
Penes E. W.f

“ There was lately a pretty big whale came in at Crawmond. It
had no whalebone, and teeth only in the lower jaw, which, accord-
ing to Sir R. Sibbald, is the characteristick of yt kind which
has ye sperma cete. You have ys figured in Jonston, tab. 42 of
his Fishes. J Diverse of our physicians were present at ye opening

* Auctarium Mussei Balfouriani e Musseo Sibbaldiano : sive Enumeratio
et Descriptio Rerum Rariorum, tam Naturalium, quam Artificialium, tam
Domesticarum quam Exoticarum : quas Robertus Sibbaldus, M.D. Eques
Auratus, Academiae Edinburgenae donavit. Edinburgh impressum per Aca-
demise Typographum, Sumptibus Academiae, 1697. In this catalogue, under
the head “ De Piscibus Viviparis Raribus,” the following specimens obtained
from this sperm whale are referred, to : — A tooth, the crystalline humour of
the eye, a fragment of the flesh and skin, and a specimen of spermaceti
from the head. “ The Sperma Ceti was lodged most of it within the skull of
it, which was of a prodigious bigness.”

+ Mr Small, the Librarian to the University and to the College of Physi-
cians, informs me that the initials “ E. W.” are in all probability those of
Dr Edward Wright of Kersie, who became a Fellow of the College in 1753.
His valuable library of works on natural history, of which the copy of the
“ Phalainologia Nova,” above referred to, formed a part, was presented, in
1761, to the College by Alexander Gibson Wright, Esq. of Cliftonhall.

X The “ Historia Naturalis,” by Joannes Jonstonus, M.D., was published
at Amsterdam in 1657. Book v. De piscibus et cetis, contains a folio plate,
tab. 42, on which is represented a great whale, 60 feet long, lying on its right
side, and presenting its abdomen, with a large pendulous penis, to the ob-
server. From the form of the head and the shape of the lower jaw it is

368 Proceedings of the Royal Society

of ye head, where they got 2 barrels of sperma cete : This filled

up the whole cranium ; they could find no other thing they could
call ye brain, if it wrere not a friable cineritious-like substance,
which seemed very improbable. They found ys sperma, not only
in ye head and spina dorsi, but (which perhaps has not been
hitherto observed) dispersed through ye whole body ; in ye glands,
whence they prest it out in considerable quantities. The chyrur-
gions spoke of buying the skeleton ; but I don’t know how it
came, ye owners disposed of all another way, so yt neither they
nor we got anything of it. Dr Sibbald got a tooth. He has made
a description of it, and says he has materials for a 2nd part of
his 1 Phalainologia.’ Our whale was a male : the penis appeared
near 7 feet without ye body. The whole length of the creature
was near 52 feet, and ye circumference of ye biggest part of it
about 30. The nether jaw was only 3 foot J about, and had 48
teeth in it. The upper jaw had sockets lined with cartilages to
receive ’em.”

Dr Wright has also inserted into the same copy of the “ Phalain-
ologia Nova” a plate containing six figures, which are marked as
follows: — Fig. 1. Balaena foemina, pinnis et cauda sinuatis; fig.
2. Balasna Macrocephala in faciem ob versa, ut dorsum appareat ;
fig. 3. Eadem in latus decumbens; fig. 4. Delphinus; fig. 5.
Phocoena; fig. 6. Pediculus Ceti Bocconi.

In explanation of this plate, Dr Wright states — “ This plate I
found in a book of original drawings of Sir Robert Sibbald ’s, which
I met with accidentally some years ago. All the explanation I
could make out is as follows : — Fig. 1. The original drawing is
marked in Sir Robert Sibbald’s own hand, ‘ A Whale cast in at
Resyth Castle.’ Figs. 2, 3, marked in Sir Robert’s hand, ‘ A Sperma
Ceti Whale;’ and in another hand, * Whaile at Monyfeith, Feb.
23, 1703 — (fig. 2) backe, to represent the taill ; (fig. 3) side; but
it did lay halfe upon its side that one Ey & a litle of the bellie was

obviously a sperm whale. The drawing has clearly been made from the
animal as it lay on the beach, as the coast line, and numerous figures of per-
sons, either gazing at the whale or on their way to see it, are carefully given.
The whole plate has an air of truth and nature which contrasts favourably
with the imaginary figures of dragons, mermaids, basilisks, griffins, and
unicorns represented in other parts of the work.

of Edinburgh , Session 1870-71. 369

sanded. 57 foots long and 56 round, tooth under, & all the skin
blackish blew, werie smooth, and as thick as a bull’s, & all white
fat within & nixt the skin.’ ”

Figures 2 and 3 are very fair representations of the back and
left side of a male sperm whale, and the plate was in all proba-
bility prepared for the second part of his “ Phalainologia,” which
does not seem, however, to have been published.

In the year 1756 a sperm whale, 63 feet long, is said to have
been stranded on the west coast of Ross-shire.*

In the year 1769 a third specimen was seen in the Forth. It
ran ashore on Cramond Island, on December 22, and was there
killed. It was described and figured by Mr James Robertson, of
Edinburgh, in the u Philosophical Transactions.”! This animal
was a male, and measured 54 feet in length, the greatest circum-
ference being 30 feet.

In the Statistical Account of Scotland, vol. v., 1793, it is stated
in the account of Unst, in Shetland, that u the spermaceti whale
sometimes wanders to this coast, and is here entangled and taken.”
The Rev. G-eorge Low, in his “ Fauna Orcadensis,” 1813, says that
the sperm whale “ is often drove ashore about the Orkneys, and
sometimes caught. One, about 50 feet long, was caught in Hoy
Sound, some years ago, from which was extracted a vast quantity
of spermaceti; as also another, which drove ashore in Hoy.”

The most recent specimen, also a male, of this animal was
washed ashore, in a much decomposed state, in July 1863, near
Thurso. The skeleton was presented to the British Museum, and
formed a part of the material from which Professor Flower has
drawn up his admirable account of tbe osteology of the sperm
whale.

This whale, in the tropical or semi-tropical seas, which more
especially are its proper habitat, moves about, as a general rule, in
large herds or “ schools.” The eight well-authenticated speci-
mens which have now been captured on the Scottish coasts have
been solitary animals, which have wandered northwards, perhaps,
in the track of the G-ulf Stream. Of these eight specimens the sex

* Jardine’s “ Naturalist’s Library, Mammalia,” vol. vi. Cetacea. Edin-
burgh, 1837.

t March 10, 1770.

370 Proceedings of the Royal Society

of three was either not recognised or has not been stated. Five,
however, are known to have been males — a circumstance of con-
siderable interest, as it serves to corroborate the statement made
by Mr Thomas Beale, in his work on the natural history of the
sperm whale, that “ the large and fully-grown males always go
singly in search of food.”

5. On the Efficient Powers of Parturition. By Dr J.
Matthews Duncan.

There can be no doubt that, among the numerous matters at
present occupying the attention of obstetricians, none is more
important than the subject of this paper. So evident is the cor-
rectness of this statement that one cannot but wonder why
attempts to arrive at the truth have been, so far as we know,
delayed till the present day. It is long since excellent researches
of an analogous kind in regard to the force of the circulation of
the blood, the power of the ventricles of the heart, were pub-
lished ; yet such researches do not seem naturally so attractive, nor
do they give promise of so valuable practical results as those into
the power of labour.

It is well known that the first and, I believe, the best results in
this inquiry have been obtained by careful deduction from experi-
ments on the tensile strength of the amniotic membrane. The
researches referred to were made quite independently, and pub-
lished soon after one another by Poppel, of Munich, and by Tait
and myself conjointly. Studying this subject, I thought of some
other modes of reaching conclusions, such as by observations on the
caput succedaneum. Means might be taken to find the force
required to raise a caput succedaneum, and the variations of force
required to raise this swelling in different degrees of thickness.
Such an investigation would, no doubt, lead to similar valuable
results, but the plan has never been employed. Again, observa-
tions might be made to ascertain the force required to rupture the
fourchette or the perineum, and thus a fact might be got which
would be of service in this inquiry. It is well known to
accoucheurs how these parts sometimes offer a successful resistance
to all the powers of labour. This resistance, if its force be ascer-

371

of Edinburgh, Session 1870-71.

tained, is of course a measure of the power employed ; at least, it
would afford a valuable result as to the limits of the power. Like
statements might be made regarding the laceration of the margin
of the cervix uteri, as a test of the power exerted at the completion
of the first stage of labour. Many methods were available, but
none were till very recently worked out.

It is probable that many intelligent and thoughtful accoucheurs
had some rough ideas as to the amount of power exerted in partu-
rition. They could not fail, in attending on ordinary labours, to
observe the strength of hand and arm required to keep back the
head too rapidly advancing over a delicate perineum. This power
is, under certain conditions, a measure of the force of the labour,
but I am not aware that any one has hitherto made the simple
and proper dynamometrical experiments to decide the amount of
force so exerted by the accoucheur. The problem may be more
exactly stated as follows : — If in an unobstructed and powerful
labour, the accoucheur, by the directly opposing pressure of his
hand on the foetal head, arrests its progress for one or several
pains, he has in the pressure of his hand a force which, added to the
small amount required to effect parturition, exceeds all the com-
bined powers of labour in this case. He may then estimate by
dynamometrical experiment what was the force he used, or what
force he is capable of applying in the way in which he actually
applied it to arrest the progress of labour. This experiment may
be varied in different ways, of which I may mention one. Let us
suppose a case of rigid vulva, the perineal resistance being over-
come, and the head retroceding during the interval between
powerful bearing down pains. Now, it is well known that in such
a case a little manual pressure from above may be enough to push
the head down again on the perineum, or to resist retrocession, or
that the first and painless part of the next pain will make the head
that has retroceded, again bulge out the perineum, before it is
forced by the powerful acme of the pain against the resisting
vulva. If, then, the practitioner opposes the advance of the head
even so far as to bulge out the perineum, he must have a nearly
exact measure of the force which the labour could bring to bear
against the vulvar obstacle.

In such experiments or practice, what force does the accoucheur

372 Proceedings of the Royal Society

exert? I have a hand well accustomed to such work, and I find,
by actual trial with an accurate dynamometer, 50 lbs. to be about
the highest power I can use, situated as I am at the bedside in at-
tendance on a case. I have ample reason, then, in such experience
to believe that very few of the most powerful labours exert a force of
50 lbs. ; that an ordinary strong labour is easily arrested by a
much smaller force than 50 lbs. ; that the great majority of labours
is accomplished by repeated efforts whose highest power never
exceeds 25 lbs. I may add that, in the great mass of short forceps
deliveries, the force required from the accoucheur, even when he
delivers the head, unaided by the natural efforts, seldom reaches
50 lbs. These statements are, to a great extent, arbitrary or
dependent on my skill as an observer, yet I feel very confident of
their accuracy.

Again, the intelligent practitioner who has observed a case of
difficult labour finished either by the long forceps or by podalic
extraction, could not but form some rough idea of the force he
used, and compare it with the force which the labour exerted in
its nugatory struggles. The force which the accoucheur thus
exerted would not be certainly the equivalent of what the labour
must have put forth in order to produce a spontaneous termination.
It would, no doubt, in most cases surpass the force which the
mother must have exerted to produce the spontaneous birth. But
it would be, nevertheless, a valuable measurement indicating a
force which in such a case the labour failed to produce. Joulin
and I have made dynamometrical experiments to make use of
such measurements in estimating the highest power of labour.

Another method of advancing our knowledge of this subject has
been followed by the Rev. Professor Haughton. This gentleman
does not, as his predecessors, examine the effects produced by the
powers of labour, and thus get results having a very distinct positive
value. He follows a plan which may be justifiable, yet which is
difficult and dangerous. He takes an almost opposite method to
that used by me. He measures the bulk and the extent of the
involuntary and voluntary muscles employed in the function, and
from these data he arrives at conclusions which he in one particular
corroborates by a simple experiment. The results arrived at are
statements of the powers of the parts, which are true if his methods

of Edinburgh, Session 1870-71.

373

are true. Even if his methods are correct, the results are not
actual values, but possible values, or statements of what may be,
not of what has been.

These results are very different from those of Poppel, Tait, and
myself, and it is one of the objects of this paper to inquire into
their value. In doing this, I shall not discuss the method, but
merely examine the results, by the aid of any obstetrical light
which I can throw upon them.

Before proceeding to this inquiry, it is to be remarked that
Haughton arrives by his method at new results which the methods
of previous observers did not afford the means of reaching. There
are, as is universally known, two great forces employed in labour —
the uterine contractions and the involuntary and voluntary bearing
down. The former of these forces is peculiar to the parturient
female. The latter, as Haughton truly observes, is not peculiar to
parturition, but is “ available to expel feces, urine, or a foetus.”
Haughton’s plan is, to examine the uterus, measure it, and through
this, arrive at a conclusion as to its power ; then to examine the
muscles which co-operate to produce bearing down, measure them,
and through this arrive at a conclusion as to their power. The
addition of the two results will, of course, give the power of labour.
As I have already said, this is a dangerous and difficult plan to
follow, and this is because there is room for error at every
step.

The conclusions which Poppel and Tait and myself enunciated
regarding the power of natural parturition stand on a completely
different and, it appears to me, far more secure footing. There
can, indeed, be scarcely any important difficulty raised regarding
them. The strength of the foetal membranes is ascertained by
experiment. Certain facts are well known regarding the rupture
of the membranes generally, and regarding their rupture in the
labours in which the membranes experimented on were produced.
These two sets of data, when put together, lead by a process of
reasoning, which it would be tedious here to recapitulate, to con-
clusions regarding the lower* limit of the power of natural labour,
and regarding the power of labour generally, which cannot, so far
as I see, be cavilled at. It is evident that this method tests only
the whole or the combined powers of labour. It can afford no hint

3 E

VOL, VII.

374

Proceedings of the Royal Society

as to the comparative value of the two forces which combine to
produce the power which is to be measured.

The results given in Professor Haughton’s paper which appear
to me to be both new and important are three. I shall first state
them, and then proceed to their examination one by one

1. The first conclusion is, that “ the uterine muscles are capable

of rupturing the membranes in every case, and possess in general
nearly three times the amount of force requisite for this purpose.”
.... “It would be a waste of power (adds Haughton) to endow
the uterus with more force than I have shown it to possess, for it
is not necessary that the uterus should complete the second stage
of labour, as the abdominal muscles are available for this purpose ;
so that by using them, and not giving the uterus more force than
is absolutely necessary for the first stage of labour, an admirable
economy of muscular power is effected.” ... “ The extreme

force of uterine contraction produces a pressure of 3402 lbs. per
square inch, which is equivalent to a pressure of 54406 lbs. acting
upon a circle of four and a-half inches in diameter, which is
assumed as the average area of the pelvic canal.”

2. The second of Professor Haughton’s new and important
conclusions is, that the action of the voluntary abdominal muscles
“ constitutes the chief part of the force employed in difficult
labours.” . . . “ The amount of available additional force given
out by the abdominal muscles admits of calculation, and will be
found much greater than the force produced by the involuntary
contractions of the womb itself.”

3. The third conclusion is, “that, on an emergency, somewhat

more than a quarter of a ton pressure can be brought to bear upon
a refractory child that refuses to come into the world in the usual
manner.” ... “ Adding together the combined forces of the

voluntary and involuntary muscles, we find —

Involuntary muscles . . = 5440 lbs.

Voluntary muscles . . = 523-65 lbs.

Total . . 577-75 lbs. av.”

I. The first of Professor Haughton’s conclusions on which I
comment is, to the effect that the unaided uterine muscle can

of Edinburgh , Session 1870-71.

375

exert a force in labour of 54 lbs., that this force is employed in
dilating the cervix and rupturing the membranes, and that it can
or does effect little more.

Now, it appears to me that Haughton limits far too much the
use of the power of the uterus. I have no doubt that the uterine
efforts not only dilate the cervix and rupture the membranes in
most cases, but also do, in most cases, perform the chief part of
the work required to bring forth the child. Although I do not
coincide with Haughton in his reflections on the economy of
muscular power, I shall not discuss the point therein raised. Yet
I cannot avoid saying that, in the present instance, his own state-
ments invalidate his reflections, for he asserts that the uterine
muscle has three times the amount of muscular power required to
do the work demanded of it. In endowing the uterus with this
great power, Haughton, in my opinion, furnishes conclusive evi-
dence against his own view as to the use of the contractions of the
uterus. For I am sure that the great mass of births, even in
difficult labours, including only the most difficult, is effected by a
force less than what Haughton ascribes to the uterine muscle
alone. I am satisfied that the whole combined powers of labour
seldom reach above 50 lbs., while Haughton gives the uterus alone
a power of 54.

I do not say Haughton is wrong in supposing that the uterus
can exert a force of 54 lbs. On the contrary, I have no reason to
doubt it. But I am sure that while easy labours require for their
whole work a force scarcely exceeding the weight of the child,
only a few difficult labours require for their whole work a force
exceeding 50 lbs.

Every accoucheur knows to some degree of exactness the force
which is required to restrain the forward movement of the child
when there is no special resistance to its advance. This power I
have measured approximatively by dynamometrical experiments,
and I find it to be at the most 50 lbs., — a power less than what
is ascribed by Haughton to the unaided uterus. In other words,
the uterus and voluntary muscles combined, stimulated to violent
effort by insuperable temporary resistance, exert a force greater
than is required to complete the labour; yet this force is generally
much less than 50 lbs., and possibly never exceeds it.

376 Proceedings of the Royal Society

It is well-known to accoucheurs that the great resistance to the
progress of the child in the second stage of labour is what is called
in obstetrics the perineum. The power of this part I do not know,
and guessing is a bad proceeding in a scientific paper. Yet I may
venture to say that no perineum would long resist a force of 50
lbs. repeatedly applied, a force less than Haughton ascribes to the
uterine muscle.

II. Haughton ’s second conclusion is that the chief force in par-
turition is furnished by the voluntary muscles. The available
power of these is (he says) 523 lbs., while that of the uterus is 54.
The whole amount of expulsive force of the voluntary muscles is,
he says, not usually employed to assist the uterus in completing
the second stage of labour; but this does not contradict the con-
clusion we have ascribed to him. The conclusion is indeed, for
Professor Haughton, inevitable, for every accoucheur knows that
the bearing down efforts, whatever may be their actual measured
power, are very strong, perhaps as strong as possible, quite fre-
quently in ordinary labours. Besides, Haughton himself expounds
his meaning in the following words : — “ It is plainly necessary that
the first stage in the expulsion of the foetus should not be intrusted
to a voluntary muscle, and hence an involuntary muscle is gradu-
ally provided, which takes the initiative and commences the pro-
cess of parturition, the completion of which is then accomplished
by the aid of voluntary muscles, to the employment of which, at
this stage, no moral objection can be raised. It is also necessary
(if the Contriver be allwise, or if the principle of least action in
nature be true), that the involuntary muscle so produced, should
not possess more or less force than is requisite for its purpose.
The uterine muscle does not grow to meet a growing resistance
(as happens frequently in other cases), and its precise degree of
strength cannot be produced by a tentative process; for in healthy
gestation the uterine muscle never tries its force against the mem-
branes it is called upon to rupture until the actual period of
parturition has arrived.”

The view expounded in these words has great authority on its
side beside that of the quoted writer, for the point therein raised
as to the relative powers and uses of the uterine and auxiliary

of Edinburgh, Session 1870-71.

377

forces of parturition is one that has been much discussed and for
a long time. The great Haller, indeed, held opinions which are
in accordance with Haughton’s view. This renowned physiologist
discarded the opinion common in his day, and now almost uni-
versally entertained, that the uterus is the main source of the power
exerted in every stage of parturition.

Haughton gives us no reason for discrediting the general opinion
of obstetricians, relying apparently on his conclusions alone re-
garding the comparative power of the two forces, that of the uterine
muscle and that of the assistant voluntary muscles. No doubt he
makes some observations intended to be corroborative as to the
economy of force and other so-called laws of nature ; but such
reflections cannot be regarded otherwise than as premature by
those who, like myself, do not adopt this writer’s conclusions upon
whose verity their justice depends.

In the course of his concise view of this question in his work on
Physiology, Haller twice takes care to express his doubts as to the
truth of his own opinions ; and he ends by appealing to anatomists
for light upon the subject. This appeal is, at least, ingenuous, for
his argument against the ordinary opinion rests greatly upon the
uterine fibres, their direction, and the direction of the force evolved
by them ; and, as Haller’s notions on this anatomical point were
very imperfect, and his mechanical ideas equally so, we need attach
no weight to this part of his argument. Besides this, however, he
has really nothing deserving the name of good evidence on his
side. He thinks the effects produced by expulsive pains greater
than the power of the uterus ; but this is evidently mere begging
the question. So also is his dependence, for aid in his judgment,
on a picture of the great struggles of the voluntary muscles.

Authors generally do, as I have said, entertain an opinion
opposed to that of Haller and Haughton. They are too numerous
to name, and no one merits special mention; for, so far as I know,
no one has distinguished himself by the novelty or elaborateness
of his arguments in support of the ordinary view that the uterus is
the chief agent in the whole process of parturition, and that the
voluntary muscles, whether stimulated by volition or by reflex
excitement, are, in a secondary position, aiding the uterus indeed
but not supplying the chief force. There is no positive value in an

378 Proceedings of the Royal Society

argument of appeal to authority, yet it is evident that the amount
of authority against him made Haller hesitate to enunciate his
own views ; and, when we consider the number, the intelligence,
and the acute attention of the obstetricians who form a majority,
scarcely differing from the whole body, in favour of our view,
we cannot but be weightily impressed in its favour.

I must admit that some of the arguments made by obstetric
authors to do regular service in defence of their view are very
weak or quite vain. I may cite examples. Cases of parturition
completed when the uterus is prolapsed, and is said to derive no
assistance from bearing down efforts, are cited. But such cases
prove almost nothing, even supposing they are correctly described ;
for there is in such cases absence of the ordinary difficulties of
labour which consist in the propulsion of the child through the
pelvis. Cases of expulsion of the child after death of the mother
are quoted. But so far as I have perused them, they are given
with a deficiency of circumstantial data such as to invalidate them
altogether. Indeed, it is, in some of them, not even shown that
the uterus acted at all ; while in all there is the assumption that
the difficulty of birth after death is as great as before it. The like
objections may be made to examples of labour in asphyxia, narco-
tism, and syncope. It lias been asserted also that narcotism by
chloroform affords evidence that the uterus is the chief agent in
parturition. But I must assert the incorrectness of this argument,
and I cannot understand wrhy Haughton should call attention to
the influence of this agent, for any argument from it is valid, so
far as it goes, only against his own views. I have, in a large
experience, never seen chloroform inhalation destroy the action of
the voluntary muscles. I believe it generally weakens their action,
and it is well known that, at the worst, it only weakens the powers
of labour. It is not known whether it weakens the uterine action or
the action of the voluntary muscles in the greatest degree. If it
does, as is alleged, when given profusely, destroy the action of the
voluntary muscles, it certainly seldom completely arrests the pro-
gress of labour. Lastly, cases of labour in paraplegic women are
cited in favour of the ordinary opinion. But I fear they do not
even appear to favour it ; and, with a view to the present question,
they cannot be held as settling anything, seeing we do not know

of Edinburgh, Session 1870-71. 879

what influence paraplegia may exert on the uterus itself. Besides,
the cases are insufficient in every way.

The arguments on which I place chief reliance are the follow-
ing:—

1. The great power of the uterus felt by the hand of the
accoucheur, as in the operation of turning, long after the rupture
of the membranes.

2. The great and sufficient power of the uterus observed in cases
where the action of the voluntary muscles is weak or restrained.

3. The regulating influence of purely uterine pains in the pro-
gress of the second stage of labour.

4. The supremely important demand for and presence of power-
ful uterine action after the expulsion of the child.

5. The arrest of the progress of labour by inertia of the uterus.
This argument appears to me unanswerable, for the condition often
occurs when there is certainly only the slightest possible resistance
to the progress of the child, when the mother ardently desires the
completion of labour, and bears down violently with this object in
view.

6. In cases of uterine inertia, such as are above described, the
practitioner may find, by pulling with the forceps from below or
pushing with the hands from above, in the absence of all partu-
rient effort, whether of the uterus or of the voluntary muscles,
that a very small force, say not exceeding the weight of the child,
is sufficient to finish a labour upon whose progress violent bearing
down efforts have had no effect.

7. The circumstance that, were the voluntary muscles the chief
agents, expulsion of the child would be in great part a voluntary
act, which it certainly is not.

8. The asserted completeness of the function of parturition in
animals in which the assistant bearing down efforts are annihi-
lated by opening the abdomen ; the process being effected by their
uterine and vaginal muscles, which are weak when compared with
that of women.

Baudelocque and Velpeau* relate cases which appear to show
that woman has very rarely voluntary power over the progress of
parturition for a time Such cases offer no difficulty when regarded
* Traite complet de l’art des Accouch. Ed. Bruxelles, p. 227.

380 Proceedings of the Payed Society

with a view to the present question. They are explicable in more
ways than one, and an illustrative statement is, for my present pur-
pose, quite sufficient. Every experienced accoucheur has seen
cases where voluntary increase of bearing down has sufficed to
expedite labours, which, if the women had been left in a sleepy,
lethargic condition, might have been protracted for an indefinite
length of time.

There can be no doubt that the uterus is a very powerful
agent in expelling the foetus from its cavity into the world —
that it is not the sole agent, and that it is assisted by the action
of the voluntary muscles. Though I have not proved absolutely
that the uterus is the chief agent in the performance of this func-
tion, yet I have no doubt that it is so; and I think that the
arguments I have adduced give this belief of the profession the
highest degree of probability. This belief does not imply that
the aid afforded by the voluntary muscles is inconsiderable or
unimportant. It only renders it quite incredible that while the
power of the uterus is 54 lbs. that of the voluntary muscles can
be 523.

III. Haughton’s conclusion, on which I wish last of all to
comment, is, “ that, on an emergency, somewhat more than a
quarter of a ton pressure can be brought to bear upon a refrac-
tory child that refuses to come into the world in the usual manner.”

In my work entitled “ Researches in Obstetrics,” to which Pro-
fessor Haughton refers, I have discussed carefully, but briefly,
this point, and announce the conclusion that the comparatively
small figure of 80 lbs. gives the highest power of labour ; and I
quote Joulin, who estimates it at somewhat above 100 lbs. I do
not deny that in exceptional circumstances a few pounds above 80
may be reached, but I feel pretty sure that seldom in the history
of woman has the figure 80 been attained, whether on an emer-
gency or not. This conclusion is arrived at by experiment and
observation— experiments on the force required to pull a child
through a contracted brim of pelvis, observations of the force used
to complete a difficult labour, which nature, in its most violent
throes, has failed to accomplish.

Every accoucheur will, I suppose, readily admit that, in a case

of Edinburgh , Session 1870-71.

381

of delivery by podalic extraction, the surgeon can exert a great
deal more force to bring the child into the world than the most
energetic labour can. Now, in these circumstances the surgeon
can use no force nearly reaching to a quarter of a ton. A very
much smaller power would rend the luckless body of the child in
pieces.

Such a power as a quarter of a ton does, in my opinion, represent
a force to which the maternal machinery could not be subjected
without instantaneous and utter destruction. To speak of a rigid
perineum resisting such a power, or the fourth part of it, would
be ridiculous. The possession and use even of a considerable portion
of such a power would render the forceps and the cephalotribe
weak and useless instruments. The mother could bray the child
as in a mortar, and squeeze it through a pelvis which would, under
other circumstances, necessitate Caesarean section. Such a power
would, if appropriately applied, not only expel the child, but also
lift up the mother, the accoucheur, and the monthly nurse all
at once. It would be dangerous not only to the mother and the
child ; it would imperil also the accoucheur. It has been cal-
culated for me, that if this force were applied just as the chief
resistance to delivery was overcome, the child would be shot out of
the vagina at the rate of thirty-six feet per second!* The blow
would be equal to the shock produced by the fall of the child from
a height of twenty-one feet.

In an early part of this paper I have said that the method of
inquiring into the subject which Haughton adopts is both difficult
and dangerous, and I think I have said enough to show that
danger has not been avoided. There must be error in Professor
Haughton’s calculation of the power produced by the action of
the voluntary muscles, or there must be error in judging of the
application of this power to the accomplishment of the function,
or there must be 'error in both. I shall not attempt to show where
the error lies, but its occurrence does not astonish me; for any one

* In making this calculation the child is taken as 7 lbs., the pressure as
580 lbs., and it is supposed to be exerted through a space of three inches —
measurements which are fair statements of the case. It is farther supposed
that the friction is negligible when compared with the forward pressure.
This is certainly the case if the forward pressure be nearly as much as is
stated by Professor Haughton as possible.

VOL. VII. 3 If

382

Proceedings of the Royal Society

who has studied the difficult subject of the retentive power of the
abdomen will recognise the difficulty of reaching conclusions as to
the power of labour by Haughton’s method. It is highly probable
that the power of the voluntary muscle is dissipated, perhaps in
compressing intestinal gases, perhaps in consequence of being mis-
directed.

Whatever may be the real source of error as to this matter, it
is highly desirable to find it out, in order that we may, by more
accurate proceedings, arrive at the true results which Haughton
hoped to reach.

The following Gentlemen were admitted Fellows of the
Society : —

Rev. William Scott Moncrieff, of Fossaway, M.A. (Camb.)

Professor A. R. Simpson.

Dr R. J. Blair Cunynghame.

Dr Cosmo Gordon Logie, Surgeon-Major, Royal Horse Guards.

Monday, 20 th February 1871.

W. F. SKENE, LL.D., Vice-President, in the Chair.

The following Communications were read : —

1. On the Pentatonic and other Scales employed in Scottish
Music. By the Hon. Lord Neaves.

Lord Neaves adverted to the peculiarity which had been observed
in many Scotch airs, that they are composed on a pentatonic scale,
and do not make use of the fourth or seventh of the gamut. It
has been said that these airs can be played on the black notes of
the pianoforte, which means that they can be played on the key of
FjJ major, of which the fourth and seventh are represented by white
notes, but are not needed. He also observed that this class of airs
could be played on the white notes of the piano, both in the key of
F and in that of Gr. They could be played on F, because, as they
do not use the fourth, they do not need ; and they could be
played on Gr, because, as they do not use the seventh, they do not
need F$. They could also, of course, be played on the key of C.

383

of Edinburgh, Session 1870-71.

Many minor airs can be played on the pentatonic scale of the
relative major; that is, airs on D$ minor can be played on the
black notes, and airs in A minor can be played on the white notes
on the pentatonic of 0 ; airs in D minor on the pentatonic of F ;
and airs in E minor on the pentatonic of G.

Specimens of major pentatonic airs are these — “Roy’s Wife,’

“ Auld Langsyne,” “ Ye Eanks and Braes/’ “ The Gypsies came,’

“ WTnstle o’er the lave o’t.”

Specimens of minor pentatonic airs — “ The Mucking o’ Geordie’s
byre,” “My tocher’s the jewel,” “Auld Robin Gray” (old set),

“ Wandering Willie,” “ Ca’ the yowes to the knowes.”

Some minor airs are composed on the pentatonic of the tone
below.

Specimens — “Adieu, Dundee” (in Skene MS.), “Blythe, Blythe.”

In several old pentatonic airs grace notes or transitional notes
have been added in modern singing or playing, but the original
pentatonic character can still be traced.

Another large class of Scotch airs are composed on the full
diatonic scale, and can be played entirely on the white notes with-
out any apparent modulation.

When these airs are on the key of C major, there is nothing
very peculiar in them, and there are many of this class. But
when they are composed on other keys, certain peculiarities
appear.

Several Scotch airs are composed in the key of G, but played on
the full diatonic scale of C, so as frequently to introduce F natural,
sometimes with a pathetic, sometimes with a comic effect. The
old set of the “Flowers of the Forest ” (Skene MS.) is an example
of the one, and the tune of “ Pease Strae ” of the other.

Other specimens are — “Bessie Bell,” “ Tullochgorum,” “Loch-
aber no more.”

Minors in the diatonic scale are often singular, as, for instance,
the air of “ My boy, Tammie,” played on the white notes. It
runs into three keys — D minor, C major, and F major.

The pentatonic scale is not peculiar to Scotch music, but it may
partly be accounted for by the fact that rude wind instruments are
apt to be defective in the fourth and fifth. The simple diatonic
scale, without other semitones, may in like manner have been used

384

Proceedings of the Royal Society

from the adoption of early harps or other stringed instruments of
a limited construction.

Scotch airs were often imitated by introducing a particular
accentuation, called the Scottish “snap,” as in the Vauxhall air,

’Twas within a mile of Edinburgh Town.”

He expressed an opinion that many airs were common to Scot-
land and the North of England, and he denied that Scotch airs
were always sombre, as had sometimes been alleged.

Airs illustrating the views above stated were played by Mr
Bridgman in a manner of which it may be allowable to say that it
gave great satisfaction to the audience.

2. On the Motion of Free Solids through a Liquid.

By Sir William Thomson.

This paper commences with the following extract from the
author’s private journal, of date January 6, 1858 : —

“ Let IT, 1 L, iPT, be rectangular components of an impul-

“ sive force and an impulsive couple applied to a solid of invariable
“ shape, with or without inertia of its own, in a perfect liquid,
11 and let u, v, w, «r, p , <r, be the components of linear and angular
“ velocity generated. Then, if the vis viva* (twice the mechanical
“ value) of the whole motion be, as it cannot but be, given by the
“ expression

“ Q = \u, u\v? + [v, v\v0- + .... + 2 [v,u\vu + 2 \w,il\wu + Z[z?,u~\z<ru +

“ where = [w, w], [v,v], &c., denote 21 constant co-efficients determin-
“ able by transcendental analysis from the form of the surface of
“ the solid, probably involving only elliptic transcendentals when
“ the surface is ellipsoidal : involving, of course, the moments of
“ inertia of the solid itself : wre must have

[w, u\u + [v, u]v + [w, u\w + [ar, u\vr + [ p , u]p + [(7, u\a- = &C.

\u, ztju + [v, -&\v + [w, ar]t0 + [ar, ™\sr + [p, isrjp + [cr , a r](7 = 2L, &C.

“ If now a continuous force X,Y,Z, and a continuous couple
“ L,M,N, referred to axes fixed in the body, is applied, and if

“ M &c., denote the impulsive force and couple capable

“ of generating from rest the motion u , v, w, w, p, <r, which exists

* Henceforth T, instead of £ Q, is used to denote the “ mechanical value,”
or, as it is now called, the “ kinetic energy ” of the motion.

• 385

of Edinburgh, Session 1870-71.

“ in reality at any time t\ or merely mathematically, if &c.,
“ denote for brevity the preceding linear functions of the com-
“ ponents of motion, the equations of motion are as follow ; —

“ resultant momentum constant;

(3) iL£ + ffliY + §*% = const.

“■ resultant of moment of momentum constant ; and

(4) + vY + + c r0i = Q, .”

These equations were communicated in a letter to Professor
Stokes, of date (probably January) 1858, and they were referred
to by Professor Eankine, in his first paper on Stream Lines, com-
municated to the Eoyal Society of London,* July 1863.

They are now communicated to the Eoyal Society of Edinburgh,
and the following proof is added : —

Let P be any point fixed relatively to the body, and at time t ,
let its co-ordinates relatively to axes OX,OY,OZ fixed in space, be

* These equations will be very conveniently called the Eulerian equations
of the motion. They correspond precisely to Euler’s equations for the
rotation of a rigid body, and include them as a particular case. As Euler
seems to have been the first to give equations of motion in terms of co-
ordinate components of velocity and force referred to lines fixed relatively
to the moving body, it will be not only convenient, but just, to designate
as “Eulerian equations” any equations of motion in which the lines of re-
ference, whether for position, or velocity, or moment of momentum, or force,
or couple, move with the body, or the bodies whose motion is the subject.

d$

dt

dli

—rr ~ Yw -}- + Jlp = L

- ¥o- + = X,^ = &c-> &c*'

dY

. . . a)

“ Three first integrals, when

X = 0, Y = 0, Z = 0, L = 0, M = 0, N = 0,
“ must of course be, and obviously are,

(2) £2 + ¥2 + W = const.

386 Proceedings of the Royal Society

x, y , z. Let PA, PB, PC be three rectangular axes fixed relatively
to the body, and (A,X), (A,Y), . . . the cosines of the nine
inclinations of these axes to the fixed axes OX, OY, OZ.

Let the components of the “impulse”* or generalized momen-
tum, parallel to the fixed axes be £, rj, £, and its moments round
the same axes A, y, v , so that if X, Y, Z be components of force
acting on the solid, in line through P, and L, M, N components of
couple, we have

dij _ d/Yj y df y

dt ' ’ dt~ ’ dt~

(6).

dX _ _ _ dfi ,, v - dv AT v v

jt = L + Zy - Yz , -£ = M + Xz - Zx , = N + Yx - Xy \

Let g, % and 3L, HU, be the components and moments
of the impulse relatively to the axes PA, PB, PC moving with
the body. We have

| =$(A,X) +g(B,X) + Z(C,X) ^

A = n (A, X) + m (B, X) + $ (C, X) + %y -

Now let the fixed axes OX, OY, OZ be chosen coincident with
the position at time t of the moving axes, PA, PB, PC, we shall
consequently have

£c = 0, y = 0 , z =
dx _ dy _ dz

It U 3 dt ’ dt

(8).

(A, X) = (B, Y) = (C, Z) = 1

(A, Y) = (A, Z) = (B, X) = (B, Z) = (C, X) = (C, Y) = 0

d( A,Y) d{ B,X)

~~It * ’ dt

d(A, Z) _ _ d(B,Z)

dt P ’ dt

“ o’ j

d(C, Y) _ H
dt

Using (7), (8), and (9) in (6) we find (1).

* See “ Vortex Motion,” \ 6, Trans. Roy. Soc. Edin. (1868).

387

of Edinburgh,. Session 1870-71.

One chief object of this investigation was to illustrate dynamical
effects of helipoidal property (that is right or left-handed asymmetry).
The case of complete isotropy, with heliyoidal quality, is that in
which the coefficients in the quadratic expression for T fulfil the
following conditions.

[w, u] = [v} v\ = \w, w\ (let m be their common value) \

[^r, w] = [p, p] = [cr, cr] ,, n „ ,, „

K w] = b,p] = O, <r] „ h „ „ „ (10).

[v, w] = [«;, w] = [w, F] = 0 ; [p, cr] = [cr, zff] = [^r, p] =0
and [u, p] = [' u , a-] - [v, cr] = [v, w] = K «r] = [w, p ] = 0 J
so that the formula for T is

T = ^{m(y + v2+.w2) + w(^2 + p2 + o-2) + 2h(u<v + vp-\-'W(r)} . (11)#

For this case therefore the Eulerian equations (1) become
d(mU(U “ m( W — wp)=X, &c.

and *& + »") = Lj *c.

dt ’

[Memorandum: — Lines of reference fixed relatively to the
body]. J

But inasmuch as (11) remains unchanged when the lines of
reference are altered to any other three lines at right angles to
one another through P, it is easily shown directly from (6) and
(9), that ; if, altering the notation, we take u , v, w to denote the
components of the velocity of P parallel to three fixed rectangular
lines, and w, p, cr the components of the body’s angular velocity
round these lines, we have

d(mu + h<zr) _ \

dt ’ C'

and dJ^±M _ Kav _ pw) = L, &c. (12>

[Memorandum: — Lines of reference fixed in space], /

which are more convenient than the Eulerian equations.

The integration of these equations, when neither force nor
couple acts on the body (X = 0, &c. ; L = 0, &c.), presents no
difficulty, but its result is readily seen from § 21 (u Vortex
Motion”) to be that, when the impulse is both translatory and
rotational, the point P, round which the body is isotropic, moves

388

. Proceedings of the Royal Society

uniformly in a circle or spiral so as to keep at a constant distance
from the “axis of the impulse,” and that the components of
angular velocity round the three fixed rectangular axes are con-
stant.

An isotropic helicoid may be made by attaching projecting
vanes to the surface of a globe, in proper positions ; for instance,
cutting at 45° each at the middles of the twelve quadrants of
any three great circles, dividing the globe into eight quadrantal
triangles. By making the globe and the vanes of light paper, a
body is obtained rigid enough and light enough to illustrate by
its motions through air the motions of an isotropic helipoid
through an incompressible liquid. But curious phenomena, not
deducible from the present investigation, will no doubt, on account
of viscosity, be observed.

Still considering only one movable rigid body, infinitely remote
from disturbance of other rigid bodies, fixed or movable ; let there
be an aperture or apertures through it, and let there be irrotational
circulation or circulations (§ 60 “ Vortex Motion ”) through them.
Let £, rj, £, be the components of the “ impulse ” at time t , parallel
to three fixed axes, and A,, fx , v its moments round these axes,
as above, with all notation the same, we still have ( 26 “Vortex
Motion”)

But, instead of for T a quadratic function of the components of
velocity as before, we now have

T = E + u] u2 + . . . + 2 \u, v\uv + . . .} . . . (13).

where E is the kinetic energy of the fluid motion when the solid
is at rest, and \u , u \u2 + . . .} is the same quadratic as before.

The coefficients [iq u~\, [ u , v], &c., are determinable by a transcen-
dental analysis, of which the character is not at all influenced by
the circumstance of there being apertures in the solid. And

Part II.

. . . (6) (repeated).

dT

instead of £ = — , &c., as above, we now have
du

of Edinburgh, Session 1870-71.

389

\

• • • (14),

where I denotes the resultant “ impulse ” of the cyclic motion
when the solid is at rest ; Z, m, n its direction cosines ; Gr its
“rotational moment,” (§ 6, “Vortex Motion”); and x) y , 2 the co-
ordinates of any point in its “ resultant axis.” These (14) with
(13) used in (6) give the equations of the solid’s motion, referred
to fixed rectangular axes. They have the inconvenience of the
coefficients [ u , w], [w, v], &c„, being functions of the angular co-
ordinates of the solid. The Eulerian equations (free from this
inconvenience) are readily found on precisely the same plan as
that adopted above for the old case of no cyclic motion in the
fluid.

The formulas for the case in which the ring is circular, has no
rotation round its axis, and is not acted on hy applied forces, though
of course easily deduced from the general equations (14), 13), (6),
are more readily got by direct application of first principles. Let
P be such a point in the axis of the ring, and A, B, such con-
stants that ^-(^Tw2 + A u2 + Bv2) is the kinetic energy due to
rotational velocity w round D, any diameter through P, and trans-
lational velocities u along the axis and v perpendicular to it.
The impulse of this motion, together with the supposed cyclic
motion, is therefore compounded of

and moment of momentum round the diameter D.

Hence if OX be the axis of resultant momentum ; ( x , y) the
co-ordinates of P relatively to fixed axes OX, OY ; 0 the inclina-
tion of the axis of the ring to 0 ; and £ the constant value of the
resultant momentum : we have

momentum in

lines through P

A u -f I along the axis
Bv perpendicular to „ „

£ cos 6 -- k.u + 1 ; - £ sin 6 - Bv ,

f y = ;

(15.)

and

3 G

VOL. VII.

390

Proceedings of the Royal Society

Hence, for 0 , we have the differential equation,

+i 0 sin 6 + fp fsin 26] =0 ' (l6'}

which shows that the ring oscillates rotationally according to the
law of a horizontal magnetic needle carrying a bar of soft iron
rigidly attached to it parallel to its magnetic axis.

When 0 is and remains infinitely small, 6, y , and y are each
infinitely small, x remains infinitely nearly constant, and the ring
experiences an oscillatory motion in period

« , Be

V[I + (A - B)£c](I + Ax) ’•

compounded of translation along OY and rotation round the dia-
meter D. This result is curiously comparable with the well-known
gyroscopic vibrations.

3. Laboratory Notes. By Professor Tait.

1. On Thermo-electricity.

Messrs J. Murray and J. C. Young have been carrying out
experimentally the idea mentioned in my former note on this
subject. (Proc. Dec. 1870.) Their first sets of observations, of
the results of which I subjoin a specimen, were made with an
iron-silver and an iron-platinum, circuit working opposite ways on
a differential galvanometer. The resistances (including the galva-
nometer coils) were in this particular experiment 53T and 25-9
B.A. units respectively, so that but very slight percentage changes
could he produced in them by the elevation of temperature of the
junctions. As one of a number of closely agreeing preliminary
trials the result is extremely satisfactory, though the exact adjust-
ment has not yet been arrived at. To show the parabolas due to
the separate circuits, and thus exhibit the advantage of the method,
I have requested the experimenters to break the circuits alter-
nately after taking each reading of the complex arrangement, and
take a rough reading. The last four columns of the table give
the results; but, as the temperatures were probably slightly different
from those in the first columns, no very direct comparison can be
instituted. A glance at the 4th, 6th, and 8th columns, however,
shows how nearly a linear relation between temperature-difference
of junctions and galvanometer deflection has been arrived at in the

391

of Edinburgh, Session 1870-71.

composite arrangement, while the separate circuits give marked
parabolas.

p.

1

p.

|

&b

|1

Sh

<2 O

6 g

§ g

EH

Et

EH

fi) *

s

1|?

s .

if?

fi

£

fi.HS

£

fi.eS

bj)

<1

fi.es

12-3° C

39-0° C

28-5

10-67

44

16-28

17

6-32

„

72

61-5

10-30

96-0

16-08

36

603

„

104

930

10-14

143-5

15-55

51-5

5-61

„

146-5

136-5

10-17

202-5

15-08

68-0

5-06

12*6

185

172-5

io-o

250-0

14-50

77-0

4-46

„

202-5

190-5

1003

268-5

14-13

79-5

4-18

12-4

229*5

219-5

10-11

298-5

13-74

81-5

3-74

„

251-5

239-0

10-0

318*0

13-30

81-0

3-38

12-5

263-0

250-5

io-o

330-0

13-16

80-0

3-19

272-0

260-0

io-o

3370

12-98

80-0

3-19

I find great difficulty

in obtain

ing wires

of the

more

infusible

metals :-

—and I

am therefore endeavouring to make a

complex

arrangement for very high temperatures with palladium and two
very different kinds of platinum. Wires of nickel, cobalt, molyb-
denum, rhodium, or iridium, or of any one of these, would be of
immense use to me, and I should be happy to hear from any one
whether there is a possibility of procuring them.

2. On Phyllotaxis.

I was recently led to consider this subject by Professor A.
Dickson, who showed me some of his beautifully-mounted speci-
mens, and explained to me the method he employs for the deter-
mination of the divergence, and of the successive leaves of the
fundamental spiral or spirals. He referred me to two terribly
elaborate papers by Bravais,* and I have since met with another
of a similar character by Naumann.f These papers certainly
cannot be supposed to present the subject from the simplest point
of view. I do not doubt that the results I have here arrived at are
to be found in some form or other in their pages, which are an-
nounced as completely elucidating the question ; but I have not
sought for them, my sole object having been to put what seem to me
the elements of the matter as simply and intelligibly as I could.

* Annales des Sciences Naturelles, 1839.
t Poggendorff’s Annalen, 1842.

392

Proceedings of the Royal Society

Let A, a, represent the same leaf in a plane development of a

branch or fir-cone
(regarded as cylin-
drical) ; 0, a leaf
which can be
reached from A
by m steps in
a right-handed
spiral, developed
into the straight

line AO, and by n steps from a in a left-handed spiral aO. These
spirals may in general be chosen so that m and n are not large
numbers (3, 5, 8, 13, &c., being very common values) ; but they
must (and can always) be so taken that m spirals parallel to aO,
and n parallel to AO, shall separately include all the leaves on the
stem or cone.

If m and n have a common factor A, there will be A — 1 leaves
(besides A) which are situated exactly on the line A a, and there-
fore the arrangement is composite, or has A distinct fundamental
spirals. If m' and n' be the quotients of m and n by A, they are to
be treated as m and n are treated below ; and this case thus merges
into the simpler one, so that we need not allude to it again.

It is obvious that, in seeking the fundamental spiral, we must
choose the leaf nearest to A a on the side towards 0, as that suc-
ceeding A or a. The fundamental spiral will thus be right-handed
if P, which is nearer to A than to a, be this leaf — left-handed if
it be p. Of course, we may have a left-handed fundamental spiral
in the former case, and a right-handed one in the latter ; but the
divergence in either will be greater than two right angles, and this
the majority of botanists seem to avoid.

Draw PQ and pq respectively parallel to a 0 and AO, then the
requisite condition is that

n \ s-\ ni

— AQ - PQ, or -aq - pq ,
m n

shall be as small as possible.

Hence, if ^ be the last convergent to and if - > m . it is
v n v n

of Edinburgh, Session 1870-71. 393

obvious that to get at P we must count /x leaves along AQ, and v

along QP. If, however, ^ ^ Vl, count v leaves along aq, and /x
v n

along qq>. P, or p: thus found is the next leaf of the fundamental
spiral to A or a ; the next is derived from it by a second applica-
tion of the same process, and so on.

There is no necessity for restricting the development, as given
above, to once round the cone. Suppose we go several times round
and that A, a, a, &c., are successive positions of the same leaf. The
processes given above may be employed, and the results will be of
the same nature. But this extension enables us to obtain (more
and more approximately, sometimes accurately) a right angle aAo,
where o is a leaf reached after several turns of the fundamental
spiral. This indicates that the leaves maybe grouped (approxi-
mately or accurately) in lines parallel to the axis of the stem or
cone. When this can be done accurately, it is easy to see that

(since one of - n-, is greater, and the other less, than the number

V [X

of leaves in one turn of the fundamental spiral) the difference of
azimuth of two successive leaves of that spiral must be expressible
in the form

o rp + sv

£ 7 r — — : — SEaH $
rm + sn

where s and r are necessarily very small positive integers in all the
ordinary cases of phyllotaxis, since they are the numbers of leaves
in AK, Ec, respectively, which are portions of the spirals on which
or parallel to which, m and n were measured.

The fraction

r/x -f sv
rm + sn

has been called the divergence of the fundamental spiral. Of its
constituents the numbers m, n, r, s are at once given by inspection
of any cone or stem, and (from m and n) fx and v are easily
calculated.

To extend this investigation to the cases in which the divergence
is altered by torsion of the cone, it is merely necessary to notice
that such a process alters only r and s. It produces, in fact, a
simple shear in the developed figure.

394 Proceedings of the Royal Society

Added, March 20 th, 1871, in consequence of some remarks made by
Professor Dickson at the Meeting of that date.

It is obvious that if the same leaf, 0, be reached from A by m
steps of a right-handed, and n of a left-handed, spiral (such that n
of the former and m of the latter contain, severally, all the leaves),
another common leaf can be reached by m - n steps of the right-
handed spiral, and n steps of a new left-handed one (these spirals
possessing the same property of severally containing, in groups of
n and m — n respectively, all the leaves). This process may be
carried on, when m and n are prime to one another, until we have
steps represented by 1 and 1, in which case we obviously arrive at
the leaf of the fundamental spiral next to A. It is better, how-
ever, to carry the process only the length of steps 1 and t, where t
is determined by the condition that 1 and t + 1 would give spirals
both right-handed or both left-handed.

Now, in the majority of cases of fir-cones, it seems that we have
t, found in this way, = 2, i.e., there are less than three leaves in a
single turn of the fundamental spiral. It is of course obvious that
there can never be less than two, and the case of exactly two
corresponds to the simplest of all possible arrangements, that in
which the leaves are placed alternately on opposite sides of the
stem. Fir-cones, therefore, give in general the arrangement next
to this in order of simplicity. Hence, for such cones, and for all
other leaf arrangements which are based on the same elementary
condition, the values of m and n for the most conspicuous spirals
must be of the forms

2 , 3 , 5 , 8 , Ac.,

1, 2, 3, 5, A-c.

These simple considerations explain completely the so-called
mysterious appearance of terms of the recurring series 1, 2, 3, 5,
8, 13, &c., &c. The other natural series, usually but misleadingly
represented by convergents to an infinitely extended continued
fraction, are easily explained as above by taking t = 3, 4, Ac., Ac.
As a purely mathematical question it is interesting to verify the
consistency of the statements just made, where the change in t is
introduced, with those above made as to the effects of torsion in
altering r and s. But this may easily be supplied by any reader
who possesses a small knowledge of algebra.

of Edinburgh , Session 1870-71.

395

Monday, §th March 1871.

Dr CHRISTISON, President, in the Chair.

The following Communications were read :• —

1. Account of the Extension of the Seven-Place Logar-
ithmic Tables, from 100,000 to 200,000. By Edward
Sang, Esq.

A bstract.

In this paper the details were given of the computations made
for extending the Table of Seven-Place Logarithms to 200,000
and of the precautions taken to ensure accuracy in the printed
work.

The calculations were originally intended for a Nine-Place Table
to One Million ; and the manuscript shows the logarithms to fifteen
places, with their first and second differences for all numbers from
100,000 to 200,000.

2. On the Place and Power of Accent in Language. By
Professor Blackie.

Professor Blackie then read a paper on “ The Place and Power
of Accent in Language.” On the subject of accent and quantity,
he remarked, especially in relation to the learned languages, the
greatest confusion had prevailed, and the existing practice was
altogether unreasonable and anomalous. In articulate sound four
things had to be distinguished — volume or bulk, force or emphasis,
elevation and depression, and prolongation or duration. English
scholars had shown an unhappy incapacity of not being able to
distinguish between stress and prolongation, and thus had been led
to introduce the general practice of pronouncing G-reek with Latin
accents. In laying down the principles by which syllabic accentua-
tion is guided, four points are to be attended to — significance,
euphony, variety, and convenience. Fashion, of course, and cus-
tom have wide sway in this domain; but in the original structure

396 Proceedings of the Royal Society

of language we have to look to significance and euphony rather
than arbitrary usage, as the main causes which determined the
place of the accent. In compound words it was natural that the
qualifying or contrasting element should he emphasised, as in the
proper Scotch pronunciation of Balfour (Coldtown), where the
accent lies on that element of the word which distinguishes it from
other Bals or towns. As to euphony, those languages are least
euphonious which, like English and Gaelic, have a preference for
the ante-penultimate accent, while those are most euphonious
which, like Latin, Greek, and Italian, abound in penultimate or
ultimate accented syllables. In respect of euphony, as well as
variety, the Greek language was superior to the Latin, in that it
allowed the accent on any of the three last places, while Latin
allowed it only on the penult and ante-penult. The attempt to
make out a special and exceptional case for Greek accents were
vain. It is perfectly clear from the statements of the ancient
Greek grammarians, that the Greek acute accent consisted not
only in the raising of the voice on the syllable, as Professor Munro
imagines, but in a greater emphasis or stress. The prejudice which
has so long existed against the use of Greek accents arose partly
from mere carelessness, partly from a notion that the observance of
the accent would interfere with the proper quantity of the vowels,
and destroy the beauty of classical verse. But this notion is alto-
gether unfounded, as classical verse, originally an inseparable part
of musical science, was not governed in any respect by the spoken
accent, but guided entirely by the rhythmical ictus or time-beat.
Practically, there was no difficulty in reading Greek prose by the
accent, and Greek poetry by the quantity. In the /re'Aos, or purely
musical part of the drama, the spoken accent naturally fell away.
In recitation a sort of compromise probably took place, which is
perfectly easy of execution. The paper included a history or review
of the doctrines of learned men and great scholars on the subject of
Greek accentuation, from Erasmus down to Chandler, Munro,
Clark, and Geldart. It was astonishing that such confusion and
beating the air about imaginary difficulties should have so long pre-
vailed on a matter comparatively so simple ; but there was not the
slightest doubt that the moment our classical teachers should recur
to living nature, instead of being governed by dead tradition in this

of Edinburgh, Session 1870-71.

39'

matter, the present monstrous, pernicious, and perplexing practice
of reading Greek with Latin accentuation must cease. Independent
of its absurdity, the loss of time occasioned by teaching one accent
to the ear, and another to the understanding, should he motive
enough for all teachers to deliver our classical schools from a yoke
which, originally imposed by sheer laziness, is now supported only
by ignorance, prejudice, and the tyranny of custom.

Monday , 20 th March 1871.

D. MILNE HOME, LL.D., Vice-President, in the Chair.
The following Communications were read : —

1. Notice of Exhibition of Vegetable Spirals. By
Professor Alexander Dickson.

Dr Dickson exhibited a number of specimens, chiefly Fir Cones
and Cacti, illustrating the principal series of vegetable spirals.
Almost all the cacti and many of the cones were from the Edin-
burgh Botanic Garden and the Museum of Economic Botany there.
As the nomenclature of the cacti in the Edinburgh garden, as in
many other botanic gardens, is in a state of considerable confusion,
the specific names will not be referred to, and the generic ones,
even, must in some cases be held as only approximately correct.
This, however, is of the less consequence as the phyllotaxis of such
plants is eminently variable even in the same species. Ten
different series or systems of spirals were illustrated by specimens,
of which the following may be noted.

I. Ordinary series, g, ?, ^ , &c.

Cones of Abies Douglasii : A. excelsa (A) ; Pinus
Coulieri (-§|) : Araucaria excelsa (U) : Araucaria im -
Iricata : Bijugates of the same series in cone of
Abies Douglasii , the solitary abnormality out of

3 IT

VOL. VII.

398

Proceedings of the Royal Society

200 cones examined ; in an Echinocactus ; and in
Abies excelsa and Pinus Pinaster (21^2)' Tnjugates in
an Echinocactus (5^3) ; and in cones of Abies excelsa and
Pinus Pinaster (^3^3) .

II. Series, g, |, ^ , &o.

Cones of Pinus Pinaster , P. Lambertiana , and Abies excelsa
: Mammillaria cone of Pinus Jeffreyi

Bijugates of same series in an Echinocactus (7^2); and
one shoot of another Echinocactus (jj^) •

ITT Q • 1 1 2 3 .

III. Senes, ^ , &c.

Echinocactus ; cone of Pinus Pinaster or possibly
Bijugate of same series in an Echinocactus (g^g)-

I V . Series, g , ^ , -q , > ^0.

Two Echinocacti .

Y. Series, g , ^ , ~,&c.

A Cereus? and Mammillaria? (^) •

-ITT Q * 11 2 3

VI. oeiies, ^ , g , , 2g 5 txc.

Melocactus and Echinocactus .

VII. Series, ^ , |, |, ^ , &c.

Echinocactus? . Bijugate of same series in the middle
region of a cone of Pinus Lambertiana in the Museum,
Edinburgh Botanic G-arden ; the two parallel spirals,

399

of Edinburgh) Session 1870-71.

here, ran to the right hand, while the single spiral at top
and bottom of the cone was left-handed,

VIII. Series, 1, ®, ~ . &c.

Echinocactus .

tv o 1 2 3 5

IX. Senes, 3 , jq, R

Echinocactus .

&c.

X. Series,

13’ 22

, &c.

Cone of Pinus Pinaster , in Museum of Edinburgh Botanic
G-arden, (A) .

Dr Dickson drew special attention to five flower spikes of
Banksia occidentalism which he had examined from the Edinburgh
Botanic Garden. These he found to exhibit four distinct arrange-
ments. One had fourteen vertical rows of bracts, from alternate
whorls of seven ; two presented thirteen verticals, from a A
arrangement ; one had also thirteen verticals, but from a A
arrangement; the fifth had twelve verticals, from a A arrange-
ment.

2. On the Old River Terraces of the Spey, viewed in con-
nection with certain proofs of the Antiquity of Man. By
the Rev. Thomas Brown, F.R.S.E.

Abstract

The author referred to the paper which he had read on the ter-
races of the Earn and Teith,* and then described similar deposits
which he had observed last autumn on the Spey, giving examples
with drawings, from the neighbourhood of Kingussie, Dalvey, and
Ballindalloch. The arguments formerly adducedf were equally con-
* Trans. Roy. Soc. Ed. xxvi. 149. + Ibid. 154-163.

400 Proceedings of the Royal Society

elusive in the Spey to show that these terraces were not old sea
beaches nor lake margins, but the fluviatile deposits of some former
epoch when the floods rose to a greater height. The problem then
came to be, In what way are we to explain the action of the river
in throwing up deposits 60, 80 feet, or even more above its bed ?
There are two ways, in one or other of which this may be accounted
for, — either by supposing the river bed to have lain on its present
level, and allowing rainfall sufficient to flood the channels up to the
requisite height ; or by supposing the bed of the stream to have been
formerly at a higher level, and that, after forming the terraces, the
current had excavated its bed down to where it now is. It is the
second of these views which has found most favour among geologists,
and various suggestions have been offered as to how the bed of the
stream was formerly elevated.

One explanation is, that at the time of the highest terrace, the
line of the valley, then comparatively shallow, was occupied by the
original rock, still to a great extent in situ. In regard to our
Scottish valleys this explanation is inadmissible. It was formerly
shown, from the position of the boulder clay,* that the rocky struc-
ture of these river-courses had been hollowed out nearly as deep as
now previously to the formation of the terraces ; but apart from
the Boulder clay the terraces themselves, as will be shown, prove
the same thing, for example, the 70 feet terrace at Kingussie.

Another explanation is, that during the last submergence of
Scotland the valleys had been filled by marine gravels, &c., and
that the river bed had been thus lifted to the requisite height.
This view, however, must also be set aside, because after that sub-
mergence, the valleys of Scotland were occupied by glaciers, which
must to a great extent have cleared out these previous marine
deposits.! Especially must this have taken place in Strathspey,
lying so high above the sea, and connected with the central moun-
tain-masses of the country. The glacier must have ploughed out
the marine debris. It was after that the terraces were formed.

There is a third suggestion, that the river had raised itself on
its own alluvium, formed the terraces, and then re-excavated its

* Trans. Roy. Soc. Ed., vol. xxvi., 171.

t Sir C. Lyell’s Antiquity of Man, p. 206. Scenery of Scotland, by Mr
Geikie, p. 847

401

of Edinburgh, Session 1870-71.

bed. But here, again, the objections are equally decisive. First ,
the raising of a river bed in this way seems to take place only when
the current has reached some comparatively level part of its course,
as in the Po or Nile. The Spey is remarkable for the steep incline
of its bed. The Ordnance Survey * shows that for nearly 30 miles
below Orantown it goes down more than 600 feet,' — fully 20 feet a
mile. The current is strong, the old terraces are high. The idea
is not for a moment to be thought of that it could have acted as the
sluggish rivers which silt up their beds. But, secondly , how did the
river, after silting up its bed, and raising itself, come to change its
action, and cut its way down? Is any such case on record appli-
cable to any river course as a whole ? If such a revolution of
river action be exceptional, or if it be unknown in nature, we
should surely not be warranted in applying it to the rivers of Scot-
land generally at the period of the terraces.

Thus the idea that the river bed had formerly been elevated is
encompassed by difficulties. In whatever form the explanation is
put, objections at once suggest themselves which would appear to
be fatal.

Turning to the other view, that the river had flowed on its pre-
sent level, we find that the one great difficulty is the vast amount
of water which would be needed to flood the channels up to the
requisite height. Mr Prestwich, referring to the Somme and some
English rivers, has calculated that it would require 500 times the
present flow of the stream to form the 80 feet terrace.f When we
look closely into the matter, however, this difficulty diminishes.
The result of 500 : 1 is obtained by taking the present flow of the
Somme at 800 square feet sectional area. That represents the
river when not in flood. As the 80 feet terrace, however, is ad-
mittedly the work of the old river when in flood, we must take the
present Somme also in flood, and that is not 800 but 3000 square
feet (Prestwich).+ The effect of this first correction is to bring
the 500 : 1 down to 133 : 1. But, further, when Mr Prestwich
comes to put all the facts together, he estimates the old Somme at
a little more than five times the present — 1 6,000 § against 3000 of

* As yet unpublished ; but these results were obligingly communicated
by Gol. Sir H. James, F.R.S.

f Phil. Trans., vol. cliv., p. 265. J Ibid., 292. $ Ibid.

402 Proceedings of the Boyal Society

sectional area — and the result is, that if we compare his own view
with that which he ascribes to his opponents, the 133 : 1 is further
diminished to 25 : 1. But there is a still more important fact to be
taken into account. In calculating the sectional area of the old
river the whole valley is assumed as empty ; but this it cannot have
been, at least here in Scotland. If the rocky structure of the valleys
was excavated, and the rock removed, how shall the floods be
raised high enough to form the terraces? There only remain
water and alluvium to fill the space. The only reasonable view is
that the area of the valley was to a large extent occupied by masses
of alluvium since removed. And this is borne out by what we
actually find — fragments of old gravelly platforms left standing to
tell of deposits which evidently were at one time far more extended.
A third correction, not less important than the others, must be on
this ground applied to Mr Prestwich’s calculation. So far from
the valley having been empty, it must to a great extent have been
filled with alluvial deposit since denuded. The difficulty raised
as to the volume of the old floods is thus to a great extent set aside.

At various points along the Spey — Kingussie, Coulnakyle, Crom-
dale — transverse sections of the valley were given, showing the
height of the terraces. From the width of the valley in these
cases (of which details were given) it appeared that a calculation
like that of Mr Prestwich in the Somme would bring out results
equally incredible as to the old floods, hut owing to the above cor-
rections this difficulty is removed, and the remarkable thing is that
the 70 feet terrace at Kingussie has been laid open in an old river
course, and the 80 feet terrace at Cromdale in a railway cutting so
as to bring out similar results to those formerly shown from the
valley of Monzie.* Explain the matter how we may, the river,
with an open valley three-fourths of a mile wide, has begun at the
bottom, on the level of its present bed, and piled tip these deposits
to the height of 70 or 80 feet. That they are the work of the
river is proved by the way in which the platform-like surface of the
terrace slopes down the stream.

The idea of ascribing these high-lying terraces simply to the
greater flooding power of some former time was suggested by a
comparison between the deposits of the Kuchil with those of the
* Trans. Roy. Soc. Ed., vol. xxvi. pp. 171, 172.

403

of Edinburgh, Session 1870-71.

Upper Earn, and of the terraces of Loch Lubnaig with those of
Loch Earn, as formerly explained.* It is confirmed by the terraces
of the Spey, and more especially by the failure of all the other ex-
planations.

Our knowledge of this whole series of deposits is as yet far too
imperfect to allow of anything like a complete theory of their for-
mation. If a suggestion might be offered, perhaps the course of
events may have been something like this. When the glacial
epoch ended, and the covering of ice and snow melted off Scotland,
there would be no small amount of debris over the face of the coun-
try, and, unprotected by vegetable covering, it would be washed
down into the valleys. Every one admits that the rivers of that
age were larger than now — how much larger it is difficult to say.
If the Spey had five times its present volume (as Mr Prestwich
suggests in the case of the Somme) it would, judging from the
present force of its current, assuredly keep its central channel open
whatever the amount of debris which came down into the valley.
Eiver-like, it would form its banks, and spread out its haughs up to
the height to which its floods could rise, when confined to its com-
paratively narrow channel. In the case supposed that height may
have been great; and these old high terraces may be the fragments
of alluvial platforms, which once spread out along the valley, where
the old floods had raised them. Before the whole facts are fully
explained, it seems probable that our ideas of the amount of water
present in these old floods may have to be enlarged.

The bearing of these facts on certain arguments for the an-
tiquity of man was considered, with special reference to the Spey
deposits. There are gravel beds along the Somme in France,
which, up to the height of 80 feet, contain flint weapons,
which are held to be of human manufacture ; and the argument
is, that the river has excavated through the rock the valley in
which it now flows — that this has been done since the deposition
of the gravels, and to allow time for such excavation their age, and
consequently the human period, must be carried back into some
vast antiquity.

But here is an important fact, which the deposits of the Spey
make still more clear in some respects than those of the Earn and
* Trans. Royal Soc. Edin., vol. xxvi, 163-166.

404 Proceedings of the Royal Society

Teith. Along our Scottish rivers there are similar high gravels,
80 feet or more above the stream ; and it is known that, pre-
viously to the time of their formation, the rocky structure of our
valleys had already been hollowed out nearly as deep as now. This
is shown at Kingussie, where the 70 feet terrace — and at Crom-
dale, where the 80 feet terrace — are seen resting on the rock
nearly on a level with the river-bed. If, then, with the rocky
bed down on its present level, the Scottish streams have managed
somehow to form those high-lying deposits, why may not the French
rivers have done the same ? In that case, the Somme would re-
quire no time for the subsequent excavation of its valley, and the
human period, so far as this argument is concerned, may not he so
long after all.

The force of this does not depend on the correctness of the views
stated above as to the formation of these terraces. Whatever was
the way in which the Scottish rivers went to work, it was after the
rock had been excavated, and the question would still be, why may
not the French rivers have done the same ?

One point seems clear, that the case of the French gravels must
be shown to differ from those of Scotland before the advocates of
extreme antiquity can prove their case from the Somme. After
admitting the case in Scotland, if a distinction is to be made in
regard to France, the burden of proof will lie with them. The
probabilities would certainly seem to be against them. Rivers
and valleys have the same laws in different countries. If the
French rivers be alleged to have acted differently from the Scottish
it may have been so, but the grounds of the difference would need
to be adequate, and the proof clear. In the present case, the
alleged distinction has reference altogether to the excavation of
the rock. In France, they say it had to be done subsequently to
the time of the terraces ; in Scotland, it must be admitted to have
been done before. Are there any grounds on which such a distinc-
tion can be made good? Was there such a difference in the for-
mation of valleys between Scotland and France?

It wdll not be alleged that the soft texture of the chalk rock
of the Somme, as contrasted with our harder rocks, can form the
ground of distinction. In France itself the same valley-systems
traverse many different kinds of rock.

of Edinburgh, Session 1870-71.

405

Nor can it be said that the submergence of Scotland as con-
trasted with the area of the Somme, which was not submerged, can
constitute the difference, for Mr Prestwich has shown * not only
that the French system of valleys has crossed into the south of
England, but that it prevails indifferently as much beyond as within
the line of submergence traced by Sir 0. Lyell. That submergence
seems in this respect to make no difference.

It is equally in vain to allege that the large amount of alluvium
in the Scottish valleys makes such a ground of distinction when
contrasted with the lesser amount of such deposits on the Somme.
The alluvium along our Scottish streams is a very variable quan-
tity as between valley and valley, and as between different portions
of the same valley. On the other hand, the amount of the Somme
gravels at Amiens and above it, is great — so great, that both Mr
Prestwich and Sir Charles Lyell argue in favour of their antiquity,
from the length of time which must have been needed to accumu-
late such a volume of debris. On the Oise also, and some neigh-
bouring streams, the amount of alluvium is described as very great.

It is enough, however, to remark, that the burden of proof lies
with the advocates of antiquity, and that its difficulties have not
been surmounted. On the other hand, there is one thing which they
may fairly be asked to do — if they maintain that the French and
Scottish valleys have been formed on different principles — to show
where the two systems meet. The French method, as we have
seen, crosses into England. No one will maintain that the Scottish
stops at the Tweed. Somewhere they must come in contact. It
would be instructive if some one would try to show us two conter-
minous vp^eys wrought on the opposite plans. The attempt would
probably evince the impossibility of drawing such a distinction.
In all that is important, the French and Scottish valley systems
go together.

The whole of these remarks are submitted as suggestions, show-
ing the need of much more complete investigation. On this whole
series of deposits we have much to learn, — far too much to admit of
anything like confident conclusions being drawn as yet. The only
safe course is to await the results of future research.

* Phil. Trans., vol. cliv. PL iv.

t Prestwich, ut sup , 286. Sir C. Lyell, “ Antiq. of Man,” p. 144.

3 r

VOL. VII.

406 Proceedings of the Royal Society

If difficulty be still felt in regard to the amount of water required
for those old floods, we might appeal to the kind of proof by which
the existence of a former glacial epoch in Scotland is established.
Who that looked to the present ice and snow of a Scottish winter,
could think it likely that glaciers once filled the valleys of the
Pentlands, and that masses of moving ice rose over the flanks of
Arthur’s Seat. We point to the rounded and striated rocks, and
say, there are the foot-prints of the old glacier, — and the thing is
proved, no matter how different may be the cold of our present
winters. And why not reason thus in regard to the old floods ?
Who that looks on the present flow of our streams could realise
floods able to raise those old 80 feet terraces? But why should
we not point to these deposits where they lie, and say, these strati-
fied gravels and bedded sands are the workmanship of the old cur-
rents, which once swept and eddied at that height down these
valleys. If this kind of evidence makes you believe in the great
old glacier all unlike our present ice, why should not similar proof
make you believe in the great old floods of a former epoch, all
unlike though they may be to our present streams ?

And yet in Strathspey, with the traces of the Moray floods all
around us, it is easier to believe these things than it would be
almost anywhere else. It was at Coulnakyle, the scene of one of
these drawings, that Captain M‘Donald, R.N., a sailor of the old
school, looked out and saw the Spey, about a mile wide, covered
with wraves, that put him in mind of Spithead in a fresh gale3 and
felt sure, as he told Sir T. D. Lauder, that he could have sailed a
fifty-gun ship from Boat of G-arten to Bellifurtli,a distance of seven
miles. The small burn of Drumlochan, which in its ordinary state
“ is hardly sufficient to keep the saw-mill going,” rose till it swept
away two bridges of twenty feet span, the column of water being
estimated at 400 square feet sectional area. As the miller of Dal-
nabo expressed it, “ the height the burns rose to that day wTas just
a’ thegither ridiculous.” In looking back to the time of these old
deposits, it is generally admitted that the volume of the rivers was
decidedly greater than it is now. Mr Prestwich, as we have seen,
assumes that the old Somme was five times the present. If we
might suppose something like this in the Spey — if, further, there
was along the valley an amount of alluvium sufficient to confine

407

of Edinburgh, Session 1870-71.

the stream to its own channel — and if, from whatever cause, there
came floods which would do in proportion for the enlarged Spey
what the floods of 1829 did for the Drumlochan Burn, it does not
appear as if the solution of the problem as to the formation of
these high terraces should be difficult. It is in this direction that
the solution is to be sought.

Monday , 3 d April 1871 .

Professor KELLAND in the Chair.

The following Communications were read : —

1. On the Gravid Uterus and the Arrangement of the Foetal
Membranes in the Cetacea. By Professor Turner.

(Abstract.)

In this memoir the author described the dissection of the gravid
uterus of an Orca gladiator, for which he was indebted to Mr James
Gatherer of Lerwick. The paper contained an account of the
uterus and appendages, the foetal membranes, the position and
general form of the foetus, and a comparison of the placentation
with that of other mammals possessing the diffused form of pla-
centa. The structure of the uterine mucous membrane, its sub-
division into a gland layer and a crypt layer, the relations of the
glands to the crypts, their structure, the arrangement of their blood-
vessels, and the much greater vascularity of the crypts than of the
glands, were especially described. The chorion, though with diffused
villi, possessed not only a small non-villous part at each pole, but a
third larger bare spot opposite the os uteri internum; the non-villous
spots corresponded, therefore, to the three uterine orifices. The
arrangement and structure of the villi, the relations of the vessels
to them and to the chorion generally were described ; the plexus
of capillaries within the villi became continuous with a network,
termed sub-chorionic, situated immediately beneath the intervillous
part of the chorion, from this latter plexus the rootlets of the umbi-
lical vein arose. The intra-villous capillary plexus lay in relation
to the system of capillaries situated in the walls of the uterine

408

Proceedings of the Royal Society

crypts, whilst the sub-chorionic lay in relation to the capillaries
situated beneath the plane of the general uterine mucous surface,
v The amnion formed a continuous bag from one horn of the chorion
to the other, but did not fsach the poles of the latter. In the left
horn, which contained the foetus, it extended to 2 inches, in the
right to 9 inches from the corresponding pole of the chorion, its
free surface was studded with small pedunculated corpuscles. The
allantois was not so extensive as the amnion. The urachus
expanded into a large funnel-shaped sac, which bifurcated when it
reached the chorion and formed a right and left cylindrical horn ;
the left reached to 7 inches from the left pole of the chorion, the
right to 21 inches from the right pole.

2. Note on some Anomalous Spectra. By IT. F. Talbot.

A recent number of Poggendorff’s u Annalen ” contains a short
but interesting paper by Christiansen, of Copenhagen, in which he
states that a hollow prism filled with the alcoholic solution of
fuchsine produces a highly anomalous spectrum, which, instead of
proceeding regularly from the red to the violet like the ordinary
solar spectrum, stops at a certain point, returns backward, then
stops again and resumes a direct course to the end. This paper by
Christiansen, kindly pointed out to me by Professor Tait, recalls to
my memory an experiment which I formerly made more than
thirty years ago, and which, with the permission of the Society, I
will briefly describe, premising, however, that I write from memory,
and without access at present to the original paper which I believe
I have still preserved. My account may therefore contain some
inaccuracies, but the general nature of the experiment was as
follows : — I prepared some square pieces of window glass, about an
inch square. Taking one of these, I placed upon it a drop of a strong
solution of some salt of chromium, which, if I remember rightly, was
the double oxalate of chromium and potash, but it may have been
that substance more or less modified. By placing a second square of
glass on the first, the drop was spread out in a thin film, but it was
prevented from becoming too thin by four pellets of wax placed at the
corners of the square, which likewise served to hold the two pieces
of glass together. The glasses were then laid aside for some hours

of Edinburgh, Session 1870-71. 409

until crystals formed in the liquid. These were necessarily thin,
since their thickness was limited by the interval between the
glasses. Of course the central part of each crystal, except the
smallest ones, was bounded by parallel planes, but the extremities
were bevilled at various angles, forming so many little prisms, the
smallest of them floating in the liquid. When a distant candle
was viewed through these glasses, having the little prisms inter-
posed, a great number of spectra became visible, caused by the
inclined edges. Most of these were no doubt very imperfect, but
by trying the glass at various points, some very distinct spectra
were met with, and these could with some trouble be isolated by
covering the glass with a card pierced with a pin-hole. It was
then seen that each prism (or oblique edge of crystal) produced two
spectra oppositely polarised and widely separated. One of these
spectra was normal ; there was nothing particular about it. The
colours of the other were very anomalous, and, after many experi-
ments, I came to the conclusion that they could only be explained
by the supposition that the spectrum, after proceeding for a certain
distance, stopped short and returned upon itself.

No accurate measurements, however, were made, because it
always happened that, after the lapse of a minute or two, the
crystals dissolved in the surrounding liquid, owing to the warmth
of the hand or eye. The presence of the liquid, however, was
necessary to give the crystals the requisite transparency, and,
moreover, the liquid virtually diminishes the angle of the prism
floating in it, which otherwise would be too great to give a good
result. I never published this experiment, because I found it
delicate and capricious, and I was reluctant to publish any facts
that might be difficult for others to verify. But I have several
times described it to Sir D. Brewster in conversation, and he always
said that he thought it very important, at the same time suggesting
that there might perhaps be some fallacy. This was because he
doubted the possibility of a spectrum being partially inverted or
returning on itself. But this doubt seems now to be wholly
removed by Christiansen’s experiment, in which there seem to be
two inversions in the spectrum, and therefore I no longer hesitate
to state the grounds on which I concluded long ago that this
phenomenon was possible.

410 Proceedings of the Royal Society

Writing entirely from memory, it is possible that I may have
fallen into some inaccuracies in this brief account, which, if it
should be the case, I trust the Society will, under the circumstance,
kindly excuse.

P.S. — Since the above remarks were written, the first number of
Poggendorff’s “ Annalen ” for the present year has been received in
Edinburgh. This contains a long article by Kundt on the subject
of Christiansen’s experiment.

He finds that anomalous spectra are given by all the aniline
colours, and by permanganate of potash. Such spectra turn back
upon themselves, generally having the green at one extremity, the
blue being situated between the green and the red.

Hence this property is possessed by an extensive class of bodies,
and must form a new and separate branch of optics. He says that
the phenomenon only occurs when a very strong solution of the
substance is employed in the form of a liquid prism of 25°. But
only the thin extreme edge of the prism is available, the thickness
of the rest rendering it opaque. He failed in the attempt to form
a solid prism by mixing collodion with the alcoholic solution, but
this might perhaps be achieved by other means. In the meantime
a wide field of experiment is open.

3. Laboratory Notes. By Professor Tait.

1. On Anomalous Spectra, and on a simple Direct-vision
Spectroscope.

When I first saw Le Roux’s account of his very singular dis-
covery of the abnormal refraction of iodine vapour, I was inclined
to attribute the phenomenon to something similar to over- correction
of an achromatic combination. In fact, if a hollow prism be filled
with a mixture of two gases or vapours, one of which is more
refractive than air, the other less refractive; while the second
body is more dispersive than the first ; it is easy to see that
Le Roux’s result might be obtained, although each of the sub-
stances employed is free from anomalous refractive properties. In
a recent conversation with Mr Talbot, I happened to mention the
subject, and I learned from him his remarkable observation just
laid before the Society. I have since, when I had an opportunity,

of Edinburgh, Session 1870-71.

411

made several trials with hollow prisms and prismatic vessels, using
various substances, such as oils of cassia and turpentine, toluol,
alcohol, saturated solutions of salts, &c., with the view of imitating,
with nearly transparent substances, the singular results obtained
by Talbot, Christiansen, and Kundt. The observations are cer-
tainly very easy in one sense, though very laborious in fact ; but I
have already produced a spectrum doubled on itself, and have no
doubt that with patience I shall be able to produce one with two
and even more inversions; though, of course, the more numerous
are the inversions the smaller is the scale of the whole phenomenon.
The easiest method seems to be to put into a hollow prism a mix-
ture of two substances of very different refractive powers, and to
immerse it in a prism or trough containing a substance of inter-
mediate refractive power. When a trough is employed, an external
glass prism may vjith advantage be used along with the combina-
tion. The sought phenomenon is, of course, obtained best near the
point of adjustment for achromatism, and is in fact very closely
connected with the investigations of Dr Blair in his attempts to
improve the achromatic telescope by using fluid lenses.

One of my hastily set-up combinations (of two liquids only) gave
me a direct-vision spectroscope complete, more powerful than one
of Browning’s excellent instruments with five glass prisms, and I
have little doubt that in this way very good results may be obtained.
But, if it be needful to examine only a small region of the spectrum
at a time, practically unlimited dispersion may be obtained by using
so very simple a combination as two approximately isosceles flint
prisms of small angle with their edges together and their adjacent
faces inclined at an angle approaching to 180°, so as to form a hollow
prism to be filled with oil of cassia. In fact, the dispersion is in
this case easily seen to be nearly proportional to the tangent of
half the angle of the oil prism. If two kinds of glass, of very
different dispersive powers, but of nearly equal mean refractive
powers, could be obtained, a permanent combination might be
easily formed on this plan, giving as much dispersion as a very
long train of ordinary prisms, and losing scarcely any light. A
slight inclination of the ends to one another will enable us to use
ordinary flint and crown for the purpose, except in so far as total
reflection may interfere. Such a combination, adjusted for the red

412

Proceedings of the Roycd Society

ray C, seems to promise to be of considerable use in observations of
the sun’s atmosphere. A somewhat similar result maybe obtained
by using a single large prism, one of whose faces, employed for
total reflection, has a very slight cylindrical curvature.

2. On a Method of illustrating to a large Audience the Composition

of simple Harmonic Motions under various conditions.

I have often felt the difficulty of illustrating, by means of Airy’s
Wave Machine, and various other complex instruments of a similar
character, the composition of plane polarised rays into a single
elliptically or circularly polarised one ; the difficulty arising chiefly
in showing separately, but in close succession, to the audience the
two vibrations which are to be compounded, and their resultant.
Lissajoux’s apparatus would exactly answer the purpose if we had
tuning-forks vibrating 10 or 15 times a second, its sole defect being
the extreme rapidity with which differences of phase are run through ;
and, in fact, I have tried metronome pendulums with mirrors attached
to them ; but I have since found the following arrangement to be
much more satisfactory. It consists simply in using plane mirrors
rotating about axes very nearly perpendicular to their surfaces. A
ray reflected. almost normally from each of two such mirrors, equally
inclined to their axes, and rotating in opposite directions with
equal angular velocities, has communicated to it a simple harmonic
vibration, whose line and phase can be adjusted at pleasure by a
touch. Two such systems of pairs of mirrors, connected by elastic
bands with an axle driven by hand, enable the operator to illustrate
every combination of two simple-harmonic motions, as well as of
circular and elliptic vibrations. By an obvious adjustment it is
easy to use, instead of equal periods of vibration, periods bearing
any desired relation to one another; and by crossing one or more
of the bands we reverse the direction of rotation in the correspond-
ing shafts. It is absolutely necessary to have adjusting screws by
which to regulate the inclination of each mirror to its axis.

3. On a simple Mode of explaining the Optical Effects of Mirrors

and Lenses.

It is very singular to notice how small a matter makes the differ-
ence between the intelligibility and unintelligibility of a demon-

of Edinburgh, Session 1870-71. 413

stration to an audience as a whole not mathematical. In no part
of Physics have I found this so marked as in the most elementary
portions of geometrical optics. Such a formula as

when interpreted directly as signifying that “the sum of the
reciprocals of the distances of the object and image from the sur-
face of a concave spherical mirror, is equal to double the reciprocal
of the radius of the mirror,” if understood at. all, is understood as a
sort of memoria technica which enables the student to make calcu-
lations; but unless he have some knowledge of mathematics it
suggests absolutely no higher meaning. If, however, we give to
the various terms of the formula their meanings in terms of the
divergence of the incident and reflected beams, and of the normals
to the reflecting surface, even the non-mathematical student easily
understands the relation signified. I am indebted to Mr Sang for
a reference to Lloyd On Light and Vision , 1831, in which this
mode of presenting the subject is introduced, but I think the term
“vergency” there used is hardly so convenient as the more com-
monly employed word divergence. Our fundamental optical fact
is that to produce the most distinct vision rays must diverge as if
from a point about ten inches from the eye. No one has any diffi-
culty in understanding this. As my object has been merely to men-
tion to the Society what I have found to be a method (however
trivial in itself, yet) of really considerable importance in teaching,
I need do no more than give one simple example of its application,
and that only to direct pencils of such small divergence that spheri-
cal aberration may be neglected, A perfectly obvious set of modi-
fications is introduced when we treat of oblique pencils, and pencils
of large divergence, but students capable of understanding these
do not require the adoption of such elementary methods of ex-
planation.

Take, then, the case of light refracted at a concave spherical sur-
face, bounding a substance denser than air. If the incident and
refracted rays make (small) angles a and /3 with the axis of the
surface, and if y be the angle between the normal at the point of

VOL, vii. 3 K

414

Proceedings of the Royal Society

incidence and the axis, these angles being the respective diver-
gences, we have rigorously by the law of refraction

sin (y - a) = p sin (y - /3) ,

or, approximately ,

y-a = p(y-(3),

or pP - a = (p - ,l)y . . . . (1),

where p is the refractive index. [This we may, if we choose,
translate into

where y is the distance of the point of incidence from the axis, and
the rest of the notation is as usual. In this form we see that, to
our approximation, the result is independent of y .]

In (1) we have y=0 for a plane surface, and p = - 1 when there
is reflection instead of refraction.

Hence for a reflecting surface the meaning of (1) is — u the sum
of the divergences of the incident and reflected rays is twice that
of the normals to the surface.” If the incident rays be parallel,
the reflected rays diverge twice as much as do the normals.

At the second surface of a thin lens (1) becomes

which, compounded with (1), gives

P' - a = (p - 1) (y - y') ,

which may be thus translated — “ A lens produces a definite change
of divergence on any direct pencil — and the change is p - 1 times
the difference of the divergences of the normals to its surfaces.”
Hence that a divergence may be changed into an equal negative
divergence, it must be equal to half the change produced by the
lens; i.e ., when the object and image are equidistant from the
lens, their common distance from it is double the focal length of
the lens.

of Edinburgh, Session 187 0-7 1 .

415

4. On the Structure of the Palaeozoic Crinoids.

By Professor Wyville Thomson.

(Abstract.)

The best known living representatives of the Echinoderm Class
Crinoidea are the genera Antedon and Pentacrinus — the former the
feather stars, tolerably common in all seas ; the latter the stalked
sea lilies, whose only ascertained habitat, until lately, was the
deeper portion of the sea of the Antilles, whence they were rarely
recovered by being accidentally entangled on fishing lines. Within
the last few years Mr Bobert Damon, the well-known dealer in
natural history objects in Weymouth, has procured a considerable
number of specimens of the two West-indian Pentacrini , and Dr
Carpenter and the author had an opportunity of making very
detailed observations both on the hard and the soft parts. These
observations will shortly be published.

The G-enera Antedon and Pentacrinus resemble one another in
all essential particulars of internal structure. The great distinc-
tion between them is, that while Antedon swims freely in the water,
and anchors itself at will by means of a set of “ dorsal cirri,” Penta-
crinus is attached to a jointed stem, which is either permanently
fixed to some foreign body, or, as in the case of a fine species
procured off the coast of Portugal during the cruise of the Porcu-
pine in the summer of 1870, loosely rooted by a whorl of terminal
cirri in soft mud. Setting aside the stalk, in Antedon and Penta-
crinus the body consists of a rounded central disc and ten or more
pinnated arms. A ciliated groove runs along the “ oral ” or
“ventral” surface of the pinnules and arms, and these tributary
brachial grooves gradually coalescing, terminate in five radial
grooves, which end in an oral opening, usually subcentral, some-
times very excentric. The oesophagus, stomach, and intestine coil
round a central axis, formed of dense connective tissue, apparently
continuous with the stroma of the ovary, and of involutions of the
perivisceral membrane ; and the intestine ends in an anal tube,
which opens excentrically in one of the interradial spaces, and
usually projects considerably above the surface of the disc. The
contents of the stomach are found uniformly to consist of a pulp

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Proceedings of the Royal Society

composed of particles of organic matter, the shields of diatoms,
and the shells of minute foraminifera. The mode of nutrition
may be readily observed in Antedon , which will live for months in
a tank. The animal rests attached by its dorsal cirri, with its
arms expanded like the petals of a full-blown flower. A current
of sea- water, bearing organic particles, is carried by the cilia along
the brachial grooves into the mouth, the water is exhausted in the
alimentary canal of its assimilable matter, and is finally ejected
at the anal orifice. The length and direction of the anal tube
prevents the exhausted water and the foecal matter from returning
at once into the ciliated passages.

In the probably extinct family Cyathocrinidse, and notably in
the genus Cyatkocrinus , which I take as the type of the Palaeozoic
group, the so-called Crinoidea tessellata, the arrangement, up to
a certain point, is much the same. There is a widely-expanded
crown of branching arms, deeply grooved, which doubtless performed
the same functions as the grooved arms of Pentacrinus ; but the
grooves stop short at the edge of the disc, and there is no central
opening, the only visible apertures being a tube, sometimes of
extreme length, rising from the surface of the disc in one of
the interradial spaces, which is usually greatly enlarged for its
accommodation by the intercalation of additional perisomatic plates,
and a small tunnel-like opening through the perisom of the edge
of the disc opposite the base of each of the arms, in continuation
of the groove of. the arm. The functions of these openings, and
the mode of nutrition of the crinoid having this structure, has
been the subject of much controversy.

The author had lately had an opportunity of examining some
very remarkable specimens of Cyatkocrinus arthriticus, procured by
Mr Charles Ketley from the upper Silurians of Wenlock, and a
number of wonderfully perfect examples of species of the genera
Actinocrinus , Platycrinus , and others, for which he was indebted to
the liberality of Mr Charles Wachsmuth of Burlington, Ohio, and
Mr Sidney Lyon of Jeffersonville, Indiana; and he had also had
the advantage of studying photographs of plates, showing the
internal structure of fossil crinoids, about to be published by Messrs
Meek and Worthen, State Geologists for Illinois. A careful
examination of all these, taken in connection with the description

417

of Edinburgh, Session 1870-71.

by Professor Loven, of Hyponome Sarsii , a recent crinoid lately
procured from Torres Strait* had led him to the following general
conclusions.

In accordance with the views of Dr Schultze, Dr Liitken, and
■Messrs Meek and Worth en, lie regarded the proboscis of the tesse-
lated crinoids as the anal tube, corresponding in every respect
with the anal tube in Antedon and Pentacrinus, and he maintained
the opinion which he formerly published (Edin. New Phil.
Jour., Jany. 1861), that the valvular “pyramid” of the Cysti-
deans is also the anus. The true mouth in the tesselated cri-
noids is an internal opening vaulted over by the plates of the peri-
som, and situated in the axis of the radial system more or less
in advance of the anal tube, in the position assigned by Mr
Billings to his “ ambulacral opening.” Five, ten, or more openings
round the edge of the disc lead into channels continuous with the
grooves on the ventral surface of the arms, either covered over
like the mouth by perisomatic plates, the inner surface of which
they more or less impress, and supported beneath by chains of
ossicles ; or, in rare cases ( Amphoracrinus ), tunnelled in the sub-
stance of the greatly thickened walls of the vault. These internal
passages, usually reduced in number to five by uniting with one
another, pass into the internal mouth, into which they doubtless
lead the current from the ciliated brachial grooves.

The connection of different species of Platyccras with various
crinoids, over whose anal openings they fix themselves, moulding
the edges of their shells to the form of shell of the crinoid, is a
case of “commensalism,” in which the mollusc takes advantage
for nutrition and respiration of the current passing through the
alimentary canal of the echinoderm. Hyponome Sarsii appears,
from Professor Loven’s description, to be a true crinoid, closely
allied to Antedon , and does not seem in any way to resemble the
Cystideans. It has, however, precisely the same arrangement as
to its internal radial vessels and month which we find in the older
crinoids. It bears the same structural relation to Antedon which
Extracrinus bears to Pentacrinus.

Some examples of different tesselated crinoids from the Burling-
ton limestone, most of them procured by Mr Wachsmuth, and
described by Messrs Meek and Worthen, show a very remarkable

418 Proceedings of the Boyal Society

convoluted plate, somewhat in form like the shell of a Scaphander,
placed vertically in the centre of the cup, in the position occupied
by the fibrous axis or columella in Pentacrinus and Antedon. Mr
Billings, the distinguished palaeontologist to the Survey of Canada,
in a very valuable paper on the structure of the Crinoidea, Cystidea,
and Blastoidea (Silliman’s Journal, January 1870), advocates the
view that the plate is connected with the apparatus of respiration,
and that it is homologous with the pectinated rhombs of Cystideans,
the tube apparatus of Pentremites, and the sand-canal of Asterids.
Messrs Meek and Worthen and Dr Lutken, on the other hand,
regard it as associated in some way with the alimentary canal and
the function of nutrition.

The author strongly supported the latter opinion. The perivis-
ceral membrane in Antedon and Pentacrinus already alluded to,
which lines the whole calyx, and whose involutions, supporting
the coils of the alimentary canal, contribute to the formation of
the central columella, is crowded with miliary grains and small
plates of carbonate of lime; and a very slight modification would
convert the whole into a delicate fenestrated calcareous plate.
Some of the specimens in Mr Wachsmuth’s collection show the
open reticulated tissue of the central coil continuous over the
whole of the interior of the calyx, and rising on the walls of the
vault, thus following almost exactly the course of the perivisceral
membrane in the recent forms. In all likelihood, therefore, the
internal calcareous network in the crinoids, whether rising into
a convoluted plate or lining the cavity of the crinoid head, is
simply a calcified condition of the perivisceral sac.

The author was inclined to agree with Mr Bofe and Mr Billings
in attributing the functions of respiration to the pectinated rhombs
of the Cystideans and the tube apparatus of the Blastoids. He did
not see, however, that any equivalent arrangement was either
necessary or probable in the crinoids with expanded arms, in which
the provisions for respiration, in the form of tubular tentacles and
respiratory films and lobes over the whole extent of the arms and
pinnules, are so elaborate and complete.

of Edinburgh, Session 1870-71.

419

5. On the Formation and Decomposition of some Chlorinated
Acids. By J. Y. Buchanan.

1. On the Rate of the Action of a Large Excess of Water on Mono-
chloracetic Acid at 100° C. — When monochloracetic acid is heated
with water, double decomposition takes place, glycollic and hydro-
chloric acids being formed ; and conversely, when glycollic acid is
heated with hydrochloric acid, it is converted into monochloracetic
acid and water. A similar reaction takes place with the two mono-
chloropropionic and corresponding lactic acids, and probably with
all their homologues.

The task which I have set myself is to study these reactions, in
so far as they are dependent upon temperature, duration of reaction,
and relative mass of reacting substances. In the present commu-
nication, I give the results of experimenting upon monochloracetic
acid with a very large, practically infinite, excess of water at
100° O.

The monochloracetic acid was purchased from Dr Marquart, of
Bonn, and rectified. What passed between 180° and 190° was
used for the following experiments : — A watery solution of it was
made which contained in a litre 32*4 grms., and showed a specific
gravity = 1*01 24, whence the chloracetic acid and the water were
mixed in the proportion of one molecule of the former to 164
molecules of the latter.

As the increase of the acidity of the solution is the measure of
the decomposition which takes place, it is easily determined by
titration. For this purpose a solution of caustic soda was gene-
rally employed, although in the earliest experiments baryta water
was made use of.* The saturating power of these reagents was

* Berthelot (Ann. de Chim. et de Pliys. [3], lxv., 401) made use only
of baryta, his objections to potash and soda being that they always contain
carbonate, and that their salts with organic acids always have a more or less
alkaline reaction. The first of these objections may be got rid of by keeping
the solution, freed from C02 in the first instance by lime water, in a number
of small bottles filled full up to their tightly fitting corks. The second I have
found not to apply to the bodies here in question. There is no doubt, how-
ever, that baryta solution does present considerable advantages in the greater
ease with which it can be procured in a state of absolute purity ; and that
any carbonic acid which it may absorb is at once eliminated, thereby, how-

420

Proceedings of the Royal Society

ascertained by means of a very carefully prepared normal sulphuric
acid, containing 49 grms. II2S04 in a litre. 10CC. of this acid
saturated 42'7 CC. caustic soda, and 4T8 CO. baryta water, whence
one litre caustic soda contains 9-3677 grms. NaHO, and one litre
baryta water 20450 grms. BaH202. 10 CC.of the above-mentioned
chloracetic acid saturated 14 7 CC. caustic soda and 144 CC. baryta
water.

In every experiment 10 CC. chloracetic acid solution were sealed
up in a tube, and introduced directly into the boiling water bath.
After the reaction was finished, it was transferred immediately to
a vessel of cold water. By this means the time of heating up to
100° and of cooling down again to the surrounding temperature
was reduced to a minimum.

The chloracetic acid solution was prepared in the middle of last
November, and although it has now stood at the ordinary tempe-
rature of the laboratory for over four months, its saturating power
has not changed to a sensible extent. It is true, however, that it
gives a slight opalescence with solution of nitrate of silver. It
appears then that the decomposition of monochloracetic acid by a
large excess of water at the ordinary temperature is infinitely slow.

In the experiments at 100° C. the same quantity, namely, 10 CC.
of the acid solution, was invariably employed, In the following
table showing the results, the first column contains the duration
of the experiment in hours ; the second the number of CC. caustic
soda or baryta water required to saturate the resulting acid, and
the third gives the percentage chloracetic acid decomposed as
calculated from column 2. No fraction smaller than 0'5 is given,
this being the limit of possible errors of observation : —

ever, altering the strength of the solution. My principal objection to it was
its great tendency to crystallise even in solutions a long way removed from
saturation.

Table

of Edinburgh, Session 1870-71.

421

Table I. — C2H3C102 + 164Ho0 at 100° 0.

Duration of
Experiment in
Hours.

Number of CC. required for
neutralisation.

Percentage of
C2H3C102
Decomposed.

Soda.

Baryta.

0

14-70

14-40

0-0

2

1555

6-0

4

16-35

11-0

6

16-85

14-5

11

18-10

23-0

14

18-80

28-0

16

19-30

31-5

18

19-85

35-0

21

20-30

38-0

24

20-95

42-5

27

21-35

45-0

30

22-15

51-5

33

22 55

53-5

37

22-95

56-0

43

23-90

62-5

48

24-45

66-0

72

25-40

76-5

96

26-20

82-0

120

27-57

87-5

144

28-00

90-5

192

28*40

93.0

332

28 95

97 0

430

29-05

97-5

The following Gentlemen were elected Fellows of the
Society : —

James Geikie, Esq.

Thomas E. Thokpe, Ph. D., Lecturer on Chemistry in the
Andersonian Institution, Glasgow.

8 L

VOL. VII.

422

Proceedings of the Royal Society

Monday , 17 th April 1871.

The Hon. LORD NEAVES, Vice-President, in the Chair.
The following Communications were read : —

1. Notes on the Antechamber of the Great Pyramid. Based
on the Measures contained in vol. ii. “ Life and Work
at the Great Pyramid,’’ by C. Piazzi Smyth. By Captain
Tracey, R.A. Communicated by St John Vincent Day,
Esq., C.E., F.R.S.E.

In considering the authority for the division of the sacred cubit
into 25 inches, we have, first, the architectural fact that the,
Queen’s chamber, containing the visible expression of that cubit,
stands in or upon the 25th course of masonry, comprising the whole
Pyramid. And here, though not strictly bearing on the case, may
be mentioned a connection between the lengths of the two pas-
sages (the first ascending, and the horizontal passages) leading to
that chamber, remarkable when expressed in inches, of which 25
make a cubit.

Thus, the length of the first ascending passage from the axis of
descending passage to north wall of Grand Gallery (see p. 54,
v. ii., L. and W.)* = 15444 B. I., or 1542-9 inches, of which 25
make a sacred or Pyramid cubit, and which for the future we will
term “Pyramid inches.”

Now, this length of 1542-9 P. I. — 25 = 1517*9 P. I. — is the
exact length of the horizontal passage from north wall of the
Grand Gallery to the north wall of the Queen’s Chamber —

E.g ., length of horizontal gallery (see ) ^ ^ ^

p. 57, v. ii., L. and W., last line), J

1-5

1517*9 P. I.

* In this paper the following abbreviations are used: “ L. and W.,” for
‘ Life and Work at the Great Pyramid ; ” B. I. = “ British Inches ; ” P. I.
— “ Pyramid Inches ” Pyramid Inch= British Inch x 1001.

423

of Edinburgh, Session 1870-71.

But on entering the Antechamber, we find this particular mea-
sure or sacred cubit we pave termed the Pyramid inch,

Zo

to avoid expressing that particular measure of length by the
algebraical x) not only typified, but expressed, and most notably
in the granite leaf, whose precise functions have never yet been
explained.

For there — on a stone immediately in front of an unmistakable
symbol of division into five — we find a raised boss, with a single
straight edge exactly | of a Pyramid or sacred cubit in length,
and consequently representing 5 of these inches.

The thickness of this boss along the whole line of 5 inches is
exactly of that line, ^ of the same cubit, or precisely the inch
we are in search of.

Further, the centre of this boss is exactly one inch from the
middle of the Antechamber, its distance from either side being
19-5 and 21*5 inches from the west and east walls respectively,
and, consequently, it is one inch to the west of centre (just as the
niche in the Queen’s Chamber, marking the whole 25 inch cubit
by the breadth of its flat top, is also 25 inches removed from the
central vertical line of the wall in which it is formed).

It may he argued that all these expressions of an inch in the
Antechamber depend upon the shape and position of a stone that
was not necessarily placed there by the architect of the Pyramid.

Let us, therefore, seek some connection with the grander fea-
tures of the building, both for the stone itself and the particular
measure of length, of which we are thus far led to consider it the
standard.

The following calculation shows that a line drawn from the
angle of the great step at an angle of 26° 18', or parallel to the
true axis of the Grand Gallery, passes about 1*13 inch below the
centre of the bottom of the upper stone forming the granite leaf,
or the one that bears the boss.

Vol ii. L. & W. pp. 93, 96. B. I.

North end of step to north side of leaf (omit boss) = 1343
,, south „ = 15055

2)284-85

Distance of centre of leaf from north end of step, 142-42

424

Proceedings of the Royal Society

Height of bottom of leaf above floor, . . 43' 7

„ lower stone of leaf, . . . 27*75

„ junction of the stones above the floor, = 71*45
Now, 142-4 x *494,ornat. tan. of Grand Gallery angle, = 70‘32

FT3 B.I.

A line || to axis of G-rand Gallery, drawn from of Great
Step, passes 1*13 B. I. below centre of joint of leaf.

P. 96 L. & W. This and the next calculation.

Distance of south wall of Antechamber from of Step = 229*6 B.I.

229‘6 x -494 (nat. tan. Grand Gallery «/) = 113*42 ,,

show that the same line produced, strikes the south wall of the
Antechamber at a height of 113*42 B. I. from the floor. As the
boss is to the west of the centre of the room, we turn to that side,
and find that the height of the granite wainscot there, where it
bears against the south wall, is 111*8 inches or 1*62 B. I. lower
than the spot indicated. But, on examining the course of the axis*
itself of the Grand Gallery when produced, the following calculation
shows that it passes through the lower stone of the leaf at a distance
of 0*8 inch below its centre on its northern side, and on being pro-
duced strikes the south wall of the Antechamber at a height above
the floor of 104*02 B. I., or just an inch above the height of the
wainscot on the east side, which reaches an altitude of 103*1 B. I.

Thus connecting the inch, the granite leaf, and the rest of the
building in a manner that none but the original Designer could
have introduced.

P. 96 L. & W.

North side of leaf (omit boss) from north side of step = 134*3 B. I.

Height of bottom of leaf above ) ^o. 7 (P 99 L & W 1
floor, . . . J * ^ * ‘ ')

One-half height of lower stone, 13*9 „

Height of centre of lower stone, 57*6
= 66*24

=■ 9*4

( Height at which axis of Gran d

= 56*8 = ■< Gallery strikes lower stone on
( north side,

or (57*6 - 56*8) or 0 8 B. I.
below centre of stone.

* That is, axis of 1st ascending passage continued through Grand Gallery.

f See next calculation.

But 134*3 x *494
and axis of ascending)
passage continued |
through Grand Gal- y
lery is 9*4 B. I. below j
^ of Stept J

of Edinburgh, Session 1870-71.

425

P. 74 L. & W. B. I.

Vertical height of Great Height of || axis = 113'42
Step — - 9*4

East, 35*8 B. I. > 104*02 = Height of

West, 36*2 true axis of Grand Gallery above the

36’ mean. ' floor.

Vertical height of northern en-
trance to Grand Gallery (p. 70

L.&W.)is 53’2 =26-6 = height of axis which subtracted

A

from 36* =

9-4 = vertical height of of Great
Step above the point where
the axis of1 first ascending
passage passes into it.

But the axis of the Grand Gallery, the most important line in
the whole building, having so signally pointed out the importance
of the lower stone of the leaf, let us examine it also in terms of
the inches we are led to connect so closely with it. Taking the
mean of all the measures given, the calculation following shows
that the cubical contents of that part of the stone not sunk in the
grooves

= 15-7 x 41 x 27-7 = 17830-5 British inches.

17-8

= 17812-7 Pyramid inches.

P. 99 L. & W.

Thickness — East end of leaf, . . 15-4

,, West ,, . . 16-

Mean, . 15-7 P. I.

Height, ..... 27*5

...... 28-

Mean, . 27-7 B. I.

P. 100 L. & W.

Width, 41 B. I. — this measure being taken on the leaf itself, and
on the same side as the boss.

Log. 15-7 = 1-1958997
„ 27-7 = 1-4424798

41* = 1-6127839

= 4*2511634 = log. of 17830-5 British inches.

426

Proceedings of the Royal Society

The Ark, or Laver by theory, and the Pyramid Coffer in prac-
tice, contain 71321-2.5 B. I. = 71,250 P. I., the quarter of which,
or 17812,5 Pyramid inches (the volume of this particular stone),
is the Chomer or Homer of sacred standard.

The remarkable result thus obtained induces a further examina-
tion of the position of this stone.

We remark that the base of this stone (lower stone) is in the
same horizontal plane as three other well defined lines of the ante-
chamber— viz., the division between the courses of the wainscot
on the east wall' and the tops of the doors in the north and south
walls.

It is to be noticed that the refined workmanship of the granite
wainscoting has been most fully developed to the south of the
leaf.

We will thus examine that portion first. The granite leaf itself
and the granite walls mark off above the horizontal plane a cer-
tain space.

The dimensions of this part of the plane are —

In length varying from (1.) 79-0 B.I. to 79T B.I.

In breadth (2.) 4L2 to 4L45 B.I.

While at the height of (3.) 27‘5 to 28 B.I. there

runs across it the joint line of the leaf.

a-)

P. 96 L. & W. — North end of step to south
side of leaf,

E. 150-3
W. 150-8

Mean 150-55

North end of step to south end of
antechamber,

Ho. do.

}

E. 229-4
W. 229-8

Length, East side, 229‘4
150-3

Mean 229-6

Do. West,

79-f

229-8

150-8

Mean 79-05

79-0 )

427

of Edinburgh, Session 1870-71.

(2.) P. 93 L. & W.— 41-45
41-2

82-65

41-325 Mean.

(3.) P. 99 L. & W.— 27-5
28-

55 -5

27-75 Mean.

The already acquired facts give us good reason to look upon the
25th part of the sacred cubit as an unit of measure that may be
safely used in at least the antechamber of the great Pyramid, and
we only argue in conformity with other teaching of the Pyramid
in assuming that the volume of the lower stone of the leaf may
also be an unit of volume for antechamber cubical measures.

Thus if we take the lowest readings, a cubical space of 27'5 x
41-2 x 79-0 B.I., or (1.) 89507*0 B.I. is marked out; or (2.) 5*019
of our volume unit.

B.I.

(1.) Log. of 27*5

41-2
79-0
B.I.

89507-0

and (2.) 895070

17830-5 UiJ

Practically 5 volumes of the lower stone of the leaf, and therefore
P-g-th of the lower course of the king’s chamber.

For that has been shown (by Professor Piazzi Smyth) equal to
2000 baths, or 50 coffers, therefore the space in the antechamber

Equals ... 50 baths

or . . . . 5 chomers

of which last our unit represents . 1

We have consequently the Hebrew* chomer standing, as it were,
at the end of a measure of 5 times its own capacity, as in the

- 1-4393327
= 1-6148972
= 1-8976271

= 4-9518570

428

Proceedings of the Poyal Society

king’s chamber has been found the coffer in one 50 times its own
content. The rest of the granite-lined chamber, of which the above
formed part, may also be worthy of consideration. Its length and
breadth are the same as that of the portion already considered,
while its height is determined by that of the containing wainscots.
But these, as we have already seen, are determined by the heights
at which the south wall is touched, the one by the axis of the (first
ascending passage produced through the) Grand Gallery prolonged
into the antechamber, and the other by a line parallel thereto
drawn from the angle of the great step. But as it would be
evidently giving either undue weight to use it alone, let us take
(as the following calculation shows) the average height of the two
—viz., (1.) 108-72 B.I.

Taking the highest readings of the dimensions, we obtain — (2.),
108-72 x 79*1 x 41 '45 B.I., or 356460-4 B.I. (3.), we find therein
19 99, &c. of the units we have seen reason to employ, or so close
on 20 as to justify our acknowledging intention in the size.

(1.)— H. of || axis, . _ . 113-47

,, grand gallery axis produced 104*07
2)217g4
108-72 mean.

(2.) Log. of 108-72 - 2-0363094
79-1 - 1-8981765

41-45 - 1-6165245

356460-4 = 5-5520104
Minus log. 17830-5 - 4*2511634

(3.) 19-99, &c. = 1-3008470

Granting that, we have another noteworthy connection estab-
lished between the antechamber and king’s chamber, as there the
volume of the lower course has been shown (by Professor Smyth)
to equal 50 coffers, or 200 of our units, while here we have its tenth
part, or 20 units equalling 5 coffers.

It will doubtless be objected that in one instance we have used
the highest, and the other the lowest readings of the measures.
Just proportion teaches that the product of the means should be
of no less value than that of the extremes.

Let us then take the means of those two sets of numbers, whose
extremes only we have been using heretofore, and employ them in

of Edinburgh, Session 1870-71.

429

connection with other dimensions of that marked horizontal plane
already alluded to.

Examination of it shows that it is broadly divided into two por-
tions, by the leaf resting on it ; and the linear measures of the two
rectangles thus formed are respectively, the northern one —

(i.) (2.)

41-7 P. 96, V. 2, L. & W. P. 99, V. 2, L. & W.

41-45 P.93, „ 21-0

41-2 „ „

41-45 mean.

{(41-45 x 2) + (21- x 2)} = 82-9 + 42 = 124-9

and the southern one —

(3.) (4.)

See (1) page 426.* See (2) page 427*

{(79-05 x 2) + (41-3 x 2)} = (158-1 + 82*6) = 240-7

British inches, 3 65*6

•36

or in Pyramid inches, 365-24

roughly divided into J and -frds of No. of days in a year.

The perimeter of the chamber at the ceiling (363 inches) had
pointed out the probability of our finding some of the external pro-
portions of the pyramid repeated here ; and as there we find the
“year'-’ in terms of 4 cubits, or 100 inches, so here we have a “year”
of inches ; and as there the grander and external year is intimately
connected with the height of the pyramid through 7 r, so here we
find, through the same medium, a connection with the length of
the chamber, a mean of three measures of which gives 116-32 for
its length in pyramid inches, for taking 365-24 as circumference,
diameter = 116-26.

P. 95 L. & W. — Length of antechamber, 116-3

... -8
... -2

Mean 116*43 British inches.

•11

116-32 Pyramid inches.
Log. of 365-24 - 2-5625783
7T - -4971499

116-26 = 2*0654284

3 m

VOL. VII.

* These numbers refer to pages of this volume.

430

Proceedings of the Royal Society

Or an approximation to 7 r, as represented by a “ year” of inches
marvellously close both in the numbers representing the circum-
ference and diameter, and reproducing here the grander proportions
of the external form of the pyramid.

It is to be remembered that the “ year” of inches was divided
roughly into i and fds, and the three stones of the ceiling and the
three cuts on the wainscot seem to point to some important divi-
sion by 3.

We have seen 7 r playing so important a part in deciding the
height of the pyramid and the length of the Antechamber, that
we may at any rate try what a division by 3 will do.

On the base of the pyramid the “ year ” which represents
circumference (or, as regards the height of the pyramid 7 r)
was expressed in units of 100 inches. Have we any chance
of finding not circumference, for we already have our “year”
of inches, but diameter, or radius, as a purely mathematical ex-
pression as regards 7 r, when expressed in say the same terms of
100 inches ?

Taking 7 r as represented by 314T59, &c. Pyramid inches, we
find diameter + radius expressed very closely, as § and | of the
height of the antechamber ( i.e ., 149*2//).

But when we divide 7 r itself (still expressed in terms of K = 100
Pyramid inches) by 3, we obtain the figures 104*72, which strike
us as being an approximation to the height of the wainscot on the
east wall (103*1); but when we refer to the grand gallery axis (to
whose connection with the east wainscot our attention has already
been drawn) we find a still closer approximation (viz., 104 06 P.I.)

to the expression of-^»
o

But is a curious expression, and not much used in calculations
o

I am conversant with, except in one instance ; but that instance
bears on the case, as it is in the calculation of volume of spheres,
cones, and also pyramids, the area of whose base is expressed in
terms of 77 -.

It may be advantageous to note here the connection between the
volumes of pyramids and spheres. The content of a pyramid is
mathematically expressed thus,

of Edinburgh, Session 1870-71 .

431

where a — area of base,
and h = height of pyramid.

But in the purely mathematical form of pyramid we are led to
consider

a — 7rR2

h

D

2

i)

, when V would equal

ttB3

3

but in a sphere,

volume = 4

7rB3

3 '

So that in the case of the great hemispherical molten sea, whose
content = 50 lavers, a pyramid of the same base and height would
contain 25 lavers, 100 homers, or five of the largest marked-off
space in the antechamber whose content has already been pointed
out.

This may certainly lead us to infer, that as up to the ante-
chamber our measures have been lineal and superficial; now, on
the other hand, wre must be prepared for cubical measures with,
perhaps, also some concerning the content of spheres, cones, or
pyramids.

Commencing our investigation at the horizontal marked plane
previously referred to, we remember in its most highly finished por-
tion that its smallest dimensions are 79 0 B. I. and 4P2 B. I., and

s 79 0 B.I.x

here we may notice that their sum ( 4T2 J , 120‘2 B.I. or

VM B.I./

120 1 P.I. is very close upon the radius of the hemisphere that
the presence of g has led us to refer to. The precise figures stand-
ing thus : —

Radius of J sphere whose volume = 3,562,500 P.I. (= lower course
of King’s Chamber = “ Molten Sea”) is 119 371 P.I.

When vol ume of sphere = 3562500 x 2 cubic inches

432 Proceedings of the Royal Society

Required its radius :

Now V. of sphere = 4 ttR3

~3

7125000 = 4 ttR3

3

R3 I 7125000
4 7 r

.-. R = y' 7125000 log. 7 125-000 = 6-8527849
4-1887902 log. N =0-6220886

o

= 119-371 3)6-2306963

119-371 = 2-0768987

But we are getting on too fast. Now in spite of the presence of
t r are we to suppose the circle squared practically, as we have
imagined, when suggesting that the area of the base of a square
pyramid might be represented by 7rR2 ?

To seek an answer to that question we must go back to that part
of our investigation, where we had reason to believe that the con-
nection between 116-3 and 365'24 was intentionally introduced
as an exponent of the relation between diameter and circumference,
and we may not unreasonably test the accuracy of our deductions
by finding the area of the circle there expressed, trusting that if
we are working in the right direction this step may lead to some
further proof of its being so.

But in so doing we should use the figures only as a guide to the
intentions of the Great Architect, and having as we believe learnt
that the “ jrnar” of inches symbolises a circle of 365-256, &c., we
may take as our starting-point the more accurate diameter repre-
356-256

sented by — or 116-264 pyramid inches.

To proceed.

The area of a circle whose diameter is 116-264 is 10,616*65.

This number in itself does not seem peculiarly suggestive, but
when we recollect how remarkably both the east wainscot and
granite floor* point to an accurately marked square of 103 Pyramid

* Viz. the east wainscot, a vertical line 103 inches high, and of the floor,
a special portion constructed in granite showing a horizontal line 103 inches
long.

433

of Edinburgh , Session 1870-71.

inches whose area = 10,609, we think we have advanced in the
right direction and shown that the builder here places for our
instruction and guidance another practical illustration of the
importance and use of 7r, its former application being lineal, and
this superficial. And here we stay to point out how these curious
proportions, coincidences, and symbols become legible when read
by the units of length and volume supplied by the architect of the
pyramid himself, and extant (let us hope) to this day in the very
spot where their use first becomes imperative.

For though the proportions remain the same whether expressed
in inches, feet, or metres, they only become vocal as it were when
read by the units there prepared and hung up near them.

What should be the next step in the process of inductive
argument ?

The sides and perimeter of this square (of 103-0 P.I.) are so
obviously connected with the length and breadth of the King’s
Chamber, as exactly J, and \ thereof, that a consideration of the
area of its floor would perhaps be the next step, guided too by the
admonition we fancy we have received on passing through the
antechamber, that cubical and not simply linear or superficial
measures should occupy us in the chamber ultimately attained.

With what results this has been done over the area of that floor,
we already know, from Taylor, Smyth, Petrie, and Day, results too
so overwhelmingly important, that though the tables of the Law,
written by the hand of the Omniscient, have been lost to man, we
have here inscribed by the great architect of the pyramid the very
essence of all legislation, so exact and so scientific in all its
branches, as far as we can penetrate, that it is indeed “ ennobling
to the mind of man to contemplate.”

2. Experiments and Observations on Binocular Vision.
By Edward Sang, Esq.

(. Abstract .)

This communication was chiefly directed to the question whether
the idea of distance be obtained from the adjustment of the eyes
to distinct vision, or from the convergence of their axes. The case
of the chameleon was cited as one in point, since that lizard

434

Proceedings of the Royal Society

directs its eyes each to a separate object, but habitually, when
about to strike its prey, brings both eyes to bear upon it. Several
experiments, mostly suggested by Wheatsone’s inquiries, were
cited, and the conclusion was arrived at, that, although the adjust-
ment for direct vision concur in the formation of the estimate of
distance, the convergence of the eyes plays the principal part.

3. On the Fall of Rain at Carlisle and the neighbourhood.

In this communication, the author offers remarks on journals
kept by Dr Carlyle, in the city of Carlisle, from 1757 to 1783
inclusive; by the Rev. Joseph Golding, at Aikbank, near Wigton,
Cumberland, from 1792 to 1810 inclusive ; and by himself at Bun-
kers Hill, two and a half miles west of Carlisle, which is situate
184 feet above the sea-level. The author gave tables showing the
quantity of rain of each month and year included in these periods.
From the averages, it appears that about twice as much rain falls
in each of the latter months of the table as in the month of April ;
and about one-third less rain falls in the first six months of the
year than in the last six months, and that April is the driest month
of the year.

4. Mathematical Notes. By Professor Tail.

1. On a Quaternion Integration.

A problem proposed to me lately by my friend T. Stevenson,
C.E., for constructing what he calls a Differential Mirror , when
attacked directly led to the equation

where a is a unit-ve ctor, perpendicular to fi.

By another mode of solution it was easy to see that the integral
must be of the form

It may be instructive to consider this question somewhat closety,
as the form of the unintegrated expression is certainly (to say the
least) at first sight unpromising.

By Thomas Barnes, M.D.

Tp - T(/3 + a Yap) = constant.

435

of Edinburgh, Session 1870-71.

The problem was : to construct a reflecting surface from which
rays, emitted from a point, shall after reflection diverge uniformly,
but horizontally. Using the ordinary property of a reflecting sur-
face, we easily obtain the first written equation. By Hamilton’s
grand “ Theory of Systems of Rays,” we at once write down the
second.

The connection between them is easily shown thus. Let w and
r be any two vectors whose tensors are equal, then

L±^y = i + 2„t-‘ + c^T-'y

= 2=t-*(1 + Ss,T-‘),
whence, to a scalar factor pres , we have

(0‘-

T -h '

Hence, putting w = U (j8 + aV ap) and r = Up, we have from the
first equation above

But

and

S.dp[Up + U(/? + aVap)] = 0.
d (/3 aV ap) = aVa dp = — dp — aSa dp ,
S . a(/3 + a V ap) = 0 ,

so that we have finally

S . dpUp — S . d(/3 + aVap)U(/3 + aYap) = 0 ,

which is the differential of the second equation above. A curious
particular case is a parabolic cylinder, as may be easily seen
geometrically. The general surface has a parabolic section in the
plane of a , /3 ; and a hyperbolic section in the plane of /?, a (3.

It is easy to see that this is but a single case of a large class of
integrable scalar functions, whose general type is

s.dpfffyP=o,

the equation of the reflecting surface ; while

S(a^ — p)dcr = 0

is the equation of the surface of the reflected wave : the integral

436

Proceedings of the lloycil Society

of the former equation being, by the help of the latter, at once
obtained in the form

Tp -f T(<n — p) = constant.

2. On the Ovals of Descartes.

The following results were obtained lately while I was consider-
iug how most simply to describe by working sections surfaces
analogous to that treated in the preceding note. They are so
elementary that it is not likely that they can be new, but as they
are novel to myself, and to several mathematicians whom I have
consulted, I bring them before the Society : —

Let two coplan ar circles be described, with centres A and B.
Take any point, C, in the line of centres, and draw a line CPQ,
cutting the circles in P and Q. Find the locus of R, the inter-
section of AP and BQ.

Expressing that CPQ is a straight line, we have, if 0 and </> be
the angles at A and B respectively,

AP sin 0 ^ BQ sin <j>

AP cos 0 =b AC BC rb BQ cos <f>
or

AP . BC sin 0 rb AO . BQ sin <f> = rb AP • BQ sin (0 + <£) ,

which, by substituting the sides of ABB for the sines of the angles
opposite them, becomes

AP . BC • BR rb AC • BQ • AR = rb AP . BQ. AB (1)

which is the general equation of Cartesian Ovals.

of Edinburgh, Session 1870-71.

437

When AP • BC = AO . BQ the curve becomes an ellipse or
hyperbola. Of this the simplest case is

AP = BQ> BO = CA.

The normal at B is in all cases parallel to

AP . BC • U(BR) =fc AO . BQ . U(AR) ,
because we have

d . AR = d . BR .

But the general equation (1), on account of the identity

AP .BC.BQrbAO.BQ.AP = db AP -BQ . AB ,

may be written more simply, as

AP.BC.RQ - AC.BQ.PR = 0, (2)

a very singular and suggestive form ; holding true, as it does, for
all four points, R, R', R", R'", in the figure.

Hence the normal is

U(BR) t U(AR)

RQ PR ’

which may he constructed by drawing at R a tangent to the circle
circumscribing the triangle PQR. When the curve is a conic this
line is parallel to CPQ, because by the condition above we have in
this case

RQ = PR.

Of course the mode of tracing here adopted is at once capable of
being effected mechanically.

The results above are easily derived from the general equation
of Cartesian Ovals

er d= e'r' = a ,

by writing it in the form

e(r0 4- e'x) rh e'(rQ' ex) — a ,

and showing from this that QP cuts AB in a fixed point.

But by a purely quaternion process it is easy to give in a very
simple form the equation of the locus of R when C is not in the line
AB. Let CA, CB, OR be denoted by a, /3 , p respectively, and let

3 N

VOL. VII.

438

Proceedings of the Royal Society

AP = a , BQ = b. Then, by expressing that CP and CQ coincide
in direction, we have at once the equation

Y . [a + aU(p - a)] [fi + bU(p - /?)] = 0 ,

in which the above results are included as a very particular case,
and whose geometrical interpretation is elegant. It is a mere
Scalar equation, since Ya/3 is a factor of the left side, and may be
omitted.

Added, May 4 th, 1871. — I have just been informed by Professor
Cayley that the above results, so far as they concern the Cartesian
Ovals, are to be found (some actually, some virtually) in Chasles’
Apergu Historique , a work of which, to my great regret, I have
never been able even to see a copy.

The following Gentleman was elected a Fellow of the
Society : —

John Smith, M.D., F.R.C.S.E.

Monday , ls£ May 1871.

Dr CHRISTISON, President, in the Chair.

The following Communications were read : —

1. On the remarkable Annelida of the Channel Islands,
&c. By W. C. MTntosh, M.D.

The extraordinary richness of the littoral region and the
deeper water surrounding Guernsey and Herm, as well as the
marked southern character of many of the Annelidan types, formed,
for instance, an excellent comparison with the ample series of
specimens which the dredgings of Mr Jeffreys in the Shetland seas
had lately brought before us ; or, again, with the valuable collec-
tions procured during the expeditions of the “ Porcupine,” in 1869
and 1870, the former chiefly from the Atlantic, the latter from the
same region and the Mediterranean.

The object of the present paper is to give a short notice, chiefly

of Edinburgh, Session 1870-71.

439

of the structural, or other, peculiarities, of the remarkable Nemer-
teans and Annelids found in this expedition, and of certain in-
teresting questions in zoology connected therewith.

Amongst the Nemerteans is the curious Ommatoplea spectabilis of
De Quatrefages, a species of much interest, in so far as its discoverer
stated that it was furnished with a peculiar horny pectinated
structure in its proboscis. Careful examination showed that the
latter has a strictly Ommatoplean anatomy, the longitudinal hands .
of the reticulated layer of the pinkish organ being very apparent.
In Prosorliochmus claparedii , Keferstein, the granules of the exter-
nal circlet of glands round the stylet-region of the proboscis are
unusually large and distinct. The granular basal sac of the central
stylet is of a peculiar shape, having a straight border and sharp
angles posteriorly, and obtuse angles at the sides anteriorly.
The pale setting of this apparatus is comparatively limited in bulk ;
and the curved fibres of the region behind the latter pass out-
wards and forwards in a very distinct manner. The development
of the ova in the bodies of the females of this viviparous species is
very similar to that of the free ova and their products in other
Ommatopleans, space being formed for the growing embryos by the
enormous dilatation of the ovisacs. Indeed, the larger young speci-
mens, which are often doubled within the body of the parent,
appear to be in cavities produced by the coalescing of many ovisacs ;
at any rate, it is clear that to describe them, as former authors have
done, as simply within the body-cavity of the worm, is wanting
in structural accuracy. It seems to he a further stage of the type
of development observed in Nemertes carcinophilus , Kolliker
( Polia involuta , Van Beneden), in which, after the deposition of
the majority, a few are left in the body of the parent for subse-
quent evolution. A still more remarkable Nemertean is the
Borlasia elisabethce, MT., from Herm, a large species with a
pointed, eyeless snout. In this form the powerful muscular layers
of the body-wall are tinted of a fine reddish hue, so that the
resemblance in this respect to the muscles of the higher animals is
striking. The proboscis is extremely slender in proportion to the
bulk of the animal, and its muscular walls are comparatively thin.
A reddish coloration was frequently observed in the living animal
at the white belts, showing that some contained fluid tinted the

440 Proceedings of the Royal Society

cutaneous tissues during its passage. On puncturing the swollen
anterior end, a copious exudation of a reddish-brown fluid occurred.
This presented many fusiform and clavate corpuscles, probably
from the proboscidian fluid ; but there were also a vast number of
minute granules, of a yellowish colour by transmitted light, though
reddish in mass, which doubtless belonged to the blood-proper.
Many of the latter bodies showed a contraction in the middle, so
as to resemble the outline of a figure of eight.

In regard to the Annelids Proper, it is found that the northern
Aphrodita aculeata and Loetmonice filicornis, Kbg., are replaced by
the southern Hermione liystrix , which occurs in great abundance in
water from 10 to 20 fathoms in depth. Amongst the Polynoidce ,
P. areolata, Grube, is remarkable in having greatly swollen cirri.
The dorsal bristles are not very robust, while the ventral are in
two sets, if the ends alone are viewed, but form a regularly dimi-
nishing series from the dorsal to the ventral surface as regards
length of tip. The scales are boldly areolated. In this species
there is a series of well-marked circular muscular fibres towards the
outer half of the vertical coat of the proboscis. The new Har-
mothoe marphysce accompanies Marphysa sanguinea in its tube.

The remarkable forms of the Phyllodocidae and Hesionidee ; the
great abundance of the Nereidce , and the uses of the latter as bait,
were next detailed.

The representatives of the Eunicidse are very plentiful. Besides
the gigantic Marphysa sanguinea , there occur Marphysa belli ,
Eunice harassii or norvegica , and Eunice gallica. The allied forms
Lysidice ninetta and Blainvillea filum are also abundant, and
impart a character to the fauna of the region. The same may be
said of Prionognatlms Kefersteini and Staurocephalus rubrovittatus.

Ghcetopterus norvegicus and other phosphorescent Annelida were
then examined, and the facts observed in these, as well as in other
luminous invertebrates were shown to give no support to the Abyssal
Theory of Light as expounded in the u Report (1869) of H. M. ship
‘ Porcupine/ ”

The structure and habits of the Annelida frequenting muddy
ground in the Channel Islands, and the examination of those and
other marine invertebrates elsewhere, exhibited grave objections to
another theory, lately brought forward by Dr Carpenter (“Porcu-

of Edinburgh, Session 1870-71.

441

pine” Report for 1870), viz., that the barrenness of the deeper parts
of the Mediterranean is due to the turbidity (from mud) of the
bottom-water.

2. Note. On the Use of the Scholastic Terms Vetus Logica
and Nova Logica , with a Remark upon the corresponding
Terms Antiqui and Moderni. By Thomas M. Lindsay,
M.A., Examiner in Philosophy to the University of Edin-
burgh.

During the earlier part of the middle ages, or until the middle
of the eleventh century, students of logic had a very incomplete
knowledge of the logical works of Aristotle. They knew the trans-
lations which Boethius had made of Porphyry’s Eio-a-ycoyi), of Aris-
totle’s Trept KareyopLMV , and of his Trepl kppaqvd a?, and they knew little
else. Their labours did not go beyond the reproduction of, and
commenting on, these old G-reek writings.

Towards the beginning of the twelfth century, however, the
gradual diffusion of knowledge had brought with it acquaintance
with the remaining treatises of Aristotle’s Organon. The old trans-
lations of Boethius were recovered, and new translations were made.
We are told that “ Jacobus Clericus of Yenetia translated from
G-reek into Latiu certain hooks of Aristotle, and commented on
them, namely, the Topica, the Analytics Prior and Posterior,
and the Elenchi, although,” adds the chronicler, “an earlier trans-
lation of these same books may he had.”* This was in 1128 a.d.
It is more than probable that Roscellinus, who flourished 1080-
1100, knew more of Aristotle’s writings than the treatises on
the Categories and on Interpretation. Abelard (b. 1079 — d. 1142)
must have known the greater part of Aristotle’s Organon, and John
of Salisbury (who died 1180), we know, knew the whole of it.

Hence, whereas at the middle of the eleventh century the know-
ledge of Aristotle was confined to acquaintance with the two first

* “ Jacobus Clericus de Yenetia transtulit de grseco in latinum qu'osdam
libros Aristotelis et commentatus est, scilicet Topica, Anal, priores et posteriores
et Elenchos, quamvis antiquior translatis super eosdem libros haberetur.”
Robert de Monte Chronica ad Ann. 1128, in Pertz, Monument, viii. 489.
Quoted from Prantl, Geschichte der Logik ii. p. 99.

442

Proceedings of the Royal Society

books of the Organon, along with the Introduction of Porphyry,
at the middle of the twelfth century there were two distinct sources
of knowledge of Aristotle’s opinions on Logic — that derived from
the “old” tradition from the books on the Categories, and on In-
terpretation, and from the Introduction of Porphyry, and that
derived from a “ new ” tradition from recovered translations made
by Boethius of the Prior and Posterior Analytics, of the Topics and
of the book on Fallacies, and from new translations.

This new tradition was looked upon with considerable mistrust
by several of the steady going old schoolmen. It disturbed their
view of logic. They had constructed a very fair well-rounded system
from the material supplied by the old tradition. It had been suffi-
cient for them then, and they wanted nothing new now. Even
supposing that these new treatises were Aristotle’s, they would not
admit them to be logical, or, if they went so far, they would not
allow them to have any real importance. The old doctrine had
done very well for them and their fathers before them, and it might
serve every one else. They saw no need for any change. On the other
hand, more enterprising students were vastly taken with these new
treatises, and found that they contained Aristotle’s real logic. They
revealed to them the doctrine of the syllogism, and its application
in demonstrative, probable, and fallacious material of knowledge.
The new tradition was Logic, the old not more than an introduction,
even if worthy of that place.

When we consider that logic, with all its verbal niceties, was
more studied than anything else in these days, we find in the very
fact of these two different traditions, and the twro ways of accepting
them, all the elements for a severe and widely extended quarrel :
and the quarrel soon arose. On the one side, the zeal shown in
studying and commenting upon these new treatises was wholly
attributed to the love of novelty, and the new opinions concerning
logic and its sphere, which were coming into fashion, were set down
as due to a restless, shallow, modern spirit. The logic of the new
tradition was called the “ Nova Logicaf and those who advocated
it, “ ModerniP On the other hand, the Moderni thought that
their opponents were prejudiced against their opinions, simply
because they were not the old ones, and they despised them as old
world thinkers, who had not the breadth of view required to accept

of Edinburgh, Session 1870-71.

443

anything, however good in itself, which differed from their old
theories. They called the logic of the old tradition the “ Vetus
Logica f and its upholders “ Antiqui .”

Now, curiously enough these terms had been applied half a cen-
tury before, and in a very different manner. When Roscellinus had
startled the orthodox world by saying that universals were only
“ flatus vocisf and had drawn many heretical conclusions in logic
and in theology, from this doctrine, his opponents said that he was
the author of a “ new ” kind of logic, and called his followers
“ moderni.” The “old ” logic, of the days of Roscellinus, treated
logic from a realist point of view, the “ new ” logic treated logic
from a nominalist point of view (so far as the words “ realist ” and
“ nominalist ” can be used with accuracy of any doctrine at this
early period of scholasticism). The Antiqui of the time of Ros-
cellinus became realists in the time of Thomas of Aquino, and
the “moderni ” were the nominalists of later days.

Here then we have a confusion in the terminology, on the one
hand Yetus Logica meant the introduction of Porphyry, the trea-
tises on the Categories, and on Interpretation ; Nova Logica, the
Prior and Posterior Analytics, the Topics and the book on Falla-
cies ; Antiqui, those who thought that Logic Proper was contained
in this Yetus Logica; Moderni, those who thought that this Nova
Logica was the true Logic. On the other hand, Yetus Logica
meant logic treated from a realist point of view ; Nova Logica,
logic treated from a nominalist point of view ; while Antiqui and
Moderni corresponded very much to the latter terms of Realist
and Nominalist.

This confusion does not really last throughout the period of
Scholasticism. The meaning of the terms did fluctuate somewhat,
as all terms do, but upon the whole they preserved a great uni-
formity of meaning. “Yetus” and “Nova Logica,” became
dissociated from “ Antiqui ” and “ Moderni,” with which they
were at first so closely united, and, curiously enough, while the
one set of terms kept to one of their primitive meanings, the other
set kept to the opposite meaning. “ Yetus ” and “ Nova Logica ”
were used of divisions of Aristotle’s Organon ; while Antiqui and
Moderni became more or less, though never quite, equivalent to
Realist and Nominalist.

444

Proceedings of the Royal Society

“ Vetus Logica,” from the middle of the twelfth down to the
beginning of the sixteenth century, meant the logic taught in the
etcraywyr] of Porphyry, and in the 7repi, Karqyoptuv and the 7repi
ippLrjvetas of Aristotle.

“ Nova Logica,” during the same period, meant the logic of
Aristotle’s avaXvriKa Trporepa, avaXvTLKa vcrrepa, to7tlkol and 7 repl
(To<jiUTTLKwv eAeyya)i/. This is the almost invariable scholastic use of
the terms. Any other is accidental and variable.

Now, this assertion is made against the greatest authority in
the history of scholastic Logic, Professor Prantl of Munich, whose
“ G-eschichte der Logik im Abendlande,” is one of the most trust-
worthy and laborious efforts in historical research. Dr Prantl
recognises, as every one must do, that the meaning given here to
“vetus” and “nova logica” was one of the principal scholastic
uses of the terms, and every quotation to be made from logical
treatises in support of our view of the question appears in his
notes, hut he seems to think that the expressions retained their
relation to the names “ Antiqui ” and “ Moderni,” and that any
signification which belongs to them apart from these names is
entirely subordinate. He connects the term “ Nova Logica ” with
the partly grammatical, partly logical additions to the doctrine
which first became popular through the Summulae Logicales of
Petrus Hispanus ; * he makes it occupy the middle place between
the “ old ” logic and the “ Ars Magna ” of Raymond Sully; and
he has proved by a quotation from a dialogue in that curious and
amusing Manuale Scholarium or Mediaeval Students’ Gruide-book,
given in Zarnacke’s Deutschen Universitaten im Mittelalter, that
when the Antiqui were hard pressed by the Moderni, they always
retired on the “ Vetus Logica” as their stronghold, f

* Prantl believes that this addition to logic is due to a Byzantian influence,
and therefore believes that the Summulae of Petrus Hispanus is almost a
Latin translation from the Greek of Psellus. Sir W. Hamilton and many
other authorities refuse to admit this Byzantian influence, and hold that the
Greek work of Psellus is a copy or translation from the Latin of Petrus
Hispanus. Prantl , Gesch. der Logibr.,\\. p. 264. Hamilton Discus. 2nded.,
p. 275.

f C. iv. De altricatione viarum et disciplinarum.

Camillus. Hunc magistrum tu quasi ad ccelum attuliste tamen modernus
est.

Bartoldus. Quid turn ?

of Edinburgh , Session 1870-71.

415

It is not to be supposed that two names, especially when embo-
died in such vague words as “old ” and “new ” should have pre-
served the same invariable meanings in every writer during a period
of three centuries. We may, therefore, admit, without prejudice
to our statement, that the terms “ Yetus ” and “ ISTova Logica ” did
bear those significations which Prautl gives to them, and did pre-
serve a more or less continuous connection with the terms
“ Antiqui ” and “ Moderni.” But it may be proved that, from
about the middle of the twelfth century down to the middle of the
fifteenth at least, the first meaning which the term Vetus Logica
would suggest to a mediaeval student was “ the logic treated in the
Predicables of Porphyry, and in the Categories and De Interpre-
tatione of Aristotle ; ” while the first meaning suggested by the
term Nova, Logica , was “ the logic treated in Aristotle’s Prior and
Posterior Analytics, his Topics, and his book on Fallacies.”

This may be directly proved from the quotations which Prantl
himself gives.

Lambert of Auxerre, who lived in the middle of the 13th
century, says, “ Logica traditur in omnibus libris logicas, qui sunt
sex, sc. liber prasdicamentorum, liber Peryermenias, qui nunc dicun-
tur vetus logica , liber Priorum, Posteriorum, Thopicorum et Elen-
chorum, qui quatuor dicuntur nova logica — Of. Prantl, iii.

p. 26.

Cam. Nihil ab eo deinceps audiam.

Bart. Eo stultior es, si doctrinam despicis. Nam non solum realistae verum
etiam moderni magnam partem philosophise consecuti sunt.

Cam. Sed versantur in sophismatibus tantum, veram doctrinam asper-
nantur.

Bart. Offendis veritatem, nam erudissimi viri reperiuntur inter modernos.
Nonne audisti, in quibusdam terris eos possidere integras universitates ?
ut Viennae Erfordiae, utque quondam hie erat. Nonne arbitraris, doctos hie
bonosque fuisse ? Et nostro aevo adhuc reperiuntur ?

Cam. Scio quidem et intelligo, sed fama eorum parva est. Elaborant solum
in parvis logicalibus et sophismaticis opinionibus.

Bart. Non recte intelligis, nam clari sunt in enunciationibus et syllogismis.
Non reperies artium studiosos, qui syllogismos ceterasque species arguments.-
tionis facilius noscant quam moderni.

Cam. Et in vera scientia nihil sciunt.

4

Bart. Quam mihi facis veram scieneiam ?

Cam. Predicabilia Porph/yrii, cathegorias AridoWm, in quibus aut parum
noveant aut nihil. — p. 11, 12.

3 o

VOL. VII.

446

Proceedings of the Royal Society

Dans Scotus, who died in 1308, calls Syllogistic, i.e., the Prior
and Posterior Analytics and the Topics, the :c Nova Logica,”
and the Categories, with the De Interpretatione, the “ Yetus
Logica.”

In the 14th century we have commentaries Super Yeterem Artem,
e.g., by Antonius Andreas, by Walter Burleigh, and by Gfratiadei
of Ascoli (Esculanus, as he is commonly called), and these are in-
variably expositions of the Predicables of Porphyry, the Categories,
and the De Interpretatione of Aristotle.

Esculanus (d. 1341) says plainly, “ Ars autem nova, quae tota
versatur circa ratiocinationem, oportet quod distinguatur secundum
diversam considerationem eius ; potest autem ratiocinatio dupli-
citer considerari, uno quidem modo simpliciter sine applicatione ad
raateriam aliquam, et alio modo considerari potest cum applicatione
ad materiam specialem. De ratiocinatio quidem sumpta in sua
comitate, agitur in libro priorum, sed ratiocinatio sumpta cum
applicatione ad materiam specialem distinguitur ; quia aut appli-
catur ad materiam demonstrativam ; ac sic agitur de ipsa, in
libro posteriorum ; aut etiam applicatur ad materiam dialecticam.
In materia autem dialecticam potest fieri ratiocinatio recta et
ratiocinatio sophistica. De ratiocinatione recta agitur in libro
topicorum ; et de ratiocinatione sophistica in libro elencho-
rum.” *

There is, however, another source of evidence which Prautl has
not in this reference carefully investigated — the regulations and
decrees of the universities. When any term whatever is found in a
university decree, we may take it for granted that its signification
there was the standard one for the time being, and when we find
the same terms occurring in the regulations of almost all the
principal universities with the same meaning, we are warranted in
adopting that meaning as the real signification of the term.

These terms, u Yetus ” and “ NovaLogica,” are frequently found
in the regulations of the mediaeval universities, and they invari-
ably mean the logic taught in the first two, and the logic taught In
the last four, of the treatises of the Organon.

* Commentaria Graciadei Esculani ordinis predieatomm. In totam Artem
veterem Aristotelis, f. 1.

447

of Edinburgh, Session 1870-71.

Thus as early as 1215 * the students of Paris University are
commanded to read the boohs of Aristotle on Logic, — both the
“ Vetus ” and the “ Nova Logica.”

In 1309 we find, among the Statuta Collegii Cluniacensis, a
statute concerning scholars studying philosophy, in which students
are told to work at — first the Summulse in the college ; then the
Vetus Logica; and lastly the Nova Logica, either in the college
or outside. f This passage is important, because it shows that the
Summulm are not part of the Nova Logica; elsewhere Summulists
are distinguished from Logicos.

In 1366, at the reformation of the Faculty of Arts, it is ordained
that students attending lectures in this faculty read the whole of
the vetus ars, four books of the Topics and the books of the
Elenclii, the Prior or the Posterior Analytics completely, and the
books De Anima in whole or in part.J

In the munimenta of the University of Oxford, published by the
Master of the Polls, we have many references to the vetus and
nova logica ; and in all cases the reference is evidently to books of
Aristotle’s Organon. §

Thus Artistae are told, in 1340, that, before they can “incept ”
in arts, they must first have sworn that they have read two logical
books at least, one of the vetus logica, and the other of the
nova. ||

In the munimenta of the University of Glasgow, of the date
1460, or thereabout, we find it enacted in the regulations about
reading in logic — “ Ordinaria vero audienda sunt hsec; primus sc.
in Veteri Arte liber universalium Porphyrii, liber Predicamentorum
Aristotelis, duo libri Peri Hermeneias ejusdem. In Nova Logica
duo libri priorum, duo posteriorum, quatuor ad minus Topicorum,
sc. primus, secundus, sextus, et octavus, et duo elenchorum. . . .
Item audiantur libri extraordinarii ... in logica textus Petrus

* Bulseus. Hist. Univ. Paris, iii. p. 82.

f Ibid., iv. p. 122.

f Item quod audierunt veterem Artem totam, librum Topicorum, quoad 4
libros, et libros Elenchorum, Priorum aut Posteriorum complete; etiam
librum de Anima in tota vel in parte. — Bui. Hist. Univ. Paris, iv. 890.

g Munimenta Acad. Oxon. 128, 417, 422. Edited by Anstey.

|| Ibid., 142, cf. 242, 286.

448

Proceedings of the Royal Society

Hispanus cunc syncathegorematibus, tractatus de distributionibus
liber sex principiorum.” *

This reference is important, because it places those grammatico-
logical treatises, which gave a distinctive character to the logic of
the moderni, outside of the “ nova logica.”

In the Liber Decanorum of the University of Prague, the Veins
ars Aristotelis is always kept separate from the books of the Prior
and Posterior Analytics, the Topics, and the book on Fallacies ; f
and this division is elsewhere referred to as that of “ Yetus ” and
“ Nova Logica.” J

Aschbach, in his history of the University of Vienna, says that
the Ars Veins treated of the Predicables of Porphyry, and of the
Categories or Predicaments, and of the de Interpretatione of
Aristotle. The Logica Nova looked at argumentation as a whole,
and considered — (1.) The Eesolution or analyses of syllogisms given
in the Prior and Posterior Analytics ; (2.) Inventive, or ways of
discovering true middle terms, given in the Topics; and (3.)
Fallacies, given in the libri Elenchorum. Prof. Aschbach shows
that Logic, as taught in Vienna, consisted of three parts— the
Vetus Logica, which was studied as an introduction; the Parva
Logicalia, for the Vienna Students were Moderni; and the Nova
Logica. § The lists which he quotes bears out his statement, with
this exception, that after some time the Parva Logicalia, not the
“ Ars Vetus,” came to be looked on as the introduction to Logic. ||

These quotations may, perhaps, serve to prove our assertion, that
the scholastic use of the terms “vetus” and “nova logica” is
almost exclusively confined to the designation of parts of the

* Munimenta Univ. Glasg., ii. 25, 26. This reference I owe to Professor
Veitch of Glasgow.

t Liber Decanorum Fac. Phil. Univ. Prag. Pars. i. pp. 83, 126.

f Ibid., p. 127. £ Ibid., p. 89, 90.

|| Ibid., pp. 95, 135, 139, 142, 144, 147, 151, 154, 161. According to these
lists a course of lectures on the Ars Vetus cost 5 groschen, but, if taken with
exercises and colloquia, or qusestiones, it cost 18 groschen. A course on the
Parva Logicalia cost 10 groschen, including quaestiones. While a course on
the Nova Logica cost 12 groschen, and 36 including qusestiones (p. 95). In
the last decade of the 14th century, the course on the Parva Logicalia con-
sisted of 104 lectures, and cost a gulden ; the length of the course on the
Vetus Logica was the same, and the fee the same ; while the courses on the
Nova Logica consisted of 132 lectures, and the fee was 35 groschen (p. 352).

449

of Edinburgh, Session 1870-71.

Organon of Aristotle — the part earlier and the part later known ;
and that the meaning of the terms did not vary with the significa-
tions of Antiqui and Moderni.

The point discussed in this note is of small importance on its
own account, but it is one step, and a rather significant one, in the
argument which tends to show that the new life in scholasticism
which expressed itself most fully in the 14th century in William
of Occam, and which afterwards developed, through the early
natural philosophers of Italy, into those scientific methods which
have rendered modern science possible, was due to the inborn
genius of western Europe, and was not a foreign growth cut from
the Greek stock and engrafted on the Latin.

3. On some Abnormal Cones of Finns Pinaster. By
Professor Alexander Dickson.

In their celebrated essay, iC Sur la disposition des feuilles curvi-
seriees,” * the brothers Bravais describe a cone of Finns Pinaster
{Pin maritime ), where the lower part of the cone exhibited second-

1 2 3 5 g

ary spirals 7 S, 12 D (series - , - , - , — , — , &c.), while towards

A o 7 1 A

the apex the arrangement, in consequence of the disappear-
ance of one of the spirals by 12, changed to 7 S, 11 D (series
112 3 5

r, -r , —r , -q , &c.).f They describe another cone of the same
o 4 7 11 lo

species, in which the lower four- fifths exhibited secondary spirals

9 S, 13 D (series 1 , | , , &c.), changing at the upper fifth

4 y lo AA

112

to 8 S, 13 D (ordinary series - , - , &c.) by suppression of one

2 o o

of the spirals by 9.J Such cases, along with some others chiefly
in the capitula of Dipsacus sylvestris , lead these authors into a dis-
cussion of the general question of the possible transition from one
arrangement to another by change in the number of secondary
spirals. As regards their “ curviserial ” forms, however, they are
disposed only to admit the occurrence of such transitions by way of

* Ann. des Sc. Nat. 2d ser. t. vii. f L. c. p. 93.

t L. c. p. 103.

450

Proceedings of the Royal Society

convergence of secondary spirals, i.e ., by abortion of one, or possibly
coalescence of two, resulting in diminution of number. For
example, after referring to the possible derivation of an arrangement

with 5 and 7 secondary spirals (series ^ | , ?I , &c.), from an

Z O 7 1 Z

ordinary one with 5 and 8, by abortion of one of the spirals by 8,
they add that “the series 1, 4, 5, 9 . . . does not admit of
explanation by the way of abortion, and that one can deduce it
from the ordinary series only by supposing a superfoetation or
addition of a new spiral among the secondary spirals by 8.”
“This hypothesis,” they continue, “appears to us altogether
improbable, since in the face of an immense number of instances
where two spirals converge into one, we cannot on the other hand
cite one (apart from rectiserial stems) where one spiral diverges into
two similar and parallel ones.”*

The two cones of Pinus Pinaster which form the immediate
subject of Dr Dickson’s paper, and for which he is indebted to the
kindness of R. Smyth, Esq., Emyvale, Co. Monaghan, Ireland, are
interesting cases of convergence of spirals. These, together with a
few other cases already noted by Dr Dickson, seem to throw some
additional light upon this question of the origin of variations in
the spiral arrangements in a given plant, where not unfrequently
spirals belonging to several distinct systems occur.

In the first of the cones received from Mr Smyth, there is at the

base a right-handed spiral (series | | > &c0

with the secondary spirals 9 S, 14 D, 23 S. A little above the base,

however, two of the 9 spirals to the left run into one, leaving, from

that point up to about the middle of the cone, an arrangement of

secondary spirals 8 S, 14 D, 22 S = a left-handed bijugate of the

1 1 2 3 5 5

series - , , &c., with divergence — About the

o 4 7 11 18 lo x 2

middle of the cone two of the 14 spirals to the right run into

one, leaving, from thence to the top of the cone, an arrangement

13

of secondary spirals 8 S, 13 D, 21 S = a left-handed — spiral of the
.112 3.

ordinary series &c.

* L. c. pp. 104, 105.

451

of Edinburgh, Session 1870-71.

The second of Mr Smyth’s cones exhibits from the base to near

5 112 3 5

the top a right-handed — spiral (series - , - , - , — , , &c.)

lo o 4 7 II lo

with secondary spirals 7 S, 11 D. Near the top of the cone, how-
ever, two adjacent scales of two of the 7 spirals to the left have
partially coalesced, and beyond that point the two spirals run
into one, leaving an arrangement of secondary spirals 6 S, 10 D —

13 2-3

a left-handed bijugate of the ordinary series - , - , - , - , &c.,

2 o o o

3

with divergence .

8 = 2

In the cone of Pinus Lambertiana, recently exhibited to the
Society, it will be recollected that at the bottom and top of the

cone there was a left-handed spiral (series \ , p , ~

23 4 5 9 14 23,

&c.) ; while in the middle was a right-handed bijugate of the series

12 3 5

- , p, - , , &c., where the divergence in each of the two gene-

Z o 7 1 Z

rating spirals =

In this cone the steepest secondary

spirals at the bottom and top were 9 D, 14 S ; while those in the
middle were 10 D, 14 S.

In connection with the above, Dr Dickson recalled attention to
the flower-spikes of Banksia occidentalis recently exhibited to the
Society, where there wTere four different arrangements, — viz., one
with secondary spirals 7 and 7 = alternate whorls of 7 (or, if pre-

ferred, a 7-jugate of the ordinary series with divergence

2 x 7;

giving 14 vertical rows ; one with secondary spirals 7 and 6
2 112

= a spiral (series g > ^ ^ ’ &c), giving 13 vertical rows; one

5 12 3 5

with secondary spirals 7 and 5 = a — spiral (series - , - , - , _

&c.), giving 12 vertical rows ; and one with secondary spirals
5

8 and 5 = a ^ spiral (ordinary series) giving 13 vertical rows.

It will be noted that, contrary to the opinion of MM. Bravais,
one arrangement does not necessarily or only originate from
another by suppression of parts. To prove this, we have only to

452

Proceedings of the Royal Society

look at the above-mentioned cone of Pinus Lambertiana, where the
arrangement in the middle region results from an augmentation of
parts as compared with the base of the cone ; while the spiral at
the top, which is the same as that at the base, is, of course,
the result of a diminution as compared with the middle. It has
been already observed by authors, moreover, that in such plants
as Cacti and succulent Euphorbias* one vertical row may be split
into two, or, conversely, two run into one, thus changing the
spiral. Now, as vertical rows are, in one sense, only to be regarded
as the steepest secondary spirals (a slight torsion readily con-
verting them into actual spirals), such cases are in all essentials
comparable to the above- described cones.

The arrangements above indicated will be rendered very readily
intelligible by the accompanying tabular views.f

Table A. — Gone of Pinus Pinaster ( Mr Smyth — No. 1).

S D

S D

S

D

S V

13

34

Top, 1 2

3 5

8

13

21 34 =

Middle, —

2 6

8

14

22 36 =

5

18x2

Bottom, — 1

4 5

9

14

23 37 =

8

37

Table B. — Gone of P. Pinaster (Mr Smyth— No. 2).

D

S D

S

D

v ,

Top, —

2 4

6

10

16 = 8—

2

Bottom, 1

3 4

7

11

»- rs

* The greater number of these plants would be reckoned as truly recti-
serial by MM. Bravais. Dr Dickson has no hesitation in referring to such
cases in this argument, as he is strongly disposed to doubt as to there being
any fundamental distinction between the “ rectiserial” and the so-called
“ curviserial” spirals of these authors.

f In these tables, under S, are indicated the numbers of spirals, generating
as well as secondary, running to the left; under D, the numbers of those run-
ning to the right; while under V are indicated the numbers of vertical rows.

453

of Edinburgh, Session 1870-71.

Table C. — Cone of Pin us Lambertiana, in Museum , Edinburgh
Botanical Garden.

S

D

S

D

S

V

£r

Top,

1

4

5

9

14

23

0

= 23

Middle,

-

2

4

10

14

24

5

~ 12 x 2

Bottom,

1

4

5

9

14

23

5

= 23

Table D represents the four different arrangements in the flower-
spikes of Banksia occidentals , placed in series so as to show how,
by slight diminution or augmentation in the number of secondary
spirals, one arrangement may be conceived to originate from
another. The directions of the spirals to right or deft are stated
arbitrarily, to suit the purpose of the diagram.

D

No. 1, —

No. 2, —

No. 3, —

No. 4, 1

Table D.

S D S D

— —77

16 7

12 5 7

2 3 5 8

V

14 =
13 =
12 =
13 =

1

2x7

2

13
5_
12
J5
• 13

It is impossible to reflect on such cases as have been adduced
and not be impressed forcibly with the idea that, as regards their
production or origination, diverse spiral arrangements are to be re-
garded as allied much more according to the numerical correspond-
ence of their secondary spirals and verticals than in proportion to the
correspondence of their angular divergences. Such cases, moreover,
show clearly how a generating spiral may change its direction on
one and the same axis.

It is perhaps rash to speculate as to how the different systems of
spirals in Fir cones originate. On the whole, Dr Dickson is inclined
to assume the bijugate of the ordinary system as the fundamental
arrangement. He is to some extent confirmed in this view by a
remarkable abnormality in a cone of P. Pinaster , gathered by
him at Muirhouse, near Edinburgh. This cone exhibits a left

3 p

VOL. VII

454 Proceedings of the Poyal Society

handed — spiral.

Zjl

At the base of the cone, however, a number of

rudimentary scales of small size and somewhat peculiar shape are
intercalated with considerable regularity among the others, so as to
appear as projections placed at the intersections of the lines formed
by the margins of the larger scales. Now, if these small scales had
been disposed with perfect regularity, and had been of equal size
with the others, there would have been a left-handed bi jugate

arrangement, with divergence

Such a cone, in fact, sug-

21x2

gests the possibility of single spirals of the ordinary series being
derived from bijugates of the same series by suppression of one
half of the scales.

Again, the ordinary trijugates are easily derivable from bijugates,
as indicated in Table E.

Table E. — Showing the possible derivation of ordinary Trijugate from
the Bijugate Arrangement.

DSD

— 3 6

2 4 6

From the ordinary trijugate, in turn, a spiral of the system, -,
2 3 5

- , — , — , &c., may be simply derived, as indicated in Table E.

y 1 4 Zo

s

9

10

V

15 =

16 =

2

5x3

3

8x2

Table E. — Showing possible derivation of a Spiral of the System,

1 1

4’ 5’

&c., from the Ordinary Trijugate.

D

S

D

S

D

S

V

1

4

5

9

14

23

37 =

_

3

6

9

15

24

39 =

Again, it is clear that by augmentation of parts, a spiral of the
112

system - , - , - , &c., may be derived from the ordinary bijugate,
o 4 7

since the converse (by diminution) actually occurs in the second
of Mr Smyth’s cones indicated in Table B.

of Edinburgh, Session 1870-71.

455

Lastly, the spiral — , series
A A

1 2 3_ 5_

4’ 9 ’ 13’ 22’

&c., which Dr

Dickson formerly noted as occurring in a cone of Finns Pinaster , in
the Museum, Edinburgh Botanic Garden, may readily he derived,
as MM. Bravais have suggested,* from a spiral of the series

1 1 2

4’ 5’ 9’

_3 _5

14’ 23

, &c., thus,

Table G-. — Showing possible derivation of a — Spiral from the System

A A

&c.

D

S

D

S

D

V

—

1

4

9

13

22 -

5

22

1

4

5

9

14

23 =

5

23

The following Gentleman was admitted a Fellow of the
Society : —

Rev. Professor Crawford.

Monday , 1 5th May 1871.

Professor CHRXSTISON, President, in the Chair.

At the request of the Council, Professor Tait gave an
Address on Spectrum Analysis.

(The following is a brief Abstract, consisting mainly of the Lecture
Notes') : —

I should not have thought of appearing before you to-night to
lecture on so hackneyed a subject, had I not been assured by
several members of the Council that such an address was really
desired by many Fellows of the Society. It is a subject to which
I have not paid very special attention, partly because it is in so
many and such good hands, and partly because (except from the
point of view of theory) it requires for its extension, especially to

* L. c. p. 103.

456

Proceedings of the Royal Society

astronomy, very costly instrumental appliances and a great sacrifice
of time. And the difficulty of transporting to the Society’s rooms
from the College the large amount of bulky and delicate apparatus
required for its proper illustration, is (as I have just found) so
great, that if on any future occasion the Society desire me to give
such an address, I shall have to make it a condition that the
meeting for that evening be held in my class-room in the Uni-
versity buildings.

The subject of spectrum analysis must always possess great
interest for this Society, inasmuch as many of its most distin-
guished promoters have been, or are, among our Fellows, ordinary
as well as honorary, and several of the most remarkable memoirs
on various parts of the subject are to be found among our publica-
tions.

The objects of spectrum analysis may be briefly enuntiated as
follows : — To make, by optical methods , the qualitative chemical ana-
lysis of (1) a self-luminous body ; (2) an absorbing medium , whether
self-luminous or not.

It is difficult now-a-days, when so many philosophers are engaged
almost simultaneously at the same problem, to decide which of
their successive steps in advance is that to which should really be
attached the title of discovery (in its highest sense) as distinguished
from mere improvement or generalisation. You have only to look
at the recent voluminous discussions as to the discoverer of the
Conservation of Energy, to see that critics may substantially agree
as to facts and dates, while differing in the most extraordinary
manner as to their deductions from them.* Some of these writers,
no doubt, put themselves out of court at once by habitually attri-
buting the gaseous laws of Boyle and Charles to Mariotte and G-ay-
Lussac. Men who persist in error on a point so absolutely clear
as this, show themselves unfit to judge in any case of even a little
more difficulty. Others, who strongly support the so-called claims
of Mayer in the matter of Conservation of Energy, and who should
(to be consistent) therefore far more strongly advocate the real
claims of Talbot, Stokes, Angstrom, Stewart, &c., to the discovery
of spectrum analysis, are found to uphold Kirchhoff as alone en-

* Some frantic partisans of Papin, &c., deny almost all credit to Watt in
the matter of the steam-engine ! No farther examples need be cited.

of Edinburgh, Session 1870-71.

457

titled to any merit in the matter. As a paper by Mr Talbot, on the
early history of the subject, is to be read this evening, I shall content
myself for the present with the remark, that, of the two objects of
spectrum analysis above named, Talbot and Herschel were unques-
tionably foremost in the enuntiation of the first ; Brewster, Angstrom ,
and especially Stokes and Balfour Stewart, in that of the second.
Why some of their statements were incomplete or inexact, and
what was required to complete or to correct them, will be more
usefully stated after I have given some preliminary explanations.

Spectrum. — Newton’s fundamental experiment.

Reason of separation of colours.

Reason of impurity.

How to obtain a pure spectrum.

Object of trying to do so.

Effect of Additional Prisms.

Note that the source of light in all these experiments has been carbon
heated to incandescence by resistance to a powerful current of voltaic
electricity.

I. Incandescent solids and liquids give generally a continuous spectrum.

Its highest radiation, and the amount of radiation of each wave
length, depend on the temperature.

Hence the necessity of using the highest temperature we can
obtain.

Illustrate by different lengths of platinum wire heated by current.

II. Gaseous bodies, incandescent, give generally a (limited) number of

perfectly definite wave lengths (though under certain circumstances
of pressure, &c., they give a continuous spectrum). The number
depends for each substance on its temperature and pressure, and their
appearance is characteristic of the substance. For, under the same
physical circumstances, we have always the same effect — as, indeed,
must be assumed to be the case, if we think physics can be studied
at all. This remark was virtually made by Carnot, and is all that
was wanting in Talbot’s earliest paper to make it the complete
statement of this first part of the subject.

Illustrate by the spectra of the incandescent vapours of
Thallium,

Lithium,

Magnesium,

Sodium.

Illustrate the conductivity of the vapour of the latter by the
increased breadth of the spectrum when it is present ; also by its
effect in improving the spectra of other substances when a weak
battery is used.

458

Proceedings of the Royal Society

Hydrogen — by induction-coil.

(Here refer again to Talbot’s paper, presently to be read.)

Spectroscopes. — Swan’s paper, in Edinburgh Transactions — Intro-
duction of Collimator — estimation of the exces-
sively minute amount of sodium required to give
the D line.

Universal Prevalence of Sodium, Lithium, &c.

Discovery of New Metals. — Bunsen — Rubidium, Caesium.

Crookes and Lamy — Thallium.

Reich and Richter — Indium.

Discoveries in Astronomy and Meteorology.

Lightning.

Aurora.

Solar prominences and corona.

Nebulae.

Comets.

Zodiacal light.

Temporary stars.

Huggins, Janssen, Lockyer, Secchi, &c.

III. Absorption by glowing gases, from otherwise continuous spectra.

Fraunhofer’s lines (Wollaston).

Reversal of sodium line (exhibit).

Hence atmospheres of sun, stars, &c.

Brewster (in Edinburgh Transactions).

Nitric peroxide — effects of heat and pressure.

Atmospheric lines.

Foucault. — Spectrum of incandescent carbon points, seen (by reflec-
tion) through the voltaic arc (which itself gives them bright)
shows the D lines reversed.

Stokes — about 1850, gave, in consequence of W. H. Miller’s very
accurate verification that the double bright line of sodium
exactly corresponds in refrangibility with the double dark line
D, the correct mechanical explanation of the phenomenon,
with the mechanical illustrations still very often employed.
Given, with general theory of solar and stellar chemistry, ever
since (annually) by Thomson in his lectures. Give it.

Angstrom — 1853. — “ Un gaz a l’etat d’incandescence emet des
rayons lumineux de la meme refrangibilite que ceux qu’il peut
absorber.”

B. Stewart (Edinburgh Transactions, 1858-9).

Extension of the Theory of Exchanges — The radiating power
of a body is equal to its absorbing power, and that for every
ray. Based on experimental facts.

Heated pottery ware, with marked pattern, looked at in the
dark.

459

of Edinburgh, Session 1870-71.

Coloured glasses lose their colour in the fire.

Kirchhoff, Oct. 1859. — Introduction of reasoning more directly
based on the Second Law of Thermodynamics.

Proof that the absorbing flame must be colder than the
source — Exception for Fluorescence.

Kirchhoff and Stewart. — Tourmaline, which polarises common light
by absorbing polarised light, gives off, when hot, polarised
light like that which it absorbs.

(Note that the discussion of the question of priority on this subject, in
papers by Stokes, Thomson, Kirchhoff, and Stewart, in the Phil. Mag.
1863, is very interesting, and may still be read with profit).

Fluorescence is Degradation of Energy.

Exhibit Stokes’ fundamental Experiments.

The question of priority just alluded to illustrates in a very
curious way a singular and lamentable, though in one sense
honourable, characteristic of many of the highest class of British
scientific men ; i.e., their proneness to consider that what appears
evident to them cannot but be known to others. I do not think
that this can be called modesty ; it is rather a species of diffidence
due to their consciousness that in general their accurate knowledge
of the published developments of science is confined mainly to
those branches to which they have specially devoted themselves.
Their foreign competitors, on the other hand (especially the
G-ermans), are often profoundly aware of all that has been done,
or, at least, have some one at hand who is, and can thus, when
a new idea occurs to them, at once recognise, or have determined
for them, its novelty, and so instantly put it in type and secure it.
Neither Stokes nor Thomson, in 1850, seems to have had the least
idea that he had hit on anything new, especially as they had a
vague recollection that Foucault had previously attacked the pro-
blem— the matter appeared so simple and obvious to them — and,
but for the fact that Thomson has given it in his public lectures
ever since (at first giving it as something well known), they might
have thus forfeited all claim to mention in connection with the
discovery. I could mention many other striking instances of this
peculiarity ; one, in fact, appeared in our own Proceedings a
few months ago ; but to consider it more closely would lead me
away from the subject of my lecture. It is sufficient to have
called attention to a want which could easily be supplied, if we

460 Proceedings of the Boyal Society

had anything in this country equivalent to the Fortschrilte dev
Physik, hut published with considerably less delay.

Detailed study of Solar Spectrum — mainly due to the labours of
two men.

Maps by Kirchhoff and Angstrom, with the number of ele-
ments proved to exist in the sun’s atmosphere.

According to Angstrom, the following numbers of bright lines given by
elements are found exactly coincident with dark lines in the solar

spectrum : —

Hydrogen,

4

Manganese,

57

Sodium,

9

Chromium,

18

Barium,

11

Cobalt,

19

Calcium ,

75

Nickel,

33

Magnesium,

4 + (3 ?)

Zinc,

m

Aluminium,

2(?)

Copper,

7

Iron,

450

Titanium,

118

He notes that Thalen has found 200 coincidences with Titanium lines.
Types of Stars — Secchi.

I. White stars — Scarcely any absorption lines, except those due to

Hydrogen, which are strongly marked. Sirius, Yega, &c.

II. Yellow stars — The Sun, Arcturus, Aldebaran, &c. — multitudes of

fine lines.

III. Nebulous bands in addition to the fine lines — « Herculis, « Orionis,
&c. In Mira Ceti these bands vary with the apparent magnitude.
Similar appearances are observed in the spectra of sun-spots. On the
contrary, Algol retains the first type through all its periodic changes.

IV. Feeble spectrum crossed by bright lines. The stars of this type are
all of small apparent magnitude ( i.e . of feeble luminosity), and
usually of a blood-red colour. Temporary Stars — bright lines of
hydrogen.

If to these be added

Y. Resolvable Nebulae — Continuous spectrum, as are those of the
nebula in Andromeda* and of many others not resolvable ; and
YI. Planetary Nebulae, and others irresolvable, such as those of Orion,
Lyra, &c., where the spectrum consists of a very few bright lines
only.

it seems to me that we have a series of indications of what (for want of a
better phrase) may be called the period of life of a star or group ; beginning
with the glowing gases developed by the impacts of the agglomerating
cold masses (YI.), * then the almost perfect spectrum of white-hot liquid or
compressed gas (V., I.), which (as it becomes colder) suffers absorption by the
rise of still colder vapours (II.) ; then, as it farther cools, nebulous bands
take the place of sharp lines (III.) ; anon the bursts of glowing gases are
* See the Abstract of my paper on Comets, Froc. R.S.E., 1868-9.

of Edinburgh, Session 1870-71.

461

brighter than the photosphere (IV.), and, finally, no light but that of these
gases is intense enough to reach us (VI.) That there is energy enough to
produce these successive developments is obvious from the fact that, even
at their immense distance, the visible portions of the nebulae of Orion and
of Argus subtend an angle of nearly four degrees.

Application of the spectroscope to determine the relative velocity of

A STAR, OR OF A GASEOUS CURRENT IN THE SOLAR PHOTOSPHERE, WITH
REGARD TO THE EARTH.

Analogy from sound.

Railway whistle.

Tuning-fork experiment.

Similar experiment with organ-pipe.

Finally, absorption by bodies at ordinary temperatures.

Coloured glasses.

Chlorophyll.

Detection of blood, changes of the blood-spectrum by
oxidation, &c., &c.

Microscopic spectroscope.

The following Communications were read : —

1. Note on the Early History of Spectrum Analysis. By
H. Fox Talbot, Hon. F.B.S.E.

Newton, in his observations on the spectrum, appears never to
have used a narrow aperture. In fact there was nothing, in the
existing state of knowledge in his day, to lead him to suppose that
this would alter the phenomena.

Wollaston was the first who observed some obscure bands in the
spectrum, by viewing with a prism the aperture left by the shutters
of his room when nearly closed. It is surprising that this acute
philosopher did not follow up the hint thus accidentally presented
to him, but contented himself with the rude observation above
mentioned.

Fraunhofer was the first who detected the wonderful system of
dark lines in the solar spectrum, by viewing a very narrow and
accurately formed aperture with an excellent prism, aided by a
small telescope. He likewise gave names to the principal dark
lines which have been generally adopted, and he measured accu-
rately their refractive indices by mounting the prism on a
graduated brass circle movable round a centre.

After completing his observations on the solar spectrum, be

3 Q

VOL. VII.

462 Proceedings of the Royal Society

turned his attention to the spectrum of the stars, of which he
described several. He likewise described the spectrum of electric
light, but only that of sparks passing through atmospheric air.
He has likewise left on record a very curious observation on the
spectrum presented by the exterior flame of a wax candle. When
the bright flame is intercepted by a screen, and only the faint ex-
terior flame viewed, he found it to consist almost entirely of homo-
geneous yellow light ; but his skill as an observer was so great that
he perceived this yellow light to consist of two distinct rays very
close together, and only separable by an excellent prism, and a
very narrow aperture. As he remembered that there was a similar
double ray in the yellow part of the solar spectrum which he had
named D, the happy thought occurred to him of transmitting solar
light through the same aperture. He did so, and found that the
two rays of the line D coincided most accurately with the double
yellow ray given by the exterior flame of a wax candle. He does
not appear to have prosecuted this interesting research further.
He merely records the fact. He was not aware that the yellow
light of the candle was in any way caused by the presence of
sodium , the existence of which in a wax candle would probably not
occur to any one, unless perhaps to an experienced chemist on the
look out for some extraneous substance.

About the same time Sir D. Brewster had been seeking for a
source of homogeneous light, for the purpose of improving the
microscope by destroying all chromatic aberration of the lenses.
See his paper of 1822 in the Transactions of the Boyal Society of
Edinburgh, vol. ix. p. 433. Although acquainted with the effect of
salt on the flame of burning alcohol, he had evidently only cursorily
examined it, since he says “ salt or nitre f which is incorrect, and
speaks of its causing the flame to yield “ insalubrious vapours.”
He therefore rejects the use of it, and merely recommends that the
alcohol should be “ largely diluted with water.” The yellow light
so obtained he refers to “ imperfect combustion” (p. 435), and not
in any way to sodium , observing that the combustion of paper,
linen, cotton, or the flame of a blow-pipe, also contain the same
homogeneous yellow light in tolerable abundance. His observa-
tions, therefore, have a certain resemblance to those of Fraunhofer.

About the year 1824 or 1825, Dr Wollaston gave one of his

of Edinburgh, Session 1870-71.

463

evening parties, to which men of science and amateurs were in-
vited, and it was the custom to exhibit scientific novelties, and to
make them the subject of conversation.

On the evening in question I brought as my contribution to the
meeting some very thin films of glass (such as are shown in glass-
houses to visitors by a workman, who blows a portion of melted
glass into a large balloon of extreme tenuity, and afterwards
crushes the glass to shivers). Such a film of glass I brought to
Dr Wollaston and his friends, and after showing that in the well-
lighted apartment it displayed a uniform appearance without any
markings, I removed it into another room, in which I had prepared
a spirit lamp, the wick of which had been impregnated with com-
mon salt. When viewed by this light, the film of glass appeared
covered with broad nearly parallel bands, which were almost black,
and might be rudely compared to the skin of a zebra. Similar
bands, but much fainter, were seen by transmitted light. All pre-
sent agreed that this curious phenomenon could only be due to the
extreme homogeneity of the light of the lamp with the salted wick,
which much exceeded any previous estimate of it. It did not
occur to any one that evening to procure a lens and a plate of
glass, in order to try the effect of the light on Newton’s rings.
But such an experiment tried soon afterwards revealed an astonish-
ing augmentation of the number of rings visible. I followed up
this observation by publishing a paper in 1826 (Brewster’s Journal,
vol. v. p. 77), in which I determined, among other things, the fol-
lowing facts, namely, that all the salts of soda gave the yellow line
D, which I therefore affirmed to be characteristic of sodium. That
the salts of potash give a violet light, together with a single red
ray situated almost at the end of the spectrum, and with no other
light near it. [Subsequently Brewster made careful observations
upon this ray, and found it to be coincident with A in the solar
spectrum, a remark wdiich recent researches with more powerful
instruments have shown to be not entirely exact. Brewster did
one great service in pointing out the fact that in inquiries like this
an achromatic telescope is not necessary.]

The following is a quotation from this paper (vol. v. p. 77): —
“ The flame of nitre contains a red ray of remarkable nature. This
red ray possesses a definite refrangibility, and appears to be cha-

464

Proceedings of the Royal Society

racteristic of the salts of potash, as the yellow ray is of the salts of
soda. If this should be admitted , I would further suggest that when-
ever the prism shows a homogeneous ray of any colour to exist in a
flame, this ray indicates the formation or the presence of a definite
chemical compound .”

Further on, speaking of the spectrum of red fire (such as is used
in theatres and in fireworks), I said, “the other lines may be attri-
buted to the antimony, strontia, &c., which enter into this compo-
sition. For instance, the orange ray may be the effect of the
strontia, since Herschel found in the flame of muriate of strontia a
ray of that colour If this opinion should be correct, and appli-
cable to the other definite rays, a. glance at the prismatic spectrum
of a flame may show it to contain substances which it would otherwise
require a laborious chemical analysis to detect .”

An early paper by Herschel has been omitted in its proper place,
the year 1822 (Transactions Eoyal Society of Edinburgh, vol. ix.
p. 455). He there shortly describes the spectra of chloride of
strontia, chloride of potassa, chloride of copper, nitrate of copper,
and boracic acid.

In 1827 (after the publication of my experiments in 1826), he
stated in the Encyclopedia Metropolitana, article on Light, p. 438,
that salts of soda give a copious and purely homogeneous yellow ;
those of potash a beautiful pale violet. He also describes the
spectra of lime, strontia, lithia, barytes, copper, and iron.

In another paper of mine (Phil. Mag. 1834, vol. iv. p. 114), the
flames of strontia and lithia are examined. The following is an
extract from this paper: — “The strontia flame exhibits a great
number of red rays, well separated from each other by dark inter-
vals, not to mention an orange, and a very definite bright blue ray.
The lithia exhibits one single red ray. Hence I hesitate not to
say that optical analysis can distinguish the minutest portions of
these two substances with as much certainty, if not more, than
any other known method.”

Another passage, taken from the same page, records the first
observation of those peculiar rays at the violet end of the spectrum,
to which some years later Herschel gave the name of the lavender
rays. “ The flame of Cyanogen separates the violet end of the
spectrum into three portions, with broad dark intervals between.

465

of Edinburgh, Session 1870-71.

The last of those portions is so widely separated from the rest as to
induce a suspicion that it may be more refracted than any rays in
the solar spectrum. This separated portion has a pale undecided
hue. I should hardly have called it violet were it not situated at
the violet end of the spectrum. To my eye it had a somewhat
whitish or greyish appearance.”

This was followed by another paper of mine “ On Prismatic
Spectra” (Phil. Mag. 1836, vol. ix. p. 3), in which the spectra of
gold, copper, zinc, boracic acid, and barytes are described.

Wheatstone, nearly at the same time, published some interesting
analogous researches. I regret not to have his paper at hand at
present, in order to give a full aoc.ount of it.

Brewster then took up the subject, and described the spectra
produced by the combustion of a great variety of substances, in a
paper printed in the Manchester meeting (1842) of the British
Association (see Proceedings of the Sections, p. 15). But in the
same page there is another short paper by Brewster, of surpassing
interest, since he there announces the fact that the bright rays
which are characteristic of artificial flames are for the most part
those which are deficient in solar light, a fact previously confined
to the line D, and discovered, as we have said, by Fraunhofer.
These observations of Brewster deserve to be quoted textually.
His paper is entitled “ On Luminous Lines in certain Flames cor-
responding to the defective Lines in the Sun’s Light.”

After noticing Fraunhofer’s beautiful discovery as to the phe-
nomena of the line D in the prismatic spectra, Sir David said —
“ He had received from Fraunhofer a splendid prism, and upon
examining by it the spectrum of deflagrating nitre, he was surprised
to find the red ray discovered by Mr Talbot, accompanied by several
other rays, and that this extreme red ray occupied the exact place
of the line A in Fraunhofer’s spectrum, and equally surprised to
see a luminous line corresponding to the line B of Fraunhofer.
In fact, all the black lines of Fraunhofer were depicted in the
spectrum in brilliant red light. The lines A and B in the spectrum
of deflagrating nitre appeared to be both double lines, and upon
examining a solar spectrum under favourable circumstances, he
found bands corresponding to these double lines. He had looked
with great anxiety to see if there was anything analogous in other

466 Proceedings of the Royal Society

flames, and it would appear that this wTas a property which belonged
to almost every flame.”

One thing only was wanting in order to complete this discovery
of Brewster’s, namely, to explain why the rays which are bright
in artificial flames should be dark in the solar spectrum. The ex-
planation of this fact was reserved for later inquirers.

The above is far from exhausting the catalogue of Brewster’s
researches on the spectrum. He made numerous measurements of
Fraunhofer’s lines and maps of certain portions of the solar
spectrum. He likewise discovered the extraordinary effect of
nitrous gas upon the spectrum transmitted through it, which
becomes covered with a vast multitude of lines, irregularly dis-
posed, but always appearing in the same places in the spectrum,
provided the density and temperature of the gas is the same.

2. On Some Optical Experiments. By H. F. Talbot, Hon.
F.R.S.E.

I. On a New Mode of observing certain Spectra.

The attention of the scientific world has been for some years
past fully awakened to the importance of observing the spectra
exhibited during the combustion of chemical substances. But in
making an extensive series of such experiments, it must often hap-
pen that the observer has to test substances of which he only pos-
sesses a very minute quantity. In that case, before he has viewed
the spectrum long enough to feel fully satisfied of its nature, his
stock of the substance is exhausted, and he is obliged to leave his
observation imperfect. He might perhaps he testing some mineral
in his cabinet, of which the native locality was unknown, and he
might surmise it to contain a new metal, from its yielding a ray
not before seen in the spectrum, yet after a short time his observa-
tions on it would come to an end, and he would have no means of
showing this ray to other observers. Some years ago the metal
thallium was so rare that it was only distributed by a few grains at
a time to those who were interested in its discovery; and many of
the rarer metals are absent from most chemical laboratories, or onjy
represented by trifling specimens. About four or five years ago I
devised a method of remedying, or, at least, greatly diminishing

of Edinburgh, Session 1870-71 . 467

this inconvenience, which, with some slight recent improvements,
I will now proceed to describe. My method was founded on a fact
which I had observed many years ago, namely, that the mere pre-
sence of a chemical substance in a flame frequently suffices to cause
the appearance of its characteristic rays, and that it is not at all
necessary that the substance should be consumed and dissipated.
This dissipation is an accident, and if by any means it could be
prevented, the flame would maintain its characters for a consider-
able time. For instance, in Brewster’s Journal for 1826, vol. v. p.
77, &c., I remarked that alcohol burnt in an open vessel, or in a
lamp with a metallic wick, gives but little yellow monochromatic
light, while if the wick be of cotton, it gives a considerable quan-
tity, and that for an unlimited time. And I added that I had
found other instances of a change of colour in flames, owing to the
mere 'presence of a substance which suffers no diminution in conse-
quence. Thus, a particle of muriate of lime on the wick of a spirit
lamp will produce a quantity of red and green rays for a whole
evening without being itself sensibly diminished.

Mindful of these experiments of 1826, when a few years ago I
wished to examine the spectra of thallium and other substances, I
adopted the following plan : — A grain, or sometimes much less, of
the substance was. placed in a piece of strong glass tube about one
inch long. Short platina wires were inserted into the tube at each
end, approaching each other within about half an inch. The ends
are then sealed by a blow-pipe, leaving enough of the platina wire
outside the tube to allow of its being soldered to a long copper wire.
One of these copper wires (with the external portion of the pla-
tinum wire soldered to it) was then coated with gutta percha for
the space of three or four inches next the tube. To coat the other
wire was found unnecessary. The mode of experimenting was as
follows. The tube in a horizontal position, having the chemical
substance nearly in its centre, was lowered into a glass of water
about two or three inches below the surface. The two wires were
then connected with a BuhmkorfFs coil, set in action by six of
Grove’s cells. When the sparks were allowed to pass through the
tube, they speedily ignited the substance, and caused it to give
forth its characteristic spectrum. Even after the sparks have been
passing for several minutes, the tube remains perfectly cold. This

468

Proceedings of the Royal Society

is the object of placing it under water, for if that precaution is not
taken the tube will sometimes become very hot, and explode. The
gutta percha covering is to prevent the spark passing through the
water, and to oblige it to pass through the tube. It is sufficient,
as I have said, to coyer one wire. If a drop of water has been
enclosed in the tube along with the chemical substance, the
colours of the spectra are displayed with more vivacity; but if this
is done, it is absolutely necessary to have the tube well under
water. The bright light given off under these circumstances by
strontia, sodium, thallium, and many other substances, is very
beautiful, and so permanent that at the close of the experiment
the original grain or half grain of the substance does not appear
diminished, and even the drop of water is found remaining
, unchanged. Provided always that the chemical substance is one
not liable to decomposition under these circumstances of heat and
moisture. In these experiments a small Ruhmkorff’s coil was
found to answer better than a very large one.

This method might be usefully applied to the illumination of
microscopic objects by homogeneous light. If the tube were
placed immediately under the stage of the microscope, the full
intensity of the yellow light would fall upon the object.

All these experiments were made in the Physical Laboratory of
the University of Edinburgh by the kind permission and assistance
of Professor Tait.

II. On the Nicol Prism.

Many years ago, when this beautiful and useful optical instrument
was new and very little known, I wrote a paper in a scientific journal
calling attention to its merits, and recommending its use. It was
first described by its inventor in Jameson’s Journal for 1828, p. 83.
The title of the paper being u On a Method of so far increasing the
Divergency of the tivo Rays in Calcareous Spar that only one Image
may he seen at a time .” This paper was reviewed in Poggendorff’s
Annalen for 1833, p. 182, who says — That he perused Mr Nicol’s
account of his invention with very little hope of its proving suc-
cessful, but that having constructed the instrument, he found that
nothing could answer more perfectly than it did. Having read
this testimony to its merits, I had one made by a London optician,

469

of Edinburgh, Session 1870-71.

which proved very successful. I then published a paper on it in
the Phil. Mag. for 1834, vol. iv. p. 289, from which I must ask
leave to make an extract, as a necessary introduction to what I
wish to say about it on the present occasion.

My paper begins by quoting the testimony of the German writer
to the merits of the instrument, and continues thus : —

“Poggendorff then goes on to say, that as Mr Nicol had not
attempted to explain the operation of the instrument, he would
endeavour to do so, in which, however, I cannot say that I think
he has been entirely successful. Now, it will he observed that the
inventor attributed the fact of the instrument’s producing only one
image to a great 1 divergency ’ which it causes in the images,
throwing one of them aside out of the field of view. The German
writer follows the same idea, but adds, that in his opinion such
divergency is caused by the Canada balsam, whose index of
refraction being 1-549, is intermediate between that of the ordinary
ray 1 654 and that of the extraordinary ray 1*483, which circum-
stance will (in his opinion) account for the rays being 1 thrown
opposite ways.’ He adds, that any one 1 who was not afraid of the
trouble ’ might easily calculate the path of both rays, a remark
which shows that his idea was that they were both transmitted,
and diverging from each other. But I find that this great diver-
gency does not, in point of fact, exist, for by inclining the
instrument a position may be found in which both images are
seen, and they are then very little separated, not more so than they
were by the same piece of spar before its bisection and cementation.
On gradually altering the position of the instrument, the second
image is not seen to move away from the first ; but at a certain
moment it vanishes suddenly without leaving the smallest trace of
its existence behind. Having thus described the appearances as
I have found them, I will give an explanation of them, which I
hope will be more satisfactory. As long as the rays composing the
images are incident upon the Canada balsam at moderate obli-
quities, it cannot exert any particular discriminating action upon
them. But when the obliquity reaches a certain point, one of the
images sulfers total internal reflexion, because the Canada balsam
is (with regard to that image) a less refractive medium than calc
spar. But with regard to the other image, it is at the same

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VOL. VII.

470 Proceedings of the Royal Society

moment a more refractive medium than the spar, and therefore it
suffers that image to pass alone.”

The preceding remarks were published in the year 1834. Soon
afterwards I perceived that if my explanation were correct, a Nicol
prism might be made, half of calc spar and half of glass. Theory
indicated this, but no actual experiment of the kind was made at
that time. Recently, however, my attention has been once more
directed to this subject, and I have had such an instrument con-
structed by Mr Bryson, optician, of Edinburgh, with a very satis-
factory result. When light has been polarised by an ordinary
Nicol prism, it is completely extinguished by the new prism held
in a proper position; whereas when two Nicol prisms are com-
bined, a small portion of light generally remains visible.

Either end of the new prism may be held foremost, a result
which was not altogether expected. An idea is prevalent that the
action of an ordinary Nicol prism is due to the circumstance that
one surface of the calc spar is left rough to scatter one of the rays.
But such is not the case. Both surfaces are highly polished by the
best makers, and the ray is not scattered, but reflected, and maybe
seen by proper management.

3. Note on a New Scotch Acidulous Chalybeate Mineral
Water. By Janies Dewar, F.RS.E.

It is generally known that this country is extremely deficient
in well-marked chalybeate waters. Plenty natural waters, con-
taining small proportions of iron, are to be met with in the
United Kingdom ; but, with the exception of those of Tun-
bridge Wells, Harrogate, Sandrock (Isle of Wight), Heartfell,
near Moffat, and Vicarsbridge, in the vicinity of Dollar, they con-
trast very unfavourably with those of the numerous spas of the
continent of Europe. If we restrict ourselves to an examination
of the chemical characters of the above-mentioned Scotch chaly-
beates, we observe that the iron is present in large quantities in
the form of sulphate, along with sulphate of alumina, on which
account they are more nauseous to invalids, and are at the present
time rather unpopular.

Recently my brother, Dr Alexander Dewar, Melrose, sent me for

of Edinburgh, Session 1870-71.

471

analysis a sample of a new well water, whose peculiarity had pre-
viously attracted his attention. A chemical examination of the
water in question showed it to be a well-defined acidulous chaly-
beate, unusually rich in carbonate of iron. The following are the
analytical details. (As the surface water gets access at present, a
very exhaustive analysis appeared unnecessary) : —

Carbonate of iron, .

17*5 grains per gallon.

Alumina, .

1*8

Silica,

8*5

Sulphate of magnesia,

7*8

Chloride of calcium,

16*0

Carbonate of calcium,

4*1

Alkaline chlorides,

11*4

Total residue,

67*1

Carbonic acid gas per gallon 40 cubic inches.

With the exception of the celebrated “ Dr Muspratt’s chaly-
beate,” at Harrogate, which contains 108 grains per gallon of
carbonate of iron, along with 16*0 grains of protochloride, I do
not know of any natural water in this country containing such a
large proportion of iron in the form of carbonate. And it is to be
observed that the water is not associated with a large quantity of
other salts.

The well whence the foregoing sample was taken has not been
long sunk, and its water is perfectly different from all of those in
its immediate vicinity. Should it maintain its present character,
I have no doubt that, judging from its own qualities, as well as
from its favourable climatic situation, along with the general
interest attached to the locality, this chalybeate is certain to
recommend itself to the medical profession.

The following Gentleman was admitted a Fellow of the
Society : —

Thomas J. Boyd, Esq.

472 Proceedings of the Poyal Society

Monday , 29 th May 1871.

Professor CHRISTISON, President, in the Chair.

The following Communications were read

1. On the Homologies of the Vertebral Skeleton in Osseous
Fishes and in Man. By Professor Macdonald.

Abstract.

After a brief notice of the seven bi-vertebral segments of the
cranium in man: —

1. The liypo-cranial, or the axis and atlas vertebrae, which is

adopted as a key to the cranial segments ;

2. Para-cranial, or occipital;

3. Wormi-epiotic parietal, or meta-cranial ;

4. Sphenoidal, or meso-cranial ;

5. Ethmo-frontal — pro-cranial ;

6. Nasal, or apo-cranial.

7. Rhino-nasal.

Professor Macdonald gave a short outline of the osteology of the
human cranium, in order to trace the homologous osteology of the
osseous fishes, or ichthyia.

The great characteristic of the vertebralia is the centro-chord, or
axis, extending through the whole length of the animal from stem
to stern, around or upon which the vertebral column has been
developed This has been demonstrated in the very earliest type,
both by the late Professor G-oodsir and Professor Owen in the
Amphioxus, where the direction of the anterior portion, as far as
the oral cleft, is to the tip of the nose from the anterior portion of
the representative of the spinal marrow. The same proof may be
adduced from the condition of the early human embryo, where
the anterior of the embryo, consisting of the pro-cranium and part
of the tubercles of the spine, are at once bent downwards, towards
the upturned coccygeal extremity of the spine, where the umbilicus
is afterwards formed, when the abdominal or ventral laminrn unite
to close in the abdomen. There is another flexure of the pro-cranium
and the meso-cranium in warm blooded vertebrata.

of Edinburgh , Session 1870-71.

473

It is very important to notice this last flexure as distinctly
marking the difference between the warm and cold-blooded animals,
and to account for the necessity of the temporal squamo-zygomatic
limb-bearing girdle connecting the anterior and posterior cranium.

From this zygoma, or limb-bearing zone or girdle, the maxilla
depends as the anterior thoracic limbs, as seen in the annulozoa
and arthrozoa. The condyle being articulated in the glenoid
cavity, it is the upper or homotype of the brachium and femur,
and the homologue of the quadratum of the bird, hypotympanic,
and of osseous fishes (28, Owen).

He then directed the attention to the reduced scale of the fish
cranium. The general form, from the great depression of the
ethmo-frontal segment, prevents the formation of apros-encephalon,
and even the meso-encephalon is crushed back into the III. or
wormi-epiotic parietal segment ; the only encephalic cavity in the
fish cranium, where not only the orbit and the convolutions and
olfactory cells, but also the whole otic sensory apparatus with the
cerebellum. This segment is closed in by the development of the
wormi-epiotic spine, which has hitherto been described by all
anatomists, from Cuvier and others on the Continent, and by Pro-
fessors Owen, Huxley, Parker, and all their followers, as the
occipital bone in the fish. A careful re-examination of the sub-
ject will correct this general and inconsiderate error. In the
osseous fishes the occipital bone still exists in the bi-vertebral con-
dition. It, however, contains the medulla oblongata, and their
long spines extend upward, as they do in the human cranium, to
nearly the wormi-epiotic spine.

Referring to the archetype of Owen, the basi-sphenoid (5.) was
shown to be the last vertebral centrum, from whence the basi- cranium
extended, without central joints, to the anterior glabella frontis.
(13, incorrectly named vomer) is in fact the premandible or incisor
bone. (13.) The vomer is a vertical, or mediastinal double osseous
septum, set on the rostrum sphenoides (olivaris) in connection with
the perpendicular plate of the ethmoid and septum nasi separating
the olfactory cells.

From (4) the wormi-epiotic tuber or spine the upper part of the
ischium is attached by a chain of transparent bent scale-bones con-
taining a muscle, seems the principal part of the pelvis; it has a large

474 Proceedings of the Royal Society

tuberosity; from the inner part the ramus rises. * From the inner and
lower surface of the tuber ischii the femur (51) descends. It is from
the inner articulation in the fishes, instead of the external aceta-
bulum in the human pelvis, that the relation between the tibia
(52) and fibula (58) is altered. The fibula is articulated within the
head of the tibia ; the femur overlaps the upper spine of the
head of the tibia. The external malleolus tibiae is very greatly pro-
longed, and forms the great osseous sub-opercular cleft, while the
internal malleolus fibulae is embedded in the skin behind the tarsal
fin.

The tarsal fin consists of calcaneum (55), astragalus (53), scaphoid
(54). These Cuvier named radius and ulna, in which he was fol-
lowed by Owen, &c. Anterior cuneiform and cuboid tarsals (56).
The phalangeal fin rays (57).

The mistaken homology of the pectoral fin for the anterior
instead of the posterior extremity baffles all chance of correct
homology, and I earnestly hope that all the living homologists will
re-examine the subject, and adopt the system which I have wrought
out for between forty and fifty years without succeeding to con-
vince the anatomists. I put forth this final appeal of the oldest of
living homologists who proposed an original scheme (my friend,
Professor G-rant, University College, London, introduced that of
the brilliant but fanciful Geoffroy St. Hilaire some years earlier),
with the firm conviction that ere long, after I have retired, the
scheme now proposed will be adopted.

* Owen’s Nomenclature.

50. Supra-scapula.

51. Scapula.

52. Coracoid.

53. Humerus.

54. Ulna.

55. Badius.

56. Carpal.

57. Metacarp-phalanges.

58. Epicoracoid.

Macdonald’s Nomenclature.

50. Ischium.

51. Femur.

52. Tibia.

53. Astragalus.

54. Scaphoid.

55. Calcaneum.

56. Tarsal.

57. Tarsal fin rays.

58. Fibula.

of Edinburgh, Session 1870-71.

475

2. Scheme for the Conservation of Remarkable Boulders in
Scotland, and for the indication of their Positions on
Maps. By D. Milne Home, Esq.

Among many geological questions which wait solution, there is
probably none more interesting or perplexing than the agency by
which Boulders or “blocs erratiques,” as the French term them,
have come to their present sites. I allude, of course, not to blocks
lying at the foot of some mountain crag from which they have
fallen by the decay or .weathering of the overhanging rocks, but to
blocks which have manifestly been transported great distances,
after being detached from the rocks of which they originally
formed part.

That many of the large isolated blocks lying on our mountain
sides and on our plains have come from a distance, and by some
means of tremendous power, is obvious even to an unscientific
observer ; and the perception of this truth by the popular mind has,
in many cases, so invested these boulders with superstitious interest,
that they have received names and given rise to legends, which
impute the transport of them to supernatural agents.

There are two circumstances which very plainly indicate that
these stones are strangers.

One is, that many of these blocks are on examination found to
be different from any of the rocks prevailing in or near the dis-
trict where they are situated.

The other is, that some of these blocks, whilst excessively hard,
— so hard that it is difficult to break off a portion with the hammer,
are nevertheless round in form — a form evidently acquired by
enormous friction — such friction as would result from being rolled
a long way over a rough surface.

The inference drawn from these two facts was confirmed when
it was discovered, as in many cases it was, that rocks of the same
nature as the block existed in a distant part of the country, and
from which, therefore, it had probably come.

These round shaped blocks were the first to attract popular
attention. The name given to them in Scotland of boulders has
no doubt been suggested by their shape.

It is accordingly only the rounded boulders which possess the

476 Proceedings of the Royal Society

traditionary names and curious legends by which many of them
are known. Such names as the Carlin’s Stane, the Witch’s Stane,
Pech or Piet’s Stone, Clachannadruid, Kirk-Stane, Pedlar’s Stane,
Thuggart Stane, and Devil’s Putting Stane, are all applicable to
rounded blocks.

When the geologist turned his attention to the subject, it was
soon discovered that there were many blocks equally entitled
to be called erratic, not round but square shaped ; and which,
though discovered to belong probably to rocks at a great distance,
yet showed signs of little or no attrition. Moreover, many of these
angular or sharp-edged blocks were comparatively soft and loose in
structure, so that they could not have been rolled, for any con-
siderable distance, without being broken or crushed into pieces, or
into sand or mud.

On a more minute inspection and study of these erratic blocks,
certain features were noticed which seemed to indicate the forces
to which they had been subjected. Thus on many of them, deep
scratches, ruts, and groovings were found, as if sharp pebbles or
stones harder than themselves had been pushed over them, or
squeezed against them under great pressure. It was also observed
that, when a block had a long and a short axis, the longer axis was
generally parallel with any well marked scratches or striae on
their surface ; and moreover that the direction of these striae fre-
quently coincided with the direction in which the block itself had
apparently come from the parent rock.

These circumstances soon led geologists to speculate on the
nature of the agencies which could have effected a transport
of the blocks. Some blocks are of enormous size, exceeding
1000 tons in weight.* Many, before they could have reached the
places where they were found, must have travelled fifty or sixty
miles, and have crossed valleys and even ranges of hills. In the
county of Berwick, for example, there is a large block of gneiss, a
rock which exists nowhere in that county or in the south of Scot-
land; and if it came from some of the hills in the Highlands, it
must have crossed, not only the valley of the Forth, but the Kil-
syth, Pentland, and Lammermoor Hills.

* The celebrated block near Neufchatel, called “ Pierre a bot,” contains
about 1480 cubic yards of stone, and is supposed to weigh about 2000 tons.

477

of Edinburgh, Session 1870-71.

Sir James Hall and Sir G-eorge Mackenzie in this Society, who
were the first to study the subject, advocated the idea of diluvial
agency. At a later period, ice in various forms was suggested as
the agent, — First, in the condition of glaciers filling our valleys ;
next, in the condition of icebergs floating over our island, whilst
under the sea; and latterly, as a great sheet or cake stretching
from the Arctic regions, and overspreading the whole of northern
Europe.

It is not my intention to discuss these theories, or say which
appears the most probable. I allude to them now, merely to in-
dicate the tremendous character of the agencies, which it is found
necessary to invoke for the solution of the problem, — agencies
all implying a very different condition of things in Scotland, as
regards configuration of surface and climate, from what now pre-
vails. These phenomena are the more interesting, because, as
most of the erratic blocks lie above all the rocks, and very free” .tly
even above the beds of clay, gravel, and sand, which consf oethe
surface of the land we inhabit, they indicate probably tk. very last
geological changes which occurred in this part of the earth’s sur-
face, and which there are some grounds for supposing, may even
have occurred since this country was inhabited by man.

The basis on .which geologists have been obliged to build their
theories, it must be admitted, is somewhat narrow. It consists
merely of observations made casually by individuals, who have
noticed certain appearances in districts of Scotland which they
happen to have visited; and, therefore, it is little to be wondered
at, that more than half a century has been required for procuring
the information, scanty as it is, which has been obtained.

What appears desirable for expediting the solution of the pro-
blem, is to organise a staff of observers, and to parcel out the
country amongst them, for the purpose of observing facts likely
to throw light on the subject, and of making these facts known
from time to time, both with a view to verification, and as a basis
for further speculation.

It has occurred to me, that the numerous natural history societies
and field clubs existing in Scotland, would be valuable agents
in this investigation; and, moreover, that individual geologists
would be pleased to co-operate in their respective districts.
vol. vn. 3 s

478 Proceedings of the Royal Society

I hope no one will think that the object for which I suggest this
investigation, is not worthy of the trouble which it implies, and of
the patronage which I ask this Society to bestow on it. These
erratic blocks bear the same relation to the history of our planet,
as the ancient standing or memorial stones do to the history of the
early races of mankind. These last-mentioned stones, — sometimes
with sculpturing on them not yet understood, — sometimes arranged
in circles or other regular forms not yet explained, — sometimes found
in connection with sepulture, are beheld and studied with interest,
on account of the gleams of light which they throw on the people
who erected them ; and popular indignation justly rises, when any
of these prehistoric records of our ancestors are destroyed or muti-
lated. The great boulder stones to which I have been referring
would, if investigated and studied, in like manner cast light
on £he last tremendous agencies which have passed over whole
regions of the earth. It is therefore important to have as many of
these b<. dders as possible discovered and examined, and to have
such of them preserved as seem worthy of study. I need not say
how rapidly, during the last century, both classes of ancient stones
have been disappearing ; and therefore, if it be desirable to pre-
serve the most remarkable boulders, or at all events to record their
existence, and their geological features, the investigation which
I advocate, cannot be too soon begun.

Alike in illustration and in recommendation of this suggestion,
I will refer to an investigation for the same object commenced two
years ago in Switzerland, and in the adjoining parts of France.
The design was twofold, — First , the conservation of remarkable
boulders situated on the Jura and in Dauphiny; and second , the
recording of their positions by maps, and of their characteristic
features by schedules.

With this view a circular was drawn out, and issued by the
Swiss Geological Commission, pointing out the scientific bearings
of the subject, and invoking the co-operation not only of provincial
societies, but also of municipal authorities in the cantons, and of
landed proprietors. A few extracts from the Swiss circular may
not be inappropriate : —

“ These erratic blocks are composed of granite, schist, or lime-
“ stone; but they rest on rocks of a different description. They

479

of Edinburgh, Session 1870-71.

were so remarkable by their number and size, that, from an
“ early period, they attracted the attention of naturalists, and
“ suggested scientific inquiries. It is, indeed, interesting to seek
“ to comprehend how enormous masses, with from 40,000 to 50,000
“ cubic feet of contents, and weighing from 800 to 1000 tons, could
“ be transported from the Alps from which they were evidently
“ detached, to spots 40 and 50 leagues distant, crossing deep
“ valleys, such as the lakes of Geneva, Neufchatel, Zurich, Con-
“ stance, Lucerne, &c.

“ This great problem has been discussed by numerous philo-
“ sophers, both of Switzerland and of foreign countries.” Then
follows a list of names, including those of our own Playfair, Lyell,
Murchison, Forbes, Tyndall, and Kamsay.

“ Unhappily,” (the circular goes on to state), “ during the last
“ 100 or 150 years, these erratics have been broken up for building
“ purposes, and even for road metal. Eecently the work of destruc-
“ tion has gone on more rapidly, and, unless stopped, the result
“ will be to obliterate all traces of one of the greatest facts in the
“ natural histor}'' of our country.

“ Though the destruction of these blocks is now advancing with
“ great rapidity, there are still a number of very large specimens
“ left, and these the Geological Commission is anxious to pre-
“ serve.”

“ The members of Archaeological Societies are interested in the
“ conservation of these blocks, for they often bear those curious
“ sculpturings, to which much importance is now justly attached.”

“ The lovers of legends must regret to see these blocks disap-
“ pearing, for ancient tradition tells how some have been flung by
“ the Devil on a poor hermit; that another bears the name of a
“ fish merchant in a town of wThich there is now no trace, &c.

“ The Geological Commission considers that the time has come
“ for appealing to all who have any power over the fate of these
“ blocks, that is to say, to individual proprietors, to communal
“ authorities, and to municipalities. The Commission also entreats
“ natural history societies, Alpine clubs, and public bodies, to co-
“ operate in this work, in order to preserve for Switzerland a
“ feature of the country, which, if not altogether peculiar to it, is
“ at all events better developed there than in any other

480 Proceedings of the Royal Society

Besides making an appeal for the conservation of boulders, the
same Swiss G-eological Commission suggested the propriety of
marking their exact position on the (government maps.

They farther expressed a hope that these measures might reach
even beyond the frontiers of Switzerland, and they referred to an
offer made hy a French geologist to draw up an account of the
Erratics of Souabe , with the view of obtaining co-operation from
that quarter.

A committee was appointed to carry out these views, supply the
necessary schedules and maps, and conduct the correspondence.

I shall next explain what resulted from the appeal. The circular
containing it was issued in the autumn of 1867, and I now quote
from a report presented to the Helvetic Society of Natural Sciences
at a meeting in August 1869, drawn up by Messrs Favre and Soret.

They state that, very soon after the commencement of the inves-
tigation, it was found desirable not to limit it to boulders, but to
include a description of enormous heaps of gravel, existing in many
districts, having the appearance of ancient moraines, and in that
view likely to throw light on the mode in which the boulders were
transported. Accordingly, instructions were given to indicate on
the maps the position of these gravel accumulations as well as of
boulders.

Messrs Favre and Soret then narrate what had been done during
the previous year in the different cantons, and from their report
I give the following extracts : —

Tn the first place, they acknowledge the liberality of Colonel
Siegfried, the Director of the Federal Topographical Department,
in supplying maps to assist in recording the observations.

They farther acknowledge the assistance which Colonel Siegfried
had given to the investigation, by issuing instructions to the
engineers surveying the slopes of the Jura, to indicate on the maps,
and to describe in their reports, any remarkable erratic blocks they
met with.

Reference is next made to the proceedings of the societies and
clubs in the different cantons. In some of the larger cantons, as
Lucerne and Vaud, the country had been divided into five and six
compartments, and a small sub-committee of members had been
appointed to explore each. In one of these cantons, the municipal

481

of Edinburgh, Session 1870-71.

authorities had given orders to the inspectors of roads and bridges
to aid in the investigation.

In the canton of Zurich , notice is taken of one remarkable block,
known as the “Stone. for the sacrifices of Hegsrutif which had
been purchased by the Society of Antiquaries, and had been
brought into the town of Zurich.

In the canton of Soleure, blocks of enormous size, and to the
number of 228, had been marked, and appointed by the municipal
authorities to be preserved, these blocks being situated on lands
belonging to the canton. The celebrated block of Steinhof, weigh-
ing about 1400 tons, had been purchased by means of a special
subscription, and made over in property to the Helvetic Society.

Several landed proprietors are named as having gifted particular
boulder stones to the societies. Thus Mr Briganti, at Monthey ,
had gifted to the Helvetic Society one block out of a remarkable
group, of which I well remember the late Principal Forbes once
spoke in this Society, and which I had lately an opportunity of
visiting. So also Mr Bonneton of GJ-eneva had presented to the
Alpine Club of that town a piece of land, containing what is
described as a magnificent boulder, and known by the name of the
“ Stone of Beauregard.”

Even the Federal Government of Switzerland had condescended
to share in what really seems to amount almost to a national
movement; for reference is made to an official communication from
the Chancellor, stating that the Council of State had caused an
order to be issued, that all erratic blocks situated in the cantonal
forests should be preserved intact, till examined by the committee.

I have had sent to me a printed report of the steps taken in the
canton of Aargau , drawn out by Professor Miihlberg. He men-
tions that one of the measures taken there, was the appointment
of a referee to inspect the boulders which were discovered, with
the view of determining whether they were worthy of being pre-
served. Professor Miihlberg mentions farther, that “the State
“ undertakes the expense of printing and postages, as well as of
“ the travelling of the canton referee to the sites of the most
“ important boulders, and had in the meantime advanced 100 francs
“ to defray expenses already incurred.”

These extracts from the reports, of which printed copies have

482

Proceedings of the Boyal Society

been kindly sent to me by Professor Favre of Geneva, show what
is doing in Switzerland for the promotion of an object which, under
the auspices of this Eoyal Society, I should wish to see taken up
in Scotland. And before concluding what I have to say about the
Swiss movement, I may refer to one circumstance which ought to
be gratifying to Scotchmen, viz., that the Swiss naturalists retain
a grateful recollection of what has been done by Scotchmen for
exploring and making known the interesting physical features of
their beautiful country. Not only have they, in specifying the
names of geologists who have written on Switzerland, included all
the Scotchmen who have done so, but I see in one of Professor
Favre’s pamphlets, written in connection with this movement,
allusion to the year 1741, “ when (he says) the English first pene-
“ trated into the valley of Chamounix,” — “and gave to that valley
“ a celebrity, which the previous visits of several bishops had not
“ obtained for it.” Professor Favre records the names of these
English visitors, and among them are “ Lord Haddington and his
“ brother, Mr Baillie.” The pamphlet mentioning these names I
sent to the present Earl of Haddington, that he might see the
courteous allusion to his ancestor; and, in returning the pamphlet,
he referred me to a paragraph in Douglas’s Peerage, which men-
tions the fact that, in the year 1740, the Earl of Haddington and
his brother, George, set out on their travels to the Continent, and
were for some time located with other friends at Geneva — one
of these being Stillingfleet, famous in his day as a naturalist, and
who in one of his works alludes to the very agreeable reunions of his
countrymen which took place at Geneva and the neighbourhood.

I will next refer briefly to the steps taken in the south of
France in co-operation with the Swiss movement. These began
by a communication from Professor Favre to Mons. Belgrand, who,
besides being President of the Geological Society of France, wras
Inspector-General of Bridges and Boads, a Government Depart-
ment. This communication, which explained the object of the
Swiss investigations, and also what was being done by the different
cantonal societies and municipalities, was referred by Mons. Ber-
trand to two members, Messrs Falsan and Chantre, to report on.

It is from their report, the remarks of Mons. Bertrand upon it,
and some notes of a subsequent date, published in the Transactions

483

of Edinburgh, Session 1870-71.

of the Geological Society of France for December 1869, that I
make the following extracts : —

The great interest attaching to the investigation is allowed by
the reporters, and a compliment is paid to the Swiss naturalists for
commencing and urging it.

Reference is made to the rapid disappearance of the boulders,
and especially limestone boulders, which were generally broken
up for limekilns. The reporters state that near Lyons, the greater
part of the boulders had been destroyed long ago, and in particular
one weighing about 150 tons, which marked the point where the
boundaries of three parishes met.

Examples, however, of remarkable boulders still untouched, with
legends attached to some, are specified, such as the “ Pierre du
Bon Dieu,” of 120 tons, and the “Pierre du Diable,” of 56 tons,
which it is strongly recommended should, with many others of less
note, be saved from destruction or injury.

Reference is then made to the steps which should be taken to
carry out these views. Circulars, it is said, should be drawn up,
and sent not only to the public departments which superintend the
management of Government or communal lands, but also to indi-
vidual landed proprietors, pointing out the scientific interest attach-
ing to these erratic blocks.

These suggestions were at once favourably responded to and
acted on. Three public departments or functionaries, viz., the
Minister of Public Works, the Director-General of Forests, and
the Prefects in each of the provinces of Savoy, High- Savoy, Ain,
Rhone, and Isere — all adjoining Switzerland — are stated to have
lent their willing co-operation.

After the project had received the approbation of the Geological
Society of France, and the promise of important official support, an
appeal to the friends of Natural Science was drawn up by Messrs
Faison and Chantre very similar to the appeal which had been
previously drawn out and issued in Switzerland. This appeal,
after describing the movement and proceedings in Switzerland,
proceeds thus: — “ Such is the object pursued vigorously in Switzer-
“ land with the co-operation of departments and of individuals.
“ Ina word, see what is going on near ourselves. Can we remain
“ outside of, and indifferent to, this scientific enterprise, especially

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Proceedings of the Royal Society

“ when Mons. Favre has asked us to engage in the same work, and
u to undertake for our country what he is doing for his ? We are
“ bound to answer this appeal. The solution of the same questions
“ ought to occupy us. These erratic phenomena abound every -
“ where in our district. The debris of rocks torn from the Alps
“ cover the plain of Eauphiny, the plateau of the Dombes, the hills
“ of Croix, Kousse, and Sainte-Foy. Already many geologists
“ have studied these erratic phenomena in our neighbourhood,
u without being able to discover a solution. The truth, when we
“ seek it, seems to fly from us ; but we must persevere and pursue
“ it till it is caught.

“ Our desire is simply to prevent the destruction of the most
“ remarkable blocks, and leave them on their natural sites, and
“ also to obtain a collection of specimens* to illustrate them, and
“ we hope that our administrations will in this object not be behind
“ those of Switzerland and the department of Haute Savoie. Their
“ example would, we doubt not, be followed by individual proprie-
“ tors, where boulders cease to be regarded as mere masses of stone
“ of unusual size, but without scientific value.”

Besides this appeal, printed copies of which were extensively
circulated, directions and schedules were drawn out to be trans-
mitted to local societies as well as to individuals who should under-
take the investigation, in particular districts, maps of these districts
being at the same time supplied.

The documents from which I have made these extracts were, as
I have said, transmitted to me by Professor Favre of Geneva. He
wrote to me at the same time, and concluded his letter by saying,
“ Voila, Monsieur, un aperpu de la marche de cette entreprise. Je
“ serai bien heureux, de le voir s’etendre a TEcosse.”

In a subsequent letter he repeats his suggestion thus : — “ Si vous
“ pouvez organiser quelque chose de semblable en Ecosse, vous
“ m’obligerez infiniment, en me tenant au courant.”

In a third letter, he says, “ Permettez moi de vous renou-
“ veller la demande que je vous ai addresse, en vous priant de me
“ tenir au courant de ce que nous ferez pour les blocs erratiques de
“ l’Ecosse, et des resultats que vous obtiendrez.”

I have given these details of the proceedings in Switzerland and
France, and quoted these passages from Professor Favre’s letters,

of Edinburgh, Session 1870-71.

485

in order both to add weight to my proposal, and show how we may
proceed to attain it.

I have alluded to the existence throughout Scotland of many
provincial societies whose objects are not inconsistent with the
investigation which I think they may be invited to engage in. Sir
Walter Elliot of Wolflee has lately been at pains to make out a
list of all the Natural History Societies and Field Clubs existing
in G-reat Britain and Ireland.

I now give this list, in so far as it applies to Scotland, in the
hope that, when our proceedings are published, this list may appear
in it, so that if any societies or clubs are seen to have been omitted,
the omission may be taken notice of and supplied.

1. Berwickshire Naturalist’s Club. ( Secretary , Mr G-eo. Tate,

Postmaster, Alnwick.)

2. Hawick Archaeological Society. (Secretary, David Watson.)

3. Tweedside Physical and Antiquarian Society.

4. Dumfries and Galloway Natural History and Antiquarian

Society.

5. Edinburgh G-eological Society. (, Secretary , Geo. A. Pan ton,

Hope Terrace.)

6. Edinburgh Naturalists’ Field Club. ( Secretary , Andrew

Taylor, 5 St Andrew Square.)

7. Glasgow Natural History Society. ( President , John Young

M.D. ; Secretary , Robert Gray, 2 Lawrence Place, Dowan-
hill.)

8. Glasgow Geological Society. (. President , John Young, M.D. ;

Secretary , Dugald Bell, 136 Buchanan Street.)

9. xklloa Society of Natural History and Archaeology.

10. Largo Field Natural History Society. ( Secretary , Charles

Howie.)

11. Perth Literary and Antiquarian Society.

12. Perthshire Society of Natural History. (. President , Dr

Buchanan White ; Secretary , A. T. Scott.)

13. Montrose Natural History Society. ( Secretary , Mr Robert

Barclay.)

3 T

VOL. VII.

486 Proceedings of the Royal Society

14. Aberdeen Natural History Society.

15. Aberdeen Philosophical Society. ( President , Professor

Ogilvie, M.D. ; Secretary , Alex. D. Milne, 37 Thistle
Street.)

16. Natural History Society, Elgin.

17. Orkney Natural History Society.

Being myself a member of one of these Societies, I know that
some of its members have devoted themselves to the subject of
boulders, and of moraine-looking deposits, occurring within the
district over which the operations of the Society extend.

Sir Walter Elliot tells me that he has information of a Field
Naturalists’ Club in England which has specially directed its atten-
tion to the boulders of the district.

It is quite true that, in Switzerland and in the south of France
boulders, considerable in size and numbers, are much more abun-
dant than in Scotland, so that little searching is required to enable
the provincial societies of these countries, to carry out the investi-
gation proposed to them.

On the other hand, let it not be imagined, that in Scotland the
boulders generally are not of such interest as to deserve the adop-
tion of proceedings similar to those now being adopted in Switzer-
land and France. Even within the limited range of my own dis-
coveries, I know and have measured eight boulders in the south-east
of Scotland, the smallest of which is 10 tons and the largest 918
tons in weight, and all possessing features more or less significant.

There are others equally large which I have heard of, but have
not seen. Moreover, almost all these boulders have old traditional
names, and many of them legends which indicate, that they have
been objects of popular and even superstitious regard.

There are two objects which ought to be aimed at. The first is
to obtain a list of all boulders which appear remarkable ; i.e ., re-
markable for size, and instructive on account of polishing, ruts
on the surface, or any other circumstance. The second is to put
down on maps, a mark to represent the exact position of boulders,
occurring in groups, or of large individual boulders.

487

of Edinburgh, Session 1870-71.

Moreover, accumulations of gravel, sand, or clay in any district,
in so far as they seem to have been produced by agents now no
longer operating in the district, should be notified.

In order to carry out these suggestions, I would venture very
respectfully to ask that the Council of this Society should pass a
Special Minute expressing approval of the subject explained in
this paper, and appointing a Committee of the Fellows of this
Society to carry out farther proceedings. The circumstance that
this Society had expressed its approval, and taken steps to aid the
investigation, would alone ensure for it a favourable consideration.

The Committee would, of course, communicate with the various
provincial societies throughout Scotland, by enclosing a copy of
this paper or an abstract of it, and intimating readiness to send the
necessary Schedules and Directions, should a willingness be ex-
pressed to enter on the investigation proposed.

I have in these remarks alluded only to the steps necessary for
discovering the existence of remarkable boulders, indicating their
position on a map, and obtaining a correct description of them.
But the other object, which also engages attention so much in
Switzerland and France, should not be lost sight of here. I allude
to the conservation of boulders. The disappearance of numerous
camps, buildings, standing stones, and other objects of archaeolo-
gical interest in all our counties, which every one now regrets, has
been owing in a great measure to ignorance on the part of the pro-
prietors and tenants on whose lands they were situated, of the
value and even nature of these objects. But this work of destruction
has been happily now stopped, and chiefly by the interference and
influence of our Society of Antiquaries. In like manner, the demo-
lition of Boulders which has been going on rapidly in Scotland,
will, I hope, be arrested, when the proprietors and tenants on whose
lands they stand, are made aware of the interest they excite, and
of what is being done to preserve them in other countries. Of
course, it would only be certain boulders which it would be desira-
ble to preserve, boulders remarkable for size, or shape, or position,
or for markings upon them; and when a report was made to
the Committee of any boulder of this description, the Committee
would judge whether an application should be made to the pro-
prietor on whose lands it was situated, to spare the stone, so that it

488

Proceedings of the Royal Society

might be preserved for examination and study. I have little doubt
that such an appeal would be attended to. Indeed, in the great
majority of cases, a proprietor would be pleased to learn, that an
object of scientific interest had been discovered on his estate, and
would be glad to have it in his power to accede to any request in
relation to it coming from a Committee of this Society.

With regard to the mode of meeting the expenses attending the
investigation and other proceedings suggested in this paper, it
occurs to me that subscriptions from individuals should be chiefly
relied on, and that the Council of this Society should only promise
such aid as the state of the Society’s funds and their appreciation
of the proceedings of the Committee, may suggest to them. The
Committee will, no doubt, make a Report at least once a year of
their proceedings, which the Council may allow to be read at a
meeting of the Society, if its contents were sufficiently interesting.

3. Note of a New Form of Armature and Break for a
Magneto-Electric Machine. By R. M. Ferguson, Ph.D.

The magneto-electric machine, which I am about to describe,
approximates in its general arrangements to Ladd’s hand-machine.
In it Mr Ladd makes use of a compound Siemens’ armature, con-
sisting of two separate armatures placed in length, and revolving
round the same axis, with their coils at right angles to each other.
The armature revolves between the poles of an electro-magnet, of
the description introduced by Mr Wilde. The electro-magnet, in
the present instance, is made of a rectangular piece of boiler-plate,
three-quarters of an inch in thickness, bent so as to form three sides
at right angles to each other, as shown (in section) in fig. 1 . The up-
right sides (P P' P) are nearly 9 inches high and 11 inches in length,
and the top of the same length is 6 inches broad. Pieces of cast-
iron (N and S) are put in the open end to form the poles of the mag-
net. About 300 yards of a double No. 14 wire, wrapped round the
upright sides, make the coil (COCO) of the electro-magnet. One
of the armatures in Ladd’s machine furnishes a current to the coil
of the electro-magnet ; the other gives out an external current.
To distinguish the two, the counterparts of which occur in the
arrangement I bring before you, I shall call the first the inter-

of Edinburgh, Session 1870-71.

489

nal current, and the second the external current ; and the coils
furnishing them I shall designate the magnetic coil and the electric
coil respectively. The action of the magnetic coil is based on
Siemens’ and Wheatstone’s principle of reciprocal increase. When
a Siemens’ armature revolves between the poles of an electro-
magnet, what feeble magnetism there may be in the iron core
generates a feeble current in the armature coil. This current, by
a commutating arrangement of revolving collar and springs, is sent
into the coils of the electro-magnet, which in consequence rises in

power. It is now able to excite a stronger armature current,
thereby rendering itself still more powerful, and this mutual action
goes on until the driving force is insufficient to continue the
action. Ladd has ingeniously turned this principle to account in
his machine, the magnetic coil of which furnishes electricity for
the electro-magnet, and this last is thereby rendered competent to
generate electricity in the electric coil available for external use.

Wishing to make a machine to give off a current equal to a few
cells of Bunsen, I thought of trying the following deviation from
Ladd’s construction : — Instead of having two separate armatures
revolving on the same axis, I thought one might serve, in which
two coils were inserted, the one at right angles to the other. In
the revolution of a Siemens’ armature there are two polarities, so

490 Proceedings of the Royal Society

to speak, one only of which is utilised, viz., that which takes place
(fig. 2) when the greatest length of the iron core lies in the line
joining the two poles ; the other polarity ensues when this main
axis is perpendicular to the line of poles (fig. 3). This second

Fig. 2. Fig. 3.

polarity is, from the less favourable position of the core, necessarily
weaker than the first; hut it struck me that it might be quite suffi-
cient to furnish the internal current, leaving to the more powerful
polarity the task of generating the external current. Another
advantage seemed to flow from this utilisation. When an armature
without coil or closed circuit revolves within a magnet, the
energy expended in its motion heats its particles. When the
core is provided with a coil and closed circuit, part of this energy,
instead of assuming the form of heat, is transmuted into the
energy of an electric current, and the electricity induced is so
much deducted from the heat that would otherwise appear in the
armature. In the ordinary construction the weaker polarity, being
unprovided with a coil, results only in heat ; but if it be furnished
with such, as in the arrangement I suggest, and its molecular
energy thereby tapped, so to speak, the heat of the armature may he
partially withdrawn in the shape of an electric current. A current
sufficient to magnetise the electro-magnet may thus be got, for no
additional expenditure of force, hut only by the conversion of heat
that would otherwise he mere waste, so far as the action of the
machine was concerned. When one of Wilde’s small machines, in
which a battery of permanent magnets is used instead of an electro-
magnet, is turned by the hand, additional resistance is felt on the
armature circuit being closed more especially by a short wire. The
current got from the armature would thus seem to be formed
partially from the conversion just mentioned, and partially from a
new access of force demanded by the creation of the current. In
the arrangement I here describe, a different action takes place, for
when the coil of the electro-magnet is disjoined from the magnetic
coil and included in the circuit of a single Bunsen cell, the feeling

of Edinburgh, Session 1870-71.

491

of diminished resistance is nearly as decidedly felt as that of in-
creased resistance in Wilde’s machine on closing the electric coil
circuit. The same feeling is not so decided in the case of the
magnetic coil, and this, no doubt, arises from its smaller dimensions ;
at any rate, there is no additional force needed. Whether this action
has its origin in an essential difference in the action of permanent
magnets and electro-magnets in these circumstances, or in some
peculiarity of construction, is immaterial to the present inquiry,
for to all appearance the armature currents cost no additional
energy, but are got entirely from the waste heat of the armature.

The core of the armature (fig. 4 a) is 11 inches long and 2J inches
in diameter. The main longitudinal cut or groove
is If inch wide and \ inch deep. The small cut
is f of an inch wide and f of an inch deep.* In
the large cut is wound the electric coil, consisting
of a cable of 8 silk-insulated wires, of an inch
iu diameter, and 82 feet long. The magnetic coil
in the small cut is made of a cable of four such
wires, 46 feet in length. The electric coil thus
contains about four times as much wire, and offers about the same
electric resistance as the magnetic coil.

The two grooves leave four protruding ends at each end of the
armature. To these are screwed a bronze cap and spindle of re-
volution (figs. 4 and 5, which are on a larger scale than fig. 4 a).

Fig. 4. Fig. 5.

A collar of wood (a) is fixed next to the spindle, and on this collar
two ferrules of iron (//fig. 5) are put, separated by the wood to
prevent contact. To these ferrules the wires from the coils ( + - )
are soldered, care being taken to prevent unnecessary contact. A
cylindrical collar (C C fig. 4) turns on the ferrules, and can be
turned round and fixed in any position by screws (s s fig. 4). The
collar is made up of three parts, two pieces of iron (one is shown
* In the figure both cuts to be shown clearly appear of the same size.

C o

Fig. 4 a.

492 Proceedings of the Royal Society

in fig. 7) cut out of the same tube and kept from touching, by being
fixed to a vulcanite ferrule ( v in fig. 6, which shows the inside of
half the collar) placed inside and between them. The ends of the
iron pieces slide on the iron ferrules beneath, and are in conducting
connection with them. Electrical contact is made by springs press-
ing on this composite collar, and which are metallically connected
with the binding screws, the poles of the armature coils. The collar
and springs at each end form the breaks or commutating arrange-
ment of their respective coils. The cross line of separation (e efig.
4) can he fixed in any position, and currents in one or different
directions thereby obtained in the course of a revolution. The
pressure of the springs against the collars is regulated by screws.

Fig. 6. Fig. 7.

When the machine is prepared for working, the cross lines of the
commutating collar of the magnetic coil are placed at right angles
to the plane of the coil, the position of maximum effect. If the
handle of the machine be turned when the circuit of the electric
coil is open, one or two turns bring the hand of the operator to
something like a dead halt ; the resistance to further motion
is so great as to challenge its continuance. If, now, the
external circuit be closed, immediate relief is felt, as if part of
the internal current had been diverted into the external circuit
from the coils of the electro-magnet. The relief thus experienced,
moreover, bears some proportion to the conductivity of the external
circuit. With an easy circuit, the work expended in turning the
handle is easy ; with a resisting circuit, the driving resistance
becomes correspondingly great. The hand is thus made to sym-
pathise with the nature of the external circuit, and the experi-
menter feels as if he were charged mechanically with a resistance
offered electrically. Suppose, for instance, we have a piece of thin
wire to heat or melt ; at first little or no driving resistance is felt,
but the moment that the wire begins to get hot, the arm becomes
charged with a heavy resistance, which grows as the wire rises in
temperature till it melts, and then suddenly the excessive no-circuit

of Edinburgh, Session 1870-71. 493

resistance is felt. The moment that there is hard work to be done
in the external circuit, the strength of the arm is put to the proof.
When water is decomposed by the machine, the strain upon the
arm does not rise beyond a certain amount, at whatever speed the
handle be driven. In working an induction coil, the load on the
arm appears capable of rising to any extent, and the length or
density of the spark bears something like a proportion to the
burden of work. With an electric resistance great enough, and an
inexhaustible driving power, there seems no limit to the electric
effect attainable, and that, too, with little increase of speed.

When a tangent galvanometer is interposed in the external
circuit, something may be learned of the way this takes place.
With an easy circuit, where little difficulty is felt in driving, a
current of about 60° may be got. When a thin wire is now inter-
posed, the needle does not reach this point, for the wire (iron wire
gL- inch in diameter) melts or ignites between 30° and 40°, and yet
while the heating lasts the strain is enormously greater than before.
If the galvanometer be inclosed in the internal circuit, and the
wire melted in the electric circuit, just at the point when the heat-
ing begins, the needle takes a sudden swing upwards. Thus, if it
be at 20° before the heating sets in, it will rise to 30°, and stay
there till the wire melts, when, if the motion be continued, it again
takes a start upwards. If the magnetic coil be detached from the
coil of the electro-magnet, and if its function be performed by one
Bunsen cell, this increase of load is not felt, a greater effect in
the external circuit being only attainable by an increase in velocity,
and the same holds with a battery of permanent magnets.

That two separate coils, by being imbedded in the same piece of
iron, should thus act upon each other seems strange. One might al-
most think that it arose from the particles of iron refusing to polarise
and unpolarise quick enough. The maximum speed of revolution
of the armature is about 2500 times a minute. The driving gear
multiplies 22 times, so that this speed is nearly as much as the
arm can effect. A particle of iron would have thus 10,000 times
to polarise and unpolarise in a minute. A little consideration will
show, however, that it is from no such incapacity on the part of
the iron ; for at the same rate of revolution, the two effects are felt
with the different circuits. Speed in these cases, therefore, has not

3 u

VOL. VII.

494 Proceedings of the Royal Society

overshot the mark. The cause of the action appears to me as fol-
lows ; — When the line of the armature (fig. 8) is vertical — when, in
fact, the strongest action is taking place in the small coil — the wires
of the large coil cut the lines of magnetic force between N and S
at right angles, the best time and the best place for a current to he
induced in them. Although, then, the longitudinal polarity of the
iron has disappeared, the coil takes up the action and makes a north
and a south end, even when the main line of the armature is up-
right, and should be free from polarity. This coil induction or
polarity is feeble, contrasted with that resulting through the iron,
and would have little effect if the coils were near each other in
size. It is only in the present case, where there is such a dis-
parity between the coils, that the interference grows to a sensible
amount. In support of this view of the matter, it may be men-
tioned that when the larger coil is connected with the electro-
magnet, little relief is felt on an easy
circuit being made for the smaller coil.
The effect of the interference is to lessen
the current induced in the smaller coil.
A particle at a, for instance (fig. 8), which
when left to the action of the poles of the
electro-magnet would give its full quota
of electric induction, is by the cross polarity magnetically forced
round, so to speak, into a less favourable position for doing
so. But how is this interference stopped by a resisting external
circuit? In this way, I imagine. The available electro-motive
power may take the form of large quantity in an easy circuit,
or little quantity in a resisting circuit. On consulting the
galvanometer in a resisting circuit, while the strength is taxed
to the utmost, the current is often found weak. It is the quantity
of electricity that is the cause of the interference, and not the work
value of the circuit. When the strength of the electric current is
great with a resisting circuit, that of the magnetic current has been
proportionally exalted.

The interference of the two coils with each other can be shown
in a simple way. When the coil of the electro-magnet is detached
from the magnetic coil and joined up with a Bunsen cell, we have,
on turning the handle, both armature coils prepared to give ex-

of Edinburgh, Session 1870-71.

495

ternal currents. If, in the circuit of the electric coil, a few inches
of fine platinum wire he included, and the circuit of the magnetic
coil half completed, so that one end of the connecting wire has only
to touch the other binding screw to close it, and the handle be put
in sufficient motion, the platinum wire becomes white hot, and this
sinks to a dull red when contact in the magnetic circuit is made.
The same takes place when the coils are reversed. Such an action
as this suggests the supposition that what appears in the second
coil is but electricity stolen from the first, and that the arrangement
effects only a convenient distribution, and not an increase of the
electricity available. I cannot, with the observations I have yet
made, say that such is not true in all cases, but in one case, at least,
the only one I have examined, such a supposition cannot be enter-
tained, and that is when both coils work together in the same
circuit. When both coils, as just mentioned, are ready to give
external currents under the magnetism induced by one Bunsen cell,
it is quite possible, by accustoming the ear to the note produced by
the springs rubbing on the revolving collars, to get the arm to work
at a uniform speed. If the cell be steady, you can, within a frac-
tion of a degree, produce the same angle in the galvanometer in
the same circumstances. I have made repeated observations in
this way as to what current the electric coil would give when act-
ing alone, as to what the magnetic coil would give, and as to what
both together would effect. The circuits in these cases consisted of
the coils themselves and the wires leading to a tangent galvano-
meter some 12 feet off, and the working of the machine and the
observing of angles were done by different persons. The resistances
in both circuits were sensibly the same. The resistance of the
electric coil was 32 inches of a G-erman silver wire in my posses-
sion, that of the magnetic coil 34, and that of the galvanometer
wire 5 inches. To these must be added the resistance introduced
by the imperfect contact of the break-springs, which, at a high
speed, and especially in the case of the machine exhibited where
the armature is not quite truly centred, must be considerable. The
difference between the two coils would thus almost disappear on the
total resistances of their respective circuits. This being the case,
the work value of the electricity appearing in each will be as the
squares of the tangents of the angles observed. Now, in all the

496 Proceedings of the Royal Society

observations I have made, tbe sum of these for the two coils sepa-
rately was approximately equal to that obtained when both currents
were sent into the galvanometer circuit. To give an idea of how
nearly this comes out, I may cite one observation repeated three
times in succession with the same result. I found the angle of
both together to be 47|°, that of the electric coil separately 40°,
and that of the magnetic coil separately 34°. Now the square of
the tangent of 47 J° is 1*1909, and the sum of those of the other
two 1*15905.

The theory of the machine, as I understand it, may be thus
shortly summed up. In one case, namely, that of an easy common
circuit, and it is likely to be more or less so in all cases, the two
coils contribute each their full quota to the total electric fund of
the armature. When the resistance of the circuits differ, this fund
is divided inversely in some function of the relative resistance, but
whether this takes place so as to excite the electro-magnet at no
original expense of driving energy is still a matter for further
determination. The results got from the machine would lead us to
suspect as much, for they compare favourably with machines where
a permanent battery of magnets is used; hut this test, though so
far satisfactory, is far from exact.

The interference of the coils seems to me to be a hopeful feature
of the arrangement, as it does not make increased power simply
dependent on increased velocity. There is a promise in it that by
adjusting the relative sizes of the coils a powerful current may be
got at a really practicable speed, and there would thus be obviated
the serious objection to this class of machines, which, however
astonishing in their power, are apt to wear themselves out by their
rapid rate of motion when kept in action for days together. Even
in the machine before you, if the collars were properly turned and
centered, so as to give good contact with the springs at all rates of
revolution, I have reason to believe that its effective speed of
revolution would be very much diminished.

In mentioning what a machine like this can do, considerable
latitude must be understood in interpreting results. The strength
or ardour of different workers may tell very differently. The only
fair way would be to give the electric effect corresponding to a
weight falling so far per second, hut this involves opportunities of

of Edinburgh, Session 1870-71.

497

experiment which I have not at my command. When I say that
6 inches of soft iron wire g1^ of an inch in diameter can he melted or
ignited by it, I only mean to say that the arm of an ordinary man,
working briskly for a second or two, can accomplish this, though it
would he hard work for him to continue the same for a minute.
A stronger arm than usual, or a more ardent labourer, would do
much more than this. A battery of six Bunsen cells, each with an
effective surface of 42 square inches, melted 5 inches of the same
wire. With an induction coil a spark of 1^ inches can he got with
an expenditure of labour that may be continued for a minute or two ;
with intense exertion a spark of 5 or even more inches may be got.
By working reasonably for a minute from 2J to 4 cubic inches of
explosive gas can he got from a voltameter ; working very hard for
a quarter of a minute at the rate of 6 inches or more may be
obtained. To turn a handle some 100 times a minute, more espe-
cially against some resistance, is not work that can he easily con-
tinued for minutes ; and such machines, when driven by the hand,
are only good for incidental, not continuous use. To keep down
the pull on the hand with a resisting circuit, the commutating
collar of the magnetic coil has to be turned round from its position
of maximum effect. There is a certain speed at which the hand
can best work, for slow and difficult motion is not so convenient
nor attended by so good results as quick and easy motion.

The machine is well adapted for an educational instrument, viz.,
for illustrating electro-magnetic action. If the electro-magnetic
coil he joined with one cell of Bunsen, and the electric coil with
five or six cells, the conditions of the machine are reversed; and now
electricity produces motion, instead of motion producing electricity.
The handle is made to go round with considerable velocity, and if
the belt that connects the gearing with the handle he removed, the
armature alone spins round at a great rate. If now the poles of
the magnetic coil be joined, the armature instantly slows, and the
slowing is all the more marked the less the resistance of the circuit
offered. The current of this new circuit can raise to a white heat
about a \ inch of fine platinum wire. It may be worth mentioning,
that the current given off by the magnetic coil under these condi-
tions is singularly steady, and that its strength is something like
inversely proportional to the circuit resistance. This slowing of

498

Proceedings of the Boy at Society

the armature seems at variance with what I have stated before, that
less instead of more driving resistance is felt in closing either of
the armature circuits, for here the new current seems to be paid for
out of the motion of the armature. The discrepancy may possibly be
accounted for by the consideration that both coils are now antago-
nistic in their action, and that whatever part of the induced current
appears in the magnetic coil, from whatever source derived, goes
directly to oppose the conditions favourable to motion, and that
between the opposing actions more heating in the core may he the
accompaniment or equivalent of slower motion. When the coil of
the electro-magnet is joined with the larger (electric) coil, so that a
wire has only to touch the unconnected binding screw to close the
circuit, and when the arm puts the machine into rapid motion, it is
brought to an instant, one might say an impotent halt, on the wire
touching the binding screw. One cannot help thinking, in trying
such an experiment, that coil-brakes or drags may be yet extensively
used in machinery.

Whether this machine he any improvement or even a rival to
existing machines, I do not pretend to say. I only wish in this paper
to bring the peculiarities of its action before the notice of the
Society.

4. Mathematical Notes. By Professor Tait.

1. On a Property of Self- Conjugate Linear and Vector Functions.

In the course of an investigation connected with the free rota-
tion of a rigid body I was led to the remark that, if £ and r\ be two
vectors related to one another so that

£ = Y.rjpr) ,

where is a self- conjugate linear and vector function, we have
also

r\ = V. £(p£ ,

(so that the relation is reciprocal) provided
S .r)Qr)'V2r) = 1 ,

which implies also the corresponding equation

S.^^=l •

499

of Edinburgh, Session 1870-71.

The surface of the third order, represented by either of the two
latter equations, is well known, and the property above shows a
curious relation between certain of its vectors and those of a central
surface of the second order. It has also interesting applications
to the lines of curvature of the surface.

If £ and 7] be unrestricted, the theorem above may be put in the
more general form that the two following equations are conse-
quences one of the other, viz. : —

£ V.rjtpy

$3 *-£(P£(P2£ $3 .rj(pr](p27]

r) __ I • £$£

.rjpr)(p2r] S* .£<p£ty2£

From either of them we obtain the equation
S<p£<P0 = S5 ,£(p£^>2£ S5 -rtf rtf2 r] ,

which, taken along with one of the others, gives a singular theorem
when translated into ordinary algebra.

2. Relation between corresponding Ordinates of two Parabolas.
Two projectiles are anyhow projected simultaneously from a
point, what is the relation between their vertical heights at any
instant ?

This simple inquiry, which was instituted in consequence of some
results recently obtained from thermo-electric experiments (see ante .
p. 311) carried on at high temperatures, where the indications given
by two separate circuits, immersed in the same hot and cold bodies,
were used as ordinate and abscissa, leads to a very curious conse-
quence.

Let

x = At (B - t)

and

y = A7(B' - t)

be any two parabolas whose axes are vertical, and which pass
through the origin. We have

A'x — Ay [- ^ A'x — Ay q

•" ii - i; -l. ' aa i ii is J'

500

Proceedings of the Royal Society

or

(k'x - A y)2 = A A' (B' - B) (ABy - A'B'a;) .

This, again, is the equation of a parabola, which passes, like the
others, through the origin, hut whose axis is no longer vertical.
The converse suggests another easy but interesting problem.

If we write £ for , rj for , and / and /' for the halves of B

and B', we easily see that the last equation above becomes

(i " V)2 =

Every parabola passing through the origin may have its equation
put in this form. Hence, as f and rj are dependent on one another
(in the thermo-electric as in the projectile case) only as being
both functions of temperature, or of time, it is obvious that we must
seek to break this expression up into a linear relation between
functions of i and y separately. A well known transformation
leads to

- jr-~-v = ±c/ -/) •

whence

Jr~- l = ±(r -/I

Jf 2 - V= =fc(T

where t is some function of time or of temperature. These give
f . = T (2/ - t) ,

V = T (2/ ~ r) •

Hence, in the thermo-electric case, if we obtain a parabola by using,
as ordinate and abscissa, the simultaneous indications of any two
circuits whose junctions are at the same temperatures/ and if one of
them gives a parabola (with axis vertical) in terms of absolute
temperature, r must be a linear function of the difference of absolute
temperatures of the junctions, and, therefore, the other circuit gives
a similarly situated parabola in terms of the absolute tempera-
ture.

h

DOSES OF' ATROPIA

ANTAGONISM BETWEEN PHYSOSTIGMA ANO ATROPIA i ATROPIA ADMINISTERED 5 MINUTES BEFORE PHYSOSTI GMA )

509

of Edinburgh, Session 1870-71.

to 12 grain; and with three and a-half times the minimum fatal
dose of physostigma, with doses of atropia ranging from *1 grain to
'2 grain. Successful antagonism could not be obtained above this
dose, and, accordingly, three and a-half times the minimum fatal
dose of physostigma would appear to be about the largest quantity
whose lethal action may he prevented by administering atropia
five minutes previously.

A similar series of experiments has been made, in which phy-
sostigma was administered five minutes before atropia, and the
results were essentially the same, excepting that the region of suc-
cessful antagonism was found to be more limited.

These results may be graphically represented by means of
diagrams. The diagram accompanying this abstract is a reduced
copy of one exhibited by the author to illustrate the series of ex-
periments above described, in which atropia was administered five
minutes before physostigma. The experiments that terminated in
death are marked by crosses, and those that terminated in recovery
by dots, while the position assigned to each experiment is deter-
mined by the doses of physostigma and atropia, calculated, when
necessary, for three pounds weight of rabbit. The doses of atropia
increase according to the distance, in a horizontal direction, from
the perpendicular line forming the left margin of the diagram, and
the increase proceeds at the rate of one-tenth of a grain for each
subdivision of the horizontal lines. The doses of physostigma
increase from below upwards, the same horizontal line always
representing the same dose of physostigma. The curved line,
a b c, separates the fatal experiments (crosses) from those which
terminated in recovery (dots), and, accordingly, it defines the region
of successful antagonism — a region further distinguished in the
diagram by the absence of shading. The darkly shaded region is
that in which antagonism is not successful, death being produced
because the doses of atropia given in combination with one or
other of the doses of physostigma employed are either too small or
too large. In the lightly shaded region, below the horizontal line
representing the minimum fatal dose of physostigma, the doses of
physostigma are too small of themselves to cause death. The
lateral extension of the diagram is, however, insufficient to exhibit
the chief interest of this region. Were the diagram extended, it

VOL. vii. 3 y

510

Proceedings of the, Eoyal Society

would show that fatal experiments occur in this region, not only
with fatal doses of atropia given in combination with less than
fatal doses of physostigma, but also with less than fatal doses
of atropia given in combination with less than fatal doses of
physostigma.

In this manner, the entire superficial area of the region of suc-
cessful antagonism has been defined, when physostigma is given
five minutes after and five minutes before atropia. In addi-
tion to this, what may be termed the thickness of the region
has been determined. For this purpose, series of experiments
were made, in each of which the doses of physostigma were the
same, and the doses of atropia varied ; while with each dose of
atropia, several experiments were made which differed from each
other by a difference in the interval of time between the adminis-
tration of the two substances. From the data thus obtained, curves
have been constructed; the dose of physostigma serving as the
base-line, the various doses of atropia as the abscissas, and the dif-
ferent intervals of time that separate successful from unsuccessful
experiments as the summits of the ordinates. When these curves
are brought into relation with a diagram of the superficial area of
the region of successful antagonism, in such a manner that the
base-lines, representing the doses of physostigma, correspond to
each other, and that the ordinates of these curves extend at right
angles to those in the diagram of the superficial area, the lateral
extension of the region of successful antagonism may be defined.
In this way, its lateral as well as its superficial extent has been
indicated with atropia and physostigma.

After defining the superficial area and the thickness of the
region of successful antagonism, it seemed of interest to ascertain
what dose of atropia is required to produce death with a dose of
physostigma below the minimum fatal. The experiments per-
formed for this purpose show that when one-half of the minimum
fatal dose of physostigma is given five minutes after atropia, so
large a dose of the latter substance as 9’8 grains is required in
order to cause death ; recovery taking place with doses ranging
from 3 to 9 '5 grains,

The minimum fatal dose of sulphate of atropia given alone was
found to be twenty-one grains for a rabbit weighing three pounds.

511

of Edinburgh, Session 1870-71.

It is, therefore, remarkable that the gf-g-ths °f a grain can prevent
a dose of physostigma, equal to the minimum fatal, from causing
death, and that the y^th of a grain is capable of rendering non-
fatal a dose of physostigma, equal to three and a-half times the
minimum fatal.

Excepting dilatation of the pupils, these minute doses of atropia,
and indeed any dose capable of antagonising the lethal action of
physostigma, are unable to produce any symptom recognisable
by a mere inspection of the animal. Still, they undoubtedly
produce energetic physiological effects — effects, however, which it
is unnecessary to describe in this brief abstract. It is sufficient to
point out that the notion, which exists in many quarters, that
rabbits can scarcely be affected by atropia is an erroneous one.

Without referring to the other results obtained in his investiga-
tion, the author pointed out, in conclusion, that unless the anta
gonism between any two active substances be examined in the
manner indicated in this communication, no satisfactory proof of
its existence can be obtained. The superficial area of the region
should always be defined, otherwise indications of antagonism
obtained by one observer will be liable to be discredited by those
who subsequently examine the subject. The first observer may
succeed in performing an experiment within the area of successful
antagonism, and thus feel satisfied of its existence ; but his suc-
cessors may fail in obtaining any proof by so varying the dose
of one or other substance as to pass the limits of the region of suc-
cess (see diagram). Feeling assured that many examples of success-
ful antagonism, besides the one he had the honour of bringing before
the Society, will yet be discovered, the author could not avoid the
conclusion that the imperfect methods of investigation hitherto
pursued are accountable for the absence of success that has attended
the numerous researches made on this subject — a subject, it need
scarcely be added, of the greatest importance to toxicology and to
scientific therapeutics.

512

Proceedings of the Royal Society

6. On the Homological Relations of the Coelenterata. By
Professor Allman, F.R.S.E.

Abstract.

In this communication an Actinozoon (Actinia) was compared
with a Hydrozoon (Hydra), and the various Sub-orders of the Hydro-
zoa were compared with one another.

The author agreed with Agassiz in regardingthe radiating cham-
bers of an Actinia as the homologues of the radiating canals of a
medusa, but he differed from him as to the true homologies of the
differentiated stomach-sac of Actinia ; for while Agassiz regards
this as represented by the proboscis or hypostome of the Hydra
inverted into its body cavity, Professor Allman maintains that it is
impossible on this supposition to conceive of the structure of Actinia;
and on comparing a Hydra with an Actinia , he imagines the tentacle
to become connate for a greater or less extent with the sides of
the hypostome and with one another, so that the hypostome of the
hydra, while retaining its normal position, will thus become the
stomach of the Actinia, and will at the same time become connected
with the outer walls by a series of radiating lamellm — the connate
tentacle walls — separated from one another by radiating chambers,
the cavities of the tentacles ; while such portions of the tentacles
of Hydra as still continue free will be represented by a single circle
of the tentacles of Actinia .

The author had formerly compared the radiating canals of a
hydroid medusa to the immersed portions of the tentacles of a
Hydra , and he still maintains this view.

The strict parallelism of a siphonophore with a hydroid was
pointed out, and each of the zooids which combine to form the
heteromorphic siphonophorous colony was shown — as indeed Hux-
ley and others had already done — to have its representative in the
hydroid colony, and to be but a slightly modified form of some
hydral zooid.

In order to understand the relations of a discophorous or
steganophthalmic medusa to the other liydrozoa , he supposes the
‘ ‘ atrium” of a hydroid medusa, or that part of the main body
cavity which is still immersed in the solid proximal portion of the

513

of Edinburgh, Session 1870-71.

umbella, at the base of the manubrium, to be expanded laterally,
and the gelatinous extoderm of its floor to be projected along four
or eight symmetrically disposed radiating lines into as many thick
pillars, which converge towards the axis, and there meet the manu-
brium, while the thin intervening portions between the pillars
become developed into generative pouches, the velum at the same
time disappearing. A hydroid medusa would thus, in all essential
points, become converted into a discophorous medusa.

A Lucernaria was conceived of by imagining a Hydra to have its
tentacles reduced to four in number, and expanded laterally until
their sides meet and coalesce ; while the hypostome continues free,
the solid hydrorhizal basis becoming at the same time extended
into a peduncle of attachment traversed longitudinally by four
canal-like prolongations of the body cavity, of else by a simple
continuation of this cavity.

Lastly, a Beroe was taken as a type of the Ctenophora, and was
conceived of as a hydroid medusa so modified as to become reduced
to the atrial region alone. The two lateral canals which spring
from the somatic cavity in Beroe , and subdivide so as to form ulti-
mately the eight meridional canals, correspond to the greatly deve-
loped basal portion of the radiating canals of the medusa, or that
portion of those canals which is still contained within the solid
summit of the umbella ; the affinities of the Ctenophora being thus
directly with the Hydrozoa instead of the Actinozoa.

The author finds the key to the homology of Beroe , and the tran-
sition between the Ctenophora and the Hydroida in the singular
ambulatory gonophore of Clavatella.

514

Proceedings of the Royal Society

The following Donations to the Society were announced : —

Agassiz (Louis). Address delivered on the Centennial Anniver-
sary of the Birth of Alexander von Humboldt, under the
auspices of the Boston Society of Natural History. 8vo. —
From the Author.

Anderson (Benjamin). Narrative of a Journey to Musardu, the
Capital of the Western Mandingoes. New York, 1870. 8vo.
— From the Author.

Asman (Dr P. H.). Proeve eener G-eneeskundige Plaatsbes-
cbrijving ven de G-emeente Leeuwarden. Utrecht, 1870.
4to. — From the Author.

Benson (Prof. Lawrence S.). Dissertation on the Principles and
Science of G-eometry. New York, 1871. 8vo. — From the Author.

Breen (Hugh). Corrections of Bouvard’s Elements of Jupiter and
Saturn. Paris, 1821. — From the Author.

Brown (Bobert, Ph. D., A.M.). Descriptions of some new or little
known species of Oaks from North-West America. (From
Ann. Mag. Nat. Hist., April 1871). 8vo. — From the Author.

On the Physics of Arctic Ice, as Explanatory of the

Glacial remains in Scotland. (From Quart. Jour. Geol. Soc.,
Feb. 1871). 8vo. — From the Author.

Colding (A.). Om Stroemningsforholdene i almindelige Ledninge-
rog i Havet. Kjoebenhavn. 4to. — From the Author.

Day (St John Vincent). On some Evidences as to the very early
use of Iron. Edinburgh, 1871. 8vo. — From the Author.

Flora Batava. Nos. 211-215. Amsterdam. 4to. — From the
King of Holland.

G-ould (Augustus A., M.D.). Keport on the Invertebrata of Mas-
sachusetts. Boston, 1870. 8vo. — From the Boston Society of
Natural History.

Journal (American) of Science and Art, conducted by Benjamin
Silliman. No. 148, 149, 150. Vol. I. Third Series, No. 1, 2,
3. New Haven. 8vo. — From the Editor.

Julian. Biology versus Theology or Life on the Basis of Hylozo-
ism. Lewes, 1870. 8vo. — From the Author.

Lea (Isaac, LL.D.). Index to Vol. Nil. of Observations on the
Oenus Unio. Philadelphia, 1869. 4to. — From the Author.

515

of Edinburgh, Session 1870-71.

Lea (Isaac, LL.D.j. A Synopsis of the Family Unionidce. Phila-
delphia, 1870. 4to. — From the Author .

Miller (Eev. Jas. N.). The true Direction and Velocity of Wind
observed from ships while sailing. London, 1870. 8vo. —
From the Author.

Packard (A. S.), M.D. Record of American Entomology for 1868.
Salem, 1869. 8vo. — From the Author.

Parrish (R. A., Jun.). Details on an Unpaid Claim on France for
24,000,000 francs, guaranteed by the Parole of Napoleon III.
Philadelphia, 1869. 8vo. — From the Author.

Pascucci (Prof. Luigi). Brevi Cenni sulle Speciality Mattei
con sunto delle Malatte Senate nella Citta di Roma 1869.
Rome 1870. 8vo. — From the Author.

Preger (Wilhelm). Die Entfaltung der Idee des Mensclien durch
die Weltgeschichte. 4to. — From the Author.

Rive (Prof. A. de la). Recherches sur la Polarisation rotatoire
magnetique des Liquides. 8vo. — From the Author.

Settimanni (Capt. Cesar). Nouvelle Theorie des principaux la-
ments de la Lune et du Soleil. Florence, 1871. 4to. — From
the Author.

Simpson (Martin). A G-uide to the G-eology of the Yorkshire
Coast. 4th Edition. London, 1868. 8vo„ — From the Author.

Sobrero (Ascanio). Notizia Storica dei Lavori fartti della Classe di
Scienze Fisiche Matematiche della Reale Accademia delle
Scienze di Torino negli aiini 1864 e 1865. 8vo. — From the
Author.

Stewart (B.). Account of Certain Experiments on Aneroid Bar-
ometers made at Kew Observatory. 8vo. — From the Author.

Strecker (Adolph). Jahresbericht iiber die Fortschritte der Chemie,
&c., fur 1868. Heft 3. Giessen. 8vo. — From the Editor.

Thayer, C. F., and Buswell, II. T. Address and Ode delivered at
the Dedication of Memorial Hall, Lancaster, 17tli June 1868.
Boston, 1868. 8vo. — From the Authors.

Thomsen (Julius). Thermochemiske undersoegelsen. Kjoeben-
havn. 4to. — From the Author.

Zittel (Carl Alfred) Denschrift auf Christ. Erich Hermann von
Meyer. Munich. 4to. — From the Author.

516

Proceedings of the Royal Society

Transactions and Proceedings oe Learned Societies and
Academies.

Amsterdam. — Jaarboek van de Koninklijke Akademie van Weten-
scliappen gevestigd te Amsterdam voor 1869. 8vo. —
From the Academy.

Processen-verbaal van de G-ewone Yergaderingen, der Kon-
inklijke Akademie van Wetenschappen, 1870. 8vo. —
From the Academy.

Verhandelingen der Koninklijke Akademie van Wetens-
chappen Deel Y. 4to. — From the Academy.

Yerslagen en Mededeelingen der Koninklijke Akademie
van Wetenschappen Natnurknnde. Deel IY. Letter-
kunde Deel XII. 8vo. — From the Academy.

Augusta , U. S. — 3d Report of the Commissioner of Fisheries
of the State of Maine, 1869. 8vo. — From the Commis-
sioner.

Baltimore. — Proceedings of the Board of Trustees of the Peabody
Institute. Nov. 1870. 8vo. — From the Institute.

Berlin.— Abhandlungen der Koniglichen Akademie der Wissens-
chaften. 1869. I., II. 4to. — From the Academy.

Monatsbericht der Koniglicli Preussischen Akademie der
Wissenschaften, Juni, Juli, August, September, October,
November, December, 1870. January, February, March,
April, 1871. 8vo. — From the Academy.

Die Fortschritte der Physik in Jahre 1867, dargestellt von
der Physikalischen G-esellscliaft zu Berlin. Jahrgang
XXIII. 8vo. — From the Society.

Yerzeichniss der Abhandlungen der Koniglicli Preussischen
Akademie der Wissenschaften von 1710-1870. 8vo. —
From the Society.

Berne. — Mittheilungen der Naturforschenden G-esellschaft in Bern
aus dem Jahre 1869. Nos. 684-711. 8vo. — From the
Society. -

Materiaux pour la Carte G-eologique de la Suisse. Liv. 7-8.
4to. — From the Natural History Society.

Birmingham. — Ninth Annual Report of the Free Libraries Com-
mittee. 1870. 8vo. — From the Committee.

517

of Edinburgh, Session 1870 -71.

Bologna. — Memorie dell Accademia delle Scienze dell Institute) de
Bologna. Tome IX. Fasc 1-4. 4to — From the Aca-
demy.

Boston. — Bulletin of the Public Library. No. 16. 1871. 8vo.

From the Library.

Proceedings of the Boston Society of Natural History. Vol.
XI1.-XIII. 8vo. — From the Society.

Brussels. — Bulletin de FAcademie Eoyale des Sciences des Lettres
et des Beaux-Arts de Belgique. Tome XXX., Nos. 7-9,
11-12 ; XXXI., Nos. 1, 2, 3, 4. 8vo. — From the Aca
demy.

Calcutta. — Journal of the Asiatic Society of Bengal. Part I., Nos.

2, 3, 4 ; Part II., Nos. 2, 3. 1870. 8vo. — From the Society.

Proceedings of the Asiatic Society of Bengal. Nos. 6, 7, 8,
9, 10, 11, 1870; Nos. 1, 2, 1871. 8vo.— From the

Society.

Cambridge (17. Si). — Memoirs of the American Academy of Arts
and Sciences. Vol. III. Part II.; IV. Part I. 4to. —
From the Academy.

Annual Report of the Librarian of Harvard University,
1863-1864 and 1869. 8vo. — From the University.

New Catalogue of Harvard College Library. 8vo. — From
the College.

Annual Reports of the President and Treasurer of Harvard
College, 1868, 1869. 8vo. — From the College.

Addresses at the Inauguration of Charles William Eliot as
President of Harvard College, 1869. 8vo. — From the

College.

Catalogue of Officers and Students of Harvard University
for 1869-70. 8vo. — From the University .

Catalogus Senatus Academici Collegii Harvardiani, 1869.
8vo. — From the College.

Catalogue of the Collection of Engravings bequeathed
to Harvard College by Francis Calley Hray. By Louis
Thies. 4to. — From the College.

Proceedings of the American Association for the Advance-
ment of Science, 1868 and 1869. 8vo, — From the Asso-
ciation.

3 z

vol. VII.

518 Proceedings of the Royal Society

Cambridge (JJ.S.') — Proceedings of the American Academy of Arts
and Sciences. Vol. II.- VIII. 8vo. — From the Academy.

Canada. — Report of Progress of Geological Survey of, for 1866-
1869. 8 vo. — From the Survey.

Cincinnati. — Annual Report of the Director of the Cincinnati
Observatory. 1870. 8vo. — From the Observatory.

Cherbourg. — Memoires de la Societe Imperiale des Sciences Natu-
relles. Tome XIII., XIV. 8vo. — From the Society.

Copenhagen. — Oversigt over det Kongelige danske Videnskabernes
Selskabs, Forhandlinger og dets Medlemmers Arheider i
Aaret 1868, No. 6; 1869, No. 4; 1870, Nos. 1, 2. 8vo.
— From the Royal Academy of Sciences.

Dorpat. — Meteologische Beobachtungen. 1869. 8vo. — From the
University of Dorpat.

Dublin. — Journal of the Royal Dublin Society. No. 39. 8vo.—

From the Society.

Edinburgh. — Transactions of the Royal Scottish Society of Arts.
Vol. VIII. Part II. 8 vo. — From the Society.

Transactions and Proceedings of the Botanical Society,
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Transactions of the Highland and Agricultural Society of
Scotland. No. 6. 8vo. — From the Society.

Journal of the Scottish Meteorological Society. Nos. 27,
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Quarterly Returns of the Births, Deaths, and Marriages
Registered in the Divisions, Counties, and Districts of
Scotland. Nos. 63 to 65. 1870. Monthly Returns of

the same from July to December 1870, and from January
to May 1871. 8vo. — From the Registrar-General.

Fourteenth Detailed Annual Report of the Registrar-General
of Births, Deaths, and Marriages in Scotland. 8vo. —
From the Registrar -General.

Forty-third Annual Report of the Council of the
Royal Scottish Academy of Painting, Sculpture, and
Architecture. 8vo. — From the Academy.

Supplement to Catalogue of the Library of the Royal College
of Physicians, 1863-70. 4to. — From the College.

519

of Edinburgh, Session 1870-71.

Frankfort. — Abhandlimgen herausgegeben von der Senckenber-
gischen Naturforschenden Gesellschaft. Band VII.
Heft 8-4. 4to. — From the Society.

Bericht iiber die Senckenbergische Naturforschende Gesell-
schaft, 1869-70. 8vo. — From the Society.

Geneva. — Memoires de la Societe de Physique et d’Histoire Natur-
elle de Geneve. Tome XX. Partie 2. 4to. — From the
Society.

Gottingen. — Abbandlungen der Koniglichen G-esellschaft der Wis-
senscbaften. Band XV. 4to. — From the Society .

Nachrichten von der K. Gesellsckaft der Wissensckaften
und der Georg- Augusts-Universitat, 1870. 12mo. — From
the Society.

Greenwich. — Astronomical and Magnetical and Meteorological
Observations made at the Royal Observatory in the year
1868. London, 1870. 4to. — From the Society.

Haarlem. — Archives du Musee Teyler. Vol. III. Fasc 1. 8vo. —
From the Museum.

Innsbruck. — Berichte des Naturwissenschaftlich-Medizinischen
Vereines in Innsbruck. Jahrgang I. Heft 1-2. 8vo. —
From the Society.

Jena. — Jenaische Zeitschrift fur Medcin und Naturwissenschaft
herausgegeben von der Medicinisch Naturwissenschaft-
lichen Gesellschaft zu Jena. Band V. Heft 3-4. Band
VI. Heft 1-2. 8vo. — From the Society.

Kasan. — Reports of the University of Kasan, 1865-1869. 8vo. —
From the University.

Kiel. — Schriften der Universitat, 1869. Band XVI. 4to. — From
the University.

Leeds. — 15th Report of the Philosophical and Literary Society,
1869-70. 8vo. — From the Society.

Leeuwarden. — Nederlandsch Kruidkundig Archief, Vijfde deel.
Viorde Stuk. 1870. 8vo. — From the Editors.

Leipzig— Berichte fiber die Verhandlungen der Koniglich Sachsis-
chen Gesellschaft der Wissensehaften zu Leipzig. Phil.
Hist. Classe. 1868, Nos. 2, 3 ; 1869, Nos. 1-3. Math.
Phys. Classe, 1869, Nos. 2-3-4; 1870, Nos. 1-2. 8vo.
— From the Royal Saxon Academy.

520

Proceedings of the Royal Society

Leipzig. — Bestimmung der Sonnenparallaxe durch Venusvoriiber-
gange vor der Sonnenscheibe mit Besonderer Beriicksichti-
gung des im Jahre 1874 eintreffenden voraberganges von
P. A. Hansen. Band IX. No, 5. 8vo. — From the Royal
Saxon Academy.

Elektrische Untersuchungen ueber die Thermo-elektrichen
Eigenschaften des Topases. Band VIII., IX. No. 4.
W. G. Hankel. 8vo. — From the Royal Saxon Academy.
Eropbile Vulgaergriechische Tragoedie von Georgios Chor-
tatzes ans Kreta. Ein Beitrag zur Geschichte der Neu-
griechischen und der Italianischen Litteratur von Conrad
Bursian. Band V. No. 7. 8vo. — From the Royal
Saxon Academy.

Tafeln der Amphitrite mit berucksichtigung der Storungen-
durcli Jupiter, Saturn, und Mars, entworfen von Dr E.
Becker. 4to. — From the Astronomical Society .
Vierteljahrsschrift der Astronomischen Gesellschaft ; Jahr-
gang V. Heft 2, 3, 4; Jahrgang VI. Heft 1. — From
the Society.

Leyden. — Annalen der Sternwarte. Zweiter Band. 1870. 4to. —
From the Observatory.

London. — Transactions of the Society of Antiquaries. Vol.

XL. Part 2. XLII. Part 2. XLIII. Part 1. 4to. —

From the Society.

Proceedings of the Society of Antiquaries, Vol. IV., Nos.

7, 8, 9. 8vo. — From the Society.

Journal of the Society of Arts, 1870-71. 8vo. — From the
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tTournal of the Boyal Asiatic Society of Great Britain and
Ireland. Vol. V. Part 1. 8vo. — From the Society.
Memoirs of the Boyal Astronomical Society, Vol. XXXVII.

Parts 1, 2. Vol. XXXVIII. 4to. — From the Society.
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Journal of the Chemical Society. September, October,
November, December, 1870. January, February, March,
April, May, June, 1871. 8vo. — From the Society.

521

of Edinburgh, Session 1870-71.

London. — Transactions of the Clinical Society, Yol. III. 8vo. —
From the Society.

A General Index to the first Twenty-Nine Volumes of the
Monthly Notices of the Royal Astronomical Society.
8vo. — From the Society.

Proceedings of the Institution of Civil Engineers. Vols.
XXIX., XXX. 8vo, — From the Society.

Catalogue of the Library of the Institution of Civil En-
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Education and Status of Civil Engineers. 8vo. — From the
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Proceedings of the Royal Geographical Society. Vol.
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Society.

Address at the Anniversary Meeting of the Royal Geo-
graphical Society, 1871, by Sir Roderick Impey Murchi-
son, Bart. 8 vo. — From the Society.

Quarterly Journal of the Geological Society. Vol. XXVI.
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Society.

Geology of the Country between Liverpool and Southport,
and Explanation of Geological Map, 90° S.E. 8vo. —
From the Geological Survey.

Catalogue of the Published Maps, Sections, Memoirs, &c.,
of the Geological Survey of the United Kingdom up to
July 1870. 8vo. — From the Survey.

Explanation of Quarter Sheet, 93° S.W., of the One-Incli
Geological Survey Map of England. 8vo. — From the
Survey.

Mineral Statistics of the United Kingdom of Great Britain
and Ireland for 1869. 8vo .—From the Geological Survey.

Annual Report of the Geologists’ Association for 1870, and
List of Members. 8vo. — From the Association.

Proceedings of the Royal Institution of Great Britain. Vol.
V. Part 7. Vol. VI. Parts 1, 2. 8vo. — From the Society.

List of Members of the Royal Institution of Great Britain
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522

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London. — Journal of the London Institution. Yol. I., Nos. 1, 2, 3, 4,
5, 6. 8vo. — From the Institution .

Journal of the Linnean Society. Yol. XI. (Botany) ;
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51, 52, 53, 54, 55. 8vo. — From the Society.

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Transactions of the Royal Society. Yol. CLX. Part I., II.

List of Members. 4to. — From the Society.

Proceedings of the Royal Society. Yol. XYIII. Nos.

122, 123, 124, 125, 126, 127, 128. 8vo, — From the Society.
Royal Society Catalogue of Scientific Papers. Yol. IV.
4to. — From the Society.

Quarterly Weather Report of the Meteorological Office.
Parts 2, 3, 4. 1869. 4to. — From the Meteorological

Committee of the Royal Society.

Report of the Meteorological Committee of the Royal So-
ciety, for Year ending 1869. 8vo. — From the Com-

mittee.

Transactions of the Royal Society of Literature. Yol. IX.

Part 3. 8vo. — From the Society.

Journal of the Statistical Society. Yol. XXXIII. Parts
3, 4. XXXIV. Part 1. 8vo. — From the Society.
Transactions of the Zoological Society. Vol. VII. Parts
3, 4, 5. 4to. — From the Society.

Proceedings of the Zoological Society, 1870. Parts 1, 2, 3.
8vo. — From the Society.

523

of Edinburgh, Session 1870-71.

London . — Reports on Experiments made with the Bash forth
Chronograph to determine the Resistance of the Air to the
Motion of Projectiles. 1865-1870. 8vo. — From, H.M.
Stationery Office.

Barometer Manual (1871). 8vo. — From the Board of Trade.

Milan. Atte della Societa Italiana di Scienze Naturali. Yol. XII.
Fasc. 4. Yol. XIII., Ease. 1, 2, 3. Yol. XIY. Ease. 1.
8vo. — From the Society.

Moscow. — Bulletin de la Societe Imperiale des Naturalistes. 1870.
Nos. 1, 2. 8 vo. — From the Society.

Munich. — Abhandlungen der koniglich. bayerischen der Wissen-
schaften. Mathematisch-Physikalischen Classe, Band X.,
Abth. 3. Philosophisch-Philologischen Classe, Band XII.
Abth. 1. — 4to. — From the Academy.

Sitzungsberichte der konigl. bayer. Akademie der Wis-
senschaften. 1870, Band I. Heft 1, 2, 4; Band II. Heft
1, 2. 8vo. — From the Society.

Neuchatel. — Bulletin de la Societe des Sciences Naturelles de
Neuchatel. Tome YIII. No. 3. 8vo. — From the Society.

New YorJc — Monthly Report of the Deputy Special Commissioner
of the Revenue in charge of the Bureau of Statistics,
Treasury Department. 1869-70. 4to. — From the Com-
missioner.

52d Annual Report of the Trustees of the New York
State Library. 1870. 8vo .—-From the Library.

81st and 82d Annual Reports of the Regents of the Uni-
versity of the State of New York. 8vo. — From the

University.

22d Annual Report of the Regents of the University of the
State of New York. (Nat. Hist. Antiq. 1869). 8vo. —
From the University.

Ohio. — 23d Annual Report of the Ohio State Board of Agriculture,
1868. Columbus, 1869. 8vo. — From the Board.

Paris. — Annales des Mines. Tome XYI1. Liv. 1, 2, 3. 8vo. —
From the Ecole des Mines.

Bulletin de la Societe de G-eographie ; Juillet, Aout, Sep-
tembre, Octobre, Novembre, Decembre 1870; Janvier,
Fevrier 1871. 8vo. — From the Society.

524 Proceedings of the Royal Society.

Paris. — Bulletin de la Societe de Geographic; Juin 1870. 8vo.
— From the Society.

Comptes-Bendus Hebdomadaires des Seances de l’Academie
des Sciences, 1870-71. 4to. — From the Academy.

Pest. — A Magyar Tudomanyos Akademie Ertesitoje; Szam 9-20,
1868; Szam 1-20, 1869; Szam 1-12, 1870. 8vo.—

From the Academy.

Ertekezesek a Matbematikai Osztaly Kdrebol Kiadja A. M.
Tudomanyos Akademia. Szam 3, 4, 1868-69. Svo. —
From the Academy.

Ertekezesek a Termeszettudomanyok Kdrebol Kiadja A. M.
Tudomanyos Akademia. Szam 13-19, 1868-69; Szam
1, 2, 1870. 8vo. — From the Academy.

Philadelphia. — Proceedings of the Academy of Natural Sciences.
Nos. 3, 4, 1869. 8vo. — From the Academy.

Proceedings of the American Philosophical Society. YoL
XI. No. 82. 8vo. — From the Society.

Quebec. — Transactions of the Literary and Historical Society. New
Series. Part 7. 8vo. — From the Society.

Rotterdam. — Nieuwe Verhandelingen van het Bataafsch Genoot-
schap der Proefondervindelijke Wijsbegeerte, Deel II.
Stuk 1. 4to. — From the Society.

St Petersburg. — Bulletin de l’Academie Imperiale des Sciences de
St Petersbourg. Tome XV. Nos. 1, 2. 4to. — From the
Academy.

Compte-Rendu de la Commission Imperiale Archeologique
pour l’Annee 1868. 4to. (Atlas Fob)— From the Com-
mission.

Memoires de F Academie Imperiale des Sciences de St Peters-
bourg. VIIe Serie. Tome XY, Nos. 5-8. 4to. — From the
Academy.

Salem, Mass. — The American Naturalist. Yol. III. ; Vol. IY. Nos.
1, 2. 8vo. — From the Peabody Academy of Science.

First Annual Report of the Trustees of the Peabody
Academy of Science 1869. 8vo. — From the Peabody

Academy of Science.

Bulletin of the Essex Institute. Yol, I. 8vo —From the
Institute.

of Edinburgh, Session 1869-70. 525

Salem , U.S. — Proceedings of the Essex Institute. Vols. I., II.,
III., YI. Part 1. 8vo —From the Institute.

Toronto. — Canadian Journal of Science, Literature, and History.

Yol. XII. No. 6 ; XIII. No. 1. 8vo. — From the Canadian
Institute.

Turin. — Atti della Reale Accademia delle Scienze Appendice.

Yol. IY. ; Yol. Y. Disp. 1-7. 8vo. — From the Academy.

Bollettino Meteorologico ed Astronomico dal Regio Osser-
vatorio, dell’ Universita, 1869. 4to. — From the University.

Upsala. — Bulletin Meteorologique Mensuel de l’Observatoire de
FUniversite. Yol. II. Nos. 1-6. 4to. — From the Uni-
versity.

Nova Acta Regies Societatis Scientiarum Upsaliensis. Yol.
YII. Fasc. 1, 2. 4to. — From the Society .

Utrecht. — Memoire sur le genre Poterion par P. Harting. 4to. —
From Society of Arts and Sciences , Utrecht.

Yerslag van het Yerhandelde in de algemeene Yergadering
van hen Provinciaal Utrechtsch G-enootschap van Kuns-
ten en Wetenschappen, 1870. 8vo. — From the Society.

Nederlandsch Meteorologisch Jaarhoek 1869. 4to. — From
the Meteorological Institute of Utrecht.

Venice. — Atti del Real Istituto Yeneto di Scienze, Lettere ed
Arti. Tomo XIY. Dispenso 6-10; Tomo XV. Hispenso
1-9. 8 vo. — From the Institute.

Victoria , Australia. — Agricultural Statistics of the Colony for
1869-70. Fol — From the Registrar-General.

Statistics of the Colony, 1869. Fol. — From the Registrar -
General.

Vienna. — Denkschriften der kaiserlichen Akademie der Wissen-
schaften. Phil. Hist. Classe, Band XIX.; Math. Nat.
Classe, Band XXX. 4to. — From the Academy.

Sitzungsberichte der kaiserlichen Akademie der Wissen-
schaften — Botanik, Zoologik, etc., Band LX. Heft 3-5 ;
B. LXI. Heft 1-5 ; B. LXII. Heft 1, 2. Mathematik,
Physik, &c., B. LX. Heft 3-5 ; B. LXI. Heft 1-5 ;
B. LXII. Heft 1-3. Philosophise^ B. LXIII., B.
LXIV., B. LXV., B. LXYI. Heft 1. 8vo. — From the
Academy.

4 a

VOL. VII.

526

Proceedings of the Royal Society

Vienna. — Almanack der kaiserlicken Akademie der Wissensehaften,
1870. 8vo. — From the Academy.

Phanologische Beobachtungen aus dem Pfianzen und Thier-
reiche von Karl Fritsch. Heft 8. Jahrgang 1857.
4to. — From the Academy.

Verhandlungen der kaiserlich-koniglichen Zoologisch-
Botanischen Gesellsehaft in Wien. Band XX. 8vo. —
From the Society.

Verhandlungen der kaiserlich-koniglichen G-eologischen
Keichsanstalt. 1869, Nos. 6-9, 10-12, 13-18; 1870,
Nos. 6, 7. 8 vo. — From the Society.

Die Fossilen Mollusken des Tertioer-beckens von Wien, von
Dr Hornes. Band II. Nos. 9, 10. 4to. — From the
Society .

Jahrbuch der kaiserlich-koniglichen G-eologischen Beich-
sanstalt. Band XIX. No. 2 ; B. XX. Nos. 2-4. 8vo. —
From the Society.

Warwick. — Thirty-fourth Annual Keport of Natural History and
Archaeological Society, 1870. 8vo. — From the Society.

Washington. — Astronomical and Meteorological Observations made
at the United States Naval Observatory during 1867.
4to. — From the United States Government.

Smithsonian Contributions to Knowledge. Vol. XVI. 4to.
— From the Institution.

Smithsonian Contributions to Knowledge. — The Trans-
atlantic Longitude as determined by the Coast Survey
Expedition for 1866. By Benjamin Apthorp Gould,
1869. 4to. — From the Smithsonian Institution.

Smithsonian Miscellaneous Collections. Vols. VIII. and
IX. 8vo. — From the Institution.

Annual Beport of the Board of Begents of the Smithsonian
Institution for 1868. 8vo. — From the Institution.

Twelfth Annual Beport of the Columbia Institution for the
Deaf and Dumb, 1869. 8vo. — From the Institution.

Beport of the Commissioner of Agriculture for 1868. 8vo.
— From the United States Government.

Monthly Beports of the Department of Agriculture for 1869.
Edited by J. B. Dodge. 8vo. — From the Editor.

of Edinburgh, Session 1869-70. 527

Washington. — Report of the Superintendent of the United States
Coast Survey for 1866. 4to. — From the Survey.
Wellington ( New Zealand). — Statistics of New Zealand for 1869.

Fol. Wellington, 1870. — From the Registrar-General .
Whitby. — Forty-eighth Report of the Literary and Philosophical
Society, 1870. 8vo. — From the Society.

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

yol. vii. 1871-72. No. 84.

Eighty-Ninth Session.

Monday , 21th, November 1871.

Sir ROBERT CHRISTISON, Bart., President, in the Chair.
The following Council were elected
President.

Sir ROBERT CHRISTISON, Bart., M.D., D.C.L.

Honorary Vice-President.

His Grace the DUKE of ARGYLL.

Professor Kelland.

The Hon. Lord Neaves.
Professor Sir William Thomson.

Vice-Presidents.

Principal Sir Alex. Grant, Bart.

Sir W. STiRLiNG-MAXWELL,Bart.
Professor W. J. Macquorn Rankine.

General Secretary — Dr John Hutton Balfour.

Secretaries to Ordinary Meetings.
Professor Tait.

Professor Turner.

Treasurer — David Smith, Esq.

Curator of Library and Museum — Dr Maclagan.

Councillors.

Professor Geikie.

Professor A. Crum Brown.
Rev. W. Lindsay Alexander.
Professor Fleeming Jenkin.
Prof. Wyville Thomson.
James Donaldson, Esq.
vol. vn.

Dr Thomas R. Fraser.

Dr Arthur Gamgee.
Alexander Buchan, Esq.
Prof. A. Dickson.

D. Milne Home, Esq.
James Leslie, Esq., C.E.

4 B

Art

530

1 roceedings of the Royal Society

Monday , 4 th December 1871.

A Marble Bust of the late Sir Roderick I. Murchison, Bart.,
by Weekes, was presented.

Although the Bust was only placed in the Hall at this time, the
offer of it to the Society was made by Sir Roderick 1. Murchison
in June 1871, in the following letter to the President : —

16 Belgrave Square, 2 6th June 1871.

My dear Professor, — As it is very improbable, indeed — nay,
almost a certainty — that I shall not be able to attend the meeting
of the British Association at Edinburgh this year, I wish to send,
as my representative, a marble bust of myself, executed by Mr
Henry Weekes, R.A., and which is on the point of completion.

I beg to be informed if the Council of the Royal Society of
Edinburgh, over which you preside, will accept this bust as a
donation from myself, in gratitude for the great honour they con-
ferred on me many years ago, by enrolling my name in their dis-
tinguished list of honorary members; also in recollection of
another great honour which they conferred on me, by granting to
me the first Brisbane gold medal for my labours in Scottish
geology. If you assent to this proposal, I will direct Mr Weekes
to transmit the bust to the Secretary of your Royal Society, in the
hope that you will place it in the same building as the busts of our
other scientific countrymen whom you have thus honoured.

I have also written to David Milne Home on this point, and
have assured him, at the same time, that I will do everything in
my power to support the memorial to the G-overnment to assist the
Royal Society of Edinburgh in carrying out their meritorious re-
searches, as signed by yourself. — An early reply will oblige, yours
sincerely,

RODERICK I. MURCHISON.

To Professor Christison,

President, tt.S. Edin.

of Edinburgh. Session 1871 --72.

531

Sir Robert Christison, Bart., the President, read the
following Opening Address : —

At the commencement of this, the 89th session of the Royal
Society of Edinburgh, I beg to congratulate you on the successful
issue of that which has just come to an end. The number of our
members has increased, in consequence both of a low proportion
of deaths among us, and likewise of an increase of new members
beyond the average ; so that, from 326 at the same period last
year, the Society has grown to 331 at the present time.

We may appeal with equal, and even more, satisfaction to the
success of our late meetings ; which, in the first place, were carried
on a full month longer than usual before exhausting the list of
communications approved by your Council as worthy of being read
before you ; and which, in the second place, attracted from first to
last unusual attendance and interest, on the part both of ourselves
and of our visitors, by reason of the variety and value of the in-
quiries communicated at them.

Nor, amidst these grounds of direct gratification on account of
the proceedings of last year in the Royal Society itself, will it
appear out' of place that I further congratulate you on the great
success which attended the late meeting in Edinburgh of The
British Association for the Advancement of Science. Whether we
consider who was the founder of this most prosperous institution —
or that the Royal Society of Edinburgh and the Association were
established very much for the same objects — or that our Fellows
have taken an active part in its proceedings, wheresoever it may
have held its meetings — or that our endeavours contributed greatly
to bring it on the recent occasion to our city — or that many of us
did much, or at least as much as we could, to receive our eminent
guests with the cordiality due to their distinction in science — we
are equally entitled to rejoice that, in respect of the number of
remarkable men who were attracted hither, the excellence of the
matter produced before the several sections, the interest of the
excursions which the unrivalled opportunities in our neighbour-
hood enabled us to offer, the oft-expressed obligations of our guests
for the reception they met from us and our fellow-citizens, and, I

532

Proceedings of the Royal Society

may add, the eight days of glorious weather, upon which in Scot-
land much of the comfort of so great an assemblage depends —
this forty-first meeting of the British Association proved in truth
to be a great success.

Although the deaths in the Society have not been numerous
during last year, we have nevertheless to lament the loss of
several of the most distinguished among our Fellows, both ordi-
nary and honorary. From the list of ordinary Fellows we have to
strike out the names, in alphabetical order, of Dr William Anderson,
Mr Charles Babbage, Mr Robert Chambers, Dr Robert Daun, Mr
Alexander Keith Johnston, Dr Sheridan Muspratt, Mr Robert
Russell, Sir William Scott, Dr Fraser Thomson, and Mr Moses
Steven. Our honorary list no longer bears the names of Sir
John Herschell, Sir William Haidinger, and Sir Roderick Impey
Murchison.

Mr Robert Russell, an eminent practical and scientific agri-
culturist in the county of Fife, was led to connect himself with the
Society by his taste for meteorological pursuits.

Sir William Scott, Baronet, of Ancrum, an enterprising country
gentleman, a soldier in his youth, and afterwards for some time
member of Parliament for his county, was well known for his
attachment to scientific society, and for the regularity of his attend-
ance at our meetings at a period when his avocations allowed him
to reside occasionally in Edinburgh.

Dr Robert Daun, Deputy Inspector-General of Army Hospitals,
also a frequent attender at one time of the meetings of the Society,
died in June last at a very great age [86]. He served his country
with distinction in the medical service of the army throughout
nearly the whole of the most momentous period, and the most
critical trials, in the military history of our country. He was
highly esteemed publicly for his knowledge in all departments of
his profession, and his powers of organisation in his own branch
of service ; and he was no less prized by his friends for his acquaint-
ance with various branches of science and literature.

533

of Edinburgh, Session 1871-72.

Dr Fraser Thomson, son of the Rev. Dr William Thomson of
Perth, and nephew of the late eminent clergyman of Edinburgh,
Dr Andrew Thomson, the first minister of St George’s parish,
graduated at the University of Edinburgh, where he had been a
distinguished student of medicine. He settled as a medical prac-
titioner in his native city, and for most of his life was much
engrossed by the cares of an extensive practice in town and
country. Rut, like many of his profession in our county towns,
he made natural history his recreation for his short leisure hours,
and applied himself eagerly to microscopical research in that
department of science. In this he acquired great expertness and
accuracy, and would easily have become an original inquirer, were
it not that his fondness for such pursuits had not fame for its
object, but simply relief from the cares and fatigues of professional
life. He died, after a short illness, in the month of October, in his
65th year.

James Sheridan Muspratt, a native of Dublin, was trained in
the science to which he dedicated his life, under two of the greatest
chemists of their day in Europe — Graham and Liebig. At the age
of twenty-three he published the results of investigations carried
on as a student in Liebig’s laboratory on the sulphites, showing
their analogy with the carbonates. Returning to Giessen three
years later, he resumed his inquiries into the sulphur acids, the
fruit of which was an interesting paper on the Hyposulphites, and
also on Sulpho-cyanic Ether. In the interval he did good service
to practical chemistry in this country by making generally known
in a translation Plattner’s standard work on the Blowpipe ; and in
1854 he published a “ Dictionary of Chemistry,” which has been
of great use in diffusing a knowledge of chemistry among those
engaged in the practical working of chemical problems. Mr
Muspratt died in the 47th year of his age.

Mr Robert Chambers, long one of the most attached and work-
ing Fellows of the Royal Society, is one of the many instances,
observed at all times in Scotland, of men raising themselves in a
short time, by the sheer unaided gifts of native talent and indomi-
table perseverance, from an obscure position in society to a promi-

534 Proceedings o f the Royal Society

nent place in public estimation. Born, as we are told by one of
his biographers, who evidently knew him and his history well, of
parents respectable, but not fortunate in life, he had to struggle
in his early years with difficulties. Nevertheless he was not pre-
vented from reaping the inestimable advantages which in Edin-
burgh a parent of even moderate means could always command,
for a son of promising parts, from an education at the High
School.

Like other prolific writers, Mr Chambers began the career of
authorship at a very early age. He must have been not above
eighteen, when, having not long before chosen for his occupation
in life that of bookseller, he determined to be publisher and author
too, projecting and conducting a periodical called the “Kaleido-
scope,” to which he himself also contributed articles from his own
pen. Soon afterwards he published “Illustrations of the Author of
Waverley ; ” and in 1823, when only twenty years old, he added
the work by which he has been longest and most familiarly known
as a writer, his “ Traditions of Edinburgh.” Work upon work
then followed in quick succession on all sorts of literary subjects,
but chiefly historical and antiquarian — works which it would be
out of place even to enumerate in so short a sketch as that to which
this brief notice must be confined.

At last, in conjunction with his elder brother, Mr William
Chambers, was begun in 1832 the now famous “ Chambers’ Edin-
burgh Journal,” — the first idea, and as such a great invention, of
a weekly periodical devoted to short productions, original, as well
as critical, on nearly all literary and also some scientific subjects,
suited for the information, as well as for the purse, not alone of
the educated classes ordinarily so called, but likewise for the edu-
cated in the humbler walks of life. This undertaking met soon
with extraordinary success — in so much, indeed, that it became
the parent of many others identical or similar in their aims, and
not affew of them not less prosperous than that of the two brothers
Chambers.

While adhering steadily to his literary tastes, and giving forth
in various works the results of his literary labours, Mr H. Chambers’
attention was turned to a totally different object of study, which
in all probability he first followed as a diversion, or distraction

535

of Edinburgh, Session 1871-72.

from the severity of professional toil. This was geology, which in
the end captivated him, and first made him an active, energetic
member of this Society. Cultivating his new pursuit with his
inherent fervour unabated, he soon became an original inquirer in
this fascinating branch of natural science. Besides making him-
self acquainted with the rock structure of many parts of his own
country, he visited as a geologist Switzerland, Norway, Sweden,
Iceland, the Faroe Islands, and parts of Canada and the United
States. Few geological amateurs, engaged in a profession usually
so engrossing as that of Robert Chambers, have acquired such
intimate knowledge of geology. Many of us can recall the interest
of his discussion of geological questions at our ordinary meetings ;
and his “ Ancient Sea Margins ” will long be known as one of the
earliest, most exact, and most lively descriptions of that particular
branch of his favourite study.

Mr Chambers was distinguished, alike in his public appearances,
as in social intercourse, by a great fund of information on most
diversified topics of interest in literature and science, by his
caution and politeness in criticism, and by his courteous kindliness
in every relation of life. In the last respect he will be long missed
by a numerous circle of attached friends, many of whom were his
fellow-members of the Royal Society of Edinburgh. In March
1871, after a tedious and enfeebling illness, borne with singular
patience, he died in the 69th year of his age.

I turn next to another no less serious loss sustained during the
past year by science and this Society in the death of Mr Alexander
Keith Johnston. Mr Keith Johnston at first intended to join the
medical profession ; but, at an early age, he betook himself to the
art of engraving, which again led him to the study of geography ;
and from that time geography became his ruling pursuit, and the
object of his professional life.

In 1830, having had occasion, during a pedestrian trip iji the
Highlands, to remark the inaccuracy of the maps of Scotland, he
published an improved collection in a Guide Book. At the same
time, to facilitate the development of his geographical enterprises,
he joined the firm of his two brothers, Sir William and Thomas
Johnston, which had been established in this city some years

536 Proceedings of the Boy a! Society

before for carrying on the business of engraving and printing, in
which they have been long famous among the skilful engravers of
Edinburgh. In his thirty-ninth year he attracted the regard of
scientific geographers at large by the publication of his “National
Atlas,” and still more, five years later, by his “Atlas of Physical
Geography,” For the task he had thus set himself he had been
thoroughly prepared by assiduous study of the best works in the
various languages of Europe, by frequent visits to many European
countries, and by acquaintance and personal intercourse with the
greatest continental geographers and travellers. Not long after-
wards Mr Keith Johnston brought out in succession a “ Dictionary
of Geography,” a “ Military Atlas ” for Alison’s “ History of
Europe,” the “Royal Atlas of Modern Geography,” and subse-
quently a variety of cheap atlases for the use of schools. By these
productions he raised himself to a position in which he had no
superior rival as a geographer in this country ; and his merit in
this respect received the stamp of the Royal Geographical Society
of London in the last year of his life by the award of the Geo-
graphical Victoria Medal.

But Mr Johnston took also great interest in almost every branch
of physical research, with many of which he had no mean acquaint-
ance, and whose cultivation in this city he seized every opportunity
to encourage and promote. Among other obligations to him, we
are greatly indebted for the foundation of “ The Meteorological
Society ” of Scotland, — an institution which, under the able direc-
tion of its present Secretary, promises important results, certain,
indeed, to be realised if the Society receive due public support in
the line of inquiry in which it has already been for some years
successfully engaged. It is also known to me that the city and
University are mainly indebted to him for the early foundation of
the Chair of Geology, through the munificence of his friend the
late Sir Roderick Murchison. At the direct instance of Mr John-
ston, and through the weight which his genuine love of science
commanded with many men of influence, Sir Roderick was induced
to alter his intentions, from a “ post-obit ” foundation, to an im-
mediate gift, of the Chair, in conjunction with a Royal Foundation
and additional endowment.

In such proceedings as these Mr Johnston did good with no

537

of Edinburgh, Session 1871-72.

ulterior view, and from no love of being what our neighbours across
the channel aptly call a “grand faiseur.” Hence we scarcely know
how much we owe to him. His extensive acquaintance with the
upper ranks of what it has become the custom to call the “ citizen
class” in Edinburgh, enabled him often quietly to direct public
opinion in the nice exercise of scientific, literary, and professional
patronage, when sound direction was greatly needed; and his
acknowledged prudence, probity, impartiality, and knowledge of
men, never failed to guide himself soundly in such conjunctures.

Throughout his whole life he was faithful and fruitful in his
calling, and no less a sincere and active Christian. Seldom has
there been a more affable, agreeable, and profitable companion in
social life in all its phases.

Although far from being a young man at his death, — for he
died in his 67th year, — we have to lament that he was struck
down while in full possession of his powerful intellect, and enjoy-
ing shortly before a vigour which promised long continuance of
his useful labours.

Wilhelm Bitter von Haidinger, one of our Honorary Fellows,
was a favourite pupil of Mohs ; who, during great part of the first
half of this century, was celebrated as one of the foremost mineralo-
gists of his day in Europe, and as the able Professor of Mineralogy
in the University of Vienna. While yet a young man, William
Haidinger possessed an extraordinary extent and accuracy of
knowledge of minerals. On account of his talents as a descriptive
mineralogist, he came to Edinburgh, about the year 1824, to
arrange and catalogue the splendid mineralogical collection of a
former curator of our Society, Mr Thomas Allan, banker in this
city,— a collection unrivalled, for extent and careful costly selec-
tion, among the private mineralogical museums of Europe. In
discharging this duty Mr Haidinger was enabled to establish
several species as new to science ; which he investigated and com-
municated to our meetings in conjunction with the late Edward
Turner, the chemist, at the time lecturer here, and soon after-
wards first Professor of Chemistry in University College, London.
Haidinger took the descriptive, Turner the analytical, part of
these inquiries ; and, in both respects, their papers are models of

4 o

VOL. VII.

538 Proceedings of the Royal Society

mineralogical investigation. I was at this time intimately ac-
quainted with Haidinger, and could well appreciate his mineralo-
gical facility and acuteness, his varied knowledge of natural history
and physical science, and his remarkable command of languages, —
so that, for example, in our own tongue, he could tell a jocular
story, make a pun, and extemporise a clever couplet,— -which I
take to be about the severest of all tests of a man’s familiarity with
a foreign language.

No one who knew him at that time could fail to see that
Haidinger would one day become a man of mark among the
mineralogists of his own land, to which he returned soon after
completing his labours in Mr Allan’s museum. He then travelled
for some time with Mr Allan’s son, Eobert, who died a few years
ago a Fellow of this Society; and the main object of the travellers
was the pursuit of mineralogy. Ere long Mohs died, and Haidinger
succeeded him in his University Chair. His office put him natu-
rally at the head of all relative Government undertakings, which
in their turn brought him promotion, till at length he filled the
highest office in his profession, that of Director of the Mineralo-
gical and Geological Survey of Austria. For his many scientific
and practical services to his country he received from his sovereign
the honour of knighthood a few years before his death, which took
place last April in, as I understand, the 71st year of his age.

Coming nearer home, I have next to deal with the scientific life
of another lost Honorary Fellow of the highest rank in Physical
Philosophy, Sir Roderick Impey Murchison, Baronet. But
though very willing, and not altogether unable, to do justice to
his remarkable labours in his science, I felt that I should be acting
with injustice to his memory, and to the claims of a far superior
biographer and eulogist, if I did not transfer from myself to Pro-
fessor Geikie the pleasing task of recalling to our recollection the
main points in the life and the work of his patron and friend.
The following summary is accordingly the tribute which Professor
G-eikie has kindly enabled the Society to pay to the fame of Sir
Roderick Murchison : —

“ Among our recent losses there is none which we have more
reason to deplore than bis. The name of Sir Roderick Murchison

539

of Edinburgh, Session 1871-72.

has been a household word in geology for nearly half a century,
not in Britain only, but also over all the world. While we share
in the wide regret at the injury which the general cause of science
sustained by his removal, we add also the sadness which arises from
the recollection of the relation which he bore to the progress of
geology in Scotland, and from what he has recently done for the
advancement of its study in the University of this city.

“ Born in 1792 at Tavadale, in Ross-shire, he was educated for
the military profession, and served during part of the Peninsular
War. But on the arrival of peace in 1815, finding that the army
no longer opened up the same prospect of activity for which he
longed, he gave up his commission, married, and settled in
England. The succeeding part of his life, prior to 1824, he used
to speak of as his “ Eox-hunting period,” when he threw himself
with all the ardour of his nature into the field sports of a country
residence. Part of that period, however, he spent abroad, making,
with his wife, tours in search of picture galleries and old art, and
keeping an elaborate diary, with criticisms on the character of the
fine arts in each tour or collection visited. It was by a kind of
happy accident that his energies were at last directed into the
channel of science, — the merit of which change was due partly to
his wife’s taste for natural history, and partly to the friendly
counsel of Sir Humphrey Davy. He joined the G-eological Society
of London, and soon became one of its most enthusiastic members.
From that time forward his love for geology, and his activity in
its pursuit, never waned. He travelled over every part of Britain,
and year after year he resorted to the Continent, traversing it in
detail from the Alps to Scandinavia, and from the coasts of France
to the far bounds of the Ural Mountains. As the result of these
journeys, there came from his pen more than a hundred memoirs,
besides two separate and classical works on 1 The Silurian System,’
and on ‘ Russia.’

“Sir Roderick was essentially a geologist, and he chose one
special branch as his own domain. Perhaps no man ever had the
same power, — which seemed sometimes almost an intuition, — of
seizing the dominant features of the geographical and paleeontolo-
gical details of a district. With a keen eye to detect the characters
as they rose before him, and a faculty of rapidly appreciating their

540 Proceedings of the Royal Society

significance, he could, as it were, read off the geology of a country
after a few traverses only, when most men would have been
puzzling over their first section. This was the secret of his broad
generalisations regarding the geological structure of a large part of
Europe, — generalisations which, though of course requiring to he
corrected and modified by subsequent more detailed investigations,
still remain true in the main, and still astound by their marvellous
grasp and suggestiveness. The leading idea of his scientific life
was to establish the order of succession among rocks, and through
that order to show the successive stages in the history of life on
our globe. With the more speculative parts of geology he meddled
little ; nor did he ever travel outside the bounds of his own science.
He early recognised the limits within which his powers could find
the fullest and most free development, and he was seldom found
making even a short excursion beyond them.

“ The special part of his work on which his chief title to fame
rests is undoubtedly his establishment of ‘ The Silurian System.’
Before his time, the early chapters of the history of life on our
globe had been but dimly deciphered. William Smith had thrown
a new flood of light upon that history by showing the order of suc-
cession among the secondary rocks of England, and had done more
than any other man to dispel the prejudices with which the
doctrines of Werner seemed naturally to fill the mind. But the
rocks older than secondary, to which Werner had given the name of
‘ Transition,’ remained still in deep Wernerian darkness. Sir
Koderick Murchison saw that it might be possible to bring order
and light out of these rocks, even as had been done with those of
more recent origin ; and that a double interest would attach to
them if, as he supposed, they should reveal to us the first begin-
nings of life upon our globe. Choosing a part of the broken land
of England where the rocks are well exposed, he set himself to
unravel their order of succession. Patiently year after year he
laboured at his self-appointed task, communicating his resulfs
sometimes in writing to his friends, sometimes in the form of a
short paper to the Geological Society of London, until at last, in
1838, he gathered up the whole into his great work, £ The Silurian
System.’ In that book the early chapters of the history of life on
the earth were first unfolded, and a system of classification was

541

of Edinburgh, Session 1871-72.

chosen with such skill that it has been found applicable, with
minor modifications, even in the most distant quarters of the globe.

“Round this early work all his after-labours seemed to range
themselves by a natural sequence. His choice had led him into
the most ancient fossiliferous rocks, and to that first love he re-
mained true. Whether in the glades of Shropshire, or the glens
of his own Highlands, among the fjelds and fjords of Norway, or
in the wilds of the Urals, it was with the Palaeozoic formations
that he mainly busied himself. They were to him a kind of patri-
mony which had claims on his constant supervision. With his
friend Sedgwick he unravelled the structure of the middle Palae-
ozoic rocks of Devonshire, and with Keyserling and De Yerneuil
he showed the true relations of the upper Palaeozoic rocks of
Russia. The Silurian, Devonian, and Permian systems, represent-
ing each a vast cycle in the history of our earth as a habitable
globe, received in this way from him their first clear elucidation,
and the very names by which they are now universally known.

“But if we seek to measure the influence which Sir Roderick
Murchison exercised on the progress of the science of the time
merely by the original work which he himself accomplished, we
should fail duly to appreciate the measure and the powrer of that
influence, and the extent of the loss which his death has caused.
Fortunate in the possession of wealth and high social position, he
was enabled to act as a constant friend and guardian to the cause
of science. He moved about as one of the representative scientific
men of his day. To no man more than to him do we owe the public
recognition of the claims of scientific culture in this country. For
he not only stood out as the acknowledged chief in his own domain,
but had also the faculty of gathering round him men of all sciences,
among whom his kindliness of nature, his courteous dignity of
manners, his tact and knowledge of the world, and his wide range
of social connections marked him out as spokesman and leader.
Nowhere were these features of his character and influence more
conspicuous than in his conduct of the affairs of the Geographical
Society, of which he was for many years the very life and soul,
and which owes in large measure to him the stimulus it has given
to geographical science.

“ Here in his own native country, and more especially here in

542 Proceedings of the Royal Society

Edinburgh, we have peculiar cause to mourn the loss of such a
man. Though his residence from boyhood had been chiefly in
London, he never to the last relinquished his enthusiastic regard
for the land of his birth. He never lost an opportunity of boasting
that he was a Scot. During the last ten years of his life he made
frequent and protracted tours in the Highlands ; and, in unravel-
ling their complicated geological structure, he accomplished one
of the most brilliant generalisations of his long and illustrious
scientific career. There is something touching in the reflection
that, after having travelled and toiled all over Europe, gaining the
highest position and rewards which a scientific man can attain, he
should at last, ripe in years and in honours, have come back to his
own Highlands, and there completed his life-work by bringing into
order the chaos of the primary rocks, and laying such an impress
on Scottish geology as had never been laid before by any single
observer. Eor these and other researches he received from this
Society the first Brisbane Medal — an honour conferred on him at
the Aberdeen meeting of the British Association, and of which he
often spoke as one that gave him the deepest gratification. He
used to boast, too, of being an honorary Fellow of this Society, and
to quote a remark made to him by the late Kobert Brown, that his
election into the list of our honorary Fellows was one of the highest
marks of distinction he could receive. His kindly interest in. our
prosperity was often expressed ; and we have a token of it in the
presentation to us of his bust by Weekes, which this evening is
formally delivered to the Society.

“ Of the closing acts of his life, there is one which cannot be
mentioned without peculiar pride — the institution of a Chair of
Greology and Mineralogy in the University of Edinburgh. He
intended to found this Chair by bequest; but on the retirement of
Dr Allman from the Chair of Natural History, he determined to
do in his lifetime what w'ould otherwise have been accomplished
not till after his death. He gave to the University a sum of
£6000 ; and the Crown having consented to add an annual grant
of £200, the Chair was founded in the spring of the present year.
Sir Roderick has not lived to witness the first beginnings of the
tuition which he had started. But long after the memory of his
personal character shall fade, men will remember the work which

of Edinburgh, Session 1871-72. 543

lie did ; they will recognise the impetus his researches have given
to geology all over the world; and let us hope also they will see
in the Chair he has founded the starting-point of a new and active
school of Scottish geology.”

I have left to the last in this biographical sketch of our lately
deceased Fellows two of the most eminent men of British science
in their day — Herschel and Babbage. For as I could not pretend
to do justice to the lives of men whose pursuits, in the highest
range of physical science, were so far removed from my own, I
think it right to keep quite apart the following eulogium, the
preparation of which my university colleague, Professor Tait, has
kindly allowed me to impose on him, and which I will give in his
own words : —

“Of Sir John F. W. Herschel and Charles Babbage, who may
be fitly mentioned together, it is not necessary that much should
be said, as their contributions to science cannot fail to he set forth
at length in the Proceedings of other Societies, with which they
were more connected than with our own. Intimate friends during
their undergraduate career at Cambridge, they joined us as ordi-
nary Fellows shortly after taking their degrees, and when they
were just commencing, along with the late Dean Peacock, what
all must consider, in spite of their other grand contributions to
science, the greatest work of their lives — the restoration of mathe-
matical science in Britain. It is impossible even now to over-
estimate the value of this service. Few know to what a state of
ignorance we had fallen at the time when Lagrange, Laplace,
Fourier, Cauchy, Poisson, and Gauss, and many others abroad,
were advancing with breathless rapidity in the track, neglected by
us, of James Bernoulli and Euler. Partly from a mistaken notion
that they were honouring Newton by adhering to his published
methods, partly owing to the British dislike to men and things
foreign, which at this time was pushed, perhaps not unnaturally,
to extreme lengths in all matters, and partly in consequence of our
long state of war with France, our mathematicians had never even
learned those unpublished methods by which Newton made his
discoveries, which, as soon as they were to some extent divined

544

Proceedings of the Royal Society

abroad, were at once estimated at their true value, and pursued
with zeal and genius.*

“ Little by little, first by translating Lacroix’s elementary treatise
on the differential and integral calculus, and by thus introducing,
in face of determined opposition, the notation of differential co-
efficients into Cambridge, so as for the first time to enable her
mathematicians to understand a foreign treatise ; secondly, by
publishing an excellent collection of examples; and thirdly, by
their separate original treatises on different special parts of analysis,
they put this country on a level with France and G-ermany, so far
at least as opportunities of progress are concerned. It is to them
mainly that we owe, not merely our modern British school of
mathematicians, which is now certainly second to none in the
world, but even the very possibility of the existence in this country
of such great departed masters as Boole and Hamilton.

“ Herschel’s 1 Treatise on Finite Differences,’ which appeared
as a supplement to the translation of Lacroix, is one of the most
charming mathematical works ever written, everywhere showing

* Professor Tait has urged me to make known a reminiscence of my youth
that at the time here referred to there were in Edinburgh, and in this Society,
no fewer than three mathematical amateurs, who, though they never made
themselves publicly felt as such, in some measure saved this corner of the
land from the censure dealt in the text. These were Sir William Miller,
Baronet, of Glenlee, better known as Lord Glenlee of the Scottish bench ;
William Archibald Cadell, of the family of Cadell of Grange, who finished
his earthly career but a few years ago ; and my own father, Professor of
Latin in our University. Lord Glenlee, a man of very retiring habits
and disposition, was usually called the first amateur mathematician in
Scotland. Mr Cadell, also a man of great reserve and shyness, neverthe-
less, in order to carry out his admiration of the modern continental mathe-
matics, contrived to obtain, during the very hottest of our struggles with
France, from that generally unyielding potentate, the First Napoleon, per-
mission, through the influence of one of the great mathematicians of Paris,
to repair to the French capital, to dwell there for seven years, and to return
unhindered to Scotland, at a period when no other Briton was known to have
put his foot on French soil without being made a detenu. My father, during
the last ten years of his life, which ended in 1820, betook himself, as his idea
of relaxation from routine professional life, to the differential calculus, and
to Newton, Bernoulli, Euler, Lagrange, Laplace, Lacroix, &c., whose works
were always at hand when not in his hands. As he made a vigorous attempt
to indoctrinate me at a very early age in his favourite pursuits, I know well
what these were, and what he knew of the kindred spirits Glenlee and
Cadell.

545

of Edinburgh , Session 1871-72.

power and originality, as well as elegance. In all these respects it
far surpasses his subsequent mathematical writings, excellent as are
many of them ; for instance his celebrated treatises on * Light ’ and
on ‘ Sound ’ in the £ Encyclopaedia Metropolitana.’ The appendix
to Lacroix which was written by Babbage, was devoted to the
‘ calculus of functions,’ a strangely weird branch of analysis, which
remains even now much as Babbage left it. That in this direction
there is a splendid field open for the inquirer, is evident to any one
who consults Babbage’s papers on it ; and it is wonderful that it
has not been greatly developed of late years, when so many mathe-
maticians, especially at home, have been found to apply themselves
almost exclusively to those branches of the science which seem the
least likely ever to have useful applications.

<{ In their after-life the careers of these great workers and
thinkers led them widely apart. Herschel devoted himself mainly
to astronomy, but also to chemistry, photography, and occasionally
to mathematics. His astronomical work is all of the very highest
class, whether it consisted in his seclusion, for several of the
best years of his life, at the Cape of G-ood Hope in the close observa-
tion of the stars and nebulas of the Southern Hemisphere ; or in
first writing, and then, as edition after edition was called for,
extending and improving his splendid semi-popular work, the ‘ Out-
lines of Astronomy,’ which none, even of men of science, can read
without deriving from it at once pleasure and profit.

“ Babbage, on the other hand, applied himself mainly to machin-
ery and manufactures. His so-called ‘ Ninth Bridgewater Treatise’
was pre-eminent even among the best of that singular series ; his
1 Economy of Machines and Manufactures ’ is still a wonder-
fully suggestive work; and his ‘Mechanical Notation’ supplies
us with an insight into the kinematics of all possible combinations
of machinery, which none can have any conception of without
making it a special subject of study. He was led to its invention
by his celebrated attempts to achieve the construction of a differ-
ence-engine, and even of an analytical engine — machines totally
unintelligible, in their conception, to the majority even of those
who are capable of understanding the nature of the work for which
they were designed. Enough was constructed, though it was a
very small part, of the first of these engines to show not only that

4 D

VOL. VII.

54:6 Proceedings of the Royal Society

the device was completely successful, but also to exhibit the ex-
traordinary talent of the inventor in such a light as to convince
scientific men that in his hands the astounding problem of con-
structing the second was capable of solution. A paltry economy
of the Treasury prevented the completion of the first engine, and
made it obvious to Babbage that there was no hope of assistance
from G-overnment to construct the second. Yet it has been allowed
by the best authorities that the money spent on the finished por-
tion of the difference-engine was far more than repaid to the
country by the extraordinary improvement in tools of every kind,
which was required for the new engine, and was at once supplied
by the fertile, inventive brain of Babbage as the work proceeded.

“ No one can read the obviously true story of this miserable
affair, as it appears in the strange autobiography of Babbage — his
‘ Passages from the Life of a Philosopher’ — without a blush for
the short-sightedness of British rulers. Had Babbage been a
Frenchman or Russian, had he even belonged to the then poor
kingdom of Prussia, do we not all feel assured that these grand
conceptions of his would long ere now have been realised as power-
ful agents in the working world, instead of lying dormant, in mould-
ering, worm-eaten plans and sections.

“ Strange the contrast between the careers of these early friends !
They began, indeed, by a grand joint success, for which alone their
memory will always be justly cherished. But while the one,
encouraged, yet never unduly elated, by success, steadily at work,
though not of late years brilliantly, ended a long and happy life,
every day of which had added its share to his scientific services;
the other, enraged by the petty persecutions of men unable to
understand scientific merit, or even its mere pecuniary value,
spending lavishly from his private fortune to be enabled to leave
to some possibly enlightened posterity a complete record of the
working details for the construction of his splendid inventions,
was never understood by his countrymen.

“ But so it has ever been in this country. Herschel’s father was
a German ; so of course we could appreciate him. Babbage was an
Englishman; the only person who took the trouble to understand
his invention was a foreigner, the skilful mathematician Menabrea,
ex-minister of Victor Emmanuel.”

of Edinburgh, Session 1871-72.

547

Observations on the Fresh Waters of Scotland.

Looking around me for some general theme suitable for the sub-
ject of this introductory address, I became oppressed with the
persuasion, that no such subject, worthy of j^our acceptance, had
been left unexhausted by the able men who have lately had to treat
of scientific topics of a general nature in circumstances akin to my
own on the present occasion. I therefore thought I might trust to
your indulgence, ^and substitute for a general address a notice of
some inquiries, which have been carried on from time to time dur-
ing my late occasional autumn holidays, and which promise results
of some interest, illustrating the hydrography of the fresh waters
of Scotland. These inquiries have in several respects been pushed
not so far as to satisfy me completely. But as I may not be able
to carry them through according to my present design, and I hope
that others may be led to interest themselves in also pursuing them,
I beg to submit the results to the Society, such as they are.

The topics I propose now to bring forward, — which are rather
diverse in nature, yet not altogether unconnected with one another,
—are three in number, — First , The composition of the water of
certain lakes and their leading streams in Scotland, and the changes
their waters undergo in the streams which the lakes feed ; Secondly ,
The temperature of these lakes at various depths ; and, Thirdly ,
The action of their waters upon lead.

I shall commence by recalling shortly the geological structure of
our country, by which in a great measure the nature of its waters
is regulated.

In the 7 primitive formations which constitute the 11 Scottish
Highlands” of ordinary speech, — for in correct language many
parts of the so-called “ Lowlands ” are as well entitled to the other
name, — we find that the mountain summits are either pointed or
rounded, but seldom table-topped ; that their spurs are commonly
rather sharply ridged; that their surface abounds in precipices,
crags, loose blocks, rocks, and stones ; and that the valleys between
them, except in the course of our largest rivers, are narrow, gravelly,
or rocky, thinly covered with vegetative soil, and consequently
little fit for plough cultivation. Not infrequently, however, the
spurs or buttresses, instead of being ridgy, are broad and flat,

548 Proceedings of the Royal Society

smoothly covered with fine heather, the favourite breeding-place
for grouse, and tolerably dry, except where small patches of peaty
bog show themselves here and there. This structure is often well
exemplified among the mountains of Grlen-Shee. Again, when the
spurs of a mountain are ridgy, the ridges are sometimes separated
from one another by an upland valley, often very grassy, especially
towards its head or “ corrie,” but likewise apt in many places to be
boggy, and there abounding in peat, and in denuding cuts which
expose the peat to atmospheric influences. Grood examples of such
upland valleys are to be seen on the Cobbler, and on its higher
northern neighbour Ben-Arnen, where they face Arrochar eastward,
and also on Ben-Lomond northward from its peak. Exposed peat
constitutes on the whole no great proportion of the surface of most
mountains in the Highlands.

It follows from this structure, that in most districts of the High-
lands rain and melted snow find little to dissolve in descending the
mountain sides ; and their steepness causes the streams to tarry a
very short time in their descent, and to drain off quickly the excess
of water in flood-time. All these circumstances combine to render
the streams and lakes of the Highlands uncommonly pure in dry
weather, and not materially less so even in heavy floods. Among
the granite ranges, such as in the G-oat-Fell district of Arran, the
streams, such as the Rosa and Sannox, are beautifully clear
and colourless in the highest floods. The temporary water-falls
which then streak the mountain slopes, present to the eye the
purest whiteness; and on filling a glass tumbler from a stream, the
water, after the instant subsidence of a few coarse particles of granite
sand, is seen to be perfectly transparent and free from colour. In
the mica-slate districts of the near G-rampians the streams are
equally pure in dry weather. But after rains they are visibly
brownish, yet so slightly that in a common water-bottle on a dinner-
table the colour may readily escape notice.

During last autumn I had frequent opportunities of examining,
in various circumstances, the water of one of these mica-slate
streamlets, which is used for supplying a villa near Loch-Gfoil-head.
The stream descends the steep eastern slope of <£ The Cruach,” a
hill which land-locks the upper part of Loch Gfoil on its west shore
at a point about a mile and a half from the Head. Although only

549

of Edinburgh , Session 1871-72.

2000 feet high, “ The Cruach ” presents an imposing, rugged,
conical sky-line to one entering Loch Goil from Loch Long. The
east face, precipitous at the summit, is entirely grassy lower down,
unless where broken by other precipices, out-cropping rocks, or
stream-courses, also always rocky. There is little peat to be seen
anywhere, and no agriculture. From various trials around Loch
Goil and Loch Lomond I am satisfied that this streamlet is a fair
type, both in its ordinary state and in its occasional variations, of
most of the streams which tumble into these sheets of water from
the mica-slate mountains around them.

When I examined this water in the end of September, after ten
days of perfectly dry weather, following a heavy twelve-hours’ rain
two days earlier, it was beautifully clear and sparkling. In the
first place, it was entirely free from colour. The absence of colour
was tested conveniently and delicately by means of a glass tube 16
inches long and six-tenths of an inch in diameter, which is nearly
filled with the water to be examined, and is held over, but not
touching, a sheet of white paper in a bright light. For security, a
very fine colourless spring water was always kept at hand for com-
parison in another tube. The slightest coloration is thus seen by
looking perpendicularly down the tube. Or it may be equally recog-
nised by looking at the surface of the water obliquely through the
upper part of the tube from a distance of 18 inches or 2 feet ; for the
colour is thrown up by the paper, and concentrated, as it were, on
the surface of the water, though the long subjacent column, as seen
through the glass, appears colourless. Very few waters, except
that of springs, withstand altogether this test of the presence of
colour.* Mr Dewar has suggested that it admits of being made a
water-chromometer, by employing for comparison,-— distilled water
being used for fixing the zero point, — a solution of some invariable
strength of a permanent per-oxide salt of iron, such as the acetate,
and diluting the solution to uniformity of depth of colour with the
water to be compared. The amount of dilution would denote the
degree of coloration relatively to a fixed standard.

In the second place, this water contained a very small propor-

* This method, devised for the occasion, I have since found to be a mere
variety, but more^convenient, of one proposed some years ago by Ur Letheby,
and adopted by the late Professor Miller.

550 Proceedings of the Royal Society

tion of saline matter. In by far the greater number of streams and
lakes in Scotland, whether Highland or Lowland, the salts met
with are the same, viz., carbonates and sulphates of the three
bases, lime, magnesia, and soda, and the chloride of their metalloids,
calcium, magnesium, and sodium. Of these the chlorides are
usually most abundant, the sulphates least so; and of the bases,
lime is commonly predominant, magnesia the contrary. But fre-
quently in the Highland streams the proportion of all is so small
that most of the ordinary liquid tests scarcely affect them. In
the water now under consideration, for example, magnesia, among
the bases, was not indicated by the alkaline phosphate of ammonia;
nor was sulphuric acid, among the acids, by nitrate of baryta;
even lime was doubtfully indicated by oxalate of ammonia;
chlorine, too, was scarcely indicated by nitrate of silver in a small
test-glass, and required a quantity amounting to six or seven
ounces to yield an undoubted faint mist; and permanganate of
potash did not denote organic matter except faintly. Acetate of
lead, however, by acting on both combined carbonic acid and
organic matter, showed a haze even in a small quantity of the
water ; and so did tincture of potash-soap, by virtue of the decom-
posing influence on it of earthy carbonates and free carbonic acid
together.

After frequent trials I am inclined to think, that for practical
purposes, when organic matter does not require to be taken into
account, we seldom need any other test for ascertaining the relative
purity and usefulness of these waters than the late Professor Clark’s
soap-test. In the present instance this denoted in several trials
only 1*04 degrees of hardness, which is equivalent to that much of
carbonate of lime in an imperial gallon of 70,000 grains of water.
From frequent observation of the effects of this and other liquid
tests, I feel assured that the total solid contents could not have
been more than a 25,000th of the water, and was probably nearer a
30,000th.

In the third place, this composition, viz., little saline and ex-
tremely little organic matter, would lead to the expectation that the
water will corrode lead. And so it does, but not powerfully. A
thin plate of lead, with 4J square inches of surface, weighing 437
rains, was suspended by a lead rod in this water. In twenty-eight

of Edinburgh, Session 1871-72. 551

days it lost only 0'42 grain in weight, and crystals of carbonate of
lead were deposited scantily. In circumstances exactly the same,
distilled water will form carbonate of lead in abundance, and the
loss of lead is 34 grains, or eight times as much.

In times of flood the condition of the water in such streamlets
necessarily undergoes change. But the difference is not so great
as might naturally be expected. In the night of 19th September
last and subsequent morning rain fell steadily at Loch Goil, and
heavily for twelve hours; and, consequently, in the forenoon of
the 20th the streamlet described above was considerably flooded.
The water, seen in bulk, was somewhat brownish ; it was even
faintly brownish in a dining-room water-bottle ; and in a 16-inch
glass tube it appeared yellowish. Nevertheless, it looked well
enough in a glass tumbler, and it was not in the slightest degree
turbid. Its purity, apart from its colour, was very great. No
liquid test for inorganic salts hut one, — not oxalate of ammonia,
not nitrate of silver, not even acetate of lead, had any visible effect.
The soap-test alone exerted any manifest action ; and this indicated
only 0*8 degrees of hardness, which is equivalent to little more
than an 80,000th of carbonate of lime in the water. In corre-
spondence with this condition, lead underwent rapid corrosion in it.
A plate, an inch and a half square, lost in twenty-eight days 3’09
grains in weight, or about -J-f ths of the loss in distilled water in
the same time ; and crystals of carbonate of lead were formed in
abundance.

I examined the same stream on a previous occasion after a furi-
ous tempest and rain-flood on the 24th August last. Much rain
had fallen at Loch Goil previously for several days. But on the
24th it fell in torrents, and for half-an-hour that forenoon like a
tropical deluge. During this period a great extent of grassy turf
was torn off in the upper part of the stream, probably by a water-
spout. In a few minutes the streamlet, already in high flood,
became a muddy tumultuous torrent in which no man could have
stood or lived ; swiftly its muddy waters spread out over the salt
water of Loch Goil ; and then meeting similar floods first at its
own side, and afterwards from the opposite shore, the united muddy
torrents covered the whole upper reach of the loch in less than
half-an-hour to the extent of two miles in length, and three-quarters

552 Proceedings of the Royal Society

of a mile in average breadth. A rainy day followed, and then four
days of uninterrupted dry weather, during which the stream
returned nearly to the same state in volume and appearance as
after the moderate flood already described. There was this differ-
ence, however, even in its composition ; nitrate of silver feebly
indicated chlorides, and acetate of lead also feebly indicated car-
bonates. The difference wss probably owing to a material differ-
ence in the direction and force of the wind. On the former occasion
the wind blew from the north-east, with no great violence, over
about 90 miles of land ; but on the latter occasion it blew with
fury from west to south-west over Loch Fyne at distances varying
from 18 to 15 miles only. In the latter case sea-spray must have
been swept up into the air and carried far by the storm. In the
former less would be raised into the atmosphere, and much would
be deposited again in passing over 90 miles of land. In 1845 I
found chlorides distinctly indicated by a white cloudiness, when
nitrate of silver was added to rain-water collected on the top of
Goat-Fell in Arran, towards the close of a violent four days’ south-
westerly gale, attended with frequent heavy rain, the sea in the
direction of the wind being 12 miles distant, and 2800 feet
below.

The facts now stated, which I have often corroborated by less
minute observation of other streams in the mica-slate district of
Loch Long, Loch Goil, and Loch Lomond, will convey some idea
of the constitution of these waters in three conditions, viz., after
high floods, moderate floods, and dry weather. To complete the
series, it is an object of interest to add their condition after very
prolonged drought. In that case the streamlets, except those fed
by small upland “ tarns,” will come at last to convey only the
water proceeding from springs ; and many not so supplied will dry
up altogether. For the composition of those which continue to
run we may look to the springs themselves which feed them, because
in their then very low state, running chiefly over rocks and stones,
their waters will contract little additional impregnation in their
course downwards. I have examined several springs in the mica-
slate district under consideration. They have generally presented
rather more saline constituents than the streams in their ordinary
state, and invariably no colour appreciable by any of the ocular

of Edinburgh, Session 1871-72. 553

tests I have used as described above. Sometimes their salts are
scanty ; but always they are quite colourless. Their solids appear
to vary from a 16,000th to a 21,000th ; and chlorides and lime-
salts are, for the most part, indicated by their proper liquid tests
rather more distinctly than in the general run of stream waters in
their ordinary state of fulness. Several small springs high on the
hill slopes have yielded these results. Similar in that respect is a
copious spring in G-len Beg, more familiarly known by the name
of Hell’s G-len, about three miles from Loch-Goil-head in the
narrow pass to St Catherine’s on Loch Fyne. This spring, which
gushes in force near the highway and close to the valley stream,
is at all times beautifully limpid, and seems to be little affected
in volume by droughts or floods. Its temperature is 41° when
the air is 64° and more, though its site is not much over 300
feet above the sea-level. Its water is perfectly colourless, but
contains rather more chlorides and earthy salts than the waters
of the streams in their ordinary condition. Another more re-
markable spring of great volume issues from the south flank of
the Cobbler, about 1500 feet perpendicular above the bottom of
Glen Croe, and leaping from rock to rock, joins the Croe about half-
way up the glen. In the very dry season of 1870, its course was the
only one which showed any water among the many which score
the steep slope of the mountain where it overlooks the glen from
the north. I found the water last autumn, after ten days of com-
plete drought, to be perfectly colourless, and to be so free from
saline matter as to be barely affected even by the delicate liquid
tests for chlorine and for lime.

As the various streams now described are the feeders of the
fresh-water lakes, which abound in the mica-slale districts, the
composition of the water of the lakes must be the same with that
of the average water of the streams. The small upland “tarns”
are peaty, owing to the peat which paves and surrounds them.
But the great low-lying lakes present very little solid matter of any
kind in their waters; their scanty salts consist of chlorides, car-
bonates, and sulphates, the bases being lime, soda, and magnesia ;
and the organic colouring matter is so small as to be discoverable
by delicate tests only. In all instances, however, our purest lake

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54 Proceedings of the Royal Society

waters in a mica-slate country are slightly — very slightly
coloured.

The water of Loch Katrine is a well-known and characteristic
example. Some years before the proposal was first entertained to
use it for supplying Glasgow, I found it to contain only a^40, 000th
of solids. When compared with a fine spring water, however, it
now presents in a 16-inch glass tube an appreciable, yet very faint,
yellowness. In hardness it indicates only O’ 65 by the soap-test,
or the equivalent of a 108,000th of carbonate of lime. In corre-
spondence with this great purity it acts powerfully on lead. In
three weeks, a lead plate one inch and a half square, lost 2*53
grains in weight, which is exactly the loss sustained in distilled
water in the same time ; and crystals of carbonate of lead were
formed in profusion.

The water of Loch Lomond is a less familiar instance of the
same kind.

Loch Lomond is twenty miles long, and at its southern or outlet
end, rather more than four miles and a half wide. Its average
elevation is only 22 feet above high-water mark. Eight miles
north of its outlet it suddenly contracts at Ross Point to rather
less than a mile across ; and the northern division of twelve miles
in length varies in breadth between a mile and only a fourth so
much. The lower wide division of the loch, at a short distance
from the shore, varies in depth on the whole from 8 to 12 fathoms ;
and these soundings continue till near Point Ross, where there is
a rapid increase to 32 fathoms. This continues to be the average
in the middle of the lake, till at the next contraction in its width,
opposite Rowardennan Point, where it singularly shallows at once
to 9, 8, and 7 fathoms. A mile further up, after another swell, it
quickly deepens at a new contraction at Rhuda Mor (the Great
Point) to 65 fathoms ; and for five miles further north the sound-
ings first steadily deepen by degrees to 105 fathoms, and then
shelve to 80 opposite Inversnaid ; above which point the lake
becomes both much narrower and greatly less deep (Admiralty
Map). My observations on its waters were made near Tarbet,
which faces the middle of the very deep five-mile reach, where the
soundings in mid-channel are never under 85, and at one place,
opposite Culness farm-house, attain the extreme depth of 100 and

of Edinburgh, Session 1871-72. 555

even 105 fathoms, — the width there being barely three-fourths of a
mile.

The surface water over these great depths is of remarkable
purity. Its saline matter is very scanty, and the colouring organic
matter equally so. Still it has a faint yellowish colour. On Sep-
tember 21st, the second day after heavy rain, incessant for twelve
hours, a white porcelain basin, 4 inches in diameter, disappeared in
18 feet of water; on 11th October, after many days of alternate
rain and drought, in 15 feet; and on 18th November, after four
days of dry weather, in 14 feet, but in feeble sunshine.* After
long drought there is little doubt that the colour would be less, for
it will be seen subsequently, that as the streams pour in fresh sup-
plies of water, there is reason to suppose that these penetrate little
before they run off, and consequently the coloured flood waterfrom the
streams will colour for some time the superficial waters of the lake.

On 18th November, the water taken from the surface of Loch

* This is a good method of ascertaining the relative colour of waters if it be
smployed with due precautions. The trial should be made in sunshine —
when the sheet of water is quite calm— between 9 a.m. and 3 p.m., so that
the sun’s rays may not fall too obliquely on the water, and with the back to
the sun, and, best of all, on the shady side of a boat. If all these conditions
be reversed, vision will penetrate scarcely half so deep as when they are all
observed. In my recent trials I have not found a white object visible at a
greater depth than 21 feet, viz., on Loch Lomond on the 6th May. But,
from observations made many years ago, I am satisfied that, after long dry
weather, some river waters will allow such an object as a white porcelain
basin to be seen at a much greater depth, with due attention to the condi-
tions now mentioned. Having a recollection of seeing it stated long ago,
that the water of the Lake of Geneva was so clear, that objects could be dis-
tinguished in it at a very great depth, I applied to Dr Coindet of Geneva for
precise informatien, for which he referred me to Professor Forel of Lausanne.
To Professor Forel’s kindness I am indebted for the following interesting
facts : — In the spring of 1869, using a white-painted sheet of iron, 15 inches
by 12, he found that the utmost depth at which it could be seen was 13
metres, or 44 feet. The transparency is much affected by locality, and very
much too by season. In winter and spring it is greatest, in summer and
autumn least. In the Bay of Morges, objects may be seen distinctly at the
bottom in winter at a depth from 13^ to 20 feet, while in summer they are
barely visible through 7 feet. This difference is greatest near the shore, at
the bottom of bays, and near villages or towns. It is least around promon-
tories, far from land, and at a distance from human habitations. In autumn
the change from obscurity to transparency usually takes place early in October,
and is completed in three days ; in summer, the reverse change takes place

556 Proceedings of the Royal Society

Lomond over a depth of 102 fathoms, or 612 feet, presented in a
16-inch tube as exactly as possible the same degree of faint yellow-
ish hue as the water of Loch Katrine. Evaporated to dryness, it
left a pale, greyish film, amounting to a 33,000th of the water. It
had only O' 70 degrees of hardness by Clark’s soap- test. Of the
other liquid reagents, acetate of lead alone caused at once a
slight haze; oxalate of ammonia and nitrate of silver had at
first no effect, but in time caused an extremely faint haziness ;
nitrate of baryta, and ammoniacal phosphate of soda had no effect
at all. When the water was much concentrated, however, sul-
phates, carbonates, and chlorides, as well as the bases, lime, soda,
and magnesia, were clearly indicated by their ordinary tests, exactly
as in the springs and streams of the adjacent country.

I examined also the water taken at the same place from the
bottom at the depth of 102 fathoms. This differed in some
respects from the surface water directly above it. It contained
the same salts. Bat nitrate of silver indicated rather less chlo-
rides; acetate of lead more carbonates; the soap-test denoted a
trifling additional hardness, namely 0*74 degrees, and the total
solids amounted to a 28,000th instead of a 33,000th. Farther,

about the beginning of May, and is more gradual. By filtering a large
quantity of turbid water, he found the obscuring cause to be a collection of
amorphous dust, living and dead diatoms, vegetable debris, a few living
infusoria and crustaceans, and debris of insect larvae and microscopic Crus-
tacea. They naturally collect slowly in the summer ; but the first cold of
approaching winter sends them quickly down with the water as it cools.

In the case of Loch Lomond, these inquiries of Professor Forel would lead
one to expect little influence from organic or inorganic dust in obscuring
water where it is so deep as at the places chosen for my observations. Accord-
ingly, the surface water was remarkably free from turbidity, or deposit on
standing at rest. But the yellowish colour, faint though it be, constitutes a
no less powerful obstruction to the penetration of light. The depth of
colour, and consequently the transparency, vary at different periods, not so
much with the seasons as with the times of floods. In advanced summer
and in autumn, the floods increase the colour decidedly, and lessen for a
time transparency. But my single observation on 6th May, when I found
the transparency greatest of all a few days after heavy north-east rain, raises
a question whether floods have the same effect in spring or the end of winter.
A probable reason for the contrary may be, that the soluble matters of the
peat-fields and stream-courses, developed by heat, growth, and atmospheric
action in summer and autumn, are much exhausted by the frequent winter
floods before the arrival of the floods of spring.

of Edinburgh, Session 1871-72.

557

although the colour is the same at the bottom as at the surface,
and very slight, it is distinctly deeper in shade when seen in a
16-inch tube; and the film left on evaporation, instead of being
light grey, is of a rather deep yellowish -brown tint.

[ May 16 th, 1872. — As supplementary to these observations, I
may here add the following, which I had an opportunity of mak-
ing on the 10th of last month : — During the five winter months
intermediate between my previous visit in November, the winter
had been unusually open. Until the middle of March, indeed, there
had been very little frost, and no severe cold. During the latter
half of March frosty northerly winds prevailed, but without any very
great fall of the thermometer. In the last days of March and first
three days of April, snow fell frequently, covering the Highland
mountains to their bases. Ben Lomond and the adjacent Arrochar
mountains shared in the change. On 4th April the wind veered
to west and south-west; bright sunshine and warmth soon dis-
solved most of the snow, and this weather continued, with scarcely
any rain, till after my visit. The ground around Loch Lomond
was consequently dry, the hill streams very low, and the streamlets
dried up, or nearly so.

The surface water corresponded with these antecedent circum-
stances. Frequent winter floods had swept from the mountains
most of the soluble matter from their beds ; and for some days the
streams, reduced to rills, would have little remaining to remove
from their stony channels. Hence the surface water was of great
purity. A white porcelain basin, two inches in diameter, was
visible at the depth of 16 feet, although a light breeze rippled the
surface. In a 16-inch tube the yellowish colour was extremely
faint. The solid contents amounted to only a 32,000th of the water,
and lost a fourth by incineration.* Nitrate of silver occasioned
in the water only the faintest haze, and oxalate of ammonia did
not visibly affect it. The soap-test indicated 0-49 of hardness,
which is equivalent to a 145,000th of carbonate of lime. In accord-
ance with its purity this water acted powerfully on lead. Action
commenced at once, loose crystals of carbonate of lead were formed

* 26,250 grains left 0'83 at 300° F., and 0 62 after incineration.

558

Proceedings of the Royal Society

in abundance, and in twenty-three days a plate an inch and a half
square lost I'll grain in weight.

The bottom water, taken where the depth was 594 feet, differed
materially in these characters. The cistern brought up some finely
comminuted peat-like matter, in which the microscope detected a
profusion of various diatoms, and two species of active microcosmic
animals. The colour of the water was deeper than that of the sur-
face, and became the same not till the addition of half its volume of
colourless distilled water. Nitrate of silver produced an immedi-
ate scanty precipitate, oxalate of ammonia scarcely any effect.
The soap-test indicated T015 of hardness, which is the equivalent
of a 69,000th of carbonate of lime. The solids amounted to a
16,000th of the water, and lost a third by incineration.* When the
water was evaporated to a tenth of its volume, nitrate of silver
indicated chlorides in abundance, nitrate of baryta sulphates feebly,
oxalate of ammonia lime sparingly, and phosphate of ammonia
magnesia faintly. The original water had no action at all on
lead. The lead plate became dull in a few hours, but no other
change ensued which the eye could discover; and in twenty-
three days the plate, which originally weighed 405*73 grains,
weighed 405*74 grains.

These differences between the bottom and surface waters were so
great, that it became desirable to repeat the examination, which I
was able to do on the 6th of the present month. A good deal of
easterly rain had fallen for some days until two days before this
visit ; but the hill streams had already become low. The waters
were collected near the same place as before, — the bottom water
from a depth of 94 fathoms, or 564 feet. The cistern brought up,
as formerly, some peaty-like matter, which speedily subsided, and
was promptly removed by decantation. Both specimens of water
were very pure. But the bottom water was more affected than the
surface water both by nitrate of silver and by oxalate of ammonia,
and its colour was decidedly deeper, so that fully more than half its
volume of colourless distilled water required to be added, to produce
the feeble tint of the water from the surface.f The peaty matter

* 13,125 grains left 0*82 grains at 300, and 0-55 after incineration.

t The cistern which brought up the water was new, made of copper, and
urnished, for valves, with spherical copper balls resting on hemispherical beds,

559

of Edinburgh, Session 1871-72.

was found by microscopical examination to abound in diatoms and
skeleton tissues of graminaceous and other vegetables. The bottom
water contained a 25,000th of solids.

It has been proposed, in projects for introducing lake water into
a town for domestic uses, to draw the water from a considerable
depth, instead of from the surface, under the supposition that the
deep water is the purest. The preceding observations show that
this is a mistake, at least in the case of some lakes. On every occa-
sion I have found the water of Loch Lomond somewhat more saline
in its deepest parts than at the surface immediately above, and
decidedly more coloured. The cause is easily understood, if the
preceding chemical examination be taken in connection with the
observations to be subsequently made on the temperature of Loch
Lomond at various depths. For the results of both inquiries con-
cur in indicating that, in the very deep parts, there is a vast body
of still water which undergoes little, or, perhaps, no change or
movement, and which, therefore, at the bottom, will become impreg-
nated with whatever is soluble in the bed on which it rests.

Let me now change the scene to the hills and the waters of the
Lowlands.

In the course of late notorious proceedings in this city for obtain-
ing a more abundant water supply, it was stated by good chemical
authorities that the water of St Mary’s Loch in Selkirkshire,
although of remarkable purity, does not exert upon metallic lead
that eroding action which is a singular property of all pure waters
previously subjected to trial. This statement was so opposed to
the principles regulating the action of waters upon lead, as pro-
pounded by me so long ago as 1829, and also to the facts brought
forward both then and in a paper read to this Society in 1842,
that I resolved to investigate the question for myself.

This undertaking, in spite of my strong repugnance and steady
refusal to be involved on either side of the Edinburgh water-con-
troversy, led indirectly to my being compelled to concern myself
with it as a parliamentary witness. But let it be clearly understood

and it was never used except for these experiments. The cistern was emptied
at once into stoppered bottles on being drawn into the boat, and was carefully
dried in a current of air with the valves open.

560 Proceedings of the Royal Society

that my inquiries were undertaken quite irrespective of all contro-
versial proceedings, parliamentary or otherwise, and for a purely
scientific object — in which point of view alone I shall now proceed
to state them. In the present place, I shall notice the lead ques-
tion slightly, reserving that inquiry for another head of my obser-
vations. At present I have to say a few words of other matters
which arose incidentally before me in the course of my inquiries.

St Mary's Loch is a lonely lake, retired among the hills of Sel-
kirkshire, 37 miles south from Edinburgh. It is three miles long,
and about half a mile in width at its broadest parts ; but it may be
said to be prolonged nearly another mile by the Loch of the Lowes
above it, which is separated only by a space of 150 yards, through
which the upper loch is joined to St Mary’s Loch by a small stream.
The lake in most parts shelves rapidly to a depth of 30 or 40 feet ;
in various parts it is said to deepen to 80, 100, and even 150 feet ;
and at a place pointed out to me as the deepest, I found 144 feet
of water. It discharges itself in a goodly body of water, by a broad,
shallow outlet to constitute the Yarrow Water. This joins the
Ettrick a mile and a quarter above Selkirk ; and the united waters,
under the name of Ettrick, are poured, after a course of about four
miles more, into the river Tweed. The Yarrow runs over 11 miles
in a right line, but 14 miles by its windings, in a very stony chan-
nel, obviously of great width in floods.

The country of the Yarrow and St Mary’s Loch is almost entirely
pastoral, except where covered at the lower end of the stream by
the beautiful woods of Bowhill, Philipshaugh, Hangingshaw, and
other country seats. Around the lake itself the land may be de-
scribed as consisting purely of pastoral hills, the attempts at arable
culture being as yet very limited, and wood hitherto a scanty and
stunted ornament. The level of the lake is almost exactly 800
feet above the sea. It is bordered everywhere, and abruptly, by
hills rising from 750 to 1000 feet above it, showing long sky-lines,
and steep slopes which present no rocks, no woods, nothing but
smooth grass, unbroken save where scored by a few stream courses,
mostly waterless in dry weather. But the Meggat Water is a
considerable permanent stream, seven miles in direct length, which
falls into St Mary’s Loch about its middle line on the north ; and
the Little Yarrow, three miles in direct length, feeds the Loch of

561

of Edinburgh, Session 1871-72.

the Lowes at its upper end. These streams, though short, are
Voluminous, because constantly supplied by numberless hill tribu-
taries.

A traveller on the loch-side sees no peat anywhere. The dis-
trict was therefore pronounced by recent one-eyed visitors to be
free from peat. An inquisitive observer might have suspected the
reverse from one of the highest surrounding hills being called
Peat-Law ; and on the high sky-line of another, a telescope would
have betrayed to him a very suspicious circumstance in a crowd of
little peat-stacks. Any one, not content with creeping along the
bottom of valleys, but familiar with the summits of the mountains
of the Scottish Lowlands, would then have known that the sky-
line seen from the loch-side is not, — as it very often is in the
primitive mountains of the Highlands, — a mere ridge, but forms
the edge of a great table-top, which, in most cases, is chiefly com-
posed of peat. In point of fact Professor G-eikie has shown last
summer, from the Government Geological Survey, that a vast pro-
portion of the hill-tops in the St Mary’s district consists of peat
table-lands.

The consequences which flow from this structure of the country
are peculiar. In dry weather the high peaty summits of the hills
will cease to supply moisture enough to drain into the streamlets
which score their sides. These will then convey to the lake chiefly
the drainage of the grassy slopes, and the produce of the scanty
springs in the lower regions. But when a rain-flood sets in, the
peat, whether previously dry or moist, will send down a profusion
of peaty water. Had the Yarrow flowed as a river through the
vale at St Mary’s, the peaty flood would have been swept quickly
down towards the sea ; and in two or three days the waters would
have recovered from their peaty impregnation. But the two lochs,
with a superficial area of two square miles, store up the peaty
water, and dole it out, like a compensation pond, for many days,
until the arrival of a fresh flood to renew it. An embankment at
the outlet, to increase the storage, would protract the outflow,
and postpone still further the recovery of the water from impurity.

These facts and views could only occur to one familiar with the
district, or going thither to study it for a practical object. When
I first went to St Mary’s Loch on the 12th and 13th June last, I

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562 Proceedings of the Royal Society

had no further acquaintance with the hill structure around than
that of an angler thirty years ago, when I probably looked more
at what came out of the loch than at anything else concerning
it. I consequently went prepossessed in its favour by the glowing
account given of its extreme purity by its admirers. My surprise,
therefore, was not small when my very first observation showed
that its water was yellow. My visit was made in circumstances
highly favourable to its condition, in splendid sunshine, being the
last two days of six weeks of extraordinarily dry weather, broken
only by a few light showers, sufficient to freshen the grass, and
little more. But I found that my white porcelain basin became at
once yellowish when dropped into the lake, acquired a lively amber
hue at the depth of 3 feet, and disappeared entirely at 12 feet,
while the sun shone brightly on the spot. I remembered well,
however, having once distinguished small pebbles in the Dumfries-
shire Esk through 16 feet of water, when spearing salmon in a still
pool, and on another occasion through 21 feet in a pool below the
Bracklinn Falls, near Callander. I afterwards tested the colour of
the loch water on a small scale, and showed it satisfactorily to
many, by comparing it with the water of Edinburgh of the same
date in two narrow glass jars, 20 inches in height, with a circular
disc of white porcelain at the bottom. The porcelain was of un-
stained whiteness as seen through the Edinburgh water, but of a
lively amber tint when looked at through the water of St Mary’s
Loch. The difference was not less marked in the narrow 16-inch
tubes. Even in dining-table water-bottles, placed on a white table-
cloth, the colour of the loch water was such as to make it evident,
that certainly nobody would drink it who could get the other. I
may add that, when I revisited the loch on 8th September, also
in bright sunshine, I found that my porcelain basin disappeared
entirely in eight feet of water ; and, nevertheless, there had been
previously ten continuous days of absolutely dry weather.

On the 12th and 13th June, I saw in the water no want of the
water-fleas, which excited so much interest and heat in the late
controversy. It may create additional interest with some to be
told that three months later they were decidedly bigger, busier,
and altogether more deserving of their vernacular name.

Before speaking of the chemical composition of the water, let

563

of Edinburgh, Session 1871-72.

me finish what may be said of the physical characters of the loch,
by noticing one not yet adverted to. Visitors in the dry season,
when the waters of the lake are somewhat shrunk, have been
much struck with the beauty of its border, — its “ silver strand.”
This is owing to a uniform beach of crowded, chiefly angular, or
partially rounded, light-grey coloured stones. The colour, however,
is not their own, but belongs to a generally dense covering of a dried-
up matter, composed of a multitude of various diatoms entangled in
the delicate lines of a finely fibrous conferva. In the fresh state
this investing matter is dark greenish-brown, close, and slimy. The
stones, therefore, give the loch, even in its shallows, a disagreeable,
dark, deep appearance, abruptly defined by the water’s edge. But
all of them out of water acquire, in drying, a light grey or greyish-
white hue. Every scientific visitor has observed, and some have
carefully examined, these stones and their covering. But, so far
as I am aware, no one has noted their full significance ; of which
more presently, when I come to speak of the Yarrow.

The water of the loch, though it is coloured, is a pure water, —
in the sense that it contains very little solid matter in solution.
It has been repeatedly analysed, and found to contain rather less
than a 20,000th part of total solids. Mr Dewar, the latest analyst,
I believe, found a 22,440th, — of which the inorganic salts consti-
tuted two-thirds [a 37,000th], and the organic matter one-third [a
55,500th]. The chief inorganic salts are the same as in the mica-
slate streams and lochs of the Highlands, and much in the same
proportion to one another. The hardness of the water was found
by Mr Dewar to be 1*30 degrees by the soap-test, or nearly twice
that of Loch Lomond surface water. Other chemists have found
more solids, some less. My own results, with water collected on
13th June, show more saline, and rather less organic, matter ;
which is no more than might have been anticipated from the long
antecedent very dry weather. I found the solid contents dried at
about 300° F. to be a 15,000th of the water ; one-fourth of this
was destroyed by slow incineration at a low red heat; and the hard-
ness was 2*0 degrees of Clark’s soap-test scale, — which is about the
fourth part of that of the present Edinburgh water supply. Water
collected three months later, on 8th September, after ten days of
complete drought, which, after a few days of showery weather,

564 Proceedings of the Royal Society

followed the very heavy floods of 24th August, contained more
colouring matter, exhibited less action with the ordinary liquid
tests for the inorganic salts, and had a hardness of L4 degree
only. I have no doubt that this water corresponded in all respects
very closely with the specimen examined by Mr Dewar.

Thus, it appears, that the waters of St Mary’s Loch — which,
with the exception perhaps of those in the primitive districts of Kirk-
cudbrightshire and Wigtownshire, may be taken as a type of the
lowland lochs at large — differ from the waters of the Highland
lakes in containing more solid matter, a little more saline matter,
and decidedly more colouring organic matter, and in being consi-
derably harder, though really belonging to the “ soft ” waters too.
Another difference is that they vary more with the season, the salts
becoming rather more abundant in long dry weather, and the
colouring matter clearly abounding more during and after floods.
Finally, a remarkable difference in property, to be discussed by-
and-by, is, that unlike the waters of the Highland lochs, that of
St Mary’s Loch does not erode lead. But first let me say a word
or two about the Yarrow Water, by which this lake discharges
itself.

The Yarrow, before uniting with the Ettrick, wdnds for 14 miles
through a narrow, bare, chiefly pastoral vale, bounded by gently
sloping hills. It is joined in this course by twenty-two tributaries,
of which only three or four are considerable streamlets, the others
being mostly rills, apt to be dried up, or nearly so, in dry weather.
The waters of the chief tributaries contain in the dry season more
salts than the main stream itself, but very much less colouring
matter, two of them, indeed, none at all appreciable even in a 16-
inch tube. The channel of the Yarrow is wide and stony, and the
stream shallow, and for the most part turbulent. In the 14 miles
it falls 220 feet. Its banks present very few human habitations.

These circumstances are favourable to the gradual diminution of
organic impregnations, partly through the decomposing influence
of fresh earthy salts added here and there by little tributaries,
partly by the slow oxidation, to which Liebig gave the name of
“ Eremacausis,” — “ quiet” or “ slow burning.” My attention was
turned very long ago, before the publication of Liebig’s views on
this subject, to the rapidity with which, by natural processes,

565

of Edinburgh, Session 1871-72.

streams rid themselves of the unnatural impurities introduced into
them by sewage, and by some of the manufactures. But I am not
aware that the process of clearing has been watched with care in
circumstances altogether natural. It occurred to me, at anyrate,
that we have in the Yarrow a most favourable opportunity for
tracing this process in the case of a natural water of a remarkable
kind, under the operation of natural causes alone. On the 8th of
September, therefore, I examined the course of the Yarrow with
some attention.

In its descent from St Mary’s Loch, it is first joined by two
unimportant rills, at that time nearly dried up by ten days of pre-
vious drought. A mile and a half below its outlet, it receives
from the north its largest tributary, the Douglas Burn, which
drains a very hilly country about five miles and a half long and
four miles wide. This stream, indeed, was at the time a small rill,
compared with the strong body of water in the Yarrow. But it
was interesting in this respect, that its water, containing more
saline matter than the main stream, and possessing the hardness
of 4*90 degrees, presented no colour at all, even when examined in
a 16-inch tube. This last fact is remarkable, because the Douglas
Bum comes very much from peat-topped hills, so that either the
peaty water of floods soon runs out in dry weather, and spring-
water is alone left, or the water clears itself by eremacausis, or in
its upper course in the way in which purification seems to be
brought about in the Yarrow.

For, when I came to examine the Yarrow immediately above
the junction of the Douglas Burn, I found to my surprise that the
colour, which at the outlet was such as to render a porcelain basin
invisible when sunk 8 feet only, was already so much reduced, in
the course of a mile and a half, as to approach the faint hue of the
waters of Loch Katrine and Loch Lomond. There was also a
slight increase of salts, as shown by the ordinary liquid tests, and
also by the hardness of the water having increased from 1*4 to 2*40
degrees.

A mile lower down another principal tributary, but inferior to
the Douglas Burn, falls into the Yarrow on the right, the Altrieve
Burn, which, however, I had not time enough to examine. Two
miles further on a similar streamlet joins from the right, the

566 Proceedings of the Royal Society

Sundkope, which, too, I could not examine. Other trifling rills,
almost dried up, join between the Douglas Burn and Yarrow kirk,
seven miles from the outlet of the lake. This point was a good
one for studying the joint eifect of atmospheric exposure through
constant agitation, and of the influx of several brooks, all probably
containing more salts than the main stream itself. Here I found
that the soap-test indicated a further increase of hardness to 3-0
degrees, and that the yellow colour in a 16-inch tube was still
further reduced, but not much.

In the next three miles and a half there are six little tributaries,
all at the time of my visit insignificant, and some quite dried up,
till we arrive at the Lewenshope Burn, which drains from the
north a considerable stretch of the Minchmoor range, described to
me as generally stony hills, without much peat. This water pos-
sessed 6*5 degrees of hardness, and so little colour that it was
barely appreciable in a 16-inch tube. In the remainder of its
course the Yarrow is joined by five more rills, either almost dried
up when I was there, or appropriated in a great measure for the
supply of mansions. Four hundred yards above its junction with
the Ettrick, I found its water to possess, as at Yarrow kirk, seven
miles higher up, 3'0 degrees of hardness, so that the comparatively
saline water of the Lewenshope had not materially increased the
salts of the Yarrow. But the colour was still more reduced, so as
to be very faint indeed, equally so with the colour of the water of
Loch Lomond.

Thus the principal loss of colour takes place in the first mile
and a half of the river’s course ; but there was also a very appreci-
able additional improvement in the longer course below, and the
final result was a nearly total removal of colour.

To what is this change owing? Does it depend entirely on the
intermixture of earthy salts from the tributaries, and on erema-
causis? I apprehend that these causes will scarcely account for
the great change effected in the first mile and a half. There may
even be a doubt whether peat-extract is particularly subject to the
process of eremacausis. It is well known to be a preservative of
organic matters, which it could scarcely be were it very subject to
decay itself ; and I find that a solution of it without any saline
matter, has undergone no change in a warm room, in a half-filled

of Edinburgh, Session 1871-72. 567

bottle, during six months. But there is a more potent agent at
work in the Yarrow. The dark, green-coated stones of the loch,
with all their characters unreduced, pave the entire channel of the
stream as low at least as the confluence of the Douglas Burn, and,
with a less abundant covering, so low at least as Yarrow kirk,
seven miles from the outlet of the lake. But there is nothing of
the kind in the chief tributaries. At the junction, for example,
of the Douglas Burn, there is an abrupt line of demarcation be-
tween the dark green, slippery stones of the Yarrow, and the stones
of the tributary, which are as naked as if they had been scrubbed
clean with a brush. I do not well see how to escape the conclu-
sion, that the confervse and diatoms of the stones live at the cost
of the peaty matter from the loch, — that peat-extract is their food
and is consumed by them. This is a ready explanation of their
excessive growth on the stones of the loch. The want of such
food equally explains the comparative absence of them from the
stony banks of Loch Lomond, and the stony channels of all the
streams of the adjacent mica-slate district.* Indeed, in the
opposite circumstance* — in some mountain tarns of the district,
resting, as they may, on peat, and surrounded by it— the slippery,
dark green, stony bottom is no uncommon occurrence.

If these views be correct, it is easy to appreciate both the un-
favourable significance in a lake of a dark-green bottom of stones,
densely covered with confervas and diatoms, and likewise their
value in a running stream ; and it may be well also not to let the
imagination run away luxuriating in every u silver strand” that
meets the eye.

The Temperature of the Deep Fresh-water Lakes of this country
has no connection with the preceding inquiries, further than that
my observations on the subject arose incidentally while I was
carrying on the inquiries in question. The results I have obtained
may interest the cultivator of physical geography, if I am right

* It has been said that stones covered with green confervse and other
diatoms do occur in Loch-Lomond. They do in bays and other shallows ;
but the covering is very thin ; and the line of such stones is narrow. Where
deep water is near there are none at the edge, and where they do occur the
dry stones close to the edge appear quite clean.

568 Proceedings of the Royal Society

in supposing that no prior observations of the kind have been
made on our deep fresh waters. [See, however, p. 574.]

In the course of the discussion of the St Mary’s Loch water-
supply scheme, opposite opinions were expressed as to the relative
advantage of drawing the water from the surface of the lake, or
from a considerable depth; and weighty arguments, of a specula-
tive nature, were advanced on both sides of the question. It
occurred to me, therefore, to consider what becomes of the deep
water. Does it escape as that of the surface must do ? And if so,
How ? It appeared to me that during a winter of such protracted
cold as that of 1870-71, the water at the bottom would probably
acquire so low a temperature, that it must long remain there. For
it can only rise again, either by its temperature falling below 39°*5,
when its density decreases instead of continuing to increase, or by
being heated by the heat of the earth beneath ; and it is unlikely
that the temperature of the entire water of a deep lake will fall
lower than 390,5, or indeed so low, in this latitude, and the heat
derived from the earth, in our latitude at the elevation of 800 feet
above the sea, must be inconsiderable. It is well known that the
bottom cannot be heated by conduction from the summer heat of
the atmosphere above, as in the case of a solid substance ;
and the effect of the penetration of the sun’s rays, by which
the water is heated to a certain depth, cannot descend very low
in a lake, the water of which is, like that of St Mary’s Loch,
so coloured as to render a very white object invisible at the depth
of 8 or 12 feet. The conclusion would be that the water at the
bottom of the deep parts of the lake, in the absence of strong
springs — of the existence of which there is neither proof nor pro-
bability— will remain at the bottom for want of a current during
the whole warm season, and perhaps longer.

When I was first at St Mary’s Loch on 12th and 13th June, I
had no suitable thermometer for taking observation of deep tem-
peratures. But Mr Dewar kindly undertook to make the necessary
trial a few days later in the same month. With a Six’s thermometer,
whose graduation was subsequently tested and found correct, he ascer-
tained that in 150 feet soundings, the temperature, being 56 at
the surface, was 46° at the bottom. When I revisited St Mary’s
Loch on 8th September, nearly three months afterwards, the inter-

569

of Edinburgh, Session 1871-72.

mediate weather having been generally fine, I found, with the
same thermometer, in 96 feet of water, near the head of the
lake, 56° at the surface and 54° at the bottom ; and in 144
feet of water, in the middle of the loch, exactly opposite the
17th milestone from Selkirk, I obtained 55° at the surface and
47° at the bottom. During three of the warmest months of last
warm season, the heat of the earth, or the sun’s rays, had heated
the water at the bottom by one degree of Fahrenheit only. I do
not well see how that water can ever rise from such a depth, unless
its temperature during the winter should fall below 39°‘5, which
is not probable.

I regret I did not take successive observations at several depths
in order to fix the upper limit of the cold substratum of water. My
time was short, for my main object on that occasion was the changes
undergone by the river Yarrow, and I contemplated a chain of
observations in more favourable circumstances at Loch Lomond.
I went to Loch Lomond on four occasions for the purpose, viz., on
September 14th, September 21st, October 11th and 12th, and
November 18th. As accurate observations were made only on the
two last occasions, I shall refer to the others only incidentally.

On 11th October, at 3 p.m., the atmospheric temperature on land
being 48°, and that of the surface water everywhere over deep sound-
ings 52°, I found in 103 fathoms of water opposite Culness, with a
Six’s thermometer by Casella, which, though not specially protected
against high pressure, was believed to be proof against such pres-
sures as it was to be subjected to, that a temperature of 43° was
indicated at 200 feet, and 410,8 steadily at 400, 500, and 618 feet.
Next forenoon at 11, 1 repeated my observations about a mile lower
down opposite Tarbet in 87 fathoms. The air was singularly still,
the atmospheric temperature on land 44°, and that of the loch on
the surface 52°, exactly as on the previous day. The following
successive temperatures were obtained at various depths : —

Surface, .

. 52o,0

150 feet, .

. 44°-5

25 feet, .

. 51°-5

200 „ . .

. 43°-0

50 „ .

. • 50°-2

o

o

CO

. 42° -0

75 „ . .

. 50°-0

400 „ . .

. 42°-0

100 „ . .

. 49° 5

518 ,, bottom,

. 42°*0

4 o

VOL. VII.

570 Proceedings of the Boyal Society

It will be observed that these temperatures correspond almost
exactly with such observations of the previous day as were made a
mile and a half further north at the same depths, where the sound-
ings were 618 fathoms. The bottom temperatures also corre-
sponded with what I had observed with a different thermometer
on September 21st, three weeks earlier. Using a cistern with
proper valves, constructed by Mr Adie, for bringing up 96 ounces
of water from the bottom, with a simple thermometer in it, I found
that on September 21st, when the surface temperature was 54°, and
also on October 11th, when it was 52°, the thermometer, on the
instrument arriving at the surface, indicated 44° in the water
brought up from the bottom, both in 87 and 103 fathoms of water.
As the heating of the cistern in ascending must have been very
nearly or altogether the same on both occasions, it follows that the
corrected temperature at the bottom, as on 11th October, was 42°
on 21st September.

On 18th November I found it to be also the same. Cold weather
had set in for a week before. The air was frosty, the ground dry
and hard, the atmosphere very clear and perfectly still. Near the
lower end of the loch, where the highway first touches it, the air
temperature was 33° at half-past eleven. At Tarbet at one p.m., it
was on land, but at the water’s edge, 37° ; in the boat, in the middle
of the loch, two feet above its surface, 42°; and in surface water,
over 610' feet soundings, 46°. At the bottom, by a Casella’s thermo-
meter, protected against pressure, and corresponding exactly in its
graduation with the unprotected one previously used, the bottom
temperature was again 42°. My design to make at the same time
another complete series of observations, was prevented by unex-
pected delays shortening my time very much, so that I had to con-
fine myself to a single additional observation, for determining more
nearly the upper limit of the cold substratum of water. At 250
feet I obtained a temperature of 420,25, and consequently the
upper limit of the water at 42° must have been as nearly as pos-
sible at 270 feet in 610 feet soundings.

Before drawing confident deductions from these observations,
they require to be repeated at other seasons. But in the
meanwhile it may be well to see what are likely to be the
results,

571

of Edinburgh, Session 1871-72.

It is plain, in the first place, that in a deep lake in this
latitude, there is a very gradual and slight increase of cold in
the warm season for the first hundred feet, viz., by 20,5 only,
then a sudden descent by 5°'0 in the next 50 feet only; next
another slow descent by 2°‘5 in 150 feet ; and finally, below
that a great substratum of 250 feet of water, and at a deeper
spot of no less than 350 feet, at the uniform temperature of 42°, or
a little less. Next, at Loch Lomond no change took place in the
temperature of the bottom water during two months of unusual
warmth for the months of September and October, and no change
at 300 feet from the surface during five weeks prior to the middle
of November.

It seems certain that the temperature of the great substratum
of cold water cannot be raised after the middle of November, when
the cold season has fairly set in. Whether it is to be lowered
during winter, or whether the substratum, without becoming colder,
will merely have its upper level raised, is a question to be settled
by observation at an early period of next spring.

In the meanwhile, abstracting the highly improbable existence
of strong springs at the great depths I have mentioned, it does not
appear how this vast cold substratum could have been moved dur-
ing last summer and autumn. Neither does it appear how it can
be moved during the winter, unless the equally great stratum above
it acquire a lower temperature than 42°, and so take its place; for
the uniformity of the bottom temperature between 21st September
and 18th November, when no additional cold could descend through
the warmer stratum above, is sufficient proof that the influence of
the heat of the earth beneath is too feeble in this latitude to make
itself sensibly felt by motion of the water.

Thus there is a probability, that when water once descends to so
great a depth as the bottom of our deep lakes, it cannot ascend
again except under rare and extraordinary circumstances. If this
view be correct, the movement of the waters of a deep lake towards
its outlet for escape, must be confined very much to the warm
water at its surface, or to no great depth, and, therefore, mainly to
the waters which are constantly supplied on all sides by its feeding
streams. This must be the case in summer and in autumn ; it may
be the case in winter also

572

Proceedings of the Royal Society

[May 18, 1872. — Circumstances having delayed the publication
of the Society’s Proceedings, I take this opportunity of adding the
result of recent and conclusive observations. These were made on
10th April and 6th May, as near as I could to the place of the
observations described above.

April 10. — The weather on this occasion was very fine and
favourable for my purpose. During the whole winter period after
November 18th, the date of the last observations, the weather
had been remarkably open. The mean temperature of the atmo-
sphere for the five intervening months, as kindly calculated for me
by Mr Buchan, Secretary of the Meteorological Society, from
observations at Balloch Castle, at the southern end of the loch,
was 10,4 higher than the average for the same months for thirteen
previous years.* Consequently, the same influence of the winter
season on the temperature of deep waters cannot be expected as in
ordinary winters, or in a hard winter, such as the preceding one of
1870-71.

When I made my observations, about 3 p.m. on 10th April, the
temperature of the air on land was 55° ; and on the water, one mile
from the shore whence the wind blew, it was 53° in the boat,
scarcely 2 feet above the surface of the lake. The following tem-
peratures were obtained, at various depths in the same place : —

Surface, .

43°-0

150 feet, .

42°T

50 feet, .

42°*6

200 „ . .

42°-0

75 „ .

42°2

594 ,, bottom,

42°*0

100 „ .

42°-2

These observations were made with Casella’s protected thermo-
meter. The thermometer in Adie’s cistern, for bringing up water
from the bottom, also stood at 42° when brought up to the surface,
the temperature of the upper warmer stratum being much too low
to affect the cistern in its passage.

May 6. — Between 10th April and this date the weather varied

* In tbe course of his calculations Mr Buchan arrived at the interesting
fact that the average mean temperature of the air during the six cold
months of these years, at the level of the lake’s surface, was 41°*7 from No-
vember 18 to April 10, cr very nearly that of the deep substratum. — See sub-
sequently, for his observat. ons , the later Proceedings of the Society.

573

of Edinburgh, Session 1871-72.
as to warmth ; but there was a large proportion of sunshine, and

little rain, till three days before, when there was

a heavy fall

with an easterly wind.

The temperature on land,

within fifty

yards of the water, was
made at 2 p.m. : —

55°.

The following observations were

Surface, .

44° -5

150 feet, .

42°-7

25 feet, .

43°-7

175 „ . .

42°-6

50 „ .

43°*5

200 „ .

42°-5

75 „ . .

43°-2

250 „ . .

42°*4

100 „ . .

43°T

300 „ .

42°T

125 „ . .

42°-8

574 l . .

42°*1

The thermometer in Adie’s cistern, when brought up full of
water from the bottom, but raised rather deliberately, stood at420,5.

It appears, from these and the preceding observations, that in
the deep parts of Loch Lomond there is a substratum of water of
several hundred feet, which, between the end of September last
and 10th April, has been steadily of the temperature of 42° ; and
that during last winter no other change has taken place, in relation
to temperature in or near it, than that the level of the cold sub-
stratum rose in the interval between 70 and 100 feet. A winter,
materially colder than the last unusually mild one, would at least
raise that level still nearer the surface. Whether it may reduce
the temperature still lower than 42°, is a question which remains
to be decided by future observation. It is still also a matter for
observation, whether the temperature of the substratum may not
rise a little during summer. For it may be reasonably said, that
the unusually hard winter of 1870-71 might have lowered the tem-
perature of the substratum in April of last year below that observed
in April of this year after a very open winter, and, consequently,
under 42°, which was the temperature observed in October. But the
difference, if any, cannot be considerable ; for it can only arise from
the heating power of the earth on which the water rests.

The water of a lake is heated in summer and autumn in three
ways — the heat of the atmosphere, that of the sun’s rays, and that
of the earth. The atmosphere will communicate its heat to so
much of the superstratum only as is disturbed, more or less, by the
wind ; and, therefore, cannot penetrate many feet. The tempera-

574 Proceedings of the Royal Society

ture of the earth at the bottom, from 500 to 600 feet under the sea-
level, should be by theory about 60° in the deepest parts; but, con-
sidering the very low conducting power of the rocky structure of the
earth, its heating power over so vast a bed of cold water must be
very feeble. The sun’s rays are at once the most energetic heating
power, that which penetrates deepest, and that which alone can
sensibly heat any part of the superstratum of water underneath
the thin bed near the surface, where it is aided by the warmth of
the atmosphere, and the stirring of the water by the wind. But
there is a limit to the sun’s penetration in such depths, when the
water, as in the case of Loch Lomond, is coloured, however slightly.
It has been imagined that the presence of springs at the bottom
may be a fourth source of influence over the temperature. If there
be any springs there, the effect must be to heat the water. But, as
there are no springs in Scotland which rise above the surface, or pre-
sent other proofs of owing their place to unusual sources of pressure,
it seems most improbable that any are so constituted as to overcome
the pressure which exists at the bottom of a very deep lake.

Every known consideration, — the great thickness of the cold
substratum, its steady low temperature, and its greater colour than
at the surface — contributes proof that this substratum can undergo
little or no movement, unless an unusually hard winter should dis-
place it by colder water from above.*]

The previous observations have extended to so great a length
that I must postpone till another opportunity the remarks which I
have prepared on the third of my promised topics — the Action of
Water on Lead.

The following Gentlemen were elected Fellows of the
Society : —

Alexander H. Lee, Esq., C.E.

Robert Lee, Esq., Advocate.

John Anderson, LL.D.

* While the preceding statements were passing through the press, my
attention was called to similar observations in Sir John Leslie’s article on
Climate in the “Encyclopaedia Britannica,” by Saussure on the Lakes of
Geneva, Thun, and Lucerne, and by the late eminent engineer, Mr James
Jardine, on Loch Lomond and Loch Katrine in 1814. Their observations
are not entirely concordant with those given above. I contemplate further
observations which may reconcile them.

of Edinburgh, Session 1871-72.

575

Monday , 18£/i December 1871.

Sir ROBERT CHRISTISON, Bart., President, in the Chair.
The following Communications were read : —

1. On the Computation of the Strengths of the Parts of
Skeleton or Open Structures. By Edward Sang.

The first part of the paper is devoted to the computation of the
strengths of the parts of a structure destined to resist given
strains, taking into account, along with those strains, the unknown
weights of the parts. The results obtained by this process neces-
sarily give the best possible arrangement of the strengths, since, if
any one part were made weaker, the whole structure would be
weakened; or, if a part were made stronger, the unnecessary
weight thus thrown upon the other parts would also go to weaken
the fabric. It is believed that this investigation has now been
given for the first time.

It was pointed out that this method enables us to determine the
utmost limit of magnitude of a structure having a given general
configuration.

The second part concerned deficient or flexible structures ; the
mode of discovering the relations among the applied pressures,
needed to cause the structure to assume a prescribed form, was
indicated.

Thirdly, the case of redundant structures was gone into. It
was observed that the absolute strains on the parts of such struc-
tures depend, not merely on their form, but also on the manner of
putting them together. The changes on these strains caused by
additional loads can, however, be computed by considering the
compressions or distensions of the parts; and it was pointed out
that the computation of these changes has been mistaken for that
of the absolute strains.

Lastly, there was investigated a new general theorem, which
may be stated as follows : —

When we apply a pressure to some point of a flexible system,

576 Proceedings of the Royal Society

the yielding is not necessarily in the direction of the pressure.
There is, however, always one direction of coincidence, and there
may be three. When there are three, if two of these form a right
angle, the third is also perpendicular to both of them.

2. On Vortex Motion. By Professor Sir William Thomson.

(Abstract .)

This paper is a sequel to several communications which have
already appeared in the Proceedings and Transactions of the Royal
Society of Edinburgh.* It commences with an investigation of
the circumstances under which a portion of an incompressible fric-
tionless liquid, supposed to extend through all space, or through
space wholly or partially bounded by a rigid solid, can be projected
so as to continue to move through the surrounding liquid with-
out change of shape ; and goes on to investigate vibrations exe-
cuted by a portion of liquid so projected, and slightly disturbed
from the condition that gives uniformity. The greatest and least
quantities of energy which a finite liquid mass of any given initial
shape and any given initial motion can possess, after any varia-
tions of its bounding surface ending in the initial shape, are next
investigated ; and the theory of the dissipation of energy in a
finite or infinite frictionless liquid is deduced. A finite space, filled
with incompressible liquid, traversed by a great multitude of parts
of itself, each very small in comparison with the average distance
of any one of the parts from its nearest neighbour, is next con-
sidered, and thus a kinetic theory of gases, without the assump-
tion of elastic atoms, is sketched; also a realisation by vortex
atoms of Le Sage’s “ gravific ” fluid consisting of an innumerable
multitude of “ ultramundane corpuscles.”

Towards the vortex theory of the elasticity of liquids and solids,
the propagation of waves along a row of vortex columns alternately
positive and negative, in a liquid contained between two rigid
parallel planes, close enough to give stability to the row of columns,
is next investigated.

In conclusion, it is pointed out that the difficulties of forming a
complete theory of the elasticity of gases, liquids, and solids, with

* Vortex Atoms. Proceedings, February 1867 ; Transactions, 1868-1869.

577

of Edinburgh, Session 1871-72.

no other ultimate properties of matter than perfect fluidity and in-
compressibility are noticed, and shown to be, in all probability,
only dependent on the weakness of mathematics.

3. On the Ultramundane Corpuscules of Le Sage.

By Professor Sir W. Thomson.

{Abstract.)

Le Sage, born at Geneva in 1724, devoted the last sixty-three
years of a life of eighty to the investigation of a mechanical theory
of gravitation. The probable existence of a gravific mechanism is
admitted and the importance of the object to which Le Sage
devoted his life pointed out, by Newton and Bumford* in the
following statements : —

It is inconceivable that inanimate brute matter should, without
“ the mediation of something else, which is not material, operate
“ upon, and affect other matter without mutual contact ; as it must
“ do, if gravitation, in the sense of Epicurus , be essential and
“ inherent in it. And this is the reason why I desired you would
“ not ascribe innate gravity to me. That gravity should be innate,
u inherent, arid essential to matter, so that one body may act upon
11 another at a distance through a vacuum , without the mediation
“ of anything else, by and through which their action and force
u may be conveyed from one to another, is to me so great an
“ absurdity, that I believe no man who has in philosophical
“ matters a competent faculty of thinking, can ever fall into it.

* On the other hand, by the middle of last century the mathematical
naturalists of the Continent, after half a century of resistance to the Newtonian
principles (which, both by them and by the English followers of Newton, were
commonly supposed to mean the recognition of gravity as a force acting
simply at a distance without mediation of intervening matter), had begun to
become more “ Newtonian ” than Newton himself. On the 4th February
1744, Daniel Bernoulli wrote as follows to Euler, “ Uebrigens glaube ich.
“ dass der Aether sowohl gravis versus solem. als die Luft versus terrain
“ sey, und kann Ihnen nicht bergen, dass ich iiber diese Puncte ein volliger
“ Newtonianer bin, und verwundere ich mich, dass Sie den Principiis
“ Cartesianis so lang adhariren ; es mochte wohl einige Passion vielleicht
“ mit unterlaufen. Hat Oott konnen eine animam, deren Natur uns unbe-
“ greiflich ist, erschaffen, so hat er auch konnen eine attractionem universalem
“ materise imprimiren, wenn gleich solche attractio supra captum ist, da
“ hingegen die Principia Cartesiana allzeit contra captum etwas involviren.”

4 H

VOL. VII.

578

Proceedings of the Boyal Society

<r Gravity must be caused by an agent acting constantly accord -
“ ing to certain laws; but whether this agent be material or
££ immaterial, I have left to the consideration of my readers.” —
Newton’s Third Letter to Bentley , February 2 5th, 1692-3.

“ Nobody surely, in his sober senses, has ever pretended to
“ understand the mechanism of gravitation ; and yet what sublime
“ discoveries was our immortal Newton enabled to make, merely
“ by the investigation of the laws of its action.” *

Le Sage expounds his theory of gravitation, so far as he had
advanced it up to the year 1782, in a paper published in the Tran-
sactions of the Royal Berlin Academy for that year, under the
title “Lucrece Newtonien.” His opening paragraph, entitled,
“ Rut de ce memoire,” is as follows : —

“ Je me propose de faire voir : que si les premiers Epicuriens
££ avoienteu; sur la Cosmographie des idees aussi saines seule-
££ ment, que plusieurs de leurs contemporains, qu’ils negligeoient
££ d’ecouter; f et sur la Geometrie, une partie des connoissances
“ qui etoient deja communes alors: ils auroient, tres probablement,
£< decouvert sans effort ; les Loix de la Gravite universelle, et sa
11 Cause mecanique. Loix ; dont l’invention et la demonstration,
“ font la plus grande gloire du plus puissant genie qui ait jamais
££ existe : et Cause , qui apres avoir fait pendant longtems, T ambition
££ des plus grands Physiciens; fait a present, le desespoir de leurs
££ sucesseurs. He sorte que, par exemple, les fameuses Regies de
££ Kepler ; trouveea il y a moins de deux siecles, en partie sur des
££ conjectures gratuites, et en partie apres d’immenses tatonnemens;
££ n ’auroient ete que des corollaires particuliers et inevitables, des
££ lumieres generales que ces anciens Philosophes pouvoient puiser
“ (comme en se jouant) dans le mechanisme proprement dit de
££ la Nature. Conclusion; qu’on peut appliquer exactement aussi,
££ aux Loix de Galilee sur la chute des Graves sublunaires ; dont
££ la decouverte a ete plus tardive encore, et plus contestee : joint
“ a ce que, les experiences sur lesquelles cette decouverte etoit
££ etablie ; laissoient dans leurs resultats (necessairement grossiers),

* An Inquiry concerning the Source of the Heat which is excited by Fric-
tion. By Count Rumford. — Philosophical Transactions, 1798.

t Yobis (Epicureis) minus notum est, quemadmodum quidque dicatur.
Vestra enim solum legitis, vestra amatis; caeteros, causa incognita, con-
demnatis. Ciceron, De natura Deorum, ii. 29.

579

of Edinburgh, Session 1871-72.

“ une latitude, que les rendoit egalement compatibles avec plusieurs
u autres hypotheses ; qu’aussi, l’on ne manqua pas de lui opposer :
“ au lieu que, les consequences du choc des Atoms; auroient ete
“ absolument univoques en faveur du seul principe veritable (des
“ Accelerations egales en Tempuscules egaux).”

If Le Sage had but excepted Kepler’s third law, it must be ad-
mitted that his case, as stated above, would have been thoroughly
established by the arguments of his u memoire ;” for the epicurean
assumption of parallelism adopted to suit the false idea of the earth
being flat, prevented the discovery of the law of the inverse square
of the distance, which the mathematicians of that day were quite
competent to make, if the hypothesis of atoms moving in all
directions through space, and rarely coming into collision with one
another, had been set before them, with the problem of determin-
ing the force with which the impacts would press together two
spherical bodies, such as the earth and moon were held to be by
some of the contemporary philosophers to whom the epicureant
“ would not listen.” But nothing less than direct observation, prov-
ing Kepler’s third law,— Galileo’s experiment on bodies falling from
the tower of Pisa, Boyle’s guinea and feather experiment, and
Newton’s experiment of the vibrations of pendulums composed of
different kinds of substance — could give either the idea that gravity
is proportional to mass, or prove that it is so to a high degree of
accuracy for large bodies and small bodies, and for bodies of dif-
ferent kinds of substance. Le Sage sums up his theory in an ap-
pendix to the “ Lucrece Newtonien,” part of which translated
(literally, except a few sentences which I have paraphrased) is as
follows : —

Constitution of Heavy Bodies .

Is*, Their indivisible particles are cages; for example, empty
cubes or octahedrons vacant of matter except along the twelve edges.

2 d, The diameters of the bars of these cages, supposed increased
each by an amount equal to the diameter of one of the gravific
corpuscles, are so small relatively to the mutual distance of the
parallel bars of each cage, that the terrestrial globe does not inter-
cept even so much as a ten- thousandth part of the corpuscules
which offer to traverse it.

580 Proceedings of the Royal Society

3d, These diameters are all equal, or if they are unequal, their
inequalities sensibly compensate one another [in averages].

Constitution of Gravific Corpuscules.

1st, Conformably to the second of the preceding suppositions,
their diameters added to that of the bars is so small relatively to
the mutual distance of parallel bars of one of the cages, that the
weights of the celestial bodies do not differ sensibly from being
in proportion to their masses.

2d, They are isolated. So that their progressive movements are
necessarily rectilinear.

3d, They are so sparsely distributed, that is to say, their dia-
meters are so small relatively to their mean mutual distances, that
not more than one out of every hundred of them meets another
corpuscule during several thousands of years. So that the unifor-
mity of their movements is scarcely ever troubled sensibly.

4:th, They move along several hundred thousand millions of
different directions ; in counting for one same direction all those
which are [within a definite very small angle of being] parallel to
one straight line. The distribution of these straight lines is to be
conceived by imagining as many points as one wishes to consider
of different directions, scattered over a globe as uniformly as pos-
sible, and therefore separated from one another by at least a second
of angle; and then imagining a radius of the globe drawn to
each of those points.

5th, Parallel, then, to each of those directions, let a current or
torrent of corpuscules move ; but, not to give the stream a greater
breadth than is necessary, consider the transverse section of this
current to have the same boundary as the orthogonal projection of
the visible world on the plane of the section.

5th, The different parts of one such current are sensibly equi-
dense ; whether we compare, among one another, collateral portions
of sensible transverse dimensions, or successive portions of such
lengths that their times of passage across a given surface are
sensible. And the same is to be said of the different currents com-
pared with one another.

7th, The mean velocities, defined in the same manner as I have
just defined the densities, are also sensibly equal.

581

of Edinburgh, Session 1871-72.

8th, The ratios of these velocities to those of the planets are
several million times greater than the ratios of the gravities of the
planets towards the sun, to the greatest resistance which secular
observations allow us to suppose they experience. For example,
[these velocities must be] some hundredfold a greater number of
times the velocity of the earth, than the ratio of 190,000* times
the gravity of the earth towards the sun, to the greatest resistance
which secular observations of the length of the year permit us to
suppose that the earth experiences from the celestial masses.

CONCEPTION, which facilitates the Application of Mathematics to

determine the mutual Influence of these Heavy Bodies and these

Corpuscules.

1st, Decompose all heavy bodies into molecules of equal mass, so
small that they may be treated as attractive points in respect to
theories in which gravity is considered without reference to its
cause ; that is to say, each must be so small that inequalities of
distance and differences of direction between its particles and those
of another molecule, conceived as attracting it and being attracted
by it, may be neglected. For example, suppose the diameter of
the molecule considered to be a hundred thousand times smaller
than the distance between two bodies of which the mutual gravita-
tion is examined, which would make its apparent semi-diameter,
as seen from the other body, about one second of angle.

2d, For the surfaces of such a molecule, accessible hut imper-
meable to the gravific fluid, substitute one single spherical surface
equal to their sum.

3d, Divide those surfaces into facets small enough to allow them
to he treated as planes, without sensible error, [&c., &c.]

Remarks.

It is not necessary to he very skilful to deduce from these
suppositions all the laws of gravity, both sublunary and universal
(and consequently also those of Kepler, &c.), with all the accuracy
which observed phenomena have proved those laws. Those laws,

* To render the sentence more easily read, I have substituted this number
in place of the following words : — le nombre de fois que le firmament con-
tient le disque apparent du soleil.”

VOL. VII.

4 i

582 Proceedings of the Royal Society

therefore, are inevitable consequences of the supposed consti-
tutions.

2 d, Although I here present these constitutions crudely and
without proof, as if they were gratuitous hypotheses and hazarded
fictions, equitable readers will understand that on my own part I
have at least some presumptions in their favour (independent of
their perfect agreement with so many phenomena), but that the
development of my reasons would be too long to find a place in the
present statement, which may be regarded as a publication of
theorems without their demonstrations.

3d, There are details upon which I have wished to enter

on account of the novelty of the doctrine, and which will readily
be supplied by those who study it in a favourable and attentive
spirit. If the authors who write on hydro-dynamics, aerostatics,
or optics, had to deal with captious readers, doubting the very exist-
ence of water, or air, or light, and therefore not adapting them-
selves to any tacit supposition regarding equivalencies or com-
pensations not expressly mentioned in their treatises, they would
be obliged to load their definitions with a vast number of specifi-
cations which instructed or indulgent readers do not require of
them. One understands u cl demi-mot” and u sano sensu” only
familiar propositions towards which one is already favourably
inclined.

Some of the details referred to in this concluding sentence of
the appendix to his “Lucrece Newtonien,” Le Sage discusses fully
in his “ Traite de Physique Mecanique,” edited by' Pierre Prevost,
and published in 1818 (G-eneva and Paris).

This treatise is divided into four books.

I. u Exposition sommaire du systeme des corpuscules ultra-
mondains.”

II. “ Discussion des objections qui peuvent s’elever contre le
“ systeme des corpuscules ultramondains.”

III. “ Des fluides elastiques ou expansifs.”

IY. “ Application des theories precedentes a certaines affinites.”

It is in the first two books that gravity is explained by the im-
pulse of -ultramundane corpuscules, and I have no remarks at pre-
sent to make on the third and fourth books.

583

of Edinburgh, Session 1871-72.

From Le Sage's fundamental assumptions, given above as nearly
as may be in his own words, it is, as he says himself, easy to deduce
the law of the inverse square of the distance, and the law of pro-
portionality of gravity to mass The object of the present note is
not to give an exposition of Le Sage’s theory, which is sufficiently
set forth in the preceding extracts, and discussed in detail in the
first two books of his posthumous treatise. I may merely say that
inasmuch as the law of the inverse square of the distance, for every
distance, however great, would be a perfectly obvious consequence
of the assumptions, were the gravific corpuscules infinitely small, and
therefore incapable of coming into collision with one another, it
may be extended to as great distances as we please, by giving
small enough dimensions to the corpuscules relatively to the mean
distance of each from its nearest neighbour. The law of masses
may be extended to as great masses as those for which observation
proves it (for example the mass of Jupiter), by making the
diameters of the bars of the supposed cage-atoms constituting heavy
bodies, small enough. Thus, for example, there is nothing to pre-
vent us from supposing that not more than one straight line of a
million drawn at random towards Jupiter and continued through
it, should touch one of the bars. Lastly, as Le Sage proves, the
resistance of his gravific fluid to the motion of one of the planets
through it, is proportional to the product of the velocity of the
planet into the average velocity of the gravific corpuscules ; and
hence by making the velocities of the corpuscules great enough,
and giving them suitably small masses, they may produce the
actual forces of gravitation, and not more than the amount of
resistance which observation allows us to suppose that the planets
experience. It will be a very interesting subject to examine
minutely Le Sage’s details on these points, and to judge whether
or not the additional knowledge gained by observation since his
time requires any modification to be made in the estimate which he
has given of the possible degrees of permeability of the sun and
planets, of the possible proportions of diameters of corpuscules to
interstices between them in the “ gravific fluid,” and of the possible
velocities of its component corpuscules. This much is certain,
that if hard indivisible atoms are granted at all, his principles
are unassailable ; and nothing can be said against the probability

584 Proceedings of the Royal Society

of his assumptions. The only imperfection of his theory is tha
which is inherent to every supposition of hard, indivisible atoms.
They must be perfectly elastic or imperfectly elastic, or perfectly
inelastic. Even Newton seems to have admitted as a probable
reality hard, indivisible, unalterable atoms, each perfectly inelastic.

Nicolas Fatio is quoted by Le Sage and Prevost, as a friend of
Newton, who in 1689 or 1690 had invented a theory of gravity
perfectly similar to that of Le Sage, except certain essential points ;
had described it in a Latin poem not yet printed; and had written, on
the 30th March 1694, a letter regarding it, which is to be found in
the third volume of the works of Leibnitz, having been communi-
cated for publication to the editor of those works by Le Sage.
Eedeker, a German physician, is quoted by Le Sage as having
expounded a theory of gravity of the same general character, in a
Latin dissertation published in 1736, referring to which Prevost
says, “ Oil l’on trouve l’expose d’un systeme fort semblable a celui
“ de Le Sage dans ses traits principaux, mais depourvu de cette
“ analyse exacte des phenomenes qui fait le principal merite de toute
“ espece de theorie.” Fatio supposed the corpuscules to be elastic,
and seems to have shown no reason why their return velocities
after collision with mundane matter should be less than their pre-
vious velocities, and therefore not to have explained gravity at all.
Eedeker, we are told by Prevost, had very limited ideas of the per-
meabilities of great bodies, and therefore failed to explain the law
of the proportionality of gravity to mass ; u he enunciated this law
“ very correctly in section 15 of his dissertation ; but the manner
“ in which he explains it shows that he had but little reflected upon
11 it. Notwithstanding these imperfections, one cannot but recog-
“ nise in this work an ingenious conception which ought to have
“ provoked examination on the part of naturalists, of whom many
u at that time occupied themselves with the same investigation.
“ Indeed, there exists a dissertation by Segner on this subject.*
“ But science took another course, and works of this nature gradu-
u ally lost appreciation. Le Sage has never failed on any occasion
il to call attention to the system of Eedeker, as also to that of Fatio.” f

* De Causa gravitatis Redekeriana.

f Le Sage was remarkably scrupulous in giving full information regarding
11 who preceded him in the development of any part of his theory.

585

of Edinburgh, Session 1871-72.

Le Sage shows that to produce gravitation those of the ultra-
mundane corpuscules which strike the cage-bars of heavy bodies
must either stick there or go away with diminished velocities.
He supposed the corpuscules to he inelastic ( durs ), and points
out that we ought not to suppose them to he permanently lodged
in the heavy body (ent asses), that we must rather suppose them
to slip off ; but that being inelastic, their average velocities after
collision must be less than that which they had before collision.*

That these suppositions imply a gradual diminution of gravity
from age to age was carefully pointed out by Le Sage, and referred to
as an objection to his theory. Thus he says, “ . . . Done., la duree
“ de la gravite seroit finie aussi, et par consequent la duree du
<£ monde.

“ Beponse. Concedo ; mais pourvu que cet obstacle ne contrihue
“ pas a faire finir le monde plus promptement qu’il n’auroit fini sans
“ lui, il doit etre considere comme nulTf

Two suppositions may be made on the general basis of Le Sage’s
doctrine : —

ls£, (Which seems to have been Le Sage’s belief.) Suppose the
whole of mundane matter to he contained within a finite space,
and the infinite space round it to be traversed by ultramundane
corpuscules ; and a small proportion of the corpuscules coming
from ultramundane space to suffer collisions with mundane matter,
and get away with diminished gravific energy to ultramundane
space again. They would never return to the world were it not
for collision among themselves and other corpuscules. Le Sage
held that such collisions are extremely rare ; that each collision,
even between the ultramundane corpuscules themselves, destroys
some energy ;J that at a not infinitely remote past time they
were set in motion for the purpose of keeping gravitation through-
out the world in action for a limited period of time; and that

* Le Sage estimated the velocity after collision to be two-thirds of the
velocity before collision.

| Posthumous. “ Traite de Physique Mecanique,” edited by Pierre Prevost.
Geneva and Paris, 1818.

x Newton (Optics, Query, 80 Edn. 1721, p. 378) held that two equal and
similar atoms, moving with equal velocities in contrary directions, come to
rest when they strike one another. Le Sage held the same ; and it seems
that writers of last century understood this without qualification when they
called atoms hard.

586 Proceedings of the Royal Society

both by their mutual collisions, and by collisions with mundane
atoms, the whole stock of gravific energy is being gradually re-
duced, and therefore the intensity of gravity gradually diminishing
from age to age.

Or, 2 d, suppose mundane matter to be spread through all space,
but to be much denser within each of an infinitely great number of
finite volumes (such as the volume of the earth) than elsewhere.
On this supposition, even were there no collisions between the
corpuscules themselves, there would be a gradual diminution in
their gravific energy through the repeated collisions with mundane
matter which each one must in the course of time suffer. The secular
diminution of gravity would be more rapid according to this sup-
position than according to the former, but still might be made as
slow as we please by pushing far enough the fundamental assump-
tions of very small diameters for the cage-bars of the mundane
atoms, very great density for their substance, and very small
volume and mass, and very great velocity for the ultramundane
corpuscules.

The object of the present note is to remark that (even although
we were to admit a gradual fading away of gravity, if slow enough),
we are forbidden by the modern physical theory of the conservation
of energy to assume inelasticity, or anything short of perfect elas-
ticity, in the ultimate molecules, whether of ultramundane or of
mundane matter; and, at the same time, to point out that the
assumption of diminished exit velocity of ultramundane corpuscules,
essential to Le Sage’s theory, may be explained for perfectly elastic
atoms, consistently both with modern thermodynamics, and with
perennial gravity.

If the gravific corpuscules leave the earth or Jupiter with less
energy than they had before collision, their effect must be to con-
tinually elevate the temperature throughout the whole mass. The
energy which must be attributed to the gravific corpuscules is so
enormously great, that this elevation of temperature would be
sufficient to melt and evaporate any solid, great or small, in a
fraction of a second of time. Hence, though outward-bound cor-
puscules must travel with less velocity, they must carry away the
same energy with them as they brought. Suppose, now, the whole
energy of the corpuscules approaching a planet to consist of trans-

587

of Edinburgh, Session 1871-72.

latory motion : a portion of the energy of each corpuscnle which
has suffered collision must be supposed to be converted by the
collision into vibrations, or vibrations and rotations. To simplify
ideas, suppose for a moment the particles to he perfectly smooth
elastic globules. Then collision could not generate any rotatory
motion; but if the cage-atoms constituting mundane matter be
each of them, as we must suppose it to be, of enormously great
mass in comparison with one of the ultramundane globules, and if
the substance of the latter, though perfectly elastic, be much less
rigid than that of the former, each globule that strikes one of the
cage-bars must (Thomson & Tait’s “ Natural Philosophy, § 301),
come away with diminished velocity of translation, hut with the
cQrresponding deficiency of energy altogether converted into vibra-
tion of its own mass. Thus the condition required by Le Sage’s
theory is fulfilled without violating modern thermo- dynamics ; and,
according to Le Sage, we might be satisfied not to inquire what be-
comes of those ultramundane corpuscules which have been in collision
either with the cage-bars of mundane matter or with one another ;
for at present, and during ages to come, these would he merely an
inconsiderable minority, the great majority being still fresh with
original gravific energy unimpaired by collision. Without entering
on the purely metaphysical question, — Is any such supposition satis-
factory ? I wish to point out how gravific energy may be naturally
restored to corpuscules in which it has been impaired by collision.

Clausius has introduced into the kinetic theory of gases the
very important consideration of vibrational and rotational energy.
He has shown that a multitude of elastic corpuscules moving
through void, and occasionally striking one another, must, on the
average, have a constant proportion of their whole energy in the
form of vibrations and rotations, the other part being purely trans-
lational. Even for the simplest case, — that, namely, of smooth
elastic globes, — no one has yet calculated by abstract dynamics
the ultimate average ratio of the vibrational and rotational, to
the translational energy. But Clausius has shown how to deduce
it for the corpuscules of any particular gas from the experimental
determination of the ratio of its specific heat pressure constant, to
its specific heat volume constant.* He found that

* Maxwell’s “ Elementary Treatise on Heat,” chap. xxii. Longman, 1871.

588

Proceedings of the Royal Society
2 1

P =

3 y-1 '

if y be the ratio of the specific beats, and /3 the ratio of the whole
energy to the translational part of it. For air, the value of y found
by experiment, is 1*408, which makes /3 = 1*634. For steam,
Maxwell says, on the authority of Eankine, /3 “may be as much
as 2*19, but this is very uncertain.” If the molecules of gases are
admitted to be elastic corpuscules, the validity of Clausius’ prin-
ciple is undeniable ; and it is obvious that the value of the ratio /3
must depend upon the shape of each molecule, and on the distribu-
tion of elastic rigidity through it, if its substance is not homo-
geneous. Farther, it is clear that the value of /3 for a set of equal
and similar corpuscules will not be the same after collision with
molecules different from them in form or in elastic rigidity, as
after collision with molecules only of their own kind. All that is
necessary to complete Le Sage’s theory of gravity in accordance
with modern science, is to assume that the ratio of the whole
energy of the corpuscules to the translational part of their energy
is greater, on the average, after collisions with mundane matter
than after inter-collisions of only ultramundane corpuscules. This
supposition is neither more nor less questionable than that of
Clausius for gases which is now admitted as one of the generally
recognised truths of science. The corpuscular theory of gravity is
no more difficult in allowance of its fundamental assumptions than
the kinetic theory of gases as at present received ; and it is more
complete, inasmuch as, from fundamental assumptions of an ex-
tremely simple character, it explains all the known phenomena of
its subject, which cannot be said of the kinetic theory of gases so
far as it has hitherto advanced.

Postscript , April 1872.

In the preceding statement I inadvertently omitted to remark
that if the constituent atoms are aeolotropic in respect to perme-
ability, crystals would generally have different permeabilities in
different directions, and would therefore have different weights
according to the direction of their axes relatively to the direction
of gravity. No such difference has been discovered, and it is

of Edinburgh, Session 1871-72.

589

certain that if there is any it is extremely small. Hence, the
constituent atoms, if aeolotropic as to permeability, must be so,
but to an exceedingly small degree. Le Sage’s second funda-
mental assumption given above, under the title “ Constitution of
“ Heavy Bodies ,” implies sensibly equal permeability in all direc-
tions, even in an aeolotropic structure, unless much greater than
Jupiter, provided that the atoms are isotropic as to permeability.

A body having different permeabilities in different directions
would, if of manageable dimensions, give us a means for drawing
energy from the inexhaustible store laid up in the ultramundane
corpuscles, thus : — First, turn the body into a position of minimum
weight; Secondly, lift it through any height; Thirdly, turn it
into a position of maximum weight ; Fourthly, let it down to its
primitive level. It is easily seen that the first and third of those
operations are performed without the expenditure of work ; and, on
the whole, work is done by gravity in operations 2 and 4. In
the corresponding set of operations performed upon a moveable
body in the neighbourhood of a fixed magnet, as much work is
required for operations 1 and 3 as is gained in operations 2 and 4;
the magnetisation of the moveable body being either intrinsic or
inductive, or partly intrinsic and partly inductive, and the part of
its aeolotropy (if any), which depends on inductive magnetisation,
being due either to magne-crystallic quality of its substance, or to
its shape.*

4. Note on Spherical Harmonics. By Professor Tait.

While engaged in some quaternion researches with reference to
Spherical Harmonics, which I hope soon to lay before the Society,

I was led to imagine that some of my results might produce a
simplification of the ordinary modes of treating the subject. The
following is the result of the attempt. It seems to make the cal-

* “ Theory of magnetic induction in crystalline and non-crystalline sub-
“ stances.” — Phil. Mag., March 1851. “Forces experienced by inductively
“ magnetised ferro-magnetic and dia-magnetic non-crystalline substances.”
— Phil. Mag., Oct. 1850. “Reciprocal action of dia-magnetic particles.” —
Phil. Mag., Dec. 1855 ; all to be found in a collection of reprinted and newly
written papers on electrostatics and magnetism, nearly ready for publication,
(Macmillan, 1872).

4 k

VOL. VII.

590

Proceedings of the Royal Society

cuius somewhat more intelligible to the beginner than the methods
employed by O’Brien and Murphy, whose works on the subject are
usually read in this country. As I am not writing a treatise, but
merely sketching a method, I shall run over the principal elemen-
tary propositions only.

1. Let

1 1
P

\i — #Q i

'(i-2 hfx+h2y>

This is possible, if h be always taken less than 1 ; and, as //, is never
beyond the limits db 1, 1, Q*, - 1 are in order of magnitude, and
the series is always convergent.

Hence we may differentiate, and we thus obtain

dL 1

d/x p

p3 " ^

and

l(a-'A) - w+3{i -,■)»• }

Also

and

72 d 1 uW-li3 .

h tt ~ = 3 — = S Qi ,

dk p p6 ’

dh p) ^ 5 { — P2 + 3 (/x — A)2 h 2 1

= 5 . a (V 4- 1) A?’Q*

(1).

(2).

The sum of the multipliers of p~5 in (1) and (2; is obviously zero.
Thus we have the equation for Qi

i(i+l)Qi + ((1-P*)f) =0 . (3).

2. From this equation, by differentiation s - 1 times with respect
to fi, we have

of Edinburgh, Session 1871-72.

591

3. Let Q j be any one of the values of Q above defined, then
Hence, integrating between the limits ”Fl of p, we have

f 4.= (.•+«) (i-.+ijy (5).

+ i +i

Applying the reduction s times, we evidently obtain

—i „„ —i

J O-/4) dll,,

dsQi dsQj

~dfd

|t + s

^ tl 1737

J Qi 0/ *7/^

(6).

4. To find the value of the integral on the right, note that
QiQj is the co-efficient of A*A^' in the expansion of

Now

(1 - 2 fxh +h2f (1 - 2^' + A'2)*

dp

a/(1 + A2 - 2 V) (1 + h'2 - 2 A»

j

+i

7IFlos-

/1+A2

2 li

1 +

l + A/;
2A'

j

1 + A2
~2/T

+ 1 +

/1 + A':
V 24'

+ 1

1 ^ a/A'(1-A) + \A(1 -AQ

a/ AA' ° \/A' (1 + A) + a/A (1 + A')

1 1 - a/ AA'

a/ AA' ° 1 + a/ AA'

592

Proceedings of the Royal Society

= -2 20

* (hhy

2i + V

In this there is no term in which the powers of h and h' are
different, hence we have

—l

J Q i Qj djL ■

in all cases unless j = i. In this special case we have

—l

/ Q? d/x
J+i

2

2* + l

(7).

(8.)

Hence the left hand member of (6) vanishes unless j = i, and in
that case we have

• to.

+1 '

We might have proved (7) from (6) by exchanging i and/, and
showing that unless i — /, we cannot have

V \J + S _ 1 / + s
1 i - s~ \j - s *

5. The equation (3), which is satisfied by Q*-, is a mere particular
case of the general equation of surface harmonics —

*•(>•+ 1) Si + + |-(W) §)=0 (10).

which maybe obtained by putting V < = Si in the ordinary equa-
tion of Laplace —

r d%^i) + 1 dfVj + d Aj _ JA _ Q

dr 2 1 — (a? d<p2 d/x\ d/xj *

after differentiating the first term. That differentiation gives, in
fact,

593

of Edinburgh, Session 1871-72.

From equation (10) we may prove, as usual, by multiplying by
S j and integrating over the unit sphere, that

i(i + 1)/ dtrSfij = j(J+ lXArSiS,- ,

the expression for either being symmetrical in i and/, so that the
integral vanishes unless i —j : or, if negative values be admitted,
unless i + j + 1 = 0.

6. We must now express S* in terms of <p and Q ». Let, then,

S< = 30 As cos. (s<p -f ai)®® . . . (11).

where As, as are virtually 2 i+ 1 arbitrary constants. Substituting
this value in (10), and supposing all the coefficients A to vanish
except As, we have

This equation is materially simplified by assuming (as is suggested
by (6) and (9) )

®f=( l-ff6*. ■ ■ ■ (13),

for with this substitution it becomes, by a process the same as ''that
of section 2 above,

(^+l)-S(S+]))(1-^ + |((l-^)S+1f) = 0.

But, by (4), putting s + 1 for s,

+ «) 0 -<■•> T + 1 (o -*"**$) - »•

Comparing these equations, and remembering that all the permis-
sible arbitrary constants have already been introduced into the
solution of (10), we have

Hence, finally,

Si = 2j A, cos. (s<p + a,)(l - ^7- .

(U)

594 Proceedings of the Royal Society

7. We may now easily find the value of
fS&fdtr

taken over the whole spherical surface. For

and

2 TT — 1

/( )^<r=//( ')d<pd(x:

o +i

f d<p cos. (sp + a,) cos. (s'<p + <v)

vanishes unless s and s' be equal, in which case its value is 7 r.
Hence, attending to § 4, and to (14),

and

f S S da~ = 0 ,

/q2 , 2 tt *■ .2 lh

S^cr _ 2i+i 20 As

i + s

• (15)-

8. Another curious expression for ©£s) is given by (4)- For
that equation gives

= - (*'(‘+l) -«(»-!)) f-!’*) 1

=+{«'+ i)-.(*-i)}{»(«+i)-(*=i)(^2)}

(S)

=(-yifi/w .... (i6).

Hence

=(-)!{S(i-/^( 7^*)* Qi • (17)-

10. let

JT+^xh + hF = 1 + hy . . . (19),

where y is a function of h and (a, never beyond the limits -f 1 and - 1.
Then

h ndy

J l + Zfxh + l? = hdf'

Hut the first equation gives, at sight,

(20),

of Edinburgh, Session 1871-72.

595

whence,

7 1 -g2 h2 d ( 1-/x2Y ,

y = H+h— 2~ + §— ) + &c->

and therefore,

1 _ dy _ d_ df /l-^Y

v l + 2/J> + Aa~<^~ 2 J + l-2 d^2\ 2 y +cC,>

which shows that

■ • (21>’

and suggests obvious simplifications of preceding results, e.g.,

c • - - (by § 8) ( - ) i+s(i - "■

&c., &c.,

[t- s \c?jtc / \ 2 / ’

11. The complete integral of

^DQ. + Ka-^f) =° . (3)

may easily be found, since a particular integral is known. Let it
be MQj, where M is a function of Then (3) gives at once

(- VQ>+2 cw*>f )f + a - = o,

- 2a , 2 dQi -4- dm
l-ju2 + Qi d/l + ~ dy* ~ °>

d/ji

whence

dM

G

dfx (1 - p2)Q,i2
Thus the complete integral is

cafiF$W

12. Let us now suppose

Si = P,Qi •

(22).

(23),

596

Proceedings of the Royal Society

where Q* is as in § 1, and P* is a function of /x and <p. The
equation (10) becomes successively

d_

d/x

/ ox d CPiQi)\ 1 d^PiQi) _

(a-^) (/;, ) + rr^ dip2 + <*+i)P.Qi=o,

Q t d2?j

— jj? dtp2

jp a, j-p,

and, finally,

+ =°-

If we put, for a moment,

= 0,

djx

(i -*■)<**

(which has a real meaning, see § 11),

and suppose Q* to be expressed in terms of v instead of /x, calling
it qi3 the equation may be written

d2Vj
dv- +

(24).

Hence it appears at once that P i cannot contain <p except in the
form of factors, such as cos. s<p, sin. stp, in the several terms of
which (as an integral of a linear equation) it must be composed.
Hence, as before,

to

P,; — h-s ®i COS.(sp + a),
and, keeping to one value of s,

of Edinburgh, Session 1871-72.

597

5. Laboratory Notes : On Thermo-Electricity. By
Professor Tait.

For some time back I have been endeavouring to prove, by ex-
periment, through great ranges of temperature, the result announced
by me in December last, viz., that the electro-motive force of a
thermo-electric circuit is in general, unless the temperature be very
high, a parabolic function of the absolute temperature of either
junction, that of the other being maintained constant.

For moderate ranges of temperature the experiment presents
little difficulty; but, when mercurial thermometers cannot be em-
ployed, a modification of the experimental method must be made.
I have employed in succession several such modifications, of which
the following are the chief : —

The simplest of all is to dispense altogether with thermometers,
and to employ two thermo-electric circuits, whose hot and whose
cold junctions are immersed in the same vessels ; and to plot the
curve whose abscissae and ordinates are simultaneous readings of
the electro-motive forces in the two circuits. In every case I have
tried the curve thus obtained is almost accurately a parabola, most of
the few deviations yet observed being in the case of silver and other
metals at temperatures not very much below their melting points —
under circumstances, in fact, in which we should naturally expect
that the law would no longer hold. There are, also, cases in which
the whole electro-motive force is so small, even for very large differ-
ences of temperature, that very much more delicate apparatus would
be required for their proper investigation. And there are cases in
which the neutral point is so far off that for moderate ranges of
temperature the curves obtained are sensibly straight lines. I
intend to examine these cases with care — the former by using more
delicate galvanometers ; the latter, by employing metals which are
practically infusible. The difficulty of obtaining wires of such
metals has been the chief one I have had to face.

If we assume the experimental curve to be a parabola, then it is
easily seen ( Proc . May 29, 1871) that in each circuit the electro-
motive force must be a parabolic function of some function of the ab-
solute temperatures of the junctions. And, as in the iron-silver,

4 L

VOL. VII.

598

Proceedings of the Royal Society

iron-zinc, iron- copper, iron-cadmium, &c., circuits, this function has
been proved to be simply the absolute temperature itself (at least,
within the range of mercury thermometers), it is probable that such
is the general law, at least for ranges of temperature short of those
which materially alter the molecular structure of the metals em-
ployed.

The second method consisted in employing two pairs of circuits,
all four hot junctions being in the same heated substance, and all
four cold junctions kept at a common temperature. The members
of each pair acted on a differential galvanometer (as explained in
Proc. Dec. 19, 1870) in such a way as to eliminate the term containing
the square of the absolute temperature. In this case the readings of
the galvanometers should be simply proportional to one another,
and likewise to the differences of absolute temperature of the junc-
tions. The method is exact in theory, but by no means easy in
practice, especially with the very limited number of metals capable
of resisting a high temperature which I could manage to obtain.
That a very exact and useful thermometric arrangement can be
made on this principle admits of no doubt, when we examine the
results of the experiments.

The third method consisted in assuming the parabolic law, and
the following consequence of it which follows directly by the use
of Thomson’s general formulse. These may easily be reproduced
as follows : — Suppose a sliding ring or clip to be passed round the
wires, so as to press together points of the wires which are at the
same temperature, t. Its effects are known by experiment to be nil,
whatever be its material. Let it be slid along so that the tempera-
ture of what is now effectively the hot junction becomes t + St, then
the two laws of thermodynamics give, respectively,

SE = J(SH + (crq — o~2) St^ ,

and

o=sn+£i^&.

Here E is the electromotive force, n the Peltier effect at a junction
at temperature t , and <rv cr2, are the specific heats of electricity in
the two metals.

of Edinburgh, Session 1871-72. 599

Hence

SE = J (oll-tSj) = J^ot .

Introducing the hypothesis, obtained from considerations of Dissi-
pation of Energy, (Proc. Dec. 19, 1870) that

= Kt, <rs = kbti

we have

JT = S = (^-^

where Tab is the well-known “ neutral point.”

Also

e ={K-h)(f-h) (t*-^),

since it vanishes for t = tv the temperature of the cold junction.
Now, if the neutral point be between such limits as 0° 0. and 300°
C., the exact determination of it is an easy matter; and this ex-

cZE

act knowledge of it greatly facilitates the determination of

which cannot be very accurately found by drawing a tangent to the
plotted curve. For if one junction be at t , the other at Ta6, we
have

= ~ “ 0**

Et and Tab - 1 are easily measured on the experimental curve, and
thus ha-hb is found. The following values have thus been
(roughly) calculated from observations. Where the neutral point
was not reached, it is put in brackets. The unit for ha - Jch is 3 or 4
2

'per cent, less than — of the electromotive force of a good G-rove’s
cell.

Fe-Cu (had)

T

265 C.

Tca ~ Jcb
-0-00147

Fe-Al

T

(387) C.

k

'a — tcb

0-00105

- Cu (good)

260

- -00145

>» ~ Arg.

Cu (bad) - Cd

(1357)

-

•00045

„ -Cd

159

- -00209

-(23)

-

•00081

„ -Zn

199

- -00189

„ -Zn

-(146)

-

•00048

„ -Ag

235

- -00151

» - Ag

- (687)

-

•00006

„ -Pb

(357)

- -00112

, , (good) - Pb

-(213)

+

•00016

,, - Brass

(318)

- -00127

Pb-Cd

-(74)

-

•00096

„ -Pt

(519)

- -00063

„ - Pd

-(188)

+

•00080

„ -Sn

(416)

- -00094

,, - Zn

-(78)

-

•00060

,, - Pd

(1908)

- *00029

„ - Ag

- (262)

-

•00026

600

Proceedings of the Royal Society

Now, it is an immediate consequence of the second law of thermo-
dynamics that, as Peltier effects are reversible with the direction of
the current, and are the only sensible thermal effects when a very
feeble current passes through a thermo-electric circuit, all of whose
parts are at one temperature, we must have

or, assuming the parabolic law,

^•fc-^)(Ta6-0 = 0.

This holds for any number of separate materials in the conductor.
As t is the same throughout, the terms involving it evidently
vanish identically; but there remains the equation
l.(ka-hb) Ta6 = 0,

establishing a relation between the specific heats of electricity in a
number of metals and the absolute temperatures of the neutral
points of each junction of two of them. Other relations may be
obtained by altering the order of the metals if there be more than
three — but they are all virtually contained in the formula for three,
which we write at full length,

(ha ~ ^b) ^ab + d£b ~ K) ^bc + (he ~ ^a) ^ca =

From the direct experiments of Le Roux on “l’Effet Thomson,” as
he calls it, it appears that h is null in lead.* At all events,
since Thomson showed that it has opposite signs in iron and copper,
we may imagine a substance for which h = 0. We may now con-
struct an improved “ Thermo-electric diagram ” to represent these
relations numerically, employing the line for this substance as
our axis of absolute temperatures ; while the ordinates perpen-
dicular to it give, for this substance employed with any other in a

circuit of two metals, the values of or or (what comes

to the same thing) the electro-motive force of a circuit whose
junctions are both very nearly at t , but have a small constant
temperature difference. This quantity corresponds with what has
been called the thermo-electric power of the circuit.

* Annales de Cljimie, 1867, vol. x. p. 277.

601

of Edinburgh, Session 1871-72.

The two oblique straight lines in the diagram belong to the metals
a , b, respectively. The tangents of their inclination to the horizontal
axis (the line of the supposed metal for which k = 0) are ka, kb — and
they cut it at the points Ta, Tg, where they are neutral to it ; cut-
ting one another at a point A whose abscissa is their own neutral
point Ta&. The only change which would, be introduced, by taking

as horizontal axis the line corresponding to a metal for which k
does not vanish, would be a dislocation of the diagram, by a
simple shear. This follows at once from the equation of one of
the lines —

v=K 0-T„).

The diagram gives the Peltier effect at the junction of a and b
for any temperature tv by drawing the ordinate at tv and completing
a rectangle cc'gf on the part intercepted, its opposite end being at
absolute zero. The area of this rectangle is to be taken positively
or negatively according as the corner corresponding to a is nearer
to, or further from, the horizontal axis than that corresponding
to b , the current being supposed to pass from a to b.

The electro-motive force in a circuit of the two metals, a and b,
with its junctions at tx and t2 respectively, is found by drawing
ordinates at these temperatures, so as to cut off triangular spaces
Acc', Add', whose vertices are at the neutral point. The difference

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Proceedings of the Royal Society

of the areas of these spaces, cdd'c', is proportional to the electro-
motive force. When the higher temperature, £3, is above the neu-
tral point, the electromotive force is the difference of the areas A cc',
Aee'. The case above mentioned, in which, by a differential
galvanometer, we get rid of the terms in £2, is obviously a process
for making the curves of. two separate complex arrangements into
parallel straight lines.

In conclusion, I may give a few instances of the comparison of
results of calculation of the neutral point of two metals from their
observed neutral points, and differences of &, as regards iron, with
calculation of the same neutral point from the portion of the curve
(assumed to be a parabola) which expresses their electro- motive
force within ranges of temperature where mercurial thermometers
can be applied.

Thus with Fe, Cd, Pb, we have from the iron circuits 0-00112
- 0-00209 = - 0-00097, while the direct experiment with Cd, Pb
gave - 0-00096.

The neutral point, as calculated from the data for the iron
circuits is - 69° C., while the calculation from direct experiment
gives -74°C.

When the quantities to be found are very small, as for instance
in the case Ag - Cu, we cannot expect to get a good approximation
by introducing a third metal. In fact, introducing Fe we find
indirectly 0-00147 - 0-00151 = - 0-00004, while the direct de-
termination gives - 0-00006.

Again with Zn and Cu, indirectly wre get

- 0-00042 and - 144° C.

Directly - 0'00048 and - 146° C.

Several of the other groups give results as closely agreeing with
one another as these, others are considerably out.

The numerical determinations above are founded entirely on a
series of experiments made for me by Messrs J. Murray and R. M.
Morrison. Mr W. Durham is at present engaged in determining
the electromotive force of contact of wires of the same metal at
different temperatures, with the view of inquiring into its relation to
ordinary thermo-electric phenomena which appears to be suggested
by some of the formulas above given.

DEFLECTIONS INDICATING MAGNETIC STRENGTH

of Edinburgh, Session 1871-72.

603

Monday , 15 th January 1872.

Professor KELLAND, Vice-President, in the Chair.
The following Communications were read : —

1. On the Relation of Magnetism to Temperature. (With
a Plate.) By D. H. Marshall, Esq., M.A., Assistant to the
Professor of Natural Philosophy. Communicated by Pro-
fessor Tait.

The following was the arrangement adopted in these experi-
ments : — A large magnet was put into a copper pot containing oil,
which was heated up by a brass Bunsen, and its temperature deter-
mined by a mercurial thermometer immersed in it. The magnet
was set magnetically east and west, and placed so as to act
with equal force on the poles of a small magnet, whose centre
was in the prolongation of its axis. This small magnet was
cemented to the back of a small concave mirror, suspended by a
single silk fibre, and placed in a glass case to guard it against cur-
rents of air. The deflections of the small magnet were measured
exactly as in the reflecting galvanometer, and since from the nature
of the arrangement, the absolute magnetism in the large magnet is
directly as the tangent of the angle of deflection of the small one,
its amount for any temperature was immediately measured by the
reading on the scale.

a

Te

N S , the poles of the fixed magnet, m its absolute magnetism.
N a = x, SN = 1. The couples indicated are those produced by
the large magnet, and the earth’s magnetism, E, on the small
magnet.

604

Proceedings of the Royal Society

For any deflection 6, if the length of the small magnet be negli-
gible compared with x, we have

[This simple formula holds, of course, however complex be the
distribution of magnetism in the large magnet, provided the rela-
tive intensities of magnetization at different parts, and their direc-
tions, remain unchanged by heating.]

Disturbances were experienced in the form of thermo-electric
currents in the pot and brass ring supporting it (these acted against
one another), but their effects were rendered insignificant by remov-
ing the flame, and allowing the whole to come to a uniform tem-
perature before reading. The direction of these currents, and there-
fore that of the disturbance to which they gave rise, could be re-
versed by changing the position of the flame relatively to the pot ;
but a smaller disturbance of a more unaccountable nature presented
itself during the heating of the pot, which did not -depend on the
position of the flame, and could not be got rid of. This latter
disturbance, which increased with the temperature, resulted in a
gradual alteration of zero, and in consequence the deflections, cor-
responding at least to the higher temperatures in the curves and
all the ordinates of the lower part of curve III., are somewhat less
than they ought strictly to be.

Curves I., II., and the upper part of curve III., show how the
absolute magnetism diminishes as the temperature of the magnet
increases ; the lower part of curve III. shows how the magnet re-
gains its power when the temperature again falls, and it is seen at
once from it that, when the magnet is allowed to cool after being
heated, the deflection corresponding to a given temperature is less
than that obtained at the same temperature when the magnet is
being heated, thus indicating a loss of magnetic power, and the
difference of the two deflections is greater the lower the tempera-
ture. It is principally on this account also that the curves I. and
II. do not coincide, for the experiments were performed on succes-
sive days, and it was found that that magnet took about two days
after such heating to acquire its original power. The magnet used

E sin.

(* + Q‘-

1

cos. 6 :

m a tan. 0 .

605

of Edinburgh, Session 1871-72.

in the experiments represented by curves I. and II. was not the
same as the one used in that represented by curve III. ; the latter
was a thin, very hard steel magnet, the former thicker and softer,
and it may be seen from the curves that the hard steel parted with
its magnetism less readily than the soft.

From these experiments it follows also that

dm
dt ’

or the rate of

change of magnetism with temperature, is not constant for each
temperature, but depends in some way or other upon the state of
the magnet.

When the above experiment was repeated with an electro-magnet
in the copper pot instead of a permanent magnet, it was found that
while at a temperature of 500° F. the power of the permanent
magnet is very much lessened, that of the electro-magnet, provided
the intensity of the current remain constant, is unaltered.

2. Note on a Singular Property of the Retina.

By Professor Tait.

While suffering some of the annoyances seemingly inseparable
from re-vaccination at too advanced an age, I was led to the curious
observation presently to be described. I was unable to sleep, ex-
cept in u short and far between ” dozes, from which I woke with
a sudden start, my eyelids opening fully. I found by trial that
this state of things became somewhat less intolerable when I
lay on my back, with my head considerably elevated. In this
position I directly faced a gas jet, burning not very brightly, placed
close to a whitish wall, and surrounded by a ground glass shade,
through which the flame could be prominently perceived. The
portions of the wall surrounding the burner were moderately illu-
minated, and hyperbolic portions above and below somewhat more
strongly. I observed, on waking, that the gas flame seemed for
a second or two to be surrounded by a dark crimson ground, though
itself apparently unchanged in colour. Gradually, after the lapse
of, at the very utmost, a couple of seconds, everything resumed its
normal appearance. As this phenomenon appeared not only to be
worthy of observation in itself, but to furnish me with something
definite to reflect upon, which is far the best alleviation of annoy-
VOL. VII. 4 M

606 Proceedings of the Poyal Society

ances similar to those from which I was suffering, I determined to
watch it, transitory as it was, feeling assured that I should have
many opportunities of observing it. After two nights’ practice, I
found myself getting dangerously skilful in reproducing it, and
decided, somewhat reluctantly, that I must give it up. What I
observed, however, has already been almost completely described
as having been seen on the very first occasion. I endeavoured to
prepare myself to note any possible difference of colour in the crim-
son field, as distinguished from mere difference of intensity of illu-
mination, and I could perceive none. I also endeavoured to
ascertain the nature of the transition from this state to the normal
one, but this was so exceedingly rapid that I could form no conclu-
sion, and I found that under the necessary circumstances of the
observation, viz., as it could be made only at the instant of awaken-
ing, it was impossible for me to estimate, even approximately, the
duration of the crimson appearance.

Several possible modes of explaining the phenomenon at once
occurred to me. Of these, however, I shall mention but three,
and give reasons for rejecting two of them, while not pretending
to specify them in the order in which they occurred to me.
It cannot be ascribed to any visual defects in my eyes, which
are normal as to colour sensations, and very perfect optically.
ls£, I imagined it might be due to light passing through the almost
closed eyelid, or through a portion of the eyeball temporarily filled
with blood. Besides feeling certain that my eyes were fully
open, I had the additional argument against this explanation, that
I could not reproduce the phenomenon by carefully and gradually
closing them, and that I am not aware that an effusion of blood
in any part of the eye could possibly disappear so rapidly. 2c?,
It might be due to diffraction either by my eyelashes or by small
particles, whether on the cornea or in the transparent substances of
the eye, coarse enough to produce nearly the same tint for some
distance round the flame. This is negatived by several considera-
tions, among which (in addition to those urged against the preced-
ing explanation) it is only necessary to mention again the facts,
that the colour is not one which can be produced by diffraction
under such circumstances, and that it appeared to be the same on
the more illuminated, as well as on the darker part of the field.

607

of Edinburgh, Session 1871-72.

3d, I suggest, as a possible explanation, but one which is more
specially in the province of the physiologist than of the natural
philosopher, that the retina (or the nerve cells connected with it?)
partakes of sleep with the other nerve cells, by which that pheno-
menon has been accounted for, and that on a sudden awakening,
the portions connected with the lowest of the primary forms of
colour are the first to come into action, the others coming into
play somewhat later, and almost simultaneously. This would
completely account for the peculiar crimson colour, and for its
uniformity of tint over the whole field, excepting the gas flame
itself, the comparative intensity of whose light may easily be sup-
posed to have simultaneously aroused all the three sensations in the
small portion of the retina on which it fell, though it is just pos-
sible that it also may have appeared crimson for an exceedingly
short period. I am not aware of any experiments or observations
having been made with reference to the subject of this note,
and I hope to have no further opportunities of making them, at
least in the way in which these were made, but the point is a
curious one, and worthy of the careful attention of all who may be
forced to consider it. Professor Clerk-Maxwell informs me that
he and others have observed that the lowest of the three colour sen-
sations is the first to evanesce with faintness of light, and that it
has been asserted to be the most sluggish in responding to the
sudden appearance of light. This, however, is not necessarily anta-
gonistic to my explanation, but will rather, if my explanation be
correct, tend to show a greater interval between the awakening of
the red, and that of the other colour sensations than that above
hinted at.

3. On the Operator £>(v). By Professor Tait.

(Abstract.)

By combining, as above, Hamilton’s linear and vector-function
with his celebrated vector square- root of the negative of Laplace’s
operator, an operator of great use in physical applications of mathe-
matics is obtained. With the notation employed in the author’s
paper “ On Green's and other Allied Theorems,” Trans. B..S.E.

608 Proceedings of the Royal Society

1870, § 17, it is shown to be generally expressible in the form of

aida + Pid(3 + 7idy>

where a, /3 , y, are any three unit vectors (not necessarily rectangu-
lar), and av /3V yv any three vectors whatever. The scalar and
vector parts of the result of its operation on a vector-function, cr-, of p
are first considered — with various interpretations, especially as to dis-
tortions, condensations, &c., in a group of points — then it is exhi-
bited in its applications to various questions ; especially to Physical
Strain, to Heat, and to Electricity. By making the constituents
of <p variable, we have a means of Deformation specially applicable
to problems such as that of Orthogonal Isothermal Surfaces.

4. Note on Pendulum Motion. By Professor Tait.

Mr Sang’s papers in recent parts of the Transactions of the
Society have reminded me of some geometrical constructions which
are to a certain extent indicated in Tait and Steeles Dynamics of a
Particle (1856). Some of these were suggested to me by a beautiful

construction given (I believe by
Clerk-Maxwell) in the Cambridge
and Dublin Math. Journal , Feb.
1854, the others by a very simple
process which occurred to me for
the treatment of oscillations in
cycloidal arcs. The former en-
ables us easily to divide the arc of
oscillation of a pendulum, or the
whole circumference if the motion
be continuous, into two, four,
eight, &c., parts, which are de-
scribed in equal times; also to
solve by simple geometrical con-
structions problems such as the
following : — Given any three
points in a circle, find how it
must be placed that a heavy
of them, may take twice as long

609

of Edinburgh , Session 1871-72.

to pass from the second to the third as it takes to pass from the
first to the second. It suggested to me the following theorem,
which really involves Mr Sang’s results, hut which appears to be
considerably simpler in treatment, this being my sole reason
for bringing it before the Society.

Let DM be a horizontal line, and let DA be taken equal to the
tangent from D to the circle BPC', whose centre C is vertically under
D. Also let PAQ be any line through A, cutting in Q the semi-
circle on AO. Also make E the image of A in DM. Then if P
move with velocity due to DM, Q moves with velocity due to the
level of E ; so that we have the means of comparing, arc for arc,
two different continuous forms of pendulum motion, in one of which
the rotation takes place in half the time of that in the other.

Let to be a small increment of the circular measure of BAP, then

arc at Q = CA . co , arc at P =

AP. PC
PQ

CO .

Also,

velocity at P = J 2g . PM = ,J • AP .

Hence,

velocity at Q = ^PQj^>Ap

9- AC
PC

• PQ.

But

PQ = VOP2 - CQ3

= »/CP2 — CR . CA (where QR is horizontal)

, /ftps _ PAa

= JCAj - -CA + AR = JCA . ER .

Hence,

AO

velocity at Q = ^Q-Jg . ER.

Thus Q moves with velocity due to the level of E, and constant
acceleration

AC2

2P02 -3-

The second process referred to above gives at once the means
of comparing continuous rotation with oscillation, as follows —

610

Proceedings of the Royal Society

Let two circles touch one an-
other at their lowest points —
compare the arcual motions of
points P and p, which are always
in the same horizontal line.
Draw the horizontal tangent
AB. Then, if the line MPp be
slightly displaced,

Arc at P AO M p AO /aM.MO AO JaU
Arc at p ~ MP ' dO ~ aO V AM . MO aON AM

Thus, if P move, with velocity due to g and level a, continuously
in its circle, p oscillates with velocity due to

g . and level AB .

Combining the two propositions, we are enabled to compare the
times of oscillation in two different arcs of the same or of different
circles.

Professor Cayley has pointed out to me that results of this kind
depend upon one of the well-known fundamental transformations
of elliptic functions. In fact, it is obvious that the squares of the
sines of the quarter arcs of vibration which the combination of the
above processes leads us to compare are (in the first figure),

CA , C'B . .

and respectively-

Calling them
we have

-j^- and -j-£ , and putting DA = a, AC = e,

1 e 1 2 J2ae + e1 2

k* ~ 2 a + e ’ ~ e + v/2^T+=? ’

of Edinburgh , Session 1871—72

61 1

Hen'ce

i

k'L

_4

k

or

J_ = 2 Jk

kx 1 + k

Lagrange’s transformation is equivalent to

and we thus have

whose application to the pendulum problem is obvious.

5. On the Decomposition of Forces externally applied to an

Elastic Solid. By W. J. Macquorn Bankine, C.E.,
' LL.D., F.B.SS. Bond, and Edin.

The principles set forth in this paper, though now (with the
exception of the first theorem) published for the first time, were
communicated to the French Academy of Sciences fifteen yearn
ago, in a memoir entitled “ de lEquilibre interieur d’un Corps
solide, elastique, et homogene,” and marked with the motto,
“ Obvia conspicimus, nubem pellente Mathesi,” the receipt of which
is acknowledged in the Cornptes Bendus of the 6th April 185T
(vol. xliv. p. 706.)

The author quotes a theorem discovered by him, and previously
published in the Philosophical Magazine for December 1855,
called “ the Principle of Isorrhopic Axes,” viz., “ Every self-

( Abstract .)

612

Proceedings of the Royal Society

balanced system of forces applied to a connected system of points,
is capable of resolution into three rectangular systems of parallel
self-balanced forces applied to the same points.”

Let X, &c., be the forces resolved parallel to any three ortho-
gonal axes ; find the six sums or integrals, ^X#, y, %Zz, 3Yz =
%Z y, %Zx = 2,Xz, Xy = ; these are called the “ rhopimetric

coefficients.” Conceive the ellipsoid of whose equation these are
the coefficients ; then for the three axes of that ellipsoid (called
the “ isorrhopic axes”) each of the last three coefficients is null ;
and the three systems of forces parallel respectively to those three
axes are separately self-balanced.

The theorem may be extended to systems of moving masses by
d2x

putting X-m- &c., instead of X, &c. If for any system of

forces, the last three rhopimetric coefficients are null, and the first
three equal to each other, every direction has the properties of an
isorrhopic axis. This, of course, includes the case in which all
the coefficients are null ; and in that case the system of forces is
said to be “ Arrhopic.” The author shows that the six rhopimetric
coefficients of a system of forces externally applied to an elastic
solid, being divided by the volume of the solid, give the mean
values throughout the solid of the six elementary stresses. Those
are called the “ Homalotatic stresses.”

If we calculate from them the corresponding externally applied
pressures, these may be called the 1‘ Homalotatic pressures.”

Take away the homalotatic pressures from the actual system of
externally applied pressures, and the residual pressures will be
arrhopic ; that is to say, their components parallel to any direction
whatsoever will be separately self-balanced, and may have their
straining effects on the solid separately determined ; and hence,
the axes to which those residual pressures are reduced may be
arbitrarily chosen, with a view to convenience in the solution of
problems.

The author then demonstrates that those problems respecting
the distribution of stress in an elastic solid, in which the stresses
are expressed by constants and by linear functions of the co-ordi-
nates, are all capable of solution independently of the coefficients
of elasticity of the substance.

of Edinburgh, Session 1871-72.

613

6. On Geometric Mean Distance. By Professor
Clerk Maxwell.

7. On a Singular Case of Rectification in Lines of the
Fourth Order. By Edward Sang, Esq.

The class of curves resulting from the formula
x = a . sin 0 , y - b . sin 2 0

are of considerable interest as occurring in various mechanical in-
quiries. When a straight wire, whose effective breadth and thick-
ness are as two to one, is fixed at one end and made to vibrate, its
free end describes a curve of which the general equation is

* = a . sin (0 -f &) , y = b . sin 2 0 ,

in which k is constant for the particular variety of curve. When

T

k — Tpr the curve becomes a parabola, and when k = o, it takes

the form above mentioned ; these phases were exhibited by me in
1832. Again, when a system of toothed wheels is deduced from a
straight rack, having a curve of sines for its outline, the points of
contact describe a curve of this class, as is shown in my treatise on
the teeth of wheels.

In attempting the rectification of these curves, we have to inte-
grate an expression of the general form

dl a2. cos 02 + 4 b2. (cos 2 6)2yd 0 ,

and for this purpose have to expand the root in an interminate
series, and then integrate each term, the result being unmanage-
able from its complexity. In one particular phase of the curve,
however, the integration can be easily effected. The above general
expression may be written

dl = { 16 b2. cos 6 4 + (a2 - 16 b2) cos $ 2 + Wf dQ ,

and we readily observe that if a2 = 32 b2, that is, if a = 4 b^/%

4 x

VOL. VII.

614 Proceedings of the Royal Society

the quantity under the radical sign becomes a square, and in this
case

d l = { 4 b . cos 6* + 2 b } d 0
= 2 b { cos 2 9 + 2 } d 0 ,

whence, on integrating, we at once obtain

l = b { sin ? 6 + 4 0 } = y 4:b 6 .

The expression for the radius of curvature also takes a very simple
form, it is

= _b___ (cos 2 0 + 2)2
~ a/ 2 sin 0

No other curve of this class, nor indeed any belonging to the more
general formula

x = a . sin (p $ + k) , y — b. sin (q 0 ) ,

seems to be susceptible of easy rectification.

These results may be exhibited geometrically thus: — Having
drawn OA, OB in the directions of the length and breadth of the
curve, and described round 0 a circle with the radius OB = OC
= &, let OA be made equal to four times CB, and an hour-glass
curve be constructed in the usual manner. Then, having as-
sumed any arc CD to represent b . 2 0 and drawn DFQ parallel to
OA, if FP be laid off equal to a . sin 0, P is a point in the curve,
and the length from 0 to P is equal to the sum of OF, and twice
the arc CD.

Hence it follows that the portion PQ of the curve, cut off by the
line DQ, is just double of the circular arc DBE, cut off by the same
line.

B

Hence it appears that the length of the quadrant OPQA of the
curve is just equal to the circumference of the circle, or that the
whole curve is equal in length to four times the circumference of
the circle described with the radius OB.

oj Edinburgh, Session 1871-72. 615

The following Gentlemen were admitted Fellows of the
{Society : —

David Maclagan, Esq., C.A.

Major Rickard.

Dr John Sibbald.

Dr J. G. Fleming.

Rev. Andrew Tait, LL.D.

David Grieve, Esq.

The Right Rev. Bishop Cotterill.

George Barclay, Esq.

Monday , 29 th January 1872.

The Hon. LORD NEAVES, Vice-President, in the Chair.
The following Communications were read : —

1. On the Wheeling of Birds. By Professor Fleeming
Jenkin.

2. Notice of a New Family of the Echinodermata. By
Professor Wyville Thomson, LL.D., F.R.SS.L. and E.,
F.L.S., F.G.S.

During the deep sea dredging expedition of H.M. ships
‘Lightning’ and ‘Porcupine,’ in the summers of 1868-69 and
1870, two or three nearly perfect specimens, and a number of frag-
ments were procured of three species of regular echinideans, which
were referred by the author to a new family, the Echinothuridae,
intermediate in their more essential characters between the
Cidaridae and the Diadematidae.

In these urchins the test is circular and greatly depressed. The
plates of the perisom are long and strap-shaped, and the inter-
ambulacral plates overlap one another regularly from the apical
towards the oral poll, while the ambulacral plates overlap in a
similar way in the opposite direction. The test is thus flexible.
The plates of the ambulacral areae are essentially within the inter -
ambulacral plates which over-lie them along their outer edges.
The ambulacral pores are tri-gem in ah arranged in wide arcs; the

616 Proceedings of the Royal Society

two pairs of pores of each arc which are nearest the centre of the
ambulacral area, pierce two small accessory plates intercalated be-
tween the ambulacral plates, while the outer pair passes through
the ambulacral plate itself near its outer extremity. The tube-
feet on the oral surface of the body are provided with terminal
suckers, supported by calcareous rosettes, while those on the apical
surface are conical and simple. The tube-feet on both surfaces
have their walls supported by wide cribriform calcareous plates.

The peristome and the periproct are unusually large. The edge
of the peristome is entire, without branchial notches, and the
peristomial membrane is uniformly plated with twenty rows of
imbricating scales, corresponding with the rows of plates of the
corona, and the rows of ambulacral tube-feet are continued as in the
Cidaridse, over the peristome up to the edge of the mouth. The
ovarial plates are unusually large ; in some of the species they are
broken up into several calcareous pieces. The ovarial apertures
are very large, and are partly filled up with membrane.

The dental pyramid is wide and strong, but somewhat low on
account of the depressed form of the test. The epiphyses of the
tooth-sockets do not form closed arches as in the Echinidae, and in
this respect resemble those of Cidaris and Diadema. The teeth
are simply grooved as in Cidaris. The spines are hollow and com-
paratively small, and the larger spines show a tendency to the spiral
arrangement of projecting teeth which is so characteristic of the
Diadematidas. The Pedicellariae are very remarkable in form,
more nearly related, however, to those of the Diadematidse than
to any others. A strong fenestrated fascia traverses the body cavity
vertically on either side of each ambulacral area, thus nearly
cutting off the ambulacral from the inter- ambulacral region, and
allowing only a small space for the coils of the intestine.

For this family, distinguished by the depressed corona of imbri-
cated plates, the peristome covered with scales through which the
rows of ambulacral double-pores are continued to the mouth, the
absence of branchial notches in the peristomial border, the
peculiar arrangement of the ambulacral pores, the heterogeneity of
the tube-feet on the oral and apical surfaces, the absence of closed
arches uniting the pairs of tooth -sockets, and the absence of
longitudinal ridges within the simple grooved teeth, the term

617

of Edinburgh, Session 1871-72.

Echinothuridae was proposed, the fossil-genus Echinothuria , saga-
ciously described by the late S. P. Woodward, from an imperfect
specimen from the upper chalk being taken as the type. The
specimens procured were referred to two genera and three species.

In the genus Phormosoma the plates of the perisom only
slightly overlap, and fit so closely as to form a complete calcareous
casing without any membranous fenestras. Although constructed
essentially on the same plan, the apical and oral surfaces of the
test differ from one another singularly in character, the oral sur-
face being almost uniformly covered with large areolar depressions
surrounding spine tubercles.

One species, Phormosoma placenta , n. sp., was dredged in deep
water off the Butt of the Lews, and some fragments were met
with in gravel from the Bockall Channel.

In the genus Calveria, the plates of both the ambulacral and
inter-ambulacral areas form large expansions towards the middle
line of the area, while the outer portions of the plates are narrow
and strap-shaped, leaving large fenestrae filled up with membrane
between plate and plate. The oral surface of the body does not
differ markedly in character from the apical.

Two species of this genus were taken, Calveria hystrix, n. sp.,
with a strong perisom, of a nearly uniform rich claret colour, from
deep water off the Butt of the Lews ; and Calveria fenestrata, n. sp.,
more delicate, with wider spaces between the plates, the body of a
greyish colour, rayed from the apical pole with bright chocolate.

It is very possible that the genus Asthenosoma, described by
Professor Gfrube, may belong to this group, but the description of
that form hitherto given is not sufficient for identification, as the
points of structure on which the families of the Echinidea are dis-
tinguished from one another are not noticed. With this exception,
the form which most nearly resembles them is Astropyga , which,
however, is in every respect, except in habit, a true Diadema , with
the peristomial margin deeply notched for external branchiae, and
all the other characters of the family.

618

Proceedings of the Royal Society

3. On frhe Principles which regulate the Incidence of Taxes.
By Professor Pleeming Jenkin.

It is well known that many taxes do not fall ultimately on the
person from whom they are in the first instance levied. The mer-
chant advances the duties imposed on goods, but the tax ulti-
mately falls on the consumer. The problem of discovering the
ultimate or true incidence of each tax is one of great importance,
and of considerable complexity. The following paper contains an
investigation of the methods by which this incidence may in some
cases be experimentally determined, and of the principles regulat-
ing the incidence in all cases, these principles being stated in a
mathematical form.

The author, in a paper published in Becess Studies, expressed
the law of supply and demand by representing what may be
termed the demand and supply functions, as curves. The ordi-
nates parallel to the axis OX, fig. 1, were prices — the co-
ordinates parallel to the axis OY were the supplies at each
price, and the demand at each price for the respective curves — the
market price is then indicated by the ordinate X of the point at
which the curves intersect, this being the only price at which
buyers and sellers are agreed as to the quantity to be transferred.

We might write the law algebraically as follows, calling y the
quantity of goods in the market, at each price x , we have y = <p x ;
and calling yx the quantity of goods demanded at each price, we
have yx = <px x ; the market price is determined by the equation
y — yL. There is, however, little or no advantage in adopting this
algebraic form, because we cannot suppose that in any instance
<px or <pxx will be any tolerably simple algebraic function, whereas
the curve for given goods might be determined experimentally by
observing from year to year variations of quantities bought or
quantities supplied at various prices.

Professor Jevons has since given a much more complex algebraic
representation of the same law, which, however, reduces itself to
the above simple form.

The graphic method may also be employed to indicate the
advantage gained by each party in trade, and to show how it may
be estimated in money. Let the two curves indicate the demand

of Edinburgh, Session 1871-72.

619

and supply at each price for a certain kind of goods. If all sellers
were of one mind, and were willing to supply all their goods at
a given price x, and were quite determined to sell no goods below
that price, the supply curve would be a mere straight line parallel
to OX, and ending abruptly at the ordinate raised at x. Similarly,
if all buyers were of one mind, and would only buy below a given
price x, but were whiling to buy all they want at that price, and no
more at any lower price, the demand curve would be a line parallel
to OX ending abruptly at the ordinate raised at x, and the price
would be quite indeterminate. If the two lines overlapped, trans-
actions might take place at any price between that at which the

Y

sellers wrere willing to sell and the buyers willing to buy ; there
would in this case be no market price. This case does not repre-
sent the true state of either buyers’ or sellers’ minds in any real
large market. There are always a few holders who would only sell if
the price were much higher than the market price, — these are the
people who expect prices to rise ; there are some who are just willing
to sell at the market price, but who will not sell a penny below; and
there are others, weak holders, who expect prices to fall, and these
would really, if pushed to extremity, sell below the market price.
This condition of things is represented by the supply curve in fig. 1.

620 Proceedings of the Royal Society

Similarly, there are a few buyers who, if pushed to extremity,
would buy some goods above market price ; some also will just
buy at market price ; some will not buy unless the price is below
market price. This is represented by the demand curve.

Now, I contend that when the market price is fixed, those
traders who are perfectly indifferent whether they buy or sell at
that price reap no benefit by the trade ; but these will be few in
number.

Looking at the demand curve, the ordinate XA from the axis .OY
to A represents the value set on some of the goods by some buyers,
but these buyers have got the goods for the sum represented by
the ordinate x = OM ; the difference between these two ordinates
XA - x is the difference in price between what was given and what
might have been given for a certain small quantity Ay of goods.
Ay is therefore the benefit reaped by buyers from the purchase
of the quantity Ay; and integrating the benefits derived from the
sale of each successive quantity, we find the area MDCBAN
represents the whole gain to buyers by the purchase of the quantity
y of goods. Similarly, it is easy to show that the area MDc&aP
represents the gain to sellers by the same transaction ; these areas
represent the gain in money. Each product j\y(x - XA) being
the product of a quantity by the gain in money per unit of quantity.

Thus the whole benefit to the two leading communities is repre-
sented by the sum of the two above named areas, and the reparti-
tion of the benefit between the two communities is perfectly
definite.

Professor Jevons has used curves to integrate what he terms the
utility gained by exchange in a manner analogous to the above ;
but utility, as he defines it, admits of no practical measurement,
and he bases his curve, not on the varying estimates of value set
by different individuals each on what he has or what he wants, but
on the varying utility to each individual of each increment of
goods. The above estimate of the gain due to trade, deduced from
the demand and supply curves as originally drawn in my Kecess
Studies’ article is, I believe, novel, and gives a numerical estimate
in money of the value of any given trade, which might be approxi-
mately determined by observing the effect of a change of prices on
the trade; the curves throughout their whole lengths could cer-

621

of Edinburgh , Session 1871—72.

tainly not, in most cases, be determined by experiment, but
statistics gathered through a few years would show approximately
the steepness of each curve near the market price, and this is the
most important information.

A steep supply curve and a horizontal demand curve indicate
that the buyers reap the chief benefit of the trade. The sellers, if
producers, may, however, be making important profits as capitalists
and labourers.

A steep demand curve and a level supply curve indicate that the
suppliers are chiefly benefited by the trade ; the community or
body which is most ready to abandon the trade if the price in-
creases a little, benefits least by the trade.

When the traders are producers and consumers, the benefits
estimated in this way as due to the trade are not the only benefits
reaped by the community from the manufacture.

In this case, what is termed the supply curve depends on the
cost of production of the article, including that interest on capital
and that remuneration for skilled superintendence which is neces-
sary to induce the producer to employ his capital and skill in that
way. The cost of production increases generally with the quantity
of the article produced, otherwise the supply curve would be a straight
vertical line ; but as a matter of fact, to produce an increase of
production a rise of price is necessary, indicating that only a few
men with little capital are content with a small rate of interest and
small remuneration for their skill, but that to induce many men
and much capital to be employed in the particular manufacture, a
large rate of interest and considerable remuneration are required,
hence the supply curve will be such as shown in fig. 2, where the
price OP is that price or cost of production which is just sufficient
to tempt a few producers to produce a little of the article.

Then if OP' is the actual cost out of pocket required to produce
a small quantity of an article, and if OP is the lowest cost at
which any manufacturer can afford to produce it, the area P'D'DM
represents the whole profit to the producing capitalist when the
price is OM. The line D'P' is not necessarily parallel to DP,'
nor vertical, the bare cost of production of the article generally in-
creases as the quantity increases; and in that case D'P' is not verti-
cal. Again, the rate of interest required to tempt additional capital

4 o

VOL. VII.

622

Proceedings of the Royal Society

into a particular field is not constant, but increases, hence P'D' is
steeper than PD. I see at present no means of experimentally
ascertaining the gain reaped by producers represented by the area
PDDP' ; it can be approximately estimated by considering the pre-
vailing rate of interest in the producing community and the amount
of capital required for the production of the unit of the article.

We see that the gain of a manufacturing capitalist may be
divided into two parts — the profit as a trader, and the interest as a
capitalist.

In safe trades, where there are few fluctuations in price, the
former gain may perhaps be the most important,; in more specu-
lative trades the latter.

There is yet a third source of gain to the manufacturing com-
munity : the labourer who produces the goods earns his wages by
the manufacture, and this is an advantage to him. In the diagram,
the area OP'D'D" represents the wages paid for labour alone.
The length of the lines between OY and P'D' represent the wages
of labour per unit of goods, increasing as the quantity of goods
required increases. This is lost to the community if the manu-
facture is stopped. Thus the whole sum paid by the consumer is
the area OMDD"; and this is made up of three parts, one of which

623

of Edinburgh, Session 1871-72.

is the profit to the trader, one the interest to the capitalist, and
one the wages of the labourer ; all these advantages are lost if the
manufacture ceases.

The gain of the labourer does not resemble the profit of the
trader, or the interest of the capitalist. The profit of the trader is
the difference between his valuation of the goods and what he
gets for them. If he does not sell his goods he still has his
goods, he only loses the profit. Similarly, if the capitalist does not
sell his capital, he still has his capital. Now, the area P'PDIP
represents the profit made by the capitalist on the particular
employment of his capital, and this is all that he loses if unable to
sell that capital ; but the area OP'D'D" represents the whole sum
received by the labourers, not their profit. The profit of the
labourer may perhaps be considered as the excess of wages which
he earns in a particular trade, over that which would just tempt
him to work rather than starve or go into the workhouse.

If the consumer purchases the article for simple unproductive
consumption, then the loss to him is only represented by the area
DMN, If, however, a community purchases goods, and consumes
them productively, then, by the cessation of the trade, they in their
turn lose the interest on the capital they employ, and the labourers
of the community lose their wages; so that, in that case, the loss
to the buyer, who cannot be classed as an immediate consumer, is
made up of three parts, similar to those enumerated in the case of
the seller.

Taxes on Trade .

Having distinguished between the three distinct advantages
given by trade, I will now consider the incidence of a tax on trade,
levied as a fixed sum per unit of goods, as one pound per ton, or
one shilling per gross.

The effect of such a tax is to produce a constant difference
between the price paid by the buyer and the price received by the
seller. The market prices are determined in the diagram of the
supply and demand curves, by the points between which a line
parallel to OX, and equal in length to the tax, can be filled between
the two curves.

Thus, if in figure 3, FN be the demand curve, and PE the
supply curve, and if the length of the line CC' be the amount of

624

Proceedings of the Royal Society

the tax per unit of goods, then OM is the market price to the
supplier, OM' the market price to the buyer and the difference
Mm' is equal to the tax.

The total amount raised by the tax from the transactions repre-
sented in the diagram, is measured by the area MCC'M'. The

portion paid by the seller is measured by the area CC"M"M. The
portion paid by the buyer is measured by the area C'/C'M'M". The
whole loss entailed by the tax on the two communities is measured
by the area MCDC'M' ; the loss to the sellers is measured by the
area CDM"M ; the loss to the buyers by the area M"DC'M' ;
both buyers and sellers suffer a loss beyond the tax they pay. This
excess of loss is represented by the area CC"D for the sellers, and
C'C"D for the buyers.

If the tax be large, the line CO' will approach the axis OX, the
tax will be unproductive, and the area CC'D representing the excess
of injury to the buyers and sellers will be large, compared with the
produce of the tax. This fact is one justification of free trade.

There is a certain magnitude of tax which will produce the
maximum revenue or value for the area MCO'M'. The ratio in
which the tax falls, in one sense, on sellers and buyers is simply
the ratio of the diminution of price obtained by the sellers to the
increase of price paid by the buyers.

It is absolutely clear that this is the proportion in which the tax
is actually paid by the two parties, although this may by no means

of Edinburgh, Session 1871-72.

625

correspond to the relative suffering inflicted on the two parties, nor
is it even the proportion in which the two parties lose by the loss
of trade profit. The whole loss of either party is, as the diagram
shows, always greater than the tax they pay. The relative total
losses of the two communities as traders, are in proportion to the
areas MCDM" and M'C'DM" ; and these areas might approxi-
mately, at least, be ascertained by experiments for this purpose,
treating OD and C^D as straight lines, we only require to know the
quantity and price of the goods before the imposition of the tax,
and the quantity and price afterwards.

Thus, if a tax of 2d. per pound were imposed on the trade in
cotton between ourselves and America, if before the tax we imported
500 million lbs. at one shilling, and after the tax 300 million lbs.
for which we paid 13Jd., and the Americans received ll|d., the
total loss to the two communities as traders would be 600 + 200 =
800 million pennies, the produce of the tax 600 million pennies.

England would pay of the tax 450 million pennies. England’s
total loss would be 600 million pennies. America would pay
of the tax 150 million pennies. America’s total loss would be
200 million pennies. The incidence would be the same whichever
government levied the tax.

It follows from the above principles, that if a holder sells unre-
servedly, trusting to the competition between the buyers to produce
the market, the whole tax falls on the seller ; the supply curve
becomes a vertical straight line. If a buyer buys unreservedly,
the whole tax falls on him ; in this case the demand curve becomes
a vertical straight line.

Thus, if sales by auction were subject to a tax ad valorem or
otherwise, and if sales were quite unreserved, the number of trans-
actions not being altered, the prices would be unaltered, but the
sellers would only get the prices minus the tax.

This case does not practically arise, because, if auctions were
really so taxed, although in each auction that occurred the sale
might be unreserved, auctions would, as a whole, be checked; fewer
people would put up their goods for sale in that way, — the prices
would rise, the number of transactions would be diminished, and
the tax would really be borne in part by the buyers and part by
the sellers.

626

Proceedings of the Royal Society

If the trade between two countries really consists in the exchange
of goods, effected by the agency of money as a unit for expressing
value, but not involving the actual transfer of coin, the above prin-
ciples show’ the whole gain by the exchange to be the sum of two
gains which each party would make by each trade if it alone
existed.

If by duties one portion of the trade be extinguished or much
diminished, both parties lose, but if the other portion of the trade
remain uninjured, then, although there may be no exchange of
commodities other than of goods for actual money, nevertheless
the full gain on that which is untaxed remains intact. Thus,
although the French may tax our goods, and so inflict a loss on
themselves and on us, this is no reason for our inflicting an addi-
tional loss on the two communities by taxing the import of their
goods.

House Rent.

I will next consider the effect of a tax on house rent.

Landlords are here the sellers, and tenants the buyers of what
may be termed a commodity ; not the house, but the loan of a
house for a term of years — the tenant buys what might be called,
by the extension of a suggestion of Professor Jevons, a house-year
from his landlord.

The difference between the house and other commodities such as
food or dress is, that the house remains, wdiereas they are consumed.
The house-year is consumed year by year, but it is reproduced year
by year without material fresh expenditure on the part of the
landlord. This permanency alters the incidence of taxation.

If the demand falls off the landlord cannot remove his house —
he cannot cease to produce his house-year, which therefore he
must dispose of. Hence, in a stationary or declining community,
where no new houses are being built, but where year after year a
sensible proportion remains unoccupied, the landlord must sell his
house-year unreservedly, and any tax imposed on house rent would
fall on him alone; that is to say, he would receive a rent dimin-
ished by the full amount of the tax, and the tenant would pay no
more rent for a house of a given class than if no tax were imposed.
The supply curve becomes a straight horizontal line, and is un-
affected by the tax ; the demand curve is equally unaffected by

627

of Edinburgh, Session 1871-72.

the tax ; the number of houses let is unaltered by the tax, but the
landlords lose as rent the whole amount raised by taxation.

This reasoning is based on the assumption, that the supply curve
has become a straight horizontal line unaffected by the tax. This
condition is altered in any prosperous or growing community.
There, new houses must be built, and a considerable number of
houses are always unlet, not because they are not required by the
community, but because the speculative builders are holding out
for higher terms. This produces a supply curve of the kind
common to all other kinds of goods. At higher prices more goods
are forthcoming. A newly imposed tax will then be distributed
between sellers and buyers, landlords and tenants in a manner
depending on the form of these curves. A sensible check will be
given to the letting of houses, tenants will be content with some-
what less good houses, and landlords with rather smaller rents.
This is the immediate effect of the tax — the greater portion would
probably fall on the landlords at first, at least in the new houses
where fresh contracts are being made. But after a few years the
conditions would have altered. New houses are only built because
the builders obtain the usual trade profit and interest on their
capital — the check to letting consequent on the imposition of the
tax will therefore diminish the supply of new houses until, owing to
diminution in supply, rents have risen to their old average. Then
builders resume their operations. The whole tax by that time will
be borne by the tenants; that is to say, if there were no tax they
would get their houses cheaper by the precise amount of the tax,
because rents so diminished would suffice to induce speculative
builders to supply them. The rents through the whole town are
ruled by those of the new districts. There is a certain relative
value between every house in the town, and if the rents of new
houses are dearer the rents of the old houses are increased in due
proportion. In fact, when new houses need to be supplied year by
year, houses are commodities which are being produced, and the
tax falls on the consumers.

The above principles determine the incidence of a tax, whether
nominally levied on the landlord or tenant, but in their application
account must be taken of the mental inertia of both landlords and
tenants, as well as of the fact that many contracts for houses are

628 Proceedings of the Royal Society

not immediately terminable. These two conditions will for the
first few years after the imposition of any new tax cause it to fall
on the party from whom it is nominally levied.

Precisely as a tax on trade not only falls on the traders, hut
injures capitalists and labourers, a tax on house rents injures the
capitalists who build houses and the labourers they employ— not
that the capitalist pays the tax, hut he is prevented from finding a
useful investment for his money owing to the diminution in the
number or quality of houses required.

Taxes on Land.

The question of the incidence of taxes on land is peculiarly in-
teresting. Land differs from all other commodities, inasmuch as
the quantity of it does not depend on the will of any producer.
The number of houses in a flourishing community does depend on
the will of speculative builders; but land can only be increased in
quantity by such processes as enclosing commons, or breaking up
private pleasure grounds. We will neglect these small disturbing
influences, and assume that all the land in a country is available for
cultivation, where such cultivation is profitable; and that the absence
of profit is the only reason for neglecting to cultivate any portion of it.

It is well known that the rent of each acre of land is simply the
excess of annual value of that acre over the annual value of the
poorest land which tenants think it worth while to cultivate. We
may classify all land according to the total return which it will
yield per acre upon capital invested in its cultivation ; and we may
draw a supply curve of land such that the ordinates will be the total
quantities of land which will return each successive percentage on
the capital required to cultivate it. The supply diminishes as the
rate of percentage increases, that is to say, there is less land which
will return ten per cent, on the capital than will return five per
cent., and still less land which will return twenty or thirty per cent.

If, therefore, tenants as a body, considered as capitalists, will not
cultivate any land which does not yield twenty per cent., there will
be far less land in the market than if they will be just satisfied with
ten per cent.

Again, all tenants are not of one mind, and we may construct a
demand curve in which the ordinates are the total quantities of

629

of Edinburgh, Session 1871-72.

land which would be let, if the land paying no rent be fixed at
each successive percentage. The actual quantity of land let will
be determined by the intersection of the two curves, and is repre-
sented by the height MD, fig. 4.

If we now build a solid on the base OD’DN, such that its height
all along each ordinate x is the number of hundreds of pounds of
capital per acre required to give the percentage corresponding to
K the length x, then we shall have a volume standing on (OD'DN),

the contents of which will measure the total annual returns from
all the land cultivated.* The rent is the volume standing on
MDN, the profit received by the farmers is the volume standing
on OD'DM, and this is in excess of what would have just
tempted them to cultivate by the volume MDP. We may,
therefore, considering the farmer as a capitalist and a trader, call
the volume on MDP his trade profit, and the volume on OD'D
the interest on his capital.

The effect of any tax on the land is to reduce the interest which
each class of land is capable of returning on the capital employed.
This it will do in very different ways according to the manner in
which the tax is levied.

* If L. 150 per acre are required to give the percentage x of any one class of
goods, the height of the ordinate perpendicular to the plane of OD'DN will
he 1-5.

4 p

VOL. VII.

630 Proceedings of the Poyal Society

If the tax be an ad valorem duty on rent, it will modify the
supply curve only between D and N. There will remain just as
much land as before capable of paying rates of interest less than
OM, but the quantity of land capable of paying the higher rates
will be diminished ; in other words, the rate of interest which the
poorest land worth cultivating pays will not be affected, for this
land pays no rent and remains untaxed — hence no land will be
thrown out of cultivation, hut the supply curve will be altered from
DN to DN', diminishing the volume representing rent, but leaving
the other quantities untouched; hence any tax assessed on rent
is paid wholly by the landlord. The amount of the tax is the
volume standing on DNN'. It is curious to remark that this
tax in no way falls on the consumer. The tax on rent sim-
ply diminishes the excess of value which some land has over
others ; no land is thrown out of cultivation, and no less capital
employed in production than before ; no one suffers but the
landlord. If, instead of being assessed on the rent, the tax is
assessed on the produce of the cultivation, the incidence of the tax
will be greatly modified. The cultivation of land will no longer
be so profitable ; i.e ., the returns from capital employed on the
land will be less ; in other words, the whole supply curve of the
land will be modified, falling everywhere if the produce taxed be
that which is produced on all qualities of land. Some' land will
fall out of cultivation, and only part of the tax will be borne by
the landlord; part will fall in the first instance on the tenant, but
he, like any other manufacturer, will recover almost the whole
of his portion from the consumer. Tenants will be injured by
the limitation of the number of transactions, and labourers by the
diminution in the amount of work required. This is the effect of
an octroi duty.

Sometimes a tax is assessed not on the rent, but on an assumed
value per acre. Such a tax can never be raised on land which pays
no rent, for the owner would rather abandon possession of the land
than pay the tax. It might, however, lead to the abandonment of
the cultivation of poorer soils ; it would then injure tenants and
consumers, although they would not pay one penny of the tax; for
taxes cannot he paid out of lands which lie waste ; assuming that
the tax is always less than the rent, as it certainly always should

of Edinburgh, Session 1871-72.

631

be, it will be paid wholly by the landlords. The tax in this case
does not diminish the supply of land.

A cognate question of great interest is, Who reaps the benefit of
any improvements in agriculture, making land return more than it
previously did ? This improvement may require, and probably will
require, increased investment of capital. The whole supply curve
will be raised; assuming the demand to remain the same, fig. SjM'T)"
will be the new increased number of acres in cultivation, but land
will be left uncultivated which would have returned the interest
OM on capital. The volume standing on D'D"N" will be much
greater than that on D'DN, for the third dimension will also have
increased ; the average rate of interest and the trade profit of the
tenant will have increased, and it is highly probable that the
volume standing on D"M"N" may be greater than that which
stood on JDNM ; but this is by no means certain. It might at first
be actually smaller. In all probability, however, the demand
curve is very nearly vertical, a small increase of profit tempting a

largely increased investment of capital in farming. If this be so,
then the landlord also reaps considerable benefit from the improve-
ment, for if the farmers were contented with nearly the same rate
of interest as before, the solid standing on DRNN'T)" which he
gains would be larger than the solid on DRM"M which he loses;
moreover, the volume on RNM", which he retains, is increased.
Labourers "and consumers also gain.

632

Proceedings of the Royal Society

4. Additional Notes on the Occurrence of the Sperm-Whale
in the Scottish Seas. By Professor Turner.

In a communication made to this Society on the 6th February,
1871, I noted the capture of a sperm-whale at Oban in May, 1829,
and I collected from various sources records of the stranding of
seven additional specimens on the Scottish coasts.

Since that communication was published, a large sperm-whale
has come ashore on the west coast of the Isle of Skye, some parti-
culars concerning which I propose to relate in this communication.

Tourists in Skye, during the past autumn, who visited Loch
Corruisk by boat from Torrin, as they sailed up Loch Scavaig, be-
came conscious, by another sense than that of sight, that a large
animal in a state of putrefaction was in their immediate vicinity.

A correspondent of the “Glasgow Herald,’’ writing in July last,
states that a great whale entered Loch Scavaig about the middle of
that month, and after floundering about, bellowing like a bull
amongst the rocks, amidst which it had become entangled, it died
after a lapse of two or three days. Large quantities of blubber
were removed from the carcase without loss of time by the neigh-
bouring fishermen, but enough of the external form remained to
enable the correspondent to give the following description : Skin
black, thick and corrugated. Head enormous, square, ending in a
flat snout some eight or ten feet across, looking like a peat stack.
Eye small, surrounded with lashes, some 16 feet from the snout.
Blower covered with a flap a foot long. Under jaw slender, shorter
than the upper, in it were thirty-six teeth shaped like the ends of
ducks’ eggs. No teeth were visible in the upper jaw. The whale
could not be short of 60 feet in length.

My attention having been directed by Sir Bobert Christison to
the newspaper report, I at once recognised from the form of the
head, jaw, and teeth, that the characters were those of the sperm-
whale ( Physeter macrocephalus ), and I determined, if possible, to
obtain a portion, if not the whole of its skeleton. The distance,
however, of the spot, where the carcase was lying, from human
habitations, and the want of proper appliances for lifting heavy
objects, have proved hindrances to the removal of the huge cranium
of the animal, but the two halves of the lower jaw, and a number

of Edinburgh, Session 1871-72. 633

of the smaller bones of the skeleton, are now in my posses-
sion.

From the examination of these bones an estimate may be formed
of the age, size, and, I believe, also the sex of the animal.

The state of ossification of the bones proved that the animal had
reached its full period of growth, for the epiphysial plates were
anchylosed to the bodies of the vertebrae, the lower jaw had attained
a great length, the radius and ulna were anchylosed together, both
at their upper and lower ends, and the various subdivisions of the
sternum were welded into one massive bone.

As some estimate may be formed of the size of the animal from
the dimensions of its lower jaw, it may be useful to give the
measurements of this bone, and at the same time to compare it
with the dimensions of some other specimens.

In the Natural History department of the Edinburgh Museum
of Science and Art is a magnificent lower jaw, which was pre-
sented many years ago by Captain William Hardie. It possesses
twenty-five teeth on one side, but only twenty-four on the other.
On the outer face of the right mandible there has been engraved a
large picture of the boats of the ship “Woodlark” of London,
Captain William Hardie, engaged in the capture of the sperm-
whale, in a school of sperm-whales, off the Banda Islands, April
7th', 1813. On the other half, a figure, 43 inches long, of a sperm-
whale has been engraved. As authentic drawings of this animal
are by no means common, and as this figure has been executed with
a considerable amount of artistic skill, and in all probability by one
well acquainted with the form and proportions of this animal, I
produce on the following page a reduced copy. In the Anatomical
Museum of the University of Edinburgh is the mandible of a young
male, presented two years ago by my pupil, Mr F. B. Archer of
Barbadoes. The animal was captured in the North Atlantic Ocean,
in the latitude of the Azores.

Professor Flower has also carefully recorded* the dimensions of
three specimens from Tasmania, in the Museum of the London
College of Surgeons, one of which is stated to be “unique on
account of its great size,” and in measuring the Edinburgh speci-
mens I have followed his plan of taking the length from the apex
* Trans, Zool, Soc. 1868.

634

Proceedings of the Royal Society

635

of Edinburgh, Session 1871-72.

of the mandible to the middle of a line drawn across the posterior
ends of the rami.

Entire

Length.

Length
of Sym-
physis.

Greatest

Girth

Behind.

Mandible from Isle of Skye,

190J

//

116

56

Proportion, ....

100

61

29

Mandible in Natural History Museum,

196

120

54

Proportion, ....

100

60

27

Mandible in Anatomical Museum,

80

381

29

Proportion, ....

100

48

36

Width

Behind.

Mandible, young skull, Tasmania,

49

21

31

Proportion, ....

100

43

63

Mandible, Tasmanian Skeleton,

Proportion, ....

174

102

72

100

59

41

Largest Tasmanian Mandible,

194

124

75

Proportion, ....

100

64

38

The specimens in the Edinburgh Museums corroborate the con-
clusions arrived at by Mr Flower, that a gradual increase in the
length of the symphysis, compared with that of the entire jaw,
takes place as age advances, and it is obvious also that the girth
behind diminishes in proportion to the increase in the length of
the jaw. This increase is without doubt co-ordinated with the
development and growth of the teeth.

Although the teeth had been removed by the fishermen, and sold
to tourists before the mandible of the Skye sperm-whale came into
my possession, yet the sockets were entire, and twenty-four on each
side could be counted, so that the animal had attained its complete
dentition. Seven loose teeth were, however, sent, all of which, with
one exception, were worn on the surface and sides of the crown. In
all, the pulp cavity was completely closed at the extremity of the
fang, and, in several, irregular outgrowths from the surface of the
fang were present. Two of the teeth, though worn at the crown,
closely corresponded in general form with the one not so affected,
and were much more slender and tapering than the remaining
four, the roots of which were much more bulky. The unworn tooth
was five inches long, and the greatest circumference of its root
inches.

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Proceedings of the Royal Society

The sternum was a massive, plate-like, triangular-shaped bone,
greatly expanded anteriorly in its transverse diameter, and grad-
ually tapering backwards to a rounded apex posteriorly. Inferior
surface, convex ; superior, concave ; anterior border, convex. ; lateral
borders varied in thickness, but were from four to five inches in
diameter at the thickest part. Four well-marked costal articular
surfaces on each lateral border. An oval hole, 6^ inches long, was
in the middle of the manubrial element of the bone, and 4% inches

Fig. 2.

Inferior surface of the sternum of the Skye sperm-whale.

further back a much smaller foramen pierced the entire thickness
of the bone. From this smaller hole a mesial and two lateral
grooves passed for some inches backwards along the inferior surface
of the bone. On the inferior surface there was no indication of the
original transverse segmentation ; on the superior surface, 19 inches
in front of the posterior end, a deep transverse fissure passed across
the bone through the middle of the third pair of costal articular
facets, but there was no trace of the original division between the
first and second segments.

Extreme length of sternum, 50 inches; transverse diameter at

637

of Edinburgh, Session 1871-72.

first pair of costal facets, 40 inches ; at second pair, 22 inches ;
at third pair, 18 inches; at fourth pair, 14 inches. This bone had
attained a more complete stage of ossification than had previously
been described or figured in the sternum of this cetacean.

The length of the third transverse segment of the sternum being
19 inches, I examined it carefully to see if any evidence of a sub-
division into smaller segments could be detected, but without
success. Moreover, I find that Professor Flower has met with

Outline sketch of the superior surface of the sternum of the
Skye sperm-whale.

great differences in the length of the terminal segment of this
bone in the specimens which he has examined. In one from
Tasmania the length was 14f inches, whilst in the Caithness
Cachalot the hinder piece is represented by a median spheroidal
nodule of bone, 4 inches in diameter, imbedded in dried cartilage.
The terminal piece of the sternum is therefore variable in its
dimensions, and the greater length in the Skye specimen is without
doubt due to the age of the animal having rendered possible com-
plete ossification of the terminal cartilage.

That the animal had reached its full growth and attained the

4 Q

VOL. VII.

638

Proceedings of the Royal Society

adult period of life is evident from the completed ossification and
the dimensions of its bones. There can be, I think, little doubt
but that it was of the male sex. For although little has been
done in the descriptions of the sperm-whale to discriminate the
sexual characters of the skeleton, yet those who have had opportuni-
ties of observing the habits of this cetacean, agree in ascribing to
the male a much greater magnitude than is acquired by the
female. That excellent naturalist, Mr F. D. Bennett, for example,*
states that the adult female does not exceed the length of thirty,
or at most thirty-five feet.

We may now pass from the most recent specimen to the
consideration of, I believe, the most ancient relic of the sperm-
whale which has yet been found in the British Islands.

In August 1871, Mr George Petrie of Kirkwall presented to
the Boyal Scottish Society of Antiquaries a tooth recently obtained
from a “ brough ” near the Howe of Hoxa, in the Isle of Sh. Bonald-
say, on a promontory opposite the Bay of Scapa. This tooth had
obviously been buried in the earth for a lengthened period, and in
all probability was co-eval with the early occupation of the
“ brough,” and may have belonged to one of its early Norse, or
even still more ancient inhabitants. This tooth has been carefully
examined by Professor Duns, Dr John Alexander Smith, and
myself, and we all agree in regarding it as the tooth of a sperm-
whale. A part of the alveolar end of the tooth, more especially on
one side, has been broken away, so that the conical-shaped pulp-
cavity is fully exposed. The free end of the crown is smooth and
rounded, such as one sees in specimens of well-worn teeth of this
animal. The length of the tooth is 5f inches, but, owing to a
part being broken off, this does not give its full length ; the greatest
girth is 6f inches.

Mr Petrie has most courteously sent me an account of the locality
in which he discovered the tooth. He says : — u I was glad to find
that the tooth was of some interest. I was led to its discovery by
a request of my friend, Mr James Fergusson, the author of the
‘ Handbook of Architecture,’ to make some excavations in the
vicinity of the Howe of Hoxa, with the view of discovering, if

Whaling Voyage, vol. ii. p. 155.

639

of Edinburgh, Session 1871-72.

possible, the tomb of the celebrated Orkneyan Jarl, Thorfinnr
who was, according to the ‘ Orkneyinga Saga,’ buried at Haug
seic5, now known as the Howe of Hoxa. The Howe is ap-
parently a long-shaped natural mound of considerable height,
on which artificial mounds were probably made, as traces of
them can still be seen, as well as of a massive stone wall
encircling a great portion of the top of the mound. On the
north end of the mound are the ruins of a large circular struc-
ture, which, on being excavated between twenty and thirty years
ago, was found to be the remains of a brough or round tower. On
proceeding to the spot last summer, and carefully examining the
mound, I found that it would involve much time, labour, and
expense to make a satisfactory examination. I determined, there-
fore, to excavate a smaller mound, evidently wholly artificial, at a
short distance from the Howe of Hoxa, but connected at one time
with it, as traces of an avenue of stones leading from the one to
the other were still to be seen. I expected to find a chambered
tomb, but to my surprise a structure resembling the ordinary
brough, but far less symmetrical than such buildings usually are,
was revealed. I am inclined to think that it was sepulchral in
character, although of a type unique, so far as my experience goes.
The passages or galleries were still roofed in many parts by flag-
stones laid across from wall to wall. The excavations did not pro-
duce many relics, but amongst these were bits of dark pottery and
several vertebrm of whale much scorched by fire. One of the ver-
tebrae, about 1 foot in diameter at the broadest part, and 9 J inches
in height, had been fashioned into a rude vessel by scooping out the
central or more porous part of the bone, as is often the case. Tt
was found about two feet beneath the surface of the mound at A,
on what appeared to be the floor of the interior of the structure,
and it and the other vertebrae were buried beneath the ruins, which
seemed to have fallen upon them. The tooth was found at B, and
not far off a piece of freestone, convex on one side and slightly
concave on the other. The concave side was tolerably smooth,
apparently due to friction of a freestone rubber passing frequently
over its surface. Similar stones were found in the brongh of
Hoxa, when it was cleared out some years ago. They much
resemble the slightly hollowed stones found at New Clrange, in

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Proceedings of the Royal Society

Ireland. I do not remember any case of a brongh which has been
explored in Orkney in which bones of the whale have not been
found.”

“ I hesitate very much to attempt even to assign a date to the

Fig. 4.

Ground Plan of structure near seashore at Hoxay, about 110 yards westward
of Howe of Hoxay, or Brough of Hoxay. Ruins excavated and planned
by George Petrie, Esq., Kirkwall, in summer, 1871. Scale, Ag-th inch
to 1 foot. A, the place where the broken vessel made out of the verte-
bra of a whale was found. B, the situation of the tooth of the sperm-
whale. 0, entrance doorway, which was roofed over with stones. D,
passage, also roofed over. E, passage where stone roof was destroyed.

structure in which the tooth was found. It may belong to the
period when the Celtic or Pictisli population by whom the islands
were occupied prior to their invasion by the Scandinavians, but I
do not think, from the general appearance of the ruins and the
character of the remains found in them, that the tooth belonged

641

of Edinburgh, Session 1871-72.

to a whale captured or driven ashore later than the Scandinavian -
Pagan period in Orkney, or say the ninth or tenth century.”

As bearing on the early history of the sperm-whale in the Bri-
tish islands, I may next refer to a passage in a memoir by the
eminent Norwegian archaeologist, Professor P. A. Munch, to
which my attention has been directed by Mr Joseph Anderson,
the curator of the Antiquarian Museum. The memoir is en-
titled “ Geographical Elucidations of the Scottish and Irish Local
Names occurring in the Sagas,”* and on pp. 128, 129, Professor
Munch, in his account of the Shetland Isles, says : — “ The island
of Yell is nearly divided into two halves by the deep fiords which
penetrate on each side, Whalefirth (Hvalfjor<5r) on the west, and
Reafirth (ReySarfjorSr) on the east. In a deed dated May 19,
1307, which speaks of the pledging of the estate Kollavagr, now
Cullavoe, one of the witnesses is a Hogni i ReySarfirSi. This
Rey'Sarfjor'Sr is clearly the above Reafirth, early contracted, or
rather corrupted, even by Norse speakers, to Rafjord.” Further,
Professor Munch states, it is very suitable that the two opposite
fiords should be called, the one Hvalfjorbr and the other Rey-
ftarfjorbr, for Reyftr (now called Ro$r or Ror, in Norway), is also a
kind of whale, the Physeter macrocephalus, black-headed sperma-
ceti whale.

If we are to accept this interpretation by Professor Munch, that
the old Norse term Reybar was equivalent to our sperm-whale, then
we should have to assume that this cetacean was so well known to
the ancient Norsemen that they had coined a word to designate it.
And it is indeed not improbable that, considering their roving
habits, they may have sailed in the seas which it most usually
frequents, and perhaps have chased it for the sake of its valuable
oil.

But from the association of this name with a particular firth in
the Shetland group of islands, it would, granting the accuracy of
Munch’s interpretation, seem as if, in the early years of the Norse
settlement, the sperm-whale had not unfrequently entered this firth,
and perhaps been captured there — a circumstance which would
show that this animal was then a much more frequent visitor of

* Memoires de la Soc. Royale des Antiquaries du Nord, 1850-1860,
Copenhague.

64:2 Proceedings of the Royal Society

the Scottish seas than we know it to be at the present day, or
indeed to have been for some centuries past.

But I think it very questionable if the interpretation given by
Professor Munch of the old word Rey<5ar can be regarded as
zoologically correct. Torfbeus, the historian of Greenland, in his
account of the cetacea which frequent the Greenland and Iceland
seas,* uses the term Reidr three times in his description of these
whales. One he terms Hrafnreidr, white in colour, of a length of
fourteen or sixteen cubits, “ branchiis etiam prseditus,” and tastes
well. A second, called Hafreidr, a whale of sixty cubits, or a little
more, which carries a small horn, and is most pleasant to eat. The
third is named Reidr, or most usually Steipireidr, which, he says,
surpasses all others in sweetness, is gentle, and not to be feared by
ships. The largest which has been caught by the Northmen equals
130 cubits, is very fat, “ branchiis gauclet,” but wants teeth. This
description by Torfaeus is much wanting in precision, and the state-
ment that the Hrafnreidr and Reidr possess branchiae would lead
one to say, if this term were understood by him in the sense in
which it is now employed, that these animals were not whales, but
fishes. It is probable, however, that the so-called branchiae in
Hrafnreidr and Steipireidr may be the plates of whalebone which
depend from the roof of the mouth of the baleen whales, and which
have a laminar arrangement not unlike the gills of a fish, and
might readily be mistaken for such by an inexperienced observer.
The absence of teeth, however, conclusively shows that these could
not be sperm whales.

Otho Fabricius, in his “ Fauna Groenlandica,”f identifies the
Hrafnreidr of Torfaeus with the fin-whale named by Linneeus
Balcena hoops ; and the Reidr or Steipereidur with the Balcena
musculus of the same naturalist. By Otho F. Miiller, | the term
Reider or Reydur is applied to two species of Baleen whales.
Mohr also, in his Natural History of Iceland, § adopts the classifica-
tion of Fabricius; and Erik Jonssou, in his Dictionary of old Norse
terms, || accepts the definition of the above naturalists. Further,

* Gronlandia Antiqua, pp. 90, 96. Havnise, 1706.

+ Hafnise, 1780, p. 36, et seq.

| Zoologicse Danicse prodromus. Hafnise, 1776.

§ Forsog til en Islandsk Naturhistorie. Copenhagen, 1786.

j| Oldnordisk Ordbog. Copenhagen, 1863.

643

of Edinburgh , Session 1871-72.

both the lexicographer and the naturalists agree in giving as the
Norse equivalent for our term sperm-whale, not Reybar, but
Burhvalr. Munch himself, also, by putting the Norwegian term
Rohr or Ror as equivalent to the older word Reybar, supplies me
with an additional argument against the latter word being regarded
as signifying sperm-whale, for Ror or Rorhval is merely our term
Rorqual, i.e ., a whale with folds and sulci extending longitudinally
along the belly, such as one sees in the Bahenopteridas or Tinner
whales, but which do not exist in the sperm-whale.

Hence we cannot regard Reafirth in Yell as having received its
name from having once been a place of resort for the sperm-
whale, or as affording any evidence that our seas were at one
time more largely frequented by these huge cetaceans than at
the present day.

But though this name loses its interest in connection with the
natural history of the sperm-whale, it acquires importance in
reference to the natural history of the rorquals. Of this group
of whales, two, viz., the common Tinner, and the species of Tin
whale, of which we had recently so fine a specimen stranded at
Longniddry, attain a length of upwards of 60 feet, and are not
uncommon in our seas. By modern zoologists, the common Tin-
ner is usually called Balcenoptera musculus ( Physalus antiquorum ),
and may be identical with the Hrafnreidr of Torfasus. The
other, the Baloenoptera Sibbaldi, has been identified by Professor
Reinhardt and myself * as identical with the Rorqual, to which the
Icelanders even at the present day apply the name of Steypir-
eythr. In all probability the firth on the east side of Yell, now
known as Reafirth, was frequented by these Rorquals, and was
named by the ancient Norse settlers, Reybarfjorbr, from this
circumstance, whilst the deep inlet of the sea on the west side of
the island, now known as Whale-firth, may have obtained its
Norse name of Hvalfjordr from having been the resort of the
“caaing” whale, which in large herds still frequents the Orkney
and Shetland seas, and is killed in great numbers by the islanders.

Tor convenience of reference, I may append a tabular statement,
compiled from the cases referred to in this and my former essay,

* See my Memoir in Trans, of this Society, p. 247, 1870.

644 Proceedings of the Royal Society

of the well-authenticated instances in which the sperm-whale has
been met with on the Scottish coasts.

Locality.

Date.

Authority.

Hoxay, Orkney, ....

9th or 10th cent.?

George Petrie.

Limekilns,

Feb. 1689

Sir R. Sibbald.

Cramond,

1701

James Paterson.

Monifieth,*

Feb. 1703

Sir R. Sibbald.

Ross-shire,

1756

Sir W. Jardine.

Cramond,

1769

James Robertson.

Hoy Sound, Orkney, . . .

About 1800

George Low.

Oban,

May, 1829

William Turner.

Thurso,

July, 1863

J. E. Gray, and
W. H. Flower.

Loch Scavaig, Skye, . .

July, 1871

William Turner.

Monday, 5th February 1872.

Sir WILLIAM THOMSON, Vice-President, in the Chair.

At the request of the Council Professor Tait gave an
Address on Thermo-Electricity.

The following Communication was read : —

1. Note on Cystine. By James Dewar, F.R.S.E.

The following observations on Cystine are a continuation of those
formerly communicated to the Society by .Dr Arthur G-amgee and
myself, during the course of the Session 1869-70, and reprinted
with addition in the “Journal of Anatomy and Physiology” for
that year ; and although really little of a novel nature to present
to the Society, still it is necessary to show some additional facts have

* In connection with this animal, I may refer to an essay in the “ Scottish
Naturalist,” dated November 1871, by Mr Robert Walker, of St Andrews, in
which he describes and figures the vertebra of a wliale, in the University
Library of that city, which he believes to be the tenth dorsal of a youngish
Cachalot. He believes it to be a relic of a whale stranded there, from which
Mr Foster, a former Regent in the University of St Andrews, obtained a para-
site which he sent to Sibbald, who figured it. He thinks that the whale
figured on the same plate, though stated to be stranded at Monifieth, may have
been this animal.

of Edinburgh, Session 1871-72. 645

been observed tending towards the synthesis of this interesting
substance.

The most important fact ascertained with regard to the chemical
relation of cystine in memoir referred to was the production of
pyruvic acid, when it was treated with nitrous acid. In this re-
action the amido residue was not alone eliminated, the sulphur also
separating as sulphuric acid, however carefully the experiment was
performed. The fear of allowing the action to proceed too far, on
the necessarily small quantity of substance operated upon, pre-
vented us from purifying the product thoroughly, and, consequently,
the analysis differed slightly from that of pure pyruvic acid. We
had no hesitation in saying, however, the acid agreed better with
the chemical characters of the syrupy modification of pyruvic acid
than with that of Wischelhaus’s carbacet oxylic acid, that we had
anticipated would be produced, and that in all probability cystine
would be found to be an amido-sulpho pyruvic.

If cystine is directly related to pyruvic acid, it must contain five
instead of seven hydrogen atoms (and this supposition agrees well
with the published analysis). The formula of the compound will
then be, C3H5N02S. On this supposition, we may derive from
pyruvic acid at least five isomers, that will all have the general
characters of cystine, although there are many other possible con-
stitutional formulas.

Pyruvic Acid.

1.

2.

oh3

ch2nh2

ch2nh;

CO

CO

CO

CO. OH

CO.SH

CSOH

3.

4.

5.

CH2 (NH2)

CH

CHS

cs

CO

CN^

CO. OH

CO. OH

CO. OH

Of the five possible cystines formulated, it is impossible to select
that of the natural substance, because of our ignorance of the inter-
mediate sulpho-acid. All attempts to replace the amido group
alone by the action of nitrous acid having failed, I have tried several
experiments, with the object of replacing the sulphur alone, with
the small quantity of cystine at my disposal.

If cystine is one of the above five substances, the replacement
VOL. vii. 4 a

646 Proceedings of the Royal Society

of the sulphur by hydrogen will generate very different bodies.
Theory enables us to predict that, in the case of bodies having the
constitutional formulae of No. (5), we ought to obtain alanine.
In that of (3) (jS) alanine, and in that of (4) amido-lactic acid
(serine), and in that of (2) amido-glycerine ; whereas it is diffi-
cult to imagine the sulphur in (1) being replaced. A success-
ful experiment in this direction ought to restrict the selection to
two possible constitutional formulas in the worst case, and syn-
thetical processes might then be attempted. It was formerly
observed that nascent hydrogen generated in an acid solution,
readily liberated sulphuretted hydrogen, and might be used as a
test for this substance. The action goes on, however, very slowly,
and it was found extremely difficult to get anything like the theo-
retical quantity of sulphur evolved. With this experience, sodium
amalgam suggested itself as being more powerful, and equally
likely to act. When cystine is dissolved in caustic soda, and
sodium amalgam added, in a few minutes it is easy to detect the
presence of a sulphide by the nitro-prusside test. The action was
allowed to proceed for several days, being occasionally rendered
acid by the addition of hydrochloric imid, and the amalgam renewed.
Ultimately the alkaline solution, after being neutralised with
hydrochloric acid, was evaporated and treated with boiling alcohol
to separate the chloride of sodium, and to dissolve any hydro-
chlorate of alanine that might be formed. After the filtrate was
evaporated, the residue still contained sulphur, from the presence
of hydrochlorate of cystine. This was separated by treating with
water, and the filtrate was boiled with oxide of lead, treated after-
wards with sulphuretted hydrogen to precipitate the dissolved lead,
and evaporated. The residue was then heated to 200 0. in a tube,
with the object of subliming the alanine. No crystalline subli-
mate was observed ; it is probable, therefore, that substances of
the constitutional formulae of 5 do not express the constitution
of normal cystine. This result is subject to a certain amount
of reservation, from the difficulty of separating a small quantity
of substance from a very large amount of secondary material
accumulated in the course of the experiment. The battery is far
better adapted to give a supply of nascent hydrogen in this case;
and an experiment male in this way looks promising, if sufficient
material was to be had.

647

of Edinburgh , Session 1871-72.

The small quantity of substance left I have employed for the
purpose of corroborating the production of pyruvic acid, when it is
treated with hydrate of baryta.

Took a decigramme of cystine, treated it in a tube with a solu-
tion of hydrate of baryta, and heated it all night to a temperature
of 130° C., opened it, and transferred contents to a beaker, boiled
to expel the ammonia produced, then added an exactly equivalent
quantity of sulphuric acid, filtered from the sulphate of baryta ;
after boiling to expel the sulphuretted hydrogen, the filtrate evapo-
rated contained a yellow syrupy acid, which contained a few crystals
under the microscope, having the appearance of Fiuck’s uvitic
acid. Ammonia was added, and gave a yellow solution, which was
evaporated on the water -bath ; it was dissolved in water, and gave
a white precipitate, with nitrate of silver, which was not distinctly
crystalline ; it also gave a white precipitate with subnitrate of
mercury, and a red colour with a crystal of sulphate of iron, and
no precipitate with sulphate of copper. The barium salt was also
found to be non-crystalline, the acid lost the power of giving a red
colour with Ferric salts after treatment with sodium amalgam,
and the composition of the silver salt agreed better with pyruvic
acid then formerly.

Considerable progress has been made in an examination of the
chemical characters and relations of the thio-pyruvic acids.
Normal thio-pyruvic acid has been obtained from the di-chlorpro-
pionic ether. When this ether is treated with excess of alcoholic
sulphide of potassium, we obtain at once a precipitate of chloride
of potassium, and a solution of the potash salt of the new acid.
When this is diluted with water, acidulated with sulphuric acid,
and shaken up with ether, the acid is obtained in yellow crystalline
plates, part of it seems to remain a viscid fluid. The lead and
silver salts are white and insoluble, blacken when heated. It pre-
cipitates mercurous salts black from the first. The calcium, barium,
iron, cadmium, and copper salts are all soluble. The potassium
and sodium salts are intensely yellow, and decompose slightly on
exposure to the air. When treated with tin and sulphuric acid,
they evolve sulphuretted hydrogen.

The thio-carboxyl pyruvic acid has not yet been obtained in a
pure state. When pyruvic acid treated with pentasulphide of
phosphorus, a violent action takes place, associated with much

618 Proceedings of the Boyal Society

frothing; and when the product is distilled, a large mass of carbon
is left in the retort, and a very small quantity of distillate is
obtained. It is probable that chloro-pyruvil, when treated with
sulphide of potassium, will give a more satisfactory yield. It is
the author’s intention to make a careful comparison of these two
acids, and to transform them into amido-acids, with the object of
making an artificial cystine ; and the results arrived at will shortly
be communicated to the Society.

The author’s stock of cystine being now exhausted, he will feel
extremely indebted to any one who would spare him a small quan-
tity for experimental purposes.

The following Gentlemen were elected Fellows of the
Society : —

George Forbes, Esq., B.A., St Catherine’s College, Cambridge.

J. Lindsay Stewart, M.D., Conservator of Forests, Punjab.

Rev. Charles R. Teape, M.A.

Monday , 19 th February 1872.

Principal Sir ALEXANDER GRANT, Bart., Vice-President,
in the Chair.

The following Communications were read : —

1. Remarks on Contact-Electricity. By Sir William
Thomson.

2. On the Curves of the Genital Passage as regulating the
movements of the Foetus under the influence of the Resultant
of the Forces of Parturition. By Dr J. Matthews Duncan.

The observer of the current literature of Midwifery finds nothing
more characteristic of it than the number of papers on the mechan-
ism of natural parturition. These papers indicate for the most
part an enlightened zeal, for they are engaged with a most im-
portant branch of this mechanism, namely, the mode of action of
the force of labour upon the foetus and upon the passages, and the
explanation thereby obtained of the changes which take place in
these as natural labour advances.

For these inquiries great additional value would accrue, were the
amount of power exerted by the combined forces of parturition

649

of Edinburgh, Session 1871-72.

well known ; but they can be carried on to a great degree of ad-
vancement, even while the amount of power exerted by the machine
is unknown, or at least unsettled.

Some of these inquiries as to the action of the force of labour
upon the foetus and passage are very easily solved, and have been
long in this condition. But the most, and by far the most, import-
ant are questions only recently raised ; and of which it may be
said that few are familiar to the profession even as questions, and
still fewer can be regarded as settled. These inquiries form the
natural sequel- to the most recent developments of our knowledge
of natural parturition. These have been chiefly engaged in de-
scribing how the foetus and the passages actually behave during
the process, while the new inquiries are destined to explain why
they so behave. These new inquiries will introduce us far more
deeply into the subject of the mechanism of labour than those
which have preceded them. They are specially difficult because
of the varying conditions of the force of labour and of the corre-
lated parts, the foetus and the passage. The former has the relations
of its parts extensively changed while the process of labour pro-
ceeds, and the latter is only produced at the time by what is called
the development of parts, as the foetus advances.

The subject to which I wish at present to direct attention is the
curves of the genital passage, and their influence on the pheno-
mena of parturition.

I. The first curve to which I direct attention is said to be at the
brim of the pelvis, and to have its convexity directed downwards
and forwards. I do not admit that the curve exists, but it is of
the utmost importance to decide the point, because, without doing
so, we cannot possibly determine the primary direction of the driv-
ing force of labour. Hitherto and now, the axis of the gravid
uterus has been and is generally regarded as coincident with the
axis of the brim of the pelvis, and to indicate the direction of the
resultant of the forces of parturition. But an elaborate attempt has
been recently made by Schatz and Schultze, especially by the former
of these authors, to demonstrate that the axis of the uterus at rest
and in action is inclined to the axis of the brim of the pelvis, at a
small angle opening forwards and upwards, and of about ten
degrees. I have just said that the axis of the uterus has been
generally considered to indicate the primary direction of the driv-

650

Proceedings of the Royal Society

ing power ; but it is evident that this can only be the case if a
variety of conditions be satisfied. Of these the following are pro-
bably principal : — the assistant driving force, which is auxiliary to
the proper uterine force, must be also directed in the axis of the
brim of the pelvis, being supposed to be uniformly applied to the
uterus by the circumjacent viscera and parts, acting like a fluid,
exerting pressure equally in all directions : the uterus must be dis-
tended with a fluid which is copious enough to prevent any part of
the walls being specially pressed upon or indented by the foetus ;
or, it must have its tendency to become spheroidal superiorly unre-
strained. Now Schatz, in addition to giving the proper uterine
driving force a posterior inclination to the axis of the brim by
ascribing to the uterine axis such an inclination, still further in-
creases the inclination of the whole driving force, by describing
the special direction of the auxiliary bearing-down driving force as
still more inclined than the direction of the uterine axis. The
resultant of the combined or whole driving forces will of course,
according to Schatz, have a direction somewhere intermediate be-
tween that of the uterine and that of the auxiliary driving forces.

Smellie’s authority is much relied upon in support of the exist-
ence of this curve. In his plates he gives the uterus this inclination
to the axis of the brim of the pelvis, both in natural cases and in cases
of deformity ; but this is not satisfactory evidence as to what lie
believed, for it is probable that in preparing his plates he did not
pay particular attention to the point. Those of them to which
reference is here made (as xii. and xiv.) are not in the proper
sense drawings or pictures, but mere plans, and might very well
have been arranged as they are, merely because in other respects
the works looked well. Dr Barnes, in his recent work on obstetric
operations, while adhering to the generally entertained view as to
the coincidence of the axis of the uterus and of the brim of the
pelvis, implies, by his descriptions and drawings, a belief that, in
most if not all cases of antero-posterior contraction of the brim of
the pelvis, the uterine axis is inclined to the axis of the contracted
brim, as Schatz believes it to be in cases generally. This is not the
place for any full criticism of what Barnes very aptly calls the curve of
the false promontory, because I confine myself to ordinary or natural
conditions. I shall merely say that this important and practically
valuable doctrine of Barnes regarding the curve of the false promon-

651

of Edinburgh, Session 1871-72.

tory is made too general. It can be true and applicable only where
the posterior uterine obliquity is present, and it is not demonstrated,
nor is it probable that this always is so, in cases of deformity.

It is extremely desirable that means should be devised for ascer-
taining the direction of the resultant of the combined forces of
parturition, and especially of the axis of the uterus in action.
The means adopted by Schatz with this object in view are not
satisfactory ; they merely go the length of showing how carefully
he entered upon the question. But it may be permitted me to
state reasons which tend to establish the ordinary opinion, and to
discountenance that of Schatz.

If the uterine axis is inclined to the brim of the pelvis poste-
riorly to its axis, we should expect to find the child’s head at the
commencement of labour, while yet above the brim, to be in a posi-
tion which has never, so far as I know, been ascribed to it in
natural cases. Smellie, in his plate xii., gives this position con-
sistently, but not truly. He could not avoid doing so, unless he
represented the child at rest as having a left lateral flexion of the
head, which would be ridiculous. His. mode of drawing the uterus
with this posterior obliquity created an exigency for him, which he
could get over only by what must be regarded as misplacement of
the head. One error thus led him into another. The erroneous
posterior uterine obliquity forced him to represent the left side as
presenting in the very commencement of labour in an ordinary
case of first cranial position with the occiput looking to the left.
I do not see how the difficulty, Smellie’s yielding to which gave
rise to error, can be avoided, except by assuming that the ordinary
view as to the axis of the pregnant uterus is correct.

At the same point where Smellie stumbled, Nrngele also fell into
error, but in an opposite direction. In his classical essay on the
mechanism of birth, describing the first position of the foetal head,
he represents it as presenting at the brim of the pelvis, which it
has not yet fully entered, more obliquely than when it has entered
it, or as having at the earliest stage its perpendicular axis more
inclined anteriorly to the axis of the brim ; and in this way he
accounts for his allegation that the right ear can generally be felt
at this time without difficulty behind the pubic bone.* Here a

* See the work of H. F. Nsegele, “ Die Lehre vom Meclianismus der
Geburt.” Mainz, 1838, S. 12.

652 Proceedings of the Royal Society

remark may be made similar to that applied to Smellie’s drawing;
namely, that the head could not be so placed unless the uterus had
an anterior obliquity, an obliquity opposite in direction to that
figured by Smellie and described by Schatz ; an obliquity quite
incompatible with Nsegele’s own description in his work on the
female pelvis •* or unless the child maintained an unnatural and
undescribed left lateral flexion of its head.

The now generally entertained views, that the axis of the uterus
coincides with the axis of the brim of the pelvis, and that the
foetal head presents at the brim directly, f have at least the merit
of evading such obvious and adverse criticism as the figure of
Smellie, and the expressed opinions of Schultze, Schatz, and of
Nmgele, are liable to be subjected to.

The great authority of Nasgele was long sufficient to give cur-
rency to his statement that the head of the foetus, as it passed
through the brim of the pelvis, had its vertical axis in a position
of anterior obliquity to the plane of the brim, an obliquity which
is appropriately designated the Nasgele obliquity, in order to dis-
tinguish it from other obliquities at the same situation. The great
argument against this view, and the only one having a final charac-
ter, is, that it is not an accurate description of what takes place ;
but in addition, it has been argued against it that it is impossible
to find a mechanism to account for it. Stoltz’s attempt to explain
its occurrence by mere lateral flexibility of the neck of the child
is insufficient, because it affords no explanation why the lateral
flexion is towards the posterior shoulder ; but the now alleged
posterior obliquity of the uterus, as regards the axis of the brim,
affords a solution which Nsegele did not foresee when he described
this obliquity as present and increasing with the increasing height
of the head in or above the true pelvis. If, adopting the kind of
nomenclature introduced by Barnes, we describe a curve of the
natural promontory, produced at the brim of the pelvis by the
posterior obliquity of the uterus, then this curve, representing a
deflection of the axis to the extent of about ten degrees, can be
easily made to account for the alleged Neegele obliquity during the
first half of the passage of the child’s head through the ligament-

* F. C. Nsegele. “ Das Weibliche Becken.” Carlsruhe, 1825.

+ See my “ Researches in Obstetrics,” p. 834, &c.

653

of Edinburgh) Session 1871 -72.

ous pelvis. For, if we suppose with Schatz that the whole power
of labour acts in an oblique line nearly corresponding to that of
the axis of the uterus, or inclined still more posteriorly, then there
will always be a tendency of the anterior half of the head, or of
that which is nearer the concavity of the curvature of the passage,
to descend first, and so produce the Naegele obliquity, if there be
uniform resistance to the advance of all parts of the head. But, as
the occurrence of Nsegele’s obliquity is now very generally denied,
any mechanism which accounts for it derives little or no support
of its own accuracy from the circumstance of its doing so.

Still another difficulty in the way of admitting the presence of
the curve of the natural promontory as the natural or ordinary con-
dition is worthy of consideration. It is justly held that in natural
labour the advance of the head through the brim of the pelvis is
impeded only by friction and imperfect dilatation or dilatability of
the soft parts ; but, if this curve of the natural promontory exists,
a new and considerable difficulty is introduced, namely, the differ-
ence between driving a body through a curved and a straight
passage — a new difficulty which it appears to me unreasonable to
admit. And this is not all ; for this addition of difficulty is not
overcome and passed when the child’s head has traversed the curve,
but lasts during most of the process of the birth of the child. If
this curve exists, the axis of the genital passage, regarded in the
antero-posterior vertical plane, has the shape of a Roman S ; its first
or upper curve, the curve of the natural promontory, having its
concavity looking backwards; its second and universally recognised
curve having its concavity looking forwards. I believe we are
nearer the truth when adopting the view at present generally en-
tertained, that, in the antero-posterior vertical plane, the genital
passage has ordinarily only one curve, having the concavity of its
axis looking forwards.

Direct therapeutical bearings of this matter are evident and
important both in natural and morbid parturition. Certain atti-
tudes of the body, by increasing or diminishing the flexion of the
iliac beams upon the sacrum, a movement which I have elsewhere
described as nutation of the sacrum,* may alter not only the dimen-
sions of certain parts, but also the relations of the axis of the
* Researches in Obstetrics, p. 148.

4 s

VOL. VII.

654 Proceedings of the Royal Society

pelvic brim to the axis of the uterus, or to the direction of the
resultant of the forces of labour. In an elaborate paper Schultze*
has attempted to show that similar results may be produced by
flexion and extension of the spine. This author assumes that
the lower lumbar vertebrae govern the uterine axis, and that the
latter is normally inclined posteriorly to the plane of the pelvic
brim. He therefore recommends that when difficulty arises at
the brim, the spine should be flexed so as to bring the axes of the
uterus and of the brim, if possible, into coincidence; and if we
admit his assumptions, there can be no doubt as to the justice of
his conclusion. For practical application, however, the proper
treatment may be stated in such a way as to offend no theory as
to axes of brim or of uterus, or so as to stand good whatever view
is held on these points. When, before labour, or while the foetal
head is still mobile above the brim, it is placed with its sagittal
suture not traversing the centre of the brim, but lying anterior to
it (as Smellie figures), then it will during early labour be pressed,
with a loss of force, against the pubes, not directly into the brim.
It will then be worth while to try whether flexion of the spine, by
putting the woman into the attitude assumed in stooping forward,
will correct the direction of the head [which I consider an unna-
tural direction]. If it corrects it, the sagittal suture will be
observed to leave the neighbourhood of the pubes and approach or
reach the middle of the plane of the brim. Again, if the uterine
axis, or the resultant of the forces of labour, has this posterior
obliquity to the axis of the brim, then, in the first half of its course
through the ligamentous pelvis, the foetal head may be expected
to show the Nasgele obliquity — that is, its half lying in the ante-
rior half of the pelvis will be lower than that in the posterior as
regards the plane of the pelvic brim, being pushed down with
greater force ; and it will be well worth while to try whether or not
flexion of the spine will correct this direction of the head [which
I consider an unnatural direction].

II. The second curvature of the pelvis, which I proceed to de-
scribe, is, like the former, situated at the brim of the pelvis; but

* Jenaische Zeitschrift fiir Medicin und Natur-Wissenschaft, iii. Band.
S. 272.

655

of Edinburgh, Session 1871-72.

of its frequent existence there can be no doubt whatever. Its
presence is indicated by the deflexion of the uterus from the
mesial line to the right or to the left ; and it is well known to be
observed at all times — that is, before, during, and after pregnancy;
but as this paper is concerned only with dynamical matters, this
deflexion or deviation is interesting only as observed during labour.
On the direction of this deflexion, to right or to left, I have no
remarks to make, but I may refer the student first to the recent
paper on this subject by Winkler,* and then to the earlier obser-
vations of Spiegelberg f on this uterine position during labour.
For my present purpose it is more important to have some idea of
the amount of deflexion which occurs. With a view to ascertain
it, however imperfectly, I examined a series of cases which I found
to present this condition. I did not, in all of these cases, make
out whether or not the deflexion persisted during uterine action ;
but I ascertained that it did so in some of them. I hope to make
further observations on this point, but such an inquiry is not essen-
tial to my present purpose, it being sufficient to know that the devia-
tion does generally persist during the so-called erection of the
uterus in a pain.

I proceeded as follows. Having the pregnant woman lying flat
on her back, I made out the position of the uterus by feeling its
outline with my hands ; this manipulation shortly induced a pain
which made the uterine form more distinct than previously; and
then I could observe the outline mark the projection of the direc-
tion of the axis on the skin, and notice its just incidence on the
outline of the fundus. Then I measured off, as on a plane, the
angle between the projection of the axis and the vertical line join-
ing theensiform cartilage and the symphysis pubis. I did not try
to have guidance from feeling the uterine angles and the parts
attached thereto, as Winkler has done in similar circumstances,
because I thought that such guidance would not ensure greater
approach to accuracy in the measurements I wished to make with
a view to purely dynamical considerations.

This angle I found in five cases to be 8, 10, 11, 14, 15 degrees
respectively, or on an average about 10 degrees. The problem now

* Jenaische Zeitschrift, iv. Band. S. 522. 1868.

t Monatsschrift fiir Geburtskunde, xxix. Band. S. 92. 1867.

656 Proceedings of the Boyal Society

to be solved, is to make out from this angle on the surface of the
spheroid what is the corresponding deflexion of the axis of the
spheroid ; and since the angle, as measured low down on the sur-
face of the abdomen lies in a plane nearly parallel to that in which
the axis of the uterus is deflected from the antero-posterior mesial
plane, the deflexion of the axis may be regarded as nearly iden-
tical in amount with the angle measured on the surface. It is
probable that this angle of deviation of the axis of the uterus from
the axis of the brim of the pelvis has important physiological and
practical bearings ; but as yet little has been made out regarding
them. It has been looked upon as affording some explanation of
the alleged comparative frequency of laceration of the cervix on
the left side in ordinary labour.* But the most interesting appli-
cation of it is to assist in accounting for the production of face
cases.f It has been shown how, under certain conditions, and
supposing a right lateral deviation of the uterus, the part of
the head on the left side of the brim — that is, the seat of the con-
cavity of the curvature, will have a greater tendency to descend —
that is, to be more powerfully pushed, downwards than the part
on the right side of the brim. Of this there can be no doubt; and
the probability of this being a true theory or explanation of face
cases is highly increased by remarking the apt manner in which
other things, known in regard to face presentations, adapt them-
selves to it.

Another ingenious dynamical theory of face presentation has
been started by Schatz. He states it as follows : — “ When the
uterus alone is in action, or when there is also acting uniform
resistance around by the walls of the pelvis, a cranial presentation
always occurs, if the occipital foramen of the foetal head at the
time of the first more important shortening of the long axis of the
uterus lies backwards from this towards the back of the foetus,
but a face presentation, if it deviates forwards from this towards
the breast side of the foetus. With the co-operation of non-
uniform resistance by the walls of the pelvis, cranial presentation
is produced if the occurring positive or negative distance of the
great occipital foramen towards the back of the foetus from the

* Edinburgh Medical Journal, June 1871, p. 1061.

t Edinburgh Medical Journal, May 1870.

657

of Edinburgh, Session 1871-72.

long axis of the uterus multiplied into the positive or negative
difference of resistance by the walls of the pelvis, is greater on
the posterior side of the foetus than the product of the same factors
on the breast side. In the opposite circumstances face presenta-
tion is produced.”* To all this ingenious theorising there can be
no objection if the conditions are assumed. But the two chief
premises are merely assumed ; they are not shown to occur ; they
are not shown to be more likely to occur in face presentation cases
than in others. Under these circumstances, I submit that there
can be no hesitation in preferring the formerly described theory of
face cases, where the corresponding assumptions or premises are not
mere assumptions, but well-known facts ; I refer to the occasional
lateral deviation of the uterus, the occasional dolichocephalous
condition of the head, and the greater liability of cases of the
second or right occipital position to be transformed into face cases
than of the first or left occipital position.

III. The last curve of the developed genital passage which falls
to be considered is the most extensive and the best known. It is
the great curve in the antero-posterior vertical plane, which begins
about the middle of the third bone of the sacrum and extends
through the outlet of the ligamentous pelvis to the outlet from the
soft parts. Its length may be greatly diminished by rupture of
the perineum, and still more if the sphincter ani is torn through.
It forms a curve, whose amount of bending varies from about 60 to
about 150 degrees.

In connection with this curve fall to be studied the synclitic and
allied movements of the foetal head during its progress, to which
Kueneke has recently directed attention, and which have been so
carefully discussed at home and abroad, f that it is unnecessary to
re-enter upon them here.

In connection with this curve have also to be studied the develop-
ment of the lower part of the genital passage, the greater
development posteriorly where the force is particularly or more
strongly applied, than anteriorly where there is little more than

* Der Geburt’s Mechanismus der Kopfendlagen, S. 72.

t See Edinburgh Medical Journal, June 1870, and the American Journal
of the Medical Sciences, October 1870, &c.

658 Proceedings of the Royal Society

counter-pressure, or pressure against a fixed wall, and that chiefly
during the temporary abeyance of the power of parturition. There
is to be noted, also, in connection with this curve, the inevitable
tendency of the force of labour, not merely to distend the perineum,
hut also to rupture it centrally, to force the presenting part through
it ; a tendency the study of which, apart from other considerations,
leaves no possible doubt as to the expediency of the practice of
supporting the perineum, a practice which can he demonstrated to
favour the maintenance of its entirety.

A novel practice, founded upon what I regard as a misapprehen-
sion of the conditions of this curvature, has been recently much
dwelt upon by Professor Schultze of Jena.* The practice has for
its object to facilitate and promote the advance of the child after
its head has reached the floor of the pelvis. It is proposed to effect
this by extension of the spine, with a view to which a hard pillow
is to be placed beneath the loins as the woman lies on her back.
The extension of the spine he believes to increase the posterior
obliquity of the axis of the uterus, and therefore of the force of
labour as exerted in this part. By the change supposed to be thus
effected in the direction of the axis of the uterus, the axis of the
force of labour is brought more nearly to the direction of the axis
of the outlet of the pelvis, whereby there is supposed to be pro-
duced a diminution of the otherwise necessary loss of power arising
from the change of direction of the passage at this part. Schultze
alleges that he has found this extension of the spine to be useful
in practice. If this utility is confirmed and ascertained, nothing,
of course, can be said against it. But for the enforcement of his
recommendation of this practice, it is evident that he trusts chiefly
to theoretical arguments; and, therefore, I proceed to examine
them, and believe I shall show that they are fallacious. Before
doing so, it is worth while to point out that the attitude recom-
mended by Schultze is a very unnatural one, and that a woman
straining in labour advanced to the stage at present under conside-
ration naturally assumes an attitude nearly opposite to that implied
by extension of the spine, an attitude of some degree of flexion,
an attitude which, keeping in view the relaxed state of the sacro-

* See Jenaische ZeitsGhrift fiir Medicin, &c. Band iii., 1867, and Lehrbuch
fur der Hebammenkunst, 1870.

of Edinburgh, Session 1871-72.

659

sciatic ligaments, may be accompanied by some degree of enlarge-
ment of the outlet by the posterior nutation of the apex of the
sacrum.

To Schultze’s theory of the facilitation of the latter part of the
second stage of labour by extension of the spine several objections
may be made. First, it is inconsistent with his views as to the
facilitation of the entry of the foetal head into the brim of the
pelvis by flexion of the spine. That view is based upon the assump-
tion that the child’s head enters the brim of the pelvis so as pretty
nearly to occupy it and have a nearly vertical axis in the axis of
the brim. If this be true of the foetal head at the brim, it will be
true of it during its course, mutatis mutandis , and it will be true
of that part of the body which occupies the brim when the child's
head is pressing on the perineum. It will be impossible, therefore,
by any change of the axis of the uterus to bring the line of the
labour force to bear upon the perineum in the direction of a straight
line as Schultze represents it. Second, the upper cylindrical solid
portion of the ligamentous pelvis, having a length of at least an
inch and a half, has a well-determined axis with which must corre-
spond the axis of any body fully occupying it, if the body is of
uniform consistence, — conditions with which the foetus nearly com-
plies. If this be the case, the direction of the force of labour will
follow the same axis, and no change of its direction above the brim
of the pelvis, however produced, can have any effect upon its direc-
tion in any part below the brim of the pelvis. Third, Schultze
forgets that his practice is intended to produce or increase posterior
obliquity of the axis of the uterus to the brim, to increase the
supposed curve of the natural promontory, and that every addi-
tional degree of that curve necessarily produces additional loss of
power. The more, then, he extends the spine he will diminish the
power of labour available at the outlet of the pelvis, instead of
increasing it, as he expects. Fourth, if Schultze’s* views, as illus-
trated by his diagrams, are correct, a dangerous amount and direc-
tion of force would be brought to bear upon the perineum, a
structure whose integrity is already sufficiently imperilled by a
force whose direction is gradually changed as the foetus passes
through the lower half of the ligamentous pelvis.

* Lehrbuch der Hebammenkunst, fig. liii.

660 Proceedings of the Royal Society

Before concluding the consideration of the great curve of the
genital passage in the anteroposterior vertical mesial plane, it is
necessary to point out an important difficulty introduced into its
study by the change in the condition of the ovum when passing
through it, as compared with the ordinary condition of the ovum
when passing the pelvic brim. Hitherto I have spoken on the
assumption that the ordinary view of the action of the power of
labour holds good at all parts of the course of the child. This
view is, that the power is uniformly applied by the concave surface
of the approximately spheroidal uterus to the uniform surface of
the approximately spheroidal ovum, in a direction corresponding
to the axis of the uterus and of the developed genital passage.
Now, this view is probably nearly correct so long as the mem-
branes are unruptured, or while no special part of the foetus
impinges on the uterus so as to injure its approximately spheroidal
form, and provided no part of the foetus impinges on the passage
so as to cause special friction or obstruction at the part impinging.
But while the great anteroposterior vertical curvature of the genital
passage is being permeated, this view is no longer tenable, although
even then it may, in a confessedly inexact way, be advantageously
kept in mind, if other more exact conditions are not stated. While
the curve is being described, the membranes are generally ruptured
and the waters more or less completely discharged; and conse-
quently the foetus is in a variety of places impinging on and chang-
ing the form of the propelling uterus, and meeting with frictional
obstruction in the passage at special points more than at others.
These changes introduce an amount of complication of the problem
which damages greatly the value of such considerations as I have
above adduced, and I see no means at present of overcoming it
and of arriving at exactness, though there is probably no insuper-
able difficulty in the matter. Another element of confusion is
introduced by the want of uniformity which exists in the composi-
tion of the foetus as a mechanical body. It is especially to be
noted that it contains a longitudinally-placed elastic beam of con-
nected vertebrae, which lies nearer the surface of the mass at one
side than at the other.

The ovum or foetus, in its passage through the developed genital
canal, is subjected in various circumstances to various rotations on

of Edinburgh, Session 1871-72.

661

some more or less longitudinally directed axis. It is also subject,
in various circumstances, to various revolutions or sinuous deflexions,
in which its long axis moves through portions of curves which are
measured by corresponding angles. On these curves and their
influence I have made a few remarks while feeling deeply their
imperfection and the need of much further observation and research.
The student who has followed the argument in this paper will have
observed the resort to inferences when direct observations would
have been preferable. This remark applies to every subject dis-
cussed in it ; and while it is to be greatly regretted that such is the
case, it is at the same time not to be forgotten that no method of
making direct and exact observations has hitherto been discovered.
The adoption of the homalographic method is surrounded with
difficulties, not only in the method itself, but also in the procuring
of subjects on which to use it ; and while results obtained by it
would be of great interest and importance, it is evident that they
would not be complete or sufficient, for they can never be other than
observations on parts in the repose of death, not in the turgescence
and action of life. Until very recently, all our knowledge of the
force of labour was on a like imperfect footing; but already ingenuity
has suggested a means of basing this subject on exact observations,
and Schatz has availed himself of these means, and greatly assisted
us to arrive at results which we regard as probably the most impor-
tant hitherto achieved in obstetric science. Till some ingenuity has
succeeded in devising means of making like exact observations to
settle the points discussed in this paper, we must be content to do
our best to reach the truth by reasoning on what we do know more
or less exactly. And it should be remembered that, by this method,
we may reach the greatest assurance, if not certainty. A boy, play-
ing with his dissected puzzle-map, may be certain that a county is
rightly placed if it fits exactly into an entire hole formed of the
conterminous boundaries of surrounding counties, especially if it
also fits in nowhere else. So a theory which suits itself to all, or
is in opposition to none, of numerous known conterminous condi-
tions, may be, provisionally at least, assumed to be correct, and such
assumption of correctness will vary with the number and testing
character of the conditions so humoured by the theory.

4 T

VOL. vxi.

662

Proceedings of the Royal Society

3. On a Method of Determining the Explosive Power of
Gaseous Combinations. By James Dewar, Esq.

( Abstract .)

The author describes an apparatus by means of which the
axplosive power of gaseous combinations can easily he deter-
mined, and from this, by Bunsen process, the temperature may
readily he calculated. The essential feature of the apparatus is
the registration of the “ compression volume ” of a given initial
volume of air, on which the gaseous explosive mixture has been
allowed to act. As the duration of the pressure is all but instan-
taneous, the well-known formula

may he employed to ascertain the final pressure, more especially as
the sudden rebound prevents any great loss of heat. In order to test
the apparatus many experiments were made with mixtures of hydro-
gen and oxygen, and the mean result arrived at was a condensa-
tion to one-fifth the original volume of air (the initial volume
being measured at 30 in. bar), when pure electrolytic gas was
employed. This is equivalent to a pressure of 9*5 atmospheres,
and therefore agrees with Bunsen’s previous determination. The
author hopes to he able to execute a series of determinations
under varying conditions of temperature and pressure.

4. Note on Sprengel’s Mercurial Air-Pump. By James
Dewar, Esq.

The ordinary Sprengel, requiring careful manipulation, and
being apt to get out of order, has not yet become an essential
piece of lecture apparatus as it ought to be. The author exhibited
to the Society two modifications adapted to lecture illustration. In
both instruments the mercury receptacle is made of iron, and instead
of the india-rubber joint of the original, a'well-ground iron stop-
cock is substituted, the portion of iron tube before the stopcock
terminating in a Y-shaped piece bored out of the solid. In the
one form the drop-tube is of glass, attached by means of marine

663

of Edinburgh, Session 1871-72.

glue ; in the other, of carefully made india-rubber tube four or
five millimetres in thickness, of a very small uniform bore, made
expressly for the purpose by the Edinburgh Rubber Company.
The iron funnel-shaped receptacles are ground at the inner apex,
so as to fit perfectly finely-ground iron tubes. By means of these
tubes the preliminary exhaustions are made by a band pump,
and then they are withdrawn. This device saves a separate joint.
The barometer tubes are attached to solid T-shaped pieces of iron
tube, and between these pieces and the main tubes each has a
small glass bulb. Both forms work for all practical purposes as
well as glass, and suit admirably for Erankland’s water analyses,
and Graham’s experiments, &c. They may be procured from
Mr Cameron, philosophical instrument maker, South Bridge, Edin-
burgh.

5. Professor Alexander Dickson exhibited a large series of
abnormal cones of Pinus Pinaster which were to form the
subject of a future communication to the Society.

The following Gentleman was balloted for and admitted
as a Fellow of the Society : —

Archibald Constable, Esq.

Monday , 4 th March 1872.

Professor MACQUOEN BANKINE, Vice-President,
in the Chair.

The following Communications were read

1. On the Connection between Chemical Constitution and
Physiological Action — Continued. On the Physiological
Action of the Salts of Trimethylsulphin. By Prof. Crum
Brown and Dr Thomas B. Fraser.

In the former parts of this investigation we studied the physio-
logical action of the salts of a considerable number of ammonium

664

Proceedings of the Boyal Society

bases — that is, of the salts formed by the union of an ether with
the nitride of one or more alcohol radicals. Thus —

(CH3)'3N

Trimethylamine
(Nitride of Methyl).

+ CHJ

Iodide of Methyl.

(CH3)4NI

Iodide of Tetramethyl-
ammonium.

(C8H14)" (CH3)N

Methylconia

(Nitride of Methyl and (C8Hl4)").

+ CHSI =

Iodide of Methyl.

(C8H14)"(CH3)2NI

Iodide of Dimethylconium.

(C^NOXN + CHJ = (CaH22NOJ'(CH3)NI

(Nitride ofToaH^NO,)'”). IoaWe of MethyI' Ioaiae of M^ylstryclmimn.

The examination of the physiological action of such salts proved
that, while differing from one another in many respects, there are
two points in which they agree — they all paralyse the end-organs
of the motor nerves, and none of them possess that stimulating
action of the spinal cord wrhich we observe in such a substance as
strychnia.

Some years ago Yon (Efele discovered that the sulphide of ethyl
forms a compound with the iodide of ethyl, exactly as the nitride
of ethyl (triethylamine) does. To this new salt he gave the name
of iodide of triethylsulphin, and from it obtained the hydrated
oxide and various other compounds of triethylsulphin. The num-
ber of known salts of this type has been increased by Cahours and
Dehn.

As there are two ways in which the salts of the ammonium bases
may be represented, — 1st, as molecular compounds of nitrides with
ethers ; and 2d, as compounds of pentad nitrogen, — so the salts of
the sulphin bases may be represented, either, 1st, as molecular com-
pounds of sulphides with ethers; or, 2d, as compounds of tetrad
sulphur.

As our physiological observations had led us to prefer the second
mode of representing the constitution of the salts of the ammonium
bases, it appeared to us that it would be of interest to examine
the physiological action of the salts of the sulphin bases. We have
accordingly commenced with the simplest salts of this type, viz.,
the salts of trimethylsulphin, and have made a number of experi-
ments with the iodide and the sulphate of that radical. The iodide
was employed in the form of pure white crystals; the sulphate,

665

of Edinburgh, Session 1871-72.

which is an excessively deliquescent salt, was employed in the
form of an aqueous solution of known strength. We found that
the action of the two salts was identical, the difference of dose
being nearly proportional to the chemical equivalent. In the case
of warm-blooded animals the symptoms observed were — increas-
ing weakness of the voluntary muscles ending with fatal doses in
asphyxia, considerable contraction of the pupils, and profuse sali-
vation.

In the case of frogs complete paralysis of the voluntary muscles
was produced, along with a remarkable stiffness of the muscles of
the anterior part of the body. By experiments conducted exactly
as described in former papers read before the Society, we proved
that the paralysis of the voluntary muscles was caused by the
destruction of the function of the motor end-organs, the nerve
trunks and the muscular fibres being still active. In fact, the
action of these salts is almost identical with that of the salts of
tetramethyl-ammonium, as formerly described by us.

We intend to continue these investigations, and to extend them
to the corresponding compounds of selenium and tellurium and
to the remarkable series of salts derived from Se(CH3)2Cl2 and
Te(CH3)2Cl2, such as Se(CH3)2OHNOs, &c.

2. On the Mean Monthly Eainfall of Scotland. By
Alexander Buchan.

So far as regards the annual amounts of the rainfall of Scotland,
deduced from observations made at 296 different places, the chief
point brought out is the enormous difference between the rainfall
of the west and that of the east ; the stations along the west coast
showing such figures as 40, 45, and 54 inches, as compared with
24, 27, and 30 inches at stations on the east coast, not situated in
the immediate neighbourhood of hills. When it is considered that
the source of the rainfall is the prevailing south-westerly winds, it
is evident that the comparative dryness of such districts as the
south shore of the Firth of Forth is due to high land lying to the
south-west, which drains the winds of a large portion of their mois-
ture in their passage across them. On the other hand, in the West
Highlands, where arms of the sea open in upon the land in all direc-

666 Proceedings of the Royal Society

tions from south round to west, the case is that of a high district,
with currents of moist air poured in upon it, and the consequence
is, an enormous rainfall, amounting, for example, at Grlencroe to
128 inches, and at the head of Lochlomond to 115 inches. Between
these extremes the amount of the rainfall varies, the variations
being dependent on the physical configuration of the surface.

The monthly average rainfall has been examined by the dis-
cussion of observations made at 126 places for long terms of years
— the number of years varying from 10 to 60, and the whole averag-
ing 21 years. Of the stations dealt with, 54 are on the west slope,
and 72 on the east slope. The mean annual rainfall for the whole
country, deduced from these averages, is 44 inches ; for the eastern
slope 38 inches, and for the western slope 50 inches, — amounts
which are probably not far from the true averages of these different
regions.

In December, the general average for the whole country is
greatly above the average monthly fall; in May it falls to the
minimum, after which it continues to increase till it again rises
considerably above the monthly average in October, to fall again,
however, to about the average in November. The curve of the
rainfall of the east, as compared with that of the west, shows the
wet and dry seasons to be less strongly marked in the east; or the
departures from the monthly averages are larger in the west.
Since, however, the curves closely resemble each other, the general
causes bringing about the deposition of rain in the west and in the
east are the same. But at all seasons the absolute amount of the
rainfall is greater in the west than in the east.

The largest monthly rainfall takes place in December in the
north-western and western districts, and in the mountainous dis-
tricts of the interior ; in January , in the south-west, the Ochil Hills,
and east of Perthshire ; whereas, at a number of places in the drier
districts, August is the month of largest rainfall.

The month of least rainfall is April , in the south of Scotland,
May in the north, and June in Orkney, Shetland, and Faro; and
it is remarkable that these same months are the months of largest
(or very large) rainfall in various extensive regions on the continent
of Europe.

of Edinburgh, Session 1871-72,

667

3. Note on the Strain-Function. By Professor Tait.

When the linear and vector function expressing a strain is self-
conjugate the strain is pure. When it is not self-conjugate, it may be
broken up into pure and rotational parts in various ways (analogous
to the separation of a quaternion into the sum of a scalar and a vec-
tor part, or into the 'product of a tensor and a versor part), of which
two are particularly noticeable. Denoting by a bar a self-conjugate
function, we have thus either

9 = if/ + V. e( ),

p = 2S( ) q~\ or f> = 5 .j ( )q-1,

where e is a vector, and q a quaternion (which may obviously be
regarded as a mere versor).

That this is possible is seen from the fact that <p involves nine
independent constants, while ^ and w each involve six, and e and
q each three. If <p' be the function conjugate to <pt we have
<p'= ^ - Y. € ( )

so that

and

2if/ = <p + <p'

2 Y. e ( ) = <P - <p'

which completely determine the first decomposition. This is, of
course, perfectly well known in quaternions, but it does not seem
to have been noticed as a theorem in the kinematics of strains that
there is always one, and but one, mode of resolving a strain into the
geometrical composition of the separate effects of (1) a pure strain,
and (2) a rotation accompanied by uniform dilatation perpendicular
to its axis, the dilatation being measured by (sec. 6-1) where 6 is
the angle of rotation.

In the second form (whose solution does not appear to have been
attempted) we have

P = ( )2-1,

where the pure strain precedes the rotation ; and from this
P'=5-2~1( ) 1 >

or in the conjugate strain the rotation (reversed) is followed by the
pure strain. From these

P'P = (?» ( ) 2— J) 1

_ -2

4 T*

VOL. VII.

668 Proceedings of the Boyal Society

and 5 is therefore to be found by the solution of a biquadratic
equation, as in Proc. R. S. E., 1870, p. 316. It is evident, indeed,
from the identical equation

S . <r-p'pp = S . ppf pa-
th at the operator p'p is self- conjugate.

In the same way

9? (. ) = 2 — 1 S2 (g ( )q~1)q

or

2 (w'p) 2_1 = (2P2-1) = <p'<p (qpq-1)

which show the relations between pp', p'p, and q .

To determine q we have

<pp.q = q*rp

whatever be p, so that

or

which gives

S.Yj(p -*)p= 0,

S . p (p' — sr) Yg = 0 ,

(p' - w) = 0 .

The former equation gives evidently

V# || Y. (9 - a (p - 5) /?

whatever be a and /? ; and the rest of the solution follows at once.
A similar process gives us the solution when the rotation precedes
the pure strain.

4. On the Motion of Bigid Solids in a Liquid circulating
Irrotationally through Perforations in them or in any
Fixed Solid.* By Sir William Thomson.

1. Let if/, p, ...be the values at time t, of generalised co-ordi-
nates fully specifying the positions of any number of solids mov-
able through space occupied by a perfect liquid destitute of rota-
tional motion, and not acted on by any force which could produce

* The title and first part ($£ 1 ... 13) are new, The remainder (§§ 14, 15)
was communicated to the Royal Society at the end of last December. — W. T.
September 26, 1872.

669

of Edinburgh, Session 1871-72.

it. Some or all of these solids being perforated, let x, x) x, &c.,
be the quantities of liquid which from any era of reckoning, up to
the time t , have traversed the several apertures. According to an
extension of Lagrange’s general equations of motion, used in Yol. I.
of Thomson and Tait’s “ Natural Philosophy,” §§ 331... 336, proved
in §§ 329, 331 of the German translation of that volume, and to
be farther developed in the second English edition now in the press,
we may use these quantities x, x) ••• as if they were co-ordinates
so far as concerns the equations of motion. Thus, although the
position of any part of the fluid is not only not explicitly specified,
but is actually indeterminate, wheni/f, <p, ... x, x) •••are all given, we

may regard x, X as specifying all that it is necessary for us to

take into account regarding the motion of the liquid, in forming
the equations of motion of the solids; so that if and 'k,

<f> ... denote the generalised components of momentum and of force
[Thomson and Taifc, § 313 (a) (5)] relatively to if/, and if

k, k, ... K, K' . . . denote corresponding elements relatively to x?
X'..., we have (Hamiltonian form of Lagrange’s general equations)

dt dxf/

dK frT

dt dx

? dt dp

d K' bT

’ dt + df

= .
= K'.

(1),

where T denotes the whole kinetic energy of the system, and b dif-
ferentiation on the hypothesis of rj, ••• k , k ... constant.

2. To illustrate the meaning of x, K, k, x) let B be one of the
perforated solids, to be regarded generally as movable, draw an
immaterial barrier surface O across the aperture to which they
are related, and consider this barrier as fixed relatively to B. Let
N denote the normal component velocity, relatively to B and O of
the fluid at any point of O; and let ffdcr denote integration over
the whole area of 12 : then

ff NAr = X

■ ■ (2);

X^fdtffKdo- .

• • (3),

which is a symbolical expression of the definition of x* To the

670

Proceedings of the Royal Society

surface of fluid coinciding with 12 at any instant, let pressure be
applied of constant value K per unit of area, over the whole area ;
and at the same time let force (or force and couple) be applied to
B equal and opposite to the resultant of this pressure supposed for
a moment to act on a rigid material surface 12 rigidly connected
with B. The “ motive” (that is to say, system of forces) consisting
of the pressure K on the fluid surface, and force and couple B as
just defined, constitutes the generalised component force corre-
sponding to x [Thomson and Tait, § 313 (&)] ; for it does no work
upon any motion of B or other bodies of the system if x is kept con-
stant ; and if x varies work is done at the rate

Kx per unit of time,

whatever other motions or forces there may be in the system.
Lastly, calling the density of the fluid unity, let k denote u circula-
tion ” * [Y. M. § 60 (a)]f of the fluid in any circuit crossing j3
once, and only once : it is this which constitutes the generalised
component momentum relatively to x [Thomson and Tait, § 313
(e)] ; for (Y. M. § 72) we have

«=/„K *. • ■ • (4),

if the system given at rest (or in any state of motion for which
k — 0) be acted on by the motive K during time t.\

3. The kinetic energy T is, of course, necessarily a quadratic
function of the generalised momentum-components, £, rj, ...k, k ... ;
with coefficients generally functions of » J/, <p , but necessarily
independent of x, ... ■ In consequence of this peculiarity it is
convenient to put

T = Q (f — olk — a 'k — &C., 7]- /3k- (3'k — &C., • • .) + ^ (k, k', . . .) (5),

* Or fFds if F denote the tangential component of the absolute velocity of
the fluid at any point of the circuit, and fds line integration once round the
circuit.

f References distinguished by the initials Y. M. are to the part already
published of the author’s paper on Yortex Motion. ( Transactions of the
Royal Society af Edinburgh , 1867-8 and 1868-9.)

f The general limitation, for impulsive action, that the displacements
effected during it are infinitely small, is not necessary in this case. Compare
$ 5 (11), below.

671

of Edinburgh, Session 1871-72.

where Q, OJ denote two quadratic functions. This we may clearly
do, because, if i be the number of the variables >7, — , and j the
number of k, k'...; the whole number of coefficients in the single

quadratic function expressing r is ^ which is equal

A

to the whole number of the coefficients + ^ 4- of the

2 2

two quadratic functions, together with the i j available quantities
a, a , /5 , . . ...

4. The meaning of the quantities a, (3,... a',... thus introduced
is evident when we remember that

dT . dT dT . dT

d£ dv~‘P’"' dK

For ; differentiating (5), and using these, we find

=

dQ

w

dQ

<V"‘ '

(6).

CO)

and using these latter,

X = .,#= -/¥?-& C^,..

(8).

Equations (8) show that - a \p, - ft <p, - a'ij/, &c., are the contribu-
tions to the flux across O, O', &c., given by the separate velocity-
components of the solids. And (7) show that to prevent the solids
from being set in motion when impulses k, k',-*- are applied to the
liquid at the barrier surfaces, we must apply to them impulses ex-
pressed by the equations

£ — a k + aV + &C., 7 } ~ @k + P'k + &C.,... . (9).

5. To form the equations of motion, we have, in the first place,

^-0 ^ -0
dX ~ ’ dx

(10),

and therefore, by (1),

dK

dt

A K,

dt c' T_,

W = K’

(ii);

672

Proceedings of the Royal Society

which show that the acceleration of k, under the influence of K,
follows simply the law of acceleration of a mass under the influence
of a force. Again (for the motions of the solids), let

£o= i — clk - o!k — &c., 7)0 = 7] - /3k - /3'k - &c.,... (12);

and let &c., denote variations of Q on the hypothesis of £01
y0i ... each constant.

hT

We have from (5), remembering that &c., denote variations

of T, on the hypothesis of £, rj, ... k, k ', ... constant,

bT_$Q dQ/ da ,da! \ dQ/ dp dp \

d\\r d\f/ dg\d\Jr dxjr drj\Kdx!/ K d\f/ c‘/ C’ + dxfs y

or, by (7)

bT IBQ (da. da \ .(dp dp . \ i

* \Kdxf} +K M + &C- ) " KKd$ + K chj, + &c- ) ' ' &c* +,
Hence by (1)

d

(13).

dt dx!/

+m + 4? + &o-) - + «&+ &°)~ &c- +^=’f - <u>-

TSow, remark that, according to the notation of (12), £0,r] 0,... are
the momentum-components of the solids due to their own motion
alone, without cyclic motion of the liquid; and therefore eliminate
ij by (12) from (14). Thus we find

d&.m , dK

dt +dxfs + adi+ “ dt +

+ &c-

which, with the corresponding equation for £0, &c., and with (11;
for k, k', &c., are the desired equations of motion.

6. The hypothetical mode of application of K, K',... (§ 1) is
impossible, and every other (such as the influence of gravity on a
real liquid at different temperatures in different parts) is impossible
for our ideal u liquid,” that is to say, a homogeneous incompres-
sible perfect fluid. Hence we have K = 0, K' = 0, and from (11)

673

of Edinburgh, Session 1871-72.

conclude that k, k,... are constants. [They are sometimes called
the “cyclic constants (Y. M. §§ 62 — 64)]. The equations of motion
(15) thus become simply

dip J1Q
dt df

+ 0

f / da dy\ /da' d(3'\ )

{ K y(£0 dif/J + K \dO dif/J^ )

+ &c.

with corresponding equations for rj0, 4, and with the following
relations from (7), between to, y0-" and if ^

7. Let

dQ . dQ ^

dt o drj0 ~

dQ
dt o"

0 , &c.

• (17).

'da d/3\ / da d/3'\

dp~*j') + K\d? ~T^)h &G-> be denoted {?,</>} ■

(18),

so that we have

• - • (19)-

These quantities {<p, if/} , {0, if/} , &c., linear functions of the cyclic
constants, with coefficients depending on tbe configuration of the
system, are to he generally regarded simply as given functions of
the co-ordinates if >, <p, 0, ... : and the equations of motion are

3F + 3? + ta +

(20).

In these (being of the Hamiltonian form) Q is regarded as a
quadratic function of to, rj0 , £0-** with its coefficients functions of
i ft, <p, 0, &c. ; and applied to it indicates variations of these co-
efficients. If now we eliminate to, Vo, to’" from Q by the linear
equations, of which (17) is an abbreviated expression, and so
have Q expressed as a quadratic function of ij/, <p, 0,.- , with
its coefficients functions of if/, <p, 0, &c. ; and if we denote by

dQ dQ

dp’ dif/ ’

&c., variations of Q depending on variations of these co-

674

Proceedings of the Royal Society

efficients ; and by &c., variations of Q depending on

variations of p, p, &c. ; we have [compare Thomson and Tait,
§ 329 (13) and (15)]

fo =

and

dQ ^
dp

Vo =

(IQ
dxj, 9

JQ= _ dQ ^ gQ

dp dp dp
and the equations of motion become
dQ

dQ

dp’

(21);

d dQ
dt dp dp

d dQ dQ
dt dp ~~ dp

+ {?, P}fi + {0, P}0 +
- {<P> P}P + <P}6 +

dp

Ttfd-70-M +

<£ -

dQ

(22).

The first members here are of Lagrange’s form, with the remark-
able addition of the terms involving the velocities simply (in
multiplication with the cyclic constants) depending on the cyclic
fluid motion. The last terms of the second members contain traces

of their Hamiltonian origin in the symbols^ , , ... .

8. As a first application of these equations, let p = 0, p = 0,
0 = 0, ... . This makes £0 =0, Vo = 0..., and therefore also
Q = 0; and the equations of motion (16), (now equations of equi-
librium of the solids under the influence of applied forces <1>,
■&c., balancing the fluid pressure due to the polycyclic motion
k, k,...), become

(b -

dp J

dp

&c.,

(23);

a result which a direct application of the principle of energy
renders obvious (the augmentation of the whole energy produced

by an infinitesimal displacement, Sp, is ^%P, and ^ Sp is the

work done by the applied forces). It is proved in §§ 724 ... 730 of a
volume of collected papers on electricity and magnetism soon to be

of Edinburgh, Session 1871-72.

675*

published, that

dij/ 3 d<p

&c., are the components of the forces

experienced by bodies of perfect diamagnetic inductive capacity
placed in the magnetic field analogous* to the supposed cyclic
irrotational motion. Hence the motive influence of the cyclic
motion of the liquid upon the solids in equilibrium is equal and
opposite to that of magnetism in the magnetic analogue.

This is proposition II. of the paper “ On the Forces experienced
by Solids immersed in a Moving Liquid,” which relates to the
forces required to keep the movable solids at rest. The present in-
vestigation shows Prop. II. of that article to be false. Compare
“Beprint,” § 740.

0. Equations (16) for the case of a single perforated movable
solid undisturbed by others, agree substantially with equations (6)
and (14) of my communication f to the Boyal Society of Edinburgh
of February 1871. The ??0, ... of the present article correspond

dT «iT

to the — - , — , &c., of the former; the L », ... mean the same in
du dv

both. The equations now demonstrated constitute an extension of
the theory not readily discovered or proved by that simple considera-
tion of the principle of momentum, and moment of momentum, on
which alone was founded the .investigation of my former article.

10. Going back to the analytical definition of in § 3 (5), we see
that when none of the movable solids is perforated, this configur-
ational function is equal to the whole kinetic energy (E), which
the polycyclic motion would have were there no movable solid,
diminished by the energy (W) which would be given up were the
liquid, which on this supposition flows through the space of the
movable solid or solids, suddenly rigidified and brought to rest.
Putting then

48 = E - W . . . (24), '

and remarking that E is independent of the co-ordinates of the
movable solids, we may put — W in place of (fj In the equations
of motion, which, for this slight modification, need not be written

* Proposition I. of article on “ The Forces experienced by Solids immersed
in a Moving Liquid” (Proceedings R. S. E., February 1870, reprinted in
Volume of Electric and Magnetic papers, §§ 733 ... 740).

t See Proceedings R. S. E., Session 1870-71, or reprint in Philosophical
Magazine, Nov. 1871.

4 u

VOL. VII.

676* Proceedings of the Royal Society

out again. W might be directly defined as the whole quantity of
work required to remove the movable solids, each to an infinite
distance from any other solid having a perforation with circulation
through it; and, with this definition, — W maybe put for in
the equations of motion without exclusion of cases in which there
is circulation through apertures in movable solids.

11. I conclude with a very simple case, the subject of my com-
munication to the Royal Society of last December, in which the
result was given without proof. Let there be only one moving body,
and it spherical; let the perforated solid or solids be reduced to an
infinitely fine immovable rigid curve or group of curves (endless, of
course, that is, either finite and closed, or infinite), and let there be
no other fixed solid. The rigid curve or curves will be called the
“core” or “cores,” as their part is simply that of core for the
cyclic or polycyclic motion. In this case it is convenient to take
for ij/, <p, 0 , the rectangular co-ordinates ( x , y, z ) of the centre of the
movable globe. Then, because the cores, being infinitely fine,
offer no obstruction to the motion of the liquid, making way for the
globe moving through it, we have

Q ~ lm(sc2 + y2 + z2) . . (25),

where m denotes the mass of the globe, together with half that of
its bulk of the fluid. Hence

/"\

c lx ? dy ‘ dz ’

and

= mx, rj0 = my, £0 = mi

A farther great simplification occurs, because in the present case
a dif/ + /3dp + ..., or, as we now have it, adx + fidy + ydz, is a
complete differential* To prove this, let V be the velocity-
potential at any point (a, b, c) due to the motion of the globe,
irrespectively of any cyclic motion of the liquid. We have

V = if

.d

. d

. d

+ y — i -
dx dy dz

)B'

* Which means that if the globe, after any motion whatever, great or
small, comes again to a position in which it has been before, the integral
quantity of liquid which this motion has caused t© cross an}' fixed area is
zero.

677*

of Edinburgh , Session 1871-72.

where r denotes the radius of the globe, and D = {(x - of -+• (y - h)2
+ (z-c)2p. Hence if N denote the component velocity of the
liquid at ( a , b , c) in any direction A, fx, v , we have
. d N

where

F

N = (4 + 4y + 4) P C)> (27)’

(*• * *> “> l’ c’> = i,,3(XJa + 4b + "Jo):

A1

D ’

Let now (a, b, c) be any point of the barrier surface O (§ 2), and
A, fx, v , the direction cosines of the normal. By (2) of § 2 we see
that the part of x due to the motion of the globe is ffNdo-, or,
by (26),

(4 + 4y + 4i)fP <*> * *’ °> C> ^

Hence, putting

(28).

(29).

ff¥ (a?, y, *, a, 5, c) dcr - U ,
we see by (8) of § 4, that

_dU _dU _ dE
a dx’ ^ dy ’V dz

Hence, with the notation of § 7 (18) for x, y,... instead of 9,...

{y, *} = 0, {z, x] = 0, {x, y} - 0.

By this and (25) the equations of motion (22), with (24), become
simply

d2x bW d2y bW d2z bW /om

X + -r-, = Y + m^2 = Z + (30).

dt2

dx ’ dt2

These equations express that the globe moves as a material particle
of mass m, with the forces (X, Y, Z) expressly applied to it, would
move in a “ field of force,” having W for potential.

12. The value of W is of course easily found by aid of spherical
harmonics, from the velocity potential, P, of the polycyclic motion
which would exist were the globe removed, and which we must sup-
pose known : and in working it out (small print below) it is readily
seen that if, for the hypothetical undisturbed motion, q denote the
fluid velocity at the point really occupied by the centre of the rigid
globe, we have

W = | fxq2 -f w

(31),

678* Proceedings of the Boyal Society

where fx denotes one and a half times the volume of the globe,
and w denotes the kinetic energy of what we may call the internal
motion of the liquid occupying for an instant in the undisturbed
motion the space of the rigid globe in the real system. To define
w , remark that the harmonic analysis proves the velocity of the
centre of inertia of an irrotationally moving liquid globe to be
equal to q , the velocity of the liquid at its centre ;* and con-
sider the velocity of any part of the liquid sphere, relatively to a
rigid body moving with the velocity q. The kinetic energy of
this relative motion is what is denoted by w. Kemark also that if,
by mutual forces between its parts, the liquid globe were suddenly
rigidified, the velocity of the whole would be equal to q; and
that \mql is the work given up by the rigidified globe and sur-
rounding liquid when the globe is suddenly brought to rest, being the
same as the work required to start the globe with velocity q from
rest in a motionless liquid.

Let P -j- ^ be the velocity potential at ( x , y , z) in the actual motion of the
liquid when the rigid globe is fixed. Let a be the radius of the globe, r
distance of ( x , y, z ) from its centre, and ffdcr integration over its surface.
At any point of the surface of the instantaneous liquid globe, the component
velocity perpendicular to the spherical surface in the undisturbed motion is

; and hence the impulsive pressure on the spherical surface re-

dr Jr — a

quired to change the velocity potential of the external liquid from P to P4-4,,
being — 4, , undoes an amount of work equal to

in reducing the normal component from that value to zero. On the other
hand, the internal velocity-potential is reduced from P to zero, and the work
undone in this process is

* This follows immediately from the proposition (Thomson and Tait’s
“ Natural Philosophy,” § 496) that any function V, satisfying Laplace’s
^2y ^2y ^2y

equation — - + — - + — — throughout a spherical space has for its mean
dx 2 dyz dzl

dY

value through this space its value at the centre. For — satisfies Laplace’s

dx

equation.

of Edinburgh, Session 1871-72.

679

Hence

W = i^Ar(P + +)f, . .

(32).

The condition that with velocity-potential P -J- 4* there is
dicular to the spherical surface, gives

no flow perpen-

O

II

e

II

Si

+

• (33).

Now let

P = P« + P.a+ +PiG)‘ +&C'

+ = *((f+ + *G), + 1 + ta.

| • (34),

be the spherical harmonic developments of P and vf, relatively to the centre
of the rigid globe as origin, the former necessarily convergent throughout the
largest spherical space which can be described from this point as centre
without enclosing any part of the core ; the latter necessarily convergent
throughout space external to the sphere. By (33) we have

= Pi

* + l

(35).

Hence (32) gives

which, by
becomes

w=#K^ip0(aP-)’

jrdaVft = 0,

(86).

Now, remarking that a solid spherical harmonic of the first degree may be
any linear function of x, y , z, put

which gives

and
1

P^ = Acc + Br+C?
£2 = A2 + B2 + C2,

(37),

~ JJ fcPi = (A2 + P2 + C2) . | .Jfdtr = gT X volume of globe = ? pq* .
Hence by (36

W = J + + +...) . (38);

and, therefore, by comparison with (31),

2.5 , 3 . 7 T

(39),

680* Proceedings of the Royal Society

13. When the radius of the globe is infinitely small,

W = .... (40),

where jx denotes one and a half times the volume of the globule,
and c[ the undisturbed velocity of the fluid in its neighbourhood.
This corresponds to the formula which I gave twenty-five years
ago for the force experienced by a small sphere (whether of
ferromagnetic or diamagnetic non-crystalline substance) in virtue
of the inductive influence which it experiences in a magnetic
field.*

14. By taking an infinite straight line for the core a simple but
very important example is afforded. In this case, the undisturbed
motion of the fluid is in circles having their centres in the core
(or axis, as we may now call it), and their planes perpendicular to
it. As is well known, the velocity of irrotational revolution round
a straight axis is inversely proportional to distance from the axis.
Hence the potential function W for the force experienced by an
infinitesimal solid sphere in the fluid is inversely as the square of
the distance of its centre from the axis, and therefore the force is
inversely as the cube of the distance, and is towards the nearest
point of the axis. Hence, when the globule moves in a plane
perpendicular to the axis, it describes one or other of the forms of
Cotesian spirals f. If it be projected obliquely to the axis, the
component velocity parallel to the axis will remain constant, and
the other component will be unaffected by that one ; so that the
projection of the globule on the plane perpendicular to the axis
will always describe the same Cotesian spiral as would be described
were there no motion parallel to the axis. If the globule be left
to itself in any position it will commence moving towards the axis
as if attracted by a force varying inversely as the cube of the dis-
tance. It is remarkable that it traverses at right angles an in-
creasing liquid current without any applied force to prevent it

® “ On the Forces Experienced by Small Spheres tinder Magnetic Influ-
ence, and some of the Phenomena presented by Diamagnetic Substances ”
{Cambridge and Dublin Mathematical Journal, May 1847); and “ Remarks on
the Forces experienced by Inductively Magnetised Ferromagnetic or Diamag-
netic Non-crystalline Substances ” {Phil. 3Iag. October 1850). Reprint of
Papers on Electrostatics and Magnetism, §$ 634-668. Macmillan, 1872.

f Tait and Steele’s “ Dynamics of a Particle,” $ 149 (15).

of Edinburgh, Session 1871-72.

681*

from being (as we might erroneously at first sight expect it to be)
carried sideways with the augmented stream. A properly trained
dynamical intelligence would at once perceive that the constancy
of moment of momentum round the axis requires the globule to
move directly towards it.

15. Suppose now the globule to be of the same density as the
liquid. If (being infinitely small) it is projected in the direc-
tion and with the velocity of the liquid’s motion, it will move
round the axis in the same circle with the liquid ; but this motion
would be unstable [and the neglected term w (39) adds to the in-
stability]. Compare Tait and Steele’s “ Dynamics of a Particle,”
§ 149 (15), Species IV., case A = 0 and AB finite ; also limiting
variety between Species I. and Species V. The globule will
describe the same circle in the opposite direction if projected with
the same velocity opposite to that of the fluid. If the globule
be projected either in the direction of the liquid’s motion or
opposite to it, with a velocity less than that of the liquid, it will
move along the Cotesian spiral (Species I. of Tait and Steele),
from apse to centre in a finite time, with an infinite number of
turns. If it be projected in either of those directions with a velo-
city greater by v than that of the liquid, it will move along the
Cotesian spiral (Species V. of Tait and Steele), from apse to asymp-
tote. Its velocity along the asymptote, at an infinite distance from
the axis, will be

where a denotes the distance of the apse from the axis, and -K— the

velocity of the liquid at that distance from the axis. If the globule
be projected from any point in the direction of any straight line
whose shortest distance from the axis is p, it will be drawn into
the vortex or escape from it, according as the component velo-

and the distance of the asymptote from the axis will be

a

Sira

882* Proceedings of the Boyal Society

city in the plane perpendicular to the axis is less or greater than
. It is to be remarked that in every case in which the globule

is drawn in to the axis (except the extreme one in which its
velocity is infinitely little less than that of the fluid, and its spiral
path infinitely nearly perpendicular to the radius vector), the spiral
by which it approaches, although it has always an infinite number
of convolutions, is of finite length ; and therefore, of course, the
time taken to reach the axis is finite. Considering, for simplicity,
motion in a plane perpendicular to the axis ; at any point infinitely
distant from the axis, let the globule be projected with a velocity
v along a line passing at distance p on either side of the axis.
Then if r denote the velocity of the fluid at distance unity from

the axis j^which is equal to J > an(^ ^ we

(41),

the polar equation of the path is

r =

cos nQ

• (42).

Hence the nearest approach to the axis attained by the glo-
bule is np , and the whole change of direction which it expe-
riences is 7 r case of - — 2*3 is represented in the

annexed diagram, copied from Tait and Steele’s book [§ 149 (15),
Species V.].

of Edinburgh, Session 1871-72.

675

Monday , 1 %th March 1872.

Professor KELLAND, Vice-President,
in the Cliair.

The following Communications were read : —

1. On the Extraction of the Square Root of a Matrix of
the Third Order. By Professor Cayley.

Professor Tait has considered the question of finding the square
root of a strain, or what is the same thing, that of a matrix of the
third order —

(a, b, c).

I d, e, f I

I 9, i I

A mode of doing this is indicated in my “ Memoir on the Theory
of Matrices” (Phil. Trans., 1858, pp. 17-37), and it is interesting
to work out the solution.

The notation and method will be understood from the simple
case of a matrix of the second order. I write

Oi, yd = ( <», ® ) 0, y),

I «, <* I

to denote the two equations, xx = ax + by, y1 = cx + dy. This being
so, putting

(*2> yd = ( «, b ) Oi> yj, = ( «, b )2 (*, y)>

I c, d I I c, d |

we arrive at the value of the squared matrix, viz.,

( a, b )2 - ( a2 + be, b(a + d) ) ,

| c, d | | c(a + d), d2 + be |

and we have similarly the third, fourth, and higher powers of a
matrix. The zero power is the matrix unity, = ( 1, 0 ) .

I 0, 1 |

The zero matrix is ( 0, 0 ), and when a matrix rs put = 0, this

I o, 0 |

means that it is a matrix of the last-mentioned form.

VOL. VII.

4 u*

676 Proceedings of the Royal Society

Consider the matrix M = ( a, b ) ; write down the equation,

1 «, I

1 a - M, b 1=0,

I c ,d - M I

where the function on the left hand is a determinant, M being
therein regarded in the first instance as a quantity, viz., this equa-
tion is

M2 - (a + d) M + ( ad - be) M° = 0 ;

and then substituting for M2, M, M°, their expressions as matrices,
this equation is identically true, viz., it stands for the four iden-
tities—

a 2 + be - (a + d) a + ad - be = 0,

b(a + d) - (a + d) b ,= 0,

c(a + d) — (a + d) c =0,

d 2 + be - (a + d) d + ad - be - 0,

and the like property holds for a matrix of any order.

To extract the square root of the matrix M = ( a, b ) ; in

I c, d\

other words, to find a matrix L = ( a, b ) such that L2 = M;

| 0, d [

that is

( a2 -(- be, b(a + d) ) = ( a, b ) ,

| c(a + d), d2 + be | | c, d j

(four equations for the determination of a, b, c, d) : —

The solution is as follows : write

I a - M, b I = M2 - pM + q ,

I c , d - M |

is here written for g-M0, and so in other cases) ; and similarly

| a - L, b I = L2 - pL -f q,

j c , d - L I

then we have

M2 - + <£=0,

L2 - pL + q = 0,

L2 = M;

and from these equations we may express L as a linear function of
M, M°, with coefficients depending on p, q; and also determine
the unknown quantities p, q in terms of p, q.

of Edinburgh, Session 1871-72.

677

We, in fact, have

L = J(M + q);

Also this gives (M + q)2 - p2M = 0, that is

M2 - (p2 - 2q) M + q2 = 0 ,
which must agree with

M2 - pM + q — 0 ;

consequently,
that is,

p2 - 2q = p, q2 = q ,

and then,

q = A /q, p = V p + 2 A? ,

L = J (M + q) ,

which is the required solution ; viz., this signifies

L = ^ a + q b ),

P ’ P

c fi + <4
p ’ P

where p, q have the above-mentioned values— a result which can
be at once verified. Observe that there are in all 1 solutions, but
these correspond in pairs of solutions, differing only in their sign ;
the number of distinct solutions is taken to be = 2.

Passing jiow to the case of a matrix of the third order,

M = ( a, b, c ) ,

| d, «, / I

I 9, h i\

let the expanded value of the determinant

a — M, b, c

d , e - M, /

9 , h , i - M

be

(M3

pM.2 + qK - r) ;

and let the required square root be

L = ( a, b, c )
I d, e, f I

I g. h> i I

VOL. VII.

678

Proceedings of the Royal Society

and p, q, r, have the like significations in regard to L. Then from
the equations —

M3 — pM2 + - r Ho,

L3 - pL 2 + qL - r = 0 ,

L2 - M,

we can express L as a linear function of M2, M, M°, with co-
efficients depending on p, q, r ; and obtain expressions for p, q, r,
in terms of p , q, r.

We have

L (M + q) - pM + r ,

that is,

L

pM + r r - pq

M + q ’ = P + M + q'

But we have

M3 - pM2 + - r = (M + q) (l’ + «M+P+HT-q)

where

- 0:= q + p,

<p = q2 + q£> + q ,

- (O = q3 + qp2 + qgr + r,

and thence

L = pqm r (M^ + 6M + <p) + p,
that is, L = £cM2 + 2/M + z, where x, yy z are given functions of p, q, r.

To determine these, observe that

that is

\/M(M + q) = pM -f r,

M3 - (p2 - 2q)M2 +' (q2 - 2pr)M - r2 = 0 ,

which must agree with

M3 - pM2 + ffM-r=0,

or we have

p2 - 2q = p, q2 - 2pr = q, r2 = r,
r = «/r,

(q2 - if = i (2q + p)r ,

whence

679

of Edinburgh, Session 1871-72.

which are the required values ; there being in all eight solutions,
but these .correspond in pairs of solutions of opposite sign, so that
the number of independent solutions is = 4. The form of the
result agrees in a remarkable manner with that obtained by Pro-
fessor Tait on totally different principles (ante, p. 316).

I annex a further investigation, starting from the assumption
that the solution is 4- yM + z ; viz., writing for

shortness —

M2 - ( a', V, c' ) ,

I d\ e':f I

• I g\ i' I

then the solution is

JM. — ( xo! 4- ya + z , xb' 4- yb , xc! + yc )

I xd' + yd , xe' 4- ye 4- z , xf + yf I
I %g' + yg , %h' + yh , % + yi + z |

where observe that only a, e, i contain z ; and that the differences
e-i, i-a, a-e are independent of z. We ought to have

a2+ eg + bd|S a
e2+ db + fh = e
i2+ hf + eg = i

b(a + e) 4- ch - b
f (e + i) + dc = /
g(i 4- a) + hd = g

d(a 4- e) + fg = d ,
h(e 4- i ) 4- gb = h,
c(i 4- a) 4- bf = c ,

viz., these nine equations should be satisfied by a common set of
values of x,y,z\ or, what is the same thing, the whole system
should be equivalent to the first triad of equations. To verify this,
observe that we can from the first triad (by the linear elimination
of z2 and z) obtain an equation of the form (x , y)3 4- x = 0 ; say
this is the equation 0=0. In fact, multiplying by e - i, i - a,
a-e and adding, the three equations give

(e - i) (i - a) (a - e) + fh (e - i) 4- g c (i - a) 4- bd (a - e)

4- a (e- i) 4- e(i-a)4- i(a-e) = 0,

where the first line contains terms of the form (x, y )3 , the second
line is linear and

= [a(e' - 1) 4- e (if - a ') 4- i (ct' - e')]x ,

viz., this is

= [(e - i)(i - a)(a - e) 4- fh(e - i) 4- gc(i -a) 4- bd(a - e)]a? .

The whole equation divides by the coefficient of x, and the result
is (x, yf 4- x = 0.

680

Proceedings of the Royal Society

Now, from any one of the remaining six equations, together
with two equations of the first triad, we can obtain the sajne result,
0 = 0. Thus, if the selected equation is b (a + e) -+- ch - b = 0, then
from the first and second equations of the triad we have
(a2 - e2) + eg - fh - {a - e) = 0 ,

and thence

(a - e)(b - ch) + b (eg - fh) - b (a - e) = 0 .

There is here the linear term b (a - e) - b (a - e), viz., this is
= \b(af - e) - b\a - e)~\x ,

which is

— [ - (a - e)ch + b(cg — fh)]x .

The whole equation divides by the coefficient of x, and gives the
foregoing equation, 0=0.

Thus the equations reduce themselves to the first triad : writing
these under the form

-(a2 -t- eg -h bd) = -(e2 + bd + fh) = l(i2 + hf -f eg) = 1

then omitting the last equation ( = 1), these are of the form
U = V = W, where [J, Y, W are homogeneous quadric functions of
x,y,z-, viz., treating these as co-ordinates they represent two
quadric cones, having a common vertex, and intersecting in 4
lines : or we have 4 sets of values of the ratios x\y\z\ or for
x, y, ^ themselves 8 sets of values ; but, as before, these correspond
in pairs, and the number of distinct solutions is taken to be = 4.

I return to the equation 0 = 0. This is found to be

(■ a - p)x - y, bx cx

dx (e - p)x — y fx

gx hx (i - p)x - y

- x = 0

(p = a + e + i as before) ; or what is the same thing, the equa-
tion is

a — p -

= 0.

e - p -

9

h

> * - P

of Edinburgh, Session J 871-72. 681

I verify this by the former solution, as follows : — We have
pq - r pq-r

y

The equation thus becomes

? ; that is, - - 0 , = - - q .

a + q, b, , c
d ,e + q, /
g , h ,i + q

(pq - r):

-v, = 0,

r)2

that is

q3 + p0* + n + r _ = 0 ,

But we have

— o) = q3 + pq2 + </q + r ,

and the equation thus becomes

q3 + pq2 + qq + r - (pq - r)2 = 0 ;

viz., substituting for p , q, r their values in terms of p, q, r, this is
the identity,

q3 + q2 (p2 - 2q) + q (q2 - 2pr) + r2 - (pq - r)2 = 0 .

An interesting case is where the given matrix M is unity ; that is

M = ( 1, 0, 0 ) .

I 0, 1, 0 I

I 0, 0, 1 |

We have here p= 3, 9 = 3, r- 1 ; the equation in q is
q4 - 6q2 - 8q -3 = 0;

that is (q- 3) (q+l)3 = 0; viz., q = 3or q = -1. Taking, as we
may do, r = q-l, we have the two solutions (p = 3, q= 3, r = 1) and

(p= -1. q| -1, r=l).

For the first of these 0= -6, <p = 21, w= -64, pq-r = 8, and
thence

L = - ^-(M2 - 6M + 21) + 3, = 1, on writing therein M = 1 ;

viz., we have L the matrix unity, a self-evident solution.

But for the second, 6= -2, <p- 1, w=0, pq-r = 0, and the

solution takes the form \/M = ^ (M - l)2 - 1. There is, in

682

Proceedings of the Royal Society

fact, a solution, containing four arbitrary constants, given (with
some misprints) in the “Memoir on Matrices,” and which (for
convenience changing the signs) is as follows : —

— a

(P + yf

(P + yf

a + ft + y

a + 13 + y

a + ft + y

(y + °0 X

- P

(* + »)£

a + P + y

a + ft + y

a + ft + y

(«+ 0'

(a +

r

“ 7

a + ft + y

a + ft + y

a + ft + y

(or, what is the same thing, we may omit the denominators,
assuming a + /3 + y=l); it is, in fact, easy to verify that this has
for its square the matrix unity. Moreover, we have, as above,
p = - 1, q S- 1, r=l.

2. Second Note on the Strain Function. By Prof. Tait.

3. Note on the Rate of Cooling at High Temperatures. By

Professor Tait.

4. Notice of a Large Boulder in the Parish of Rattray, and
County of Perth, having on one of its sides Cups and
Grooves, apparently artificial. By D. Milne Home.

About a year ago, the Council of this Society appointed a Com-
mittee to make inquiry about boulders in Scotland.

The Committee intend to submit to the Council a general report
of their proceedings, showing the progress made.

The object of the present notice is to give to the Society an
account of one of the boulders reported to the Committee, as a
specimen of the information which they have been obtaining.

The Rev. Mr Herdman, minister of Rattray, in Perthshire, sent
to the Committee an answer to their circular, specifying the follow-
ing boulders and standing stones in his parish : —

of Edinburgh, Session 1871-72. 683

!!s£, A stone known from time immemorial as the Standing Stone
of Glenballoch .

This boulder is angular, and rudely pyramided in form. Its entire
height is 12 feet. At its base it is about 8 feet square; and half-
way up, about 6 feet square. Its weight is estimated at about 25
tons.

It rests on what Mr Herdman describes as a firm, hard, dry,
sandy, reddish yellow clay, called by the farmers of the district,
till.

On one side of this stone,- viz., that facing the glen, on the north
bank of which it stands, there are cuttings or incisions, which Mr
Herdman, and others skilled in archaeology who have examined
them, believe to be artificial. These incisions are of two kinds :
First , hemispherical cavities, about twelve or thirteen in number ;
and second , grooves which on some points touch or run into these
cavities.

2 d, In another part of the same estate, viz., of Craighall,
belonging to Colonel Clark Rattray, there is a spot known as “ The
Stannin’ Stanes.” This name occurs in the parish records, Mr
Herdman says, so far back as 300 years. There was a small farm
long known by the name of “ Stannin’ Stanes and about forty years
ago, there were dwelling-houses at the place, forming a hamlet
which bore the same name.

Though there is only one large stone at this place, Mr Herdman
is of opinion that it once had companions. These have disappeared.
They are probably in dykes and cattle sheds, not far off.

The stone which remains, is, in length above ground, about 5
feet, and is about 4 feet square. It is believed to be sunk in the
ground 3 feet. Its weight is estimated at 8 or 9 tons. It stands
upright.

3d, There is a group of stones, each containing about 7 cubic
yards of rock, and each weighing, probably, about 14 tons, situated
on the farm of Gflenballoch, not far from the large stone first men-
tioned. Lines joining these 4 stones would form an irregular square.
The intervals between the stones are from 9 to 12 feet. The stone
at the south-west angle is higher than the others, reaching to
a point 5 feet above the ground. The other three stones lie on their
sides.

684

Proceedings of the Royal Society

4th, There is another group of stones , five or six in number, on
Hatton Hill, about 500 yards to the east of the hill top, and about
20 feet below its level. Each of these stones is on average about
a cubic yard in solid content, and weighs about two tons.

Hatton Hill is at its top about 900 feet above the sea. The farm
of G-lenballoch, on which most of the other stones are, is about 750
feet above the sea.

To revert now to the stone first mentioned, the annexed wood-
cut will give an idea of its shape. The cups or cavities on its
sides — which, however, are not well shown on the diagram — are
from 2 to 3 inches in diameter, and from half an inch to one inch
deep. The grooves are about half an inch deep and about half
an inch wide.

The cup-shaped cavities were first noticed about fourteen or
fifteen years ago, by the Eev. Mr Herdman, and were shown by him
to Dr Wise, a well-known archaeologist. At that time the part of
the stone above the surface of the ground measured about 9£ feet

of Edinburgh, Session 1871-72.

685

from the top, and in that part of the stone there were only five or
six cups discernible ; plaster casts of these, however, were taken
and sent to the Society of Scottish Antiquaries. No doubt was
entertained by those who then examined the stone and the casts,
that these cup cavities were artificial and not natural.

About six years ago the late Sir James Simpson turned his atten-
tion to the subject of these antique and mysterious cuttings and
sculpturings, and drew out a memoir on the subject, illustrated by
numerous lithographs, which was published by the Society of
Antiquaries.

Mr Herdman having heard of this inquiry, was induced to make
a farther examination of the stone, and had some of the earth cleared
away from its sides. He then discovered other hemispherical cavities
sharper and more distinct than those in the higher and more ex-
posed part of the stone, and which greater distinctness he natu-
rally ascribed to the covering of earth by which they had been
protected from the weather. He also on this occasion observed
that there were grooves or ruts on the surface of the stone, in the
parts which had been covered up, and which were prolonged
into grooves on the upper part of the stone where they were more
faint.

It will be seen from the diagram, — first, that on the middle of
the stone and near the cups there are two long grooves, with a
cross groove at two places ; second, that at the right hand there is
a zigzag groove ; and third , that at the left hand there is a
straight groove, running up vertically, but more faint than the
others. The second and third of these grooves were only dis-
covered lately, and in consequence of investigations for the Boulder
Committee.

Whenever the discovery of these additional cups and grooves
was made, Mr Herdman lost no time in sending an account of them
to Sir James Simpson. But by this time his memoir had been
printed ; and the only notice which appears in that memoir of
the G-lenballoch Stone, is in the following terms, p. 15 : —

“ Circle at Craighall , Perthshire. — Cup excavations exist upon an
erect stone standing at a megalithic circle behind Craighall House,
Blairgowrie. The cups are five or six in number, and placed in a
group near the foot of the stone.”

4 Y

VOL. VII.

686

Proceedings of the Royal Society

The account is incorrect in several particulars. Instead of there
being only five or six cups, there are thirteen or fourteen. The
four vertical and three transverse grooves are not mentioned. There
is no reason to suppose that a circle of stones ever existed here. In
fact the rapid slope of the ground, where the boulder stands, would
have prevented such a circle being made. Megalithic circles are
always on a flat piece of land. Sir James Simpson was never at
G-lenballoch, as he told Mr Herdman himself shortly before his
death.

Whilst to Mr Herdman belongs the merit of discovering these
markings, the still greater merit belongs to him of having saved
this boulder from the fate which has befallen several others in his
parish, and hundreds, or probably thousands, equally curious
throughout Scotland. The boulder stands within the precincts of
a field which bears good crops, and as it was a considerable obstruc-
tion to farming operations, the tenant about six years ago was
preparing to break it up, and the more especially as he was then in
want of stones for a new farm-house. His intentions having
become known, the Rev. Mr Herdman would have applied to the
proprietor himself had he been at home, to save the boulder. But
he was abroad ; and so the factor was appealed to, and fortunately
with success.

The tenant has several times since thrown out dark hints about
the inconvenience to which he is exposed by the presence of this
boulder in an arable field, and also by the occasional visits of the
curious to examine it. He has recently spoken of the damage
done to his “ neeps ” by Mr Herdman’s excavations ; and it was
only after much persuasion that Mr Herdman obtained from him
a promise in these words, “ Weel, I’ll lat the stane alane, if you
dinna howk muckle mair about it.” Notwithstanding this assur-
ance, Mr Herdman thinks it might be as well that the Royal
Society Committee should communicate with the proprietor, Col.
Clark Rattray, and ask him to give strict orders for the preservation
of the boulder.

These remarks apply to the G-lenballoch stone only in its archaeo-
logical relations. But it is probably also interesting geologically.
Mr Herdman states that he has not much knowledge of rocks, and
no experience in geological researches. Nevertheless, the facts

687

of Edinburgh, Session 1871-72.

related by him suggest some questions of considerable importance.
He has bad the kindness to send chips of all the stones specified
by him. Mr Herdman describes them as, in his opinion, a black
coloured trap. But they appear to be all bits of micaceous schist.
The prevailing rock in the parish of Battray is a coarse red sand-
stone— probably Old Bed Sandstone, containing thick beds of coarse
conglomerate.

The nearest rocks of micaceous schist are in the hills to the
north and west. How far off they are it is not stated, nor how
much higher in level than Battray parish. But it is pretty evi-
dent that all these boulders came from the hills, and by natural
agency of some kind. The stone of Glenballoch, weighing as it
does 25 tons, must have come in that way, and it is almost certain
that it now occupies the spot and position on which it was
originally placed. The other stones specified by Mr Herdman
probably do not now occupy their original site and position, as
they seem to have been set up for the purposes — whatever these
were — for which they were wanted. Probably the group of stones
near the top of Hatton Hill are in their original position, for
they do not seem to be artificially arranged ; and, moreover, it is
not uncommon to find boulders in heaps near the tops of hills,
as if these hills had somehow obstructed the farther progress of
the agent (whatever that was), which transported the boulders,
and caused it to discharge its cargo on or near the top of the
hill.

Assuming, then, that the stone of Glenballoch is an erratic from
some northern or westerly point, one question would be, What
caused the transporting agent to drop it at the place where it
now stands ? Why should it not have been carried farther ? Per-
haps an examination of the country might suggest data to aid in
the solution of this question.

The position of the houlder and its attitude appear to deserve
attention, provided it can be correctly assumed that they were
received by natural and not by human agency.

Mr Herdman states that the boulder stands in a field which slopes
pretty rapidly down towards a stream, running through a narrow
glen. This field seems to form one side of that glen, or small
valley, through which, he says, there was formerly a pass much

688 Proceedings of the Royal Society

frequented between Craighall and Banff; and “ balloch ” is a
Celtic word for “pass.” How high above the bottom of the glen
the boulder stands, Mr Herdman does not explain. The boulder,
therefore, stands in rather a critical position ; and considering
its great weight, it does not seem likely that it could have been
put into that position by human agency.

Then its attitude is singular, because boulders having a longer
and shorter axis are generally and naturally found lying with their
longer axis parallel with the ground ; but this boulder has its
longer axis vertical, and stands on a basis of only 8 feet square. Tf
the present position and attitude are those it received when it fell
from the agent which transported it, what was the nature of the
agent which allowed it to fall, so as to take that attitude ?

The two theories for the transport of such boulders are land ice ,
as by a glacier, and floating ice , as by an iceberg or ice floe.
Whether the country between Rattray parish and the mountains to
the north is of such a nature as to have allowed the formation of a
glacier may be a question, but supposing it were, which of these
two ice agents, glacier or floating ice, would have been most likely
to cause this pear-shaped block to fall into the position and attitude
which it occupies? This is a question as much for a mathe-
matician as for a geologist to solve.

5. On the Fruiting of the Ipecacuan Plant ( Cephaelis
Ipecacuanha , Rich.) in the Royal Botanic Garden. By
Prof. Balfour.

The cultivation of the Ipecacuan plant in this country has
received an impetus from the demand on the part of His Gfrace the
Duke of Argyll, for a large supply of fresh plants for India. The
object of the India office is to cultivate the plant extensively, and
thus prevent the evils which might arise from scarcity of a drug
which is so important in the treatment of dysentery. The risk of
such an occurrence is due to the mode in which the plant is
gathered in Brazil, and the want of care in preserving it. A similar
fate threatens Ipecacuan as that which has occurred in the case of
Cinchona.

689

of Edinburgh, Session 1871-72.

The Secretary of State for India has, in the first place, endeavoured
to introduce the plant from this country — leaving for after considera-
tion the propriety of getting specimens sent direct from Eio Janeiro
to India. The plants in this country have been supplied from
various sources. The original specimen, cultivated by Sir William
Hooker in Glasgow, came from Liege, and the Messrs Lawson have
imported recently a quantity of specimens from Belgium and
Germany. In the Boyal Botanic Garden of Edinburgh we are in-
debted for specimens — first, to Sir William Hooker; and, secondly,
to Dr Gunning of Palmeiras, Bio Janeiro. Sir Bobert Christison
has taken a warm interest in the subject, and has aided much in
procuring specimens. Mr M‘Nab found that by cutting the root of
the original garden plant he could propagate it easily, and in this
way he secured a large stock. He gave to the Botanical Society
of Edinburgh a notice of his mode of cultivation. This account
was printed for the India office, and copies of it were extensively
distributed. The specimens from Bio Janeiro were treated in a
similar manner.

The plants were sent to India in Wardian cases, sometimes under
charge of gentlemen of the forest department going to India, and
sometimes without any one in charge. The results have been very
successful.

The Duke of Argyll has forwarded to me a report by Dr G. King,
superintendent of the Botanic Garden, Calcutta, to whose care the
cases were consigned.

From Dr G. King, Superintendent , Botanic Garden , Calcutta , to the
Secretary to the Government of Bengal.

“ I have the honour to report, for the information of Government,
the arrival from England of five consignments of Ipecacuanha
plants. Eive of these consignments, consisting of a single case
each, were brought out under the care of Messrs Walton, Whittall,
Jellicoe, Ferrais, and Gamble, officers newly appointed to the
Forest Department. The sixth, consisting of three closed Wardian
cases, came as deck-baggage on board the Suez Canal steamer,

1 City of Mecca,’ under the special care of no one.

“ As will be seen by the following tabular statement, the total
number of plants despatched from England was 277. On arrival

690 Proceedings of the Royal Society

in Calcutta 15 plants were found to be dead, and 36 in a sickly
state, leaving a balance of 226 healthy.

Healthy.

Sickly.

Dead.

Total.

Brought by Mr Walton,

12

121

,, Mr Jellicoe,

26

"i

30 | 120

,, Mr Ferrais,

12

12 {“Botanic

„ Mr Gamble,

27

2

5

34 | Garden.

„ Mr Whittall, .

Received ex 1 City of Mecca,’

26

4

2

32 J

149

4

4

157 Lawson

Total, .

226

36

15

277

“ It will be observed that the mortality and sickness has been
greatest amongst the plants brought out under the care of the
members of the Forest Department. I have no doubt this result
is due to over-kindness during the voyage. The plants have been
apparently freely watered and over-shaded ; and in the close and
moist atmosphere of the cases, unnatural forced growth has been
the result. Mr G-amble’s consignment is an exception, the plants
brought out by him being in quite as good health as those that came
untended in the ‘ City of Mecca.’ The condition of the latter is
wonderfully good, and indicates extreme care in the selection of
plants, and in the mode of packing them.

“ As soon as the plants shall have recovered a little from their
journey, I propose to despatch them to Sikkim.

<c I take this opportunity of stating that the twelve plants
brought out in July last by Mr Walton were forwarded to Sikkim
three months ago, and that eleven of them are now in excellent
order ; the twelfth unfortunately died during the journey to
Sikkim.

u The condition of the eleven plants just alluded to, of the five
old plants formerly sent from this garden to Sikkim, and of the
young ones propagated from them, leads me to entertain hopes that
in that province the Ipecacuanha experiment will be attended with
great success.”

A question has been started whether there are not plants in
India which may be used as Ipecacuan. One of these is the
Tylophora asthmatica , W. et A., an Asclepiadaceous plant, which

of Edinburgh, Session 1871-72.

691

lias been known under various names : — Gynanchum Ipecacuanha ,
Willd.; Asclepias asthmatica , Roxb. FI. Ind.; Gynanchum vomitorium ,
Lam. Dr Roxburgh and Dr Anderson used the plant for dysentery
in India with great success.

There are some peculiar features in the plant now under culti-
vation which require investigation, and I am not able to give a
full paper on the whole subject until further cultivation. The
plant which has been long in the garden has flowered regularly.
Even the young cuttings have sent forth their flowers. The plant,
on the other hand, sent from Rio Janeiro, although treated in the
same way as the other, has not flowered.*

The former, although flowering freely, has not produced perfect
fruit until the present year. The plants were carefully fertilised
by the application of the pollen of one flower to the stigma of
another. Ey this means we have secured a number of fruiting
specimens, and I nowT exhibit fruiting plants with drawings of the
fruit and sections.

The fruit is drupaceous, of a dark purple colour, shining and
glossy on the outside. It is about the size of a large currant, and
when ripe it falls off easily. Each fruit contains two seeds. These
are seen in the section of the fruit. The albumen of the seed is
very hard. I have not seen any figure of the fruit in botanical
works containing plates of the plant. There is a resemblance
between it and that of Psychotria emelica.

We expect that some of the seeds will ripen, and that we shall
then be able to propagate the plant from seed.

The following Gentlemen were elected Fellows of the
Society : — ■

George Seton, M.A. Oxon., Advocate.

Captain Charles Hunter.

* Since this communication was made the plant has flowered, and has
shown peculiarities in the relative length of the stamen and pistil. July 1872.

692

Proceedings of the Royal Society

Monday , ls£ April 1872.

Professor Sir BOBERT CHRISTISON, Bart., President,
in the Chair.

The following Communications were read : —

1. On Cardiocarpon. By Professor Duns, D.D., F.R.S.E.,
New College.

The attention of the Society was called to many beautiful speci-
mens of Sphenopteris laid on the table. These had been obtained
by Dr Duns and his predecessor, Dr Fleming, from the old work-
ings in the Burdiehouse limestones, near Edinburgh, well known
from Hibbert’s Memoir (1835), and from the papers of more recent
observers. The species exhibited were chiefly S. artemisicefolia
and S. affinis. An Antholite (A. Pitcairniae) was also shown, in
which the pedicels that spring from the flower-like buds in the
axils of the bracts, sub-opposite in the spike, are well represented.
The author then referred to Cardiocarpon, Brong., and to the
species named by Brongniart, Bindley, and Hutton, and more
recently by Dawson and Lesquereux. It was pointed out, that
very many Cardiocarpa occur in association with the specimens of
Sphenopteris on the table. On three of these alone there are
above 160. Of these, some are almost globular, others are oval.
Some taper to a single sharp point ; others, and the majority, have
an acute bifid apex. In many the medial ridge is not seen, in
others it is highly marked. In a few this ridge has an excurrent
appearance, both at the apex and at the supposed point of attach-
ment to the plant. Many of the forms are so placed as to present
an appearance of organic connection with the Sphenopterides. The
author then showed that it “ is needful to guard against a tendency
to give undue importance to the mere fact of association. If in
other departments this has lead to most erroneous inferences, it
will he sure to mislead in the study of pakeobotany. Some weight
is, no doubt, to be given to the fact, but to use it to any extent as
a guide in determining the affinities of fossil plants is, to say the
least, not safe. Principal Dawson has pointed to the occurrence

693

of Edinburgh, Session 1871-72.

of Cardiocarpa along with the stems of Sigillaria as corroborative
of the theory of the conifer or cycad character of Sigillaria.
He says, “ Some botanists, conspicuous among whom is Brongniart,
hold that Sigillaria were gymnospermous plants allied to Cycadacese.
Others are disposed to regard them as Acrogens, and as closely

allied to Lycopodiacese In favour of the former

view we may adduce the exogenous structure of the stem of
Sigillaria , and the obvious affinity of its tissues to these of conifers
and cycads, as well as the constant association with trees of this
genus of the evidently phanerogamous fruits, known as Trigono-
carpum and Cavdiocarpum.” And he adds, “ The higher Sigillarice
unquestionably resemble cycads in the structure of their stems.
Their long, rigid, narrow leaves may be compared to single pinnae
of the leaves of cycads. Their cord-like rootlets, as I have
ascertained by actual comparison, are similar to those of cycads.
If their fruit was of the nature of Cardiocarpon or Trigonocarpum,
this would also correspond.” (See Quarterly Journal of the Geo-
logical Society , May 1871.) This assumes throughout that palseo-
botanists are agreed as to the nature of these fossil fruits, which is
far from being the case.

In August 1870, Mr C. W. Peach, to whom Scottish natural
science is so much indebted, found specimens of Cardiocarpon
organically united with a plant long known by the nam e, Antholites
Pitcairnice. The specimens were obtained from carboniferous
shale at Cleuch, near Falkirk. Specimen No. 16, on the table, is
Antholites Pitcairnice , from shale near Bathgate. By the kindness
of Mr Peach, I am able to show the Society an example of Antho-
lites with the fruit organically attached. The importance of this
discovery is at once recognised. In a department where facts are
the letters, and their association the words by which we read the
history of creative manifestation, every worker will acknowledge
the value of an observation like that referred to, even though he
may not see his way to accept views implying generic identity
between the fruit now associated with Antholites and Cardiocarpon.
On the assumption of this identity, Mr Carruthers has recently
limited the term Antholites to the place, or rather the use assigned
to it by Brongniart — “ Les especes indeterminable sont generale-
ment designees sous le nom d’ Antholites.” — Prod. p. 149. In-

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694

Proceedings of the Royal Society

stead of Antholites Pitcairnice , Lindley, lie has proposed Gardio-
carpon Lindleyi , Carruthers. ( ' Geolog . Mag., Feb. 1872., pp. 54-57.)
Along with a figure of the Falkirk specimen, another is given from
an unknown locality, supposed to be from mines in Derbyshire.
The fruit on the latter is regarded as similar to Cardiocarpon
acutum of Lindley.

It was stated that, so far as the author is aware, there is no
certain record as to the form of the fructification of such Sphenop-
terides as S. artemisicefolia and)#, affinis , or, indeed, of any of the
species closely related to these by their bipinnate leaf and the
deep pinnatifid segments of their leaflet. G-oeppert and Unger’s
statement, that* the fructification is “ punctiform or marginal,” may
be true of species like S. dilata , or S. latior (Dawson), but these
differ widely from the specimens now noticed, though they bear
some resemblance to living forms. As regards S. artemisicefolia ,
Brongniart himself has said, that he has not been able to find the
least resemblance between it and living ferns. It was shown that
this remark is especially applicable to S. affinis. The question
seemed to be raised by what might be said to be the almost constant
association of Cardiocarpa with these two species, “ Have they
their proper place under the genus Sphenopteris ? ” Dr Duns
stated in conclusion, that while these species must still be regarded
as true ferns, and while the idea even of organic connection
between such forms as the samaroid fruit Cardiocarpon and the
species S. artemisicefolia , and S. affinis is opposed to all accepted
views of plant affinity, yet the association, as shown in the numerous
specimens on the table, is so frequent, and often so remarkably like
organic, as to call for the attention of observers.

2. On the Composition of the Flesh of the Salmon in the
“Clean” and “Foul” condition. By Sir Bobert Christison,
Bart.

Having had occasion lately to fill up some blanks in a table of
the Nutritive Value of different kinds of Food, I was unable to
find for the purpose an analysis of the flesh of the Salmon.
I have therefore made such an analysis as is necessary ; and as

of Edinburgh, Session 1871-72. 695

the results may be useful to others, I beg to offer them to the
Society,

I first examined the composition of a very fine “ Clean ” fish,
caught in the estuary of the Tay in May last year, and weighing
20 pounds. I have never seen a finer fish from that far-famed
salmon-river.

I have also, in contrast with this, examined a “Foul” fish, or
Kelt, taken in the beginning of March last from a pool where
spawned fish are known to congregate at that season in the Isla, a
principal tributary of the Tay. It weighed 27 pounds the day
after it was caught, and would probably have weighed 35 pounds
in good condition. In order to account for my being in lawful
possession of such an article, I must mention that I owe it to the
consent of the Commissioners for the Tay Fisheries, whose kind-
ness in presenting, for a scientific object, what otherwise cannot be
easily obtained without infringing the law, may receive, as I hope,
some return in the additional proof which analysis supplies of the
inferiority of the salmon as food when in the state of a Kelt, and
the folly of destroying it before it recovers condition.

The clean salmon of last May presented abundance of fat under
the skin, and in masses betwixt the muscles. Avoiding all accu-
mulations of fat in mass, I cut one piece of muscle from the
dorsal region a little in front of the dorsal fin, and another from
the ventral region directly opposite ; so that the one should repre-
sent the “ thick,” and the other the “thin,” of a slice of salmon
Four hundred grains of each being cut into fine chips about twelve
hours after the fish was caught, each was separately exhausted by
ether ; and the ether was distilled off at a gentle heat. When the
residual oil was deprived of a little adhering alcohol and water by
heating it gently for an hour in an open vessel, it had a bright
amber colour, and a strong odour not very different from that of
cod-liver oil. The fibrous residuum was dried at 212° till it ceased
to lose weight. A portion of the dry residue was incinerated in
order to determine the fixed saline constituents. The difference
denoted the dry nitrogenous nutritive principles, fibrin, albumen,
and extractive matter usually called osmazone.

696

Proceedings of the Royal Society
The results were as follows: —

Oil

Dorsal.

16-66

Abdominal.

20-4

Mean.

18-53

Fibre, albumen, ex-
tractive matter .

J 20-57

18-82

19-70

Saline matter

0-88

0-88

0-88

Water

61-89

59-90

60-89

100-00

100-00

10000

The Kelt of last March was as ugly a specimen of the Salmo
Salar as I have ever seen. It was 38 inches long, weighed 27
pounds, and was very lank in the belly, soft in the flesh, much
lacerated in the dorsal fin and tail, and of a uniform, disagreeable,
mottled-grey colour over the entire skin. In its structure other-
wise it was a true male salmon. I subjected it to analysis in the
same way as the clean fish, with the following results. The ana-
lysis was made about forty-eight hours after the fish was caught ;

and in the interval it was shut up in

a box, so that there could not

have occurred any appreciable loss by evaporation.

Dorsal.

Abdominal .

Mean.

Oil ...
Fibrin, albumen, extrac- j

1-2

1

1-30

1-25

tive matter . j

Saline matter [inferred

• 16-92

)

17-22

17-07

from the former ana- j
lysis]

l 0-88

0-88

8-88

Water

81-0

80-60

80-80

100-00

100-00

100-00

Thus it appears — 1. That the nitrogenous solids of a Clean
salmon, and its oil or fat, constitute together in round numbers 38
per cent of its flesh ; the remaining 62 per cent being water, with
a little saline matter (0-9 per cent.). 2. That the fat and the nitro-
genous constituents are nearly equal to one another. 3. That there
is decidedly more fat in the “ thin” or abdominal region than in

697

of Edinburgh, Session 1871-72.

the “ thick” or ’dorsal region, hut somewhat less of nitrogenous
constituents. 4. That there is very little difference in constitution
between the dorsal and abdominal regions of a “Foul” fish or
Kelt. But, 5. That the Kelt is a much more watery fish than the
clean salmon ; and that this is slightly owing to a deficiency in
nitrogenous ingredients, but much more to an enormous deficiency
of oil or fat, — which is reduced to almost a sixteenth only of its
amount in a clean-run fish.

I am not aware of any good authority for the prevalent notion
that a Kelt is unwholesome food. But it is plain from the foregoing
analysis, that the Parisian gastronome, — who, before the late
stringent measures against river-poaching in Scotland during close-
time, consumed a large proportion of Scottish Kelts, — must have
been indebted for his enjoyment therein much more to his cook
than to his fish. On the other hand, it is easy to see why an Api-
cius, whose taste has been cultivated on the banks of a Scottish
salmon-river, should wonder how any one can imagine, that the
delicate flavour of a fish in good condition is improved by besmear-
ing it with butyraceous sauces, simple or compound.

3. On Recent Estimates of Solar Temperature.

By James Dewar, Esq.

(Abstract.)

After referring to the recent discussion on the temperature of
the sun, in which Secchi, Zollner, Yicare, Deville, and Ericsson have
taken part, the author proceeds to group all the known methods
of arriving at a knowledge of high temperatures under eight
different processes. The following table gives the names of the
physicists who have specially employed each process, together with
the principle on which it is founded : —

(1.) Guyton and Daniell, Prinsep, &c. — Expansion of Solids and
Gases.

(2.) Draper. — Refrangibility of Light.

(3.) Clement and Desormes, Deville. — Specific Heat.

(4.) Becquerel, Seamens. — Thermo-Electricity and Electric Con-
ductivity.

698 Proceedings of the Royal Society

(5.) Bunsen, Zollner. — Explosive Power of G-ases.

(6.) Newton, Waterston, Ericsson, Secchi. — Badiation.

(7.) Thomson, Helmholtz. — Mechanical Equivalent of Heat.

(8.) Deville, Debray. — Dissociation.

After treating of the great disparity of opinion regarding the
temperature of the sun, the author proceeds to detail how it is pos-
sible, from the known luminous intensity of the sun, to derive a
new estimate of solar temperature. This calculation is based on a
definite law relating temperature and luminosity in the case of
solids, viz., the total luminous intensity is a parabolic function of
the temperature, above that temperature where all kinds of luminous
rays occur. So that if T is a certain initial temperature, and I its
luminous intensity, a a certain increment of temperature, then we
have the following relation : —

T + n (a) = n2 1 .

The temperature T is so high as to include all kinds of luminous
rays, viz., 990° C., and the increment a is 46° C. This formula
expresses well the results of Draper, and I have used his numbers
as a first approximation. It results from the above equation,
that at a temperature of 2400° 0., the total luminous intensity will
be 900 times that which it was at 1037° O. Now, the temperature
of the oxyhydrogen flame does not exceed 2400° C, and we know
from Eiseau and Eoucalt’s experiments that sunlight has 150
times the luminous intensity of the lime light ; so that we only
require to calculate at what temperature this intensity is reached
in order to get the solar temperature. This temperature is
16,000° C.,in round numbers. Enormously high temperatures are
not required, therefore, to produce great luminous intensities, and
the temperature of the sun need not, at least, exceed the above
number. Sir William Thomson, in his celebrated article, “ On the
Age of the Sun’s Heat,” says, “ It is almost certain that the sun’s
mean temperature is even now as high as 14,000° C.,” and this is
the estimate with which the luminous intensity calculation agrees
well.

of Edinburgh, Session 1871-72.

699

4. On the Temperature of the Electric Spark. By
James Dewar, Esq.

(Abstract.)

The author begins this paper by calculating the highest hypo-
thetical temperature that could be produced by the chemical
combination of the most energetic elements if all the heat evolved
could be thrown into the product. This would not exceed 19,500°
C. in the case of silica, and 15,000° O. in the oxides of aluminum and
magnesium, and these are the highest results. The estimation of
the temperature of the electric spark is based on the thermal value
of each spark, together with the volume of the same. The
methods of observing these quantities are fully detailed in the
memoir. The general result may be stated thus, — the tempera-
ture of the electric spark used in the experiments ranged between
10,000° C. and 15,000° O.

The following Gentlemen were admitted Fellows of the
Society : —

James Thomson Bottomley.

Thomas Knox, Esq.

Dr D. Argyll Robertson.

Monday , \5th April 1872.

Professor KELLAND, Vice-President, in the Chair.

The following Communications were read : — ■

1. On the Action of Water on Lead. By Sir Bobert
Christison, Bart.

After summarising the conclusions at which he had arrived from
numerous experiments made more than forty years ago, as published
in his Treatise on Poisons, and in the Transactions of this Society,
the author alluded to various blanks left at that time in the inquiry
which had not been yet filled up, and to various criticisms and
doubts which had been recently expressed relative to the facts and
principles formerly announced.

700 Proceedings of the Royal Society

The general results of the former inquiries are — 1 That the
purest waters act the most powerfully on lead, corroding it, and
forming a carbonate of peculiar and uniform composition ; 2. That
all salts impede this action, and many prevent it altogether, some
of them in extremely minute proportion ; and 3. That the proportion
of each salt required to prevent action is nearly in the inverse ratio
of the insolubility of the compound which its acid forms with the
oxide of lead. The effect of certain inorganic and organic ingre-
dients of water in modifying the preservative power of the salts
was not investigated, but has been since made the subject of nume-
rous observations and inquiries by others, chiefly, however, of a
desultory nature, some of them much too succinctly described, and
some also of questionable accuracy.

The first part of the present paper dealt with the influence of
inorganic substances. The second part, on the influence of organic
matters, was reserved for a subsequent article.

It had been denied thatwater acts by reason, and in the ratio,
of its purity; and it had even been alleged that distilled water
itself does not act, if really quite pure. The author, however, had
invariably found the reverse, and could assign no other explanation of
these statements except some error in manipulation. For example,
a very pure spring water was sent to him from the south of England,
with the assurance that it had been found to be incapable of attach-
ing lead. But, on making trial of it, he had found it act with an
energy not inferior to that of distilled water. Also, it had been
stated that ordinary distilled water is apt to contain a trace of
nitric or nitrous acid, from nitrates incidentally present in the
water subjected to distillation ; and that such water, it distilled
after the addition of a little potash to fix the acid thoroughly,
yields a distillate which has no action on lead. But when the
author prepared distilled water in this way, with great care to
prevent the access of impurities from other sources, the only
result was that the action was even greater than that of the
ordinary distilled water of the laboratory, and so great as he had
never observed before.

An interesting statement had been made by Dr Nevins, that
some salts appear to allow of a certain action going on when they
are present largely in water, although their influence, when they

701

of Edinburgh, Session 1871-72.

exist in very small proportion, is to act as preventives. The
author sometimes obtained the same result, and found the action
such as might prove dangerous. But its limit requires to be de-
fined ; and there is reason to suppose that the proportion required
to permit action will be found so great as never occurs in the instance
of waters applicable to household use.

It has been also stated, but in general terms, without experi-
mental proof, that the presence of carbonate of soda, even in a
hard water, takes away the preventive influence of other salts, and
enables water to dissolve lead. There appears to be some founda-
tion for this statement. But here, too, it is necessary to fix what
is the limit to such influence before its importance can be valued.
Moreover, as bicarbonate of soda appeared to the author to have
no such effect, and this is the usual form of the carbonate in
natural waters, the practical importance of the fact is inconsiderable.

The author called attention to some observers not having under-
stood the nature of the corrosive action of water on lead, and having
confounded it with other causes of corrosion. Thus the true action
has been confounded with the corrosive action of potent agents
accidentally coming in contact with the metal in presence of water,
— as, for example, when a lead pipe has been led through fresh
mortar which is frequently or permanently kept moist, or when
lumps of fresh mortar have been allowed to fall upon the bottom
of a lead cistern. Several remarkable examples of rapid corrosion
of this local kind were exhibited. The true or simple action of
water had been not infrequently confounded also with the effects
of galvanic action. Thus, if a lead pipe or cistern be soldered
with pewter-solder, and not with lead, erosion takes place near
the line of junction of the solder with the lead, of which character-
istic examples were shown. The presence of bars of other metals
crossing lead, or bits of them lying on it, will also develope the
same action ; and some facts seem to point to the same property
being possessed in a minor degree by some stony and earthy sub-
stances. This observation may explain the local erosion sometime
observed in cisterns containing hard water ; since, if galvanic action
be excited, it will be increased by saline matter existing more
largely in these waters than in soft, or comparatively pure, water.

Lastly, some observers have contradicted former statements,

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VOL. VII.

702 Proceedings of the Royal Society

because in certain circumstances, which led them to anticipate
no action, they nevertheless found lead in water, but only in
extremely minute and unimportant proportion. The test for lead,
the hydrosulphuric acid, when employed in the way now usually
practised, is so delicate as to detect that metal dissolved in ten
million parts of water, and even more. But facts warrant the con-
clusion that the impregnation must amount to at least ten times
as much before water can act injuriously on man, however long
it may be used.

2. On the Preservation of Iron Ships. By
James Young, Esq., of Kellie.

My attention was called in January last year to the rusting of
iron vessels by observing that the bilge water of my yacht (the
“Myanza,’’ 214 tons) was much discoloured by red oxide. Knowing
that bilge water is apt to become acid, and thus to attack iron, the
result was easily accounted for. Even when the water does not
become acid, we may expect some action on the iron to take place
when sulphuretted hydrogen exists, as it frequently does there, in
which case, first a sulphide, then an oxide, and some sulphate, are
formed. The remedy seemed to be easy, because the acid can be
neutralised by lime. This earth would also prevent the formation
of sulphuretted hydrogen.

I put this immediately into practice, adding lime until the bilge
water was alkaline ; and samples were taken every fourteen days,
which showed the amount of rust to be rapidly diminishing. After
six months the liquid became perfectly clear, so that the cure is
complete. The yacht is a composite one, and the action is there-
fore greater than in iron vessels generally, because of the copper
or cupreous bolts which are used. These bolts cause galvanic
currents with the iron, and greatly assist in its oxidation and
solution.

As a very little lime will last a long period, the plan causes
neither trouble nor expense. Seeing in the newspapers that the
destruction of the “ Maegara ” was attributed to the action of bilge
water, I thought that my experience might be of some value.

oj Edinburgh, Session 1871-72.

703

3. First Eeport by the Committee on Boulders appointed
by the Society.

In April 1871, a paper was read in this Society proposing a
scheme for the conservation of boulder or erratic blocks in Scotland,
in so far as they were remarkable for size or other features of
interest. The Council of the Society approved of the scheme,
appointed a committee to carry it out, and agreed to aid in meeting
the expense of any circulars which might be necessary for con-
ducting the inquiries.

The objects of the committee were twofold. They were first to
ascertain the districts in Scotland where any remarkable boulders
were situated ; and, second, to select those which might be deemed
worthy of preservation, with the view of requesting landed proprie-
tors and tenants of farms not to destroy them.

The labours of the committee have as yet been directed only to
the first of these objects.

In order to procure information, they drew out a set of printed
queries, applicable to boulders apparently above 50 tons in weight,
in order to ascertain the parishes in which they were situated, and
the names of the proprietor and tenant on whose lands they were;
and also to learn other features, such as the nature of the rocks
composing the boulders, their form, and the existence of striations
upon them. Inquiry was also made whether the boulders had any
traditional names or popular legend connected with them, or ex-
hibited any artificial markings.

The committee thought that, with a view to the conservation of
the boulders, the greater the interest which could be shown to
attach to them, the more chance there would be of inducing pro-
prietors and tenants to preserve such as the committee might
select for preservation.

Besides queries about boulders, there was one query directed to
ascertain the occurrence of kaimes or eskars , i.e., long banks of sand
and gravel, as some persons imagined that the agents which trans-
ported boulders might have had some relation with, or might throw
some light on those which were concerned in the formation of those
deposits.

Circulars containing queries, a copy of the minute of Council

704

Proceedings of the Royal Society

approving of the scheme, and appointing a committee, and an ab-
stract of the paper read in the Society in April 1871, explaining
the scheme, were transmitted to the ministers of all rural parishes
in Scotland.

About 700 circulars were issued. After the lapse of six months
about 100 answers were received.

The committee, on considering these, were of opinion, that in
making their queries applicable only to boulders exceeding 50
tons in weight, they had probably erred, by excluding many boulders
of interest, and to this circumstance they attributed the small
number of answers sent.

They therefore resolved to issue another circular containing the
same queries as before, to cover boulders exceeding 20 tons in
weight. This circular was addressed to parochial schoolmasters, as
the committee feared that they might be considered troublesome, if
they made a second application to ministers of parishes.

This second circular brought to the committee a large amount
of information, and they desire now to express their cordial thanks
to both classes of reporters for responding so readily.

When the committee was appointed, an expectation was ex-
pressed that they should, from time to time, lay before the Society
some account of their proceedings, and of the progress made by
them.

In now proceeding to the performance of this duty, the committee
will confine themselves to a statement of facts communicated, and
avoid at present attempting to draw conclusions from these facts.

1. In order to show the situations of the boulders reported on,
the committee have drawn up a list,* according to counties, giv-
ing the names of the parishes where boulders occur, adding shortly
any particulars regarding them, such as size, nature of the rock
composing the boulder, direction of the longer axis, striations,
popular naihes, and legend, if any.

They have also, on a general map of Scotland, indicated by a red
cross the exact position of the most remarkable boulders.

From this table and map, it will be seen that Aberdeenshire pos-
sesses the largest number of boulders, and also the boulders of
greatest magnitude.

This list is in the Appendix.

of Edinburgh, Session 1871-72. 705

Boss and Cromarty stand next, then Perth, Argyll , Inverness ,
Kirkcudbright , and Forfar.

2. In regard to size , the largest boulder reported is one of granite,
in the parish of Pitlochry, called u Clach Mhor” (big stone), being
about eight yards square, and estimated about 800 tons.

There are two boulders between 500 and 600 tons weight, one in
Boss, the other in The Lewis.

There are three boulders between 200 and 500 tons, seven be-
tween 100 and 200 tons, twenty between 50 and 100 tons.

3. With regard to the nature of the rocks composing the boulders,
the largest reported are of granite, though there is one known to
the convener of the committee, still larger, of conglomerate, in
Doune parish. The most numerous are composed of compact
greenstone; but these are generally of small size. The next
most numerous class are of grey granite. There are also many of
gneiss, grey-wacke, and conglomerate.

4. The boulders reported generally differ in regard to the nature of
the rocks composing them, from that of the rocks of the district in
which they are situated ; and, in many of the reports, reference is
made to the district from which the boulder is supposed to have come.

Thus, in those parts of Perthshire, Forfarshire, and Kincardine-
shire where the old red sandstone formation prevails, and over
which multitudes of granite, gneiss, and conglomerate boulders are
lying, most of the reporters have no hesitation in pointing out that
the parent rock is in the Grampian range, lying to the north or
west. So also in Wigtonshire, where the greywacke formation pre-
vails, and on which many boulders of grey granite are lying, the
general opinion is that they came from the granite hills of Kirk-
cudbrightshire.

But where a boulder happens to be of a species of rock the same
as that of the rocks of the neighbourhood, it is more difficult to
recognise it as a true erratic. Hence, in the Lewis, where there are
huge single blocks of gneiss, which is also the prevailing rock of
the country, the reporters say that they cannot tell whether these
blocks are erratics or not.

5. The boulders mentioned in the reports are of various shapes.
Some approach a cube, well rounded of course on the corners and
sides. That is the shape mostly possessed by granite boulders.

706 Proceedings of the Royal Society

Others again are of an oblong shape, and this is particularly the case
with whinstone and greywacke boulders. The difference in this
respect is probably mainly due to a difference in the natural struc-
ture of the parent rocks.

A point of some importance occurs in regard to oblong-shaped
boulders.

The direction of their longer axis , in the great majority of cases,
is stated to coincide with the direction in which they have come
from the parent rock, when the situation of that rock has been
ascertained. Thus, in Auchterarder parish, there is a boulder 10
feet long by 6 broad, the longer axis of which points north-west. In
Auchtergaven parish there is a granite boulder 10 feet long by 8
broad, the longer axis of which points due north. In Menmuir
parish, Forfarshire, there are two large granite boulders, the one

14 by 9, and the other 13 by 9, the longer axis of which points
north-west. In each of these cases the reporters seem satisfied of
the situation of the parent rock, and in each case the longer axis of
the boulder points towards it.

It appears, also, that where there are natural striations or ruts on
the boulders, these almost always run in a direction parallel with
the longer axis ; and that when there are striae crossing these, the
number of such oblique striae are comparatively few.

6. Notice in the reports is taken of the remarkable positions occu-
pied by some boulders.

Thus, the Ardentinny report refers to a large boulder called
u'Glachan XJdalain ,” or the nicely balanced stone,* so-called, as the
reporter states, because “ it stands on the very edge of a precipice,
and must have been gently deposited there.” In the same parish
there is another boulder, called “ The Giant's Putting Stone. It is
pear shaped, and rests on its small end. It looks,” says the re-
porter, “ as if a push would roll it over.”

In Menmuir parish (Forfarshire), two boulders are reported, each
from 30 to 40 tons in weight, and perched on or near the top of a
hill, having come there, as the reporter thinks, from a parent rock

15 miles distant, with several valleys intervening.

Cases of the same kind are reported from islands.

On Iona, near the top of the highest hill in the island, which is
* Another translator represents this word to mean “ of the swivel.”

707

of Edinburgh, Session 1871-72.

about 250 feet above the sea, there is a great boulder of granite.
There is no granite in the island. The nearest place where that
rock occurs is in the Boss of Mull, with an arm of the sea intervening.

In the Island of Eday, in Orkney, there is a conglomerate
boulder, called the “ Giant's Stone f about 8 tons in weight, near the
top of a hill — the only one in the island — about 300 feet high.
There is no conglomerate rock in Eday. But conglomerate rock
occurs in the Island of Stronsay, situated to the south-east, a few
miles distant.

7. The report from the parish of Benholm (Forfarshire), by the
Rev. Mr Myres, gives information and suggestions to the committee
of considerable interest. On the sea coast of that parish, two sets
of boulders are described. One set are supposed to have come from
the Grampian range many miles to the north-west, and consist of
granite and gneiss rocks. But another set, also consisting of pri-
mitive rocks, are believed to be derived from a different source
altogether, viz., from the great beds of conglomerate rock, which
forms a band crossing the whole of Scotland from Stonehaven
and Bervie, in a south-west direction, to Dumbarton and Rothesay.
Some of the rounded masses in the conglomerate are stated to be
several feet in diameter, and a few present appearances of striation ;
a fact which, if established, would seem to prove that, at a very
early period indeed, ice action had existed, and had formed boulders
just as it did at a later period.

This report from Benholm parish was read lately at a meeting of
the Geological Society of Edinburgh, and was illustrated by drawings
and specimens which afforded strong evidence of the correctness of
these views.

8. With regard to kaims or long embankments of gravel or sand,
there are twenty-three parishes reported to the committee as con-
taining them.

They appear to be most numerous in Aberdeenshire, Eorfarshire,
and in the east of Perthshire. In Kemnay parish there is a kaim
said to be 2J miles long, running east and west. In Airlie parish
there is a kaim 2 miles long, also running east and west. In Fet-
tercairn parish, Kincardineshire, and also in Tarbet parish, Ross-
shire, there are several kaims parallel to, and not far distant from,
one another.

708 Proceedings of the Royal Society

In two cases the reporters, who seem to have visited Switzer-
land, whilst mentioning kaims in their parishes, express an opinion
that they are evidently lateral and terminal moraines.

In several cases, oddly enough, these kaims exist at much the
same level above the sea, viz., between 700 and 800 feet, which
happens also to be the height of similar deposits in Berwickshire
and Mid-Lothian.

The committee wish it to be understood, that in the present
report, they confine themselves simply to a statement of the
information received. They do not think it would be wise as
yet to attempt to draw theoretical conclusions. Almost every
day they are receiving more answers to their circulars; and
they think that the wider the basis for considering the important
geological questions connected with the transport of boulders and
the formation of kaims, there will be the more probability of reach-
ing the truth.

One object which the committee have in view in explaining the
nature of the information communicated to them, is to show and
to acknowledge the deep debt of gratitude which this society lies
under to the gentlemen who have responded to the circulars of
the committee.

But whilst the information supplied is undoubtedly valuable, the
committee cannot but feel the truth of what many of the reporters
themselves modestly and properly state, that they are so little
acquainted with geology or mineralogy, that they may not have
correctly understood the queries, or they may not have made their
observations in the way necessary to answer the queries. Moreover,
the committee itself may not in all cases have rightly understood
the answers given.

Having regard to these considerations, the committee would
very much desire that the boulders reported should be ex-
amined by experienced geologists, who should at the same
time make a survey of the district, in order to see whether it
presents any special features bearing on the nature of the agency
by which the boulders were transported. The information in the
reports received by the committee would greatly facilitate such an
inspection, as they indicate not only the parish and the farm where

of Edinburgh, Session 1871-72. 709

the boulder is situated, but generally record other features of
interest.

The committee entertain a hope, that were this wish on their
part made known, some geologists, who may be either resident in
Scotland or who may purpose to visit Scotland during the course
of the ensueing summer or autumn, might offer their services in
the way, and for the purpose now suggested. In that case, the
committee would willingly lend the reports which they have received,
on condition that the results of the inspection were made known
to the committee.

The committee will place in the library of this Society, the list
of boulders before referred to, showing the parishes in each county
in which the boulders and kaims are situated, so that any person
may see where these parishes are, and be able to judge whether it
would be convenient for him to visit these.

Were this list published, and generally circulated, good would
result in another way. As it would show all the parishes from
which reports of remarkable boulders and kaims had come, some
persons might be able to discover parishes from which reports had
been omitted to be sent, and if these were pointed out to the
committee, they would make the requisite inquiry.

II. The committee proceed next to notice points of archaeological
interest connected with boulders.

1. The committee were surprised with the large number of
individual boulders possessing names by which they were known
in the district.

The names may be classified under several heads : — First , there
are names having reference to the agency by which the boulders
were supposed to have come into the district. Second , there are
names indicative of the use to which boulders were put. Third ,
there are names making the boulders commemorative of certain
events.

Many of the boulders, besides having a name, have also a legend ,
which explains and illustrates the name.

The Giant's Stone , FingaVs Putting Stone , the Witches’ Stone ,
the Carlin Stone , Heathens , Hell Stones , the Deil’s Stone ,
the DeiVs Putting Stone , the Deil’s Mither’s Stone , — these are
among the names, almost all in the Gaelic language, which ap-

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Proceedings of the Royal Society

pareutly were given to account for the way in which particular
boulders came into the district. *

To show that this was the origin and object of the names, a few
of the legends, as stated in the reports, may be given. They in-
dicate, no doubt, a very deplorable state of ignorance and credulity;
but they indicate also that in many cases our forefathers had
satisfied themselves that the boulders had been transported into the
district. Their perplexity was how to account for their transport.
Not knowing anything of glaciers or icebergs, they had to resort to
supernatural agency for an explanation. A few examples may be
given.

Reference has already been made to a large conglomerate boulder
near the top of a hill, in the Island of Eday, one of the Orkneys.
It goes under the name of u Giant's Stone." The legend for it is,
that it was flung by a giant from the Island of Stronsay. Now, as
already stated, there is no conglomerate rock which could have
supplied the boulder in Eday Island, but there is in Stromsa.

So also in the Island of Sanday, one of the Orkneys, there is a
granite or gneiss boulder ; the legend about which is, that it was
thrown from the Shetland Islands by a giantess, who had been
jilted by a Westray man. She intended to throw it into Westray,
but she made a bad shot, and it fell into the Island of Sanday.
There is no rock which could have produced the boulder in Sanday,
but there is abundance of it in the Shetlands.

About 1 \ miles west of St Andrew’s in Fife, there is a large con-
glomerate boulder, and the legend about it is, that when the “ Four
hnockit steeple ” in that town was being built, a giant who lived at
Drumcarro Crags, a hill about 5 miles to the north-west of St
Andrews, was indignant, and resolved to demolish the edifice. He,
therefore, got the largest stone he could find, and borrowing his
mother’s apron, he made a sling of it, and threw it at St Andrews.
But the stone being too heavy, the apron broke, and the stone did
not quite reach its destination, and there it has lain ever since.
There is no conglomerate rock where the boulder lies, but there is
at or near Drumcarro Crags.

* The Rev. Mr Joass of Golspie refers to a boulder in Sutherland, called “ Clach
Mhic Mhios,” or stone of the Manthold son, believed to have been thrown from a
hill two miles off by Baby Fingalian.

711

of Edinburgh, Session 1871-72.

The Witches’ Stone, which is on the estate of Pitferran, near
Dunfermline, has this legend : A witch who lived among the hills
to the west, wishing to confer a favour on the Pitferran family, re-
solved to give them a cheese-press, the heaviest she could find. She
selected a large block of basalt of the proper shape, and carried it in
her apron, which, however, broke under the load before she reached
the family residence ; and there it has lain ever since. There is no
rock of that kind near Dunfermline, but there is to the west-
ward.

In the parish of Carnwath there are one or two spots where theie
are or have been groups or collections of whinstone boulders, be-
tween the river Clyde and a hill of whinstone, known by the name
of the Yelpin Craigs. The distance between the river and this
hill is three or four miles. These heaps of boulders have from time
immemorial gone by the name of Hellstanes, insomuch that places
near them are called Hellstanes Loan , Hellstanes Gate , &c. The
legend is, that Michael Scott and a great band of witches, wishing
to dam back the Clyde, gathered stones at the Yelpin Craigs , and
were bringing them towards the Clyde, when one of the young
witches, groaning beneath her load, cried out, “ Oh Lord, but I am
tired.” As soon as she uttered the sacred name, the spell broke,
the stones fell down, and have remained there ever since.*

There are many legends founded on the agency of the devil, and
on his hatred of churches and clergy. Thus near the old church
of Invergowrie, now in ruins, there is a large whinstone boulder,
called the Paddock Stone. The legend about it is, that the devil,
going about in Fife, descried the church shortly after it was begun
to be built, and wishing to stop the work, threw a large stone at it
across the Frith of Tay. There is no whinstone rock at or near Inver-
gowrie, but there is abundance of it immediately opposite in
Fife.

In the parish of Kemnay (Aberdeenshire), there is a boulder of
grey granite, called the DeviVs Stone , estimated to weigh about
250 tons, which lies not far from the old kirk. There is no rock
of that nature in Kemnay parish, but there is at Bennachie, a hill
about seven or eight miles to the westward. The legend explain-

* This legend is given more fully in “ Scenery of Scotland,” p. 314, by Professor
Geikie.

712 Proceedings of the Royal Society

ing how this boulder came from Bennachie forms the subject of a
ballad,* a few verses of which may he given.

“ It was the feast o’ Sanct Barnabas,

I’ the merry month o’ June,

When the woods are a’ i’ their green livery,

And the wild birds a’ in tune ;

“ And the priest o’ Kemnay has gaen to the kirk,

And prayed an earnest prayer,

That Satan might for aye be bund
To his dark and byrnand lair.

“ And aye the haly organ rang,

And the sounds rose higher, higher,

Till they reached the Fiend on Bennachie,

And he bit his nails for ire.

4‘ And he lookit east, and he lookit west,

And he lookit aboon, beneath ;

But nocht could he see save the haul’ grey rocks
That glower’d out through the heath.

“ He lifted aloft a ponderous rock,

And hurl’d it through the air ;

4 ’Twere pity ye sud want reward
For sae devout a prayer ! ’

“ The miller o’ Kemnay cries to his knave,

‘ Lift up the back sluice, loon !

For a cloud comes o’er frae Bennachie
Eneuch the mill to droon.’

“ The boatman hurries his boat ashore.

And fears he’ll be o’er late ;

Gif yon black cloud come doon in rain,

It ’s fit to raise a spate.

44 But the ponderous rock came on and on,

W ell aimed for Kemnay Kirk ;

And cross’d it field, or cross’d it flood.

Its shadow gar’d a’ grow mirk.

44 But the fervent prayers o’ the haly priest,

And the power o’ the Sanct Anne,

They turn’d the murderous rock aside.

And foil’d the foul Fiend’s plan.

* From 44 Flights of Fancy and Lays of Bon Accord.” By William Cadenhead
Aberdeen. Edinburgh : Oliver and Boyd, 1853.

713

of Edinburgh, Session 1871-72.

“ And it lichted doon frae the darken’d lift,

Like the greedy Erne bird, —

And there it stands i’ the atild kirk-lands,

Half-buried in the yird.”

These legends, in explanation of the transport of Scotch boulders,
are of the same nature as the legend which professes to explain how
the Blue Stones of Stonehenge came to Salisbury Plain in England.
Jeffrey of Monmouth, who was the first author to write a descrip-
tion of Stonehenge, says that certain of the stones were brought
by Merlin and a band of giants from Ireland. Mr Fergusson,
in his book on Ancient Stone Monuments, recently published,
says that some geological friends of his have told him, that
these blue stones of Stonehenge are a species of trap, which is not
known in England, but is well known in Ireland; and therefore
Mr Fergusson supposes that they probably were brought from Ire-
land in ships. It seems quite as likely that these blue stones were
boulders, and were brought from Ireland by natural agency, and
deposited on Salisbury Plain in that way. There are strong proofs
to show that there was an agency of some kind which swept over
Ireland from the westward, and brought boulders across what is
now the Irish Channel to the south-west districts of England.

In these legends we see the efforts of the people in those early
times to account, in the best way they could, for the transport of
boulders into their districts. It is evident that they had investi-
gated the subject, and had made considerable approaches to the
truth. Finding that many of these great blocks differed in com-
position from all the rocks of the district where the blocks lay,
and inferring that their rounded shapes were probably due to
friction, they inferred that they must have come into the district
from some distant quarter ; and this inference was confirmed by
discovering that in certain other districts there was rock of the
same description as the blocks. But how blocks exceeding 100 tons
weight could have been brought many miles, and over a tract of
country uneven and broken in its surface, their knowledge of
nature’s laws did not enable them to explain. The only agency
which they could think of was superhuman and supernatural; and
hence the invention of such legends as assumed the agency of
Merlin, giants, Michael Scott, witches, and the devil.

714 Proceedings of the Royal Society

2. The second class of names by which particular boulders are
known, have reference to the uses to which these stones were
put.

In remote periods in the history of Scotland, when there were no
maps, roads, or even names of parishes, it was important to have
some other means of indicating spots or districts where people
required to congregate for special purposes.

One of the boulders reported to the Committee (in the Island of
Harris), still goes by the name of “ Clachan Treudachf or the Oa-
th ering Stone.

What were the special purposes for which our early forefathers
gathered together is of course not easily discovered. But the
ancient names of the boulders seem to throw light on the sub-
ject. (1.) Such names as “ Clach- sleuchdaidhf or Stones of Wor-
ship (in the parish of Kirkmichael) ; “ Clach an t-Tobairt or Stone
of Sacrifice ; “ Clach na Greinef Stone of the Sun ; “ Clach na
JiAnnaitP Stone of Victory, (a Scandinavian deity); and “ Clach
mhor a Chef G-reat Stone of Che, (another deity), seem very plainly
to indicate that these boulders were used as trysting-places for
worship ; and they were all the more suitable if they were looked
upon with superstitious awe, on account of their supposed connec-
tion with spiritual agency. On two of the boulders reported to
the Committee, there are artificial circular markings, other examples
of which are very numerous throughout Scotland ; and though
archaeologists are not yet agreed as to the meaning of these marks,
one theory is, that they were symbols of a religious character. It
is well known that these great stones were in some way or other,
hindrances to the reception and diffusion of Christianity in most
of the countries of Western Europe ; for between the years 500 and
800 there are numbers of decrees and edicts requiring these stones
to be destroyed, as being objects of superstition. There are some
arch geologists who go so far as to maintain that the word “ Kirk ”
is actually synonymous with the word “ Circle,” meaning the circle
of stones where Celtic worship was performed.

(2.) Another use to which these boulders were applied was
Sepulture. There is in Berwickshire, a boulder known by the name
of the “ Pech or Piet’s Stone,” round which human bones in very
large quantities were found a few years ago ; and similar discoveries

of Edinburgh, Session 1871-72. 715

have been made at boulders in many other districts, especially
where they formed circles.

If these great boulders were used as places of worship, it was
natural that they should also be used for sepulture, on account ot
the supposed sanctity of the place. Indeed, the fact of a place
having been used for sepulture, creates of itself a presumption that
it was used also for worship.

(3.) Another important purpose for which the boulders were
used, was for the trial of offenders and the issuing of judicial sen-
tences. Thus, in Little Dnnkeld parish, there is a large boulder
called “ Glacli a mhoidf * or Stone of the place of Justice, where
the baron of the district could try offenders , with right to hang or
drown those convicted. In Ayrshire there is another large boulder
called the Stone of Judgment , for the barony of Killochan. Several
large rocking stones have been reported. In ancient times, when
very rude tests of guilt or innocence were employed, the rocking
stone was used in the trial of persons accused of crimes.

“ It moves obsequious to the gentlest touch,

Of him whose breast is pure. But to the traitor,

Though even a giant’s prowess nerved him,

It stands as fixed as Snowdon.”

(4.) There are boulders which are known to have been used as
trysting places for military gatherings; a large boulder on Cul-
loden Moor is one example. It was on a whinstone boulder called
The Bore Stone , that Eobert Bruce planted his standard before the
Battle of Bannockburn. A sandstone boulder on the Borough
Muir, near Edinburgh, was the gathering point for the army col-
lected by James IV. before the Battle of Flodden. Both of these
stones are in existence. The Bannockburn stone is protected by
an iron grating. The other stone is also preserved, being fixed on
a wall near Morningside parish church, having on it a brass plate ,
bearing an inscription, given by the late Sir John Forbes.

(5.) Some boulders are said to have been used as trysting places
for the contracting of engagements , such as matrimonial contracts,
and others less important. There is a boulder in the parish of
Coldstream (Berwickshire), called the Grey Stone from its colour
at which within the last hundred years marriages took place. The
* New Stat. Acc. vol. x. p. 1007.

716 Proceedings of the Boyal Society

bride and bridegroom stood on tiptoe on each side of the stone and
joined hands over the top, whilst the friends of each party sur-
rounded the stone to witness the engagement. The Stone of Odin,
in the Orkneys, at which marriages were celebrated, was held in
peculiar veneration; for in one case where a man was pro-
secuted for deserting his wife, it was stated to be an aggravation
of his offence, that they had been married at the Stone of Odin.

3. A third class of names given to boulders had relation to them
as commemorative of important events.

Thus there is in Badenocli the “ Clach an Charra,” or Stone of
Vengeance, so called because a profligate and tyrannical feudal
baron was killed by his own people near it.*

There is in Lewis the “ Clach D'hoisf or Stone of D’hois, a
boulder of gneiss, weighing about 120 tons. It is called after a
person named D’hois, who slew a giant near the boulder, and who
also himself died immediately after, from the wounds received in
the conflict.!

4. Some boulders were used to mark the boundaries of estates,
parishes, and counties, and are still in many parts of Scotland
recognised as affording evidence on that subject.

In Ross-shire, the boundary between the districts of Urray and
Contin is marked by the boulder called u Clachloundroniy

A great boulder is said to indicate the spot where the three
counties of Dumfries, Ayr, and Lanark meet.

The line of boundary between England and Scotland was in the
eastern borders originally indicated by boulders, several of which
still remain.

5. Some of the boulders have curious popular predictions con-
nected with them.

Thus, near Invergowrie, on the north side of the Frith of Tay,
there were in the days of Thomas the Rhymer two boulders
entirely surrounded by the water, of which the seer sang —

“ When Gows of Gowrie come to land
The day of judgment’s near at hand.”

These two boulders, called the Grows (probably because always
frequented by sea-gulls), are now no longer surrounded by water.

* Proceedings Soc. of Scotch Antiquaries, voi. vi. 328.

t This Boulder and its legend reported to the committee by Captain Thomas,
R.N.

of Edinburgh, Session 1871-72. 717

But it is not they which have come to land, the land has come to
them.

In the parish of Crieff a boulder of whinstone is reported, with
a vein of white quartz through and partially round it, in con-
sequence of which the stone has from time immemorial been
known as the Belted Stane. The prediction about it is, that the
white belt will gradually increase in length till it envelopes the
stone ; and that whenever the two ends meet, a great battle will be
fought, on which occasion a king will be seen mounting his horse
at the stone, — ■

‘ ‘ 'Twixt the Gartmore Gap and the Belted Stane
The nobles blnid shall run like a stream.”

Geologists, however, are of opinion that there is not much chance
of the quartz vein extending.

Perhaps some persons may think that the time of the Royal
Society should not be taken up by any allusion to these absurd
popular legends. There are, however, good reasons for referring
to them. In the first place, they are evidence of the extraordinary
ignorance and superstition which prevailed in former times in our
own land, and even at no very distant date. In the second place,
the archseological and even historical associations with which many
of the boulders are invested, may induce many proprietors to take
an interest in them and save them from destruction, if the com-
mittee think them worthy of preservation.

There is even yet among our fellow-countrymen a considerable
amount of interest felt in these boulders, and particularly such as
have traditionary names and legends ; and it is to this feeling that
several are indebted for their preservation. Professor Geikie at
the last meeting of the British Association told this anecdote of
the Ayrshire boulder, known as the Killochan Stone of Judgment.
An enterprizing tenant, a stranger to the district, finding this
stone much in his way, was preparing to blow it up with gun-
powder. His intention becoming known, some of the old residenters
went to the laird’s factor and asked whether he knew what was
intended. On his stating that he did not, he was entreated to pre-
vent the stone from being destroyed. The proprietor was com-
municated with, and the new tenant was interdicted from meddling

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718 Proceedings of the Royal Society

with the stone. Shortly afterwards this inscription was put on
the stone, — “ The Baron's Stone of Killochan.” *

It is a boulder of blue whin stone, on which stands the market
cross of Inverness. For some reason or other, it is preserved as
the Palladium of the town, ever since the battle of Harlaw in the
year 1411. It is called “ Clack na cudden f or “ Stone of the tubs,”
from the circumstance that the people carrying water from the
river used long ago to rest their tubs on it. It was till lately in
the middle of the street ; but Having ceased to be of use, when
water was brought into the town by pipes, it was removed to the
side of the street opposite to the town hall, with the old cross of
the town and the Scottish arms resting on it. “ Clack na cudden
hoys,” is a nom de guerre for Invernessians ; and “ All our friends
round clack na cudden f is a toast given in many a distant land.

In the parish of Rattray, there is a remarkable boulder of mica-
ceous schist, weighing about 25 tons, of which some account was
given a short time ago in this Society. It bears a number of
artificial markings of a very ancient date. The tenant of the farm
on which it is situated proposed to blow it up. Some of the in-
habitants having heard of this, went to the minister of the parish,
and begged him to take steps to save the old stone of Grlenballoch.
The proprietor being on the Continent, the rev. gentleman ap-
plied to the factor, and through his good offices saved the stone.
This gentleman being still under anxiety about it, lately requested
this committee to communicate with the proprietor, Colonel Clark
Rattray, with the view of obtaining from him a promise that the
stone should be preserved. Colonel Clark Rattray was accordingly
written to by the convener of the committee, and he at once ac-
ceeded to the request.

There is on the shore at Prestonpans, on the south side of the
Firth of Forth, a large basaltic boulder, which has long been
known under the name of “ Johnny Moat.” The Convener wish-
ing to see this boulder, he went out from Edinburgh a few weeks
ago by rail to Tranent Station, and walked towards the shore in
search of it. Between the railway station and Prestonpans he met
a boy, whom he stopped, and telling him that he had come to see

* An account of this boulder was published in Macmillan’s Magazine for
March 1868, by Professor Geikie.

719

of Edinburgh^ Session 1871-72.

the boulder called “ Johnny Moat,” he asked the way. The boy
pointed it out at once. Three or four other persons in succession,
two of them women, had to be asked the same question before the
spot was reached. Every one knew “ Johnny Moat .” The last
person accosted was a fisherman, and he volunteered to be guide.
He seemed somewhat suspicious of the stranger’s intentions; for
after reaching the stone, he remained beside him till he saw it
was only to measure its dimensions and make a sketch of it, that
he had come. From what was observed during this visit, it was
evident that every inhabitant of Prestonpans, not only knew of the
boulder, but took a personal interest in it, and would sternly resist
any attempt to destroy it.

It is satisfactory to find this popular feeling still prevailing to
some extent. But the feeling is not of itself sufficient to prevent
the wholesale destruction which is going on in many parts of Scot-
land. Thus, the minister of Bendochy reports to the committee,
that “ on the rising ground behind his manse, there was a circle of
large stones, boulders, standing on their ends (Druidical) ; but
some years ago they were removed. The place is yet called ‘ The
Nine Stanes

There was formerly a rocking stone in Aberdeenshire, estimated
at about 50 tons weight ; but it has now been converted into field
dykes.

Numberless cases of the same kind can be specified.

It is therefore most necessary to take steps to preserve what re-
main of these megalithic relics ; and it is especially gratifying to
the committee to be able to state, that the movement towards
this object, made by this Society, has met with general approval.

The British Association, at its last meeting, so highly approved
of the scheme, that it appointed a committee of some of its most
influential geologists to carry out a similar scheme for England
and Ireland.

In the last number of the “ Geological Magazine,” there is a lauda-
tory notice of the object and operations of the committee; and the
readiness with which all parties applied to in Scotland have re-
sponded to the circulars of the Committee, proves how much they
also approve, to say nothing of express commendations contained
in individual reports. Even in Switzerland notice has been taken

720 Proceedings of the Royal Society

of our Scottish movement, and in very complimentary terms; for
a few weeks ago, a pamphlet by Professor Favre of Geneva was
received by the convener, alluding to our Society’s movement in
this matter, and anticipating important results from it.

List of Boulders reported to Royal Society , arranged by Counties
and Parishes.

Aberdeen.

Aberdeen (Town).— In excavating for foundation of house in Union
Street, boulder of black sienite, 6x5x4 feet found. No
rock like it in situ nearer than Huntly or Ballater, about 30
miles to NAY. or W. Under surface of boulder, striated.
The direction of striae coincides with the longer axis of
boulder, viz., about east and west. Preserved, and set up in
Court of Marischall College. (Reporter — Professor Nicol.)
Ballater. — On top of Morven, 3000 feet above sea, several granite
boulders, unlike rock of hill, and apparently from mountains
to west. (Jamieson, “ Geol. Soc. Jour.,” xxi. p. 165.)
Belhelvie. — Gneiss boulder, about 8 feet diameter, called the “ Caple
Stone,” near parochial school. Rocks in situ ; near it are
granite. (Reporter — Alex. Cruickshanks, Aberdeen.)

Sienite boulder, in a wall, King Street Road , about 3-J x 2
feet. The face covered with striae parallel to longer axis.
Cairney Granite Quarry , 3 miles N.W. of Aberdeen, and about 400
feet above sea. When boulder clay removed, surface of rock
found to be smoothed and grooved in a direction E.N.E. and
W.S.W. (true.) (Reporter — Alex. Cruickshanks, Aberdeen.)
Bourtie. — 1. Four Greenstone boulders, supposed to be Druidical ;
what is called “The Altar Stone,” 16x6x5 feet, weighs
about 18 tons. 2. Boulder, about 20 tons. Longer axis E.
and W. Called “Bell Stane,” the church bell having once
hung from a post erected in it. 3. Whinstone boulder, about
20 tons, on Barra Hill, called “Wallace’s Putting Stane,”
24 feet in circumference. Legend, that thrown from Ben-
nachie Hill, distant about nine miles to west. 4. Whinstone
boulder, called “Piper’s Stone.” Origin of name given.
5. Whinstone boulder, called “ Maiden Stane.” Tradition

of Edinburgh, Session 1871-72. 721

accounting for name. 6. Several' Druidical circles described.
(Reporters — Rev. Dr Bisset, and Mr Jamieson of Ellon.)
Braemar. — At bead of Grlen Sluggan, several large erratics. These
stand exactly on watershed or summit level. Near shooting-
lodge there, a cluster of four or five immense angular granite
boulders. They touch one another, and may be fragments of
one enormous mass. The adjacent rock is quartz. These
blocks situated at end of a long low ridge or mound, which
extends from south extremity of Ben Avon Hills, and which
strewn thickly over with great granite blocks. The mound
composed of a mixed debris of earth and stones, and is appar-
ently a moraine. The adjoining mountain of “ Cairn a
Drochid ” is composed of quartz and granite. On top of it
are large granite boulders, many of which situated on quartz
rock. (Reporter — Mr Jamieson, Ellon, in letter to convener.)
Chapel Garioch. — Boulder, 19 x 15 J x 11 1 feet, weighing about 250
tons above ground. Height above sea 280 feet. Rests on
drift. Longer axis E. and W. Legend, that thrown from
Bennachie Hill to north-west. The rock of boulder differs
from rocks adjoining. Kaims abound in parish. (Reporter —
Rev. G-. W. Sprott.)

Cruden. — In Boddom Dean, a granite boulder called “ The Hang-
ing Stone,” measuring 37 feet in circumference and 27 feet
over it, resting on several small blocks of granite. Supposed
to be Druidical. Half a mile east there is another of 20 tons.
(Buchan’s Peterhead, published in 1819, and James Mitchell,
Boddam.) Huge granite boulder, called 11 The Grray Stone
of Ardendraught,” broken up in 1777 to build walls of Parish
Church. It was the stone on which “ Hallow” fires* used to
be lighted. (Jamieson, “ G-eol. Soc. Jour.,” xiv. p. 525.)

* “ Hallow ” fires were lighted on 31st October, and were called “ Saimli-
theine.” The “ Beil-theine ” fires were lighted on 1st May. These prac-
tices, formerly general in the Highlands of Scotland, were probably connected
with the worship of the sun, whose departure in autumn, and return in spring,
were signified by these rites. The Rev. Mr Pratt published an account of
Buchan in the year 1858, and states (page 21), “ Hallow fires are still kindled
on the eve of Ali Saints, by the inhabitants of Buchan — from sixty to eighty
fires being frequently seen from one point.” ( Old Stat. Acct. of Scotland,
vol. xi. p. 621, and vol. xii. p. 458.)

722

Proceedings of the Royal Society

At Menie Coast G-uard Station, granite boulder, 54 feet in
circumference and 7 feet above ground ; also a greenstone
boulder, 78 feet in circumference and 6 feet above ground.
(Jamieson, “ Geol. Soc. Jour.,” xiv. p. 513.)

Near the “ Bullers of Buchan,” there stands “ The Hare or
Cleft Stone,” which marks the boundary between the parishes
of Cruden and Peterhead. G-ranite 9x8 feet, 160 feet above
sea. (Pratt’s “Buchan,” 1858, page 47, and James Mitchell,
Boddam.)

In this parish, and to north, numerous mounds and ridges
of gravel, called at one place “Hills of Fife,” at another,
“ Kippet Hills.” The generic name of these mounds and
ridges in this part of Scotland, is Celtic word “Druim” or
“ Drum.” They are composed sometimes of sand, more fre-
quently of gravel. The gravel consists of fragments of rock,
generally from westward. They are always well rounded, by
the friction they have undergone. They sometimes reach a
size of 2 feet in diameter. The pebbles are chiefly gneiss.

On top of some of the knolls and ridges there are large
boulders. There is one, near Menie, being a coarse crys-
talline rock, with a greenish tint, 8x5 feet. Another
boulder of greenstone lies near it. Very frequently a stratum
of red clay lies over the gravel ridges, encircling the base of
boulders, indicating that after the gravelly ridges had been
formed, and the boulders deposited, muddy sediment had been
deposited in deep water. (Jamieson, “ Gfeol. Soc. Journ.”)

The following additional information sent by Mr James
Mitchell, Boddam : —

No. 1 boulder, in a ravine at Bullers of Buchan, granite,
14 x 8 x 5 feet. About 15 feet above sea.

No. 2 boulder, on confines of Cruden and Peterhead.
Granite, 18 x 12 x 5^ feet (above ground), 290 feet above sea.

No. 3, half a mile to E. of No. 2, a granite boulder, 13 x 9
x 5 feet, at a height of 260 feet above sea.

Along the south side of Peterhead Bay, and as far as Buchan
Ness, the shore is strewed with blocks of granite, gneiss, trap,
and sandstone ; many of them belonging to rocks not found
nearer than 20 or 30 miles.

723

of Edinburgh, Session 1871-72.

A belt of gravel and calcareous sand forms a semicircular
arc, with a radius of about 3 miles from the coast, passing
through Crudens and Slains. The most conspicuous hillock
in the line is a narrow Kaim in Slains parish, called the Kipet
Hill , — the abode of fairies and elf bulls.

Compact groups of boulders form lines generally in a N.E.
and S.W. direction. But a large number have been sown
broadcast.

Culsalmond (G-arioch). — Boulder of blue gneiss, 6i x 2i feet, known
as the Newton Stone, containing Ogham and other very antique
inscriptions. (Professor Nicol in letter to Convener.)

Ellon. — At junction of Ythan and Ebrie, sienitic greenstone boulder,
22 x 9^- x 8J> feet, resting on gneiss. Near same place, another
still larger. All these boulders have come from W. or W.N.W.
(Jamieson, in letter to Convener.)

Glass (5 or 6 miles west of Huntly). — Five blocks called “ Glachan
Duibh ” (Black Stones), on Tod Hill. G-irth of each about 50
feet, and height from 10 to 12 feet. Being of same rock as
hill, not certain whether brought from a distance. Other
boulders on hill apparently different from adjoining rocks.
Height above sea about 1000 feet. (Reporter — J. F. Macdonald,
parochial schoolmaster.)

Kemnay. — Boulder, 38 x 30 x 10J feet, about 300 feet above sea ;
longer axis, E. and W. Boulder, 35 x 30 x 10 feet, about 325
feet above sea; longer axis N. and S. Boulder, 25 x 23 x 8 feet,
about 325 feet above sea ; longer axis, E. and W. Boulder,
28 x 25 x 8 feet, about 325 feet above sea; longer axis N. and S.
Boulder, 30 x 28 x 10 feet, about 360 feet above sea; longer
axis, N. and S. Boulder, 33 x 27 x 6 feet, about 360 feet above
sea; longer axis, N. and S. Boulder, 21 x 20 x 3 feet. All
these boulders are blue gneiss, whilst rocks adjoining are a
coarse grey granite. On Quarry Hill, situated to north, 600
feet above sea, the rocks show striations indicating movement
from west. Kaimes in valley parallel with valley running
N.E. and S.W. for two or three miles. Legend, about devil
throwing boulders at church from Bennachie Hill, situated to
N.W. about eight miles. See ballad in Report. (Reporter —
Rev. Gleorge Peter, M.A., parish minister.)

724

Proceedings of the Roycd Society

Logie Coldstone.- — This "parish thirty miles N.W. of Aberdeen.
Surrounded at N.W. by amphitheatre of hills, of which
Morven 2850 feet high. It contains numerous mounds of
gravel and sand, in layers, showing action of water. They
have the form of “kaims.” Though there are no boulders,
there are pebbles up to a cwt. or more, imbedded in water-
worn gravel and fine sand. The pebbles are of same rock as
adjoining hills — gneiss, granite, and hornblende. Two sin-
gularly shaped mounds, one 60 feet high, the other com-
posed entirely of sand. They resemble the terminal moraines
seen in the G-rindelwald and other parts of Switzerland.
Some years ago a number of boulders (from 3 to 6 tons in
weight) were destroyed at a place situated to the north of
this. They were of a soft, bluish granite, differing from any
granite rock within a distance of nine or ten miles. One of
these boulders might weigh 20 tons. This place had all the
appearance of an ancient lake. The boulders may have been
brought to it by same agency as that now seen on the Marjelin
See, near Aletsch Glacier. (Reporter — J. G. Michie, school-
house, Coldstone, Tarland.)

New Deer. — A great number of boulders, from 1 cwt. to several
tons, lie in a sort of line for more than a mile S.E. from farm
of Green of Savoch, as far, at least, as the hill of Coldwells
and Toddlehills, in parish of Ellon. Elsewhere they are
mostly on surface. Locally called “ Blue Heathens.” On
Whitestone Hill, Ellon, and on Eudwick Hill, chalk flints
are exceedingly abundant. (Reporter — James Moir, Savoch,
by Ellon.)

In this parish formerly there was a rocking-stone, called
“ The Muckle Stone of Auchmaliddie.” On the Hill of Culsh,
formerly a Eruidical circle. About seventy years ago the
stones were carried away to aid in building a manse. Farm
where situated still called, “ The Standing Stones of Culsh.”
(Rev. J. Pratt’s Account of Buchan, 1858.)

Towie. — Stone of unhewn granite, standing about 7 feet above
ground, on north side of river Eon, near bridge. Sup-
posed to be Eruidical (“ New Statistical Account ” of
parish).

of Edinburgh, Session 1871-72.

725

Argyll.

Appin. — Granite boulder 20x18x11 feet, about 290 tons.
Differs from adjoining rocks. Longer axis N.E. Striated.
Apparently has come from head of valley, which to N. or
N.E. There is also a line of boulders ; — rocks striated in direc-
tion of glen. (Beporters — James M'Dougall and Sir James
Alexander, who sends a sketch.)

Ardentinny. — 1. Boulder, called “Pulag”* (Big Bound Stone),
about 30 tons. In critical position on edge of cliff. 2.
Boulder, called (t G-iant’s Putting Stone,” pear-shaped, and
rests on small end. 3. Boulder, called “ Clachan Udalain”
(nicely-balanced stone), larger. (Beporter — Bev. Bobert

Craig.)

Buncansburgh (near Kilmallie). — G-ranite boulder, 7 x 5J x 5 feet,
called “ Trysting Stone.” Tradition. There are larger
boulders nearer Ben Nevis. (Beporter — Patrick Gordon, min.,
Q. S. Duncansburgh, Fort-William.)

Dunoon (Kirn). — Trap boulder, 21 x 14 x 7 feet, about 164 tons.
The adjoining rocks are mica schist and clay slate; striated.
Photograph sent. (Beporter — Bev. James Hay, minister of
Kirn.)

Glencoe. — Trap boulder, about 90 feet in girth and about 10 feet
high. It is nearly round, and lies on an extensive flat, so
that very conspicuous from a distance. (Beporter — Captain
White, B.E.)

Inishail (North of Inverary). — Granite boulder about 8 feet above
ground, called “ Bob Boy’s Putting Stone,” about 1 mile from
Taynuilt Inn on Oban road, about 60 feet above sea. A moun-
tain of same rock about 1 mile distant. Longer axis, E. and
W. Due west from above about 1^ miles, another boulder
on a ridge on side of Loch Etive, in Muckairn parish.
Several large boulders on road between Dalmally and Tyndrum ;
also on road between Tyndrum and Black Mount, about 4
or 5 miles from Tyndrum. A fine boulder on Corryghoil
farm (Mr Campbell) between Inishail and Dalmally. (Be-

* Another translator states that “ Pulag ” in Gaelic means a “ dome.”

VOL. VII.

5 D

726

Proceedings of the Royal Society

porter — Eev. Eobert M. Macfarlane, minister of Glenorcky
and Inishail).

Inverchaolain. — Gneiss boulder, 10^ x 7x5| feet, about 30 tons.
Called “ Craig nan Cailleacb ” (Old Wife’s Eoek). Differs
from rocks of district. At head of Loch Striven, many
boulders, same as rocks. (Eeporter— John E. Thompson,
schoolmaster, Inellan.)

Iona (Island). — Granite boulder, 24 x 18 x 6 feet, 190 tons. Longer
axis N.W. There are a great many others, chiefly on E.S.E.
side of island, opposite to Eoss of Mull, from which boulder
supposed to have come. On other hand, Duke of Argyll is
said to consider that the granite of the boulder is not the
same variety as that of Eoss. There are several boulders
oddly placed near top of highest hill on N.W. side. (Eeporter
— Allan M‘Donald, parish schoolmaster.)

Kilbrandon (Easdale by Oban). — On Lord Breadalbane’s estate,
grey granite boulders from 21 to 28 feet in girth, and standing
from 3 to 4 feet above ground. Longer axis generally N.W.
Euts or grooves on tops and sides of some, bearing N.W.
These boulders sometimes single, sometimes in groups, some-
times piled on one another. Occur at all levels from shore
up to hill tops. No granite in situ nearer than Mull, which
is 15 or 20 miles distant to N.W. (magn.) (Eeporter —
Alexander M‘Millan, schoolmaster, Kilbrandon.)

Kilmallie. — Boulder, 12 x 10 x 10 feet, about 100 tons. There is
another, said to be larger, in the distant moors ; also quartz
boulder, about 9 feet square, supposed to have come from Glen-
finnan, about 15 miles to N.W. by W. (Beporters — Eev. Arch.
Clerk, and C. Livingston, schoolmaster.)

Kilmore and Kilbride (near Oban). — Granite boulder, 12 feet long;
diameter of shortest axis, 5 feet ; longer axis, E. and W. A
few feet above sea mark. Adjacent rocks conglomerate.
Another stone, about 200 yards distant, called “ Dog Stone,”
of which photograph sent. It is a conglomerate. (Eeporter
— C. M‘Dougall, Dunollie, Oban).

Lismore (Island of). — Boulders of granite, red and grey, lie on the
limestone rocks of the island. An old sea terrace described, as
encircling the island, on one part of which a cave, from the

727

of Edinburgh, Session 1871-72.

crevices of which shells picked by Reporter (Alexander Car-
michael, Esq., of South Uist, Lochmaddy, who refers also to
the Rev. Mr Macgrigor, minister of Lismore).

Saddell (Kintyre). — Several small granite boulders, though there
are no granite rocks in Kintyre. A good many whinstone
standing stones. (Reporter — Rev. John G. Levach, Manse of
Saddell.)

South of Campbelton, many granite boulders, like Arran
granite, one near Macliarioch, 4x5x2 feet. (Reporter — Pro-
fessor Nicol, Aberdeen.)

At Southend, a boulder of coarse grey granite, about 18 feet
in circumference, and weighing more than 3 tons, now broken
up.

Another granite boulder, about 12 feet in circumference.

Two boulders of sienite, each 2 or 3 tons, about 200 feet
above sea.

No granite rocks in neighbourhood. Rocks chiefly lime-
stone and red sandstone. (Reporter — D. Montgommerie,

Southend parish school.)

Ayr.

Coylton . — Granite boulder, 11 x 1\ x 5 feet, about 30 tons.
Longer axis N. and S. There are four more boulders, about
4, 8, and 12 tons. They form a line running N. and S.
Legend, that King Coil dined on large boulder. (Reporter —
Rev. James Glasgow.)

Dailly. — Granite boulder about 36 tons on Killochan Estate, called
“ The Baron’s Stone.” About 100 feet above sea. Lies
on Silurian rocks. Apparently derived from granite hills
situated S.S.E., near Loch Doon, about 13 miles distant.
Boulder proposed to be blown up by tenant of farm. But old
inhabitants interposed, and an inscription put on it by pro-
prietor, Sir John Cathcart, in these terms, “ The Baron’s
Stone of Killochan.” Granite boulders of various sizes, on
hill slopes, south of river Girvan. One on Maxwelton farm
800 feet above sea, contains 240 cubic feet. Another, 16 feet
long, on top of Barony Hill above Lannielane, mostly buried
under turf. Level mark on it by Ord. surveyors of 1047 feet
above sea.

728

Proceedings of the Royal Society

Doone Loch. — Two miles south of, — a granite boulder, about
25 x 20 x 12 feet, called “ Kirk Stane.” (Seen by Convener.)

Girvan. — Thousands of granite boulders for miles along shore near
Turnberry Point, and some whinstones. Rocks in situ sand-
stone. (Reporter — Superintendent of Turnberry Lighthouse
works.)

Along coast 4 miles south, in a ravine, two boulders of
altered G-reywacke. Largest, 17 x 13 feet, and weighs 180
tons. Other weighs about 100 tons. Have probably come
from hills to S. or S.E.

Maybole. — Granite boulder, flat and oblong, on slope of hill above
river Doon, on Aucbindrane, at height of 230 feet, known as
Wallace’s Stone, from tradition, that a rude cross carved on it
represents the sword of that hero. (These cases from Dailly,
Girvan, and Maybole, communicated by Professor Geikie).

Banffshire.

Banff. — In district between Banff and Peterhead, beds of glacial
clay, of a dark blue colour, very similar to beds in Caithness,
and probably drifted from Caithness. Near Peterhead, many
boulders of granite and trap. One of these, 4jx 2-jr x 1 feet,
a fine grained tough trap, of a greenish colour, not known
in situ in Aberdeenshire, but occurs in Caithness. (Jamieson,
“ Geol. Soc. Jour.,” xxii. p. 272.)

Royn^'e.“Hypersthene boulders along shore, and found for some
miles running S.W. Supposed to have come from rock to
S.E., called “ Boyndie Heathens.” (Reporter — James Hunter,
Academy, Banff.)

Fordyce. — A line of boulders can be traced running through
parishes of Ordiquhill, Marnock, Grange, Rothiemay, and
Cairney, in a direction S. and N. The boulders are a
blue whinstone. In Ordiquhill parish, boulders, so close as
to almost touch. They are called “ Heathens.” 500 feet
above sea. (Reporter — Parish minister.)

Caithness.

Punnet. — Conglomerate boulder of small size, apparently from
“Maiden Pap” Hill, thirty miles to south. Several large

of Edinburgh, Session 1871-72. 729

boulders in parishes of Olrich and Cannesby. (Reporter —
Robt. Campbell, parish schoolmaster.)

Thurso. — Near Castletown, large granite boulder, which supposed
to have come from Sutherland.* Between Weydale and Stone-
gun, several large conglomerate boulders.

Wick. — Three large boulders, differing from adjoining rocks,
weighing from 20 to 60 tons. One is a conglomerate,
apparently from mountains twenty miles to south. f (Reporters
— John Cleghorn and J. Anderson.)

G-ranite boulder, 12 feet long, in drift, striated. Frag-
ments of lias, oolite, and chalk flints, in same drift. Striations
of rocks and boulders in Caithness indicate a general move-
ment from N.W., i.e., from sea.

Dumfries.

Kirkconnell. — Granite boulder, about 9 feet diameter, 20 to 30
tons; 700 feet above sea, called “ Deil’s Stone.” Differs
from adjoining rocks. Granite rocks in Spango Water,
about three miles to north. (Reporter — R. L. Jack (Geolog.
Survey).)

Tynron. — Three whinstone boulders, each weighing from 20 to 30
tons ; also several conglomerate boulders. All have appa-
rently come from N.W. (Reporter — James Shaw, school-
master, Tynron, Thornhill.)

Wamphray. — Large whinstone boulder. King Charles II. halted
with his army and breakfasted here. (Reporter — Parish
minister.)

Edinburgh.

Arthur Seat. — On west side of, boulders of limestone, supposed to
have come from west. Rocks at height of 400 feet above sea,
smoothed and striated in direction N.W.

Between Arthur Seat and Musselburgh, boulders smoothed
and striated. Strise run from N.W. and W.N.W. (Roy. Soc.
of Ed. Proceedings, vol. ii. p. 96.)

* Rev. Mr Joass, of Golspie, states that granite occurs at a less remote

locality.

t Rev. Mr Joass states that conglomerate rock occurs to the westward at a

less distance.

730

Proceedings of the Royal Society

Pentland Hills. — 1. Mica-slate boulder of 8 or 10 tons. Supposed
by Mr Maclaren to liave come from Grampians, 50 miles to N.,
or from Cantyre, 80 miles to W., about 1400 feet above sea.
2. Greenstone boulder, 12 or 14 tons. Nearest greenstone
rock in situ , 500 or 600 feet lower in level to N.W. 3. Sand-
stone boulder, about 8 tons, differing from adjacent rocks.
(The above mentioned in Maclaren’s “ Fife and Lothians,” p.
300.) 4. Greenstone boulder, about 10 tons, near Dreghorn.

(Fleming’s “ Lithology of Edinburgh,” p. 82.)

West Colder. — Whinstone boulder, 8x7x7 feet, about 28 tons.
Adjoining rocks are sandstone. (Reporter — S. B. Landells,
teacher.)

Elgin.

Dallas. — Numbers of small granite boulders found here, which
supposed to have come from Ross-shire.

Duffus. — On Roseile Estate, conglomerate boulder called, “ Hare, or
Witch’s Stone,” 21 x 14 x 4 feet, longer axis N.W. Farm
named “ Keam,” from being situated on a sandy ridge.

Elgin. — 1. Conglomerate boulder on Bogton farm, 4 miles south of
Elgin, 15 x 10 x 8 feet, about 80 tons. Longer axis is E.N.E.,
called “ Carlin’s Stone.” Also a smaller one, called the
“ Young Carlin,” to N.W. about half a mile. 2. Conglome-
rate boulder, 4x4x3 feet, about 3 tons. 3. Gneiss boulder,
13 x 8 x 6 feet, about 46 tons, called “ Chapel Stone.”
Situated west of Pluscardine Chapel. 4. Sienite boulder,
12 x 8 x 3 feet, about 13 tons. 5. Sienite boulder, 8x6x2
feet, about 7 tons. The rocks in situ are all Old Red Sandstone.
On Carden Hill, rocks smoothed and striated ; — the direction
of striae N.W. (Reporter — John Martin, South Guildry Street,
Elgin.)

Forres. — Conglomerate boulder, 9| x 8 x 8 feet, about 44 tons,
called “ Doupping Stone.” (Reporter — John Martin.)

Llanbryde , St Andrews. — Gneiss boulder, 15 x 9 x 7 feet, about 70
tons, in bed of old Spynie Loch, called “ Grey Stone ; ” longer
axis is N.N.E. and S.S.W. (Reporter — John Martin.)

New Spynie. — Four conglomerate boulders, lying on Old Red
Sandstone rocks. (Reporter — John Martin.)

731

of Edinburgh, Session 1871-72.

Bodies. — Six hornblende boulders, lying on gneiss rocks ; dimen-
sions and positions given. (Beporter — John Martin.)

Fife.

Balmerino. — Mica schist (?) boulder, 12x9x8 feet; destroyed
some time ago. (Beporter — James Powrie, Esq., Beswallie,
Forfar.)

Grail. — Granite boulder, K) x 8 x 6 feet, called Blue Stone o’
Balcomie,” close to sea margin at East Neuk. Also trap
boulder, 12 x 8 x 7i feet. (Beporter — Captain White, B.E.)

Dunfermline. — Whinstone boulder, 17 x 15 x 6 feet, about 114 tons,
called “ Witch Stone.” Legend. (Beporter- — Bobert Bell,
Pitconocbie.)

Leslie. — Kaim of sand and gravel near village, 100 to 300 feet
wide, and 20 feet high, cut through by a brook. (Beporter —
John Sang, C.E., Kirkcaldy.)

Newburgh. — On shore, near Flisk point, boulder of sienitic gneiss,
about 15 tons. Legend is, that a giant who lived in Perth-
shire hills flung it at Flisk church. (Dr Fleming, “ Lithology
of Edinburgh,” p. 83.)

West Lomond. — Hill about 1450 feet above sea, boulder of red
sandstone and porphyry lying on carboniferous limestone.
(John Sang, C.E., Kirkcaldy.)

Forfar.

Airlie. — A remarkable kaim running two miles eastward from
Airlie Castle. (Beporter — Daniel Taylor, schoolmaster.)

Barry. — Granite, sienite, and gneiss boulders and pebbles, on shore,
and also on raised beaches, 11 and 45 feet respectively above
sea level. (Beporter — James Proctor.)

Benliolm. — Huge granite boulder, called “ Stone of Benholm,” now
destroyed. Boulders on sea shore, of granite and gneiss, many
of which are supposed to have come out of the conglomerate
rocks, which occur here in situ. One boulder 18x12x3 feet,
another 12x6x4 feet. “ Stone of Benholm,” stood on apex
of a Trap knoll. The Trap knoll presents a surface of rock,
which has apparently been ground down and smoothed by
some agent passing over it from west ; the exact line of move-

732

Proceedings of the Royal Society

ment seems 10° to 20° south of west (magn.) In this Trap
knoll there are agate pebbles, which have been mostly all
flattened on west side, and been left steep and rough on east
sides. Small hills which range in a direction north and south
are scalloped, as if some powerful agent passing over them
from westward had scooped out the softer parts. Hills rang-
ing east and west, form a ridge with a tolerably level surface.
G-ourdon Hill and Craig Davie show marks of great abrasion.
(Reporter — Rev. Mr Smart Myers, parish minister.)

Garmyllie. — Granite or gneiss boulder, from 7 to 10 tons. Differs
from rocks near it. It lies on a height. Called “ The Cold
Stone of the Crofts.” Supposed to have come from hills thirty
miles to north. (Reporter — Rev. G-eorge Anderson.)

Cortachy. — Whinstone (?) boulder, 13 x 10 x 8 feet, about 78 tons
Longer axis E. and W. Supposed to have come from a trap
dyke situated to N.W. Legend, that thrown from N.W
(Reporter — Rev. G-eo. G-ordon Milne.)

Mr Powrie of Reswallie reports a mica schist boulder as
situated in South Esk river, about 60 or 80 yards below bridge,
and within Earl of Airlie’s park. Parent rock supposed to be
2 or 3 miles to N.W. This boulder probably same as that
mentioned by Rev. Mr Milne.

Farnell. — Boulder x 7^ x 2^ feet, about 12 tons. Supposed to

have come from N.W. about thirty miles. (Reporter — Rev.
A. O. Hood, parish minister.)

Inverarity. — Two grey granite boulders, from 2 to 5 tons each ;
destroyed some time ago. (Reporter — Rev. Patrick Steven-
son.)

Kirkden.— Kaims, 440 paces long, running E. and W. ; slope on
each side from 22 to 30 paces; composed of gravel and sand.
(Reporter — Rev. James Anderson.)

Kirriemuir. — A number of granite boulders in centre of parish,
both grey and red. They lie chiefly between Stronehill and
Craigleahill. Supposed to have come from Aberdeenshire.

Two kaims on Airlie Estate, one 100 yards long and 30 feet
high, N.W. and S.E. on Upper Clintlaw Farm; other on Mid
Scithie Farm, about 200 yards long and 30 feet high. At
south base of Criechhill, a group of kaims, apparently

733

of Edinburgh, Session 1871-72.

caused by confluence of great streams from N.E. and N.W.
glens.

Old Eed Sandstone rocks in S. of parish. Igneous rock
towards N. at Craigieloch.

Slate rocks in Lintrathan and Kingoldrum. (Reporter —
David Lindsay, Lintrathan, by Kirriemuir.)

Liff. — 1. Mica schist boulder, 8x6x4 feet, called “ Paddock
Stone.” Legend. Longer axis, N. and S. One report bears
that it is whinstone, and may have come from Pitroddie
Quarry, fourteen miles west. 2. Two boulders of mica schist,
each 8 or 10 tons, called “ Glows of Gowrie,” noticed by
Thomas the Rhymer. 3. A Druidical circle of nine large
stones — three mica schist, one granite, five whinstone. Central
stone, longer axis N. and S. (Reporters —James Powrie,
Esq., Reswallie,' Forfar ; P. Anthony Anton, St Regulus
Cottage, St Andrews.)

Menmuir . — 1. Granite boulder, 14 x 9 x 4 feet, about 36 tons.
Longer axis N. and W. Striated. Called the “ Witch
Stone.” 2. Granite boulder, 13 x 9 x 4 feet, about 34 tons.
There are many others smaller. (Reporter — Rev. Mark

Anderson, Menmuir, Brechin.)

Montrose. — On Garvock and other hills, strise on rocks point
W. by N.”, i.e., obliquely across the hills, which range W.S.W.
and E.N.E.

On Sunnyside Hill, pieces of red shale found, derived from
rocks in situ many miles to N.W. at a locality 100 feet lowest
level.

Large blocks of gneiss, several tons in weight, occur, which
must have come from Grampians, many miles farther to west.
(James Howden, “Edin. Geol. Soc. Trans.” vol. i. p. 140.) J

Bescobie. — Mica slate boulder, 13x7x7 feet, near top of Pits-
candly Hill, lying on drift. Rocks in situ Old Red Sandstone.
Sir Charles Lyell says it came from Creigh Hill, about seventeen
miles to W.N.W. Longer axis N. by E. 550 feet above sea.
Yalley of Strathmore lies between boulder and parent rock, and
there are several hills also between boulder and parent rock,
higher than boulder. Many smaller boulders of old rocks on
same hill. (Reporter— James Powrie, Esq., Reswallie, Forfar).

VOL. VII. 5 E

734 Proceedings of the Royal Society

St Vigeans. — Gneiss boulder, now destroyed. Supposed to have
come from mountains situated to N.W. If so, it had to cross
valleys and ridges of hills. Kaims in parish full of granite
and gneiss boulders. (Reporter — Rev.William Duke, minister.)

Hebrides.

Barvas. — On Estate of Sir James Mafcheson, a monolith, called
Clack an Trendack, or “ Gathering Stone.” Height above
ground, 18 feet 9 inches, and girth 16 feet. (Eeporter —
Eev. James Strachan.)

Harris. — A large boulder on a tidal island, broken into two frag-
ments, 100 feet apart. (Eeporter — Alex. Carmichael.)

North Uist. — On a small island called Caneum, north of Locli-
maddy Bay, there are two boulders of Laurentian gneiss,
which, though 100 feet apart, are evidently the two fragments
of one block. The rocks in situ are also gneiss ; but there is
no hill or cliff near, from which the block could have fallen or
come. One boulder weighs about 15, the other about 50 tons.
They are both on the sea-beach, with a ridge or isthmus of
rock between them. The boulders have each a side — in the
one concave, and in the other convex — which face one another,
and correspond exactly in shape and size. The edges of these
two sides (viz., the convex and concave) are sharp, whereas
the other sides in both boulders are rounded, suggesting that
the original block had undergone much weathering or other
wearing action before being fractured. The larger boulder
rests fantastically and insecurely on two smaller blocks.
Eeporter thinks the boulder brought by ice, and that it fell
from a height, and was split by the fall.

In Long Island the hills even to the summits are covered
with blocks and boulders. As a rule the edges of these are
sharp, whereas the native rock, whether low down or high up,
is glaciated, grooved, and striated to a very remarkable degree.
The best places to see these marks are where drift, covering
them, has been recently removed. They are obliterated in the
rocks, which have been much weathered. (Eeporter — Alex.
Carmichael, Esq., South Uist, by Lochmaddy.)

The Lewis. — (Q. S. Parish of Bernera. On farm of Ehisgarry, be

735

of Edinburgh, Session 1871-72.

longing to Lord Dunmore.) Gneiss boulder, 8j x 7 x 3 feet.
Longer axis N. and S. 30 feet above sea. Striated N. and S.
Striae from 2 to 4 feet long. Same rock as those in situ.
Called “ Craig nan Ramh.” (Reporter — Rev. Hugh Macdonald,
Manse, Bernera.)

The Lewis (Stornoway, Tolsta). — A rocking stone of gneiss
12 x 5 x 4^ feet. Longer axis N.W. and S.E. About 200 feet
above sea. Rocks in situ also gneiss. There are boulders
of trap, apparently brought from eastward, where there are
trap dykes. At a corner of a rocky hill near Tolsta, there are
huge pieces of rock lying, suggesting idea of having been
broken off by an iceberg. On Park Farm, beside a loch, there
is a solitary boulder. Near Stornoway Tile Works, a boulder
of Cambrian rock, supposed to have come from mainland to
eastward. (Reporter — Mr Peter Liddell, Gregs, by Stornoway.)

Stornoway. — Several boulders occur near Garabast, of a rock similar
to that which exists at Gairloch, on mainland to east (about
35 miles across the sea). There is also a large standing stone
at Paible. (Reporter — Henry Caunter, Esq., Stornoway.)

In Forest of Harris, and beween Fincastle and Glen Ulled ale,
there are many evidences of (supposed) ice action, viz., rocks
smoothed and striated, and boulders lying in lines. (Reporter —
Capt. Thomas, R.N.)

Report by Mr Campbell of Islay.

The well-known author of “Frost and Fire,” who has studied the
subject of the transport of boulders, not only in Scotland, but
in many foreign lands on both sides of the Atlantic, has sent
to the Committee a report, from which the following extracts
are made : —

“ I find in Scotland, upon ridges which separate rivers,
marks of glaciation upon a large scale. These enable me to
say, with tolerable certainty, that the ice which grooved rocks
in the Outer Hebrides, at low levels, near sounds, moved from
the ocean in the direction which tides now follow in the straits
beside which the striae are found.

“ The conclusion at which I have arrived, by the examina-
tion of all these phenomena, boulders included, is, that a
system of glaciations prevailed in Scotland, which can be ex-

736 Proceedings of the Royal Society

plained by the system now existing in Greenland. There, a
vast system of Continental ice, as great in area as all India,
radiates seawards, and launches icebergs, which move about
in tides and currents. This system certainly existed in Scot-
land previous to the smaller system.

“ Following any glen in Scotland, say Glenfyne, the smaller
system of glaciation follows the course of the river (as in
Switzerland), and the course of the tides in the sea loch (as
glaciers do in Greenland) ; and, furthermore, often overruns
low watersheds, and runs out to sea in some direct line. The
striae which mark the run of ice from the head of Glenfyne to
Lochgilphead, run over a col and down Loch Killisport. They
run past Tarbert, down both sides of Ceantyre and Arran, and
out to sea. At Ormsary, by the roadside, and on the sea-beach,
is a train of large boulders to which the usual legends are
attached. One was thrown from Knapdale at a giant who was
eating a cow on the other side of the loch. One of these
boulders close to Ormsary House, at a small roadside cottage,
is the biggest I have seen in Scotland. I did not try to
ascertain whence it came. I think it was pushed a short dis-
tance only. But the striae and trains of blocks show that it
moved from N.E. to S.W. along the general line of hollows in
the Western Highlands.

“ On the outer islands in Scotland are marks equivalent
to those so conspicuous on shore. In the Long Island, from
Barra Head to the Butt of Lewis, the whole country glaciated,
and the boulders everywhere perched upon the hills. Where
surface newly exposed, the striations and smooth polishing so
perfect and fresh, that marks can be copied as brasses are copied
in churches by antiquaries. I showed to you samples taken
last year in Barra and Uist. I have a large series taken
wherever I have wandered. These enable me to say, with
tolerable certainty, that the ice which grooved rocks in Outer
Hebrides at low levels, near sounds, moved from the ocean in
the direction which tides now' follow in the straits, beside
which the striae are found. For example, the grooves upon the
flat at Iochdar, at the north end of South Uist, aim directly
at the Cuchullin Hills in Skye. At the Mull of Ceantyre, at a

737

of Edinburgh , Session 1871-72.

great height above the sea, grooves aim at Rhinns of Islay
parallel to the run of the tides. And so it is at a great many
other places all round the coast.”

In a letter from the same gentleman to Mr Carmichael, of
South Uist, dated 29th March 1872, the following passages
occur : —

“ Glacial striae occur upon fixed rocks in Tiree, Minglay,
Barra, South and North Uist.. They correspond with a direc-
tion from the N.W., or thereabouts.

il The striae abound, and are especially fresh in the low
levels, and opposite to hollows in hills, which would be under
water, and traversed by tides, if those levels were now to sink
a few hundred feet. The hills, so far as I have examined
them, are ice- worn to the very top. Transported blocks are
scattered all over these islands. In some places regular
boulder-clay is left in patches. Under the clay, the rocks are
smooth as polished marble. The boulders, so far as I have
been able to ascertain, are of the same rock as the rock of the
islands named. Boulders in Tiree, for example, may have
come from Uist or Barra. They are perched upon the highest
hill-top in Tiree.

“ I was unable to find any sample of the rocks of Skye in
Uist or in Tiree.”

Inverness.

Kilmallie. — Boulder, fully 2000 feet above sea, on summit of a
hill, 12 x 10 feet. Another still larger among the mountains
between Loch Shiel and Loch Arkaig. Also boulder drifts
and moraines in numbers. (Reporter — Rev. Archibald Clerk,
Kilmallie Manse.)

Kilmallie (near Ardgour). — Quartz and mica boulders, nearly
round, and remarkable on bare hill side. Different from
adjacent rocks. 110 feet above sea. Same kind does not
occur nearer than G-lenfinnan, situated fifteen miles to N.W.
by W. (Reporter — C. Livingston, parochial schoolmaster.)

Kilmonivaig (Glengarry, N.W. of Fort William), Estate of Edward
Ellice, M.P. — Boulder on Monerrigie Farm, near Lochgarry,
about 16J feet long at base, and 23 feet at top, and about 9
feet high. Round at top. Quartzite rock. No rock in situ near.

738

Proceedings of the Roy at Society

Longer axis N. and S. Several boulders on Leek Farm, near
Loch Lundie, considerably larger. Some of boulders examined
by Mr Jolly, school inspector, Inverness, and found by him
to be striated. On Faicheam Ard Farm boulders very peculiar,
being entirely different from all rocks in neighbourhood.
Have been objects of curiosity to many geologists. The
boulders generally arranged in groups, except at Faicheam Ard,
where piled on one another. They rest on gravel. At Leek,
near Iron Suspension Bridge, rocks in situ well striated.

There are “ kaims” in another part of parish. At mouth of
Glengarry a delta of fine gravel. In Lochaber also, along
banks of Spean and Lochy. (Beporter — Parochial School-

master.)

Kiltarlity (on Lord Lovat’s lands). — A group of boulders called
whinstones. Bock of same kind il a little southwards.”
Dimensions of two largest are (1.) 15 feet long, 9 feet high,
10 feet broad; (2.) 8 feet long, 6^ feet high, 13 feet broad.
Longer axis of both E. & W. Angular in shape. Several
natural ruts on both 4 or 5 feet long, running N.W. About
300 feet above sea. (Schoolmaster’s schedule, but omitted to
be signed.)

Kingairloch (near Fort William). — Boulder, 5x5x4 feet, about 5
tons; 8 feet above sea. Different from adjacent rocks. (Be-
porter — D. Cameron, teacher.)

Kingussie. — Boulder of a slaty rock, 15J x 12 x 9, about 120 tons.
Longer axis, E. & W. Called u Fingal’s Putting Stone.”
About 900 feet above sea. Several other large boulders near
Laggan Free Church. (Beporter — Cluny M'Pherson, Cluny
Castle, Kingussie.)

Lochaber . — Near summit of Craig Dhu, between Gflens Spean and
Boy, a black sienite boulder, 14 x 8 x 4 feet. On same hill
lower down, boulders of red granite and felspar. (Observed
by Professor Nicol and Mr Jamieson of Ellon. Mr Jamieson
states that parent rock is in G-len Spean, to S.E. of Craig
Dhu, and at a level far below boulders.) (“Lond. G-eol. Soc.
Journal,” Aug. 1862 and Aug. 1863.)

On second G-lenroy shelf, near the 11 Gfap,” a boulder of
sienite, 8x7x4 feet. (Beporter — Professor Nicol.)

739

of Edinburgh, Session 1871-72.

Morvern (near Fort William). — G-rey granite boulder, called
“ Clach na’m Buachaillean.” Length — North side, 17 yards;
south side, 7\ yards; 17 yards “round about;” 13 yards
“ round top from ground to ground ; ” 11^ yards “ across middle
from ground to ground.” A large boulder to east of above on
a hill about 2640 yards distant, and “ peculiarly laid upon
other smaller stones.” (Schoolmaster’s schedule, but omitted
to be signed.)

Kincardine.

Banchory. — On property of John Michell, Esq. of G-lessel, not far
from G-lessel Railway Station, a boulder called the “ Bishop’s
Stone;” circumference 44 feet, height above ground 8 feet,
estimated to weigh 70 tons ; bluish granite, differing from
adjoining granite rocks. An ancient stone circle of boulders
about 200 yards distant. (Reporter — Sir James Burnett of
Crathes.)

The hill of Farre, situated two miles to north, forms an
elongated range, running E. and W. Rocks on it glaciated,
the strias running about E. and W., i.e., nearly coincident
with valley of Dee. (Reporter — Thos. F. Jameson, Ellon.)

Fettercairn. — No boulder now left in parish, of any size. Long
banks of gravel and sand occur, running parallel to one
another. (Reporter — A. 0. Cameron, parish schoolmaster.)

Maryculter. — Boulder, 5| x 6 x 6 feet, about 14 tons. Longer axis
N. and S. Rock of boulder considered same as rock situated
to eastward. (Reporter — David Durward.)

Kirkcudbright,

Galloway. — A great accumulation of blocks at head of Loch Valley
at Loch Narroch. Among these are blocks of the peculiar
graphic granite of Loch Enoch to the north, so that these
blocks must have been carried from Loch Enoch southwards
into the basin of Loch Neldricken, on to the spur of Craignaw
between it and Loch Valley, and still onwards right over
Craiglee and its deep scooped lake basins into G-len Trool.
Craiglee is remarkable for the number of perched blocks, some
of immense size, scattered over its ridges and highest peaks.

740

Proceedings of the Royal Society

The many boulders along its ridgy crest give the appearance
of an old broken -toothed saw.

Throughout the whole region travelled blocks and boulders
occur, even to the summit of the Merrick, the highest peak
south of the G-rampians (2764 feet). One set of perched
blocks is interesting, viz., poised blocks, known as Rocking
Stones. Such blocks are natural, and have been placed by no
human hands. Their exquisite balance is the result of the
weathering of the block and of the rock below, caused by wind
and storm.

There are well-marked striated rock surfaces more than 1600
feet above the sea-level.

Various moraines described, as stretching across valleys like
ramparts, and forming dams to existing lakes. (William
Jolly in “Edin. G-eol. Soc. Trans.” i. 155.)

Kells . — On Craigenbay Farm, a grey whinstone boulder, about 10
feet high and 17 feet long, with girth of 54 feet; 800 feet
above sea. Longer axis N. and S. (Reporter — Robert
Wallace, Auchenbrack, Tynron.)

Kirhbean. — Grey G-ranite boulder, 16x91x71? feet, and girth
about 38 feet, weighing about 80 tons. On sea shore at
Arbigland. Longer axis, S.E. by E. Superficial groovings
on top and S.W. front running N.N.W. Rests on free-
stone.

Criffel is about 3 miles to N.N.W. Granite rock there
same as boulder. In all the glens, between sea shore and
Criffel, numerous granite boulders generally in lines parallel
with glens. Several kaims 40 to 50 feet high, run from J to
^ mile. (Reporter — Rev. James Fraser, Colvend Manse, by
Dalbeattie).

Penninghame.— Granite boulders chiefly, supposed to have come
from Minnigaff Hills, situated to N.E. Larger boulders on
watersheds between Lochs Dee and Troul. (Reporters — Rev.
William M‘Lean, parish minister, and Rev. George Wilson,
F.C. minister.)

Twynholm. — Granite boulder, supposed to have come from Gallo-
way Hills, six or seven miles to westward. Several Druidical
circles. (Reporter — Rev. John Milligan, Manse of Twynholm.)

of Edinburgh, Session 1871-72.

711

Lanark.

Carluke. — Sandstone boulder, 20 x 14 x 14 feet, about 290 tons.
Called “Samson’s Sling Stone.” Doubtful if an erratic.
(Eeporter — D. E. E.j

Carnwath . — Whinstone boulders in large heaps. Supposed to have
come from “Yelpin Craigs,” three or four miles to north.
Legend about Michael Scott and witches. (Eeporter — Eev.
Mr M‘Lean.)

Nairn.

Auldearn. — A great many boulders in this parish, of old rocks, and
lying chiefly on Old Eed Sandstone rocks. Chiefly conglome-
rates, and apparently derived from same kind of rock, cha-
racterised by pebbles in it of angular quartz or hornstone,
liver coloured. These boulders all lie on sides of hills facing
N.W., and they have generally one of their sides smooth
which fronts the west. (Eeporter — James Eennie, school-

master.)

Ardclach. — At Eaemore Burn, about 270 feet above sea, and 5
miles distant from sea, a conglomerate boulder with five sides,
measuring altogether about 17 yards, and 3 yards above
ground. Surrounded by hills of no great height ; but lowest
of these is to N.W. Fragments in conglomerate of quartz,
hornstone, sienite, felspar, and other very hard rocks. The
block is scarcely rounded at its edges and corners. (Eeporter
— Dr G-regor, Nairn.)

Cawdor. — On hill of Urquenay, the following boulders — 1. At top
of hill, about 690 feet above sea, conglomerate called “ Clach
na Gillean,” or “ Young man's stone,” in girth about 54 feet,
and height 10 feet. It rests on bare granite rock. 2. Half-
way down hill, about 580 feet above sea, conglomerate called
“ Clach na Cailleach,” or “ Old wife’s stone,” in girth about 54
feet and height 15 feet. It seems to rest on drift gravel.
3. At foot of hill, and at east end of a kaim of gravel and
sand, about 300 feet above sea, conglomerate called “ Clach an
oglach ,” or “ Boy’s stone,” in girth about 69 feet, and average
height about 9 feet.

Within policy woods of Cawdor Castle, on side of a burn

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VOL. VII.

742 Proceedings of the Royal Society

facing W.N.W., a conglomerate boulder about 250 feet above
sea, in girth about 100 feet, and about 12 feet high.

The above four conglomerate boulders lie on granite rocks.

On Piper’s Hill, where rocks in situ are Old Red Sandstone,
a conglomerate boulder, on the side of a kaim facing N.W.,
weighing about 10 tons. Above sea about 300 feet.

No conglomerate rock of the same hard description in
Nairnshire. On the granite rocks there lie boulders of sand-
stone, evidently transported from the north, where the Old Red
Sandstone only exists, in the low country. (Reporters — W.
Stables, Esq., commissioner; and his clerk, Mr John G-rant,
Cawdor Castle.)

Croy, — Conglomerate boulder, called “Tomreach,” about 15 feet
high, and girth of 27 yards. About 300 or 400 feet above
sea. Sketch sent. (Reporter — -Captain White, R.E.)

Orkney and Shetland.

Bressay (Shetland). — A number of boulders consisting of a coarse
white sandstone at various heights, viz., from 40 to 360 feet
above sea. They lie on east side of island, and are conjec-
tured to have come from Norway. Largest boulder, 10 x 7 x 4
feet. Longer axis, N.W. Distinct groovings N.E. and S.W.
(true); some of them 3 inches deep. (Reporter — School-

master ?)

Eday (Orkney). — Conglomerate boulder, 12 x 7 x 1J feet, about 8
tons. Longer axis N.E. Situated near top of hill, about 250
feet above sea. Called “ Giant Stone.” Legend, as to it
being thrown from island of Stronsay. No conglomerate in
Eday, but there is in Stronsay. (Reporter — G\ Miller, school-
master, Cross and Burness.)

Frith and Stennis (Orkney). — Pebbles of white freestone on the
hills. No white freestone rock in district ; all red sandstone,
(Reporter — Robert Scarth .)

Jlousay Island (Shetland). — On a cliff, 200 feet above sea, there
are loose blocks resting on rounded knolls and polished rock,
all polished before the burthen they now bear was thrown upon
them. Some of the stones hang on ridges on the rounded
sides of the bill.

74:3

oj Edinburgh , Session lb>71-72.

Lerwick (Shetland). — At Lunna, a large block, broken into two,
called the “ Stones of Stoffus,” but uncertain whether erratics.
(Reporters — James Irvine, teacher, and Robert Bell, pro-
prietor.)

North Unst. — Here ice action plain. The serpentine rock has
suffered severely. Ruts and striae on it W.N.W. A hill 500
feet high, whole of upper part of which for 150 feet from top
polished. Striated stones and blocks also plentiful. All over
Unst the rocks show signs of abrasion, and in many places
deposits of drift, inclosing stones of all sizes, some of which
are rounded and striated.

In the Island of Ueay , large perched blocks, some many
tons in weight, lie scattered about everywhere.

Thus then, at both ends, and in the middle of this group of
islands, traces of glacial action have been found. (Peach,
Brit. Assoc. Rep. 1864.)

Sunday (Orkney). — Gfneiss boulder, 7 x 2-J x 6 feet, about 14 tons.
Rocks of island are Old Red Sandstone. At Stromness, thirty
miles to S.W., gneiss rocks occur in situ , also in Shetland
Islands to north. Legend, that thrown from Shetland. (Re-
porter— G-. Miller, schoolmaster, Cross and Burness.)

Sumburgh Head (Shetland). — Conglomerate boulder, lying over
sandstone. (Reporter — William Lawrence, teacher.)

Walls (Orkney). — Lydian stone boulder, 9x7x6 feet, about 28
tons. Large quantities of granite boulders scattered over
hills; valleys show glacier and iceberg agency. (Reporter —
James Russell, teacher.)

Peebles.

Kirkurd. — Three boulders of gneiss or'trap (?) differing from adja-
cent rocks. (Reporter^ — James Palmey, schoolmaster, Kirkurd,
Dolphinton.)

Newlands. — Remarkable kaims. (Reporter — E. Blacklock, school-
master.)

Perth.

Aberfeldy (Tullypowrie village). 1. On north side of village, a
considerable assemblage of schist boulders, the rocks in situ
being clay slate. Most of boulders round in shape as if rolled.

744 Proceedings of the Royal Society

One large boulder angular, 16 x 14 x 7 feet, named “ Clach
Chinean,” or “ Stone of Doom.” These boulders all rest on
heaps of drift, much resembling a moraine. On the opposite
or south side of the valley there are similar masses of drift,
containing, however, stratified beds of sand and gravel.

2. About 2 miles north of Tullypowrie village, near the hills,
two very large boulders of mica slate occur, about 1500 feet
above sea. They rest apparently on a heap of drift. They
are both cubical in form, and with sharp angles, as if never
exposed to friction. One of them measured, and found to be
71 feet in girth and 17 feet high. The hills are more than J
mile distant. They must have been brought by ice of some
kind, and let down without violence ; for a fall from any height
would have probably caused such large masses to break in
pieces. The adjoining hills form a range to N. and W., reach-
ing fully 700 feet above the boulders. But to N.W. (magn.)
of the boulders, and within a J mile a passage occurs through
the hills, the level of which is only about 200 feet above the
boulders. They might have come through this passage, carry-
ing the boulders and stranding them where they now lie.
These boulders, called “ Clach M‘had,” or “ Stones of the
Fox.”

3. Above Pitnacree House, a boulder of schist resembling
hypersthene, 15 x 111 x 4 feet above ground. It is called
“ Clack odhar,” or “ Dun Stone.” No hills are near it, and
it differs from all rocks in situ near it. (Reporter — Mr
M‘Naughton, merchant, Tullypowrie).

Arngask . — Rocking stone of mica slate, in Glenfarg (“ New Statis-
tical Account,” vol. x. p. 888).

Auchterarder. — Boulder, 10x6x2 feet, about 8 tons. Longer axis
N.W. Called “ Wallace’s Putting Stone.” (Reporter — Rev.
Dr Nisbet, Edinburgh.)

Auchtergaven. — Granite boulder, 10x8x3 feet, about 8 tons; 260
feet above sea. Longer axis N. and S. Called the “ Deil’s
Stone.” Has numerous and distinct “cup” markings on its
sides. Supposed to have come from mountains situated thirty
miles to north. Has been mutilated by slices cut off it for
building, &c. Several standing stones and Druidical circles in

of Edinburgh, Session 1871-72. 745

this parish, composed of boulders. (Reporter — William Dull,
schoolmaster.)

Bendochy. — Formerly a Druidical circle of nine large stones, now
destroyed, but name still preserved of “ Nine Stones.” Long
kaims of gravel or sand, which supposed may have caused
river Tay to fall into sea at Montrose. (Reporter — Rev. Dr
Barty.)

CaJlendar (Stirling). — Gneiss boulder on top of Bochastle Hill,
called “Samson’s Putting Stone,” 14x9x9 ft., resting on
conglomerate rock. Longer axis N.E. Sketch sent, showing
unstable position. Has come from westward. (Reporter — J.
B. Hamilton, Leny.)

Collace. — Large stones said to be here. Query, — are they erra-

tics? (Reporter — Peter Norae, schoolhouse, Collace.)

Comrie. — Four boulders of whinstone, and one of granite, 13x9x7^
feet, weighing about 20 tons. Longer axis N. and S. (Re-
porter— Wm. F. Swan.)

Crieff. — 1. Conglomerate boulder, 16 x 10 x 5% feet, about 64 tons,
“ Witches’ Stone.” 2. Conglomerate boulder, 19 x 10 x 5 feet,
about 70 tons. 3. Red granite boulder, 8J x 4J x 4 feet,
called “ Cradle Stone.” (Reporter — Rev. Dr Nisbet, Edin-

burgh.)

At Abercairney, dark grey granite boulder, about 20 tons.
(Reporter — C. Home Drummond Moray; and Rev. Thomas
Hardy, parish minister.)

In Glen Turret, appearances of ancient moraines, described
in letter by Mr Sang, C.E., Kirkcaldy.

Doune (near Kilbride). — Conglomerate boulder, about 900 tons.
(Described in Estuary of Forth, by Mr Milne Home.)

Dron. — Whinstone rocking stone, 10 x 7 feet. Stands on bare
rock (“ New Statistical Account,” vol. x. 364).

Errol. — Several boulders, differing from adjacent rocks. Said to
be indicated on Ordnance Survey maps.

Fortingall. — Gneiss boulder, 24x16x13 feet, called “ Clach an
Salaine,” from people who brought trees out of Black Wood of
Rannoch, resting them on it. Height above sea 2500 feet.
Rocks in situ clay slate. Longer axis N.W. (Reporter — Mr
Fletcher Menzies.)

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Proceedings of the Royal Society

Fowlis. — Two dark grey granite boulders, 10 x 7 x 4 feet, and
12x6x4 feet. Supposed to have been used as places of
worship or sepulture, in very ancient times. (Reporter — Rev.
Thomas Hardy.)

Killiecrankie (Tennandry Parish). — Blue limestone boulder,
6 x 5J- x 4 feet. Supposed to have come from “ Ben y Gloef
a hill to N.N.E., across valley 500 feet deep ; plan of district
sent. Granite boulder, also mentioned ; has come from North.
(Reporter — Rev. Patrick Grant, Tennandry Manse.)

Kilspindie. — Seven granite boulders, from 5 to 6 tons weight. Five
form a belt or row having N.W. direction. All differ from
adjacent rocks. (Reporter — J ames M‘Kerracher, schoolmaster,
by Errol.)

Kirkmichael. — Rocking stone, 7 x 5 x 2J feet, about 3 tons, whin-
stone. (?) Several tall stones near it, called “Olachan
Sleuchdaidh ” (Stones of Worship). — (‘‘New Statistical
Account,” vol. x. p. 737.)

Logie Almond. — Whinstone boulder, 8 or 10 feet square, about 48
tons, called “ The Ker Stone,” about 600 feet above sea, on
north bank of River Almond, opposite to Glenalmond College.
Probably* as there is a great peat moss near, the name has
reference to the moss, “ char” being the Gaelic for peat.

There is another boulder called u Cul na Cloich,” or Stone
Nook. A stream forms a nook or angle with the drain or ridge
on which the boulder stands. It is a conglomerate, and rests
on Old Red Sandstone. Another conglomerate boulder occurs
at S.E. corner of the farm of Risk. (Reporter — Rev. Patrick
Macgregor, Logie Almond Manse.)

Meihven (Auchtergavin Parish). — Whinstone boulder, about 10
feet high, oval shaped, standing on small end, called “ Sack
Stone.” No rock of same kind near. 800 feet above sea.
(Reporter — William Duff, schoolmaster.)

Monzie. — In Glen Almond, a large stone, 8 feet high, near side of
river, nearly cubical, called Clach-Ossian , said to mark grave
of that poet. (“ New St. Acct.” of parish, vol. x. 264.)

Pitlochrie. — 1. On road to Straloch, mica slate boulder, called
“ Gledstone,” about 1800 feet above sea. Lying on drift of
gravel and stratified sand. Rocks adjoining clay slate.

747

of Edinburgh , Session 1871-72.

About 8 tons weight. Legend, that this stone gave name to
Gladstone family, an infant having been found at it by a shep-
herd, who took it home to his wife, who nursed it.

2. Near parish church of Straloch, a huge boulder of very
coarse granite, called u Clack m’kor,” or ‘ * Big stone,” about 24
feet diameter, and about 20 feet high. Supposed to weigh
about 800 tons. Adjoining rocks clay slate. Many other
boulders of mica slate and quartzite beside it. Supposed to
have come from north through a valley. (Reporter — Rev.
Dr Robertson, Straloch.)

Rattray. — Mica schist boulder, 12x6x6 feet, about 25 tons,
called “ Glenballoch Stone.” Has cup and groove markings
on south side. There are other boulders in Druidical circles.
They have all come from hills to N. or N.W. (Reporter —
Rev. Mr Herdman, Rattray.)

Renfrew.

Kilbarckan. — Porphyry boulder, 22 x 17 x 12 feet, about 300 tons.
Longer axis E. and W., called “ Clach a Druidh ” (Stone of
’Druid)? Legend. Boulder differs from adjacent rocks. Same
rock seen in hills 2 or 3 miles to west and north. (Reporters,
— Robert Graham, D.D. ; and R. L. Jack (Geol. Survey).)

Ross and Cromarty.

Alness. — In forest of Gildermoy, a very large granite boulder re-
ported by Earl of Selkirk.

Applecross. — Three large boulders, one near shore at Rassel, called
u Clach Oiu ” weighing about 60 tons, other two about 30 tons,
each called respectively “ Clack Mkoir ” and “ Clack Van.”
Used as landmarks from the sea. Kaims at Ardbain and
Ardrishach, extending each more than two miles along coast.
(Reporter — William Ross, schoolhouse, Applecross.)

Ben Wyvis.— N.W. shoulder of, presents whole acres of rock, swept
bare of soil, rounded and polished. Boulders of a peculiar
veined granite have come from the Derry More (tract situated
to west of Ben Wyvis), and been carried eastward to Moray
Erith. These boulders found half-way up Ben Wyvis, also in
valleys of Alness and Ault Grand, In Strathgarve some of

748

Proceedings of the Royal Society

the blocks are as big as cottages. Their size lessens towards
E. No boulder of same kind seen on West Coast. (Nicol
“ Geol. of N. of Scot./’ p. 70.)

Garnock. — Five large boulders, each weighing about 20 tons. Each
has a G-aelic name. One, a boundary stone. (Reporter —
James Watson, schoolhouse, Strathconon, Beauly.)

Edderton . — Granite boulder, 23 x 19 x 12 feet, weighs about 290
tons. Longer axis N.E. Two others, not quite so large.
All differing from adjacent rocks. (Reporter — Rev. Ewen
M‘Ewen, parish minister.)

Rev. Mr Joass states that this word is derived from u Garbli ”
— “ rough the Gaelic for “ Hill of the Pitcher ,” on account
of shape, its sides being almost vertical. (Rev. Mr Joass.)

Rev. Mr Joass of Golspie states, that the boulders here
referred to are on a shelf or terrace about 900 feet above sea,
and that their parent rock is at Carn na Cuinnaig about 12
miles to N.W.

He adds, that the boulders specified, as in the parishes of
Tain and Tarbat, are probably from same source. The granite
is peculiar. (See Tain and Tarbat farther on.)

j Fannich Mountains. — Boulder of grey gneiss, with garnets.
30 x 10 x 5 feet, described in letter to Convener by J. F.
Campbell of Islay ; 2700 feet above sea ; angular. Situated
on watershed. Called “Clach mhor na Biachdoil.” A train
of large boulders to be seen in a valley not far off. Rocks
also smoothed and striated. Lines of striation parallel with
valleys.

Foddarty. — Boulder, 14 x 8 x 5 feet, about 40 tons. About 6 feet
above sea ; shape, angular ; Druidical. Another with inscrip-
tion illegible. Supposed to commemorate a battle between
two clans. (Reporter, parish schoolmaster.)

Lochalsh. — Gneiss boulder, 9x7x8 feet; longer axis E. and W.,
striated. Boulder differs from adjacent rocks. Same rock
said to be at Glenelg, 5 or 6 miles to south.

Boulder called after Fingal. Quartz, 7-J x 7 x 5 feet. Longer
axis, N.W. ; striated. At Loch Carron, said to be a kaim or
diluvial bank. (Reporter — Duncan Sinclair, parish school,

Lochalsh.)

of Edinburgh, Session 1871-72.

749

Lochgair. — One granite boulder, 28 x 17 x 16 feet, about 56 0 tons
striated. Two granite boulders, 23 x 10J x 7 feet, about 120
tons. One of these said to be on top of a hill, and called
“ San del Stone.” Legend. There are three other boulders of
smaller size. Rocks in situ are granite. (Reporter — John
MacKillop, schoolmaster.)

Shieldag (Loch Oarron). — Granite boulder, 16 x 10 x 10 feet, about
120 tons. Longer axis E. and W. There is another large
boulder. Both said to be in precarious positions. (Reporter
— Rev. Alex. C. MHntyre, Shieldag Manse, Dingwall.)

Tain. — Granite boulder, 18 x 12 x 8J feet, about 60 tons. Plan
and section of boulder given. Rocks of district are Old Red
Sandstone. South shore of Dornoch Frith said to be thickly
strewed with granite blocks, whilst none on north shore.
(Reporter — Robert Gordon.)

Tarbat. — Seven or eight large boulders of gneiss and granite.
Places, dimensions, and names specified, with sketches of
boulders. Also, kaims of clay running E. and W. in parallel
lines. One a mile long. (Reporter — Rev. George Campbell,
parish minister.)

West Coast. — Vestiges of moraines, lateral and terminal, from
glacier generated in valley occupied by Loch Fuir, N. of Loch
Maree. (Nicol “ Geol. Soc. Jour.,” xiv. p. 170.)

Roxburgh.

EcJcford. — Two kaims, each from 100 to 300 yards long, from 50
to 60 feet high. (Reporter — Parish schoolmaster.)

Jedburgh. — Porphyry boulder, supposed to have come from Dunion
Hill, which is 2 miles to west. Formerly granite boulder on
Dunion. Supposed to have come from Galloway or Dumfries
now destroyed. A whinstone boulder, above Bedrule Bridge.
(Reporters — Rev. Archibald Craig and Rev. Dr Ritchie.)

Melrose. — Greywacke boulder, round shaped, called u Samson’s
Putting Stone.” (Reporter — Parish schoolmaster.)

Stirling.

Alloa. — Basaltic boulder, 13 x 11 j x 11 feet. Longer axis N. and S.
Called “ Hair Stane.” About 70 feet above sea. (Reporter — -
Parish minister.)

5 G

VOL. VII.

750

Proceedings of the Royal Society

Campsie. — Rocks glaciated. Striations W.S.W. & W.N.W. (Re-
porter— Rev. Thomas Monro, D.D.)

Fintray. — Boulders in a group, called “ Gowk Stones.” Have
apparently come down valley. (Reporter — R. L. Jack (Geol.
Survey).)

Kilsyth. — Mica Slate boulder, 7 x 5 x 2J feet, about 6 tons. 1250
feet above sea. Parent rock supposed to be 15 miles to north.
(Reporter — R. L. Jack (Geol. Survey).)

Ochils. — On watersheds of, at about 2000 feet, boulder of mica
schist fall of garnets, apparently from Grampians to N.W.
(Jamieson, “ Geol. Soc. Jour.,” xxii. p. 166.)

St Ninians. — Boulder about 200 tons, at height of 1250 feet above
sea. (Reporter — R. L. Jack (Geol. Survey).)

Strathblane. — Conglomerate boulder, 8x4x3 feet, about 7 tons.
Longer axis W. 20° N. 1803 feet above sea. Parent rock
supposed to be to N.W. (Reporter — R. L. Jack (Geol.
Survey).)

Sutherland.

Assynt. — Two arge boulders, one at Unapool, the other at Stron-
chrubie, called “ Clach na Putain ” (Stone of the Button).
(Reporter — Angus M‘Ewen, parochial schoolmaster.)

Clyne. — Remarkable kaims, apparently moraines (lateral and ter-
minal) in valley of Brora. Also, rocks striated at Brora
quarry. Strias run N.W. (Reporter — M. Myron.)

Golspie. — Old Red Sandstone boulder, 16 x 10 x 4 feet, lying on
Oolite rocks. Longer axis, N.N.W. ; sub-angular. Sketch
sent. About 248 feet above sea. Three smaller boulders of
Old Red Sandstone lie about 100 yards to S.E. of the above.
The Old Red Sandstone formation is situated to north and west,
about 3 miles from boulder. Terminal and lateral moraines
occur in Brora valley, broken up by diluvial action into ridges
and hummocks. (Reporter — Rev. James Joass, minister of
Golspie.)

On the whole N.W. coast from Cape Wrath southwards,
numerous “ Perched ” boulders occur on summits and sides of
hills, in the most exposed positions. Especially numerous
around Loch Maree. (Nicol “ Geol. Soc. Journal,” xiii. pp.
29, 39.)

751

of Edinburgh, Session 1871-72.

Boulders of large size on top of Applecross Hills. Rocks
below, striated. Direction of striae S. 20° W. (true.) (Re-
porter— Nicol of Aberdeen.)

Wigtownshire.

Olasserton. — Granite boulder, 9x6x6 feet, about 24 tons. Longer
axis N.E. Two small boulders to east of above, and in a line
with it. These boulders supposed to have come from moun-
tains to N.E., across arm of sea. Kaims in parish, full of
granite pebbles. (Reporter — Archibald Stewart.)

The following Gentleman was elected a Fellow of the
Society : —

Thomas B. Christie, M.D., F.R.C.P.E.

Monday , §th May 1872.

D. MILNE HOME, LL.D., Vice-President, in the Chair.

The following Communications were read : —

1. On the Chemical Efficiency of Sunlight.

By James Dewar, Esq.

Of all the processes proposed to measure varying luminous in-
tensities by means of chemical effects, not one has yet been
expressed in strictly dynamical measure. This is owing to the
very small amount of energy to be measured necessitating very
peculiar processes for its recognition. The chemical actions gene-
rally induced by light are of the “Trigger” or “Relay” description ;
that is, bear no necessary relation to the power evolved by the
transformation. There is one natural action of light continuously
at work of a very different kind in the decomposition of carbonic
acid by plants, necessitating a large absorption of energy, and thus
enabling us to ascertain the proportion of the radiant power
retained, through the chemical syntheses effected.

So far as I am aware, the following passage extracted from
Helmholtz’s Lectures “On the Conservation of Energy,” delivered

752 Proceedings of the Royal Society

at the Royal Institution in 1864, and published in the “ Medical
Times and G-azette,” contains the first estimate of the chemical effi-
ciency of sunlight. “ Now, we have seen already, that by the life
of plants great stores of energy are collected in the form of com-
bustible matter, and that they are collected under the influence of
solar light. I have shown you in the last lecture that some parts
of solar light — the so called chemical rays, the blue and the
violet which produce chemical action — are completely absorbed
and taken away by the green leaves of plants ; and we must sup-
pose that these chemical rays afford that amount of energy which
is necessary to decompose again the carbonic acid and water into
its elements, to separate the oxygen, to give it back to the atmo-
sphere, and to collect the carbon and hydrogen of the water and
carbonic acid in the body of the plant itself. It is not yet possible
to show that there exists an accurate equivalent proportion between
the power or energy of the solar rays which are absorbed by the
green leaves of plants, and the energy which is stored up in the
form of chemical force in the interior of the plants. We are not
yet able to make so accurate a measurement of both these stores
of energy, as to be able to show that there is an equivalent pro-
portion. We can only show that the amount of energy which the
rays of the sun bring to the rank is completely sufficient to produce
such an effect as this chemical effect going on in the plant. I
will give you some figures in reference to this. It is found in a
piece of cultivated land producing corn or trees, one may reckon
per year and per square foot of land 0-036 lb. of carbon to be pro-
duced by vegetation. This is the amount of carbon, which during
one year, on the surface of a square foot in our latitude, can be
produced under the influence of solar rays. This quantity, when
used as fuel and burnt to produce carbonic acid, gives so much
heat that 291 lbs. of water could be heated 1° C. Now we know
the whole quantity of solar light which comes down to one square
foot of terrestrial surface during one second, or one minute, or one
year. The whole amount which comes down during a year to one
square foot is sufficient to raise, the temperature of 430,000 lbs. of
water 1° C. The amount of heat which can be produced by fuel
growing upon one square foot during one year is, as you see from
these figures, a very small fraction of the whole amount of solar

of Edinburgh, Session 1871-72. 753

heat which can be produced by the solar rays. It is only the
1477th part of the whole energy of solar light. It is impossible
to determine the quantity of solar heat so accurately that we could
detect the loss of so small a fraction as is absorbed by plants and
converted into other forms of energy. Therefore, at present, we
can only show that the amount of solar heat is sufficient to pro-
duce the effects of vegetable life, but we cannot yet prove that this
is a complete equivalent ratio.” This estimate is, strictly speaking,
the mean agricultural efficiency of a given area of land, cultivated as
forest, and considering that active growth only takes place during five
months in the year, we may safely adopt g^o-th of the total energy
of sunlight as a fair value of the conserved power, on a given area
of the earth’s surface in this latitude during the course of the
summer. As chlorophyll in one or other of its forms is the sub-
stance through which light becomes absorbed, and chemical
decomposition ensues, it would he interesting to acquire some idea
of the storage of power, effected by a given area of leaf surface
during the course of a day, and to compare this with the total
available energy. Here we are dealing with strictly measurable
quantities, provided we could determine the equation of chemical
transformation.

Boussingault’s recent observations on the amount of carbonic acid
decomposed by a given area of green leaf seem to me to afford
interesting data for a new determination of the efficiency of sun-
light. In his experiments made between the months of January
and October under the most favourable circumstances in atmo-
spheres rich in C02 one square decimetre of leaf has decomposed in
one hour, as a mean 5'28 cc of C0.2, and in darkness evolves in the
same period of time 033 cc of C02. In other words, one square metre
of green surface will decompose in twelve hours of the day, 6336
cc of C02, and produce in twelve hours of the night 396 cc of C02.

This quantity of carbonic acid decomposed does not represent
the whole work of sunlight for the time, as water is simultaneously
attacked in order to supply the hydrogen of the carbo-hydrates.
Boussingault, in summing up the general results of his laborious
researches on vegetable physiology, says, “ Si l’on envisage la vie
vegetale dans son ensemble, on est convaincu que la feuille est la
premiere etape des glucoses que, plus ou moins modifies, on trouve

754

Proceedings of the Royal Society

repartis dans les diverses parties de l’organisme ; que c’est la feuille
qui les elabore aux depens de l’acid carbon ique et de l’eau.” —
P. 415, Am. de Chemie, tom xiii. The fundamental chemical
re-action taking place in the leaf, may therefore be represented
as follows : —

(1) C0,0 + H20 - CO,H2 + 0,0

(2) 6(CO.H2) = CAA

In the first equation carbonic acid and water are simultaneously
attacked with the liberation of a volume of oxygen equal to that
of the original carbonic, together with the formation of a substance
having the composition of methylic aldelyde. The second equation
represents the condensation of this aldelyde into grape sugar. The
transformation induced in (1) necessitates the absorption of a large
amount of energy ; and if we neglect the heat evolved in the
combination of nascent CO and H2, which can be shown to be very
little, the calculated result is made a maximum : whereas the con
densation of (2) being attended with an evolution of heat, diminishes
considerably the amount of power required. Happily Frankland’s
direct determination of the thermal value of grape sugar leaves
no doubt as to the true equivalent of work done in its formation.
Taking the following thermal value C0,0 = 68,000, H2, O = 68,000,
C6H1206 # 642,000, 1c centimetre of C02 decomposed as in (1)
would require 6*06 gramme units of heat, or its light equivalent;
whereas the complete change into grape sugar of the same amount
of carbonic acid requires only 4 *78 gramme units. But we have
seen before 1 square decimetre of green leaf functions at the
rate of 5 *28cc of carbonic acid assimilated per hour, therefore
(5*28) x (4*78) = 25*23 represents the number of gramme heat
units conserved through the absorption of light in the above
period of time. Pouillet estimates the mean total solar radiation
per square decimetre exposed normally to the sun’s rays in or near
Paris per hour as 6000 gramme units, so that 6000 - 25*23 =
represents the fraction of the entire energy conserved. The esti-
mate is by no means too little, as Boussingault has shown the leaf
may function at twice the above rate for a limited time.

In connection with equation (1), above given, as representing
the action of sunlight on the leaf, it is worthy of remark, that

755

of Edinburgh, Session 1871-72.

supposing the carbonic acid and water equally efficient as absorb-
ing agents of the vibratory energy (although each has a specific
absorption for certain qualities of rays), then the decomposition of
the two compound molecules may take place continuously side by
side, owing to the equality of the thermal equivalents of carbonic
oxide and hydrogen. We already know, from the laborious re-
searches of Tyndall, how thoroughly aqueous vapour retains
thermal radiations ; and Janssen has further shown that the same
substance has a strong absorptive action on the rays of light of low
refrangibility (just those rays that are in part selected by chloro-
phyll), producing the well-known atmospheric lines of the solar
spectrum. The presence, therefore, of varying quantities of
aqueous vapour in the atmosphere in all probability produces a
considerable difference of rate in the decomposition effected by the
leaf, and may, in fact, end in carbonic acid and water being
attacked in another ratio than that given as the fundamental
equation of decomposition. Thus the same plant in different
atmospheric conditions may elaborate different substances.

2. On the Eainfall ol the Continents of the Globe. By
Alexander Buchan, Secretary of the Scottish Meteoro-
logical Society.

This paper was illustrated by two large charts of the world
showing, by isohyetal lines, the rainfall over the different conti-
nents in January and July; two large charts showing the months
of least and greatest rainfall in Europe, north Africa, and west
Asia; and by six sets of smaller charts of thirteen each, showing,
by isohyetal lines, the monthly and annual rainfall of Europe,
Asia, Australasia, North America, Africa, and parts of South
America. The data laid down on these eighty-two charts were
taken from a Table comprising about 2000 good averages of rain-
fall, calculated or collected by the author.

On comparing the results of the rainfall with the author’s charts
of Atmospheric Pressure and Prevailing Winds, published in the
Society’s Transactions,* the broad principles regulating aqueous
precipitation are chiefly these : —

* Yol. xxv. p. 575, et seq.

756 Proceedings of the Royal Society

1. When the prevailing wind has previously traversed a large
extent of ocean, the rainfall is moderately large.

2. If the winds are at the same time advancing into colder
regions, the rainfall is largely increased ; and if a range of moun-
tains lie across their onward path, the rainfall is also thereby
largely increased on the side facing the prevailing winds, and
reduced over the regions lying on the other side.

3. If the winds, though arriving from the ocean, have not tra-
versed a considerable extent of it, the rainfall is not large.

4. If the winds, even though having traversed a considerable
part of the ocean, yet on arriving at the land proceed into lower
latitudes, or regions markedly warmer, the rainfall is small or nil.

3. On the Lunar Diurnal Variation of Magnetic Declination
at Tre van drum, near the Magnetic Equator. By J. A.
Broun, F.R.S.

The author gives the results derived from different discussions of
nearly eighty thousand observations, made hourly during the eleven
years 1854 to 1864. They are as follows : —

1. That the lunar diurnal variation consists of a double maximum
and minimum in each month of the year.

2. That in December and January the maxima occur near the
times of the moon’s upper and lower passages of the meridian ;
while in June and July they occur six hours later, the minima
then occurring near the times of the two passages.

3. The change of the law for December and January to that for
June and July does not happen, as in the case of the solar diurnal
variations, by leaps in the course of a month (those of March and
October), but more or less gradually for the different maxima and
minima.

4. While the lunar diurnal variation changes the hours of
maxima and minima more gradually than the solar diurnal varia-
tion, it also makes the greatest change at different times ; thus the
solar diurnal variation changes completely during the month of
March, or from February to April, while the lunar diurnal varia-
tion makes the greatest change, from April to May. The second

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great change which happens for the sun, between September and
November, occurs earlier, or between September and October for
the moon.

5. The range of the variation is greatest in January, and is least
in May and October ; the arc, including the mean diurnal variation
for January, from eleven years’ observations, being nearly 0'*5,
while in the latter months the ranges were nearly O'- 18 and 0H4
respectively; the range for July being 0'‘26.

The author states, that, in a paper already published,* be has
shown that the range of the diurnal variation amounts sometimes
to five minutes (5'-0), which, from the less value of the horizontal
force, would be equivalent to about twelve minutes (12'*0) in Eng-
land ; and that the diminution of range appearing in the mean of
many lunations is due to the combination of variations following
different laws.

6. The ranges of the mean lunar and mean solar diurnal varia-
tions thus obey different laws with reference to the period of the
year; the range of the former in January being nearly double that
in any month from May to September, while the range of the latter
in August is nearly double that in January.

In the discussion for the change of the law which might be due
to the moon’s passing from one hemisphere to the other, the author
found different results for different months of the year ; this led
him to perform the calculations in a new way, described by him,
in which the law derived from observations made during the day
is separated from that obtained from observations made during the
night. From this discussion it follows —

7. That the action of the moon on the declination needle is, in
every month of the year, greater during the day than during the
night; the range of the oscillation in January and June being nearly
four times greater during the day than during the night, the ratio
being less in the intermediate months.

When the results are derived from the forenoon hours only, or
from the afternoon hours only, the range in January is six times
greater than that derived from the night hours only.

It also appears that the law derived from the night hours varies
little in the course of the year ; it is only that derived from the
* Trans. Koy. Soc., Edin. vol. xxiv. p. 673

5 H

VOL. VII.

758 Proceedings of the Royal Society

day hours which becomes inverted in passing from January to July.
It follows —

8. That the principal, if not the only, cause of change in the
amount of the lunar action at Trevandrum, near the magnetic
equator, for the moon on different meridians, depends on whether
the sun is shining on the place of the needle or not.

The author finds —

9. That the area of the curve representing the lunar diurnal
variation in the mean of the group of months, October to April, for
the half orbit about Perigee, is to that for the other half orbit as
1T8 : 1 ; while for the group of months, May to September, the
ratio is 1*31 : 1 ; the moon’s action appearing to diminish more
rapidly with the distance from the earth, when both moon and earth
are farthest from the sun. As the mean distances of the moon from
the earth in the two half orbits are nearly as 1 to T07, it appears
that the mean range for Perigee and for Apogee, derived from both
groups, varies nearly as the inverse cube of the distance, as in the
case of the tides.

Monday , 20 th May 1872.

Professor Sir ROBERT CHRISTISON, Bart., President,
in the Chair.

The following Communications were read : —

1. Some Helps to the Study of Scoto-Celtic Philology,
by the Hon. Lord Neaves.

(Abstract.)

Lord Neaves read a paper entitled “ Some Helps to the Study of
Scoto-Celtic Philology,” in which, after noticing the mistaken
tendencies of the Celtic scholars of former times, both Irish and
Scotch, as to the origin and affinities of G-aelic, and adverting to
the fact now firmly fixed that it was an Aryan or Indo-Germanic
tongue, he submitted a statement of some of the imitations or
disguises which words underwent or assumed in passing into G-aelic.
Thus it was a peculiarity of Gaelic to avoid the letter p, which it

759

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did in various ways. Sometimes it dropped that letter, as when
it changed the Latin Pater into Athir , the Latin piscis into iasg,
plenus into l&n, &c. Sometimes it changed the p into a gutte'ral
c, g, or ch, as seachd for septem , feasgar for vesper. It did this
even in borrowed words, as when the Church term Pasch for Easter
was changed into Caisg ; the Latin purpur into corcur. It was
another peculiarity of Gaelic to omit the letter n before certain
other consonants, so that centum became cead , guinque became coig ,
■mensis, mios ; infernum , ifrinn ; inter , eadar. The Latin v or
English w was generally represented in Gaelic at the beginning of
words by f: thus vir,fear; verus, fior ; vinum, fion ; rates, faidh ;
&c. The old Irish word for a widow was fedb. Two remarkable
prefixes occurring frequently in Gaelic, do and so, correspond to
similar prefixes du and su in Sanscrit : do and du meaning “ evil or
difficulty,” and so and su meaning “ goodness or facility.” These
prefixes are very abundant in those two languages at the two
extremes of the Aryan field, but though represented also in Greek,
are scarcely or very slightly perceptible in the intermediate tongues.

An attention to these and other' changes which words undergo
in passing into Gaelic would greatly facilitate the study of this
remarkable tongue, which it is not creditable to Scotchmen to
neglect as they have done. The comparative forms of the inflec-
tions of words also deserve attention, and on this subject reference
might be made to an interesting lecture on the Gaelic, by Professor
Geddes of Aberdeen.

2. Some Observations on the Dentition of the Narwhal
(Monodon monoceros). By Professor Turner.

The author expressed his concurrence with those anatomists who
hold that the two tusks of the narwhal are situated in sockets
in the superior maxillary bones, and not, as was stated by the
Cuviers, in the premaxillse, or partly in the pre- and partly in the
superior maxillae. He then proceeded to relate some further observa-
tions on the dentition of the narwhal, and pointed out, both in the
skull of a young male and in those of three well grown foetuses,
an elongated canal on each side of the upper jaw, parallel and
inferior to the tusk socket, which had the appearance of a socket

760 Proceedings of the Royal Society

for a supplementary tooth, although none protruded from it. In
the young male a minute denticle was seen at the bottom of this
socket.

He then described a dissection he had made of the upper jaw of
a male foetus, 74 inches long, given him by Mr C. W. Peach, in
which, imbedded in the gum on each side, were two well-formed
dental papillae, barely visible to the naked eye. Each papilla was
contained in a well-defined tooth sac. Calcification of the papillae
or of the wall of the tooth sac had not commenced. The minute
structure of these embryonic teeth was next described. The more
anterior of the two papillae was T2oths inch behind the tip of the
jaw, and the more posterior lay about y^th inch behind the
anterior.

No rudimentary teeth were found in the lower jaw.

The formation of bone had only just begun in the fibrous matrix
of the maxillary bones ; hut in the lower jaw a very decided ossifica-
tion of the fibrous membrane investing the cartilage of Meckel had
commenced.

3. On the occurrence of Ziphius cavirostris in the Shetland

Seas, and a comparison of its Skull with that of Sowerby’s
Whale ( Mesoplodon Sowerhyi). By Professor Turner.

This paper contained a brief historical sketch of Ziphius cavi-
rostris. The skull of a specimen caught at sea in 1870, off Hamna
We, Northmaven, Shetland, was then described, and this skull was
compared with previously recorded specimens. A brief historical
sketch of Sowerby’s whale was then given, a skull in the Edinburgh
Museum of Science and Art was described, and reasons were
advanced for associating it with the genus Mesoplodon rather than
with Ziphius.

4. On the Maternal Sinus Vascular System of the Human
Placenta. By Professor Turner.

The author gave a brief sketch of the various theories which
have been advanced by Velpeau, R. Lee, Braxton Hicks, the
Hunters, Owen, Weber, J. Reid, J. Groodsir, Virchow, Kolliker, Van

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Der Kolk, Arthur Farre, and Ercolani regarding to the relations of
the maternal blood-vessels to the placenta and chorionic villi. He
then proceeded to state the results of his own observations on various
specimens of placentae, some of which had been separated at the
full time, others prematurely, and on three specimens attached to
the uterine wall. Two of these latter were from women at or
about the full period of gestation, whilst the third was from a
woman who died undelivered in the sixth month of pregnancy. In
one of the attached specimens a pipe had been introduced into a
uterine vein in the broad ligament, and a coloured gelatine in-
jection had been passed along the venous sinuses in the muscular
wall, and the utero-placental veins into the placenta. The utero-
placental veins were followed through the decidua serotina, and were
seen to pierce the uterine surface of the placenta. The walls of
these veins were so delicate that they tore through on the appli-
cation of very slight force. Thin sections made through the
placenta and the adjacent part of the uterine wall permitted the
author to trace a direct continuity of the injection within the
placenta with that within the utero-placental veins and uterine
sinuses, and showed the one to be continuous with the other. The
injection also passed into veins of considerable size, situated within
the decidua reflexa, near the attached border of the placenta.
In another attached specimen, the intra-placental sinus system
was injected with coloured gelatine from a pipe inserted into one
of the uterine arteries, and the injection of the system of inter-
communicating spaces within the placenta was as readily made as
in the specimen where the injection was passed through the uterine
vein. In the third attached specimen, the injecting pipe was
introduced into the cut face of a section through the placenta itself,
and the intra-placental sinus system was not only distended, but
some of the injection had even entered the utero-placental veins.

Thin sections of the injected placentse had been made and ex-
amined both with low and high powers of the microscope. Draw-
ings, greatly enlarged, of the appearances seen on examining these
sections were shown to the Society, and the author pointed out that
these were to be regarded as actual representations of the objects,
and not, as had previously been almost universally the case, mere
diagrammatic conceptions of what the anatomist might consider to

762 Proceedings of the Royal Society

be the character of the arrangement. The chorionic villi were seen
in these sections to be cut across longitudinally, obliquely, and trans-
versely, and the villi were not in contact with each other by their
surfaces, hut separated by intermediate freely-communicating spaces,
filled with coloured gelatine. These spaces constituted the intra-
placental maternal sinus vascular system. Thin sections examined
with high powers showed multitudes of red-blood corpuscles lying
in the coloured gelatine, which corpuscles had undoubtedly been
in these sinuses before the injection had been passed into them,
and from their position were the corpuscles of the maternal blood.
The ready manner in which the injection flowed into the intra-
placental sinuses, either when passed directly into the placenta,
or through the artery, or through the vein, the regularity and
uniformity of the pattern produced by the injection when set,
and the abundance of blood corpuscles present in the sinuses,
mingled with the injection, seemed to the author to substantiate
the view that these sinuses are a natural system of intercom-
municating spaces for the transmission of the maternal blood
through the interior of the placenta; and not as some have main-
tained, artificially produced by the extravasation of injection from
the uterine vessels into the placenta.

The author then proceeded to describe the structure of the
chorionic villi, to show their relations to the decidua serotina and
the decidual bars which pass into the interior of the placenta, and
to discuss the views which have been advanced, whether the villi
hang naked in the maternal blood, or whether they are invested
either by a prolongation of the lining membrane of the maternal
blood-vessels, or by the cells of the decidua, or by both.

The following Gentleman was admitted a Fellow of the
Society : —

Rev. Hugh Macmillan, LL.D.

of Edinburgh, Session 1871-72.

763

Monday , 3d June 1872.

Professor W. J. MACQTJOBN BANKINE, Vice-President,
in the Chair.

The following Commnnications were read : —

1. On Dimorphic Flowers of Cepliaelis Ipecacuanha , the
Ipecacuan Plant. By Professor Balfour.

I have reported already to the Society (p. 688) the results of the
cultivation of the Ipecacuan plant in the Botanic G-arden, and its
successful propagation by Mr M‘Nab by root-cutting. By this
means it has been sent in considerable quantity to Calcutta, under
the direction of the Secretary of State for India. From the Garden
at Kew, in 1863, a plant was sent out to Dr King, and of late he
has been successful in propagating it by cuttings of the stem above
ground. So that from both sources there seems to be every prospect
of the plant being extensively cultivated in India, the climate of
which in many places is favourable for its growth. The so-called
root of the Ipecacuan may be said to be composed of a sort of under-
ground stem capable of producing leaf-buds, as well as true roots.

I have already stated that the plants in the Botanic Garden have
been derived from two sources, — one from a plant sent by Sir Wm,
Hooker more than 40 years ago, and which he had procured from
Mr M‘Koy of Liege ; the other is from plants sent from Bio
Janeiro by Dr Gunning. There is an apparent difference in the
characters of the plants from these two sources, but not such as to
amount to a specific distinction. Hooker’s plant has flowered
pretty freely, but never produced fruit until last year, when the
pollen was artificially applied from one flower to another. All the
plants from this source have long stamens and short styles.

The plants sent by Dr Gunning have grown well, but it is only
recently that they have flowered, and now there are several speci-
mens in flower, and some are fruiting after artificial impregnation.
In this series of plants there are evident dimorphic flowers. In
some the stamens are long and the style is short ; while in others
the style is long, projecting much beyond the corolla, while the
stamens are short.

764 Proceedings of the Royal Society

It would appear that successful fertilisation may be effected by
applying the pollen from the long stamens to the stigma of the
long styles.

The partial fruiting which took place in the heads of flowers in
the Hookerian plants may have depended on the fact that there
were only produced flowers with long stamens and short styles, and
although when pollen was applied from one flower to another
fertilisation was effected, still it was by no means fully successful,
only two or three of the flowers in the head producing fruit. The
flowers are sweet-scented with a delicate odour.

One of the largest plants has the following dimensions : —

Height of plant, .... 12^- inches.

Length of leaves, . . 5 „

Breadth of leaves, . . .2 ,,

Peduncle (length), ... 1 inch

Greatest circumference of stem, . ,,

2. On the Crinoids of the “ Porcupine ” Deep-Sea Dredging
Expedition. By Professor Wyville Thomson.

Seven species belonging to the Echinoderm order Crinoidea,
were procured during the “ Porcupine ” dredging expeditions of
1869 and 70. Pour of these belong to the free section of the order,
and are referred to the genus Antedon.

1. A. escrichtii , J. Muller.

This fine species is abundant off the coast of Greenland, but so far
as I am aware, it does not occur in the seas of Scandinavia.
Several hauls of the dredge in the cold area in the channel between
Scotland and Faeroe, yielded many examples, the largest of which,
however, fell somewhat short of the dimensions of the largest
specimens from Greenland. Antedon escrichtii was associated in
the Faeroe channel with Ctenodiscus crispatus , an Asteridean which
had been met with previously only in the Greenland seas. A
single example of a pentacrinoid in an early stage was found
associated with Antedon escrichtii. It resembled closely the larva
of Antedon sarsii, but the specimen was not sufficiently perfect for
a critical examination.

765

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2. A. sarsii, Duben and Koren.

More or less complete specimens or fragments of this widely-

distributed species came up in nearly every one of the deep hauls
of the dredge, from the Faeroe Islands to Gibraltar. One or two
small examples of the pentacrinoid were procured in the Faeroe
Channel.

3. A. rosaceus , Linck.

Frequent in water of moderate depth. Many examples of the
form known to continental naturalists under the name of A.
mediterraneus , Lam. sp., were dredged in the Mediterranean off the
coast of Africa. I do not feel satisfied that this is identical with
Antedon rosaceus of the coast of Britain, although the two specific-
names are usually regarded as synonyms. There is a great
difference between them in habit ; a difference which it is difficult
to define.

4. A. celticus , Barrett.

This species, which is at once distinguished by the extreme
length of the dorsal cirri, is abundant at depths of 40 to 60 fathoms
in the Minch, and we also met with it in local patches to 150
fathoms off the north coast of Scotland.

The remaining three Crinoids belong to the section of the Order
which are permanently stalked. Two of the three are new to
science, and the third was discovered in the year 1864 by G-. 0.
Sars, in the deep water off the Loffoden Islands.

Up to the present time two recent species have been described
belonging to the Family Pentacrinid^e. Both of these were known
only from the deep water of the seas of the Antilles. Since the
discovery of the first of these in the year 1755, they have been
regarded with special interest, both on account of their great
beauty, and of the singular relation which they bear to some of the
most abundant and characteristic fossils of the palaeozoic and
mezozoic formations.

Pentacrinus asteria , L , the species first described by Guettard,
and afterwards very carefully worked out by Johannes Muller, has
a stem sometimes nearly a metre in length consisting of a multitude
of discoidal joints about every seventeenth of which bears a
circle of five long cirri which spread out rigidly and abruptly

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VOE. vri.

766 Proceedings of the Royal Society

from the joint, turning down hooklike towards the tips. Each
cirrus consists of about 36 joints. The nodal joint, that is to say
the joint modified for the insertion of the cirri, is single; but it is
united to the joint beneath by a peculiar suture with much of the
character of a syzygy, Most of the examples of P. asteria which
have reached Europe have had the stem recently broken. In one
however in my possession, the stem, which is unusually short, had
evidently given way at one of these joints long before the death of
the animal, for the surface of the terminal joint is smoothed and
rounded, and the terminal row of cirri are curved over it. This
example, at all events, must have lived for some time free.

In Pentacrinus asteria , the basal plates of the cup project like
small round buttons over the ends of the salient angles of the first
stem joint. The first radials are connected with the second radials
by a true joint with muscles and ligaments, and the second radial is
united to the radial axillary by a syzygy. There are from 70 to 120
pinnated arms. There is constantly a syzygy on each branch at the
first joint beyond each bifurcation, but there are few syzygies on
the arms after their last bifurcation, although in some specimens
one is met with here and there.

All the examples of P. asteria in European museums have lost the
soft parts and the disk; but I have one example which is com-
plete. The mouth is central, and five radial grooves pass from the
edge of the mouth-opening to the proximal ends of the arms, and
become continuous with the brachial grooves, dividing with each
bifurcation. The perisom of the disk is covered with irregular
calcareous plates, and at the free inner angles of the interradial
spaces these plates become closer, and form a solid kind of boss ;
but there are no distinct oral plates. A rather long anal tube
occupies the centre of one of the interradial spaces.

Pentacrinus mulleri , CErstedt, seems to be more common than P.
asteria especially off the Danish West Indian Islands. The whole
animal is more delicate in form. The stem attains nearly the
same height, but is more slender. The nodes occur about every
twelfth joint and at every node two stem-joints are modified. The
upper joint bears the facets for the insertion of the cirri, and the
second is grooved to receive the thick basal portions of the cirri,
which bend downwards for a little way closely adpressed to the

767

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stem before becoming free. The cirri are much shorter than in
P. asteria. The syzygy is between the two modified joints. In
all complete specimens which I have seen, the stem has evidently
been separated for long at one of these syzygies. I described some
years ago a specimen in which this was the case, and suggested
that in that instance the animal had lived for some time free.
I have since seen several other examples in the same condition,
and I believe that the disengagement at a certain stage of growth
is habitual. The arrangement of the joints and syzygies in the cup
is the same in P. mulleri as in P. asteria , only the syzygy between
the second radial and the radial axillary is not so complete. The
arms are more delicate, and appear never to exceed thirty in num-
ber. The number of syzygies is very variable; sometimes they are
confined, as in P. asteria, to the first joint after a bifurcation, and
sometimes they occur at intervals all along the arms. The struc-
ture of the disk is the same as in P. asteria , but its texture is more
delicate, and the calcareous pieces are smaller and more distant.

On the 21st of July 1870, Mr Gwyn Jeffreys, dredging from
the <{ Porcupine,” at a depth of 1095 fathoms, latitude 39° 42' N.
long. 9° 43' W., with a bottom temperature of 4°-3 0., took about
twenty specimens of a handsome Pentacrinus involved in the
hempen tangles attached to the dredge.

1. P. wyville-thomsoni , Jeffreys.

This species is intermediate in some of its characters between
P. asteria and P. mulleri , it approaches the latter however most
nearly. In a mature specimen the stem is about 120 mm. in
length and consists of five to six internodes. The whorls of cirri
towards the lower part of the stem are 40 mm. apart, and the
internodes consist of from thirty to thirty-five joints. The cirri
are rather short, and stand out straight from the nodal joint
or curve slightly downwards. There are usually eighteen joints
in the cirri, the last forming a sharp claw. As in P. asteria
the nodal joint is single, and a syzygy separates it from the
joint immediately beneath it which does not differ materially in
form from the ordinary internodal stem-joints. All the stems of
mature examples of this species end inferiorly in a nodal joint
surrounded by its whorl of cirri, which curve downwards into a

768 Proceedings of the Royal Society

kind of grappling root. The lower surface of the terminal joint
is in all smoothed and rounded, evidently by absorption, showing
that the animal has long been free. This character I have
already noted as occurring in some specimens of P. mulleri and
in one at least of P. asteria. I have no doubt whatever that it is
constant in the present species, and that the animal lives loosely
rooted in the soft mud, and may change its place at pleasure
by swimming with its pinnated arms : that it is, in fact, interme-
diate in this respect between the free species of Antedon and
the permanently rooted fossil crinoids.

A young specimen of P. wyville-thomsoni gives the mode in
which this freedom is acquired. The total length of this specimen
is 95 mm., of which the head occupies 35 mm. The stem is
broken off in the middle of the eighth internode from the head.
The lowest complete internode consists of 14 joints, the next
of 18, the next of 20, and the next of 26 joints. There are
8 joints in the cirri of the lowest whorl, 10 in those of the
second ; 12 in those of the third, and 14 in those of the fourth.
This is the reverse of the condition in adult specimens, in all
of which the numbers of joints in the internodes, and of joints
in the cirri, decrease regularly from below upwards. The broken
internode in the young example and the three internodes above
it are atrophied and undeveloped ; and suddenly at the third node
from the head the stem increases in thickness and looks as if
it were fully nourished. There can be no doubt that in early life
the Crinoid is attached, and that it becomes disengaged by the
withering of the lower part of the stem.

The structure of the cup is the same as in P. asteria and P.
mulleri. The basals appear in the form of shield -like projections
crowning the salient angles of the stem. Alternating with
these we have well-developed first radials forming a closed ring
and articulating to free second radials by muscular joints. The
second radials are united by a syzygy to the radial axillaries,
which as usual give off each two first brachials from their bevelled
sides. A second brachial is united by syzygy to the first, and
normally this second brachial is an axillary, and gives off two
simple arms ; sometimes, however, the radial axillary originates
a simple arm only from one or both of its sides, thus reducing the

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total number of the arms, and sometimes one of the four arms
given off from the brachial axillaries again divides, in which case
the total number of arms is increased. The structure of the disk
is much the same as in the species of the genus previously known.

The Apiocrinid^: to which the remaining two fixed Crinoids
must be referred, differ from all other sections of the order in the
structure of the upper part of the stem. At a certain point consi-
derably below the crown of arms the joints of the stem widen
by the greater development of the calcified ring, the central cavity
scarcely increasing in width. The widening of the stem-joint
increases upwards until a pyriform body is produced, usually very
elegant in form, in which one would suppose looking at the out-
side that the viscera were lodged. It is, however, nothing more
than a symmetrical thickening of the stem, and the body cavity
occupies a shallow depression in the top of it inclosed within the
plates of the cup ; the basals and radials are much thicker and
more fully calcified than in other crinoids, but they are normally
arranged.

The stem is usually long and simple, until near the base, where
it forms some means of attachment; either as in the celebrated
pear encrinites of the forest-marble, a complicated arrangement of
concentric layers of cement which fix it firmly to some foreign
body ; or as in the chalk Bourguetticrinus and in the recent Bhizo-
crinus , an irregular series of jointed branching cirri.

The Apiocrinim: attained their maximum during the Jurassic
period, where they are represented by numerous and fine species
of the genera Apiocrinus and Millericrinus. The chalk genus
Bourguetticrinus shows many symptoms of degeneracy. The head
is small, and the arms are small and short. The arm joints are so
minute that it is difficult to make up anything like a complete
series from the separate fragments scattered through the chalk in
the neighbourhood of a cluster of heads. The stem, on the other
hand, is disproportionately large and long, and one is led to suspect
that the animal was nourished chiefly by the general surface absorp-
tion of organic matter, and that the head and special assimilative
organs are principally concerned in the function of reproduction.
The genus Rhizocrinus possesses all the essential characters of
the family.

770

Proceedings of the Royal Society
1. R. lofotensis , M. Sars.

This species was discovered in the year 1864, at a depth of about
300 fathoms, off the Loffoden Islands, by Gr. 0. Sars, a son of
the celebrated Professor of Natural History in the Uuiversity
of Christiania; and it was described in detail by the latter in the
year 1868. It is evidently a form of the Apiocrinidee still more
degraded than Bourguetticrinus, which it closely resembles. The
stem is long and of considerable thickness in proportion to the
size of the head. The joints of the stem are individually long
and dice-box shaped, and between the joints spaces are left on
either side of the stem alternately, as in Bourguetticrinus , and in
the pentacrinoid of Antedon for the insertion of fascicles of con-
tractile fibres. Towards the base of the stem branches spring from
the upper part of the joints ; and these, each composed of a suc-
cession of gradually diminishing joints, divide and re-divide into a
bunch of fibres which expand at the ends into thin calcareous
laminae, clinging to small pieces of shell, grains of sand — anything
which may improve the anchorage of the crinoid in the soft mud
which is nearly universal at great depths.

In Bhizocrinus the basal series of plates of the cup are not dis-
tinguishable. They are masked in a closed ring at the top of the
stem, and whether the ring be composed of the fused basals alone,
or of an upper stem-joint with the basals within it forming a
“ rosette ” as in the calyx of Antedon , is a question which can
only be solved by a careful tracing of successive stages of develop-
ment. The first radials are likewise fused,, and form the upper wider
portion of the funnel-shaped calyx The first radials are deeply
excavated above for the insertion of the muscles and ligaments
which unite them to the second radials by a true (or moveable)
joint. One of the most remarkable points in connection with this
species is, that the first radials, the first joints of the arm, are
variable in number, some examples having four rays, some five, some
six, and a very small number seven in the following proportions.
Out of seventy-five specimens examined by Sars, there were —

15 with 4 arms.

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of Edinburgh, Session 1871-72.

This variability in so important a character, particularly when
associated with so great a preponderance in bulk of the vegetative
over the more specially animal parts of the organism, must un-
doubtedly be accepted as indicating a deterioration from the
symmetry and compactness of the Apiocrinidse of the Jurassic
period.

The anchylosed ring of first radials is succeeded by a tier of free
second radials, which are united by a straight syzygial suture to
the next series — the radial axillaries. The surface of the funnel-
shaped dilation of the stem, headed by the ring of first radials, is
smooth and uniform, and the second radials and radial axillaries
present a smooth regularly arched outer surface. The radial
axillaries differ from the corresponding joints in most other known
crinoids in contracting slightly above, presenting only one arti-
culating facet, and giving origin to a single arm. The arms, which
in the larger specimens are from 10 to 12 mm. in length, consist of
a series of from about twenty-eight to thirty-four joints, uniformly
transversely arched externally, and deeply grooved within to
receive the soft parts. Each alternate joint bears a pinnule
alternating on either side of the axis of the arm, and the joint
which does not bear a pinnule is united to the pinnule-bearing
joint above it by a syzygy : thus joints with muscular connections
and syzygies alternate throughout the whole length of the arm.

The pinnules, twelve to fourteen in number, consist of a uniform
series of minute joints united by muscular connections. The grooves
of the arm and of the pinnules are bordered by a double series of
delicate round fenestrated calcareous plates, which, when the animal
is contracted and at rest, form a closely imbricated covering to the
nerve and the radial vessel with its delicate cmcal tentacles. The
mouth is placed in the centre of the disk, and radial canals, equal
in number to the number of arms, pass across the disk, and are
continuous with the arm grooves. The mouth is surrounded by a
row of flexible cirri arranged nearly as in the pentacrinoid of
Antedon , and is provided with five oval calcareous valve-like plates
occupying the interradial angles, and closing over the mouth at
will. A low papilla in one of the interradial species indicates the
position of the minute excretory orifice.

Bhizocrinus lofotensis is a very interesting addition to the British

772 Proceedings of the Royal Society

Fauna. We met with it in the Faeroe Channel in the year 1869, —
three examples, greatly mutilated, at a depth of 530 feet, with a
bottom temperature of 60,4 C. Station 12 (1868) — Several occurred
attached to the beards of Holtenice off the Butt of the Lews,
and specimens of considerably greater size were dredged in 862
fathoms off Cape Clear. The range of this species is evidently very
wide. It has been dredged by G. 0. Sars off the north of Norway;
by Count Pourtales, in the Gulf-stream off the coast of Florida ; by
the naturalists on board the u Josephine” on the “ Josephine Bank”
near the entrance of the Strait of Gibralter; and by ourselves
between Shetland and Faeroe, and off Ushant and Cape Clear.

The Genus Bathycrinus (n. g.) must also apparently be re-
ferred to the Apiocrinid^!, since the lower portion of the head
consists of a gradually expanding funnel-shaped piece, which seems
to be composed of coalesced upper stem-joints.

1. B. gracilis (n. sp.).

The stem is long and delicate, in one example of a stem alone,
which came up in the same haul with the one perfect example
which was procured, it was 90 mm. in length. The joints are
dice-box shaped as in Rliizocrinus , long and delicate, towards the
lower part of the stem 3*0 mm. in length by 0-5 mm. in width in
the centre, the ends expanding to a width of 1*0 mm. As in
Rhizocrinus , the joints of the stem diminish in length towards
the head, and additions are made in the form of calcareous laminse
beneath the coalesced joints which form the base of the cup.

The first radials are five in number. They are closely opposed,
but they do not seem to be fused as in Rliizocrinus , as the sutures
show quite distinctly. The centre of each of the first radials
rises into a sharp keel, while the sides are slightly depressed
towards the sutures, which gives the calyx a fluted appearance,
like a folded filter paper. The second radials are long and free
from one another, joining the radial axillaries by a straight
syzygial union. They are most peculiar in form. A strong
plate-like keel runs down the centre of the outer surface, and the
joint is deeply excavated on either side, rising again slightly
towards the edges. The radial axillary shows a continuation of
the same keel through its lower half, and midway up the joint the

773

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keel bifurcates, leaving a very characteristic diamond-shaped space
in the centre towards the top of the joint. Two facets are thus
formed for the insertion of two first radials. The number of arms
is therefore ten. The arms are perfectly simple, and in our single
specimen consist of twelve joints each. There is no trace of
pinnules, and the arms resemble in character the pinnules of Rhizo-
crinus. The first brachial is united to the second by a syzygial
joint, but after that the syzygies are not repeated, so that there is
only one of these peculiar junctions in each arm. The arm-grooves
are bordered by circular fenestrated plates as in Rliizocrinus.

Certain marked resemblances in the structure of the stem, in the
structure of the base of the cup, and in the form and arrangement
of the ultimate parts of the arms, evidently associate Bathycrinus
with Rliizocrinus; but the differences are very wide. Five free
keeled and sculptured first radials replace the uniform smooth ring
formed by these plates in Rliizocrinus. The radial axillaries give
off each two arms, thus recurring to the more usual arrangement
in the order, and the alternate syzygies on the arms, which form so
remarkable a character in Rliizocrinus , are absent.

Only one nearly complete specimen and a detached stem of this
very remarkable species were met with, and they were both brought
up from the very greatest depth which has as yet been reached
with the dredge, 2435 fathoms, at the mouth of the Bay of Biscay,
200 miles south of Cape Clear.

3. Laboratory Notes. By Professor Tait.

1. On Thermo-electricity: Circuits with more than one Neutral
Point. (With a Plate.)

Having lately obtained from Messrs Johnson & Matthey some
wires of platinum, and of alloys of platinum and iridium, I formed
them into circuits with iron wire of commerce ; and noticed that
with all, excepting what is called “ soft ” platinum, there is more
than one neutral point situated below the temperature of low white
heat, and that at higher temperatures other neutral points occur.
This observation is, in itself, highly interesting ; but my first im-
pression was one of disappointment, as I imagined it depended on
some peculiarity of the platinum metals, which I had hoped would

5 K

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774 Proceedings of the Royal Society

furnish me with the means of accurately measuring high temper-
atures (by a process described in previous notes of this series). As
this hope may possibly not be realised, I can as yet make only
rough approximations to an estimation of the temperatures of these
neutral points.

So far as I am aware, the phenomenon discovered by Cum-
ming and analysed by Thomson has hitherto been described
thus : When the temperature of the cold junction is below the
neutral point, the gradual raising of the temperature of the
other produces a current which increases in intensity till
the neutral point is reached, thenceforth diminishes; vanishes
when one junction is about as much above the neutral point
as the other is below it, and is reversed with gradually in-
creasing intensity as the hot junction is farther heated. To
discover how my recent observation affects this statement, I first
simply heated one junction of a circuit of iron and (hard) platinum
gradually to whiteness, by means of a blowpipe, and observed the
indications of a galvanometer — both during the heating and during
the subsequent cooling when the flame was withdrawn. The heat-
ing could obviously not be effected at all so uniformly as the
cooling; but, making allowance for this, the effects occurred in
the opposite order, and very nearly at the same points of the scale
in the descent and in the ascent. [I have noticed a gradual dis-
placement of the neutral points when the junction was heated and
cooled several times in rapid succession ; hut as my galvanometer,
though it comes very quickly to rest, is not quite a dead-heat
instrument, I shall not farther advert to this point till I have made
experiments with an instrument of this more perfect kind, which
is now being constructed for me.] The observed effect of heating,
then, was a rise from zero to 110 scale divisions when the higher
temperature was that of the first neutral point, then descent to 95
at a second neutral point, then ascent to a third, descent to a
fourth, neither of which could be at all accurately observed, and
finally ascent until the junction was fused.

With an alloy of 15 per cent, iridium and 85 per cent, platinum,
the galvanometer rose to 53’5 at a neutral point, then fell to — 50
at a second, then rose to a third at — 39’5, and thence fell, but I
could not observe a possible fourth neutral point on account of the

of Edinburgh, Session 1871-72. 775

fusion of the iron. As shown on the plate, the first of these occurs
at about 240° 0. of a mercurial thermometer.

With another alloy supposed to be of the same metals, but of
which I do not yet know the composition, also made into a junction
with iron, the behaviour was nearly the same, but the readings at
the successive neutral points were 28, - 137, - 132. The tempera-
ture of the first is about 200° 0. by mercurial thermometer.

An iron-palladium circuit showed no neutral points within the
great range of temperatures mentioned above ; though it showed
a remarkable peculiarity which must be more closely studied, as it
appears to point to the cause of the above effects in a property of
iron. It was therefore employed to give (very roughly) an indica-
tion of the actual temperatures in these experiments. But as for
this purpose it is necessary to measure the simultaneous indica-
tions of two circuits whose hot and whose cold junctions are respec-
tively at the same temperatures, I was obliged to employ a steadier
source of heat than the naked flame. I therefore immersed the hot
junctions in an iron crucible containing borax glass, subsequently
exchanged for a mixture of fused carbonate of soda and carbonate
of potash; but, to my surprise, the former of these substances at a
red heat disintegrated both the platinum and the alloy, and thus
broke both circuits without sensibly acting on the iron, while the
mixture (evidently by the powerful currents discovered by Andrews,
Phil. Mag. 1837) interfered greatly with the indications of the
thermo-electric circuit, as will be seen by the dotted curve in the
plate. [I may remark here that the deviations of this curve from
its form when these currents are prevented are quite easily observed
and plotted by the process next to be mentioned, sq that the study
of the Andrews’ effect may be carried out with great accuracy by my
method.] Finally, determining to dispense altogether with fused
salts, which conduct too well besides acting on the metals, I simply
suspended a red-hot bombshell, vent downwards, in such a way that
the hot junction was near its centre. This arrangement worked
admirably, until a white heat was required, for this melted the
shell. In its place a wrought iron tube (an inch in bore, four
inches long, half an inch thick, and closed at the upper end) has
been substituted and answers excellently. It does not cool too fast
for accurate reading at the higher temperatures, and by elevating

776 Proceedings of the Royal Society

it by degrees from over the hot junction we can make the cooling
fast enough at the lower ranges. In fact, I believe that if I do
not succeed in getting a sufficient number of practically infusible
metals to construct my proposed thermometric arrangement, I may
be able to make a fair approximation to temperatures by simple
time observations made with the hot tube, surrounded by some
very bad conductor, such as sand, where the surface in contact
with the air is always comparatively cool, and where therefore we
can accurately calculate the rate of cooling.

Curves I., II., III., in the plate were drawn by means of this
apparatus. The hot junction consisted of an iron wire, a palladium
wire, and (for the several curves in order) — I. Hard platinum;
II. Pt 85, Ir 15 ; III. The other alloy of Pt and Ir. The free
ends of the palladium wire, and of the platinum or alloy, were
joined to iron wires, and the junctions immersed in test-tubes filled
with water resting side by side in a large vessel of cold water.
The other ends of these three iron wires, and the wires of the
galvanometer, were led to a sort of switch, by means of which
either circuit could be instantly made to include the galvanometer.
Readings were taken of each circuit as fast after one another as
possible (with the galvanometer I employed about 6 '5 seconds was
the necessary interval), and the mean of two successive readings of
one circuit was taken as being at the same temperature as that of
the intermediate reading of the other.

The indications of these curves are very curious as regards the
effect of even small impurities on the thermo-electric relations of
some metals. It is probable, from analogy, that the curve for iron
and 'pure platinum, in terms of temperature, would be (approxi-
mately, at least ; even if it should be the iron, and not the platinum
metal, which is represented by a broken or curved line) a parabola
with a very distant vertex. And it appears probable that when
the wire of curve III. is analysed it will be found to contain even
a larger percentage of iridium (?) than that of curve II.

I find, by tracing these curves on ground glass, allowing for the
difference between temperatures and the indications of an Fe-Pd
circuit, and superposing them on a nest of parabolas with a com-
mon vertex and axis, that they can be closely represented by suc-
cessive portions of different parabolas (with parallel axes) whose

r

of Edinburgh^ Session 1871-72.

777

tangents coincide at the points of junction, though the curvature
is necessarily not continuous from one to the other. Hence, as at
least a fair approximation to the electro-motive force in. terms of
difference of temperature in the junctions, we may assume a para-
bolic function, which up to a certain temperature belongs to one
parabola, then changes to another without discontinuity of direc-
tion, and so on.

Hence either the iron, or the hard platinum and the platinum -
iridium alloys, will be (approximately, at least) represented on my
form of Thomson’s thermo-electric diagram ( ante p. 601) by broken
lines, of which the successive parts are straight. This, contrasted
with the (at least nearly) straight lines for pure metals, seems
to show that some bodies take successively different states ( i.e .,
become different substances ) at certain u critical ” temperatures, re-
taining their thermo-electric properties nearly unchanged from one
of those critical points to another.

The curve marked IV. in the figure was obtained by plotting
against each other the simultaneous indications of the alloy of curve
III. and iron, and of the alloy of curve II. and iron, so as to avoid
any disturbance from possible peculiarities of palladium. Then, to
obtain an idea of the share taken by iron in the results, it was found
that the electro-motive force in a circuit formed by the two alloys,
or by either with hard Pt, is (for a very great range of temperature)
sensibly proportional to the temperature difference of the junctions.

The same result is easily seen from the plate, if we notice that
the difference of corresponding ordinates in any two of curves I.,
II., III., is nearly proportional to the corresponding abscissa. Now,
it seems a less harsh supposition that the lines representing pla-
tinum and its alloys are nearly straight and parallel, while that of
iron is a broken line, than that the latter should be straight and
the former all broken at the same temperatures. On the other
hand, this latter hypothesis would make k alternately negative and
positive in iron, while the former would only require the platinum
metals to have values of k alternately less and more negative than
that of iron.

1 may add that none of the above-mentioned effects can be due
to altered electric resistance of the heated junctions, because the
galvanometer resistance was about 23 B. A. units, while that of the

778

Proceedings of the Royal Society

iron and platinum wires together was in each case not more than
one such unit. The palladium-iron circuit was so much more
powerful than the others that a resistance coil of about 146 B. A.
units had to be inserted in its course.

Assuming, for a moment, that, as above suggested as at least
approximately true, in one of the wires we have cr — kxt up to
the temperature tv cr = k.2t up to temperature t.2, &c., we have by
the two equations of thermo-dynamics —

e = j(sn + sry^+vv*)

»- +si C"?*-

Now, if both junctions be under tx , and if cr = kt for the other wire,

8E = J (8n -{- kx - ktSf)

0 = 8— + (kx - k)8t ,

and we have as before, t0 being temperature of cold junction,

?■-(*!-*)( T-0
E = - ^1°).

But from tx to t2 we have

5 =

Now, at t - tx these formulas must agree, so that

C = ft - <„) {ft, - *) T, - (4, - 4) T - (4, - 4j) ,

whence

rp _ (&2 — 4- (&J — &)T

1 h2-k

0 = 0,- Oft, - 4,)( t, - ^ ) = 1(4,* 40ft - 0*.

and

779

of Edinburgh, Session 1871-72.

I reserve farther developments of this subject until I have made
a sufficient number of experiments with both junctions at high
temperatures,, particularly when these are two of the series of
neutral points ; and especially until I mana'ge to settle, by one at
least of several processes which have occurred to me, whether the
multiple neutral points depend upon peculiarities in the behaviour
of the iron, or of the platinum, or of both.

[Added during 'printing. — I have since made out that the lines
of the diagram are approximately straight, and parallel to the lead
line, for the platinum metals, that of hard platinum being below the
lead line, while those of most of the other alloys are above it, and
that the multiple neutral points depend upon the peculiar sinuosity
of the line for iron. I have also obtained curious results of a some-
what similar kind with steel wire. The method I employed was
to^explore the part of the thermo-electric diagram included between
the lines of gold and palladium, by making a multiple arc of these
two metals, and varying the ratio of their separate resistances. But
I reserve details until I have carefully examined the behaviour of
nearly pure iron.]

2. On a Method of Exhibiting the Sympathy of Pendulums.

While making some magnetic experiments lately with Mr Fox
Talbot, I happened to notice that two equal rectangular pieces of
tin plate, when standing nearly parallel to one another on the pole
of a large electromagnet, acted on one another so that a vibration
communicated to either was in a few seconds handed over to the
other, and vice versa.

The definiteness of the result led me to try the experiment with
ordinary bar magnets. Taking two large magnetised bars of almost
exactly equal mass, I suspended them with their axes in the same
horizontal line, so that their (small) vibrations were executed in
that line, their undisturbed periods being very nearly equal, and
the distance between them (when at rest) so small compared with
their lengths, that we need consider only the magnetic action of
the two poles nearest together. With this apparatus the transfer
of energy from one pendulum to the other is most beautifully
exhibited, for if one only be in motion at starting, the magnets

780 Proceedings of the Royal Society

alternately come sharply to rest at successive equal intervals of
time. This arrangement makes an excellent and instructive class
experiment, and its value may be greatly increased by placing round
the exterior end of one of the magnets a vertical coil of copper -
wire connected with a distant galvanometer. The nature of the
motion of this magnet at any instant is readily deciphered from
the signals given by the reflected light on the galvanometer scale,
which is also visible to the whole class. A more complex, hut
with practice easily intelligible, signal is given by placing the coil
round the contiguous ends of the magnets.

The extension of this arrangement to three, four, and more equal
magnets, all vibrating in one line, and of nearly equal mass,
magnetic power, and (independent) period is of course obvious, and
forms a beautiful mechanical illustration of the solution of a differen-
tial equation.

In thinking how most simply to explain such results to an
elementary class, I was led to the following, which can hardly he
new, though I have never met with it, but which is certainly not
as well known as it ought to be. Take first the case of the two
equal magnets.

Since there are but two moving parts of the system, and each
has but one degree of freedom, it is obvious that if we can find two
different forms of motion of the system which, once established,
will persist for ever, any motion whatever of the system must he a
mere superposition of these two modes with arbitrary amplitudes
and epochs. Now, one such mode is obviously the motion of the
pendulums as one piece at their equilibrium distance from one
another. As the magnetic force does not vary during this motion,
the time of vibration is that of either pendulum when left to itself.
The other fundamental mode is that in which the centre of inertia
of the two remains fixed, i.e ., the simultaneous displacements of
the two magnets are equal and in opposite directions. The time
of small oscillations now will evidently be the same as if one of the
magnets were held fixed and its magnetic strength doubled. It
will, therefore, be shorter or longer than the former period, according
as the poles presented to one another attract or repel, and its
actual value is easily calculated. Hence, as these small motions
separately can be represented by expressions such as cos ( mt + c),

of Edinburgh, Session 1871-72.

781

cos ( m't + e7); the period of any complex vibration is , and

therefore at intervals of — ■ the configuration of the magnets

will be the same to a spectator who changes the side from which
he regards them in successive such intervals. Thus, if one magnet
was originally at rest, the two will alternately be reduced to rest.

When there are three equal magnets, it is easy to see that one
fundamental mode is a swing of the whole as one piece, a second
(if we suppose like or unlike poles adjacent to each other at each
gap) is the middle magnet and the centre of inertia of the other
two fixed, and the third has also the centre of inertia fixed, but the
two extreme magnets are at each instant equally deflected in the
same direction, while the middle one has a double deflection to the
opposite side. It is troublesome, but not difficult, to think out the
fundamental modes for four and even far five magnets ; hut it would
be a waste of time to try it in that way for more.

Generally if xr denote the displacement at time t of the rth
magnet, and if we assume the masses, magnetisation, and gaps to be
equal, we have

xr + n2xr = fx + ^ “ (_a + Xr+1 _ Xry^

= ^ (xr- 1 + Xr+1 - 2av) ,

except for the ends of the series where r- 1, and r = m, the number
of magnets.

Hence, multiplying by \r and adding, we have

where

£ + = 0 ,

€ = % A rxr

It will be sufficient to work this out for three magnets. Here, if

we put -^-5 = e , we have
war

o L

VOL. VII.

782

Proceedings of the Royal Society

^ = — 2, or \ = A3, besides A2 = -0;
A, A,

whence

l2

-1 e

. /V2

= 1 , or - 2 , or 0 .

Thus jf = n 2, or w2(l + 3e), or n2(l + e). There is no farther
difficulty in applying the method to magnets of different masses or
magnetic strengths ; but it is interesting to observe that, by pro-
perly adjusting the gaps in terms of the masses and magnetisation
of the bars, any set of magnets whatever can be brought to behave
(for small oscillations) as if they were in all respects equal to each
other and arranged at equal distances.

When there is an infinite series of magnets arranged in this way
the equation above may be written

where

, D*r = ®r + i,

of which the general integral is easily found.

When the number of magnets (m) is finite, and they are arranged
in a closed curve, we have the conditional equation

In this case the general solution may be elegantly expressed in
terms of the mth roots of unity. It leads to some curious proper-
ties of determinants, whose development will form an excellent
exercise for the student. Thus, writing in succession 1 , 2 , ...., m
for r ; and putting

(Dm - 1 )xr = 0.

of Edinburgh , Session 1871-72. 783

the first of the above equations gives, by the help of the second,
after the elimination of the displacements

l - 2
1

1

1

1-2 1
1 1-2 1

&c.

1

1 - 0.

-2 1
1 1-2

This is a particular case of the determinant,

p q r s

2 p q r

y z p q

* P 2

y z p

which, equated to zero, gives the result of elimination of 6 between
the equations

p + q0 + r6* + + zdm~1 = 0,

er - 1 = 0.

Its factors are obviously to be found by substituting in succession
the several mth roots of unity in the expression

p + qO + + z6m~1 .

The form of its minors, on which depends the solution of the pen-
dulum question, follows easily from these properties; and from
them we in turn easily obtain the value of the same determinant
when bordered, as it will be in the pendulum case if the series of
magnets be finite and not closed. The question forms a very in-
teresting illustration of the linear propagation of disturbances in a
medium consisting of discrete, massive, particles — when only con
tiguous ones act on one another. For, if we put

d_

D = ea dv >

784 Proceedings of the Royal Society

and alter the value of //,, we have by taking a small,

[©■— £)■]—>

which, with n = 0 , is the usual equation for sound, provided the
particles repel one another. Of course we can easily extend the
investigation so as to include the more complex cases where the
mutual actions of all the poles are taken into account. The result
is not altered in form ; but it might he curious to inquire whether
the retention of n2 in the equation might not give some hints as to
the formation of a dynamical hypothesis of the action of transparent
solids on the luminiferous ether. This, however, I cannot enter
upon at present.

4. On Some Quaternion Integrals. Part II. By Professor
Tait.

(Abstract.)

Commencing afresh with the fundamental integral

ffS.Vrds = ffS.l Jvrds,
put

cr = u/3

and we have

fff( S . p V) uds =Jfu S . PVv ds ;
from which at once

fjf^7uds=fruVvds, . . . (a),

or

fff'VTds=ffVv.Tds. . . . (V).

Putting uxt for t, and taking the scalar, we have

fff (S (rV) . uL + ux S . Vt) ds — ff rqS . Uvt ds

whence

^'(SQV) <3~+ <rS . Vt) ds = ff <r S . Uvt ds . . (c).

As one example of the important results derived from these
simple formulae, I take in this abstract the following, viz. : —
jUTY.(J.<r Ui/) rds -#cr~S . Uvr ds - /fVv S . <rrds ,

of Edinburgh, Session 1871-72. 785

where by (c) and (a) we see that the right hand member may be
written

= #(S • (tV) . Vr - VS . cnr) ds

= -ffV- V(v<r)rds (d).

This, and similar formulas, are applied in the paper to find the
potential and vector-force due to various distributions of magnetism.
To show how this is introduced, I briefly sketch the mode of ex-
pressing the potential of a distribution.

Let cr be the vector expressing the direction and intensity of
magnetisation, per unit of volume, at the element d$. Then if the
magnet be placed in a field of magnetic force whose potential is u,
we have for its potential energy

E = - fj] ${cr^uds

= JJf u$(ycr)d<s - Jf u$. Vivcrds .

This shows at once that the magnetism may be resolved into a
volume-density S(V<r), and a surface-density -S.Uvo~. Hence,
for a solenoidal distribution,

S. = 0.

What Thomson has called a lamellar distribution {Phil. Trans.
1852), obviously requires that

S . erdp

be integrable without a factor; Le., that

Y . V<r~ = 0.

A complex lamellar distribution requires that the same expression
be integrable by the aid of a factor. If this be u} we have at once

Y . V{ucr ) = 0,
or

S . <rVc t - 0.

786 Proceedings of the Royal Society

With these preliminaries we see at once that (d) may be written

f/YfY.crVvfds = -Jjpr.TV.Vcrds -JjfY.^rds +#SaV.«fe.

Now, if r — V^^, where r is the distance between any external

point and the element d<s , the last term on the right is the vector-
force exerted by the magnet on a unit pole placed at the point.
The second term on the right vanishes by Laplace’s equation, and
the first vanishes as above if the distribution of magnetism be
lamellar, thus giving Thomson’s result in the form of a surface
integral.

Another of the applications made is to Ampere’s Directrice de
V action electrodynamique , which ( Quarterly Math. Journal , Jan.
1860) is the vector-integral

f Ypdp

J iy ’

where dp is an element of a closed circuit, and the integration
extends round the circuit. This leads again to the consideration
of relations between single and double integrals.

[Here it may be well to note that, by inadvertence, I wrote cr
for r towards the end of the abstract of the former part of this
paper, thus giving the result a false generalisation depending on
the fact that r had been made subject to the condition

S . Vr = 0 ,

while no such restriction was imposed on a~. With this restriction
most of the results already given ( Proc . ante p. 320) are correct,
but the general forms in the paper itself are as follows, being
deducible at once from the first expression in the abstract : —

jfS . U vV*<rds -jfS . Ui/VS . Ycrds = /S . Ycrdp ,

and

JfUvWds -ffS . VvY . VP ds =/Y {dPV) P ;
giving finally

f/Y . U vWtfc - . UvV . YVcrds - /V . Y(dpV)<r .]

of Edinburgh, Session 1871-72. 787

Returning to the electrodynamic integral, note that it may be
written

so that, by the corrected formula just quoted, its value as a surface
integral is

JJ S . UvV . V * <h -ff UvV2 l- ds.

Of this the last term vanishes, unless the origin is in, or infinitely
near to, the surface over which the double integration extends.
The value of the first term is seen (by what precedes) to be the
vector-force due to uniform normal magnetisation of the same
surface.

Also, since

vUp = ~ Tp’

we obtain at once

-l

whence, by differentiation, or by putting p + a for p, and expanding
in ascending powers of Ta (both of which tacitly assume that the
origin is external to the space integrated through, i.e ., that Tp no-
where vanishes), we have

- "-f/fW - ff T" * - >

and this, again, involves

The interpretation of these, and of more complex formulae of a
similar kind, leads to many curious theorems in attraction and in
potentials. Thus, from (a) we have

f*.

788

Proceedings of the Royal Society

which gives the attraction of a mass of density t in terms of the
potentials of volume distributions and surface distributions. Put-
ting

o' = it + jt2 + kt3 ,

this becomes

Iff

ya-ds

-Iff

Up . erdq

=ff

TJv . a~ds

By putting cr = p, and taking the scalar, we recover a formula
given above ; and by taking the vector we have

Y ff VvTJpds = 0 .

This may he easily verified from the formula
/Pdp = V JjfXJv . yldds ,

by remembering that

vTp = Up .

Again if, in the fundamental integral, we put
(T = tJJp ,

we have

~ ff/% =ff® ■ VvVpds ■

5. On the Currents produced by Contact of Wires of the
same Metal at different Temperatures. By W. Durham,
Esq. Communicated by Professor Tait.

At the suggestion of Professor Tait, I undertook the investiga-
tion of the momentary thermo-electric current developed when two
conductors or wires of the same metal are brought into contact, the
one being at a different temperature from the other.

Platinum was chosen as the most suitable metal to experiment
with, in the first instance, as it is free from the interfering action
of oxidation at high temperatures.

789

of Edinburgh, Session 187] -72.

The following arrangement of apparatus was employed : —

1. A long iron bar, one of those used by the late Principal
Forbes in his experiments on the conduction of heat, was heated
at one end in the usual manner. This formed the source of heat at
once steady and graduated, so that, by contact with it at various
parts, the platinum wire experimented with could be kept at any
required temperature.

2. Small glass tubes were fitted into holes in the bar at regular
intervals, and turned over a little at the edge in the form of a lip.
These served the double purpose of preventing metallic contact with
the bar (and thus introducing ordinary thermo-electric currents),
and also served as guides to the same point of contact in each
experiment.

3. A small iron bar kept at the temperature of the room.

4. A reflecting galvanometer (with somewhat massive mirror
and magnet, so as to “ integrate”), with a scale placed at the dis-
tance of six feet, so that the smallest deflection of the needle could
be readily observed and measured.

5. Two pieces of the same platinum wire connected with the
galvanometer in the usual manner.

The mode of working was as follows The free end of one of the
platinum wires rested on the small bar, and was thus kept at the
temperature of the room. The free end of the other wire was
placed in one of the glass tubes on the heated bar, and, while in
that position, and after it had attained the temperature of the bar
at that particular spot, the wire from the small bar was brought
into contact with it, and the sudden deflection of the galvanometer
needle noted.

With this arrangement very good and steady results were
obtained when care was taken to keep the wires perfectly clean,
and to apply the same amount of pressure in making contact in
every experiment, because any deficiency of contact increased the
resistance so as greatly to affect the currents.

The results show that for platinum wire the current, as indicated
by the deflection of the galvanometer needle, is exactly as the dif-
ference of temperature between the two wires.

To show the steadiness of the results, I give the details of one
experiment —

h m

VOL. VII.

790

Proceedings of the Royal Society

Temperature
of Hole.

Difference of
Temperature.

Galvanometer Deflection.

Mean.

No. 1.

325° C.?

310°?

215, 220, 225, 220, 225, 235, 240, )
230, 240, 240, 237, 245, 235,
220, 250, 230, . . J

► =231-7

2.

00

o

CM

193°

140, 140, 135, 130, 142, 130, 130, )
130, 132, 128, 132, 130, 130, (
185, 130, 132, 135, 140, 140, (
140, 130, 135, 135, . . J

■ = 134-

3.

144°

129°

90, 90, 90, 92, 90, 85, 85, 90, 85, )
87, 85, 85, 90, 85, 80, 80, 90, 1
85, 90, 90, , . J

[• = 85-

4.

103°

88°

62, 60, 60, 60, 55, 60, 55, 60, 60, ]
60, 60, . . . J

| = 69-27

6.

78°

63°

42, 42, 44, 44, 44. 40, 50, 47, 50, ]
47, 50, . . . j

| = 45-5

6.

66°

41°

38, 35, 32, 30, 30, 32, 35, 35, 33, ‘
35, 35, 35, 35, 35, 35, 38, 38,
35, 35, 38,

| = 34-7

The following are the means of a great number of experi-
ments, the mean values of the current being all multiplied by a
common factor : —

No. 1. No. 2. No. 3.

Difference of
Temperature
In Degrees
Cent.

Current.

Difference of
Temperature
in Degrees
Cent.

Current.

Difference of
Temperature
in Degrees
Cent.

Current.

21°

19-

50°

55-5

9°

9-6

30°

30-

53°

64-5

14°

13-

42°

38-3

63°

68-

20°

19-

60°

59-

68°

70-

28°

26-

88°

89-

74°

73-

39°

34-

92°

90-

88°

89-

61°

65-

134°

132-5

105°

101-

84°

76-

136°

135-

109°

105-

124°

120-

139°

138-

129°

127*

131°

120- ?

140°

142-

152°

120- ?

196°

192-

167°

161-5

?

314-

193°

201-

2

266-

2

347-

With the same apparatus as in the foregoing, I next tried heat-
ing both wires considerably above the temperature of the room,

791

of Edinburgh, Session 1871-72.

till, however, keeping one wire at a higher temperature than the
other. The result in this case was as in the former. The current

was exactly as the difference of temperature,
the means of the experiment : —

The following

Temperatures in Degrees Cent.

Current.

203° — 142° = 61° .

64-5

142° — 100° = 42° .

48-

100° — 76° = 24° .

30-

With more sensitive galvanometer, — -

320°?— 205° = 115°? .

120- *

205° — 143° = 62° .

64-5

143° — 102° 41° .

42*

102° — 76° = 26° .

28-5

6. Eemarks on the Deep-Water Temperature of Lochs
Lomond, Katrine, and Tay. By Alexander Buchan.

In the communications made by Sir Bobert Christison to the
Society in December and April last on the deep-water temperature
of Loch Lomond, from observations made by him with a Miller-
Casilla thermometer, these important facts were stated : —

(1.) On 12th October 1871, the temperature at the surface was
52-°0, from which it fell, on descending, till at 300 feet below the
surface it stood at 42°-0, and this temperature of 42°*0 was uni-
formly maintained at greater depths or to 518 feet, the depth of
the loch at the place of observation.

(2). On 18th November following, the surface temperature was
46o,0; at depth of- 250 feet, 420,25 ; at 270 feet and lower depths,
42°-0.

(3.) On the 10th April 1872, the temperature at the surface was
43°-0 ; at 150 feet, 42°*1 ; and from 200 to 594 feet, 42°-0.

Hence it appears that there is a stratum of water of considerable
thickness at the bottom of this loch of uniform temperature ; that
the upper surface of this stratum of deep water of uniform tempera-
ture was about 100 higher on the 10th of April than it was in the

* Results varied considerably owing to working so near the flame — varying
from 104° to 126°‘

792

Proceedings of the Royal Society

beginning of winter, or on the 18th November; and that this deep
water temperature probably remains constantly at, or very near,
42° 0.

Sir Bobert asked me for a statement of the temperature of the
air at Loch Lomond from 18th November 1871 to 10th April
1872, or during the time that the cold stratum of water of the
uniform temperature of 42o,0 had increased about 100 feet in
thickness. This I have prepared from the observations made at
Balloch Castle, by Mr David Hill, the observer of the Scottish
Meteorological Society at that place, Balloch Castle is at the foot
of the loch, and 72 feet above its surface. The table showed the
mean temperature of each day during the time, — the mean of the
maximum and minimum temperatures of each day being assumed
as the mean temperature of that day. Of this table an abstract is
given below, from which it appears that the mean temperature,
from

November 18 to 30 was 38° 0, or 2°-5 below the average,

December

1 „ 31

5)

39°*4,

„ 0°-4

>>

January

1 „ 31

))

40°- 8,

,, 2° -3 above

y>

February

1 „ 29

1)

43°-3,

» 3°-3

5)

jj

March

1 „ 31

}}

43°-6,

» 2°-l

V

>J

April

1 „ 10

>>

45°*6,

» 1°'4

>>

))

The average temperature of the 145 days was 4L7, which 10,4
above the average of past years.

Taking the observed mean temperature of each day for Edin-
burgh as calculated by the late Principal Forbes,* and applying to
these the differences observed between Balloch Castle and Edin-
burgh, the normal temperature of each day at Balloch Castle was
calculated. In this way the divergence of the temperature of each
of the 145 days from its normal was ascertained. The amount for
each day was given in a table, — temperatures above the average
being given in red ink, under the average in blue. An abstract of
this table is given below, from which it appears that there were
four cold, and four mild periods, as under : —

Trans, of the Society, vol. xxii. p. 351.

793

of Edinburgh, Session 1871-72.

Cold Periods.

November 18 to December 10, or 23 days, 4°'6 under average,
December 20 „ ,, 23, ,, 4 „ 30,9 „

January 5 „ January 10, ,, 6 ,, 1°*0 ,,

March 20 „ April 6, ,, 18 „ 3o,0 ,,

Average, 51 days, 30,4 „

Mild Periods.

December 11 to December 19, or 9 days, 4°T above average,

,, 24 ,, January 4, „ 12 ,, 3°*5 „

January 11 „ March 19, ,, 69 „ 3°’9 „

April 7 „ April 10, ,, 4 „ 6°-0 „

Average, 94 days, 4°*0 „

Hence during this period the temperature was under the average
of the season on 51 days, the deficiency amounting to a mean of
30-4; and above the average on 94 days, the excess amounting to
a mean of 4o,0. The most markedly mild period extended over 69
days, viz., from 11th January to 19th March, during which the
temperature was on an average of 30,9 above that of the season;
and as already stated, the temperature was, for the whole period of
145 days, 10,4 above the average.

It may be concluded that in ordinary winters the stratum of
water of uniform temperature will be thicker than Sir Eobert
Christison found it to be this year in the beginning of spring; in
other words, that it will be nearer the surface than 170 feet.

In the end of last week, Mr James Leslie, C.E., kindly sent me
some highly interesting and valuable observations on the deep-
water temperature of Lochs Tay, Katrine, and Lomond, made by
the late Mr James Jardine, C.E., in 1812 and 1814. These I
have now very great pleasure in laying before the Society. They
were taken in fathoms, and the temperature in degrees centigrade
which are here reduced to Eng. feet, and degrees Fah.

* The general results of these observations were given by Sir John Leslie
in his “ Treatises on Various Subjects of Natural and Chemical Philosophy,”
Edinburgh 1838, p. 281.

794 Proceedings of the Royal Society

Observations of the Deep-Water Temperature of Lochs Tay , Katrine,
and Lomond , by the late James Jar dine, Esq., G.E.

Depth.

Loch Tay.
Aug. 12, 1812.

Loch Katrine.
Sept. 3, 1814.

Loch Katrine.
Sept. 7, 1812.

Loch Lomond
Sept. 8, 1812.

Surface

57°-2

56°*8

57°-9

59°*5

30 feet

56°- 7

60

49°-6

5o"-9

90

45°-5

440.4

120

440.4

43V-5

150

43°'3

• . .

180

42°*3

210

43°*2

41°*5

240

...

41°*7

300

))

...

41 °* 5

360

...

41°*5

...

420

41°’ 9

...

...

480

;;

4l°-7

41°*4

41°*7

540

y)

41°*5

600

>>

...

...

41°*5

These results are strikingly accordant with those obtained by
Sir Robert Christison, The difference as regards the deep-
water temperature of Loch Lomond may he, and probably is, only
instrumental.

These observations were made in the summer and early autumn,
or when the temperature of the sea and of lakes is about the
annual maximum. Taken in connection with Sir Robert’s observa-
sions, they warrant the conclusion that the deep-water temperature
of Loch Lomond remains during the whole year either absolutely
at, or very nearly at, the low figure of 42o,0.

The observations also show that this is not a peculiarity of Loch
Lomond, hut that it is also a characteristic of Lochs Katrine and
Tay, and most probably of other deep waters.

The mean annual temperature of the air at Loch Lomond, from
the mean at Balloch Castle, calculated on the 13 years’ average,
ending 1869, is 48o,0,* which is 6o,0 higher than the uniform
deep-water temperature of the loch. The deep-water temperature

* In this and following temperatures 0o,2 has been added, in order to bring
them to the level of the loch, which is 72 feet lower than the thermometers at
Balloch Castle.

of Edinburgh, Session 1871-72. 795

is, therefore, not determined by the mean annual temperature of
air over this part of the earth’s surface.

From Forbes’ “Climate of Edinburgh, ”it is seen that the tempera-
ture there is under the annual mean from the 21st October to the
26th April. Assuming that this holds good for Ballocli Castle,
then the mean temperature for the cold half of the year will be,
from —

October

21 to 31, .

46°-0

November

1 to 30, .

41°-7

December

1 to 31, .

40°-9

January

1 to 31, .

38°‘6

February

1 to 28, .

39°-8

March

1 to 31, .

40°-5

April

1 to 26, .

45°-8

The mean of these 188 days is therefore 410,4.

The close approximation of this temperature of 410,4 to 42o,0,
the deep-water temperature of the loch, is such as to suggest that
it is the mean temperature of the cold half of the year which deter-
mines the temperature of the lowest stratum of water at the bottom
of deep lakes , so long as the deep-water temperature does not fall
below that of the maximum density of the water. As this prin-
ciple, if established, would be of great importance in many ques-
tions of physical research, such as the deep-water temperature of
the Mediterranean Sea, which Dr Carpenter has very accurately
ascertained, in its connection with the larger question of general
oceanic circulation, it well deserves further investigation.

796

Proceedings of the Royal Society

Donations to the Society during the Session 1871-72 —
Agassiz (Alexander). Application of Photography to Illustrations
of Natural History; with Two Figures printed by the Albert
and Woodbury processes. 8vo. — From the Author.

Anderson (John), M.D. Note on the Occurrence of Sacculina in
the Bay of Bengal. 8vo. — From the Author .

— — — On some Indian Keptiles. 8vo. — From the Author.

— — Description of a New G-enus of Newts from Western Tunan.
8vo. — From the Author.

Note on Testudo Phayrii. 8vo. — From the Author.

— Description of a New Cetacean from the Irrawaddy River,

Burmah. 8vo.— From the Author.

— On Three New Species of Squirrels from Upper Burmah

and the Kakhyen Hills, between Burmah and Yunan. 8vo. —
From the Author.

On Eight New Species of Birds from Western Yunan, China.

8 vo. — From the Author.

— Notes on some Rodents from Yarkand. 8vo. — From the

Author.

■ Description of a New Species of Scincus. 8vo. — From the

Author.

■ A Report on the Expedition to Western Yunan. 4to. —

From the Author.

Baudet (P. J. H.). Leven en Werken, van Willem Jansz, Blaeu.

Utrecht, 1871. 8vo. — From the Author.

Bergman (Jo. Theod.). Memoria Ludovici Caspari Valckenarii.

Rheno-Trajecti, 1871. 8vo. — From the Author.

Bert (M. P.). Influence des diverses couleurs sur la Vegetation.
4to. —FVom the Author.

Blade (M. Jean Francois). Etudes sur 1’Origine des Basques.
8vo. — From the Author.

- Defense des Etudes sur l’Origine des Basques. 8vo. —

From the Author.

Blanford (W. T.). Observations on the Geology and Zoology of
Abyssinia, made during the progress of the British Expedition
to that Country in 1867-68. 8vo. — From the Indian Govern-
ment.

797

of Edinburgh, Session 1870-71.

Blyden (Rev. Edward W.). Appendix to Benj. Anderson’s
Journey to Musadu. New York, 1870. 12mo. — From the

A uthor.

Blytt (A.). Christiania, Omegns Phanerogamer og Bregner. 8vo. —
From the Author.

Bonnel (J. F.). Essai sur les Definitions Geometriques. Paris, 1870.
8 vo. — From the Author.

Boott (Francis), M.D. Illustrations of the Genus Carex. Part IV.

London, 1867. Fol. — From the Author.

Boyle (W. R. A.). The Tribute of Assyria to Biblical History.
London, 1868. 8vo. — From the Author.

Literature under the Shade of Great Britain. In a Letter

to the Right Hon. W. E. Gladstone. London, 1870. 8vo. —
From the Author.

Brigham (W. T.). Historical Notes on the Earthquakes of New
England, 1638-1869. 4to. — From the Author.

Notes on the Eruption of the Hawaiian Volcanoes, 1868.

Boston, 1869. 4to. — From the Author.

The Colony of New Plymouth and its relation to Massa-
chusetts. Boston, 1869. 8vo. — From the Author.

Contributions of a Venerable Savage to the Ancient History

of the Hawaiian Islands. Boston, 1868. 8vo. — From the
Author.

Cox (E. T.). First Annual Report of the Geological Survey of
Indiana during the year 1869. 8vo. — From the Author.

Day (St John Vincent), C.E. On Asbestos, with special reference
to its Use as Steam-Engine Packing. Glasgow, 1872. 8vo.
— From the Author.

Delesse (M.). Revue de Geologie pour les Annees 1867 et 1868.

Tome VII. Paris, 1871. 8vo. — From the Author.

Dole (Sandford B.) A Synopsis of the Birds of the Hawaiian
Islands. Boston, 1869. 8vo. — From the Author.

Erlenmeyer (Dr Emil). Die Aufgabe des Chemischen Unterrichts
gegeniiber den Auforderungen der Wissenschaft und Technick.
Munchen, 1871. 4to. — From the Author.

Everett (Prof. J. D.). On the General Circulation and Distribution
of the Atmosphere. 8vo. — From the Author.

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VOL. VII.

798 Proceedings of the Royal Society

Fayrer (J.), M.D., C.S.I. The Thanatophidia of India; being a
Description of the Venomous Snakes of the Indian Peninsula,
with an Account of the Influence of their Poison on Life.
London, 1872. Fob — From the Author.

Frauenfeld (George Bitter von). Die Grundlagen des Vogelschutz-
gesetzes. Wien, 1871. 8vo.— From the Author.

Friis (Prof. J. A.). Salbmagirje (Lappish. Salmebog). Christiania,
1871. 12mo. — From the Author.

Fuchs (Dr C. W. C.). Die Kiinstlich dargestellten Mineralien nach
G. Bose’s Krystallo-chemischen Mineralsysteme geordnet.
Haarlen, 1872. 4to. — From the Author.

Gabba (Luigi). Bapporti sui Progressi delle Scienze. Milano,
1870. 8vo. — From the Author.

Gamgee (Sampson). On the Treatment of Fractures of the Limbs.
8vo. — From the Author.

Geikie (James). On Changes of Climate during the Glacial
Epoch. 8vo. — From the Author.

Grant (Bobert E.), M.D. Umrisse der Vergleichenden Anatomie.

Leipzig, 1842. 8vo. — From the Author.

Grundfjeldet (I.). Om Skuringsmoerker Glacialformationen og
Terrasser. Kristiania, 1871. 4to. — From the Author.

Hall (Townshend M.), F.G.S. Topographical Index to the Fellows
of the Geological Society of London. 8vo. — From the Author.
Hauer (Franz Bitter v.) Zur Erinnerung an Wilhelm Haidinger.

Vienna, 1871. 8vo. — From the Author.

Haug (Dr Martin). Brahma und die Brahmanen. Munich, 1871.
4to. — From the Author.

Heller (Prof. Cam). Die Zoophyten und Echinodermen des Ad-
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Hoeufft (Jacobi Henrici). Urania, Carmen Didascalicum Petri
Esseiva. Amstelodami, 1870. 8vo. — From the Author.

Jervis (Cav. Guglielmo). B. Museo Industriale Italiano Illus-
traziari delle, Collizione Didattica. Parte Prima. 8vo. — From
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Korosi (Josef). Vorlanfiger Bericht uber die Besultate der Pester.

Volkszahlung vom Jahre, 1870. 8vo. — From the Author.
Kuntsler (Gustav). Die unseren Kulturpflanzen Schadlichen In-
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Mackinder (D.), M.D. Clinical notes. 8vo. — From the Author.

Maxwell (J. Clerk), LL.D. Theory of Heat. 12mo. — From the
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Mueller (Ferdinand von), M.D. New Vegetable Fossils of Victoria.
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Muir (J.), D.C.L., LL.D. Original Sanskrit Texts on the Origin
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Neilreich (Dr August). Die Vegetation sverhaltnisse von Croa-
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Nicholson (II. Alleyne), M.D. Monograph of the British Grap-
tolitidse. Part I. 8vo. — From the Author.

Nowicki (Prof. Dr Max.). Ueber die Weizenverwiisterin Chlorops
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Pacini (Prof. Filippo). SulT Ultimo Stadio del Colera Asiatico.
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Packard (A. S.), M.D. Record of American Entomology for 1869.
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800

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Quatrefages (A. de). La Eace Prussienne. Paris, 1871. 12mo.

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Eeid (Hugo). Memoir of the late David Boswell Eeid, M.D.,
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Eive (A. de la) et E. Sarasin. De l’Action du Magnetisme sui-
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Eiver Engineering. Second Edition, 1872. 8vo. — From the
Author.

Stratton (Thomas), M.D., E.N. The Affinity between the Hebrew'
Language and the Celtic. Edinburgh, 1872. 8vo. — From
the Author.

Strecker (Adolph). J ahreshericht iiber die Fortschritte der Chemie,
etc., fur 1869. Heft, 1, 2, 3. Giessen. 8vo. — From the Editor.

Struve (Otto). Jahresbericht am 29 Mai 1870 dem Comite der
Nicotai-Hauptsternwarte. St Petersburg, 1870. 8vo. — From
the Author.

Studer (B.) Index der Petrographie und Stratigraphie der
Schweiz und ihrer Ungebungen, Bern. 1872. 8vo. — From the
Author.

Thomsen (Julius). Undersgelser over Basernes Neutralisation -
svarme. Kjobenhavn, 1871. 4to. — From the Author.

Topinard (Dr Paul). Etude sur les Eaces Indigenes de l’Australie.
Paris, 1872. 8vo. — From the Author.

of Edinburgh, Session 1870-71. 801

Tschermak (Gustav). Mineralogische Mittheilungen, Jahrgang.

1871. Heft 1. 8vo. — From the Author.

Vollenhoven (S. C. Snellen van), Ph.D. Laatste Lijst van
Nederlandsche Schildaleuge’lige Insecten ( Insecta Coleoptera).
Haarlem, 1870. 4to. — From the Author.

Wells (Walter). The Water Power of Maine. Augusta, 1869.
8 vo. — From the Hydrographic Survey.

Transactions and Proceedings of Learned Societies,
Academies, Etc.

Amsterdam. — Jaarboek van de Koninklijke Akademie van Weten-
schappen gevestigd te Amsterdam voor 1870. 8vo. —
From the Academy.

Processen-verbaal van de G-ewone Vergaderingen der Kon-
inklijke Akademie van Wetensckappen, 1871. 8vo. —
From the Academy.

Yerslagen en Mededeelingen der Koninklijke Akademie
van Wetenschappen. Afdeeling Natuurkunde. Deel Y. —
Afdeeling Letterkunde. Deel I. 8vo. — From the Aca-
demy.

Verhandelingen der Koninklijke Akademie van Weten-
schappen. Afdeeling Letterkunde. Deel YI. — Natuur-
kunde. Deel XII. 4to. — From the Academy.

Flora Batava. Nos. 216-217. 4to. — From the King of
Holland .

Baltimore. — Fourth and Fifth Annual Keports of the Provost to
the Trustees of the Peabody Institute. 1871-72. 8vo. —
From the Institute.

Batavia. — Observations made at the Magnetical and Meteorological
Observatory at Batavia. Yol. I. Fob —From the Govern-
ment.

Berlin. — Abhandlungen der Koniglichen Akademie der Wissen-
schaften. 1870. 4to. — From the Academy.

Monatsbericht der Koniglich Preussischen Akademie der
Wissensohaften. 1871, May, Juni, Juli, August, Septem-
ber, October, November, December. 1872, January, Feb-
ruar, Marz, April. 8vo. — From the Society.

802

Proceedings of the Boyal Society

Beitrsege sur Geologischen Karte der Schweiz herausgege-
ben von der Geologischen Commission der Schweiz.
Naturforsch. Gesellschaft auf Kosten der Eidgenossen-
schaft. 1872. 4to. — From the Commission.
Mittheilungen der Naturforschenden Gesellschaft in Bern,
aus dem Jahre 1870. Nos. 711-744. 8vo. — From the

Society.

Bologna. — Memorie dell Accademia delle Scienze dell Instituto
di Bologna. Serie II. Tomo Y. Fasc. 3, 4. Tomo
VI., VII., VIII., IX., X. Serie III. Tomo I., II. Fasc.
1. 4to. — From the Academy.

Eendiconto delle Sessioni dell Accademia delle Scienze dell
Istituto di Bologna. Ann. Accademic. 1865-66, 1866-
67, 1867-68, 1868-69, 1870-71, 1871-72. 8vo.— From
the Academy.

Boston. — Bulletin of the Public Library. Nos. 18, 19, and 20. 8vo.
— From the Library.

Bourdeaux. — Memoires de la Societe des Sciences Physiques et
Naturelles de Bordeaux. Tome VI. No. 3 ; Tome
VIII. Parts 1, 2, 3. 8vo. — From the Society.

Brussels. — Annuaire de l’Observatoire Royale de Bruxelles, par A.
Quetelet. 1871. 12mo. — From the Observatory.

Annales de l’Observatoire Royale de Bruxelles publies aux
frais de l’Etat, par le directeur A. Quetelet. Tome XX.
4to. — From the Observatory. 4

Annuaire de l’Academie Royale des Sciences, des Lettres et
des Beaux-Arts de Belgique. 1871. 12mo. — From the

Academy.

Bulletin de l’Academie Royale des Sciences, des Lettres et
des Beaux-Arts de Belgique. Tome XXXI. Nos. 6-8;
XXXII. Nos. 9-12 ; XXXIII. Nos. 1-6, XXXIV. Nos.
7-8. 8 vo. — From the Academy.

Biographie Nationale publi4e par l’Academie Royale des
Sciences, des Lettres et des Beaux-Arts de Belgique.
Tome III. Part 1. 8vo. — From the Academy.

Memoires de l’Academie Royale des Sciences, des Lettres
et des Beaux-Arts de Belgique. Tome XXXVIII.
4to. — From the Academy.

803

of Edinburgh, Session 1871-72.

Brussels. — Memoires couronnes et Memoires des Savants Etrangers
publiees par l’Academie Royale des Sciences, des Lettres
et des Beaux-Arts de Belgique. Tome XXXY. XXXYI.
4to. — From the Academy.

Calcutta. — Journal of the Asiatic Society of Bengal. Part I. Nos.

1- 3 ; Part II. Nos. 1-4, 1871. Part I. No. 1 ; Part

II. No. 1, 1872. 8vo. — From the Society.

Proceedings of the Asiatic Society of Bengal. Nos. 3-13,

1871; Nos. 1-5, 1872. 8vo. — From the Society .

Memoirs of the Survey of India, Pala3ontologia. Yol.

III. Nos. 1-13. Ser. YI., YII. 4to. — From the Sur-
vey.

Memoirs of the Geological Survey of India. Yol. YII.

Parts 1-3. 8 vo. — From the Survey.

Records of the Geological Survey of India. Yol. II. Parts

2- 4; Yol. III.; Yol. IY. Parts 1-4. 8vo. — From the
Survey.

Account of the Operations of the great Trigonometrical
Survey of India. Yol. I. 4to. — From the Survey.

Report of the Commissioners appointed to inquire into the
Origin, Nature, &c., of Indian Cattle Plagues, with
Appendices. 1871. Folio. — From the Indian Govern-

ment.

California. — Memoirs of the Academy of Sciences. Yol. I. Parts
1, 2. 4to. — From the Academy.

Proceedings of the Academy of Sciences. Yol. IY. Parts
1-4. 8 vo. — From the Academy.

Cambridge (U. Si). — Annual Report of the Trustees of the Museum
of Comparative Zoology at Harvard College for 1870-71.
8vo. — From the College.

Bulletin of the Museum of Comparative Zoology at Harvard
College, Cambridge, Mass. Yol. II. Nos. 1-3; Yol. III.
No. 1. 8vo. — From the College.

Illustrated Catalogue of the Museum of Comparative
Zoology at Harvard College. Nos, 3-6. 8vo.— From
the College.

Memoirs of the American Academy of Arts and Sciences
Yol. X. Part 1. 4to. — From the Academy.

804

Proceedings of the Royal Society

Cambridge ( U.S .) — The Complete Works of Count Rumford, pub-
lished by the American Academy of Arts and Sciences.
Yol. I. 1870. 8 vo. — From the Academy.

Proceedings of the American Association for the Advance-
ment of Science. 1870. 8vo. — From the Association.

Cape of Good Hope. — Results of Astronomical Observations made
at the Royal Observatory, Cape of Good Hope, in the
year 1856. 8vo. — From the Observatory.

Catania. — Atti dell Accademia G-ioenia de Scienze Naturali de
Catania. Serie Terza. Tomo II., 1868; tomo III.,
1869. 4to. — From the Academy.

Cherbourg. — Catalogue de la Bibliotheque de la Societe Imperiale
des Sciences Naturelles. Part I. 8vo. — From the So-
ciety.

Memoires de la Societe Imperiale des Sciences Naturelles.
Tome XV., XVI. 8vo. — From the Society.

Christiania. — Annexe & la Statistique Officielle du Royaume de
Norvege pour Fannee 1869. 4to. — From the Govern-
ment of Norway.

Beretning om Skolevaesenets Tilstand i Kongeriget Norges
Landdistrikt for Aarene 1864-66, og Rigets Kjbstseder og
Ladesteder for Aaret 1867. 4to. — From the Government
of Norway.

Driftsberetning for Kongsvinger-Lillestrom Jernbane, i
Aaret 1869. 4to. — From the Government of Norway.

Driftsberetning for Hamar-Elverum- Jernbane, i Aaret 1869.
4to. — From the Government of Norway.

Tabeller vedkommende Norges Handel og Skibsfait, i Aaret
1869. 4to. — From the Government of Norway.

Driftsberetning for Norsk Hovid- Jernbane, i Aaret 1869.
4to. — From the Government of Norway.

Fattig-Statistik for 1867. 4to. — From the Government of
Norway.

Beretninger om Norges Fiskerier, i Aaret 1868, 1869.
4to. — From the Government of Norway.

Beretning den Hoiere Landbrugsskole i Aas, i Aarene fra
April 1867 til April 1870. 4to. — From the Government
of Norway.

805

of Edinburgh, Session 1871-72.

Christiania. — Beretning Rigets Oeconomiske Tilstand, Aarene
1861-1865. Andet Hefte. 4to. — From the Government
of Norway.

Criminalstatistiske Tabeller for Kongeriget Norge for Aaret
1866, samt den Kongelige Norske Regjerings Under-
danigste Indstilling af 3 Juni 1870. 4to. — From the
Government of Norway .

Nyt Magazin for Naturvidenskaberne. Bind XYII. Hefte
1-3; Bind XVIII. Hefte 1-3. 8vo. — From the Royal
University of Norway.

Le Neve de Justedse et ses Glaciers par le de Sene. 4to. —
From the University.

Det Kongelige Norste Frederiks-Universitets Aarsberetning
for 1869-1870. 8vo. — From the University.

Tabeller vedkommende Skiftevoesenet i Norge, Aaret 1868.
Tilligemed opgave o ve de efter Overformynder-
Regnskaberne for Aaret 1868-1869, under rigets Over-
formynderiers Bestyrelse Henstaaende Midler samt den
Kongelige Norske Regjerings Underdanigste Indstilling
af 15 Juli 1870, 12 Sept. 1871. 4to. — From the Govern-
ment of Norway.

Den Norske Statstelegrafs Statistik for 1869. 4to. — From
the Government of Norway.

Det Norske Meteorologiske Instituts Storm Atlas udgivet
med Bestand af Videnskabs-Selskabet i Christiania. Fol.
— From the Institute.

Forhandlingeri Videnskabs-Selskabet. Aaren. 1869,1870.
8vo. — From the Society.

Norsk Meteorologisk Aarbog for 1869-1870. 4to — From
the Meteorological Institute.

Connecticut. — Transactions of the Connecticut Academy of Arts
and Sciences. Vol. I. Part 2; Vol. II. Parti. 8vo.—
From the Academy.

Copenhagen. — Oversigt over det Kongelige danske Videnskabernes
Selskabs Forhandlinger og dets Medlemmers Arbeider i
Aaret, 1870, No. 3; 1871, Nos. 1, 2. 8vo. — From the Society.

Dorpat. — Meteorologische Beobachtungen 1866, 1868, 1870, 1871.
8 vo. — From the University of Dorpat.

5 o

VOL. vir.

800 Proceedings of the Royal Society

Dresden.— Nova Acta Academiae Oaesarese Leopoldino-Carolinas
Grermanicse Naturae Curiosorum. Vol. XXXV. 4to. —
From the Academy .

Dublin . — ’Tables of Iris, computed with regard to the Perturbations
of Jupiter, Mars, and Saturn, including the perturbations
depending on the square of the mass of Jupiter. By
Francis Briinnow, Ph.D., F.R.A.S. 4to. — From the

Royal Astronomical Society.

Astronomical Observations and Researches made at Dunsink.
Part I. 1870. 4 to. — From the Board of Trinity College.

Edinburgh. — Astronomical Observations made at the Royal Ob-
servatory, Edinburgh, by Charles Piazzi Smyth, F.R.SS.L.
and E., F.R.A.S., F.R.S.S.A., Professor of Practical
Astronomy, and Astronomer Royal for Scotland. Vol.
XIII. for 1860-1869, with additions to 1871. 4to. —
From the Royal Observatory.

Report presented to, and read before, the Board of Visitors,
appointed by Government for the Royal Observatory, at
their Visitation held on Thursday, 27th July 1871. 4to. —
From the Royal Observatory.

Scottish Meteorology, 1856-1871, computed at the Royal
Observatory. 4to. — From the Royal Observatory.

Quarterly Return of the Births, Deaths, and Marriages,
registered in the Divisions, Counties, and Districts of
Scotland. Nos. 16 to 19, with Supplement. Monthly
Returns of the same from July 1871 to July 1872. Seven-
teenth. Annual Report of the same for 1871. Census of
Scotland, 1871, Fol. — Edinburgh, 1872. 8vo. — From
the Registrar-General.

Eighth Decennial Census of the Population of Scotland,
taken 3rd April 1871. Vol. I. Fol. — From the Registrar-
General.

Transactions of the Highland and Agricultural Society of
Scotland. Vol. IV. 8vo. — From the Society.

Transactions and Proceedings of the Botanical Society.
Vol. XI. Part 1. 8 vo. — From the Society.

Journal of the Scottish [Meteorological Society. Nos.
31-35. 8vo — From the Society.

807

of Edinburgh^ Session 1870-71.

Erlangen — Sitzungsberichte der Physiealisch - Medicinischen
Societat zu Erlangen. Heft 3. 8vo.—From the Society.

Frankfort. — Abhandlungen herausgegeben von der Senckenbergi-
scben Naturforschenden Gesellschaft. Band VIII. Heft
1, 2. 4to. — From the Society.

Bericht iiber die Senckenbergiscbe Naturforschenden
Gesellschaft in Frankfort am Main, 1870-71. 8vo.—
From the Society.

Geneva . — Memoires de la Societe de Physique et d’Histoire
Naturelle de Geneve. Tome XXI. Part 1.— Table des
Memoires. Tomes I.-XX. 4to. — From the Society.

Glasgow. — Proceedings of the Philosophical Society — Vol. VII.
No. 3 ; Vol. VIII. No. 1. — 8vo. From the Society .

Transactions of the Geological Society. Vol. III. Supple-
ment. 8 vo. — From the Society.

Gottingen. — Abhandlungen der Koniglichen Gesellschaft der Wis-
senschaften. Band XVI. 8vo. — From the Society.

Nachrichten von der K. Gesellschaft der Wissenschaften
und der Georg- Augusts-Universitat, aus dem Jahre 1871.
8vo. — From the University.

Greenwich. — Astronomical and Magnetical and Meteorological
Observations made at the Boyal Observatory in the year
1870. 4to . — From the Observatory.

Haarlem. — Archives Neerlandaises des Sciences Exactes et
Naturelles publiees par la Societe Hollandaise a Haarlem.
Tome V. Liv. 4, 5 ; Tome VI. Liv. 1-5 ; Tome VII.
Liv. 1-3. 8vo. — From the Society.

Archives du Musee Teyler. Vol. III. Fasc. 2. 8vo. — From
the Museum.

Helsingfors. — Bidrag till Finlands Officiela Statistik V. Temper-
aturforhallanden i Finland 1846-1865. Heft 1. 4to. —
From the Society of Science.

Bidrag till Kannedom af Findlands Natur och Folkutgifna
af Finska Vetenskaps-Societeten Sjuttonde Haftet. 8vo.
— From the Society.

Acta Societatis Scientiarum Fennicas. Tomus IX. 4to. —
From the Society .

808 Proceedings of the Royal Society

Helsingfors. — Ofversigt af Finska Yetenskaps-Societetens For-
kandlingar. 1870-1871. 8vo. — From the Society.

Innsbruck. — Berichte des N aturwissenschaftlich-Medizinischen
Yereines in Innsbruck. Jahrgang II. Heft 1-3. 8vo. —
From the Society.

Jena— -Jenaiscke Zeitschrift fur Medicin und Naturwissenschaft
herausgegeben von der Medicinisch Naturwissenschaft-
lichen G-esellschaft zu Jena. Band YI. Heft 3, 4. 8vo. —
From the Society.

Kasan. — Reports of the University of Kasan, 1864—1868. 8vo.—

From the University .

Kiel. — Schriften der Universitat. 1870, Band XVII. ; 1871, Band
XVIII. 4to. — From the University. .

Leeds. — Report of the Proceedings of the Geological and Polytechnic
Society of the West Riding of Yorkshire, 1870. 8vo. —
From the Society.

The Fifty-First Report of the Council of the Leeds Philoso-
phical and Literary Society, 1870-71. 8vo. — From the
Society.

Leipzig.— Vierteljahrsschrift der Astronomischen Gesellschaft ;

Jahrgang VI. Heft 2-4; VII. Heft 1. 8vo. — From the
Society.

Berichte iiber die Verhandlungen der Koniglich Sachsischen
Gesellschaft der Wissenschaften zu Leipzig ; Math. Phys.
Classe, 1870, Nos. 3, 4; 1871, Nos. 1-3. 8vo. — From
the Royal Saxon Academy.

Elektrodynamische Maassbestimmungen Insbesendere iiber
das Princip der Erhaltung der Energie, von Wilhelm
Weber. Band X. No. 1. 8vo. — From the Royal Saxon
Academy.

Zur Experimentalen Aesthetik, Von Gustav Theodor
Fechner. Band IX. No. 6. 8vo. — From the Royal Saxon
Academy.

Untersuchung des Weges eines Lichtstrahls durch eine
beliebige Anzahl von brechenden spharisclien Ober-
flaclien. P, A. Hansen. 8vo.~- From the Royal Saxon
Academy.

of Edinburgh, Session 1871-72.

809

Lisbon .• — Catalogo das Publicacoes da Academia Real das Sciencias
de Lisboa. 8vo. — From the Academy.

Memorias da Academia Real das Sciencias de Lisboa, Classe
de Sciencias Mathematicas, Physicas e Naturaes, Nova
Serie. Tomo IV. Parte 1, 2. 4to. — From the Academy.

Liverpool. — Proceedings of the Literary and Philosophical Society
of Liverpool. Nos. 23, 24. 8vo. — From the Society.

Transactions of the Historic Society of Lancashire and
Cheshire. Yol. XI. 8vo. — From the Society.

London— Journal of the Royal Asiatic Society of Great Britain
and Ireland. Yol. Y. Part 2 ; Yol. VI. Part 1. 8vo. —
From the Society.

A General Index to the First Thirty-Eight Volumes of the
Memoirs of the Royal Astronomical Society. 8vo. — From
the Society.

Monthly Notices of the Royal Astronomical Society for
1871-72. 8vo. — From the Society.

Memoirs of the Royal Astronomical Society. Yol. XXXIX.
Part 1. 4to. — From the Society.

Astronomical, and Magnetical, and Meteorological Observa-
tions, made at the Royal Observatory in the year 1869.
London, 1871. 4to. — From the Society.

Journal of the Chemical Society. 1871, July August, Sep-
tember, October, November, December; 1872, Yol. X.,
January, February, March, April, May, June, July,
August, Sept. 8 vo. — From the Society.

Proceedings of the Royal Geographical Society. Yol. XY.
Nos. 2-5 ; XYI. Nos. 1-3. 8vo. — From the Society.

Journal of the Royal Geographical Society. Yol. XL. 8vo.
- — From the Society.

Memoirs of the Geological Survey of Great Britain. London,
1870. 8vo. — From the Survey.

Quarterly Journal of the Geological Society. Yol. XXVII.
Parts 3, 4; Yol. XXVIII. Parts 1-3. 8vo . — From the
Society.

Memoirs of the Geological Survey of England and Wales.
Yol. IY. 8vo. — From the Survey .

810 Proceedings of the Royal Society

London. — Memoirs of the Geological Survey of the United King-
Decade XIII. 8vo. — From the Survey.

Journal of the London Institution. Yol. I. Nos. 7-15.
8vo. — From the Society.

Proceedings of the Koyal Institution of Great Britain. Yol.

VI. Parts 3, 4. 8vo. — From the Society.

Index to Proceedings of the Institution of Civil Engineers.

Yol. XXI. to XXX. 8vo. — From the Society.

Proceedings of the Institution of Civil Engineers. Yols.
XXXI., XXXII., XXXIII. Part 1 ; XXXIY. Part 2.
8vo. — From the Society.

Transactions of the Pathological Society. Yol. XXII. 8vo.
From the Society.

The Journal of the Koyal Horticultural Society. Vol. III.

Parts 9, 10. 8vo. — From the Society.

Quarterly Journal of the Meteorological Society. Yol. I.

New Series. Nos. 1-3. 8vo. — Fiom the Society.
Proceedings of the Meteorological Society. Yol. Y. Nos.

55, 56. 8 vo. — From the Society .

Quarterly Weather Report of the Meteorological Office,
Parts 1-4, 1870; Part 1, 1871. 4to. — - From the Meteo-
rological Committee of the Royal Society.

A Discussion of the Meteorology of the Part of the Atlantic
lying north of 30° N. for the Eleven Days ending 8th
February 1870 ; with Chart and Diagrams. 4to. — From
the Royal Society.

Proceedings of the Geologists’ Association. Yol. II. Nos.
1-6. Annual Report for 1871. 8vo. — From the Associa-
tion.

Proceedings of the Society of Antiquaries. Yol. Y. Nos.

1-3. 8vo.- — From the Society.

Journal of the East India Association. No. II. 8vo.—
From the Association.

Currents and Surface Temperature of the North Atlantic
Ocean, from the Equator to Latitude 40° N. for each month
of the year ; with a General Current Chart. 4to. — From

the Royal Society.

811

of Edinburgh, Session 1871-72.

London . — Proceedings of the Royal Society. Nos. 129-136. 8vo.
— From the Society.

Report of the Meteorological Committee of the Royal So-
ciety, for the Year ending 1870-71. 8vo. — From the

Committee .

Royal Society Catalogue of Transactions, Journals, &c.
8vo. — From the Society.

Royal Society Catalogue of Scientific Papers. Yol. V.
4to. — From the Society.

Contributions to our knowledge of the Meteorology of
Cape Horn and the West Coast of South America. 1871.
4to. — From the Meteorological Committee of the Royal
Society.

Transactions of the Royal Society. Yol. CLXI. Part 1.
4to. — From the Society .

Correspondence concerning the Great Melbourne Tele-
scope, in three Parts. 1852-1870. 8vo . — From the Royal
Society.

Transactions of the Royal Society of Literature. Yol. X.

Part 1. 8 vo. — From the Society.

Transactions of the Clinical Society. Yols. IV. V. 8vo. —
From the Society.

Proceedings of the Royal Medical and Chirurgical Society.
Vol. YI, No. 8; Yol. VII. Nos. 1, 2. 8vo .-From the
Society.

Transactions of the Royal Medical and Chirurgical Society.

Yol. L1Y. 8vo.' — From the Society.

General Index to the first Fifty-Three Volumes of the
Medico-Chirurgical Transactions. 8vo. — From the

Society.

Proceedings of the Mathematical Society. Nos. 35-47.
8vo. — From the Society.

Journal of the Society of Arts for 1871-72. 8vo.— From

the Society.

Transactions of the Linnean Society. Yol. XXVII. Parts
3, 4; XXVIII. Parts 1, 2 ; XXIX. Part 1. 4to.— From
the Society.

812 Proceedings of the Royal Society

London. — -List of the Linnean Society. 1870-1871. 8vo, — From
the Society.

Journal of the Linnean Society. Vol. XII. (Botany) ;
Yol. XIII. (Botany), Nos. 65-67; Yol. XI. (Zoology),
Nos. 52-54. 8vo. — From the Society.

Proceedings of the Linnean Society, Session 1870-71,
1871-72. 8vo. — From the Society.

Journal of the Statistical Society. Yol. XXXIV. Parts
2-4; Yol. XXXY. Parts 1-3. 8vo. — From the Society.

Statistical Beport of the Health of the Navy, for the year
1869. 8vo. — From the Admiralty.

Proceedings of the Zoological Society. 1871, Parts 1-3 ;
1872, Part 1. 8vo. — From the Society.

Transactions of the Zoological Society. Yol. VII.
Parts 6-8 ; Yol. VIII. Parts 1, 2. 4to. — From the
Society.

Catalogue of the Library of the Zoological Society. 8vo.—
From the Society.

A Descriptive Catalogue of the Calculi and other Animal
Concretions, contained in the Museum of the Royal
College of Surgeons of England. Supplement I. 4to. —
From the College.

Revised List of the Vertebrated Animals now or lately
living in the Hardens of the Zoological Society. 1872.
8 vo. — From the Society.

Lyons. — Annales de la Societe Imperiale d’Agriculture, Histoire
Naturelle et Arts Utiles de Lyon. Quatrieme Serie.
Tome I., II. 8vo. — From the Society.

Memories de FAcademie Imperiale des Sciences Belles-
Lettres et Arts de Lyon. Classe des Lettres. Tome
XIY. — Classe des Sciences. Tome XVIII. 8vo. — From
the Academy .

Maine. — Report of the Commissioners of Fisheries of the State
of Maine for the year 1870. 8vo. — From the Commis-
sioners.

Manchester. — Proceedings of the Literary and Philosophical Society.
Yol. XI. No. 1. 8vo .—From the Society.

of Edinburgh, Session 1871-72. 813

Milan. — Memorie del Beale Istituto Lombardo di Scienze e
Lettere. Classe di Lettere e Scienze Morali e Politio^.
Vol. XI. Della II. Serie III. Fasc. 3; Yol. XII. Fasc.

1, 2, 3, 4. — Classe di Scienze Matematiche e Naturali.
Yol. XI. Fasc. 3; Yol. XII. Fasc. 1, 2. 4to. — From the
Institute .

Atti della Societa Italiana di Scienze Naturali. Vol. XIY.

Fasc. 3, 4; Yol. XY. Fasc. 1. 8vo. — From the Editor.
Bendiconti Eeale Istituto Lombardo di Scienze e Lettere.
Serie II. Yol. II. Fasc. 17-20; Yol. III. Fasc. 1-15,
16-20; Yol. IY.; Yol. Y. Fasc. 1-7. 8vo .—From the

Institute.

Moscow. — Bulletin de la Societe des Naturalistes. 1860, Nos.

2, 3, 4; 1870, Nos. 3, 4; 1871, Nos. 1-4. 8vo .—From
the Society.

Nouveaux Memoires de la Societe Imperiale des Naturalistes
de Moscow. Tome XIII. Liv. 2, 3. 4to. — From the
Society.

Munich. — Sitzungsberichte der konigl. bayer. Akademie der Wis-
senscbaften. 1870, Band II. Hefts 3, 4. — Pkilosophisch-
Philologischen und Historiscben Classe. 1871, Hefts
1-6; 1872, Heft 1. — Mathematisch-Physikalischen

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Catalogus Codicum Manu Scriptorum Bibliotheca

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the Compilers.

5 p

vol. vii.

814 Proceedings of the Royal Society

Neuchatel. — Bulletin de la Societe des Sciences Naturelles de
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815

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816

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817

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Mineral Statistics of tke Colony for 1871. Fol. — From the
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818 Proceedings of the Royal Society

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of Edinburgh, Session 1870-71. 819

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Society.

INDEX.

Acid, Thebo-lactic, 103.

Acids, Chlorinated, their Formation
and Decomposition, 419.

Address on the Educational System
of Prussia, 309.

on the Results of the more

recent Excavations on the Line of
the Roman Wall in the North of
England, 350.

on Spectrum Analysis, 455.

on Thermo-Electricity, 644.

Africa, Eastern, Lake Basins of, 122.

Aggregation in the Dublin Lying-in
Hospital, 38.

Air-Pump, Sprengel’s Mercurial, 662.

Allman (Professor) on the Genetic
Succession of Zooids in the Hy-
droida, 168.

on the Homological Relations

of the Coelenterata, 512.

Alpine Lake-Basins, Geological Struc-
ture of, 33.

Andrews (Dr Thomas) on the Heat
disengaged in the Combination of
Acids and Bases (2d Memoir),
174.

Annelida of the Channel Islands, 438.

Archer (T. C.), Note on two species of
Foraminifera, and on some Objects
from the Nicobar Islands of great
Ethnological interest, 353.

Arrow-Poison, Kombi, 99.

Assured Lives, the Rate of Mortality
of, 115.

Atomic Volume of Solid Substances,
70.

Atropia, Experimental Research on
the Antagonism between its Actions
and those of Physostigma 506.

Babbage (Charles), Obituarv Notice
of, 543.

Balfour (Professor) on Dimorphic
Flowers of Gephaelis Ipecacuanha , the
Ipecacuan Plant, 763.

YOL. VII.

Balfour (Professor) on the Fruiting
of the Ipecacuan Plant ( Gephaelis
Ipecacuanha , Rich.) in the Royal
Botanic Garden, 688.

Barcaple, Lord, Obituary Notice of,
242.

Barnes (Dr Thomas) on the Fall of
Rain at Carlisle and in the neigh-
bourhood, 434.

Begbie( James), Obituary Notice of, 2.

Birds, the Wheeling of, 615.

Blackie (Professor) on the Place and
Power of Accent in Language, 395.

on the Principles of Scientific

Interpretation in Myths, 44.

Blood, Notes of some Experiments on
the Rate of its Flow through Tubes
of narrow diameter, 193.

Boulder, Notice of a large, 682.

Boulders, List of, in Aberdeen, 720 ;
Argyll, 725 ; Ayr, 727 ; Banffshire,
728; Caithness, 728; Dumfries,
729 ; Edinburgh, 729 ; Elgin, 730 ;
Fife, 731; Forfar, 731; Hebrides,
734; Inverness, 737 ; Kincardine,
739; Kirkcudbright, 739; Lanark,
741 ; Nairn, 741 ; Orkney and Shet-
land, 742 ; Peebles, 743 ; Perth,
743 ; Renfrew, 747 ; Ross and Cro-
marty, 747; Roxburgh, 749; Stir-
ling, 749; Sutherland, 750; Wigton-
shire, 751.

— — Remarkable, Scheme for the
Conservation of, 475.

■ First Report by the Com-

mittee on, 703.

Bow (Robert H.) on Change of ap-
parent Colour by Obliquity of
Vision, 155.

Bow seen on the Surface of Ice, 69.

Brain-Work, Facts as to, 145.

Brand (William), Obituary Notice
of, 6.

Break for a Magneto-Electric Machine,
488.

5 Q

822

Index.

Broun (J. A.) on the Lunar Diurnal
Variation of Magnetic Declination
at Trevandrum, near the Magnetic
Equator, 756.

Brouncker’s Method, Extension of, 56.

Brown (Dr A. Crum), Note on an Ice
Calorimeter, 321.

and Dr T. R. Fraser, on the

Physiological Action of Salts of
Trimethylsulphin, 663.

Brown (Rev. Thomas) on the Old
River Terraces of the Earn and
Teith, 41.

on the Old River Terraces of

the Spey, viewed in connection
with certain Proofs of the Antiquity
of Man, 399.

Bruce (Dr J. Collingwood), Address on
the Results of the more recent Exca-
vations on the Line of the Roman
Wallin the North of England, 350.

Buchan (Alexander) on the Mean
Monthly Rainfall of Scotland, 665.

on the Rainfall of the Con-
tinents of the Globe, 755.

Remarks on the Deep-Water

Temperature of Lochs Lomond,
Katrine, and Tay, 791.

Buchanan (J. Y.) on Thebo-lactic
Acid, 103.

On the Formation and De-
composition of some Chlorinated
Acids, 419.

Calorimeter, 321.

Capillary Action, Theories of, 160.

Capillary Attraction, Remarks on the
Theory of, 308.

Cardiocarpon, 692.

Cayley (Professor) on the Extraction
of the Square Root of a Matrix of
the Third Order, 675.

Cephaelis Ipecacuanha, Rich., 688, 769.

Cetacea, Gravid Uterus and Foetal
Membranes in, 407.

Chambers (Robert), Obituary Notice
of, 533.

Christie (John), Theory of Construc-
tion of the Great Pyramid, 162.

Christison (Sir Robert, Bart.), Open-
ing Address, 1871-72, 531.

on the Composition of the

Flesh of the Salmon in the
“ Clean ” and “ Foul ” condition,
694.

on the Fresh Water of Scot-
land, 547.

on the Action of Water on

Lead, 699.

Ccelenterata, the Homological Re-
lations of, 512.

Colour, Apparent Change of, by
Obliquity of Vision, 155.

Cones, Abnormal, of Pinus Pinaster,
449, 663.

Contact-Electricity, Remarks on, 648.

Coventry (Andrew), Method of Econo-
mising our Currency, 39.

Crinoids, the Structure of the Palaeo-
zoic, 415.

of the Porcupine Deep-Sea

Dredging Expedition, 764.

Currency, Method of Economising,
39.

Currents produced by Contact of
Wires of the same Metal at differ-
ent Temperatures, 788.

Cystine (C3H7N02S), 201, 644.

Dalzell (Dr Allen), Obituary Notice
of, 7.

Daun (Robert, M.D.), Obituary Notice
of, 532.

Deas (Francis) on Spectra formed by
Doubly Refracting Crystals in
Polarised Light, 172.

Descartes, Ovals of, 436.

Dewar (James). Note on the Atomic
Volume of Solid Substances, 70.

Note on Inverted Sugar, 77.

on the Oxidation Products of

Picoline, 192.

Note on a New Scottish

Acidulous Chalybeate Mineral
Water, 470.

Note on Cystine, 644.

■ Note on Sprengel’s Mercurial

Air-Pump, 662.

on a Method of determining

the Explosive Power of Gaseous
Combination, 662.

— on Recent Estimates of Solar

Temperature, 697.

* on the Temperature of the

Electric Spark, 699.

on the Chemical Efficiency of

Sunlight, 751.

■ and Dr Arthur Gamgee, on

Cystine, 201.

Dickson (Prof. Alexander), Remarks
on Vegetable Spirals, 397.

on some Abnormal Cones of

Pinus Pinaster, 449.

— Exhibition of a large series of

Abnormal Cones of Pinus Pinaster ,
663.

Donations to the Library, 209, 514,
796.

Index.

823

Dublin Lying-in Hospital, Note on
Aggregation in the, 38.

Duncan (Dr Matthews), Note on
Aggregation in the Dublin Lying-in
Hospital, 38.

• on the Efficient Powers of

Parturition, 370.

on the Curves of the Genital

Passage as regulating the move-
ments of the Foetus under the in-
fluence of the Resultant of the
Forces of Parturition, 648.

■ and Dr Arthur Gamgee,

Notes of some Experiments on the
Rate of Flow of Blood and some
other Liquids through Tubes of
narrow diameter, 193.

Duns (Professor) on Cardiocarpon,
692.

Durham (W.) on the Currents pro-
duced by contact of Wires of the
same Metal at different Tempera-
tures, 788.

Dyce (Robert), Obituary Notice of, 9.

Earn and Teith, Old River Terraces
of, 41.

Echinodermata, Notice of a new
Family of, 615.

Electricity, the Flow of, on Conduct-
ing Surfaces, 79.

Electric Spark, the Temperature of
the, 699.

Equations, Note on Linear Partial
Differential, 190.

Euclid I. 4, Note on Professor Bain’s
Theory of, 178.

Fellows Elected, 39, 42, 51, 69, 114,
122, 166, 171, 308, 322, 350, 353,
382, 421, 438, 455, 574, 615, 648,
663, 691, 699, 751, 762.

— Statement regarding number,

32.

Ferguson (R. M.), Note of a new
Form of Armature and Break for
a Magneto-Electric Machine, 488.

Flourens, Obituary Notice of, 10.

Foraminifera, Two Species of, 353.

Forbes (James David), Obituary
Notice of, 11.

Forces, Reciprocal Figures, Frames,
and Diagrams of, 53.

Experienced by Solids im-
mersed in a Moving Liquid, 60.

— Decomposition of, 611.

Fraser (Dr Thomas R.) on the Kombi

Arrow-Poison ( Strophanthus hispi-
dus, DC.), 99,

Fraser (Dr Thomas R.), an Experi-
mental Research on the Antago-
nism between the Actions of
Physostigma and Atropia, 606.

— and Professor Crum Brown,

on the Physiological Action of
Salts of Trimethylsulphin, 663.

Fresh Water of Scotland, Observa-
tions on, 547.

Gamgee (Dr Arthur) and Dr J.
Matthews Duncan, Notes of some
Experiments on the Rate of Flow
of Blood and some other Liquids
through Tubes of narrow diameter,
193.

* and James Dewar, on Cystine,

201.

Gaseous Combinations, Method of
determining the Explosive Power
of, 662.

Geikie (Archibald), on the Geological
Structure of some Alpine Lake-
Basins, 33.

Geometric Mean Distance, 613.

Graham (Thomas), Obituary Notice
of, 13.

Grant (Principal Sir Alex.), Address
on the Educational System of
Prussia, 309.

Haidinger (W. Ritter von), Obituary
Notice of, 537.

Harmonic Motions, the Composition
of Simple, 412.

Harmonics, Note on Spherical, 589.

Heat Disengaged in the Combination
of Acids and Bases (2d Memoir), 174.

Herschell (Sir John F. W.), Obituary
Notice of, 543.

Hunter (Adam), Obituary Notice of,
240.

Hydroida, on the Genetic Succession
of Zooids in, 168.

Ice, Bow seen on the Surface of, 69.

Ice Calorimeter, 321.

Indian Life and Society in the Age
when the Hymns of the Rigveda
were composed, 119.

Ipecacuan Plant, on the Fruiting of,
in the Royal Botanic Garden, 688.

( Cephaelis Ipecacuanha ), on

Dimorphic Flowers of, 763.

Jenkins (Professor Fleeming) on the
Wheeling of Birds, 615.

on the Principles which Regu-
late the Incidence of Taxes, 618.

824

Index .

Johnston (Alexander Keith), Obituary
Notice of, 535.

Johnston (Keith), junior, on the Lake-
Basins of Eastern Africa, 122.

Kombi Arrow-Poison, 99.

Laboratory Notes in Physical Science,
206.

On Thermo-Electricity, 308,

390, 597.

On Phyllotaxis, 391.

On Anomalous Spectra and a

simple Direct- Vision Spectroscope,
410.

On a simple Mode of explain-
ing the Optical Effects of Mirrors
and Lenses, 412.

On a Method of illustrating to

a large Audience the Composition
of simple Harmonic Motion under
various conditions, 412.

On Thermo-Electricity (Cir-
cuits with more than one Neutral
Point), 773.

On a Method of exhibiting

the Sympathy of Pendulums, 779.

Lake-Basins, Geological Structure of
some Alpine, 33.

of Eastern Africa, 122.

Language, on the Place and Power of
Accent in, 395.

Languages, Primitive Affinity be-
tween the Classical and the Low
German, 167.

Laycock (Thomas, M.D.), Facts as to
Brain-Work, 145.

Lead, Action of Water on, 699.

Leitch (W.), a simple Method of
Approximating to the Wave-Length
of Light, 179.

Le Sage, Ultramundane Corpuscules,
577.

Library, Donations to, 209, 514, 796.

Lichens, Experiments on the Colorific
Properties of, 43.

Light, a simple Method of Approxi-
mating to the Wave-Length of,
179.

Lindsay (Lauder, M.D.), Experiments
on the Colorific Properties of
Lichens, 43.

(Thomas M.), on the use of

the Scholastic Terms Vetus logica
and Nova logica , with a Remark
upon the corresponding Terms
Antiqui and Moderni, 441.

Lines of the Fourth Order, a singular
case of Rectification in, 613.

Lochs, Deep-Water, Temperature of,
791.

Logarithmic Tables, Account of the
Extension of the Seven-Place, from
100,000 to 200,000, 395.

Macdonald (Professor) on the Homo-
logies of the Vertebral Skeleton in
the Osseous Fishes and Man, 472.

MTntosh (W. C.) M.D., on the Re-
markable Annelida of the Channel
Islands, 438.

on the Structure of Tubifex,

166.

Magnetism, Relation of, to Tempera-
ture, 603.

Maitland (Francis Edward), Obituary
Notice of, 242.

Marshall (D. H.) on the Relation of
Magnetism to Temperature, 603.

Martius (Charles Frederick Philip
von), Obituary Notice of, 20.

Mathematical Notes. On a Quater-
nion Integration, 434.

— On the Ovals of Descartes, 436.

On a Property of Self-Conju-
gate Linear Vector Functions, 498.

Relation between Correspond-
ing Ordinates of Two Parabolas,
499.

On some Quaternion Transfor-
mations, 501.

On an Expression for the

Potential of a Surface Distribution,
&c., 503.

Matrix of the Third Order, on the
Extraction of the Square Root of,
675.

Maxwell (J. Clerk) on Reciprocal
Figures, Frames, and Diagrams of
Forces, 53.

on a Bow seen on the Surface

of Ice, 69.

on Geometric Mean Distance,

613.

Meikle (James) on the Rate of Mor-
tality of Assured Lives, 115.

Mesoplodon Sowerbyi, 760.

Milne-Home (D.), Opening Address,
Session 1870-71, 232.

Scheme for the Conservation

of Remarkable Boulders in Scot-
land, and for the Indication of their
Positions on Maps, 475.

Notice of a Large Boulder in

the Parish of Rattray, and County
of Perth, having on one of its
Sides Cups and Grooves, apparently
artificial, 682.

Index .

825

Mineral Water, Note on a New
Scottish Acidulous Chalybeate, 470.

Mirrors and Lenses, Optical Effects
of, 412.

Monodon monoceros, 759.

Mortality, the Kate of, in Assured
Lives, 115.

Motion, the most General, of an
Incompressible Perfect Fluid, 143.

of an Incompressible Fluid in

Two Dimensions, 142.

■ of a Heavy Body along the

Circumference of a Circle, Addi-
tional Note on, 361.

of Free Solids through a

Liquid, 384.

Muir (John), Notes on Indian Society
and Life, 119.

Muir (William), Obituary Notice of,

22.

Murchison (Sir Roderick Impey,
Bart.), Bust of, 530.

Obituary Notice of, 538.

Music, Scales employed in Scottish,
382.

Muspratt (James Sheridan), Obituary
Notice of, 533.

Myths, Principles of Scientific Inter-
pretation in, 44.

Narwhal, some Observations on the
Dentition of the, 759.

Nasmyth (Robert), Obituary Notice
of, 245.

Neaves (Hon. Lord). Opening Ad-
dress, Session 1869-70, 2.

Primitive Affinity between

the Classical and the Low German
Languages, 167.

on the Pentatonic and other

Scales employed in Scottish Music,
382.

Some Helps to the Study of

Scoto-Celtic Philology, 758.

Nicobar Islands, Objects from, 353.

Nicol Prism, 468.

Obituary Notices, 2, 241, 532.

Office-Bearers, 1869-70, 1; 1870-71,
231; 1871-72, 529.

Opening Address, Session 1869-70, 2 ;
Session 1870-71, 232; Session
1871-72, 531.

Operator <p (v), 607.

Optical Experiments, 466.

Osseous Fishes, Homologies of their
Vertebral Skeleton, 472.

Parturition, Efficient Powers of, 370.

Parturition, Resultant of the Forces
of, 648.

Pendulum Motion, 608.

Pendulums, a Method of Exhibiting
the Sympathy of, 779.

Penny (Frederick), Obituary Notice
of, 25.

Pettigrew (Dr James Bell), on the
Physiology of Wings ; being an
Analysis of the Movements by
which Flight is produced in the
Insect, Bat, and Bird, 336.

Philology, Study of Scoto-Celtic, 758.

Physiology of Wings, 336.

Physostigma, an Experimental Re-
search on the Antagonism between
the Actions of, and Atropia, 506.

Picoline, on the Oxidation Products
of, 192.

Pinus Pinaster, Abnormal Cones of,
449, 663.

Placenta, on the Maternal Sinus Vas-
cular System of the Human, 760.

Polarised Light, Spectra formed by
Doubly Refracting Crystals in, 172.

Prussia, Address on the Educational
System of, 309.

Pyramid, Theory of Construction of
the Great, 162.

Notes on the Antechamber of

the Great, 422.

Quaternions, Note on Linear Diffe-
rential Equations in, 311, 784.

Integrals, 318.

— Integration, 434.

Rain, Proposed Method of ascertain-
ing the Temperature of Falling,
170.

the Fall of, at Carlisle and in

the Neighbourhood, 434.

Rainfall, of Scotland, the Mean
Monthly, 665.

of the Continents of the

Globe, 755.

Rankine (W. J. Macquorn), Letter
from, regarding Diagrams of Forces
and Framework, 171.

— on the Decomposition of Forces

externally applied to an Elastic
Solid, 611.

Retina, Note on a Singular Property
of, 605.

Rigveda. Indian Life and Society in
the Age when the Hymns of the
Rigveda were composed, 119.

River Terraces of the Earn and
Teith, 41.

826

Index.

River Terraces of the Spey viewed
in connection with certain Proofs
of the Antiquity of Man, 399.

Russell (Robert), Obituary Notice of,
532.

Salmon, the Composition of the
Flesh of the, in the Clean and
Foul Condition, 694.

Sang (Edward), on the Extension of
Brouncker’s Method, 56.

* — Motion as to Order of Busi-

ness, 160.

Remarks on the Theories of

Capillary Action, 160, 308.

Note on the Motion of a

Heavy Body along the Circum-
ference of a Circle, 361.

Account of the Extension of the

Seven-Place Logarithmic Tables,
from 100,000 to 200,000, 395.

Experiments and Observations

on Binocular Vision, 433.

on the Computation of the

Strengths of the Parts of Skele-
ton or Open Structures, 575.

on a Singular Case of Rectifi-
cation in Lines of the Fourth
Order, 613.

Scott (Sir William, Bart.), Obituary
Notice of, 532.

Seal, Bones found in Red Clay, near
Grangemouth, 105.

Seller (William), Obituary Notice of,
26.

Ships, Iron, the Preservation of, 702.

Skeleton, Vertebral, the Homologies
of, 472.

Simpson (Sir James Young), Obituary
Notice of, 247.

Smith (W. R.) on the Flow of Elec-
tricity in Conducting Surfaces, 79.

— Note on Professor Bain’s

Theory of Euclid I. 4, 176.

Solids, the Forces experienced by,
Immersed in a Moving Liquid 60.

■ Rigid, Motion of any Number

of, 668.

Spectra, formed by Doubly Refract-
ing Crystals in Polarised Light, 172.

■ Anomalous, 408, 410.

on a New Mode of Observing,

466.

Spectrum Analysis, Address on, 455.

• Note on the Early History of,

461.

Sperm Whale, Additional Notes on
its Occurrence in the Scottish Seas,
632.

Spey, Old River Terraces of the,
Viewed in Connection with Cer-
tain Proofs of the Antiquity of
Man, 399.

Spirals, Vegetable, 397.

Stevenson (Thomas), Proposed Method
of ascertaining the Temperature of
Falling Rain, 170.

Strain-Function, Note on, 667.

Second Note on, 682.

Slrophanthus hispidus, DC., 99.

Structures, Open, Computation of the
Strength of, 575.

Sugar, Note on Inverted, 77.

Sunlight, Chemical Efficiency of, 751.

Syme (Professor James), Obituary
Notice of, 270.

Tait (Professor) on the most General
Motion of an Incompressible Perfect
Fluid, 142.

on the Steady Motion of an

Incompressible Fluid in Two Di-
mensions, 142.

on Green’s and other Allied

Theorems, 168.

Note on Linear Partial Dif-
ferential Equations, 190.

Notes from the Physical

Laboratory of the University, 206.

Laboratory Notes on Thermo-

Electricity, 308.

Note on Linear Differential

Equations in Quaternions, 311.

on some Quaternion Integrals,

318.

on Thermo-Electricity, 390.

• on Phyllotaxis, 391.

Anomalous Spectra, and on

a Simple Direct Vision Spectro-
scope, 410.

on a Method of Illustrating to

a Large Audience the Composition
of Simple Harmonic Motions under
various conditions, 412.

■ on a Simple Mode of Ex-

plaining the Optical Effects of
Mirrors and Lenses, 412.

on a Quaternion Integration,

434.

— on the Ovals of Descartes,

436.

Address on Spectrum Ana-
lysis, 455.

on a Property of Self-Con-
jugate Linear Vector Functions,
498.

Relation between Correspond-
ing Ordinates of Two Parabolas, 499.

Index.

827

Tait (Professor) on some Quaternion
Transformations, 501.

on an Expression for the

Potential of a Surface Distribution,
&c., 503.

Note on Spherical Harmonics,

689

On Thermo-Electricity, 597.

Note on a Singular Property

of the Retina, 605.

On the Operator <p (v), 607.

Note on Pendulum Motion,

608.

Address on Thermo-Electri-
city, 644.

Note on Strain-Function, 667.

Second Note on the Strain-

Function, 682.

• Note on the Rate of Cooling

at High Temperatures, 682.

on Thermo-Electricity — (Cir-
cuits with more than one Neutral
Point), 773.

on a Method of Exhibiting

the Sympathy of Pendulums, 779.

on some Quaternion Integrals,

784.

Talbot (H. F.), Note on some Anoma-
lous Spectra, 408.

Note on the Early History of

Spectrum Analysis, 461.

on some Optical Experi-
ments—

I. On a New Mode of Observing

certain Spectra, 466.

II. On the Nicol Prism, 468.

Taxes, on the Principles which Re-
gulate the Incidence of, 618.

Temperature, Rate of Cooling, 682.

Solar, Recent Estimates of,

697.

— Remarks on the Deep-Water

Temperature of Loch Lomond,
Loch Katrine, and Loch Tay, 791.

Terms, Scholastic, Vetus logica and
Nova logica , with a Remark upon
the corresponding Terms Antiqui
and Moderni, 441.

Thebo-Lactic Acid, 103.

Theorems, Green’s, and other Allied,
168.

Thermo-Electricity, 597.

(Circuits with more than one

Neutral Point), 773.

Thomson (Fraser, M.D.), Obituary
Notice of, 533.

Thomson (Sir William) on the Forces
experienced by Solids Immersed in
a Moving Liquid, 60.

Thomson (Sir William) on the
Equilibrium of Vapour at a Curved
Surface of Liquid, 63.

• on the Motion of Free Solids

through a Liquid, 384.

on Vortex Motion, 575.

on the Ultramundane Cor-

puscules of Le Sage, 577.

Remarks on Contact - Elec-
tricity, 648.

on the Motion of any Number

of Rigid Solids of any Shapes
through a Liquid in a State of
Irrotational Cyclic Motion, having
for its Core any Fixed Rigid Per-
forated Solid, 668.

Thomson (Professor Wyville), Ad-
dress on the Condition of the
Depths of the Sea, 144.

on the Structure of the

Palaeozoic Crinoids, 415.

Notice of a New Family of

the Echinodermata, 615.

on the Crinoids of the “ Por-
cupine ” Deep-Sea Dredging Ex-
pedition, 764.

Tracey (Captain), Notes on the Ante-
chamber of tbe Great Pyramid, 422.
Trevandrum, Magnetic Declination at,
756.

Trimethylsulphin, on tbe Physiolo-
gical Action of the Salts of, 663.
Tubifex, the Structure of, 166.

Turner (Professor), Preliminary No-
tice of the Great Fin Whale cap-
tured at Longniddry, 34.

on the Bones of a Seal, 105.

on the Capture of a Sperm

Whale on the Coast of Argyllshire,
with a Notice of other Specimens
caught on the Coast of Scotland,
365.

on the Gravid Uterus, and

Arrangement of the Foetal Mem-
branes in the Cetacea, 407.

Additional Notes on the Oc-
currence of the Sperm Whale in
the Scottish Seas, 632.

Some Observations on the

Dentition of the Narwhal ( Mono-
don monoceros), 759.

on the Maternal Sinus Vas-
cular System of the Human Pla-
centa, 760.

on the Occurrence of Ziphius

cavirostris in the Shetland Seas, and
a Comparison of its Skull with that
of Sowerby’s Whale ( Mesoplodon
Sowerbyi ), 760.

828

Index .

Vapour, the Equilibrium of, at a
Curved Surface of Liquid, 63.

Vision, Change of Apparent Colour
by Obliquity of, 155.

Certain Phenomena applied

in Solution of Difficulties connected
with the Theory of, 355.

Experiments and Observa-
tions'on Binocular, 433.

Vortex Motion, 575.

Wardrop (James), Obituary Notice of,
30.

Whale, Great Fin, Preliminary No-
tice of, 34.

Whale, Sperm, Capture of, on the
Coast of Argyllshire, 365.

Wings, Physiology of, 336.

Wires of same Metal, Currents pro-
duced by Contact of, 788.

Wyld (R. S.), Certain Phenomena
applied in Solution of Difficulties
connected with the Theory of
Vision, 355.

Young (James) on the Preservation
of Iron Ships, 702.

Ziphius cavirostris , 760.

PRINTED BY NEILL AND COMPANY, EDINBURGH.

<\ PROCEEDINGS

ROYAL SOCIETY OF EDINBURGH.

SESSION 1869-70.

CONTENTS.

Monday , 6th December 1869.

PAGE

Opening Address. Session 1869-70. By the Hon. Lord

Heaves, Vice-President, .... 2

Monday , 2 Oth December 1869.

On the Geological Structure of some Alpine Lake-Basins.

By Archibald Geikie, Esq., F.B.S., . . . 33

Preliminary Notice of the Great Pin Whale, recently

stranded at Longniddry. By Professor Turner, . 34

Note on Aggregation in the Dublin Lying-in Hospital. By

Dr Matthews Duncan, . . . 1 38

/

Monday , 3 d January 1870. ‘

On a Method of Economising our Currency. By Andrew

Coventry, Esq., . . . 39

On the Old Biver Terraces of the Earn and Teith, viewed
in connection with certain Geological Arguments for
the Antiquity of Man. By the Bev. Thomas Brown,
Edinburgh, .... . . 41

Monday , 17 th January , 1870.

Experiments on the Colorific Properties of Lichens. By

W. Lauder Lindsay, M.D., E.B.S.E., F.L.S., . . 43

On the Principles of Scientific Interpretation im Myths*
with Special Beference to Greek Mythologyl 4§y Pro-
fessor Blackie, . . . , 44

' y} [ Turn over.

11

Monday , 7tli February 1870.

PAGE

i Reciprocal Figures, Frames, and Diagrams of Forces.

By J. Clerk Maxwell, Esq., F.R.SS. L. & E., . 53

0)i the Extension of Brouneker’s Method. By Edward

Sang, Esq., . . . . . .56

On the Forces experienced by Solids immersed in a Moving

Liquid. By Sir William Thomson, . . .60

the Equilibrium of Vapour at a Curved Surface of Liquid.

By Sir William Thomson, . . . .63

On a Bow seen on the Surface of Ice. By J. Clerk

Maxwell, Esq., F.R.SS. L. & E., . . 69

Monday , 21 st February 1870.

Note on the Atomic Volume of Solid Substances. By James
Dewar, Esq., Lecturer on Chemistry, Veterinary College,
Edinburgh, ...... 70

Note on Inverted Sugar. By James Dewar, Esq., Lecturer

on Chemistry, Veterinary College, Edinburgh, . 77

On the Flow of Electricity in Conducting Surfaces. By
W. R. Smith, M.A., Assistant to the Professor of
Natural Philosophy in the University of Edinburgh.
Communicated by Professor Tait. (With a Plate.) . 79

On the Kombi Arrow-poison ( Strophanthus hispidus, DC.)
of the Manganja district of Africa. By Dr Thomas R.
Fraser, . • . . . . 99

On Uhebo-lactic Acid. By J. Y. Buchanan, M.A., . 103

On the Bones of a Seal found in Red Clay near (Grange-
month, with Remarks on the Species. By Professor
CORNER, , . . . . .105

Monday \ 7th March 1870.

On the Rate of Mortality of Assured Lives as experienced
by Ten Assurance Companies in Scotland from 1815
to 1863. By J. mes Meikle, Esq. Communicated by
Professor Tait, _. . . . .115

Notes on Indian Society, and Life in the Age when the
Hymns of the Bigveda were composed. By John Muir,

D.O.L., LL.D., Ph.D„ 119

Monday, 21 st March 1870.

> .... r in ' ake Basins of Eastern Africa, By Keith Johnston,

Jan.., Esq., F.R.G-.S., . . . . .122

continv i ion of Contents, see pp. 3 and 4 of Cover.

iii

PAGE

On the Steady Motion of an Incompressible Perfect Fluid

in Two Dimensions. By Professor Tait, . . 142

On the most general Motion of an Incompressible Perfect

Fluid. By Professor Tait, .... 143

Monday , 4 th April 1870.

Address by Professor Wyyille Thomson on the “ Condition

of the Depths of the Sea,” , 144

Monday , 18£A April 1870.

Facts as to Brain-Work; in Illustration of the New and
Old Methods of Philosophical Inquiry in Scotland.

By Thomas Laycock, M.D., .... 145

On Change of Apparent Colour by Obliquity of Vision. By

Egbert H. Bow, C.E,, F.B.S.E., . . • 155

Monday , 2 d May 1870.

Remarks on the Theories of Capillary Action. By Edward

Sang, Esq., F.E.S.E., ..... 160

Theory of Construction of the Great Pyramid. By John
Christie, Esq. Communicated by the Eev. W, Lindsay
Alexander, D.D., ..... 162

On the Structure of Tubifex, By W. C. MTntosh, M.D., . 166

Monday , l§th May 1870.

Primitive Affinity between the Classical and the Low German

Languages. By the Hon. Lord Neaves, . .167

On the Genetic Succession of Zooids in the Hydroida. By

Professor Allman, . . . . .168

On Green’s and other Allied Theorems. By Professor Tait, 168
Proposed Method of ascertaining the Temperature of Falling

Bain. By Thomas Stevenson, F.B.S.E., Civil Engineer, 170

Monday , Qth June 1870.

Letter from Professor W. J. Macquorn Bankine as to

Diagrams of Forces in Framework, . . . 171

On Spectra formed by Doubly Befracting Crystals in

Polarised Light. By Francis Deas, LL.B., F.B.S.E., . 172

On the Heat Disengaged in the Combination of Acids and
Bases. Second Memoir. By Thomas Andrews, M.D.,

F.B.S., Hon. F.R S.E., .... 174

PAGE

iv

Note on Professor Bain’s Theory of Euclid I. 4. By Wm.
Robertson Smith, M.A., Assistant to the Professor of
Natural Philosophy. Communicated by Professor Tait, 176
A Simple Mode of xApproximating to the Wave-Length of
Light. By W. Leitch, Assistant to the Professor of
Natural Philosophy in the University of Glasgow.
Communicated By Professor Tait, . * . 179

Note on Linear Partial Differential Equations. By Professor

Tait, . . . . . . 190

On the Oxidation Products of Picoline. By James Dewar,
F.R.S.E., Lecturer on Chemistry, Yeterinary College.

Edinburgh, • \ 192

Notes of some Experiments on the Rate of Flow of Blood
and some other Liquids through tubes of narrow
diameter. By J. Matthews Duncan, M.D., F.R.S.E.,
and Arthur Gamgee, M.D., F.R.S.E., . . 193

On Cystine (CLT7N02S). By James Dewar, F.R.S.E.,
Lecturer on Chemistry, Yeterinary College, Edinburgh,
and Arthur G-amgee, M.D., F.R.S.E., Lecturer on
Physiology, at Surgeon’s Hall, Edinburgh, . .201

Notes from the Physical Laboratory of the University. By

Professor Tait. (With a Plate), . . . 206

Donations to the Society, . 209

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

SESSION 1852-3.

CONTENTS.

Monday , 6tli December 1852.

PAGE

1. On a supposed Meteoric Stone, alleged to liave fallen in Hamp-

shire in September 1852. By Dr George Wilson, . .147

2. On the Glacial Phenomena of Scotland, and parts of England.

By Robert Chambers, Esq., . . . . 148

Donations to the Library, . . . . .153

Monday. 20th December 1852.

On the supposed occurrence of Works of Art in the Older Deposits.

By James Smith, Esq. of Jordanhill, . . . • 158

Tuesday , 4th January 1853.

1. On the Optical Phenomena and Crystallization of Tourmaline,

Titanium, and Quartz, within Mica, Amethyst, and Topaz.

By Sir David Brewster, K.H., D.C.L., F.R.S., and Y.P.R.S.
Edin., . . . . . . 158

2. On the Absolute Zero of the Perfect Gas Thermometer ; being

a Note to a Paper on the Mechanical Action of Heat. By
W. J. Macquorn Rankine, Esq., . . . .160

Donations to the Library, ; . . . .161

PAGE

11

Monday , 1 7 th January 1853.

1 . On a simplification of the Instruments employed in Geographical

Astronomy. By Professor C. Piazzi Smyth, . . .161

2. On the Mechanical Action of Heat, Section YI. : — A review of

the Fundamental Principles of the Mechanical Theory of
Heat ; with remarks on the Thermic Phenomena of Currents
of Elastic Fluids, as illustrating those Principles. By W. J.
Macquorn Rankine, Esq., . .... 162

Donations to the Library, . . . . 168

Monday , 7 th February 1853.

1. On the Structural Characters of Bocks. By Dr Fleming, . 169

2. Observations on the Speculations of the late Dr Brown, and of

other recent Metaphysicians, regarding the exercise of the
Senses. By Dr Alison, . . . . 170

Donations to the Library, . . . . . 172

Monday , 21st February 1853.

On the Summation of a Compound Series, and its application to a

Problem in Probabilities. By the Bight Bev. Bishop Terrot, 173

Monday , 7 th March 1853.

1. On the Species of Fossil Diatomaceas found in the Infusorial

Earth of Mull. By Professor Gregory, . . .176

2. On the Production of Crystalline Structure in Crystallised

Powders, by Compression and Traction. By Sir David Brew-'
ster, K.H., D.C.L., F.B.S., V P.B.S. Edin., . . 178

3. On the Structure and Economy of Tethea, and on an undescribed

species from the Spitzbergen Seas. By Professor Goodsir, 181
Donations to the Library, . . . . . 182

Monday , 21st March 1853.

On Circular Crystals. By Sir David Brewster, K.H<, D.C.L.,

F.B.S., V.P.B.S.E,, Associate of the Institute of France, 183
Donations to the Library, , . . . T88

For continuation of Contents see p. 3 of Cover.

Ill

Monday , 4 th April 1853.

PAGE

1. On Nitric Acid as a source of the Nitrogen found in Plants.

By Dr George Wilson, . . . . .189

2. Observations on the Amount, Increase, and Distribution of

Crime in Scotland. By George Makgill, Esq. ofKemback, 190

Monday , 18 th April 1853.

1 . Notice of recent Measures of the Ring of Saturn. By Professor

C. Piazzi Smyth, . . . . . 192

2. Chemical Notices. By Professor Gregory, . . . 193

3. Observations on the Structural Character of Rocks. Part II.

By Dr Fleming, . . . . .197

4. Some Observations on Fish, in relation to Diet. By Dr John

Davy, . . . . . . 197

Donations to the Library, . . . . . 198

. V' ^

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

SESSION 1853-4.

CONTENTS.

Monday , December 1853.

PAGE

Remarks on the Torbanehill Mineral. By Dr Traill, . 199

Notice of the Blind Animals which inhabit the Mammoth Cave

of Kentucky. By James Wilson, Esq,, . . 200

Donations to the Library, . . . .201

Monday , 19^ December 1853.

Additional observations on the Diatomaceous Earth of Mull, with
a notice of several New Species occurring in it, and Re-
marks on the value of Generic and Specific Characters in
the Classification of the Diatomaceae. By William Gre-
gory, M.D., Professor of Chemistry, . . . 204

On the Physical Appearance of the Comet 3, of 1853. By

Professor C. Piazzi Smyth, . . . . 207

Tuesday , 3d January 1854.

On the supposed Sea-Snake cast on shore in the Orkneys in
1808, and the Animal seen froiprH.M.S. Daedalus in 1848.

By Dr Traill, . Sr>' • ; . . 208

Donations to the Library, . . 216

[Turn over.

*

11

Monday, 1 6th January 1854.

PAGE

What is Coal? By Dr Fleming, . . . 216

Monday, 6 th February 1854.

Observations on the Structure of the Torbanehill Mineral, as

compared with various kinds of Coal. By Prof. Bennett, 217

Monday, 20th February 1854.

On certain Vegetable Organisms found in Coal from Fordel.

By Professor Balfour, . . . .218

Monday, 6th March 1854.

On the Impregnation of the Ova of the Salmonidm. By John
Davy, M.D., F.R.SS. Lond. & Edin , Inspector-General of
Army Hospitals, . . . . .219

Account of a remarkable Meteor seen on 30th September 1853.

By William Swan, Esq., .... 220

On the Mechanical Action of Heat. By W. J. Macquorn

Rankine, C.E., F.R.SS. Lond. & Edin., &c. . , 223

Donations to the Library, .... 224

Monday, 20 th March 1854.

On the Total Invisibility of Red to certain Colour-Blind Eyes.

By Dr George Wilson, . «• . . . 226

Donations to the Library, . . . .22 7

Monday, 3 d April 1854.

On a ]STew Hygrometer, or Dew-Point Instrument. By Pro-
fessor Connell, ..... 228

On the Stability of the Instruments of the Royal Observatory.

By Professor Piazzi Smyth, .... 229

On a General Method of effecting the substitution of Iodine for
Hydrogen in Organic Compounds, and on the properties of
Iodo-Pyromeconic Acid. By Mr James Brown, Assistant
to Thomas Anderson, ...... 235

Donations to the Library, . . . . . .236

For continuation of Contents, see page 3 of Cover.

Ill

Monday, 17 th April 1854.

PAGE

Notice of the Completion of the Time-Ball Apparatus. By

Professor C. Piazzi Smyth, .... 238

On the Mechanical Energies of the Solar System. By Profes-
sor William Thomson, . . . .241

Monday, ls£ May 1854.

On the Action of the Halogen Compounds of Ethyl and Amyl
on some Vegetable Alkaloids. By Henry How, Assistant
to Professor Anderson of Glasgow, .... 244

On the Mechanical Value of a Cubic Mile of Sunlight, and on
the possible density of the Luminiferous Medium. By
Professor W. Thomson. ..... 253

Account of Experimental Investigations to answer questions ori-
ginating in the Mechanical Theory of Thermo-Electric
Currents. By Professor W. Thomson, • . . 255

Dynamical Theory of Heat, Part VI. continued. A Mechanical
Theory of Thermo-electric Currents in Crystalline Solids.

By Professor W. Thomson, . . . . . 255

On the Structure of Diatomacea. By E. W. Dallas, Esq. . 256

Donations to the Library, ...... 259

N - % '> H ^

PROCEEDINGS

or THE

ROYAL SOCIETY OF EDINBURGH.

SESSION 1854-5.

CONTENTS.

Monday , 4th December 1854.

PAGE

Farther Experiments and Remarks on the Measurement of
Heights by the Boiling Point of Water. By Professor
J. D. Forbes, . . . . .261

On the Chemical Equivalents of Certain Bodies, and the Re-
lations between Oxygen and Azote. By Professor Low, 263
Donations to the Library, . . . .263

Monday , 18^ December 1854.

Some Observations on the Salmonidee. By John Davy,
M.D., F.R.S., Lond. and Edin., Inspector-General of
Army Hospitals, . . . .267

On the Structural Character of Rocks. Part III., embrac-
ing remarks on the Stratified Traps of the neighbourhood
of Edinburgh. By Dr Fleming, . . . 268

Donations to the Library, . . . . 269

[ Turn over.

PAGE

11

Tuesday , 2d January 1855.

Notes on some of the Buddhist Opinions and Monuments of
Asia, compared with the Symbols on the Ancient Sculp-
tured “ Standing Stones” of Scotland. By Thomas A.
Wise, M.D., ..... 272

Notes on the extent of our knowledge respecting the Moon’s

Surface. By Professor C. Piazzi Smyth, . 274

On the Interest strictly Chargeable for Short Periods of
Time. By the Bev. Professor Kelland, . . 274

Donations to the Library, . . . .276

Monday , 1 5th January 1855.

Some additional Experiments on the Ethers and Amides of
Meconic and Comenic Acids. By Henry How, Esq.
Communicated by Dr Anderson, . .277

On a Bevision of the Catalogue of Stars of the British Asso-
ciation. By Captain W. S. Jacob, H.E.I.C., Astro-
nomer at Madras. Communicated by Professor C.
Piazzi Smyth, ..... 279

Notice of Ancient Moraines in the Parishes of Strachur and

Kilmun, Argyleshire. By Charles Mac laren, Esq., 279

Monday , 5th February 1855.

On the Properties of the Ordeal Bean of Old Calabar, West-
ern Africa. By Dr Christison, . . . 280

Experiments on the Blood, showing the effects of a few
Therapeutic Agents on that Fluid in a state of Health
and of Disease. By James Stark, M.D., F.B.C.P., 282

Extracts from a Letter from E. Blackwell, Esq., containing
Observations on the Movement of Glaciers of Chamouni
in Winter. Communicated by Professor Forbes, . 283

Monday , 19 th February 1855.

On the Mechanical Action of Heat Supplement to the
first Six Sections and Section Seventh. By W. J. Mac-
quorn Bankine, Esq., C.E., F.B. SS. Lond. and Edinb., 287

[For continuation of Contents , see page 3 of Cover.

On an Inaccuracy (having its greatest value about 1") in the
usual method of computing the Moon’s Parallax. By
Edward Sang, Esq., . . . .292

Monday , 5th March 1855.

On Annelid Tracks in the Exploration of the Millstone Grits
in the South-west of the County of Clare. By Bobert
Harkness, Esq., F.G.S., Professor of Geology, Queen’s
College, Cork, . . . . .294

On Superposition. By Professor Kelland, . . 296

On the Colouring Matter of the Bottlera tinctoria. By
Thomas Anderson, M.D., Begius Professor of Chemis-
try in the University of Glasgow, . . .296

Donations to the Library, .... 298

Monday , \§th March 1855.

Experiments on Colour as perceived by the Eye, with Be-
marks on Colour-Blindness. By James Clerk Max-
well, Esq., B.A., Trinity College, Cambridge. Com-
municated by Professor Gregory, . . .299

Notice of the Occurrence of British newer Pliocene Shells
in the Arctic Seas, and of Tertiary Plants in Greenland.

In a letter from Dr Scoular of Dublin. Communicated
by James Smith, Esq., of Jordanhill, . . 301

Monday , 2 d April 1855.

Account of Experiments to ascertain the amount of Prof.

Wm. Thomson’s “ Solar Befraction.” By Prof. C.
Piazzi Smyth, ..... 302

On the Extent to which the Theory of Vision requires us to
regard the Eye as a Camera Obscura. By Dr George
Wilson, ..... 303

Besearches on the Amides of the Eatty Acids. By Thomas
H. Bowney, Ph.D., Assistant to Dr Anderson. Com-
municated by Dr Anderson, . . . 305

iv

Monday , \Qth April 1855.

PAGE

Notice of Some new Forms of British Fresh- Water Diato-
macese. By William Gregory, M.D., Professor of
Chemistry, ..... 306

On Glacial Phenomena in Peebles and Selkirk Shires. By

Robert Chambers, Esq., &c., . . . 308

Preliminary Notice on the Decompositions of the Platinum
Salts of the Organic Alkalies. By Thomas Anderson,
M.D., Regius Professor of Chemistry in the University
of Glasgow, . . . . .309

On the Volatile Bases produced by Destructive Distillation
of Cinchonine. By C. Greville Williams, Assistant
to Professor Anderson, Glasgow University, . 314

Monday , 30th April 1855.

Remarks on the Coal Plant termed Stigmaria. By the Rev.

Dr Fleming, . . . . .316

On Errors caused by Imperfect Inversion of the Magnet in
Observations of Magnetic Declination. By William
Swan, Esq., ..... 318

On the Accuracy attainable by means of Multiplied Obser-
vations. By Edward Sang, Esq., . .319

A - H h

PROCEEDINGS

OF THE

ROYAL SOCIETY OE EDINBURGH.

SESSION 1855-56.

CONTENTS.

Monday , 26th November 1855.

PAGE

On the Occurrences of the Plague in Scotland during the
Sixteenth and Seventeenth Centuries. By Robert
Chambers, Esq., . . . . 326

On a Problem in Combinations. By Professor Kell and, 326
Occurrence of Native Iron in Liberia, in Africa. From a
Letter of Dr A. A. Hayes, Chemist, Boston, U.S., to
Professor H. D. Rogers. Communicated by Dr Gre-
gory, ..... 327 •

Donations to the Library, . . . . 328

Monday , llth December 1855.

Geological Notes on Banffshire. By R. Chambers, Esq.,

F.R.S.E., &c., .... 332

On the Physical Geography of the Old Red Sandstone Sea
of the Central District of Scotland. By Henry Clif-
ton Sorby, F.G.S. Communicated by Professor Bal-
four, ..... 334

Donations to the Library, . . . . 334

11

Monday , 7 th January 1856.

PAGE

Remarks by Professor Cliristison in delivering the Keith

Medal to Dr Anderson of Glasgow, . . 337

Geometry a Science purely Experimental. By Edward

Sand, ..... 341

Notice respecting recent Discoveries on the Adjustment of

the Eye to Distinct Vision. By Professor Goodsir, 343

Monday , 2\st January 1856.

Memoir of Rear-Admiral Sir John Franklin. By Sir John
Richardson, C.B. Communicated by Professor Bal-
four, ..... 347

On the Geological Relations of the Secondary and Primary
Rocks of the Chain of Mont Blanc. By Professor
Forbes, ..... 348

Monday , 4 th February 1856.

On the Turkish Weights and Measures. By Edward

Sang, Esq., ..... 349

Observations on Polyommatus Artaxerxes, the Scotch Argus.

By Dr W. H. Lowe, .... 349

On Solar Light, with a Description of a Simple Photometer.

By Mungo Ponton, Esq., . . . 355

Monday , 18£/i February 1856.

On certain Cases of Binocular Vision. By Professor Wil-
liam B. Rogers. Communicated by Professor Kel-
land, ..... 356

Theory of the Free Vibration of a Linear Series of Elastic

Bodies. Part I. By Edward Sang, Esq., . 358

[For continuation of Contents see page 3 of Cover .

Ill

Monday , 3d March 1856.

PAGE

Observations on the Diatomaceous Sand of Glenshira. Part
II. Containing an Account of a number of additional
undescribed Species. By William Gregory, M.D.,
F.B.S.E., Professor of Chemistry in the University of
Edinburgh, . . . . . 358

Theory of the Free Vibration of a Linear Series of Elastic

Bodies. Part II. By Edward Sang, Esq., . 360

Monday , 17 th March 1856.

An Account of some Experiments on certain Sea-Weeds of
an Edible kind. By John Davy, M.D., F.E.S., Lond.
and Edin., &c., .... 363

On the Deflection of the Plumb-Line at Arthur’s Seat, and
on the Mean Density of the Earth. By Lieutenant-
Colonel James, R.E. Communicated by Professor
Forbes, ..... 364

On the Possibility of combining two or more independent
Probabilities of the same Event, so as to form one de-
finite Probability. By Bishop Terrot, . 366

Donations to the Library, . . . . 367

Monday , 7 th April 1856.

On Atmospheric Manoscopy, or on the direct Determi-
nation of the Weight of a given bulk of Air with
reference to Meteorological Phenomena in general,
and to the Etiology of Epidemic Diseases. By Dr
Seller, ..... 368

Researches on Chinoline and its Homologues. By C. Gre-
ville Williams. Communicated by Dr T. Ander-
son, ...... 370

On Fermat’s Theorem. By H. Fox Talbot, Esq., F.R.S., 371

IV

PAGE

On the Transmission of the Actinic Rays of Light through
the Eye, and their relation to the Yellow Spot of the
Retina. By George Wilson, M.D., . . 371

Donations to the Library, . . . . 375

Monday , 21st April 1856.

On the Prismatic Spectra of the Flames of Compounds

of Carbon and Hydrogen. By William Swan, Esq., 376
On the Laws of Structure of the more disturbed Zones of the
Earth’s Crust. By Professor H. D. Rogers, of the
United States, . . . . 378

On a Property of Numbers. By Balfour Stewart, Esq.

Communicated by Professor Kelland, . . 390

Analysis of Craigleith Sandstone. By Thomas Bloxam,

Esq., Assistant-Chemist, Industrial Museum, with a
Preliminary Note by Professor George Wilson, 390

Donations to the Library, . . . . 395

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

SESSION 1856-57.

CONTENTS.

Monday , ls£ December 1856.

PAGE

Opening Address, Session 1856-57. By Bishop Terrot, 398
On the Minute Structure of the Involuntary Muscular Tissue.

By Joseph Lister, Esq., F.B.C.S. Eng. and Edinb.
Communicated by Dr Christison, . • 413

Donations to the Library, . . * • 416

Monday , 15th December 1856.

On the Ovum and Young Fish of the Salmonidse. By Wil-
liam Ayrton, Esq. Communicated by Professor All-

man, . . • • • •

Notice of the Yendace of Derwentwater, Cumberland, m a let-
ter addressed to Sir William Jardine, Bart., by John

Dayy, M.D., . . • • i 1

On the Paces of the Western Coast of Africa. By Colonel
Luke Smyth O’Connor, C.B., Governor of the Gambia.
Communicated by Professor Kelland,

Donations to the Library, .

[ Turn over .

428

429

429

433

PAGE

ii

Monday , 5 th January 1857.

Some Remarks on the Literature and Philosophy of the

Chinese. By the Rev. Dr Robert Lee, . 433

Observations on the Crinoidea, showing their connection with
other branches of the Echinodermata. By Fort-Major
Thomas Austin, F.G.S. Communicated by Professor
Balfour, . . . . . 433

Donations to the Library, . . . . 435

Monday , 19$ January 1857.

On the application of the Theory of Probabilities to the ques-
tion of the Combination of Testimonies. By Professor
Boole. Communicated by Bishop Terrot, . 435

On New Species of Marine Diatomaceee from the Firth of
Clyde and Loch Fine. By Professor Gregory. Illus-
trated by numerous, drawings, and by enlarged figures, all
drawn by Dr Greville, . . . 442

Short Verbal Notice of a simple and direct method of Comput-
ing the Logarithm of a Number. By Edward Sang, Esq., 451
Donations to the Library, . . . . 451

Monday , 2d February 1857.

On the Urinary Secretion of Fishes, with some remarks on this
secretion in other classes of Animals. By John Da yy,
M.D., F.R.SS. London and Edinburgh, . 452

On the Reproductive Economy of Moths and Bees ; being an
Account of the Results of Von Siebold’s Recent Re-
searches in Parthenogenesis. By Professor Goodsir, 454
On the Principles of the Stereoscope ; and on a new mode of

exhibiting Stereoscopic Pictures. By Dr W. Macdonald, 455
Donations to the Library, . . . . 455

Monday , 16$ February 1857.

On the Crania of the Kaffirs and Hottentots, and the Physical
and Moral Characteristics of these Races. By Dr Black,

F.G.S. , 456

On a Roche Moutonnee on the summit of the range of hills
separating Loch Fine and Loch Awe. In a letter from
the Duke of Argyll to Professor Forbes, . 459

[ For continuation of Contents see page 3 of Cover .

Ill

PAGE

On M. J. Nickles’ claim to be the Discoverer of Fluorine in
the Blood. By George Wilson, M.D., F.R.S.E., Re-
gius Professor of Technology in the University of Edin-
burgh, ..... 463

Donations to the Library, .... 469

Monday , 2 d March 1857.

On the Functions of the Spinal Cord. By Professor Hughes

Bennett, ..... 470

On the Delta of the Irrawaddy. By T. Login, C.E., Pegu.

Communicated by William Swan, Esq., . 471

Notice of a Collection of Maps. By A. K. Johnston, Esq., 477

Monday , 16$ March 1857.

Notice respecting Father Secchi’s Statical Barometer, and on

the Origin of the Cathetometer. By Professor Forbes, 480
History of an Anencephalic Child. By Dr Simpson, . 482

On certain Laws observed in the Mutual Action of Sulphu-
ric Acid and Water. By Balfour Stewart, Esq. Com-
municated by Dr G. Wilson, . . . 482

Donations to the Library, .... 485

Monday , 6$ April 1857.

On the Structure of the Pedicellina. By Professor Allman, 486
On a Case of Lateral Refraction in the Island of Teneriffe.

By Professor C< Piazzi Smyth, . . 487

On Insect Vision and Blind Insects. By Andrew Murray,

Esq., ... . . . 487

On the mode in which Light acts on the Ultimate Nervous
Structures of the Eye, and on the relations between Sim-
ple and Compound Eyes. By Professor Goodsir, 489

Donations to the Library, .... 495

Monday , 20$ April 1857.

On the recently discovered Glacial Phenomena of Arthur’s

Seat and Salisbury Crags. By Robert Chambers, Esq. 497

IV

PAGE

On a Dynamical Top, for exhibiting the Phenomena of the
Motion of a system of invariable form about a Fixed
Point ; with some suggestions as to the Earth’s Motion.

By Professor Clerk Maxwell, . . 503

On the true Signification of certain Reproductive Phenomena

in the Polyzoa. By Dr Allman, . . 504

On the Destructive Distillation of Animal Matters. Part IV.

By Dr Anderson, Glasgow, . . . 505

Analysis of Specimens of Ancient British, of Red Indian, and

of Roman Pottery. By Murray Thomson, . 505

Theory of Linear Vibrations. Part VI. Alligated Vibra-
tions. By Edward Sang, . . . 507

Donations to the Library, . . . . 508

Index, . . . . . 511

Title and Contents, vol. iii.

/'VI

/ & /n

\

i 'l i «>