A

It 0 6
/

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

PROCEEDINGS

OF

THE ROYAL SOCIETY

EDINBURGH.

VOL. XXXIV.

NOVEMBER 1913 to JULY 1914.

2 3(8'!^

EDINBURGH:

PRINTED BY NEILL AND COMPANY, LIMITED.

MDCCCCXIV,

CONTENTS.

PAGE

Presentation of Bust of Lord Kelvin. (With Frontispiece ), ... 1

1. Opening Address by the President, Professor James Geikie, LL.D., D.C.L.,

F.R.S., F.G.S., delivered at the First Ordinary Meeting for the Session, held
on November 3, 1913, ........ 4

2. Observations on the Auditory 0 gan in the Cetacea. By Principal Sir Wm.

Turner, K.C.B., D.C.L., F.R.S. Issued separately December 31, 1913, . 10

3. Note on a Siliceous Sponge of the Order Hexactinellida from South Shetland.

By Principal Sir William Turner, K.C.B., D.C.L., F.R.S. Issued separately
December 31, 1913, ........ 23

4. Some Factorable Minors of a Compound Determinant. By Professor W. H.

Metzler. Issued separately December 31, 1913, . . . .27

5. The Theory of Bigradients from 1859 to 1880. By Thomas Muir, LL.D.

Issued separately February 19, 1914, ...... 32

6. The Kinetic Energy of Viscous Flow through a Circular Tube. By Professor

A. H. Gibson, D.Sc., University College, Dundee. Issued separately
February 19, 1914, ........ 60

7. The Axial Inclination of Curves of Thermoelectric Force : a Case from the

Thermoelectrics of Strained Wires. By John M‘Whan, M.A., Ph.D.,
Lecturer in Mathematics in the University of Glasgow. Communicated by
Professor Andrew Gray, LL.D., F.R.S. Issued separately March 20, 1914, . 64

8. The Path of a Ray of Light in a Rotating Homogeneous and Isotropic Solid.

By E. M. Anderson, M.A., B.Sc. Communicated by The General Secretary.

Issued separately March 20, 1914, . . . . . . 69

9. Principia Atmospherica : a Study of the Circulation of the Atmosphere. An

Address delivered at the request of the Council before the Royal Society of
Edinburgh, on December 1, 1913. By W. N. Shaw, LL.D., Sc.D., F.R.S.,
Director of the Meteorological Office, Reader in Meteorology in the University
of London. Issued separately March 23, 1914, . . . . 77

10. Enzymatic Peptolysis in Germinating Seeds. By Dorothy Court, B.Sc., Carnegie

Research Fellow. Communicated by Professor E. Westergaard. Issued
separately March 26, 1914, . . . . . . .113

11. A Study of the Curvatures of the Tasmanian Aboriginal Cranium. By L. W. G.

Buchner, Victorian Government Research Scholar in the Anthropology
Department of the University of Melbourne. Communicated by Professor
R. J. A. Berry. (With Three Folding Tables.) Issued separately April 28,

1914,

128

VI

Contents.

I’AGE

12. The Place in Nature of the Tasmanian Aboriginal as deduced from a Study of

his Calvaria. — Part II. His Relation to the Australian Aboriginal. By
Richard J. A. Berry, M.D. Edin., Professor of Anatomy in the University of
Melbourne ; and A. W. D. Robertson, M.D. Melb., Government Research
Scholar in the Anatomy Department of the University of Melbourne. (With
One Folding Table.) Issued separately April 29, 1914, . . . 144

13. A Chemical Examination of the Organic Matter in Oil-Shales. By John B.

Robertson, M.A., B.Sc., Carnegie Scholar. Communicated by Dr J. S. Flett,

F.R.S. Issued separately July 15, 1914, . . . . . 190

14. Notes on the Atmospheric Electrical Potential Gradient in the Industrial Dis-

tricts around Leeds. By Dan. W. Steuart and Ingvar Jorgensen. Com-
municated by James A. S. Watson, B.Sc. Issued separately July 14, 1914, . 202

15. On the Hall and the Transverse Thermomagnetic Effects and their Temperature

Coefficients. By F. Unwin, M.Sc., Assistant Lecturer in Physics, Heriot-
Watt College, Edinburgh. Communicated by Professor F. G. Baily. Issued
separately August 4, 1914, ....... 208

16. Some Factorable Continuants. By W. H. Metzler, Ph.D. Issued separately

September 3, 1914, . . . . . . . . 223

17. The Analytical Study of the Mechanism of Writing. By James Drever, M.A.,

B.Sc. Communicated by Dr Alexander Morgan. Issued separately September

3, 1914, . . . . . . . . .230

18. Abnormal Echinoids in the Collection of the Royal Scottish Museum. By

James Ritchie, M.A., D.Sc., Royal Scottish Museum ; and James A. Todd,

M.A., B.Sc. Communicated by William Eagle Clarke. (With a Plate.)

Issued separately September 4, 1914, ...... 241

19. Description of a Projection-Model of the 600-Cell in Space of Four Dimensions.

By D. M. Y. Sominerville, M.A., D.Sc., Lecturer in Mathematics, University
of St Andrews. (With a Plate.) Issued separately September 29, 1914, . 253

20. Changes of Electrical Resistance accompanying Longitudinal and Transverse

Magnetizations in Iron and Steel. By Professor C. G. Knott, D.Sc. Issued
separately December 14, 1914, ....... 259

Obituary Notices —

Dr A. C. L. G. Gunther, M.A., Ph.D., M.D., LL.D., F.R.S., etc., . . 269

John Sturgeon Mackay, M.A., LL.D., ...... 278

Professor John Gibson, ........ 285

Appendix —

Laws of the Society, . ...... 293

The Keith, Makdougall-Brisbane, Neill, and Gunning Victoria Jubilee Prizes, . 298

Awards of the Keith, Makdougall-Brisbane, Neill, and Gunning Victoria Jubilee

Prizes, .......... 300

Proceedings of the Statutory General Meeting, October 1913, 305

Proceedings of the Ordinary Meetings, Session 1913-1914, . . . 306

Proceedings of the Statutory General Meeting, October 1914, . . . 312

Accounts of the Society, Session 1913-1914, , 313

Contents. vii

PAGE

Appendix — continued.

The Council of the Society at January 1915, ..... 319

Alphabetical List of the Ordinary Fellows of the Society at January 1915, . 320

List of Honorary Fellows of the Society at January 1915, . . . 337

List of Ordinary Fellows of the Society elected during Session 1913-1914, . 339

Honorary Fellows and Ordinary Fellows deceased and resigned during Session

1913-1914 . . . . . ... . .339

List of Library Exchanges, . ..... 340

List of Periodicals purchased by the Society ..... 364

Additions to Library during 1914, by Gift or Purchase .... 368

Index, ........... 370

PROCEEDINGS

OF THE

lnstifuf/

APR 18 1914

JVat:

ROYAL SOCIETY OF EDINBURGH.

SESSION 1913-14.

Part I.] VOL. XXXIV. [Pp. 1-112.

CONTENTS.

NO. PAGE

Presentation of Bust of Lord Kelvin. (With Frontispiece), . 1

I. Opening Address by the President, Professor James Geikie,

LL.D., D C.L., F.R.S., F.G.S., delivered at the First Ordinary
Meeting for the Session, held on November 3, 1913, . 4

II. Observations on the Auditory Organ in the Cetacea. By

Principal Sir Wm. Turner, K.C.B., D.C.L., F.R.S., . . 10

{Issued separately December 31, 1913.)

III. Note on a Siliceous Sponge of the Order Hexactinellida from
South Shetland. By Principal Sir William Turner, K.C.B.,

D.C.L., F.R.S., . . ... . .23

{Issued separately December 31, 1913.)

IY. Some Factorable Minors of a Compound Determinant. By

Professor W. H. Metzler, . . ; . .27

{Issued separately December 31, 1913.)

Y. The Theory of Bigradients from 1859 to 1880. By Thomas

Muir, LL.D., 32

{Issued separately February 19 1914.)

YI. The Kinetic Energy of Yiscous Flow through a Circular Tube.

By Professor A. H. Gibson, D.Sc., University College, Dundee, 60

{Issued separately February 19, 1914.)

EDINBURGH :

Published by ROBERT GRANT & SON, 107 Princes Street, and
WILLIAMS & NORGATE, 14 Henrietta Street, Covent Garden, London.

MDCCCCXIY.

Price Six Shillings and Sixpence.

REGULATIONS REGARDING THE PUBLICATION OF PAPERS
IN THE PROCEEDINGS AND TRANSACTIONS OF THE
SOCIETY.

The Council beg to direct the attention of authors of communications to
the Society to the following Regulations, which have been drawn up in
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1. Manuscript of Papers. — As soon as any paper has been passed
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5 Special Discussion of Papers accepted for Publication. —
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the consent of the author, select this paper for Special Discussion. In the
case of such papers advanced proofs will be sent to the members of the
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tribution. A paper selected for Special Discussion will be marked with an
asterisk (*) and placed first on the Billet for the day of reading. Any
following papers for that day may be adjourned or held as read if the
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6. Communications not submitted for Publication, such as
Demonstrations of Experiments, Statement of Scientific Problems, etc.,
may be received by the Council, and may also be selected for Special
Discussion. The Council does not undertake to publish any notice of such
communications in the Proceedings or Transactions of the Society.

[Continued on page iii of Cover .

► *

Proc. Roy. Soc. Edin. ]

[Yol. XXXI Y.

THE RIGHT HON. LORD KELYIN, G.C.Y.O., F.R.S.,
President of the Royal Society of Edinburgh, 1873-1878, 1886-1890,
and 1895-1907.

[. Frontispiece

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

YOL. XXXIV.

1913-14.

Presentation of Bust of Lord Kelvin.

The General Statutory Meeting of the Royal Society of Edinburgh was
held in 24 George Street on Monday, 27th October 1913, at 4.30 p.m.

Principal Sir William Turner, K.C.B., President, in the chair.

Before the transaction of the usual business, the bust of Lord Kelvin
(see frontispiece), which had been gifted to the Royal Society of Edinburgh
by Lady Kelvin, was presented by Professor Crum Brown, acting for Lady
Kelvin, and received by the President for the Society.

Professor Crum Brown said : —

“ Mr President, Fellows of the Royal Society of Edinburgh,
Ladies and Gentlemen, — Lady Kelvin, knowing the great interest Lord
Kelvin always took in the Royal Society of Edinburgh, and knowing also
the high admiration and warm affection of the Fellows of the Society for
their late President, has, with thoughtful kindness, expressed the wish to
give this beautiful bust, by Mr Shannan, to remain in the rooms of the
Society as a permanent memorial, and has asked me to present it in her
name. I feel very highly honoured by Lady Kelvin’s request. I have had
the great privilege of intimate acquaintance with Lord Kelvin since my
boyhood, and it is impossible for me to tell how much I owe to him.

“ I shall not attempt a review of Lord Kelvin’s work or character, but I
may remind you of his supreme love of truth and of his intense interest in
everything, however apparently trivial, connected with the constitution or
with the working of the physical universe. These were the prime motives
to his work, and he carried it out in the same spirit. Having formulated a
problem, he followed the straightest road to its solution. Of course he
encountered difficulties : these he did not evade, he surmounted them. To

do so he had often to invent and construct special instruments of wholly

VOL. xxxiv. 1

2 Proceedings of the 'Royal Society of Edinburgh. [Sess.

novel type. These were always marked by singular ingenuity, and designed
so that they do the work for which they were made with the greatest
possible accuracy. Lord Kelvin was a great mathematician. We all
remember the “ green books,” always at hand, in which he worked out the
mathematical analysis of the data obtained in his experiments, and of any-
thing else he wished to subject to mathematical treatment. He was never
at a loss to find the mathematical key. He made no show of abstruse
formulae. In his mathematical as in his experimental work he took the
most direct and the simplest way consistent with accuracy. Lord Kelvin
was no intellectual miser. When, in the course of his scientific work, he
came across something which could be so applied as to be of practical
use, he developed this application, and thus became the inventor of
truly scientific instruments, differing in character from those he made for
purely scientific purposes only in this, that they are also used and very
highly prized by those who are not necessarily scientific, who perhaps do
not care about the dissipation of energy or vortex motion. These practical
men come, by using Lord Kelvin’s inventions, to see that pure science is not
vain ; they come to know something of the tree from its fruit. Lord Kelvin
was quite free from selfishness or jealousy. He rejoiced in his own work
and discoveries ; he rejoiced also in the discoveries of others. I recollect very
well his enthusiasm over the work of Becquerel, of Crookes, of Dewar, of
Graham Bell, and of many others. In the questions of first importance to
man, where science gives no help, Lord Kelvin was a humble and devout
disciple. In Lady Kelvin’s name I hand over to the Royal Society of
Edinburgh, through you, Sir, as President, this beautiful work of art and
striking likeness of Lord Kelvin, one of the greatest discoverers in pure
science, a true benefactor of mankind, our honoured President and dear
friend.”

After the bust was unveiled, Sir William Turner received it in the name
of the Society with the following words : —

“ I feel sure that no more appropriate Fellow of the Society could have
been chosen to act as spokesman on this occasion than our dear colleague
and friend, Professor Crum Brown. He has given so admirable a summary
of Lord Kelvin’s character and intellectual power as one of the great
scientific men of the age that I need not attempt to follow him in that
direction. But, speaking as the President of the Society, and speaking in
regard to the man who immediately preceded me in the presidential chair,
I think it might be useful and instructive to say a few words about Lord
Kelvin as Fellow of the Royal Society of Edinburgh. I find that Lord
Kelvin joined the Society in 1847. He remained a Fellow for sixty years.

3

1913-14.] Presentation of Bust of Lord Kelvin

Two years after he joined the Society, he made his first communication,
which was printed in our Transactions for the year 1849. It is interesting
to note that this communication was on the subject of heat, and for ten
years after that date he produced a series of most important memoirs
on heat and other forms of activity, showing himself to be one of the
most active-minded and original-minded men engaged in physical science.
Our Transactions are a valuable record of all the early work which
he gave to the world; and he looked upon the Society as the medium
through which his ideas were to be submitted to the consideration of his
fellow men of science.

“ I can only refer to the numerous communications Kelvin made to the
Society ; and it is interesting to note that there was a communication from
him in our Proceedings for 1906, the year before he died. This was a
great feature in Lord Kelvin’s intellectual career — he had an active mind
to the end. The last communication published in our Proceedings was on
the initiation of deep-sea waves. The sea and the deep sea exercised
indeed an important influence over his practical career. As we all know,
it was through Lord Kelvin’s investigations that the laying and the
commercial working of the Atlantic cable were brought about, and his
improved compass has been a boon to all seamen. In 1873 Kelvin was
elected our President for the period of five years. In 1886 he was for a
second time chosen for a similar period. He had served for four years of
the second period when the Council of our Society received an informal
intimation from the Council of the Royal Society of London that they wished
Lord Kelvin to be their President. It was felt that it would be difficult
to discharge the duties of this office if he remained President of the
Edinburgh Royal Society. Accordingly it was suggested that we might
be able to surrender Lord Kelvin to the Royal Society of London. This
our Council agreed to do ; and in 1890 Lord Kelvin became their President.
When in 1895 he retired from his Presidentship in London, he was for the
third time appointed our President, and he continued in this office till his
death in 1907. We can at once understand how Lady Kelvin should feel
desirous that, so far as marble can perpetuate personality and expression,
there should be such a perpetual memorial of her great husband in the
building of the Society which he had adorned in the double capacity of
Fellow and President. I ask Professor Crum Brown, as the mouthpiece of
Lady Kelvin on this occasion, to be good enough to convey to her Ladyship
our most devoted and hearty thanks for this admirable bust of her late
husband, which will form one of the precious possessions of the Society.”

4

Proceedings of the Royal Society of Edinburgh. [Sess.

I. — Opening Address by the President, Professor James Geikie,

LL.D., D.C.L., F.R.S., F.G.S., delivered at the First Ordinary Meeting
for the Session, held on November 3, 1913.

Gentlemen, — For the high honour you have done me in electing me to the
Presidency of this, the premier scientific Society of Scotland, I offer you
my grateful thanks. I am proud indeed that you should have deemed me
not unworthy to succeed the eminent men who have heretofore occupied
this chair. My complacency, however, is tempered, if not subdued, by the
consciousness of my own limitations. But if I cannot, like my predecessors,
add lustre to the office I hold, I can at least endeavour to devote all my
energies to the performance of its duties.

It is matter of sincere congratulation that our Society continues to
prosper, and to keep up its reputation by the number and value of its
contributions to the stock of knowledge. During the past session no fewer
than 46 papers were communicated. Of these 19 dealt with chemical and
physical subjects; 19 were zoological; 3 botanical; 2 geological ; while
pure mathematics, engineering, and anthropology were each represented
by one paper. In addition to these papers, two addresses were delivered
at the request of the Council — one being physiological and the other
astronomical.

During the session, I regret to say, our Society has sustained not a few
losses — twenty-three of our fellow-members having died. Of this number,
some will be long remembered by us not only for the distinction of their
own careers, but for the active part they took in conducting the affairs of
the Society.

Ramsay Heatley Traquair, M.D., LL.D., F.R.S., F.G.S. . . . Dr
Traquair became a Fellow of the Society in 1874, and served many years
on the Council — his first term of office being from 1875 to 1878, and his last
from 1904 to 1910, when he acted as Vice-President. He communicated
many important papers to the Society, and was awarded the Makdougall-
Brisbane and Neill Medals. Dr Traquair died on 24th November 1912,
. . . [See Obituary Notice, Proceedings , vol. xxxiii. pp. 336-341.]

John William Shepherd, Glasgow, was elected in 1897. He died on
26th November 1912.

5

1913-14.] Opening Address by the President.

Andrew Jamieson, M.Inst.C.E. . . . He was elected a Fellow of the
Society in 1882, and died on 4th December 1912. . . . [See Obituary
Notice, Proceedings , vol. xxxiii. pp. 334, 335.]

Sir George Howard Darwin, K.C.B., M.A., LL.D., F.R.S., second son
of the famous naturalist, was born in 1845, and died on 7th December 1912.
After a brilliant career at Cambridge, he became barrister in 1874, but
subsequently returned to Cambridge and devoted himself to mathematical
science, and in 1883 was elected Plumian Professor of Astronomy and Experi-
mental Philosophy. He is the author of many important and suggestive
papers, a number of which appeared in the Proceedings and Philosophical
Transactions of the Royal Society, of which Society he became a Fellow
in 1879, and was the recipient of the Copley and Royal Medals. The great
merits of his original researches have been recognised by many Universities
at home and abroad, and by learned Academies and Institutions all the
world over, who have enrolled his name among their hon. members. He
was elected an Honorary Fellow of this Society in 1897.

Lieut.-Col. Frederick Bailey obtained his commission in the Royal
Engineers in 1859, and went to India in 1864, where he served in the
Bhutan Expedition of 1864-5, for which he obtained a medal. In 1871 he
was attached to the Indian forest service, in which department he remained
for close on twenty years, having during that long period occupied several
very important posts. So highly were his services appreciated by the
Indian Government that he was eventually appointed Inspector-General
of Forests. In 1890 temporary illness compelled him to return to this
country. About this time the importance of Forestry as a branch of
University education had been recognised by the institution of a Lecture-
ship on the subject in the University of Edinburgh, and Lieut.-Col. Bailey
was called upon to become first lecturer. He threw himself with charac-
teristic zeal into his work, and soon gained the confidence of his students
and the admiration of his colleagues. It is chiefly due to his indefatigable
exertions that a degree in Forestry was eventually instituted by the
University Court. Nor can it be doubted that it is to his energy and
enthusiasm that the subject of Forestry now occupies so prominent a
position not only in the University of Edinburgh but in Scotland generally.
Lieut.-Col. Bailey also found additional outlets for his energies as an active
member of the Royal Scottish Arboricultural Society, and as Secretary of the
Royal Scottish Geographical Society. This latter post he occupied with
conspicuous ability for many years, until the increasing work of his Lecture-

6

Proceedings of the Royal Society of Edinburgh. [Sess.

ship compelled him in 1903 to resign. For four years longer he retained
his position at college, when, to the regret of his colleagues, failing
health obliged him to retire. Lieut.-Col. Bailey was elected a Fellow of
the Society in 1894, and served one term on the Council (1896-99). His
death took place on 21st December 1912.

John M£ Arthur, F.C.S., Sussex. . . . He was elected to the Fellowship
of the Society in 1888, and died on 19th December 1912. . . . [See Obituary
Notice, Proceedings, vol. xxxiii. p. 333.]

Robert M. Ferguson, Ph.D., LL.D., who died on 31st December
1912, at the advanced age of 84, was elected a Fellow in 1868, and served
three terms on the Council. He acted also as the representative of the
Society on George Heriot’s Trust. . . . [See Obituary Notice, Proceedings,
vol. xxxiii. pp. 342-345.]

A. Beatson Bell, advocate, of Kilduncan, Kingsbarns, Fife, and a
former Chairman of H.M. Prison Commissioners for Scotland, died on
6th January 1913, in his 81st year. He was elected a Fellow in 1886,
and served three terms on the Council. Mr Bell was all his life much
interested in educational matters, having acted as a director of Edinburgh
Academy, a governor of Donaldson’s Hospital, and a governor of the
Trust for Education in the Highlands. He held various other important
positions, such as director of the Royal Institution for the Home Relief
of Incurables, and director of the Royal Sick Children’s Hospital. He
was also a Fellow of the Royal Scottish Society of Arts, and served as
President of that Society from 1897 to 1899.

George Alexander Gibson, D.Sc., M.D., LL.D., F.R.C.P.E., was elected
a Fellow in 1881, and served one term on the Council. He died on 18th
January 1913, in his 59th year. I need not attempt to appraise Dr
Gibson’s position as a medical man — we know that he was a brilliant
member of his profession, respected and beloved by all who knew him.
It is hardly too much to say that the premature death of this distinguished
physician has been mourned by the whole community, and has been felt
as a great loss to this Society.

Sir William White, K.C.B., F.R.S., London, was elected a Fellow in
1890. Sir William, who has been called “ the father of the modern British
Navy,” had a most notable career. With no advantages of fortune or social
position, he worked his way in the Naval service from the humble posi-
tion of a shipwright apprentice to the important position of Director of

7

1913-14.] Opening Address by the President.

Naval Construction. Under his superintendence some two hundred and
fifty ships of various types were added to our Navy at a cost of about one
hundred millions sterling, and for the work of construction of that great fleet
Sir William was ultimately responsible. He died on 27th February 1913,
in the 68th year of his age.

J. J. Kirk Duncanson, M.D., studied medicine at Edinburgh and various
medical schools on the Continent. He graduated M.D. at the University of
Edinburgh in 1871, was elected to the Fellowship of our Society in 1890,
and died on 12th March 1913.

Walter Whitehead, F.R.C.S.E., was formerly Professor in Clinical
Surgery in Victoria University, Manchester; past-President of the British
Medical Association ; and author of many important works in surgery. He
was elected a Fellow in 1881, and died on 19th August 1913.

James Gordon MacGregor, D.Sc., LL.D , F.R.S., Professor of Natural
Philosophy in the University of Edinburgh, passed away very suddenly on
21st May 1913. He was elected to our Fellowship in 1880, and served one
term on the Council. His genuine character had endeared him to a wide
circle of friends, who could not but appreciate his kindly, frank manner and
engaging simplicity ; while the whole-hearted zeal with which he devoted
himself to his duties gained the admiration of his colleagues. Professor
MacGregor was a sterling man, whose premature death was deeply
regretted.

William Colin Mackenzie, M.D., F.R.C.S., Melbourne, Australia, who
was elected a Fellow of the Society in 1905, was Demonstrator in Anatomy
in the University of Melbourne.

John Penny, M.B., C.M., D.Sc., Cumberland, elected 1900, died 19th
June 1913. He was a distinguished medical graduate of Edinburgh
University, who afterwards specialised in the Department of Public Health,
and obtained the degree of D.Sc. Although as a medical officer of health
his time was largely occupied, he yet engaged actively in research, and con-
tributed a number of important papers to various medical publications.

William Gayton, M.D., M.R.C.P., M.R.C.S., etc., was elected to the
Fellowship of the Society in 1900, and died in August 1913. He was
Medical Superintendent of the N.W. Fever Hospital, and for thirteen years
of Homerton Small -pox Hospital. Dr Gayton was the author of various
papers on vaccination and small-pox.

8

Proceedings of the Royal Society of Edinburgh. [Sess.

James M‘Cubbin, B.A., Kilsyth, was elected a Fellow of the Society in
1899, and died on 2nd September 1913. He was latterly Rector of the
Burgh Academy, Kilsyth.

Hugh Marshall, D.Sc., F.R.S., Professor of Chemistry, Dundee Uni-
versity College, was elected a Fellow in 1888, and died on 6th September 1913,
at the early age of 46. He had a distinguished career at the University of
Edinburgh, graduating as D.Sc., in his 21st year, a triumph which, so far
as I know, is unique. He was for a number of years assistant to Professor
Crum Brown, and Lecturer in the University on Mineralogy and Crystallo-
graphy, until his appointment to the chair of Chemistry at Dundee in 1908.
Although his time was much occupied in teaching, Professor Marshall yet
found time to engage in original research, and published various valuable
papers on chemical and crystallographical subjects. The quality of this
research work was attested by the award of the Gunning “ Joseph Black ”
Prize of the University, and of the Keith Prize and Medal of this Society,
as also by his election to the Fellowship of the Royal Society of London.

Alexander Macfarlane, M.A., D.Sc., LL.D., Ontario, Canada, was
elected in 1878, and died in September 1913, aged 62. He greatly dis-
tinguished himself as a student of mathematics in the University of
Edinburgh, where he graduated as D.Sc. — his thesis, “ On Electric Sparks
in Air,” appearing subsequently in the Transactions of this Society. For
some time he acted as assistant to the late Professor Chrystal, and in 1885
was appointed Professor of Physics in Texas University. He latterly
devoted much attention to the study and development of vector algebras,
his latest communication on the subject having been read before the
Congress of Mathematicians which met at Cambridge in 1912.

Sir Walter Noel Hartley, D.Sc., F.R.S., was elected in 1877, and died
on 11th September 1913. He was Hon. Fellow of King’s College, London,
and for some time Professor of Chemistry in the Royal College of Science
for Ireland. He was author of works on air and its relations to life, and on
water, air, and disinfectants, and communicated a number of papers to the
Royal Society of London, the Fellowship of which he attained in 1884. He
contributed also to the Journal of the Iron and Steel Institute, the Trans-
actions of the Chemical Society, and to the publications of various other
scientific institutions. Amongst the honours conferred upon him in re-
cognition of his work he was awarded the Longstaff Medal of the Chemical
Society for researches in spectro-chemistry.

9

1913-14.] Opening Address by the President.

John Macmillan, M.A., D.Sc., M.B., C.M., etc., Edinburgh, was elected
in 1876, and died on 7th October 1913. He was a brilliant student, first at
St Andrews, where he graduated as M.A., and afterwards at the Uni-
versity of Edinburgh, where he obtained the degree of B.Sc. Later on he
entered upon the study of medicine at the same university, and graduated
M.B., C.M., subsequently passing as B.Sc. in Public Health, and finally
obtaining the doctorate of science. With such an academic career Dr
Macmillan could hardly fail to make his mark in his profession, and by his
medical brethren he was held in the highest esteem. As Lecturer in
Medical Jurisprudence in the Extra-mural School of Medicine, Edinburgh,
he was much appreciated by his pupils ; while as a practitioner he endeared
himself to his patients by his unfailing kindness and sj^mpathy.

Sir John Batty Tuke, M.D., D.Sc., LL.D., was elected in 1874, and
served three terms on the Council; he died on 13th October 1913.
Born in 1835, in Yorkshire, he came early to Edinburgh, and graduated in
medicine in 1856. Shortly afterwards he went to New Zealand, where he
was attached to the colonial forces as surgeon, becoming senior medical
officer on the outbreak of the Maori War in 1860. On his return to this
country he devoted himself especially to the treatment of mental diseases,
and soon attained eminence in his profession. He occupied many im-
portant positions as a medical man, and was twice elected to represent
the Universities of St Andrews and Edinburgh in Parliament. During
his term of office he naturally took great interest in all educational matters,
and for these services, as well as for his eminence as a physician, he
obtained honorary degrees from Trinity College, Dublin, and the University
of Edinburgh. As member of Parliament for the Universities of Edinburgh
and St Andrews he was of great service in pressing the claims of the
Society upon the Government during the negotiations in regard to the
removal of the Society from the Royal Institution to its present premises
in George Street.

William Donaldson, M.A., was elected in 1896, and died on 16th
October 1913. For over thirty years he was headmaster and controller of
Viewpark School — a private educational institute in this city. He was
devoted to his profession, and held in high esteem by all who knew him —
and by none more so than his pupils.

10

Proceedings of the Royal Society of Edinburgh. [Sess.

II. — Observations on the Auditory Organ in the Cetacea.

By Principal Sir Wm. Turner, K.C.B., D.C.L., F.R.S.

(Read December 1, 1913. MS. received December 2, 1913.)

Early in September of this year I received from the Falkland Islands
a box, dispatched by Mr G. Millen Coughtrey, a former student of the
University, now an employe in the New Zealand Whaling Company. It
contained a number of specimens which illustrated the anatomy of the
auditory apparatus in the Cetacea. The whales were caught in the South
Atlantic, mostly at South Shetland, though some were from Graham’s Land,
at which place he had been whaling last season.

External Auditory Meatus and Earwax.

The Cetacea do not possess an auricle or pinna of the ear. A small
external opening capable of admitting a probe may be seen, when carefully
looked for, at the side of the head, behind the outer angle of the eye. It
is the orifice of the external auditory meatus, which penetrates the cutis
and the thickness of the blubber to reach the tympano-petrous bone in
which the essential parts of the organ of hearing are situated. The length
of the meatus varies in different species. The lumen of the meatus may
easily be overlooked, but it widens in its course, especially as it approaches
the tympanic bone. It is usually destroyed in removing the blubber,* and
has not received much attention in cetological literature.

The presence in it of a ceruminous secretion, the earwax, has, however,
been occasionally noted. Thomas Buchanan, surgeon in Hull nearly a
century ago,f described and figured in 1828 dissections of the meatus and
tympanum in the Greenland whale, Balcena mysticetus. He saw in the
meatus an unctuous cerumen of a greyish-blue colour, “but in no great
quantity.” He thought that the collapsed state of the orifice, the great
length of the meatus, its winding course, a valve-like obstruction about its
middle, and the unctuous secretion tended to prevent the passage of sea
water down the auditory canal, in which none was present in the specimens

* Robert Gray, “ Auricular Opening and External Auditory Meatus in Balcena
mysticetus Journal Anat. and Phys ., vol. xxiii., 1889.

t Physiological Illustrations of the Organ of Hearing , London, 1828. Hull at that time
was the great shipping port of the whaling industry.

11

1913-14.] The Auditory Organ in the Cetacea.

he dissected. Carte and Macalister described * the meatus in Balcenop-
tera rostrata as lined by a pseudo-mucous membrane of modified cuticle,
arranged in three longitudinal folds, and filled with a dark, greyish sebaceous
substance produced in ceruminous glands, the openings of which were
visible on the mucous membrane. The most recent account of the meatus
and its contents has been, given by D. G. Lillie, j* He described in Baloe-
noptera musculus the opening of the meatus, its course to the tympanum,
where the lumen widened to 1^ inch diameter, and its relation to the mem-
brana tympani. The meatus contained a solid plug of wax, the base or
deep end of which was cup-like and moulded on the convex sac-like surface
of the membrana tympani, which projected into the deep end of the
meatus. The cup was about 1 inch deep and 1J inch in breadth. The
plug of wax was about 5 inches long, and its outer part formed a thin
flattened rod which lay in the inner half only of the meatus. Lillie stated

Fig. 1. — Plug of earwax from meatus o LMegaptera longimana, slightly reduced in size.

that the meatus appeared to be full of water, in which the wax and the
tympanic sac were immersed.

Mr Coughtrey’s collection contained several good specimens of plugs
of dark, yellowish-brown earwax.

Megaptera longimana. — A plug from each auditory meatus of a hump-
backed whale, captured January 1913, was sent. One was complete, the
other was not so perfect: they were 150 and 159 mm. (6 and inches)
long respectively. The tympanic end, 22 mm. (about J inch) broad and
10 mm. thick, was hollowed into a cup 22 mm. deep, which without doubt
had been in close apposition with the convex sac-like tympanic membrane
that had occupied the deep expanded part of the meatus (fig. 1). The plug
gradually diminished in diameter, and at the opposite end it was flattened,
only 12 mm. broad and 1 mm. thick. The surfaces of the plug were marked
with shallow ridges and furrows which extended in its long diameter.

A much smaller plug, 112 mm. long, was included in the collection.
The tympanic end, not cup-like, had apparently been broken, its transverse
diameter was 12 mm., and it rapidly narrowed to a point at the opposite

* Trans. Roy. Soc. London , 1867.

t Proc. Zool. Soc. London , p. 769, 1910, with figures and plate.

12

Proceedings of the Royal Society of Edinburgh. [Sess.

end. The specimen was not labelled, but had probably been from the
meatus of another Megaptera.

Balcenoptera sibbaldi. — A single plug of earwax from one meatus of a
Blue Whale, captured in South Shetland in 1912, was sent. It had been
injured at the tympanic end, and only a portion of the cup-like cavity had
been preserved. The plug was 50 cm. (nearly 20 inches) long, 26 mm.
(1 inch) broad, and 12 mm. thick at its deep end. It gradually diminished
in breadth and thickness, so that the opposite outer end, though 20 mm.
(| inch) broad, was only 3 mm. thick, and possessed a flattened, ribbon-like
aspect (fig 2, A). The surfaces of the plug were fluted longitudinally, and

Fig. 2. — Earwax from meatus of Balcenoptera sibbaldi , natural size. A, outer fourth of plug with
thin flattened end to the right ; B, tympanic end with cup -like depression.

had doubtless been adapted to ridges and furrows on the surface of the lining
membrane of the meatus. Cough tre}T had noted that the plug gave a very
good impression of the canal in which it was situated. The tympanic end
of a second plug, 80 mm. long, 34 mm. in greatest breadth, and 15 mm.
thick, had been preserved. The cup-like cavity was nearly complete and
was 15 mm. in depth (fig. 2, B).

The length of the auditory meatus in the Cetacea bears a proportion to
the thickness of the blubber on the side of the head. If the wax plug
were in every case of equal length with the meatus, it would be a gauge to
the thickness of the blubber, but in the specimen dissected by Lillie the
plug was not equal in length to the meatus. I am not acquainted with
any exact measurement of the thickness of the blubber on the side of the
head in Megaptera. Sir John Struthers in his account of the Tay

13

1913-14.] The Auditory Organ in the Cetacea.

Megaptera* gave 4 inches in the fore part of the carcase and 3 inches
further back as the thickness of the blubber, but the length of the wax
club in the South Shetland Megaptera indicated a greater thickness on
the side of its head. In the Longniddry B. sibbaldi which I dissected in
1869-70 f the blubber on the top of the beak and cranium was 8 to 15
inches thick, whilst in front of the dorsal fin it was 12 to 16 inches, and
behind that fin 14 to 21 inches.

Tympano-petrous Bones.

The collection contained the following specimens : —

Megaptera longimana. — (a) Right and left tympano-petrous bones of the
Humpbacked Whale, from a specimen captured in 1913 near Bryde Island,
Graham’s Land; the tympanies were 109 and 113 mm. (4J and 4J inches)
respectively in length. ( b ) Left tympano-petrous tympanic, 108 mm. long,
(c) Right and left tympanies, 106 mm. long, (d) Right tympanic, 107
mm. long.

Balcenoptera sibbaldi. — (a) Three pairs of tympano-petrous bones of
the Blue Whale from South Shetland, captured 1912, and (b) a single left
tympanic. The tympanies as a rule varied in length from 121 to 129 mm.,
but one pair measured exceptionally 146 and 148 mm. (about 5f inches).

Balcenoptera musculus. — A pair of tympano-petrous bones from a
whale captured at Admiralty Bay, South Shetland, in November 1912, is
labelled B.W., i.e. Blue Whale. The examination of these specimens
satisfied me that the tympanic differed from that bone in B. sibbaldi in
several particulars, as follows : It possessed a deep groove on the outer
surface parallel and close to the posterior border, which gave to that border
a more definite character than was the case in B. sibbaldi. On the other
hand, it did not possess the long broad groove parallel to and bounding
the outer side of the lower border, which gave rise in sibbaldi to a very
prominent keel; the Eustachian end of the tympanic cleft was also less
scooped out than in sibbaldi. The tympanic was 125 mm. long, 89 high,
and 77 in greatest breadth. In one of the pair the opisthotic process of
the petrous was entire, 435 mm. long by 135 mm. in greatest breadth,
almost identical in its dimensions with those of a large B. sibbaldi.

Differing from Sibbald’s Whale in several particulars, the tympanies
more closely corresponded in their characters with B. musculus, so that I
am disposed to regard this pair of specimens as from that species.

* Anatomy of the Humpbacked Whale, Edinburgh, 1889.

t Account of the great Finner Whale, stranded at Longniddry, Trans. Boy. Soc.
Edin.} vol. xxvi., 1870.

14

Proceedings of the .Royal Society of Edinburgh. [Sess.

This series of tympanies are of importance in showing that the
Balsenopteridse, Megaptera longimana, Balcenoptera sibbaldi, and B.
musculus, which frequent the North Atlantic and are; captured in Scottish
waters, are also denizens of the South Atlantic. The University Museum
also contains a pair of tympanic bones from Balcenoptera borealis,
Rudolphi’s whale, the Sye Whale, from the South Atlantic,* captured in
1911, which is also a Scottish species.

Many naturalists have described with more or less detail the tympano-
petrous bones in the whalebone and toothed whales. I have also figured
in my descriptive Catalogue f the characters of the tympanies in a large
number of species. The additions to the collection through the recent gift
of Mr Coughtrey have enabled me to study more completely the relations
of the tympanic and petrous bones to each other, to the chain of tympanic
ossicles, and the approximate arrangement of the membrana tympani and
the external auditory meatus. Carte and Macalister had previously given a
careful description of the tympano-petrous in Balcenoptera rostrata, and
Struthers had recorded their characters in Megaptera longimana, but the
dissections of D. G. Lillie of the region in Balcenoptera musculus are much
more complete, as he had the advantage of studying the bones along with
the associated soft parts. The University collection contains specimens of
these bones in both the whalebone and toothed whales ; they corresponded
with each other in general characters, though with modifications in detail,
which expressed specific and generic differences. In no specimen, however,
had the external meatus, the tympanic membrane, and the Eustachian tube
been preserved.

The following description is based on the characters of the tympano-
petrous bones in Balcenoptera sibbaldi, \ though with specific modifications it
applies generally to the baleen whales. The tympanic bone was keeled on
its inferior surface. Its outer surface was convex and marked by an
oblique, strong, relatively wide groove-like depression which divided it into
an anterior and a posterior part, the latter of which was the larger. The
upper border of this surface was sinuous and was connected by a broad
posterior pedicle to the under-border of the long, flattened, winglike opis-
thotic process of the petrous. The anterior surface of the posterior pedicle
was hollowed, smooth, directed towards the tympanic cavity and the meatus,

* Catalogue, p. 58 ( G . Bpt., 5). I described a Scottish specimen in Journ. Anat. and
Phys ., April, 1882.

+ The Marine Mammals in the Anatomical Museum of the University of Edinburgh ,
London, 1912 ; also “ The Right Whale of the North Atlantic ( Balcena biscayensis )” in Trans.
Boy. Soc. Edin ., vol. xlviii. part 4, 1913.

I The University Museum now contains eighteen tympanic bones of Sibbald’s Whale.

15

1913-14.] The Auditory Organ in the Cetacea.

and had evidently been invested by the tympanic membrane (fig. 3, Au),
where it formed the cul-de-sac which projected into the auditory meatus ;

Fig. 3. — Outer aspect of left tympano-petrous bones of Balcenoptera sibbaldi , natural size. A,
anterior end, P, posterior end of tympanic ; Au, indicates the region adjoining the external
auditory meatus covered by the tympanic membrane and the place of projection into meatus of
tympanic membrane ; l , lip-like process of sinuous border with which malleus is fused ; M,
head of malleus ; S, head of stapes in funnel-like depression on inner wall of tympanum ; L,
labyrinthine part of petrous ; Pr, pre-otic, and Op, opisthotic parts of petrous cut across ; Ap,
anterior, and Pp, posterior tympano-petrous peduncles. The incus is not figured, as it would
have obscured the stapes.

the smooth surface was bounded by a rough area, to which had doubtless
been attached the deep end of the wall of the meatus. The sinuous border

16

Proceedings of the Royal Society of Edinburgh. [Sess.

in front of the posterior pedicle was at first concave, then somewhat elevated,
and was succeeded by a narrow, deep groove, which formed the posterior
boundary of a strong curved process. I have elsewhere * named this process
lip-like or mallear, for the malleus was fused with it ; it ascended towards
but did not touch the under surface of the labyrinthine part of the petrous,
and ended in a free rounded edge (fig. 3, l). At its front was the wide
groove-like depression which separated the posterior from the anterior part
of the outer surface of the tympanic. The upper border of this part of the
surface was connected by a broad anterior pedicle *j* to the pre-otic division
of the petrous. The labyrinthine or proper periotic division of the petrous
was relatively small ; it lay between and gave origin to the pre-otic and
opisthotic divisions of the bone, and it formed the roof and inner wall of
the tympanic cavity (fig. 3, L).

The gap between the anterior and posterior pedicles, the sinuous border,
and the edge of the labyrinthine roof had without doubt been associated
with the membrana tympani, and through the large part of the gap
behind the lip-like process the sac-like prolongation of this membrane had
projected into the lumen of the meatus, the wall of which had been attached
to the margin of the gap.

Buchanan, in his Illustrations (op. cit.), figured dissections of the dilated
tympanic end of the meatus in Balcena mysticetus, and showed the sac -like
surface of the tympanic membrane, which formed a convex projection into
its lumen and was enclosed by its wall. He stated the sac to be divided
internally into a major and a minor concavity by a valve-like membranous
process from the wall, to the whole length of which the slender process of
the malleus was attached, whilst the handle was connected with the outer
edge of the osseous tympanum. Buchanan adopted the view of Sir Everard
Home, that the membrana tympani had a muscular layer, to which he
added a reticulated nervous plexus situated subjacent to the cuticle.
KnoxJ saw in Balcenoptera rostrata a bag-like projection of the membrana
tympani projecting into the auditory meatus; he stated that in a foetal
Balcena mysticetus the membrane, though thick, is not muscular. The
presence of muscular and nerve fibres in the membrane is not now accepted.
Lillie, in his excellent description and figure of the membrana tympani in
B. musculus, showed that it formed a sac, not unlike the finger of a glove,
about 3 inches long and § inch in diameter, which projected into the dilated

* Marine Mammals , op. cit. pp. 20, 74.

t The anterior and posterior pedicles in Balcenoptera rostrata were thin plates of bone
and were very easily fractured.

tj; Catalogue of Anatomical Preparations of the JVhale, Edinburgh, 1838.

17

1913-14.] The Auditory Organ in the Cetacea.

lumen of the auditory meatus, where its somewhat rounded end fitted into
the cup-like base of the plug of wax. By its opposite end it was con-
tinuous with the membranous lining of the tympanic cavity. A ligament
about 1 inch long and 5 mm. broad sprang from the upper part of the
sac, passed towards the tympanic cavity under the malleo-incal joint, and
became attached to the manubrium of the malleus. The tympanic sac and
the ligament were together about 4 inches long.*

The Tympanic Ossicles are frequently missing in museum specimens,
and I have carefully looked for them in the bullse of the whales in the

Fig. 4. — Chain of left tympanic ossicles, tympanic cavity and cleft of Balcenoptera sibbaldi, natural
size seen from above. A, anterior end of tympanic ; E, Eustachian end of cleft ; Ap, anterior
tympano-petrous peduncle cut across ; l , lip-like process of sinuous border ; M, malleus with
two processes fused with anterior border of lip ; I, incus ; S, stapes : their several articula-
tions are represented.

University collection. The incus, owing to the diarthrodial joints between
it and the malleus and stapes being apt to give way, is seldom present, even
when the malleus and stapes with their firmer attachments have been
preserved.

The Ossicles in B. sibbaldi will now be described. The upper end of the
Malleus consisted of a rounded head with a groove separating it from the
part of the bone which had on its inner aspect two articular surfaces for
the incus set at an angle to each other. The diameter of the conjoined head
and articular part was 16 mm. From the lower part of the head, a process
descended, 18 mm. long, which was fused in its entire length with the
anterior border of the lip-like process of the sinuous border of the tym-
panic (fig. 4). A second descending process, parallel and close to the

* I have figured in Marine Mammals a similar sac in Hyperoodon.

VOL. XXXIV.

2

18

Proceedings of the Royal Society of Edinburgh. [Sess.

preceding, was similarly attached to the lip. These processes were brittle,
and if the tympanic was roughly handled they easily broke and the malleus
became detached and lost. The Incus had a body, 8 mm. in diameter, on
which were two concave articulations for the malleus. A short, sharp
process projected from the posterior surface and nearly reached the roof of
the tympanic cavity. From the inner aspect sprang a longer curved process
which, together with the body, measured 14 mm. ; at its free end was an
oval facet for the stapes. The Stapes had a corresponding facet on its head,
from which a pair of short relatively thick legs arose, to end in the plate-
like foot of the stirrup. A very thin layer of bone passed between the legs
and was pierced by a minute foramen. The stapes, 11 mm. long, occupied
a funnel-shaped depression in the inner or petrosal wall of the tympanum,
and its oval foot, 8 mm. in diameter, was attached to the fenestra ovalis
of the cochlea (fig. 4).

As the fusion of the malleus with the tympanic gave to the Cetacea
an exceptional character as compared with other mammals, I may state
the species in which I have noted this arrangement. In the whalebone
whales I saw it in Balcena mysticetus and biscayensis, in Balcenoptera
musculus, sibbaldi, borealis, rostrata, and in Megaptera longimana. In
the toothed whales I saw it in Hyperoodon, Phocsena, Globicephalus,
Grampus, Delphinus, Tursiops, and apparently in Monodon. In several
other species in the University Museum the malleus was not in place and
had not been preserved. It should be stated that previous observers have
noted the fusion of the malleus with the tympanic in certain species. Knox
saw it * in Balcenoptera sibbaldi and rostrata ; Carte and Macalister spoke
of it in B. rostrata as a process of the tympanic bone, from the margin of
whose centre it projected; Dwight described it in B. musculus as co-ossified
with the tympanic by a processus longus, which had a deep groove anteriorly ;
Lillie in B. musculus as fused to the inner edge of the lip of the tympanic.

Different views have been expressed regarding the morphology of the
processes of the malleus. By some, the process fused with the tympanic
lip has been regarded as the manubrium or handle of the bone. Possibly
the two parallel processes which I have figured in B. sibbaldi were only a
twin-like arrangement of this process. Others, again, have considered the
fused process to be the long slender (gracilis) process of the human anatomist.
Buchanan, whilst recognising the handle as always attached to the outer

* Knox, Catalogue , pp. 14, 21, who named the species Balcena maximus borealis and
minimus ; Carte and Macalister, op. cit. ; Dwight in Memoirs of Boston Society of Nat. Hist.,
vol. ii. ; Lillie, Proc. Zool. Soc. London , 1910 ; Turner in Marine Mammals and in Memoir
on Balcena biscayensis , Trans. Roy. Soc. Edin ., vol. xlviii., 1913.

19

1913-14.] The Auditory Organ in the Cetacea.

-edge of the osseous tympanum, described in B. mysticetus the valvular
fold of the tympanic membrane as attached to the whole length of the
gracilis, or slender process. Lillie, again, considered that the only attach-
ment of the membrane to the malleus in B. musculus was through the
connection of the ligament to a short process, which he regarded as the
manubrium, whilst the fused process was the processus gracilis. The de-
velopment of these processes requires to be studied before their morphology
can be precisely determined.

The inner surface of the tympanic bone was separated from the outer by
the tympanic cavity, the upper internal border of the former surface was thick,
rounded, and striated, where it turned over into the cavity (fig. 4). This
border was distant from the sinuous upper border of the outer surface by
the width of the tympanic cleft, which extended forwards from the posterior
pedicle to the anterior or Eustachian notch of the cleft. In the whalebone
whales the cleft was approximately horizontal, though in the genus Bahama
it had a deep notch at its anterior end.* In the toothed whales the cleft
inclined downwards at this end and opened by a mouth immediately above
the anterior end of the inferior surface. The Eustachian tube had not been
preserved in my specimens. Mr Lillie has been more fortunate, and he has
described in B. musculus a sac-like prolongation of the tympanic membrane
through the Eustachian notch into the pterygoid fossa, from which the
Eustachian tube proper arose as a relatively narrow canal, about one
foot long, which extended forwards to open into the naso-pharyngeal
chamber.

Observations have been made in several toothed whales on the arrange-
ment of the membrana tympani and its prolongation forwards into the
sinuses in the cranio-facial bones. Buchanan described and figured the
membrane in the Narwhal (Monodon) as nearly circular, concave towards
the meatus, convex towards the tympanic cavity ; the manubrium of the
malleus was, he said, attached to it. In the University Museum is the
tympanic of a well -grown foetal Narwhal about 5 feet 5 inches long.j-
The lip-like process of the sinuous border was prominent, and the gap
between it and the posterior peduncle was occupied by the dried tympanic
membrane, which did not bulge outwards towards the meatus. The malleus
incus and stapes were present. The malleus had been attached to the lip-
like process, but owing to the fragility of the bone it had broken away.
The auditory arrangements in the Porpoise ( Phoccena communis) were

* See the figures in my Memoir on the North Atlantic Balcena biscayensis , Travs. Roy.
,Soc. Edin ., 1913.

t Proc. Roy. Soc. Edin., vol. ix. p. 10?, 1876.

20

Proceedings of the Royal Society of Edinburgh. [Sess.

figured by Monro secundus * who described a concave tympanic membrane
at the bottom of the meatus ; a communication between the cavity of the
tympanum and other cavities analogous to the human frontal, sphenoidal
and maxillary sinuses ; an Eustachian tube which connected the tympanic
cavity with the nasal chamber. The prolongation of the tympanic
membrane into the air sinuses in these bones of the skull, as well as into
the palate bone, has been described by Rappj* in the porpoise, and by
Claudius l in Delphinus delphis, together with the relations of the ossicles
to the tympanic membrane and the communication of the Eustachian tube
with the cavity.

The Petrous in the large whales is a heavy massive bone interlocked
with the base of the skull, consisting of three definite divisions, a central
labyrinthine part which contained the cochlea, vestibule, and semicircular
canals, in which the auditory nerve was distributed ; a short anterior pre-
otic process and a long posterior opisthotic process, as an example of
which Balcenoptera sibbaldi may be described (rig. 3). The Labyrin-
thine division had a rough upper surface in relation to the basis cranii ; a
smooth under surface characterised by a large bluntly conical projection,
which was directed outwards towards the tympanic, but separated from it
by the cleft in the tympanic bulla. This surface also formed the roof and
inner wall of the tympanic cavity ; in it was a funnel-like depression in
which the stapes was situated and was attached by its foot to the fenestra
ovalis of the cochlea. The inner aspect of the petrous was prolonged and
perforated by the large canals for the passage to the labyrinth of the
divisions of the auditory nerve, and by smaller foramina and canals.

The Pre-otic was an irregular conical mass which projected forwards to
end in a more or less pointed process, it was continuous with the labyrinthine
division, and was connected with the tympanic by the anterior pedicle ; it
occupied a depression in the squamous temporal above the pterygoid fossa.
The Opisthotic, so-called mastoid, was a long flattened wing-like plate
continuous with the labyrinthine division, and connected with the tympanic
by the posterior pedicle. In one of my specimens of B. sibbaldi it was
17 inches (432 mm.) long, and in another 5J inches (134 mm.) broad. It
was locked into a groove between the squamous-temporal and the ex-
occipital. In a Megaptera the greatest length was 235 mm., and the
greatest breadth 100 mm. ; in B. musculus, 200 by 70 mm. ; in B. rostrata ,
70 by 35 mm.

* “On Fishes,” p. 45, Edinburgh, 1785.

t Die Gehorwerkzeuge der Cetaceen, Tubingen, 1836. Die Cetaceen, Stuttgart, 1837.

J Physiologische Bemerkungen iiber das Gehororgan der Cetaceen , Kiel, 1858.

21

1913-14.] The Auditory Organ in the Cetacea.

The auditory apparatus in the Cetacea has been modified in adaptation
to the aquatic life of an air-breathing mammal, which can respire only
during the relatively short period when the nasal opening or blowhole
is above the surface of the water. There can be no doubt that the tym-
panic cavity contains air, which it obtains during inspiration through the
communication of its Eustachian tube with the naso-pharyngeal chamber.
The immersion of the side of the head in the water renders unnecessary
the development of an external auricle, capable of being turned in different
directions to receive aerial sound waves, and the question naturally
arises, how can sound waves be conveyed so as to impress the nerve
apparatus in the whale’s labyrinth ?

On this matter different opinions have been expressed. Buchanan
considered * that the Eustachian tube and not the external meatus
■“ conducted the pulsations of sound into the tympanum,” causing
vibratory movements of its membrane and corresponding action in the
chain of ossicles; whilst the meatus, through the width of its tympanic
end, facilitated the vibratory movements of the sac-like prolongation of
the membrane into it. This view has not, however, been accepted.

Others have regarded the vibrations as excited by the aerial sound
waves propagated down the external meatus, which directly impressed the
membrane and were then conveyed by the chain of ossicles to the fenestra
ovalis and labyrinth. As against this view it should be kept in mind that
in the Cetacea the period is short and infrequent during which the external
aperture is exposed to the air ; waves of sound could be transmitted only
interm ittingly and not to much purpose. Sufficient evidence now exists
that in the whalebone whales the meatus is blocked with a large
plug of wax ; the lumen, therefore, cannot be occupied with air to permit
the transmission through this medium of sound weaves. On the other
hand, the wax-plug is a solid body closely moulded in these whales on the
;sac-like membrane of the tympanum. As such it would doubtless transmit,
as the cranial bones themselves can do, sound waves generated in the sur-
rounding water, which would produce vibratory movements of the tympanic
membrane and the chain of ossicles. In the baleen whales sufficient
pressure exists in the air of the tympanum to produce the convex pouch-
like projection of the membrane into the auditory meatus.

Some years ago Claudius wrote an interesting memoir on this subject, f
and argued that in the Cetacea the sound waves were not directly
transmitted by the Eustachian tube, the meatus auditorius, or through

* Op. cit.

t Ueber das Gehororgan der Cetaceen, Kiel, 1858.

22

Proceedings of the Royal Society of Edinburgh. [Sess.

the bones of the head to the nerves in the labyrinth ; but that the waves,
detached themselves from the bones and thus impressed the air contained in
the tympanic cavity and in the sac-like projection of its membrane in the-
baleen whales, and its prolongations into the accessory sinuses in the
dolphins. The waves might then act in two ways, either through the
fenestra ovalis and fenestra rotunda, by impressing the lymph in the
divisions of the labyrinth and through it the end organs of the auditory
nerve, or by setting in movement the chain of ossicles which have as
their fixed point of attachment the malleo-tympanic interossification.

Claudius, therefore, thought that the sound waves reached the head of
a Cetacean through the water in which it lived ; that they were trans-
mitted by the bones of the head to the air in the tympanic cavity, and
that the waves generated in it directly caused vibrations through the
fenestra ovalis and rotunda in the lymph in the labyrinth, as well as along
the chain of bones, and impressed the nerve end organs. This view
of the mode of excitation of the auditory nerve seems to be the most
satisfactory.

{Issued separately December 31, 1913.)

1913-14.] Siliceous Sponge of the Order Hexactinellida.

23

III. — Note on a Siliceous Sponge of the Order Hexactinellida from
South Shetland. By Principal Sir William Turner, K.C.B.,
D.C.L., F.K.S.

(Read December 1, 1913. MS. received December 2, 1913.)

The specimen was presented to me by Mr G. Millen Coughtrey, who
obtained it in Admiralty Bay, South Shetland, lat. 62° S., and long. 58° W.,
in 1912. It was procured in about 20 fathoms, and was brought to the
surface when the ship’s anchor was weighed. It consisted of white, delicate,
thread-like spicules collected into two tufts or bundles. At the first glance
the threads might easily have been mistaken for white hair, but they
would not burn ; neither were they calcareous, for they were not acted on
by mineral acids. From their vitreous appearance they were obviously
siliceous and indeed were not unlike spunglass. Their aspect and com-
position led me to regard them as belonging to a siliceous sponge, but the
body of the sponge was wanting. In its absence one had to rely on the
characters of the tufts and spicules in attempting to determine the genus
of the sponge.

One tuft was about 40 cm. (16 inches) long, and 3J cm. at its greatest
transverse diameter. The thread-like spicules were compacted and inter-
laced together at the proximal and mid parts of the tuft, but at the distal
end it was somewhat dishevelled. It contained many hundred spicules
and seemed as if it had belonged to one sponge. The smaller tuft was not
so compact and might possibly have been divided into two parts, one for
each of two smaller sponges.

The threads were the basalia or basal spicules of the sponge, which
had grown downwards from the base of its body and had penetrated the
mud on the floor of the sea in which the sponge lived. In weighing the
ship’s anchor the tufts of basal spicules had been drawn up at the same
time. The spicules were so brittle that it was difficult to pick a single
one out of the tuft without breaking it, but with care I obtained examples
30 cm. (12 inches) long. The spicules were smooth on the surface,
translucent, and the transverse diameter ranged from 35 to 92 jm. In
many of the smaller sizes the appearance of a narrow canal in the long
axis of the spicule was seen, but in the wider spicules no structural
differentiation was observed. One end of the spicule was frequently

24

Proceedings of the Royal Society of Edinburgh. [Sess.

attenuated to a fine point, though often it was broken abruptly; the
opposite end was sometimes broken, at others it terminated in a very
minute knob (scarcely visible to the naked eye), which, when magnified, was
seen to be the rounded end of the basal spicule from which four hook-
like processes equal in length arose ; they were recurved in their direction,
almost parallel to the long axis of the spicule, and formed an anchor-like
arrangement which assisted in fixing the sponge in the mud (figure).

A close examination of the tufts showed that a number of the spicules,
more especially near the proximal part of the tuft, had attached to them
globular blackish specks, 300 to 320 ju in diameter, which contrasted in
colour with the white spicules. Under low magnification they looked like
very minute grains, and had with strong transmitted light a greyish-blue

Anclior-like end of basal spicule of siliceous sponge, South Shetland.

tint. Neither Canada balsam nor treatment with acetic acid and glycerine
made the centre translucent, but the thinner periphery permitted greyish -
blue-tinted siliceous microscopic flakes or scales to be seen, which, when
superimposed on each other, gave opacity to the object. Owing to their
hardness and brittleness, attempts failed to make sections through them.
They seemed to be aggregations of siliceous plates attached to the spicule,
the purport of which was difficult to explain.

A brown substance was occasionally seen to surround some of the basal
spicules in the proximal part of the tuft. The largest example was 6 mm.
long and was fusiform. From its structure it was essentially a fragment
of the body of the sponge which had adhered to the basal spicules. In
part it contained nuclear-looking bodies embedded in a granular protoplasm,
but a number of ray-like spicules were also present. Many of these were
four-rayed tetracts, which radiated horizontally from a common centre, and
the largest specimens measured 0*5 mm. between the tips of opposite rays.

25

1913-14.] Siliceous Sponge of the Order Hexactinellida.

Others were much smaller, 0‘2 mm. between their tips, and in many five or
six rays could be seen, one or two of which had been broken across at or
near the common centre ; the type, therefore, was hexact. In the middle of
the centre was a very minute circle, from which a line passed along the axis
of each ray almost to its tip. The rays were sometimes smooth, but more
usually slightly roughened near the tip and faintly serrated at the sides.
Mingled with the ray-like spicules were numerous disc-shaped Diatoms,
which varied in their dimensions from 77 to 96 /u across the face of the
disc. They had doubtless lived in the mud in which the basal tuft had
been anchored.

As the siliceous sponges have been described by Professor F. E. Schulze
in an elaborate memoir in his Challenger Report on the Hexactinellida,*
I have examined the text and figures so as to identify, if possible, the
species from the characters presented by the basal spicules. The length
and thickness of the tufts and the number of spicules varied materially in
different genera and species, but in the genera Hyalonema and Pheronema
species existed in which the basal tuft of spicules attained a considerable
length. Schulze gave as a character of Hyalonema a tuft consisting of
long and strongly developed basal spicules which projected downwards
from the centre of the lower end of the body, and the spicules themselves,
either wholly, or for the most part, had four-toothed anchors. He stated
that in H. sieboldii the total length of the body and tuft varied from 50
to 80 cm., and as the body occupied 10 to 15 cm. of that length, the basal
tuft varied from 30 to 60 cm., and broke up at the lower end in a brush-like
manner. This species inhabits the seas of Japan. In H. affine the tuft
was 47 cm. long, but only 8 mm. broad. Wyville Thomson dredged in the
sea north of the Butt of Lewis, from a depth of 450 to 500 fathoms,
Hyalonemata in which the root tuft measured 40 cm. or more. In Phero-
nema carpenteri, obtained in the sea north of Scotland, as well as off the
coast of Brazil, a number of slender tufts, only 1 to 2 mm. in breadth, the
spicules of which were 30 to 40 cm. long, interlaced abundantly in the felt-
work of the basal tuft. Wyville Thomson considered that in the larger
specimens the tufts may measure several decimetres. Schulze stated that
other species of this genus also possessed long basal spicules.

Schulze has figured Numerous examples of four- and six-rayed spicules
in the bodies of the sponges in the Hexactinellida group. In my specimen
the rayed spicules found in the basal tuft did not properly belong to it,
but had accidentally become intermingled with the basal spicules. Schulze
specially referred to the lower end of the body of Hyalonema as containing

* Yol. xxi. part 53, 1886.

26

Proceedings of the Royal Society of Edinburgh. [Sess.

four-rayed, tetract spicules. In the length of the tuft and in the numerous
spicules which composed it, this sponge had also affinities with Hyalonema,
though none of Schulze’s figures had so bulky a tuft. Hyalonema sieboldii ,
however, seems to be the sponge which most closely corresponds with it in
this particular.

Two other questions of interest arise out of this specimen, viz. : the
locality and the depth from the surface. Schulze, in his map, showed the
distribution of the order Hexactinellida, and localised a small species,
Rossella antarctica (Carter), obtained by Sir James Ross in 1839-43, as far
south as lat. 74*5°, at a depth of 300 fathoms ; also a small species, Polyrhabdus
oviformis (Schulze), obtained by the Challenger in lat. 62*26°, in 1975
fathoms. With these exceptions no other specimen of this order, which
from the size of the basal tuft was obviously a large species, had previously
been obtained so near the Antarctic circle as 62° S. In his chapter on the
bathymetrical distribution of the Hexactinellida, Schulze gave several
species as dredged from a depth at and near 100 fathoms ; but the depth
of only 20 fathoms, given by Mr Coughtrey for the South Shetland specimen,
localises Hyalonema in a shallower sea than had previously been recorded.

( Issued separately December 31, 1913.)

1913-14.] Factorable Minors of a Compound Determinant.

27

IV. — Some Factorable Minors of a Compound Determinant.
By Professor W. H. Metzler.

(MS. received April 17, 1913. Bead November 3, 1913.)

If we start with a determinant A of order n, and, using exclusive umbral
notation, take the minor

Mee

(n\m\k)

a 1

(n | m | k)

(n | m | k)

a 2

(n | m | k)

(n I m | k) \
a x \

(n\m\/c) L

a \ /

mk

of the (n — 7c)th compound of A, Sylvester * has shown that

M = A

(n | m)
( n | m)

. (A)

Besides this, Muir j- has considered another type of minor which breaks
up into factors. It may be obtained from M by putting k = m— 1, and in
place of the combinations — 1), . . . 1) indicating the

a 1 am

selections of rows for the elements we take the combinations 12 . . . m— 1,
23 . . . m, 34 . . . m+1, . . . mm + 1 . . . 2n — 2, where for definiteness
of statement we suppose a = 1, and (n \ m) = 12 . . . m. Thus the theorem

a

given in Muir is

12 ... m- 1

23 ... m

mm + 1 .

. . 2m -2

(n\m\m — T)
\ l i

(n | m | m - 1)
1 2

(n m

l

i m — i)

m

23 ... m + 1

34 ... m + 2

A .

( n | m)

(n | m)

l

l

m . . . 2m — 3

( n | m)

l

(B)

In both these theorems the combinations indicating the selection of row
numbers are definite. In Sylvester’s theorem they are the same as the
selection of the column numbers. In Muir’s the first one is the same, and
the rest may be obtained by a definite sliding process.

The object of the present paper is to show that there are a large number
of other minors which break up into factors, and to give a general theorem
(C) which includes these two as special cases.

Theorems (A) and (B) are readily proved by the method used by the

* Philosophical Magazine , 1851.
t A Treatise on Determinants , Art. 93.

28

Proceedings of the Royal Society of Edinburgh. [Sess.

author in 1897.* Starting with a particular case of the general theorem
(C), where m = 5 and k = 3, and using a similar method, we have on
multiplying

1 2 3

4 5
4 5

M=

%

— 4

--5

-34

1-35

1-45

2 3 4

2 3 5

2 4 5 j

|3 45

\

1 2 4

1 2 5

1 3 4

13 5

1 4 5

2 3 4

2 35

2 4 5 |

345

)

3 5

i 3 4

2 5

2 4

2 3 j

1 5

1 4

13

1 2

\

3 5

3 4

2 5

2 4

2 3

1 5 |

1 4

13

1 2

)

where the positions indicated by the dashes in M may be filled with any
numbers from the set 12 ... n, as long as (1) no two numbers in the
same element are alike, for in that case every element in that row of M
would be zero; (2) the row numbers in the fth row of M and the com-
plementary with respect to m of the column numbers in the fth column
of M have no numbers in common, for if they had then the corresponding
element in the principal diagonal of the product would be zero, and
therefore the product zero; the product

M.N = A10.

45

— 3 4 51

--345

-23451

-2 3 45

-2345i

1 2345

i 1 2 3 4 5

12345’

1 2 3 45

12345’

1 23 45

12345’

1 2 345

N = A6 .

1 2 3 4 5
1 2 3 4 5

45

- - 3 4 5

--345

- 2 3 4 5

- 2 3 4 5

- 2 3 4 5

1 2 3 4 5

1 2 3 4 5

'12345

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

For the product has every element on one side of the principal diagonal
zero, and therefore it equals the product of the elements along the principal
diagonal.

By Sylvester’s theorem

and dividing out the common factor from both sides we have

M = A4

where of course the numbers in the places indicated by the dashes are the
same with which we started in M.

It will be observed that the 4 in the row numbers of the second row
of M, the 5 in the third row, the 3 and 4 in the fourth, the 3 and 5 in
the fifth, etc., are what make all the elements on one side of the principal
diagonal of the product vanish and the minor break up into factors. This
is true independent of the numbers (under the restrictions named) in the
places indicated by the dashes.

* Metzler, “Compound Determinants,” American Journal of Mathematics , vol. xx.
No. 3.

29

1913-14.] Factorable Minors of a Compound Determinant.

The row of M which has the three arbitrary row numbers is the same
(viz. the first) as the column of M which has the column numbers 12 3.
That is, the three arbitrary row numbers are associated with the column
numbers 12 3, and it is obvious that they might have been associated with
any of the ten combinations of the numbers 1 2 3 4 5 taken three at a time.
Thus, for instance, associating them with the combination 2 3 4, we have
the minor

(

—

--5

1 --

-45

1-4

1-5

3 4 5

1 3 4 ;

1 35

145

\

2 3 4

2 3 5

12 3

2 45

1 2 4

125

3 4 5

134!

1 35

145

1 5

1 — 4 5 1

1 — 4 5

1-345

1-345

1-345

1 2 3 4 5

12345*

1 2 3 45*

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

If in M we put in the place of the dashes the same numbers as those in
the column numbers with which they are associated, the six factors other
than A4 are all equal, and we have Sylvester’s theorem.

If 1c = 4 and we take the minor

12 34
12 3 4

123-
12 3 5

1 2--
1245

1

13 45

2 3 4 5

M=

which equals

A •

and put in the place of the dashes 8, 7 8, 6 7 8, 5 6 7 8, respectively, so that

MW

1 2 3 4-

12 3 —

1 2 j

1

1 2 3 4 5

1 2 3 4 5

1 2 3 451 '

1 2 3 4 51

1234

1234

1238
12 35

1 2 7 8 j 116 7 8
1245 1345

5 6 7 8
2 3 4 5

we have

M = A •

1 2 3 4 8

1 2 3 7 S

[1 2 6 7 8

1 2 3 4 5

1 2 3 4 5

* 1 2345

1 5 6 7 8
1 2 3 4 5

which is an example of Muir’s theorem.

In the general case the theorem is simple, though its statement is a
little cumbersome.

Take any one of the — A combinations (n\m \ k), (n\m\ Jc), . . .

a 1 a. 2

(n\m\ k), say the /3th or (n\m \ k) to start with, and arrange the set into

a \ a /3

groups as follows : —

1st group containing 1 combination consisting of (n | m 1 Jc).

a (3

2nd group containing (m — k)l combinations, consisting of those which
have in common the first (Jc — 1) only of the numbers of (n | m 1 1c).

a £

30

Proceedings of the Boyal Society of Edinburgh. [Sess.

(h l)st group containing (m — Jc + h— 1)A combinations, consisting of
those which have in common the first (k — h) only of the numbers
of (n\m \ k).

a jS

(/c + l)th and last group containing (m— 1)* combinations, consisting of
those which do not contain the first number in (n\m\ k).

a J8

Let

(n\m\tc\Ic-h)(cm), (* = 0, 1, 2, . . . (m-k + h- 1) -1)

a 0 1 1 h

represent the combinations of the (/& + l)st group. By giving h in this
the values from 0 to k, it will represent the combinations of each group.

Let the first combinations in the 1st, 2nd, . . . (& + l)th groups, ar-
ranged in this order, be represented by

(n | m | k ), (n \ m \ k ), . . . (n\m\k)i
Po Pi a Pk

respectively, and let
p — 1 k

a FT Tal

0 0

(n \m\ k )

a p h+i

(n\m\k\k-h)(cW)

a P 1 1

(p = (m-k + h — 1 )ft)

represent the determinant whose elements along the principal diagonal
arranged in the above order are

(n | m | k)

a 1

(n\m\ k)

a 2

(?i | m | k)

a \

(n | m k)

a 1

>

(■ n | m | k)

a 2

(n\m\k)

a \

Then the determinant

(n | m | k )

p - 1 k

d^a in III

0 0

(n | m)

a

(b<k-h))(+))(n\m\ k )

a Ph+i

A(m_1 k (C)

where (b^ ll)) represents any set of (k — h) of the numbers 1 2 3 ... n, as
long as (1) (bf h))(c^) has no two numbers alike; and (2) no numbers
in (Jbf h)) and (n | m | k ) are alike.

a p +t
h

1913-14.] Factorable Minors of a Compound Determinant. 31

For if we multiply D by

p - 1 k

A ITT IM

0 0

/\(n\m\ k )
/ a Ph+i

\ \ {n\m\ k)

\ 1 a fth+i

which by Sylvester’s theorem is equal to

^ (n | m) 3

a

(ji | m)

the resulting determinant will have every element on one side of the
diagonal zero, and therefore equal to the product of the elements along the
diagonal. Dividing out the common factor from both sides, we get the

o o 7 o

result given.

Syracuse University,
March 1913.

(Issued separately December 31, 1913.)

32

Proceedings of the Royal Society of Edinburgh. [Sess.

V. — The Theory of Bigradients from 1859 to 1880.

By Thomas Muir, LL.D.

(MS. received June 9, 1913. Read November 17, 1913.)

My last communication in reference to the history of bigradients ( Proc .
Roy. Soc. Edin., xxx. pp. 396-406) brought the record up to the year
1859. The present paper continues it to the year 1880.

Bruno, F. Faa di (1859).

[Theorie Generale de l’Elimination, .... x + 224 pp. Paris.]

In his section on the highest-common-divisor (pp. 47-52) Bruno, denoting
the rth Sturmian remainder of

%xm + a^xm~x + • • • •, &0a?m_1 + b4xm~2 + • • • ■

by Rr, finds for it the expression

where \r and Rr/Ar are the “ allotrious factor ” and “ simplified residue ” of
Sylvester (1853). He must, however, have overlooked the question of sign,
for the example which he gives, namely,

1

% ai a2

X2 +

a0 <h aB

x +

a0 ax a4

b0 \ 52

K bl h

bo \

(

b1

. b0 52

CO

hO

o

as the first Sturmian remainder of

+ a4x2 + • • . + a4 , b0xs + b ^ + b2x + bz
is incorrect in this particular.

33

1913-14.] The Theory of Bigradients from 1859 to 1880.

In the section on the properties of the resultant (pp. 68-81) he recalls
Richelot’s theorem of 1840, that if w be a common root of the equations

a^xm + apcm~x + • • • = 0 , b^xn + \xn~x + • • * = 0

whose resultant is R, then we have

0R ,

0R .

. ?R

daQ '

0ax

* dam

0R

. 3R .

0R

3 V

1 06x : '

' ' '' Mn

This is not brought forward as a theorem in determinants, hut for com-
parison, when n = m, with Jacobi’s theorem of 1835 to the effect that the
■signed primary minors associated with the elements of any row of Bezout’s
condensed eliminant

■are proportional to

aobi

^0^2 I ! ®o^3 I "t" I ^lb2

m

wm x, wm 2, . . . , IV , 1 .

In the section on common roots (pp. 81-84) he obtains such a root when
it is solitary by taking any one of these three series of proportionals and
dividing one member of the series by the member immediately following.
When the number of such roots is lc he has recourse to the Sturmian
remainders previously found, stating for comparison Lagrange’s set of
conditions : *

R = 0,

02R _ 0*-^

da2m ’ ’ bak~l

0.

Trudi, N. (1862).

[Teoria de’ Determinant:, .... xii + 268 pp. Napoli.]

To Trudi is due the first methodical exposition of bigradients, a nineteen-
page chapter of the first part ( Teoria ) of his text-book being specially
devoted to them, and several chapters of his second part (Applicazioni)
making constant use of them.

The nineteen-page chapter or section (§ xi., pp. 94-112) bears the head-
ing “ Matrici e determinanti a due scale.” It contains, first of all, careful
explanations of the various expressions which he finds necessary to use in

* Lagrange. Reflexions sur la resolution algebrique des equations. Nouv. Memoires
. . . Acad. . . . Berlin , 1770, 1771 : or (Euvres completes , iii. pp. 205-421 (227-229).

VOL. XXXIV. 3

34

Proceedings of the Royal Society of Edinburgh. [S

ess.

a special sense while dealing with such determinants ; for example, scala ,
scala, di grado r, scala diretta, scala inversa, scala completa, etc. He next
gives an account of the simple properties of bigradient arrays, or, as he calls
them, two-scale matrices, and introduces a notation for them, writing

j {ao)r

I (\)s

to denote the bigradient array in which the elements a0, av . . ., am are
repeated r times, and the elements b0, bv . . ., bn are repeated s times, a0 and
b0 when furthest to the left being in the first column, and am and bn when
furthest to the right being in the last column. Clearly, the notation would
have been less imperfect if written

(“o> •

• • ) ^"m)r 1

! (&», •

. . , u !

For example, the bi gradient array

°0

cq

«8

<q

ah

“6

a7

•

ao

«1

a2

a3

ai

«5

«6

a7

•

a0

<q

a2

«3

ai

°5

a6

a7

bo

h

K

h

\

•

K

\

h

h

\

h

h

h

^2

h

h

K

h

h

K

might with fair appropriateness be denoted by

(«o> •

• • j ar)s

1 (K ■

• • > ^4)6

the only weak point then being that the introduction of the 6 is uncalled
for, on account of the necessary equality of m + r and n + s, either of which
specifies the number of columns in the array. It is a convenience, however,
to have both the outside suffixes 3, 6 in front of us, because their sum
gives the number of the rows, a sum we should otherwise have to know
from m + 2r — n. Instead of all the determinants of such an array being
viewed, as hitherto, of equal prominence, Trudi only concerns himself with
the first two of the ten, namely, those which have in common the first eight
columns of the array. These n — r+ 1 determinants he designates not very
happily “ the successive determinants of the array.” The name “ principal ”
which he gives to the first determinant of all may be advantageously
translated “ leading.”

35

1913-14.] The Theory of Bigradients from 1859 to 1880.

The number of bigradient arrays associated with the two sets of
elements

’ ' • ’ K ^1’ • ' ’ ’

is evidently n : thus, in the case where m,n = 7,4 the arrays are

(%< • •

• . «r)x

(ao> • •

• > ^7)2

(®o> . .

. , oq)3

«o>* ■

. . , & 7)4

(K ■ ■

•.M4

f

■ ■

• . *4)5

>

(K ■ ■

• 5

I ? 1

K • •

■ ..sa

the last, where r = n, being square, and therefore preferably written in
the form

I («0» • • • » I

I (&0. • ' • 5 ^4)7 I ’

These and other preliminaries being settled, he is in a position to deal
with an important theorem on the subject of what we may call the con-
densation of a bigradient array. The proof given is, unfortunately, not
at all so simple as it might have been. We shall therefore substitute for
it one of our own, which Trudi himself would probably have devised had
he been aware of Cayley’s work of 1845. Taking, first, a case in which
m = n, say the case

a0

“1

«2

*4

•

a0

“2

«B

a4

«o

ai

a2

«3

“4

\

h

*4

h

h

^4

%

h

K

h

h

(«o> • •

. , a4)3

or

00. • •

• 5 ^4)3

we multiply the determinant

1

1

0
r-c>

1

1

~h

-h

~ ^2

a0

cq

a2

a0

ai

a0

by the given array in column-by-column fashion, obtaining {Hist., ii. p. 34)

^0 ^2

aB

«4

a0

a2

«3

«4

•

\ («0. • •

. . , a4)g

. . a0

ai

a2

«8

a4

1 00. • ■

■ • . £4)3

r

1 “(A 1

1 «062 1

KVI

1 aA 1

1 <*A 1

I S63 1 + 1 aA 1

1 «064 1 + 1 « A 1

l | !

«0&3 1

1 «o64 1 + I af3 I

1 «A 1 + 1 ,%&3 i

1 «2&4 1 1

36

Proceedings of the Royal Society of Edinburgh. [Sess.

Of the seven identities included in this the first two are Trudi’s, and these
he writes in combination, thus —

ao

a4

a2

‘h

•

ao

a j

« 2

as

a4

%

a\

a2

a3

a 4

h

bB

b 4

b»

h

h

h

K

\

h

h

bs

b\

1 aohi 1

1 a0^2 1

1 a0^3 i

1 %bi \

1 aJ,2 1

1 a0^3 I 4* 1 ai^2 !

1 Vk 1 + 1 aA 1

I «A 1

1 a(fo3 j

| a(fi4 1 4 | |

| axb4 1 + ! a.2bB j

1 «2&4 1 1

meaning thereby that the determinants got by leaving out the 7th column
on the left and the 4th on the right are equal to one another, and also
those determinants got by leaving out the 6th column on the left and the
3rd on the right.*

He then draws attention to the fact that the two-line determinants
involved in the array on the right are principal minors of the array

d rv CL-y Cic) Clo d*

and he formulates a mnemonic rule like Sylvester’s {Hist., ii. p. 340) for
the formation of the condensed array. His own illustrative examples are

a

b

c

d

.

. a

b

c

d

au - bt

av - d

ax - dt

a

b

c

d

ax — dt

=

av - d

bx - du

.

t

u

V

X

+ bv — cu

. t

u

V

X

ax- dt

bx - du

cx - dv

t

u

V

X

a

b

c

d

a

b

c

d

au - bt

av - d

ax - dt

t

u

V

X

av — d

ax - dt

bx — du

t

u

V

X

+ bv — cu

a

b

c

d

_

|| au - bt.

, av — d,

ax - dt |

t

u

V

X

* With Cayley the assertion

Ii %

« 2

aB

a4 1

= \\xi

x2

x3

x4

II \

b 3

\ II

II Vi

V2

V 3

Vi

included 6 equations, whereas with Trudi it only includes 3, namely, the first 3 of Cayley’s
6 : and with Cayley the assertion

al

a2

C*3

a4

xi

x2

Xo j

*1

b2

h

\

—

! Vi

V2

y3 1

C1

C2

C3

c4

was meaningless, whereas with Trudi it includes 2 equations. Since in the former case
Trudi’s 3 equations are known to necessitate the other 3, there is clearly no good reason for
refusing to profit by the new usage. What is common to any two arrays which Trudi may
equate is the excess of the number of columns over the number of rows : and evidently if
his excess be 5, the number of included equations is 5 + 1.

37

1913-14.] The Theory of Bigradients from 1859 to 1880.

where each array on the left is got from the one that precedes it by
deleting the first row, the first column, and the last row ; and each array
on the right by merely deleting the last row. It is noted that the leading
determinant of the condensed array is axisymmetric.

Lastly, it is pointed out that cases where m>n present almost no
additional difficulty, as they are readily brought under the foregoing.
Thus, if the case be

we have only to take

I (a, b, c, d, e, f)2 I
I (t, u, v)5 j

a b c d e f

0 0 0 t u v

for our generating array and proceed exactly as before, the results being

a

b

c

d

e

f

r

a

b

c

d

e

f

at

au

av

t

u

V

at

au + bt

av + bu

bv

t

u

V

=

at

au + bt

av + bu + ct

bv + cu

cv

az

t

u

V

au

av + bu

bv + cu

cv + du — et

dv - ft

t

u

V

av

bv

cv

dv - ft

ev - fu

u v

a b c d e f

t u v
t u v .

t u v .

t u v

t

u

V

t

u

V

=

t

u

V

au

av + bu

bv + cu

cv + du — et

dv - ft

av

bv

cv

dv -ft

eu —fu

-

t

u

V

•

t

u

V

t

u

V

.

au

av + bu

bv + cu

Cv + du — et

dv -ft

The requisite division by a3 (in general am n) may be performed by
removing the a’s one at a time, or by using the divisor in the form

a b c
a b .

Another theorem of a similar kind but introduced for a different
purpose, namely, for dilatation rather than condensation (pp. 129-131), is

(*o

K),

(-r

• • • , Or

38 Proceedings of the Royal Society of Edinburgh,

where the c s are determinants defined by the postulated identity

[Sess.

a{)x'" + • • •
b^xn + • • •

q0xr‘

+ ... Hr

b0x"

(see under Recurrents ) and where a- = r + 1 + f (m — n)(m — n — 1). For
example, when m = 5, n = 4, r = 2 the identity is

ao

al

Ctcy

® 3

a4

a 5

\

b

h

b

b

•

a 0

ai

as

a4

°5

\

b

b

_ (-1)*

ao

a ,

b

b

b

« 3
b
b

«4

&4

«B

7,

co

co

C1

C1

C2

C2

C3

CS

V

\

co

C2

C3

b

b

b

b

b

b

b

b

Trudi’s proof consists in evolving the second member from the first, but
here again it is simpler to use Cayley’s multiplication-theorem of 1845.
Thus, taking the second array as multiplier and the determinant

1 .....

1

1 ....

. . -qi 1 . . .

-0i "0o * 1 • •

-01-00 • . . 1 .

- 00 1

as multiplicand we at once find the product to be

co

c]

C2

C3

•

co

C1

62

C3

C0

C1

C2

C3

b

b2

h

b

.

b

b

h

b

b

b

\

•

b

b

b

\

which is equal to

c0

C2

CO

. c0

C1

^2*

C3

.

co

C1

C2

C3

. \

h

b

^3

b

\ \

b

V

(b ■

■ • ^4)2

(co • ■

• • 5 ^3)3

as was to be proved.

39

1913-14.] The Theory of Bigradients from 1859 to 1880.

The use to which this second theorem is put (pp. 132-137) is in
connection with the division-process for finding the highest-common-
divisor of two integral functions, and, in particular, with the modification
of the said process employed by Sturm in obtaining his so-called
“remainders.” From the general theorem* connecting dividend, divisor,
quotient, and remainder we know that the coefficients of the first remainder
in such a process are proportional to the successive determinants of a
bigradient array composed of the coefficients of the dividend and divisor.
We thus also know that this remainder having been made the divisor and
the previous divisor the dividend, the new remainder must be expressible
in like fashion. In the second bigradient array thus arising, however, one
of the two sets of elements is complicated, being in fact the successive
determinants of the previous array : and what Trudi’s “ dilatation ” theorem
enables us to do is to supplant it by another array whose elements are
simply the coefficients of the original functions. In this way the theorem
finally reached is : The coefficients of the rth remainder Rr arising in the
course of the performance of Sturms division-process on

a^xm + . . . + am , b0x11 + ... + bn

are equal to the successive determinants of the array

(a0, . .

■ , a,n)r

(b0 . ■ .

.,K) \

divided by the product of the squares of the first coefficients of all
the preceding remainders and by b0m-n+1 and by the sign-factor
( _ xive rth remainder, when divested of the threefold divisor

here specified, ar say, Trudi follows Sylvester in calling the residuo
semplificatofr and denotes by pr, so that R r = pr/ar. For example, when
the originating functions A and B are

axi + bxB + ex1 + dx + e,
px* + qx2 + rx + s,

* See under Recurrents.

t A most natural and helpful notation for such a remainder would he

II Oo, . . . , a.m)r II ( xn~r ,. 1).

II (&o, bn) II

Thus, in the case here used for purposes of illustration, the remainders would be written

a b

c d e j

(x“, x , 1),

|| {abed

e h II

. p

q r s \

l| (p q r

s)3 |l

P <1

r s . 1

1

40

Proceedings of the Royal Society of Edinburgh. [Sess.

the three Sturmian remainders in their “ simplified ” or disencumbered
form are

a

b

c

a

b

d I

a

b e

V

2

+

<M

8

V

T p “H

p s

V

<1

r

p

<1

s \

p

<1 •

a

b

0

d

e

a

b

c

d .

a

b

0

d

a

b

o e

V

d

r x +

V

q s

p

d

r

s

P

d

r . |

V

d

r

s

p

d

r

s

abode
abode
a b c d e

p q r s

p q r s

p q r s

p q r s

the removed encumbrances being the factors

a

b

c

2

P

d

1

p2

V

d

r

p2

a

b

0

2’

p2

a

b

0

d

e

2

P

d

a

b

0

d

p

d

r

p

d

r

p

d

r

s

p

d

r

s

.

respectively. The general expression for the factor, ar, connecting the
simplified and unsimplified forms of a remainder is readily got (pp. 138-139)
in Sylvester’s way by using the fact that the product av_xa r is equal to the
square of the first coefficient of pr. For, this is the same as saying that, if
we denote the first determinant of

by Dr, we have
and these lead to

and

where

j (a0 , ... , am)r j|

I (6q , . . . , &n) ||

l2 2

— T)2

= j . . . • Dt-i

a,

a2ju,+l

1 d m • • • ’

a1 = (~ . b

m—n+

0

41

1913-14.] The Theory of Bigradients from 1859 to 1880.

An important observation made in passing is that any simplified
remainder can be condensed into a single determinant : for example, the
three just given are equal to

a

b

ex 2 + dx + e

a b

A

P

qx 2 rx + s

or

• V

B

V

! 1

rx2 + sx

p a

Bx

a b c

d ex

a b

c d Ax

a b

c dx + e

a

be A

p

q rx-rS

or

. . p q B

• P 2

r sx

• P <

q v Bx

p q r

s

p q r s B x 2

a b c

d e

Ax2

a b

c d

e Ax

a

b c

d A

V d

r B

• . p

q r

s Bx

• V 2

r s

. Bx2

p q r

s

. Bx3

,

where, be it remarked, the ultimate forms, namely, those explicitly involv-
ing A and B, are Cayley’s of 1848.

Cayley’s relation between any three consecutive ‘‘simplified remainders”
is next given (pp. 140-142), the proof arising quite naturally and being
mainly dependent on the equality ar_1ar = Dr-i- Thus, taking the equations
that indicate the nature of the division-process, namely,

A = QiB-R,

B = Q2Bi — R2

b] — Q3B2 — 1*3

b-2 = “ B4

and substituting pr/ar for Rr, we obtain

cq • A = cqQj-B - pj

ala2 ’ B = a2Q2‘Pl “ a]*P2
a2a3-pi = a1a3Q3 *p2 - cqcq-pg

a3a4’P2 = a2a4Q4'P3 “ a2a3'P4

In this way there results the general equation

Or-lOr • Pr-a. = ar-2arQr’Pr-l “ ar_2a r_1-pr ,
Hr— 1 * Pr— 2 ar— 2arQr’Pr— 1 — ^r—2’Pr •>

and thence

42

Proceedings of the Royal Society of Edinburgh. [Sess.

showing that pr_2 and pr have different signs for any value of x that makes
Pr^ vanish.

Proceeding from the above-noted Cayleyan mode of expressing the
“simplified remainders,” Trudi puts forward (pp. 145-152) another mode,
each remainder now appearing as a sum of a multiple of A and a
multiple of B ; or, in Sylvester’s words,* as a syzygetic function of A and B.
For example, the three remainders above given he considers in the form

1

A +

a b

. p

B

p

<1 •

p

q

X

a

b

c

d

X

A +

a

b

c

d

a

b

c

1

a

b

c

V

<1

P

q

1

V

<Z

r

V

q

r

X

p

Q

r

s

p

q

r

8*

X 2

and generally he writes

Pr I Ur.A + Vr.B ,

where it is readily seen that as regards x

- 1,

Ur is of the degree r

V,

UrA

y,b

and where, as we know,

Pr

m — n + r
m + r - 1
m + r

h

r— 1 f

n — r .

Observation also shows that the coefficients of the highest powers of x in
Ur, Vr are H^D^, afir_x respectively. By substituting the new forms
for pr_2, pr_v pr in Cayley’s relation

By— l * Pr— 2 CtT_20tTQr * Pr— 1 “t ' pr 0 ,

there is obtained

(D^Lj • Ur_2 — ar_2arQr ■ Ur_1 + D^_2 • Ur)A

+ ( • Vr_2 — ar_2arQr • Vr_x + D^_2 • Vr)B = 0 ;

and, as Trudi proves that this can only hold when the coefficients of A and
B vanish, it follows that each of the two series of functions

B"o 5 1^1 5 • • • 5 B"n+1 5 V0 , Y"i , . . . , yn+l

* It is worth noting that it was in this connection that the word “ syzygetic ” was first
used, the full title of the memoir of 1853 (which clearly had considerable influence on Trudi)
being “ On a theory of the syzygetic relations of two rational integral functions, comprising
an application to the theory of Sturm’s functions, and that of the greatest algebraical
common measure.”

1913-14.] The Theory of Bigradients from 1859 to 1880. 43

has one of the Stnrmian properties which the p’s have been shown to
possess.

As regards the highest-common-divisor (pp. 142-144) his result is :
In order that two functions may have a common divisor of the k*/l degree,
it is necessary and sufficient that the first determinant of each of the last
k of their bigradient arrays shall vanish: and, when this holds, the
coefficients of the divisor in question are the successive determinants of
the (n — k)<A array. For example, the functions being

cLqX* + ape1 + . . . + «8 , bpxb + bYx^ + ... + bb ,
their bigradient arrays are

(«0. • •

• > as)\

1 («0 . • '

• • > “3)2

1 (ao > • •

• . «s)j

(«o . ■ •

• ’ ^3)4

(«<>>••

a

00

Cr<

ft,,-.

■ > h)

, life,-

• , h)

(V-

)

(V--

• . h)

and the proposition states that if the first determinant of each of the last
three arrays vanishes, the functions have the common cubic factor

(<*o> •

X

(60. •

At a later stage (p. 151) there is given the supplementary proposition
that the quotients resulting from dividing A and B by the said highest-
common-divisor are, save for an unimportant factor in each case, the
coefficients of B and A in Trudi’s form of the (n — k + iy/l “ simplified
remainder ” — that is to say, are Vn_*+1 and Un_fe+1 as before defined.

The closely related question concerning the common roots of two
equations he deals with at length in a section devoted to elimination
(pp. 161-178). Starting with the proposition that, u and v being integral
functions of x, uA-f-tB must vanish for any common root of the equations
A = 0, B = 0, he next points out that u and v may be so chosen as to make
uA + tB of a low degree in x, even of the degree zero. In the latter
extreme case uA + vB must contain the eliminant as a factor, and if in
addition it be of the proper degree in the coefficients of A and B it is the
eliminant pure and simple. Attention is then called to the fact that the
division-process for finding the highest-common-divisor of A and B, or the
Sturmian modification of this process, supplies a series of pairs of functions
like u and v, and in particular that the last ££ simplified remainder ” Dn, as
satisfying all the requirements mentioned, is the eliminant. The condition
for the existence of more than one common root is investigated in like
manner. If the number of the roots in question be h, the degree-number
of wA + tB cannot be less than h Founding on this, it is asserted that

44

Proceedings of the Royal Society of Edinburgh. [Sess.

functions of the form uA-ffB whose degree-number is less than k must
vanish identically, and that therefore in particular the last k “ simplified
remainders” of A and B must so vanish. In the next place, proof is
adduced that the vanishing of these remainders is equivalent to the vanish-
ing of their first coefficients : and finally, there is reached the following
variant to the above proposition regarding the highest-common-divisor :
In order that the equations A = 0, B = 0 may have k common roots, it is
necessary and sufficient that Dn, Dn_i, . . . , Dn_k+1 vanish : and, this being
the case, the equation of the said common roots is pn_k = 0. The fact that
the vanishing of the first coefficients of the “ simplified remainders ” implies
in each case the vanishing of all the coefficients following the first is merely
commented on in passing. Attention, however, is more fully drawn to the
important fact that the existence of the condensation-theorem makes it
possible to put every proposition, which, like the foregoing, involves
bigradients, into an alternative form. Thus, the condition that the
equations

x 3 + aqje2 + a2x + «3 = 0 t
x? + b-jX + b2 = 0 j

may have two roots in common is, according to the said proposition, the
vanishing of

1 oq a.2 az

1 oq a2 cis
. . 1 \ b2

. 1 \ b2 .

1 \ b2 . .

and this by the condensation-theorem is the same as the vanishing of

a2

1

b2 + cl-Jj 1 — a2
alb2 - aB

oq&2 — <^3

Cltpbc) ?

1 Jh

Zq b2 -f* CL-fj-y ei>2 |

Bezout’s “ abridged method ” and Sylvester’s “ dialytic ” method, which
resemble each other in involving elimination of successive powers of a
common root, are only introduced by Trudi for purposes of corroboration.
In connection with the former method there is noted Sylvester’s theorem *
that the derived equations provide also an alternative way of obtaining the
Sturmian “ simplified remainders,” the first remainder being the non-zero
member of the first equation, the second remainder being the result of
eliminating the highest power of x from the first two equations, the third
remainder the result of eliminating the two highest powers of x from the

* See Art. 5 of “ On a theory of the syzygetic relations . . .”

45

1913-14.] The Theory of Bigradients from 1859 to 1880.

first three equations, and so on. In other words, if the set of equations
derived from A = 0, B = 0 by Bezout’s method be

c llxm~1 + c12xm~2 + ... +clm = 0^
c21xm_1 + C22xm~2 + . . . +C2m = 0 |-

then the second, third, . . . “ simplified remainders ” of A and B are

11 Cl2Xm " "f C13^m 3 ’

• • + cm

21 ^22*^ "" "t“ ^23*^ '

. . +

i r r r xm~3 4-

C11 c12 '13*^ ^ - 0

• +Cim

^21 ^22 ^23*^ + , .

• ^2 m

C31 ^32 CS2pC "t • •

• +C3 m

Proceeding from this, Trudi then says that if the non-zero members of the
said derived equations he denoted by Yv Y2 . . . , the “ simplified remainders ”
can clearly be put in the form

V.

cn Y,

C11

C12 Yj

r Y i
°21 x 2 1 *

C21

c Y

C22 X 2

C31

r Y

c32 x 3

and, as by definition

Yx — cLqB ’

Y2 = (u0x + aq)B - (b0x + 6j)A ,

Y3 = ( a ^x2 + ax x + a2)B - (bQx2 + bxx + &2) A ,

it follows that the said remainders have still another form, namely,

0

1

CO
■ ^0

ao

P> -

cn

K |A,

| c21 a0a; + oq

C21

i<r

+

&

0

C11 C12 ao

P> -

C11

C12 ^0

c2X c22 *t* oq

^21

^-'22 b0x -)- b j

Cgi ^'gq a^x2 4- (x-^Kj 4- cl2

C31

Cg2 b^x2 -{- byC + b2

— a result easily shown, by the use of the condensation-theorem, to be in
agreement with a previous one in which the determinant coefficients of A
and B are bigradients. He is also careful to note that although here, as
usual, n is taken equal to m, no real restriction is thereby made, the case
where m>n being viewable as a case in which the coefficients of xn+1, xn+ 2,
. . . , xm in B are equal to 0. For example, if the given equations be

ax 4 + bx 3 + ex2 + dx + e = 0 i
qx2 + rx + s = 0 f

46

Proceedings of the Royal Society of Edinburgh. [Sess.

Bezout’s derived equations (although not in Bezout’s nor Trudi’s notation)

are

a bxB + cx 2 + dx + i

\

= 0,

qx2 4- ra + s

ax + b cx2 + dx + e

qx2 + rx + s

ax2 + bx + c dx + e

q rx + s

= °.

ax 3 + bx2 + cx + d e

qx + r s

j = 0

or, in their usual form,

aq . x 2 + ar . x + as =

aqxB + (ar + bq)x2 + (as + br)x + bs =
arxB + (as + br)x 2 + (bs + cr - dq)x + (cs - eq ) =
asxB + bsx 2 + (cs - eq)x + (ds - er) =

0^

0

0

0^

We then have for the simplified remainders of the 1st and 0th degrees the
determinants

aq

ar ,

,x + as

ar + bq

(as + br) .

, x+bs

as + br

(&

s + cr - dq) ,

&

+

Ci

05

1

aq

ar

as

aq ar +

bq

as + br

bs

ar as +

br

bs + cr - dq cs - eq

as bs

cs — eq

ds - er

being only careful to note that both of these contain the irrelevant factor
a2. Trudi, however, does not point out that this factor would not have
troubled us if we had noted at the outset that for the first two derived
equations we might have substituted

qx2 + rx + s = 0
qxB + rx 2 + sx = 0,

thus using Sylvester’s method of derivation for the first m — n equations
and Bezout’s for the remaining n, as Rosenhain had shown in 1844.*

The case where B is the derivate of A receives special attention (pp. 152-
160), the object of course being to show that the quantities Dr, Ur, Vr are
then expressible in terms of sums of like powers of the roots of the equation
A = 0. The reason for the possibility of this transformation lies in the fact
that the coefficients

h, ^1 ) ^2 ’ • • • • 1

* Crelle’s Journ xxviii. p. 269.

47

1913-14.] The Theory of Bigradients from 1859 to 1880.

are then equal to

^0^1 ’ ^0^2 "h ^2,l?0 ’ ....

a.Sr

a0Sn-l + • • • + an-lS(i

and that in addition we have

(cKq , C8j , . . . , dn $ Sn , Sn_ i ,

K J 5 • • • 5 an \ SJl+l J Sn 5

(«0 J ^1 J • - • 5 $ Sn+2 > Sw+1 5

®0) = °»

*i) = 0,

s9) = 0,

The results arrived at are
D, = a *

°o °i

Sn So

«r-l

Sr

sr+1

°r+l

Sr+2

= 0 when r>n - 1

V,. — tto

tl =

. *1

$9

sr-l

1

S2

S3

. sr

X

! S3

*4

Sr+1

X 2

r+1 5

S0

*1

s2 . .

. . Sr_!

Sl

tS>2

s3 . .

. .

so

S2

S3

S4 • *

. . sr+1

S0X + Sj

S3

S4

% • •

• . Sr_|_ 2

S0X 2 + Sj# + s2

r+1-

Here again, however, Trudi loses his opportunity from not being acquainted
with Cayley’s multiplication-theorem of 1845, the use of which enables us
to transform not only Dr, but the whole bigradient array of which Dr is the
first determinant. In fact, it gives us for the case under consideration
another condensation-theorem. For example, when

A = a^x5 + cqa?4 + * • - + a5

and we consequently have to consider the four “ simplified remainders ”

(®o > • •

•» “5)1 1

(x*, x\ X, 1),

I (“o."

•5 ^5)2

(x2, X , 1),

•> ^5)3

|(*, 1).

(«<>>••

•.“5)4

•> ^4)2 '

II (6o,..

•? ^4)3

•^4)4

!(»«,••

•>*4)5

we find the condensation-results

48

Proceedings of the Royal Society of Edinburgh. [Sess.

(»».'•

• 5 ai)‘i

• . w I

I («o > •

• • . “5)4

l (6, , •

• • . *4)5

so

*1

s2

a0S3

a0s4

4- ajSg

si

’S2

S3

%S4

a0S5

+ alS4

S2

S3

*4

<*0*5

CLqSq

+ “lS5

S3

S4

8^

a0s6

a

0S7

+ «1«6

S0

S1

S2

S3

S4

*1

S2

S3

S4

%

^2

S3

S4

So

S6

*3

8 4

S3

**6

S7

I *4

S5

S6

S~

h

5

all in agreement with Cayley’s original result of 1846 (Hist, ii. pp. 162-164).
Taking the second of these for proof, we multiply unity columnwise by the
given bigradient array, obtaining

1

-*o

I

ao

«1

a2

CO

e

*5 •

1 .

-*o ~si

ao

ax

a2 a?j

a4 a5

. 1

•

\

\ b2

CO

1 *

\

\

\ h

*4 •

1

K

h

b2

b3 b4

ao

ai

a2

a3

a4

a5

. a0

ai

a2

a3

a4

«5

\

K

\

^3

%9i

a0S2 + <Vl

(^0^3 4" CL]$2

4- a2

*1

«0S4+ • •

. a0s5 + . . .

a0s2

CLq^3 "t

aQS4 "t

+ ^2

S2

%s5+ • ‘

• aose + • • •

%90

a0Sl + alS0

UqS 2 + tqSj + 0 2‘S‘o

a0S3 ’ •

. «0s4+ . . .

a0S2 + al*l

a0S3 + CllS2 + a2’Sl

%94 + • •

• a0s5 + • • •

«o«2

ao*z + a4s2

^o,94 ”t ^1^3 4- ei2s2

a0*5 4 • •

. a0s6+ . . .

and thence the final form desired.

The question of the existence of multiple or repeated roots in an equation
is next taken up (pp. 178-196), the main result being: The equation A = 0
will admit of only k distinct roots of the first determinant of each of the
last n— k bigradient arrays arising from A, and its derivative vanishes:
and this condition being fulfilled, the equation of the said roots will be got
by equating to 0 the determinant formed by replacing the last column of
Dk by k zeros and the 0th, l6’*, 2nd, . . . , kfot powers of x. For example,
A and its derivate being

xb + x 4 - 5a,s - x2 + Sx + 4 ,

5x 4 + 4a:3 - 1 5a:2 - 2a: + 8 ,

49

1913-14.] The Theory of Bigradients from 1859 to 1880.

and it having been found that the first determinants of the arrays

I (l,...,4)l

(1 . • • • . 4),

<1 ..... 4),

! (5, . . . , 8)2

(5, . . .,8),

1 ?

(5 , • . . , 8)4

5

(5 , . . . , 8)s

have the values

54, 0, 0, 0,

the proposition states that the number of distinct roots of the equation
A = 0 is 2, i.e. 5 — 3, and that the equation of these two roots is

11-5-5.

. 1 1 -5 .

. . 5 4 1

5 4-15 x

5 4 -15 -2 x2

0.

As a matter of fact, this equation is 54}(x+.2)(x—l) = 0, and A=(x + 2)2

{x-lf.

Lastly, Trudi takes up Sturm’s theorem for determining the number of
roots of an equation which lie between two given values. In dealing with
it he brings forward a new series of functions as a substitute for Sturm’s
series, namely,

%

•

>

a0 aY

«2

%

K

1

' «0

al

« 2

\

X

1

■ \

X

\ b1 b2 bs x2

Further, he points out that the individual members of this series can be
lowered in grade by the use of his condensation-theorem, thus providing
a variant of the series. He also notes that by means of the theorem which
we have extended above into another condensation-theorem they can be
transformed into

so

1 A

H ^

> ao

so

S1

1

S1

X

S1

S2

X

S2

h

X 2

and so he arrives by a different route at Joachimsthal’s series of 1854
{Hist., ii. p. 171).

Trudi’s work on bigradients, extending to 94 pages if both Teoria and
Applicazioni be included, has suffered undeserved neglect. Why this
should have been the case it is a little difficult to understand, its only
demerits being an occasional wordiness, a not very acceptable notation,

and a paucity of concrete examples. In his preface (p. vii) he tells us
VOL. xxxiv. 4

50 Proceedings of the Royal Society of Edinburgh. [Sess.

that it was first communicated in a number of papers to the Naples
Academy of Sciences in the year 1857. This being so, it was two years
in advance of Zeipel’s memoir on the same subject {Hist., ii. pp. 370-372)
and Bruno’s text- book, a fact which it is important for the reader to recall
if any small point of similarity between two modes of treatment should
attract attention.

Salmon, G. (1866).

[Lessons Introductory to the Modern Higher Algebra. 2nd ed.
viii + 296. Dublin.]

In a table of resultants (pp. 283-285) the final expansion of R25 is given?
and the discriminant of {a, b, c, d, e \ x 4, xsy, ... , y 4).

Sardi, C. (1866) : Rajola, L. (1866) : Torelli, G. (1866).

[Questione 47. Giornale di Mat., iv. pp. 239-240 : solution by L. Rajola,
iv. p. 297.]

[Teorema sui determinant a due scale, e soluzione della questione 47.

Giornale di Mat., iv. pp. 294-296.]

We have already seen how, from equating two forms of the resultant of
a pair of rational integral equations, interesting identities may be obtained
{Hist., i. p. 487 at bottom: ii. pp. 369-370, 374-375). Another instance is
here reached, the forms of eliminant used being Sylvester’s bigradient and
the eliminant which arises from successively substituting the roots of one
of the equations in the non-zero member of the other equation and taking
the product of the resulting expressions. If in connection with the latter
we make use of Spottiswoode’s determinant expression {Hist., ii. p. Ill)
for such a non-zero number, the identity evolved will be purely and almost
alarmingly determinantal.

Baltzer, R. (1864, 1870, 1875).

[Theorie und Anwendung der Determinanten, ... 2te Aufl. 3te Aufl.

4te Aufl. Leipzig.]

Putting (§ 11, 4)

A{x) = a0xm + aqa?™-1 + • • • + am = a0(x - a1){x - a2) . . . {x - am) | __

B(a?) = b0xn + lxxn~x +••• + &„ = b0(x - j8x)(aj - /32) ... {x - f3n) f > n

51

1913-14.] The Theory of Bigradients from 1859 to 1880.

and supposing x to be one of the roots of the equation B(oj) = 0, Baltzer
predicates the n equations

0 = [am- A(x)} 4 ctm-ix + 4 ■ • ■

0 = {am - A(x)}x 4 +

0 = {am- A{x)}x2 4

and the m equations

0 = bn 4 bn_xx + bn_2x 2 4
0 = bnx 4 bn_^t? 4

0 = bnx 2 4

and so deduces

am-A(x) am_x am_ 2

am-A(x) am_x

am - A(x) .

= 0,

which must thus be the equation in A(x) whose roots are A(/81), A (/32), ...,
A (/3n). Since the coefficient of the highest power of A(x) in it is

( — 1 )nb0m} it follows that

(-])*Jg‘.A0S1)A082)...A (pn) =

am

«m-l

V 2 • • • •

CLm

am- ....

a ....

K- 1

bn.2 ....

bn

bn~ 1 ....

bn ....

n+m )

as Hesse in 1858 had shown by direct transformation.

The bigradient form of resultant is also used (§ 11, 7) to show that when
A and B are of the same degree

resultant (A, B4AA) = resultant (A, B).

A fresh proof is given of Jacobi’s theorem * that if (p be a given
function of the (m + n — l)*;i degree in x, it is possible to determine two
functions u , v of the (n — l)t}l, (m — l)th degrees so as to have

wA4vB = S c/>,

* Grelle’s Journ xv. (1835) p. 108, where however m=n.

52

Proceedings of the Royal Society of Edinburgh. [Sess.

where S is Sylvester s bigradient. This consists simply in taking the
1 +n-\-m equations

and deducing

=

^m+n—1 d" Cm+n_2X + C

/y»2

m+n—Z'v

+ • •

. . \

A |

G,m +

+

V 2«2

+ • •

xA =

amx

+

+ . •

x2A =

amx 2

+ . .

B =

bn + bn_xX

+

bn_2x2

+ . .

II .

bnx

b r2

un- !•*'

+ . .

A

xA

^m+n— 1 ^ m+n— 2 ^ m+n —

cim am_i dm_2
• eLm etm_ i

0.

B

xB

bn- 1

bn

bn- 2

+n+m

Jacobi’s theorem of 1835 regarding Bezout’s condensed eliminant
suggests the similar theorem regarding the bigradient eliminant,* namely,
if w be a common root of the equations

a0xm + aYxm~x + • • • = 0, bQxn + bp?1-1 + • • • = 0 ,

then the signed primary minors associated with any row of

(a0, , am)n

are proportional to

wm+n~\ Wm+n~\ ... ,10, 1.

In dealing with the highest-common-factor of A and B and with the
subject of elimination Baltzer profits far less than he ought to have done
from the work of Trudi, whom indeed he does not mention.

Isic, E. (1873): Janni, V. (1874).

[Sul grado della risultante. Giornale di Mat., xi. p. 253.]

[Sul grado dell’ eliminante del sistema di due equazioni. Giornale di
Mat., xii. p. 27.]

* Gordan (1870) in quoting the two from Baltzer says that mn of the primary minors
of the former eliminant are secondary minors of the latter. , {Math. Annalen , iii. p. 356.)

53

1913-14.] The Theory of Bigradients from 1859 to 1880.

The bigradient form of eliminant is here used in the establishing of the
proposition that if the coefficients ar, br, be functions of the rth degree in one
and the same variable y, the eliminant is of the (mnf degree in the same
variable. Janni’s proof, though not quite so good as it might have been,
is the more interesting. The eliminant being

a0 ai a2 a3

• (Xq ax ^3

\ b\ ^2 5

he, in effect, multiplies the columns in reverse order by y°, yl, y 2, ys, y 4
respectively, and then divides the rows in order by y 4, yz, y2, y1, y a
respectively, thus obtaining

V/

«i2/_1 a2y~2 asV~3
«o a\V~X

\ y h

hy 2 bi y b2

\y2 \y

y 3

In this equivalent form the elements of the first two rows are all now of
the degree 0 in y , and those of the last three rows are all of the degree 2,
whence comes at once the desired result.

It should be noted that the procedure shows each term to be of the
( mnff degree in y ; in other words, that the eliminant is homogeneous.
Also, dispensing in the end with y, we may deduce the isobarism of the
eliminant, its weight being mn.

Zeuthen, H. G. (1874): Madsen, V. H. O. (1875).

[En Bemaerking om Beviserne for Hovedsoetningen om Elimination
mellem to algebraiske Ligninger. Tidsskrift for Math. (3), iv.
pp. 165-171.]

[En Bemserking om Sylvesters dialytiske Eliminationsmethode.
Tidsskrift for Math. (3), v. pp. 144-145.]

Zeuthen repeats Salmon’s mode of 1859 {Hist., ii. pp. 373-374) of using
Euler’s treatment of two integral equations in x which have more than one
common root : he is, however, more detailed, and takes the number of roots
to be p.

54

Proceedings of the Royal Society of Edinburgh. [Sess.

Lemonnier, H. (1875, 1878).

[Theoremes concernant les equations qui ont des racines communes.
Comptes-Rendus .... Acad, des Sci. (Paris), lxxx. pp. 111-112,
252-255.]

[Memoire sur 1’elimination. Annates de Vlfcole Norm. Sup. (2), vii.
pp. 77-96, 151-214.]

Lemonnier’s condition for the equations

%xm + ■ • • + am = 0, b0xn + ••• + &„ = 0

having k common roots is different from Trudi’s, but fortunately for com-
parison is very easily expressed in Trudi’s notation. It is * that the first
k determinants of

: K> ' '

• 5 ®m)n—k+ 1

1 (&<)>••

shall vanish, and the first determinant of

(“o. • •

• ? ®>m)n—k

• j l*n)m—k

shall not vanish. The former part of the condition recalls Zeipel’s of 1859 :
the latter is an important necessary adjunct. When, however, the equation
of the common roots

\(xk, a*-1, . . . , a?0) = 0

{aQ > • •

• 5 am)n-k j

• j bfim-k 1

happens to be given along with the condition, it is less necessary to mention
the latter part, as the determinant involved is the coefficient of xk in the
said equation.

Muir, T. (1876).

[New general formulae for the transformation of infinite series into
continued fractions. Trails. Roy. Soc. Edin., xxvii. pp. 467-471.]

[On the transformation of Gauss’ hypergeometric series into a continued
fraction. Proc. London Math. Soc., vii. 112-118.]

The fundamental theorem, which is established in two different ways,
is not essentially different from Heilermann’s of 1845 (Hist., ii. p. 361).
The second of the two ways is the more interesting. Beginning with the
series

a0 + ape + ap? + ap? + ••••, or /0 ,
b0 + bp + bp? + bp3 + ••••, or fi ,

* This is in accordance with the statement in § 13 of the complete memoir, and is
somewhat different from that first published.

55

1913-14.] The Theory of Bigradients from 1859 to 1880.

and subtracting b0 times the first from a0 times the second, and dividing
the result by x, we obtain

a0

ai I

+

a0 ^2

X +

I ao as

\

bQ ^2

1 b0 b3

or /2 say ;

and by subtracting | ajbx | times the second from b0 times this third series
and dividing by x there results

ao aY

■ \

«2

\

+

tt0 CLy

• \ \

x +

CIiq CL-^ CL 4

• ^1 ^3

%? + • • • , or /8 say ;

\ ^1 ^3

\ \ h4,

and so on. The outcome is

a0 4- axx + a2x2 + • • • • 61 q ^

b0 + bjX + b2x2 + • • • 0o - -j- _ O3P q^q^x

1 °2 ~ -q— -

C73

where 0O, 6V 02, • • • • are the first terms of f0, fv f2 . . . respectively.

Yent^jols, . (1877).

[Sur un probleme comprenant la theorie de l’elimination. Gomptes-
Rendus . . . Acad, des Sci. (Paris), lxxxiv. pp. 546-549.]

Ventdjols’ subject would have been much better described by Lemonnier’s
title of 1875. In substance nothing fresh is brought forward.

Dickson, J. D. H. (1877).

[A class of determinants. Trans. Roy. 80c. Edin ., xxviii. pp. 625-631.]
[The numerical calculation of a class of determinants, and a continued
fraction. Proc. London Math. Soc., x. pp. 226-228.]

The determinants here considered are the bigradients dealt with by
Heilermann (1845) and Muir (1876). They also arise in the same connection.

Mansion, P. (1878).

[Sur l’elimination. Bulletin . . . Acad . . . . de Belgique, xlvi. pp. 899—
903.]

What is interesting here is Mansion’s mode of obtaining the evanescent
bigradient array that results from the existence of common roots. The
equations being

A(aj) = a0cc5 + ... +a5 = 0, B(x) =* + . . . + &4 = 0

56

Proceedings of the Royal Society of Edinburgh. [Sess.

and the common roots a, /3, y, it follows that

am an A (a)

am a” aA(a)

am an B(a)

am an aB(a)

am an a2B(a)

pm p* AOS)

/3~ 0* pm

/T /3n B (P)

/3m / 3n (3B((3)

/ 3m (3n /32B(/3)

T 7“ A(y)

5

7” 7" yMy)

5

7“ 7“ b<7>

im T 7 B(y)

5

T yn 72B(y)

are all equal to 0 ; so that, if we temporarily write

(m , n , p) for the alternant | a m/3nyp | ,

we have

(mn5)a0 + (mni)^ + (mn?>)a.2 + (mn2)as + (mn\)ab + (mnO)ab — 0

(mw6)a0 + (innbya-^ + (mni)a2 + ( mn3)as + (mn2)a4 + (mnl)a5 = 0

(mn4:)b0 + (mu 3)b1 + (mn2)b2 + (mnl)b^ + (mn0)b4 = 0
(mn5)b0 + (mni)bl + ( mn3)b.2 + ( mn2)b 3 + (mn\)b4 = 0

(mn6)b0 + (mn5)b1 + (mni)b2 + (mn3)bs + (mn2)b4 = 0.

Here, however, by taking any two of the numbers 0, 1, 2, 3, 4, 5, 6 as
values for m, n two of the alternants will disappear, and we shall be able
to eliminate the five others, the final and complete result thus being in
Cayley’s notation

%

a2

00

al

ab

ao

ai

aB

a4

“5

\

h

b2

h

*4

h

h

h

For example, putting m, n equal to 0, 1, then equal to 0, 2, and finally
equal to 1, 2, we should have the particular three results which in accord-
ance with our usage under Trudi we might write

(a0 , . .

■

(*„ ■ •

• ■ > ^t)s !

All this, however, is considerably modified from Mansion’s exposition.

Gunther, S. (1879).

[Eine Relation zwischen Potenzen und Determinanten. Zeitschrift f.
Math. u. Phys., xxiv. pp. 244-248.]

The subject here is simply the evaluation of the bigradient which is the
discriminant of (xm+2 — l)/(x— 1), the result being

(m + 2)m.

For example, when m is 2,

1111.

. 1111
12 3..

. 12 3.

. 1 2 3

42.

57

1913-14.] The Theory of Bigradients from 1859 to 18.80.

Gunther’s proof is unnecessarily lengthy. The determinant can be readily
transformed into one whose diagonal has for its elements 1 repeated m + 1
times and m + 2 repeated m times, and whose other terms all vanish. For
example, when m is 2, the requisite operations are

row5 - row4 + row2 ,
row4 - row3 + row4 ,
row3 — row2 — rowq .

Mansion, P. (1879).

[On the equality of Sylvester’s and Cauchy’s eliminants. Messenger of
Math., ix. pp. 60-63.]

Mansion’s proof is not essentially different from the process of applying
Trudi’s condensation-theorem to Sylvester’s bigradient. The additional
fact, to which Mansion draws attention, namely, that many minors of the
one eliminant have equivalents among the minors of the other, is also
virtually included in Trudi. Thus, the four identities which Mansion
indicates in the form (see his fig. 11)

(Zq cq a2 aB a4 cl^ a,^ .

G t>2 bB

where the X’s, /Ps, Ps stand for

&i a0b2 + a1b1 af)B + alb2 + afb4 af>B + a2b2 + «3&4 - a4b0 a2bs + aBb2 - abb0 aBbB -

b2 a0bB + af)2 aYbB + a2b2 a2bB + aBb2 + a,b0 aBb.3 - a6b0 + a4b2 abhx a4bB - aQb l

h aA aA aA ~ a6ho aA - a A aA~a6b2

are only four of the ten noted by Trudi, the others being excluded, so to
speak, by drawing three vertical dotted lines on the right of each determi-

*0

al

a2

«3

a4

ab

%

ao

ai

a2

a3

a4

ft

\

\

\ ■

h

\

\

K

h

CO

\

h

h

■

b2

b0 bx

b3

\ bi b2

CO

oq

*<

K

P i H H

ft

V1 v2 v3

V4

V5

ne

/*e

58 Proceedings of the Royal Society of Edinburgh. [Sess.

nant instead of continuing the horizontal dotted lines all the way towards
the right.

From the foregoing there is probably no serious omission of papers
dealing directly with bigradients and in particular with the bigradient
eliminant. But, as it is possible to study the subject of the common roots
of two intregral equations without direct reference to bigradients, and as
the other determinants that may then be used can generally be transformed
into bigradients, it will doubtless be of service to the student of determinants
to give the following list of titles of papers on elimination. When taken
together with the preceding papers on the same subject they will also be
helpful to the student of the theory of equations : —

1870. Gordan, P. Ueber die Bildung der Resultante zweier Gleichungen.

Math . Annalen, iii. pp. 355-414.

187 2. Naegelsbach, H. Ueber die Resultante zweier ganzen Functionen.

Zeitschrift f. Math. u. Phys., xvii. pp. 333-346.

1876. Darboux, G. Sur la theorie de lelimination entre deux equations

a une variable. Bull, des Sci. Math., x. pp. 56-64 : (2) i. pp.

54-64.

1877. Rouche, E. Sur l’elimination. Nouv. Annates de Math. (2), xvi.

pp. 105-113.

1877. Igel, B. Einige Satze und Beweise zur Theorie der Resultante.

Sitzungsb. . . . Akad. d. TFiss. (Wien), lxxvi. pp. 145-168.

1877. Forestier, C. Exposition succincte de quelques methodes d’elimi-

nation entre deux equations. Mem. de V Acad, des Sci.

(Toulouse) (7), ix. pp. 142-163.

1879. Biehler, C. Sur la theorie des equations. Dissert. 60 pp.

Paris.

1879. Falk, M. Sur la methode de l’elimination de Bezout et Cauchy.

Nova Acta Reg. Soc. (Upsala), x. No. 15, 36 pp.

1879. Hioux, V. Note sur la methode d’elimination Bezout-Cauchy.

Nouv. Annates de Math. (2) xviii. pp. 289-295.

1879. Mansion, P. Sur l’elimination. Bull. . . . Acad. . . . Belgique

(2), xlvi. pp. 899-903: xlvii. pp. 532-541: xlviii. pp. 463-472,

473-490, 491-526.

The papers of Falk and Manson devote some little space to reviewing
the work of their predecessors, and are therefore additionally helpful. They
do not, however, mention Trudi, nor indeed does any one of the other
writers of the period.

59

1913-14.] The Theory of Bigradients from 1859 to 1880.

It may be noted as a significant fact in connection with the history
of the subject that in 1876 the editors of the Nonvelles Annates found
themselves called on to republish Cauchy’s important paper of 1840 (see
Hist., i. pp. 240-243). Its reprint occupies pp. 385-416, 433-451 of vol. xv.
of the second series. On this account, save for junior readers, the
“ exposition succincte ” above noted was quite unnecessary.

LIST OF AUTHORS

whose

1859. Bruno, F. Faa di .

1862. Trudi, N.

1866. Salmon, G.

1866. Sardi, C., etc. .

1864- Baltzer, R. .

1870. Baltzer, R. .

1875. Baltzer, R. .

1873. Isis, E. .

1874. Janni, V.

1874. Zeuthen, H. G.

ritings are herein dealt with.

32

1875. Madsen, V. H. O.

33

1875. Lemonnier, H.

50

1878. Lemonnier, H.

50

1876. Muir, T. .

50

1877. Ventejols

50

1877. Dickson, J. D. H.

50

1878. Mansion, P. .

52

1879. Gunther, S. .

52

1879. Mansion, P. .

53 !

53

54
54

54

55
55

55

56

57

{Issued separately February 19, 1914.)

60

Proceedings of the Royal Society of Edinburgh. [Sess.

VI. — The Kinetic Energy of Viscous Flow through a Circular
Tube. By Professor A. H. Gibson, D.Sc., University College,
Dundee.

(MS. received October 11, 1913. Read December 15, 1913.)

In the stream-line flow of a viscous fluid through a circular pipe of radius
a, the velocity of flow at any radius x is given by

where

v = k(a2 - x2),

k=— . .

4 fx dl

From this it follows that the kinetic energy of the moving column per
unit volume is given by

— I 27rxv3dx
2gJo

I — . 2t rife* [a{aPx
2 g Jo

- 3 cfix3 + 3 a2xb - x7)dx

w

2 9

Jtt Wa8.

(1)

The mean velocity v of flow through such a tube is given by

v = J ka 2,

so that the apparent kinetic energy, or the product of the mass flow and
one-half the square of its mean velocity, is

— • ira2[^ka2f
2 Q

= “ • (2)

The true kinetic energy is therefore twice that calculated as in (2)
from the mean velocity.

In the majority of experiments carried out to determine the co-
efficient of viscosity of a fluid, the head necessary to maintain a
measured velocity of flow through a tube of known diameter and length

1913-14.] Viscous Flow through a Circular Tube.

61

is measured, and the coefficient //. is then determined from Poiseuille’s
equation,

h = ^ (3)

Where h is measured by the difference of pressures at piezometer
orifices at two points in the wall of the tube, this equation is rigorously
true. Where, however, as is more often the case, the upper end of the
tube projects into a reservoir of the fluid, while its lower end discharges
freely, the head being measured from the free surface in the reservoir
to the centre of the discharging end of the tube, the true equation
becomes

h — 32/^_j_ k.E. of discharge + head loss at entrance to tube. . (4)

The two last terms become decreasingly important as the length of the
tube increases, but, with a fairly short tube, account for a very appreciable
portion of the whole head. In many cases in which the details of viscosity
experiments have been published, the kinetic energy of discharge has been
calculated erroneously from the mean velocity as in formula (2), while

various allowances, varying from zero to have been made for the head

9

loss at entrance to the tube. In a thin- walled tube projecting into a
reservoir, the loss at entrance, with an inviscid fluid, may readily be shown

to be equal to while the effect of viscosity is to reduce this loss some-
what. As the walls of the tube become thicker the conditions approximate
more nearly to that of a tube whose end opens flush with the sides of the
reservoir, in which case, in large tubes conveying water, the loss is

approximately ‘5^-. The true value of this loss for any actual projecting

Zg

tube may therefore be expected to be given by c^- , where c increases with

^9

the relative thickness of the walls, and, for such a fluid as water, has a
value somewhere between -5 and kO.

The following experiments have been carried out with a view of
checking the accuracy of the deductions leading to formula (1), and
of determining the value of c for tubes of small bore. In each case
the tube used projected for some distance into the upper reservoir
and discharged freely at its lower end. The head from the free
surface in the reservoir to the centre of the outlet was measured, and
the discharge was collected and measured. The fluid was water,

62 Proceedings of the Royal Society of Edinburgh. [Sess.

and the purely viscous loss was calculated from Poiseuille’s value
of ju, viz.,

•0000181

^ 1 + -03368* + -00022 W

Three tubes were used, of the following dimensions : —

Tube.

Diameter in cm.

Length.

Cm.

Ratio

external

Internal .

External.

internal
diameter =m.

A

*0715

•1073

4-29

1*50

B

*1470

*1960

6-66

1*33

C

*2580

•9000

38*20

3*50

For tubes A and 13, £=14-2° C., making [x= *0000119.

For tube C, £=12*9°C., „ /* = *0000123.

Since the pressure in the interior of the jet at the point of discharge

T

is greater than atmospheric by an amount — , where T is the surface tension

and r the radius of the jet, the effective head is less by this amount than
the measured head.

Thus, for tube A, T = *073 grms. per cm. ; — = 2*028 cm.

r

„ B, T = '073 „ ; 1 = 1-00 „

r

„ C, T = -075 „ ; 1=0-57 „

r

This correction is applied in the following tables, which give the
experimental results.

Tube A.

Loss of head in cm.

v 2

Experiment.

Total.

In viscous
resistance.

Due to T
at outlet.

Residue

(-*©■

V

c. per sec.

L

1

16-50

12-400

2-028

2-072

39-00

•775

2-68

2

16-22

12-200

55

2-002

38*40

*750

2-68

3

8-48

5*980

55

0-475

18*82

*1805

2-63

4

8*35

5*870

55

0*452

18-48

•1740
Mean =

2-60

2-65

1913-14.] Viscous Flow through a Circular Tube.

63

Tube B.

Loss of head in cm.

Experiment.

Total.

In viscous
resistance.

Due to T
at outlet.

Besidue

K>

V

c. per sec.

v2

w

1c.

1

16-02

8-155

1-000

6-865

69-60

2-470

2-78

2

16-64

8-390

55

7-250

71-30

2-595

2-80

3

12-56

6-905

55

4655

58-75

1-760

2-65

4

11-81

6-550

55

4-260

55*70

1-581

2-69

5

7-50

4-501

55

1-999

38-23

0-745

2-68

6

7-46

4-490

55

1-970

38-20

0-744
Mean =

2-65

2-71

Tube C.

1

16-90

11-98

0-57

4-35

57-90

1-705

2-55

2

16-60

11-85

55

4-18

56-90

1-646

2-54

3

12-43

9-30

55

2-56

44-65

1-015

2-53

4

12-55

936

55

2*62

44-95

1-029

2-54

Mean =

2-54

From these results it appears that the sum of the residual losses is
between 2*5 and 3*0 times — . Of this, the kinetic energy of discharge

accounts for 2~. The remainder, incurred at entry to the tube, is equal

* 9

to Ctz- , where c has mean values as follow : —

2g

Ratio

outer diameter

1-33

1-50

3-50

inner

(=m)

Mean value of c

•71

•65

•54

1

2 - V

•70

•64

•52

m2

The value of c appears to increase slightly with an increase in speed.
Its mean values over the range of values of m occurring in the experi-
ments are given with fair accuracy by the relationship

and as this also satisfies the two extreme conditions, i.e. makes c = 1 when
m=l, as in a thin- walled tube, and makes c — m 5 when m is very large,
values calculated by this relationship are probably fairly accurate for all
intermediate values of m.

(. Issued separately February 19, 1914.)

64

Proceedings of the Royal Society of Edinburgh. [Sess.

VII. — The Axial Inclination of Curves of Thermoelectric Force : a
Case from the Thermoelectrics of Strained Wires. By John
M‘Whan, M.A., Ph.D., Lecturer in Mathematics in the University of
Glasgow. Communicated by Professor Andrew Gray, LL.D., F.R.S.

(MS. received October 17, 1913. Read February 16, 1914.)

In a communication to the Royal Society of Edinburgh,* Mr J. D. Hamil-
ton Dickson has examined with great care the valuable results of Professors
Dewar and Fleming on the thermoelectromotive forces of various couples,
and has come to the conclusion that the curve representing the thermo-
E.M.F. is in every case a parabola whose axis is, not vertical as had always
been assumed, but inclined a definite though very small angle to the
E.M.F.-axis.

This remarkable result has led me to go back to some experiments
which I made a few years ago on the thermoelectric properties of longitu-
dinally strained metal wires, to see if by any chance the same phenomenon
might be detected there, and in one instance (only) I have been able to
establish its existence unmistakably. The experiments in question, which
I have described elsewhere, j* were made on couples consisting each entirely
of one and the same pure metal ; but one wire of the couple might be subjected
to any desired longitudinal tension while the other remained unstrained.
The temperatures of the junctions were the same in all the experiments,
one junction being steam-heated, the other water-cooled.

On reference to the curves showing the relation of the tension in the
strained wire to the thermo-E.M.F. of the couple, only one was found to be of
parabolic shape, namely, that for nickel. The E.M.F.’s in non-magnetic
metals nearly all obey a straight-line law up to the point where overstrain
sets in : the only other magnetic metal tested, bismuth, gave no simple
relation between E.M.F. and strain. A closer examination of the nickel-
curve showed that, while it afforded good grounds for suspecting an in-
clination of the axis, the observations had been neither numerous enough
nor of the high order of accuracy necessary for certainty, and it was
accordingly decided to repeat the experiment. This repetition proved
extremely laborious, and only after some five or six attempts (each necessitat-

* Trans. R.8.E. , xlvii. 737-791, 1910-11.
t Diss., Gottingen, 1911.

65

1913-14.] Inclination of Curves of Thermoelectric Force.

ing the mounting of a fresh and freshly annealed wire) was the accompanying
curve, the figures for which appear in Table I., obtained, in which only one
of the thirty plotted points lies appreciably wide.

Table I.— Table showing Loads carried by Strained Wire (Mean Diameter
0-682 mm.) and Corresponding E.M.F.’s, reduced to Mean Temperature-
Range of 75° C. June 4, 1913.

Load (kg.) .

E.M.F. (volt x 106)

0

0-600

0-5

2-101

1

3-459

1-5

4-732

2

5-932

2-5

7T20

3

8-261

3-5

9-318

4

10-300

4-5

11-289

5

12T41

5 5

12-920

6

13-718

6-5

14-471

7

15-092

7-5

15-649

8

16-101

8-5

16-299

9

16-833

Q-F,

17-080

10

17*211

10-5

17330

11

17-363

11-5

17-302

12

17-178

12-5

16-970

13

16-661

13-5

16-272

14

15-800

14-5

15-260

It may be remarked, with reference to this curve and the table of values,
that the loads given as abscissae do not include the weight (175 gm.) of
the weight-pan. This accounts largely, though not entirely, for the fact
that “zero” load on the curve shows an E.M.F. of 0-60 xlO-6 volt; the
unavoidable manipulation of the annealed wire in mounting it (and
consequent slight strain) gave rise to an observed E.M.F. at (true) zero
load of about 0*066 X 10-6 volt, which accounts for the remainder of
the discrepancy. During the experiment — which lasted some eight con-
secutive hours — it was, of course, impossible to secure that the temperatures
inside the steam jacket and cold-water jacket which surrounded the
two junctions of the couple should remain constant. Besides the unavoid-
able small variations due to the replenishment of the boiler and other
incidental parts of the experiment, there comes into play a very con-
siderable thermoelastic cooling effect* at the junctions as the load is
increased. Thus, though these junction-temperatures, which were read
between every two galvanometer readings, proved fairly steady in the
neighbourhood of 97° C. and 21° C. respectively, varying at most by about
half a degree, for greater accuracy all the observations of E.M.F. used in
plotting the curve were reduced by interpolation to a mean temperature-
difference of 75° C. The reduction was easily performed from a series of
temperature-E.M.F. curves for different constant loads, prepared in connec-
tion with the original experiments.

Examination of the Curve. — The curve, when drawn to a large scale

* Loc. cit ., pp. 36-43.

VOL. XXXIV.

5

66

Proceedings of the Royal Society of Edinburgh. [Sess.

LOAD

67

1913-14.] Inclination of Curves of Thermoelectric Force.

(1 inch = 05 kg. for abscissae, = 10~6 volt for ordinates), was examined to
determine (i.) if it was a parabola, and (ii.) if so, if its axis was vertical or
inclined. The method of examination differed from that employed by
Dickson, in that it was first tacitly assumed that the curve was a parabola,
the fact that the midpoints of several parallel chords were found to lie on
one straight line giving support to this assumption, while not completely
justifying it. The straight line in question then gave the direction of the
axis. To determine the vertex of the curve, the tangent to it at right
angles to the axial direction was drawn : this is easily performed with
considerable accuracy by the aid of a long slip of glass having one straight
line ruled on it all its length, and a shorter one at right angles across the
slip. The shorter one is made to cover the determined axial direction, and
then slid along it until the longer one just touches the curve. (The glass
is, of course, turned with the lines next the paper.) The axis was then
drawn at right angles to the tangent at the vertex, and the focus determined
by trial, again with the glass slip, by finding the point on the axis whose
distance from the vertex was half its perpendicular distance from the curve.
This determined the latus rectum. Lastly, the inclination of the curve-
axis to the E.M.F.-axis was measured roughly by protractor and (much
more accurately) by square-counting, to find its tangent. The results of
these various measurements were :

Co-ordinates of vertex . . (22*48", 17*34")

Length of latus rectum .... 25*2"

Axial inclination,

(i.) by protractor (mean of 8 readings) . 3° 54' (about)

g

(ii.) by square-counting (tan o> = Y^g) . 3° 48'

From these data it is now possible to calculate the equation of the parabola,
and the final stage of the work is then the verification that the values
given in Table I. satisfy this equation to a sufficient degree of accuracy.
The equation, as calculated to seven significant figures for each coefficient,
was

9956077a?2 - 1322564 xy + 43922 if - 407990900* + 279653900 y - 206538300 = 0.

For any assigned value of x the equation gives two values of y, one of which,
since the coefficient of y 2 is very small compared with the other coefficients,
will be practically infinite (and negative). Neglecting these infinite solu-
tions as foreign to the problem, Table II. gives a comparison of the E.M.F.’s

(y) corresponding to various loads f~) as calculated from this equation.

68

Proceedings of the Royal Society of Edinburgh. [Sess.

and the E.M.F.’s actually observed at the same loads. The agreement is at
once sufficiently obvious : from the arrangement of the signs in the column

Table II.

Load (kg.).

Calculated value
of E.M.F.

(Volt)

Observed value
of E.M.F.

< 106).

Difference.

0

0-641

0-600

+ 0-041

1

3-547

3-459

+ 0-088

2-5

7-307

7-120

+ 0-187

4

10-511

10-300

+ 0-211

5

12-326

12-141

+ 0-185

6

13-877

13-718

+ 0-159

7*5

15-685

15-649

+ 0-036

9

16-855

16-833

+ 0-022

10

17-262

17-211

+ 0-051

11

17-362

17-363

- o-ooi

12-5

16-915

16-970

- 0-055

14-5

15-148

15-260

-0-112

of differences it seems probable that the determination of the axial in-
clination has been slightly at fault (rather too large), and that a more
accurate determination would make the agreement still more striking.
As it is, the initial assumption that the curve is a parabola appears sufficiently
justified.

{Issued separately March 20, 1914.)

1913-14.] Path of Ray of Light in Rotating Solid.

69

VIII. — The Path of a Ray of Light in a Rotating Homogeneous
and Isotropic Solid. By E. M. Anderson, M.A., B.Sc. Com-
municated by The General Secretary.

(MS. received November 3, 1913. Read January 19, 1914.)

The path of a ray of light in irrotationally moving media was first
investigated mathematically by Fresnel, who showed that to account for
the observed phenomena it is necessary to suppose that, the aether being

fixed, the medium imparts - — — of the amount of its own motion, resolved

in the line of the refracted ray, to the advancing disturbance. This
conclusion is also a necessary consequence of the modern Theory of
Relativity, which, while holding that, with reference to axes with regard
to which the medium is stationary at any point, the speed of light depends
only on the refractive index, for any other system leads to the above result.

Using this formula, it is possible to calculate the path of a ray of light
in a rotating homogeneous and isotropic solid, when the velocity produced
by rotation is small compared to that of light itself. We shall first
consider the case of a body rotating about an axis fixed in space, and at

right angles to the line joining two points A and B, through which we
will suppose the path to pass. If r be the distance of the disturbance
at any moment from this axis, and cp the angle made by the ray with
the direction of r produced ; if further co be the velocity of rotation, and
c the speed of light ; then the total velocity of the ray is

c wr sin 4> (/jl2 - 1)

70

Proceedings of the Koyal Society of Edinburgh. [Sess.

or

where

D =

D + Er sin <f> ,
and E = o>—

[X /x-

Then the condition for a brachistochrone is first evidently that the-
path shall lie entirely in the plane of rotation, and further

8 f — =0,

J D + E?’ sin (j>

or, neglecting the second order of small quantities

\ f ds j, f i

dsEjr sin <f>

= 0.

If we consider the part of the brachistochrone intercepted between
A and B, then Jcfe is the total length of the curve AB, while Jds r sin 0
is twice the area traced out by the radius vector.

It is easy to see that, while an increase of the length of the path leads
to an increase in the time taken, an increase in the area covered by the
radius vector will have the opposite effect, if area be reckoned positive
when swept out in the direction in which the solid is rotating. The last
equation may be interpreted to mean that for any slight deviation from
a brachistochrone these two causes of variation must exactly balance, and
that they will do so if an increase in length is accompanied by D/2E times
the same increase in area. Substituting we find

D fxc
2E==2oi(^-l)'

It is easy to show that a curved path, with a certain radius of curvature,

constant within the limits already assigned, will satisfy the above condition.
In the first place, it is a well-known theorem, and may be proved by the

71

1913-14.] Path of Ray of Light in Rotating Solid.

calculus of variations, that for any given length of line joining two points
A and B (fig. 2), that form of curve which subtends a maximum area with a
third point O in the same plane is an arc of a circle. We shall not, however,
use this result, but another which follows from it, or may be regarded as
the last step in its demonstration, namely, that if AFDGB be the circular
arc of required length, and ACDEB a slight variation from it having
exactly the same length, then the areas 0 ACDEB and 0 AFDGB are
equal to the first order of small quantities.

If now (fig. 3) we consider ALB as a possible circular path for light
in the rotating solid, and let APB be any slight deviation from it, in the
same plane, but not necessarily of the same length as ALB ; then if the
lengths of the two curves be not the same, let AMB be the circular

arc joining A and B which has the same length as APB. Then by the
theorem just stated AMB and APB subtend the same area at any point in
their plane to the first order of small quantities. Thus the time taken by
an ethereal disturbance to traverse the paths AMB and APB will be equal
with the same degree of accuracy.

Let us next consider the difference of length, and of area subtended by
the two circular arcs ALB and AMB. Let R be the centre of the chord
AB, and C and D the respective centres of the two circles. If then

Ah = a

AT) = p

AC = p + e,

then the area enclosed by the two arcs is

72

Proceedings of the Royal Society of Edinburgh. [Sess.

which equals

2e( p sin _1—

V P Jo 2 - aV

P Jp2 - a2'

The difference in length of the two arcs is

the former result divided by p, where p is the radius of curvature.

Thus the area enclosed between two nearly coincident circular arcs,
ending at the same points, is p times their difference of length. Also, from
what we have already seen, the difference in the area subtended at any
point in its plane by a circular arc and any slight deviation from it will
be p times the difference in length of the two curves. This assumes that
the point of subtension is so situated that the area swept out by the radius
vector is wholly positive or wholly negative. Obviously, for a point on
the concave side the difference of area will be of the same sign as the
difference in length, while for a point on the convex side the sign will be
opposite.

Now, we have seen that the condition for a brachistochrone in the case
we are considering is that an increase of length in the curve between any
two points shall be accompanied by an increase of area subtended at the

centre of rotation of times the amount, area being counted

2co(Ju2— 1) 6

positive when traced out in the same direction as the body is rotating.
This condition is obviously satisfied by a circular arc whose radius of
curvature

c p,

W 2(p? - 1)

and which is concave or convex to the centre of rotation according as the
wave motion with regard to that centre is in the same or in the opposite
direction to the rotation.

We will next consider the case where the medium, in addition to its
rotatory motion, has an uniform translatory motion v, as before, small com-
pared to the velocity of light. If 6 be the angle between the direction
of the ray and that of v, the total velocity is

c <or sin <jf>(/x2 - 1) fcos0(/x2-l)

~+ ^2 + ^2 ’

where

D + Er sin </> + F cos 0 ,
tr _ v( A*-2 ~ 1 )

73

1913-14.] Path of Ray of Light in Rotating Solid.

The condition for a brachistochrone is

ds

D + E?' sin $ + F cos 0
or to the first order of small quantities

= 0

fs-‘j

dsFr sin <£ dsF cos 0

D2

D2

= 0.

Now, as the projection of the path AB on a line drawn parallel to v
is a constant, the last term vanishes, and we therefore arrive at our
previous result.

In both this and the previous case the curves calculated are those
followed in space with regard to the assumed axes of no velocity. The
paths traced out in the solid itself can be deduced as follows. It is easy
to show that a ray which penetrates the rotating body in a straight line,

with velocity - , will leave a trace in the solid of curvature } which will
fk c

he convex to the centre of rotation if the ray be moving with regard

to the centre in the direction of rotation. The actual curvature of the

o / 2 1 \

path of light is — — in the opposite direction. By subtraction we

Cfk

get — as the curvature of the path traced out in the solid ; the radius of

Cfk

curvature is ~ , and the curve will be convex or concave to the centre
2oo

of rotation according as the radius vector of the disturbance moves along
with or against the rotation. This result will apply to both the cases
so far considered.

We have next to deal with the case in which the path of the ray is not in
the plane of rotation. Let us consider what path will be followed between

two points A and B in a medium rotating about an axis LM (fig. 4). Let
P be the plane passing through A and perpendicular to LM ; 0 the point

74

Proceedings of the Royal Society of Edinburgh. [Sess.

of intersection of that axis; C the projection of B on P. Join CA and AB,
and let \fs0 be the angle CAB. Let ADB be a possible path for light
between A and B, and let AEC be its orthogonal projection on P. Let
\]s be the angle between any element of the curve and the corresponding
element of the projection; r the distance of the latter element from the
point O, and (p the angle it makes with the direction of r produced. Then
the speed of light at any point on ADB is

c • , , fX2 - 1

- + cor sin <jt> cos if/ ™ - ,

/x ^

or

D + Er sin <£ cos if/ ,

where D and E have the same meanings as before. The condition for a
brachistochrone is therefore

v fds s f

‘ h-s)

Er sin cos i J/ds
IP

If now ds' be the element of the projection corresponding to any element
ds, ds ' = ds cos \fs, and our condition may be written

s fds « fEr sin d>ds A

sJd-s]—w-=0

Let Q be the cylindrical surface whose generators are parallel to LM,
and which passes through the curve ADB and its projection. Then it is
evident that for any curve on Q joining A and B the latter half of the
expression vanishes. Hence the curve of this class which most nearly
satisfies the brachistochrone condition is the shortest in length, or otherwise
the curve for which \{s is constant.

We may therefore confine ourselves to curves for which this condition
is fulfilled. Denoting the length of the arc AEC by l, and that of CB by a,

tan^ = T’ and C0S^ = -Jiha?’

The condition may therefore be written

As

fds' _

JT~

1, we get

g fds Jl2 + a2 _ « f Er sin <pds' _ ~

J D^ J W

Ihl ^ f E?’ sin <pds _ n

or in other words, being the rectilineal angle CAB, the increase of area
subtended at O by the curve AEC must be ^ C^-r^Q times its increase of
length, to the first order of small quantities. From this it follows that

75

1913-14.] Path of Ray of Light in Rotating Solid.

the radius of curvature of the projected curve is f CQS V'oM > The curve

^ J 2o)(m2-1)

itself follows from this condition and the fact that \Js is constant.
Within the limits considered it is part of a circular helix. Its radius of

curvature is /L— in a direction perpendicular to the axis of

2o> cos yfr0(nA2— 1)

rotation. This conclusion holds good whether or not we consider our
rotating body to have also a translatory motion with regard to the axes
of reference.

Note on Mr Anderson’s Paper. By Sir Joseph Larmor,

M.P., F.R.S.

Mr E. M. Anderson’s elegant argument may be paraphrased as
follows : —

Let v he any coplanar velocity of the medium, and set E = v(/ul2— 1)/m2
and D = c/iul; then the time of passage of a ray restricted to any artificial
path is

f— — , approximately J- f ds - J— [e cos <f> . ds .

J D + E cos <f> ^ J DJ D2J ^

Now

J E cos <f>ds = ^ v cos (f>ds ,

where the integral expresses, for a complete circuit, the circulation of the
medium in the sense introduced by Lord Kelvin into Hydrodynamics.
Here a circuit can be completed by any unvaried return path. Now, in
coplanar Kinematics, the circulation round the contour of any area is
|2cod(area), where co is the velocity of differential rotation or the vorticity.
When co is uniform, the time of passage of the ray is, for a ray in the plane
of motion,

ST = A (length) - CyL (area).

Now, when the length is maintained constant, S (area) = 0 for all possible
variations when the curve is a circular arc. Therefore, as Mr Anderson
reasons, when the length also is allowed to vary

S(area) = AS(length),

where the value of A can be calculated from the circular form. A particular
circular arc can then he selected which will make St vanish for all small
variations of its form without restriction to constant length ; and this will
be the path of an unconstrained ray.

76

Proceedings of the Royal Society of Edinburgh. [Sess.

If an additional uniform velocity is imposed at right angles to this
coplanar (or rather uniform laminar) motion, the vorticity will remain
unaltered ; thus, in the expression for St (the ray being now free of
any restriction to a plane) the area that occurs will be that of the
projection on the plane of the laminar motion. Now, even in the most
general coplanar motion, when the vorticity is not uniform, Jo)c£(area)
will be stationary for small variations which leave the length unvaried,
only when the curve is a geodesic on the cylinder, perpendicular to
the laminar motion, on which it lies; for otherwise a displacement of
the curve, considered as a thread, on the cylinder will make it slack,
and the cylinder can be expanded to take in more area. This geodesic,
as it would unroll into a straight line, will have the length of its projection
on the plane of the laminar motion unvaried while the shape of the cylinder
thus varies. The shape of the cross-section of the cylinder on which the
ray lies will therefore be such that for given length of its arc Jwd( area)
is stationary. In particular, if co is uniform, it will be an arc of a circle.*
This brings us to Mr Anderson’s result, in a somewhat extended form.

If a uniform material medium is in motion through the aether with
vorticity co restricted to be constant in magnitude and direction, all rays
of light travel in it along helices traced on cylinders of constant radius

C fl

2co ju2—l
vorticity.

* The same argument establishes that a flexible conductor carrying an electric current
in a uniform magnetic field will when free assume the form of a circular helix ; ef. Proc.
Lond. Math. Soc., vol. xvi., 1884, p. 169.

cos'll, having their axes in the direction of the constant

(Issued separately March 20, 1914.)

1913-14.]

Principia Atmospherica.

77

IX.— Principia Atmospherica: a Study of the Circulation of the
Atmosphere. An Address delivered at the request of the Council
before the Royal Society of Edinburgh, on 1st December 1913. By
W. N. Shaw, LL.D., Sc.D. , F.R.S., Director of the Meteorological
Office, Reader in Meteorology in the University of London.

(Read December 1, 1913. MS. received December 12, 1913.)

Introduction.

Every science has two aspects or two stages in its development. In the
first, the inductive stage, observations are made and compiled, and axioms or
laws are laid down. In the second or deductive stage the laws are applied
by syllogistic reasoning, mathematical or otherwise, to elicit conclusions
which either disclose new facts or show the inevitable connection between
facts already known, and, in either case, complete the claim of the study to
the rank of a science.

The different sciences vary greatly in the stage of development which
they present. The science of geometry has almost forgotten the origin of
its own laws and axioms, and occupies itself with the most complicated
deductive propositions, the forms of which are used to guide the deductions
of other sciences. Biology is still in the inductive stage: no one ventures
yet to predict in what form the horse will be found a million or even a
thousand years hence.

These different aspects of science appeal with different force to different
types of human mind. Observers are comparatively rare ; true inducers,
those who have the patience and the insight to arrange the facts and
formulate the underlying laws, are extremely rare; deducers, those who
draw conclusions, not always mathematical or strictly logical, make up the
balance of the human race.

Many years ago, in 1862, Dr Alexander Buchan, in a contribution to this
Society which was subsequently elaborated in a volume of the results of
the Challenger Expedition, laid the foundations of our inductive know-
ledge of the atmospheric circulation by a series of maps of the distribution
of pressure over the surface of the globe. With great pleasure I take the
opportunity afforded to me by your invitation to address you on recent
developments of the science of meteorology, particularly in the investigation
of the upper air, to put before you a representation of the knowledge of

78

Proceedings of the Koyal Society of Edinburgh. [Sess.

the atmospheric circulation as it presents itself to my mind, arranged in the
normal scientific form, with axioms which represent inductive laws, with
postulates or lemmas which represent groups of observed facts, and with
propositions leading to conclusions which are susceptible of verification.

Synopsis.

Section I. — Axioms or Laws of Atmospheric Motion.

1. The Law of the Relation of Motion to Pressure.

In the upper layers of the atmosphere, the steady horizontal motion of the air at any
level is along the horizontal section of the isobaric surfaces at that level, and the velocity is
inversely proportional to the separation of the isobaric lines in the level of the section.

2. The Law of the Computation of Pressure and of the Application of the Gaseous Laws.

The pressure at any point in the atmosphere and at any instant is the weight of the
column of air which stands upon one unit of horizontal area containing the point. The
numerical values of pressure, temperature, and density at any point of the atmosphere are
therefore related by the usual formulae for the gaseous laws.

3. The Law of Convection.

Convection in the atmosphere is the descent of colder air in contiguity with air relatively
warmer.

4. The Law of the Limit of Convection.

Convection in the atmosphere is limited to that portion of it, called the troposphere, in
which there exists a sensible fall of temperature with height. The upper layer of the
atmosphere, in which there is no sensible fall of temperature with height and therefore no
convection, is called the stratosphere.

5. The Law of Saturation.

The amount of water vapour contained in a given volume of air cannot exceed a certain
limit, which depends upon the temperature and upon nothing else.

Section II. — Lemmas or Postulates.

Lemma 1. — In the stratosphere, from 11 kilometres upwards it is colder in the high
pressure than in the low pressure at the same level; and in the troposphere, from
9 kilometres downwards to 1 kilometre, it is warmer in the high pressure than in the low
pressure at the same level. [W. H. Dines, M.O., 2106.]

Lemma 2. — The average horizontal circulation in the Northern hemisphere in January
between 4 kilometres and 8 kilometres consists of a figure-of-eight orbit from west to east
along isobars round the pole, with lobes over the continents and bights over the oceans.

The average circulation at the surface is the resultant of the circulation at 4 kilometres
combined with a circulation in the opposite direction of similar shape due to the distribution
of temperature near the surface. [L. Teisserenc de Bort, Ann. du Bureau Central Mete'oro-
logique , 1887 ; and W. N. Shaw, Proc. Roy. Soc ., vol. lxxiv. p. 20, 1904.]

1913-14.] Principia Atmospherica. 79

Section III. — Propositions.

Proposition 1. — To define the conditions for the persistence of the existing motion of the
atmosphere.

Proposition 2. — To show that the rate of increase of pressure-difference per kilometre

of height is 34-2 L ( ^ ^ ) ; and hence that the distribution of pressure in the strato-

& 6 \ d p) *

sphere is the dominant factor in the circulation of the air at the surface ; that the inter-
mediate layers between 4 kilometres and 8 kilometres exert little influence upon the
distribution of pressure.

Proposition 3.- — To show that the wind velocity across the slope of pressure at any level
is proportional to 0 ; and thence to show how to utilise observations of the pressure

and temperature to calculate the wind velocity at any level.

Proposition 4. — To show that the wind velocity generally increases with height until the
substratosphere is reached, and falls off with increase in height in the stratosphere.

Proposition 5. — To show how the distribution of pressure and temperature in the
upper air can be calculated from the observations of structure represented by a sounding
with a pilot balloon, and thence to account for the local distribution of rainfall when an
upper current from the north-west crosses a lower current from the south-west.

Proposition 6. — To account for the average general circulation over the Northern
hemisphere in the four-kilometre level as set out in Lemma 2.

Section I. — Axioms or Laws of Atmospheric Motion.

The time has arrived when it seems possible and desirable to formu-
late the laws and principles which can be effectively employed at the
present day in the explanation of many of the recognised phenomena of
the structure and circulation of the atmosphere, and to illustrate their
application. These laws and principles are the result of observations some-
times suggested or controlled by theory. They are of the nature of
axioms or inductions, about the validity of which a good deal of discussion
is possible. Into that discussion I do not now propose to enter. The
axioms really depend for their justification upon their effectiveness in
explaining observed facts. They are set out as follows : —

1. The Law of the Relation of Motion to Pressure.

In the upper layers of the atmosphere, the steady horizontal motion
of the air at any level is along the horizontal section of the isobaric
surfaces at that level, and the velocity is inversely proportional to the
separation of the isobaric lines in the level of the section.

The line of argument in favour of this law, which cannot strictly speak-
ing be either verified or contradicted by any available process of observa-
tion, is as follows : The condition specified in the law is the condition of

80

Proceedings of the Royal Society of Edinburgh. [Sess.

kinematic equilibrium towards which all atmospheric motions tend, and
have tended either since the earth began to rotate as it does now, or the
atmosphere was first formed, whichever of those events is the later in time.
Any deviation from the equilibrium state is by infinitesimal steps during
which readjustment to the equilibrium condition has been taking place
automatically. Hence any finite difference from the equilibrium state can
only occur in quite exceptional conditions. Consequently if there is an
ascertained difference from the equilibrium condition it requires explanation
just as the divergences from the uniformity contemplated by the First Law
of Motion require explanation.

An allowance for “ curvature of path ” is one of the differences of which
account may have to be taken. Its importance depends upon the latitude.
For* the half of the globe north of 30° N. and south of 30° S. it is generally
negligible, but near the equator it becomes the paramount consideration in
the question of the persistence of distribution. Thus rotary systems, small
or large, are the only possible isobars for a synchronous chart of an
equatorial region, if one were drawn. The long sweeps of “ parallel isobars ”
with which we are concerned in this paper would be inadmissible there.

Near the surface there is always a component of motion along the
gradient from high pressure to low pressure. In this region the friction
due to obstacles and to the viscosity of the air prevents the steady state
being reached, and in consequence the centrifugal force due to the
velocity of motion is not adequate to balance the pressure.

This modification of the general principle in the case of surface air may
be inferred from the fact that in all maps of the distribution of pressure
and wind at the surface there is evidence of a flow across the isobars.
The maps are not always conclusive, as they are for sea level and not
station level ; but no person of experience will doubt the general truth of
the statement, which in books often takes the form of postulating con-
vergence towards centres of low pressure and divergence from centres of
high pressure.

2. The Law of the Computation of Pressure and of the Application of

the Gaseous Laws.

The pressure at any point in the atmosphere and at any instant is
the weight of the column of air which stands upon one unit of horizontal
area containing the point.

This principle assumes that the motion of the air is so slow that the
hydrostatical forces are not interfered with. Explosion or elastic wave-
motion would invalidate the law. It therefore assumes that the

81

191 3-14. J Principia Atmospherica.

atmosphere is free from explosions and elastic wave-motions, or that their
effect is so small that it does not enter into meteorological calculation.

It follows that the numerical values of pressure, temperature, and
density at any point of the atmosphere are related by the usual formulae
for the gaseous laws. In other words, when due allowance is made for
the difference of composition in consequence of the variation in the amount
of water vapour or other possible causes, the relation p = ROp holds, where
p, 0 , p are the pressure, temperature (on the absolute scale), and density of
the air, and R is a “constant” which is altered by an alteration in the
composition of the air, but not by other causes.

3. The Law of Convection.

Convection in the atmosphere is the descent of colder air in con-
tiguity with air relatively warmer.

The law is advisedly stated in this form (although objections may be
taken to it for want of strictness) because the driving power of the
convective circulation comes from the excess of density of the descending
portion, and the excess of density in atmospheric air is due in nearly all cases
to low temperature. Differences of density might be caused by differences
of pressure or by differences in the amount of moisture contained in equal
volumes. But finite differences of pressure cannot persist in contiguous
masses of air ; the amount of water vapour in air at the ordinary tempera-
tures with which a meteorologist has to deal is only a small fraction of the
whole mass, and the colder the air is, the less water vapour is required to
saturate it. Consequently, although it would be possible in a physical
laboratory to display a sample of air which, though warmer, is yet denser
than another cooler sample on account of the humidity of the latter, the
conditions would not easily occur in nature, and the motive power for
convection would be exceedingly small. Such cases may therefore be left
out of account, and we may consider that, of two contiguous masses of air,
the colder is the denser.

The law of convection is usually stated with regard to the warmer
part of the convective circulation, and takes the briefer form that warm
air rises. The general adoption of this briefer form is due to the fact that
the warming of air at the surface is a matter of common knowledge, and it
occurs in the daytime, when its effects in producing a local convective
circulation are often quite distinctly visible. The form which is adopted
here, however, is preferable, because in any case it is the cooler and heavier
air in the neighbourhood which must be looked for if the true cause of

the circulation is to be found ; and, although on the smaller scale the

VOL. xxxiv. 6

82

Proceedings of the Royal Society of Edinburgh. [Sess.

heavier air is not far to seek, it is not so easily identified on the scale of a
meteorological chart.

Convection in the atmosphere may also be due to the variation in
the gravitational acceleration due to the motion of the air with reference
to the earth.

The gravitational acceleration depends partly on the statical attraction
of the earth’s mass and partly on the centrifugal action due to rotation.
The ordinary values of the constant of gravitation assume the rotation to
be that of the solid earth, and the acceleration of gravity upon air moving
over the earth’s surface is consequently different from that for calm air.
Hence the air which forms part of a westerly wind is specifically lighter
than air at the same temperature and pressure which is calm ; and, on the
other h^tnd, air which forms part of an easterly wind is specifically heavier.
These variations in what, contrary to the usual convention, may rightly be
called the “ specific gravity of the air ” have not yet been generally taken
into account in meteorological practice, but they are of real significance,
and are the subject of certain classical papers by von Helmholtz and
Brouillin on the circulation of the atmosphere.

4. The Law of the Limit of Convection.

Convection in the atmosphere is limited to that portion of it in which
there exists a sensible fall of temperature with height.

This portion, which comprises about three-fourths of the atmosphere, is
called the troposphere , and is a layer of air about 10 kilometres thick
surrounding the whole earth. It is surrounded by an outer spheroid of
air comprising the remaining fourth part of the atmosphere, which is
called the stratosphere , in which there is no sensible fall of temperature
with height. The boundary between these two layers is not at a fixed
height ; it is apparently a flexible, and therefore deformable, surface, but it
is not penetrable by air.

The height of the boundary differs in different latitudes, being highest
over the equator and getting gradually lower towards the poles ; it differs
also in different localities, being higher over an area of high pressure than
over one of low pressure. The local differences are due to deformations of
the boundary by the accumulation or withdrawal of air from underneath.
At any place the boundary oscillates about a mean position which should
be regarded as the height of the boundary of the stratosphere for the
place. There is no physical reason why the boundary of the stratosphere
should not be penetrated. All that is required to produce that effect is an
accumulation of air warm enough to cause upward convection. All that

1913-14.] Principia Atmospherica. 83

can be said is that there is no example of the approach to such an ac-
cumulation. There are a sufficient number of examples in which there is
a reversal of fall of temperature just below the stratosphere, and these
show that the stratosphere has, if anything, a little to spare in the way of
resistance against penetration. Hence, from the point of view of meteoro-
logical theory we regard the stratosphere as impenetrable.

5. The Law of Saturation.

The amount of water vapour contained in a given volume of air
cannot exceed a certain limit which depends upon the temperature and
upon nothing else.

This is really simply a statement of Dalton’s law of the saturation of a
gas with the vapour of a liquid, but it is quoted here partly because it
refers to the only form of variation in chemical composition to which the
meteorological atmosphere is subject, and also partly in order to avoid a
misapprehension that is very widespread. It is a well-known physical
principle that when a vapour is condensed the “ latent heat of vaporisation,”
which, in the case of water vapour, is very large, is liberated. The state-
ment of the principle is not complete ; it should go on to say that the
condensation cannot take place unless provision has been made for dispos-
ing of the heat which will be liberated. In the case of the atmosphere it
is often assumed that no provision of the kind is required, and that the air
will, in consequence, be warmed by the heat set free. Herein lies the mis-
apprehension. Vapour of water in air will not condense unless the air is
cooled, and the amount of condensation will be limited by the amount of
the cooling.

It should, however, be noted that the wording of the law as here given,
namely, that the limiting amount of water vapour depends upon the
temperature and upon nothing else, implies a statement about the atmo-
sphere about which it is necessary to be explicit. Since Dalton’s law was
enunciated, the researches of Aitken and others have shown that the cooling
of a mass of air below the “ saturation point ” causes condensation only if
there are nuclei upon which drops of water can form. In the absence of
such nuclei, laboratory experiments have shown that condensation does not
take place until the limits of saturation have been largely exceeded ; “ four-
fold saturation ” is necessary in such a case. Air without nuclei cooled
below its “ saturation point ” is said to be supersaturated, and the statement
of the law of saturation as set out implies that supersaturation does not
exist in the free air. This is another case in which there is no physical
reason to prevent anyone imagining circumstances in which supersaturation

84

Proceedings of the Royal Society of Edinburgh. [Sess.

might exist ; all that can he said is that no such circumstances have been
demonstrated, and the ready formation of clouds at all heights seems to
indicate that such circumstances are quite unlikely. Hence the meteoro-
logist is entitled to infer, as the result of a meteorological though not of a
physical law, that condensation in the form of cloud, or if necessary of
rain, will always accompany the reduction of temperature of the air below
the point of saturation, and the amount of condensation will depend upon
the reduction of temperature and upon nothing else.*

These five laws express the special principles with which the meteoro-
logist must approach the consideration of the circulation of the atmosphere,
with all its complexities and its perplexities. The rest must depend upon
the application of the ordinary principles of dynamics and physics to the
results of observations which indicate the pressure, temperature, and density
of the air in its actual condition when under consideration. It is my object
in this paper not to discuss or to justify these principles, but to show how
far they lead us in the explanation of some of the more general phenomena
of the atmospheric circulation.

The form which has been adopted for this communication has been
chosen for the purpose of drawing a distinction between the inductive, the
observational, and the deductive aspects of the questions which are treated.
Just as, in the cases of motion treated in text-books of dynamics, there is
ample opportunity for discussion as to the form of words which shall be
used for the laws of motion and the grounds for their acceptance or re-
jection, starting from the consideration that there never has been an actua]
example of a body free from the action of force, so, in the case of atmo-
spheric motion, there is no lack of opportunity for the discussion of the laws
as here set out, starting from the consideration that no actual case can be
quoted in which we are certain that the laws are strictly obeyed. And
further, just as in the case of the dynamics of the heavenly bodies the
whole subject is reduced to a manageable form by setting out to explain
the changes of motion and their causes instead of pondering over the
ultimate origin and cause of the state of motion which exists at any
particular epoch, so in the study of the circulation of the atmosphere we
may profitably turn our attention to the changes in the motion related to
the varying distributions of pressure, and leave for the time being the
endeavour to give a short answer to the question, “ What is the ultimate

* The supersaturation of atmospheric air is discussed in Dr Alfred Wegener’s Thermo-
dynamik der Atmosphare, Leipzig, J. A. Barth, 1911. Humidities, by the hair hygrometer,
up to 107 per cent, are cited on p. 254 of that work.

85

1913-14.] Principia Atmospherica.

cause of any given distribution of pressure, with its attendant atmospheric
motion ? ”

We proceed, therefore, first to define in two lemmas the average con-
dition of the atmosphere which we wish the reader to keep in mind, and
secondly to apply the laws which have been already enunciated to make
certain deductions or establish certain propositions with regard to the
circulation of the atmosphere, which are set out in the synopsis.

Section II. — Lemmas or Postulates.

Lemma 1.

In the stratosphere from 11 kilometres upwards it is colder in the
high pressure than in the low pressure at the same level ; and in the
troposphere, from 9 kilometres downwards to 1 kilometre, it is warmer
in the high pressure than in the low pressure at the same level.

Proof. — Table of average values of pressure and temperature at different levels over high
pressure (1031 mb.) and low pressure (984 mb.) at the surface ; with pressure differences
and temperature differences at each level. Compiled from the diagram and tables of
W. H. Dines, F.R.S., in Geophysical Memoirs , No. 2, M.O. Publication, 2106.

Table I.

Pressure.

Diff.

Diff.

Temperature.

Low

High

A p

A0

Low 984 mb. High 1031 mb.

K.

mb.

mb.

mb.

°A.

°A.

°A.

15

116

123

7

14

135

146

11

-

9

224

215

13

157

171

14

-

11

226

215

12

183

201

18

-

8

225

217

11

212

235

23

-

4

225

221

10

247

273

26

+

1

225

226

9

288

317

29

+

7

226

233

8

335

366

31

+

13

227

240

7

388

422

34

+

15

232

247

6

449

483

34

+

14

240

254

5

516

552

36

+

13

248

261

4

591

628

37

+

12

255

267

3

675

713

38

+

9

263

272

2

767

807

40

+

8

269

277

1

870

913

43

+

4

275

279

0

984

1031

47

+

3

279

282

Standard deviation of P9 13 -8 mb.

Standard deviation of Ps 14T.

Correlation coefficient between the variations of P9 and Ps from the means for the
month (English ascents) ‘80.

The table which is here given summarises the results of an important
investigation by Mr Dines into the relation between the changes of pressure

86

Proceedings of the Royal Society of Edinburgh. [Sess.

at the 9-k. level and the corresponding changes at the surface. The
changes which he dealt with were chronological, and I have extended the
conclusion in applying it to topographical differences. This extension is
justified if the places between which the differences are to be taken are
sufficiently close together to be influenced by the same barometric system,
and if the chronological sequence is followed in individual cases. That the
latter condition is generally satisfied is shown by the high correlation
coefficient between the variations at 9 k. and at the surface.

The conclusion as to the relation between temperature and pressure in
the upper air which is drawn from this table is supported by the gradual
evolution of meteorological ideas on the subject. Originally it was assumed
that high pressure meant relatively dense air and low pressure relatively
light air from the surface upwards. Sometimes temperature and sometimes
moisture was held accountable for the levity; but the view first put
forward by von Hann that, in ordinary circumstances, the air over high
pressure is warmer than that over low pressure has gradually developed
until it may now be regarded as an accepted principle in meteorology. It
is borne out by the simultaneous soundings which have occasionally been
obtained from places within the same barometric system ; and apparently
the disturbances in the specified order are mostly confined to the lowest
reaches of the atmosphere. This last point also is well illustrated by the
figures of the table, which show a gradual falling off, on the average, of the
temperature differences in the lowest three kilometres.

Lemma 2.

The average horizontal circulation in the Northern hemisphere in
January between 4 kilometres and 8 kilometres consists of a figure-of-
eight orbit from west to east along isobars round the pole, with lobes
over the continents and bights over the oceans.

The average circulation at the surface is the resultant of the circula-
tion at 4 kilometres combined with a circulation in the opposite direction
of similar shape due to the distribution of temperature near the surface.

[L. Teisserenc de Bort, Ann. du Bureau Central Meteorologique, 1887 ;
and W. N. Shaw, Proc. Boy. Soc., vol. lxxiv. p. 20, 1904.]

This lemma is introduced in order to supply the reader with a suitable
general picture of the atmospheric circulation in the upper air, and the
modification which it must undergo in the lowest layers in consequence of
the distribution of temperature near the surface. As will be seen from
Proposition 2, which follows, the similarity of pressure-distribution at all
heights depends upon the equality of A 6/0 and Ap/p. Consequently, a

1913-14.] Principia Atmospherica. 87

circulation along parallels of latitude from west to east in which the air
nearer the poles is the colder is a circulation which may remain practically
identical at all heights, and is suggestive of durability and persistence.

The distribution of pressure at the 4-k. level given by M. Teisserenc de
Bort suggests that the actual circulation in the upper air is not a circu-
lation along parallels of latitude, but yet is an approximation thereto, being
something intermediate between a circle and a figure-of-eight.

That the circulation at the 4-k. level remains of the same general character
up to the 8-k. level is suggested by the fact that in those regions distribution
of temperature is such as to cause very little change in pressure-differences,
in accordance with the formula of Proposition 2.

It may be remarked that the distribution was calculated by M. L.
Teisserenc de Bort from the distribution of pressure and temperature at
the surface, and is subject to two uncertainties : first, the reduction of the
original pressure readings to sea-level ; and secondly, their further reduc-
tion to the 4-k. level. The uncertainties arise from the uncertainty in the
values of the temperature of the air “ below the ground ” in the reduction
to sea-level, and above the ground in the reduction to the 4-k. level. To a
certain extent these two uncertainties compensate each other in the
important features of the result, and the conclusion as to the circulation
at which M. Teisserenc de Bort had arrived, is supported by the results of
Hildebrandsson’s discussion of the international cloud observations (see
Hildebrandsson and Teisserenc de Bort, Les Bases de la Meteorologie dyna-
mique, vol. ii., Gauthier- Villars, Paris), and by other considerations of a
more general character.

The statements of these two lemmas are based upon observation and
are, therefore, liable to modification or correction in detail as the results of
observation become more conclusive. They are, however, sufficiently well
established to justify their use in the further consideration of meteoro-
logical problems.

Section III. — Propositions.

We now proceed to the consideration of the propositions which are set
out in the Synopsis. I shall deal in detail with only three of the pro-
positions, numbered 1, 5, and 6 respectively, because the remaining three,
numbered 2, 3, and 4, have already been dealt with in a paper communicated
to the Scottish Meteorological Society, with the title of “ The Calculus of
the Upper Air, and the Results of the British Soundings in the International
Week of May 5-11, 1913.” The paper is published in the Journal of the
Society for 1913.

88

Proceedings of the Royal Society of Edinburgh. [Sess.

Proposition 1. — The Conditions necessary to maintain a Steady
Atmospheric Current.

The conditions which must be complied with if a steady current is to
be persistently maintained must satisfy the first law, the law of relation of
motion to pressure.

The law prescribes that the velocity V is related to the pressure
gradient y, density p, latitude X, and the angular velocity of the earth’s
rotation w, by the equation

F=y/(2a>p sin X).

Provided that the latitude X remains constant during the persistence of the
current, this condition presents no difficulty ; the flow will always be de-
termined by the distance apart of the isobars, but the auxiliary condition
that the current shall not change its latitude implies that the isobars are
parallel to the circles of latitude. Hence we may infer that, neglecting a
very small correction for curvature, a circulation round the pole along
isobars parallel to the circles of latitude is a “ steady ” circulation which
will be persistently maintained. The only forces which will interfere with
it are frictional forces due to the relative motion of adjacent layers of air,
and, except in the immediate neighbourhood of the ground where friction
is aided by turbulent motion, these are extremely small. Hence a west-to-
east circulation or an east-to-west circulation in the upper air, once steady
will remain so, unless it is disturbed by changes of pressure- distribution.

But, on the contrary, when the air movement is from south to north
or from north to south, or has any component which gives a motion across
the circles of latitude, a change in sin X has to be dealt with.

Motion from South to North.

We propose to deal first with a current moving from south to north.
We shall suppose the current to be uniform over the section from the one-
kilometre level upivards. We leave out the lowest kilometre because we
know that it is disturbed by quasi-frictional forces at the surface.

In this case the value of sin X is increasing, and therefore greater pressure-
difference is required to get the same quantity of air through the same
section. But the pressure-difference is limited by the isobars, which are by
hypothesis supposed steady. Any convergence of the isobars themselves
provides its own remedy, because the gradient velocity is inversely pro-
portional to the distance. We have, therefore, only to deal with the
change in sin X in the formula

F=y/(2 mp sin X).

1913-14.]

Principia Atmospherica.

89

Let L be the width of the current, and H its depth ; then the flow over the
whole section Lx H is LHV ; and by the equation of continuity this must
be constant as the stream flows northward.

Now

LHV=nHLy ,

2(0/0 sin A.

and Ly is the pressure-difference, A p, between the two sides of the current.
LHV is constant ; hence, differentiating, we get

q _ dH dp d sin A
~H~J
or

sin A

dJLJ±+ CotX0X.

H p

Now p can only alter by variation of pressure, temperature, or composition ;
change of pressure is ruled out because the motion is along isobars ; change
of temperature will be very slight because there is no change of pressure,
and there are no other causes of any appreciable change of temperature ;
and change of composition can only occur in consequence of condensation.
By Law 5, in the absence of change of temperature no change of composi-
tion will occur. Hence

dp/p = 0,

and

— cot ASA.

H

Ln other words, the thickness of the moving layer must increase fractionally
by the amount cotXSX for the change of latitude <5A. If latitude is ex-
pressed in degrees and not in circular measure as differentiation supposes, we

must introduce the factor and thus the formula becomes

180

4 ^=-0175 cot A.

H aX

Hence, in order that a current may persist over any stretch from south to
north, it is necessary that the thickness of the moving layer should increase
fractionally to the extent of '0175 cot \ for every degree of latitude which
it crosses.

We have assumed the layer to be unlimited above, and limited below by
the one-kilometre level. To provide for the additional air by increasing
the height above the selected base-level would result in altering the
pressure : that mode of operation is therefore excluded by the condition of
maintenance of the current as steady. Consequently we must suppose the
additional thickness to be provided by encroachment upon the lowest

90

Proceedings of the Royal Society of Edinburgh. [Sess.

kilometre : that region is already supposed to be occupied by an extension
of the current which is disturbed by surface friction ; hence, unless there is
a continual flow-off of air from below the one-kilometre level, the steady
state cannot be maintained.

The south-to-north current implies a high pressure on the eastern side
and a low pressure on the western side, and near the surface there is a
component of flow from high to low across the isobars. Hence we may
suppose a case in which the northward-flowing current is maintained steady
by the flow-off from east to west in the surface layer. We proceed to
calculate the amount of this east-to-west current which will suffice to draw
off the increase of the current above 1 kilometre.

We suppose, for the purpose of calculation, that the east-to-west com-
ponent is uniform over the lowest half kilometre of the western section.
The fractional increase of thickness in the upper layer has been shown to
be ’0175 cot X for each degree of advance northward. The increase of the
thickness is the same over each elementary layer of height into which the
whole thickness can be divided ; consequently the air to be removed is the
fraction -0175 cot X of the transverse vertical section at every level. If
the removal is confined to the lowest half kilometre, which contains a
fraction of the atmosphere approximately one-twentieth of the whole, it
follows that a fraction 20 x ‘0175 cot X of the lowest half -kilometre layer
has to be removed for each degree of advance northward.

For each metre of advance northward, therefore, a fraction ^ X 0175 cot X

llTlxlO3

of the lowest half-kilometre layer has to be removed ; and, similarly, for

each metre per second of the wind velocity from south to north a fraction

20 x -0175 cot X i t i 7

— — — — — must be removed every second.

-L JL _L I X JL v/

Suppose that the breadth of the advancing current which is supposed
to be maintained steady is L kilometres, the westerly flow at the western
end of the lowest half kilometre must carry away air at the rate of

20 x 0175 cot X x l kilometres per second, or there must be a cross com-
UlTxlO3

ponent of wind there amounting to

20 x *0175 cot X
HIT

xL metres per second.

If the cross wind be referred to the width of a current expressed in
degrees of longitude at the latitude X, and if l be the width of the current
in degrees, we get

L = 111T cos XL

Whence it follows that in order to maintain a south-to-north current of V

91

1913-14.]

Principia Atmospherica.

metres per second there must be a cross wind leaving the lowest half
cos2A

kilometre of "35 — IV metres per second.

sin A

We have supposed the drainage to take place entirely in the lowest
half kilometre, which represents one-twentieth of the atmosphere. The
same result might be produced by a distributed cross-flow throughout the

western vertical section of the moving air of *0175 C-?S ^P metres per second.

We may therefore sum up the conclusion as follows: —

In order that a current across circles of latitude from south to north
with a breadth of l degrees of longitude may 'persist unaltered at any level,
it is necessary that air should be drawn away from the moving air at that

level to the extent of *0175 CQS ^ IV metres ver second.

sin A

The use of the surface layer, to draw off the excess of air which would
otherwise prevent the persistence of a current across circles of latitude, is
quite appropriate in the case of currents with a south-to-north component.
According to the rider to Law 1, such a current certainly exists, and it only
requires its magnitude to be adjusted in order that persistence may be secured.
Fora current extending over 10° of longitude in lat. 45° the cross component

CROSS SECTION OF 9 Kl LO MET RES &K.TO 10K] OF
A S. TO N.CURRE NX 5'WIDE'MAINTAINECT IN LATHS'

w

DOWNWARD FLOW. OF 0175
*TMOSP"£f?r FOR each Decker
OF L AT n UOC CR OSS CO

K 5* LO/VG: il

Fig. 1.

at the extreme west of the lowest half kilometre would have to be two
and a half times the steady south wind above, and that hardly occurs in
practice ; but there are a variety of ways of accounting for any discrepancy
between the calculated and observed cross-wind in case the south-to-north
current is actually maintained. Hence the diagram, fig. 1, representing
the conditions for maintenance of a south wind across a section of 5° of
longitude is not unreasonable.

92

Proceedings of the Royal Society of Edinburgh. [Sess.

The representation is, moreover, borne out by the facts which are known
as to the distribution of temperature in the atmosphere. For the seven
kilometres between the 1-k. level and the 8-k. level the temperature on the
“ high ” side is “ too warm,” and therefore represents the effect of a down-
ward flow while the pressure is maintained.* Hence it seems possible for
the conditions for the maintenance of a south-to-north current to be realised
in practice, though the adjustment would be delicate and might certainly be
transient.

Motion from North to South.

Persistence in the reverse of the case just described, that is to say, in
the case of a current flowing from north to south, is in one respect more
difficult and in another more easy.

What we havev to provide for here is not the thickening but the
shrinkage of the current in consequence of the decrease of sin X as successive
circles are crossed. The numerical result applies equally, but in the opposite
sense. Thus a current of velocity V flowing from north to south requires
that air should be fed wTith an inflow which, if distributed over the whole

side, would be *0175

cos2X
sin X

IV at any level at which the wind velocity is

Vt in order to avoid fractional shrinkage of *0175 cot X per degree of
advance. It is more difficult to see how the air could be supplied ; but the
shrinkage of the current while the distribution of pressure which controls
it is maintained presents little difficulty if the current in question may be
supposed to remain an upper air-current and therefore subject only to the
pressure-distribution appropriate to the current. To explain the persist-
ence of a current in the lower layers would make greater demands upon
one’s ingenuity, because the introduction of the necessary air would, as a
rule, alter the distribution of pressure below, and limitations to prevent
that alteration would have to be invented. Hence the maintenance of a
current from north to south at all levels requires some artifice for the
continuous production of the necessary pressure-distribution. The difficulty
is further aggravated by the fact that, just as in the case of the south-to-
north current, there is a flow-off from “ high ” to “ low ” in the surface
layers ; but unfortunately it flows away from where it is required to make
up the loss due to change of latitude, and consequently that loss as well as
the loss by shrinkage has to be made good if the northerly current is to be
maintained.

Putting the two currents side by side as in fig. 2, we see that the supply
* See the paper in the Journal of the Scottish Meteorological Society already referred to.

93

1913-14.] Principia Atmospherica.

for the north-to-south current may possibly come from the surplus of the
south-to-north current, but it cannot be along the surface. It must be remem-
bered that, so far as our information goes, we have no reason from observa-
tions for supposing that the relation between pressure and temperature in a
northerly current is different from that in a southerly current, though the
evidence is not quite conclusive, because the former has been less frequently
the subject of investigation. The air supply ought, therefore, to be carried out
in a similar manner in both cases. Persistence in this case, therefore, requires
the surplus of the adjacent southerly current and the outflow from the
northerly itself both to be delivered to the northerly current in the upper
layers in order that the proper temperature distribution may be obtained.

CROSS SECTION OF 9 Kl LOMETRES&K TO lOK] OF
TWO CURRENTS S. TO N. AND N. TO S. EACH
5‘ WIDE MAINTAINED IN LAT4 5.'

Such a combination of circumstances may fairly be regarded as exceptional,
and therefore the maintenance of a northerly current must be regarded as
exceptional.

Changes from the Steady State.

To complete the process of maintenance of the steady current from the
north we should have to imagine the whole of the outflow in fig. 2 towards
the “low” from both sides conveyed to the upper part of the northerly
current, and thus transferred from low pressure to high pressure as well as
from low level to high level. It is possible to make out a process with the
aid of the law of convection if the two currents are at different tempera-
tures. In such a case the surfaces of equal pressure may be so sloped as to
produce an apparent flow across isobars from low to high ; but we have no
such obvious and automatic explanation to give in the case of the northerly
current as in the case of the outflow of the southerly current. And,
indeed, it was not intended to adduce the conditions for persistent main-
tenance with the object of claiming that they are generally satisfied in
practice. On the contrary, the adjustment of the outflow in the southerly

94

Proceedings of the Royal Society of Edinburgh. [Sess.

current to the conditions of persistence must be fortuitous and unlikely to
be maintained for long ; the adjustment of conditions for the maintenance
of a northerly current is even more fortuitous. The reason for setting out
the conditions of maintenance is rather to show that natural conditions of
atmospheric currents are not, as a rule, those of persistence but of change.
If the conditions of persistence which have been set out are not realised,
the currents will change, and by Law 1 changes in currents imply changes
in the distribution of pressure. Consequently, an atmospheric system
which includes northerly or southerly currents has within itself elements
and causes of change in the distribution of pressure. It is therefore
unnecessary to attribute all changes to outside causes. It is preferable to
consider the causes of the changes which are inherent in cases in which we
cannot suppose the conditions of maintenance satisfied, and to regard
external causes of change which are known to exist as supplementary.

It follows that we have not to regard a quiescent atmosphere all over
the globe as the starting-point of our explanation of the present condition,
but we have rather to regard the circumstances of transition from one
set of conditions to another.

We may add some notes upon practical cases.

Persistent Southerly Current.

The maintenance of a southerly current has been shown to be a question
of adjustment of velocities, and a southerly current lends itself comparatively
easily to persistence. Examples of a persistent southerly current across
the parallels of Northern Europe furnish a well-recognised type of weather
that seems to resist the incursions of cyclones from the west. A southerly
current often extends throughout the vertical section of the atmosphere, as
might be expected from the automatic thickening described above.

Persistent Northerly Current.

On the other hand, a northerly current requires constant reinforcement,
and yet a northerly current, persistent for days over the North-Eastern
Atlantic, is by no means unknown. It is possible that the necessary air
in this case may be supplied by the gravitational flow of cold air off
Greenland or Northern Siberia, which must contribute a large amount of
air to the surface layers above the North-Eastern Atlantic.

Replacement of a North-Easterly Current by a South-Westerly Current.

An example of the disturbance of persistence frequently occurs in the
case of a north-easterly current with a south-westerly current above it, a

95

1913-14.] Principia Atmospherica.

case which is referred to in Mr Cave’s book on the Structure of the Atmo-
sphere in Clear Weather as a frequent precursor of weather of the thunder-
storm type, accompanied by the setting in of the south-westerly wind.
The distribution of temperature is such as to change the direction of the
pressure-gradient near the surface. Consequently the outflow from high
to low goes from under the upper “ low ” to under the upper “ high.” The
necessity for the thickening of the southerly current is therefore not re-
lieved by the outflow, but accentuated thereby. At the same time the
north-easterly current has to get thinner, so it is gradually replaced by the
south-westerly current settling down to the surface. The appropriate re-
distribution of pressure at the surface accompanies the redistribution of
air-currents in the vertical section.

These examples are adduced because it seems not improbable that they
give us the opportunity of watching the operation of the causes of change
which are inherent in any actual state of atmospheric motion.

Let me summarise the attitude which seems to me to be appropriate
for the meteorologist to take up in face of the complexities of the atmo-
spheric circulation, by again referring to the position of the astronomer
before the final enunciation of the laws of motion. Imagine the perplexity
of the astronomer who, finding the heavenly bodies moving in all sorts of
directions with all sorts of velocities, set himself to explain the motion
which each possessed. To him the laws of motion bring the assurance that
it is not necessary for him to explain why a body moves ; it is the changes
of motion which should occupy his attention. So the meteorologist, looking
at the circulation of the atmosphere in obedience to the distribution of
pressure, has not to ask himself why the pressure is high here or low
there, but rather, “ Is the distribution persistent, and if not, are the causes
of change inherent in the existing circulation sufficient to account for the
changes ? ” If it be said that, after all, the problem remains the same and
the point of view is immaterial, it is right to remember that in astronomy
the change in the point of view has simply reduced chaos to law.

From what has been already said, it appears that a steady state of
persistent motion of the earth’s atmosphere is in the highest degree im-
probable, because it can only occur in a combination of circumstances which
are independently fortuitous ; but it is desirable to call attention to a possible
case of motion which is quasi-persistent in consequence of two concurrent
and persistent infractions of the conditions of steadiness.

If we suppose the south-to-north and north-to-south currents of fig. 2
placed back to back so as to form an anticyclonic section instead of the
cyclonic section represented in fig. 2, we find in juxtaposition a south-

96

Proceedings of the Royal Society of Edinburgh. [Sess.

to-north current which must get rid of air, and a north-to-south current
which must have air in order to maintain itself, and all that is required in

order to maintain both currents is a transverse flow of *0175 C?S^L IV at

sm \

any level where the current velocity is V from the south-to-north current
to the north-to-south current. We cannot accept this transverse motion as
a part of steady motion, because the motion would not be strictly speaking
along the isobars as prescribed by Law 1. But if we could persistently
take the momentum necessary for the perturbation of the steady motion in
compliance with Law 1 out of the general west-to-east circulation, we

High

10

9

South-

>

North -

8

to-

•0175

to-

7

North

sm a

South

6

current

1

current

5

4

V

•0175^^zr

Sill A

3

‘ ‘ Too warm ”

>

‘ ‘ Too warm ”

2

I

1

1

1

<$- - - 1° long. > long. - ->

Fig. 3. — South-to-North current V1 supplying its own bottom outflow
Uj and maintaining a parallel North-to-South current V2 and its
bottom outflow U2 by transference of air across the ‘ ‘ high ” ridge.

could have both the southerly and northerly currents maintained. It is
not unreasonable to suppose that, as a westerly circulation has to be
diverted northward to produce the northward circulation, the westerly
momentum at the various levels may produce the effect described. In
this case we should have the permanence of the anticyclonic distribution
maintained by the persistent infraction of the law of relation of pressure
to wind. At the same time a flow-off at the bottom outwards in both
cases has to be supplied, and in consequence there is a downward flow
under permanent conditions of pressure over both sides of the ridge of
“ high ” which would give the necessary warming of the air of a high-
pressure region. Hence the case represented in fig. 3 seems to furnish a
possible example of a high-pressure region maintained in a quasi-steady
condition by a transfer of air across the isobars in consequence of the

97

1913-14.] Principia Atmospherica.

uncompensated momentum ; the flow-off on either side at the bottom from
“ high ” to “ low ” denoted by U1 and U2 being provided by the adjustment
of the currents V1 and V2.

Whether or not this be a true explanation, it certainly agrees with
common experience in regarding a high-pressure area as more easily main-
tained persistently than a “ low.1’

Propositions 2, 3, and 4.

These propositions, which deal with the application of the formula for
change of pressure-difference with height (the unit of height being the
metre), viz.

to explain the dominance of the stratosphere and the lack of importance of
the troposphere in the distribution of pressure at the surface, to compute
the wind- velocity from the pressure-difference at any height and to explain
the observed falling off of wind-velocity with height in the stratosphere,
have been dealt with in the paper communicated to the Scottish Meteor-
ological Society, and the work need not be repeated here, especially as
Proposition 5 makes use of the same equations.

Proposition 5. — The Calculation of the Distribution of Pressure and

Temperature in the Upper Air from the Observations of Structure

represented by Soundings with a Pilot Balloon.

A pilot balloon gives primarily the horizontal direction and velocity of
the wind at successive heights, so that we may suppose that we have the
horizontal direction and velocity of the wind at each kilometre as the data
for the calculation.

The first step is to resolve the wind-velocity into two components,
west to east and south to north.

By the application of Law 1 we can then compute the pressure-difference
for 100 kilometres in the south-to-north direction and the west-to-east
direction.

Thus, if A p is the pressure-difference for a distance L taken along the
direction of the wind velocity V, if 6, in absolute degrees, and p, in milli-
bars, are the temperature and pressure, X the latitude, go the angular
velocity of the earth’s rotation, and R the constant of the characteristic
equation for air, we have

y_ R 0 Ap _ g 6 Ap
2o> sin \ p L p L

And since both velocity and pressure-difference, or gradient, are vector

VOL. xxxiv. 7

98

Proceedings of the Royal Society of Edinburgh. [Sess.

quantities, we get for the northward and westward components of the
pressure-gradient per hundred kilometres

ANy=l|-(WtoE)

and

AwP = l^ T(S to N),

where (W to E) and (S to N) indicate the components of the wind- velocity
resolved in those two directions.

Now from a pilot balloon ascent we cannot get the value of p/0 for the
special occasion of the ascent, but there is really little variation from time
to time of this ratio. For the greater part of the troposphere variations of
pressure and temperature go together, and the whole range of variation
of 0 for any particular time of year is less than 10 per cent., and the whole
range of variation of p is of the same order. Consequently a mean value
of p/0 may be taken as a first approximation for the purposes of the
calculation.

The following is a table of average values of p/0 : —

Table II. — Table for Values of p/e at Different Levels —
Average of Results in “Geophysical Journal,” 1912.

Height,

kilo-

metres.

p/e.

Height,

kilo-

metres.

Pie.

Height,

kilo-

metres.

p/e.

Height,

kilo-

metres.

pie.

20

•26

15

•53

10

1*18

5

2-11

19

•28

14

•64

9

1-35

4

2-35

18

•32

13

•75

8

1-52

3

2-61

17

•39

12

•87

7

1-70

2

2-91

16

•46

11

1-02

6

1-90

1

Gd.

3*24

3-55

Having thus computed the pressure-difference for 100 kilometres, in
two directions at right angles, for the level of each kilometre, we may next
obtain by subtraction the change of pressure-difference for each kilometre.
The use of the mean value for p/0 will not altogether invalidate the process,
because the variation from kilometre to kilometre depends generally on the
ordinary diminution of pressure with height rather than on any extra-
ordinary distribution of temperature.

Substituting the value of the rate of increase of pressure-difference per
kilometre of height in the equation

dAP_oA.oP(M AP
dh~ “ 6\0 p

99

1913-14.] Principia Atmospherica.

and again assuming a value of 0/p, we can compute Ad provided we have a
value of 6 which can properly be substituted in the equation.

Here again we must have recourse to the mean value, as we have no
observation of actual temperature at the time ; but, again, the error made is
not fatal to the practical success of the calculation, because 0 comes in as a
factor which affects the scale of the variation ; it does not affect the sign.
By taking the mean value for the month instead of the actual value the
error is probably less than 10 per cent., and the whole error of employing
mean values for actual values probably amounts to less than 20 per cent. ;
and in considering the distribution of pressure and temperature in the
upper air we are not yet in a position to reject observations and informa-
tion which may be in error by as much as a fifth.

Consequently we may properly use the calculation here indicated to
give at least a rough but working idea of the distribution of pressure and
temperature at successive levels in the atmosphere when we know the
velocity and direction of the wind there.

The errors in p/0 and 0 are less important in considering the nature of
the distribution, because the same values, right or wrong, are used for both
components at the same level.

The following table of monthly averages gives values which may be
used in the absence of any special information for the particular occasion : —

Table III. — Average Temperature at Different Levels for Months.

1. For British Isles. Taken from “Geophysical Memoirs,” No. 2 (W. H. Dines).

Height,

kilo-

metres.

Jan.

Feb.

Mar.

April.

May.

June.

July.

Aug.

Sept.

Oct.

Nov.

Dec.

14

216°

217°

219°

221°

222°

223°

222°

221°

219°

217°

216°

215°

13

216

217

219

221

222

223

223

221

219

218

217

216

12

217

218

219

220

221

222

222

221

221

219

218

217

11

217

217

217

219

220

221

222

222

221

220

219

218

10

220

220

220

222

224

225

226

226

226

224

223

221

9

224

223

224

226

229

231

234

233

233

231

228

225

8

230

229

230

232

236

238

241

241

241

238

235

332

7

237

236

237

239

242

245

247

248

247

245

241

238

6

243

243

244

246

249

252

255

255

254

251

249

245

5

250

249

250

252

256

259

261

262

261

258

255

252

4

257

256

257

259

262

265

267

268

267

264

261

258

3

263

262

263

265

268

271

273

274

273

270

267

264

2

267

266

267

270

273

276

278

279

278.

275

272

269

1

271

271

273

276

279

282

283

283

281

279

275

272

Gd.

276

276

277

282

285

288

289

289

286

283

280 1

277

I give in Table IY. a specimen of the calculation as applied to the
results of a sounding with a pilot balloon on April 29, 1908.

Table IV. — Computation of Pressure Distribution and Temperature Distribution from
Pilot Balloon Ascent of April 29, 1908.

100

Proceedings of the Koyal Society of Edinburgh. [Se

0’

0

X
1 <*>
%

O 0 ^ CO 0

. CD CD CO ^ 05 £-

^ H CM CM

+ + + 1 + +

d

0

X

\<

CM O CM iC5 05 CM
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1913-14.] Principia Atmospherica. 101

I have used this method for the calculation of the distribution of
pressure and temperature in the cases represented by photographs of models
in Mr C. J. P. Cave’s book on the Structure of the Atmosphere in Clear
Weather * which includes that given in detail on p. 100. Some of the
results are given below — the problem being understood to be stated thus :
Given the wind-velocity at any point, to find co-ordinates for drawing the
isobar for the next higher millibar and the isotherm for the next higher
degree of temperature. It will be remembered that the isobar over the
point of observation itself is to be taken parallel to the wind direction in
accordance with Law 1, and the direction of the isothermal lines will be
taken parallel to the line joining the computed co-ordinates, so that the
distribution of pressure and temperature is to be represented each by two
parallel lines, the co-ordinates giving their direction and their distance apart.

1. Sounding of May 5, 1909, 6h. 43m. p.m.

“ Solid Current ” ; Wind approximately uniform in direction and velocity
from 2 kilometres to 10 kilometres.

Table V.

Height.

Distance of next higher
isobar in kilometres.

|

Distance of next higher
isotherm in kilometres.

k.

k.

k.

k.

k.

9-10

143 N

233 E

93 N

93 W

8-9

143 N

181 E

1000 N

1250 E

7-8

123 N

291 E

454 S

54 E

6-7

114 N

292 E

137 N

74 W

5-6

99 N

141 E

100 S

139 W

4-5

77 N

110 E

832 N

58 E

3-4

67 N

187 E

303 S

909 W

2-3

. 58 N

144 E

769 N

196 W

1-2

54 1ST

353 E

270 N

49 E

0-1

In this case it is interesting first to notice the gradual separation of the
isobars with increasing height and consequently diminishing density. This
is the ordinary condition for the velocity remaining invariable with height.

Secondly, it is noteworthy that the separation of the isotherms is
generally large and also very irregular, showing approximate equality of
temperature in any layer, but great want of conformity between one
layer and another. Such variations in the distribution of temperature may
easily be accounted for by local convection producing changes of tempera-
ture and possibly clouds, and it leads us to reflect that the convection
* Cambridge University Press, 1912.

102

Proceedings of the Royal Society of Edinburgh. [Sess.

which produces local clouds will also produce local modifications of
temperature and consequently local modifications of pressure and wind
velocity. If we ask whether such local variations of temperature and wind
are at all probable, we have only to refer to the records of the ascents
of registering balloons and of anemometers, or of pilot balloon ascents,
to give an affirmative answer.

Nothing is more noteworthy than the irregular variations in tempera-
ture-difference as given by a pair of soundings with registering balloons,
and the curious local irregularities of wind disclosed by pilot balloon
ascents. Hitherto it has been customary, on quite general grounds, to
regard them both as possibly due to the uncertainties of observation. We
now see that they may equally well be important evidence of complication
in the structure of the atmosphere.

Those whose temperament inclines them that way have still the
possibility of uncertainties in observation to fall back upon ; but the better
plan would seem to be to arrange for simultaneous ascents of registering
balloons and pilot balloons, so that the actual and computed distribution
of temperature may be compared. The interesting feature of the compari-
son would be that, if the method of computation here indicated (with its
acknowledged uncertainties in taking mean values for p/6 and 0 instead of
actual values) should prove serviceable, then one pilot balloon ascent gives for
practical purposes almost as much information as three registering balloons.

Apart from the uncertainties which have been mentioned, the con-
clusions as to the distribution of temperature and pressure are incontrovert-
ible by those who accept Law 1, and per contra if the conclusions are
sustained Law 1 receives its most complete vindication.

2. Sounding of September 1, 1907.
Westerly Wind rapidly increasing aloft.
Table VI.

Height.

Distance of next higher
isobar in kilometres.

Distance of next higher
isotherm in kilometres.

k.

k.

k.

k.

k.

4

68 S

oo E or W

86 S

119 E

3

77 S

400 W

44 S

555 E

2

139 S

294 W

119 S

185 W

1

196 S

526 W

43 S

80 E

The increase in the intensity of the pressure-distribution with height
is clearly shown, and finds its explanation in a steep temperature gradient
from south to north.

1913-14.]

Principia Atmospherica.

103

3. Sounding of November 6, 1908, 10h. 55m. a.m.

Reversal of Direction from E.S.E. in the lowest three kilometres
to W.N.W. in the reach from 4 kilometres to 9 kilometres.

Table VII.

Height.

Distance of next higher
isobar in kilometres.

Distance of next higher
isotherm in kilometres.

k.

k.

k.

k.

k.

8-9

185 S

356 W

96 S

312 W

7-8

204 S

356 W

416 S

770 W

6-7

200 S

416 W

294 S

189 W

5-6

233 S

435 W

139 S

625 E

4-5

344 S

665 W

101 S

109 W

3-4

5000 S

4000 E

119 S

270 W

2-3

588 N

416 E

286 S

108 W

1-2

100 N

142 E

24 S

65 W

0-1

77 N

172 E

34 N

40 E

The gradual diminution of velocity up to 4 kilometres, where the
isobars become very wide apart, is well marked in the second and third
columns ; and it is seen that the reversal is to be accounted for by a rapid
rise of temperature to the south-west in the second and third kilometres,
with a similar distribution of temperature of less marked character in
the higher layers.

It will be noticed that in the second and third kilometres, where the
reversal is determined, the slope of temperature is opposite to the slope of
pressure, a condition which we have already noticed as being characteristic
of large change of pressure-difference with height. In the sixth kilometre
the next higher isotherm is found a long way off on the east instead of on
the west, as in the layers above and below. The change is not really very
. large, as the temperature conditions are nearly uniform in that region as
regards the west-to-east direction, but it furnishes a reminder of the close
association which we must expect to find between slight changes in
temperature distribution and in the direction and force of the wind.

4. Sounding of April 29, 1908.

North-Westerly Current in the Upper Layers crossing a Lower
Current from the South- West.

This is the example of which the details of the working are shown in
the table on p. 100, and it is one of great interest, because it is characteristic

104 Proceedings of the Royal Society of Edinburgh. [Sess.

of the advance of a well-developed cyclonic depression from the westward.
It has long been recognised, by seamen and other observers of weather, in
observations of upper clouds which are seen to be moving from the north-
west while the surface winds are coming from the south-west. It is one
of the surest signs of the rainfall which occurs in the front of a cyclonic
depression. The table already given shows the values of A Np and A wp for
each kilometre level, and the values of A^d and Awd computed from the
changes in the pressure-differences for successive kilometre steps. We
may note here an ambiguity of notation, which we ought to find some
means to remove, and which ought at least to be made clear. In the table
A p and A# are used to indicate the slope of pressure and of temperature in
the two directions N. and W. Thus in the table, when A p or Ad is positive
for a given direction, it is to be understood that it represents the fall of
pressure in that direction. But the usual convention of the differential
calculus is that an increase in the quantity represented is indicated by a
positive value of the difference. The ambiguity arises from the use of the
convenient symbol A to denote the difference, while the meteorological
practice is to think of gradient as represented by downward slope. I have
not found any convenient new symbol to use instead of A to indicate a
negative difference, so the ambiguity remains for the present, though I feel
that an apology is due for it.

In order to present in a table the corresponding values of A p and Ad
for the same level, I have taken the means of the two values of A p for the
top and bottom of the kilometre to which Ad refers. This practice is,
perhaps, rather doubtful, but except in Table VI. it has been followed in
the tables already given, so I adhere to it in this one.

Converting by simple inversion the figures for Ap and Ad per 100
kilometres into distances along the axis of the intercepts of the next higher
isobar and isotherm respectively, we obtain the following : —

Table VIII.

Height.

Distance of next higher
isobar in kilometres.

Distance of next higher
isotherm in kilometres.

k.

k.

k.

k.

k.

5-6

84 S

143 W

60 S

102 W

4-5

109 S

263 W

64 S

50 W

3-4

141 S

2000 W

135 S

132 W

2-3

131 S

526 E

244 N

125 W

1-2

141 S

312 E

93 S

909 E

0-1

200 S

232 E

270 S

222 W

1913-14.]

105

Principia Atmospherica.

In this table the gradual conversion of a southerly component into a
northerly component associated with higher temperature to the westward
is very noticeable.

It will be seen that the isobars above 4 kilometres are, roughly speak-
ing, at right angles to those in the lowest kilometre, which is, of course, in
accordance with the wind observations ; but that the isotherms, with some
fluctuations, particularly in the second kilometre, are similarly arranged at
the top and at the bottom. That is to say, the upper winds are flowing
from the north-west with the higher temperature on the south-west side,
while the lower winds are moving transversely from the south-west with a
distribution of temperature parallel to that of the upper air, but in this case
the isotherms are across the wind.

These results are represented in fig. 4, which was originally drawn to
the same horizontal scale as the larger chart of the Daily Weather Report,
and it is clear that in the lowest stage the columns of warmer air brought
in by the south-westerly current are being carried underneath the parallel
columns of the upper current. Up to 4 k., where the wind has become
westerly, we have a distribution which produces the same effect. The
wind is always carrying warmer air under colder air, and as, by Proposi-
tion 1, a southerly current tends to thicken and a northerly current to give
way, the pushing under of the warmer air becomes more effective, until
instability occurs and rainfall sets in. The irregularities which are shown
in the distribution of temperature are probably due to previous convectioiia

We have here, therefore, the assurance of rainfall conditions as the
south-westerly wind pursues its course under the north-westerly in front
of the approaching depression. The rainy condition of that part of a
depression is thus directly accounted for.

The characteristic rainfall of a cyclonic depression is generally associated
with a general convergence of the surface isobars, but this hypothesis is
difficult to follow into details, because the convergence is general over the
area, while the rainfall is local. The analysis of the conditions of the upper
air here set out shows that there is good reason for rainfall in the upper
layers, to which the doctrine of general convergence cannot safely be held
to apply.

To the examples which are taken from Mr Cave’s work, I may add one
for October 16, 1913, which was reported to me by Mr J. S. Dines in con-
nection with his work for the branch Meteorological Office at South
Farnborough.

On that day, at Pyrton Hill, where the sounding was made, there was

06 Proceedings of the Royal Society of Edinburgh. [Sess.

5 -6k

4-5

3-4k

sl

\

r

N Y

1

sl

' x

+t?r>b. ^

<

7^"* 1

\

s of isobars and isotherms
£ 1 J 1° — \Ktlomtbss

scale, of wind velocity

9 20 3,°

J I

7/ieCeo per second

2-3i

1-2

0-1

Fig. 4. — Pilot balloon sounding, April 29, 1908. North-west wind over south-
west : characteristic of an advancing depression.

The arrow shows the direction and velocity of the wind ; the full line, the position of
isobar next above that which passes through the station. The dotted line through the 0
shows the isotherm passing through the station ; the parallel dotted line, the isotherm
for one degree higher than that of the station.

107

1913-14.] Principia Atmospherica.

a sudden change of wind between 1100 and 1500 metres height from a
reasonably steady wind from nearly due south into one almost as steady
from due north, the change being accomplished within half a kilometre.
The analysis in this case shows for the layer between 500 and 1100 metres
a temperature distribution in isotherms nearly north and south with the
warmer air on the east, and above 1500 metres an entirely different dis-
tribution with isotherms nearly east and west, and cold to the northward.
The intermediate layer, 400 kilometres thick, showed a very rapid increase
of temperature to the west — as much as 7° C. per hundred kilometres.

The complete arrest of the northerly current and production of a calm
by the annihilation of the gradient between 1100 and 1500 metres is very
remarkable, but nevertheless a real fact. The accompanying temperature
difference is probably due to a strong temperature “ inversion ” at a height
of about 1500 metres at the place of observation and of 1100 metres at a
place 100 kilometres distant to the west. On that occasion it lasted for
some time, as it was found an hour afterwards by a second balloon ; but it
must be remembered that it was a region of no velocity, and therefore the
relatively warm and cold airs were not moving. In order to get them
away, either convection must take place or a gradient must be created.

Proposition 6. — The General Circulation of the Atmosphere in the
Northern Hemisphere.

The reasoning in this proposition is more general in form than that of
the foregoing propositions. The extension of our knowledge tends more and
more to strengthen the conclusion that the proximate cause of the varia-
tions of pressure in the region of the British Isles must be looked for in the
layer at a height of about 7 to 9 kilometres ; it is the layer of maximum
wind- velocity just under the stratosphere, and it is also the layer within
which must be located a rapid transition of slope of temperature. Below it,
as set out in Lemma I., the slope of temperature follows the slope of
pressure ; above it, the slope is in the opposite sense. The mechanism by
which the changes of pressure are produced is unknown ; but this much is
apparently true, that within the layer referred to, the relation between the
pressure and temperature of the air at two places on the same level is that
of adiabatic expansion. Above the critical layer where this relation holds,
the air in the high-pressure area is “ too cold,” and below it, for 5 or 6 kilo-
metres at least, it is “too warm.”* We may suppose that air becomes “too
warm ’* by the dynamical warming of downward convection, and, perhaps, also
* See Journal Scottish Met. Soc., 1913, loc. cit.

108 Proceedings of the Royal Society of Edinburgh. [Sess.

that it becomes “ too cold ” by piling np under the stratosphere and readjust-
ment of the several layers within the stratosphere, so that pressure on the
sample which causes the bulging is reduced, while that over the surrounding
regions is increased.* Radiation is left out of account — whether rightly or
wrongly, it is not possible at this stage to say.

The motion of the critical layer is on the average from west to east, but
not invariably so, and apparently the temperature-relations which have
been described are not dependent upon wind direction. Other phenomena,
so far as they have been observed, seem to indicate a similar symmetry,
but there is no sufficient evidence for supposing that the phenomena are
necessarily centred locally. In fact, according to the distribution of isobars
at 4 kilometres computed by Teisserenc de Bort (Lemma II.), the average
motion does not differ much from a circulation round the pole which, once
set up, might be persistent with little change if it was everywhere
adjusted to the barometric gradient. The actual motion, however, certainly
does change, and is, in fact, constantly changing.

Let us consider the conditions of Teisserenc de Bort’s average isobars
and the forces which are available to produce the perturbations of a
supposed original circumpolar circulation indicated thereby. I have
already remarked that, for such a circulation as that represented by
Teisserenc de Bort, the isobars for 4 kilometres may fairly be accepted as
applicable at 7 kilometres also, because the changes of pressure-difference
between 4 kilometres and 7 kilometres are in ordinary circumstances very
slight.

Taking the average map for January, it will be noticed that the
isobars at 4 kilometres are clearly not circles round the pole. If they
were so, a steady circulation would be a natural conclusion. It has been
already postulated in Lemma II. that they are in reality indented ovals or
approximate figures-of -eight with the lobes over the Asiatic and American
continents and the inward bends over the two oceans. I purpose consider-
ing first the effect of convection as a possible cause of the deviation from
the circular shape. The shape which we have to explain is exactly
opposite of that which is often shown on synchronous charts of the
distribution of pressure at the surface of the Northern hemisphere in
winter, and which has “ highs ” over the continents and “ lows ” over the
oceans. I remark in the first place that, to derive the figure-of-eight shape
from the circular shape, one cannot rely simply upon the nutation of a
west-to-east circulation round the pole ; one must superpose either a pair of

* See a note on the Perturbations of the Stratosphere in Publication 202 of the
Meteorological Office.

1913-14.] Principia Atmospherica. 109

anticyclonic systems, elongated north or south, over the oceans, or a pair
of cyclonic systems over the continents, of which we can at present only
determine the southern portions ; or we might arrive at the actual shapes
by adjustments of both kinds. If we assumed positions for the original
circular isobars, it would be a simple matter to give numerical values of
the superposed anticyclones or cyclones. But the circumpolar circular
isobars are hypothetical, and, at the present stage, the numerical work
indicated would be unremunerative. Let us assume, however, such an
initial circumpolar system, and consider the physical forces which would
disturb its motion.

The only force immediately at hand is that of gravity, due indirectly
to the cooling of the surface air on the land and frozen sea in the arctic
night operating in accordance with Law 3, the law of convection. This
may produce a real effect of some magnitude on land-slopes. It is not,
I think, necessarily effective over level surfaces, because there is no slope
down which the cooled air can flow.

I have always hesitated about the common explanation of the trade-
winds and other well-known phenomena based upon the reverse process of
surface-heating. Surface-heating and surface-cooling necessarily produce
a certain amount of expansion and contraction, but not necessarily any
continuous convection current. Convection requires the juxtaposition of
warm air and cold air, and, if the region is big enough, the result of
surface-heating may easily give rise to a heated volume of air surrounded
by isobars and air-currents that prevent any continuous process of general
convection. Local convection there would be, but that need only extend
high enough up to take up the day’s heat. All the main air-currents of
the globe have pressure-distributions to guide them. They cannot usefully
be called convection currents.

So, if we had, say, a million square miles of level ice round the pole,
I cannot see that the cooling of that area need produce any considerable
effect upon the distribution of pressure ; but if the cooling takes place on
slopes, we at once get the force of gravity to help, and one can no more
suppose the downward flow of the air to be stopped than the flow of a
river to be permanently arrested. Hence there must be in winter a
continual flow of air off the great land-areas of the Northern hemisphere
if they have any slope. The air-fall off Greenland, for example, must be
enormous. Every description by explorers in the Antarctic seems to
support the suggestion of a great cold-air cascade from the Antarctic
continent. How much flows, and where it flows to, I cannot say ; ulti-
mately it must find its way to warmer latitudes by some route or other ;

110 Proceedings of the Boyal Society of Edinburgh. [Sess.

but these air-flows must be a real cause of alteration in the distribution of
pressure, and it is to the land-slopes which are losing heat that we may
trace an indubitable influence, and therefore a disturbance of the uniformity
of circulation. Apart from compensation, a flow-off of 1 metre thickness
of air would mean a reduction of pressure by 0*1 millibar.*

Similar phenomena must of course happen locally, and they are well
known in mountainous regions, though we can hardly expect the smaller
local examples to show much effect in the distribution of pressure over
the globe.

But we may assume that cold land-slopes in winter are the cause of a
constant abstraction of air from the lowest layers of the atmosphere in
those regions. The cold air flows away by gravity, and since the surface
pressure is apparently still maintained, the efforts to redress the loss of air
have to be carried out in the upper atmosphere and in accordance with its
laws ; consequently we should expect to find a cyclonic circulation in the
level in which the replacement is taking place. The cyclonic circulation
may operate to prevent the pressure being made up overhead, but it cannot
prevent the cold air from flowing downhill unless the reduction of pressure
is enough to reduce the density by as much as the low temperature
increases it, and this is a difficult task, for near sea-level it takes more
than 3 millibars loss of pressure to make up for a single degree loss of
temperature.

Hence we may suppose that the constant drainage of the land-areas
would result in the superposition of a cyclonic distribution at high level
over them, and the continental lobes of Teisserenc de Bort’s isobars for the
upper air may well be due to this cause.

But the .cause is obviously a very variable one, depending upon the
distribution of cloud and other circumstances. Statistically, its effect upon
the circulation of the upper air is to exaggerate the pressure gradient for
westerly winds over the temperate zones of the continents, and to diminish
the gradient northward. Thereby we introduce into the circulation local
accentuation of current, which must be disposed of by some dynamical
process.

* The facts which are here represented are sometimes taken as indicating the formation
of anticyclones over the Arctic and Antarctic land-areas. When those areas are represented
by plateaus 10,000 or 15,000 feet in height, the surface anticyclone may become merely a
hypothetical construction supposed to occupy the space which is really occupied by land
and not by air at all. To a considerable extent the great Asiatic and American anticyclones
depend upon the reduction of observations to sea-level under conditions which can have no
real existence. The mountain slope might possibly operate, in the maintenance of a
cyclonic circulation in the upper air, much like the hole in the bottom of a basin, and the
actual land-surface at the high level might therefore be a region of cyclonic circulation.

Ill

1913-14.] Principia Atmospherica.

The next step in the consideration rests upon the fact that by superpos-
ing a cyclonic depression upon the circumpolar circulation we displace a
part of that circulation to the southward and reduce the northern part.
Taking the case of Teisserenc de Bort’s map for January, the westerly run
of isobars over America and Asia is about 10° to 20° of latitude lower than
over the oceans, and these two positions of westerly circulation have to be
connected by isobars which cross the parallels of latitude, and therefore
have a south-to-north and a north-to-south component respectively. There-
fore, they can only be maintained persistently under the conditions set out
in Proposition 1. Now, it has been shown in the discussion of Proposition 1
that permanence of a quasi-steady character might be realised in the case
of an anticyclonic ridge having a south-to-north current on its western side,
and vice versa, provided that momentum was being taken out of the
westerly circulation in order to provide a slight eastward deviation from the
isobars setting to the north. Such a case would be fairly represented by the
deviation from circular isobars shown over the oceans on Teisserenc de Bort’s
map for January, and hence the form of those isobars may be arrived at by
the influence of a steady flow-off of air down the land-slope of the Arctic
regions and the steady deviation of the wind from the direction of the
south-west to north-west isobars on the western sides of the oceans in con-
sequence of the momentum of the westerly circulation.

Meanwhile, what happens to the cold air which has run off the land-
areas ? That has to be steered about by the distribution of pressure in the
upper air as modified by any special peculiarities of temperature in the
lower regions, and all sorts of complications may arise from this cause. So
far as it goes, its density tends to set up high pressure over the regions
which it covers, and so to make a slope of pressure southward and cause
easterly winds on its southern side. Whenever in a mass of air tempera-
ture-fall is in the opposite direction to pressure-fall, great change in the
horizontal distribution of pressure underneath is the result, and many of
our local variations of pressure may fairly be attributed to the reactions
which these cold masses of air offer to the attempt (in the end futile) on
the part of the upper air to steer them round the pole from west to east.
By their eastward motion these masses of cold air are always reminding us
that if left to themselves, without the overpowering guidance of the
pressure-distribution of the upper air, they would form a circulation round
the pole in opposition to the circulation of the upper air, with which they
are in perpetual conflict.

112

Proceedings of the Royal Society of Edinburgh. [Sess.

Turbulent Motion.

In the study which has been the subject of the foregoing pages we
have always considered the motion of the air to he regulated by a dis-
tribution of pressure balanced by the rotation of the earth, except in regard
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present communication.

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MODEL INDEX.

Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly
injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol. , 1902, pp.

Cells, Liver, — Intra-cellular Canaliculi in.

E. A. Schafer. Proc. Roy. Soc. Edin., vol.

Liver, — Injection within Cells of.

E. A. Schafer. Proc. Roy. Soc. Edin., vol.

, 1902, pp.
, 1902, pp.

IV

CONTENTS.

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VII. The Axial Inclination of Curves of Thermoelectric Force: a
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(. Issued separately March 20, 1914.)

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Part IX.] VOL. XXXIV. [Pp. 113-208.

CONTENTS.

NO. PAGE

X. Enzymatic Peptolysis in Germinating Seeds. By Dorothy
Court, B.Sc., Carnegie Research Fellow. Communicated
by Professor E. Westergaard, . . * . . 113

( Issued separately March 26, 1914.)

XI. A Study of the Curvatures of the Tasmanian Aboriginal
Cranium. By L. W. G. Buchner, Victorian Government
Research Scholar in the Anthropology Department of the
University of Melbourne. Communicated by Professor
R. J. A. Berry. (With Three Folding Tables), . .128

(Issued separately April 28, 1914.)

XII. The Place in Nature of the Tasmanian Aboriginal as deduced

from a Study of his Calvaria. — Part II. His Relation to
the Australian Aboriginal. By Richard J. A. Berry, M.D.

Edin., Professor of Anatomy in the University of Melbourne;
and A. W. D. Robertson, M.D. Melb., Government Research
Scholar in the Anatomy Department of the University of
Melbourne. (With One Folding Table), . . 144

(Issued separately April 29, 1914.)

XIII. A Chemical Examination of the Organic Matter in Oil Shales.

By John B. Robertson, M.A., B.Sc., Carnegie Scholar.
Communicated by Dr J. S. Flett, F.R.S., . . 190

(Issued separately July 15, 1914.)

[ Continued on page iv of Cover.

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[Continued on page iii of Cover.

1913-14.] Enzymatic Peptolysis in Germinating Seeds.

113

X. — Enzymatic Peptolysis in Germinating Seeds. By Dorothy
Court, B.Sc., Carnegie Research Fellow. Communicated by
Professor E. Westergaard.

(Read December 15, 1913. Revised MS. received February 10, 1914.)

In a previous paper ( Proc . Roy. Soc. Edin., vol. xxxi. p. 342) a method was
described for measuring small degrees of enzymatic peptolysis, and in a
subsequent paper {Proc. Roy. Soc. Edin., vol. xxxii. p. 251) the conditions
were dealt with under which such experiments could be carried out with
the greatest possible guarantee of sterility combined with the least inter-
ference with the reaction.

The intention was to employ these methods for the purpose of pursuing
the main object of research — the activation of zymogens in germinating
seeds — and it was accordingly decided to carry through a series of ex-
periments on germinating barley. This material was selected on account
of the readiness with which it may be obtained.

The presence of proteolytic and peptolytic enzymes in germinating
barley has been previously described by Weis {C. R. Carlsberg Lab., vol. v.
p. 127), Vines {Ann. Bot., xvi. 1), and Abderhalden and Dammhahn {Zeit-
schrift fur physiol. Chemie, lvii.).

Weis, working with a watery extract of crushed germinated barley,
found evidence of proteolytic as well as peptolytic activity, and it was
therefore decided to use a similar extract in some preliminary experiments.
For this purpose 900 grms. of material were crushed in a mincing
machine and extracted with 700 c.c. chloroform wrater for twenty hours.
The liquid was expressed in a hand-press, filtered, neutralised with sodium
bicarbonate, and divided into three portions. One of these was made
slightly acid ( = '2 per cent, lactic acid), one was made alkaline ( = T per
cent. NaHCo3), and one remained neutral. One gramme of Pepton Roche
was dissolved in 10 c.c. of each of these preparations, T c.c. chloroform
added, and the mixture incubated at 37°. It was somewhat surprising to
find that though the digestion was carried on for several days no deposit
of tyrosin was obtained.

At the same time another experiment was carried out with the same
material for the purpose of determining the relative activities of the

embryo and endosperm of the seed. The embryos were carefully dissected

vol. xxxiv. 8

114

Proceedings of the Royal Society of Edinburgh. [Sess.

out, ground with sand and a 1 per cent, solution of Pepton Roche, filtered,
and the filtrates digested at 37° C., 1 per cent, chloroform being added.
This procedure was also followed out with the residues and with a sample
of the whole seed. In each of these cases, as before, a number of the
digestions were allowed to remain neutral, while others were acidified and
made alkaline respectively. An entirely negative result was obtained from
these experiments also.

The experiments described above were repeated several times with
different samples of material, the digestions were carried out within a wide
temperature range (15°, 25°, 37°, 50°), and the period of incubation was
extended to as much as three weeks. It thus became obvious that an
invariable negative result could not be due to any accident, but to the
absence of a peptase capable of splitting off tyrosin from Pepton Roche.
It was therefore decided to carry through a final experiment in order
to investigate the matter fully.

For this purpose a sample of germinating barley was ground up in a
mincer, extracted for twenty-four hours with chloroform water, and pressed
in a hand-press. The liquid was freed from suspended particles by means
of a centrifuge. This extract will, in the following pages, be referred to as
Extract A.

The residue from the press was then ground with sand and kieselguhr,
with the addition of a little water, in the Buchner mortar, and then subjected
to a pressure of 300 kg. per sq. cm. in the Buchner hydraulic press. The
liquid obtained in this way, and freed from solid matter as before, will be
referred to as Extract B.

Twelve flasks were made up, each containing 5 c.c. 20 per cent. Pepton
Roche solution and 5 c.c. Extract A, while another twelve were similarly
prepared with Extract B, T c.c. chloroform being added to each as anti-
septic. Three of each series were digested at each of the following
temperatures — 15°, 25°, 37°, 50°. At the same time a similar number of
flasks containing 5 c.c. 10 per cent. Pepton Witte solution instead of the
Pepton Roche were placed at the same temperatures, a series of controls
being prepared for the latter experiment by precipitating the material at
once with excess of tannic acid. The digestions were examined from day
to day, and whenever a deposit was found it was filtered off and the
identity of the tyrosin established by means of Morner’s reaction, the corre-
sponding Pepton Witte digestions being precipitated with tannic acid at the
same time.

The first deposits of tyrosin were produced within six days in the diges-
tions containing Extract B, at 25° and 37° respectively; the next ones

19 13- L 4.] Enzymatic Peptolysis in Germinating Seeds. 115

being formed after a period of fourteen days in the Extract B digestions at
15°. The remainder of the digestions gave negative results after three weeks’
incubation, when the experiment was discontinued and the Pepton Witte
digestions precipitated. The filtrates from these were used in the manner
described by Weis (l.c.) for determining the degree of peptolysis which
had taken place during incubation, expressed in terms of cubic centimetres
of N/10 alkali, this latter figure representing the ammonia formed during
the determination of the nitrogen contained in 5 c.c. of the filtrate, by
Kjeldahl’s method.

The results of the experiment may be seen in the following tables

Extract A, with

1. Pepton Witte.

Temperature

of

Digestion.

Titrations.

Average.

Control.

Difference
(indicating enzyme
action).

15°

1. 2.
8*9, 9T,

3.

9*5

9T6

14*9

5-74

25°

6-0, 5-5,

5-6

5-7

15-3

9-6

37°

6T, 6’1,

—

6T

15*3

9*2

50°

8-3, 8-4,

—

8*35

15-5

7'15

2. Pepton Roche.

The whole of this series of digestions gave negative results.

Extract B, with
1. Pepton Witte.

Temperature

Difference

of

Titrations.

Average.

Control.

(indicating enzyme

Digestion.

action).

1. 2. 3.

15°

13*25, 12-55, 12-55

12-78

15-8

3-0

25°

7-7, 7-4, 7-1

7-4

16-8

9-4

37°

7-2, 8-2, 6-65

7-35

16-85

95

50°

10-15, 9-0,

9-55

16-0

6-45

2.

Pepton Roche.

15°. Positive result observed after fourteen days.
25°. Strongly positive result within six days.

37°. Positive result also within six days.

50°. Negative result.

116 Proceedings of the Royal Society of Edinburgh. [Sess.

The total result of the experiment may, for the sake of comparison, be
expressed as follows : —

Results of Peptolysis.

Temperature.

Pepton

Witte.

Pepton Roche.

A.

B.

A.

B.

15°

5*74

3-0

Negative.

14 days.

25°

9*6

9-4

6 „

37°

9*2

95

6 „

50°

7T5

6*45

Negative.

These results seem to indicate the presence in germinating barley of
two different peptolytic enzymes, one of which can be readily extracted
with water, while the other is apparently of the nature of an endo-enzyme
and can only be obtained by destroying the cells of the seed tissues. The
existence of these two enzymes is further indicated by the fact that their
temperature curves differ materially. The optimum temperature for both
seems to be between 25° and 37°. At 50°, however, while the hydrolysis of
Pepton Witte proceeds vigorously, being considerably more marked than
at 15°, the action on Pepton Roche seems to be inhibited, since no separation
of tyrosin has ever been observed at this temperature. On the other hand,
a slow but quite distinct action takes place at 15°.

The inhibition of the Pepton Roche digestion at 50° was further
accidentally demonstrated in this way. A number of digestions which had
been incubated at 15° and 50° for six days, with a negative result, were
put aside and overlooked for a couple of weeks. It was then found that
those which had been at 15° for the whole period gave a distinct deposit of
tyrosin, while those which had previously been exposed to a temperature
of 50° showed no such deposit. Apparently the Pepton Roche digestion
is not only prevented at 50° but the activity completely destroyed, while,
as has been previously demonstrated, the hydrolysis of Pepton Witte pro-
ceeds vigorously at this temperature.

The digestions were all examined for the presence of moulds or bacteria,
partly by microscopic examination and partly by adding a drop of the
material to sterile meat-extract gelatine and incubating at 20°. This
examination invariably showed the absence of any development of bacteria
or fungi. In a few cases only, an isolated Penicillium spore seemed to
have survived.

For the sake of certainty on this point another experiment was devised.
The barley was crushed, mixed with sand and kieselguhr, and ground in

117

1913-14.] Enzymatic Peptolysis in Germinating Seeds.

the Buchner mortar. A suitable quantity of Pepton Roche solution was
then added and the resulting mass subjected to a pressure of 300 kg. per
sq. cm. in the Buchner press. The expressed liquid was freed from sus-
pended particles by means of the centrifuge, and then passed through a
Chamberland filter into sterilised Pasteur flasks, which were afterwards
placed at the same temperatures as were employed before.

The results obtained from this experiment were similar to those
obtained before with regard to the separation of tyrosin — a strongly
marked reaction at 25° and 37°, a less marked but distinct reaction at 15°,
and no reaction at 50°.

Part of the contents of the flask which had been incubated at 25°, and
which had given the heaviest deposit of tyrosin, were transferred to a
Pasteur flask containing sterilised glucose-Pepton Witte solution and further
incubated at 25°. The contents of the flask were found to remain sterile
throughout the whole period of incubation, which extended over several
weeks, proving conclusively that the peptolysis was not due to any
development of micro-organisms.

The presence in germinating barley of two distinctly different peptases
having be,en thus established, the next step in the main research became
that of ascertaining at what period the activation of the above-mentioned
peptases takes place, in order that the conditions influencing the activation
might be finally studied in detail.

For the purpose of elucidating this point, the peptolytic activity was
determined from time to time in a sample of barley during germination
and the results confirmed, firstly, with another quantity of the same sample,
and secondly, by repeating and extending the experiment with a different
sample.

The examination was in each case commenced with the ungerminated
barley, and was continued in the first two instances for seventeen days, in
the last instance for twenty-nine days. The germination took place under
the conditions usually observed in the preparation of malt, and the samples
were examined at intervals of from two to four days.

The water content was determined in every sample withdrawn for
examination, by placing 5 grms. of the ground material in a weighing
bottle, covering it with absolute alcohol, and drying it in a hot- water oven
for twenty-four hours.

500 grms. of barley were disintegrated in a mincing machine and
ground in a Buchner mortar with 500 grms. of sand and a suitable quantity
of water to make a firm paste. This was placed in a Buchner press and
subjected to a pressure of 350 kg. per sq. cm. for about one hour, when no

118

Proceedings of the Royal Society of Edinburgh. [Sess.

more liquid could be expressed, and the extract was finally made up with
distilled water to 350 c.c.

The liquid was freed from suspended particles by means of a centrifuge,
and was thereafter divided into two portions, one of which was mixed with
a solution of Pepton Witte in such quantities as to give a concentration of
2 per cent, peptone, whilst 10 per cent, of Pepton Roche was dissolved in
the other.

The liquids were then placed, in quantities of 10 c.c., in a number of
small bottles, each of which received in addition T c.c. of chloroform.
Excess of tannic acid and a trace of sodium acetate were added to half of
those bottles containing Pepton Witte, while the remainder of these and all
those containing Pepton Roche were placed in an incubator at 35° C.

The Pepton Witte digestions were withdrawn after forty-eight hours’
incubation, precipitated with tannic acid and sodium acetate, and, along
with the controls, which were precipitated before digestion, filtered and *
used for determining the amount of nitrogen contained in 5 c.c. of the
filtrate, Kjeldahl’s method being employed.

The increase in nitrogen, expressed in cubic centimetres of N/10
alkali, was, as before, taken as an indication of the amount of peptolytic
activity during digestion.

This difference was, in all cases where ungerminated barley was em-
ployed, within the limits of experimental error, and the resting seed of
barley may therefore be regarded as containing only in extremely small
quantities, if at all, a peptase capable of catalysing the hydrolysis of the
polypeptids contained in Pepton Witte.

A peptase of this nature was, however, found to be rapidly produced
during germination, as will be seen below.

In the following tables, the first column shows the number of days from
the time when the barley was steeped in water to the time when the
sample was withdrawn for examination, while the second column gives the
degree of peptolytic activity expressed in cubic centimetres of N/10 acid
neutralised by the ammonia formed during the Kjeldahl process, and in
each case corrected for the amount of moisture contained in the sample.

The Pepton Roche digestions were examined from day to day, and a
note was made of the minimum number of days within which a deposit of
tyrosin was formed.

Although there is no experimental evidence to show that under the
conditions of the experiment, and especially considering its duration, the
time required to produce a precipitate is inversely proportional to the
degree of activity, it is nevertheless obvious that, the greater the peptolytic

1913-14.] Enzymatic Peptolysis in Germinating Seeds. 119

activity, the more rapidly will the tyrosin be precipitated, and vice versa.
The figures obtained in this way are therefore sufficient indication of the
degree of activity, provided that they are expressed in a manner capable
of direct comparison, and they are therefore, in the following tables,
expressed in terms of a unit which, under the conditions of the experiment,
would produce the first indication of tyrosin in 100 days. The amount of
moisture contained in the samples has here, as in the case of the Pepton
Witte digestions, been taken into consideration, the figures shown being
calculated for dry material. These results are given in the third column.

Table I.

Number
of days.

Pepton Witte.

Pepton Roche.

4 j in water

o-oo

4T3

2-80

8-56

6

7-59

8-25

8

11-60

20-45

10

11-60

37-40

13

11-20

45-30

15

11-0

58-70

17

11-32

34-60

Table 11.

0\ • ,

o-oo

2-45

4 > m water

6'24

7-88

6

9-16

12-40

10

11-50

24-90

12

12-05

24-40

13

14-60

43-35

15

13-27

34-60

17

13-48

24-06

Table III.

01 •

. m water

4f

o-oo

4-49

2-20

6-30

6

7-83

7-40

8

9-77

16-76

10

9-83

24-30

12

9-81

35-00

15

14-10

42-50

17

12-75

75-40

19

1215

41-20

20

10-55

3940

22

11-22

38-95

24

11-12

Lost.

26

13-72

31-57

29

12-84

25-50

120 Proceedings of the Royal Society of Edinburgh. [Sess.

It is obvious from the whole nature of the experiment, and from the
manner in which the different samples were obtained, that a certain amount
of irregularity must be expected in the results. Such fluctuations, however,
have not been found to be nearly so serious as was anticipated. The fact
that the maximum degree of activity is reached somewhat later in the third
than in the first and second experiments is easily explained by the fact that
an entirely different variety of barley was used, while the other irregularities
are so small that they cannot obscure the evidence of the experiments, to
the effect that, of the two forms of activity, the one rises sharply from
nothing in the ungerminated seed till it reaches its maximum, after which
it remains fairly constant during the remainder of the experiment. On the
other hand, the activity in the second case rises comparatively slowly from
slightly above zero in the ungerminated seed till it reaches its maximum a
few days later than in the former case, after which it rapidly falls again.

The presence of both of these forms of activity in germinating barley
having been thus demonstrated, it seemed desirable to investigate the
existence of similar enzymes in material of widely different origin. For
this purpose the strongly proteolytic and peptolytic enzyme, Bromelin,
contained in the juice of the fruit of Ananassa sativa, was selected. In
order to make the experiments more complete, it was decided to carry out
parallel digestions, using as substrate in one case the alcohol-soluble
protein of wheat, and in the other a solution of Pepton Witte.

The digestions were carried out partly in presence of the natural acidity
of the juice, partly with a juice that had been neutralised, and partly with
a portion made slightly alkaline with sodium bicarbonate. In each case
5 c.c. of the juice was employed, and three digestions were carried out with
each substrate and each reaction.

The following series of digestions were accordingly prepared : —

(a) 2 grms. protein + 5 c.c. water + 5 c.c. juice.

(b) 5 c.c. 4 per cent. Pepton Witte solution + 5 c.c. juice.

( c ) 5 c.c. 10 per cent. Pepton Roche solution -f 5 c.c. juice.

As usual, half of the digestions (a) and ( b ) were precipitated before
digestion with tannic acid ; the others, along with (c), being digested at 37°.
After twenty-four hours (a) and ( b ) were withdrawn and precipitated, the
nitrogen contents of the filtrates estimated, and the amount of peptolysis ex-
pressed as before. The results are given in the following table, and show that
a very strong proteolysis and peptolysis had taken place. The corresponding
Pepton Roche digestions, however, showed no deposit of tyrosin, even after
three weeks’ incubation, and it is therefore safe to conclude that bromelin
does not decompose this polypeptid. Whether an enzyme capable of doing

1913-14.] Enzymatic Peptolysis in Germinating Seeds. 121

so is present in the cells of the fruit, and might be extracted by the
Buchner method, was not determined at the time.

Juice of An an ass a sativa on
1. Protein.

Reaction of
Medium.

Titrations,
[c.c. N/10 NaOH]

Average.

Control.

Difference

(indicating

enzyme

action).

Acid

2-5, 2-55, —

2*52

8-5

60

Neutral ....

6*6, 7-0, 57

6'46

8T

1-64

Alkaline ....

6-8, 6-6, 5*7

6-4

8-6

2-2

2. Pepton Witte.

Acid .....

2*4, 2'4, —

2-4

5-6

32

Neutral ....

4-4, 4-1, —

4*25

5-9

1-65

Alkaline ....

5-2, 5-5, 6-0

5-56

6-0

•44

3. Pepton Roche.

The whole of this series gave negative results.

About the same time a number of fungi were gathered, ground to pulp
with sand in a mortar, and the juice pressed out in the hand -press. The
preparations thus obtained were used in a similar series of experiments,
the only difference being that the digestions were in this case confined to
the natural reaction of the extracts, in all cases slightly acid.

The results were as follows

Fungus.

Protein Digestions.

Pepton Witte Digestions.

Titrations.

Aver-

age.

Con-

trol.

Diff.

Titrations.

Aver-

age.

1 n

Con-

trol.

Diff.

Lycoperdon gemmatum

9-2,

9-35,

9T5

9-23

9-45

•22

5*6, 5-3, 5-2

5-36

8-4

3*0

Hyphaloma capnoides .

8-75,

8-95,

8-85

8-85

9-5

•65

5-8, 5-9, 5-7

5-8

8-5

2-7

Hyphaloma trichaloma

9-15,

9-0,

9-2

9:12

9-4

•28

6-1, 61, 6T

6T

8-4

23

Russula emetica .

9'1,

9-2,

9T

9T3

9*3

T7

6-8, 6-7 —

6-75

8-6

1*85

Boletus badens

8-9,

8*7,

8-9

8'83

93

•5

5 3, 5*5, 5-4

5*4

8-3

2-9

Laccaria laccata .

10*0,

9-85,

9-6

9-8

9-85

•05

6-9, 6*7, 7-0

6-86

8-8

1-94

Hydnum repandum

.9-3,

9*1,

9-2

9-2

93

T

7-0, 6-6, 6-4

6-6

8-7

2T

Amanita rubescens

7-0,

7-6,

7*5

736

8-9

1-54

3-9, 4-0, 4T5

4-0

7-7

3*7

Amentopsis strangulata

7*7,

7-65

8-0

7-78

8-9

1-12

4-7, 4-7, 4-5

4-63

7‘8

317

Pepton Roche.

The whole of these gave negative results.

122

Proceedings of the Royal Society of Edinburgh. [Sess.

From this it will be seen that a distinct peptolytic action is found in all
cases on Pep ton Witte, and a slight action in some cases on the protein.
The result of the Pepton Roche experiment remained negative after several
weeks. Neither was it determined in this case, however, if the cell
contents obtainable by the Buchner process would be capable of hydrolys-
ing Pepton Roche, as the small quantities of the material available did
not allow of the use of this method. It would, however, seem probable
that a considerable proportion of the cell contents must have been liberated
during the grinding, since sand was employed, and since the tissue of these
fungi is by no means difficult to disintegrate. It would therefore seem
almost safe to assume the entire absence of this enzyme in all the cases
in question.

For further information, a series of experiments was carried out with
the ordinary cultivated mushroom, which can be bought in quantities. The
preparations were made as in the case of barley, Extract A being obtained
by grinding in an ordinary mortar and expressing in a hand-press, while
Extract B was obtained from the residue by the Buchner method. The
following results were obtained : —

Agaricus campestris. — Extract A.

Substrate.

Titrations.

Average.

Control.

Difference.

Protein ....
Pepton Witte
Pepton Roche

5-3, 5-4, 5*3
1-7, 1'9, 1*5
Positive

5*36

P7

result obtaine(

6-8

6*0

1 within 24 ho

1*44

4-8

urs.

Extract B.

Protein ....
Pepton Witte
Pepton Roche

8-8, 9-2, 9T5
6-8, 6*4, —

Positive resull

9-05

6*6

b obtained onh

9-2

73

l after 7 days5

T5

•7

digestion.

These results show at once the presence of a tyrosin-separating enzyme,
and also that this, as well as the other forms present in this material, had
been extracted in the first pressing, the amount remaining in the residue
being doubtless removable by washing. To obtain confirmation of the
presence of this enzyme in Agaricus, another quantity was ground with
sand and kieselguhr and expressed in the Buchner press. Digestions similar
to those just described were carried out with the following results : —

1913-14.] Enzymatic Peptolysis in Germinating Seeds.

123

Agaricus campestris — Extract on

Protein .
Pepton Witte
Pepton Roche

Titrations.

Average.

Control.

5-9, 6-0, 6T

6-0

7-3

2-8, 2-3, 2-35

2-5

6-3

Positive result-

—marked.

Difference.

1-3

3-8

A number of experiments similar to those just described have also been
carried out, using as material Saccharomyces cerevisice, Penicillium glaucum,
Aspergillus niger.

In the case of Saccharomyces cerevisice three experiments were
carried out: —

I. Washed and pressed yeast was extracted for twenty-four hours with
chloroform water, and the filtered liquid allowed to act on the protein,
Pepton Witte, and Pepton Roche as before, at 37° C., using the same concen-
trations as in the previous experiments. Three digestions were carried
out with each substrate, and in the case of the protein and Pepton Witte
two controls were precipitated before digestion.

The Pepton Roche digestions did not give any precipitate of tyrosin
within three weeks, thus indicating the absence of this form of activity
in the extract. The other digestions were all precipitated after twenty-four
hours’ incubation and used for nitrogen determination in the usual manner,
with the following results : —

Titrations.

Average.

Control.

Difference.

Protein ....

9-3, 9T, 9T5

9T8

9T0

*08

Pepton Witte

7-9, 7-6, 7-8

7*77

8*5

•27

II. Washed and pressed yeast was ground with sand and kieselguhr in
the Buchner mortar, the liquid expressed in the usual manner and freed
from suspended particles by means of a centrifuge. Digestions similar to
those described above were carried out, using 2 c.c. of the liquid in each
case and adding distilled water to obtain the same concentrations of the
substrate.

All the Pepton Roche digestions gave a strong deposit of tyrosin within
twenty-four hours.

The other digestions were all precipitated after twenty-four hours’ incuba-

124 Proceedings of the Royal Society of Edinburgh. [Sess.

tion, and the nitrogen content determined in the usual way. The results
were as follows : —

Titrations.

Average.

Control.

Difference.

Protein ....

87, 8*6, 8-5

86

9*3, 9T

0-6

Pepton Witte

4T, 4T5, 4-2

4-15

8-0, 8-2

3-95

III. A watery extract was first obtained, as in the first experiment, and
the residue subjected to the Buchner method process in order to obtain the
cell contents. The same conditions were observed as in the previous experi-
ments, with the difference that the digestions were carried out with Pepton
Witte and Pepton Roche only and that four temperatures were employed,
viz. 15°, 25°, 37°, 50°.

The results will be seen from the following table : —

Extract A, with Pepton

Witte.

Temperature.

Titrations.

Average.

Control.

Difference.

15°

7-9, 7-4, 8-2

7-83

7 '9

•07

25°

8-3, 8-5, 7-9

8*23

8-5

•27

37°

8-0, 8-0, 8-0

8-00

8-0

•00

50°

7-9, 8-0, 8-0

7-97

8T

T3

Extract A, with Pepton

Boche.

All results were negative.

Extract B, with Pepton Witte.

15°

6-0, 6*4, 5-9

6T0

7-60

1-50

25°

2-35, 2-5, 2-8

2-55

7-60

5 05

37°

2-4, 2-0,

2-20

7-50

5*30

50°

3-6, 3-6, 33

3-76

7*40

394

Extract B, with Pepton

Roche.

15°,

. Slight positive result within twenty-four hours.

25°.

Strong

55

55

37°.

55 55

55

>5

50°.

Negative result at the end of three weeks.

In the case of Penicillium glaucum and Aspergillus niger, pure cultures
were developed in sterilised 10 per cent, malt extract in large flasks at
room temperature. After several weeks a large growth had taken place,

125

1913-14.] Enzymatic Peptolysis in Germinating Seeds.

and all the cultures were in a state of fructification. As much as possible
of the liquid was then poured off and discarded, while the liquid remaining
amongst the mycelium was expressed by means of the hand-press. This
was retained for experiment as Extract A.

The mycelium was then ground in the usual way in the Buchner
mortar and pressed in the Buchner press. In this way two liquids were
obtained from each of the fungi — a medium, and a mycelium extract-
Digestions were made as before with these preparations, using protein,
Pepton Witte, and Pepton Roche as substrates. The results may be seen
in the following tables : —

Penicillium glaucum — Extract A (Hand-press Extract) on

Titrations.

Average.

Control.

Difference.

1. Protein ....

8-3, 8T5, 8T5

8-2

9-45

1-25

2. Pepton Witte

8-4, 8-7, 8-2

8-46

8-9

•44

3. Pepton Roche

All negative.

Extract B (Buchner Extract) on

1. Protein ....

6-4, 7*0, 6-7

6-7

8-8

2*1

2. Pepton Witte

4-8, 5*0, 5-2

5-0

8-6

3-6

3. Pepton Roche

All negative.

Aspergillus niger — Extract A on

Titrations.

Average.

Control.

Difference.

1. Protein ....

8-0, 7*0, 7-5

7-5

9*3

1-8

2. Pepton Witte

6*2, 6*1, 6-0

6T

8-9

2-8

3. Pepton Roche

Negative result.

Extract B on

1. Protein .

6-75, 6-9, 6-3

6-65

8-3

D65

2. Pepton Witte

2-2, 2-5, —

2-35

6-8

4-45

3. Pepton Roche

In the apparently complete absence of the Pepton Roche hydrolysing
activity in Penicillium glaucum, a striking contrast is shown with Asper-
gillus. In view of the close relationship existing between these fungi, it
was thought desirable to ascertain if Penicillium could be brought to

126

Proceedings of the Royal Society of Edinburgh. [Sess.

produce this enzyme. A sterilised solution of sugar and Pepton Roche was
made up and infected with a pure culture, and then incubated at 20° for
several months. The development was, however, so small that it was
quite impossible to carry out any examination of the mycelium, and no
deposit of tyrosin appeared in the culture medium.

The results obtained with the watery extracts of Saccharomyces are so
slight that they must be regarded as being within the limits of experi-
mental error. It is, however, possible that more active preparations could
have been obtained by prolonged extraction or by addition of sodium
chloride as suggested by Vines (Ann. Bot., vol. xviii. p. 289, 1904). The
results are, however, in conformity with the statement made by that author,
to the effect that a rapidly prepared watery extract of yeast has no proteoly-
tic action, and with those of Geret and Hahn (Buchner, Die Zymasegdhrung ,
1903, p. 287) that the Buchner extract possesses a much stronger proteolytic
action than that exhibited by the living yeast towards its substrate, and
that the proteolytic and peptolytic activity is due to a cell enzyme.

Whether this enzyme, as suggested by Geret and Hahn (l.c.), is of the
nature of a tryptase has already been rendered doubtful by the works of
Bokorny (Beihefte, Bot. Gentr., vol. xiii. p. 235, 1903), who suggested that an
enzyme of the pepsin group is also present, and Vines (l.c.), who found
evidence of the presence of an ereptase.

In this connection, the results obtained with the Buchner extract
(Extract B), which are shown in the preceding tables, are of interest.

In the first place, it will be noticed that there is a strong peptolytic
activity against Pepton Roche as well as against Pepton Witte. Secondly,
the decomposition of Pepton Roche, as in the case of barley, is inhibited at
50°, whereas the hydrolysis of Pepton Witte proceeds vigorously at that
temperature. Thirdly, assuming the activity on Pepton Roche to be in-
versely proportional to the time required for producing the first indication
of tyrosin, this activity is, in the case of Saccharomyces, much more pro-
nounced as compared with the action on Pepton Witte than in the case of
barley, a fact which further supports the view of the non-identity of the
two enzymes. Further, the proteolytic activity exhibited by the Buchner
extract of Saccharomyces is very slight in comparison with the peptolytic
activity, a fact which becomes even more striking when the results are
compared with the corresponding figures obtained with Penicillium and
Aspergillus. Finally, it would seem highly unlikely that the proteolysis
and the peptolysis are catalysed by the same enzyme, as in that case the
primary reaction would need to be accelerated in at least the same degree
as the secondary one, which is obviously not the case.

1913-14.] Enzymatic Peptolysis in Germinating Seeds. 127

Whether the comparatively slight proteolytic activity observed in the
present investigation in the Buchner extract of yeast, and previously
described by other observers (Geret and Hahn, Vines, etc.), is due to a
trypsin or a pepsin is uncertain ; but it is fairly evident that the peptolysis
is almost entirely due to different agents, and it would further seem highly
probable that these agents are similar to the two peptases found in ger-
minating barley, if they are not identical with them.

(Issued separately March 26, 1914.)

128

Proceedings of the Royal Society of Edinburgh. [Sess.

XL— A Study of the Curvatures of the Tasmanian Aboriginal
Cranium. By L. W. G. Buchner, Victorian Government Re-
search Scholar in the Anthropology Department of the University
of Melbourne. Communicated by Professor R. J. A. Berry.
(With Three Folding Tables.)

(MS. received December 9, 1912. Read January 19, 1914.)

The extinction of the Tasmanian aboriginal in 1876 closed, for all practical
purposes, the further scientific study of this ancient and highly interesting
race, and it appeared almost certain that our knowledge of this people
would remain dependent on the earlier works of those who were fortunate
enough to have studied them during life, and on the few remains housed
in such fortunate centres as London, Paris, Edinburgh, Oxford, and
Cambridge.

Fortunately, just at the moment when it seemed most improbable that any
further specimens of Tasmanian crania would be discovered — the number
known to be in existence up to 1909 having been given by Turner as
seventy-nine, — Berry and Robertson published in the Proceedings of the
Royal Society of Victoria (1) and the Anatomischer Anzeiger (2) an
account of a further discovery of fifty-two. This discovery, important
though it undoubtedly was, would not materially have greatly advanced
Tasmanian craniology, had not the dioptrograph and diagraph just been
invented. By the use of the former ingenious and accurate instrument,
Berry and Robertson were enabled to record the whole of their fifty-two
crania — forty of which were absolutely new to science — in such a way
as to make any craniological investigations on these skulls available in
any part of the world.

The great importance of this method was immediately realised, amongst
others, by Professor Sergi of Rome, who hastened to avail himself of this
unexpected increase in the wealth of Tasmanian material available, in order
to study anew the form of the Tasmanian skull by means of his own
highly original modes of investigation. The results have been made
available to us in his recently published “ Tasmanier und Australier,
Hesperanthropus tasmanianus , spec.” (3).

The publication of Berry and Robertson’s Atlas has also made it
possible for any investigator to apply any of the recently introduced
craniological and morphological methods of skull analysis to the Tasmanian
cranium, quite apart from the possession of the skulls or otherwise, and

1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 129

thus Tasmanian cranial work is no longer confined to those fortunate
centres already mentioned, nor is it impossible now to apply modern
methods to a race long extinct. It is therefore clear, in view of those
enormous advantages, that Berry and Bobertson are correct when they say
“ that all known existing Tasmanian crania, whether in Europe, America,
or Australia, ought to be similarly recorded, and thus made available for
study in all parts of the world, and for all time.”

It will only be by the publication of similar works that any appreciable
advance will be made in comparative craniological research. So many and
varied methods of examination have been made on the Tasmanian and
other crania, that it becomes imperative to secure some suitable method
by which all the recorded observations may be referred to one common
standard.

It is, therefore, most important that similar works on the European
and other races should be published, so that a detailed system of com-
parative research may be instituted with the Australian and Tasmanian
aboriginal crania.

The morphology and general characters of the Tasmanian crania have
been the subject of research by such investigators as Barnard Davis (4),
Topinard (5, 6), de Quatrefages and Hamy (7), Flower (8), Williamson (9),
Wieger (10), Klaatsch (11), Garson (12), Harper and Clarke (13), Duckworth
(14), and Turner (15). Still more recently, Berry, Robertson, and Cross (16,
17, 18) have made some important contributions to the subject, and have
paid considerable attention to the biometric study of certain cranial obser-
vations based on Schwalbe’s “ form analysis.” They selected this system
of investigation in order “ to determine with some degree of certainty
the final position of the Tasmanian with reference to the anthropoids,
Pithecanthropus , Homo primigenius , and Homo sapiens, both extinct and
recent.” They have succeeded, in some measure, in establishing the relative
position of the Tasmanian aboriginal with the forms just quoted, by
employing this investigational method. In view of these objects, it was
absolutely necessary for Berry and Robertson to employ the glabella-inion
plane as their working base-line, though they agree with Turner that this
glabella-inion plane is not the best “ from which to estimate the length of
the cerebral part of the cranial cavity,” for, in their opinion, the nasion-
inion plane coincides more closely with the cerebral length than either the
glabella-inion or Turner’s nasio-tentorial plane.

As the nasion-inion is, therefore, important as a base-line, and as there
is no reason why the present investigation should not employ it, I have

directed some attention to it, as also to certain cranial proportions and
VOL. xxxiv. 9

130 Proceedings of the Royal Society of Edinburgh. [Sess.

indices based on it, and referred to later. Two of these curvature indices,
calculated in accordance with the procedure laid down by Schwalbe (19),
have already been published by Berry and Robertson. They were
estimated by taking the proportion which the length of the chord bears
to the length of the arc, the latter being taken as 100. Klaatsch (20),
on the other hand, in his work on the Australian and other skulls,
estimates these indices of curvature quite differently, and says : “ To
properly appreciate a sloping forehead, the only part of practical im-
portance is that between the glabella and bregma. The simplest way of
determining it, though not employed so far as I am aware, is to measure
the greatest distance of the curved surface of the frontal from the
glabella-bregma line (i.e. the chord of frontal curvature), and to form
an index comparing this greatest distance with the length of the glabella -
bregma line.”

By multiplying the length of the greatest distance of the chord from
the arc by 100, aUd dividing by the length of the chord, he constructs his
index of curvature for the ossa frontale, parietale, et occipitale. It will
thus be seen that Klaatsch’s index expresses the ratio of the maximum
distance of arc from chord to the length of the chord, the latter being
taken as 100.

I am not at all convinced that the above method will do all that
Klaatsch endeavours to claim for it. It will, of course, be admitted that
as a method of determining the amount of curvature it fulfils its purpose ;
but, in my opinion, it fails to express the degree of the recession of the
forehead, for, as demonstrated by Schwalbe and others, the sloping forehead
can only be estimated by angular measurements on a suitable base-line.
It is, therefore, extremely difficult to see how Klaatsch’s method of dealing
with the chord of the os frontale and its distance from the arc without the
use of any base-line whatsoever can express the recession or otherwise
of the forehead.

This apart, it is an excellent method of determining the degree of
curvature of the bone, and is probably preferable to Schwalbe’s method,
though, it may be noted, the degree of curvature of any cranial bone can
now be estimated directly by means of Mollison’s cyclometer.

Turner (21) and Cunningham (22) have also estimated the curvatures of
various longitudinal osseous segments of the skull in a somewhat similar
manner to Klaatsch, but do not construct an index of curvature. They
simply record the greatest distance of the arc from its chord, and, in the
case of the os frontale, prefer the nasion-bregma or total frontal arc and
chord to the glabella-bregma measurements.

TABLE I.— THE INDIVIDUAL AND GENERALISED RESULTS OF

EXAMINATION OF FIFTY-TWO TASMANIAN ABORIGINAL CRANIA.

[To face V. 131.

Proc. Roy. Soc. Edin ., Yol. XXXIV.]

Biichner — >

Probable Sex >

Serial Number >

1

2

3

Present Location of Specimen-^

Tasmaniai

Nature of Observation.

Original Number of Specimen-^

4288

4291

4300

“1

1

Nasion-Inion Length.

177

182

178

i

i

2

Bregma Angle.

59

60

+

64

—

3

Frontal Angle.

84*5

90

87

"n

4

Lambda Angle.

78

80-5

82

5

Opisthion Angle.

35

31-5

6

Frontal Arc.

123

133

+

143

1

7

Frontal Chord.

108

114

116-5

1

8

Greatest Distance of Arc from Chord.

25

27

29

1

9

Occipital Arc.

122

119

110

1

10

Occipital Angle.

113

112

—

li

11

Inion- Opisthion Chord.

56

55

1

>.

12

Total Sagittal Curvature.

366

387

398

J

13

Total Longitudinal Circumference.

497

522

— n

4

14

Vertical Transverse Arc.

280

297

309

4

15

Basal Transverse Diameter.

143

+

145

137

■

16

Total Vertical Transverse Diameter.

423

442

446

J

17

Preauricular Curve.

226

239

260

%

18

Postauricular Curve.

286

+

294

279

A

19

Total Horizontal Circumference.

512

533

539

5

L. W. G. Buchner.

1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 131

The objects of the present research are : —

1. To record certain craniometrical curvilinear and angular measure-
ments, the latter being based on the nasio-inion plane.

2. To estimate the degree of flattening, or otherwise, of the Tasmanian
aboriginal crania.

3. To estimate the evolutionary position of the Tasmanian from a
study of certain of his cranial curvatures.

It has already been pointed out that, as one of the main objects of
the Tasmanian work of Berry and Robertson was a comparison of the
Tasmanian evolutionary relationship with that of Pithecanthropus erectus ,
they were compelled to employ the glabella-inion plane as their base. As
the present work is freed from this disability, one of its first objects is to
restate certain already recorded Tasmanian measurements on the new
base — the nasio-inion plane — a base which it has already been shown
Berry and Robertson prefer, where possible. As it is not proposed to do
more than record these figures, they are simply set forth in Table I , and
will not herein be again referred to. Suffice it to state that there are now
available on both base-lines a large number of Tasmanian measurements for
future comparison of other races by subsequent observers, and that, in each
instance, the number of Tasmanians so recorded is the largest on record.

The material on which the present work is based will be found in Berry
and Robertson’s “ Dioptrographic Tracings in Four Normse of Fifty-two
Tasmanian Crania ” (23). In Table I. the angular and certain curvilinear
measurements are estimated from the median sagittal drawings, that is,
a tracing in the norma lateralis. The remainder of the observations in
Table I. were recorded by Professor Berry and Dr Robertson on the
original crania, wrhilst they were engaged in their investigations in
Tasmania in 1909, and they are now made available for scientific study
for the first time. I have to express my thanks to these authors for
permission to utilise their figures.

These observations, to the number of nineteen, are set forth in
Table I., and are as follow : —

1. The nasion-inion length.

2. The bregma -nasion-inion angle. This angle corresponds with
Schwalbe’s bregma angle, which has already been recorded by Berry
and Robertson on the Tasmanian crania which form the subject of the
present research.

3. The frontal angle.

4. The nasion-inion -lambda angle. The lambda angle has already been
recorded by Berry and Robertson, based on the glabella-inion plane.

132

Proceedings of the Royal Society of Edinburgh. [Sess.

5. The nasion -inion -opisthion angle. Also recorded by Berry and
Robertson, as the opisthion angle, based on the glabella-inion plane.

6. The total frontal arc. Nasion to bregma.

7. The total frontal chord. Nasion to bregma.

8. The length of the greatest distance of the arc from the chord.

9. The length of the total occipital arc. Lambda to opisthion.

10. The occipital angle, enclosed by the lambda-inion and the inion-
opisthion chords.

11. The length of the inion-opisthion chord.

12. The total sagittal curvature.

13. The total longitudinal circumference.

14. The length of the vertical transverse arc.

15. The length of the basal transverse diameter.

16. The length of the total vertical transverse diameter.

17. The length of the preauricular curve.

18. The length of the postauricular curve.

19. The length of the total horizontal circumference.

In Table I. the individual and generalised observations just referred to
of fifty-two Tasmanian crania have been set forth. The probable sex,
the serial number, the present location, and the original number of each
skull are set forth in the four upper horizontal lines. In the two vertical
columns on the left, the numbers and names of the observations recorded,
and the nature of the observation, are set forth. In the vertical columns
1 to 52, inclusive, are set forth the individual measurements of each skull.

The male and female cranial observations have been recorded in separate
columns. The four vertical columns immediately on the right of the male
observations record the number of observations made, the average figures
for each observation together with the minimum and maximum figures
for that observation. The four vertical columns immediately on the right
of the female observations record like results, and for both sexes combined
the figures are set forth in the four vertical columns on the extreme right
of the Table.

No. 48 has been shown to be a juvenile subject; all the observations
recorded upon it have been uniformly omitted from the final results.

For the purposes of determining the range of variation of each observa-
tion, the minimum and maximum figures are denoted by means of a
— or + sign.

Of the observations set forth in Table I., 4 and 5 and 8 to 12 are
original ; Nos. 13-19 are the original observations already referred to ;
Nos. 3, 6, and 7 have already been published by Berry and Robertson

1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 133

(18), but they have been incorporated in the present work for necessary
reasons. For further explanation of the observations of the median
sagittal curvatures in Table I., the reader is referred to fig. 1, where the
method of determining the various measurements is displayed.

As regards the degree of flattening or otherwise of the Tasmanian
aboriginal crania, it is very important to notice that Duckworth (24), in
his recently published (1912) Prehistoric Man, says, “The flatness of a
cranial arc is but one of many characters awaiting research,” and adds,

Br

“ More research is needed.” In the same work, he also states that “ Dr
Sera (25) has been led to pay particular attention to the remarkably
flattened cranial vaulting ” of certain crania previously mentioned in
Duckworth’s work. He also adds that, “as a rule, this flattening has been
regarded as representative of a stage in the evolution of a highly developed
type of human skull from a more lowly, in fact a Simian one. This
conclusion is challenged by Dr Sera. The position adopted is that a
flattened skull need not in every case owe its presence to such a condition
as an early stage of evolution assigns to it. Environment, for which we
may here read climatic conditions, is a possible and alternative influence.
If sufficient evidence can be adduced to show that the flattened cranial

134 Proceedings of the Royal Society of Edinburgh. [Sess.

arc in the Neanderthal skull does actually owe its origin to physiological
factors through which environment acts, the status of that type of skull
in the evolutionary sequence will be materially affected. . . . The
Gibraltar skull is flattened owing to its low place in evolution. But as
regards the flatness of the brain case (called the platycephalic character)
of the Neanderthal calvaria and its congeners (as contrasted with the
Gibraltar specimen) Dr Sera suggests dependence upon the particular
environment created by glacial conditions.”

It is thus obvious that the degree of flattening or otherwise is, in view
of modern opinion, an important present-day field of research, and its
estimation for the Tasmanian is the chief object of the present work. The
investigation of the problem is, however, very considerably handicapped
by the fact that Sera’s original paper is not available in Melbourne, in
either its original form or in any adequate abstract. With this important
reservation, I have estimated the degree of curvature, or flattening of the
glabello-bregmatic arc of the frontal, total parietal arc, and superior
occipital arc of the os occipitale by Klaatsch’s “index of curvature,” all
the observations having been made upon the median sagittal plane of the
Tasmanian life-size tracings already referred to. For a diagrammatic
explanation of the observations thus recorded, the reader is referred
to fig. 1.

The following twelve observations have thus been recorded : —

Os Frontale.

1. The length of the glabella-bregma arc.

2. The length of the glabella-bregma chord.

3. The length of the greatest distance of the arc from the chord.

4. The index of frontal curvature (Klaatsch).

Os Parietale.

5. The length of the bregma-lambda or parietal arc.

6. The length of the bregma-lambda or parietal chord.

7. The length of the greatest distance of the arc from the chord.

8. The index of parietal curvature (Klaatsch).

Os Occipitale.

9. The length of the lambda-inion or superior occipital arc.

10. The length of the lambda-inion or superior occipital chord.

11. The length of the greatest distance of the arc from the chord.

12. The index of occipital curvature (Klaatsch).

The individual measurements of each of the above, together with
minimum, average, and maximum results for the whole series of fifty-two
Tasmanian crania, are set forth in Table II., which is uniform throughout

f

TABLE in.— THE INDIVIDUAL AND GENERALISED RESULTS OF THE EXAMINATION OF FIFTY-ONE AUSTRALIAN ABORIGINAL CRANIA.

Proc. Roy. Soc. Edin Vol. XXXIV.]

[THE EX AM IN ATI

Unsexed

Nature of Observation.

Serial Number

23

24.

25

26

1

Glabella- Bregma Arc.

118

107

112

124

2

Glabella-Bregma Chord.

110

99

110

H7[

3

Greatest Distance of Arc from Chord.

20

21

15

21

4

Index of Frontal Curvature (Klaatsch).

18-1

21*2

13*6

rJ

5

Bregma-Lambda Arc.

120

117

120

131

6

Bregma- Lambda Chord.

110

107

114

123

7

Greatest Distance of Arc from Chord.

23

23

22

24

8

1 Index of Parietal Curvature (Klaatsch).

20-9

21*4

19*2

11

9

Lambda- Inion Arc.

56

50

60

5^

10

Lambda- Inion Chord.

52

48

58

5;

11

Greatest Distance of Arc from Chord.

9

6

8

4

12

Index of Occipital Curvature (Klaatsch).

+

17-3

12*5

13*7

1

L. W. G. Buchner.

Proc. Roy. Roc., Min., Vol. XXXIV.] 1

TY-Tl

Buchner >

r

Nature of Observation.

Serial Number >

1

2

3

No.

1

2

3

4

The Glabella- Bregma Arc.

109

121

+

12{j

32

_

The Glabella-Bregma Chord.

103

111

+

11$

32

The greatest Distance of Arc from Chord.

19

20

j

32

The Index of Frontal Curvature (Klaatsch).

18-4

18-1

17f

32

5

The Bregma-Lambda Arc.

121

135

+

145

29

6

The Bregma-Lambda Chord.

111-5

121

+

127

30

7

The greatest Distance of Arc from Chord.

23

26

+

28j

30

8

The Index of Parietal Curvature (Klaatsch).

19-9

21-5

22

30

9

The Lambda- Inion Arc.

64

63

57

30

10

The Lambda- Inion Chord.

62

62

56

30

11

The greatest Distance of Arc from Chord.

8

7

3

30

12 !

The Index of Occipital Curvature (Klaatsch).

12-9

11-1

5-1

30

L. W. G. Buchner.

1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 135

with Table I. As in Table I., No. 48 of Berry and Robertsons Atlas
is omitted from the final results, as it is known to be a juvenile.

For comparative purposes I have recorded the same twelve observations
on forty Australian aboriginal crania. The resulting figures are set forth
in Table III., in precisely the same manner as those for the Tasmanian in
Table II.

In the Australian table I have also included eleven crania from Klaatsch’s
work, and the entire table thus deals with fifty-one Australian crania, i.e.
with precisely the same number as there are Tasmanians.

The source of my own forty original Australian crania is Berry and
Robertson s“ Dioptrographic Tracings in three Normse of Ninety Australian
Crania ” (26), now in the press. As only forty of the original drawings
have as yet been returned from the printer, it was not possible for me to
utilise the whole ninety. For permission to avail myself of this work
I have to thank Professor Berry and Dr Robertson. My Australian
material will eventually be found, therefore, to include plates numbered
1 to 40, norma A, of the atlas of tracings just referred to. The whole of
this series of Australian crania is quite new, and has not previously been
recorded scientifically.

The indices of curvature of the several segments of the median sagittal
curve of the fifty-one Tasmanian and fifty-one Australian crania may be
summarised and compared with certain selected objects recorded by Klaatsch,
as follow : —

Curvature index of glabello-bregmatic curve of the os frontale : —

1 Pithecanthropus erectus (Klaatsch)
3 Spy-Neanderthal (Klaatsch) .

51 Australians (Klaatsch and Buchner)
51 Tasmanians (Buchner) .

7*53

133

181

18*7

As Klaatsch’s index of curvature expresses the ratio which the length
of the greatest distance of the arc from the chord bears to the length of
the chord, the latter being taken as 100, it follows from the above that the
Tasmanian possesses the most highly curved glabello-bregmatic arc of any
of the objects compared.

The curvature index of the os parietale, as worked out by Klaatsch’s
method, and compared with the same objects as before, is as follows : —

1 Pithecanthropus erectus (Klaatsch) . . . 9*68

3 Spy-Neanderthal (Klaatsch) ..... 17*04

51 Australians (Klaatsch and Buchner) . . . 20*2

51 Tasmanians (Buchner) ...... 20*5

136

Proceedings of the Royal Society of Edinburgh. [Sess.

Here again the Tasmanian possesses the most highly curved parietal
arc, whilst the Australian again occupies third place, a little inferior to the
Tasmanian. If these results be read in association with the known
physiological functions of those portions of the brain which lie subjacent
to the parietal arc, they become of real and striking significance.

Dealing in the same way with the superior occipital index of curvature,
we achieve the following results : —

1 Pithecanthropus erectus (Klaatsch)
51 Australians (Klaatsch and Buchner)
51 Tasmanians (Buchner) .

3 Spy-Neanderthal (Klaatsch) .

. 4*76

. 10-9

. 11 T

. 14T7

Here the several objects have changed places — the Spy-Neanderthal group
having the most highly curved superior occipital arcs, whilst the Tasmanian
still retains his more advanced position over the Australian. It is difficult
to account for the increased degree of superior occipital curvature in the
Spy-Neanderthal group, but as regards the Australians and Tasmanians
it is interesting to observe that, in all its segments, the median sagittal
curvature of the Australian calvaria is less pronounced than in the
Tasmanian, that is, the Australian has a flatter skull, as regards curvature,
than has the Tasmanian.

In a previous publication (27) I recorded the range of variation
on fifty-two Tasmanian crania for twenty-seven observations based on
Klaatsch’s cranio-trigonometrical methods. The figures expressive of this
range of variation were so small as to warrant the conclusion which I then
drew, that the Tasmanian is a pure race. By totally different methods
Berry and Robertson (28), in a memoir as yet unpublished, but now ready
for the press, have arrived at identical conclusions.

I have, therefore, again recorded the range of variation for the twelve
observations set forth in Table II. of the present work, in order to ascertain
if my former conclusions would be sustained.

The results attained from the present and previous works just referred
to are, for the Tasmanian, as follows : —

Present Work.

Degree of Sagittal Curvature.

Males .... 8*9

Females . . 7 ’8

Both sexes . . . 10 3

Previous Work.

Twenty-seven Cranio-trigonometrical
Observations.

Males . . . .7-9

Females . . .7*5

Both sexes . . . 9’9

1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 137

The range of variation of the combined observations, from these two works,
is therefore, for the Tasmanian, as follows :• —

Males 8*4

Females ..... 7*6

Both sexes . . . .10*1

The manner of estimating the range of variation by a single figure was
dealt with in my previous work. The result is so surprisingly low
as to justify the statement already made, that the Tasmanian is a homo-
geneous race.

Passing now to the third and last purpose of the present work, namely,
an estimate of the evolutionary position of the Tasmanian, as deduced from
a study of the relative degree of curvature of the various segments of the
calvaria as herein described, I propose to deal with the subject on somewhat
similar lines to those adopted by Berry and Robertson.

It will be remembered that these authors, in conjunction with Dr Cross,
introduced some strikingly original methods, in their attempt to place the
Tasmanian in his correct evolutionary position as compared with certain
supposed lower morphological forms. Their work was based solely on
twenty-seven of the “ form analysis ” measurements of Schwalbe, and it
seems to me desirable to ascertain if their final conclusions will be
sustained by like methods based on completely different observations.

With this object in view, I shall, therefore, deal with the degree of
flattening of the skull as studied in this work, and I shall employ as
objects of comparison the crania of the chimpanzee, Pithecanthropus
erectus, Gibraltar, Spy-Neanderthal, Brtix, Galley Hill, Brunn, Cro-Magnon,
Australian, Tasmanian, and European.

The sources from which I have obtained the necessary data are as
follow : —

For the anthropoid I have utilised certain observations already
published by Berry and Robertson (18).

For Pithecanthropus I have utilised the necessary observations already
recorded by Klaatsch (20) in his memoir on the Australian skull.

For the Gibraltar skull the observations have been calculated from the
diagrams furnished by Sollas (29).

For the Spy-Neanderthal group the observations have been calculated
from median sagittal diagrams in Schwalbe’s monograph on Pithecan-
thropus erectus (19).

For the Briix, Galley Hill, Briinn, and Cro-Magnon crania the observa-
tions have been calculated by me from median sagittal diagrams furnished
by Schwalbe (30) and Klaatsch (31).

138 Proceedings of the Royal Society of Edinburgh. [Sess.

The Australian and Tasmanian measurements are the original con-
tributions to the subject of the present work.

For the European the observations have already been recorded by
Klaatsch.

In grouping these several objects of comparison together for purposes
of calculation, I have regarded the Neanderthal and Spy crania as a
homogeneous group, and have dealt with the Galley Hill, Brux, and Brtinn
crania in a like way, and for like reasons. To the former procedure there

Cro-Magnon.

European.

Galley Hiil-Brux-Briinn.

Tasmanian.

Australian.

Spy-Neanderthal.

Gibraltar.

Pithecanthropus erectus.

Anthropoid ape.

Fig. 2.

can be no objection, and for the inclusion of the Galley Hill skull with
those of Brux and Briinn I have been largely influenced by the recently
expressed opinions of Duckworth (24).

For the mathematical estimation of the relative evolutionary positions
of the Tasmanian and the other objects of comparison, I have adopted the
ingenious methods introduced by Cross. I have not, however, deemed it
necessary to prolong the calculations beyond what Cross terms the
“ composite order.” The working of the method is illustrated in Tables
IV., V., and VI.

1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 139

The final result is displayed graphically in fig. 2, and numerically in
Table VI.

Table IV.

Nature of Observation.

Anthropoid.

Pithecanthropus.

1

Spy- Neanderthal.

Gibraltar.

Galley Hill-
Brux-Biiinn.

Australian.

d

‘3

3

0Q

as

EH

Cro-Magnon.

European.

1

Glabella-Bregma Arc .

92

no

124

135

110-2

119-9

138

2

Glabella-Bregma Chord

87

93

108

119

108

105-2

123

no’

3

Greatest Distance of
Arc from Chord

7

14-3

| 20-7

19-6

18-8

24

24

4

Index of Frontal Cur-
vature

753

13T3

17-5

18-1

18-7

19-5

21-8

5

Bregma-Lambda Arc .

62

103

119-6

126-6

121-2

125-8

135

133

6

Bregma-Lambda Chord

93

112

...

116-3

114-7

113

123

112

7

Greatest Distance of
Arc from Chord

9

18-3

21

23-2

23 3

26-5

24

8

Index of Parietal Cur-
vature

9-68

17-04

17-3

20-2

20-5

21-6

21-4

9

Lambda-Inion Arc

30

57*3

58-5

60

55-7

58-5

63

i 10

Lambda-Inion Chord .

42

54

38

60-6

55-2

55-5

60-75

63

11

Greatest Distance of
Arc from Chord

2

7-6

5

8-2

6-1

6-1

8 2

11

12

Index of Occipital Cur-
vature

4-76

14-17

13*1

13-3

10-9

11-1

13*4

17-46

Table V.

Nature of Observation.

Maximum.

| Anthropoid.

Pithecanthropus.

Spy-Neanderthal.

Gibraltar.

Galley Hill-
Briix-Briinn.

Australian.

Tasmanian.

1 Cro-Magnon.

European.

1

Glabella-Bregma Arc .

46

0

18'

32

43

18-2

19-9

46

2

Glabella- Bregma Chord

36

0

6

21

32

21

18-2

36

23

3

Greatest Distance of Arc
from Chord

17

0

7-3

13-7

12-6

11-8

17

17

4

Index of Frontal Curvature

14-3

0

5-6

10

10-6

11-2

12

14-3

5

Bregma-Lambda Arc .

73

o'

41

57-6

64-6

59-2

63-8

73

71

6

Bregma-Lambda Chord

30

0

19

23-3

21-7

20

30

19

7

Greatest Distance of Arc
from Chord

17-5

0

9-3

12

14-2

14-3

17-5

15

8

Index of Parietal Curvature

11-92

0

7-36

7-62

10-52

10-82

11-92

11-72

9

Lambda-Inion Arc

33

|

0

27-3

28-5

30

25-7

28-5 1

33

10

Lambda-Inion Chord .

25 |

4

16

0

22-6

17-2

17-5

22-8

25

11

Greatest Distance of Arc
from Chord

9

0

5-6

3

6-2

41

4T

6-2

9

| 12

1

Index of Occipital Curvature

12-7

0

9-41

8-34

8'54

6T4

6-34

8-54

12-7

140 Proceedings of the Royal Society of Edinburgh. [Sess.

Concerning the Tasmanian and Australian, it will be seen that these
results confirm absolutely the conclusions previously drawn by Berry,
Robertson, and Cross ; and it will also be subsequently found that, as regards
the placing of the Australian on the minus side of the Tasmanian, these
results confirm those about to be published by Berry and Robertson (28).

The Gibraltar skull appears herein between Pithecanthropus erectus
and the three Spy-Neanderthal crania. This lowly position may, however,

Table VI.

Nature of Observation.

Number.

Anthropoid.

Pithecanthropus.

Spy- N ean d erthal .

____

Gibraltar.

Galley Hill-
Brux-Briinn.

i

Australian.

o3

S3

g

02

Eh

Cro-Magnon.

European.

1

Glabella-Bregma Arc

6

0

2*35

4-17

[

5-61

2-37

2*60

6-00

2

Glabella-Bregma Chord .

7

0

l'I7

4-08

6*22

4-08 1

3-54

7*00

4-47

3

Greatest Distance of Arc
from Chord .

6

0

2-58

4-84

4-45 1

i 4T6

6-00

6-00

4

Index of Frontal Curva-
ture ....

6

0

2*35

4-20

4-45

4-70

5-04

6*00

5

Bregma-Lambda Arc

7

0

3 93

5*52

6T9

5-68

6T2

7-00

6-81

6

Bregma-Lambda Chord .

6

0

3-80

4-66

4-34

4*00

6-00

3-81

7

Greatest Distance of Arc
from Chord .

6

0

3*19

4T1

GO

4-90

6-00

5-14

8

Index of Parietal Curva-
ture ....

6

0

3-70

3-84

5-30

5-45

6-00

5*90

9

Lambda-Inion Arc .

6

0

4-96

5T8

5-45

4-67

5T8

6-00

10

Lambda-Inion Chord

7

1T2

4-48

0

6 33

4-82

4-90

63-8

7-00

11

Greatest Distance of Arc
from Chord .

7

0

4-35

233

4-82

3T9

3T9

4-82

7*00

12

Index of Occipital Curva-
ture ....

7

0

5T9

4-60

471

3-38

3-49

4-71

7-00

Total ....

0

8-57

48-38

12T1

60-98

51-60

52-23

70-95

59T2

Possible Maximum .

20

77

77

27

77

77

77

77

65

Relative Position

0

•111

•628

•315

1

•792

•670

•678

•921

•912

be due to the fact that I have only dealt with four measurements, inasmuch
as it is well known that the Gibraltar calvaria is imperfect; or, on the
other hand, it may be really due to the lowly position claimed for
this skull by Keith and others.

That the Galley Hill-Brux-Briinn group appear on the plus side
of the Tasmanian-Australian series need cause no surprise, because they are
herein dealt with as a group, and not singly as in Cross’s work. Even the
latter observer placed one of them on the plus side and the other two on
the immediate minus side of the Tasmanian.

1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 141

Working, then, on totally different craniological lines, it is sufficiently
obvious that, as regards the Tasmanian-Australian type — the “ Hesper-
anthropus tasmanianus, spec.” of Sergi, — the present work sustains the
thesis of Berry and Robertson that the “ lately extinct Tasmanians recall
the mental level of eolithic man in Britain we can quite believe ; but that
either the Australian or the Tasmanian carries us back nearly to the
Neanderthal physical type, we must, as the result of the present investiga-

tion, deny, because the physical construction of the Tasmanian is herein
certainly shown to go back only so far as the Galley Hill type at furthest,
and more than this cannot be maintained with any degree of scientific
certainty.”

REFERENCES.

(1) Berry, R. J. A., and A. W. D. Robertson, “Preliminary Communication
on 'Fifty-three Tasmanian Crania, forty-two of which are now recorded for the
first time,” Proc. Roij. Soc. of Viet., vol. xxii., N.S., pt. i., 1909, pp. 47-58.

(2) Berry, R. J. A., and A. W. D. Robertson, “Preliminary Account of the
Discovery of Forty-two hitherto unrecorded Tasmanian Crania,” Anat. Anz., Bd.
xxxv. pp. 11-17, 1909.

142

Proceedings of the Royal Society of Edinburgh. [Sess.

(3) Sergi, G., “ Tasmanier und Australier, Hesperanthropus tasmanianus ,
spec.,” Arclniv fur Anthrop ., Neue Folge, Bd. xiii., Heft 3, 1912.

(4) Barnard Davis, “ Osteology and Peculiarities of the Tasmanians,” Natuur.
Kund. Verhandl. der Hollandsche Maatschap. der Wetenschap, 3 verz., Deel ii.,
No. 4, Haarlem, 1874.

(5) Topinard, P., “ Etude sur les Tasmaniens,” Mem. de la Soc. d’ Anthropologie,
tome iii. p. 307, 1872.

(6) Topinard, P., “ Examen des mesures craniometriques adoptees par le
Thesaurus Craniorum de Barnard Davis et en particulier de celles de la serie des
Tasmaniens,” Revue d’ Anthropologies tome ii. p. 99, 1873.

(7) Quatrefages and Hamy, Crania Ethnica , Texte et Atlas, Paris, 1882.

(8) Flower, W. H., Osteological Catalogue , Museum Royal College of Surgeons
of England, pt. i., “Man,” London, 2nd edition, 1907.

(9) Williamson, G., “ Observations of the Human Crania in the Museum of
the Army Medical Department, Fort Pitt, Chatham,” Dub. Journ. Med. Science ,
vol. xxiii., vol. xxiv. p. 42, May and August 1857.

(10) Wieger, G., Katalog der anthropologischen Sammlung des Anatom ischen
Institute zu Breslau, Festgabe, Braunschweig, 1884.

(11) Klaatsch, H., “Bericht ueber einen anthrop. Streifzug nach London,”
Zeit.f. Eihnologie, Heft 6, p. 875, 1903.

(12) Garson, J. G., Chapter on “Osteology” in Ling Roth’s The Aborigines of
Tasmania, 1899.

(13) Harper, W. E., and A. H. Clarke, “Notes on the Measurements of the
Tasmanian Crania in the Tasmanian Museum, Hobart,” Papers and Proc. Roy. Soc.
Tasmania , 1897, pp. 97-110.

(14) Duckworth, W. L. H., “ Craniological Notes on the Aborigines of
Tasmania,” Journ. Anthrop. Inst., vol. xxxii. p. 177, 1902; and Studies from the
Anthropological Laboratory, Cambridge, 1904.

(15) Turner, Sir W., “The Aborigines of Tasmania: pt. ii., The Skeleton,”
Trans. Roy. Soc. Edin., vol. xlvii., pt. iii. (No. 16), pp. 411-454, 1910.

(16) Berry, R. J. A., A. W. D. Robertson, and K. S. Cross, “A Biometrical
Study of the Relative Degree of Purity of Race of the Tasmanian, Australian, and
Papuan,” Proc. Roy. Soc. Edin., vol. xxxi., pt. i. (No. 2), 1910.

(17) Cross, K. S., “On a Numerical Determination of the Relative Positions of
certain Biological Types in the Evolutionary Scale, and of the Relative Values
of various Cranial Measurements and Indices as Criteria,” Proc. Roy. Soc. Edin.,
vol. xxxi., pt. i. (No. 4), 1910.

(18) Berry, R. J. A., and A. W. D. Robertson, “ The Place in Nature of the
Tasmanian Aboriginal as deduced from a Study of his Calvaria : pt. i., His
Relations to the Anthropoid Apes, Pithecanthropus , Homo primigenius , Homo
fossilis , and Homo sapiens ,” Proc. Roy. Soc. Edin., vol. xxxi., pt. i. (No. 3), 1910.

(19) Schwalbe, G., “Studien iiber Pithecanthropus erectus Dubois,” Zeitschrift
fur Morphologie und Anthropologie, Bd. i., Heft 1, p. 16 et seq., 1899.

(20) Klaatsch, H., “The Skull of the Australian Aboriginal,” Reports from the
Path. Lab. of the Lunacy Dept. N.S. W., vol. i. p. 45 et seq.

1913-14.] Curvatures of the Tasmanian Aboriginal Cranium. 143

(21) Turner, Sir W., “The Craniology, Racial Affinities, and Descent of the
Aborigines of Tasmania,” Trans. Roy. Soc. Edin., vol. xlv., pt. ii. (No. 17),
pp. 365-403, 1908.

(22) Cunningham, D. J., “The Australian Forehead,” Anthropological Essays
presented to E. B. Tylor, 1907.

(23) Berry, R. J. A., and A. W. D. Robertson, “ Dioptrographic Tracings in
Four Normse of Fifty-two Tasmanian Crania,” Trans. Roy. Soc. Viet., vol. v., 1910.

(24) Duckworth, W. L. H., Prehistoric Man , Cambridge, 1912.

(25) Sera, Dr, Archivio jper V Antropologia e per la Etnologia , xl., fasc. 3-4,
quoted by Duckworth under (24).

(26) Berry, R. J. A., and A. W. D. Robertson, “ Dioptrographic Tracings in
Three Normse of Ninety Australian Crania,” now in the press, Trans. Roy. Soc.
Viet.

(27) Buchner, L. W. G., “An Investigation of Fifty-two Tasmanian Crania by
Klaatsch’s Cranio-trigonometrical Methods,” Proc. Roy. Soc. Viet., vol. xxv., new
series, pt. i., pp. 122-135, 1912.

(28) Berry, R. J. A., and A. W. D. Robertson, “The Place in Nature of the
Tasmanian Aboriginal, as deduced from a Study of his Calvaria : pt. ii., His Relation
to the Australian Aboriginal,” Proc. Roy. Soc. Edin., vol. xxxiv., pt. ii.. No. 12, 1914.

(29) Sollas, W. J., “ On the Cranial and Facial Characters of the Neanderthal
Race,” Phil. Trans., B, vol. exeix., 1907.

(30) Schwalbe, G., “Das Schadelfragment von Briix und verwandte Schadel-
formen,” Zeit.fiir Morph, und Anthrop., Sonderheft, Mai 1906.

(31) Klaatsch, H., “ Die Fortschritte der Lehre von den fossilen Knochen-
resten des Menschen in den Jahren 1900-1903,” Merkel und Bonnet's Ergebnisse
der Anatomie und Entioickelungsgeschichte, vol. xii. pp. 545-551, 1903.

{Issued separately April 28, 1914.)

144

Proceedings of the Royal Society of Edinburgh. [Sess.

XII. — The Place in Nature of the Tasmanian Aboriginal as
deduced from a Study of his Calvaria. — Part II. His Rela-
tion to the Australian Aboriginal. By Richard J. A. Berry,

M.D. Edin., Professor of Anatomy in the University of Melbourne;
and A. W. D. Robertson, M.D. Melb., Government Research
Scholar in the Anatomy Department of the University of
Melbourne. (With One Folding Table.)

(MS. received December 9, 1912. Read January 19, 1914.)

Introduction.

In December 1910 we published, in conjunction with Dr K. Stuart Cross,
in the Proceedings of the Royal Society of Edinburgh (1, 2, 3, 4) a series
of four papers dealing with the relations of the Tasmanian aboriginal to
Pithecanthropus erectus and to primitive man generally. In an earlier
publication, published in the Transactions of the Royal Society of Victoria
(5), we also made available the material upon which our Tasmanian work
was based. In the present publication we propose to deal with the
question of the relationship of the Tasmanian aboriginal to the Australian,
with a view to deciding, if possible, the vexed questions as to whether
the Tasmanian and the Australian are one and the same race, or, if not,
if the Australian is a homogeneous or a heterogeneous race.

Literature.

In one of our previous communications (2) we have dealt fairly ex-
haustively with the views of the two opposed schools into which the
study of the Australian aboriginal has divided scientific ethnologists.
On the one hand there are Keane, Flower and Lydekker, Topinard, Tylor,
Curr, de Quatrefages, and Mathew, who hold the Australian to be an
impure race — that is, to have resulted from a cross; on the other hand
there are Klaatsch, Schoetensack, and other German savants, who hold
that the Australian is a pure type and that the Tasmanian is but an
insular variation of that type. This subject has also been still further
dealt with by one of us in another publication (6), so that it is unnecessary
here to pursue the question further. The more recent literature bearing
on this question will be dealt with as occasion demands in the subsequent
parts of this paper.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 145

Sources of the Material.

For the purely Australian part of the present investigation we have
availed ourselves of 100 Australian aboriginal crania, none of which
have ever previously been examined by any scientist. Of these, numbers
1 to 50, both inclusive, are from the Anatomy Museum of the University
of Melbourne : the remaining 50 are from the National Museum, Melbourne ;
and for their use we have to thank the Director of the Museum, Professor
Spencer, as also his assistants, Messrs Kershaw and Walcott.

Of these 100 crania it is most important to note that all with the
exceptions of numbers 43 to 50, both inclusive, are Victorian crania ; the
eight exceptions are from Queensland. It follows therefore that 92 per
cent, of our Australian crania are derived from sources in the vicinity
of the Murray River, or roughly from a district south of the thirty-fifth
parallel of latitude ; the importance of this lies in the fact that there
cannot be any question of racial impurity due to admixture with the
Malay element, which is not infrequently the case with Australian crania
derived from the Northern Territory or other portions of the Australian
Continent in the vicinity of the Malay Peninsula.

For the purposes of comparison with the Tasmanian, our material is
naturally that of our recent Tasmanian work, to which reference has
already been made.

For other comparative purposes, to which reference will subsequently
be made, we have availed ourselves of material derived from the Catalogue
of the Royal College of Surgeons of London. The material so utilised
comprised 19 Andamanese Islander crania, and 90 crania of modern
Italians.

In addition to this we have also availed ourselves of certain data
published by Schwalbe for the Spy-Neandertal group of crania.

Technique.

In the case of the 100 Australian aboriginal crania dioptrographic
tracings in four normse were recorded of all by means of Martin’s
dioptrograph, each skull being orientated in the Frankfort plane in the
Kubuskraniophor. Selections from these tracings are now in the printer’s
hands, and will be published in due course.

Observations recorded.

On the dioptrographic tracings there have been recorded the measure-
ments of the 27 observational counts previously employed by us in the

VOL. XXXIV. 10

146

Proceedings of the Royal Society of Edinburgh. [Sess.

Tasmanian work, and to which the reader is referred. These, it will be
remembered by those who have seen that work, are the data employed
by Schwalbe in his examination of the Pithecanthropus, Spy, Neandertal,
and other calvaria. To these 27 observations there have been added, in
the case of the Australian, 5 other observations employed by Klaatsch
(7), as follows : —

A. The nasio-inion length.

B. The glabella-lambda length.

C. The lambda-glabella-inion angle.

D. The distance of the bregma foot-point from the glabella on the

glabelladambda line.

E. The bregma foot-point-glabella-lambda index — that is, the proportion

which the distance of the bregma foot-point from the glabella
on the glabella-lambda line bears to the glabella-lambda length,
the latter being taken as 100.

The complete series of measurements employed will be readily seen
in fig. 1.

In addition to the foregoing 32 observational points of the form analysis
of the Australian aboriginal skull, we have also recorded and employed for
purposes of comparison a second series of ordinary craniological observa-
tions as follows : —

1. Maximum cranial length.

2. Maximum cranial breadth.

3. The cephalic index.

4. Cranial height.

5. The height index.

6. The basi-nasal length.

7. The basi-alveolar length.

8. The alveolar index.

9. The nasal height.

• 10. The nasal width.

11. The nasal index.

12. The orbital width.

13. The orbital height.

14. The orbital index.

The necessary figures for the above in the cases of the Australian and
Tasmanian have been obtained from our own original material. In the
cases of the Andamanese Islanders and the modern Italians they have been
obtained from the Catalogue of the Royal College of Surgeons of London.

1913-14.] The Place in Nature of the Tasmanian Aboriginal.

147

Fig. 1. — Median Sagittal Section through an Adult Male Australian Aboriginal Skull. (Victoria
No. 18. From the Anatomical Museum of the University of Melbourne.) To illustrate
Schwalbe’s form analysis of the skull, as employed in the present investigation.

X. The nasion.

G. The glabellar point.

A. The upper limit of the glabellar curve.

P. The maximum point of the frontal curvature.

B. The bregma.

C. The maximum point of the calvarial height.

X. The maximum point of the parietal curvature.
L. The lambda.

I. The in ion.

0. The opisthion.

H. The calvarial height foot-point.

G.I. The glabella-inion length.

G.L. The glabella-lambda length.

N.I. The nasio-inion length.

C.H. The calvarial height.

D. The bregma foot-point on the glabella-inion

line.

E. The bregma foot-point on the glabella-lambda

line.

Gr.H. The distance of the calvarial height foot-
point from the glabella.

G.I). The distance of the bregma foot-point from
the glabella on glabella-inion line.

G.E. The distance of the bregma foot-point from
the glabella on glabella-lambda line.

B.G.I. The bregma angle.

F. G.I. The frontal angle.

N.B. The frontal chord.

N.A. The glabellar chord.

A. B. The cerebral chord.

B. L. The parietal chord.

G. P.B. The angle of frontal curvature.

B.X.L. The angle of parietal curvature.

L.I.G. The lambda angle.

L.G.I. The lambda-glabella-inion angle.

O.I.G. The opisthionic angle.

148

Proceedings of the Royal Society of Edinburgh. [Sess.

The 32 Form Analysis Measurements of the Australian Skull.

For the display of the 32 observational counts made upon each one of
the hundred Australian aboriginal crania with which this memoir deals,
we propose, for purposes of comparison, to adopt the same procedure
as employed by us in our former work upon the Tasmanian (3). The
individual results of the entire series of 100 crania are, therefore, set forth
in a table of measurements (Table XXVIII.). This table will form a
valuable means of comparison and contrast with the similar table published
by us for the Tasmanians (3), the more so as the two tables deal with what
is probably the largest consecutive series of Tasmanian and Australian
crania yet dealt with, namely, 52 Tasmanian and 100 Australian crania.

In the Tasmanian work just referred to, in addition to publishing a
complete table of all measurements, we dealt with each observational count
separately. This procedure was adopted in order to form a first estimation
of the evolutionary position occupied by the Tasmanian under each observa-
tional count. We regard it as important to form a like opinion for the
Australian, so that it is necessary, even at the risk of reiteration, to record
the same tables here with the Australian included. We have, however, taken
the opportunity whenever it was afforded, to increase the numbers of the
objects of comparison. In the several tables now to follow the results are
set forth, just as they were for the Tasmanian, in a progressive series from
the lowest figure to the highest, or in the reverse way according to the scale
of evolution, and each table also shows not only those with which the com-
parison is made, but also those which are excluded from the comparison.

Table I. — Comparison of the Calvarial Height (Kalottenhohe).

Minimum.

Average.

Maximum.

1. An adult male chimpanzee

48*5

2. Pithecanthropus erectus ....

62

3. Gibraltar ......

85

4. Briix

85

5. Three Spy-Neandertal ....

81

85-3

88

6. Four Kalmucks

88

90-7

94

7. One hundred Australians, unsexed .

79-5

95

108

8. Galley Hill ......

97

9. Forty-eight Tasmanians, unsexed

87

97

108

10. Eight Veddahs

94

99-2

107

11. Thirty-four Europeans, unsexed

91

99-9

115

12. Twenty-three Dschagga negroes

84

100

1155

13. Egisheim

100

14. Cro-Magnon ......

101

15. Briinn

103

16. Stangenas ......

106

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 149

Table II. — Angle of Frontal Curvature measured on the Glabella

Bregma Chord.

Minimum.

Average.

Maximum.

1. An adult Gibbon

160

2. Three Spy-Neandertal ....

150

153-3

159

3. Pithecanthropus erectus ....

148-5

153-2

158

4. One hundred Australians, unsexed .

123-5

139-6

153

5. Fifty Tasmanians, unsexed

131-5

139-5

149

6. Seven Europeans .....

127

135-4

148

7. Four Dschagga negroes ....

122

131-5

136-5

Gibraltar, Briix, Galley Hill, Brunn, Cro-Magnon, Veddahs, Kalmucks,
Egisheim, and Stangenas absent.

Table III. — Comparison of the Calvarial Height -Breadth Index.

Minimum.

Average.

Maximum.

1. An adult male chimpanzee

42-9

2. Pithecanthropus erectus ....

46-6

3. Three Spy-Neandertal ....

55-4

56-7

57-9

4. Gibraltar ......

57-4

5. Four Kalmucks .....

62-1

63-3

64-8

6. Briix .......

63-3

7. Cro-Magnon ......

66-8

8. Forty-four Tasmanians, unsexed

65-9

72-2

79-2

9. Four Europeans, unsexed

69

72-4

76-2

10. One hundred Australians, unsexed .

60-2

72-7

85-4

11. Briinn .......

74-1

12. Galley Hill

74-6

13. Four Veddahs .....

69-6

76-9

82-9

Dschagga negroes, Egisheim, and Stangenas absent.

Table IV. — Comparison of the Bregma Angle.

1. An adult male chimpanzee

2. Pithecanthropus erectus .

3. Three Spy-Neandertal

4. Gibraltar ....

5. Briix

6. Galley Hill ....

7. Stangenas ....

8. Brunn .....

9. Cro-Magnon ....

10. One hundred Australians, unsexed

11. Forty-five Tasmanians, unsexed

12. Four Kalmucks

13. Egisheim ....

14. Twenty-four Dschagga negroes

15. Forty Europeans

Minimum.

Average.

Maximum.

39-5

34

37-5

41*

45

47-5

50-5

50

50-5

51

51-1

52

52-5

54

54

49

54-7

60

51-5

56

64

55

56-5

57

58

53

58-6

63-5

54

59-9

68

Veddahs absent.

* Employed for comparative purposes.

150 Proceedings of the Royal Society of Edinburgh. [Sess.

Table V. — Comparison of the Calvarial Height Index (Kalottenhohen-Index.)

Minimum.

Average.

Maximum.

1. Pithecanthropus erectus ....

34-2

2. An adult male chimpanzee

35-1

3. Three Spy-Neandertal ....

40-9

44-9

47

4. Gibraltar

45-4

5. Briinn

47*6

6. Galley Hill ......

48-2

7. Cro-Magnon ......

50

8. Briinn

51-2

9. One hundred Australians, unsexed .

44-9

53

61-5

10. Four Kalmucks .....

52*8

54-5

84-9

11. Stangenas

54*6

12. Egisheim ......

55-5

13. Forty-four Tasmanians, unsexed

48-3

56-1

62-7

14. Eight Veddahs .....

54-6

58*4

62-9

15. Twenty- three Dschagga negroes

52-1

59-8

67-1

16. Thirty- two Europeans ....

54-4

59-8

66-2

Table VI. — Comparison of the Calvarial Height Half-Sum Glabella-Inion
Length plus Breadth Index.

Minimum.

Average.

Maximum.

1. An adult male chimpanzee

38-6

2. Pithecanthropus erectus ....

39-4

3. Three Spy-Neandertal ....

47

48-9

50

4. Gibraltar

50-7

5. Galley Hill

50-8

6. Briix

54*8

7. Cro-Magnon ......

57-2

8. Four Kalmucks .....

57-1

58-7

60-2

9. Briinn

60-5

10. One hundred Australians, unsexed .

52-3

61-3

69-9

11. Forty-four Tasmanians, unsexed

55-2

63

69-5

12. Five Europeans, unsexed

60-9

65-8

69-8

j 13. Four Veddahs .....

61-2

66-6

71-5

Egisheim, Stangenas, and Dschagga negroes absent.

Table VII. — Comparison of the Length of the Parietal Arc.

Minimum.

Average.

Maximum.

1. An adult female chimpanzee .

62

2. Pithecanthropus erectus ....

93

103

113

3. Briix

108

4. Gibraltar ......

111

5 Seventeen Maories, unsexed

101

117

127

6. Three Spy-Neandertal ....

119

119-6

120

7. Forty-eight Tasmanians, unsexed .

112

125-8

145

8. One hundred Australians, unsexed .

109

125-9

147

9. Galley Hill

132

10. One European .....

133

11. Cro-Magnon ......

135

12. Briinn

139-5

Egisheim, Stangenas, Dschagga negroes, Veddahs, and Kalmucks absent.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 151

Table VIII. — Comparison oe the Frontal Angle.

Minimum.

Average.

Maximum.

1. Pithecanthropus erectus ....

52*5

2. An adult male chimpanzee

56

3. Three Spy-Neandertal ....

57-5

64-8

70

4. Gibraltar ......

73

5. Briix .

74-7

6. Briinn .......

75

7. Galley Hill

82

8. Cro-Magnon ......

83

9. Four Kalmucks .....

80

85-2

91

10. One hundred Australians, unsexed .

71

85-2

100

11. Forty-four Tasmanians, unsexed

72

86

96

12. Egisheim

89

13. Stangenas

92-5

14. Forty Europeans, unsexed

73

92-5

103

15. Twenty-four Dschagga negroes

88

100-3

110

Veddahs absent.

Table IX. — Comparison of the Bregma Foot-Point Positional Index.

Minimum.

Average.

Maximum.

1. An adult male gibbon ....

63-4

2. Pithecanthropus erectus ....

39-7

44-1

50-2

3. Stangenas ......

38-9

4. Briix .......

37-3

5. Three Spy-Neandertal ....

34-8

36-6

40-1

6. Gibraltar ......

35-2

7. Galley Hill

34-3

8. One hundred Australians, unsexed

29-2

34-1

38-8

9. Briinn

. .

34

10. Forty-four Tasmanians, unsexed

26

33-5

40-6

11. Egisheim ......

33-3

12. Four Kalmucks

30-1

32-8

37-4

13. Cro-Magnon

32-6

14. Twenty-four Dschagga negroes

26-6

32-1

37-2

15. Forty-five Europeans, unsexed

22-2

30-4

35-7

Veddahs absent.

152

Proceedings of the Poyal Society of Edinburgh. [Sess.

Table X. — Comparison oe the Lambda Angle,

Minimum.

Average.

Maximum.

1. Nearest anthropoids ....

43

55-5

68

2. Pithecanthropus erectus ....

66

3. Neandertal ......

66*5

67

Spy i

67

68

4. Gibraltar ......

69

5. Cro-Magnon ......

70

6. Galley Hill

74

7. Briinn .......

78

8. One hundred Australians, unsexed .

70

79*5

90

9. Briix .......

80

10. Forty-six Tasmanians, unsexed

74

80-5

88

11. Stangenas ......

81-5

12. Modern Man . . . .

78

81-5

85

Egisheim, Dschagga negroes, Veddahs, and Kalmucks absent.

Table XI. — Comparison of the Opisthionic Angle.

Minimum.

Average.

Maximum.

1. Pithecanthropus erectus ....

64

2. Nearest anthropoids ....

50

59*5

69

3. Spy 1

54

Neandertal

51-5

4. Galley Hill

42

5. Briinn

42

6. Thirty-eight Tasmanians, unsexed .

34-5

40-6

47

7. One hundred Australians, unsexed

31

40

51-5

8. Gibraltar

36

9. Recent Man ......

31

35-5

40

10. Cro-Magnon ......

34

Egisheim, Stangenas, Briix, Dschagga negroes, Veddahs, and Kalmucks absent.

Table XII. — Comparison of the Length of the Frontal Arc.

Minimum.

Average.

Maximum.

1. An adult male chimpanzee

92

2. Pithecanthropus erectus ....

100

110

120

3. Four Kalmucks

110

115-2

120

4. Three Spy-Neandertal ....

115

124

133

5. Seventeen Maories, unsexed .

116

125

135

6. Five Europeans, unsexed

121

125-6

130

7. Forty-seven Tasmanians, unsexed .

113

126

143

8. Gibraltar

126

9. One hundred Australians, unsexed .

116

126-8

143

10. Briix

135

11. Galley Hill ......

135

12. Briinn

135

13. Cro-Magnon

138

Egisheim, Stangenas, Dschagga negroes, and Veddahs absent.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 153

Table XIII. — Comparison of the Length of the Chord of the Pars
Cerebralis of the Os Frontale.

Minimum.

Average.

Maximum.

1. An adult female chimpanzee and a gibbon

55

2. Gibraltar ......

82

3. Spy-Neandertal .....

77

83-6

87

4. Pithecanthropus erectus ....

80

87-5

95

5. Eleven Europeans, unsexed

87

92-1

101

6. Fifty Tasmanians, unsexed

73

93-7

106-5

7. Galley Hill

95

8. Five Dschagga negroes ....

94

95-8

97

9. One hundred Australians, unsexed .

85

95-9

112

10. Briinn .......

96

11. Cro-Magnon ......

97-5

12. Briix

99

Egisheim, Stangenas, Kalmucks, and Veddahs absent.

Table XIV. — Comparison of the Length of the Chord of the Os Frontale.

Minimum.

Average.

Maximum.

1. An adult male chimpanzee

87

2. Four Kalmucks

98

103-8

107-5

3. Pithecanthropus erectus ....

96

104

112

4. Fifty Tasmanians, unsexed

97

109-5

120

5. Seventeen Maories, unsexed .

103

110

119

6. One hundred Australians, unsexed .

100

110-8

124

7. Gibraltar

111

8. Five Europeans, unsexed

109

112-5

118-5

9. Three Spy-Neandertal ....

108

114

119

10. Briix

114

11. Galley Hill ......

120

12. Briinn .......

123

13. Cro-Magnon ......

123

Egisheim, Stangenas, Dschagga negroes, and Veddahs absent.

Table XV. — Comparison of the Parietal Frontal Arc Index.

Minimum.

Average.

Maximum.

1. Briix ......

80

2. An adult female chimpanzee .

82-6

3. Pithecanthropus erectus ....

71-1

85-8

102-7

4. Gibraltar. ......

88

5. Seventeen Mariories, unsexed .

81

93-3

104

6. Three Spy-Neandertal ....

89-4

96-8

104-3

7. Galley Hill

97-7

8. Cro-Magnon

97-8

9. One hundred Australians, unsexed .

87-7

99-3

113-9

10. Forty-five Tasmanians, unsexed

85-8

99-7

114-1

11. Briinn .......

103-3

12. One European .....

109-9

Egisheim, Stangenas, Dschagga negroes, Veddahs, and Kalmucks absent.

154

Proceedings of the Royal Society of Edinburgh. [Sess.

Table XVI. — Comparison of the Distance of the Bregma Foot-Point
from the Glabella.

Minimum.

Average.

Maximum.

1. Pithecanthropus erectus ....

72

81-5

91

2. Briix .......

75

3. Three Spy-Neandertal ....

67

72-3

81

4. An adult male chimpanzee

72

5. Galley Hill

69

6. Briinn .......

67-5

7. Gibraltar ......

66

8. Cro-Magnon ......

66

9. One hundred Australians, unsexed

51-5

61-2

74

10. Forty-four Tasmanians, unsexed

45

58-7

71-5

11. Four Kalmucks .....

51-5

54*6

61

12. Twenty-four Dschagga negroes

41

53-9

62-5

13. Thirty-five Europeans, unsexed

40

51-3

61

Egisheim, Stangenas, and Veddahs absent.

Table XVII. — Comparison of the Length of the Parietal Chord.

Minimum.

Average.

Maximum.

1. Briix .......

100-5

2. Pithecanthropus erectus ....

104

3. Seventeen Maories, unsexed .

92

104

110

4. Three Spy-Neandertal ....

104

107-7

113

5. Gibraltar ......

108

6. Forty-eight Tasmanians, unsexed .

99-5

113

127

7. One hundred Australians, unsexed .

98

114-6

137

8. Galley Hill

120

9. Cro-Magnon ......

123

10. Briinn .......

127-5

Anthropoids, Egisheim, Stangenas, Dschagga negroes, Veddahs, Kalmucks,
and Europeans absent.

Table XVIII. — Comparison of the Curvature Index of the Os Frontale.

Minimum.

Average.

Maximum.

1. Pithecanthropus erectus ....

93-3

94-6

96

2. An adult male chimpanzee

94-5

3. Three Spy-Neandertal ....

89-4

92-8

93-9

4. Briinn .......

91-1

5. Four Kalmucks .....

88-3

90-1

92-8

6. Five Europeans, unsexed

87-4

89-5

91-1

7. Cro-Magnon ......

89-1

8. Galley Hill

88-8

9. Gibraltar ......

88

10. One hundred Australians, unsexed .

81-3

87-4

90-8

11. Forty- seven Tasmanians, unsexed .

81-4

87-1

97-5

12. Stangenas ......

85-2

13. Briix

84-4

Egisheim, Dschagga negroes, and Veddahs absent.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 155

Table XIX. — Comparison of the Distance of the Foot-Point of the
Calvarial Height from the Glabella.

1. Pithecanthropus erectus

2. An adult male gorilla

3. Four Kalmucks

4. Forty- one Europeans, unsexed

5. One hundred Australians, unsexed

6. Forty-five Tasmanians, unsexed

7. Gibraltar ....

8. Briinn .....

9. Three Spy-Neandertal

10. Briix

11. Galley Hill ....

12. Cro-Magnon ....

Minimum.

Average.

Maximum.

70

80*5

91

84

76

86-3

95

78

95-8

112-5

88

101-1

123

85

101-9

115-5

105-7

110

103

111

123

111

111

121-5

Egisheim, Stangenas, Dschagga negroes, and Veddahs absent.

Table XX. — Comparison of the Glabella-Cerebral Chord Index.

| Minimum.

Average.

Maximum.

1. Gibraltar

43

2. An adult female orang ....

40

3. Three Spy-Neandertal ....

34-4

39-6

43-1

4. Cro-Magnon

32-3

5. Briinn .......

31-2

6. Pithecanthropus erectus ....

25-2

27-6

30

7. Egisheim ... . .

27-5

8. Five Dschagga negroes ....

23-3

27-4

30-3

9. Eleven Europeans, unsexed

21-4

26-6

31-8

10. Fifty Tasmanians, unsexed

17-6

25-5

35-6

11. Galley Hill

25-2

12. Briix

24-2

13. One hundred Australians, unsexed .

15-6

23-6

33-5

14. Stangenas ......

•*

i

18-6

Kalmucks and Veddahs absent.

156

Proceedings of the Royal Society of Edinburgh. [Sess,

Table XXI. — Comparison of the Maximum Breadth.

1

|

Minimum.

Average.

Maximum.

1. An adult male chimpanzee

..

113

2. Four Veddahs .....

123

129-7

135

3. Briix .

130

4. Galley Hill

130

5. One hundred Australians, unsexed .

120

130-7

143

6. Pithecanthropus erectus ....

133

7. Nineteen Andamanese Islanders, unsexed

128

133

141

8. Forty-eight Tasmanians, unsexed .

120

134-7

145

9. Fifteen Maories, unsexed

128

136

141

10. Briinn .......

139

11. Five Europeans (Germans), unsexed .

137

142-4

149

12. Ninety Europeans (Italians), unsexed

124

142-5

155

13. One hundred and seventy-six Europeans

(Scotch), unsexed ....

128

143-6

159

14. Four Kalmucks .....

140

146

148

15. Gibraltar ......

148

16. Three Spy-Neandertal ....

146

150-3

153

17. Cro-Magnon .....

151

Egisheim, Stangenas, and Dschagga negroes absent.

Table XXII. — Comparison of the Curvature Index of the Os Parietale.

Minimum.

Average.

Maximum.

1. Gibraltar ......

97-2

2. Three Spy-Neandertal ....

90-4

93-7

96-3

3. Briix

93

4. Pithecanthropus erectus . . .

92?

5. Briinn .......

91-3

6. Cro-Magnon ......

91-1

7. One hundred Australians, unsexed .

81-6

91

103-6

8. Galley Hill

90-9

9. Forty-seven Tasmanians, unsexed

83-8

90

97-6

Anthropoids, Egisheim, Stangenas, Dschagga negroes, V eddahs, Kalmucks,
and Europeans absent.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 157

Table XXIII. — Comparison of half the Sum of the Glabella -Inion Length

plus the Breadth.

Minimum.

Average.

Maximum.

1. An adult female gorilla ....

129

2. Four Veddahs

142-5

149-5

153-5

3. Forty-four Tasmanians, unsexed

140-5

154

164-5

4. Four Kalmucks .....

148-5

154-3

161

5. Briix

155

157-5

6. One hundred Australians, unsexed .

143

155-05

166

7. Five Europeans, unsexed

153

156-8

159

8. Pithecanthropus erectus ....

157

9. Galley Hill

165-5

10. Gibraltar ......

167-5

11. Briinn .......

170

12. Three Spy-Neandertal ....

172

174-3

177

13. Cro-Magnon

1

176-5

Egisheim, Stangenas, and Dschagga negroes absent.

Table XXIV. — Comparison of the Calvarial Height Foot-Point
Positional Index.

Minimum.

Average.

Maximum.

1. Pithecanthropus erectus ....

38-6

44-4

50-2

2. Four Kalmucks .....

43-6

52-6

56-8

3. Briinn .......

54-7

• •

4. Galley Hill

55-2

5. Three Spy-Neandertal ....

52

55-7

60-8

6. Forty-one Europeans, unsexed

48-8

56-2

66-9

7. One hundred Australians, unsexed .

44-8

56-3

65-3

8. Gibraltar

56-5

9. Forty-four Tasmanians, unsexed

53-1

59

64-8

10. Briix

60(61-6)

11. Cro-Magnon . .

60-1

12. An adult female gorilla ....

61-8

Egisheim, Stangenas, Dschagga negroes, and Veddahs absent.

158

Proceedings of the Royal Society of Edinburgh. [Sess.

Table XXV. — Comparison oe the Glabella -Inion Length.

Minimum.

Average.

Maximum.

1. An adult male gorilla ....

147

2. Four Kalmucks

157

166-2

174

3. Twenty- three Dschagga negroes

145

167-4

180

4. Thirty-one Europeans, unsexed

155

168

184

4. One hundred and fifty-four Europeans,

unsexed ......

154

169-3

199

5. Eight Veddahs .....

160

169-8

176

6. Forty-four Tasmanians, unsexed

157

173-1

188

7. One hundred Australians, unsexed .

162

179-5

196

8. Pithecanthropus erectus ....

181

9. Briix

185 (180)

10. Gibraltar ......

187

11. Three Spy-Xeandertal ....

196

198-6

202

12. Galley Hill ......

201

13. Briinn

201

14. Cro-Magnon

202

Egisheim and Stangenas absent.

Table XXVI. — Comparison of the Length of the Chord of the
Pars Glabella of the Os Frontale,

Minimum.

Average.

Maximum.

1. An adult female orang ....

20

2. One hundred Australians, unsexed .

15

22-3

29-5

3. Forty-nine Tasmanians, unsexed

18

23-8

29

4. Pithecanthropus erectus ....

24

5. Briix

24

6. Galley Hill

24

7. Eleven Europeans, unsexed

19-5

24-5

28

8. Five Dschagga negroes ....

27

26-4

28-5

9. Briinn

30

10. Cro-Magnon

31-5

11. Three Spy-Neandertal ....

30

33-1

37-5

12. Gibraltar ......

36

•*

Egisheim, Stangenas, Kalmucks, and Veddahs absent.

Table XXVII. — Comparison of the Angle of Parietal Curvature.

Minimum.

Average.

Maximum.

1. Pithecanthropus erectus ....

150

2. Chimpanzee ......

149

3. Three Spy-Neandertal ....

142-5

142-6

143

4. Galley Hill

139

5. One hundred Australians, unsexed .

125

135-7

145

6. Briinn .......

135

7. Forty-nine Tasmanians, unsexed

125-5

134-3

141-5

8. Cro-Magnon old man ....

134

9. One European (Schwalbe)

129

Gibraltar, Briix, Kalmucks, Veddahs, Dschagga negroes, Egisheim,
and Stangenas absent.

Pm Boy.. Sots. Min., [Vol. XXXIV.]

Table XXVIII.— THE INDIVIDUAL AND GENERALISED RESULTS OE THE EXAMINATION • OF ONE HUNDRED AUSTRALIAN CRANIA.

i Roberson Serial Nuvil

III

21 22 23

35 \ 36 I 37

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90-47

S0-47\ 91-40 i

,00-00

92-10

91-94

: 89-68

91-53

89-47

83-80

92-03

92-51

89-91

92-54

93-04

90-57

93-84

Wsi

92-21

12

30-01

90-15

-

90-15

92-56

85-29

92-98

92-03

100

8i-66'

ISMS

103-07

|132

131

135

134

[133-5

129

|l34

132-5

|l36-5

®fr

|l35 :!

136

137

134 |l38

132

139 136-5 132

137-5

132

136 j

136 |

140

138 136 |

|M

134

137

137

134

138

137 |137;

134

133

m -

140

138

141

137

100

126

135-77

145

\l01-63

763-77

88-18

766-70

767-26

763-37

765-42

| 96-47

766-66

96-80

104-00

I 93-70

96-18

165-66 764-91 96-66

| 93-27 1 98-33 ]l62

■43]

94-65

|j63-96

102-23 |

.

lift

95-48 j 93-93

92-68

92-74

97-66

99-23

101-69

98-38

95 cz\^^

|®0

98-42

97-65

95-27

108-80

91-20

96-46

100

IB

99-32

113-90

76

84

83

80

76

[84

77

!>0 |

76

84

82

75.5

79

75 [83

78

m 77

79

78

74 -

81

73

, 70

70

78

IW

81

82

81

74

77

78

Mi

.80

IB

.80

81

83

81

(H

100

70

79-56

90

45

38

34

37

40

34

31

33

38

43

46-5

I48

38

45 |

39

45 | 41

42

41

'ISfl

35

38-5

43

41

34-5

39

38

38

38

41

49-5

39

41

42

42

35

44

M 1

35

45

m

1 31

40-06

51-5

Present Location of :Specim

University, Melbou:

Original Number of Special

M. M. M. M. M.

8 11 II 12 I 13

12989 13006a 12995

13026

Glabella-Inion Length*,

Nasio-Inion Length.

Calvarial Height.

190

159 171 171

94-5 96 108'

172 170 174

52-87\ 52'

48-6S 53-24

54-31 \ 54-54\ 60-67 \ 54-46 1 55-55 55-05

4 Maximum Breadth.

137' 136 137 137

50-57 51-42 56-33
32 |l23 |l2S

mnigam of Glabella-Inion Length -

70-93 69-54\ 77-55 75-55 73

35 69-OS 70-541 72-69 79-33

3-57] :

148-5 157-5 164-5

166 153-5 149-5

57-27 63-14 1 64-77 62

22 56-21 61-60 62-17 64-641 63-5

9-34 57-65

60-53\ 65-46

right Boob-Point from Glabella.

1-10 1 58-37 56-52 57

90-5 107

56-54 1 54-21 58-04 51-42 \ 60-11 54-92 1 59-4

52-80\ 61-66

63-40 57-45

5 71 85

88 88 . 86

50 55 54

57-5 55 5'

Distance of Bregma Foot-1

■1

75 37-17 32-53 34-48 33-6

Glabella -Lambda Length.
Lambda-G34holla-Inion Angle.

1-89 \ 34-19 33-8

161 172 176

17 16 21

Distance of Bregma Foot-Poin

a Glabella on Glabella-Lambda Lin<

46-17 41-34

49-19 50-26 47-82 48-25

M^nPh^&fjFrontal Chord.

16-5 116 106

121 114

87-39 \ 90-33 87-40

Angle of Frontal Curvature.

Length of Chord of Pars Glabellaris.

ngtli of Chord of Pars Cerebralis

150 143 136

29 26-5 22-5 15-5

Length of Parietal Arc.

Length of Parietal C

54 1 26-63 27-53 27-36 27-37 25-73 75-30 76-47

)-79 23-36 <

129 121 110

96-24 1 !

92-66 i mm

vAh'gle. of Parietal Curvature. .

R. J. A. Berry and *Di§/A. W. D. Robertson.

89-34 1 102-9

J137 |l 36 1 145 |l31-5 |lS

127 133 134

55-37 94-24

76-5 75 77

40 43 39

V

Table XXIX.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 159

Stangenas.

14-62

| 8-64
11-21

10-79

8- 84

9- 66

7-79

7-18

78-73

91-69

•8586

Briinn.

CD !>OT)(^COI>rHCDlC<N^M(NC5'cHOCOQO©JOQOeO<M®
OO ;^OCpr^r-lOcpcOI>'Cp'>^COQpoOcpC5l^'THt^Cit^OT)HOJ
cb <©©d5Gbd5cb©c©i©c©c©c©»ocb»ocb4<cbcbcb'iHiOTH

r— 1 iH iH

166-94

co

oq

©

oq

•7755

Cro-Magnon.

lO WOOOlMlOCOtNOJ^lMlOCOlOHODNlOOCOilOOffiN
CO ;oW©-f©NHWG0NN©^Mt^l0»0Hl0O>0i01>iy|

cb G©©cbi^cbc»HibiAd5cbcb^^^^cbcbiocbiOHio^

168-21

215-23

1 — 1
00

Egisheim.

13-09

11-80

11-70

9-8*5

10-86

4-56

2-69

64-55

78-57

•8215

Dschagga

Negroes.

1 13-09
57-6

i 12-15
14-07

12-90

11-30

8-40

7-68

4-59

89-94

96-80

©
1 oq

05

Europeans.

bt'OOt'tOHDHCDiOCC^HNO CO CD CO t" 00 ©

0®ffiOiOQO'#t^q5CO'^I>COHTt<^ ] ©q rf< OO CO ‘(MrHCD ;

cb^©cb-^©cb©H©i^cbi>cbi^db 4i cb ^-h -cH cb h

178-25

206-79

©

oq

©

00

Veddahs.

12- 89
11-41

13- 30
11-17

2-42

2-39

53-58

62-31

•8598

Tasmanians.

CO>0-^>OCO'^iO'^®®(NHl>0(M-^HHCO»0'<iM>(MI>OOH

coHaoco©i^io©i^c^Hao©^©coco©q''cHHHio©'i^©<©q

cb-^05©cb©i^o5©©cocoiAiO'i^cbcbcbcbiocbcbcb'-Hio-^H

172-36

©

05

©

cq

oq

oo

©

t-*

Galley Hill.

CO T)(lO®t'DOOOO,0(NCOH(MQOI>OD'^©COiO®OOH

co ;cpcococow9>9Qpj>Diu9^THoaocoM'^H(cioc»'^
cb ocbi^'^cot^ocoiococbiA'^cb'^'cHThiocbcb^HrHcb'^

154-24

co

oq

i s

1 oq

•7166

Australians.

CKMHOCOODCOOOHt^TjKMOMO^t^OHCDOO^DaD
OOHOOCOOiOOOi005Clffl-ft^QOcp®OCOI>lOOOHH^
; p^^odiodii^cbocbcDcbco^-^iocbiocbiocbcbcbrHiorli

163-39

220-99

1 co
©
co
c-

Kalmucks.

10-73

6- 85

10- 94

11- 15
8-02

8-83

11-04

4-65

4-02

7- 48

3-73

0-93

I 4-78

2-95
| 0-82

96-92

lO

©

cb

•6775

Spy-

Neandertal.

DiOCODOOH(N(Ml>OOHHDl>ODO©DOO^XCOa)'cH

COCODI>(»'7iCOCOCOOCO'^CO'^CqiOiO^OOO'^l^C5rHDI>

dsrH^ioio-^cDcbdi^cbcDOcb-^cbi-Hr-H^rHibf-HiOrHcbcb

111-57

220-99

•5049

Briix.

ao lOCODDiOONH ©q © t- h lO © ^ ® ffi CO 1> ©

©q ;ooooco^n-^Oi^i— i ,coof oo ^ooio^ooio ; ©

ds Ai^i^©io*b©© cb©co©H©cb4i©cbcbcb>H 'cb

124-43

©

t"

05

©

oq

•5931

Gibraltar.

00 NffilCCOOCOI>HNHCD100HCDI>'<# I> © ©q io

©q ;oo^HaocowrHowooipi>oco>p^o © ^ ©q ; h

05 ^I^CD-^lO»OOvbt:'CDiO>CicbTH^-ilo4lOiOO-<chrH * h

r— 1

124-25

207-63

•5485

Pithecan-

thropus.

CO t" LO oqcD t> O H©N>fl CO © 00 ©

CO ©q CO 00 0505 cpcpo-f loooiocq

MHHOOO^OCDMOCOCoilHOOOOTtlcbcbMOOO

51-92

220-99

•2349

Anthropoid.

lOO lo oo lO -«cH . 00 CO 00 loco

i—i io 05 i—i cpcp.ocooo ; r^co;

ooo^noooooorboooosb © © © © © h ©

10-66

206-79

•0515

Maximum.

I (NDHOt^t'00OHCD'^(NDC0t'O'^l0l>00©>i(»0O©
©t-^©orHHffl©coxcqoco^^co^ipHicioiot^co©
-^^i-Hcb-^rH05cbi^-id5iAd5d5Gbd'Gbi0GbcDiAiocbi0'-HG-^

I—i 1 — 1 1 — 1 I—I I—I I—I I—I

220-99

05cqoq©qo5'^05CDoor-HrH©qTtiiocoo5iO'^TjHcDioiocoo5ioo5
^OHHt'Ht'HOOOHOOCO'^l>ffii<THt'<MXDrtOO®cO
t-coio<McocorH©qior-r-co©qoo-itfi05©©05ioiOTtHc©iOTlHio
©©©©©©©©00 00 00 00 001>t^©t^Ir^iOi©Tt<'^'^i— i©io

Total .

Pos. )
Max. /

3 ®

Ph Pm

No.

i— ioqco-^iocDt^oo©©i— icqco-^io©r^oo©©rHcqcoTt<t^ro
hi— ii— ii— iHHHHr— i^noqcqoqcqoqcq1^

160

Proceedings of the Royal Society of Edinburgh. [Sess.

Table A. — Comparison of the Nasio-Inion Length.

Minimum.

Average.

Maximum.

1. Four Kalmucks .....

154

162*5

169

2. Twenty Europeans, unsexed

154

168

178

3. Pithecanthropus erectus ....

. .

168

4. Forty-four Tasmanians, unsexed

144

169*7

183

5. One hundred Australians, unsexed .

157

173*8

191

6. Gibraltar

182*1

7. Cro-Magnon old man ....

194*2

8. Three Spy-Neandertal ....

192

196*3

199

Anthropoids, Briix, Galley Hill, Veddahs, Dschagga negroes, Egisheim, Briinn,

and Stangenas absent.

Table B. — Comparison of the Glabella-Lambda Length.

Minimum.

Average.

Maximum.

1. Pithecanthropus erectus .

171

2. Forty-eight Tasmanians, unsexed .

162

173*2

189

3. Gibraltar ......

177

4. One hundred Australians, unsexed .

161

178*6

194

5. Egisheim ......

185

6. Briix (Schwalbe) .....

185

7. Three Spy-Neandertal (Klaatsch) .

185

185*3

186

8. Cro-Magnon old man (Klaatsch)

193

9. Galley Hill

194

10. Briinn .......

197

Anthropoids, Gibraltar, Kalmucks, Veddahs, Europeans, and
Dschagga negroes absent.

Table C. — Comparison of the Lambda-Glabella-Inion Angle.

Minimum.

Average.

Maximum.

1. Pithecanthropus erectus (Klaatsch) .

10

2. Three Spy-Neandertal (Schwalbe) .

15

15*8

16*5

3. Galley Hill (Klaatsch) ....

17

4. Briinn (Klaatsch) .....

17

5. One hundred and sixty-eight Australians

(Berry, Robertson, and Klaatsch),

unsexed . .

13*5

17*1

22*5

6. Cro-Magnon old man (Klaatsch)

17*5

7. Fifty- three Tasmanians (Berry, Robertson

and Klaatsch), unsexed

15

18

23

8. Briix (Schwalbe’s estimation)

20

9. Forty-three ancient Egyptians (Schwalbe)

15

20*7

29

10. Twenty-five Dschagga negroes (Schwalbe)

17

21*5

28

11. Thirty-five Europeans (Schwalbe) .

17*5

22

30

12. Gibraltar (Sollas) . . . .

24?

Anthropoids, Kalmucks, Veddahs, Egisheim, and Stangenas absent.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 161

Table D. — Comparison of the Distance of the Bregma Foot-Point from
the Glabella on the Glabella- Lambda Line.

1

Minimum.

Average.

Maximum.

1. Pithecanthropus erectus (Klaatsch)

79-5

2. Gibraltar ......

82-2?

3. Forty-eight Tasmanians, unsexed

65

82-3

96

4. One hundred Australians, unsexed .

73

85-3

101

5. Galley Hill (Klaatsch) ....

91-5

6. Cro-Magnon old man (Klaatsch)

91-5

7. Briinn (Klatsch)

92-7

8. Three Spy-Neandertal (Klaatsch)

98

9. Briix (Schwalbe estimated)

100-5

Anthropoids, Kalmucks, Veddahs, Europeans, Dschagga negroes, Egisheim,
and Stangenas absent.

Table E. — Comparison of the Bregma Foot-Point Glabella-Lambda Index.

Minimum.

Average.

Maximum.

1. Pithecanthropus erectus ....

46-4

2. Gibraltar .....

46-4?

3. Forty-eight Tasmanians, unsexed

40-1

46-7

51-8

4. Briinn .......

47

5. Galley Hill

47-1

6. One hundred Australians, unsexed .

40-9

47-2

53-1

7. Cro-Magnon old man .

47-4

8. Three Spy-Neandertal ....

52-8

9. Briix

54-3

Anthropoids, Kalmucks, Veddahs, Europeans, Dschagga negroes, Egisheim,

and Stangenas absent.

In the foregoing tables there are several points to which we should like
to direct particular attention.

Firstly, as regards the tables, Nos. I. to XXVII. are those already
employed in our previous Tasmanian work (3). Tables A to E inclusive
comprise the additional observations which we then stated we intended to
employ in our Australian researches, and which are, therefore, now included.
It is a matter of congratulation that we are enabled to incorporate the five
additional observations not previously made upon the Tasmanian. Mr L.
W. G. Buchner, a recently appointed Victorian Government Research
Scholar in the Physical Anthropological Laboratory of the University of

Melbourne, has been engaged in an examination of the Tasmanian facial
VOL. xxxiv. 11

162 Proceedings of the Royal Society of Edinburgh. [Sess.

skeleton, and has kindly furnished us with the necessary Tasmanian data
under Tables A to E inclusive for comparison with the Australian.

Secondly, as regards the numerical order of the Tables. In our previous
Tasmanian work, Tables I. to XXVII. were simply set forth in the accidental
order in which the observations were recorded. Our fellow-worker, Dr
K. Stuart Cross, subsequently showed (4) that these morphological observa-
tions were not all of equal morphological value. He set them forth in their
correct order of value, and in this vrork we have arranged Tables I. to
XXVII. in Dr Cross’s order. Table II. of the Tasmanian work becomes
therefore now Table I., Table XVII. similarly becomes Table II., and so on
as determined by Dr Cross. Tables A to E still retain their accidental
order of observation.

Thirdly, as already stated, additional objects of comparison have been
incorporated in the present tables whenever it was possible to secure
accurate data. It is, however, a matter for regret that so few figures
dealing with the morphological form analysis of the human skull on the
lines advocated by Schwalbe and Klaatsch are as yet available, and hence,
although extended, the present tables are not even yet as complete as we
should have desired. If our colleagues in Europe would undertake the
necessary researches on British long and round barrow skulls, on modern
Europeans, on pre-historic and modern Egyptians, and so forth, the problem
of the true place in Nature of the Australian and Tasmanian aboriginal
inhabitants would be rendered simpler. These difficulties notwithstanding,
a comparison of our previously published Tasmanian tables with those now
incorporated will show that the latter have been increased. Thus the
Egisheim and Stangenas primitive crania have been included (Frederic, 8)
whenever the necessary figures were available. The 17 Maories first
mentioned in Table VII. are from the work of Mollison (9). The
Andamanese Islanders and the 90 Italians incorporated in Table XXI. are
from the Royal College of Surgeons Catalogue of Osteology, and have been
worked out therefrom by ourselves. The 176 Europeans (Scotch) mentioned
in the same table are from the work of Sir William Turner (10).

The Relative Evolutionary Positions of the Australian and

the Tasmanian.

In our previous Tasmanian communication we stated that we thought
the Australian would stand on the plus side of the Tasmanian — that is to
say, we confidently expected to find that the Australian would be a more
highly evolved morphological type than the Tasmanian. This expectation

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 163

has not, however, been realised. Mr W. M. Holmes, of the Natural
Philosophy Department of this University, has been good enough to apply
Cross’s mathematical formula to the results of the observations recorded in
the several tables. He finds the Australians are represented by the figure
0*739, and the Tasmanians by 0*779. The complete results are graphically
represented in fig. 2, and numerically in Table XXIX. An examination
of fig. 2 will demonstrate that the Australian, as regards his skull type, is
less highly evolved, morphologically, than is the Tasmanian. How far this
result agrees with one’s preconceived conceptions, it is difficult to say ; but
probably an extract from Nature of th$ 14th July 1910, taken from a
review of Professor Keith’s Hunterian Lectures on the Anatomy and
Relationships of the Negro and Negroid Races , best reconciles the position.
It is there stated that “ an analysis of the cranial features of the aborigines
of Tasmania and of Australia shows that we have in these two races an
early stage in the differentiation of the negro and negroid races of mankind.
The Tasmanian is the most primitive type of negro yet discovered; the
Australian, on the other hand, although deeply pigmented and less Simian
in some features than the Palaeolithic European, is the most primitive
representative of the negroid race. Negroid as he is, the native Australian
represents a stage in the evolution of the dominant non-negroids of the
northern hemisphere. It is a remarkable fact that the negro and negroid
races occur side by side, not only in Australasia, but in Asia proper and
in Africa.”

If this be the case, our results would appear to harmonise with the
views expressed in the above quotation, for our work simply shows that, as
regards his cranium at all events, the negroid Australian has not progressed
quite so far in the evolutionary scale as has the Tasmanian negro.

Are the Australians and the Tasmanians One and the

Same Pace ?

If we have interpreted the above extract from Nature correctly, it
would appear to be the opinion of the reviewer that the Australians and
the Tasmanians are, in effect, different types, if not, indeed, different races.
Sir William Turner, too, would appear to hold the same view, for, in
his “ The Craniology, Racial Affinities, and Descent of the Aborigines of
Tasmania” (11), he states : “From the consideration of these characters the
skulls support the opinion, based on the study by so many observers of
the external features, that the existing aborigines of Australia are distinct
from the Tasmanians, although the presence, in a proportion of the natives

164 Proceedings of the Royal Society of Edinburgh. [Sess,

prehistoric and recent forms of man.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 165

of South and West Australia, of skulls in which the height was less than
the breadth, the not infrequent sunk sagittal suture, the more marked
parietal eminences, and the antero-posterior parietal depressions, point to a
possible amount of intermixture and racial affinity of these Australian
tribes with the Tasmanians.”

The Breslau school of anthropologists apparently hold the directly
opposite view, for Basedow (12), a pupil of Professor Klaatsch, states that
“ the few superficial characteristics of the Tasmanian skull are not sufficient
proof of his different origin from the Australian. It appears much more
probable that in consequence of the comparatively recent separation of
Tasmania from the mainland the Tasmanians have from that time first
inherited their superficial differential characteristics.” Basedow concludes
by stating quite bluntly that the “ Tasmanian was an insular form of the
genuine Australian.” The pupil’s view is apparently held by the master,
for we find Klaatsch stating that “ the Tasmanians do not show any nearer
relationships to other races than the Australians.” He adds that the
separation of the two races probably occurred a very long time ago
Alsberg (13) would appear to agree with Klaatsch.

Between the two extreme views above quoted there appears to be an
intermediate opinion represented by Haddon, Keane, and many other
anthropologists. For the illustration of this school of thought one char-
acteristic quotation must suffice, though it would be easy to multiply
examples. Haddon (14), in his Races of Man and their Distribution ,
published in 1911, says: “It is generally believed that Australia was
originally inhabited, or at all events in parts, by Papuans or Negritoes,
who wandered on foot to the extreme south of that continent. When
Bass’ Strait was formed, those who were cut off from the mainland formed
the ancestors of the Tasmanians, who never advanced beyond an early
stage of Stone-Age culture. Later, a pre-Dravidian race migrated into
Australia, and overran the continent and absorbed the sparse aboriginal
population. Since then they have practically remained isolated from the
rest of the world. Their languages bear no relation to the Austronesian or
Oceanic linguistic family.” A somewhat similar view was advanced by
one of us in 1909 (Berry, 6).

Whether the divergent views as to the commonality of race of
Australians and Tasmanians be quoted in extenso or but briefly as above, it is
clear that all are based on either pure theory or on certain slight superficial
osteological resemblances or differences according to the opinions of
the author.

We now propose to submit this question of the community of race or other-

166

Proceedings of the Royal Society of Edinburgh. [Sess.

wise of the Australian and Tasmanian to a somewhat severe proof. Whatever
may be the result, it must be remembered that it is the first time that such
an attempt has been made on the lines of strictly severe scientific analysis ;
and further, that in submitting the question to such proof, we are now
enabled to deal with the largest numbers of Australian and Tasmanian
crania which have ever yet been employed ; and lastly, that the application
of such an analysis to what previously has been mere theory is due to the
introduction of some ingenious craniological methods by Dr Th. Mollison,
formerly of Zurich, and now of Dresden.

In 1908 Mollison published in the Zeitschrift fur Morphologie und
Anthropologie his “ Beitrag zur Kraniologie und Osteologie der Maori ” (9).
In this paper he introduced for the first time what he then termed the
“ Abweichungsindex.” The object of what in English we should term the
“ variation index ” is to discover if two skulls belong to one and the same
race or not, and the procedure adopted is as follows : —

Multiply the distance of the individual from the average value of the
standard type group by 100, and divide the product by the sum of the
extremest distance of the group on the minimum or maximum side of the
variation breadth. Thus a standard group of skulls (see fig. 3) has an
average greatest breadth value of 135, and a cephalic index average value
of 76. Another skull to be compared with this group has a greatest
breadth of 126 and a cephalic index of 64. The question to be answered
by the variation index is, Does this skull belong to the same race as the
standard group or not ? The distance of the doubtful skull from the
average value of the standard group is for the greatest breadth 9, and for
the cephalic index 12. Multiply these figures, both of which are on the
minimum range of variation side of the standard group, by 100, and divide
by the greatest range of variation of the standard group on the maximum
or minimum side as the case may be : in this case the minimum side. The
correct figures will therefore be found in the example quoted by subtract-
ing for the greatest breadth 129 from 135, and for the cephalic index 70
from 7 6. In each instance the difference is 6. If this calculation be worked
out in the manner indicated, it will be found that the variation index for
the imaginary object to be compared with the standard group is, for the
greatest breadth 150, and for the cephalic index 200.

To compare the variation indices of a large number of characteristics,
draw a straight line which shall be supposed to pass through the average
figures of each characteristic. Parallel to this draw two lines at arbitrary
distances and supposed to represent the minimum and maximum range of
variation of each observation from the average for the same; in each

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 167

instance the distance of the minimum or maximum parallel from the line
of average measurement is supposed to represent 100 per cent.

The variation index for the object to be compared is now set at its
correct distance from the average line on the plus or minus side. Connect
these several points together, and a graph is at once constructed which, if

Greatest

Breadth.

Maximum Range of Variation— 141

Average Value

—135

Minimum Range of Variation.— 129

Cephalic

Index.

83

76

70

0

100%.

Skull to be compared with

TYPE GROUP.

1. Subtract 126 from 135 =

1. Subtract 129 from 135 =

2. Subtract 64 from 76 =
2. Subtract 70 from 76 =

9 x 100
6

12 x 100
6

150.

200.

Fig. 3. — To illustrate Mollison’s Yariation Index.

it lies within the parallels, is proof that the compared stock is of the same
race as the original group. If it be outside, then the compared object and
the original group are not of the same species. A glance at the figure
referred to (fig. 3) will illustrate the whole method of working Mollison’s
variation index, and will also demonstrate the fact that the suppositious
skull to be compared with the crania of the standard group or type is of a
different race. Mollison’s original paper contains some highly instructive
examples of the working of this index. Amongst other things he was

168

Proceedings of the Royal Society of Edinburgh. [Sess.

enabled to prove that a skull in the Zurich collection alleged to be that of
a Maori was not a Maori skull, but that of an Australian aboriginal.

It must not be supposed that in adopting Mollison’s method we are
breaking new ground. His method has already been adopted by Czeka-
nowski (15) for the solution of a problem almost precisely similar to that
with which we are confronted — namely, the racial affinities of the Central
African pigmies ; by Oppenheim, in his “ Zur Typologie des Primaten-
craniums ” (16) ; and by Radlauer (17) ; and we believe that we are correct
in stating that all these authors have accepted the correctness of Mollison’s
methods and have abided by the conclusions to which that method led them.

In fig. 4 the Tasmanian is taken as the basis. The 32 morphological
observations made by us upon the cranium are indicated by the numbers
1 to 27, and the letters A to E, inclusive. The centre line in that figure
labelled “ Tasmanian average ” is supposed to represent the average values
for these 32 observational counts on the Tasmanian cranium. At an
arbitrary distance from this centre line are drawn two parallel lines which
indicate the maximum and minimum ranges of variation of the Tasmanian
from the average, and which are uniformly treated throughout as being
equal to 100 per cent. The Australian “ variation index ” is plotted in for
each of the 32 counts of the investigation, and is indicated in the figure by
the dotted line. It will be clearly evident that the Australian “ variation
index” falls altogether within the Tasmanian maximum and minimum
ranges of variation, thus proving conclusively, according to Mollison, that
Australian and Tasmanian are one and the same race.

Mollison, in the paper already referred to, speaking of his variation
index, says, “ Schon fur die Yergleichung in einem einzelnen Merkmal ist
dieses Verfahren zweckmassig. Sien voller Wert zeigt sich aber erst dann,
wenn wir eine grossere Reihe von Merkmalen vor uns haben, bezuglich
deren wir die Stellung des Individiums zu der Grupp beurteilen sollen.”

As Mollison is clearly of opinion that his method will always furnish
more accurate results if the procedure be made to include as large a number
of observations as possible, we have thought it desirable to supplement
these 32 morphological observations of the form analysis of the skull by an
additional series of craniological observations specially recorded by us on
both Australian and Tasmanian for this special purpose and which have
little or nothing to do with the form analysis of the skull.

These additional observations are 14 in number as given on page 146,
and have been specially selected by us for two reasons : firstly, because
they have nothing to do with the measurements and angles concerned in
our investigation of the form analysis of the skull ; and secondly, because

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 169

\

170 Proceedings of the Royal Society of Edinburgh. [Sess.

they are those uniformly recorded in the Osteological Catalogue of the
Royal College of Surgeons of England, and have, therefore, enabled us to
make use of any further comparative data which we desired — an oppor-
tunity of which, as will be seen later, we have availed ourselves.

It will be noticed that one measurement, and one only, is common to
the 32 form analysis counts and the 14 general craniological observations,
and that is the maximum breadth. We have, however, availed ourselves
of an increased number of Tasmanian skulls under this count from one of
our previous communications, and this fact explains the slight divergence
in the results obtained.

The total number of observations now available — namely, 46, composed

Fig. 5. — The Tasmanian Variation Index for 14 craniological observations
plotted out upon the Australian as the basis.

of the 32 form analysis counts and the 14 craniological observations — is the
largest number which has yet been employed for the working out of
Mollison’s variation index. Mollison himself only employed some 24
observations, Czekanowski about 28, Oppenheim 8, and Radlauer 20.

In fig. 5 these 14 general craniological observations are set out with
the Australian as the base. The Tasmanian variation index is plotted
out in a dotted line, and the results conform in every respect to those
already obtained by the 32 form analysis figures. In all cases the varia-
tion index falls altogether within the maximum and minimum range of
variation, thus again proving conclusively, according to Mollison’s method*
that Australian and Tasmanian are one and the same race.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 171

The Physical Relations of the Australian and Tasmanian to
the Spy-Neandertal Race.

It has repeatedly been stated that the Australian aboriginal is, in his
physical construction, so closely related to the Spy-Neandertal men as to
justify the assumption that they are of the same race, or at all events have
been derived from the same stock. Thus Klaatsch (18) says, “ The general
formation of the skull capsule and the form of the facial skeleton have
led him to the conclusion that the Australian and the Neandertal race
have many features in common as heirlooms from a common primitive
stock from which the Australian and the Neandertal race have developed
in different directions.”

von Luschan (19) probably shares this belief, for he says, “The primi-
tive qualities or characters (Eigenschaften) of the Australian show a con-
siderable amount of similarity with similar characteristics of the oldest
European man, which possibly underlies a real relationship.”

Stratz (20), in advancing his ideas for the correct racial divisions of
mankind, says that amongst the “ protomorphic ” races he regards the
modern Australian as amongst those which stand nearest to the oldest
monogenetic common primitive stock.

Schoetensack (21), in advancing his theory that man originated in
Australia, states that in Pliocene times the fauna of Australia contained
not even one single dangerous rival for the evolution of man. Many
human varieties could have developed themselves under these conditions,
and the modern Australian is even to-day extraordinarily rich in varieties ;
the closely allied form relations of the oldest European human species
(Spy-Neandertal) turns one’s thoughts towards the emigration of such a
variety.

Alsberg (13) agrees with Klaatsch as to the primitive nature of the
Australian and points to the Neandertal species as a step in the ancestral
series.

In view of the above opinions — and they could be multiplied — we thought
that it would be of some interest to apply Mollison’s variation index to the
alleged relationship of Australian and Spy-Neandertal. For this purpose
we have employed the 32 form analysis observations only, as it is obvious
that the 14 general craniological characteristics, including as they do
orbital and nasal measurements and indices, are not available for the Spy-
Neandertal group.

In fig. 6 the variation index of the three Spy-Neandertal crania is
plotted out upon our 100 Australians as a basis. A glance at the resulting

172 Proceedings of the Royal Society of Edinburgh. [Sess.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 173

graph will show that here a totally different result is produced than in the
similar graphs for Tasmanians and Australians. If Mollison’s index be a
correct guide to this question of similarity of race, it is clear that here we
are dealing with two entirely different races. The Spy-Neandertal varia-
tion index graph is seen to be highly irregular, and is by no means confined
within the maximum and minimum range of Australian variation.

This fact is still more strikingly brought out in fig. 7, where the
Tasmanian is taken as the basis, and on it are plotted out the variation
indices for the Australian and the Spy-Neandertal group. The variation
index for the Australian is seen to be very uniform and to fall altogether
within the Tasmanian range of variation, whilst that for the Spy-Nean-
dertal group is most irregular and is altogether outside the range of varia-
tion more often than within it. This figure conclusively demonstrates one
or other of two things : either that Mollison’s variation index is not a
reliable guide to the differentiation of race, or that the views quoted as to
the unity of type of Australian and Spy-Neandertal are erroneous. It
must, we think, be admitted by any fair-minded critic that one or other
of the two things must therefore, in future, be eliminated from scientific
discussion.

A closer glance at the variation index for the Spy-Neandertal race on
either the Australian or the Tasmanian (figs. 6 and 7) will show that,
notwithstanding the marked irregularity of the graph, the index occa-
sionally falls within the range of variation. In the case of both the
Australian and the Tasmanian this happens 13 times out of 32. If
Mollison’s variation index be, indeed, any reliable guide to this question
of differentiation of race, then the most we can admit for the alleged
relationship of Australian to Spy-Neandertal is that they have something
in common, but that that something is so little that the view of commonality
of race between the two must be abandoned. We agree therefore with
Schwalbe (22), wTho says, “ The Australians are certainly a primitive race,
but have nothing whatever to do with Homo primigenius”

The Relationship of Australian and Tasmanian to a Supposed
Pure Race like the Andamanese.

The next use which we propose to make of Mollison’s variation index
is to test the relationship, if any, of the Tasmanian and Australian
with a supposed homogeneous race like the Andamanese Islanders. This
will be a useful comparison, because it has been thought by some observers
that the Australians are very closely akin to these Islanders. Quite apart

174

Proceedings of the Koyal Society of Edinburgh. [Sess.

Fig. 7. — The Australian Variation Index and the Spy-Neandertal Variation Index plotted out upon the Tasmanian as the basis.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 175

from this the comparison will be of interest, inasmuch as certainly both
Tasmanians and Andamanese have long been isolated from contact with
other races.

For the purposes of this comparison we have been compelled to make
use of the 14 general craniological observations only, the reason being
that we have had no means of access to the necessary figures for the form
analysis of the Andaman Islanders skull. In fact we do not believe such
figures exist. The data that we have been able to employ are derived from
the Osteological Catalogue of the Royal College of Surgeons of England.
They comprise 19 skulls of Andamanese upon which we have utilised the
necessary figures for the 14 general craniological observations.

In fig. 8 the Andamanese Islander is utilised as the base. Upon this
are plotted out the variation indices for both Australian and Tasmanian.
The resulting graphs are again highly irregular and, according to Mollison,
are sufficient proof that the Australian-Tasmanian race is something dif-
ferent from the Andamanese Islander. A closer inspection of the graphs
will, however, show that the Australian-Tasmanian variation indices fall
within the Andamanese range of variation 7 times out of 14 — that is, in
50 per cent. If this index of Mollison tells us anything at all, it is that,
notwithstanding the difference in race, the Australian-Tasmanian race
is more nearly related to the Adamanese Islander than to the Spy-
Neandertal group.

The Relationship of Australian and Tasmanian to a Heterogeneous
Race like the Modern Italian.

The last use which we propose to make of Mollison’s variation index
is to test the racial relationships of the Australian and Tasmanian with an
admittedly heterogeneous race like the modern Italian. We have selected
the modern Italian for this comparison for three reasons : firstly, because
the modern Italian is admittedly and undoubtedly a mixed or impure race ;
secondly, because modern Italians and the indigenous inhabitants of
Australia and Tasmania cannot possibly have any racial relationships in
common ; and thirdly, because the Catalogue of the Royal College of
Surgeons of England enabled us to command a sufficiently large number
of Italian data, namely 90, to eliminate the possibility of error due to
the use of insufficient numbers.

In this comparison we have again been restricted to the 14 general
craniological observations, and for the same reasons as in the case of the
Andamanese Islanders.

176

Proceedings of the Royal Society of Edinburgh. [Sess.

1913-14.1 The Place in Nature of the Tasmanian Aboriginal. 177

o

In fig. 9 the modern Italian is utilised as the base, and upon it is plotted
out the Australian variation index. As the latter falls within the extreme
ranges of variation of the former, the graph would lead us to believe, if
Mollison’s index be indeed a reliable guide to racial affinities, that the
Australian aboriginal and the modern Italian are one and the same race —
a conclusion which, we take it, will not be credited by any anthropologist,
certainly not by ourselves.

It may well be, that, in view of this extraordinary result, some anthro-
pologists will be inclined to discredit Mollison’s index altogether and refuse
to accept it as a means of distinguishing diverse racial types. On the
other hand, there are the undoubted facts that in the hands of Mollison

Fig. 9. — The Australian Variation Index for 14 craniological observations plotted
out upon the Modern Italian as the basis.

himself, and in the work of Czekanowski, Oppenheim, Radlauer, and our-
selves it has given results which confirm the conclusions attained from other
sources and which would lead to the supposition that it is a fairly accurate
method of eliminating racial types one from the other; but the Italian-
Australian-Tasmanian comparison just instituted seems to prove conclusively
that the index is not an infallible guide and that its findings must be
regarded with a considerable amount of caution. For ourselves, for
reasons to be presently adduced, we have been led to the conclusion that
Mollison’s variation index is only a reliable guide to racial difference
provided the range of variation of one, at least, of the racial types compared
is but small. It is perfectly obvious to anyone who has worked with the
index that as the range of variation increases it gradually encroaches on

the variation index and eventually necessitates the latter falling within
VOL. xxxiv. 12

178 Proceedings of the Royal Society of Edinburgh. [Sess.

the former and thus gives rise to the reductio ad absurdum results of our
modern Italians, Australians, and Tasmanians.

The Range of Variation.

We now propose to consider the very important question of the range
of variation in the Australian, Tasmanian, and the other homogeneous and
heterogeneous races selected by us for comparison, in order to see what light
such a study throws on the vexed question of the purity of origin or
otherwise of the Australian aboriginal.

Almost every author who has investigated Australian osteology has
been impressed with the great range of variability displayed by his results.
Thus Klaatsch (23) says that the study of the variability of the Australian
is of the greatest significance. Wetzel (24), from his researches as to the
amount of variation in the vertebral column of the Australian, came to the
conclusion that the total amount of variation in the osseous vertebrate
column of the Australian is considerably greater than in the European, but
that, on the other hand, the variation in individual sections is less in the
Australian than in the European, and that females are the least variable.
Stratz (20), in advancing his theory of the racial division of mankind, states
that the protomorphic races — especially the Australians — are characterised
by great individual variability. Schoetensack (21) also states that the
modern Australian is even to-day extraordinarily rich in varieties. It is
unnecessary to multiply examples of the current belief that the Australian
is extraordinarily rich in his range of variation, because, as will now be
shown, our investigations confirm this view.

Of the Tasmanian there are necessarily fewer opinions, for the sufficient
reason that he was extinct before it was realised how important this study
of the range of variability is. In discussing, therefore, the range of varia-
tion exhibited by the Tasmanian we are practically breaking new ground,
apart, of course, from the generally accepted belief that as a homogeneous
race the Tasmanian would tend to display a less extended range of varia-
tion than in undoubted heterogeneous races.

Comparison of the Range of Variation in Supposed Pure Races
like the Andamanese and Tasmanians with an Admitted
Heterogeneous Race like the Modern Italian, with the object
of Establishing the Place of the Doubtful Australian.

In order to appraise the amount of variation in the pure, mixed, and
doubtful races selected for the comparison now to be established, we have

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 179

selected the Tasmanian as the basis. In fig. 10 the maximum and minimum
range of variation of this race is represented by two horizontal lines which
are supposed to pass through the extremes of variation uniformly regarded
as being equal to 100 per cent. If, for example, the average maximum
breadth of a series of Tasmanian skulls be found to be 135 with a minimum
breadth of 120, the range of variation on the minimum side would be 15.
If now the average maximum breadth of a series of Australian crania be

o

found to be 131 with a minimum of 120, the range of variation would be
11 and the relative values of the Tasmanian and Australian ranges of
variation would be expressed by the formula as 15 (Tasmanian) is to 100
so is 11 (Australian) to the answer, namely 73 in round numbers. As the
data from which our fig. 10 is compiled include other skulls besides those
specifically dealt with here and taken as stated from the Royal College of
Surgeons Catalogue, we can only indicate generally the process by which
the results are attained. We may, however, add that the very greatest
care has been taken in the calculations, which have been made throughout
by mechanical appliances.

The most cursory glance at the graph shows that the range of variation
is in the Australian greater than in the Tasmanian. It further shows
that certain individual Australians are at a much lower position in the
evolutionary scale than are the most lowly of the Tasmanians ; that certain
individual Australians have, on the other hand, attained a higher position
than have the most highly evolved Tasmanians ; whilst lastly, the applica-
tion of Cross’s formula demonstrates that the average Australian remains
at a slightly lower level in the evolutionary scale than does the average
Tasmanian.

Concerning the Andamanese the same graph, fig. 10, demonstrates
that, as judged by the range of variation, the Andamanese are an even
purer race than are the Tasmanians, but that, with one or two exceptions,
the most advanced Andamanese has not attained so high a position in the
evolutionary scale as have either the Tasmanian or the Australian.

Regarding the primary object of the graph, it will be evident that the
Australian, in his maximum and minimum ranges of variation, is more
closely related to the admittedly mixed race — the Italian — than to the two
supposed pure races. To test the point still further, we have submitted the
range of variation in all the compared races to a numerical proof. The
race taken as the basis, the Tasmanian, is regarded as possessing an amount
of variation equal to 100 per cent. The variations of the other races are
calculated therefrom in percentages, added together and divided by the
number of observations — 14. As both the maximum and minimum series

180

Proceedings of the Royal Society of Edinburgh. [Sess.

Australian

Modern Italian

TAfMMlAN (SAX^UM
10M

Andamanese

TA&MANiAJN MINIMUM

RANGE OF VARIATION

ZBqL

Fig. 10. — The Ranges of Variation of the Australian, Modern Italian, and Andamanese for 14
general craniological observations plotted out upon the Tasmanian as the basis, and expressed
in percentages of the latter.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 181

have to be taken into consideration, the divisor is naturally twice 14. The
results are as follows : —

Supposed homogeneous races —
Andamanese .
Tasmanians

Admitted heterogeneous race —
Modern Italians
Race of doubtful origin —
Australians

62*7 per cent.
1000 „

130 per cent.

141*9 per cent.

Summary of the Observed Facts.

In view of the complicity of the problem now under consideration, it
would seem advisable here to recapitulate the new facts brought out in the
present paper before we pass to their interpretation.

1. The present work contains the detailed measurements of 32 form
analysis measurements of 100 Australian aboriginal crania not previously
examined. The measurements so recorded are those introduced by Schwalbe
and Klaatsch, and have been previously utilised by us for some 52 Tasmanian
crania.

2. The present work also incorporates, but does not give the detailed
measurements of, 14 observations of a general craniological character, but
more particularly on the face, of the above-mentioned 100 Australian and
52 Tasmanian crania.

3. For purposes of comparison the corresponding series of measurements,
wherever available, have been worked out from other sources for 3 Spy-
Neandertal crania, 19 Andamanese Islanders, and 90 modern Italians.

4. The data resulting have been utilised in order to see what evidence
they afford as to the purity of stock or otherwise of the Australian ; hence
the races selected for comparison have been specially chosen as representa-
tives of either admittedly pure races or of equally undoubted impure races.

5. The use of Mollison’s variation index shows that Tasmanians and
Australians are a common stock, and that both these races are very much
more closely related to each other than they are to either Spy-Neandertal
or Andamanese.

6. Mollison’s index is shown to be an unreliable guide to the differentia-
tion of race once the range of variation in one or both of the compared
stocks exceeds a certain limit. What this limit is requires further proof,
but is certainly exceeded by Australians and modern Italians. A study of
the range of variation shows that the Australian agrees much more closely

182 Proceedings of the Royal Society of Edinburgh. [Sess.

with an admittedly impure race like the modern Italian than with supposed
pure stocks like the Andamanese or the Tasmanians.

7. A study of the mean values of all the observations recorded as shown
by Cross’s method of dealing with such calculations proves that the average
Australian is not such a highly evolved type as was the average Tasmanian.

Interpretation of the Facts.

Biasutti (25), in a recently published paper the original of which is not,
unfortunately, available to us in Melbourne, has apparently devoted some
attention to Tasmanian and Australian literature, and assumes therefrom
that the Tasmanian is the older of the two types, was developed on the
Australian mainland, and migrated thence to Tasmania. The Australian
race has been developed from this primitive type and has preserved itself
as a mixture, and by insular isolation.

It is impossible for us, under the circumstances, to say whether Biasutti
regards his theory as either new or original ; but it is hardly necessary to
add that it is neither one nor the other, and we only notice the work at all
for the simple reason that its author revives the opinion that the Australian
aboriginal is a mixed type resulting from a cross, presumably with the
older and more primitive Tasmanian type ; and this, be it noted, is the only
theory which fits the facts adduced in this, and our other papers, as also
certain other well-known ethnological, cultural, and linguistic data.

Professor Sergi of Rome has recently published a most important mono-
graph on the racial affinities of the Tasmanian and Australian, under the
title “ Tasmanier und Australier ( Hesperanthropus tasmanianus spec.) ”
(26). We consider ourselves indeed fortunate that the amount of detailed
work in our present paper has so far delayed publication as to enable
Professor Sergi to be first in the field, and this for reasons which will shortly
be apparent.

In this work Sergi has availed himself of the Tasmanian material
recently made available by us in our “ Dioptrographic Tracings in Four
Normae of Tasmanian Crania ” (5), as also of certain crania in Cambridge
and elsewhere, and of the recent valuable contributions of Turner (11) and
others. Of our own work Sergi states that he prefers to use the skull
tracings delineated in the publication just referred to, because they are
exact dioptrographic outlines in four normae of the skulls recorded, and
adds that when a sufficient number of crania are so studied, their outlines
can easily replace direct observation on the skulls themselves.

From a study of these crania Sergi deduces the fact that they are

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 1 83

lophocephalic, as are also many Australian crania. He states, therefore,
that lophocephaly is an absolutely characteristic feature of a certain type of
skull widely spread throughout the islands of the Pacific Ocean and which
he recognises as the Tasmanian-Australian skull type. The geographical
distribution of the lophocephalic Tasmanian-Australian skull is given by
Sergi as extending from the Hawaii Islands in the north to New Zealand
in the south, and from Australia in the west to Easter Island in the east,
all inclusive. For the primeval home of this skull type Sergi, for reasons
with which we are not especially concerned, but which seem sound, instances
the American continent. For the primitive parent of this skull type he
further proposes the name Homo tasmanianus, and adds that, whilst it is
difficult to state exactly when he wandered into the Pacific Ocean from
America, it is not improbable that the migration took place in late Pliocene
or early Quaternary times and that he took with him no domestic animals
of any kind. Homo tasmanianus wandered over the Australian continent
into Tasmania, and, becoming isolated there, eventually developed into the
Tasmanian aboriginal of recent times, and for him Sergi proposes the name
Hesperanthropus tasmanianus spec.

The many difficulties attending the Australian aboriginal are solved,
says Sergi, by assuming that on the Australian continent there subsequently
entered a Polynesian element, and in Sergi’s own words : “ die Kreuzung
der Polynesier mit den urspriinglichen Australieneinwohnern tasmanischen
Urspriings erzeugte eine Bastardvarietat, welche die heutigen Australier
sind . . . die Australier hy bride Tasmanier waren.” For us this quotation
is of such vital import that we may, perhaps, be pardoned for translating it
as follows : —

“ The crossing of the Polynesian with the original inhabitants of
Australia of Tasmanian origin begot a bastard variety — the Australian
aboriginal of to-day . . . the Australian aboriginal is a hybrid Tasmanian.”

For the hybrid Australian Sergi proposes the name Hesperanthropus
tasmanianus polynesianus, var. hybrida.

The thesis here briefly set forth Sergi ably supports by many facts and
different lines of evidence. With these lines of evidence we are not here
specially concerned, nor are we vitally interested at the moment with the
Polynesian character of the cross assumed by the distinguished Italian
anthropologist. For ourselves we should have assumed an earlier cross
than that emanating from the Polynesian element. This, however, is a
minor point contrasted with the more important fact that Sergi, working
by different methods and with additional material from other sources, comes
to precisely the same results as ourselves — namely, commonality of origin

184 Proceedings of the Royal Society of Edinburgh. [Sess.

and race of Tasmanians and Australians with the latter subsequently
resulting from a racial cross with the primitive stock.

To Sergi’s theory, based, be it remembered, on facts which he has firmly
established, let us now apply our own results.

Commonality of origin of Australians and Tasmanians is shown in the
present work by the results of Mollison’s variation index for Australian and
Tasmanian. On no other grounds can the remarkably uniform results
attained by us with this index be explained. Read in conjunction with
Sergi’s study of lophocephaly we regard Homo tasmanianus as proved.

That the Tasmanian aboriginal was as nearly as possible the pure
descendant of Homo tasmanianus we regard as certain on account of (1)
the results attained by Sergi himself; (2) the remarkably small range of
variation found in the Tasmanian for the observations of the present work •
(3) the equally small amount of variation recorded by Buchner (27) in his
recent works on Tasmanian prognathism, craniotrigonometry, and curvature
indices ; and (4) the close approach to unity for the coefficients of correlation
already recorded by us in our biometrical study of the Tasmanian (2). It
is thus clear that the morphological studies of Sergi, the craniological
researches of Buchner and ourselves, and the biometrical work of Dr Cross
and ourselves all alike testify to the purity of type of the Tasmanian and
the truth of Sergi’s hypothesis.

That the Australian aboriginal is a hybrid is, we believe, proved by (1)
the results recently recorded by Sergi ; (2) the study in the range of
variation adduced in the present work — a study which clearly proves that
the Australian is more variable than an admittedly crossed race like the
modern Italian ; (3) our own previously recorded study in the Australian
coefficients of correlation ; and (4) Broca’s statement, quoted by Topinard
(28), that it is only when the variations reach 15 or 18 per cent, that we
can say with certainty that they are due to mixture of race. In the
present work the Australian range of variation has been proved to be
40 per cent, more than in the Tasmanian.

If it be argued that we deduce too much from this range of variation —
a study as yet largely in its infancy as regards the precise meaning to be
attached to it — we reply in the words of Cossar Ewart, than whom there
is no greater living authority on the subject of variation by crossing of
types (29) : —

“ Domestic animals reproduce themselves with great uniformity if kept
apart ; but the moment one mixed up two different races, strains, or breeds,
one did something that was difficult to put in words, but the result was
what has been best described as an epidemic of variations.”

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 185

Were we to interpolate in the above quotation the words “such as
Homo tasmanianus and another primitive stock ” after the words “ strains
or breeds,” and add at the end “ resulting in the Australian aboriginal,” it
might stand as a perfect exposition of our views on the hybrid ity of the
Australian.

The hybrid character of the Australian is still further supported by
Lapicque (30), Baudouin (30), and Kruger-Kelmar (31), and by such well-
known ethnological facts as the use of the boomerang and throwing-stick
in Australia and their absence in Tasmania ; the presence of a domesticated
animal, the dingo, in Australia and its complete absence in Tasmania ; and
the more evolved cultural character of the Australian flints as opposed to
the more primitive Tasmanian type of instrument. The total absence of
domesticated animals amongst the Tasmanians is further proof of their
great antiquity.

The study of language, too, indicates — some would say proves — the
hybrid character of the Australian. No physical anthropologist would
rely solely on linguistics as a proof of origin of race. Taken, however,
in conjunction with somatology and ethnology, it is a valuable line of
research. Mathew (32) has pretty well established the hybrid element
in the Australian aboriginal, and here we find physical anthropology,
range of variations, ethnology, and linguistics all alike pointing distinctly
to the impurity of stock of the Australian.

But what of the other side ? So far as our study of the literature
enables us to judge, there are only some — to use his own word —
“ superficial ” observations of Klaatsch, various unsupported theories of
Schoetensack, Stratz, and others, the recent work of Basedow, and the
difficulties — prior to the publication of this and the recently issued
memoirs of Turner and Sergi — experienced by all in adequately explaining
the position of the Australian. Basedow, it is true, boldly declared the
Tasmanian to be but an insular type of Australian ; but as von Luschan
(33) has dealt pretty trenchantly with this observer, we need not further
consider him. There is nothing whatsoever in the environment, climate,
animal or plant food of Australia and Tasmania, to account for the
differences in types of Australians and Tasmanians, and for the enormous
range of variation of the former. As regards the last-mentioned point,
it is indeed rather the reverse. Dr Cherry, Professor of Agriculture in
this University, assures us, as the results of his own observations and
experiments, that the soil of the Australian continent is peculiarly deficient
in phosphorus and that, relative to the soils of the European and other
continents, those of Australia are in a miocene or pliocene condition.

186 Proceedings of the Royal Society of Edinburgh. [Sess.

Sofer (34), too, distinctly states that external influences do not affect
races, whilst Doncaster (35) stresses heredity rather than environment.
Here, then, is nothing to account for the excessive range of variation of
the Australian as compared with the Tasmanian, and we are thrown back
on the hypothesis already furnished — namely, hybridity, and the explana-
tion of same as given by Ewart.

From a study of the question in all its phases we are, therefore, forced
to the conclusion that the Australian is a hybrid.

One other interesting fact results from our study of the hybridity
of the Australian aboriginal as deduced from his range of variation, and
that is that the result of the cross has not benefited the race from the
evolutionary standpoint. The modern-day Australian aboriginal stands
rather nearer the anthropoid ape, or the common ancestor, than did the
Tasmanian. Isolated individuals of the Australian race have, on the
other hand, surpassed the Tasmanian. These facts are evidenced in the
present work by the application of Cross’s formula to all the evolutionary
objects under comparison and by the study of maximum and minimum
ranges of variation for Australian and Tasmanian.

Results.

In conclusion we may say that, as a result of our prolonged study
of Australian and Tasmanian craniology — a study which has now occupied
us over five years and is still in progress, — we are led to the following
conclusions : —

1. The Australians and Tasmanians are the descendants of a common
late Pliocene or early Quaternary stock which, for want of a better term,
may be called with Sergi, Homo tasmanianus. H. tasmanianus had a
wide range of distribution within the the islands of the Pacific Ocean
(Sergi).

2. The Tasmanian aboriginal was the almost unchanged offspring of
this type, but evolved on his own lines and in his own way.

3. The Australian aboriginal is the result of a cross between the
primitive Homo tasmanianus and some other unknown race — Polynesian,
according to Sergi; Dra vidian, according to Mathew — and is, therefore,
a hybrid. From the evolutionary standpoint the result of the cross,
whilst it has not been favourable to the race as a whole, has benefited
individual members of it. Once evolved, the Australian has, like the
Tasmanian, progressed on his own lines and in his own way.

4. Both Australian and Tasmanian have attained, morphologically,
to a higher stage in the evolutionary scale than is usually supposed.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 187

5. Neither Australian nor Tasmanian have any direct relationship
with Homo primigenius as represented by the crania of the Spy-
Neandertal men. The superficial points of cranial resemblance are
explicable solely on the grounds of the remoteness of the ancestry. In
the Spy-Neandertal crania we see them as they were ; in the modern
Australian-Tasmanian type as they have evolved.

6. The range of variability of structure is, in the Australian, as great
as in any other known race of impure origin ; in the Tasmanian, on
the other hand, it is as small as in any other known or supposed
pure race.

7. Mollison’s variation index as a test of type must be read in
conjunction with the range of variation.

LITERATURE.

(1) Robertson, A. W. D., “ Craniological Observations on the Lengths, Breadths,
and Heights of a Hundred Australian Aboriginal Crania,” Proc. Roy . Soc. Edin.,
vol. xxxi., 1910-11, pp. 1-16.

(2) Berry, R. J. A., A. W. D. Robertson, and K. S. Cross, “ A Biometrical
Study of the Relative Degree of Purity of Race of the Tasmanian, Australian, and
Papuan,” Proc. Roy. Soc. Edin ., vol. xxxi., 1910-11, pp. 17-40.

(3) Berry, R. J. A., and A. W. D. Robertson, “ The Place in Nature of the
Tasmanian Aboriginal as deduced from a Study of his Calvaria ; Part i., His
Relations to the Anthropoid Apes, etc.” Proc. Roy. Soc. Edin., vol. xxxi., 1910-11,
pp. 41-69.

(4) Cross, K. S., “On a Numerical Determination of the Relative Positions of
certain Biological Types in the Evolutionary Scale, and of the Relative Values of
various Cranial Measurements and Indices as Criteria,” Proc. Roy. Soc. Edin., vol.
xxxi., 1910-11, pp. 70-84.

(5) Berry, R. J. A., and A. W. D. Robertson, “ Dioptrographic Tracings in
Eour Normse of Fifty-two Tasmanian Crania,” Trans. Roy. Soc. Viet., vol. v. pt. i.,

1910.

(6) Berry, R. J. A., “ A Living Descendant of an Extinct (Tasmanian) Race,”
Proc . Roy. Soc. Viet., vol. xx., N.S., 1907.

(7) Klaatsch, H., “The Skull of the Australian Aboriginal,” Reports from
Path. Lab. of Lunacy Dept., N.S.W., vol. i., pt. iii., 1908, pp. 43-167.

(8) Frederic, J., “ Das Schadelfragment von Stangenas in Schweden,” Zeit. f.
Morph, u. Antlirop., vol. xi., 1908, p. 317.

(9) Mollison, Th., “Beitrag zur Kraniologie und Osteologie der Maori,” Zeit. f.
Moyph. u. Anthrop., vol. xi., 1908, p. 529.

(10) Turner, Sir William, “The General Characters of the Crania of the
People of Scotland,” Journ. Anat. and Phys., vol. xxxvii., 1903, pp. 392-408.

188

Proceedings of the Royal Society of Edinburgh. [Sess.

(11) Turner, Sir William, “The Craniology, Racial Affinities, and Descent of
the Aborigines of Tasmania,” and “ The Aborigines of Tasmania,” Trans. Roy. Soc.
Edin ., vol. xlvi., 1908, and vol. xlvii., 1910.

(12) Basedow, H., “Der Tasmanierschadel, ein Insulartypus,” Zeit. f. Ethnol .,
vol. xlii., 1910.

(13) Alsberg, C. L., “Keuere Probleme der menschlichen Stammesentwicklung,”
Arch. Rassen- u. Ges.-Biol. , Band iii., p. 28.

(14) Haddon, A. C., Races of Man and their Distribution , Miller & Co.,
London, 1912.

(15) Czekanowski, H., “ Yer wandschaf tsbeziehungen der zentralafrikanischen
Pygmaen,” Korr.-Blatt. d. deutsch. Gesell. Anthrop ., Ethnol. u. Urgeschichte, vol. xlii.,
1910, p. 101.

(16) Oppenheim, S., “Zur Typologie des Primatencraniums,” Zeit. /. Morph, u .
Anthrop., vol. xiv., 1911, pp. 1-204.

(17) Radlauer, C., “Beitrage zur Anthropologie des Kreuzbeines,” Gegenbaur’s
morph. Jahrbuch , Band xxxviii., 1908, pp. 322-447.

(18) Klaatsch, “Das Gesichtsskelett der Neandertalrasse und der Australier,”'
Verb. anat. Ges., 22. Vers., Berlin, 1908, pp. 223-273.

(19) von Luschan, “ Keuhollandische Typen,” Korr.-Blatt. d. deutsch. Gesell.
Anthrop ., Ethnol. u. Urgeschichte , vol. xl., 1909.

(20) Stratz, C. H., “Das Problem der Rasseneinteilung der Menschheit,”
Arch.f. Anthropoid vol. xxix., 1903, p. 189.

(21) Schoetensack, O., “Die Bedeutung Australiens fiir die Heranbildung
des Menschen aus einer niederen Form,” Zeit. f. Ethnol ., Jahrg. xxxiii., 1 901 ,
p. 127.

(22) Schwalbe, G., “ Uber das Schadelfragment von Briix und seine Bedeutung
fiir die Urgeschichte des Menschen,” Verhand. des anthrop. Congr. zu Salzburg ,
August 1905.

(23) Klaatsch, H., “Ergebnisse meiner australischen Reise,” Korr.-Blatt. d .
deutsch. Gesell. Anthrop ., Ethnol. u. Urgeschichte , vol. xxxviii., 1907.

(24) Wetzel, G., “Die Wirbelsaule der Australier. Erste Mitteilung : Das
Volumen der knochernen Wirbelsaule und ihre Abschnitte,” Zeit. f. Morph, u.
Anthrop., vol. xii., 1909.

(25) Biasutti, R., “ I Tasmaniani come forma d’ Isolamento Geografico,” Arch.
V Antropol., vol. xl. p. 108.

(26) Sergi, G., “ Tasmanier und Australier. ( Hesperanthropus tasmanianus,
spec .),” Archiv f. Anthrop., Neue Folge, Band xi., 1912, p. 201.

(27) Buchner, L. W. G., “ An Investigation of Fifty-two Tasmanian Crania by
Klaatsch’s Craniotrigonometrical Methods,” and “A Study of the Prognathism of
the Tasmanian Aboriginal,” Proc. Roy. Soc. Viet., vol. xxv., 1912 ; also the “Curva-
ture Indices of the Tasmanian Aboriginal Cranium,” ready for publication.

(28) Topinard, P., Anthropology, Chapman & Hall, London, 1890.

(29) Ewart, J. Cossar, “Discussion on Heredity in Disease,” Scot. Med. and
Surg. Journ., vol. vi., 1900, p. 308.

(30) Lapicque and Baudouin, Discussion on Zaborowki’s “ Metis d’Australien
et d’ Anglais,” Bull. Soc. d’ Anthrop., 5th series, vol. viii. p. 384.

1913-14.] The Place in Nature of the Tasmanian Aboriginal. 189

(31) Kruger-Kelmar, P., Beitrdge zur vergleichenden Ethnologie und Anthro-
pologie der Neuhollander, Polynesier und Melanesier , Inaug. Diss. Gottingen, 1905.

(32) Mathew, Eaglehawk and Grow , David Nntt, London, 1899.

(33) von Luschan, “ Zur Stellung der Tasmanier in anthropologischen System,”
Zeit.f . Ethnol., Jahrg. xliii., 1911, p. 287.

(34) Sofer, L., “ Uber die Plastizitat der menschlichen Passe,” Arch. Rassen- u.
Ges.-Biol., Jahrg. v., p. 660.

(35) Doncaster, Heredity , Cambridge University Press, 1911.

{Issued separately April 29, 1914.)

190 Proceedings of the Royal Society of Edinburgh. [Sess.

XIII. — A Chemical Examination of the Organic Matter in Oil-
Shales. By John B. Robertson, M.A., B.Sc., Carnegie Scholar.
Communicated by Dr J. S. Flett, F.R.S.

(MS. received February 28, 1914. Read March 16, 1914.)

Historical.

Investigations into the nature of the organic matter in oil-shales began
at the time of the famous Torbanehill case in 1854, when experts attempted
to settle the question as to whether the substance known as “ Torbanite ”
or “ Boghead Mineral ” was a coal or an oil-shale. Several witnesses at the
trial (Gillespie v. Russel, Session Papers , 1854) maintained that the oil-
producing material in the Mineral was of organic origin, while others
pronounced it to be bituminous and produced by subaqueous eruptions.
T. S. Traill, M.D., proposed for the Boghead Mineral the name “ Bitumenite,”
as it seemed to him to “ consist of much bitumen, mingled with earthy
matter” {Trans. Roy. Soc. Edin., 1857, xxi. p. 7). Dr Redfern (Quart.
Journ. Micros. Soc., 1855, x. pp. 118-119), on the other hand, supposed the
round orange-yellow bodies which occur in torbanite to have had their origin
in “ a mass of vegetable cells and tissues which have been disintegrated and
otherwise changed by maceration, pressure, and chemical action, and
subsequently solidified.” C. E. Bertrand and B. Renault (Bull. Soc. Hist.
Nat. Autun, 1892-3) on microscopic examination have classed these bodies
as the remains of gelatinous algae which have been altered by bacterial
action. They ascribe the genus “ Pila ” to those occurring in the northern
and “Reinschia” to those found in the southern hemisphere, class the
bacteria as “ micrococci,” and represent the transformation of the vegetable
matter by the equation

C12H20Oio = 2C2H3 + 5C02 + 3CH4 + 2H.

This equation is purely empirical, although no doubt carbon dioxide,
methane, and hydrogen are products of bacterial action upon organic matter.
Recently this view has been disputed by E. C. Jeffrey (Rhodora, vol. xi.
p. 61), who has subjected bogheads to a chemical treatment with nitric
and hydrofluoric acids before making sections, and has affirmed that
“ the so-called algae ” are in reality “ the strongly sculptured megaspores
of vascular cryptogams.” Dr W. Scheithauer (Oil-Shales and Tars, 1913)

191

1913-14.] The Organic Matter in Oil- Shales.

expresses the opinion that the remains of dead animals form part of the
organic material. This view is discussed later.

Lastly, J. Schuster (. Neues Jahrbuch f Mineralogie, 1912, Bd. ii. p. 33)
objects to the algal theory, and states that the yellow bodies are in some
cases concretions of resin, and in others spherulites of silica, calcspar, or
siderite.

Little chemical work has been done on the subject beyond a few
ultimate analyses for purposes of the above-mentioned trial. D. R. Steuart
(' Oil-Shales of the Lothians, 1912, p. 164) prepared artificial shale from
lycopodium dust and Florida fuller’s earth, and obtained from it on distilla-
tion oil and ammonia in quantities similar to those obtained from torbanite.
He also pointed out that there is very little in torbanite or in ordinary oil-
shales which can be extracted by petroleum spirit, benzene, carbon di-
sulphide, or ether, and that therefore the substance cannot be of the nature
of petroleum, bitumen, or resin.

Experimental.

In order to determine whether the organic matter varied in composition,
and, if so, what was the nature and extent of the variation, ultimate analyses
were made of thirteen samples of oil -shales. The methods of analysis used
were the same as those employed by Strahan and Pollard in their analyses
of coals ( The Coals of South Wales, 1908, p. 6), except in the case of
carbon and hydrogen determinations, where Walker and Blackadder’s
modification of the Dennstedt combustion furnace was used. The samples
were powdered in an agate mortar until sufficiently fine to pass through a
90-mesh sieve, then dried in a toluene-bath at 105°-107° C. for an hour.
No boat was used in the combustions, the powdered shale being mixed with
the copper oxide. The ash was determined separately by igniting the shale
in a muffle at bright red heat.

The Kjeldahl method was employed for the nitrogen estimations, a gram
of shale being used for each determination. The sulphur was estimated
by heating one gram of the shale with five grams of sodium carbonate in
a muffle till all the carbon was burned, digesting with warm water, filtering,
acidifying the filtrate with hydrochloric acid (after the addition of 10 c.c.
bromine solution to secure complete oxidation), and precipitating the
sulphate formed with barium chloride.

It was found that a slight correction was necessary in the hydrogen and
ash determinations, there being present in the shales hydrous minerals from
which the water was not expelled at 105° C. The amount of this water
was estimated by heating a weighed quantity of the shale to a temperature

192 Proceedings of the Royal Society of Edinburgh. [Sess.

between 200° and 250° C. in a current of dry nitrogen, and collecting the
water evolved in a calcium chloride tube. Little or no oil was given off
at this temperature, but to secure that none was retained in the calcium
chloride tube a current of dry air was passed through it for twenty minutes
after each experiment. In a distillation of torbanite under a pressure of
1 mm., no perceptible quantity of oil was produced until a temperature of
380° C. had been attained by means of an electric furnace. The correction
thus applied in no case exceeded 0T5 deduction from the hydrogen per-
centage, or L35 addition to the ash percentage. The detailed analyses are
given below along with the works’ yield of oil and ammonium sulphate
where these are known. The samples of Dunnet shale are from a bore at
Broxburn, each one representing one foot of the seam in vertical thickness
from the top downwards. The last two analyses are those of specimens of
“ burnt ” shales occupying the positions of the “ Maybrick ” and “ Curly ”
seams of the Pumpherston shales in a bore at Knightsbridge, and described
by R. G. Carruthers ( Oil-Shales of the Lothians, 1912, p. 88). He puts
forward the theory that these shales have been “ burnt ” or rendered useless
not through the proximity of any igneous rock, but through the oil having
been distilled off from them by the heat evolved from the oxidation of
pyrites dust in the underlying tuff beds.

The relatively high percentage of oxygen in sample 12 might be con-
sidered to lend support to this theory, but this is somewhat negatived by
the much lower oxygen percentage in sample 13. The high nitrogen
percentages in each show, however, that whatever changes the shale has
undergone, the nitrogenous matter has heen the last to be affected.

List of Shales Analysed.

1. Dunnet — Top foot (Broxburn).

2. ,, 2nd „

3. „ 3rd „

4. ,, 4th

5. „ 5th „

6. „ 6th „

7. Camps — Flat portion (Pumpherston).

8. Camps — Inclined portion (Pumpherston).

9. Broxburn (Pumpherston).

10. Torbanite (Armadale).

11. Australian Commonwealth.

12. “ Burnt ” Shale — “ Maybrick ” (Knightsbridge).

13. “ Burnt ” Shale — “ Curly ” (Knightsbridge).

1913-14.] The Organic Matter in Oil-Shales.

193

Data of Analyses.

I. — Determination op Carbon and Hydrogen.

No. of
Shale.

Weight

taken.

C02

found.

H20

found.

Carbon
per cent.

Hydrogen
per cent.

Carbon
per cent.
(Average.)

Hydrogen
per cent.
(Average.)

1 (a)

•6309

•2347

•0924

10-15

1-63

(b)

•5657

•2134

•0838

10-29

1-65

10*22

1-64

2 (a)

•6226

•2869

•0953

12-57

1-70

(b)

•4704

•0720

1-70

(c)

•4052

•1873

•0643

12-61

1-76

12-59

1-72

3 (a)

•3415

•2024

•0689

16-16

2-24

(b)

•3374

•1983

•0681

16-03

2-24

16-09

2‘24

4(a)

•2938

•1999

•0660

18-52

2-50

(b)

•3521

•0786

2-48

(c)

•3303

•2233

•0729

18-44

2-45

18*48

2-48

5 (a)

•3386

•2422

•0769

19-51

2-52

(b)

•3208

•2264

•0750

19-25

2-60

(c)

•3464

•2512

•0780

19-77

2-50

19-51

2-54

6 (a)

•5936

•3546

•1171

16-29

2-19

(b)

•3781

•0781

2-30

(c)

•3575

•0744

2-31

(d)

•3590

•2165

•0729

16**44

2;26

16-36

2-26

7 (a)

•2450

•1979

2203

(b)

•2474

•1986

•0653

21-90

2-93

21-96

2-93

8 (a)

•3558

•1318

•0567

10-10

1-77

(b)

•4118

•1534

•0655

10-16

1-77

10*13

1*77

9 (a)

•3694

•3382

•1260

24-97

3-79

(b)

•2831

■2576

•0967

24-80

3-79

24-88

379

10 (a)

•1160

•2780

•0861

65-34

8-25

(b)

•1181

•2864

66-13

(c)

•1016

•2447

65-69

(d)

•0970

•0735

8-42

(«)

•0988

•0746

8-39

65-72

8-35

11 (a)

0885

•0626

7-86

(b)

•0900

•2093

63-60

(o)

•0851

•0601

7-85

i (d)

•0856

•1994

63-56

63-58

7-86

12 (a)

•5025

•1085

•0451

5-89

Too

(b)

•9977

•2193

•0843

5-99

0-94

(c)

•5985

•1333

•0525

6-07

0-97

5-98

0-97

13 (a)

•8383

•2459

■0921

8-00

1-22

(b)

•6971

•2123

•0830

8-30

1-32

8-15

1-27

YOL. XXXIY.

13

194

Proceedings of the Royal Society of Edinburgh.

II. — Determination of Nitrogen.

No. of Shale.

Weight

taken.

Nitrogen

found.

Nitrogen
per cent.

Nitrogen
per cent.
(Average.)

1(a)

•9984

•004766

0*48

w

1*0008

•005057

0-51

0*49

2 (a)

1-0025

•005538

0-55

(b)

*9969

•005104

0-51

0-53

3(a)

1-0046

•006161

0 61

• (6)

•9999

005989

0-60

0*61

4 (a)

•9976

•006810

0-68

(b)

1-0015

•006569

0-66

0*67

5 (a)

1-0019

•006746

0-67

W

1-0020

•007100

0-71

0-69

6(a)

1-0017

•005925

0-59

(6)

1-0020

•006166

0-62

0-60

7(a)

1-0031

•006182

0-62

(&)

1-0033

•006907

069

0*65

8 (a)

1-0011

•005361

0-54

(6)

•9971

•005313

0-53

0*53

9(a)

•9971

•006585

0-66

(b)

•7123

•005071

0-71

0*68

10 (a)

•9985

•006311

0-63

• • •

(6)

1-0039

•006327

0-63

0-63

11(a)

•9984

•007986

0-80

. . .

(b)

1-0009

•008147

0-81

0-81

12 (a)

1-0004

•007736

0-77

• . .

W

•9946

•007223

0-73

0-75

13

1-0001

•01233

1-23

III. — Determination of Sulphur.

No. of Shale.

Weight

taken.

Barium

Sulphate

found.

Sulphur
per cent.

Sulphur
per cent.
(Average.)

1 (a)

•997

•0682

0-94

...

(b)

1-005

•0659

0-90

0-92

2 (a)

1-004

•0871

1-19

(b)

•998

•0860

1-18

lib

3(a)

1-005

•1277

1-75

(b)

1-005

•1262

1-73

1-74

4(a)

1-003

•0953

1-31

(b)

1-003

•0953

1-31

1*31

5 (a)

1-006

•0992

1-36

(b)

1-006

•0990

1-36

1*3*6

6(a)

•998

•1982

2-73

(6)

1-000

•1970

2-71

2*72

7(a)

•998

•0914

1-26

(b)

•997

•0912

1-26

1-26

8 (a)

1-002

•0382

0-52

<b)

1-004

•0395

0-54

0-53

9 (a)

1-005

•0589

0-81

(b)

1-004

•0583

0-80

0*80

10 (a)

1-004

•0196

0-27

(b)

•999

•0213

0-29

0*28

11 (a)

1-002

•0285

0-39

(b)

•997

•0336

0-46

0-43

12 (a)

•997

•0511

0-70

(b)

1-002

•0483

0-66

0*68

13

1-002

•1716

2*35

[Sess.

1913-14.] The Organic Matter in Oil-Shales.

195

IV. — Determination of Ash.

No. of Shale.

Weight

taken.

I

Ash.

Ash

per cent.

1

Ash

per cent.
(Average.)

1(a)

•2025

•1655

81-73

(&)

•1995

•1629

81*65

81*69

2(a)

•2054

•1629

79-30

W

•1965

•1553

79-02

79-16

3 (a)

•2013

•1514

75-21

W

•1998

•1496

74-87

75*04

4(a)

•2032

•1506

74-11

(6)

•1982

•1469

74-13

74*12

5 (a)

•2027

1455

71-78

W

•1974

•1430

72-43

72-11

6(a)

•2002

•1493

74-58

(6)

•2009

•1499

74*64

74-61

7(a)

•2050

•1413

68-92

(6)

•2070

•1418

68-48

68-70

8(a)

•2023

•1674

82-75

(6)

•1962

•1612

82-15

82-45

9(a)

•1997

•1215

60-81

(6)

•1997

•1216

60-87

60-84

10 (a)

•6994

•1237

17*68

(&)

•6998

•1234

17-63

17-66

11(a)

*7036

•1581

22-47

(6)

*7063

•1586

22-46

22-47

12 (a)

•2009

•1669

83-10

W

•2007

•1659

82-68

82-89

13 (a)

•1961

•1653

84*29

(6)

•1963

•1656

8435

84-32

V. — Correction for Hydrogen Minerals.

NTo. of Shale.

Weight

taken.

Weight
of Water.

Hydrogen
per cent, to
be deducted.

Ash

per cent, to
be deducted.

1

1-1199

•0094

0*09

0-84

2

■9110

•0034

0-04

0-37

3

1-0799

•0054

0-06

0-50

4

•9638

■0038

0-04

0-39

5

•8944

•0048

0-06

0-54

6

1-0090

•0046

0-05

0-46

7

•6948

•0042

007

0-60

8

1-0027

•0065

0-07

063

9

•5275

•0056

0-12

1-06

10

•5310

•0038

0-08

0-72

11

•6088

•0030

005

0-49

12

1-0041

•0135

0-15

1-35

13

1-0303

•0107

012

1-04

General Results of Analyses.

196

Proceedings of the Royal Society of Edinburgh. [Sess,

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1913-14.] The Organic Matter in Oil-Shales.

197

Discussion of Analytical Data.

Strahan and Pollard have adopted the “ carbon-hydrogen ratio ” (C/H)
as a basis for the classification of coals, and have found it to vary from 12 -9
in “ per-bituminous ” coals to upwards of 30 in anthracites. A variation in
a smaller degree can be seen in the shales, the limits in the above analyses
being 5*96 and 8*14. In all cases the ratio is lower than in the coals. The
analyses show that the organic matter varies considerably in constitution
in different shales. The most interesting fact revealed, however, is the
connection between the carbon-hydrogen ratio and the yield of oil. The
law would seem to be established that the yield of oil varies directly as the
percentage of organic matter , and inversely as a function of the carbon-
hydrogen ratio. This is strikingly shown by comparing analyses 3 and 4,
where the same oil yield is obtained from the two samples, the excess of
2*4 per cent, of carbon in 4 being neutralised by its higher carbon-hydrogen
ratio of 7*57 as compared with 7*38 in 3. It is still more evident on a
comparison of Nos. 7 and 8, where the oil yield in the latter is actually 1*5
gallons more than in the former, although the carbon percentages are 10*13
and 21*96 respectively, the explanation being that in 8 the carbon-hydrogen
ratio is only 5*96, whereas in 7 it is comparatively high, viz. 7*68. It is
thus shown that the all-important factor in shale analysis is the determina-
tion of the relative percentage of hydrogen present, and that an approxi-
mate analysis of a sample into volatile matter, coke, and ash may not shed
so much light on its oil-producing properties as an ultimate carbon and
hydrogen analysis.

Action of Solvents on Shale.

Mention has already been made of the fact that very little is extracted
from shale by the common organic solvents. Dichlorhydrin, a high boiling
solvent (b.p. 174° C.) was tried without success, but pyridine (b.p. 117° C.)
was found to be an effective solvent.

The Committee on Explosions in Mines (2nd Report, 1912) has investi-
gated the solubility of coals in pyridine and shown that quantities of extract
may be obtained varying from 3*7 to 38*8 per cent, on the ash-free dry coal.
Torbanite and Broxburn shale were both completely extracted with pyridine,
and it was found that 4*92 and 3*29 per cent, respectively of the ash-free
dry shale was dissolved. If then, as is suggested in the report of the above
committee, the extracted material represents the resinous part of the coal
(the small percentages are from semi-bituminous, and the high from bitu-
minous, coals), it is evident that only a very small portion of the organic
matter in shale is of a resinous character.

198 Proceedings of the Royal Society of Edinburgh. [Sess,

The extracts were obtained by treating the finely divided shale with
pyridine in a Soxhlet extraction apparatus until the solvent siphoning over
was no longer coloured, distilling off the pyridine at 60° C. under reduced
pressure, transferring the semi-solid residue to a watch-glass and drying it
in a vacuum desiccator over sulphuric acid. The extracts were dark brown
in colour and showed a tendency to crystallise in radiating needles. They
gave the following results on analysis : —

Extract from Torbanite.

(1) *0864 gave ‘0694 H90 and *2590 C02

(2) -0808 „ -0653 | „ -2467 „

(3) -0679 „ -0560 „ *2042 „

(4) *0684 „ -2088 „

0 = 81-75
C = 83-26
0 = 82-01
0 = 83-26

Average . . C = 82*57 per cent.

*5031 gave "005023 N2 N = l-00 per cent.

•502 „ -0138 BaS04 S = -38 „

H = 8-93
H = 8-98
H = 9-16

H = 9-02 per cent.

Extract from Broxburn Shale.

•0726 gave -0768 H20 and -2196 C02

From Torbanite.

0 82-57
H 9-02
N 1-00
S -38
(by difference) O 7*03

100-00

0 = 82*49 per cent. H = 11 -75 per cent.

From Broxburn Shale.

C 82-49
H 11-75

S > not estimated.

These extracts are in all probability mixtures, as small proportions of
them are dissolved by alcohol, benzene, etc.

Action of Nitric Acid on Shales.

Carrick Anderson (Jour. Soc. Chem. Ind., 1898, vol. xvii. p. 1018)
described the action of nitric acid on coals, and gave analyses of the
products obtained from seven different samples. These products are acids,
and the product from any coal is always of constant composition provided
an excess of acid is used. As it seemed possible that a comparison of these
acids with any similar compounds which might be obtained from shales and
other substances might throw some light on the origin and nature of the
organic matter in shale, an endeavour was made to obtain similar deri-
vatives from the following: — (1) Torbanite, (2) Broxburn shale, (3) New-
battle cannel coal, (4) peat from Glenfalloch, (5) lycopodium spore dust,
and (6) an organic sludge consisting mainly of decomposed leaf and root
remains, microscopic algse, diatoms, and bacteria. From all of these, except

199

1913-14.] The Organic Matter in Oil-Shales.

the last, derivatives were obtained. In the case of the organic sludge,
oxidation, even although moderated by careful cooling, was sufficiently
vigorous to change most of the oxidisable material into oxalic acid and
carbon dioxide. The finely divided material was evaporated to dryness
with excess of concentrated nitric acid, the solid residue treated with
ammonia solution, filtered, and the acid precipitated from the filtrate by the
addition of dilute hydrochloric acid. This precipitate was filtered, washed
with water till free from chloride, and dried in a vacuum over sulphuric
acid. In the experiments with lycopodium and with peat the first action
had to be moderated by cooling. The substance obtained from lycopodium
was light brown in colour and gummy. All the other preparations were
more or less dark brown in colour, hard, and brittle. They all contained
traces of sulphur and a small amount of ash. In no case was the whole of
the organic matter converted into acid, there being formed in all the
preparations a larger or smaller quantity of oxalic acid. A small quantity
of powdered torbanite, after being repeatedly treated with nitric acid and
ammonia as above, was examined under the microscope. The residue was
found to consist of inorganic materials, with here and there particles of
organic matter which had been prevented from going into solution through
being enveloped in inorganic materials. These acids form insoluble salts
with some metallic radicals such as silver, lead, copper, iron, cobalt, and
barium. They gave the following figures on analysis (neglecting traces of
sulphur and ash) : —

Acid from Torbanite.

(1) -0784 gave *0533 H20 and T765 C02 0 = 61*39

(2) -0964 „ -0632 „ „ *2162 „ 0 = 61*13

Average . . C = 61*26 per cent.

(1) *5993 gave *02189 N2 N = 4*38

(2) *4993 „ *02181 N2 N = 4*37

Average . . N = 4*37 per cent.

Acid from Broxburn Shale.

(1) *0937 gave *0576 H20 and *2040 C09 0 = 59-38

(2) -0897 „ -0533 „

(3) -0947 *2079 „ 0 = 59*87

Average . . 0 = 59*62 per cent.

*5065 gave *02175 N2 N = 4*29 per cent.

Acid from Cannel Coal.

(1) -0991 gave -0474 H20 and *1934 C02 0 = 53*22

(2) *1146 „ *0576 „ „ *2270 „ 0 = 54*01

Average . . 0 = 53*61 per cent.

N = 3*92 per cent.

= 7*55
= 7*29

7*42 per cent.

H = 6*83
H = 6*60

H = 6*72 per cent.

31

*5008 gave *01963 N2

200

Proceedings of the Royal Society of Edinburgh. [Sess.

Acid from Peat.

•0557 gave *0274 H20 and ’1081 C02 0 = 52*93 per cent. H = 5*47 per cent.

•0976 „ *004477 N2 N = 4-59 per cent.

Acid from Lycopodium.

(1) *1051 gave -0891 H90 and -2334 C02 C = 60 56 H = 9*42

(2) -1006 „ *0848 „ *2204 „ C = 59*75 H = 9*37

Average . . C = 60 ’15 per cent. H = 9-39 per cent.

(1) -4966 gave *01904 N2 N = 3*83

(2) *5106 „ *01916 „ N=3*77

Average . . N = 3*80 per cent.

Acids obtained from Shales, etc.

Torbanite.

Broxburn

Shale.

Cannel Coal.

Peat.

Lycopodium.

c

61*26

59*62

53*61

52*93

60*15

H

7*42

6*72

5*44

5*47

9*39

N

4*37

4*29

3*92

4*59

3*80

O

(by difference)

26*95

29*37

37*03

37*01

26*66

100*00

100*00

100*00

100*00

100*00

The estimation of the metallic radicals in the silver and ammonia salts
of the acids from torbanite and Broxburn shale confirm these analyses, and
point to the empirical formulae : —

From : —

Torbanite. Broxburn Shale. Cannel Coal. Peat. Lycopodium.

c16h24no5 c16h22no6 c16h19no8 c13h17no7 c19h35no6

The empirical formulae calculated from Carrick Anderson’s coal-acid
analyses are : — C14H9N06 (Ell) ; C15H9N05 (Splint) ; C15H9N05 (Gas) ;
Cl7H10NO7 (Virgin); Cl7H10NO6 (Lower Drumgray); C16H10NO6 (Bannock-
burn Main); and C21H13N08 (Kilsyth Coking).

These substances, which are evidently all of the same nature, can be
arranged into a series commencing with lycopodium acid where the
hydrogen is relatively highest, and passing through torbanite, Broxburn
shale, peat, and cannel coal-acids to ordinary coal-acids where the hydrogen
is relatively lowest. It being recognised that the first and last terms of the
series represent derivatives of pure vegetable matter and of highly meta-
morphosed vegetable matter respectively, the probable conclusion is that
the intermediate terms represent different stages in the alteration of
vegetable matter. This does not, of course, infer that the process of change

201

] 913-14.] The Organic Matter in Oil- Shales.

has been through the above steps, as no doubt the different substances
experimented on were produced under different conditions of moisture,
temperature, bacterial action, etc. Each product may, however, represent
the end point of a definite series of reactions produced by definite condi-
tions. The close relationship between the formulae for the shale acids, peat
acid, and cannel coal-acid may signify a definite stopping-place in the
process of decomposition of vegetable matter, the carbon having increased
at the expense of the hydrogen and highly complex substances having been
formed.

There would seem to be no experimental ground for concluding that
animal remains are mingled with this vegetable product, as on careful
examination no trace of phosphates could be found in samples of torbanite,
Broxburn, Camps, or Dunnet shales, and as the lime in the ash of shales is
low, varying from a “ trace ” to P55 per cent. ( Oil-Shales of the Lothians,
1912, pp. 159, 161).

Summary.

1. The carbon-hydrogen ratio varies in the oil-shales from 6 to 8 and
over. The lower this ratio the larger is the amount of oil produced from a
definite percentage of organic matter. The carbon-hydrogen ratio is, in
all the shales examined, lower than that of ordinary bituminous coals.
The oil-shales are thus distinct from coals, although the richer varieties
may approach cannel coals in properties.

2. There is but little resinous substance in oil-shales, the main bulk of
the organic material being insoluble in organic solvents.

3. The organic substance in oil-shale is a decomposition product of
vegetable matter (originally algse, spores, or simply concretions of macerated
organic material) similar in nature to that found in peat and in cannel
coal, and produced by a definite combination of external conditions.

In conclusion, I desire to thank Dr Flett for suggesting the lines of this
research ; Mr R. G. Carruthers, Mr D. Tait, Mr D. R. Steuart, F.I.C., Mr Wm.
Caldwell, and Messrs Muir & Co. for assistance in securing samples ; and
Professor Walker, Dr J. E. Mackenzie, Dr Gordon, and Dr Campbell for
their advice, assistance, and criticism throughout the research.

{Issued seyaralely July 15, 1914.)

202 Proceedings of the Boyal Society of Edinburgh. [Sess.

XIV. — Notes on the Atmospheric Electrical Potential Gradient in
the Industrial Districts around Leeds. By Dan. W. Steuart and
Ingvar Jorgensen. Communicated by James A. S. Watson, B.Sc.

(MS. received February 13, 1914. Read March 16, 1914.)

The atmosphere of industrial districts is characterised by the pollution
which it receives from smoke, comprising solid matters like carbon, tar,
and mineral ash, and gaseous constituents such as S02 and C02.

Much work has now been done with regard to the ionisation of gases
by various means.* Small ions, with a velocity of 1*6 cms. per second in
an electric field of 1 volt per cm., have long been known to exist in the
atmosphere. About ten years ago Langevin,f working in Paris, demonstrated
the presence of large ions in addition, velocity 1/3000 cm. per second.
M'Clelland and Kennedy J described the formation of large ions in the
products of combustion, and later Kennedy, § comparing town and country
air, found in town air (Dublin) a larger number of ions, due to combustion
processes ; the large ions being increased, and to some extent at the expense
of the small ones. Aitken [| has shown that the various products of
combustion include nuclei of condensation and of spontaneous condensa-
tion, due largely to the presence of sulphur in the fuel. As the envelope
which transforms small into large ions often consists of water, these two
sets of results may be correlated to some extent. Eve,H for example,
concluded that dust, smoke, or mist in air causes a transformation of small
into large ions. Several sizes of ions are now known to exist in air,
commencing with the small ions and with decreasing velocities as the
size increases.**

The foregoing researches indicate that ionisation by combustion and
the presence of combustion products in the air may be essential factors in
the phenomena of atmospheric electricity in industrial districts.

The following notes deal with measurements of potential gradients

* J. J. Thomson, Conduction of Electricity through Gases. H. A. Wilson, Electrical
Properties of Flames and Incandescent Solids , 1912.

t Comptes Rendus, 1905, p. 233.

J Proc. Roy. Irish Acad., 1912, xxx., A, No. 5.

§ Proc. Roy. Irish Acad., 1913, xxxii., A, No. 1.

|| These Proceedings , 1912, xxxii., Part 2, No. 16, and earlier.

IT Phil. Mag., ccxxxv. p. 257.

** Cf. Sutherland, Phil. Mag., 1909, p. 341.

1913-14.] Atmospheric Electrical Potential Gradient. 203

in such districts in the neighbourhood of Leeds, and with a few experi-
ments designed to suggest an explanation of certain abnormalities, as
compared with previous records. Our apparatus * comprised a Lutz
flame collector on an ebonite rod, an Exner electrometer for measuring
potential differences to 800 volts, and a Braun electrometer for read-
ings over 800. All measurements were made at a height of 1 metre
from earth.

Curve A. — These measurements were made on a grass field near
Kirkstall Forge, Leeds. The wind was blowing from the forge chimneys
about 150 yards away ; the tops of the chimneys being a little below the

A.

level of the instruments. During forty minutes the potential gradient
varied rapidly between 720 and 2200 volts per metre.

On another day the instruments were 350 yards from these chimneys
in the same direction, and the smoke caused a variation between 300
and 2250 during thirty-five minutes. A few hours later, owing to a
change in the wind, most of the smoke blew somewhat to our right,
and the variations were in consequence only from 120 to 300 during
twenty minutes.

On another occasion we were half a mile from the forge in the same
direction, and during fifty minutes the reading was never below 630.
At this same spot, with the same wind direction and on two different
days, the minimal readings were 390 during ninety minutes and 120
in twenty minutes, depending on the amount of smoke which reached
the collector.

* For the loan of the apparatus we are indebted to Prof. J. H. Priestley.

204 Proceedings of the Eoyal Society of Edinburgh. [Sess.

5:

With a different wind direction the
smoke from the forge was rising rapidly
out of the valley and drifting over a hill.
At the top of the hill the smoke was still
mostly going right over our heads,** and
the readings in forty minutes were from
140 to 220, while 50 yards down the slope
during thirty minutes the variations were
from 75 to 130.

Curve B was taken near Garforth
colliery, seven miles east of Leeds. It
shows readings taken at distances of 100,
350, and 880 yards from a tall chimney
when the wind was blowing smoke towards
the instruments. About two hours after
the last reading was made the instruments
were taken to a position about half a mile
to the windward of the chimney, and
during twenty minutes the reading was
never above 135.

It will be seen that fresh smoke reach-
ing the collector caused an increase in the
positive potential gradient. We commonly
got readings of over 800 volts at distances
over a mile from large chimneys. The
interpretation of these measurements is
slightly complicated owing to the ordinary
variations in the potential gradient due to
other causes. It is consequently more con-
venient to study the effect of smoke by
means of passing trains, as in that case the
smoke effect is limited to a definite interval
of time, as will be seen from the following
curve.

Curve C. — A slight wind was blowing
from a railway 300 to 400 yards away
(wind direction roughly at right angles
to the railway). The ground level was
below the level of the railway, and smoke
from trains was wafted slowly down to

0001

205

1913-14.] Atmospheric Electrical Potential Gradient.

ex:

A

VOLTS PER METRE.

°o

cvj

206

Proceedings of the Royal Society of Edinburgh. [Sess.

the instruments. The passage of a train is marked, and the effect of its
smoke came several minutes later.

Train 1. No visible smoke.

„ 2. A little white smoke.

„ 3. Copious white smoke.

„ 4. No visible smoke.

„ 5. No visible smoke.

„ 6. No visible smoke.

7. Two trains

(a) Dense black smoke.

( b ) No visible smoke.

No effect was recorded, probably owing to some slight variation in the
wind.

Train 8. White smoke.
„ 9. White smoke.

10. Two trains

(a) Dense black smoke.

( b ) No visible smoke.

In the case of the white smoke the colour is due to moisture, and all
whiteness had generally disappeared long before the smoke reached the
instruments. Wilson concluded that the positive ions in a bunsen flame
consist of charged molecules of the gases present. Similarly solid particles
do not seem to be necessary for the carriage of the positive charge in
smoke.

These potential gradient measurements confirm the conclusions of others
that by combustion a considerable amount of ionisation is produced ; but
as the effect is always to produce an increase of the positive potential
gradient, more positive than negative ions may be formed.

By burning considerable quantities of benzene, methylated spirits, and
sulphur, separately and simultaneously in the open, at distances up to
25 yards from the collector, and under various meteorological conditions we
were unable to reproduce the smoke effect. On burning these substances
in the laboratory we found that the cooled combustion gases, in each case,
contained both positive and negative ions,* and in approximately equal
numbers as far as we could gauge with the apparatus at our disposal.
The mixed products of combustion would contain C02, S02, S03, carbon
particles, water vapour, and nuclei both of condensation and of charge,
as in the case of coal smoke.

We consider, therefore, that the ionisation giving rise to the largely

* L. Bloeh, Annates de Ghemie et de Physique, xxii. and xxiii. Reoglie and Brizard,
Comptes Rendus, 1909, p. 146.

1913-14.] Atmospheric Electrical Potential Gradient. 207

increased potential gradient must produce many more positive than
negative ions, due to some characteristic of the mechanism of the com-
bustions investigated. Such is the case, for example, with ionisation by
certain incandescent particles at moderately high temperatures.* In the
cases cited the effluent gases would have been subjected to a temperature
of perhaps from 600 to over 1000° C.+

This work was done during the summers of 1912 and 1913 in connection
with other smoke experiments being conducted at Leeds University. In
studying the effects of smoke on plant growth it is very desirable to have
some means of measuring the concentration of noxious smoke gases in the
atmosphere, and we hoped that this object might be attained by measure-
ments of the air potential gradient. It does not seem, however, as if these
would give much guidance.

Summary.

The general effect of products of combustion would be to cause a
transformation of the small ions of the air into large ions, which, acting
alone, would tend to decrease the air conductivity. Ionisation by flames,
however, adds to the number of ions in the air, so that the size of the ions
might be increased without the conductivity of the air diminishing. In
the case of the fresh smoke direct from the forge or colliery chimney-
stalks or railway engines of our experiments, it is suggested that com-
bustion in the furnaces would result in an ionisation producing more
positive than negative ions. It is only where similar conditions obtain
that we should expect such large increases in the positive potential
gradient, due to smoke, as we have recorded.

* H. A. Wilson, loc. cit.

t Rusby, Journal of Franklin Inst., July 1913.

(. Issued separately July 15, 1914.)

208

Proceedings of the Royal Society of Edinburgh. [Sess.

XY. — On the Hall and the Transverse Thermomagnetic Effects
and their Temperature Coefficients. By F. Unwin, M.Sc.,
Assistant Lecturer in Physics, Heriot-Watt College, Edinburgh.
Communicated by Professor F. G. Baily.

(MS. received May 5, 1914. Read June 15, 1914.)

Introduction.

Of the more recent researches on the subject of this paper, mention may
be made of the work of H. Zahn * on the sralvanomavnetic and thermo-

O

magnetic effects in various metals. Zahn has measured these effects in
many different metals, and has used his results to test the electron theory
of the properties of metals as developed by P. Drude. He has also
determined in some cases the temperature variation of the effects.

The author of the present paper has confined his attention to the
thermomagnetic transverse effects and the Hall effect. These have been
measured in magnetic fields of various strengths and at temperatures
varying over a range of about 100 Centigrade degrees.

The experiments were carried out with a view to obtaining some light
on the electron theory, and the ratios of the effects are discussed in relation
to this theory.

Definition of the Coefficients of the Effects and the
Convention with respect to the Signs.

In accordance with the custom of other workers, the Hall coefficient is
denoted by R, the Thermomagnetic Temperature Effect by S, and the
Thermomagnetic Potential Effect by Q.

The directions of the effects corresponding to positive values of these
coefficients are indicated by the diagrams (fig. 1) given below; it being
understood that the magnetic field is in each case directed downwards
at right angles to the plane of the diagram.

The value of S is found as usual by calculating the transverse
temperature difference in a plate 1 cm. broad placed in unit magnetic field,
when the temperature gradient along the axis is 1° C. per cm.

The value of Q is found by calculating the transverse E.M.F. (in
electromagnetic units) under the same conditions.

* Ann. d. Phys., xiv. p. 886, 1904.

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MODEL INDEX.

Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly
injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol. , 1902, pp.

Cells, Liver, — Intra-cellular Canaliculi in.

E. A. Schafer. Proc. Roy. Soc. Edin., vol.

Liver, — Injection within Cells of.

E. A. Schafer. Proc. Roy, Soc. Edin., vol.

, 1902, pp.
, 1902, pp.

IV

CONTENTS.

NO. PAGE

XIV. Notes on the Atmospheric Electrical Potential Gradient in
the Industrial Districts around Leeds. By Dan. W. Steuart
and Ingvar Jorgensen. Communicated by James A. S.
Watson, B.Sc., ...... 202

{Issued separately July 15, 1914.)

XV. On the Hall and the Transverse Thermomagnetic Effects and
their Temperature Coefficients. By F. Unwin, M.Sc., Assis-
tant Lecturer in Physics, Heriot-Watt College, Edinburgh.
Communicated by Professor F. G. Baily, . . . 208

{Issued separately , 1914.)

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SESSION 1913-14.

Part III.] VOL. XXXIV. [PP- 209-371.

CONTENTS. .

NO. ' PAGE

XVI Some Factorable Continuants. By W. H. Metzler, Ph.D., . 223

{Issued separately September 3, 1914.)

XVII. The Analytical Study of the Mechanism of Writing. By
James Drever, M.A., B.Sc. Communicated by Dr
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(. Issued separately September 3, 1914.)

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{Issued separately September 4, 1914.)

XIX. Description of a Projection-Model of the 600-Cell in Space
of Four Dimensions. By D. M. Y. Sommerville, M.A.,

D.Sc., Lecturer in Mathematics, University of St Andrews.

(With a Plate), ...... 253

{Issued separately September 29, 1914.)

XX. Changes of Electrical Resistance accompanying Longitudinal
and Transverse Magnetizations in Iron and Steel. By
Professor C. G. Knott, D.Sc., .... 259

{Issued separately December 14, 1914.)

[' Continued on page iv of Cover .

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[Continued on page iii of Cover.

1913-14.] The Hall and Transverse Thermomagnetic Effects. 209

In the case of the Hall effect, the value of R is calculated for unit
potential gradient instead of for unit current density, as it would seem that
the coefficient calculated in this way should be more directly comparable
with the coefficients S and Q. The value of R, therefore, is the transverse

R

s

Q

4-

Warm

- —

Electric \
Current ^

Heat

Current

Heat x.
Current

—

Cold

+

Fig. 1.

E.M.F. (electromagnetic units) in a plate of unit breadth when placed in
unit magnetic field, the potential gradient along the axis being 1 electro-
magnetic unit per cm.

Apparatus.

The specimen plate, abed (fig. 2), to be tested was soldered to two
copper lugs L, L, which were themselves soldered to two brass tubes T, T.
These tubes were fixed to a wooden frame, which served as a support.

The breadth of the specimen plate was in all cases about 2 cm., and the
distance between the lugs about 5 cm. The thickness differed for the
different specimens, but was in all cases less than a millimetre. Wires
were soldered to the brass tubes to enable an electric current to be sent
through the plate for the Hall effect measurement.

Five copper-constantan thermocouples were soldered to the plate at five
points A, B, C, D, E. The three points E, B, and D were on the axis
of the plate, while A and C were on a line perpendicular to this axis
and passing through B. The distances between B and the other points
were approximately 1 cm., but the actual distances were measured for
each plate.

The thermocouples were made of line wire (No. 42 S.W.G.), so as to
avoid as far as possible any cooling effect due to conduction of heat along
the wires.

Two water jackets J, J, 8 cm. by 5 cm. and about 1 mm. thick, were
placed one on each side of the plate, and were kept at a distance of 0*84 cm.
apart by brass distance-pieces, thus forming a kind of box enclosing the

specimen plate. The space between the plate and these jackets was filled

VOL. xxxiv. 14

210

Proceedings of the Royal Society of Edinburgh. [Sess.

with loosely packed cotton- wool. These jackets were found to be necessary
in order to bring the plate to a stationary condition as regards temperature.
In some cases they were supplied with cold water, and in others with steam.

The electromagnet used was of the “ ironclad ” type, and was designed
by Professor Baily and built up in the workshops of the Heriot-Watt College.
The pole-pieces had a maximum diameter of 20 cm. and were coned
down to a pole face of 5 cm. diameter. Each pole carried an exciting coil

1/vVJ

/aA

of 880 turns, so that with a current of 20 amperes a magneto-motive force
of 35,200 ampere-turns was obtained. This was found to produce a field
strength of about 20,000 C.G.S. units.

Measuring Arrangements.

The free ends of the wires of the five thermocouples were soldered
to stouter copper wires, and these junctions were kept in a Thermos flask,
by which means their temperature was maintained constant for the length
of time required for the observations.

1913-14.] The Hall and Transverse Thermomagnetic Effects. 211

The ten copper wires from this junction box were led to a small
distributing board (fig. 3). Two similar moving coil galvanometers
were used, and these were connected to the distributing board through
the keys Px and P2. The measured low resistances Sx and S2 formed
portions of the galvanometer circuits and served as potentiometer wires.
They carried currents supplied by the accumulators V1 and V2, and
regulated by the resistance boxes Rx and R2.

One of the measuring circuits was connected to the contacts H and I

Fig. 3.

on the distributing board, and the other to the contacts J and K ; the
galvanometers could thus be easily connected to any of the couples or
to the separate wires of different couples.

Method of Observation.

Thermomagnetic Effects.

The brass tubes were supplied respectively with aniline vapour and
steam, or aniline vapour and cold water, or steam and cold water, as the
case might be, so as to produce the required temperature gradient, and
the jackets were supplied with cold water or steam according to circum-
stances. When the plate had attained a steady state, the temperatures at E,
B, and D were determined by means of the corresponding thermocouples.

212

Proceedings of the Eoyal Society of Edinburgh. [Sess.

The copper wires belonging to the junctions at A and C were then
connected to one of the galvanometer circuits, and the constantan wires

of the E.M.F.’s in these two circuits were taken, first when the magnetic
field was zero, and afterwards with magnetic fields of known strength in
each direction. The thermoelectric force between copper and constantan
at various temperatures being known from the results of a special
experiment, the transverse temperature difference and the transverse
potential difference due to the magnetic field could then be calculated,
and hence the values of S and Q.

Calculation of the Transverse Temperature Difference
and Potential Difference.

Before the magnet is excited there will be a certain difference of
temperature between A and C. Let 0 be this difference, A being at
a higher temperature than C. On account of this there will be an

E.M.F., E, acting from A to C in the copper circuit, and an E.M.F., e,
acting from A to C in the constantan circuit. If M and N are the
thermoelectric powers of the metal of the plate with respect to copper
and constantan respectively, there will be the relations : —

When the magnetic field is excited, the temperature difference 0 is
altered to some value 0 + SO, and at the same time a transverse potential
difference is set up. Let this potential difference, measured from A to C,
be denoted by V.

Let the new values of E and e be E + <SE and e -f Se.

There will be the relations : —

from A and C to the other galvanometer circuit. Simultaneous readings

E= -M0
e= -N 0

(1)

(2)

E + SE = V-M (6 + 8$)
e + 8e = Y_N (0 + S0)

(3)

(P

Now, by subtraction of (4) from (3),

(E - e) + (SE - Se) = (N - M)0 + (N - M )S0
and from (1) and (2),

E-e = (N-M )6;

therefore

SE-8e = (N-M)S0,

or

1913-14.] The Hall and Transverse Thermomagnetic Effects. 213

Now (N — M) is the thermoelectric power of copper with respect to
constantan, and is known from the results of a special experiment. The
value of SO can therefore be calculated from the observations <5E and Sec
Again, by (1) and (2),

E_M
e ~N’

so that (3) and (4) may be written

E + SE = V - M(0 + SO)

(e + $e)x- = Vx?-M(0 + S0),
e e

from which
and hence

y_e8E-E8«
e - E

The transverse potential difference V can thus be determined from the
observations E, e, <5E, and $e.

Hall Effect.

The tubes and jackets were supplied with steam or cold water in order
to bring the plate to the required temperature. A current of 10 amperes
was passed through the plate, and the temperatures at E, B, and D were
measured ; observations being taken also with the current reversed, in order
to correct for any direct action of the current on the E.M.F.’s at the
junctions.

The copper wires at A and C were then connected to one galvanometer
circuit and the constantan wires at A and C to the other, and readings
were taken with magnetic field zero and also with known magnetic fields
in each direction. From these readings the transverse E.M.F. due to the
magnetic field could be calculated.

The potential gradient along the axis of the plate was determined by
connecting the copper wires at E and D to one galvanometer and the
constantan wires at E and D to the other, and taking readings with both
directions of the current.

The value of R was then calculated in accordance with the definition
given.

No correction was made for the influence of the Transverse Galvano-
magnetic Temperature Effect, as, in the case of the metals tested, this
effect is very small.

214

Proceedings of the Royal Society of Edinburgh. [Sess.

Results.

Nickel: — Thickness of plate = 0-275 mm.

The thermomagnetic temperature and potential effects were measured
in magnetic fields of various strengths and at three temperatures, namely,
43° C, 61-5° C., and 126° C.

Temperature of Plate = 43° C.

Temperature of Plate = 61 *5° C.

Temperature of Plate = 126° C.

Magnetic

Field.

S x 10".

Q x 104.

Magnetic

Field.

SxlO7.

Q x 104.

Magnetic

Field.

S x 107.

Q x 104.

2,000

-7T0

-3P0

2,900

-5*55

- 78-0

4,200

-6-80

-29*5

4,800

-515

-76-5

6,500

-6-62

-27-5

6,800

-4-70

-68*5

8,300

-5-78

-23*5

8,500

-5*30

-34-5

8,300

- 4T7

-58-6

14,500

19,100

-3-50

- 14-5

12,000

-3-01

1—41*4

-2*78

-1P5

17,350

— 2T2

-29-0

21,900

- 2-42

-10-0

22*600

— 2-*25

-14*5

22,100

-1*78

-23*5

...

22,800

- 1-74

-22-2

The coefficients S and Q are both negative, and vary greatly with the
strength of the magnetic field. The numerical value of the coefficients
decreases as the field strength increases.

An increase of temperature causes a decrease in the numerical value of
S, but a very large increase in the numerical value of Q.

Magnetic

Field.

Range of
Temperature.

Temperature
Coefficient of S.

Temperature
Coefficient of Q.

8,500 |

43° C.-6P5° C.

- 0-0039

+ 0-027

61*5° 0.-126° C.

- 0-0033

+ 0-011

22,000 |

43° C.-61-50 C.

- 0-0028

+ 0-026

61-5° 0.-126° C.

- 0-0035

+ 0-009

Hall Effect. — This was measured in magnetic fields of strength varying
from 2000 to 22,000 units, and at temperatures of 14° C. and 101° C.

Temperature of Plate = 14° C.

Temperature of Plate = 101° C.

Field.

R x 107.

Field.

R x 107.

2,050

-9-10

2,100

-12-0

3,800

-8-95

4,060

-10-9

6,300

-8-10

6,400

- 10-0

8,200

-7T0

9,500

- 7-27

14,300

-4-50

18,800

-3'59

21,750

- 3-21

21*900

- 3*48

1913-14.] The Hall and Transverse Thermomagnetic Effects. 215

The coefficient R is negative and varies with the field strength in
practically the same way as S and Q.

Increase of temperature increases the numerical value of R.

Temperature coefficient of R in field of 6,400 units = +00025.

1 | 22,000 „ =+0-0010.

Iron. Thickness of plate = 0*51 mm.

Thermomagnetic Temperature and Potential Effects. — These were
measured in magnetic fields varying from 2000 to 22,000 units, and at
temperatures of 48*6° C., 71*5° C., 97-9° C., and 129-2° C.

Temperature of Plate
= 48-6° C.

Temperature of Plate
= 71-5° C.

Temperature of Plate
= 97-9° C.

Temperature of Plate
= 129-2° C.

Field.

S x 107.

Q >

<104.

Field.

SxlO7.

Q x 104.

Field.

S x 107.

Q x 104.

Field.

S x 107.

Q x 104.

2,100

+ 5-75

+

10*0

2,000

+ 6*45

+ 10-8

2,100

+ 7-16

+

12*8

2,000

+ 6-05

+ 10-9

4,000

+ 5-44

+

10*2

4,000

+ 6-27

+ 9-7

4,300

+ 6-24

+

11-7

4,500

+ 6-98

+ 10-1

6,500

+ 5-20

+

10-1

6,000

+ 6-00

+ 10-5

6,300

+ 6-10

+

11-5

6,650

+ 6-31

+ 10*4

8,550

+ 5-47

+

10-6

8,300

+ 5-82

+ 10-4

9,250

+ 6*26

+

10-6

8,200

+ 6-25

+ 10-5

11,300

+ 5'54

+

10*9

11,400

+ 6*08

+ 10-3

11,500

+ 6-21

+ 10-3

14,800

+ 5-48

+

10-6

14,900

+ 5-92

+ 10-8

16,400

+ 5-85

+

ii-6

14,250

+ 6-12

+ 9-9

17,600

+ 5-26

+

9-9

17,550

+ 5*72

+ 97

20,300

+ 5-65

+

10-5

19,300

+ 5-70

+ 9'2

22,650

+ 4-88

+

9-1

22,500

+ 5-40

+ 8*7

23,300

+ 5*30

j.

9-5

22,100

+ 5-39

+ 8*6

The coefficients S and Q. are both positive ; they decrease slightly as
the magnetic field is increased. As the field approaches the value 20,000
units, a more rapid decrease in the values of S and Q is observed.

Field.

Range of
Temperature.

Temperature
Coefficient of S.

Temperature
Coefficient of Q.

22,500 1

48-6° C.-71-50 C.
71-5° C.-97'9° C.
97-9° C.-129-20 C.

+ 0-0045
zero
zero

- 0-002
+ 0-005
- 0-002

Up to about 70° C. the value of S increases considerably with
rising temperature, but between 70° C. and 130° C. it remains nearly
constant.

The variation of Q is not so simple. As the temperature is
increased the value of Q at first decreases, then increases, and finally
decreases again.

216 Proceedings of the Royal Society of Edinburgh. [Sess.

Hall Effect. — This was measured in magnetic fields of strengths varying
from 2000 to 22,000 units, at temperatures of 13-3° C. and 99-8° C.

Temperature of Plate = 13-3° C.

Temperature of Plate = 99-8° C.

Field.

R x 107.

Field.

R x 107.

2,250

+ 6-60

1,950

4-965

4,050

4-8-75

5,500

+ 6T0

6,400

4-8-83

8,450

4-6T7

9,500

4-9*00

15,000

4-6-26

14,850

17,300

+ 8 95

19,000

4-6-06

+ 8-70

22,600

4-5-73

22,600

+ 8-01

The coefficient R is positive ; it decreases with increasing field, very
slightly at first, but more rapidly as the field approaches 20,000 units.

Increase of temperature produces a very marked increase in the
value of R.

Temperature coefficient of R in field of 6,400 units = +0*0052.

„ „ „ 22,600 „ =+0*0046.

Copper. Thickness of plate = 0-063 mm.

Thermomagnetic Temperature and Potential Effects. — These were
measured in magnetic fields of three different strengths, and at three
temperatures, viz. 43*9° C., 70-7° C., and 125’8° C.

Temperature of Plate
= 43-9° C.

Temperature of Plate
= 70-7° C.

Temperature of Plate
= 125-8° C.

Field.

S x 107.

Q x 104.

Field.

SxlO7.

Q x 104.

Field.

SxlO7.

«C

X

I—1

©

7,850

-2'04

+ 1-61

7,900

-1-75

+ 1-53

7,700

-1-74

+ 1-48

13,550

-2-20

+ 1-67

13,650

- 1-84

+ 1-53

13,000

- 1-80

+ 1-47

21,400

-2-27

+ 1*69

21,400

-1-86

+ 1-55

21,150

-1-74

+ 1-47

The effects are of opposite signs, S being negative and Q positive.
The values of S and Q are only slightly affected by the strength of the
magnetic field.

Increase of temperature causes a diminution in the numerical values of
both S and Q, and the rate of diminution decreases as the temperature rises.

Temperature coefficient of S in field of 21,000 units for range —

43 9° C. to 70-7° C.= -0-0068.
„ „ „ „ 70-7° C. to 125-8° C.= -0 0012.

„ „ Q „ 43-9° C. to 70-7° C. = - 0-0031.

70-7° C. to 125-8° C. = -0-0009.

1913-14.] The Hall and Transverse Therm omagnetic Effects. 217

Hall Effect. — This was measured in magnetic fields of strengths of about
8000 and 22,000 units, and at temperatures of 15 6° C. and 99'8° C.

Temperature of Plate = 15*6° C.

Temperature of Plate = 99 ‘8° C.

Field.

E x 107.

Field.

E x 107.

8,200

-2-61

8,000

-2-00

22,000

-2-76

21,500

-2-06

The coefficient R is negative and is but slightly affected by the strength
of the magnetic field. The numerical value of R decreases very consider-
ably with increasing temperature.

Temperature coefficient of R in field of 22,000 units = — 0-0038.

Zinc. Thickness of plate — 015 mm.

Thermomag netic Temperature and Potential Effects. — These were
measured in magnetic fields of three different strengths, and at temperatures
of 46-4° C., 74-4° C, and 128-3° C.

Temperature of Plate
= 46-4° C.

Temperature of Plate
= 74-4° C.

Temperature of Plate
= 128-3° C.

Field.

S x 107.

Q x 104.

Field.

S x 107.

Q x 104.

Field.

SxlO7.

Q x 104.

7,700

+ 1-04

+ 1-24

7,700

+ 0-95

+ 1-35

7,700

+ 0-83

+ 1-30

13,500

+ 1-05

-h 1*26

13,300

+ 0-98

+ 1-34

13,500

+ 0-80

+ P26

21,100

+ 1-06

+ 1-32

21,200

+ 0-97

+ 1-44

21,400

+ 0-82

+ 1-20

The coefficients S and Q are both positive, and they vary slightly
with variation of magnetic field. The value of S decreases steadily
with increasing temperature. The value of Q increases up to a certain
temperature, beyond which an increase in temperature produces a de-
crease in Q.

Temperature coefficient of S in field of 21,000 units for range —

46*4° C. to 74-4° C. = - 0-0030.
74-4° C. to 128-3° C.= -0-0030.
46-4° C. to 74*4° C.= +0-0032.
74-4° C. to 128-3° C.= -0 0031.

Q

218 Proceedings of the Royal Society of Edinburgh. [Sess.

Hall Effect. — This was measured at temperatures of 15‘9° C. and
101*5° C.

Temperature of Plate = 1 5 9° C.

Temperature of Plate = 101-5° C.

Field.

R x 107.

Field.

Rx 107.

7,700

+ 1-40

7,800

+ 0-95

13,200

+ 1-41

13,770

+ 0-98

21,300

+ 1-43

21,300

+ 0-99

The coefficient R is positive, and increases slightly with increasing
magnetic field, but decreases with increasing temperature.

Temperature coefficient of R in field of 21,300 units = —0*0037.

Aluminium. Thickness of plate = 0*25 mm.

Thermomagnetic Effects. — These were measured at 40° C.

Coefficient S in field of 22,700 units = — 6*3 x 10 ~8.

Q „ 22,700 „ 3-9xl0-5.

Hall Effect. — This was measured at 14*5° C.

Coefficient R in field of 21,600 units = — 1T5 X 10 "7.

Discussion of Results.

It will be seen from the following table that, although the Hall and
thermomagnetic temperature effects vary both in magnitude and sign

R

from metal to metal, the ratio is for all the metals tested of the same

k5

positive sign, and does not vary greatly in magnitude. The ratio is not
greatly affected by change of temperature, except in the case of nickel.

Metal.

Nickel
Iron .
Copper
Zinc .

Aluminium

Field.

Value of Ratio -5 .

O

Temperature
44° C.

Temperature
100° C.

8,500

1*32

1-83

23,000

1-37

1-90

8,000

1-34

1-44

22,000

1-36

1-49

8,000

1-18

1-15

21,000

109

1T8

8,000

1-19

1-07

21,000

1-20

1-09

22,700

1-83

1913-14.] The Hall and Transverse Thermomagnetic Effects. 219

The ratio ^ varies from metal to metal. It is positive for all the
metals tested except copper. The values are given in the following table : —

Field strength = 21 ,000.

Metal.

at 45° C.
Jti

-§at 100° C.

JLV»

Nickel
Iron . . .

Copper

Zinc ....
Aluminium

+ 3'25 x 103
+ l-39xl03
- 0'68 x 103
+ T07x 103
+ 0-34xl03

1

+ 6 0 xlO3
+ 1T8 x 103
- 0’73 x 103
+ 1*40 x 103

It may he of interest to consider these results in their relation to the
electron theory. In the development of this theory some difficulty arises
in explaining the variation of the signs of the transverse effects. Drude *
in his investigation assumes the existence of positive and negative carriers
both taking part in the transmission of the heat and electric currents.
Drude finds the following expressions for the Hall and thermomagnetic
transverse effects : —

r t =

\ x1 + x2 )

Q = — + °"2^2^/l)

( T

® = l2/2)’

CCT

where

„ „ _d(log »j)

1 dt ’ 2 W~ ’

y1 = eVj, y2 = ev2,

cr1 = e2vln1, cr2 = e2v2n2 , a = <r1 + <x2.

and n2 are the numbers of positive and negative carriers respectively
in each unit volume of the metal.

e = the magnitude of the charge on each carrier.

and v2 are the average velocities impressed on the positive and
negative carriers respectively by unit electric field.
p and c are constants.

Now if x1 and x2 have the same sign, R and S are both differential effects
* Ann. d. Phys ., vol. i., 1901.

+ The expression for R given by Drude has been multiplied by <r in order to make it
applicable to the coefficient R as defined in this paper.

220 Proceedings of the Royal Society of Edinburgh. [Sess.

and may of course vary in sign from metal to metal, but R and S will both
have the same sign in the same piece of metal. This is quite in accordance
with experiment.

In the case of the coefficient Q, it will be seen that a diversity of sign
can only occur if xx and x2 have opposite signs, which is not a very likely
proposition. In any case, there would be no reason to expect any close
relation between the sign of Q and the sign of R. Experiment shows,
however, that these coefficients have in general, though not always, the
same sign.

R

Again, in order to account for the fact that the ratio -g has nearly

the same value for all metals, it must be supposed that one group of
carriers is of small importance compared with the other.

It would seem, therefore, that the difference in the signs of the
transverse effects in different metals must be referred to some cause
other than the participation of positive as well as of negative carriers
in the transmission of the current.

Sir Joseph Thomson * has suggested that the reversal of the Hall
effect in iron may be due to the fact that the magnetic field close to a
molecule is in the opposite direction from the magnetic field in the free
space between molecules. The Hall effect would thus be a differential
effect, and the reversed sign would be easily accounted for.

A. W. Smith f has put this to the test of experiment by measuring
the Hall effect in iron at various temperatures up to 1000° C. No
reversal of the sign of the Hall effect was observed, although iron loses
its magnetic properties at a temperature considerably below 1000° C. A
simple inspection of the values of the Hall effect for different metals
is sufficient to show that there is no direct relation between the sign
of the Hall effect and the magnetic properties of the metal, for the
effect is positive in both iron and zinc, while it is negative in both
nickel and copper.

Nevertheless, a differential action such as Thomson has suggested would
carry us far towards an explanation of the experimental results, if it could
be supposed to occur in all metals whether magnetic or not. Such a
differential action would apply with equal force to all the transverse
effects, and would thus account for the experimental relation between
R and S. The fact that the relation between Q and R is not so simple
is not difficult to understand, for in the case of the thermomagnetic effect
the temperature gradient in the plate sets up a potential gradient along

* Corpuscular Theory of Matter.

t Phys. Rev., Jan. 1910.

1913-14.] The Hall and Transverse Thermomagnetic Effects. 221

the plate, and this will have an effect on the value of Q. In consequence
of this, it is not to be expected that the ratio ^ will be so nearly

constant as |

On examining the experimental results, it will be seen that there is
no simple relation between the temperature coefficient of Q and those of
R and S. This is easily accounted for by the fact, previously pointed out,
that the potential effect is influenced by causes other than those which
determine the other two effects. On the other hand, some relation is to
be expected between the temperature coefficients of R and S.

On the assumption that only negative carriers need be considered,
the electron theory leads to the expressions

R = A

eXu

S = B

eXu

I^T

j

where e = the electronic charge
A = mean free path,

u= ^/njean square velocity of electrons,

«T = K.E. of electron at absolute temperature T due to its linear
motion.

A and B are factors depending upon the distribution of the magnetic
field within the metal.

Now, if R and S are influenced in the same way by the distribution

R

of the magnetic field, the value of is unity, and should be independent

o

both of field strength and temperature. There is a rough approximation
to this in the case of copper and zinc. In the case of iron the value of
R

g-, although considerably greater than unity, does not vary greatly with

variation of either field strength or temperature.

In the case of nickel, however, a very considerable discrepancy is
apparent. It is difficult to account for this discrepancy except on the
assumption that the values of R and S do not depend in quite the same
way upon the distribution of the magnetic field. This is not inconceivable,
since in the case of the heat current the electrons are moving with
velocities which remain constant between two collisions, whereas in the
case of the electric current the velocities of the electrons are subject to an
acceleration.

The galvanomagnetic temperature effect, which has not been considered
in this paper owing to the difficulty experienced in measuring it in such

222

Proceedings of the Royal Society of Edinburgh. [Sess.

metals as copper, zinc, and aluminium, is of considerable theoretical
interest. In accordance with the theory of the differential field, the sign
of this effect should change along with the sign of the Hall effect, whereas
in accordance with Drude’s statement of the theory it should be of the
same sign in all metals. Zahn has measured the effect in several metals,
but it so happens that, owing to the metals used, no definite conclusions
can be drawn from the results. The author hopes to carry out further
experiments on this point.

( Issued separately August 4, 1914.)

1913-14.]

Some Factorable Continuants.

223

XVI. — Some Factorable Continuants. By W. H. Metzler, Ph.D.

(MS. received May 15, 1914. Read June 15, 1914.)

1. In the Transactions of the South African Philosophical Society for
January 1905, Dr Thomas Muir gives the most general continuant resolvable
into factors by means of a given set of line-multipliers. He starts with
the multipliers and determines the continuant resolvable by them. At the
end of his paper he gives another continuant and its factors, but not the
line-multipliers, which he says “ is equally interesting in itself and equally
full of promise as a base for investigation.” Throughout his paper Muir
is dealing with one of the two determinant factors of order n into
which every centro-symmetric continuant of order 2 n can be broken up.
Starting with the larger continuant of which Muir’s is a factor, one of the
objects of this paper is to determine a set of row and column multipliers
that will cause the continuant to break up into quadratic factors and
thence into linear factors. Other and more general types of con-
tinuants are given which these same multipliers reduce to quadratic
factors. Another and more convenient way to determine the factors
of these determinants is obtained in the form of reduction formulas.
It is also shown how, for the two parts of order n into which the
larger continuant of order 2n breaks up, the linear factors come out
by reduction.

2. The determinant in question is

T =

a

(~n- l)fi
2rc-l

!.(/? + 'In - 2) (2rc-2)(/?+l)

3-2 n 'In - 3

■2.Q8+2rc-3) (2rc-3)Q8 + 2)

5 - 'In ! 'In - 5

(2»-2)(/i+l) „ l.(/3 + 2»-2)
2/4 — 3 3-2 n

(2m- l)j8
2n- 1

a

2 n

{a2-£2}{a2-(/? + 2)2} . . . (a2-(/3 + 2rc-2)2},

224 Proceedings of the Royal Society of Edinburgh. [Sess.

and the multipliers are

C2A-1 +

k(2n - 4& - 3)

1)

C2*+l

(2 n - 2 k ■
k + h-1

k-l.\h ' (2w - 2k + l){2n — 2A? — 1 ) . . . (2% - 2k + 1 - 2 . h^l)

(2 n - 4& + 3)(2?i - 4& + 1) . . . (2% - 4& + 3 - 2 . A - 1 'jp .

V = r;C2fc+2^-l +

C2& +

&(22i-4&+l)^

(2tt-2£-l)°2A:+2 + ‘ * ‘

| |^ + 7t~1 (2?t-4A:+l)(2?i-4fe-l). . .(2n-4&+l-2.~fe^l)0; ^ +

lAzl* I* ’ (2n-2fc-l)(2n-2&-3). .. (2»-2&-l -2.1^1) 2*+21
(A-l)(2w-4A + 5)1

+ (->

(2n-2* + l)
|fc-l

-R2&-2 + • • •

(2?i-4& + 5 + 4 . h

1)(2 n - A.k + 3)(2w- - 4fc + 5) ,

b»+i

| k-h-l , \h

k(2n - 4^ + 3)t,

■KsSfc-r

(2 n

{2u — 4k -f- 3 + 2 . li — 2)p .

: -&2k-2h +

(2 n - 2& + 1)

„ \k
+ (~)h-

{2n-2k + l){2n-2k + Z). . . (2?i - 2&+ 1 +2 . h- 1)

4fc+3+4. fr-l)(2tt-4& + l)(27i-4fr + 3). . . (2ro-4fc + l + 2. ft-2)R^ +

| ^ (2w-2fc + l)(2w-2& + 3). . . (2?i-2fc + l + 2. fc-1)

where C* and R, represent the ith column and jth row respectively.

3. The work of finding these line-multipliers will not be given here,
though a few words as to the method used may be of interest. A series of
consecutive non-zero elements along and parallel to the principal diagonal,
beginning with that in the 2rth row and 2rth column, were written down,
and the various multipliers for these general rows and columns determined
under the conditions that when all the operations were completed the result-
ing determinant was such that all the elements, say below the principal
diagonal, were zero, except those in the odd places of the line immediately
below the principal diagonal, in which case the determinant obviously breaks
up into quadratic factors, each of which is the difference of two squares.

4. As an illustration take the determinant of order eight

a 0 !

ft + 6 6(0 + 1

- o

2(0 + 5)

-3

3(0 + 4)
- 1

5(0 + 2)

4(0 + 3)

1

4(0 + 3)

3(0 + 4)

1 " -1
5(0 + 2) 2(0 + 5)

a -3

3

6(0 + 1)

0 + 6

-5

0

1913-14.] Some Factorable Continuants,

and perform the operations

225

Cj + C3 + C5 + c7 ,

C2 + C4 + C6 + C8 ,

E8 + 9E6 - 5E4 - 5R2 ,
Rr + E5-|E3-4E1,

C3 + fc5 + fC7, C5-C7,
C4 + |C6-CS, C6 - 9C8 ,

-^G _ f-^4 - > -^4 “ -^2 ’

R5 - f R3 + tRj. » R3-Ri,

and we have

a f3

(3 a 108 + 1)

0 a f(/3 + 2)

!(£ + 2)' a 4(0+3)

0 a M±l)

-K/8 + 4) a

0 a

- 5

- 5(/3 + 6) a

= (a2 - /32)(a2 - 0 + 22)(a2 ~/3 + 4 2)(a2 - /3 + 62)
= (<2 + + (3 + 2)(a + (3 + 4)(a + (3 + 6)

(a-0)(a-0-2)(a-0-4)(a-0-6).

5. Other and more general types of continuants than Ttt given in art. 2,
whose quadratic factors are brought out by the same set of line-multipliers,
are the following :

(2 n-W
2 n - 1

a + (2n — 2)y b (2»-2)(q + y)

3-2 n 2n - 3

2{^+ (2w - 3)8} a (2w - 3)(0 + 28)
5-2 n 2n- 5

(2n-2XP+_S) fi + ( 2n-2)S

2n - 3 3-2 n

(2n — l)a
274-1

2w

= {a&-a0}{a5-(a + 2y)(0 + 2S)} . . . - (a + 2» - 2. y)(fi + 2n - 2 . 8)},

VOL. XXXIV. 15

226

Proceedings of the Poyal Society of Edinburgh. [Sess.

and

T =

(2n - l)a(/5 + 2n-2)
2 n - l

y(S + 2n - 2) , (2n - 2) { S(y + 2n - 3) + y }

3 - 2n 2w - 3

2{/3(a+2w-3) + a}
5 - 2n

(2n - 3){a(/S + 2n - 4) + 2/3}
2n-5

(2n - 2){a(/3 + 2n — 3) + (3}
2n-3

/3( a + 2 n - 2)

3 -2n

(2n-l)8(y+2w-2) &

2ra~ 1

= {ab - a(P + 2 n - 2)8(y + 2n - 2)} - (a . (3 + 2n - 4 + 20)(8 . y + 2n - 4 + 2y) j . . .

{ah - (3(a + 2 n- 2)y(8 + 2w - 2)}.

If in T6 we change the sign of /3 and S, which is equivalent to changing
the signs of the elements below the principal diagonal, the signs between
the terms of the binomial factors would be plus instead of minus.

6. If in T& we put :

(1) b — a, a = f3, and y = S — 1, it reduces to Ta ;

(2) y = ^ = 0, all the factors are alike and we have

Tb = (ab -a f3)n,

or if, in addition, b = a and a = 3,

T,=K-^r.

(3) y — — a and S = — (3, two factors become alike and

T& = (ab - a/3)2(ab - 9 af3) . . . (ab -2 n- 32‘af3) ;

(4) a = y — = y and b = a, then

T„=(<j2_12)(a2_ 32) . _ . («2_2n-l2).

This, as far as the factors are concerned, is equivalent to putting
a = f3 = y = S = 1,

or « = y = and /3 = S = k, where k is any number,

or p — a-2n—l, y = S= —2.
or i3 = a = 2n—l,y = S——l;

Some Factorable Continuants.

227

1913-14.]

(5) /3 = — a = 2n— 1, y = — 8 = 2, then

T, = (a2+l2)(a2 + 32) # . . («2 + 2^Tl2)j
which is Elliott’s form.*

(6) a = /3 = 0, y = S = 1 , and b = a, then

T& = a2(a2 — 22)(a2 - 42) . . . (a* - 2n^22) ;

(7) a — 6 = 1, y — S = i, and b = a, then

T& = (a2-l2)(a2-22) . . . (a2 -ft2);

(8) a = — ft = 1, y = — S = ^, and b = a, then

T& = (a2 + l2)(a2 + 22) . . . (a2 + ft2).

7. If in Tc we put :

(1) S = a, y = /3, and b = a, then

T ={a2- a2(/3 +2 ft - 2)2} {a2 - (a . (3 + 2n - 4 + 2/1)2} . . . {a2 - £2(a + 2tz - 2)2} ;

(2) S = y = /3 = a and b = a, then

Tc = {a1 - a2(a + 2ft - 2)2}’1 ;

(3) S = y = /3 = a = b = a, then

Tc = a2w(2ft + a - 1 )w(3 - a - 2 n)n,
or if a -f 2tz — 2 = a;, then

Tc = (l2-a2)B(a;-2ft-2)B.

If a = 1, then

Tc=2*{n(l-ft)}»;

(4) <S = y = /3 = a = l, b = a = x(2n — 1), then

Tc = (2ft - l)2?1(x2 - l2)w.

If = Tc = 0.

8. It will be observed that in (2) of articles 6 and 7 we have a
determinant of the 2r&th order expressed as the Tith power of a determinant
of the second order.

From (4) of article 7 it is seen that the determinant

x 1

1 2 n - 2

3 — 2 n 2?i — 3

2 2n - 3
5 - 2ft X 2ft - 5

- (*2-iy.

i

X ■

3-2 ft

1 x

* Proceedings of London Mathematical Society, vol. xxxiii. p. 229.

228

Proceedings of the Koyal Society of Edinburgh. [Sess.

9. There is another and simpler way of getting the factors of these
continuants. For instance, if in Ta we add to every odd column the sum
of all the odd columns which follow it, and add to every even column the
sum of all the even columns which follow it, then subtract from every row
the second row above it, the determinant breaks up into (a2 — /32) and a
determinant of order (2 n — 2), which on interchanging the denominators of
conjugate elements is a determinant of exactly the same form with n one
less and /3 two more. Thus, if Ta be represented by f2n(a, /3), then

/*»(«, /?) = («2-/32)/2n-2(«, £ + 2).

In precisely a similar manner, if T& is represented by /2n(a&, a/3), then
f2n(ab, a/3) = (ab - a/3)/2w_2(a&, a + 2y . /? + 23),
and if Tc is represented by f2n(ab, a/3, yS), then

fojcib, a/5, yS) = {ab - a(/5 + 2 n- 2)8(y + 2n - 2 )}f2n,2(ab, a/3 + 2/3, yS + 2y).

10. It is easily seen that if Tft is represented by fn(a) . F^a), then

fn(a) = (a+2n- l) ./n_!( - a) = (a - 2 n- l)(a - 2n - 3) ./„_2( a)

and

Fn(a) = (a - 2n - 1) . F,t( - a) = (a - 2 n- l)(a + 2n - 3) . FM_2(a),

which shows that the signs between the terms of the factors are alternately
positive and negative for fn(a), and negative and positive for Fn(a).

The operations which show this are the following : —

(1) Add all the other columns to the first.

(2) Add to every column after the first the second column following it.

(3) Subtract from each row the second row above it.

(4) Subtract the first row from the second.

(5) Interchange the denominators of conjugate elements in the reduced
determinant.

11. If in T& we put b — a, a = (3, and S = y, then it breaks up into factors
which we may represent by fn(a, a, y) and F n(a, a, y), where fn{a, a, y) is
the sum of two terms, and Fn(a, a, y) the difference of the same two terms.

Using the same set of operations, it is seen that

/»(«> a> y) = (« + <*)/„_!(«, a + 2y, y)

and

Fn(a, a, y) = (a- a)Fn_j(a, a + 2y, y).

That is, the linear factors of T& with the positive sign between the terms
all belong to fn(a, a, y), and those with the negative sign all belong to
F «(«> y).

Some Factorable Continuants.

229

1913-14.]

Similarly, if in Tc we put b = a, S = a, and y = b, and if

Us

ii

o

£—4

a, a /3) . F n(a,

a/3),

then

i(a,

ii

f

[a + a{(3 + 2 n -

- 2)/n_i(a,

a/3 + 2/J)}

and

F,

iO,

aj8) = ■

[a - a{/3 + '2n -

- 2)Fn_1(a.

,<*,8 + 2/3)}

Syracuse University,
28 th April 1914.

{Issued separately September 3, 1914.)

230

Proceedings of the Royal Society of Edinburgh. [Sess.

XVII. — The Analytical Study of the Mechanism of Writing.

By James Drever, M.A., B.Sc. Communicated by Dr Alexander
Morgan.

(MS. received March 16, 1914. Read June 1, 1914.)

In the new and rapidly developing experimental science known as Ex-
perimented Padagogik ” in Germany, “ Pedagogie experimental ” in
France, and “ Experimental Pedagogy ” or “ Experimental Education” in
this country and in America, two well-marked and not entirely consistent
tendencies have been hitherto manifest. On the one hand, there has been
a tendency, more particularly in Germany, to develop the work in the
new field on the lines of experimental psychology, and to employ almost
exclusively the apparatus and methods of that science. On the other hand,
there has been a tendency, to a very marked extent in this country and in
America, to endeavour to carry on experimental work entirely without the
aid of exact and elaborate apparatus, eschewing, even regarding as “ tabu,”
the methods of the psychological laboratory. Both tendencies are perhaps
more or less inevitable, and both to a certain extent may be said to have
been justified by results. Nevertheless, there are certain obvious dangers
and defects inherent in both, and the whole situation is itself dangerous
for the new science.

If we commit ourselves too exclusively to the employment of psycho-
logical apparatus and the method of the psychological laboratory, there
is danger of our experimental education becoming merely a branch of
experimental psychology, which might involve in the first place the
neglect of certain fields of study, in which such methods and apparatus are
quite inapplicable, and, in the second place, a dangerous warping of our
attitude, aim, and evaluation, consequent upon our psychological view-
point and our restricted field. If, again, we endeavour to carry on our
experimental work as far as possible without the use of exact and elaborate
apparatus, no objection can be made to the thing in itself, but the tempta-
tion is strong to avoid such detailed and fine analytical work as demands
the use of precise measuring apparatus, and more or less elaborate recording
apparatus, which in the long run is almost bound to lead to our science
becoming exceedingly unscientific, by our contenting ourselves with experi-
mental investigations of the kind that any teacher can carry out in
any schoolroom, and then deluding ourselves with the idea that elaborate
and complex statistical treatment of our results will give them scientific

1913-14.] Analytical Study of the Mechanism of Writing. 231

validity. Worst o£ all is the antagonism between the two groups of
workers in the same field, which is all the more dangerous because the one
group is mainly composed of psychologists, who know little of the practical
work of education, and rather look down upon the practical teacher, and
the other group of practical teachers, who have merely a superficial
acquaintance with laboratory psychology, and distrust the psychologist.

This condition of unstable equilibrium, if it can be so described, has
characterised the early stages in the development of other experimental
sciences in the past, notably of experimental psychology itself. The con-
dition will pass, but only when the new science comes to its own in a
developed laboratory equipment, and a developed technique, which are
peculiar to itself and not merely borrowed from another science. It is
obvious that experimental pedagogy must always owe a considerable debt
to experimental psychology, and also that a great deal of good work may
be done with the simplest apparatus. But there are certain fundamental
problems of the school, and of life from the school point of view, all
analytic problems demanding accurate analytical methods, which must be
entirely ignored or only superficially noticed, if we confine ourselves to
either or both of these lines of approach. It would seem, therefore, that
some of the most interesting, and, if not the most important and practically
valuable, at any rate most significant work in the new field is that which
undertakes the analytical study, under laboratory conditions and by means
of laboratory apparatus, of complex processes characteristic of the work of
the school, from the teacher’s rather than the psychologist’s point of view.

Such complex processes as reading, writing, and reckoning, either as
acquired ££ dexterities ” or in the acquiring, may be cited as illustrating the
field for analytical investigation offered by the school. To the extent that
such processes are fundamental in school work, their investigation should
logically occupy a central position in the new experimental science. Con-
siderable progress has already been made, chiefly in Germany and America,
in the analytical study of the reading process. The main purpose of the
present paper is to indicate how a similar study may be made of the
writing process. This purpose will be best achieved by describing some
pieces of apparatus which have been devised with a view to the analysis of
various elements in the mechanism of writing; for the analysis of the
various factors involved in writing is obviously the first step towards its
scientific study. The three pieces of apparatus described are all intended
to isolate elements in the manual mechanism, and they all yield graphic
records which may be examined at our leisure and compared with the
actual writing itself.

232

Proceedings of the Royal Society of Edinburgh. [Sess.

I. Hand Movement Apparatus.

The chief movements made in writing are those of the forearm, of the
hand, and of the fingers. Of these the only movements presenting any
difficulty for analysis are those of the fingers, and the finger movements
are at the same time the most interesting. The isolation of the finger
movements can be obtained by a process of elimination. In the actual
writing we have the resultant of all the movements. The hand movement
is the resultant of all the movements except those of the fingers. Hence,
if we can trace the hand movement, the difference between this and the
writing will give us the part played by the finger movement.

Professor Charles H. Judd has devised and described an apparatus for
tracing the hand movement during writing ( Genetic Psychology for
Teachers, New York, 1907). Our apparatus is an improved form of this.
In Judd’s apparatus a broad strip of metal, bent so as to grip the fifth
metacarpal bone of the right hand, is bent back a second time on its upper
surface, so as to hold a wooden pin, to which a tracing arrangement is
attached by a short metal bar with hinges at each end, allowing free move-
ment in the plane of the wooden pin and the writing or tracing style. The
tracing style is cylindrical in shape and brought to a rounded point with
slits so as to hold ink like a pen point, while it moves freely in a longi-
tudinal direction through a range of about 1J inches within a light frame.
The point is kept resting on the paper by gravity alone, and the longi-
tudinal play is intended to allow for different inclinations of the back of
the hand to the plane of the paper in different individuals and at different
points in the writing.

Judd’s apparatus is defective in several respects. In the first place, the
position of the tracing arrangement is itself very awkward, since its plane
is almost parallel to the back of the hand, and in writing it seems to drag
along the surface of the paper, sometimes interfering considerably with the
movement of the hand, and always distracting the attention of the writer.
In the second place, the joints are not sufficiently rigid and the free move-
ment at the joints intensifies the dragging and distracting behaviour of the
tracing style, while it also allows the hand to move without the tracing
point moving. In the third place — and this is the chief defect — gravity
cannot be relied upon to keep the point constantly on the surface of the
paper, especially where there are sudden and rapid changes in the inclina-
tion to the paper of the back of the hand.

In order to remedy these defects and get an apparatus on which we can
rely for a true record of the hand movement, it is necessary to attach the

1913-14.] Analytical Study of the Mechanism of Writing. 233

tracing arrangement differently to the metal strip, to keep the writing
point against the surface of the paper by means of a spring, and to prevent
such movement of the whole tracing arrangement as will tend to cause it
either to fail to respond to any movement of the hand, or to interfere with
the attention of the writer or his free hand movement. In the apparatus
shown (fig. 1) these objects are secured by attaching a metal pin tangen-
tially to the metal strip where it curves over on to the back of the hand,
and fitting the tracing arrangement to a tube which passes over this pin
and is movable along the pin, being fastened by a screw in any position
that may be necessary for adjustment. All the joints are arranged for

adjustment and not for free movement. Finally, by means of a spiral
spring the tracing point after adjustment is kept in contact with the paper.
The trace itself is given by a capillary glass tracing tube or by a lead
pencil, the holder for which occupies the place of the tracing style in
Judd’s apparatus.

As an indication of the kind of work that may be done with this
apparatus, some tracings are shown (fig. 2), but the results hitherto obtained
may also be briefly summarised.

1. Normally, in careful adult writing, and more especially in pen writing,
the finer movements in the formation of the letters are due to the fingers.
As the writing is increased in speed, the hand may take over a larger and
larger share of the movement, until with very rapid writing the movements
are sometimes nearly all hand movements.

2. The main movement of the hand in writing is alternately a rotation
about an axis in the wrist and about an axis in the elbow with careful

234

Proceedings of the Royal Society of Edinburgh. [Sess.

writing, but as the writing increases in speed the rotation about the wrist
axis tends to disappear.

3. In the writing of children the part played by finger movement
is very variable. In general, hand movement predominates even in

oCiXtbu A w.

iO+uJ&r-

the formation of the letters, but this must not be regarded as a
universal principle.

II. Grip Pressure Apparatus.

So far as the writer knows, no one has hitherto attempted to obtain a
record of the pressure of grip in writing. The problem undoubtedly
presents considerable difficulties, but is a very interesting one. The
apparatus shown (fig. 3), which would therefore appear to be the first
attempt to get such a record, has several more or less obvious defects, but

1913-14.] Analytical Study of the Mechanism of Writing. 235

may be regarded as indicating the general lines upon which any such
apparatus must be constructed. The essential part of the apparatus is
the arrangement for receiving the grip in such a way as to enable us to
record its pressure. This is constructed of rubber and is double walled.
In its construction two teats are used, a large and a small. These are
placed one inside the other, the space between their walls being filled with
mercury and sealed. Finally, a narrow glass tube is passed into the inner
space, and that too is filled with mercury until the mercury stands about
two inches up the tube.

To begin with, a single teat was used, but it was found that, immediately
under the fingers, with a moderately firm pressure, all the mercury was
expelled, and the rubber sides pressed together. Consequently it was
impossible to record the full pressure with this arrangement. This defect
is remedied by the double teat, arrangement with the sealed space between

Fig. 3.

the walls. The record of grip pressure is obtained in the usual way by
connecting the upper end of the glass tube, which projects above the metal
holding tube, by means of rubber tubing to a recording tambour.

The most serious defect of this apparatus is its weight, and this is
largely due to the use of mercury. It might be possible to replace the
mercury with a lighter liquid, if one could be obtained which neither
affected the rubber nor evaporated to any great extent from the inner
space. It is impossible to use merely an air space between the teats, since
this makes the holding part of the apparatus much too soft and introduces
thereby a very disturbing factor.

III. Point Pressure Apparatus.

The pressure on the writing point itself has already received a con-
siderable amount of attention, and has been made the basis for several
interesting discussions, bearing not only on the psychology of writing, but
also on the study of defective and feeble-minded children, and of the effects
of drugs like alcohol on the motor co-ordinations in writing.

Hitherto the apparatus employed to record what is called par excellence
writing pressure has in every case recorded the pressure on the writing
surface rather than on the writing point. Kraepelin employed what he
called a “ Schriftwage,” which consisted of a plate supported by springs

236

Proceedings of the Boyal Society of Edinburgh. [Sess.

and mechanically connected to a lever for recording on a smoked surface.
The paper was placed on the pressure plate and the pressure in writing
on the paper was recorded by the recording lever. Meumann similarly
employed a pressure plate, but supported it on an air cushion pneumatically
connected with a recording tambour. The chief defect of any such arrange-
ment, apart from the complications introduced into the writing process
itself, is that variations in pressure on the writing plate may be due to
variations which have no necessary connection with the writing itself, but
are the result of more or less accidental changes in the position of the
hand or wrist relatively to the plate.

The original form of the apparatus shown (fig. 4), which has now been
modified in some minor respects, was first described by the writer in the
Journal of Experimental Pedagogy , March 5, 1913. The essential feature
of the apparatus is that it records the pressure upon the writing point

Fig. 4.

itself by receiving the pressure of the top end of the writing instrument
on a receiving tambour. To this a holding tube is attached into which
either pencil or pen is slipped. By means of a guiding tube, which serves
as a holder, the pressure is kept normal to the surface of the tambour.
In order to lessen friction, as well as to prevent side movements of the pen
or pencil, a ring — or sometimes two — is placed inside the guiding tube, and
this just allows the pen or pencil to move freely up and down. By
connecting the receiving tambour with a recording tambour we get the
record of point pressure. It is not yet certain whether a light spiral spring
inside the receiving tambour, in such position that the writing instrument
presses against it, is an advantage or not.

For the two pressure recording instruments the names “Grip Pressure
Cheirograph ” and “ Point Pressure Cheirograph ” might be suggested.
Both of them might be found serviceable, not merely in the study of writing
pressure for the purposes of the science of experimental pedagogy, but in
the science and practice of medicine for the diagnosis of defects in motor
co-ordination ; as we have indicated, writing pressure, that is point pressure,
has already been studied to some extent from this point of view. The
study of grip pressure might also be expected to throw some light on
writers’ cramp.

1913-14.] Analytical Study of the Mechanism of Writing. 237

IV. Results of Study of Writing Pressure.

Traces obtained with the two pieces of pressure apparatus are shown
(fig. 5). At the same time it might be well to indicate some of the more
important results obtained in the investigation of writing pressure.

VnCTUlTT'

Fig. 5.

I. to III. Point pressure tracings from children. Time record in seconds by Jacquet Chronograph.

la. Child of six. Words “ The cow gives us milk. ”

lb. Child of six (first attempt at script). Words “ A man can.”

lc. Child of six (printing). Words “ A man can run.”

Ila. Pencil writing, and II&. Pen writing of child of eight. Words “ Moray House School,” written twice in
each case.

III. Child of eleven. Pencil writing. Words “ Moray House School,” written twice.

IV. and V. Point pressure tracings from adults. Time record in J secs, by vibrating spring.

IVa. Pencil writing, ordinary rate. Words “ Moray House School,” written twice.

IV&. Pencil writing by same subject, maximum rate. Words “ Moray House School,” written four times.

V. Pen writing, slow and fast. Words “ Moray House School, written once slow and twice fast.

VI. and VII. Grip pressure tracings from adults and child of eleven. Time records for adults in i secs, and for
child in secs.

Via. Adult pencil writing. Words “ Moray House School.”

VI6. Adult pen writing. Words “ Moray House School Moray.”

VII. Child’s pencil writing. Words “Moray House School ” twice, slow and fast.

The most interesting results are probably those indicative of the
differences between adult writing and child writing. The grip pressure of
the adult nearly always shows a rhythmical rise and fall of pressure, which
is almost as regular in the tracing as the vibrations in the tracing of a

238

Proceedings of the Royal Society of Edinburgh. [Sess.

tuning fork, although with increased speed of writing the amplitude of the
pressure changes sensibly diminishes. The rhythm is also shown in
children’s writing from about the age of ten, but the irregularities are very
marked. It is difficult to get any reliable results with our grip pressure
apparatus at an earlier age. Analogous phenomena appear in the case
of point pressure. The point pressure trace of adult writing shows a
characteristic “ rippled ” top on each wave of pressure, indicating more or
less rhythmical increase and diminution of pressure. In the child’s writing
this characteristic is entirely absent before the age of about eleven, and we
have for our pressure trace either a more or less continuous line, or a line
that is simply “ crooked,” without any regularity in its crookedness. These
phenomena are probably in the main phenomena of co-ordination, but they
also have a psychological interest, as we shall see presently.

A second characteristic difference between adult and child writing may
be regarded as due partly also to co-ordination phenomena and partly to
psychical phenomena. It is well known that the practised reader does not
recognise the several letters of a word individually, nor does he speak them
individually, in reading a word, but reads the word, as it were, with a single
total impulse, either of recognition or of speech. Similarly, the adult writer
writes a word, not with a separate impulse for each letter, but with a single
impulse for the whole word. In learning to write, however, the child
learns first to draw the shapes of the letters, and there is a separate impulse
for each stroke or letter or group of letters, according to the drawing unit
with which the child is dealing, and this gradually changes from the stroke
to the letter, from the letter to the group of letters, from the group of
letters to the whole word, as the child progresses. These differences are
well indicated in the point pressure traces. The adult trace shows at once
that each word is written as a whole. The child, learning to write, shows
equally unmistakably the units for which there is a single drawing
impulse.

Even when the child is taught from the beginning to write continuously,
the traces can still be easily distinguished by the lack of rhythmical
pressure variations in the child’s trace. This difference, although in the
main a phenomenon of co-ordination, is at the same time indicative of the
nature of the psychical impulse that guides the writing. It is due in part
to the fact that writing is a form of language, while drawing is not. The.
rhythm is present because it is the word that is before consciousness, not
the shape or figure to be drawn.

Moreover, the language unit is the sentence, not the word, and this
is generally clearly shown both in speech and in reading. Are there any

1913-14.] Analytical Study of the Mechanism of Writing. 239

traces of this in writing ? There are to some extent. In adult writing we
can often mark off the phrases, at any rate, by the subordination of the
individual pressures for each word to a single maximum pressure on some
part, usually the end, of the phrase. While the child is drawing and not
writing we naturally look in vain for any such characteristic. It must
be noted, however, that the writing of clerks, whom we may consider
professional writers, tends to lose this last language mark and tends to
show an approximately uniform pressure.

x

1

JJ

\AA/VVV\A/V\/VV

n

-jx

m

HZ

— 1/ ry^— ' 1

a

\_

5

Ld

v — f

i

JUt

ijv ““1

Fig. 6.

I. “ Masculine ” type.

II. “ Feminine ” type.

III. “Mechanical ” or “ Clerical” type.

IV. Right-hand writing, and

V. Left-hand writing without practice by
same subject.

Previous workers have sought to distinguish, on the basis of point
pressure traces, different types of writing and writers (fig. 6). As an
introduction to any such attempt, it must be stated emphatically that the
point pressure trace is as characteristic of an individual as] his hand of
writing or his signature, and even in left-handed writing, without practice
with the left hand, individual characteristics reveal themselves in the
pressure trace. Nevertheless, it does seem as if there were distinct types of
writer. Two adult types have been generally distinguished by previous
investigators. The one tends to show a single maximum of pressure for
each word or phrase written as a whole, and tends to increase writing
pressure with increased speed of writing ; the other tends to show several

240 Proceedings of the Royal Society of Edinburgh. [Sess.

maxima of pressure in the word or phrase, or to write with an approxi-
mately uniform pressure, as in the case of clerk’s writing already cited, and
also tends to show decrease of pressure with increased speed of writing.
The first has been called the “ masculine ” type, the second the “ feminine.”
It seems desirable, however, to distinguish the two varieties appearing
under the second type, and to recognise three types. The “ clerk ” type is
quite as marked as either of the others, and is quite as distinct from the
“ feminine ” as the “ feminine ” from the “ masculine.” Another characteristic
mark of this third or “ clerk ” type is that the writing speed is normally
very near the maximum. When such writers are asked to increase their
speed, they may do so to a slight extent, but often all that happens is a
breaking down of the uniformity of pressure ordinarily shown without any
significant increase of speed, and sometimes the speed actually decreases
as an accompaniment of this breakdown of pressure uniformity, while the
subject thinks he is writing faster than before. A better name for this
“ clerk ” type, and more descriptive of its chief characteristics, might be
“ mechanical ” type.

There seems little reason to doubt that a considerable development of
our knowledge of the writing process will take place along the lines of
investigation indicated in this paper. We might even look forward to the
founding of a real science of graphology. At all events, many points of
interest to the teacher, and some of interest to the nerve and brain
specialist, the alienist, or the general physician must be revealed.

(Issued separately September 3, 1914.)

1913-14.] Abnormal Echinoids in the Royal Scottish Museum. 241

XVIII.— Abnormal Echinoids in the Collection of the Royal
Scottish Museum. By James Ritchie, M.A., D.Sc., Royal
Scottish Museum ; and James A. Todd, M.A., B.Sc. Communi-
cated by William Eagle Clarke. (With a Plate.)

(MS. received May 16, 1914. Read June 1, 1914.)

CONTENTS.

PAGE

I. Introductory Notes on Regulation, Duplication op Parts, Relation op

Ocular Plates to Coronal Growth, and Condition op Specimens . 241

II. Examples op Incomplete Development ..... 243

(i) Amblypneustes ovum.

(ii) Echinus esculentus.

III. Total Variation prom Five to Six-rayed Form — Echinus esculentus . 247

IV. Explanation op Plate ........ 252

I.

»

“ Echini are a particularly good group in which to study questions of
variation, because here variations can usually be expressed in very
definite terms of numerical or other equally positive character.” * On
this account, and because, in spite of much description, the variants liable
to occur in sea urchins have not yet been exhausted, the three specimens
described below are recorded. Each of these exhibits a pronounced
abnormality in the major symmetries. Two of them resemble another
abnormal echinoid in the same collections, already discussed in Proc. Zool.
Soc., f in lacking part of a definite ambulacrum ; but the means by which
the tests have accommodated themselves to changed conditions of growth
differ markedly in each of the three cases. The third specimen exhibits, in
place of the normal five-radiate arrangement, almost perfect hexamery —
a type of abnormality very different from that of the first two specimens.
For in these the distortion is due to incomplete development caused by
interference with the processes of growth, while there the hexamery is a
fundamental change in symmetry, is congenital in origin, and probably
represents the type of variation known as duplication of parts.

* R. T. Jackson, “ Phvlogeny of the Echini, with a Revision of Palaeozoic Species,5’ in
Mem. Boston Soc. Nat. Hist., vol. vii., 1912, p. 51.

t Ritchie and MTntosh, Proc. Zool. Soc., 1908, p. 646.

VOL. XXXIV.

16

242

Proceedings of the Royal Society of Edinburgh. [Sess.

Before proceeding to the description of these specimens, we would draw
attention to a few facts of more general interest.

I. Regulation. — It is clear that where so large an area as an ambul-
acrum or inter-ambulacrum ceases to grow, after temporary development,
much rearrangement in plates is necessary in order that the potential gulf
in the test should be spanned. Two distinct modes of regulation occur.
In the first place, the remaining plates in the neighbourhood of the
abnormality may themselves wholly compensate for the deficiency by
abnormal development in length and breadth. Such is the case in the
Echinus esculentus already referred to, where, an ambulacrum only having
dropped out, the two inter-ambulacral series of areas 4 and 5 have, by orderly
increase, shared in filling in the space ; * or in Philippi’s case of Echinus
melo ,*j* where the place of an ambulacrum with its associated inter-ambul-
acral series ( i.e . a ray) is taken by a single inter-ambulacral series from each
of areas 1 and 5.

Or, in the second place, orderly growth of normal series of plates may
be replaced or supplemented by the addition of abnormal plates varying
much in shape and size. These are sometimes arranged with an approach
to bilateral symmetry, as in inter-ambulacral areas 2 and 3 of the Ambly-
pneustes described by Hawkins, J and as in the Amblypneustes described
below (text-fig. 1), or they may form an irregular medley, as in the
specimen of Echinus esculentus here described (Plate, fig. 1).

It seems to be a general rule, however, that neither of these modes of
regulation altogether compensates for the primary disturbance, for in every
case growth seems to have been retarded, and the abnormal area is indicated
by a depression in the test and occasionally by a marked distortion of the
apical area from its normal position.

II. Duplication of Parts. — Various stages of the phenomenon of duplica-
tion have been described in Echinoids (see p. 250). These have represented
duplicity only in partial degree, but it is possible that the hexamerous
Echinus described below exhibits almost perfect duplication of both
ambulacral and inter-ambulacral areas, and so completes the series of
duplication stages.

III. Ocular Plates and Coronal Growth. — It is generally held that the
growth of new plates in ambulacral and inter-ambulacral series proceeds
from the oculars. The case is stated strongly by Lambert. §

* Proc. Zool. Soc ., 1908, p. 646.

+ Archiv f. Naturg ., iii. p. 241, pi.

f Proc. Zool. Soc., 1909, text-fig. 227.

§ Lambert, “Note sur un cas de monstrosite de l’apex chez YEchinocorys vulgaris ”
Bull. Soc. Yonne , 1890, xliv.

1 9 13-1 4.] Abnormal Echinoids in the Royal Scottish Museum. 243

“ Les centres vita ax de l’apex sont dans les ocellaires et non dans les
genitales, et c’est seulement a l’abri et au contact des ocellaires que se
torment les nouvelles annles ambulacraires ou que naissent les anules inter-
radiales.” Again Jackson, in his monumental and masterly monograph,*
says : “ The ocular plates seem to exert a controlling influence in the building
up of the corona, as below and in immediate contact with the oculars
originate the coronal plates both ambulacral and inter-ambulacral ” (p. 35).
And again : “ If this is true, then the loss of an ocular would cause a failure
to develop of the plates that normally went with it ; also an abnormal
position of an ocular should cause an abnormal distribution of the associ-
ated coronal plates ” (p. 36).

The present abnormal specimens offer two comments on these statements.
In the hexamerous Echinus esculentus, the ocular of the posterior
ambulacrum (say VI.) is wholly subtended by genital 5, which extends
some distance on both sides of it (Plate, fig. 2, and text-fig. 3). Yet
this derangement of the ocular as regards its relations with the genital
plates has not affected the growth of the coronal plates, which spring in
normal manner from the sides of the ocular. On the other hand, in each
of the deficient Echinus esculentus and Amblypneustes one ocular plate is
awanting, and nevertheless coronal plates have still continued to be formed
all along the exposed margins of the genitals (text-figs. 1 and 2). These
plates are very irregular in shape and do not belong to the normal coronal
series, but are sufficient to show that the growth areas are not associated
in any essential way with the ocular plates.

IV. Preservation of Specimens. — It may be worth drawing attention to
the fact that the specimens, though dried, had not been “ cleaned.” In two
cases, therefore, the sex was able to be distinguished from the shrivelled
reproductive organs, and in one case examination of the cruder internal
structures was made.

II. Examples of Incomplete Development.

(i) Amblypneustes ovum (Lamarck).

The specimen is a male example of Amblypneustes ovum collected at
the National Park, Wilson’s Promontory, Victoria, N.S.W., in October 1910,
and presented to the Museum among a number of others by Lord Carmichael
of Skirling.

The test, when examined, was dry and denuded of spines. Its maximum

* Jackson, R. T., “The Phytogeny of the Echini, with a Revision of the Palaeozoic
Species,” Mem. Boston Soc. Nat. Hist., vol. vii., 1912.

244

Proceedings of the Royal Society of Edinburgh. [Sess.

horizontal diameter was 3’7 cm., its height 3*2 cm. It possesses five am-
bulacral and five inter-ambulacral areas, but ambulacrum IV. (Loven’s nota-
tion) has its apical extremity separated from the apical system by about
1 cm., and possesses no corresponding ocular plate. The space intervening
between the apex of the incomplete ambulacrum and the apical system is
filled in by an aggregation of modified inter-ambulacral plates, more or
less irregularly arranged, but with each individual plate approximately
symmetrical about its longitudinal diameter. Retardation in the growth

3-

-- CL

lu-

ll

Fig. 1. — Incomplete Development in Amblypneustes ovum. Apical area and surrounding

coronal plates x 4^.

of this area seems to have had the effect of preventing the apical system
from attaining its customary polar position, so that, though still centrally
placed ( i.e . immediately above the mouth), it is overtopped in height by
the upper parts of radial areas I. and II. The apical system, but for the
absence of the ocular plate corresponding to the incomplete ambulacrum,
presents the normal pentagonal sjunmetry. A minor irregularity appears
in inter-ambulacral area V., where, about 1 cm. from the edge of the peri-
stome, there is a small papillary excrescence about 4 mm. in diameter.
This is due to modification in three of the inter-ambulacral plates, two of
which are occluded, and the intercalation of three additional small demi-
plates which give rise to the protuberance.

1913-14.] Abnormal Echinoids in the Royal Scottish Museum. 245

A general type of regulation occurs in the Echinus described by Ritchie
and MTntosh (loc. cit.), where a simple increase in the length of the inter-
ambulacral plates compensated for and bridged the potential gulf left by
the disappearance of the ambulacrum. But here the mode of regulation
is essentially different. It would seem that before the ambulacrum ceased
to be formed some disturbance occurred in the growth area, for a couple of
exceedingly large inter-ambulacral plates in proper series have been formed.
Subsequently to the assumed damage the ocular plate was cast off or
absorbed, and then a large growth area at the external margins of the two
genital plates became continuous and gave rise to an enormous median,
roughly triangular plate which succeeds the detached end of the ambul-
acrum and terminates two half -rows of inter-ambulacral plates. The
remaining space between this and the apical system is filled in, not by
regular inter-ambulacral plates, but by a group of irregular casual plates,
the group being roughly symmetrical about a median longitudinal axis.

This type of regulation is a stage between the complete unharmed
inter-ambulacral areas (exhibited in the Echinus esculentus described by
Ritchie and MTntosh, or in areas 4 and 5 of the Amblypneustes recorded
by Hawkins *), and the complete disappearance of a total ray, as occurs in
the specimens recorded by Bell-)- and Philippi.!;

Soft Parts. — So far as could be distinguished, the badly preserved
genitalia presented the normal five-partite arrangement and contained
male elements.

(ii) Echinus esculentus, Linn.

The specimen was obtained by Mr F. G. Pearcey in the Cromarty Firth
at a depth between 8J to 16 J fathoms. It contained shrivelled female
reproductive organs. Even in the dry condition in which it was preserved,
when still covered with spines, it showed marked irregularity of outline.
This in plan was trapezium-shaped. There was a distinct flattening of
the test in the part which lay between the vertex and the long side of the
trapezium, and the apical system was so distorted that it lay on this
flattened surface, only one edge reaching up to the summit of the test.
The maximum horizontal diameter of the test was 5 cm., its height 3 cm.
There were the usual five teeth in Aristotle’s lantern.

The spines having been removed, there was revealed the type of
abnormality shown by the specimen of Amblypneustes described above,
but in a more extreme degree; for here ambulacrum V. had almost dis-

* Hawkins, Proc. Zool. Soc., 1909, part ii. p. 714, figs. 226-230.

t Bell, Jour. Linn. Soc., vol. xv., 1881, p. 126, pi. v.

\ Philippi, see Bateson, Materials for the Study of Variation , London, 1894, p. 443, fig. 137.

246 Proceedings of the Royal Society of Edinburgh. [Sess.

appeared (Plate, fig. 1). The peristome and mouth parts were normal,
but in the apical system abnormality was strikingly apparent. The
genital plates of areas 1, 2, and 3 (the last split into two segments) were
present approximately in their normal positions, and associated with them,
in the customary arrangement, were the oculars I., II., III., and IV. It is
certainly remarkable that in spite of the spreading out of the plates
surrounding the periproct not one of the oculars was “ insert.” The
remainder of the periphery of the periproct was bounded by a single rank

171-

Fig. 2. — Incomplete Development in Echinus esculentus. Apical area and surrounding
coronal plates x 3 ; gen. 5, supposed 5th genital plate.

of small plates, each more or less rectangular in outline, with several
smaller triangular plates thrust in to complete the almost circular outline
of the series. This abnormal series contained in all nineteen plates and
demi-plates, with two additional small circular plates between ocular I.
and the margin of the periproct. The plates were similar in size and
shape, and the majority bore primary tubercles, but one, the third from
ocular I., was perforated by a distinct pore and possibly represents genital 5,
although in the dried state no genital products were associated with it.
The madreporite was divided into two lobes, both perforate.

Outside the ambulacral area the derangement and consequent regulation
was exceedingly extensive. Apart from the one disturbed area, the

1913-14.] Abnormal Echinoids in the Royal Scottish Museum. 247

“ morphological units ” have remained intact, so that the left row of
inter-ambulacrum 4 and the right row of inter-ambulacrum 5 were
practically normal and were associated normally with the ambulacral areas
in their respective “ arms.” On the other hand, the inter-ambulacral rows
of arm V. bent away from their ambulacral area, the intervening space
thus created being filled in by irregular small plates. But they ceased to
exist at about the level of the truncated ambulacrum. Still a large area,
measuring 12‘5 mm. in height from the termination of the truncated
ambulacrum to the apical chain of plates, and 28 mm. from side to side,
remained to be accounted for. This was filled in by a series of irregular and
generally small plates arranged in lines roughly parallel to the circular
periphery of the periproct. Considerable flattening has taken place in this
growth area, which has thus been covered with the minimum of material.

Of ambulacrum V. only about 1 cm. remained. The two pore rows,
instead of approaching each other and meeting aborally to form a closed
area, were parallel throughout, the open aboral end being filled in by small
plates; The individual rows of ambulacral plates in the disturbed area
have suffered in different ways. The row to the left was perfect so far as it
went as regards pore-pairs, but the right-hand row was shorter and for the
latter half of its length was destitute of pores, except for three scattered and
imperfect pore-pairs.

Aristotle’s lantern was removed, and showed the normal skeletal
arrangements.

Soft Parts. — The dried remains of the soft parts were unsatisfactory.
Three genital glands or portions of them were present, corresponding to the
genital pores in areas 1, 2, and 3, but there was no trace of gland in
connection with the abnormally situated pore supposed to be genital 5.
The intestine was much broken, but it was noted that an upward loop in
the middle of the abnormal area actually crossed the lower portion of the
apical area, and that the intestine doubled on itself towards the anus in
area 4, instead of, as usually occurs, in area 3.

III. Total Variation from Five to Six-rayed Form.

Echinus esculentus, Linn.

Only one cake of this type has been observed in the collections — an
example of Echinus esculentus, Linn., obtained in the Cromarty Firth by
Mr F. G. Pearcey, at a depth between 8J and 16 \ fathoms. Examination
of the shrivelled reproductive organs proves it to have been female.

The specimen was preserved in a dry condition and, even clothed with

248 Proceedings of the Royal Society of Edinburgh. [Sess.

spines, it presented an unusually depressed appearance, the maximum
diameter being 10 cm., the height 5 cm. Yet the hexradiate symmetry
was so little apparent that it had escaped notice.

On the test denuded of spines the presence of six ambulacra and
six inter- ambulacra was very marked, depression in the inter-ambulacral
areas giving the ambitus an approach to regular hexagonal shape. A
peculiar feature is common to all the inter-ambulacral areas. These,
instead of narrowing gradually towards their subtending genital plates,
widen out about a centimetre from the summit, so that the recently formed
plates are as large as, or even larger than, some of their predecessors. On

Fig. 3. — Hexamery in Echinus esculentvs. Apical area x 2^ ; m, madreporite.

the aboral surface hexamery is apparent in the peristome. Six teeth are
present, the lantern itself is six-partite, the elements of the parts being
normal, while the buccal tube feet are arranged in six pairs.

The apical system, while presenting a hexradiate appearance, is less
regular. The genital plates are five in number. Those in areas 2, 3, and 4
(according to Loven’s system, and assuming that the madreporite retains its
normal position in area 2) are normal in shape and position. Genital plate
5 has a greater lateral diameter than usual ; opposite area 5 it is normal
in shape, but it is continued for a short distance opposite area 6. The
remainder of the apical system is filled in by a double plate which subtends
both of the areas 1 and 6. This is practically equivalent to two normal
plates laterally adnate. The genital pores are normal in position, there

1913-14.] Abnormal Echinoids in the Royal Scottish Museum. 249

being two individuals on the double plate. The pore on genital plate 3
is doubled, the apertures being incompletely separated.

There are six oculars. Those opposite ambulacral areas II., III., IV.,
and V. are normal in shape and position. Ocular VI. lies in a notch in
genital 5, by which plate alone it is subtended ; and ocular I. lies in a
similar notch opposite the middle of the double genital plate. Each of
these is about half the usual size.

The anus lies nearest to the right-hand corner of genital 5.

The removal of Aristotle’s lantern disclosed the fact that, in the soft
parts also, hexamery prevailed, for the reproductive organs were developed
in six equal inter-radial rays. The alimentary canal, although longer than
usual, followed the normal course even in detail, for the intestine doubled
upon itself in inter-ambulacral area 2, and its last point of attachment was
in inter-ambulacral area 3, as in normal specimens.

Clear cases of spontaneous variation in the major symmetries of sea
urchins are very rare. Of the most likely of such cases — those in which
complete rays are added — few have been recorded, and still fewer have been
satisfactorily described. As Bateson in his Materials for the Study of Varia-
tion, 1894, mentions only two cases of “ total variation to a six-rayed form,”
and as Jackson’s list (op. cih, 1912, p. 46) omits several recorded cases, we
give the following short summary of all the examples of “total” hexamery we
have been able to discover, with the view of simplifying future researches : —

Recorded Cases of Total Hexamery.

Regularia.

(1) Amblypneustes sp. : hexamerous specimen (no further description).
Haacke, Zool. Anz., 1885, p. 506.

(2) Echinus eseulentus : 6 teeth, pairs of buccal tube feet, ambulacral
and inter-ambulacral zones, ocular and genital pores, ocular and genital
plates, two of the latter adherent — described in present paper.

(3) Tripneustes eseulentus : 6 teeth, ambulacra and inter-ambulacra,
oculars and genitals, two of the latter adherent. Jackson, Mem. Boston
Soc. Nat. Hist., vol. vii., 1912, p. 46.

(4) Toxopneustes lividus : 6 teeth, pairs buccal tube feet, ambulacra,
genitals, and oculars. Ribaucourt, Gomptes rendus Ac. Sci., vol. cxlvi., 1908,
p. 92.

(5) Paracentrotus (Strong ylocentrotus) lividus (artificially reared) :
6 teeth, terminal tentacles, and ambulacra. Delage, Gomptes rendus Ac.
Sci., vol. cxlv., 1907, p. 546.

250

Proceedings of the Royal Society of Edinburgh. [Sess.

(6) Strong ylocentrotus drobachiensis : 6 teeth, ambulacra, inter-ambu-
lacra, oculars, and genitals, two of the latter adherent. Jackson, op. cit.,
p. 47.

(7) Strongylocentrotus drobachiensis as No. 6.

(8) Species unnamed — hexamerous specimen (no further description),
seen by Ribaucourt and mentioned by him, loc. cit.

Irregularia.

(9) Galerites albogalerus : 6 ambulacra and inter-ambulacra. Meyer,
Nov. Acta Ac. L. G. Nat. Cur., vol. xviii., 1836, p. 294, pi. xiii., figs. 6
and 7.

(10) Galerites sp., six-rayed. Laur., S. B. Ges. Isis, 1894, p. 6.

(11) Pyrina ovulum : a sixth ray added at posterior, displacing periproct,
6 oculars, 5 genitals. Seguin, Feuill. Nat., ser. 4, No. 376, 1902, p. 81,
figs. 1 and 2.

The descriptions of many of these specimens are insufficient to indicate
whether or not the hexamerous arrangement prevailed in all the organs.
As to the Pyrina ovulum recorded by Seguin, that author suggests that
the addition of a fifth genital plate and corresponding ocular indicates a
reversion to an earlier and more typical symmetry than that of Pyrina.
Of those regular sea urchins which have been described with any attempt
at detail, perfect hexamery appears to have prevailed in cases 4 and 5 of
the above list, all the organs having been, so far as one can judge, perfectly
formed. The origin of such cases cannot be further particularised than as
due to spontaneous meristic variation.

In the case of the Echinus esculentus here described the apical area
gives a clue to the situation of the abnormality. Oculars II., III., IV., and
Y. are similar in size, whereas the remaining two oculars resemble each
other in being each about half the size of a normal individual. This fact,
and the irregularity of the neighbouring genital plates, indicate that the
additional areas were added in the right posterior segment. Further, the
union between genitals 1 and 6 suggests that the latter is an imperfect
double of the former, the imperfection of the duplication making necessary
the abnormal compensatory extension of genital 5. We suggest, then, but
with reserve, that this Echinus may represent a case of almost perfect redupli-
cation of radii, inter-ambulacral area 1 and its flanking series of ambulacra
being repeated in area 6 with its associated ambulacral series. If such be
so, the present specimen comjDletes the series of already known cases of
partial reduplication of radii (see Bateson, Materials for Study of Variation,

1913-14.] Abnormal Echinoids in the Royal Scottish Museum. 251

p. 446). Stewart has described an example of Amblypneustcs griseus, in
which an ambulacrum only was imperfectly duplicated ; Cotteau a specimen
of Hemiaster batnensis, in which an ambulacrum only was completely
duplicated ; Gautier an Hemiaster latigrunda, in which an ambulacrum
was completely duplicated and an inter-ambulacrum imperfectly ; and in
the present Echinus esculentus both ambulacral and inter-ambulacral series
show perfect duplication.

Along with our Echinus must be reckoned the specimens of Tripneustes
esculentus and Strongylocentrotus drobachiensis (two cases) described by
Jackson; for in all of these, two of the six genital plates are adherent,
apparently indicating again the residue of the almost perfect duplication
of a ray. Regarding this curious phenomenon of two fused genitals with
an ocular between them which he found in the only cases (three in number)
of complete hexamery discovered amongst 50,000 sea urchins, Jackson
says : “ It is certainly most extraordinary that this parallel structure
should exist in three specimens, and indicates what I have elsewhere
pointed out, how very definite extremely rare variation may be.” It adds
to the wonder, and to the evidence of definiteness of particular variations,
that the specimen above described, belonging to still a different genus from
Jackson’s, should repeat for a fourth time in hexamerous Echini this
curious abnormality.

The evidence as to means of growth-compensation controverts the find-
ings of Jackson, who found that £‘ in the six-rayed specimen [. Tripneustes
but also in his other specimens] evidently the space gained to add the extra
ambulacrum and inter-ambulacrum is attained by building ambulacra of
practically the usual width, but narrowing all the inter-ambulacra equally
to much less than the usual width. This emphasises the conclusion
gathered from normal Echini that the inter-ambulacrum is essentially a
space-filler and adapts itself to fill what space is available between the
ambulacra which are the most essential structures.” In view of these
statements the six-rayed Echinus was compared, as to relative proportions
of ambulacra and inter-ambulacra, with a normal specimen of, as nearly as
possible, the same size, with these results : —

Circumference
at Ambitus.

Average Width
of Inter-ambu-
lacral Areas.

Average Width
of Ambulacral
Areas.

Normal Echinus
Six-rayed Echinus .

318 mm.
314 mm.

41 mm.
33 mm.

23 mm.
19 mm.

252

Proceedings of the Royal Society of Edinburgh. [Sess.

Clearly the ambulacral areas have suffered reduction here as well as the
inter-ambulacral, and the extent of reduction in the two types of area is
roughly proportional, the diameter relationship between the ambulacral
and inter-ambulacral areas of the normal specimen being as 1 to 1*783, and
of the six-rayed specimen as 1 to 1*737. The proportionally greater loss
in diameter of the inter-ambulacra is obviously too small to support
Jackson’s statement.

EXPLANATION OF PLATE.

Eoman and Arabic numbers mark the ambulacral and inter-ambulacral areas
according to Loven’s notation.

Eig. 1. Incomplete development in Echinus esculentus . Moray Firth specimen
viewed from flattened, abnormal aspect, showdng the termination of imperfect
ambulacrum V., the very numerous and irregular regulation plates or “space-fillers”
in the corona, and the asymmetrical position and abnormal plates of the apical
area. x 2. m = madreporite.

Fig. 2. Hexamery in Echinus esculentus. Apical aspect of Moray Firth specimen.
Natural size.

(Issued separately September 4, 1914.)

Proc. Roy. Soc. Edin.

Vol. XXXIY. Plate I.

Ritchie and Todd— Abnormal Echinoids.

Photo, by James Ritchie.

M'Farlane Erskine, Edin.

1913-14.]

Projection-Model of the 600-Cell.

253

XIX. — Description of a Projection-Model of the 600-Cell in Space
of Four Dimensions. By D. M. Y. Sommerville, M.A., D.Sc.,
Lecturer in Mathematics, University of St Andrews. (With a Plate.)

(Read May 4, 1914. MS. received June 1, 1914.)

§ 1. In 1880 Stringham 1 proved that in space of four dimensions there
exist six and no more regular rectilinear figures, whose boundaries are
regular polyhedra. The same result was arrived at independently by
Hoppe 2 in the following year. In 1883 Schlegel 3 gave an extensive
investigation of the same problem, and constructed projection-models of
the six regular figures, which were exhibited at the Magdeburg meeting
of the Society of German Naturalists in 1884. This series of models was
published by the firm L. Brill of Darmstadt and is obtainable from their
successors, Martin Schilling in Leipzig.

The models are constructed of brass wire and silk threads, and represent
projections of the figures in ordinary space in such a way that there is no
overlapping of boundaries. In each case the external boundary of the
projection represents one of the solid boundaries of the figure. Thus the
600-cell, which is the figure bounded by 600 congruent regular tetrahedra,
is represented by a tetrahedron divided into 599 other tetrahedra ; 20
tetrahedra meet at every vertex and 5 at every edge; 12 edges meet at
each point; the total number of vertices is 120. At the centre of the
model there is a tetrahedron, and surrounding this are successive zones of
tetrahedra. The boundaries of these zones are more or less complicated
polyhedral forms, cardboard models of which, constructed after Schlegel’s
drawings, are also to be obtained from the same firm.

§ 2. The model which was constructed and exhibited by the present
writer represents an exact stereographic projection of the 600-cell, i.e. the
centre of projection is taken on the circumscribed hypersphere, and in fact
is one of the vertices of the figure. The projection of this vertex would
therefore be at infinity, and the 12 edges which meet there would be
represented by lines proceeding to infinity from the vertices of the regular
icosahedron, which is the outermost accessible boundary of the projection,

1 “ Regular Figures in ^-dimensional Space,” Amer. J. Math., 3, 1-14.

2 “ Regelmassige linear begrenzte Figui en von vier Dimensionen,” Arch. Math., Leipzig,
67, 29-44.

3 “ Theorie der homogenen zusammengesetzten Raumgebilde,” Halle, Nova Acta Acad.
Leo'p., 44, 343-459.

254

Proceedings of the Royal Society of Edinburgh. [Sess.

In the model these infinite edges have been omitted, so that the model is
to that extent incomplete. The projection of the vertex which is opposite
the centre of projection forms the centre of the model, and the successive
zones of vertices are very simple and regular. Starting from the outside —

Zone A is the vertex at infinity (1 vertex).

Zone B is a regular icosahedron (12 vertices).

Zone C is a regular dodecahedron (20 vertices).

Zone D is a regular icosahedron, whose vertices are not joined to one
another. In the model these vertices are joined to the vertices of zone C
by wires painted black, forming pyramids on the faces of the dodecahedron
(12 vertices).

Zone E, the mesial zone, is the semi-regular polyhedron called the
icosidodecahedron, which is bounded by 20 triangles and 12 pentagons
(30 vertices).

Zone — D is similar to zone D, and its vertices are joined by black wires
to the vertices of zone — C, forming pyramids on the faces of a dodecahedron
(12 vertices).

Zone — C is similar to C, i.e. a regular dodecahedron (20 vertices).

Zone — B is similar to B, i.e. a regular icosahedron (12 vertices).

Zone — A is the centre (1 vertex). (Total number of vertices 120.)

The edges which join up the vertices of each zone are of brass wire,
and, with the exception of the edges joining zones C, D, and — C, — D, the
edges joining different zones are of differently coloured silk threads. All the
threads which join the vertices of the same two zones, and those of the cor-
responding zones on the other side of the mesial zone, are of one colour.

§ 3. The model has been constructed so that the radius of the circum-
scribed hypersphere is 8 cm.

In making the calculations for the lengths of the edges great use has
been made of Schoute’s valuable paper,1 which gives the co-ordinates of the
120 vertices in the most symmetrical form, and tabulates the connecting
edges. In Schoute’s system of numbering, the 120 vertices are numbered
from 1 up to 60, and from — 1 to — 60 for the opposite vertices. With
reference to the special arrangement of the vertices in the stereographic
projection, whereby one vertex is singled out as centre of projection,
another system of numbering allows of a more compact table of connecting
edges. The vertices of each zone are numbered separately, and so also are
the rings or zones of vertices of each zone. A pair of opposite vertices of

1 “ Regelmassige Schnitte und Projectionen des Hundertzwanzigzelles und Sechs-
liundertzelles im vierdimensionalen Raume,” Amsterdam, Verh. K. Akad. Wet. (le. Sect.),
II. No. 7 (1894).

255

1913-14.] Projection-Model of the 600-Cell.

any zone are numbered ±n. Thus, e.g., B 3 and — B — 3 denote opposite
vertices of the 600-cell. For the mesial zone — E is the same as E, and
— E 3 is the same as E 3.

In zones B and D, the icosahedra, the vertices are numbered 0 ; 1, 2, 3,
4, 5; -1, -2, -3, -4, -5; 0.

In zone C, the dodecahedron, they are numbered 1, 2, 3, 4, 5 ; 1, 2, 3,
4,5; -1, -2, -3, -4, -5; -1, -2, -3, -4, -5.

In zone E, the icosidodecahedron, they are numbered 1, 2, 3, 4, 5;
1, 2, 3, 4, 5; 13, 24, 35, 41, 52, -13, -24, -35, -41, -52 (or 31, 42, 53,
14, 25); etc.; i.e. the 10 vertices of the equator of this zone are represented
by the pairs of numbers which represent the vertices of the adjacent rings
to which they are connected, and 31 is the same as —13.

§ 4. In order that reference may be made to Schoute’s tables, Table I. gives
the numbers in the present system, which correspond to Schoute’s numbers.
No. 4 of his system, which is on the axis of w, is taken as centre of projec-
tion. Then — 4 is — A, the centre of the model. The numbers corresponding
to the negative numbers of Schoute’s system are obtained by changing B,
C, D into — B, — C, — D, and changing the sign of the number.

Table II. gives the edges of the 600-cell.

Table III. gives the co-ordinates of the vertices, according to Schoute,
but the plane of x, y, z has been moved so as to pass through A, i.e . w has
been changed into 2 (e + lj-m The symbol e = j5.

Table IV. gives the lengths of the edges of the projection.

§ 5. In the projection a number of groups of points become coplanar.
These are the projections of points which lie in the same hyperplane
passing through the centre of projection. The groups of points in the
original figure which are so projected form zones of the same form as the
zones B, C, D, E, and their centres lie in the zones B, G, D, E respectively.
Thus, taking the point BO as centre, we have the icosahedron —

A; B 1, 2, 3, 4, 5; C 1, 2, 3, 4, 5; BO, j

which is projected into a plane figure.

With centre Cl we have first the icosahedron —

B 0, 3, 4 ; C 1, 2, 5 ; B 0, 3, 4 ; E 1, 3, 4,
and next the dodecahedron —

A; B - 1, 2, 5; C 3, 4, 2, - 3, - 4, 5 ;

-Cl; - B 0, 3, 4 ; E, 2, 5, 2, 5, 13, 14,

and this last is projected into a plane figure.

256

Proceedings of the Royal Society of Edinburgh. [Sess.

With centre DO we have the icosahedron —

BO; Cl, 2, 3, 4, 5; E 1, 2, 3, 4, 5 ; -DO;
the dodecahedron —

B 1, 2, 3, 4, 5 ; D 1, 2, 3, 4, 5 ; E 1, 2, 3, 4, 5 ; -Cl, 2, 3, 4, 5 ;
and the icosahedron —

A ; C 1, 2, 3, 4, 5 ; - D 1, 2, 3, 4, 5 ; -BO,

and the last figure becomes a plane figure in the projection.

With centre El we have the icosahedron —

C3,4; D 0, 1 ; E 2, 5, 3, 4 ; - D 0, 1 ; - C 3, 4,
the dodecahedron —

BO, 1; C 2, 5, 3, 4 ; D 2, 5 ; E 3, 4, 31, 41 ;

-BO, 1; -02,5,3,4; -D 2, 5;
the icosahedron —

B 2, 5 ; C 1, - 1 ; E 2, 5, 35, 42 ; - C 1, - 1 ; - B 2, 5 ;
and the icosidodecahedron —

A; B3,4, -3, -4; C 2, 5, - 2, - 5 ; D 3, 4, - 3, - 4 ; El, - 1,25,52;

- A ; - B 3, 4, - 3, - 4 ; - C 2, 5, - 2, - 5 ; - D 3, 4, - 3, - 4,

the latter being projected into a plane figure.

§ 6. The equations of transformation for the stereographic projection
with centre at the point A, i.e. the origin, and plane of projection w =
2 (e + 1), are :

x _ y _ z _ 2(e + 1)
x' y z w'

where x', y', z', w' are the co-ordinates of a vertex of the 600-cell and x, y, z
those of its projection.

Table I. — Notation for the 120 Vertices of the 600-cell, (a) Schoute’s
Notation, (b) Notation used in the Present Paper.

a.

b.

a.

b.

a.

b.

a.

b.

a.

b.

1

E

52

13

B

0

25

B

2

37

B

3

49

E

2

2

E

1

14

B

1

26

B

5

38

B

4

50

E

5

3

E

1

15

B-

1

27

B-

5

39

B-

4

51

E

4

4

A

16

-B

0

28

-B

2

40

-B

3

52

E

-3

5

C

5

17

C

1

29

D

2

41

C

5

53

E

5

6

c

2

18

C-

1

30

D

5

42

C

2

54

E

2

7

c

4

19

C

1

31

D-

5

43

C-

2

55

E

42

8

c-

-3

20

-c

1

32

-D

2

44

-c

5

56

E

53

9

-c

5

21

D

0

33

C

4

45

D

3

57

E

3

10

c

3

22

D

1

34

c

3

46

D

4

58

E

4

11

0-

-4

23

D-

1

35

c-

3

47

D-

■4

59

E

41

12

-C

2

24

-D

0

36

-c

4

48

-D

3

60

E

13

1913-14.]

Projection-Model of the 600-Cell.

257

Table II. — The Edges of the 600-cell.

(To complete the table (1) perform a cyclic permutation of the numbers 1, 2, 3, 4, 5 in each
row, keeping 0 unaltered ; (2) change the sign of every number in a row ; (3) change A, B, 0, D
into - A, — B, - C, - D and vice versa.)

A joined to each B.

B 0 joined to A ; B 1, 2, 3, 4, 5 ; C 1, 2, 3, 4, 5 ; D 0.

1 „ „ A; BO, 2, -3, -4, 5; C-l, 3,4, 3,4; D 1.

Cl „ „ B 0, 3, 4 ; C 1, 2, 5 ; D 0, 3, 4 ; E 1, 3, 4.

1 „ „ B- 1,3, 4; Cl, -3,-4; D - 1, 3, 4; El, 13, 14.

DO „ „ B 0 ; C 1, 2, 3, 4, 5 ; E 1, 2, 3, 4, 5 ; - D 0.

1 „ „ Bl; C-l, 3,4,3, 4; E 1, 31, 41, 3, 4 ; -Dl.

El „ „ C 3, 4 ; D 0, 1 ; E 2, 5, 3, 4 ; - D 0, 1 ; - C 3, 4.

1 „ „ Cl, 1; D 3,4; E3, 4,13,14; -D 3,4; -Cl, 1.

13 „ „ C 1,-3; D- 1,3; El,- 3, 53, 14; -D-l, 3; -Cl, -3.

Table III. — Co-ordinates of the Vertices of the 600-cell. Edge = 4.

(The order of the combinations of sign, corresponding to the vertices going from left to

right in a row, is + + , 4 — , — f, . To complete the table change all the signs in

each row.)

‘

X

y

z

X

y

z

A : w=0
- A : w = 4(e + 1)

1 °

0

0

D : w= 2e ; - I) : w= 2e + 4

B : w=e- 1 ; -B:w=3e + 5

0, 1

2, -5

3, 4

0

e + 3

— (e + 1)

— (e + 1)
0

e + 3

e + 3
±(e + l)
0

oohoc)

i

H

0

e + 1
±2

+ 2
0

e + 1

e+1

±2

0

E : w = 2(e + 1)

C : w=e + 1 ; -C : -M? = 3(e+1)

52

1

1

3, 13,41,- 4

2,- 3, 5,- 4
5, 42, 2, 35

2(e+ 1)
0
0
2

±(e+l)
±(e + 3)

0

2(e+l)

0

±(e + 3)
2

±(e + l)

0

0

2(e+ 1)
±(e + 1)
± (e + 3)
2

1, 1

4, 3

5, -2
5, 2

-3,-4

0

±2
e + 3
±(e+l)
±(e + l)

e + 3
0

±2
e+1
e + 1

±2
e + 3
0

e + 1

-(e+1)

VOL. XXXIV.

[Table IV.

17

258

Proceedings of the Eoyal Society of Edinburgh. [Sess.

Table IV. — Lengths of Edges of the Projection of the 600-cell.

Joining

Zones.

No. of
Edges.

Length of Edge, when—

Edge of
600-cell = 30.

Radius of Circumscri
= 30.

ibed Hypersphere
= 1.

- B to -

B

30

6(5 - e)

6(3e— 5)

0-3416

-o „ -

C

30

20

10(e-l)

0-4120

-C „ -

•D

60

10(e-l)V3

10(3 - e)V3

0-4411

E „

E

60

30

15(e - 1)

0-6180

B „

C

60

6e\/10 + 2e

6e\/10 - 2e

1*0515

G „

C

30

60

30(e - 1)

1-2361

B „

B

30

30(3 -fe)

30(e + 1)

3-2361

B „

A

12

oo

00

00

-A „ -

B

12

3\/10(5 - e)

6eV5 - 2e

0-3249

-B „ -

C

60

2e\/6(5 - e)

4 VI 5(5 -2e)

0-3752

-B „ -

D

12

12e\/5 - 2e

6e 50 — 22e

0-4016

-c „

E

60

10V6

5(e — l)V6~

0-5046

-D „

E

60

15(e-l)V2

15(3 - e)V2

0-5402

-B „

D

12

6eVlO-2e

12eV5-2e

0-6498

E „

D

60

6e\/5 + e

6eV& - e

0-7435

E „

C

60

30V2

15(e - 1)V2

0-8740

D „

B

12

12e\/5 + 2e

6eV10 + 2e

1-7013

0 „

B

60

30(1 + e)

60

2-0000

The accompanying plate represents a symmetrical orthogonal plane
projection of the three-dimensional projection on exactly \ the scale of the
model. Zones B and — B are in black, C and — C are in red, and E is in
blue. The vertices are denoted as in the text, but for compactness the
“ minus ” is put as a mark over the letter or number.

{Issued separately September 29, 1914.)

SOMMERVILLE: FOUR DIMENSIONAL FIGURE.

1913-14.] Resistance of Iron in Crossed Magnetic Fields. 259

XX. — Changes of Electrical Resistance accompanying Longi-
tudinal and Transverse Magnetizations in Iron and Steel. By
Professor C. Gr. Knott, D.Sc.

(Read May 4, 1914. MS. received October 1, 1914.)

Int January 1913 I communicated a paper on the changes of resistance of
nickel when subjected to a combination of longitudinal and transverse
magnetic fields (1). The following paper contains an account of exactly
similar experiments with iron and steel.

Each steel or iron strip formed the core of an anchor-ring coil which
was double-wound, with two exactly equal coils of copper wires. When
the current was passed through the two contiguous coils in series in the same
direction the metal cores were magnetized longitudinally. When the current
was passed in opposite directions through the two coils there was no
magnetization produced in the cores, but the heating effect was the same
as in the first case. At the beginning of each experiment the current was
applied in the latter or unmagnetizing arrangement, and was sustained for a
sufficient time to permit the temperature to become practically constant.
With reversal of the current in the one half of the enveloping coil a longi-
tudinally magnetizing force was established within the region occupied
by the iron or steel core. By means of a succession of reversals and re-
reversals the core could be subjected to a cyclical variation of magnetizing
force, while the temperature remained practically constant.

Six layers of the magnetizing coil were wound round each core, the
number of windings in each layer being in accordance with the following
table.

Layer.

Number of Windings

in Magnetizing Coil.

Steel Core.

Iron Core.

I.

156

184

II.

130

176

III.

120

184

IV.

128

180

V.

112

186

VI.

160

180

Total Windings

806

.

1090

260

Proceedings of the Royal Society of Edinburgh. [Sess.

The steel core formed a circle of 6 cm. diameter, and the iron core one of
7*3 cm. diameter. The larger size of the iron core accounts for the greater
number of windings in each layer.

Applying the usual approximate formula, we find that a current of one
ampere passing through the magnetizing coils will produce fields of 53*7
and 59*6 in the steel-core and the iron-core anchor-ring respectively.

The transverse field was applied by means of a specially designed
electromagnet with cylindrical pole pieces, the air gap between which
could be altered with ease. The anchor-ring coil under investigation was
placed symmetrically in the air gap, so that the axis of the anchor-ring
passed through the centres of the pole pieces. The magnetic fields
established in the air gap for various lengths of air gap and strengths of
current passed through the coils of the electromagnetic were measured by
means of a Grassot Fluxmeter. The lines of force established in the air
gap ran across the coiled strip of iron or steel, that is, transverse to the
direction in which the resistance was being measured.

The method of experimenting was identical with that described in
detail in the former paper (1).

The iron or steel strip formed the greater part of one arm of a Wheat-
stone Bridge, an approximate balancing being secured by adjustment of
the point of contact on a stretched wire. The combined system of con-
ductors forming the Wheatstone Bridge was made part of a circuit
through which a small steady current was passed from a secondary cell.
When this current was flowing steadily through the circuit, one of the
known resistances in the Bridge was altered slightly in a definite manner
by introducing a large resistance shunt in parallel with this resistance.
The deflection obtained on the galvanometer, being due to a measurable
disturbance in the balance, was essentially a standardizing of the deflec-
tion. This calibrating shunt being thrown out of connection, the iron or
steel strip which formed the opposing branch in the Bridge was then
magnetized. The disturbance due to this cause at once declared itself by
a corresponding deflection on the galvanometer scale. This deflection,
taken in conjunction with the deflection formerly produced in the standard-
izing experiment, gave the means of calculating the change of resistance
accompanying a given magnetization.

The galvanometer used in these experiments was a D’Arsonval galvano-
meter of the Ayrton-Mather design, and was found eminently satisfactory
on account of its steadiness and sensitiveness.

As in the previous experiments with nickel, the deflections were obtained
by reversing the steady current through the Wheatstone Bridge, the

1913-14.] Resistance of Iron in Crossed Magnetic Fields. 261

reading produced when the current was in the one direction being sub-
tracted from the mean of the readings immediately preceding and succeed-
ing with the current in the other direction. Five successive sets of such
triplets of readings were taken as quickly as possible : (1) with no magnetiz-
ing force applied, (2) with the magnetizing force applied in, say, the positive
direction, (3) with no magnetizing force applied, (4) with the magnetizing
force applied in the negative direction, (5) with no magnetizing force
applied. Each triplet gave a first difference of deflections ; and from the
five first differences two second differences were obtained by subtracting the
second from the average of the first and third, and the fourth from the
average of the third and fifth. The average of these two second differences
was the final value of the deflection due to the application of the magnetis-
ing force. By means of the standardizing experiment this final value was
reduced to absolute measure in the form c^N/N, where N is the resistance
of the iron or steel strip.

The calibration experiment involved the observation of at least nine
distinct readings ; and the final value of the deflection in the experiment
just described involved fifteen distinct readings. Hence the value of any
one of the ratios, c?N/N, is deduced from twenty-four distinct galvanometer
readings.

A complete set of observations for any given pair of fields, the one
longitudinal and the other transverse, required four groups of the fifteen
readings just described. The first group was obtained with no transverse
field, the longitudinal field being put on and removed twice with change of
direction between the first and second applications. In the second group
the transverse field was applied and kept steadily in action, the longitudinal
field being put on and off with reversal of direction as before. In the third
group the longitudinal field was kept steadily applied in its turn, and the
transverse field was put on and off exactly as the longitudinal field was
manipulated during the first and second groups. Finally, in the fourth
group the longitudinal field was thrown off altogether and the transverse
field applied and removed by itself in a cyclic manner, as was done with
the longitudinal field in the first group.

The field which was put on and off with reversal of direction is dis-
tinguished as the “ cyclic field ” ; and the other, which for the time is being
maintained, is called the “ steady field.”

For other details of the method, and for the investigation of the complete
theory, reference may be made to the earlier paper.

In the Appendix, which contains all the measured values of the changes
of resistance, and in what follows here, the horizontal field will be re-

262 Proceedings of the Royal Society of Edinburgh. [Sess.

presented by h and the transverse field by t. The corresponding changes of
resistance will be represented by capital letters H and T in accordance with
the following convention.

The four changes of resistance which form one set will be H, H(T), T,
T(H), with the meanings

H = effect of cyclic h, no transverse field existing;

H(T) = „ „ „ h superposed on steady transverse field ;

T= „ „ „ t, no longitudinal field existing ;

T(H) = „ „ „ t superposed on steady longitudinal field.

Results for Steel: dN/NxlO4.

Longitudinal

Field.

i

Transverse Fields in ( ).

(864)

(1282)

(2141)

(3781)

(53-7)

H

4- 2*84

+ 2-72

4- 2-77

4- 2-89

H(T)

4- 0*3

+ o-i

4- 0-19

4- 0-01

T

- 4*59

- 5-53

- 6-29

- 7-05

T(H)

- 7"55

- 9-12

- 9-86

- 1037

(843)

(1268)

(2111)

(3706)

(104)

H

4- 5T5

+ 5-19

4- 5-29

+ 4-75

H(T)

+ 0-86

+ 0-31

4- 0-29

+ 0-22

T

- 4-44

- 5-64

- 6'31

- 6-73

T(H)

-10-34

-11-39

-12-25

-12-4

(606)

(1268)

(3706)

(157)

H

*+ 6-47

+ 6-69

. + 6-45

H(T)

+ 3-12

4- 1-08

4- 0*5

T

- 3-99

- 5-91

- 6-77

T(H)

- 7-75

- 12-53

...

-14-3

Results for Iron: dN/N x 104.

Longitudinal

Field.

Transverse Fields in ( ).

(898)

(1282)

(2156)

(3796)

(59-6)

H

4- 3-83

+ 4-58

4- 3-76

4- 3-79

H(T)

4- 1-17

4- 0-49

4- 0-36

4- 0-04

T

- 2-7

- 5-48

- 7-84

- 8-98

T(H)

- 4 92

-10-11

-11-51

-12*46

(1282)

(2156)

(3781)

(120-4)

H

+ 6-25

+ 6-83

+ 6-24

H(T)

4- 2-43

+ 0-52

+ 0-09

T

- 5-73

- 7-97

- 9-41

T(H)

- 10-83

- 13-0

-15-8

1913-14.] Resistance of Iron in Crossed Magnetic Fields. 263

The various values are tabulated in the foregoing tables. The bracketed

o o

numbers in the first column on the left give the values of the longitudinal
fields ; and the bracketed numbers in the horizontal rows give the values
of the transverse fields. The remaining numbers are the changes of resist-
ance produced by the field or combination of fields indicated by the symbol
in the second column.

In these experiments there is no evidence of what others have observed,
namely, an increase of resistance in low and moderate transverse fields.
For example, Grunmach (2), in three out of the four recorded experiments
with iron, obtained increase of resistance up to fields of 7000 or 8000 Gauss,
after which the change became a decrease rapidly increasing in value as
the field was taken stronger. In like manner, he obtained with nickel an
increase of resistance up to field 700, and thereafter decrease as the trans-
verse field was made stronger.

I have always been very doubtful of the reality of this initial increase
of resistance ; and a recent paper by Messrs W. Morris Jones and
J. E. Malam (3) seems to me to establish the fact that when nickel is ac-
curately placed in the transverse field the change of resistance is always a
decrease. In my own earlier experiments with nickel spirals in transverse
fields I was never satisfied that I had the spiral absolutely perpendicular
to the field until I had got rid of this apparent initial increase in low fields.
When very thin wires are used, the difficulty of eliminating all chance of
a resolved longitudinal effect becomes greatly increased. For the change
of resistance depends undoubtedly upon the magnetization within the
metal. In very thin wires the transverse magnetization cannot be very
much greater than the transverse magnetizing force, whereas in the
early stages the longitudinal magnetization is much greater than the
longitudinal magnetizing force. A little consideration will show that
a comparatively small resolved component of the magnetizing force along
some part of the wire may easily be accompanied by a longitudinal
magnetization large enough to produce a resistance change of positive
sign able to overbalance the very small decrease due to the transverse
magnetization.

All this danger of having present an uneliminated longitudinal com-
ponent is obviated in the experiments now described by the use of ribbons
instead of wires of iron and nickel. For in the first place it is a compara-
tively simple matter to set the coiled strip or ribbon with its width
accurately along the lines of force ; and in the second place, even if the ad-
justment were not quite accurate, the magnetization along the width of the
metal would be considerable, so that any possible resolved longitudinal

264

Proceedings of the Royal Society of Edinburgh. [Sess.

effect would not be large enough to mask the effect of the transverse
field. It seems to me, therefore, that attempts to explain the supposed
increase of resistance in low transverse fields are quite uncalled for.
What requires theoretical explanation is the decrease of resistance of
both iron and nickel in transverse fields, and the increase of resistance
in longitudinal fields.

This conclusion receives further support that in the case of cobalt
Grunmach (2) obtained only a decrease of resistance. The cobalt was not
in the form of a thin wire, hut was a strip 02 mm. thick and 0*5 mm. broad
coiled in a double flat spiral. With such a form there was less chance of
error of adjustment. Consequently no increase of resistance was obtained
in the lower fields.

With the doubtful exception of tin in the lowest field, all the other
metals experimented with by Grunmach showed increase of resistance in
transverse fields (2). These metals were silver, cadmium, tantalum,
platinum, tin, gold, palladium, zinc, copper, and lead.

Through the kindness and by the help of Principal A. Crichton Mitchell,
late of Travancore, I am able to add to these mercury. Professor Mitchell
prepared a thin mercury column in a spiral glass tube of a convenient size
to be inserted in the air-gap of the electromagnet which I used for
establishing the transverse fields in the present experiments. Substituting
the mercury spiral for the iron or steel ribbon in the arrangement described
above, I measured the change of resistance in four different fields. The
results are given in the following short table, in which the first row gives
the values of the transverse -field in Gauss, and the second the correspond-
ing changes of resistance per 10,000.

Change of Resistance of Mercury in Transverse Magnetic Fields.

Tranverse Field.

2064

3801

5263

6473

cZR/R. 104

+ 0T1

+ 0-31

+ 0-43

+ 0-64

The relation between these sets of numbers is not linear, nor does a
parabolic law satisfy them very satisfactorily. Nevertheless, assuming the
formula dR/R = Af2, where t is the transverse field, we find

A = 1'7 x 10~12,

a result of the same order as for other non-magnetic metals.

[Note added November 19, 19 — My attention has been drawn to a
paper published in 1910 in the Nuovo Cimento (5), in which Dr G. Rossi

1913-14.] Resistance of Iron in Crossed Magnetic Fields. 265

gives certain results for the change of resistance of mercury in a transverse
magnetic field. Treating his numbers in the same way, I find that A
has the value 6 x 10~13 or 5 x 10-13 for mercury filaments of diameter
0-7 mm. or 0'5 mm. respectively. The diameter of the mercury filament
used in the experiment just described was almost exactly 1 mm. The
discrepancies are considerable ; and j Jo is difficult to believe that the effect
in mercury should depend on the diameter of the filament within the
limits indicated.]

Now in field 3750 the corresponding changes of resistance per 10,000 in
iron and steel are respectively — 6 ‘9 and —9*2, that is, twenty or thirty
times the numerical value for mercury.

In the earlier experiments with nickel the highest transverse field
reached was only 815 ; but it was obvious that in much higher fields the
change of resistance would not exceed the value — 95 x 10-4, that is, about
ten times the value for steel. Changes numerically equal to those given
above for iron and steel were obtained for nickel in fields of only twenty
and thirty Gauss respectively.

It is well to bear in mind that, as proved in the earlier paper, the
numerical value of the change due to a given transverse field is a function
of the width of the strip of the magnetic metal, for the simple reason that
on that width also depends the value of the magnetization.

I now pass on to the consideration of the main object of the research,
namely the influence of a steadily maintained magnetic field upon the
changes of resistance due to a cyclically applied field at right angles to the
former.

With regard to the numbers given in the Table three pages back, it
should be noted that the last figure in the measured changes of resistance
is of no value, being well within the limits of experimental error.

The smaller number of data for the iron strip was due to the overheat-
ing of the magnetizing coil round the strip and the consequent breaking
down of the insulation between the contiguous turns of the coil. But the
nature of the results is obviously the same in both metals, and may be
expressed qualitatively in the following words : —

1. Under the influence of longitudinal magnetization the electric resist-
ance of iron and steel is increased ; but this increase is notably diminished
when the longitudinal magnetizing force is superposed cyclically upon a
steadily sustained transverse magnetization. In the highest transverse
fields used the change of resistance due to the superposed longitudinal field
was in most cases very small, being a small fraction of the value when the
longitudinal field acted alone.

2 66 Proceedings of the Royal Society of Edinburgh. [Sess.

2. Under the influence of a transverse magnetization the electric resist-
ance of iron and steel is diminished ; and this diminution becomes markedly
greater when the transverse field is superposed cyclically upon a steadily
maintained longitudinal field. In certain cases the change of resistance
due to the transverse magnetizing force was more than doubled when this
field was superposed upon the steadily maintained longitudinal field.

It will be seen on referring to my earlier paper on the behaviour of
nickel under crossed magnetic fields (1) that as regards the effect of the
steady longitudinal field upon the change of resistance accompanying the
application of a transverse field, exactly the same kind of phenomena are
obtained with the iron and steel.

On the other hand, as regards the effect of the steady transverse field upon
the change due to the superposed longitudinal field, there was a peculiarity
in the behaviour of nickel which is not found in the case of iron or steel.
This peculiarity was that when the steady transverse field was above a
certain value the change of resistance due to the superposed longitudinal
field altered in sign, that is, the resistance was diminished, not increased.

In the earlier experiments with nickel the arrangements did not permit
the application of such large fields as were possible in the later experiments
with iron and steel. Yet much greater values of the resistance change
were obtained with the nickel than with the iron or steel, although these
were subjected to much higher magnetizing forces. This will appear from
the comparisons made in the short table below, in which -the changes of
resistance in practically the same strengths of magnetizing fields are set
side by side. The approximate values of the fields are given below each
group of measurements.

Changes of Resistance per 10,000.

Longitudinal Field Cyclic.

Transverse Field Cyclic.

Nickel.

Steel.

Iron.

Nickel.

Steel.

Iron.

H

+ 66

+ 2-8

+ 3-7

T

- 91

-4*3

-2-7

H(T)

-17

+ 0-3

+ 1*2

T(H)

-192

-7-6

-4-9

h=

60

54

60

t =

800

700

900

t =

800

800

900

h 4

60

54

60

The main features of the phenomena here described are contained in
this short table. The similarity of the effects produced in iron and nickel
suggests that we are dealing with a fundamental property of ferromagnetic

1913-14.] Resistance of Iron in Crossed Magnetic Fields. 267

substances ; but of this we cannot be certain until the same experiments
have been carried out with cobalt. I hope also to be able to make a similar
study of the properties of bismuth. Meanwhile, I leave over any further
theoretical discussion. I cannot, in fact, add anything to what was said in
the earlier paper ; and I am not aware that anyone has been able to make
even a plausible suggestion as to the molecular mechanism on which these
phenomena in crossed magnetic fields depend.

My thanks are due to Miss J. G. Dunlop and Miss M. Jazewska, who
determined for me with great care the change with temperature of the
resistance of the iron ribbon.

Appendix.

Results as reduced in Laboratory Note-Book, arranged approximately
ACCORDING TO DATE IN THE YEAR 1913.

The numbers in the columns headed Resistance Change give the changes of resistance,
estimated per 10,000, of the metal strip.

h and £ represent respectively the longitudinal and transverse fields.

The temperatures are calculated from the resistances of the metal ribbon.

Iron.

Date,

Fields,

Temp.

Cvclic

Field.

Steady

Field.

Resistance

Change.

Date,

Fields,

Temp.

Cyclic

Field.

Steady

Field.

Resistance

Change.

July 22

h

None

+

3-69

h= 59-6

h

+ £

+

1T2

£ = 898

h

-£

+

1-22

37° C.

h

None

+

3-96

h

+ £

+

1T7

£

None

-

2'7

£

+ h

-

4-72

£

-h

-

5-12

h = 59-6

h

None

+

4-58

July 23
h= 120-4

h

None

+ 6-25

£ = 1282

h

£

+

0*49

£ = 1282

h

£

+ 2-43

37° C.

t

None

-

5-88

160° C.

£

None

- 5-73

£

h

-

10T1

£

h

- 10-83

£

None

-

5-09

h = 59-6

h

None

+

3-76

ft = 120-4

h

None

+ 6-83

£ = 2156

h

£

+

0-36

£ = 2095

h

£

+ 0-52

37° C.

£

None

-

7-84

160° C.

£

None

- 7-97

£

h

-

11-51

£

h

- 13-9

k = 59’6

h

None

+

3-79

7i= 120

h

None

+ 6-24

£ = 3781

h

£

+

0-04

I £ = 3796

h

£

+ 0-09

37° C.

t

None

—

8-98

160° C.

t

None

- 9-41

£

h

—

12*46

£

h

-15-8

268

Proceedings of the Koyal Society of Edinburgh. [Sess.

Steel.

Date,

Fields,

Temp.

Cyclic

Field.

Steady

Field.

Resistance

Change.

Date,

Fields,

Temp.

Cyclic

Field.

Steady

Field.

Resistance

Change.

July 26

h

None

+ 2*84

July 25

h

None

+ 5-15

h = 53-7

h

£

+ 0-30

h— 104

h

£

-1- 0-86

£ = 864

£

None

- 4*59

£ = 843

£

None

- 4-44

34° C.

£

h

— 7'55

70° C.

£

h

- 10-34

h= 53-7

h

None

+ 2-72

h = 104

h

None

+ 5-19

£ = 1282

h

£

+ o-io

£ = 1268

h

£

+ 0-31

34° C.

£

None

- 5 53

70° C.

£

None

- 5-64

£

h

- 9-12

£

h

-11-39

h = 53-7

h

None

+ 2-77

h = 104

h

None

+ 5-29

£ = 2141

h

£

+ 009

£ = 2111

h

£

+ 0-29

34° C.

£

None

- 6-29

70° C.

£

None

- 6-31

£

h

- 9-86

£

h

-12-25

h = 53-7

h

None

+ 2-89

h= 104

h

None

+ 4-75

£ = 3781

h

£

+ o-oi

£ = 3706

h

£

+ 0-22

34° C.

£

None

- 7-05

70° C.

£

None

- 6-73

£

h

- 10*73

£

h

-12-4

July 29-30

h= 158

h

None

+ 6-47

£ = 606

h

£

+ 3-12

160° C.

t

None

- 3-99

£

h

- 7-75

h= 156

h

None

+ 669

£=1268

h

£

+ 1-08

160° C.

£

None

- 5-91

£

h

-12-53

h= 156

h

None

+ 6-45

£ = 3706

h

£

+ 0-50

160° C.

£

None

- 6-77

£

h

-14-3

REFERENCES.

(1) C. G. Knott, “Changes of Electrical Resistance accompanying Longitudinal
and Transverse Magnetizations in Nickel,” Proc. R.S.E., xxxiii, p. 200 (1913).

(2) L. Grunmach, “Uber den Einfluss transversaler Magnetisierung auf die
electrische Leitungsfahigkeit der Metatle,” Ann. d. PhysiJc , vol. xxii, p. 141, 1906.

(3) W. Morris Jones, B.Sc., and J. E. Malam, “The Electrical Resistance of
Nickel in Magnetic Fields,” Phil. Mag., April 1914.

(4) C. G. Knott, “Magnetization and Resistance of Nickel at High Tempera-
tures,” Part 2, 1906, Trans. R.S.E., xlv, p. 547.

(5) G. Rossi, “Variazioni di resistenza del mercurio e delle amalgame di bismuto
nel campo magnetico.” 11 Nuovo Cimento, 1911, serie vi, tomo ii.

( Issued separately December 14, 1914 )

1913-14.]

Obituary Notices.

269

OBITUARY NOTICES.

Dr A. C. L. G-. Giinther, M.A., Ph.D., M.D., LL.D., F.R.S., etc.

By William C. MTntosh.

(Read June 15, 1914.)

The death of Dr Albert Charles Lewis Gotthilf Giinther, who was elected
to the Honorary Fellowship of this Society in 1895, has deprived science of
the most distinguished ichthyologist of his day, and one whose labours in
other departments of zoology were no less noteworthy. He was born in
Esslingen in South Germany on the 3rd October 1830, his father being
“ Siftungs-Commissar ” in Esslingen and “ Estates-Bursar ” in Mohringen,
a descendant of a family which had been known in the locality for hundreds
of years — indeed the Swabian branch of the Gunther family was settled in
and about Mohringen on the Filder Plateau at the beginning of the fifteenth
century. His mother was Eleonora Nagel, whose family originally came
from Bremen. Albert was the eldest son, and was sent for his early
education to the Gymnasium at Stuttgart (1837-47); and subsequently he
studied at the Universities of Tubingen (1847-52, 1856-57), Berlin (1853),
and Bonn (1854-55), thus gaining a wide experience of University life and
a breadth of culture which had an important influence on his future career.
Descended from a line of clergymen, family tradition destined him for the
ministry of the Lutheran Church, for which, indeed, he was trained at the
Theological College of Tubingen, and for which he passed the qualifying
examination. His natural bent, however, was wholly in another direction,
and, after taking the degree of Ph.D. in 1852, he decided to study science
and medicine, taking the degree of M.D. at the same University in 1862.
Before this, however, he had chosen zoology as the field of his labours, and
had published his first paper on a Distome as well as a treatise on Fische des
Neckars, with the coloured figure of a form new to the river (1853), and a
Randbuch der medicinischen Zoologie (1858). Visiting England in 1855, he
met Sir Richard Owen and Dr John Edward Gray, who had been interested in
the former work, and a friendship sprang up between them — resulting in the
selection of Dr Giinther, in October 1857, to arrange and describe the Fishes,
Amphibians, and Reptiles in the British Museum ; as well as to prepare

270

Proceedings of the Royal Society of Edinburgh. [Sess.

catalogues of the greater part of the collections. Thus settled with definite
work before him, and amidst congenial surroundings, Dr Gunther laboured
incessantly at his great task ; and though the apartments, which were cellar-
like, in the old Museum in Bloomsbury were far less cheerful than in the
New Natural History Museum at South Kensington, yet his interest and
energy never flagged. From the first the Fishes, Batrachians, and Reptiles
were prominent in his studies, though Birds and Mammals also received
due attention, as shown in various papers to the Zoological Society. Thus
his work in the latter group ranged from monkeys, carnivores, rodents, and
ungulates to marsupials, and from diverse parts of the globe. Besides
accounts of recent birds, he, along with Mr Newton, investigated the extinct
birds of Rodriguez. Only a lifelong experience, rigid accuracy, and great
natural ability could have enabled him to grasp the salient points of forms
pertaining to such diverse types, and this not in single species, but often in
hundreds, and whose close resemblances or intricacies of structure were in
themselves sources of perplexity.

The extraordinary activity with which he laboured is demonstrated by
the long list of his works, memoirs, and papers on all the groups mentioned.
Amongst the more important are such as The Geographical Distribution
of Reptiles (1858), in which he had forestalled many interesting features
subsequently described by others ; the memoir on Ceratodus, the lung-fish
of the Burnett and Mary rivers of Queensland ; that on the structure of
Hatteria (Sphenodon) from New Zealand; “ On the Giant Tortoises”; and
the vast array of papers on the Fishes, Amphibians, Reptiles, and occasion-
ally Birds and Mammals, of every important British expedition, as well as
collections from every quarter of the globe — from Pole to Pole, and from
river, lake, sea, and land. The mere perusal of the titles of his papers is no
light task, whilst every one is the record of a painstaking, laborious research.
Mr E. A. Smith, one of his colleagues, estimates that, besides the works and
larger memoirs, there were about 300 papers published in the Journals of
the London Societies, and that the whole of his writings occupy about ten
thousand pages, illustrated by a very large number of fine plates and
text-figures. It is a record remarkable alike for its unswerving devotion
and notable results, and affords a splendid example to younger men. He
accomplished much of this work when burdened with the cares of adminis-
tration, preparing official reports “ in connection with individual members
of the staff, monthly and annual reports of progress and work accomplished,
the supervision and editing of catalogues and guides issued by his depart-
ment, besides the consideration of all proposed acquisitions ” * and the con-
* E. A. Smith, Zoologist , March 1914, p. 115.

1913-14.] Obituary Notices. 271

tinual correspondence. Moreover, to his fellow- workers, such as Charles
Darwin and A. Russel Wallace, he was of much service in the chapters on
the distribution and classification of Fishes, Amphibians, and Reptiles.

The memoir on Geratodus in the Philosophical Transactions is one of
special interest, as it details the structure and relationship of a Dipnoan
fish, the ancestors of which were separated by the long gap between the
present and the Devonian and Carboniferous periods. Yet the persistence
of type, as pointed out by Dr Gunther, is most remarkable. Further, those
early representatives were not the beginners of a series, “ but the last of
many preceding developmental stages.”

His labours in the British Museum resulted in the issue of eight volumes
of the Catalogue of the Fishes, a work of immense research, patient in-
vestigation, and accurate description. In this work (4000 pages) he pays
a tribute to Johannes Muller’s ordinal arrangement, though he was not
satisfied that the coalesced pharyngeal bones are of sufficient importance to
unite the Acanthopterygii and Malacopterygii into one order. An idea of
the vast labour spent on this task may be obtained by glancing at the
number of species dealt with, no less than 6843 being well established,
whilst 1682 others are doubtful. The carrying out of this gigantic task in
the cellars of the old British Museum in Bloomsbury shows the indomitable
energy of the investigator as well as his thorough grasp of the subject. It
is indeed doubtful if such a task will ever again be attempted on the same
lines, at least without the physical collapse of the investigator. Two
volumes of a Catalogue of Batrachia salientia and Colubrine snakes
complete the series of ten volumes. Moreover, the Ray Society published
his fine work, with numerous illustrations by Ford, on the Reptiles of British
India. His daily work in the British Museum ranged over snakes from
West Africa and South America to those from Siam and Australia ; fishes
from the most recent British dredging expeditions, those from fresh waters
in every quarter of the globe, and from the neighbouring seas ; amphibians
from widely distant regions ; birds and mammals from diverse localities,
and often of great interest. Amongst his other works are the Challenger
volumes on the shore and deep-water fishes collected in the great expedition.
The subject of the deep-sea fishes had long been of special interest to
Dr Gunther, and we may imagine the delight he felt in the study of no
less than 266 species belonging to this category— many of weird form, with
remarkable sensory appendages and phosphorescent organs. As he himself
has stated, the Challenger series laid a broad and sure foundation to our
knowledge of the abyssal fish-fauna, and he incorporated all the most
recent work of the Norwegian, American French, and British investigators

272

Proceedings of the Royal Society of Edinburgh. [Sess.

of the deep sea. In the introduction to this fine treatise his experienced
remarks on phosphorescence and on the nature and distribution of deep-sea
fishes are of great value and interest. This volume is illustrated by no less
than 72 plates, many of them double, and admirably drawn by Mintern
Bros., the successors of G. H. Ford.

His report on the shore fishes collected by the Challenger was
published before the preceding treatise, and comprised an account of 1400
species, of which 94 were new to science. Only a skilled ichthyologist
could thus have worked out the collection with such rapidity, for it was
issued in 1886, when Sir Wyville Thomson was still at the head of affairs.
Rare forms from the tropical Atlantic, Bermuda, the temperate zone of
the South Atlantic, of the Antarctic Ocean, the temperate zone of the
South Pacific, of Japan, and the neighbouring regions were accurately
described and figured. This and the foregoing volume would alone have
made a reputation. Moreover, it gave Dr Gunther an opportunity of
widening our views with regard to the mutual relations of the fishes of
deep and shallow water, and of demonstrating the wide range of many
forms both in depth and locality.

One of his greatest services to the science of zoology as a whole, and one in
which his work has directly proved a boon to all his fellow- workers, is the
Record of Zoological Literature , which he founded in 1867 and edited for
several years. Investigators have thus a ready means of making themselves
acquainted with contemporary work in every country. This step alone
would have earned the thanks of every zoologist, and its continuance to-day
by the Zoological Society shows its permanent importance. The work must
have given Dr Gunther much thoughtful labour and care, and could only
have been undertaken by one in a central position, and with the co-operation
of a wide circle of zoological friends at home and abroad.

His Introduction to the Study of Fishes (1880) is another treatise
which has had a widespread popularity — from the masterly way in which
the author handled a subject to which he had devoted the best part of
his life. No student of the group can find a more comprehensive yet
concise treatise in any language, and none having an equal amount of
reliable information. His chapters on the distribution of fishes — geological
and geographical — are especially full of experienced remarks.

Though Dr Gunther in his early days made a few of his own drawings,
he soon became so occupied that it was necessary to employ others, and
he was fortunate in securing for many years the services of G. H. Ford —
who was facile princeps in lithography during his day, and who in the
delineation of the lower vertebrata has never been surpassed — and he

1913-14.] Obituary Notices. 273

acquired a special skill in illustrating the memoirs of Dr Giinther, whose
appreciation of a fine drawing was ever forthcoming.

Entering the British Museum in 1857, he by and by was appointed on
the staff, and he rose step by step till in 1875 he became Keeper of the
Zoological Department in succession to his friend Dr J. E. Gray, and he
held this post for twenty years. His record in this institution is remark-
able— as beneficial to the Museum as creditable to himself. His catalogues
have already been alluded to, and the vast array of original contributions
to the Royal, Zoological, and Linnean Societies formed an unbroken
succession from first to last. The latter alone would have made a great
reputation, yet they were but fragments of his daily work in perfecting
the numerous collections committed to his care, in carrying out the
endless duties of administration, and in devising improvements. More-
over, the construction of the New Natural History Museum at South
Kensington, the scheme of Sir Richard Owen, likewise gave him increased
responsibilities in connection with the arrangement of the galleries and
cases, and still more with the transfer of the vast and valuable collections
to their new premises. This task, perhaps, brought out the administrative
talents and practical skill of the Keeper of the Department more promi-
nently than anything else, and well merited the special minute of the
Trustees on its successful completion. Amidst the array of vans, lorries,
cabs, and conveyance by hand, no specimen of value was lost or broken.
Nor was the rearrangement in the new Museum less successfully carried
out, though not a few serious obstacles were encountered. Thus when the
cases for the mammals on the ground floor were being arranged, it was
found that the architect’s ornamental projections on the walls were inimical
to satisfactory adjustment, and thus this Class had to be placed on the
first floor. He also insisted on the advantages of a separate building for
specimens preserved in spirit, both for the greater safety of the extensive
collections in jars, and for the security of the other portions of the
magnificent building.

Some idea of the extent of the National Collection may be gained when
it is mentioned that in 1880 there were 1,300,000 zoological specimens,
and that when Dr Gunther retired in 1895 there were 2,245,000. Known
all over the world for his labours in zoology, and having an extensive
acquaintance with naturalists and travellers, much of this progress was
due to his tact and personal influence — and, it may be added, to his personal
example, for from his earliest days he was a field-naturalist as well as
a scientific author, and he never missed an opportunity of adding to the

collections in the British Museum, whether as the result of his own
VOL. xxxiv. 18

274 Proceedings of the Royal Society of Edinburgh. [Sess.

dredging and collecting expeditions, or by securing from friends such rare
forms, for example, as Leptocephali.

In connection with the fittings of the National Collection at South
Kensington, it is also interesting to remember that he favoured the con-
struction of metal cases instead of wood, though the Government did not
adopt this plan — probably on the score of expense. He was indeed one of
the earliest in this country to show the advantages of such cases now fitted
up in the most advanced museums. Further, from an early period of his
career in the Museum he saw the importance of having a reference library in
addition to a general library in connection with the Zoological Department,
and he persistently exerted himself to carry out this aim. The severance
of the collections from the proximity of the great library in Bloomsbury
made this the more necessary, and now the New National History Museum
has an important and invaluable general as well as a special zoological
library — an inestimable boon to visiting naturalists as well as to the staff.

Yet another side of Dr Gunther’s services in the British Museum merits
attention, viz. the development of the systematic work in the Museum.
Thus he succeeded in increasing the scientific staff gradually from 4 to 13,
and by a skilful modification of the duties of the attendants he managed
to relieve the trained men from menial duties and enlist their services
in highly skilled museum-work. Thus the scientific staff had at their
disposal a body of experienced and reliable practical aids, so that their
progress was rendered both rapid and satisfactory.

His services as a Vice-President of the Royal and Zoological Societies,
and President of the Linnean Society, must have entailed a large absorp-
tion of his time and energies — especially as many of his memoirs and
papers were communicated to one or other.

It might be supposed that one so constantly and so actively engaged
in the pursuit of science had little time for attending to the interests of
visitors to the collection. Yet, if he had done nothing more than in-
augurated the fascinating and instructive cases containing the nesting
of birds as now exhibited in the Museum, such would have been memor-
able. No feature in the great collection is more popular than these life-
like illustrations of the British nesting birds of both sexes, their eggs,
newly hatched young, and their environment. As he himself has stated,
it was essential that the actual birds which made the nest, with their
eggs or young, should be secured, and the surroundings taken from the
spot, the only artificial elements being flowers, leaves, or structures which
could not be preserved satisfactorily. In the case of such birds as the
bustard and the ruff, the remarkable plumage and attitudes of the males

1913-14,] Obituary Notices. 275

form an additional attraction in these charming scenes. None but a
skilful field -naturalist in whose mind the actual scenes had imprinted
themselves could have designed these wonderful cases ; and Dr Gunther
has often said that he gained as much real knowledge from Nature as from
the splendid libraries at his command.

His work in the other departments, viz. Mammals and Birds, was no less
noteworthy. Every important and unimportant expedition consigned to
him the fishes, amphibians, and reptiles, and occasionally the birds and
mammals, and his conscientious treatment of them was uniformly the
same, whilst his personal influence with the collectors was a constant
source of rich additions to the National Museum.

By Dr Gunther’s recommendation many valuable collections were added
to the British Museum, such as the Gould Collection of Birds, the Oates
Collection of the Birds of Pegu, Goodwin- Austin’s Indian Birds, the Sclater
Collection of Birds, Capt. Shelley’s African Birds, the Saville-Kent Corals,
the Baly Collection of Phytophaga, the Bates Collection of Heteromera,
the Zeller Lepidoptera, the Keyserling Arachnida, the Moore Indian Lepido-
ptera, the Pascoe Coleoptera, the Morelet Land and Freshwater Shells, the
Atkinson Coleoptera and Rhynehota, the Grote North American Lepido-
ptera, and the Parke Foraminifera.

His great knowledge of zoology and ichthyology in particular, as
well as his familiarity with the habits of animals, caused his services to be
much sought after by Government Commissions and municipal bodies in
regard to their fresh waters. Thus he reported on the pollution of the
Thames and on that of several trout and salmon rivers. His evidence on
the pollution of the Lower Thames was of great importance as well as
conclusive, for his careful experiments proved the effects of such on fishes,
and he indicated the length of time they would survive in various kinds of
polluted water, e.g. sewage, effluents from gas-works, ink-works, etc. He
went, for instance, minutely into the question, surveying the Lower Thames
in a steam- vessel placed at his disposal by the Metropolitan Board of Works,
and thus was enabled to give reliable advice to that body. His evidence
in connection with the “ yellow fins” of the Allan Water was another
example of his acuteness and caution in dealing with a contested point.

Moreover, Dr Gunther was ever ready to encourage local collections of
objects of natural history, and his gifts to provincial museums, of tame
birds for private parks and aviaries, are gratefully remembered. One of
his last donations was that to the University Museum of St Andrews, to
which he presented about fifty exquisitely coloured birds, ranging from
Reeve’s pheasant and the capercaillie to humming-birds, the group of the

276 Proceedings of the Royal Society of Edinburgh. [Sess.

Pittas being especially noteworthy for their striking coloration. The
majority came from the collection of A. Russel Wallace, though some, such
as the young kestrels, were reared by himself.

Since he came to England in 1856 he took an interest in the marine
fauna — indeed in that year a local publication included his contributions
to the marine fauna of Brighton. His holidays were generally devoted
to the increase of the Museum’s marine or freshwater fishes and other
forms. At St Andrews he collected in a day or two various fishes and
ten species of marine annelids. An excellent sailor, he sometimes was the
only effective naturalist on board a boat or yacht, as, for example, when
the distinguished Professor Kolliker of Wurzburg requested his aid off the
south coast of England. His tanks for the preservation of the large fishes
always accompanied him in these excursions. None enjoyed the freedom
of forest, moor, or hill, or the quietude of a river bank more than he, and
thus he gained an intimate knowledge of Nature — both animate and inani-
mate— so important for the head of the Zoological Department of the
National Museum. This knowledge, gained by close observation on the
Continent of Europe, in Britain, and in the adjoining seas, made him a
delightful companion, and there were few who were more welcome than he
at the country-seats both of England and Scotland. Moreover, he was an
excellent shot — a reminiscence, perhaps, of his military experiences in South
Germany — and an expert angler. At one time he took an active interest
in the introduction of the Sheat-fish ( Siluris glanis) to English waters, and
with success ; but the voracious habits of these large fishes proved disastrous
to the salmonoids, and the attempt was not repeated.

Quite lately he prepared for the Trustees a brief account of the changes
in the British Museum (Natural History) from 1858 to 1895 — that is, during
the period of his official connection with the institution. The continuous
stream of important additions, many of which were due to the influence of
the Keeper himself, the increase of the assistants, the inauguration of
systematic publications by the staff, the transference of the greatest collec-
tion of the kind in the world from the old to the new quarters, and the
introduction of every modern improvement in arrangement, are told with
the characteristic modesty and restraint of the veteran investigator.

Dr Gunther was the recipient of many honours both at home and
abroad. He was a Vice-President of the Royal and Zoological Societies,
President of the Linnean Society, President of the Biological Section of the
British Association, and a Fellow of most of the learned societies at home
and abroad. He was awarded a Royal Medal by the Royal Society, and
the Gold Medal of the Linnean Society.

1913-14.] Obituary Notices. 277

Dr Gtinther had a tall, somewhat lightly-built, wiry physique which
for nigh sixty years stood without a break the stress and strain of official
life, the unhealthy atmosphere in the old cellar in the basement at
Bloomsbury, and the incessant demands of scientific work. His hair was
fair, eyes blue, and his complexion fresh. Throughout his long period of
public service, he was never known to have sick-leave. Of strong person-
ality, and resolute when he had once formed a conclusion, yet he was not
only an agreeable colleague, but a warm friend to a large circle of acquaint-
ances. In his home he was one of the kindest parents, ever ready to
sacrifice himself for the happiness of his family, who had an equally warm
attachment to him. Of active habit, and delighting in his garden and his
pets, he was ever busy and cheerful. His first home at Hampton Wick,
and those subsequently at Surbiton and at Kew Gardens, all reflected the
tastes of an enthusiastic naturalist whose pleasure lay in everything with
life. His myrtles and other shrubs and trees at Surbiton, his maiden-hair
tree and collection of rare shrubs and plants at Kew Gardens, his aviaries,
house-pets, and his observations on the birds in Kew Gardens, were a
never-failing source of interest and information to himself and others.
His health suffered some years ago from a severe attack of pneumonia, but
lately was satisfactory until an abdominal affection necessitated an opera-
tion from which he did not rally. He was buried in the quiet cemetery
at Richmond, mourned by a large circle of scientific friends.

Dr Gunther was twice married. His first wife, Roberta MTntosh, of
St Andrews, made the exquisite coloured figures of marine animals, many
of which have been published by the Ray Society ; their son, Robert,
is a Fellow and Tutor of Magdalen College, Oxford, and the author of
various able works and memoirs. Dr Gtinther’s second wife, who, with a
son, survives him, was Theodora Dowrish Drake, from Cornwall, a lineal
descendant of a brother of Sir Francis Drake.

Dr Gtinther will ever be remembered as a great systematic zoologist
who had early and independently worked out many of the problems of
the distribution of animals which subsequently were more prominently
associated with other names, as an original investigator and facile princeps
in Fishes, Amphibians, and Reptiles, and as a man of untiring energy, re-
markable power of penetration, and of great administrative capacity. More-
over, the interests of the public and of scientific workers at home and
abroad were ever safe in his hands. Nowhere will the results of his life-
long labours be more keenly appreciated than in the British Museum, the
distinguished staff of which paid the last tribute to the veteran zoologist
in the peaceful cemetery at Richmond.

278 Proceedings of the Royal Society of Edinburgh. [Sess.

John Sturgeon Mackay, M.A., LL.D. By George Philip, M.A., D.Sc.

(Read July 6, 1914.)

The task which the Society has entrusted to me of putting on record some
suitable memorial of the life and work of Dr John S. Mackay is one which
I feel honoured in undertaking. At the same time I am conscious of my
own limitations in attempting to give to the scientific world a biographical
notice of one who was rightly looked on as one of the most learned men of
the day, and who possessed all the graces which a well-stored mind can
bestow, along with those subtle and ingratiating qualities of the heart
which cast such a magnetic influence on all who were privileged to know
him. Dr Mackay was, in very truth, the beau ideal of a scholar and a
gentleman, and death has removed from the circle of his friends one who
will long be missed. His death took place at his residence, 69 North-
umberland Street, Edinburgh, on March 25 of this year.

John Sturgeon Mackay was born at the village of Auchencairn, Kirk-
cudbrightshire, on October 22, 1843, so that at the time of his death he was
in his seventy-first year. While he was yet an infant, his parents removed
to Perth, and there he spent his boyhood and received his early education.
At Perth Academy he showed that aptitude for learning which later
brought him great distinction, and it is well to note here that his preliminary
education laid the foundation of both his linguistic and mathematical
studies. The biographer of the late Professor Chrystal in the Society’s
Proceedings makes a similar remark ; so that we have these two con-
spicuous instances at least of men who combined mathematical with
classical or linguistic talent. One would fain recall here the advice given
by Lagrange to Cauchy’s father when consulted by him as to the proper
education for his boy : “ Do not allow your son to open a mathematical
book nor to touch a single diagram until he has finished his classical
studies.” To the end Dr Mackay was a strenuous supporter of the old-
fashioned classical education, and never ceased to deplore the modern trend
of early specialisation, holding that preliminary education ought to be
devoted to the cultivation of all the faculties, and not to the development
of any one at the expense of the others.

After a school career that gave great promise of later distinction,
Dr Mackay proceeded to St Andrews University, where he followed the

1913-14.] Obituary Notices. 279

usual course at that time imposed on aspirants to a degree. The highest
honours in mathematics and classics were won by him, and one of his
fellow-students, himself a man of eminence, has told me that he was looked
upon as the ablest man of his year. His original intention on leaving the
University was to enter the ministry of the United Presbyterian Church,
and with that in view he attended the Theological Hall in connection with
that body in Edinburgh. Theology, as it was presented to him fifty
years ago, was not to his taste, and he decided to renounce his intention of
qualifying for admission to the Church, and to take up teaching as a
profession. His first situation was on the mathematical staff of his old
school, Perth Academy, so that, as he was fond of relating, he had as a
predecessor William Wallace, afterwards the eminent occupant of the
Chair of Mathematics in Edinburgh University. His stay in Perth was
short — two years, 1 think, — and in 1866 he received an appointment as
mathematical master in Edinburgh Academy, an institution which retained
his services until he retired in 1904. His long connection with this well-
known school had far-reaching effects both on the school and on Hr Mackay
himself. To the very last he took unabated interest in all that pertained
to the life of the school, and showed the most unswerving loyalty to every-
thing connected with it. Indeed, at the beginning of the present year,
when his eyesight failed him, he was engaged in compiling a register of
pupils who attended the Academy since its establishment in 1824. Many
of his pupils have risen to great eminence in various walks of life, both at
home and abroad, and few of them revisited Edinburgh without spending
some hours with their old master, whom they were proud to reckon among
their friends. His affection for his pupils was real and genuine, and he
followed their careers with a truly paternal interest.

Dr Mackay was singularly well suited for a teacher. His ready sympathy
and kindly disposition immediately secured for him the goodwill of his
pupils, while his great learning and nobility of character were so evident
that they must have exercised a very powerful influence for good on the
whole school. His well-stored mind was ever ready to give of its contents ;
and, while some men in such circumstances look on their learning as
wasted, Dr Mackay, quite otherwise, thought nothing too good for his
boys. A pupil of his own, a distinguished man of letters of this city, has
put on record the following appreciation, and I cannot do better than quote
his words : “ In reviewing the list of those with whom he happens to have
been brought into contact, the present writer can think of few more richly
endowed than he with the qualities which really matter. He was eminently
straight, he was eminently loyal, and he was eminently magnanimous. It

280 Proceedings of the Royal Society of Edinburgh. [Sess.

is of less consequence, yet not to be recalled without a pang, that he had
a delightful sense of humour, which, coupled with the control he possessed
over his vast stores of learning, rendered him the most charming of com-
panions. A school may reckon itself fortunate which has inscribed on
the roll of its masters the name of so learned, so accomplished, and so good
a man as was John Sturgeon Mackay.” *

His retirement from active duty dates from 1904, and as he was com-
paratively vigorous he looked forward to a period of great usefulness. He
still spent two months or so of the year on the Continent, and also con-
tinued his mathematical researches. But latterly his intimate friends
noticed a diminishing vitality, and although he came back every year
refreshed and invigorated by the change, it was evident that the heavy
self-imposed strain of many years was now beginning to tell on him. In
January of this year, failing eyesight was the first indication that things
were not right; and as this condition grew steadily worse, it became evident
that it was symptomatic of very serious weakness, and after lingering for
a few weeks he passed peacefully away on Wednesday, March 25. Having
his time so fully taken up with more congenial pursuits, Dr Mackay took
little or no interest in those affairs that bring men prominently into the
public eye. To his friends he showed a warm and affectionate disposition ;
stimulating in his criticism but never censorious, he had the happy faculty
of saying the right thing and doing the right thing at the right time.
Anything in the nature of sham, morally or intellectually, was specially
abhorrent to him, and he very readily detected it. But those who showed
even in a small degree an inclination to do something more than merely
“ put in the day ” found in him a staunch friend, willing to do his utmost
in assisting them in their work, and by his kindly and well-directed
counsel enabling them to bring their labours to a happy issue. His
reputation for accurate scholarship extended beyond the confines of his
own country, and he was frequently appealed to for information by
savants all over the world. Included among his intimate friends were
such well-known men in the domain of mathematical science as Neuberg,
d’Ocagne, Laisant, and Aubert in Belgium and France, Moritz Cantor in
Germany, and Robert Tucker in our own country.

The Royal Society did him the honour of electing him to a Fellowship
in the year 1882 ; and although he admitted the prior claims of the Edin-
burgh Mathematical Society for his support in the matter of original
papers, he did useful work as a member of the Council and also as a
member of its Library Committee. By making him an Honorary Fellow
* See Edinburgh Academy Chronicle for May of this year.

1913-14.] Obituary Notices. 281

ten years ago, the Society showed its appreciation of the great service
Dr Mackay rendered to scientific learning. His extensive knowledge of
books was recognised by his appointment as a member of the Permanent
International Bibliographical Association. His alma mater , the Univer-
sity of St Andrews, readily granted him the highest distinction she could
offer and in 1884 conferred on him the degree of LL.D. He served two
periods as Examiner in Mathematics in St Andrews, and for many years
he occupied a similar position on the Examining Board of the Chartered
Accountants’ Society of Scotland. He was elected by the Edinburgh
Mathematical Society as its first President, and it is not the least of his
claims to our remembrance that he gave such whole-hearted support to
its affairs that it was a constant pleasure to him to see it grow from a
small beginning, with a membership of two score, to its present position of
influence, with a membership of two hundred and fifty scattered over the
four quarters of the globe. His zeal for the welfare of the Society never
diminished, and until within the last few years, when his health began to
decline, he was seldom absent from its meetings. As was to be expected
from such an accomplished French scholar as he was, he took a very
prominent part in the work of the Franco-Scottish Society, and attended
several of its excursions through France.

In giving an account of the scientific work of the late Dr Mackay, it
will be simplest to deal with it in the historical order of its development.
At the outset, it is no exaggeration to say that the whole domain of pure
geometry, in so far as it deals with plane figures, came under his notice, and
a list of his published papers will show that he enriched almost every part
of the subject by discoveries of more or less importance. A very prominent
place must be assigned to his knowledge of Greek geometry. His great
command over Latin and Greek made him singularly well qualified to deal
with this fascinating subject, and only a mere chapter of accidents prevented
him from obtaining the full honour to which his labours entitled him.
The seventeenth- and eighteenth-century geometers like Commandinus,
Edmund Halley, and Robert Simson had studied and edited, as far as they
could, the works of Archimedes, Apollonius, Euclid, and Diophantos, and
fairly complete collections of the works of these mathematicians were
available ; but very little attention had been paid to the writings of Pappus,
one of the latest of the Alexandrian school of mathematicians. Dr Mackay
made up his mind to supply the defect, and for many years he spent his
vacations working patiently and laboriously at the MSS. of Pappus in the
British Museum and in the Continental libraries, collating and translating
them. He had practically finished his task, when Hultsch, the celebrated

282

Proceedings of the Royal Society of Edinburgh. [Sess.

German commentator, published his three-volume edition of Pappus, and
Dr Mackay took no further steps to bring his out. This is all the more
regrettable as British scholarship could well have stood a native edition of
Pappus ; and although Dr Mackay very magnanimously admitted that his
Pappus was in no way superior to that of Hultsch, it is not to be doubted
but that mathematical literature would have been greatly richer to-day if
his book had been published. I understand that Sir T. L. Heath is soon
to add Pappus’ “ Mathematical Collections ” to his excellent editions of
Archimedes, Apollonius, Diophantos, and Euclid, and so remove the stigma
that English mathematicians are no longer interested in Greek mathematics.
Dr Mackay was unfortunate, too, in coming so soon after Allman, whose
researches in Greek geometry appeared first in Hermathena and afterwards
in book form. These circumstances to a certain extent robbed him of the
full honour due to his original work, but, nevertheless, he was looked upon
as one of the foremost living authorities on Greek mathematics. His
reviews of Heath’s Diophantos and of Gow’s History of Greek Mathematics
in the Academy give us an insight into his grasp of the subject, and
make us regret all the more that we have not a work from his own pen
dealing with the early history of geometry. He was par excellence the
man to have done it.

These studies naturally led on to the work of the Scottish geometers,
Robert Simson and Matthew Stewart, who were more Euclid than Euclid
himself in their methods of geometrical analysis, and Dr Mackay subjected
their works to a most exhaustive examination. To mention only one of
the results that followed from this, I might note that he finally settled the
question as to who was the original discoverer of the so-called Simson Line,
and he showed that Robert Simson has no claim to that honour, but that
the theorem in question is due to William Wallace, who published it under
a nom de plume in the Mathematical Repository (old series), ii, 111.*
Popular periodicals of the type of the Repository , the Lady's and Gentle-
man's Diary, etc., were forms of mathematical literature that flourished
in our country from the middle of the eighteenth to the middle of the nine-
teenth century, and were supported very greatly by non-academic mathe-
maticians. These journals gave incontestable proof that mathematical
science, and particularly geometry, was very widely studied in our country,
and was a source of pleasure and amusement to many whose daily avoca-
tions required physical rather than intellectual energy. Many of the
problems dealt with were of a high order, and afterwards formed a
prominent part of geometrical science. The existence of the nine-point
* See Dr Mackay’s paper in Edin. Math . Soc. Proc ., vol. ix.

1913-14.] Obituary Notices. 283

circle, properties of symmedians and symmedian points, etc., were early
discussed in the diaries. Dr Mackay made a close study of these journals,
and the results of his labours were communicated to the French
Association for the Advancement of Science at their Congress at Besangon
in 1893, in a paper entitled “ Notice sur le journalisme mathematique en
Angleterre.”

Dr Mackay ’s original papers were practically all published in the
Proceedings of the Edinburgh Mathematical Society, and they constitute
the most valuable record in our language of the geometry of the triangle.
It is quite impossible to give here even the titles of all his papers, but
it may be stated that no earnest student of any branch of plane geo-
metry can afford to neglect his writings.* They deal with the nine-point
circle, the six scribed circles of a triangle, isogonals, symmedians, and
isogonic centres of a triangle. Perhaps his most valuable contributions
are “ The Triangle and its Six Scribed Circles,” published in vol. i, vol. ii,
and vol. xi of the above Proceedings , and “ The Symmedians of a Triangle
and their Concomitant Circles,” in vol. xiv. The first of these two occupied
several years of his leisure, and to make it as complete as possible he enlisted
the services of such well-known geometers as Tucker, Neuberg, Fuhrmann,
and d’Ocagne. We may judge of the completeness of the work when we
know that it occupied 1600 quarto pages of MS. His paper on the
“ Symmedians of a Triangle ” made known for the first time in an English
journal the remarkable properties of the K points and of the Tucker
group of circles which have as particular cases the first and second
Lemoine circles, the Taylor circle, and the Adams’s circle.

Dr Mackay was also the author of the articles “ Calendar ” and
“ Geometry ” in Chambers’s Encyclopaedia, and “ Euclid ” in Encyclopaedia
Britannica. The interesting and learned article on “ Numeration ” in the
jubilee volume of the Chartered Accountants’ Association of Scotland is
also from his pen.

Of his books the most important is his Elements of Euclid (W. & R.
Chambers, Edinburgh, 1884). Like many others, it is based on the well-
known edition of Robert Sim son, but it shows a vast improvement on
any previous text-book. Every page of it shows evidence of ripe scholar-
ship, and it possesses what no other text-book we know possesses, viz.
references to original memoirs and authorities and full historical notes.
Writers of mathematical text-books in general carefully avoid introducing
such personal elements, and thereby in our view make a very great

* A list of these papers will be found in the index volume of the Edinburgh Mathe-
matical Society.

284

Proceedings of the Royal Society of Edinburgh. [Sess.

mistake. The idea that the subject has reached its present condition by
the labours of many workers, largely obscure, is very helpful to learners,
and gives a humanistic trend to the study of geometry. A Key to the
Elements was published in 1885.

It is almost needless to say that Dr Mackay did not view with favour
the departure from the Euclidean sequence. He held that some logical
sequence is necessary, and that Euclid’s is superior to any more recent
innovations. Signs are not wanting that his views are now being shared
by a growing number of mathematicians, who detect in our present
system too much looseness and slovenliness. He was requested to write
a text-book of geometry in accordance with the recent movement ; and
although he complied with the request and produced his Plane Geometry ,
books i-iii in 1904, and books iv-v in 1905, they naturally have not
the characteristic features of the earlier work. His Arithmetic Theoretical
and Practical appeared in 1899, and forms one of the soundest and
most illuminating books we have on the subject.

This short account of his work will show the great service Dr Mackay
rendered to mathematical learning, and the loss the scientific world has
sustained by his death.

1913-14.]

Obituary Notices.

285

Professor John Gibson. By Principal A. P. Laurie, D.Sc.

(MS. received October 26, 1914. Read December 7, 1914.)

John Gibson was born in Edinburgh on May 13, 1855, and was educated
at Edinburgh Academy. He afterwards studied chemistry at Heidelberg
under Bunsen, Kirchhoff, Kopp, and others, working for five consecutive
sessions in Bunsen’s laboratory, and graduating in 1876 as Doctor of
Philosophy.

On returning to Edinburgh, he became assistant under Professor Crum
Brown; later on, in 1881, being appointed chief assistant in the laboratory,
where he taught for eleven years. In 1892 he was appointed Professor of
Chemistry in the Pleriot-Watt College, a post which he held up to the day
of his death.

Gibson was, above all things, an analyst. He seems to have developed
his original interest in chemical analysis under Bunsen, and to the end of
his life he remained in the very first rank of analysts, and always regarded
that part of the teaching in the department as of the utmost importance.

As an example of his capacity for analytical research, we cannot do
better than take his report on “ An Analytical Examination of Manganese
Nodules, with special reference to the Presence or Absence of the Rarer
Elements,” which was published in the Challenger Reports — “ Deep Sea
Deposits,” in 1891, and involved an original research in analytical methods.
All those who had the good fortune to be students under him have benefited
by his enthusiastic appreciation for, and exact knowledge of, analytical
methods.

While in Edinburgh University, Gibson carried out a large number of
observations for the Fishery Board on the composition of sea waters, more
especially in the North Sea, and he also made an investigation into some
of the rare earths. Years of investigation were devoted to the study of
these rare earths, and the separation of pure salts from them. Unfor-
tunately, all that ever was published on this subject was a short paper on
“ Glucinum ” in the Transactions of the Chemical Society, 1893.

Gibson always approached the problem of publication with great un-
willingness. When once he completed a research, his interest carried him
on to fresh investigations, and it was with great difficulty that he could be
persuaded to put pen to paper with a view to publication. As a conse-
quence of this, many valuable researches have been lost to science, and this

286 Proceedings of the Royal Society of Edinburgh. [Sess.

is especially the case in connection with glucinum, cerium, lanthanum, and
didymium. Large quantities of the minerals were worked up, pure salts
prepared, and much work was done, which has no doubt since been con-
firmed by others, although it may be questioned whether even now all
Gibson’s results have been re-established.

About the time when the paper on glucinum was published, Gibson
started some experiments on the effects of light on such changes as the
conversion of chlorine water into hydrochloric acid, the resulting observa-
tions being published in a short paper on “ Photochemical Action ” in the
Proceedings of the Royal Society of Edinburgh in February 1897. This
was followed by a short paper, “ A Preliminary Note on a Characteristic of
Certain Chemical Reactions ” ( Proc . Boy. Soc. Edin., Dec. 1897). The origin
of these papers was as follows : In studying the action of light on these
mixtures, Gibson discovered the fact that the amount of change depended
on whether the final result of the reaction was to increase the electrical
conductivity of the solution as a whole or to diminish it, there being a
tendency for any such solution to move in the direction of increased
electrical conductivity. This led him further to investigate the question as
to how far other reactions, apart from those caused by light, were influenced
by these conditions.

No particular physical value had been, so far, associated with the
electrical conductivity of a system as a whole, and the whole direction of
research was proceeding towards experiments on very dilute solutions,
with a view to the application of the laws laid down by van’t Hoff,
Arrhenius, Kohlrausch, and Nernst to the problems of electrochemistry.
It was probably for this reason that more attention has not been directed
to the very interesting results obtained by Gibson in this direction.

In the preliminary paper already referred to he gives examples of the
law that many chemical reactions are governed by the tendency of a
solution to develop a state of maximum conductivity in the system, these
examples being : the dehydration by hydrochloric acid of hydrated
cobaltous chloride ; the dehydration of sugar by sulphuric acid ; the re-
duction of chromic anhydride by hydrochloric acid ; the oxidation of
hydrogen iodide by sulphuric acid ; and the oxidation of nitric oxide by
nitric acid.

In order to carry these investigations further, he decided to redetermine
the conductivity curves of some of the best known acids and salts, and
devoted a great deal of time and labour to these measurements, with the
result that there can be no doubt that the most exact conductivity curves
that we have for hydriodic, hydrobromic, and hydrochloric acids, and

1913-14.] Obituary Notices. 287

ammonium bromide, lithium bromide, and sodium bromide, are those
determined by Gibson ; whilst for these experiments he devised his
electrically controlled thermostat, which is a very perfect instrument
of its kind.

The main interest of his work, however, remains as before the study of
the relation between maximum conductivity and certain types of chemical
change. He showed, for instance, the close relation between this and the
precipitation of salts from solution by hydrochloric acid ; the behaviour of
aqueous solutions of hydrogen chloride towards dissolved oxygen and
dissolved chlorine respectively; the oxidation of hydrogen chloride in
aqueous solution by chromic acid ; the action of hydrochloric acid as an
esterifying agent ; and the action of hydrogen chloride on acetal-
dehyde, aldol, and crotonaldehyde, and of hydrochloric acid on cobalt
chloride. In addition, he investigated the decomposition of aqueous solu-
tions of hydrogen iodide ; the behaviour of nitric acid when exposed to
light ; and, in more detail, the action of sulphuric acid on sucrose and on
formic acid. In all these cases he proved quite definitely that the limit to
which the reaction was carried was fixed by the point at which the system
as a whole reached its maximum conductivity, and that many reactions
were reversed on each side of this maximum conductivity point, proceeding
in opposite directions when once the maximum of the curve had been
passed.

It is, of course, evident that there are a large number of reactions which
are not governed by this condition, and this is one of the reasons why for
many years Gibson hesitated to publish his results, as he wished to get
some definite law by which he could distinguish between reactions which
were governed by the maximum conductivity and those that were not.

It is probably safe to say from his results that all chemical systems
which are electrolytes tend towards the point of maximum conductivity,
although there may be other forces at work which are sufficiently powerful
to conceal this tendency ; but whenever we are dealing with balanced
reactions in which a very small change of conditions will make the re-
action proceed the other way, we find the maximum conductivity of the
system is the governing condition. There can be no doubt that we have
therefore to look for the widest application of this principle when dealing
with plant and animal life, where we have such a delicate balance constantly
occurring between two possible directions of chemical change.

Gibson has shown the application of his theory to the change from
sugar to starch, and again from starch to sugar, in the leaf of the plant,
and he also made a considerable number of experiments — which, un-

288

Proceedings of the Royal Society of Edinburgh. [Sess.

fortunately, will now never be published — on the influence on enzymatic
reactions of the same condition. His experiments on mustard powder and
on crushed bitter almonds have already been published in the paper
on “ The Significance of Maximum Specific Electrical Conductivity in
Chemistry” {Trans. Roy. Soc. Edinburgh, xlviii, Part I, No. 6). These
will be found well worthy of study by those who are interested in plant
chemistry and in enzymatic changes. It is certainly open to question
whether one of the controlling conditions of enzymatic reactions will not
be found to be the nature of the mineral salts that are present, and the
amount of dilution or concentration required to bring the solution of the
salt to its maximum conductivity point.

John Gibson was elected a Fellow of the Royal Society of Edinburgh
in 1877, and twice served as a member of Council, from 1892 to 1894 and
from 1897 to 1900. He was of great service to the Council when papers
of a chemical nature were under consideration.

Gibson had just completed the fitting up of the new laboratories at the
Heriot-Watt College, and had only entered into possession of them for a
couple of months, when his death occurred, on January 1, 1914.

It was a peculiarly hard stroke of fate that he should not have had
the opportunity of enjoying for a longer time those laboratories in which
he had taken so great an interest, and to the completion of which he had
for so long; looked forward.

The following is a list of his papers published in the Society’s Pro-
ceedings and Transactions : —

In the Proceedings, R.S.E.

1. On some Laboratory Arrangements. April 2, 1883. Yol. xii.

2. On Peroxides of Zinc, Cadmium, Magnesium, and Aluminium (with
R. M. Morrison). Read July 5, 1880 : published 1885 in vol. xiii.

3. On Papers by MM. Haas, Cleve, and Lecoy de Boisbaudran, on the
Production of Peroxides by means of Peroxide of Hydrogen. April 6,
1885. Yol. xiii.

4. The Action of Sodium Carbonate and Bromine on Solutions of
Cobalt and Nickel Salts. February 17, 1890. {Abstract.) Yol. xvii.

5. Manganese Deposits in Marine Muds (along wdth R. Irvine).
January 9, 1891. Yol. xviii.

6. On the Chemical Composition of Sea-water. July 3, 1893. Yol. xx.

7. On Photo-chemical Action. February 15, 1897. Yol. xxi.

8. Preliminary Note on a Characteristic of Certain Chemical Reactions.
December 6, 1897. Yol. xxii.

1913-14.] Obituary Notices. 289

9. On a Thermostat electrically heated and regulated (Title only).
February 5, 1900. Yol. xxiii.

10. On certain Relations between the Electrical Conductivity and the
Chemical Character of Solutions (Title only). May 6. 1901. Vol. xxiii.

11. Preliminary Note on the Conductivity of Concentrated Aqueous
Solutions of Electrolytes. November 6, 1905. Vol. xxvi.

12. Eight papers, with others. June 22, 1908. Yol. xxviii.

13. On an Electrically Controlled Thermostat and other Apparatus for
the Accurate Determination of the Electrolytic Conductivity of Highly
Conducting Solutions (with G. E. Gibson). June 22, 1908. Yol. xxx.

14. On the Precipitation of Soluble Chlorides by Hydrochloric Acid
(with R. B. Denison). August 20, 1910. Yol. xxx.

In the Transactions, R.S.E.

1. On the Relationship between Concentration and Electrolytic Con-
ductivity in Concentrated Aqueous Solutions. May 11, 1905. Yol. xlv.

2. The Significance of Maximum Specific Electrical Conductivity in
Chemistry. Read July 13, 1908: published October 20, 1911. Yol. xlviii.

VOL. xxxiv.

19

APPENDIX.

CONTENTS.

PAGE

LAWS OF THE SOCIETY ....... 293

THE KEITH, MAKDOUG ALL-BRISBANE, NEILL, AND GUNNING VICTORIA JUBILEE

PRIZES ........ 298

AWARDS OF THE KEITH, MAKDOUGALL-BRISBANE, NEILL, AND GUNNING

VICTORIA JUBILEE PRIZES ...... 300

PROCEEDINGS OF THE STATUTORY GENERAL MEETING, OCTOBER 1913 . 305

PROCEEDINGS OF THE ORDINARY MEETINGS, SESSION 1913-1914 . . 306

PROCEEDINGS OF THE STATUTORY GENERAL MEETING, OCTOBER 1914 . 312

ACCOUNTS OF THE SOCIETY, SESSION 1913-1914 . . . 313

THE COUNCIL OF THE SOCIETY AT OCTOBER 1914 . . . 319

ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY AT

JANUARY 1, 1915 . . . . . . 320

LIST OF HONORARY FELLOWS OF THE SOCIETY AT JANUARY 1, 1915 . 337

LIST OF ORDINARY FELLOWS OF THE SOCIETY ELECTED DURING SESSION

1913-1914 ....... 339

HONORARY FELLOWS AND ORDINARY FELLOWS DECEASED AND RESIGNED

DURING SESSION 1913-1914 ...... 339

LIST OF LIBRARY EXCHANGES . . . . . .340

LIST OF PERIODICALS PURCHASED BY THE SOCIETY ... 364

ADDITIONS TO LIBRARY DURING 1914, BY GIFT OR PURCHASE . . 368

INDEX . . . . . . . .370

Laws of the Society.

293

LAWS OF THE SOCIETY,

As revised October 26, 1908.

[By the Charter of the Society (printed in the Transactions, vol. vi. p. 5), the Laws cannot he
altered, except at a Meeting held one month after that at which the Motion for alteration
shall have been proposed.]

I.

THE ROYAL SOCIETY OF EDINBURGH shall consist of Ordinary and Title.
Honorary Fellows.

II.

Every Ordinary Fellow, within three months after his election, shall pay Two The fees of
Guineas as the fee of admission, and Three Guineas as his contribution for the Fefiowsresiding
Session in which he has been elected ; and annually at the commencement of every in Scotland-
Session, Three Guineas into the hands of the Treasurer. This annual contribution
shall continue for ten years after his admission, and it shall be limited to Two
Guineas for fifteen years thereafter.* Fellows may compound for these contributions
on such terms as the Council may from time to time fix.

III.

All Fellows who shall have paid Twenty-five years’ annual contribution shall be Payment to

J cease after

exempted from further payment. 25 years.

IY.

The fees of admission of an Ordinary Non-Resident Fellow shall be £26, 5s., Fees of Non-
pay able on his admission ; and in case of any Non-Resident Fellow coming to reside ordinary
at any time in Scotland, he shall, during each year of his residence, pay the usual rellows-
annual contribution of £3, 3s., payable by each Resident Fellow; but after payment
of such annual contribution for eight years, he shall be exempt from any further
payment. In the case of any Resident Fellow ceasing to reside in Scotland, and
wishing to continue a Fellow of the Society, it shall be in the power of the Council Resident!
to determine on what terms, in the circumstances of each case, the privilege of
remaining a Fellow of the Society shall be continued to such Fellow while out of
Scotland.

* A modification of this rule, in certain cases, was agreed to at a Meeting of the Society held on
January 3, 1831.

At the Meeting of the Society, on January 5, 1857, when the reduction of the Contribu-
tions from £3, 3s. to £2, 2s., from the 11th to the 25th year of membership, was adopted, it was
resolved that the existing Members shall share in this reduction, so far as regards their future
annual Contributions.

294 Proceedings of the Eoyal Society of Edinburgh.

Defaulters.

Privileges of

Ordinary

Fellows.

Numbers

unlimited,

Fellows entitled
to Transactions
and Pro-
ceedings.

Mode of
Recommending
Ordinary
Fellows.

Honorary
Fellows, British
and Foreign.

y.

Members failing to pay their contributions for three successive years (due
application having been made to them by the Treasurer) shall be reported to the
Council, and, if they see lit, shall be declared from that period to be no longer
Fellows, and the legal means for recovering such arrears shall be employed.

VI.

None but Ordinary Fellows shall bear any office in the Society, or vote in the
choice of Fellows or Office-Bearers, or interfere in the patrimonial interests of the
Society.

VII-.

The number of Ordinary Fellows shall be unlimited.

VIII.

All Ordinary Fellows of the Society who are not in arrear of their Annual
Contributions shall be entitled to receive, gratis, copies of the parts of the Trans-
actions of the Society which shall be published subsequent to their admission, upon
application, either personally or by an authorised agent, to the Librarian, provided
they apply for them within five years of the date of publication of such parts.

Copies of the parts of the Proceedings shall be distributed to all Fellows of the
Society, by post or otherwise, as soon as may be convenient after publication.

IX.

Candidates for admission as Ordinary Fellows shall make an application in
writing, and shall produce along with it a certificate of recommendation to the
purport below,* signed by at least four Ordinary Fellows, two of whom shall certify
their recommendation from personal knowledge. This recommendation shall be
delivered to the Secretary, and by him laid before the Council, and shall be exhibited
publicly in the Society’s rooms for one month, after which it shall be considered by
the Council. If the Candidate be approved by the Council, notice of the day fixed
for the election shall be given in the circulars of at least two Ordinary Meetings of
the Society.

X.

Honorary Fellows shall not be subject to any contribution. This class shall
consist of persons eminently distinguished for science or literature. Its number
shall not exceed Fifty-six, of whom Twenty may be British subjects, and Thirty-six
may be subjects of foreign states.

* “ A. B., a gentleman well versed in science (or Polite Literature, as the case may be), being
“ to our knowledge desirous of becoming a Fellow of the Royal Society of Edinburgh, we hereby
‘ ‘ recommend him as deserving of that honour, and as likely to prove a useful and valuable
“Member.”

Laws of the Society.

295

XI.

Personages of Royal Blood may be elected Honorary Fellows, without regard to Royal
the limitation of numbers' specified in Law X.

XII.

Honorary Fellows may be proposed by the Council, or by a recommendation (in Recommenda-
the form given below*) subscribed by three Ordinary Fellows ; and in case the Fellows.
Council shall decline to bring this recommendation before the Society, it shall be
competent for the proposers to bring the same before a General Meeting. The
election shall be by ballot, after the proposal has been communicated viva voce from Mode of
the Chair at one Meeting, and printed in the circulars for Two Ordinary Meetings
of the Society, previous to the day of election.

XIII.

The election of Ordinary Fellows shall take place only at one Afternoon Ordinary Election of
. . d Ordinary

Meeting of each month during the Session. The election shall be by ballot, and Fellows.

shall be determined by a majority of at least two-thirds of the votes, provided

Twenty-four Fellows be present and vote.

XIY.

The Ordinary Meetings shall be held on the first and third Mondays of each Ordinary
month from November to March, and from May to July, inclusive ; with the Meetmgs-
exception that when there are five Mondays in January, the Meetings for that
month shall be held on its second and fourth Mondays. Regular Minutes shall be
kept of the proceedings, and the Secretaries shall do the duty alternately, or accord-
ing to such agreement as they may find it convenient to make.

XV.

The Society shall from time to time publish its Transactions and Proceedings. The Trans-
For this purpose the Council shall select and arrange the papers which they shall actlons'
deem it expedient to publish in the Transactions of the Society, and shall super-
intend the printing of the same.

XVI.

The Transactions shall be published in parts or Fasciculi at the close of each How Published.
Session, and the expense shall be defrayed by the Society.

* We hereby recommend —

for the distinction of being made an Honorary Fellow of this Society, declaring that each of us
from our own knowledge of his services to {Literature or Science , as the case may be) believe him
to be worthy of that honour.

(To be signed by three Ordinary Fellows. )

To the President and Council of the Royal Society
of Edinburgh.

296 Proceedings of the Royal Society of Edinburgh.

The Council.

Retiring

Councillors.

Election of
Office-Bearers.

Special

Meetings ; how
called.

Treasurer’s

Duties.

Auditor.

General

Secretary’s

Duties.

XVII.

That there shall be formed a Council, consisting — First, of such gentlemen as
may have filled the office of President ; and Secondly, of the following to be annually
elected, viz. : — a President, Six Vice-Presidents (two at least of whom shall be
Resident), Twelve Ordinary Fellows as Councillors, a General Secretary, Two
Secretaries to the Ordinary Meetings, a Treasurer, and a Curator of the Museum
and Library.

The Council shall have power to regulate the private business of the Society.
At any Meeting of the Council the Chairman shall have a casting as well as a
deliberative vote.

XVIIL

Four Councillors shall go out annually, to be taken according to the order in
which they stand on the list of the Council.

XIX.

An Extraordinary Meeting for the election of Office-Bearers shall be held annually
on the fourth Monday of October, or on such other lawful day in October as the
Council may fix, and each Session of the Society shall be held to begin at the date
of the said Extraordinary Meeting.

XX.

Special Meetings of the Society may be called by the Secretary, by direction of
the Council ; or on a requisition signed by six or more Ordinary Fellows. Notice
of not less than two days must be given of such Meetings.

XXI.

The Treasurer shall receive and disburse the money belonging to the Society,
granting the necessary receipts, and collecting the money when due.

He shall keep regular accounts of all the cash received and expended, which
shall be made up and balanced annually ; and at the Extraordinary Meeting in
October, he shall present the accounts for the preceding year, duly audited. At
this Meeting, the Treasurer shall also lay before the Council a list of all arrears due
above two years, and the Council shall thereupon give such directions as they may
deem necessary for recovery thereof.

XXII.

At the Extraordinary Meeting in October, a professional accountant shall be
chosen to audit the Treasurer’s accounts for that year, and to give the necessary
discharge of his intromissions.

XXIII.

The General Secretary shall keep Minutes of the Extraordinary Meetings of the
Society, and of the Meetings of the Council, in two distinct books. He shall, under
the direction of the Council, conduct the correspondence of the Society, and super-
intend its publications. For these purposes he shall, when necessary, employ a clerk,
to be paid by the Society.

Laws of the Society.

297

XXIV.

The Secretaries to the Ordinary Meetings shall keep a regular Minute-book, in Secretaries to
which a full account of the proceedings of these Meetings shall be entered ; they Meetings,
shall specify all the Donations received, and furnish a list of them, and of the
Donors’ names, to the Curator of the Library and Museum ; they shall likewise
furnish the Treasurer with notes of all admissions of Ordinary Fellows. They shall
assist the General Secretary in superintending the publications, and in his absence
shall take his duty.

XXV.

The Curator of the Museum and Library shall have the custody and charge of curator of
all the Books, Manuscripts, objects of Natural History, Scientific Productions, and ub?a?™and
other articles of a similar description belonging to the Society ; he shall take an
account of these when received, and keep a regular catalogue of the whole, which
shall lie in the hall, for the inspection of the Fellows.

XXVI.

All articles of the above description shall be open to the inspection of the Use of Museum
Fellows at the Hall of the Society, at such times and under such regulations as the andLlbrary*
Council from time to time shall appoint.

XXVII.

A Register shall be kept, in which the names of the Fellows shall be enrolled Register Book,
at their admission, with the date.

XXVIII.

If, in the opinion of the Council of the Society, the conduct of any Fellow is Power of
unbecoming the position of a Member of a learned Society, or is injurious to the Expulsion*
character and interests of this Society, the Council may request such Fellow to
resign ; and, if he fail to do so within one month of such request being addressed to
him, the Council shall call a General Meeting of the Fellows of the Society to
consider the matter ; and, if a majority of the Fellows present at such Meeting
agree to the expulsion of such Member, he shall be then and there expelled by the
declaration of the Chairman of the said Meeting to that effect ; and he shall there-
after cease to be a Fellow of the Society, and his name shall be erased from the
Roll of Fellows, and he shall forfeit all right or claim in or to the property of the
Society.

298

Proceedings of the Royal Society of Edinburgh.

THE KEITH, MAKDOUGALL-BRISBANE, NEILL, AND
GUNNING VICTORIA JUBILEE PRIZES.

The above Prizes will be awarded by the Council in the following manner : —

I. KEITH PRIZE.

The Keith Prize, consisting of a Gold Medal and from £40 to £50 in Money,
will be awarded in the Session 1915-1916 for the “best communication on a scientific
subject, communicated,* in the first instance, to the Royal Society during the
Sessions 1913-1914 and 1914-1915.” Preference will be given to a paper con-
taining a discovery.

II. MAKDOUGALL-BRISBANE PRIZE.

This Prize is to be awarded biennially by the Council of the Royal Society of
Edinburgh to such person, for such purposes, for such objects, and in such manner
as shall appear to them the most conducive to the promotion of the interests of
science ; with the proviso that the Council shall not be compelled to award the
Prize unless there shall be some individual engaged in scientific pursuit, or some
paper written on a scientific subject, or some discovery in science made during the
biennial period, of sufficient merit or importance in the opinion of the Council to
be entitled to the Prize.

1. The Prize, consisting of a Gold Medal and a sum of Money, will be awarded
at the commencement of the Session 1914-1915, for an Essay or Paper having
reference to any branch of scientific inquiry, whether Material or Mental.

2. Competing Essays to be addressed to the Secretary of the Society, and trans-
mitted not later than 8th July 1914.

3. The Competition is open to all men of science.

4. The Essays may be either anonymous or otherwise. In the former case,
they must be distinguished by mottoes, with corresponding sealed billets, super-
scribed with the same motto, and containing the name of the Author.

5. The Council impose no restriction as to the length of the Essays, which may
be, at the discretion of the Council, read at the Ordinary Meetings of the Society.

* For the purposes of this award the word “ communicated ” shall be understood to mean the
date on which the manuscript of a paper is received in its final form for printing, as recorded by
the General Secretary or other responsible official.

299

Keith, Brisbane, Neill, and Gunning Prizes.

They wish also to leave the property and free disposal of the manuscripts to the
Authors ; a copy, however, being deposited in the Archives of the Society, unless
the paper shall be published in the Transactions.

6. In awarding the Prize, the Council will also take into consideration any
scientific papers presented* to the Society during the Sessions 1912-13, 1913-14,
whether they may have been given in with a view to the prize or not.

III. NEILL PRIZE.

The Council of the Royal Society of Edinburgh having received the bequest of
the late Dr Patrick Neill of the sum of £500, for the purpose of “the interest
thereof being applied in furnishing a Medal or other reward every second or third
year to any distinguished Scottish Naturalist, according as such Medal or reward
shall be voted by the Council of the said Society,” hereby intimate :

1. The Neill Prize, consisting of a Gold Medal and a sum of Money, will be
awarded during the Session 1915-1916.

2. The Prize will be given for a Paper of distinguished merit, on a subject of
Natural History, by a Scottish Naturalist, which shall have been presented* to the
Society during the two years preceding the fourth Monday in October 1915, — or
failing presentation of a paper sufficiently meritorious, it will be awarded for a work
or publication by some distinguished Scottish Naturalist, on some branch of Natural
History, bearing date within five years of the time of award.

IV. GUNNING VICTORIA JUBILEE PRIZE.

This Prize, founded in the year 1887 by Dr R. H. Gunning, is to be awarded
quadrennially by the Council of the Royal Society of Edinburgh, in recognition of
original work in Physics, Chemistry, or Pare or Applied Mathematics.

Evidence of such work may be afforded either by a Paper presented to the
Society, or by a Paper on one of the above subjects, or some discovery in them
elsewhere communicated or made, which the Council may consider to be deserving
of the Prize.

The Prize consists of a sum of money, and is open to men of science resident in
or connected with Scotland. The first award was made in the year 1887.

In accordance with the wish of the Donor, the Council of the Society may on
fit occasions award the Prize for work of a definite kind to be undertaken during
the three succeeding years by a scientific man of recognised ability.

* For the purposes of this award the word ‘ ‘ presented ” shall be understood to mean the date
on which the manuscript of a paper is received in its final form for printing, as recorded by the
General Secretary or other responsible official.

300 Proceedings of the Royal Society of Edinburgh.

AWARDS OF THE KEITH, MAKDOUGALL - BRISBANE,
NEILL, AND GUNNING VICTORIA JUBILEE PRIZES.

I. KEITH PRIZE.

1st Biennial Period, 1827-29.— Dr Brewster, for his papers “on his Discovery of Two New
Immiscible Fluids in the Cavities of certain Minerals,” published in the Transactions of
the Society.

2nd Biennial Period, 1829-31. — Dr Brewster, for his paper “on a New Analysis of Solar
Light,” published in the Transactions of the Society.

3rd Biennial Period, 1831-33. — Thomas Graham, Esq., for his paper “on the Law of the
Diffusion of Gases,” published in the Transactions of the Society.

4th Biennial Period, 1833-35. — Professor J. D. Forbes, for his paper “on the Refraction and
Polarization of Heat,” published in the Transactions of the Society.

5th Biennial Period, 1835-37. — John Scott Russell, Esq., for his researches “on Hydro-
dynamics,” published in the Transactions of the Society.

6th Biennial Period, 1837-39. — Mr John Shaw, for his experiments “on the Development
and Growth of the Salmon,” published in the Transactions of the Society.

7th Biennial Period, 1839-41. — Not awarded.

8th Biennial Period, 1841-1843. — Professor James David Forbes, for his papers “on
Glaciers,” published in the Proceedings of the Society.

9th Biennial Period, 1843-45. — Not awarded.

10th Biennial Period, 1845-47. — General Sir Thomas Brisbane, Bart., for the Makerstoun
Observations on Magnetic Phenomena, made at his expense, and published in the Trans-
actions of the Society.

11th Biennial Period, 1847-49. — Not awarded.

12th Biennial Period, 1849-51. — Professor Kelland, for his papers “on General Differentia-
tion, including his more recent Communication on a process of the Differential Calculus, and
its application to the solution of certain Differential Equations,” published in the Transac-
tions of the Society.

13th Biennial Period, 1851-53. — W. J. Macquorn Rankine, Esq., for his series of papers
“on the Mechanical Action of Heat,” published in the Transactions of the Society.

14th Biennial Period, 1853-55. — Dr Thomas Anderson, for his papers “on the Crystalline
Constituents of Opium, and on the Products of the Destructive Distillation of Animal
Substances,” published in the Transactions of the Society.

15th Biennial Period, 1855-57. — Professor Boole, for his Memoir “on the Application of
the Theory of Probabilities to Questions of the Combination of Testimonies and Judgments,”
published in the Transactions of the Society.

16th Biennial Period, 1857-59. — Not awarded.

17th Biennial Period, 1859-61. — John Allan Broun, Esq., F.R.S., Director of the Trevandrum
Observatory, for his papers “on the Horizontal Force of the Earth’s Magnetism, on the
Correction of the Bifilar Magnetometer, and on Terrestrial Magnetism generally,” published
in the Transactions of the Society.

18th Biennial Period, 1861-63. — Professor William Thomson, of the University of Glasgow,
for his Communication ‘ ‘ on some Kinematical and Dynamical Theorems. ”

19th Biennial Period, 1863-65. — Principal Forbes, St Andrews, for his “Experimental
Inquiry into the Laws of Conduction of Heat in Iron Bars,” published in the Transactions
of the Society.

20th Biennial Period, 1865-67. — Professor C. Piazzi Smyth, for his paper “on Recent
Measures at the Great Pyramid,” published in the Transactions of the Society.

21st Biennial Period, 1867-69. — Professor P. G. Tait, for his paper “on the Rotation of a
Rigid Body about a Fixed Point,” published in the Transactions of the Society.

22nd Biennial Period, 1869-71. — Professor Clerk Maxwell, for his paper “on Figures,
Frames, and Diagrams of Forces,” published in the Transactions of the Society.

301

Keith, Brisbane, Neill, and Gunning Prizes.

23rd Biennial Period, 1871-73. — Professor P. G. Tait, for his paper entitled “First Approxi-
mation to a Thermo-electric Diagram,” published in the Transactions of the Society.

24th Biennial Period, 1873-75. — Professor Crum Brown, for his Researches “on the Sense of
Rotation, and on the Anatomical Relations of the Semicircular Canals of the Internal Ear.”

25th Biennial Period, 1875-77.— Professor M. Forster Heddle, for his papers “on the
Rhombohedral Carbonates, ” and “on the Felspars of Scotland,” published in the Transac-
tions of the Society.

26th Biennial Period, 1877-79. — Professor H. C. Fleeming Jenkin, for his paper “on the
Application of Graphic Methods to the Determination of the Efficiency of Machinery,”
published in the Transactions of the Society ; Part II. having appeared in the volume for
1877-78.

27th Biennial Period, 1879-81. — Professor George Chrystal, for his paper “on the Differ-
ential Telephone,” published in the Transactions of the Society.

28th Biennial Period, 1881-83. — Thomas Muir, Esq., LL.D., for his “Researches into the
Theory of Determinants and Continued Fractions,” published in the Proceedings of the Society.

29th Biennial Period, 1883-85. — John Aitken, Esq., for his paper “on the Formation of
Small Clear Spaces in Dusty Air,” and for previous papers on Atmospheric Phenomena,
published in the Transactions of the Society.

30th Biennial Period, 1885-87. — John Young Buchanan, Esq., for a series of communica-
tions, extending over several years, on subjects connected with Ocean Circulation,
Compressibility of Glass, etc. ; two of which, viz., “On Ice and Brines,” and “On the
Distribution of Temperature in the Antarctic Ocean,” have been published in the Proceedings
of the Society.

31st Biennial Period, 1887-89. — Professor E. A. Letts, for his papers on the Organic
Compounds of Phosphorus, published in the Transactions of the Society.

32nd Biennial Period, 1889-91. — R. T. Omond, Esq., for his contributions to Meteorological
Science, many of which are contained in vol. xxxiv. of the Society’s Transactions.

33rd Biennial Period, 1891-93. — Professor Thomas R. Fraser, F.R.S., for his papers on
Strophanthus hispidus, Strophanthin, and Strophanthidin, read to the Society in February
and June 1889 and in December 1891, and printed in vols. xxxv. , xxxvi., and xxxvii.
of the Society’s Transactions.

34th Biennial Period, 1893-95. — Dr Cargill G. Knott, for his papers on the Strains produced
by Magnetism in Iron and in Nickel, which have appeared in the Transactions and
Proceedings of the Society.

35th Biennial Period, 1895-97. — Dr Thomas Muir, for his continued communications on
Determinants and Allied Questions.

36th Biennial Period, 1897-99. — Dr James Burgess, for his paper “on the Definite Integral

— — / e ~pdt, with extended Tables of Values,” printed in vol. xxxix. of the Transactions
o

of the Society.

37th Biennial Period, 1899-1901. — Dr Hugh Marshall, for his discovery of the Persulphates,
and for his Communications on the Properties and Reactions of these Salts, published in the
Proceedings of the Society.

38th Biennial Period, 1901-03.— Sir William Turner, K.C.B., LL.D., F.R.S., &c., for his
memoirs entitled “ A Contribution to the Craniology of the People of Scotland,” published in
the Transactions of the Society, and for his “ Contributions to the Craniology of the People
of the Empire of India,” Parts I., II., likewise published in the Transactions of the Society.

39th Biennial Period, 1903-05. — Thomas H. Bryce, M.A., M.D., for his two papers on “The
Histology of the Blood of the Larva of Lepidosiren paradoxa , ” published in the Transactions
of the Society within the period.

40th Biennial Period, 1905-07.— Alexander Bruce, M.A., M.D., F.R.C.P.E., for his paper
entitled “ Distribution of the Cells in the Intermedio-Lateral Tract of the Spinal Cord,”
published in the Transactions of the Society within the period.

41st Biennial Period, 1907-09. — Wheelton Hind, M.D., B.S., F.R.C.S., F.G.S., for a paper
published in the Transactions of the Society, ‘ ‘ On the Lamellibranch and Gasteropod Fauna
found in the Millstone Grit of Scotland.”

42nd Biennial Period, 1909-11. — Professor Alexander Smith, B.Sc., Ph.D., of New York,
for his researches upon “Sulphur” and upon “Vapour Pressure,” appearing in the
Proceedings of the Society.

43rd Biennial Period, 1911-1913. — James Russell, Esq., for his series of investigations
relating to magnetic phenomena in metals and the molecular theory of magnetism, the
results of which have been published in the Proceedings and Transactions of the Society,
the last paper having been issued within the period.

302

Proceedings of the Royal Society of Edinburgh.

II. MAKDOUG ALL-BRISBANE PKIZE.

1st Biennial Period, 1859. — Sir Roderick Impey Murchison, on account of his Contributions
to the Geology of Scotland.

2nd Biennial Period, 1860-62.— William Seller, M.D., F.R.C.P.E., for his “ Memoir of the
Life and Writings of Dr Robert Whytt,” published in the Transactions of the Society.

3rd Biennial Period, 1862-64.— John Denis Macdonald, Esq., R.N., F.R.S., Surgeon of
H.M.S. “ Icarus,” for his paper “on the Representative Relationships of the Fixed and Free
Tunicata, regarded as Two Sub-classes of equivalent value ; with some General Remarks on
their Morphology,” published in the Transactions of the Society.

4th Biennial Period, 1864-66. — Not awarded.

5th Biennial Period, 1866-68. — Dr Alexander Crum Brown and Dr Thomas Richard
Fraser, for their conjoint paper “on the Connection between Chemical Constitution and
Physiological Action,” published in the Transactions of the Society.

6th Biennial Period, 1868-70. — Not awarded.

7th Biennial Period, 1870-72.— George James Allman, M.D., F.R.S., Emeritus Professor of
Natural History, for his paper “on the Homological Relations of the Coelenterata,” published
in the Transactions, which forms a leading chapter of his Monograph of Gymnoblastic or
Tubularian Hydroids — since published.

8th Biennial Period, 1872-74. — Professor Lister, for his paper “on the Germ Theory of
Putrefaction and the Fermentive Changes,” communicated to the Society, 7th April 1873.

9th Biennial Period, 1874-76. — Alexander Buchan, A.M., for his paper “ on the Diurnal
Oscillation of the Barometer,” published in the Transactions of the Society.

10th Biennial Period, 1876-78. — Professor Archibald Geikie, for his paper “on the Old
Red Sandstone of Western Europe,” published in the Transactions of the Society.

11th Biennial Period, 1878-80. — Professor Piazzi Smyth, Astronomer-Royal for Scotland, for
his paper “on the Solar Spectrum in 1877-78, with some Practical Idea of its probable
Temperature of Origination,” published in the Transactions of the Society.

12th Biennial Period, 1880-82. — Professor James Geikie, for his “Contributions to the
Geology of the North-West of Europe,” including his paper “on the Geology of the
Faroes,” published in the Transactions of the Society.

13th Biennial Period, 1882-84. — Edward Sang, Esq., LL.D., for his paper “on the Need of
Decimal Subdivisions in Astronomy and Navigation, and on Tables requisite therefor,” and
generally for his Recalculation of Logarithms both of Numbers and Trigonometrical Ratios,
— the former communication being published in the Proceedings of the Society.

14th Biennial Period, 1884-86. — John Murray, Esq., LL.D., for his papers “On the Drainage
Areas of Continents, and Ocean Deposits,” “ The Rainfall of the Globe, and Discharge of
Rivers,” “ The Height of the Land and Depth of the Ocean,” and “The Distribution of
Temperature in the Scottish Lochs as affected by the Wind.”

15th Biennial Period, 1886-88. — Archibald Geikie, Esq., LL.D., for numerous Communica-
tions, especially that entitled “ History of Volcanic Action during the Tertiary Period in the
British Isles,” published in the Transactions of the Society.

16th Biennial Period, 1889-90. — Dr Ludwig Becker, for his paper on “ The Solar Spectrum at
Medium and Low Altitudes, ” printed in vol. xxx vi. Part I. of the Society’s Transactions.

1 7th Biennial Period, 1890-92. — Hugh Robert Mill, Esq., D.Sc., for his papers on “The
Physical Conditions of the Clyde Sea Area,” Part I. being already published in vol. xxxvi.
of the Society’s Transactions.

18th Biennial Period, 1892-94. — Professor James Walker, D.Sc., Ph.D., for his work on
Physical Chemistry, part of which has been published in the Proceedings of the Society, vol.
xx. pp. 255-263. In making this award, the Council took into consideration the work
done by Professor Walker along with Professor Crum Brown on the Electrolytic Synthesis of
Dibasic Acids, published in the Transactions of the Society.

19th Biennial Period, 1894-96. — Professor John G. M‘Kendrick, for numerous Physiological
papers, especially in connection with Sound, many of which have appeared in the Society’s
publications.

20th Biennial Period, 1896-98.— Dr William Peddie, for his papers on the Torsional Rigidity
of Wires.

21st Biennial Period, 1898-1900. — Dr Ramsay H. Traquair, for his paper entitled “ Report on
Fossil Fishes collected by the Geological Survey in the Upper Silurian Rocks of Scotland,”
printed in vol. xxxix. of the Transactions of the Society.

Keith, Brisbane, Neill, and Gunning Prizes. 303

22nd Biennial Period, 1900-02. — Dr Arthur T. Masterman, for his paper entitled “The
Early Development of Cribrella oculata (Forbes), with remarks on Echinoderm Development,”
printed in vol. xl. of the Transactions of the Society.

23rd Biennial Period, 1902-04. — Mr John Dougall, M.A., for his paper on “An Analytical
Theory of the Equilibrium of an Isotropic Elastic Plate,” published in vol. xli. of the
Transactions of the Society.

24th Biennial Period, 1904-06.— Jacob E. Halm, Ph.D., for his two papers entitled “Spectro-
scopic Observations of the Rotation of the Sun,” and “ Some Further Results obtained with
the Spectroheliometer,” and for other astronomical and mathematical papers published in
the Transactions and Proceedings of the Society within the period.

25th Biennial Period, 1906-08. — D. T. Gw ynne- Vaughan, M.A., F.L.S., for his papers,
1st, “On the Fossil Osmundacese,” and 2nd, “ On the Origin of the Adaxially-curved Leaf-
trace in the Filicales,” communicated by him conjointly with Dr R. Kidston.

26th Biennial Period, 1908-10. — Ernest MacLagan Wedderburn, M.A., LL.B., for his
series of papers bearing upon “The Temperature Distribution in Fresh-water Lochs,” and
especially upon “The Temperature Seiche.”

27th Biennial Period, 1910-12.— John Brownlee, M.A., M.D., D.Sc., for his contributions
to the Theory of Mendelian Distributions and cognate subjects, published in the Proceedings
of the Society within and prior to the prescribed period.

III. THE NEILL PRIZE.

1st Triennial Period, 1856-59. — Dr W. Lauder Lindsay, for his paper “ on the Spermogones
and Pycnides of Filamentous, Fruticulose, and Foliaceous Lichens,” published in the Trans-
actions of the Society.

2nd Triennial Period, 1859-61. — Robert Kaye Greville, LL.D., for his Contributions to
Scottish Natural History, more especially in the department of Cryptogamic Botany,
including his recent papers on Diatomacese.

3rd Triennial Period, 1862-65. — Andrew Crombie Ramsay, F.R.S., Professor of Geology in
the Government School of Mines, and Local Director of the Geological Survey of Great
Britain, for his various works and memoirs published during the last five years, in which he
has applied the large experience acquired by him in the Direction of the arduous work of
the Geological Survey of Great Britain to the elucidation of important questions bearing on
Geological Science.

4th Triennial Period, 1865-68. — Dr William Carmichael MHntosh, for his paper “on the
Structure of the British Nemerteans, and on some New British Annelids,” published in the
Transactions of the Society.

5th Triennial Period, 1868-71. — Professor William Turner, for his papers “on the Great
Finner Whale ; and on the Gravid Uterus, and the Arrangement of the Foetal Membranes
in the Cetacea, ” published in the Transactions of the Society.

6th Triennial Period, 1871-74. — Charles William Peach, Esq., for his Contributions to
Scottish Zoology and Geology, and for his recent contributions to Fossil Botany.

7th Triennial Period, 1874-77. — Dr Ramsay H. Traquair, for his paper “on the Structure
and Affinities of Tristichopterus alatus (Egerton),” published in the Transactions of the
Society, and also for his contributions to the Knowledge of the Structure of Recent and
Fossil Fishes.

8th Triennial Period, 1877-80. — John Murray, Esq., for his paper “ on the Structure and
Origin of Coral Reefs and Islands,” published (in abstract) in the Proceedings of the Society.

9th Triennial Period, 1880-83. — Professor Herdman, for his papers “on the Tunicata,”
published in the Proceedings and Transactions of the Society.

10th Triennial Period, 1883-86.— B. N. Peach, Esq., for his Contributions to the Geology and
Palseontology of Scotland, published in the Transactions of the Society.

11th Triennial Period, 1886-89. — Robert Kidston, Esq., for his Researches in Fossil Botany,
published in the Transactions of the Society.

12th Triennial Period, 1889-92. — John Horne, Esq., F.G.S., for his Investigations into the
Geological Structure and Petrology of the North-West Highlands.

13th Triennial Period, 1892-95. — Robert Irvine, Esq., for his papers on the Action of
Organisms in the Secretion of Carbonate of Lime and Silica, and on the solution of these
substances in Organic Juices. These are printed in the Society’s Transactions and
Proceedings.

304

Proceedings of the Royal Society of Edinburgh.

14th Triennial Period, 1895-98. — Professor Cossar Ewart, for his recent Investigations con-
nected with Telegony.

15th Triennial Period, 1898-1901. — Dr John S. Flett, for his papers entitled “The Old Red
Sandstone of the Orkneys ” and ‘ ‘ The Trap Dykes of the Orkneys, ’* printed in vol.
xxxix. of the Transactions of the Society.

16th Triennial Period, 1901-04. — Professor J. Graham Kerr, M.A., for his Researches on
Lepidosiren paradoxa, published in the Philosophical Transactions of the Royal Society,
London.

17th Triennial Period, 1904-07. — Frank J. Cole, B.Sc., for his paper entitled “ A Monograph
on the General Morphology of the Myxinoid Fishes, based on a study of Myxine,” published
in the Transactions of the Society, regard being also paid to Mr Cole’s other valuable contri-
butions to the Anatomy and Morphology of Fishes.

1st Biennial Period, 1907-09. — Francis J. Lewis, M.Sc. , F.L.S., for his papers in the Society’s
Transactions “ On the Plant Remains of the Scottish Peat Mosses.”

2nd Biennial Period, 1909-11. — James Murray, Esq., for his paper on “Scottish Rotifers
collected by the Lake Survey (Supplement),” and other papers on the “Rotifera” and
“ Tardigrada, ” which appeared in the Transactions of the Society — (this Prize was awarded
after consideration of the papers received within the five years prior to the time of award :
see Neill Prize Regulations).

3rd Biennial Period, 1911-13. — Dr W. S. Bruce, in recognition of the scientific results of his
Arctic and Antarctic explorations.

IV. GUNNING VICTORIA JUBILEE PRIZE.

1st Triennial Period, 1884-87. — Sir William Thomson, Pres. R.S.E., F.R.S., for a remark-
able series of papers “on Hydrokinetics,” especially on Waves and Vortices, which have
been communicated to the Society.

2nd Triennial Period, 1887-90. — Professor P. G. Tait, Sec. R.S.E., for his work in connection
with the “ Challenger” Expedition, and his other Researches in Physical Science.

3rd Triennial Period, 1890-93. — Alexander Buchan, Esq., LL.D., for his varied, extensive,
and extremely important Contributions to Meteorology, many of which have appeared in the
Society’s Publications.

4th Triennial Period, 1893-96. — John Aitken, Esq., for his brilliant Investigations in
Physics, especially in connection with the Formation and Condensation of Aqueous Vapour.

1st Quadrennial Period, 1896-1900. — Dr T. D. Anderson, for his discoveries of New and
Variable Stars.

2nd Quadrennial Period, 1900-04. — Sir James Dewar, LL.D., D.C.L., F.R.S., etc., for his
researches on the Liquefaction of Gases, extending over the last quarter of a century, and
on the Chemical and Physical Properties of Substances at Low Temperatures : his earliest
papers being published in the Transactions and Proceedings of the Society.

3rd Quadrennial Period, 1904-08. — Professor George Chrystal, M.A. , LL.D., for a series of
papers on “ Seiches,” including “The Hydrodynamical Theory and Experimental Investiga-
tions of the Seiche Phenomena of Certain Scottish Lakes. ”

4th Quadrennial Period, 1908-12. — Professor J. Norman Collie, Ph.D., F.R.S., for his
distinguished contributions to Chemistry, Organic and Inorganic, during twenty-seven
years, including his work upon Neon and other rare gases. Professor Collie’s early papers
were contributed to the Transactions of the Society.

Meetings of the Society.

305

PROCEEDINGS OF THE STATUTORY GENERAL MEETING
Beginning the 131st Session, 1913-1914.

At the Annual Statutory Meeting of the Royal Society of Edinburgh, held in the Society’s
Lecture Room, 24 George Street, on Monday, October 27, 1913, at 4.30 p.m.

Principal Sir, Wm. Turner, K.C.B. , President, in the Chair.

Before the ordinary business of the Meeting commenced, Professor Crum Brown, in the name
of Lady Kelvin, presented to the Society a Marble Bust of the late Lord Kelvin, and the
President, Sir Wm. Turner, received the Bust in the name of the Society. (For account of the
Ceremony of the Presentation and Reception, see Proceedings, vol. xxxiv, pp. 1-3.)

The Minutes of the last Statutory Meeting, October 28, 1912, were read, approved, and signed.

On the motion of Dr Horne, seconded by Mr Jas. Currie, Mr John Alison and Mr J. B.
Clark were appointed Scrutineers, and the ballot for the New Council commenced.

The Treasurer’s Accounts for the past year, 1912-1913, were submitted; these, with the
Auditors’ Report, were read, and approved.

The Scrutineers reported that the following Council had been duly elected : —

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President
James Burgess, C.I.E., LL.D., M.R.A.S.,

Professor T. Hudson Beare, M.Inst.C.E.,

Professor F. 0. Bower, M.A., D.Sc., F.R.S.,

Professor Sir Thomas R. Fraser, M.D., LL.D., ^ Vice-Presidents.

F. R.C.P.E., F.R.S.,

Benjamin N. Peach, LL.D., F.R.S., F.G.S.,

Professor Sir E. A. Schafer, M.R.C.S., LL.D., F.R.S.,,

Cargill G. Knott, D.Sc., General Secretary.

Robert Kidston, LL.D., F.R.S., F.G.S., \ Secretaries to Ordinary

Professor Arthur Robinson, M.D., M.R.C.S., J Meetings.

James Currie, M.A. , Treasurer.

John S. Black, M.A. , LL.D., Curator of Library and Museum.

ORDINARY MEMBERS OF COUNCIL.

Professor T. H. Bryce, M.A., M.D.

William Allan Carter, M.Inst.C.E.
Andrew Watt, M.A.

James H. Ashworth, D.Sc.

James Gordon Gray, D.Sc.

Professor R. A. Sampson, M.A., D.Sc., F.R.S.
Professor D’Arcy W. Thompson, C.B., B.A.,
F.L.S.

Professor E. T. Whittaker, Sc.D., F.R.S.
Principal A. P. Laurie, M.A., D.Sc.

Professor J. Graham Kerr, M.A., F.R.S.
Leonard Dobbin, Ph.D.

Ernest Maclagan Wedderburn, M.A.,
LL.B.

^°CGeorge^Heriot’s^rast)n } William A llan CaETER, M.Inst.C.E.

On the motion of Professor F. 0. Bower, thanks were voted to the Scrutineers.

On the motion of Mr Hewat, thanks were voted to the Auditors, Messrs Lindsay, Jamieson
& Haldane, and they were reappointed.

On the motion of Dr Knott, thanks were voted to the Treasurer, Mr James Currie.

YOL. XXXIV.

20

306

Proceedings of the Royal Society of Edinburgh. [Sess.

PROCEEDINGS OF THE ORDINARY MEETINGS,
Session 1913-1914.

FIRST ORDINARY MEETING.

Monday , November 3, 1913.

Professor James Geikie, LL.D., D.C.L , F.R.S., F.G.S., President, in the Chair.

The President opened the Session with a short Address.

The following Communications were read : —

1. Atmospheric Electric Potential Results at Edinburgh during 1912. By G. A. Cause,
M.A. , D.Sc., and G. Shearer, M.A., B.Sc. ( With Lantern Illustrations.)

2. Some Factorable Minors of a Compound Determinant. By Professor W. H. Metzler,
A.B., Ph. D.

3. An Analytical Theory of the Equilibrium of an Isotropic Elastic Rod of Circular Section.
By Dr John Dougall. Communicated by Professor G. A. Gibson, LL.D.

The following, nominated for Honorary Fellowship, were balloted for, and duly declared
elected : —

As British Honorary Fellows : —

1. Horace Lamb, M.A., Sc.D. , D.Sc., LL.D., F.R.S., Professor of Mathematics in the
University of Manchester.

2. Sir William Turner Thiselton-Dyer, K.C.M.G., C.I.E., M.A., LL.D., F.R.S., formerly
Director of the Royal Botanic Gardens, Kew.

As Foreign Honorary Fellows : —

1. George Ellery Hale, F.M.R.S., Director of the Mount Wilson Solar Observatory
(Carnegie Institute of Washington).

2. Emil Clement Jungfleisch, Mem. Inst. Fr., Professor of Organic Chemistry in the
College of France, Paris.

3. Santiago Ramon y Cajal, F.M.R.S., Professor of Histology and Pathological Anatomy in
the University of Madrid.

4. Vito Yolterra, F.M.R.S., Sc.D., Ph.D., Professor of Mathematics and Physics in the
University of Rome.

5. Charles Ren& Zeiller, Mem. Inst. Fr. , Professor of Plant Palajontology in the National
Superior School of Mines, Paris.

SECOND ORDINARY MEETING.

Monday , November 17, 1913.

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President, in the Chair.

The following Communications were read : —

1. On the Fossil Flora of the Staffordshire Coal Fields. Part III. — The Fossil Flora of the
Westphalian Series of the South Staffordshire Coalfield. By Dr R. Kidston, F.R.S. ( With
Lantern Illustrations. )

2. Sphcerostoma ovale ( Conostoma ovale et intermedium , Williamson), a Lower Carboniferous
Ovale from Pettycur, Fifeshire, Scotland. By Professor Margaret J. Benson, D.Sc. Com-
municated by Dr R. Kidston, F.R.S.

3. Studies on the Pharmacological Action of Tetra-alkyl-ammonium Compounds. I. — The
Action of Tetra-methyl-ammonium Chloride. By Professor C. R. Marshall, M.D. ( With
Lantern Illustrations.)

4. The Theory of Bigradients from 1859-1880. By Dr Thomas Muir, F.R.S.

The following Candidate for Fellowship was balloted for, and duly declared elected : —
Edward Philtp Harrison, Ph.D.

1913-14.]

Meetings of the Society.

307

THIRD ORDINARY MEETING.

Monday , December 1, 1913.

Professor J. Hudson Beare, B.Sc., M. Inst.C.E., "Vice-President, in the Chair.

At the request of the Council the following Address was delivered : —

Principia Atmospherica : A Study of the Circulation of the Atmosphere. By W. N. Shaw,
LL.D., Sc.D., F.R.S. , Director of the Meteorological Office, London. ( With Lantern
Illustrations. )

The following Communications were also read : —

1. Observations on the Auditory Organ in the Cetacea. By Principal Sir William Turner,
K.C.B.

2. Note on a Siliceous Sponge of the Order Hexactinellida from South Shetland. By Principal
Sir William Turner, K.C.B.

The following Candidates for Fellowship were balloted for, and declared duly elected : — John
William Pare, M.B., C.M. (Edin.), M.D., L.D.S. (Eng.), William Fraser, William Barron
Coutts, M.A., B.S., Alfred Oswald, and John Edward Gemmell, M.B., C.M. (Edin.).

FOURTH ORDINARY MEETING.

Monday , December 15, 1913,

Professor James Geikie, LL.D., D.C.L. , F.R.S. , F.G.S. , President, in the Chair.

The following Communications were read : —

1. Obituary Notice of Dr R. M. Ferguson. By Dr A. E. Scougal, M.A.

2. Studies on the Pharmacological Action of Tetra-alkyl-ammonium Compounds. II. — The

Action of Tetra - ethyl - ammonium Chloride. III. — The Action of Methyl - ethyl - ammonium

Chlorides. By Professor C. R. Marshall, M.D. ( With Lantern Illustrations.)

3. Enzymatic Peptolysis in Germinating Seeds. — Parts I. and II. By Miss Dorothy Court,
B.Sc. Communicated by Professor E. Westergaard, Ph. D.

4. The Kinetic Energy of Viscous Flow through a Circular Tube. By Professor A. H. Gibson,
D.Sc.

5. Polychseta of the Family Nereidse collected by the Scottish National Antarctic Expedition.
By L. N. G. Ramsay, M.A., B.Sc. Communicated by Dr J. H. Ashworth.

FIFTH ORDINARY MEETING.

Monday , January 19, 1914.

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S. , President, in the Chair.

The following Communications were read : —

1. The Place in Nature of the Tasmanian Aboriginal as deduced from a Study of his Calvaria.
Part II. — His Relation to the Australian Aboriginal. By Professor R. J. A. Berry and Dr
A. W. D. Robertson.

2. A Study of the Curvatures of the Tasmanian Aboriginal Cranium. By Mr L. W. G. Buchner.
Communicated by Professor R. J. A. Berry. (In the absence of Professor Berry a brief account
of the above two papers was given by Dr Gerald Leighton.)

3. The Path of a Ray of Light in a Rotating Homogeneous and Isotropic Solid. By E. M.
Anderson, M.A., B.Sc. Communicated by the General Secretary.

4. The Anatomy of a New Species of Bathydoris and the Affinities of the Genus: Scottish
National Antarctic Expedition. By T. J. Evans, M.A. Communicated by Dr J. H. Ashworth.
( With Lantern Illustrations. )

5. On the Genus Porponia and related Genera : Scottish National Antarctic Expedition. By
Professor Oskar Carlgren. Communicated by Dr W. S. Bruce. {With Lantern Illustrations.)

The following Candidates for Fellowship were balloted for, and declared duly elected : —
Joseph Pearson, D.Sc., F.L.S., Director of the Colombo Museum, and Marine Biologist to the
Ceylon Government, Colombo Museum, Ceylon; Spencer Mort, M.B., Ch. B., Medical Super-

308

Proceedings of the Royal Society of Edinburgh. [Sess.

intendent, Edmonton Infirmary, London, N. ; and Charles Gloyer Barkla, D.Sc., F.R.S.,
Professor of Natural Philosophy in the University of Edinburgh, Littledene, 34 Priestfield
Road, Edinburgh.

Mr W. B. Coutts, D.Sc., M.A., signed the Roll, and was duly admitted a Fellow of the
Society.

SIXTH ORDINARY MEETING.

Monday , February 2, 1914.

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President, in the Chair.

At the request of the Council the following Address was delivered : —

Notes on the Evolution of Antarctica. By T. W. Edgeworth David, C.M.G., Hon. D.Sc.
Oxon., F.R.S., Professor of Geology in the University of Sydney, N.S.W. ; Scientific Officer with
the Shackleton Expedition, 1907-09 ; Leader of Party which reached South Magnetic Pole. ( With
Lantern Illustrations. )

SEVENTH ORDINARY MEETING.

Monday , February 16, 1914.

Professor James Geikie, LL.D., D.C.L. , F.R.S. , F.G. S., President, in the Chair.

The following Communications were read : —

1. The Axial Inclination of Curves of Thermoelectric Force : A Case from the Thermoelectrics
of Strained Wires. By John M‘Whan, M.A., Ph.D. Communicated by Professor Andrew
Gray, LL.D., F.R.S.

2. Rupture Strains in Beams and Crane Hooks. By Angus R. Fulton, B.Sc., A. M. Inst.C.E.
Communicated by Professor A. H. Gibson, D.Sc.

3. A Description of the Systematic Anatomy of a Foetal Sea-Leopard ( Stenorhynchus leptonyx),
with Remarks upon the Microscopic Anatomy of some of the Organs. By Harold A. Haig,
M. B., B.S., M.R.C.S. Communicated by Professor Arthur Robinson, M.D., M.R.C.S. ( With
Lantern Illustrations. )

The following Candidates for Fellowship were balloted for, and declared duly elected : — Robert
John Harvey-Gibson, M.A., F.L.S., Professor of Botany, University of Liverpool, 22 Falkner
Square, Liverpool, and John Noble Jack, Professor of Agriculture to the County Council of
Sussex, Kingscote, The Avenue, Lewes, Sussex.

EIGHTH ORDINARY MEETING.

Monday, March 2, 1914.

Professor Sir E. A. Schafer, F.R.S., Vice-President, in the Chair.

The following Communications were read : —

1. The Electrolytic Treatment of Lead Poisoning. By Professor Sir Thomas Oliver, M.D.,
LL.D., F.R.C.P., and Mr T. M. Clague. ( With a Demonstration and with Lantern
Illustrations. )

2, The Aborigines of Tasmania. Part III. — The Hair of the Head, compared with that of
other Ulotrichi, and with Australians and Polynesians. By Principal Sir William Turner, K.C.B.

NINTH ORDINARY MEETING.

Monday, March 16, 1914.

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President, in the Chair.

The following Communications were read : —

1. Stalk-eyed Crustacea Malacostraca of the Scottish National Antarctic Expedition. By the
Rev. T. R. R. Stebbing, M.A., F.R.S. Communicated by Dr J. H. Ashworth.

309

1913-L4.] Meetings of the Society.

2. Note on the Atmospheric Electrical Potential Gradient in Industrial Districts. By Mr
Daniel W. Steuart and Mr Ingvar Jorgensen. Communicated by James A. S.
Watson, B.Sc.

3. A Chemical Examination of the Organic Matter in Oil-Shales. By John B. Robertson,
M.A., B.Sc. Communicated by Dr J. S. Flett, F.R.S. ( With Lantern Illustrations.)

Mr William Fraser signed the Roll, and was duly admitted a Fellow of the Society.

TENTH ORDINARY MEETING.

Monday , May 4, 1914.

Professor James Geikie, LL.D., D.C.L., F.R.S. , F.G.S., President, in the Chair.

The following Communications were read : —

1. Description and Exhibition of a Four-Dimensional Model. By Dr D. M. Y. Sommervtlle.

2. Changes of Electrical Resistance accompanying Longitudinal and Transverse Magnetisations
in Iron and Steel. By Dr C. G. Knott.

3. Rocks from Gough Island, S. Atlantic : Scottish National Antarctic Expedition. By Dr
Robert Campbell. Communicated by the President. ( With Lantern Illustrations.)

ELEVENTH ORDINARY MEETING.

Monday , May 25, 1914.

Dr B. N. Peach, F’.R.S., Vice-President, in the Chair.

The following Communications were read : —

1. On the Inheritance of Certain Characters of the Wool of Sheep. By A. D. Darbishire,
M.A., and Mr M. W. Gray. {With Lantern Illustrations.)

2. On a New Species of Sclerocheilus, with a Revision of the Genus. By Dr J. H, Ashworth.

TWELFTH ORDINARY MEETING.

Monday, June 1, 1914.

Professor James Geikie, LL.D., D.C.L., F.R.S,, F.G.S., President, in the Chair.

The Council awarded : —

1. The Neill Prize for the biennial period 1911-1912, 1912-1913 to William Speirs Bruce,
LL. D. , in recognition of the scientific results of his Arctic and Antarctic explorations.

2. The Keith Prize for the biennial period 1911-1912, 1912-1913 to Mr James Russell,
for his series of investigations relating to magnetic phenomena in metals and the molecular theory
of magnetism, the results of which have been published in the Proceedings and Transactions of
the Society, the last paper having been issued within the period.

The above prizes will be presented at the Ordinary Meeting on July 6, 1914.

The following Communications were read : —

1. The Analytical Study of the Mechanism of Writing. By James Dreyer, M.A., B.Sc.
Communicated by Dr Alexander Morgan. ( With Exhibition of Apparatus and Lantern
Illustrations. )

2. The Pinna-Trace in the Ferns. By R. C. Davie, M.A., B.Sc. Communicated by Professor
Isaac Bayley Balfour, F.R.S. ( With Lantern Illustrations.)

3. Abnormal Echinoids in the Collection of the Royal Scottish Museum. By Dr James
Ritchie and James A. Todd, M.A. , B.Sc. Communicated by William Eagle Clarke. ( With
Lantern Illustrations. )

The following signed the roll, and were admitted Fellows of the Society : Dr J. W. Pare, Dr
Alex. C. Cumming, Mr James B. Ritchie, Mr Basil A. Pilkington, and Mr Theodore E.
Salyesen.

310 Proceedings of the Royal Society of Edinburgh. [Sess.

THIRTEENTH ORDINARY MEETING.

Monday , June 15, 1914.

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President, in the Chair.

The following Communications were read : —

1. Obituary Notice of Albert C. L. G. Gunther, M.A., M.D., Ph.D., F.R.S. By Professor
W. C. MTntosh, F.R.S.

2. The Fossil Osmundacese, Part V. By Dr R. Kidston, F.R.S. , F.G.S., and Professor
D. T. Gwynne-Yaughan, M.A. ( With Lantern Illustrations.)

3. The Hall and the Transverse Thermomagnetic Effects and their Temperature Coefficients.
By F. Unwin, M.Sc. Communicated by Professor F. G. Baily. ( With Lantern Illustrations.)

4. Some Factorable Continuants. By Professor W. H. Metzler, Ph.D.

5. Atlantic Sponges collected by the Scottish National Antarctic Expedition. By Miss Jane
Stephens. Communicated by Dr W. S. Bruce.

The following Candidates for Fellowship were balloted for, and duly declared elected : —
Alexander Gibb, A.M.Inst.C.E., and Robert Durward Clarkson, B.Sc., M.D., F.R.C.P.E.
Mr Peter Ramsay signed the Roll, and was duly admitted a Fellow of the Society.

FOURTEENTH ORDINARY MEETING.

Monday , July 6, 1914.

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President, in the Chair.

The following Prizes were presented : —

1. The Neill Prize for the biennial period 1911-1912, 1912-1913 to William Speirs
Bruce, LL.D., in recognition of the scientific results of his Arctic and Antarctic explorations.

2. The Keith Prize for the biennial period 1911-1912, 1912-1913 to Mr James Russell, for
his series of investigations relating to magnetic phenomena in metals and the molecular theory of
magnetism, the results of which have been published in the Proceedings and Transactions of the
Society, the last paper having been issued within the period.

Neill Prize Award, 1911-13.

The Neill Prize for the period 1911-1913 is awarded to Dr W. S. Bruce, a distinguished
traveller and naturalist. Dr Bruce, as the Fellows of the Royal Society of Edinburgh well know,
has spent his life in the exploration of Arctic and Antarctic seas and lands. He began his work
more than twenty years ago by a voyage to certain islands of the Antarctic Ocean ; in recent
years he has especially explored the Archipelago of Spitzbergen ; and in 1902 to 1904 he led the
Scottish National Antarctic Expedition through its adventurous voyage to a successful issue.

Dr Bruce’s many voyages, and especially the expedition of the Scotia , have led to the
advancement of knowledge in many departments of science. With the science of geography itself,
with the actual survey of new lands and seas, other Societies than this are peculiarly concerned.
But as far as living memory goes back, the Royal Society of Edinburgh has been proud to
encourage, with all its sympathy, and to help with all the means in its power, those discoveries,
biological and physical, which follow and reward the explorations of the scientific traveller.

In the Transactions of our Society there have appeared, during several recent years, a long
series of papers based on the results of the Scotia Expedition ; in which papers new organisms
from almost every group of the Animal Kingdom have been described, and in which important
questions of physics, of meteorology, and of oceanography have been discussed. These many
writings, by many hands, bear witness to the wisdom with which a great expedition was planned,
to the enthusiasm with which its leader animated his band of men, and to the foresight and untiring
industry which watched for and laid hold of the opportunities of discovery.

Keith Prize Award, 1911-13.

Mr Russell’s work, published mainly in our Transactions , dates from the early years of the
century. In his first paper he discussed the problem of magnetic shielding in hollow iron
cylinders, distinguishing the cases in which a transverse field existed alone, or had superposed
upon it either a circular or a longitudinal field. This work was experimental, but its results were
compared with those of the usual approximate theory. An investigation was also given of the
inductions produced by mutually perpendicular fields, and the effects were co-ordinated for the
first time and shown to be consistent with the results of the theory of molecular magnetism.

311

1913-14.] Meetings of the Society.

Phenomena were discussed with regard to which considerable difference of opinion existed, and
decisive results were obtained.

Mr Russell’s work was next directed to an investigation of the effect of an oscillating magnetic
field upon iron magnetised by a non-oscillating-field, and a careful discrimination was made,
for the first time, between the cases in which the former field was first established, or conversely.
Co-directed and perpendicularly directed fields were used, in the latter case possible disturbances
due to the establishment of the oscillating field by means of a current flowing in the iron itself
being for the first time avoided. Interesting and important results were obtained, and were
applied to the formation of new views regarding the action of certain magnetic detectors used in
wireless telegraphy.

The preceding investigation led to a similar one in which mechanical vibrations were employed,
and Mr Russell’s anticipation that similar results would be obtained was verified. Iron, nickel,
and steel were investigated, both in the annealed and the tempered conditions, and general
conclusions were obtained, while other interesting problems were suggested.

One fact — the dependence of the neutral point in a hysteresis loop upon the intensity of the
vibrational disturbance — was further investigated in a subsequent paper, and the apparently
discordant results of other observers were harmonised. In a connected investigation on the effect
of load and vibration upon magnetism in nickel, Mr Russell supplemented work of Ewing and
Chree, upon iron and cobalt respectively, published in the Philosophical Transactions , and
established the existence of a “ cyclic ” Yillari reversal.

Mr Russell is an experimenter of great skill and resource. A visit to his private laboratory
reveals how one man can do the work of three. And he is an accurate and acute reasoner. In
his lengthy series of experimental inquiries, he has co-ordinated old, disconnected, or even
seemingly discordant results, and has established new facts and new views. Throughout his
whole work his aim has been to co-ordinate and explain highly complicated phenomena as the
very direct results of the ideas of the molecular theory of magnetism based upon a simple view,
given in his first paper, of the structural condition of a magnetic metal demagnetised by decreasing
reversals. This is most noticeable in his latest paper which was communicated within the period
of the present award. When the theory of magnetism in a medium crystallised on the cubic
system is extended to an averagely random collocation of crystals, Mr Russell’s work will, with
other work, form a touchstone.

The following Communications were read

1. Obituary Notice of John Sturgeon MacKay, M.A., LL.D. By Dr George Philip,
George Watson’s College.

2. Temperature Observations in Loch Earn. — Part II. By E. M. Wedderburn, D.Sc., and
A. W. Young, M.A. {With Lantern Illustrations.)

3. Contributions to the Geology of South Georgia. By D. Ferguson, M.I.M.E., with reports
based on his collections by Professor J. W. Gregory, D.Sc., F.R.S., and G. W. Tyrrell,
A.R.C.Sc., F.G.S. {With Lantern Illustrations.)

The following Candidates for Fellowship were balloted for, and duly declared elected : —

Alfred Frank Tredgold, L.R.C.P., M.R.C.S. , Hon. Consulting Physician to National
Association for the Feebleminded; Francis John Lewis, D.Sc., F.L.S., Professor of Biology,
University of Alberta ; Archibald M‘Kendrick, F.R.C.S.E., D.P.H., L.D.S.

312

Proceedings of the Royal Society of Edinburgh.

PROCEEDINGS OF THE STATUTORY GENERAL MEETING
Ending the 131st Session, 1913-1914.

At the Annual Statutory Meeting of the Royal Society of Edinburgh, held in the Society’s
Lecture Room, 24 George Street, on Monday i October 26, 1914, at 4.30 p.m.,

Professor James Geikie, President, in the Chair,

the Minutes of the last Statutory Meeting, October 27, 1913, were read, approved, and signed.

On the motion of Dr Knott, seconded by Dr Horne, Dr J. R. Milne and Mr A. G.
Burgess were appointed Scrutineers, and the ballot for the New Council commenced.

The General Secretary announced that the Council had granted leave of absence to Mr G. A.
Stewart, Librarian, and Mr W. J. Beaton, Assistant Librarian, so as to enable them to join
His Majesty’s forces. The Council had also felt it advisable to close the Society’s Rooms on
Saturdays at one o’clock.

The Treasurer’s Accounts for the past year, 1913-1914, were submitted.

Professor Bower moved the approval of the Treasurer’s Report, and also votes of thanks to the
Treasurer and the Auditors, who were. reappointed. This was agreed to.

The Scrutineers reported that the following Council had been duly elected : —

Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President.
Professor T. Hudson Beare, M.Inst.C.E., \

Professor F. 0. Bower, M.A. , D.Sc., F.R.S.,

Professor Sir Thomas R. Fraser, M.D., LL.D.,

F.R.C.P.E., F.R.S.,

Benjamin N. Peach, LL.D., F.R.S., F.G. S. ,

Professor Sir E. A. Schafer, M.R.C.S., LL.D., F.R.S
The Right Hon. Sir J. H. A. Macdonald, K.C. B
P.C., LL.D., D.L., F.R.S., M.Inst.E.E.,

Cargill G. Knott, D.Sc., General Secretary.

Robert Kidston, LL.D., F.R.S., F.G.S.,

Professor Arthur Robinson, M.D., M.R.C.S.,

James Currie, M.A. , Treasurer.

John S. Black, M.A., LL.D., Curator of Library and Museum.

> Vice-Presidents.

j Secretaries to Ordinary
I Meetings.

ORDINARY MEMBERS OF COUNCIL.

James Gordon Gray, D.Sc.

Professor R. A. Sampson, M.A., D.Sc., F.R.S.
Professor D’Arcy W. Thompson, C.B., B.A.,
F.L.S.

Professor E. T. Whittaker, Sc.D., F.R.S.
Principal A. P. Laurie, M.A., D.Sc.

Professor J. Graham Kerr, M.A., F.R.S.

Leonard Dobbin, Ph.D.

Ernest Maclagan Wedderburn, M.A.,
LL.B.

W. B. Blaikie, LL.D.

John Horne, LL.D., F.S.S., F.G.S.

R. Stewart MacDougall, M.A., D.Sc.

W. A. Tait, D.Sc., M.Inst.C.E.

SOOi^o4ePH“T™s°t: } W— Allan CaKTEE, M.InstC.E.

Abstract of Accounts.

313

ABSTRACT

OF

THE ACCOUNTS OF JAMES CURRIE, ESQ.

As Treasurer of the Royal Society of Edinburgh.

SESSION 1913-1914.

I. ACCOUNT OF THE GENERAL FUND.

CHARGE.

1. Arrears of Contributions at 1st October 1913 ....... £106 1 0

2. Contributions for present Session : —

1. 141 Fellows at £2, 2s. each ...... £296 2 0

127 Fellows at £3, 3s. each ...... 400 1 0

£696 3 0

Less — Subscription for present Session, included in

1913 Accounts ...... 330

£693 0 0

2. Fees of Admission and Contributions of eleven new

Resident Fellows at £5, 5s. each . . . . . 57 15 0

3. Fees of Admission of eight new Non-Resident Fellows at

£26, 5s. each 210 0 0

4. Commutation Fees in lieu of future Contributions of two

Fellows ......... 45 3 0

3. Contribution for 1914-1915 paid in advance

4. Interest received —

Interest, less Tax £23, 4s. 10^d. . . £369 1 7

Annuity from Edinburgh and District Water Trust, less

Tax £3, 2s. 2d 49 7 10

5. Transactions and Proceedings sold ..... ...

6. Annual Grant from Government . ...... .

7. Income Tax repaid for year to 5th April 1914 ......

1005 18 0

2 2 0

418 9 5
140 1 1

600 0 0
25 18 11

Amount of the Charge

£2298 10 5

DISCHARGE.

1. Taxes, Insurance, Coal and Lighting

Inhabited House Duty ......

Insurance .......

Coal, etc., to 24th August 1914 ....

Gas to 12th March 1914 .....

Electric Light to 18th September 1914 .

Water 1913-14 .....

£063
9 0 9

20 18 6
0 4 10

7 19 8
4 4 0

£42 14 0

Carry forward

£42 14 0

314

Proceedings of the Royal Society of Edinburgh.

2. Salaries

General Secretary .
Librarian

Assistant Librarian
Office Keeper
Treasurer’s Clerk .

3. Expenses of Transactions : —

Neill & Co., Ltd., Printers .

Do. (for illustrations)

M'Farlane & Erskine, Lithographers
Hislop & Day, Engravers
Orrock & Son, Bookbinders
John Fowler & Co., Engravers
Alex. Ritchie & Son, Lithographers

4. Expenses of Proceedings : —

Neill & Co., Ltd., Printers

Do. (for illustrations)

Hislop & Day, Engravers
Alex. Ritchie & Son, Lithographers
M‘Farlane & Erskine do.

5. Books, Periodicals, Newspapers, etc."": —

Otto Schulze & Co., Booksellers
James Thin, do.

R. Grant & Son, do.

W. Green & Son, Ltd., do.

International Catalogue of Scientific Literatui
Robertson & Scott, News Agents .

Egypt Exploration Funds Subscription .

Ray Society do.

Palseontographical Society do.

Orrock & Son, Bookbinders .

T. & A. Constable, Printers .

Brought forward

£42 14 0

6. Expenses in Connection with Napier Tercentenary Reception :
E. Sawers, Purveyor
H. Dambmaun ....

Gillies & Wright, Joiners
A. Coutie & Son, do.

G. Waterston & Sons, Ltd., Stationers
Tait & Francis, Florists
Attendants, Extra Cleaning, Posts, etc.

7. Other Payments : —

Neill & Co. , Ltd., Printers .

E. Sawers, Purveyor .....
S. Duncan, Tailor (uniforms)

Lantern Exhibitions, etc. , at Lectures .
Lindsay, Jamieson & Haldane, C.A., Auditors
Post Office Telephone Rent .

A. Cowan & Sons, Ltd. .

G. Waterston & Sons, Ltd.

Gillies & Wright, Joiners
R. Graham, Slater
Mackenzie & Moncur, Ltd.

Oliver Typewriter Co. , Ltd.

Burn Bros., Plumbers .

Petty Expenses, Postages, Carriage, etc.

8. Interest Paid on Borrowed Money : —

Makerstoun Magnetic Meteorological Observation Fund

£100

0

0

120

0

0

49

3

4

86

14

0

25

0

0

£430

10

11

2

16

0

109

0

6

6

18

2

108

11

0

8

9

0

44

3

0

£281

13

7

1

1

0

12

4

9

9

0

0

2

10

0

£109

15

8

64

0

9

7

6

. 4

1

8

6

17

0

0

2

0

6

4

4

0

1

1

0

1

1

0

24

6

6

0

16

0

EPTION : -

£15

2

4

6

5

0

5

7

10

4

10

0

3

18

6

1

10

0

3

12

6

£68

5

0

35

17

10

11

18

0

10

10

0

6

6

0

10

0

0

10

9

6

6

16

6

21

16

8

8

5

4

2

16

3

24

6

0

2

7

3

89

8

2

380 17 4

710 8 7

306 9 4

233 0 3

40 6 2

309 2 6

5 5 2

Carry forward

£2028 3 4

Abstract of Accounts.

315

Brought forward

9. Irrecoverable Arrears of Contributions written off
10. Arrears of Contributions outstanding at 1st October 1914 : —
Present Session .........

Previous Sessions .........

. £2028 3 4

2 2 0

£59 17 0
61 19 0

121 16 0

Amount of the Discharge

Amount of the Charge

Amount of the Discharge ........

Excess of Receipts over Payments for 1913-1914

Deduct Floating Balance due by the Society at 1st October 1913 .

Eloating Balance in favour of the Society at 1st October 1914

Being —

Balance due by Union Bank of Scotland, Ltd., on Account

Current
Balance in hands of Librarian

Deduct Loan from the Makerstoun Magnetic Observation Fund

£237 5

£2152 1 4

£2298 10 5
2152 1 4
£146 9 1

123 16 2

£22 12 11

£243 11
220 18

£22 12 11

II. ACCOUNT OF THE KEITH FUND

To 1st October 1914.

CHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at

1st October 1913 ............ £62 10 7

2. Interest Received

On £896, 19s. Id. North British Railway Company 3 per cent.

Debenture Stock for year to Whitsunday 1914, less Tax

£1, 11s. lid. . . . £25 6 3

On £211, 4s. North British Railway Company 3 per cent. Lien

Stock for year to 30th June 1914, less Tax 7s. 7d. . 5 19 1

31 5 4

3. Income Tax repaid for year to 5 th April 1914 1188

£95 14 7

DISCHARGE.

1. James Russell — Money Portion of Prize 1911-13 ...... £49 19 1

2. Alexander Kirkwood & Son, Engravers, for Gold Medal . . . . 16 0 0

3. Balance due by Union Bank of Scotland, Ltd., on Account Current at

1st October 1914 ............ 29 15 6

£95 14 7

III. ACCOUNT OF THE NEILL FUND

To ls£ October 1914.

CHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at

1st October 1913 ............ £49 3 0

2. Interest Received : —

On £355 London, Chatham and Dover Railway 4^ per cent. Arbitration

Debenture Stock for year to 30th June 1914, less Tax 19s. 4d. . . . 15 0 2

3. Income Tax repaid for year to 5 th April 1914. . . . . . 0188

£65 1 10

316 Proceedings of the Koyal Society of Edinburgh.

DISCHARGE.

1. Dr Wm. S. Bruce — Money Portion of Prize 1911-13 ...... £15 19 0

2. Alexander Kirkwood & Son, Engravers, for- Gold Medal . . . . . 16 0 0

3. Balance due by Union Bank of Scotland, Ltd., on Account Current at

1st October 1914 33 2 10

£65 1 10'

IV. ACCOUNT OF THE MAKDOUGALL- BRISBANE FUND

To 1st October 1914.

CHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st

October 1913 £165 19 1

2. Interest received

On £365 Caledonian Railway Company 4 per cent. Consolidated Preference

Stock No. 2 for year to 30th June 1914, less Tax 17s. 4d. . . . 13 14 8

3. Income Tax repaid for year to 5th April 1914 ....... 0 17 0

£180 10 0

DISCHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at

1st October 1914 £180 10 9'

V. ACCOUNT OF THE MAKERSTOUN MAGNETIC METEOROLOGICAL

OBSERVATION FUND

To 1st October 1914.
CHARGE.

1. Balance due by General Fund at 1st October 1913 £220 13 6

2. Interest received on Balances due by General Fund at Deposit Receipt Rates

to 1st October 1914 552

DISCHARGE.

1. Donation to the Funds of the Napier Tercentenary Celebration .

2. Balance due by General Fund at 1st October 1914

£225

18

8

£5

0

0

220

18

8

£225

18

8

VI. ACCOUNT OF THE GUNNING VICTORIA JUBILEE PRIZE FUND

To 1st October 1914.

(Instituted by Dr R. H. Gunning of Edinburgh and Rio de Janeiro.)

CHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st

October 1913 £41 15 4-

2. Interest received on £1000 North British Railway Company 3 per cent.

Consolidated Lien Stock for year to 30th June 1914, less Tax £1, 16s. 2d. . 28 3 10

3. Income Tax repaid for year to 5th April 1914. 115 O'

£71 14 2

Abstract of Accounts.

317

DISCHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st

October 1914 £71 14 2

STATE OF THE FUNDS BELONGING TO THE ROYAL
SOCIETY OF EDINBURGH

As at 1st October 1914.

1. GENERAL FUND—

1. £2090, 9s. 4d. three per cent. Lien Stock of the North British Railway

Company at 75 per cent., the selling price at 1st October 1914

2. £8519, 14s. 3d. three per cent. Debenture Stock of do. at 75 per cent., do.

3. £52, 10s. Annuity of the Edinburgh and District Water Trust, equivalent

to £875 at 154 per cent., do. .........

4. £1811 four per cent. Debenture Stock of the Caledonian Railway Company

at 100| per cent., do. ..........

5. £35 four and a half per cent. Arbitration Debenture Stock of the London,

Chatham and Dover Railway Company at 106 \ per cent., do. .

6. Arrears of Contributions, as per preceding Abstract of Accounts .

£1567 17 0
6389 15 8

1347 10 0

1820 1 1

37 5 6
121 16 0

£11,284 5 3

Add Floating Balance in favour of the Society, as per preceding Abstract
of Accounts

22 12 11

Amount . . £11,306 18 2

Exclusive of Library, Museum, Pictures, etc., Furniture of the Society’s Rooms at
George Street, Edinburgh.

2. KEITH FUND—

1. £896, 19s. Id. three per cent. Debenture Stock of the North British

Railway Company at 75 per cent., the selling price at 1st October 1914

2. £211, 4s. three per cent. Lien Stock of do. at 75 per cent., do. .

3. Balance due by Union Bank of Scotland, Ltd., on Account Current .

Amount

£672 14
158 8

29 15

£860 17 10

3. NEILL FUND—

1. £355 four and a half per cent. Arbitration Debenture Stock of the London,

Chatham and Dover Railway Company at 106| percent., the selling price

at 1st October 1914 £378 1 6

2. Balance due by Union Bank of Scotland, Ltd., on Account Current . . 33 2 10

Amount . . . £411 4 4

4. MAKDOUGALL-BRISBANE FUND—

1. £365 four per cent. Consolidated Preference Stock No. 2 of the Caledonian

Railway Company at 94| per cent., the selling price at 1st October 1914 £344 18 6

2. Balance due by Union Bank of Scotland, Ltd., on Account Current . . 180 10 9

Amount . . . £525 9 3

5. MAKERSTOUN MAGNETIC METEOROLOGICAL OBSERVATION FUND—

Balance due by General Fund at 1st October 1914 ..... £220 18 8

318

Proceedings of the Royal Society of Edinburgh.

6. GUNNING VICTORIA JUBILEE PRIZE FUND — Instituted by Dr Gunning of Edinburgh
and Rio de Janeiro —

1. £1000 three per cent. Consolidated Lien Stock of the North British Railway

Company at 75 per cent., the selling price at 1st October 1914 . . £750 0 0

2. Balance due by Union Bank of Scotland, Ltd. , on Account Current 71 14 2

Amount . . £821 14 2

Edinburgh, 15^ October 1914. — We have examined the six preceding Accounts of the
Treasurer of the Royal Society of Edinburgh for the Session 1913-1914, and have found them to be
correct. The securities of the various Investments at 1st October 1914, as noted in the foregoing
Statement of Funds, have been exhibited to us.

LINDSAY, JAMIESON & HALDANE, C.A.,

Auditors.

Council of the Society.

319

THE COUNCIL OF THE SOCIETY,

January 1915.

President.

JAMES GEIKIE, LL.D., D.C.L., F.R.S., F.G.S., Professor of Geology in the
University of Edinburgh.

V ice-Presidents.

T. HUDSON BEARE, M.Inst.C.E., Professor of Engineering in the University of Edinburgh.
FREDERICK 0. BOWER, M.A., D.Sc., F.R.S., F.L.S., Regius Professor of Botany in the
University of Glasgow.

Sir THOMAS R. FRASER, M.D., LL.D., Sc.D., F.R.C.P.E., F.R.S., Professor of Materia
Medica in the University of Edinburgh.

BENJAMIN N. PEACH, LL.D., F.R.S., F.G.S., formerly District Superintendent and Acting
Palaeontologist of the Geological Survey of Scotland.

Sir EDWARD ALBERT SCHAFER, M.R.C.S., LL.D., F.R.S., Professor of Physiology in the
University of Edinburgh.

The Right Hon. Sir J. H. A. MACDONALD, P.C., K.C., K.C.B., F.R.S., M.InstE.E.,
Lord President of the Second Division of the Court of Session.

General Secretary.

CARGILL G. KNOTT, D.Sc., Lecturer on Applied Mathematics in the University of Edinburgh.

Secretaries to Ordinary Meetings.

ROBERT KIDSTON, LL.D., F.R.S., F.G.S.

ARTHUR ROBINSON, M.D., M.R.C.S., Professor of Anatomy in the University of Edinburgh.

Treasurer.

JAMES CURRIE, M. A.

Curator of Library and Museum.

JOHN SUTHERLAND BLACK, M.A., LL.D.

Councillors.

JAMES GORDON GRAY, D.Sc., Lecturer on
Physics in the University of Glasgow.

RALPH A. SAMPSON, M. A., D.Sc., F.R.S.,
Astronomer Royal for Scotland, and Pro-
fessor of Astronomy in the University of
Edinburgh.

D’ARCY W. THOMPSON, C.B., B.A., F.L.S.,
Professor of Natural History in the
University College, Dundee.

EDMUND T. WHITTAKER, Sc.D., F.R.S.,
Professor of Mathematics in the University
of Edinburgh.

A. P. LAURIE, M. A., D.Sc., Principal of the
Heriot-Watt College, Edinburgh.

JOHN GRAHAM KERR, M.A., F.R.S., Pro-
fessor of Zoology in the University of
Glasgow.

LEONARD DOBBIN, Ph.D., Lecturer on
Chemistry in the University of Edin-
burgh.

ERNEST MACLAGAN WEDDERBURN,
M.A., LL.B. , W.S., D.Sc.

W. B. BLAIKIE, LL.D.

JOHN HORNE, LL.D., F.R.S., F.G.S.

R. STEWART MacDOUGALL, M.A., D.Sc.

W. A. TAIT, D.Sc., M.Inst.C.E.

By a Resolution of the Society, January 19, 1880, Principal Sir WILLIAM TURNER,
K.C.B., D.C.L., F.R.S., having filled the office of President, is also a Member of Council.

Society’s Representative on George Heriot’s Trust.
WILLIAM ALLAN CARTER, M.Inst.C.E.

Office, Library, etc., 22, 24 George Street, Edinburgh. Tel. No., 2881.

320

Proceedings of the Royal Society of Edinburgh.

ALPHABETICAL LIST OF THE ORDINARY FELLOWS
OF THE SOCIETY,

Corrected to January 1, 1915.

N.B. — Those marked * are Annual Contributors.

B. prefixed to a name indicates that the Fellow has received a Makdougall-Brisbane Medal.

K. .. ,, „ Keith Medal.

N. ,, ,, ,, Neill Medal.

Y. J. ,, „ ,, the Gunning Victoria Jubilee Prize.

C. ,, ,, ,, contributed one or more Communications to the

Society’s Transactions or Proceedings.

Date of
Election.

1898

1898

1911

1896

1871

C.

1875

1895

C. K.

v. j.

1889

1894

1888

C.

1906

1893

1883

1905

1905

1903

1905

1881

C.

1906

1899

1893

1910

C.

1907

1911

C.

* Abercromby, the Hon. John, LL.D., 62 Palmerston Place, Edinburgh

Adami, Prof. J. G. , M.A. , M.D. Cantab., F.R.S., Professor of Pathology in M‘Gill
University, Montreal

* Adams, Archibald Campbell, A.M.Inst.Mech.E., A.M.Inst. E.E., Consulting

Engineer, 1 Old Smithhills, Paisley

* Affleck, Sir Jas. Ormiston, M.D., LL.D., F.R.C.P.E., 38 Heriot Row, Edinburgh

Agnew, Sir Stair, K.C.B., M.A., formerly Registrar - General for Scotland,)
22 Buckingham Terrace, Edinburgh 5 1

Aitken, John, LL.D., F.R.S., Ardenlea, Falkirk

Service on
Council, etc.

1882-85,

1886-89,

1891-93,

1895-98.

* Alford, Robert Gervase, M.Inst. C.E., Three Gables, Woodburn Park Road, Tun-

bridge Wells, Kent

Alison, John, M.A., Head Master, George Watson’s College, Edinburgh
Allan, Francis John, M.D., C.M. Edin., M.O.H. City of Westminster, West-
minster City Hall, Charing Cross Road, London
Allardice, R. E., M.A., Professor of Mathematics in Stanford University, Palo
Alto, Santa Clara Co. , California 10

Anderson, Daniel E., M.D., B.A., B.Sc.f Green Bank, Merton Lane, Highgate,
London, N.

Anderson, J. Macvicar, Architect, 6 Stratton Street, London
Anderson, Sir Robert Rowand, LL.D., 16 Rutland Square, Edinburgh
Anderson, William, F.G.S., P. O. Box 635, Sydney, New South Wales, Australia

* Anderson, William, M.A. , Head Science Master, George Watson’s College, Edin-

burgh, 29 Lutton Place, Edinburgh 15

Anderson-Berry, David, M.D. , LL.D., F.R.S.L., M.R.A.S., F.S.A. (Scot.),
Versailles, Highgate, London, N.

* Andrew, George, M. A. , B. A. , H. M. I. S. , Balwherrie, Strathearn Road, Broughty Ferry
Anglin, A. H., M.A., LL.D., M.R.I.A., Professor of Mathematics, Queen’s

College, Cork

Appleton, Colonel Arthur Frederick, F.R.C.V.S., Nylstroom, Smoke Lane, Reigate
Appleyard, James R., Royal Technical Institute, Salford, Manchester 20

* Archer, Walter E., 17 Sloane Court, London, S.W.

Archibald, E. H., B.Sc., Professor of Chemistry, Syracuse University, Syracuse,
N.Y., U.S.A.

* Archibald, James, M.A., Head Master, St Bernard’s School, 1 Leamington Terrace,

Edinburgh

* Ashworth, James Hartley, D.Sc., Lecturer on Invertebrate Zoology, University of

Edinburgh, 4 Cluny Terrace, Edinburgh

Badre, Muhammad, Ph.D., Almuneerah, Cairo, Egypt 25 I

1912-14.

1907

Date of

Electior

1896

1877

1905

1892

1902

1889

1886

1883

1910

1903

1914

1882

1904

1874

1887

1895

1904

1913

1888

1897

1892

1893

1882

1887

1906

1900

1887

1893

1897

1904

1880

1907

1884

1897

1904

1898

1894

1872

1886

Alphabetical List of the Ordinary Fellows of the Society.

321

* Baily, Francis Gibson, M.A., M.Inst.E.E. , Professor of Electrical Engineering,

Heriot-Watt College, Edinburgh, Newbury, Colinton, Midlothian
Balfour, I. Bayley, M.A., Sc.D., M.D., LL.D., F.R.S., F.L.S., King’s Botanist
in Scotland, Professor of Botany in the University of Edinburgh and Keeper
of the Royal Botanic Garden, Inverleith House, Edinburgh
Balfour-Browne, William Alexander Francis, M.A., Barrister-at-Law, 26 Barton
Road, Cambridge

* Ballantyne, J. W. , M.D., F.R.C. P.E., 19 Rothesay Terrace, Edinburgh

Bannerman, W. B., C.S.I., M.D., D.Sc., Surgeon General, Indian

Medical Service, Madras, India 30

Barbour, A. H. F., M.A., M.D., LL.D., F.R.C.P.E., 4 Charlotte Square, Edinburgh
Barclay, A. J. Gunion, M.A., 729 Great Western Road, Glasgow
Barclay, G. W. W., M.A., Raeden House, Aberdeen

* Barclay, Lewis Bennett, C.E., 13 Cargill Terrace, Edinburgh

Bardswell, Noel Dean, M.D., M.R.C.P. Ed. and Lond. , King Edward VII. Sana-
torium, Midhurst 35

* Barkla, Charles Glover, D.Sc. , F.R.S. , Professor of Natural Philosophy in the

University of Edinburgh, Littledene, 34 Priestfield Road, Edinburgh
Barnes, Henry, M. D., LL.D., 6 Portland Square, Carlisle
Barr, Sir James, M.D., LL.D., F.R.C. P. Lond., 72 Rodney Street, Liverpool
Barrett, Sir William F., F.R.S., M.R.I.A., formerly Professor of Physics, Royal
College of Science, Dublin, 6 De Vesci Terrace, Kingstown, County Dublin
Bartholomew, J. G., LL.D., F.R. G.S., The Geographical Institute, Duncan
Street, Edinburgh 40

Barton, Edwin H., D.Sc., A. M.Inst.E.E., Fellow Physical Society of London,
Professor of Experimental Physics, University College, Nottingham

* Baxter, William Muirhead, Glenalmond, Sciennes Gardens, Edinburgh

Beard, Joseph, F.R.C.S. (Edin.), M.R.C.S. (Eng.), L.R.C.P. (Lond.), D.P.H.
(Camb.), Medical Officer of Health and School Medical Officer, City of Carlisle,
15 Brunswick Street, Carlisle

Beare, Thomas Hudson, B.Sc., M.Inst.C.E., Professor of Engineering in the
University of Edinburgh (Vice-President)

* Beattie, John Carruthers, D.Sc., Professor of Physics, South African College,

Cape Town 45

Beck, Sir J. H. Meiting, Kt., M.D., M.R.C.P.E., Drostdy, Tulbagli, Cape
Province, South Africa

* Becker, Ludwig, Ph.D., Regius Professor of Astronomy in the University of

Glasgow, The Observatory, Glasgow

Beddard, Frank E., M.A. Oxon., F.R.S. , Prosector to the Zoological Society of
London, Zoological Society’s Gardens, Regent’s Park, London
Begg, Ferdinand Faithfull, 5 Whittington Avenue, London, E.C.

Bell, John Patrick Fair, F.Z.S., Fulforth, Witton Gilbert, Durham 50

* Bennett, James Bower, C.E., 5 Hill Street, Edinburgh
Bernard, J. Mackay, ofDunsinnan, B.Sc., Dunsinnan, Perth

* Berry, George A., M.D., C.M., F.R.C.S., 31 Drumsheugh Gardens, Edinburgh
Berry, Richard J. A., M.D. , F.R.C.S.E., Professor of Anatomy in the University

of Melbourne, Victoria, Australia

*■ Beveridge, Erskine, LL.D., St Leonards Hill, Dunfermline 55

Birch, De Burgh, C.B. , M. D., Professor of Physiology in the University of Leeds,
8 Osborne Terrace, Leeds

t Black, Frederick Alexander, Solicitor, 59 Academy Street, Inverness

Black, John S., M.A., LL.D. (Curator of Library and Museum), 6 Oxford J
Terrace, Edinburgh J

Blaikie, Walter Biggar, LL.D., The Loan, Colinton
: Bles, Edward J., M.A. , D.Sc., Elterholm, Cambridge 60

' Blyth, Benjamin Hall, M.A., V.P.Inst.C. E., 17 Palmerston Place, Edinburgh
Bolton, Herbert, M.Sc., F.G.S., F.Z.S., Director of the Bristol Museum and Art
Gallery, Bristol

Bottomley, J. Thomson, M.A., D.Sc., LL.D., F.R.S., F.C.S., 13 University
Gardens, Glasgow

Bower, Frederick O., M.A. , D.Sc., F.R.S., F.L.S., Regius Professor of Botany (
in the University of Glasgow, 1 St John’s Terrace, Hillhead, Glasgow J
(Vice-President) i

XIV.

Service on
Council, etc.

1909-12.

1888-91.

1909-12.

1907-1909.

V-P

1909-

1891-94.

Cur.

1906-

1914—

1887-90,

1893-96,

1907-09.

V-P

1910-

21

322

Date of

Election.

1884

1901

1903

1886

1907

1912

1895

1893

1901

1907

1864

1913

1898

1911

1883

1885

1909

1912

1906

1898

1870

1887

1905

1902

1894

1887

1888

1896

1887

1897

1910

1893

1894

1905

1904

Proceedings of the Koyal Society of Edinburgh.

Service on
Council, etc.

Bowman, Frederick Hungerford, D.Sc. , F.C.S. (Lond. and Berl.), F.I.C.,
A.Inst.C.E., A.Inst.M.E., M.Inst.E. E., etc., 4 Albert Square, Manchester 65
Bradbury, J. B., M.D., Downing Professor of Medicine, University of

Cambridge

* Bradley, 0. Charnock, M.D., D.Sc., Principal, Royal Veterinary College,

Edinburgh

Bramwell, Byrom, M.D., F. R.C.P.E., LL.D. , 23 Drumsheugh Gardens, Edinburgh

* Bramwell, Edwin, M.B., F.R.C.P.E., F.R.C.P. Lond., 24 Walker Street, Edin-

burgh

Bridger, Adolphus Edward, M.D. (Edin.), F.R.C.P. (Edin.), B.Sc. (Paris), B.L.

(Paris), Foley Lodge, Langham Street, London, W. 70

Bright, Charles, M. Inst.C.E., M.Inst.E. E., F.R.A.S., F.G.S., Consulting

Engineer to the Commonwealth of Australia, The Grange, Leigh, Kent, and
Members’ Mansions, Victoria Street, London, S.W.

Brock, G. Sandison, M.D., 6 Corso d’ltalia, Rome, Italy

* Brodie, W. Brodie, M.B., Thaxted, Dunmow, Essex

Brown, Alexander, M.A., B.Sc., Professor of Applied Mathematics, South African
College, Cape Town

Brown, Alex. Crum, M.A., M.D., D.Sc., F.R.C.P.E., LL.D., F.R.S., Emeritus
Professor of Chemistry in the University of Edinburgh, 8 Belgrave Crescent,"
Edinburgh 75

* Brown, Alexander Russell, M.A., B.Sc., Science Master, Buckhaven Junior

Student Centre, Norfield, Buckhaven

* Brown, David, F.C.S., F.I.C., J.P., Willowbrae House, Willowbrae Road,

Edinburgh

* Brown, David Rainy, Chemical Manufacturer (J. F. Macfarlan & Co.),

93 Abbeyhill, Edinburgh

Brown, J. J. Graham, M.D., F.R.C.P.E., 3 Chester Street, Edinburgh
Brown, J. Macdonald, M.D., F.R.C.S., 64 Upper Berkeley Street, Portman
Square, London, W. 80

* Brownlee, John, M.A., M.D., D.Sc., Ruchill Hospital, Biisland Drive,

Glasgow

* Bruce, Alexander Ninian, D.Sc., M.D. , 8 Ainslie Place, Edinburgh

* Bruce, William Speirs, LL.D., Director of the Scottish Oceanographical Laboratory,

Edinburgh, Antarctica, Joppa, Midlothian

* Bryce, T. H., M.A., M.D, (Edin.), Professor of Anatomy in the University of

Glasgow, 2 The University, Glasgow

Buchanan, John Young, M.A., F.R.S., 26 Norfolk Street, Park Lane,

London, W. 85

Buist, J. B., M.D., F.R.C.P.E., 1 Clifton Terrace, Edinburgh
Bunting, Thomas Lowe, M.D., 27 Denton Road, Scotswood, Newcastle-on-Tyne

* Burgess, A. G., M.A., Mathematical Master, Edinburgh Ladies’ College,

64 Strathearn Road, Edinburgh

* Burgess, James, C.I.E., LL.D., Hon. A.R.I.B.A., F.R.G.S., Hon. M. Imp.

Russ. Archseol. Soc., and Amer. Or. Soc., M. Soc. Asiat. de Paris,
M.R.A.S., IT. Corr. M. Batavian Soc. of Arts and Sciences, and Berlin Soc.
Anthrop., H. Assoc. Finno-Ugrian Soc., 22 Seton Place, Edinburgh
Burnet, Sir John James, Architect, 18 University Avenue, Hillhead, Glasgow 90
Burns, Rev. T., D.D., F.S.A. Scot., Minister of Lady Glenorchy’s Parish Church,
Croston Lodge, Chalmers Crescent, Edinburgh

* Butters, J. W. , M.A., B.Sc., Rector of Ardrossan Academy
Cadell, Henry Moubray, of Grange, B.Sc., Linlithgow

* Caird, Robert, LL.D., Shipbuilder, Greenock

* Calderwood, Rev. Robert Sibbald, Minister of Cambuslang, The Manse, Cambuslang,

Lanarkshire 95

Calderwood, W. L., Inspector of Salmon Fisheries of Scotland, South Bank, Canaan
Lane, Edinburgh

* Cameron, James Angus, M. D., Medical Officer of Health, Firhall, Nairn
Cameron, John, M.D., D.Sc., M.R.C.S. Eng., Anatomy Department, Middlesex

Hospital Medical School, London, W.

* Campbell, Charles Duff, Scottish Liberal Club, Princes Street, Edinburgh

1907-10.

1890-93.

1865-68,

1869-72,

1873-75,

1876-78,

1911-13.

Sec.

1879-1905.

V-P

1905-11.

1909-12.

1911-14.

1878-81,

1S84-86.

1895-98.

1899-1902.

V-P

1908-14.

Date of

Election.

1899

1910

1905

1901

1905

1898

1898

1908

1882

1899

1912

1874

1891

1911

1903

1909

1913

1875

1904

1904

1888

1904

1909

1886

1872

1894

1891

1905

1914

1911

1908

1875

1907

1903

1887

1870

1886

Alphabetical List of the Ordinary Fellows of the Society.

323

c.

c.

c.

y. j.

c,

o.

* Carlier, Edmund W. W., M.D., M.Sc., F.E.S., Professor of Physiology, University,

Birmingham 100

Carnegie, David, M.Inst.C.E., M.Inst.Mech.E., M.I.S. Inst., 33-35 Charterhouse
Square, London, E.C.

* Carse, George Alexander, M. A., D. Sc. , Lecturer on Natural Philosophy, University

of Edinburgh, 3 Middleby Street, Edinburgh
Carslaw, H. S. , M.A., D.Sc. , Professor of Mathematics in the University of
Sydney, New South Wales

Carter, Joseph Henry, F.R.C.V.S., Stone House, Church Street, Burnley,
Lancashire

* Carter, Wm. Allan, M.Inst.C.E., 32 Great King Street, Edinburgh (Society’s

Representative on George Heriot’s Trust) 105

Carus- Wilson, Cecil, F.R.G.S., F.G.S., Waldegrave Park, Strawberry Hill,
Middlesex, and Sandacres Lodge, Parkston e-on-Sea, Dorset
Cavanagh, Thomas Francis, M.D., The Hospital, Bella Coola, B.C., Canada
Cay, W. Dyce, M.Inst.C.E., 39 Victoria Street, Westminster, London
Chatham, James, Actuary, 7 Belgrave Crescent, Edinburgh

Chaudhuri, Banawari Lai, B.A.(Cal. ), B.Sc. (Edin.), Assistant Superintendent,
Natural History Section, Indian Museum, 120 Lower Circular Road, Calcutta,
India 110

Chiene, John, C.B., M.D., LL.D., F.R.C.S.E., Emeritus Professor of Surgery in
the University of Edinburgh, Barnton Avenue, Davidson’s Mains

* Clark, John B., M.A. , Head Master of Heriot’s Hospital School, Lauriston,

Garleffin, Craiglea Drive, Edinburgh

* Clark, William Inglis, D.Sc., 29 Lauder Boad, Edinburgh

* Clarke, William Eagle, F.L.S., Keeper of the Natural History Collections in the

Royal Scottish Museum, Edinburgh, 35 Braid Road, Edinburgh
Clayton, Thomas Morrison, M.D. , D.Hy., B.Sc., D.P. H., Medical Officer of
Health, Gateshead, 13 The Crescent, Gateshead-on-Tyne 115

* Cleghorn, Alexander, M.Inst.C.E., Marine Engineer, 14 Hatfield Drive, Kelvinside,

Glasgow

Clouston, Sir T. S., M.D., LL.D., F.R.C.P.E., 26 Heriot Row, Edinburgh
Coker, Ernest George, M.A., D.Sc., Professor of Mechanical Engineering and
Applied Mechanics, City and Guilds Technical College, Finsbury, Leonard
Street, City Road, London, E.C.

Coles, Alfred Charles, M. D., D.Sc., York House, Poole Road, Bourne-
mouth, W.

Collie, John Norman, Ph.D., D.Sc., LL.D., F.R.S., F.C.S., F.I.C., F.R.G.S.,
Professor of Organic Chemistry in the University College, Gower Street,
London 120

* Colquhoun, Walter, M.A. , M. B., 18 Walmer Crescent, Ibrox, Glasgow

* Comrie, Peter, M.A., B.Sc., Head Mathematical Master, Boroughmuir Junior

Student Centre, 1 9 Craighouse Terrace, Edinburgh
Connan, Daniel M., M.A.

Constable, Archibald, LL.D., 11 Thistle Street, Edinburgh

Cook, John, M.A. , LL.D., formerly Principal, Central College, Bangalore, Director
of Meteorology in Mysore, and Fellow, University of Madras, India, 9 Cobden
Crescent, Edinburgh 125

*' Cooper, Charles A., LL.D., 41 Drumsheugh Gardens, Edinburgh

* Corrie, David, F.C.S., Nobel’s Explosives Company, Polmont, Stirlingshire

* Coutts, William Barron, M.A. , B.Sc., 33 Dalhousie Terrace, Edinburgh

* Cowan, Alexander C., Papermaker, Valleyfield House, Penicuik, Midlothian
Craig, James Ireland, M. A., B. A. , Controller of the Department of General Statistics,

14 Abdin Street, Cairo : The Koubbeh Gardens, near Cairo, Egypt 130

Craig, William, M.D. , F.R.C.S. E. , Lecturer on Materia Medica to the College of
Surgeons, 71 Bruntsfield Place, Edinburgh

* Cramer, William, Ph.D., Lecturer in Physiological Chemistry in the University of

Edinburgh, Physiological Department, The University, Edinburgh
Crawford, Lawrence, M.A., D.Sc., Professor of Mathematics in the South African
College, Cape Town

Crawford, William Caldwell, 1 Lockharton Gardens, Colinton Road, Edinburgh
Crichton-Browne, Sir Jas., M.D., LL.D., D.Sc., F.R.S., Lord Chancellor’s Visitor
and Vice-President and Treasurer of the Royal Institution of Great Britain, 45
Hans Place, S.W., and Royal Courts of Justice, Strand, London 135

Croom, Sir John Halliday, M. D., F.R.C.P.E., Professor of Midwifery in the
University of Edinburgh, late President, Royal College of Surgeons, Edin-
burgh, 25 Charlotte Square, Edinburgh

Service on
Council, etc.

1911-14.

1884-86,

1904-06.

324

Date of

Electior

1914

1898

1904

1885

1912

1884

1894

1869

1905

1906

1904

1884

1888

1876

1885

1897

1904

1881

1867

1905

1882

1901

1866

1910

1908

1901

1904

1903

1892

1899

1906

1893

1904

1904

1875

1913

1906

1897

1884

1879

1902

Proceedings of the Poyal Society of Edinburgh.

* Cumming, Alexander Charles, D.Sc., Lecturer in Chemistry, University, Edin-

burgh, 16 Kilmaurs Terrace, Edinburgh

* Currie, James, M.A. Cantab. (Treasurer), Larkfield, Goldenacre, Edin- /

burgh \

* Cuthbertson, John, Secretary, West of Scotland Agricultural College, 6 Charles

Street, Kilmarnock

Daniell, Alfred, M.A., LL.B. , D.Sc., Advocate, The Athenseum Club, Pall Mall,
London 140

* Darbishire, Arthur Dukinfield, M.A., Lecturer in Genetics at the University of

Edinburgh

Davy, R., F. R.C.S. Eng., Consulting Surgeon to Westminster Hospital, Burstone
House, Bow, North Devon

* Denny, Sir Archibald, Bart., LL.D., Cardross Park, Cardross, Dumbartonshire
Dewar, Sir James, Kt., M.A., LL.D., D.C.L., D.Sc., F.R.S., V.P.C.S., Jacksonian

Professor of Natural and Experimental Philosophy in the University of
Cambridge, and Fullerian Professor of Chemistry at the Royal Institution of
Great Britain, London

* Dewar, James Campbell, C.A., 27 Douglas Crescent, Edinburgh 145

'Dewar, Thomas William, M.D. , F.R.C.P., Kincairn, Dunblane

Dickinson, Walter George Burnett, F.R.C.V.S., Boston, Lincolnshire
Dickson, the Right Hon. Charles Scott, K. C., LL.D., 22 Moray Place, Edinburgh
Dickson, Henry Newton, M.A., D.Sc., 160 Castle Hill, Reading
Dickson, J. D. Hamilton, M.A. , Senior Fellow and formerly Tutor, St Peter’s
College, Cambridge 150

Dixon, James Main, M.A., Litt. Hum. Doctor, Professor of English, University
of Southern California, Wesley Avenue, Los Angeles, California, U.S.A.
Dobbie, James Bell, F.Z.S., 12 South Inverleith Avenue, Edinburgh
Dobbie, Sir James Johnston, Kt., M.A., D.Sc., LL.D., F.R.S., Principal of the
Government Laboratories, London. 4 Vicarage Gate, Kensington, London, W.
Dobbin, Leonard, Ph. D., Lecturer on Chemistry in the University of Edinburgh, f
6 Wilton Road, Edinburgh \

Donaldson, Sir James, M.A., LL.D., Principal of the University of St
Andrews 155

Donaldson, Rev. Wm. Galloway, F.R.G.S., F.E.I.S., The Manse, Forfar
Dott, David B., F. I.C., Memb. Pharm. Soc., Ravenslea, Musselburgh
Douglas, Carstairs Cumming, M.D., D.Sc., Professor of Medical Jurisprudence
and Hygiene, Anderson’s College, Glasgow, 2 Royal Crescent, Glasgow
Douglas, David, 22 Drummond Place, Edinburgh

Douglas, Loudon MacQueen, Author and Lecturer, 3 Lauder Road, Edinburgh 160
Drinkwater, Harry, M.D., M.R.C.S. (Eng.), F.L.S., Lister House, Wrexham,

North Wales

Drinkwater, Thomas W., L.R.C.P.E., L.R.C.S.E., Chemical Laboratory, Surgeons’
Hall, Edinburgh

Dunlop, William Brown, M.A., 4a St Andrew Square, Edinburgh
Dunstan, John, M.R. C.V.S., Inversnaid, Liskeard, Cornwall
Dunstan, M. J. R., M.A., F. I.C., F.C.S., Principal, South-Eastern Agricultural
College, Wye, Kent 165

Dutliie, George, M.A. , Inspector-General of Education, Salisbury, Rhodesia
Dyson, Sir Frank Watson, Kt., M.A., LL.D., F.R.S., Astronomer Royal, Royal
Observatory, Greenwich
Edington, Alexander, M. D., Howick, Natal
Edwards, John, 4 Great Western Terrace, Kelvinside, Glasgow
Elder, William, M.D., F.R.C.P.E., 4 John’s Place, Leith 170

Elliot, Daniel G. , American Museum of Natural History, Central Park West,
New York, N.Y., U.S.A.

Elliot, George Francis Scott, M.A. (Cantab.), B.Sc., F.R.G.S., F.L.S., Drumwhill,
Mossdale

Ellis, David, D.Sc., Ph.D., Lecturer in Botany and Bacteriology, Glasgow and
West of Scotland Technical College, Glasgow
Erskine- Murray, James Robert, D.Sc., 4 Great Winchester Street, London, E.C.
Evans, William, F.F.A., 38 Morningside Park, Edinburgh 175

Ewart, James Cossar, M.D., F.R.C.S.E., F.R.S., F.Z.S., Regius Professor off
Natural History, University of Edinburgh, Craigybield, Penicuik, Mid--J
lothian I

Ewen, John Taylor, B.Sc., M.I.Mech.E., H.M. Inspector of Schools, 104 King’s
Gate Aberdeen

Service on
Council, etc.

Treas.

1906-

1872-74.

1905-08.

1904-07

1913-

1870-78.

1907-10.

1882-85,

1904-07.

V-P

1907-12.

Date of

Election.

1878

1900

1910

1875

1907

1888

1883

1899

1907

1904

1888

1898

1899

1911

1906

1900

1872

1904

1892

1910

1896

1867

1914

1891

1891

1907

1888

1901

1899

1867

1909

1880

1861

Alphabetical List of the Ordinary Fellows of the Society.

Ewing, Sir James Alfred, K.C.B., M.A., B.Sc., LL.D., M.Inst.C.E., F.R.S.,
Director of Naval Education, Admiralty, Froghole, Edenbridge, Kent
Eyre, John W. H., M. D. , M.S. (Dunelm), D.P. H. (Camb. ), Guy’s Hospital
(Bacteriological Department), London

* Fairgrieve, Mungo M'Callum, M.A. (Glasg.), M. A. (Cambridge), Master at the

Edinburgh Academy, 37 Queen’s Crescent, Edinburgh 180

Fairley, Thomas, Lecturer on Chemistry, 8 Newton Grove, Leeds
Falconer, John Downie, M.A., D.Sc., F.G.S., Lecturer on Geography, The
University, Glasgow.

Fawsitt, Charles A., Coney Park, Bridge of Allan

Felkin, Robert W. , M. D., F.R. G.S., 47 Bassett Road, North Kensington,
London, W.

* Fergus, Andrew Freeland, M.D. , 22 Blythswood Square, Glasgow 185

* Fergus, Edward Oswald, 12 Clairmont Gardens, Glasgow

* Ferguson, James Haig, M.D., F.R.C.P.E., F.R.C.S.E., 7 Coates Crescent,

Edinburgh

Ferguson, John, M.A., LL.D., Professor of Chemistry in the University of
Glasgow

* Findlay, John R., M.A. Oxon., 27 Drumsheugh Gardens, Edinburgh

* Finlay, David W., B.A., M.D. , LL.D. , F.R.C.P., D.P.H., Emeritus Professor of

Medicine in the University of Aberdeen, Honorary Physician to His Majesty
in Scotland, 23 Dundonald Road, Glasgow, W. 190

Fleming, John Arnold, F.C.S., etc., Pottery Manufacturer, Woodburn, Rutherglen,
Glasgow

* Fleming, Robert Alexander, M.A. , M.D. , F.R. C.P.E. , Assistant Physician, Royal

Infirmary, 10 Chester Street, Edinburgh

* Flett, John S., M.A., D.Sc., LL.D., F.R.S., Director of the Geological Survey of

Scotland, 33 George Square, Edinburgh

Forbes, Professor George, M.A., M.Inst.C.E., M.Inst.E.E., F.R.S., F.R.A.S.,
11 Little College Street, Westminster, S.W.

Forbes, Norman Hay, F.R.C.S.E. , L.R.C.P. Lond., M.R.C.S. Eng., Corres.
Memb. Soc. d’Hydrologie medicale de Paris, Druminnor, Church Stretton,
Salop 195

* Ford, John Simpson, F.C.S., 4 Nile Grove, Edinburgh

* Fraser, Alexander, Actuary, 17 Eildon Street, Edinburgh

* Fraser, John, M.B., F.R. C.P.E., formerly one of H.M. Commissioners in

Lunacy for Scotland, 54 Great King Street, Edinburgh

Fraser, Sir Thomas R., Kt., M.D., LL.D., Sc.D., F.R. C.P.E., F.R.S., Professor
of Materia Medica in the University of Edinburgh, Honorary Physician to J
the King in Scotland, 13 Drumsheugh Gardens, Edinburgh. (Vice-
President)

* Fraser, William, Managing Director, Neill & Co., Ltd., Printers, 17 Eildon Street,

Edinburgh 200

* Fullarton, J. H., M.A., D.Sc., 23 Porchester Gardens, London, W.

* Fulton, T. Wemyss, M.D. , Scientific Superintendent, Scottish Fishery Board,

41 Queen’s Road, Aberdeen

* Galbraith, Alexander, Superintendent Engineer, Cunard Line, Liverpool, 93

Trinity Road, Bootle, Liverpool

Galt, Alexander, D.Sc., Keeper of the Technological Department, Royal Scottish
Museum, Edinburgh

Ganguli, Sanjiban, M.A., Principal, Maharaja’s College, and Director of Public
Instruction, Jaipur State, Jaipur, India 205

Gatehouse, T. E., A.M. Inst.C.E., M.Inst.M.E., M.Inst.E.E.. Fairfield, 128 Tulse
Hill, London, S.W.

Gayner, Charles, M.D., F.L.S.

* Geddes, Auckland C., M.D. , Professor of Anatomy, M'Gill University, Montreal,

Canada

Geddes, Patrick, Professor of Botany in University College, Dundee, and Lecturer
on Zoology, Ramsay Garden, University Hall, Edinburgh
Geikie, Sir Archibald, O.M., K.C.B., D.C.L. Oxf., D.Sc., LL.D., Ph.D., Late Pres.
R.S., Foreign Member of the Reale Accad. Lincei, Rome, of the National Acad,
of the United States, of the Academies of Stockholm, Christiania, Gottingen,
Corresponding Member of the Institute of France and of the Academies of
Berlin, Vienna, Munich, Turin, Belgium, Philadelphia, New York, etc.,
Shepherd’s Down, Haslemere, Surrey 210

325

Service on
Council, etc.

1888-91.

1870-73,

1877-79,

1883-86,

1894-97.

V-P

1911-

1869-72,

1874-76,

1879-82.

326

Date of

Election.

1871

1914

1909

1914

1910

1912

1910

1890

1911

1900

1880

1907

1909

1911

1898

1910

1901

1899

1913

1897

1891

1898

1883

1910

1909

1910

1886

1897

1905

1906

1905

1910

1899

1907

Proceedings of the Royal Society of Edinburgh.

Geikie, James, LL. D. , D.C.L., F.R. S., F. G.S., formerly Professor of Geology
in the University of Edinburgh (President), Kilmorie, Colinton Road,-
Edinburgh

Gemmell, John Edward, M.B., C.M., Hon. Surgeon Hospital for Women and
Maternity Hospital ; Hon. Gynaecologist, Victoria Central Hospital, Liscard,
28 Rodney Street, Liverpool.

* Gentle, William, B.Sc., 12 Mayfield Road, Edinburgh

* Gibb, Alexander, A.M. Inst.C. E., St Martin’s Abbey, by Perth

* Gibb, David, M.A., B.Sc., Lecturer in Mathematics, Edinburgh University,

15 South Lauder Road, Edinburgh 215

* Gibson, Arnold Hartley, D.Sc., Professor of Engineering, University College, Dundee

* Gibson, Charles Robert, Lynton, Mansewood, by Pollokshaws

Gibson, George A., M.A., LL.D., Professor of Mathematics in the University of j
Glasgow, 10 The University, Glasgow \

Gidney, Henry A. J. , L.M. and S. Socts. Ap. (Lond.), F.R.C.S. (Edin.), D.P.H.
(Camb.), D.O. (Oxford), Army Specialist Public Health, c/o Thomas Cook &
Sons, Ludgate Circus, London

Gilchrist, Douglas A., B.Sc., Professor of Agriculture and Rural Economy,
Armstrong College, Newcastle-upon-Tyne 220

Gil ruth, Ueorge Ritchie, Surgeon, 53 Northumberland Street, Edinburgh
Gilruth, John Anderson, M-.R.C.V.S., D.V.Sc. (Melb.), Administrator, Govern-
ment House, Darwin Northern Territory, Australia

* Gladstone, Hugh Steuart, M.A., M.B.O.U., F.Z.S., 40 Lennox Gardens, London,

S.W.

Gladstone, Reginald John, M.D., F.R.C.S. (Eng.), Lecturer on Embryology and
Senior Demonstrator of Anatomy, Middlesex Hospital, London, 22 Regent’s
Park Terrace, London, N.W.

* Glaister, John, M.D., F.R.F.P.S. Glasgow, D.P.H. Camb. , Professor of Forensic

Medicine in the University of Glasgow, 3 Newton Place, Glasgow 225

Goodall, Joseph Strickland, M.B. (Lond.), M.S.A. (Eng.), Lecturer on Physiology,
Middlesex Hospital, London, Annandale Lodge, Vanbrugh Park, Blackheath,
London, S.E.

Goodwillie, James, M.A., B.Sc., Liberton, Edinburgh
’‘'Goodwin, Thomas S., M.B., C.M., F.C.S., 25 Worple Road, Isleworth, and
Derwent Lodge, London Road, Spring-grove, Isleworth, Middlesex

* Gordon, William Thomas, M.A., D.Sc. (Edin.), B.A. (Cantab.), Lecturer in

Geology, University of London, King’s College, Strand, W.C.

Gordon-Munn, John Gordon, M.D., Heigham Hall, Norwich 230

* Graham, Richard D., 11 Strathearn Road, Edinburgh
*Gray, Albert A., M.D., 4 Clairmont Gardens, Glasgow

Gray, Andrew, M.A., LL.D., F.R.S., Professor of Natural Philosophy in the J
University of Glasgow

Gray, Bruce M ‘Gregor, C.E., A.M. Inst.C. E., Westbourne Grove, Selby, York-
shire

* Gray, James Gordon, D.Sc., Lecturer in Physics in the University of Glasgow, 11

The University,. Glasgow 235

* Green, Charles Edward, Publisher, Gracemount House, Liberton

Greenfield, W. S. , M.D., F.R.C. 1J. E. , LL.D., Emeritus Professor of General
Pathology in the University of Edinburgh, Kirkbrae, Elie, Fife
Greenlees, Thomas Duncan, M.D. Edin., Rostrevor, Kirtleton Avenue, Weymouth,
Dorset

* Gregory, John Walter, D.Sc., F. R. S.; Professor of Geology in the University of

Glasgow, 4 Park Quadrant, Glasgow

Greig, Edward David Wilson, M.D., B.Sc., Captain, H.M. Indian Medical
Service, BycullaClub, Bombay, India 240

Greig, Robert Blyth, LL.D., F.Z.S., Board of Agriculture for Scotland, 29 St
Andrew Square, Edinburgh

* Grimshaw, Percy Hall, Assistant Keeper, Natural History Department, The Royal

Scottish Museum, 49 Comiston Drive, Edinburgh

* Guest, Edward Graham, M.A., B.Sc., 5 Newbattle Terrace, Edinburgh

* Gulliver, Gilbert Henry, D.Sc., A.M.I.Mech.E., 99 Southwark Street, London,

S.E.

Service on
Council, etc.

1882-85,

1888-91,

1897-99.

V-P

1892-97.
1900-05.
P. 1913-

1905-08.

1912-13.

1903-06.

V-P

1906-09.

1913-

1908-11.

Date of

Election.

"l911

1883

1911

1910

1911

1905

1899

1876

1896

1914

1888

1869

1914

1881

1880

1892

1893

1890

1900

1908

1890

1881

1908

1894

1902

1904

1885

1911

1881

1896

1904

1897

1912

1893

Alphabetical List of the Ordinary Fellows of the Society.

* Gunn, James Andrew, M. A., M.D., D.Sc., Department of Pharmacology, University

Museum, Oxford 245

Guppy. Henry Brougham, M. B., Rosario, Salcombe, Devon

* Guy, William, F.R. C.S. , L.R.C.P. , L.D.S. Ed., Consulting Dental Surgeon, Edin-

burgh Royal Infirmary ; Dean, Edinburgh Dental Hospital and School ;
Lecturer on Human and Comparative Dental Anatomy and Physiology, 11
Wemyss Place, Edinburgh

Gwynne- Vaughan, D. T., F.L.S., Professor of Botany, 14 London Road,
Reading

Hall-Edwards, John Francis, L.R.C.P. (Edin.), Hon. F.R.P.S., Senior Medical
Officer in charge of X-ray Department, General Hospital, Birmingham,
141a and 141b Great Charles Street (Newliall Street), Birmingham

* Halm, Jacob E. , Ph.D. , Chief Assistant Astronomer, Royal Observatory, Cape]

Town, Cape of Good Hope 250

Hamilton, Allan M‘Lane, M.D., LL.D., 36 East 40th Street, New York, U.S.A.
Hannay, J. Ballantyne, Sorbie, 10 Balgillo Terrace, Broughty Ferry

* Harris, David Fraser, B.Sc. (Lond.), D.Sc. (Birm. ), M. D. , F. S.A. Scot., Professor

of Physiology in the Dalhousie University, Halifax, Nova Scotia
Harrison, Edward Philip, Ph.D., Professor of Physics, Presidency College, Uni-
versity of Calcutta, The Observatory, Alipore, Calcutta
Hart, D. Berry, M.D., F.R. C.P.E. , 5 Randolph Cliff, Edinburgh 255

Hartley, Sir Charles A., K.C.M.G., M.Inst.C.E., 26 Pall Mall, London
Harvey- Gibson, Robert John, M.A., F. L.S., D.L. for the County Palatine of
Lancaster, M. R.S.G.S. , Professor of Botany, University of Liverpool, 22
Falkner Square, Liverpool

Harvie-Brown, J. A., of Quarter, LL.D., F.Z.S., Dunipace House, Larbert,
Stirlingshire

Haycraft, J. Berry, M.D., D.Sc., Professor of Physiology in the University College
of South Wales and Monmouthshire, Cardiff

* Heath, Thomas, B.A., formerly Assistant Astronomer, Royal Observatory, Edin-

burgh, 11 Cluny Drive, Edinburgh 260

Hehir, Patrick, M. D. , F.R.C.S.E. , M.R.C.S., L.R.C. P.E., Surgeon -Captain,
Indian Medical Service, Principal Medical Officer, H.H. the Nizam’s Army,
Hyderabad, Deccan, India

Helme, T. Arthur, M.D., M.R.C.P., M.R.C.S., 3 St Peter’s Square, Manchester
Henderson, John, D.Sc., A. Inst.E.E., Kinnoul, Warwick’s Bench Road, Guild-
ford, Surrey

* Henderson, William Dawson, M.A. , B.Sc., Ph.D., Lecturer, Zoological Laboratories,

University, Bristol

Hepburn, David, M. D., Professor of Anatomy in the University College of South
Wales and Monmouthshire, Cardiff 265

Herdman, W. A., D.Sc., F.R.S., Past Pres. L.S., Professor of Natural History in
the University of Liverpool, Croxteth Lodge, Ullet Road, Liverpool

* Hewat, Archibald, F.F.A., F.I.A., 13 Eton Terrace, Edinburgh

Hill, Alfred, M.D. , M.R.C.S., F.I.C., Valentine Mount, Freshwater Bay, Isle of
Wight

* Hinxman, Lionel W., B.A., Geological Survey Office, 33 George Square,

Edinburgh

Hobday, Frederick T. G. , F. R.C.V. S., 6 Berkely Gardens, Kensington,

London, W. 270

Hodgkinson, W. R., Ph.D., F.I.C., F.C.S., Professor of Chemistry and Physics
at the Ordnance College, Woolwich, 89 Shooter’s Hill Road, Blackheath, Kent
Holland, William Jacob, LL.D. St Andrews, etc., Director Carnegie Institute,
Pittsburg, Pa., 5545 Forbes Street, Pittsburg, Pa., U.S.A.

Horne, John, LL.D., F.R.S., F.G.S., formerly Director of the Geological Survey _
of Scotland, 12 Keith Crescent, Blackhall, Midlothian

Horne, J. Fletcher, M.D., F.R.C.S.E., The Poplars, Barnsley

* Horsburgh, Ellice Martin, M.A. , B.Sc., Lecturer in Technical Mathematics,

University of Edinburgh, 11 Granville Terrace, Edinburgh 275

Houston, Alex. Cruikshanks, M.B., C. M., D.Sc., 19 Fairhazel Gardens, South
Hampstead, London, N.W.

* Houstoun, Robert Alexander, M.A. , Ph.D., D.Sc., Lecturer in Physical Optics,

University, Glasgow, 11 Cambridge Drive, Glasgow
Howden, Robert, M.A., M.B. , C.M., D.Sc., Professor of Anatomy in the University
of Durham, 14 Burdon Terrace, Newcastle-on-Tyne

327

Service on
Council, etc.

1902-05,

1906- 07.
1914-

V-P

1907- 1913.

328

Date of

Election.

1899

1883

1910

1886

1911

1887

1887

1908

1912

1904

1904

1914

1875

1894

1889

1901

1912

1906

1900

1895

1903

1874

1905

1888

1907

1912

1909

1908

1903

1891

1913

1908

1886

1907

1880

1883

1878

Proceedings of the Royal Society of Edinburgh.

Howie, W. Lamond, F.C.S., 26 Neville Court, Abbey Road, Regent’s Park,
London, N.W.

Hoyle, William Evans, M.A., D.Sc., M.R.C.S., Director of the Welsh National
Museum ; Crowland, Llandaff, Wales 280

Hume, William Fraser, D.Sc. (Lond.), Director, Geological Survey of Egypt,
Helwan, Egypt

Hunt, Rev. H. G. Bona via, Mus.D. Dub., Mus.B. Oxon., The Yicarage, Burgess
Hill, Sussex

Hunter, Gilbert Macintyre, M.Inst.C.E., M.Inst.E.S., M.Inst.M.E., Resident
Engineer Nitrate Railways, Iquique. Chile, and Maybole, Ayrshire
Hunter, James, F.R.C.S.E., F.R.A.S., Rosetta, Liberton, Midlothian
Hunter, William, M.D., M.R.C.P.L. and E. , M.R.C.S., 54 Harley Street,
London 285

Hyslop, Theophilus Bulkeley, M.D., M.R.C.P.E., 5 Portland Place, London, W.

* Inglis, Robert John Mathieson, A.M.Inst. C.E., Engineer, Northern Division,

North British Railway, Tantah, Peebles
Innes, R. T. A., Director, Government Observatory, Johannesburg, Transvaal

* Ireland, Alexander Scott, S.S.C., 2 Buckingham Terrace, Edinburgh

Jack, John Noble, Professor of Agriculture to the County Council of Sussex,
Kingscote, The Avenue, Lewes, Sussex 290

Jack, William, M.A., LL.D. , Emeritus Professor of Mathematics in the University
of Glasgow

Jackson, Sir John, C.Y.O., LL.D., 48 Belgrave Square, London
James, Alexander, M.D., F.R.C. P.E., 14 Randolph Crescent, Edinburgh
*Jardine, Robert, M.D., M.R.C.S. F.R.F.P.S. Glas., 20 Royal Crescent,
Glasgow

* Jeffrey, George Rutherford, M.D. (Glasg.), F.R.C.P. (Edin.), etc., Bootham Park

Private Mental Hospital, York 295

* Jehu, Thomas James, M.A., M.D., F.G.S., Professor of Geology in the University

of Edinburgh

*Jerdan, David Smiles, M. A., D.Sc., Ph.D., Temora, Colinton, Midlothian
Johnston, Col. Hemy Halcro, C.B., Late A.M.S., D.Sc., M.D., F.L.S., Orphir
House, Kirkwall, Orkney

* Johnston, Thomas Nicol, M.B., C.M., Pogbie, Humbie, East Lothian

Jones, Francis, M.Sc. , Lecturer on Chemistry, 17 Whalley Road, Whalley Range,
Manchester 300

Jones, George William, M.A. , B.Sc. , LL. B., Scottish Tutorial Institute,
Edinburgh and Glasgow, 25 North Bridge : Coraldene, Kirk Brae, Liberton,
Edinburgh

Jones, John Alfred, M.Inst.C.E., Fellow of the University of Madras, Sanitary
Engineer to the Government of Madras, c/o Messrs Parry & Co., 70 Grace-
church Street, London

* Kemp, John, M.A. , Sea Bank School, North Berwick

Kennedy, Robert Foster, M.D. (Queen’s Univ., Belfast), M.B., B.Ch. (R.U.I.),
Assistant Professor of Neurology, Cornell University, New York, 20 West
50th Street, New York, U.S.A.

Kenwood, Henry Richard, M.B., Chadwick Professor of Hygiene in the University
of London, 126 Queen’s Road, Finsbury Park, London, N. 305

* Kerr, Andrew William, F.S.A. Scot., Royal Bank House, St Andrew Square,

Edinburgh

*Kerr, John Graham, M.A., F.R.S., Professor of Zoology in the University/
of Glasgow \

Kerr, Joshua Law, M.D., The Chequers, Mittagong, Sydney, Australia

* Kerr, Walter Hume, M.A., B.Sc., Lecturer on Engineering Drawing and Structural

Design in the University of Edinburgh

Kidd, Walter Aubrey, M.D., 12 Montpelier Row, Blackheath, London 310

Kidston, Robert, LL.D., F.R.S., F.G.S. (Secretary), 12 Clarendon Place, J
Stirling

* King, Archibald, M.A., B.Sc., formerly Rector of the Academy, Castle Douglas ;

Junior Inspector of Schools, La Maisonnette, Clarkston, Glasgow
King, W. F., Lonend, Russell Place, Trinity, Leith

Kinnear, the Right Hon. Lord, P.C., one of the Senators of the College of Justice, 2
Moray Place, Edinburgh

Kintore, the Right Hon. the Earl of, P.C., G.C. M.G., M.A. Cantab., LL.D.
Cambridge, Aberdeen and Adelaide, Keith Hall, Inverurie, Aberdeenshire 315

Service on
Council, etc.

1888-91.

1904-07,

1913-

1891-94,

1903-06.

Sec.

1909-

Alphabetical List of the Ordinary Fellows of the Society.

329

Date of
Election.

1901

1907

1880

1886

1878

1910

1885

1894

1910

1905

1910

1903

1874

1910

1914

1905

1889

1912

1912

1903

1903

1898

1884

1888

1900

1894

1887

1907

1883

1903
1905
1397

1904

1886

* Knight, Rev. G. A. Frank, M.A., 52 Sardinia Terrace, Hillhead, Glasgow

* Knight, James, M.A., D.Sc., F.C.S., F.G.S., Head Master, St James’ School,

Glasgow, The Shieling, Uddingston, by Glasgow

!. K.

Knott, C. G., D.Sc., Lecturer on Applied Mathematics in the University of
Edinburgh (formerly Professor of Physics, Imperial University, Japan)-;
(Gen. Secretary), 42 Upper Gray Street, Edinburgh

C.

C.

c.

c.

c.

!. K.

c.

Laing, Rev. George P. , 1 7 Buckingham Terrace, Edinburgh

Lang, P.R. Scott, M.A., B.Sc., Professor of Mathematics, University of St Andrews 320

* Lauder, Alexander, D.Sc., F. I.C., Lecturer in Agricultural Chemistry, Edinburgh

and East of Scotland College of Agriculture, 13 George Square, Edinburgh

Laurie, A. P., M.A., D.Sc., Principal of the Heriot-Watt College, Edinburgh |

* Laurie, Malcolm, B.A., D.Sc., F.L.S., 19 Merchiston Park, Edinburgh

* Lawson, A. Anstruther, B.Sc., Ph.D., D.Sc., F.L.S., Professor of Botany, Univer-

sity of Sydney, New South Wales, Australia

* Lawson, David, M.A. , M.D., L.R.C.P. and S.E., Druimdarroch, Banchory,

Kincardineshire 325

*Lee, Gabriel W., D.Sc., Palaeontologist, Geological Survey of Scotland, 33 George
Square, Edinburgh

* Leighton, Gerald Rowley, M.D., Local Government Board, 125 George Street,

Edinburgh

Letts, E. A., Ph.D., F.I.C., F.C.S., Professor of Chemistry, Queen’s College, Belfast
Levie, Alexander, F.R.C.V.S., D.Y.S.M., Veterinary Surgeon, Lecturer on
Veterinary Science, Veterinary Infirmary, 12 Derwent Street, Derby
Lewis, Francis John, D.Sc., F. L.S., Professor of Biology, University of Alberta,
Edmonton South, Alberta, Canada 330

* Lightbody, Forrest Hay, 56 Queen Street, Edinburgh

Lindsay, 'Rev. James, M.A., D.D., B.Sc., F.R.S.L., F.G.S., M.R.A.S., Corre-
sponding Member of the Royal Academy of Sciences, Letters and Arts, of
Padua, Associate of the Philosophical Society of Louvain, Annick Lodge,
Irvine

* Lindsay, John George, M.A., B.Sc. (Edin.), Science Master, Royal High School,

33 Lauriston Gardens, Edinburgh

* Linlithgow, The Most Honourable the Marquis of, Hopetoun House, South

Queensferry

Liston, William Glen, M.D., Captain, Indian Medical Service, c/o Grindlay. Groom
& Co.. Bombay, India 335

* Littlejohn, Henry Harvey, M.A., M.B., B.Sc., F.R.C.S.E., Professor of Forensic

Medicine, Dean of the Faculty of Medicine in the University of Edinburgh,
11 Rutland Street, Edinburgh

* Lothian, Alexander Veitch, M.A. , B.Sc., Training College, Cowcaddens, Glasgow
Low, George M., Actuary, 11 Moray Place, Edinburgh

Lowe, D. F., M.A., LL.D. , formerly Head Master of Heriot’s Hospital School,
Lauriston, 19 George Square, Edinburgh
Lusk, Graham, Ph.D., M.A. , Professor of Physiology, Cornell University Medical
College, New York, N.Y., U.S.A. 340

* Mabbott, Walter John, M.A., Rector of County High School, Duns, Berwickshire
M'Aldowie, Alexander M., M.D., Glengarriff, Leckhampton, Cheltenham
MacAlister, Donald Alexander, A.R.S.M., F.G. S., 26 Thurloe Square, South

Kensington, London, S.W.

M‘Bride, P., M.D., F.R.C.P.E., 10 Park Avenue, Harrogate, and Hill House,
Withy pool, Dunster, Somerset

*M‘Cormick, Sir W. S., M.A., LL.D., Secretary to the Carnegie Trust for the
Universities of Scotland, 13 Douglas Crescent, Edinburgh 345

* Macdonald, Hector Munro, M. A., F.R.S., Professor of Mathematics, University of

Aberdeen, 52 College Bounds, Aberdeen

* Macdonald, James A., M.A., B.Sc., H.M. Inspector of Schools, Stewarton,

Kilmacolm

* Macdonald, John A., M.A., B.Sc., King Edward VII. School, Johannesburg,

Macdonald, the Right Hon. Sir J. H. A. (Lord Kingsburgh) P.C., K.C., K.C.B.,
LL.D., F.R.S., M.Inst.E.E., Lord Justice- Clerk, and Lord President of the |
Second Division of the Court of Session, 15 Abercromby Place, Edinburgh

Service on
Council, etc.

1894-97,

1898-01,

1902-05.

Sec.

1905-1912.
Gen. Sec.
1912-

1908-11,

1913-

1910-13.

1908-11.

1889-92.

330

Date of
Election.

1904

1886

1901

1910
1888
1885

1897
1878

1903

1911

1869

1895

1914

1873

1912

1900

1910

1911

1894

1904

1910

1904

1869

1899

1888

1913

1907

1898
1913

1908

1912

1913

1880

1909

Proceedings of the Poyal Society of Edinburgh.

c.

o.

o.

!. N.
C.

). B.
0.

0.

c.

0.

a

c.

c.

c.

Macdonald, William, B.Sc. , M. Sc. , Agriculturist, Editor Transvaal Agricultural
Journal , Department of Agriculture, Pretoria Club, Pretoria, Transvaal 350
Macdonald, William J., M.A., LL.D., 15 Comiston Drive, Edinburgh

* MacDougall, R. Stewart, M.A., D.Sc., Professor of Biology, Royal Veterinary

College, Edinburgh, 9 Dryden Place, Edinburgh
Macewen, Hugh Allan, M. B., Ch.B., D.P. H. (Lond. and Camb.), Local
Government Board, Whitehall, London, S.W.

M'Fadyean, Sir John, M.B., B.Sc., LL.D., Principal, and Professor of Comparative
Pathology in the Royal Veterinary College, Camden Town, London
Macfarlane, J. M., D.Sc., Professor of Botany and Director of the Botanic Garden,
University of Pennsylvania, Philadelphia, Pennsylvania, U.S.A. 355

* MacGillivray, Angus, C.M., M.D., D.Sc., 23 South Tay Street, Dundee
M'Gowan, George, F. I.C., Ph. D., 21 Montpelier Road, Ealing, Middlesex

* MTntosh, Donald C. , M.A., D.Sc., 3 Glenisla Gardens, Edinburgh

MTntosh, John William, A.R.C.V.S., 14 Templar Street, Myatts Park,
London, S.E.

MTntosh, William Carmichael, M.D., LL.D., F.R.S., F.L.S., Professor of Natural
History in the University of St Andrews, Pres. Ray. Society, 2 Abbotsford
Crescent, St Andrews 360

* Macintyre, John, M.D., 179 Bath Street, Glasgow

* M ‘Kendrick, Archibald, F.R.C.S.E., D.P.H., L.D.S., 2 Coates Place, Edinburgh

M'Kendrick, John G. , M.D., F.R.C.P.E., LL.D., F.R.S., Emeritus Professor of^
Physiology in the University of Glasgow, Maxieburn, Stonehaven

V

M ‘Kendrick, Anderson Gray, M.B. , Major, Indian Medical Service, Officiating
Statistical Officer to the Government of India, The Pasteur Institute, Kasauli,
India

*M‘Kendrick, John Souttar, M.D., F.R.F.P.S.G., 2 Buckingham Terrace,
Glasgow 365

* Mackenzie, Alister, M.A., M.D., D.P.H., Principal, College of Hygiene and

Physical Training, Dunfermline

* M‘Kenzie, Kenneth John, M. A., Master of Method to Leith School Board,

24 Dudley Gardens, Leith

* Mackenzie, Robert, M.D., Napier, Nairn

* Mackenzie, W. Leslie, M.A., M.D., D.P.H., LL.D., Medical Member of the Local

Government Board for Scotland, 4 Clarendon Crescent, Edinburgh

* MacKinnon, James, M. A., Ph.D., Professor of Ecclesiastical History, Edinburgh

University, 12 Lygon Road, Edinburgh 370

* Mackintosh, Donald James, M.V.O., M.B., C.M., LL.D., Supt. Western Infirmary,

Glasgow

Maclagan, R. C., M.D., F.R.C.P.E., 5 Coates Crescent, Edinburgh
Maclean, Ewan John, M. D., M.R.C.P. Lond., 12 Park Place, Cardiff
Maclean, Magnus, M.A., D.Sc., M.Inst.E.E., Professor of Electrical Engineering
in the Royal Technical College, 51 Kerrsiand Terrace, Hillhead, Glasgow
*M‘Lellan, Dugald, M. Inst.C.E., District Engineer, Caledonian Railway, 42
Ormidale Terrace, Murrayfield, Edinburgh 375

* Macnair, Peter, Curator of the Natural History Collections in the Glasgow

Museums, Kelvingrove Museum, Glasgow
Mahalanobis, S. C., B.Sc., Professor of Physiology, Presidency College, Calcutta,
India

Majumdar, Tar ak Nath, D.P.H. (Cal.), L.M.S., F.C.S., Health Officer, Calcutta,
IV., 37 Lower Chitpore Road, Calcutta, India
Mallik, Devendranath, B.A., B.Sc., Professor of Physics and Mathematics,
Patna College, Bankipur, Bengal, India

Maloney, William Joseph, M.D.(Edin.), Professor of Neurology at Fordham
University, New York City, N.Y., U.S.A. 380

Marchant, Rev. James, F.R.A.S., Director, National Council for Promotion of
Race- Regeneration ; Literary Adviser to House of Cassell ; 42 Great Russell
Street, London, W.C.

Marsden, R. Sydney, M.D., C.M., D.Sc., D.P.H., Hon. L.A.H. Dub., M.R.I.A.,
F.I.C. , M.O.H., Rowallan House, Cearns Road, and Town Hall, Birkenhead

* Marshall, C. R. , M.D., M.A., Professor of Materia Medica and Therapeutics,

Medical School, Dundee, Arnsheen, Westfield Terrace, West Newport,
Fife

Service on
Council, etc.

1914-

1885-88.

1875-78,

1885-88,

1893- 94,
1900-02.

V-P

1894- 1900.

Alphabetical List of the Ordinary Fellows of the Society.

331

Date of
Election.

1882

1901

1903

1912

1913

1885

1898

1911

1906

1902

1901

1888

1902

1885

1908

1910

1909

1905

1905

1904

1886

1899

1889

1897

1900
1899

1911

1906

1890

1887

1896

1892

1914

1901
1892
1874

1888

C.

c.

0.

J. B.

C.

C.

1 B.

0.

0.

c.

c.

c.

0.

c.

!. K.

C.

Marshall, D. H., M.A., Professor, Union and Alwington Avenue, Kingston,
Ontario, Canada

* Marshall, F. H. A., Sc. D., Lecturer on Agricultural Physiology in the Uni-

versity of Cambridge, Christ’s College, Cambridge 385

^ Martin, Nicholas Henry, F.L.S., F.C.S., Ravenswood, Low Fell, Gateshead

* Martin, Sir Thomas Carlaw, LL.D., J.P. , Director, Royal Scottish Museum,

4 Gordon Terrace, Edinburgh

Masson, George Henry, M.D., D.Sc., M.R.C.P.E., Port of Spain, Trinidad,
British West Indies

Masson, Orme, D. Sc. , F. R. S. , Professor of Chemistry in the University of Melbourne

* Masterman, Arthur Thomas, M.A., D.Sc., Inspector of Fisheries, Board of

Agriculture, Whitehall, London 390

Mathews, Gregory Macalister, F.L.S., F.Z.S., Langley Mount, Watford, Herts
*Mathieson, Robert, F. C.S. , Rillbank, Innerleithen
Matthews, Ernest Romney, A. M.Inst. C.E., F.G.S., Chadwick Professor of
Municipal Engineering in the University of London, University College,
Gower Street, London, W.C.

* Menzies, Alan W. C. , M.A. , B.Sc., Ph. D. , F.C.S., Professor of Chemistry,

Princeton University, Princeton, New Jersey, U.S.A.

Methven, Cathcart W., M.Inst.C.E., F.R.I.B.A., Durban, Natal, S. Africa 395
Metzler, William H., A. B. , Ph.D. , Corresponding Fellow of the Royal Society
of Canada, Professor of Mathematics, Svracuse University, Svracuse, N.Y.,
U.S.A.

Mill, Hugh Robert, D.Sc., LL.D., 62 Camden Square, London

* Miller, Alexander Cameron, M.D., F.S.A. Scot., Craig Linnlie, Fort-William,

Inverness-shire

* Miller, John, M.A., D.Sc., Professor of Mathematics, Royal Technical College,

2 Northbank Terrace, North Kelvinside, Glasgow
Mills, Bernard Langley, M.D., F.R.C.S.E., M.R.C.S., D.P.H., Lt.-Col.

R. A. M.C., formerly Army Specialist in Hygiene, 84 Grange Crescent, Sharrow,
Sheffield 400

* Milne, Archibald, M.A., B.Sc., Lecturer on Mathematics and Science, Edinburgh

Provincial Training College, 108 Comiston Drive, Edinburgh

* Milne, C. H., M.A., Head Master, Daniel Stewart’s College, 4 Campbell Road,

Mur ray field, Edinburgh

* Milne, James Robert, D.Sc., Lecturer on Natural Philosophy, 11 Melville Crescent,

Edinburgh

Milne, William, M.A., B.Sc., 70 Beechgrove Terrace, Aberdeen

* Milroy, T. H., M. I)., B.Sc., Professor of Physiology in Queen’s College, Belfast,

Meloyne, Malone Park, Belfast 405

Mitchell, A. Crichton, D.Sc., Hon. Doc. Sc. (Geneve), formerly Director of Public
Instruction in Travancore, India, 103 Trinity Road, Edinburgh
Mitchell, George Arthur, M.A., 9 Lowther Terrace, Kelvinside, Glasgow

* Mitchell, James, M.A., B.Sc., Cruach, Lochgilphead

* Mitchell-Thomson, Sir Mitchell, Bart., 6 Charlotte Square, Edinburgh

Modi, Edalji Manekji, D.Sc., LL.D., Litt.D., F.C.S., etc., Proprietor and Director of
Arthur Road Chemical Works, Meher Buildings, Tardeo, Bombay, India 410
Moffat, Rev. Alexander, M.A., B.Sc., Professor of Physical Science, Christian
College, Madras, India

Mond, R. L., M.A. Cantab., F.C.S., Combe Bank, near Sevenoaks, Kent
Moos, N. A. F. , L.C.E., B.Sc., Professor of Physics, Elphinstone College, and
Director of the Government Observatory, Colaba, Bombay, India

* Morgan, Alexander, M.A., D.Sc., Principal, Edinburgh Provincial Training

College, 1 Midmar Gardens, Edinburgh

Morrison, J. T., M.A., B.Sc., Professor of Physics and Chemistry, Victoria
College, Stellenbosch, Cape Colony 415

Mort, Spencer, M. D., Ch.B., F.R.C.S.E., Medical Superintendent, Edmonton
Infirmary, London, N.

Moses, O. St John, I.M.S., M.D., D.Sc., F.R.C.S., Captain, Professor of Medical
Jurisprudence, 26 Park Street, Wellesley, Calcutta, India
Mossman, Robert C. , Acting Editor, British Rainfall Organization’s Publications,
63a Burntwood Lane, Wandsworth Common, London, S.W.

Muir, Thomas, C.M.G., M.A. , LL.D., F.R.S., Superintendent-General of Educa-
tion for Cape Colony, Education Office, Cape Town, and Mowbray Hall,
Rosebank, Cape Colony

Muirhead, George, Commissioner to His Grace the Duke of Richmond and Gordon,
K.G., Spey bank, Fochabers , 420 I

Service on
Council, etc.

1902-04.

1885-88.

V-P

1888-91.

332

Date of

Election.

1907

1887

1891

1896

1907

1907

1902

1888

1897

1906

1898

1884

1880

1878

1906

1888

1888

1886

1895

1914

1908

1905

1914

1892

1901

1886

1892

1881

1907

1914

1904

1889

1887

1893

1913

1889

1907

1914

Proceedings of the Royal Society of Edinburgh.

Muirhead, James M. P. , J.P., F. R.S.L. , F.S.S., c/o Dunlop Rubber Co., Ltd.,
3 Wallace Street, Fort, Bombay

Mukhopadhyay, Asutosh, M.A., LL.D., F.R.A.S. , M.R.I.A., Professor of Mathe-
matics at the Indian Association for the Cultivation of Science, 77 Russa
Road North, Bhowanipore, Calcutta, India

Munro, Robert, M.A., M.D., LL.D., Hon. Memb. R.I.A., Hon. Memb.J
Royal Society of Antiquaries of Ireland, Elmbank, Largs, Ayrshire j

Murray, Alfred A., M.A. , LL.B., 20 Warriston Crescent, Edinburgh
' Murray, James, Hill Farm Bungalow, Froxfield, Hants 425

Musgro.ve, James, M.D., F.R.C.S. Edin. and Eng., Bute Professor of Anatomy,
University of St Andrews, The Swallowgate, St Andrews
Mylne, Rev. R. S. , M.A., B.C. L. Oxford, F.S.A. Lond. , Great Amwell, Herts
Napier, A. D. Leith, M.D., C.M., M.R.C.P., 28 Angas Street, Adelaide,
S .A.fisti'ciliR

Nash, Alfred George, B.Sc., F.R.G.S., C.E., Belretiro, Mandeville, Jamaica, W.I.

* Newington, Frank A., M.Inst.C.E., M.Inst.E.E., 7 Wester Coates Road, Edin-

burgh 430

Newman, Sir George, M.D., D.P.H. Cambridge, Lecturer on Preventive Medicine,
St Bartholomew’s Hospital, University of London : Grim’s Wood, Harrow
Weald, Middlesex

Nicholson, J. Shield, M.A., D.Sc., Professor of Political Economy in the)
University of Edinburgh, 3 Belford Park, Edinburgh 1

Nicol, W. W. J., M.A. , D.Sc., 15 Blacket Place, Edinburgh

Norris, Richard, M.D., M.R.C.S. Eng., 3 Walsall Road, Birchfield, Birmingham

* O’Connor, Henry, A. M.Inst.C.E., 1 Drummond Place, Edinburgh 435

Ogilvie, F. Grant, C.B., M.A., B.Sc., LL.D., Secretary of the Board of Education

for the Science Museum and the Geological Survey, and Director of the
Science Museum, 15 Evelyn Gardens, London, S.W.

Oliphant, James, M.A. , 11 Heathfield Park, Willesden Green, London
Oliver, James, M.D., F.L.S., Physician to the London Hospital for Women,
123 Harley Street, London, W.

Oliver, Sir Thomas, M.D. , LL.D.. F. R.C.P., Professor of Physiology in the
University of Durham, 7 Ellison Place, Newcastle-upon-Tyne

* Oswald, Alfred, Lecturer in German, Glasgow Provincial Training College,

Nordheim, Bearsden, Glasgow 440

Page, William Davidge, F.C.S., F.G.S., M.Inst.M.E., 10 Clifton Dale, York
Pallin, William Alfred, F.R. C.Y.S. , Major in the Army Veterinary Corps,
c/o Messrs Holt & Co., 3 Whitehall Place, London
Pare, John William, M.B., C.M., M.D., L.D.S., Lecturer in Dental Anatomy,
National Dental Hospital, 64 Brook Street, Grosvenor Square, London, W.
Parker, Thomas, M.Inst.C.E., Severn House, Iron Bridge, Salop

* Paterson, David, F.C. S., Lea Bank, Rosslyn, Midlothian 445

Paton, D. Noel, M.D., B.Sc., F.R.C.P.E., F.R.S.;
the University of Glasgow, University, Glasgow

Professor of Physiology in

Paulin, Sir David, Actuary, 6 Forres Street, Edinburgh

Peach, Benjamin N., LL.D., F.R.S., F.G.S. (Vice-President), formerly District |
Superintendent and Acting Palaeontologist of the Geological Survey of 4
Scotland, 72 Grange Loan, Edinburgh

* Pearce, John Thomson, B.A., B.Sc., School House, Tranent

Pearson, Joseph, D.Sc., F.L.S., Director of the Colombo Museum, and Marine
Biologist to the Ceylon Government, Colombo Museum, Ceylon 450

* Peck, James Wallace, M.A., Chief Inspector, National Health Insurance, Scotland,

83 Princes Street, Edinburgh

Peck, William, F.R.A.S. , Town’s Astronomer, City Observatory, Calton Hill,
Edinburgh

Peddie, Wm. , D.Sc., Professor of Natural Philosophy in University College,
Dundee, Rosemount, Forthill Road, Broughty Ferry
Perkin, Arthur George, F.R.S., 8 Montpellier Terrace, Hyde Park, Leeds

* Philip, Alexander, M.A. , LL.B., Writer, The Mary Acre, Brechin 455

Philip, Sir R. W., M.A. , M. D., F.R.C.P.E., 45 Charlotte Square, Edinburgh
Phillips, Charles E. S., Castle House, Shooter’s Hill, Kent

* Pilkington, Basil Alexander, 20 Queen’s Avenue, Blackhall, Midlothian

Service on
Council, etc.

1894-97,

1900-03.

V-P

1903-08.

1885-87,

1892-95.

1897-1900.

1901-03.

1894-97

1904- 06,
1909-12.

1905- 08,

1911- 1912.
V-P

1912-

1904-07

1908-11.

Date of

Election.

1905

1908

1911

1906

1886

1888

1902

1892

1875

1908

1903

1911

1898

1897

1899

1884

1914

1911

1891

1904

1900

1883

1889

1902

1902

1913

1908

1914

1913

1908

1875

1914

1906

1898

1880

1900

1896

1902

Alphabetical List of the Ordinary Fellows of the Society.

* Pinkerton, Peter, M.A., D.Sc., Rector, High School, Glasgow, 44 St James’s

Street, Hillhead, Glasgow

* Pirie, James Hunter Harvey, B. Sc. , M.D., F. R. C.P. E., Bacteriological Laboratory,

Nairobi, British East Africa 460

* Pirie, James Simpson, Civil Engineer, 28 Scotland Street, Edinburgh
Pitchford, Herbert Watkins, F.R.C.V.S., Bacteriologist and Analyst, Natal

Government, The Laboratory, Pietermaritzburg, Natal
Pollock, Charles Frederick, M.D., F.R.C.S.E., 1 Buckingham Terrace, Hillhead,
Glasgow

Prain, Sir David, Lt.-Col., Indian Medical Service (Retired), C.M.G., C.I.E., M.A.,
M.B., LL.D., F. L.S., F.R.S., For. Memb. K. Svensk. Vetensk. Akad. ; Hon.
Memb. Soc. Lett, ed Arti d. Zelanti, Acireale ; Pharm. Soc. Gt. Britain ; Corr.
Memb. K. Bayer Akad. Wiss. , etc. ; Director, Royal Botanic Gardens, Kew,
Surrey

* Preller, Charles Du Riche, M.A., Ph.D., A.M.Inst.C.E., 61 Melville Street,

Edinburgh 465

* Pressland, Arthur J. , M. A. Camb. , Edinburgh Academy
Prevost, E. W. , Ph.D., Weston, Ross, Herefordshire

* Pringle, George Cossar, M.A. , Rector of Peebles Burgh and County High School,

Bloomfield, Peebles

* Pullar, Laurence, Dunbarney, Bridge of Earn, Perthshire

Purdy, John Smith, M.D.,_ C.M. (Aberd.), D.P. H. (Camb.), F.R.G.S., Chief
Health Officer for Tasmania, Islington, Hobart, Tasmania 470

* Purves, John Archibald, D.Sc., 13 Albany Street, Edinburgh

* Rainy, Harry, M.A., M.B., C.M., F.R.C.P. Ed., 16 Great Stuart Street, Edinburgh

* Ramage, Alexander G., 8 Western Terrace, Murrayfield, Edinburgh

Ramsay, E. Peirson, M.R. I.A. , F.L.S., C.M.Z.S. , F.R.G.S., F.G.S., Fellow of
the Imperial and Royal Zoological and Botanical Society of Vienna, Curator
of Australian Museum, Sydney, N. S. W.

* Ramsay, Peter, M.A., B.Sc. , Head Mathematical Master, George Watson’s

College, 63 Comiston Drive, Edinburgh 475

* Rankin, Adam A., Vice-President, British Astronomical Association, West of

Scotland Branch, 324 Crow Road, Broomhill, Glasgow, W.

* Rankin e, John, K.C., M.A., LL.D., Professor of the Law of Scotland in the

University of Edinburgh, 23 Ainslie Place, Edinburgh
Ratcliffe, Joseph Riley, M.B., C.M., c/o The Librarian, The University,
Birmingham

Raw, Nathan, M.D. , M.R. C.P. (London), B.S., F. R.C.S., D.P.H., 66 Rodney
Street, Liverpool

Readman, J. B., D.Sc., F.C.S., Belmont, Hereford 480

Redwood, Sir Boverton, Bt., D.Sc. (Hon.), F. I.C., F.C.S., A.Inst.C.E., The
Cloisters, 18 Avenue Road, Regent’s Park, London, N.W.

Rees-Roberts, John Vernon, M.D., D.Sc., D.P.H., Barrister-at-Law, National
Liberal Club, Whitehall Place, London

Reid, George Archdall O’Brien, M.B., C.M., 9 Victoria Road South, Southsea,
Hants

Reid, Harry Avery, F.R.C.V.S., D.V.H., Bacteriologist and Pathologist, .Depart-
ment of Agriculture, Wellington, New Zealand

* Rennie, John, D.Sc., Lecturer on Parasitology, and Assistant to the Professor of

Natural History, University of Aberdeen, 60 Desswood Place, Aberdeen 485
Renshaw, Graham, M.B., M.R.C.S., L.R.C.P., L.S.A., Surgeon, Bridge House,
Sale, Manchester

* Richardson, Harry, M.Inst.E.E., M.Inst.M.E., General Manager and Chief

Engineer, Electricity Supply, Dundee and District, The Cottage, Craigie,
Broughty Ferry

Richardson, Linsdall, F.L.S., F.G.S., Organising Inspector of Technical Educa-
tion for the Gloucestershire Education Committee, 10 Oxford Parade,
Cheltenham

Richardson, Ralph, W.S., 10 Magdala Place, Edinburgh

* Ritchie, James Bonnyman, B.Sc., Science Master, Kelvinside Academy, Glasgow 490

* Ritchie, William Thomas, M.D., F.R.C.P.E., 9 Atholl Place, Edinburgh
Roberts, Alexander William, D.Sc., F.R.A.S., Lovedale, South Africa
Roberts, D. Lloyd, M.D., F.R.C.P.L., 23 St John Street, Manchester

* Robertson, Joseph M ‘Gregor, M.B., C.M., 26 Buckingham Terrace, Glasgow

* Robertson, Robert, M.A., 25 Mansionhouse Road, Edinburgh 495

* Robertson, Robert A., M.A. B.Sc., Lecturer on Botany in the University of St

Andrews

333

Service on
Council, etc.

334

Date of
Election.

1896

1910

1881

1909
1906

1902
1880

1904

1906
1914
1912

1903
1903

1891

1900

1885

1880

1889

1902
1871
1908
1900

1911

1900

1903

1901
1891

1882

1885

1911

1907

1880

1899

1880

1910

Proceedings of the Eoyal Society of Edinburgh.

c.

0.

!. K.

C.

C.

0.

C.

C.

!. K.
C.

C.

* Robertson, W. G. Aitchison, D.Sc., M.D., F.R. C.P.E., 2 Mayfield Gardens, Edin-

burgh

* Robinson, Arthur, M.D., M.R.C.S., Professor of Anatomy, University of Edin-J

burgh, 35 Coates Gardens, Edinburgh (Secretary) 1

Rosebery, the Right Hon. the Earl of, K.G., K.T., LL.D., D.C.L. , F.R.S.,
Dalmeny Park, Edinburgh

* Ross, Alex. David, M.A. , D.Sc., F. R.A. S., Professor of Mathematics and Physics,

University of Western Australia, Perth, Western Australia 500

* Russell, Alexander Durie, B.Sc., Mathematical Master, Falkirk High School,

Dunaura, Heugh Street, Falkirk

* Russell, James, 22 Glenorchy Terrace, Edinburgh

Russell, Sir James A., M.A., B.Sc.,M.B., F.R.C.P.E., LL.D., Woodville, Canaan
Lane, Edinburgh

Sachs, Edwin O. , Architect, Chairman of the British Fire Prevention Committee,
Vice-President of the International Fire Service Council, 8 Waterloo Place,
Pall Mall, London, S.W.

Saleeby, Caleb William, M.D., 13 Greville Place, London 505

* Salvesen, Theodore Emile, 37 Inverleith Place, Edinburgh

* Sampson, Ralph Allen, M.A., D.Sc., F.R.S., Astronomer Royal for Scotland,

Professor of Astronomy, University, Edinburgh, Royal Observatory, Edinburgh

* Samuel, John S. , 8 Park Avenue, Glasgow

* Sarolea, Charles, Ph.D., D.Litt., Lecturer on French Language, Literature, and

Romance Philology, University of Edinburgh, 21 Royal Terrace, Edinburgh
Sawyer, Sir James, Kt., M.D., F.R.C.P., F.S.A., J.P., Consulting Physician to
the Queen’s Hospital, 31 Temple Row, Birmingham 510

* Schafer, Sir Edward Albert, M.R.C.S., LL.D., F.R.S. (Vice-President), I

Professor of Physiology in the University of Edinburgh |

Scott, Alexander, M.A., D.Sc., F.R.S., 34 Upper Hamilton Terrace, London, N.W.
Scott, J. H., M.B., C.M., M.R.C.S., Professor of Anatomy in the University of
Otago, New Zealand

Scougal, A. E., M.A., LL.D., formerly H.M. Senior Chief Inspector of Schools
and Inspector of Training Colleges, 1 Wester Coates Avenue, Edinburgh
Senn, Nicholas, M.D., LL.D., Professor of Surgery, Rush Medical College,
Chicago , U. S. A . 515

Simpson, Sir A. R., M.D., Emeritus Professor of Midwifery in the University of
Edinburgh. 52 Queen Street, Edinburgh

* Simpson, George Freeland Barbour, M.D., F.R.C.P.E., F.R.C.S.E., 43 Manor

Place, Edinburgh

* Simpson, James Young, M.A. , D.Sc., Professor of Natural Science in the New

College, Edinburgh, 25 Chester Street, Edinburgh
Simpson, Sutherland, M.D., D.Sc. (Edin.), Professor of Physiology, Medical
College, Cornell University, Ithaca, N.Y., U.S.A., 118 Eddy Street, Ithaca,
N.Y., U.S.A.

Sinhjee, Sir Bhagvat, G.C.I.E., M.D., LL.D. Edin., H. H. the Thakur Sahib
of Gondal, Gondal, Kathiawar, Bombay, India 520

* Skinner, Robert Taylor, M.A., Governor and Head Master, Donaldson’s Hospital,

Edinburgh

* Smart, Edward, B.A., B.Sc., Tillyloss, Tullylumb Terrace, Perth

* Smith, Alexander, B.Sc., Ph.D., Department of Chemistry, Columbia University,

New York, N.Y., U.S.A.

Smith, C. Michie, C. I.E., B.Sc., F.R.A.S. , formerly Director of the Kodaikanal and
Madras Observatories, Winsford, Kodaikanal, South India
Smith, George, F.C.S., 5 Rosehall Terrace, Falkirk 525

* Smith, Stephen, B.Sc., Goldsmith, 31 Grange Loan, Edinburgh

Smith, William Ramsay, D.Sc., M.D., C.M., Permanent Head of the Health
Department, South Australia, Belair, South Australia
Smith, William Robert, M.D., D.Sc., LL.D., Professor of Forensic Medicine and
Toxicology in King’s College, University of London, and Principal of the
Royal Institute of Public Health, 36 Russell Square, London, W.C.

Snell, ErnestHugh, M.D., B.Sc., D.P.H. Camb., Medical Officer of Health, Coventry
Sollas, W. J., M. A., D.Sc., LL.D., F.R.S., Fellow of University College, Oxford,
and Professor of Geology and Palaeontology in the University of Oxford 530

* Somerville, Robert, B.Sc., Science Master, High School, Dunfermline, 31 Cameron

Street, Dunfermline

Service on
Council, etc.

1910-1912.

Sec.

1912-

1912-

1900-03,

1906-09.

V.P.

1913-

Date of

Election.

1889

1911

1882

1896

1874

1906

1891

1914

1912

1910

1886

1884

1888

1902

1889

1906

1907

1903

1905

1912

1885

1904

1898

1895

1890

1870

1899

1892

1885

1907

1905

1887

1911

1896

1903

1906

1887

1906

1880

1899

1912

Alphabetical List of the Ordinary Fellows of the Society.

Somerville, AVm. , M.A. , D.Sc., D. Oec., Sibthorpian Professor of Rural Economy
and Fellow of St John’s College in the University of Oxford, 121 Banbury
Road, Oxford

* Sommerville, Duncan M‘Laren Young, M.A., D.Sc., Professor of Pure and

Applied Mathematics, Victoria College, Wellington, New Zealand
Sorley, James, 82 Onslow Gardens, London

* Spence, Frank, M.A., B.Sc., 25 Craiglea Drive, Edinburgh 535

Sprague, T. B., M.A., LL.D., Actuary, 29 Buckingham Terrace, Edinburgh
Squance, Thomas Coke, M.D., F.R.M.S., F.S.A.Scot., Physician and Pathologist

in the Sunderland Infirmary, President Sunderland Antiquarian Society,
Sunderland Naturalists’ Association, 15 Grange Crescent, Sunderland

* Stanfield, Richard, Professor of Mechanics and Engineering in the Heriot-Watt

College, Edinburgh

* Steggall, John Edward Aloysius, M.A. , Professor of Mathematics at University

College, Dundee, in St Andrews University, Woodend, Perth Road, Dundee
Stephenson, John, M. B., D.Sc. (Lond.), Indian Medical Service, Professor of
Biology, Government College, Lahore, India. 540

* Stephenson, Thomas, F.C.S., Editor of the Presenter, Examiner to the Pharma-

ceutical Society, 9 Woodburn Terrace, Edinburgh
Stevenson, Charles A., B.Sc., M.Inst.C.E., 28 Douglas Crescent, Edinburgh
Stevenson, David Alan, B.Sc., M.Inst.C.E., 84 George Street, Edinburgh
Stewart, Charles Hunter, D.Sc., M.B., C.M., Professor of Public Health in the
University of Edinburgh, Usher Institute of Public Health, Warrender
Park Road, Edinburgh

* Stockdale, Herbert Fitton, Director of the Royal Technical College, Glasgow,

Clairinch, Upper Helensburgh, Dumbartonshire 545

Stockman, Ralph, M.D., F.R.C.P.E., Professor of Materia Medica and Therapeutics
in the University of Glasgow

Story, Fraser, Professor of Forestry, University College, Bangor, North Wales

* Strong, John, M.A., Rector of Montrose Academy, Peel Place, Montrose
Sutherland, David W. , M.D., M.R.C.P. , Captain, Indian Medical Service,

Professor of Pathology and Materia Medica, Medical College, Lahore, India
Swithinbank, Harold William, Denham Court, Denham, Bucks 550

* Syme, William Smith, M.D. (Edin. ), 10 India Street, Glasgow

Symington, Johnson, M.D., F.R.C.S.E., F.R.S., Professor of Anatomy in Queen’s
College, Belfast

* Tait, John W., B.Sc., Rector of Leith Academy, 18 Netherby Road, Leith
Tait, William Archer, D.Sc., M.Inst.C.E., 38 George Square, Edinburgh
Talmage, James Edward, D.Sc., Ph.D., F.R.M.S., F.G.S., Professor of Geology,

University of Utah, Salt Lake City, Utah, U.S.A. 555

Tanakadate, Aikitu, Professor of Natural Philosophy in the Imperial University
of Japan, Tokyo, Japan

Tatlock, Robert R., F.C.S. , City Analyst’s Office, 156 Bath Street, Glasgow

* Taylor, James, M. A. , Mathematical Master in the Edinburgh Academy
Thackwell, J. B. , M.B., C.M., 423a Battersea Park Road, London, S. W.

Thompson, D’Arcy W. , C.B., B.A. , F. L.S., Professor of Natural History in)
University College, Dundee 560 j

* Thompson, John Hannay, M.Sc. (Durh.), M.Inst.C.E., M. Inst.Mech.E., Engineer

to the Dundee Harbour Trust, Sorbie, 10 Balgillo Terrace, Brough ty Ferry

* Thoms, Alexander, 7 Playfair Terrace, St Andrews

Thomson, Andrew, M.A., D.Sc., F.I.C., Rector, Perth Academy, Ardenlea,
Pitcullen, Perth

* Thomson, Frank Wyville, M.A., M.B., C.M., D.P.H., D.T.M., Lt.-Col. I.M.S.

(Retired), Bonsyde, Linlithgow

* Thomson, George Ritchie, M.B., C.M., General Hospital, Johannesburg, Transvaal 565
Thomson, George S., F.C.S. , Ferma Albion, Marculesci, Roumania

* Thomson, Gilbert, M.Inst.C.E., 164 Bath Street, Glasgow

Thomson, J. Arthur, M.A., LL.D., Regius Professor of Natural History in the
University of Aberdeen

Thomson, James Stuart, F.L.S. , Zoological Department, University, Manchester
Thomson, John Millar, LL.D., F.R.S., Professor of Chemistry in King’s College,
London, 18 Lansdowne Road, London, W. 570

* Thomson, R. Tatlock, F.C.S., 156 Bath Street, Glasgow

Thomson, Robert Black, M.B., Edin., Professor of Anatomy, South African
College, Cape Town

335

Service on
Council, etc.

1885-87.

1903-05.

1892-

1914-

1892-95,

1896-99,

1907-10,

1912-

1906-08.

336

Date of

Election.

1870

1882

1876

1911

1914

1888

1905

1906

1861

1895

1898

1889

1910

1911

1891

1873

1902

1886

1898

1891

1907

1901

1911

1900

1910

1907

1911

1911

1896

1907

1903

1904

1896

1909

1896

Proceedings of the Royal Society of Edinburgh.

Service on
Council, etc.

Thomson, Spencer C., Actuary, 10 Eglinton Crescent, Edinburgh
Thomson, Wm., M.A., B.Sc., LL.D., Registrar, University of the Cape of Good
Hope. University Buildings, Cape Town

Thomson, William, Royal Institution, Manchester 575

* Tosh, James Ramsay, M.A., D.Sc. (St Ands.), Thursday Island, Queensland,

Australia

Tredgold, Alfred Frank, L.R.C.P., M.R.C.S., Hon. Consulting Physician to National
Association for the Feeble-minded, 6 Dapdune Crescent, Guildford, Surrey
Turnbull, Andrew H., Actuary, The Elms, Whitehouse Loan, Edinburgh

* Turner, Arthur Logan, M.D., F.R.C.S.E., 27 Walker Street, Edinburgh

* Turner, Dawson F. D., B.A., M.D., F.R.C.P.E., M.R.C.P., Lecturer on Medical

Physics, Surgeons’ Hall, Physician in charge of Radium Treatment, Royal
Infirmary, Edinburgh, 37 George Square, Edinburgh 580 r

Turner, Sir William, K.C.B., M.B., F.R.C.S.L. and E., LL.D., D.C.L., D.Sc.,
F.R.S. , Late Pres. R.S.E., Knight of the Royal Prussian Order Pour le ,
Merite, Principal and Vice-Chancellor of the University of Edinburgh,
6 Eton Terrace, Edinburgh

Turton. Albert H., M. I.M.M., 171 George Road, Erdington, Birmingham

* Tweedie, Charles, M.A. , B.Sc., Lecturer on Mathematics in the University of

Edinburgh, Duns, Berwickshire

Underhill, T. Edgar, M.D., F.R.C.S.E., Dunedin, Barnt Green, Worcestershire
Vincent, Swale, M.D. Lond., D.Sc. Edin., etc., Professor of Physiology, University
of Manitoba, Winnipeg, Canada 585

* Walker, Henry, M.A. , D.Sc., Head Physics Master, Kilmarnock Academy and

Technical School, 30 M‘Lelland Drive, Kilmarnock

* Walker, James, D.Sc., Ph.D., LL.D., F.R.S., Professor of Chemistry in the

University of Edinburgh, 5 Wester Coates Road, Edinburgh
Walker, Robert, M.A., LL.D., University, Aberdeen

* Wallace, Alexander G., M.A., 56 Fonthill Road, Aberdeen

Wallace, R., F.L.S. , Professor of Agriculture and Rural Economy in the University
of Edinburgh 590

Wallace, Wm., M.A., Belvedere, Alberta, Canada

* Walmsley, R. Mullineux, D.Sc., Principal of the Northampton Institute, Clerken-

well, London

Waters, E. Wynston, Medical Officer, H.B.M. Administration, E. Africa, Malindi,
British East Africa Protectorate, via Mombasa

* Waterston, David, M.A., M.D., F. R.C.S.E. , Professor of Anatomy, University,

St Andrews

* Watson, James A. S., B.Sc., etc., Assistant in Agriculture, University of Edin-

burgh, 15 Dick Place, Edinburgh 595

* Watson, Thomas P., M.A., B.Sc., Principal, Keighley Institute, Keighley

* Watson, William John, M.A., LL.D. Aberdeen, B.A. Oxon., Professor of Celtic

Languages and Literature, University, Edinburgh, 17 Merchiston Avenue,
Edinburgh

* Watt, Andrew, M. A., Secretary to the Scottish Meteorological Society, 6 Woodburn

Terrace, Edinburgh

Watt, James, W.S., F. F.A., 24 Rothesay Terrace, Edinburgh

* Watt, Rev. Lauclilan Maclean, B.D., Minister of St Stephen’s Parish, 7 Royal

Circus, Edinburgh 600

Webster, John Clarence, B.A., M.D., F.R.C.P.E., Professorof Obstetrics and Gynae-
cology, Rush Medical College, 1748 Harrison Street, Chicago, 111., U.S.A.

* Wedderburn, Ernest Maclagan, M.A., LL.B., W.S. , D.Sc., 7 Dean Park Crescent,

Edinburgh

* Wedderburn, J. H. Maclagan, M.A. , D.Sc., 95MercerStreet, Princeton, N.J., U.S.A.
Wedderspoon, William Gibson, M.A., LL.D., Indian Educational Service, Senior

Inspector of Schools, Burma, The Education Office, Rangoon, Burma
Wenley, Robert Mark, M.A., D.Sc., D.Phil. , Litt.D., LL.D., D. C.L., Professor
of Philosophy in the University of Michigan, Ann Arbor, U.S.A. 605

* Westergaard, Reginald Ludovic Andreas Emil, Ph.D., Professor of Technical

Mycology, Heriot- Watt College, Hafnia, Liberton, Edinburgh
White, Philip J., M.B., Professor of Zoology in University College, Bangor, North
Wales

1866-68,

1895-97.

1913-

Sec.

1869-91.

V-P

1891-95,

1897-1903.

P.

1908-1913.

1907-10.

1903-05,

1910-13.

1912-14.

1913-

List of Honorary Fellows, etc.

337

Date of
Election.

1911

1912
1879
1908

1910 C.
1900

1911
1902

1895

1882

1891

1902

1908

1886 C.

1884

1911

1890

1896

1882

1892

1896

1904

C.

* Whittaker, Charles Richard, F. R.C.S, (Edin.), F.S.A. (Scot. ), Lynwood, Hatton

Place, Edinburgh

* Whittaker, Edmund Taylor, Sc.D., F.R.S., Professor of Mathematics in the

University of Edinburgh, 35 George Square, Edinburgh
Will, John Charles Ogil vie, of Newton of Pitfodels, M.D. , 17 Bon- Accord Square,
Aberdeen 610

* Williamson, Henry Charles, M.A., D.Sc. , Naturalist to the Fishery Board for

Scotland, Marine Laboratory, Aberdeen

* Williamson, William, 9 Plewlands Terrace, Edinburgh
Wilson, Alfred C. , F.C.S., Yoewood Croft, Stockton-on-Tees

* Wilson, Andrew, M.Inst. C.E., 51 Queen Street, Edinburgh

* Wilson, Charles T. R., M.A., F.R.S., 21 Grange Road, Cambridge, Sidney

Sussex College, Cambridge 615

Wilson -Barker, David, R.N.R., F. R.G.S., Captain-Superintendent Thames Nautical
Training College, H.M.S. “Worcester,” off Greenhithe, Kent
Wilson, George, M.A. , M.D., LL.D.

* Wilson, John Hardie, D.Sc., University of St Andrews, 39 South Street, St

Andrews

Wilson, William Wright, F.R.C.S.E., M.R.C.S., Cottesbrook House, Acock’s
Green, Birmingham

* Wood, Thomas, M.D. , Eastwood, 182 Ferry Road, Bonnington, Leith 620

Woodhead, German Sims, M.D. , F.R.C.P.E., Professor of Pathology in the

University of Cambridge

Woods, G. A., M.R.C.S., 1 Hammelton Road, Bromley, Kent

* Wrigley, Ruric Whitehead, B.A. (Cantab.), Assistant Astronomer, Royal Observa-

tory, Edinburgh

Wright, Johnstone Christie, Conservative Club, Edinburgh

* Wright, Sir Robert Patrick, Chairman of the Board of Agriculture for Scotland,

Kingarth, Colinton, Midlothian 625

Young, Frank W., F.C.S., H.M. Inspector of Science and Art Schools,
32 Buckingham Terrace, Botanic Gardens, Glasgow
Young, George, Ph.D., “ Bradda,” Church Crescent, Church End, Finchley,
London, N.

* Young, James Buchanan, M.B., D.Sc., Dalveen, Braeside, Liberton

Young, R. B., M.A., D.Sc., F.G.S., Professor of Geology and Mineralogy
in the South African School of Mines and Technology, Johannesburg,
Transvaal

Service on
Council, etc.

1912-

1887-90.

LIST OF HONORARY FELLOWS OF THE SOCIETY

At January 1, 1914.

HIS MOST GRACIOUS MAJESTY THE KING.

Foreigners (limited to thirty-six by Law X).

Elected,

1897 Emile Hilaire Amagat, Membre de l’lnstitut, St Satur, Cher, France.

1900 Arthur Auwers, Belle vue-Strasse 55, Berlin-Lichterfelde, Germany.

1900 Adolf Ritter von Baeyer, Universitat, Miinchen, Germany.

1905 Waldemar Christofer Brogger, K. Frederiks Universitet, Christiania, Norway.

1905 Moritz Cantor, Gaisbergstrasse 15, Heidelberg, Germany.

1902 Jean Gaston Darboux, Secretariat de l’lnstitut, Paris, France.

1910 Hugo de Vries, Universiteit, Amsterdam, Holland.

1905 Paul Ehrlich, K. Institut fur Experimentelle Therapie, Sandhofstrasse 44, Frankfurt-a.-M.,
Germany.

1908 Emil Fischer, Universitat, Berlin, Germany.

1910 Karl F. von Goebel, Universitat, Miinchen, Germany.

1905 Paul Heinrich von Groth, Universitat, Munchen, Germany.

1888 Ernst Haeckel, Universitat, Jena, Germany.

1913 George Ellery Hale, Mount Wilson Solar Observatory (Carnegie Institution of Washington),
Pasadena, California, U.S.A.

1883 Julius Hann, Universitat, Wien, Austria.

1913 Emil Clement Jungfleisch, College de France, Paris, France.

1910 Jacobus Cornelius Kapteyn, Universiteit, Groningen, Holland.

vol. xxxiv. 22

338

Proceedings of the Royal Society of Edinburgh.

Elected

1897 Gabriel Lippmann, Universite, Paris, France.

1895 Carl Menger, Wienix., Fuchstallerg, 2, Austria.

1910 Elie Metchnikoff, Institut Pasteur, Paris, France.

1910 Albert Abraham Michelson, University, Chicago, U.S.A.

1897 Fridtjof Nansen, K. Frederiks Universitet, Christiania, Norway.

1908 Henry Fairfield Osborn, Columbia University and American Museum of Natural History,
New York, N.Y., U.S.A.

1910 Wilhelm Ostwald, Gross-Bothen, bei Leipzig, Germany.

1908 Ivan Petrovitch Pawlov, Wedenskaja Strasse 4, St Petersburg, Russia.

1910 Frederick Ward Putnam, Peabody Museum of Harvard University, Cambridge, Mass. ,

1889 Georg Hermann Quincke, Bergstrasse 41, Heidelberg, Germany.

1913 Santiago Ramon y Cajal, Universidad, Madrid, Spain.

1908 Magnus Gustaf Retzius, Hogskolan, Stockholm, Sweden.

1908 Augusto Righi, Regia Universita, Bologna, Italy.

1913 Yito Volterra, Regia Universita, Rome, Italy.

1905 Wilhelm Waldeyer, Universitat, Berlin, Germany.

1905 Wilhelm Wundt, Universitat, Leipzig, Germany.

1913 Charles Rene Zeiller, Ecole Nationale Superieure des Mines, Paris, France.

Total, 33.

British Subjects (limited to twenty by Law X).

1900 Sir David Ferrier, Kt., M.A., M.D., LL.D., F.R.S., Emer. Professor of Neuro-Pathology,
King’s College, London, 34 Cavendish Square, London, W.

1900 Andrew Russell Forsyth, M.A. , Sc.D., LL.D., Math.D. , F.R.S., Chief Professor of
Mathematics in the Imperial College of Science and Technology, London, formerly
Sadlerian Professor of Pure Mathematics in the University of Cambridge, Imperial
College of Science, London, S.W.

1910 Sir James George Frazer, D.C.L. , LL.D., Litt.D., F.B.A. , Fellow of Trinity College, Cam-
bridge, Professor of Social Anthropology in the University of Liverpool, Trinity College,
Cambridge.

1908 Sir Alexander B. W. Kennedy, Kt., LL.D., F.R.S., Past Pres. Inst. C.E. , 1 Queen Anne
Street, Cavendish Square, London, W.

1913 Horace Lamb, M.A., Sc.D., D.Sc., LL.D., F. R.S. , Professor of Mathematics in the
University of Manchester.

1908 Sir Edwin Ray Lankester, K.C.B., LL.D., F.R.S. , 29 Thurloe Place, S. Kensington,
London, S.W.

1910 Sir Joseph Larmor, Kt., M.A., D.Sc., LL.D., D.C.L. , F.R.S. , M. P. University of Cambridge
since 1911, Lucasian Professor of Mathematics in the University of Cambridge, St John’s
College, Cambridge.

1900 Archibald Liversidge, M.A., LL.D., F.R.S., Em.-Professor of Chemistry in the University of
Sydney, Fieldhead, Combe Warren, Kingston, Surrey.

1908 Sir James A. H. Murray, LL.D., D.C.L., D.Litt., Ph.D., Litt.D., F.S.A., Corresp. Member
of the Institute of France, etc., Editor of the Oxford English Dictionary, Oxford.

1905 Sir William Ramsay, K.C.B*, LL.D., F.R.S., formerly Professor of Chemistry in the
University College, London, 19 Chester Terrace, Regent’s Park, London, N.W.

1886 The Rt. Hon. Lord Rayleigh, O. M., P.C. , J.P. , D.C.L., LL.D., D.Sc. Dub., F.R.S., Corresp.
Mem. Inst, of France, Terling Place, Witham, Essex.

1908 Charles Scott Sherrington, M.A., M.D., LL.D., F.R.S., Waynflete Professor of Physiology in

the University of Oxford, Physiological Laboratory, Oxford.

1913 Sir William Turner Thiselton-Dyer, K.C.M.G., C.I.E., M.A., LL.D., F.R.S., formerly
Director of the Royal Botanic Gardens, Kew ; The Ferns, Witcombe, Gloucester.

1905 Sir Joseph John Thomson, D.Sc., LL.D., F.R.S., Cavendish Professor of Experimental
Physics, University of Cambridge, Trinity College, Cambridge.

1909 Sir Thomas Edward Thorpe, Kt. , C.B. , D.Sc., LL.D., F.R.S., formerly Principal of the

Government Laboratories, Imperial College of Science and Technology, South Kensington,
London, S.W., Wliinfield Salcombe, South Devon.

Total, 15.

Ordinary Fellows of the Society Elected.

339

ORDINARY FELLOWS OF THE SOCIETY ELECTED

During Sessio7i 1913-14.

(Arranged according to their date of election.)

17 th November 1913.

Edward Philip Harrison, Ph.D.

1st December 1913.

William Barron Coutts, M.A., B.Sc. John Edward Gemmell, M.B., C.M. (Edin.).

William Fraser. Alfred Oswald.

John William Pare, M.B., C.M. (Edin.), M.D., L.D.S. (Eng.).

19 th January 1914.

Spencer Mort, M.D., Ch.B., F.R.C.S.E. Joseph Pearson, D.Sc., F.L.S,

16th February 1914.

Robert John Harvey-Gibson, M.A., F.L.S. , D.L. for the
County Palatine of Lancaster, M.R.S.G.S.

John Noble Jack.

25 th May 1914.

Alexander Charles Cumming, D.Sc. Graham Renshaw, M.B., M.R.C.S., L.R.C.P.,

Basil Alexander Pilkington. L.S.A.

Peter Ramsay, M.A., B.S.C. James Bonnyman Ritchie, B.Sc.

Theodore Emile Salvesen.

15th June 1914.

Alexander Gibb, A.M.Inst.C.E.

6th July 1914.

Francis John Lewis, D.Sc., F.L.S.

Archibald M‘Kendrick, F.R.C.S.E., D.P.H., L.D.S.

Alfred Frank Tredgold, L.R.C.P., M.R.C.S.

ORDINARY FELLOWS DECEASED AND RESIGNED

During Session 1913-14.

DECEASED.

James A. Macdonald, M.A., B.Sc.

John Sturgeon Mackay, M.A., LL.D.

Sir John Murray, K.C.B., LL.D., Ph.D.,
D.Sc., F.R.S.

R. Traill Omond.

RESIGNED.

Rev. John H. Burn. Charles B. Boog Watson.

John Gibson, Ph.D.

J. W. Inglis, M.Inst.C.E.

Lieut. George J ohnstone, R. N. R.
John Macallan, F.I.C.

FOREIGN HONORARY FELLOW DECEASED.

Eduard Suess.

BRITISH HONORARY

Sir Robert Stawell Ball, Kt., LL.D., F.R.S.,
M.RJ.A.

Coh Alexander Ross Clarke, C.B. , R.E.,
F R S

Sir David Gill, K.C.B., LL.D., F.R.S.

FELLOWS DECEASED.

Albert C. L. G. Gunther, Ph.D., F.R.S.
George William Hill.

Alfred Russel Wallace, O.M., LL.D.,
D.C.L., F.R.S.

340 Proceedings of the Royal Society of Edinburgh. [Sess.

List of Library Exchanges, Presentations, etc.

1. Transactions and Proceedings of Learned Societies, Academies,

ETC., RECEIVED BY EXCHANGE OF PUBLICATIONS, AND LlST OF

Public Institutions entitled to receive Copies of the
Transactions and Proceedings of the Royal Society of
Edinburgh. {For convenience certain Presentations are included
in this List.)

T.P. prefixed to a name indicates that the Institution is entitled to receive Transactions and
Proceedings. P. indicates Proceedings.

AFRICA (BRITISH CENTRAL).

Zomba. — Scientific Department. Meteorological Observations, Fol. {Presented
by H.M. Acting Commissioner and Consul-General .)

AMERICA (NORTH). {See CANADA, UNITED STATES, and MEXICO.)

AMERICA (SOUTH).

t.p. Buenos Ayres (Argentine Republic). — Museo Nacional. Anales.
p. Sociedad Physis. Boletin.

Oficina Meteorologica Argentina. Anales. ( Presented .)

Cordoba —

t.p. Academia Nacional de Ciencias de la Republica Argentina. Boletin.

t.p. National Observatory. Annals. — Maps.

t.p. La Plata (Argentine Republic). — Museo de La Plata.

Lima (Peru). Cuerpo de Ingenieros de Minas del Peru. Boletin. ( Presented .)
p. Montevideo (Uruguay). — Museo Nacional. Anales (Flora Uruguay).

t.p. Para (Brazil). — Museu Paraense de Historia Natural e Ethnographia. Boletin.
p. Quito (Ecuador). — Observatorio Astronomico y Meteor ologico.

Rio de Janeiro (Brazil) —
t.p. Observatorio. Annuario. — Boletin Mensal.

p. Museu Nacional. Revista (Archivos).

Santiago (Chili) —

t.p. Societe Scientifique du Chili. Actes.

p. Deutscher Wissenschaftlicher Verein.

p. San Salvador. — Observatorio Astronomico y Meteor ologico.

Valparaiso (Chili). — Servicio Meteor ologico. Annuario. {Presented.)

AUSTRALIA.

Australasian Association for the Advancement of Science. — Reports. {Pre-
sented.)

341

1913-14.] List of Library Exchanges, Presentations, etc.

Adelaide —

p. University Library.

p. Royal Society of South Australia. Transactions and Proceedings. — Memoirs,
p. Royal Geographical Society of Australasia ( South Australian Branch).
Proceedings.

Observatory. Meteorological Observations. 4 to. ( Presented .)

Brisbane —

t.p. University of Queensland.

p. Royal Society of Queensland. Transactions.

p. Royal Geographical Society ( Queensland Branch). Queensland Geographical
J ournal.

p. Government Meteorological Office.

p. Water Supply Department.

p. Geelong (Yictoria). — Gordon Technical College.
t.p. Hobart. — Royal Society of Tasmania. Proceedings.

Melbourne —

Commonwealth Bureau of Census and Statistics. Official Year Book.

By G. H. Knibbs. ( Presented .)

National Museum. Memoirs. ( Presented .)

t.p. University Library.

p. Royal Society of Victoria. Proceedings. — Transactions.

Perth, W.A. —

p. Geological Survey. Annual Progress Reports. — Bulletins.

Government Statistician’s Office. Monthly Statistical Abstract. ( Presented .)
Sydney —

t.p. University Library. Calendar. — Reprints of Papers from Science Laboratories.
t.p. Department of Mines and Agriculture ( Geological Survey ), N.S.W.

Records. — Annual Reports. — Palaeontology. Mineral Resources.
t.p. Linnean Society of New South Wales. Proceedings.
t.p. Royal Society of New South Wales. Journal and Proceedings,
p. Australian Museum. Records. — Reports. — Memoirs. — Catalogues.

N.S.W. Government. Fisheries Report. ( Presented .)

AUSTRIA.

Cracow —

t.p. Academie des Sciences. Rozprawy Wydzialu matematyczno-przyrodniezego
(Proceedings, Math, and Nat. Sciences Cl.). — Rozprawy Wydzialu
filologicznego (Proc., Philological Section). — Rozprawy Wydzialu his-
toryczno-filozoficznego (Proc., Hist.-Phil. Section). — Sprawozdanie Komisyi
do badania historyi sztuki w Polsce (Proc., Commission on History of Art
in Poland). — Sprawozdanie Komisyi fizyjograficznej (Proc., Commission
on Physiography). — Geological Atlas of Galicia; Text, Maps. — Bulletin
International, etc.

Gratz —

t.p. Naturwissenschaftlicher Verein fur Steiermark. Mittheilungen.
p. Chemisches Institut der K. K. Universitat.
p. Lemberg. — Societe Scientifique de Chevtchenko .

342

p.

T.P.

T.P.

T.P.

P.

P.

P.

P.

T.P.

T.P.

T.P.

T.P.

P.

T.P.

T.P.

T.P.

T.P.

Proceedings of the Royal Society of Edinburgh. [Sess.

Prague —

Deutscher Nat. -Med. Vereinfilr Bohmen “Lotos.” — “Lotos.”

K. K. Stermvarte. Magnetische und Meteorologische Beobachtungen.
Astronomische Beobachtungen.

K. Bohmische Gesellschaft. Sitzungsberichte : Math.-Naturw. Classe; Phil -
Hist.-Philol. Classe.— Jahresbericht, — and other publications.

Ceshd Akademie Cisare Frantiska Josef a pro Vedy Slovesnost a Umeni.
Almanach. — Yestnik (Proceedings). — Rozpravy (Transactions) : Phil.-
Hist. Class ; Math.-Phys. Cl. ; Philol. Cl. — Historicky Archiv. — Bulletin
International, Resume des Travaux presentes, — and other publications of
the Academy.

Sarajevo (Bosnia). — The Governor-General of Bosnia-Herzegovina. Ergebnisse
der Meteorologischen Beobachtungen.

Trieste —

Societa Adriatica di Scienze Naturali.

Museo Civico di Storia Natnrale.

Osservatorio Marittimo. Rapporto Annuale.

Vienna —

Kais. Akademie der^ Wissenschaften. Denkschriften : Math.-Raturwissen-
schaftliche Classe ; Philosophisch-Historische Classe — Sitzungsberichte
der Math.-Raturwissenschaftlichen Classe; Abtheil. I., II.a, II.b, III.;
Philosoph.-Historische Classe. — Almanach. — Mittheilungen der Erdbeben
Commission.

K. K. Geologische Reichsanstalt. Abhandlungen. — Jahrbiicher. — Verhand-
lungen.

Oesterreiclnsche Gesellschaft fur Meteorologie. Meteorologische Zeitschrift.

K. K. Zoologisch - Botanische Gesellschaft. Verhandlungen. — Abhand-
lungen.

K. K. N aturhistorisches Hofmuseum. Annalen.

K. K. Central- Anstalt fur Meteorologie und Erdmagnetismns. Jahrbiicher.

4to. — Allgemeiner Bericht und Chronik. 8vo. (Presented.)

K. K. Militar Geographisclies Institut. Astronomisch-Geodatischen Arbeiten.
— Astronomische Arbeiten. 4to. — TAngenbestimmungen. 4to. — Die

Ergebnisse der Triangulierungen. 4to. ( Presented .)

Zoologisches Institut der Universitdt und der Zoologisch en Station in Triest.
Arbeiten . ( Purchased,. )

BELGIUM.

Brussels —

Acadernie Roy ale des Sciences , des Lettres et des Beaux Arts de Belgique.

Memoires. — Bulletins. — Annuaire. — Biographie Rationale.

Musee Royal JHistoire Naturelle. Memoires.

Musee du Congo. Annales. — Botanique. Zoologie. Ethnographie et.
Antliropologie. Linguistique , etc.

V Ohservatoire Royal de Belgique , Uccle. Annuaire. — Annales Astronomiques
— Annales Meteorologiques.— Annales. — Physique du Globe. — Bulletin
Climatologique.— Observations Meteorologiques.

1913-14.] List of Library Exchanges, Presentations, etc.

343

T.P.

P.

T.P.

T.P.

P.

P.

T.P.

P.

P.

T.P.

T.P.

P.

T.P.

T.P.

T.P.

P.

T.P.

Brussels — continued —

Societe Scientifique. Annales.

Societe Beige d’ Astronomie. Ciel et Terre. ( Purchased .)

Ghent. — University Library.

Louvain. — University Library.

BOSNIA-HERZEGOYINA. (Bee AUSTRIA.)

BULGARIA.

Sofia. — Station Gentrale Meteorologique de Bulgarie. Bulletin Mensuel. — *
Bulletins Annuaires.

CANADA.

Edmonton (Alberta). — Department of Agriculture. Annual Report. —
(Presented.)

Halifax (Nova Scotia). — Nova Scotian Institute of Science. Proceedings
and Transactions.

Kingston. — Queen’s University.

Montreal —

Natural History Society. Proceedings.

Canadian Society of Civil Engineers. Transactions. — Annual Reports.
Ottawa —

Royal Society of Canada. Proceedings and Transactions.

Geological Survey of Canada. Annual Reports. — Palaeozoic Fossils. — Maps,
Memoirs, and other Publications.

Literary and Scientific Society. Transactions.

Quebec. — Literary and Philosophical Society. Transactions.

Toronto —

University. University Studies. (History. Psychological Series. Geological
Series. Economic Series. Physiological Series. Biological Series.
Physical Science Series. Papers from the Chemical Laboratory.) etc.
Canadian Institute. Transactions.

Royal Astronomical Society of Canada. Journal. — Astronomical Handbook.

CAPE COLONY. (See UNION OF SOUTH AFRICA.)

Colombo —
Museum.

CEYLON.

Spolia Zeylanica. Annual Report.

Hong Kong —

Royal Observatory.

CHINA.

Monthly Meteorological Bulletin. — Report.

344

Proceedings of the Royal Society of Edinburgh. [Sess.

DENMARK.

Copenhagen—

t.p. Academie Royale de Copenhague. Memoires : Classe des Sciences. — Oversigt.
p. Naturhistorisk F overling. Videnskabelige Meddelelser.

p. Danish Biological Station. Report.

Conseil Permanent International pour V Exploration de la Mer. Publications
de circonstance. — Rapports et Proces-Verbaux de Reunions. — Bulletin des
Resultats acquis pendant les croisieres periodiques. — Bulletin Statistique.
( Presented .)

Kommissionen for Havundersogelser. Meddelelser : Serie Fiskeri. Serie
Plankton. Serie Hydrografi. — Skrifter. ( Presented .)

University (. Zoological Museum). Reports of the Danish Ingolf-Expedition.
(Presented.)

EGYPT.

t.p. Cairo. — School of Medicine. Records.

Ministry of Finance" (Survey Dept. : Archaeological Survey of Nubia).
Bulletin, Reports, Papers. (Presented.)

ENGLAND AND WALES.

Birmingham —

p. Philosophical Society. Proceedings.

University. Calendar. (Presented.)

Cambridge —

t.p. Philosophical Society. Transactions and Proceedings.

t.p. University Library. — Observatory. Report. — Observations.

t.p. Cardiff. — University College of South Wales.

Coventry. — Annual Report of the Health of the City. (Presented by Dr Snell.)
p. Essex. — Essex Field Club. The Essex Naturalist.

t.p. Greenwich. — Royal Observatory. Astronomical, Magnetical, and Meteorological
Observations. — Photo-heliographic Results and other Publications.
t.p. Harpenden (Herts.). — Rothamstead Exp. Station. (Lawes Agricultural Trust.)
Leeds —

t.p. Philosophical and Literary Society. Reports,

p. Yorkshire Geological and Polytechnic Society. Proceedings.

Liverpool —

t.p. University College Library.

p. Biological Society. Proceedings and Transactions,

p. Geological Society. Proceedings.

London —

p. Admiralty. Nautical Almanac and Astronomical Ephemeris. — Health of the
Navy (Annual Report).
t.p. Anthropological Institute. Journal.

345

1913-14.] List of Library Exchanges, Presentations, etc.

London — continued —
t.p. Athenaeum Club.

British Antarctic Expedition , 1907-09. Reports on Scientific Investigations.
( Presented . )

t.p. British Association for the Advancement of Science. Reports.
t.p. British Museum ( Copyright Office). Reproductions from Illuminated

Manuscripts.

t.p. British Museum. Natural History Department. Catalogues, Monographs,
Lists, etc. National Antarctic Expedition, 1901-0 If. Publications.
t.p. Chemical Society. Journal. Abstract of Proceedings,

p. Faraday Society. Transactions.

t.p. Geological Society. Quarterly Journal. — Geological Literature. — Abstract of

Proceedings.

t.p. Geological Survey of the United Kingdom. Summary of Progress. Memoirs,

p. Geologists’ Association. Proceedings.

t.p. Hydrographic Office.

t.p. Imperial Institute.

t.p. Institution of Civil Engineers. Minutes of Proceedings, etc.

t.p. Institution of Electrical Engineers. Journal.

p. Institution of Mechanical Engineers. Proceedings.

t.p. International Catalogue of Scientific Literature. [Purchased.)

t.p. Linnean Society. Journal: Zoology; Botany. — Transactions: Zoology;

Botany. — Proceedings,
p. Mathematical Society. Proceedings.

p. Meteorological Office. Report of the Meteorological Committee to the Lords
Commissioners of H.M. Treasury. — Reports of the International Meteoro-
logical Committee. — Hourly Readings. — Weekly Weather Reports. —
Monthly and Quarterly Summaries. — Meteorological Observations at
Stations of First and Second Order, and other Publications. Geophysical
Journal. — Geophysical Memoirs.

Mineralogical Society of Great Britain and Ireland. Mineralogical Magazine
and Journal. ( Presented .)

National Antarctic Expedition, 1901-0 If.. ( Presented .)

Optical Society. Transactions. ( Purchased .)
p. Pharmaceutical Society. Journal. — Calendar,

p. Physical Society. Proceedings.

t.p. Royal Astronomical Society. Monthly Notices. — Memoirs.
t.p. Royal College of Surgeons.

t.p. Royal Geographical Society. Geographical Journal.

t.p. Royal Horticultural Society. Journal.

t.p. Royal Institution. Proceedings.

p. Royal Meteorological Society. Quarterly Journal.

t.p. Royal Microscopical Society, Journal.

p. Royal Photographic Society. Photographic Journal.

t.p. Royal Society. Philosophical Transactions. — Proceedings. — Year-Book. —
National Antarctic Expedition, 1901-01f, Publications; and other
Publications.

Royal Society of Arts. Journal.

TP.

346

Proceedings of the Royal Society of Edinburgh. [Sess.

London — continued —
t.p. Royal Society of Literature. Transactions. — Reports.
t.p. Royal Society of Medicine. Proceedings.

t.p. Royal Statistical Society. Journal.

t. p. Society of Antiquaries. Proceedings. — Archseologia ; or Miscellaneous Tracts
relating to Antiquity.

Society of Chemical Industry. Journal. ( Presented .)

Society for Psychical Research. Journal. — Proceedings. (Presented by

W. C. Crawford , Esq.)

Solar Physics Committee. Annual Report, and other Publications.
(Presented.)

t.p. United Service Institution.

t.p. University College. Calendar.

t.p. University.

t.p. Zoological Society. Transactions. — Proceedings.

t.p. The Editor of Nature. — Nature.

t.p. The Editor of The Electrician. — Electrician .

t.p. The Editor of Science Abstracts. — Science Abstracts.

Manchester —

t.p. Literary and Philosophical Society. Memoirs and Proceedings.
t.p. University . — Publications — Medical Series. Public Health Series. Anatomical

Series. Physical Series. Biological Series. Lectures. Manchester Museum
(University of Manchester). Annual Reports — Notes from the Museum,
p. Microscopical Society. Transactions and Annual Report.

Ne wcastle-on-Tyne —

p. Natural History Society of N oi'thumberland , Durham , etc. Transactions.
t.p. North of England Institute of Milling and Mechanical Engineers. Transac-
tions.— Annual Reports.

Cullercoats Dove Marine Laboratory. Annual Report. (Presented.)
p. Literary and, Philosophical Society.

University of Durham Philosophical Society. Proceedings. (Presented.)
p. Norwich. — Norfolk and Norwich Naturalists’ Society. Transactions.

Oxford —

t.p. Bodleian Library.

p. Ashmolean Society. Proceedings and Report.

p. Raddiffe Observatory. Results of Astronomical and Meteorological Obser-
vations.

University Observatory. Astrographic Catalogue. (Presented.)
p. Penzance. — Royal Geological Society of Cornwall. Transactions.

t.p, Plymouth. — Marine Biological Association. Journal.

Richmond (Surrey) —
t.p. Kew Observatory.

p. Scarborough. — Philosophical Society.

t.p. Sheffield. — University College.

Southport. — Meteorological Observatory. Results of Observations. Joseph
Baxendell, Meteorologist. (Presented.) .

t.p. Teddington (Middlesex). — National Physical Laboratory. Collected
Researches. — Annual Reports.

347

1913-14.] List of Library Exchanges, Presentations, etc.

p. Truro. —Royal Institution of Cornwall. Journal.

York —

t.p. Yorkshire Philosophical Society. Reports.

FINLAND.

Helsingfors —

Academics Scientiarum Fennicce. Annales. Sitzungsberichte. — Documenta
Historica. {Presented.)

Hydrographisch Biologisch Untersuchungen. { Presented .)
t.p. Societas Scientiarum Fennica {Societe des Sciences de Finlande). Acta
Societatis Scientiarum Fennicae. — Ofversigt. — Meteorologisches Jahrbuch.
— Bidrag till Kannedom om Finlands Natur ocb Folk.
t.p. Societas pro Fauna et Flora Fennica. Acta. — Meddelanden.
p. Societe de Geographie de Finlande. Fennia. — Meddelanden.

FRANCE.

Besancon. — TJniversite Observatoire National. Bulletin Chronometrique et
Bulletin Meteorologique. {Presented.)

Bordeaux—

t.p. Societe des Sciences Physiques et Natur elles. Memoires. — Observations

Pluviometriques et Thermometriques. — Proces-Verbaux des Seances,
p. Societe de Geographie Commerciale. Bulletin.

Id Observatoire. Catalogue Photographique du Ciel.
p. Cherbourg. — Societe Nationale des Sciences Naturelles et Mathematiques.

Memoires.

p. Concarneau. — College de France {Laboratoire de Zoologie et de Physiologie

Maritime). Travaux Scientifiques.
p. Duon. — Academie des Sciences. Memoires.

Lille —

t.p. Societe des Sciences.

t.p. Societe Geologique du Nord. Annales.— Memoires.

p. TJniversite de France . Travaux et Memoires.

Lyons —

t.p. Academie des Sciences, Belles Lettres et Arts. Memoires.

t.p. Societe d’ Agriculture, Histoire Nat. et Arts. Annales.

t.p. TJniversite. Annales, Nouv. Serie : — I. Sciences, Medecine. II. Droit,

Lettres.

p. Societe Botanique. Annales. — Nouveaux Bulletins,

p. Societe Linneenne. Annales.

Marseilles —

tp. Faculte des Sciences. Annales.

p. Societe Scientijique Industrielle. Bulletin.

t.p. Montpellier. — Academie des Sciences et Lettres. Memoires : Section des
Sciences ; Section des Lettres ; Section de Medecine. Bulletin Mensuel.

348

Proceedings of the Royal Society of Edinburgh. [Sess.

t.p. X antes. — Societe Scientifique des Sciences Naturelles de VOuest de la France.
Bulletin.

t.p. Nice. — L’Observatoire. Annales.

Paris —

t.p. Academie des Sciences. Comptes Rendus. — Observatoire d’Abbadia :

Observations, 4to, and other Publications.
t.p. Academie des Inscriptions et Belles-Lettres. Comptes Bendus.
t.p. Association Frangaise pour V Avancement des Sciences. Comptes Rendus.

t.p. Bureau International des Poids et Mesures. — Proces-Yerbaux des Seances,

— Travaux et Memoires.
t.p. Bureau des Longitudes. Annuaire.

p. L’ficole des Pouts et Ghaussees.

t.p. Ministere de la Marine ( Service Hydrographique.) Annales Hydro-

graphiques. Expedition de Charcot, 1903-05. (See Presentation List.)
t.p. Ecole des Mines. Annales des Mines.

t.p Ecole Normale Superieure. Annales.

t.p. Fcole Polytechnique. Journal,

p. Ecole Libre des Sciences Politiques.

t.p. Institut Oceanographique. Annales.

t.p. Ministere de V Instruction Publique. Expedition de Charcot, 1908-10. (See

Presentation List.)

t.p. Musee Guimet. Revue de l’Histoire des Religions. — Annales. — Bibliotheque
d’Etudes.

t.p. Museum d’Histoire Naturelle. Nouvelles Archives. — Bulletin.
t.p. L' Observatoire. Rapport Annuel sur l’Etat de l’Observatoire. — Annales. —

Memoires. — Carte Photographique du Ciel. Fol. — Catalogue Plioto-
graphique du Ciel. 4to.

L’ Observatoire d’ Astronomie Physique de Meudon. Annales. (Presented.)
t.p. Societe Nationale d’ Agriculture. Bulletins. — Memoires.
p. Societe d’ Anthropologie. Bulletin et Memoires.

t.p. Societe Nationale des Antiquaires. Memoires. — Bulletin.

t.p. Societe de Biologie. Comptes Rendus.

t.p. Societe d1 Encouragement pour V Industrie Nationale. Bulletin.

t.p. Societe Frangaise de Physique. Journal de Physique.^ — -Annuaire. — Proces-
Yerbaux.

t.p. Societe de Geograpliie. La Geographie.

t.p. Societe Geologique de France. Bulletins. — Memoires (Paleontologie).

p. Societes des Jeunes Naturalistes et d1 Etudes Scientifiques. Eeuilles des

Jeunes Naturalistes.

t.p. Societe Mathematique. Bulletin.

p. Societe Philomatliique. Bulletin.

t.p. Societe Zoologique. Bulletin. — Memoires.

p. Revue Generate des Sciences Pures et Appliquees.

t.p. Rennes. — Societe Scientifique et Medicate de VOuest. Bulletin.

Toulouse^ —

t.p. TJniversite. — Faculte des Sciences. — U Observatoire. Annales.

p. Academie des Sciences. Memoires.

1913-14.] List of Library Exchanges, Presentations, etc.

349

GERMANY.

Berlin —

Carte Geologigue Internationale de V Europe. Livres I.— VIII. (complete).

( Presented .)

t.p. K. Akademie der Wissenschaften. Abhandlungen. — Sitzungsberichte.
t.p. Physikalische Gesellschaft. Fortschritte der Physik : lte Abtheil ; Physik
der Materie. 2te Abtheil ; Physik des Aethers. 3e Abtheil ; Kosmische
Physik. — Y erhandlungen.

t.p. Deutsche Geologische Gesellschaft. Zeitschrift, — Monatsberichte.

p. Deutsche Meteorologische Gesellschaft. Zeitschrift.

p. Konigl. Preussisches Meteorologisches Institut.

p. Gesellschaft Naturforschender Freunde. Sitzungsberichte. — Archiv fair

Biontologie.

p. Kgl. Technische Hochschule. Programm.

t.p. Zoologisches Museum. Mitteilungen.

Bonn —

p. Naturhistorischer Verein der Preussischen Rheinlande und Westfalens. Yer-
handlungen.

Niederrheinische Gesellschaft fur Natur- und Heilkunde. Sitzungsberichte.
{Presented.)

t.p. Bremen. — N aturwissenschaftlicher Verein. Abhandlungen.
p. Brunswick. — Verein fur Naturwissenschaft. Jahresberichte.
p. Carlsruhe. — Technische Hochschule. Dissertations,

p. Cassel. — Verein filr Natur kunde. Berichte.

t.p. Charlottenburg. — Physikalisch-Technische Reiclisanstalt. Abhandlungen.
p. Chemnitz. — Naturwissenschaftliche Gesellschaft. Berichte.
t.p. Dantzic. — Naturforschende Gesellschaft. Schriften.

I V estpreussischer Botanisch-Zoologischer Verein. Bericht. {Presented.)
Erlangen —

t.p. University . Inaugural Dissertations,

p. Physikalisch-Medicinische Societat. Sitzungsberichte.

t.p. Frankfurt-am-Main. — Senckenbergische Naturforschende Gesellschaft. Ab-
handlungen.'— Berichte.

p. Frankfurt-am-Oder. — N aturwissenschaftlicher Verein. Helios,

p. Freiburg- i Br. — Naturforschende Gesellschaft. Berichte.

Giessen —

t.p. University. Inaugural Dissertations.

p. Oberhessische Gesellschaft fur Natur- und Heilkunde. Berichte.

t.p. Gottingen. — K. Gesellschaft der Wissenschaften. Abhandlungen, Neue Folge :
Math.-Phys. Classe ; Phil.-Hist. Classe. — Nachrichten : Math.-Phys. Cl. ;
Phil. -Hist. Cl.; Geschaftliche Mittheilungen. — (Gelehrte Anzeigen.
Purchased.)

Halle —

t.p. K. Leopold- Car olinisch- Deutsche Akademie der Naturforscher. Nova Acta
( Y erhandlungen) . — Leopoldina.
t.p. Naturforschende Gesellschaft. Abhandlungen.
p. Verein fur Erdkunde. Mittheilungen.

350

Proceedings of the Royal Society of Edinburgh. [Sess.

Halle — continued —
p. Naturwissenschaftlicher Verein fur Sachsen und Thuringen.
p. Deutsche Mathematiker Vereinigung. Jahresbericht.

Hamburg —

t.p. Kaiserliche Marine Deutsche Seewarte. Annaleu der Hydrographie, etc. —
Jahresbericht.

t.p. Naturwissenschaftlicher Verein. Abhandlungen aus dem Gebiete der Natur-
ivissenschaften. — Verhandlungen.

t.p. N aturhistorisches Museum. Jahrbuch. — Beihefte. — Mitteiiungen.

p. Verein fur Naturwissenschaftliche Unterlialtung. Verhandlungen.

t.p. Hannover. — Naturhistorische Gesellschaft. Jahresbericht.
t.p. Helgoland. — K. Biologisches Anstalt. Wissenschaftliche Meeresunter-
suchungen (Abtheilung Helgoland).

t.p. Jena. — Medicinisch-Naturwissenschaftliche Gesellschaft. Jenaische Zeitschrift
fiir Naturwissenschaft. — Denkschriften.

Kiel —

t.p. Universitdt. Dissertations.

t.p. Kommission zur Wissenschaftlichen Untersucliung der Deutschen Meere,

Wissenschaftliche Meeresuntersuchungen (Abtheilung Kiel),
p. Naturwissenschaftlicher Verein fur Schleswig-Holstein. Schriften.

t.p. Konigsberg. — University.

Leipzig —

Furstlich Jablonowskisclie Gesellschaft. Preisschriften. ( Presented .)
t.p. Konigl. Sdchsische Gesellschaft der Wissenschafteu. Berichte : Math.-Phys.

Classe; Philologisch-Historisclie Classe. — Abhandlungen der Math.-Phys.
Classe ; Phil. -Hist. Classe.

t.p. Editor of Annalen der Physik. Annaleu der Physik.
p. Naturforschende Gesellschaft. Sitzungsberichte.

Deutsche Mathematiker Vereinigung. ( See Halle.)
p. Lubeck. — Geographische Gesellschaft und N aturhistorisches Museum. Mitteil-

ungen.

p. Magdeburg. — Naturwissenschaftlicher Verein. Abhandlungen u. Berichte.

t.p. Munich. — K. Bayerische Akademie der Wissenschaften. Abhandlungen:
Mathematisch-Physikalische Classe ; Philosophisch-Philologische Classe ;

Historische Classe. — Sitzungsberichte: Mathematisch-Physikalische Classe;
Philosophiseh-Philol. und Historische Classe.— Jahrbuch.

K. Sternwarte. Neue Annalen. ( Presented .)
p. Offenbach. — Verein fiir Naturkunde. Berichte.

p. Osnabruck. — Naturwissenschaftlicher Verein. Jahresbericht.

t.p. Potsdam. — Astrophysikalisches Observatorium. Publikationen.
p. Regensburg. — Historischer Verein von Oberpfalz und, Regensburg. Verhand-

lungen.

p. Rostock-i-M. — Naturforschende Gesellschaft. Sitzungsberichte und Abhand-

lungen.

p. University.

t.p. Strassburg. — University. Inaugural Dissertations.

Bureau Central de V Association International de Sismologie. Publications.
(. Presented . )

351

1913-14.] List of Library Exchanges, Presentations, etc.

t.p. Stuttgart. — Verein fur vaterlandische Naturkunde in Wiirttemberg.
Jahresliefte.

t.p. Tubingen. — University. Inaugural Dissertations.

GREECE.

Athens —

t.p. University Library.

t.p. Observatoire National. Annales.

HAWAIIAN ISLANDS.

p. Honolulu. — Bernice Pauahi Bishop Museum of Polynesian Ethnology.

Occasional Papers. — Fauna Hawaiiensis. — Memoirs.

HOLLAND.

Amsterdam—

t.p. Kon. Akademie van Wetenschappen. Verhandelingen : Afd. Natuurkunde.

lste Sectie. 2fce Sectie ; Afd. Letterkunde. — Yerslagen en Mededeelingen ;
Letterkunde. — Yerslagen der Zittingen van de Wis- en Naturkundige
Afdeeling. — Jaarboek. — Proceedings of the Section of Sciences. — Poemata
Latina.

t.p. Koninklijk Zoologisch Genootschap 11 Natura Artis Magistral Bijdragen

tot de Dierkunde.

p. Wiskundig Genootschap. Nieuw Archief voor Wiskunde. — Wiskundige

Opgaven. — Revue Semestrielle des Publications Mathematiques.

p. Delft. — itcole Poly technique. Dissertations.

t.p. Groningen. — University. Jaarboek.

t.p. Haarlem. — Hollandsche Maatschappij der Wetenschappen. Naturkundige
Yerhandelingen. —Archives Neerlandaises des Sciences Exactes et
Naturelles.

t.p. Musee Teyler. Archives.

t.p. Helder. — Nederlandsche Dierkundige Vereeniging. Tijdschrift.

t.p. Leyden. — The University.

p. Nijmegen. — Nederlandsche Botanische Vereeniging. Nederlandsch Kruidkundig

Archief. — Yerslagen en Mededeelingen. — Recueil des Travaux Botaniques
N eerlandaises.

t.p. Rotterdam. — Bataafsch Genootschap der Proefondervindelijke Wijsbegeerte.
Nieuwe Yerhandelingen.

p. Utrecht. — Provinciaal Utrechtsch Genootschap van Kunsten en Weten-

schappen. Yerslag van de Algemeene Yergaderingen. Aanteekeningen
van de Sectie Yergaderingen. 8vo.

Koninklijk Nederlandsch Meteorologiscb Institut. Observations Oceano-
graphiques et Meteorologiques. — CEuvres Oceanographiques. ( Presented .)

L' Observatoire. — Recherches Astronomiques. ( Presented .)

352

Proceedings of the Royal Society of Edinburgh. [Sess.

HUNGARY.

Buda-Pesth—

t.p. Magyar Tudomanyos Ahademia [. Hungarian Academy). Mathemat. es
term^szettud. kozlenienyek (Communications Math, and Nat. Sciences). —
Nyelvtud. kozlemenyek (Philology). — Mathemat. es termeszettud. Ertesito
(Bulletin, Math, and Nat. Sciences). — Nyelvtudom. Ertekezesek (Philol.
Memoirs). — Tortenettud. Ertekezesek (Historical Memoirs).— T&rsadalmi
Ertekezesek (Memoirs, Political Sciences). — Archseologiai Ertesito. — Rap-
ports.— Almanack. — Mathematische und Naturwissenschaftliche Berichte
aus Ungarn. — And other publications of the Hungarian Academy, or works
published under its auspices.

t.p. Kir-Magy. Termeszettudomanyi Tarsulat ( Royal Hungarian Society of Nat.
Sciences).

p. Magyar Kirdlyi Ornithologicii Kozpont [ Royal Hungarian Central-Bureau
for Ornithology). Aquila.

ICELAND.

p. Reikjavik. — Islenzha Fornleifafelag.

INDIA.

Bangalore. — Meteorological Results of Observations taken at Bangalore,
Mysore, Ilassan, and Chitaldroog Observatories ; Report of Rainfall Regis-
tration in Mysore. ( Presented by the Mysore Government.)

Bombay —

t.p. Royal Asiatic Society [ Bombay Branch). Journal.

t.p. Elphinstone College.

Archaeological Survey of Western India. Progress Reports. ( Presented .)

Government Observatory. Magnetic and Meteorological Observations.
[Presented.)

Burma. — Reports on Archaeological Work in Burma. ( Presented by the

Government.)

Calcutta —

t.p. Asiatic Society of Bengal. Journal and Proceedings. — Memoirs'.

Board of Scientific Advice for India. Annual Report. ( Presented .)

Ethnographical Survey [ Central Indian Agency). Monographs. [Presented.)

t.p. Geological Survey of India. Records. — Memoirs. — Palaeontologia Indica.

t.p. Meteorological Office, Government of India. Indian Meteorological Memoirs.
— Reports. — Monthly Weather Review.

Archaeological Survey of India. Epigraphia Indica. — Annual Reports. [Pre-
sented by the Indian Government.)

Botanical Survey of India. Records. 8vo. [Presented by the Indian
Government.)

Imperial Library. Catalogue. [Presented.)

Linguistic Survey of India. Publications. [Presented by the Indian

Government.)

1913-14.] List of Library Exchanges, Presentations, etc. 353

Calcutta — continued —

Royal Botanic Garden. Annals. ( Presented .)
t.p. Indian Museum. Annual Reports. — Records. — Memoirs. — Catalogues, etc.

Great Trigonometrical Survey. Account of Operations. — Records. —
Professional Papers. 4to. ( Presented .)

Fauna of British India, including Ceylon and Burma. 8vo. ( Presented by
the Indian Government.)

Indian Research Fund Association. Indian Journal of Medical Research.
{Presented.)

Scientific Memoirs, by Medical Officers of the Army of India. 4to.
( Presented .)

p. Coimbatore. — Agricultural College and Research Institute.

Madras —

t.p. Literary Society.

Observatory. Report on the Kodaikanal and Madras Observatories.

8vo. — Bulletins. — Memoirs. ( Presented .) 4to.

Government Central Museum. Report. ( Presented .)

A Descriptive Catalogue of the Sanskrit MSS. in the Government Oriental
Manuscripts Library, Madras. By M. Seshagiri Sastri. 8vo. {Presented
by the Government of Madras.)

Rangoon. {See Burma.)

Simla. Committee for the Study of Malaria. Transactions (Paludism).
{Presented by the Sanitary Commissioner.) 8vo.

IRELAND.

Belfast —

p. Natural History and Philosophical Society. Proceedings.

t.p. Queen's University. Calendar.

Dublin —

t.p. Royal Irish Academy. Proceedings. — Transactions. — Abstract of Minutes.
t.p. Royal Dublin Society. Scientific Proceedings. — Economic Proceedings. —
Scientific Transactions.
t.p. Library of Trinity College.

t.p. National Library of Ireland.

p. Dunsink Observatory.

Department of Agriculture and Technical Instruction for Ireland — Fisheries
Branch. Reports on the Sea and Inland Fisheries of Ireland (Scientific
Investigations). 8vo. — Geological Survey Memoirs. {Presented by the

Department.) 8vo.

ITALY.

Bologna —

t.p. Accademia di Scienze delV Istituto di Bologna. Memorie. — Rendiconti.

University Observatory. Osservazioni Meteorologiche. {Presented.)
t.p. Catania. — Accademia Gioenia di Scienze Naturali. Atti. — Bolletino Mensile.
t.p. Societa degli Spettroscopisti Italiani. Memorie.
t.p. Genoa. — Museo Civico di Storia Naturale. Annali.
p. Messina. — Reale Accademia Peloritana. Atti.

VOL. xxxiv. 23

354 Proceedings of the Royal Society of Edinburgh. [Sess.

Milan-
as. Osservatorio di Brer a. Publicazioni. ( Presented .)

t.p. Reale Istituto Lombardo di Scienze , Lettere , ed Arti. Memorie : Classe di
Scienze Mat. et Nat. ; Classe di Lettere Scienze Storiche e Morali. —

Rendiconti.

Modena —

t.p. Regia Accademia di Scienze, Lettere, ed Arti. Memorie.
p. Societd dei Naturatisti. Atti.

t.p. Naples. — Societd Reale di Napoli. Accademia di Scienze Fisiche e Matema-
tiche. Memorie. — Rendiconti. Accademia di Scienze Morali e Politiche.
Atti. — Rendiconti. Accademia di Archeologia, Lettere e Belle Arti.

Atti. — Rendiconti. — Memorie.
t.p. Stazione Zoologica. Mittheilungen.

t.p. R. Istituto d.lncoraggiamento. Atti.

p. Museo Zoologico della R. Universita. Annuario.

t.p. Padua. — R. Accademia di Scienze, Lettere, ed Arti. Atti e Memorie.
t.p. Palermo. — Societd di Scienze Naturali ed Economiche. Giornale di Scienze
Naturali ed Economiche.

p. Pisa. — Societd Italiana di Fisica. “II Nnovo Cimento.”

Rome —

t.p. R. Accademia dei Lincei. Classe di Scienze Fisiche, Math, e Nat. Memorie.

— Rendiconti. Classe di Scienze Morali, Storiche e Filol. — Notizie degli

Scavi di Antichita. — Rendiconti. — Memorie. — Annali delh Islam.
t.p. Accademia Ponteficia dei Nuovi Lincei. Atti. — Memorie.
t.p. Int. Institute of Agriculture. Monthly Bulletins.

t.p. R. Comitato G-eologico. Memorie descrittive della Carta Geologica. —

Bollettino.

t.p. Societd Italiana di Scienza (detta dei XL.). Memorie.
p. Sassari. — Istituto Fisiologico della R. Universita di Sassari. Studi Sassaresi.

Turin —

t.p. Reale Accademia delle Scienze. Memorie. — Atti.

Osservatorio della R. Universita. Osservazioni Meteorologiche. 8vo,
( Presented .)

t.p. Venice. — R. Istituto Veneto di Scienze, Lettere, ed Arti. Atti. — Osservazioni
Meteorologiche.

JAMAICA.

p. Kingston. — Institute of Jamaica.

JAPAN.

p. Formosa. — Bureau of Productive Industry. leones Plantarum Formosanarum.

p. Sendai. — Tohoku Imperial University. Science Reports. — Tohoku Mathe-
matical Journal.

Tokio —

t.p. Imperial University of Tokio ( Teikoku-Daigaku ). Calendar. — College
of Science. Journal. — Medicinische Facultdt der Kaiserlich-Japanischen

Universitat. Mittheilungen.

355

1913-14.] List of Library Exchanges, Presentations, etc.

Tokio— continued —

p. Zoological Society. Annotationes Zoologicse Japonenses.

p. Asiatic Society. Transactions,

p. Deutsche Gesellschaft fur Natur- und Volkerkunde Ostasiens. Mittheilungen.

p. Imperial Museum.

Earthquake Investigation Committee. Bulletin. ( Presented .)
t.p. Kyoto. — Imperial University (College of Science and Engineering). Memoirs.

JAVA.

Batavia —

t.p. Bataviaasch Geriootschap van Kunsten en Wetenschappen. Verhandelingen. —
Tijdschrift voor Indische Taal-, Land- en Yolkenkunde. — Notulen.
t.p. Magnetical and Meteorological Observatory. Observations. — Regenwaar-

nemingen in Nederlandsch-Indie. — Verhandelingen.
p. Kon. Natuurkundige Vereeniging. Natuurkundig Tijdschrift voor Neder-
landsch-Indie.

LUXEMBOURG.

p. Luxembourg. — Elnstitut Royal Grand-Ducal. Archives trimestrielles.

MAURITIUS.

t.p. Royal Alfred Observatory. Annual Reports. — Magnetical and Meteorological
Observations.

MEXICO.

Mexico —

t.p. Musee National d’Histoire Natur elle. La Xaturaleza, etc.

t.p. Sociedad Cientifica “ Antonio Alzate.” Memorias.

t.p. Observatorio Meteorologico-Magnetico Central. Boletin Mensual.

p. Istituto Geologico. Boletin. Papergones.

p. Academia Mexicana de Ciencias Exactas, Fisicas y Natur ales.

p. Tacubaya. — Observatorio Astronomico. Annuario. — Boletin.

MONACO.

t.p. Monaco. — Musee Oceanographique. Bulletins. — Resultats des Campagnes

Scientifiques.

NATAL. (See UNION OF S. AFRICA.)

NEW SOUTH WALES. (See AUSTRALIA.)

NEW ZEALAND.

Wellington —

t.p. New Zealand Institute. Transactions and Proceedings.

New Zealand Government. Statistics of New Zealand. — The New Zealand
Official Handbook. (Presented by the Government.)

Colonial Museum and Geological Survey. Publications. (Presented.)

356

Proceedings of the Royal Society of Edinburgh. [Sess.

NORWAY.

t.p. Bergen. — Museum. Aarsberetning. — Aarbog. — An Account of the Crustacea
of Norway. By G. 0. Sars.

Christiania —

t.p. K. Norske Frederiks Universitet. Nyt Magazin for Naturvidenskaberne. —
Archiv for Mathematik og Naturvidenskab.
t.p. Meteorological Institute. Jahrbuch.

Videnskabs-Selskab. Forhandlinger. — Skrifter (Math. Nat. Kl.). [Presented .)
p. Stavanger. — Museum. Aarshefte.

t.p. Throndhjem. — Kgl. Norske Videnskabers Selskab. Skrifter.
p. Tromso. — Museum. Aarshefter. — Aarsberetning.

PHILIPPINE ISLANDS.

p. Manila. — Bureau of Science. Ethnological Survey Publications. Bureau of

Forestry. Annual Report.

PORTUGAL.

t.p. Coimbra. — University. Annuario. Archivo Bibliographico. — Revista.

Lisbon —

t.p. Academia das Sciencias de Lisboa. Boletim. — Actas.
t.p. Sociedade de Geographia.

Observatorio do Infante D. Luiz. Annaes. ( Presented .)

Porto. Academia Polytechnica. Annaes Scientificos.

QUEENSLAND. {See AUSTRALIA.)

ROUMANIA.

Bucharest —

t.p. Academia Romana. Analele. Bulletin de la Section Scientifique. — Also
Publications relating to the History, etc., of Roumania. Bibliografia
Romanesca. — Catalogues, etc.
p. Institut Meteor ologique. Analele.

RUSSIA.

t.p. Dorpat (Jurjew). — University. Inaugural Dissertations. — Acta. — Sitzungs-
berichte der Naturforscher Gesellschaft bei der Universitat. — Schriften.
t.p. Ekatherinebourg. — Societe Ouralienne d: Amateurs des Sciences Naturelles.
Bulletin
Kazan —

t.p. Imperial University. Uchenuiya Zapiski.

p. Societe Physico-Mathematique de Kazan. Bulletin.

t.p. Kiev. — University. Universitetskiya Isvyaistiya.

1913-14.] List of Library Exchanges, Presentations, etc. 357

Moscow —

t.p. Societe Imperiale des Naturalistes . Bulletin. — Nouveaux Memoires.
t.p. V Observatoire Imperial. Annales.

t.p. Societe Imperiale des Amis dHistoire Naturelle, d Anthropologie et
d' Ethnographie.
t.p. Imperial University.

t.p. Musee Poly technique.

p. Observatoire Magnetique et Meteorologique de VUniversite Imperiale.

p. Odessa. — Societe des Naturalistes de la Nouvelle Russie. Zapiski.
t.p. Poulkova. — Nicolai Hauptsternwarte. Publications. — Annales.

St Petersburg —

t.p. Academie Imperiale des Sciences. Memoires : Classe Phys.-Math. ; Classe
Hist.-Phil. — Bulletins.

t.p. Commission Sismique Permanente. Comptes Rendus. — Bulletin.

t.p. Comite Geologique. Memoires. — Bulletins. — Carte Geologique : Region

Aurifere d’lenissei : de 1’ Amour : de Lena.

Commission Royale Russe pour la Mesure dun Arc de Meridien au Spitzberg.
Missions Scientifiques pour la Mesure d’un Arc de Meridien au Spitzberg
enterprises en 1899-1902, sous les auspices des Governements Suedois et
Russe. Mission Russe. 4to. ( Presented .)
t.p. Imperial University. Scripta Botanica.

t.p. Institut Imperial de Medecine Experimentale. Archives des Sciences

Biologiques.

t.p. Physikalische Central-Observatorium. Annalen.

t.p. Physico-Chemical Society of the University of St Petersburg. Journal.

t.p. Russian Ministry of Marine.

p. Imperial Russian Geographical Society.

p. K. Miner alogische Gesellschaft. Verhandlungen (Zapiski). — Materialien zur
Geologie Russlands.

p. Societe des Naturalistes ( Section de Geologie et de Miner alogie). Travaux et
Supplements.

p. Societe Astronomique Russe.

p. Tiflis. — Physikalisches Observatorium. Beobachtungen.

SCOTLAND.

t.p. Aberdeen. — University Library. Calendar. — University Studies. — Library

Bulletin.

p.

Berwickshire. — Naturalists ’ Club. Proceedings.

T.P.

Dundee. — University College Library.
Edinburgh —

T.P.

Advocated Library.

P.

Botanical Society. Transactions and Proceedings.
Carnegie Trust for the Universities of Scotland.

Report. ( Presented .)

P.

Faculty of Actuaries in Scotland. Transactions.

P.

Fishery Board for Scotland. Annual Reports.

Scientific Investigations. —

Salmon Fisheries. Fifth Report of the Fishery and Hydrographical Investi-
gations in the N. Sea and Adjacent Waters (1908—1911). Fol. Lond. 1913.

358

p.

T.P.

P.

P.

T.P.

T.P.

P.

T.P.

T.P.

T.P.

P.

T.P.

P.

T.P.

P.

T.P.

P.

P.

T.P.

T.P.

P.

P.

T.P.

T.P.

T.P.

T.P.

P.

P.

T.P.

Proceedings of the Royal Society of Edinburgh. [Sess.

Edinburgh — continued —

Geological Society. Transactions.

Geological Survey of Scotland. Memoirs, Maps, etc. ( Presented by H.M.
Government.)

Highland and Agricultural Society of Scotland. Transactions.

Mathematical Society. Proceedings. — Mathematical Notes.

Pharmaceutical Society. ( North British Branch).

Registrar-General’ s Returns of Births, Deaths, and Marriages. (Presented.)
Royal Botanic Garden. Notes.

Royal College of Physicians.

Royal College of Physicians’ Laboratory. Laboratory Reports.

Royal Medical Society.

Royal Observatory. Annals. — Annual Report.

Royal Physical Society. Proceedings.

Royal Scottish Academy. Annual Reports. (Presented.)

Royal Scottish Geographical Society. Scottish Geographical Magazine.

Royal Scottish Society of Arts. Transactions.

Scottish Meteorological Society. Journal.

Scottish National Antarctic Expedition. Publications. (Presented.)
University Library. Calendar.

Glasgow —

Geological Society. Transactions.

Royal Technical College. Calendar. (Presented.)

Inst, of Engineers and Shipbuilders in Scotland. Transactions.

Marine Biological Association of the West of Scotland. Annual Report.
See Millport.

Natural History Society. — Glasgow Naturalist.

Royal Philosophical Society. Proceedings.

University. Calendar.

University Observatory.

Millport. — Marine Biological Association of the West of Scotland . Annual
Report.

Perth. — Perthshire Society of Natural Science. Proceedings.

St Andrews. — University Library. Calendar.

SPAIN.

Madrid —

Real Academia de Ciencias Exactas , Fisicas y Naturales. Memorias. —
Re vista. — Annuario.

Instituto Geologico de Espaha. Boletin. — Memorias.

Vilafranca del Panades (Cataluna). — Observatorio Meteorologico.

SWEDEN.

Gothenburg. — Kongl. Vetenskaps och Vitterhets Samhdlle. Handlingar.

Lund. — University. Acta TJniversitatis Lundensis (Fysiografiska Sallskapets
Handlingar. — Theologi. — Medicina).

1913-14.] List of Library Exchanges, Presentations, etc. 359

t.p. Stockholm. — Kong. Svenska Vetenskaps-Akademie. Handlingar. — Arkiv for
Zoologi. — Arkiv for Matematik, Astronomi och Fysik. — Arkiv for
Botanik. — Arkiv for Kemi, Mineralogi och Geologi. — Meteorologiska
Iakttagelser i Sverige. — Astronomiska Iakttagelser. — Lefnadsteckningar. —
Arsbok. — Accessionskatalog. — Meddelanden fr&n K.Vetenskaps Akademiens
Nobelinstitut. — Les Prix Nobel.

p. Svenska Sallskapet for Antropologi och Geograji. Ymer.

Commission Roy ale Suedoise pour la Mesure Pun Arc de Meridien au
Spitzberg. Missions Scientifiqnes pour la Mesure d’un Arc de Meridien
au Spitzberg entreprises en 1899-1902, sous les auspices des Gouverne-
ments Suedois et Russe. Mission Suedoise. 4 to. ( Presented .)

Ups ala—

t.p. Kongliga Vetenskaps Societeten {Regia Societas Scientiarum). Nova Acta.

t.p. University. Arsskrift. — Inaugural Dissertations (Medical and Scientific). —
Bulletin of the Geological Institution.

Observatoire de V Universite. Bulletin Meteorologique Mensuel.

SWITZERLAND.

t.p. Basle. — Naturforschende Gesellschaft. Verhandlungen.

Bern —

Commission Geodesique Suisse. Arbeiten. {Presented.)
t.p. Societe Helvetique des Sciences Naturelles. {Allgemeine Schweizerische

Gesellschaft fiir die gesammten Naturwissenschaften.) Comptes Rendus. —
Actes (Verhandlungen). — Nouveaux Memoires.
p. Naturforschende Gesellschaft. Mittheilungen.

t.p. Geneva. — Societe de Physique et PHistoire Naturelle. Memoires. — Comptes
Rendus.

p. Lausanne. — Societe Vaudoise des Sciences Naturelles. Bulletin. — Observations

Meteorologiques.

Neuchatel —

t.p. Societe des Sciences Naturelles. Bulletin,

p. Societe Neuchateloise de Geographic. Bulletin.

Zurich —
t.p. University.

t.p. Commission Geologique Suisse. Beitrage zur geologischen Karte der

Schweiz.

t.p. Naturforschende Gesellschaft. Vierteljahrsschrift.
p. Schioeizerisclie Botanische Gesellschaft. Berichte (Bulletin).

Schweizerische Meteor ologische Central- Anstalt. Annalen. 4 to. {Presented.)

TASMANIA. {See AUSTRALIA.)

TRANSVAAL. {See UNION OF S. AFRICA.)

360 Proceedings of the Royal Society of Edinburgh. [Sess.

TURKEY.

p. Constantinople. — Societe Imperiale de Medecine. Gazette Medicate d’Orient.

UNION OF SOUTH AFRICA.

Cape Town —

p. Royal Society of South Africa. Transactions.

t.p. Royal Astronomical Observatory. Reports. — Annals. — Meridian Observations.
— Independent Day Numbers.

p. Geological Commission (now Survey). Annual Reports.
t.p. South African Museum. Annals.

p. South African Association for the Advancement of Science. Journal.

J OHANNESBURG

t.p. Geological Society of South Africa. Transactions and Proceedings.
t.p. Union Observatory. Circulars.

Pietermaritzburg —

p. Geological Survey of Natal. Annual Reports. — Reports on the Mining
Industry of Natal.

t.p. Government Museum. Annals. — Catalogues.

Pretoria —

Dept, of Mines — Geological Survey. Reports. — Memoirs. — Maps. [Presented.)
t.p. Transvaal Museum. Annals.

UNITED STATES OF AMERICA.

Albany —

t.p. New York State Library. Annual Reports. — Bulletins.

State Museum. Annual Reports. — Bulletin. Neiv York State Education
Department. Annual Reports,
p. Allegheny. — Observatory. Publications, etc.

p. Ann Arbor. — Michigan Academy of Sciences. Reports. ( University .)
p. Annapolis (Maryland). — St John’s College.
p. Austin. — Texas Academy of Sciences. Transactions.

t.p. Baltimore. — Johns Hopkins University. American Journal of Mathematics. —
American Chemical Journal. — American Journal of Philology. — University
Studies in Historical and Political Science. — Memoirs from the Biological
Laboratory. — U ni versity Circulars .

Johns Hopkins Hospital. Bulletins. — Reports. ( Presented .)
t.p. Maryland Geological Survey. Publications.

Maryland Weather Service. Reports. [Presented.)

Peabody Institute. Annual Reports. [Presented.)

Berkeley (California) —

t.p. University of California. — University Chronicle. — Reports of Agricultural
College. — Publications (Zoology, Botany, Geology, Physiology, Pathology
and American Archaeology and Ethnology). — Memoirs.

Academy of Pacific Coast History. Publications.

361

1913-14.] List of Library Exchanges, Presentations, etc.

Boston —

t.p. Bowditch Library.
t.p. Boston Society of Natural History. Memoirs. — Proceedings. — Occasional
Papers.

t.p. American Academy of Arts and Sciences. Memoirs. — Proceedings,
p. Brooklyn. — Institute of Arts and Sciences. Museum Reports. — Bulletins,

p. Buffalo. — Society of Natural Sciences. Bulletin.

California. ( See San Francisco, Sacramento, Berkeley, Mount Hamilton,
Mount Wilson and Stanford.)

Cambridge —

t.p. Harvard University. — Museum of Comparative Zoology. Memoirs. —
Bulletins — Annual Reports.

t.p. Astronomical Observatory , Harvard College. Annals. — Annual Reports. —
Observatory Circulars.

p. Chapel Hill (North Carolina). — E. Mitchell Scientific Society. Journal,
p. Charlottesville. Philosophical Society , University of Virginia. Bulletin ;

Scientific Series and Humanistic Series. — Proceedings.

Chicago —

t.p. Field Museum of Natural History. Publications : Geological Series ;

Botanical Series ; Zoological Series ; Ornithological Series ; Anthropo-
logical Series. — Annual Reports,
p. University of Chicago.

t.p. Yerkes Observatory ( University of Chicago). Publications,
p. Academy of Sciences. Bulletins. — Special Publications.— Bulletins of the
Natural History Survey.

Cincinnati —

p. Observatory (University). Publications. — University Record,

p. Society of Natural History. Journal.

t.p. Cleveland (Ohio). — Geological Society of America. Bulletins.
t.p. Clinton (Iowa). — Litchfield Observatory , Hamilton College.

Colorado Springs. — Colorado College. Colorado College Studies. (Pre-
sented.)

p. Connecticut. — Connecticut Academy of Arts and Sciences. Transactions.
— Memoirs.

p. Davenport. — Academy of Natural Sciences. Proceedings,

p. Denver (Colorado). — Scientific Society of Colorado. Proceedings.
t.p. Des Moines (Iowa). — Iowa Academy of Sciences. Proceedings,
p. Garrison, N.Y. — Editor, American Naturalist.

t.p. Granville (Ohio). — Denison University and Scientific Association. Bulletin of
the Scientific Laboratories.

p. Indianopolis. — Indiana Academy of Sciences. Proceedings.

Iowa City —

p. Geological Survey. Annual Reports.

p. State University. Laboratories of Natural History. Bulletins. — Contribu-
tions from the Physical Laboratories.

Iowa. ( See Des Moines.)

Ithaca (N.Y.) —

p. The Editor, Physical Review. (Cornell University.)

362

Proceedings of the Royal Society of Edinburgh. [Sess.

Ithaca (N.Y.) — continued —

p. The Editors, Journal of Physical Chemistry. (Cornell University.)
t.p. Lawrence (Kansas). — University of Kansas. Science Bulletin (University
Quarterly).

p. Lincoln (Nebraska). — University of Nebraska. Agricultural Experiment
Station. Bulletins.

Madison —

t.p. Wisconsin University. Washburn Observatory. Observations,

p. Wisconsin Academy of Sciences , Arts , and Letters. Transactions,
p. Geological and Natural History Survey. Bulletins,

p. Massachusetts. — Tufts College Library. Tufts College Studies,

p. Meriden (Conn.). — Meriden Scientific Association.

Michigan. ( See Ann Arbor.)

Minneapolis (Minn.) —

T I University of Minnesota. Studies. — Bulletin of the School of Mines.

( Geological and Natural History Survey of Minnesota. Reports,
p. Botanical Survey.

Missouri. (See St. Louis and Rolla.)

p. Mount Hamilton (California). — Lick Observatory. Bulletins. — Publica-

tions.

t.p. Mount Wilson (California). — Solar Observatory . Contributions. — Reports.
t.p. Newhaven (Conn.) — Yale College. Astronomical Observatory of Yale University.

Transactions. — Reports,
p. New Orleans. — Academy of Sciences.

New York —

t.p. American Mathematical Society. Bulletins. — Transactions.

t.p. American Museum of Natural History. Bulletins. — Memoirs. — American

Museum Journal. — Annual Reports. — Anthropological Papers. — Guide
Leaflets. — Handbook Series. — Monograph Series,
p. American Geographical Society. Bulletin,

p. American Institute of Electrical Engineers. Proceedings.

New York. (See also Albany.)

Philadelphia —

t.p. American Philosophical Society for Promoting Useful Knowledge. Proceedings.

— Transactions.

t.p. Academy of Natural Sciences. Proceedings. — Journal.

t.p. University of Pennsylvania. Publications : — Philology, Literature, and

Archaeology, Mathematics, etc. Contributions from the Zoological and
Botanical Laboratories. University Bulletins.— Theses. — Calendar.
t.p. Geological Survey of Pennsylvania.

p. Wagner Free Institute of Science. Transactions,

p. Geographical Society. Bulletin,

p. Commercial Museum.

p. Portland (Maine). — Society of Natural History. Proceedings,
p. Princeton, N.J. — University. Annals of Mathematics. — University Obser-
vatory. Contributions.

p. Rochester. — Academy of Science. Proceedings.

t.p. Rolla (Miss.).-— Bureau of Geology and, Mines. Biennial Reports, etc.

1913-14.] List of Library Exchanges, Presentations, etc. 363

t.p. [Salem. — Essex Institute.

Saint Louis —

t.p. Academy of Sciences. Transactions,

p. Missouri Botanical Garden. Annual Reports,

p. Washington University. University Studies.

t.p. San Francisco (California). — Academy of Sciences. Proceedings. — Memoirs.
— Occasional Papers.

Stanford (California). — University. Publications. ( Presented .)
p. Topeka. — Kansas Academy of Science. Transactions.

t.p, Urbana. — University of Illinois. Bulletins of State Geological Survey , State
Laboratory of Natural History , and Engineering Experiment Station .

Washington —

t.p. U.S. National Academy of Sciences. Memoirs.
t.p. Bureau of Ethnology . Annual Reports. — Bulletins.
t.p. U.S. Coast and Geodetic Survey. Annual Reports, etc.
t.p. U.S. Commission of Fish and Fisheries. Reports. — Bulletins.
t.p. U.S. Naval Observatory. Reports. — Observations.

t.p. U.S. Geological Survey. Bulletins. — Annual Reports. — Monographs. —

Geologic Atlas of the United States. — Mineral Resources. — Professional
Papers. — Water Supply and Irrigation Papers.

Geological Society of America. ( See Cleveland.)
t.p. Weather Bureau. (Department of Agriculture.) Monthly Weather Review.

— Bulletins. — Reports. — Bulletin of the Mount Weather Observa-
tory (now embodied in Monthly Weather Review).
t.p. Smithsonian Bistitution. Miscellaneous Collections. — The same (Quarterly
Issue). — Contributions to Knowledge.- — Reports. — Annals of the Astro-
physical Observatory. — Harriman Alaska Expedition, Yol. XIV. 4to.
t.p. Surgeon-General’s Office. Index Catalogue of the Library. 4to.
t.p. Carnegie Institution of Washington. Year-Books. — Publications. Classics

of International Law. — Carnegie Foundation for the Advancement of
Teaching. Annual Report. — Bulletin.
t.p. American Association for the Advancement of Science. Proceedings,
p. U.S. National Museum. Bulletins. — Reports. — Proceedings. — Contributions
from the U.S. National Herbarium.

p. Department of Agriculture. ( Division of Economic Ornithology and
Mammalogy.) Bulletin,
p. U.S. Patent Office.

Washington Academy of Sciences , Journal of the. (Purchase.)

Bureau of Standards. Department of Commerce and Labour. Bulletins.
(Presented. ) — Technologic Papers.

Wisconsin. (See Madison.)

VICTORIA. (See AUSTRALIA.)

364

Proceedings of the Royal Society of Edinburgh. [Sess.

List of Periodicals and Annual Publications added to the
Library by Purchase, etc.

Periodicals not found in this List will be found in Exchange List.

Annuals ( Works of Reference ), see end of List.

Acta Mathematica.

American Journal of Science and Arts.

* Naturalist.

* Journal of Mathematics.

* Chemical Journal.

* Journal of Philology.

Anatomischer Anzeiger.

Erganzungshefte.

Annalen der Chemie (Liebig’s).

* der Physik.

* der Physik. (Beiblatter.)

Annales de Chimie.

d’Hygiene Publique et de Medecine Legale.

de Physique.

des Sciences Naturelles. Zoologie et Paleontologie.

des Sciences Naturelles. Botanique.

Annali dell’ Islam. (Presented.)

Annals and Magazine of Natural History (Zoology, Botany, and Geology).

of Botany.

* of Mathematics. (Princeton, N.J.)

Anthropologie (L’).

Arbeiten-Zoologisches Institut der Universitat und der Zoologischen Station in Triest.

* Archiv for Mathematik og Naturvidenskab.

* Archiv fur Biontologie.

Archives de Biologie.

de Zoologie Experimental et Generale.

* des Sciences Biologiques.

des Sciences Physiques et Naturelles.

Italiennes de Biologie.

* Arkiv for Matematik, Astronomi och Fysik. (Stockholm.)

* for Kemi, Mineralogi och Geologi. ,,

* — - — for Botanik. „

* for Zoologi. ,,

Astronomie (L’).

Astronomische Nachrichten.

Astrophysical Journal.

Athenaeum.

Bericht iiher die Wissenschaftlichen Leistungen in der Naturgeschichte der niederen
Thiere. Begriindet von R. Leuckart.

Bibliotheque Universelle et Pevue Suisse.

See Archives des Sciences Physiques et Naturelles.

* Received by exchange.

1913—14.]

365

Purchases, etc., for the Library.

Biologisches Centralblatt.

Blackwood’s Magazine.

Bollettino delle Pubblicazioni Italiane. ( Presented .)

Bookman.

Botanische Zeitung.

Botanisclies Centralblatt.

Beiheft.

British Bainfall.

Bulletin Astronomique.

des Sciences Mathematiques.

Mensuel de la Societe Astronomique de Paris. See L’Astronomie.

Cambridge British Flora. By C. E. Moss.

Catalogue of Scientific Papers, 1800-1900. Subject Index.

Centralblatt fiir Bakteriologie und Parasitenkunde.

fiir Mineralogie, Geologie und Palseontologie.

Ciel et Terre.

Contemporary Review.

Crelle’s Journal. See Journal fiir Reine und Angewandte Mathematik.

Dictionary, New English. Ed. by Sir J. A. H. Murray.

Dingler’s Polytechnisches Journal.

Edinburgh Medical Journal.

Review.

Egypt Exploration Fund. Publications.

* Electrician.

Encyklopadie der Mathematischen Wissenschaften.

Engineering.

English Mechanic and World of Science.

* Essex Naturalist.

Fauna und Flora des Colfes von Neapel.

Flora.

Fortnightly Review.

* Gazette Medicale d’Orient.

* Geographical Journal.

* Geographical Magazine (Scottish).

* Geographie (La).

Geological Magazine.

Gottingische Gelehrte Anzeigen.

Indian Antiquary.

Engineering. {Presented. )

Indian Journal of Medical Research. {Presented.)

Intermediate (L’) des Mathematiciens.

International Catalogue of Scientific Literature.

Internationale Revue der Gesamten Hydrobiologie und Hydrographie.

Jahrbiicher fur Wissenschaftliche Botanik (Pringsheim).

Jahresbericht liber die Fortschritte der Chemie und verwandter Theile anderer
Wissenschaft.

Journal de Conchyliologie.

* Received by exchange.

366 Proceedings of the Koyal Society of Edinburgh.

Journal des Debats.

de Mathematiques Pures et Appliquees.

de Pharmacie et de Chimie.

* de Physique.

— — des Savants.

ftir die Eeine und Angewandte Mathematik (Crelle).

fur Praktische Chemie.

of Anatomy and Physiology.

of Botany.

of Pathology and Bacteriology.

* of Physical Chemistry.

* of the Boyal Society of Arts.

of the Society of Chemical Industry. ( Presented .)

— of the Washington Academy of Sciences.

Knowledge.

Manual of Conchology.

* Mathematische und Naturwissenschaftliche Berichte aus Ungarn.

Mind.

Mineralogical Magazine. {Presented.)

Mineralogische und Petrographische Mittheilungen (Tschermak’s).

Monist.

* Nature.

(La).

Neues Jahrbuch ftir Mineralogie, Geologie, und Palaeontologie

Beilage.

Nineteenth Century.

Notes and Queries.

Nuova Notarisia (De Toni).

* Nuovo Cimento ; Giornale di Fisica, Chimica e Storia Naturale.

* Nyt Magazin for Naturvidenskaberne.

Observatory.

Optical Society, London, Transactions.

Page’s Engineering Weekly. {Presented.)

Palseontographical Society’s Publications.

Petermann’s Mittheilungen.

— - Erganzungsheft.

* Pharmaceutical Journal.

Philosophical Magazine. (London, Edinburgh, and Dublin.)

* Photographic Journal.

* Physical Beview.

Plankton-Expedition Ergebnisse.

Quarterly Journal of Microscopical Science.

of Experimental Physiology.

Quarterly Review.

Ray Society’s Publications.

Registrar-General’s Returns (Births, Deaths, and Marriages). {Presented.)
Resultate der Wissenschaftliche Erforschung der Balatonsees.

* Received by exchange.

[Sess.

367

1913-14.] Purchases, etc., for the Library.

Review of Neurology and Psychiatry.

* Revue Generate des Sciences Pures et Appliquees.

Philosophique de la France et de l’Etranger

Politique et Litteraire. (Revue Bleue.)

Scientifique. (Revue Rose.)

* Semestrielle des Publications Mathematiques,

Saturday Review.

Science.

* Science Abstracts.

Progress.

Scotsman.

Scottish Naturalist.

Symons’s Meteorological Magazine.

Thesaurus Linguae Latinae.

Times.

Zeitschrift fur die Naturwissenschaften.

fiir Krystallographie und Mineralogie.

fiir Wissenschaftliche Zoologie.

Zoological Record.

Zoologische Jalirbiicher. Abteilung fiir Anatomie und Ontogenie der Tiere.

Abteilung fiir Systematik, Geographie und Biologie der Tiere.

Abteilung fiir Allgemeine Zoologie und Physiologie der Tiere.

Zoologischer Anzeiger.

Jahresbericht.

Annuals (Works of Reference).

Annuaire du Bureau des Longitudes.

Slater’s Directory. (Scotland.)

County Directory. (Scotland.)

Edinburgh and Leith Directory.

English Catalogue of Books.

Medical Directory.

Minerva (Jahrbucb der Gelehrten Welt).

Minerva (Handbuch der Gelehrten Welt).

* Nautical Almanac.

Oliver & Boyd’s Almanac.

University Calendars : — St Andrews, Edinburgh, Aberdeen, Glasgow, London
University College, Birmingham, Belfast, Sydney, N.S.W. ; also Calendar of
Royal Technical College, Glasgow.

W er ist’s ?

Whitaker’s Almanack.

Who’s Who.

Who’s Who in Science (International).

Willing’s Press Guide.

Year-Book of Scientific and Learned Societies of Great Britain and Ireland.
Zoological Record.

* Received by exchange.

368

Proceedings of the Royal Society of Edinburgh. [Sess.

Additions to Library by Gift or Purchase.

Andoyer (H.). Nouvelles Tables Trigometriques Fondamentales (Logarithmes).

4to. Paris, 1911. ( Presented by the Author.)

Burckhardt (J. -Ch.). Table des Diviseurs pour tous les nombres du Deuxieme
Million. 4to. Paris, 1814. ( Purchased .)

Cauchy (Augustin). QEuvres completes. lle Serie, Tome XI. 4to. Paris, 1913.

(Presented by the “ Academie des Sciences” Paris.)

Charcot (Dr Jean). Expedition Antarctique Francaise. Deuxieme (1908-1910).
Documents Scientifiques. Sciences Physiques ; Sciences Naturelles. (Several
parts.) 4to. Paris, 1913. ( Presented by the “ Minister e de V Instruction

Publique ,” Paris.)

Coal .Resources of the World. Yols. I.— III. and Atlas. Published under the
auspices of the XII. International Geological Congress, Canada, 1913. 4to.
Toronto, 1913. (Purchased.)

Commission of Conservation, Canada. Fourth Annual Report, 1913. (Committee
on Waters and Water Powers) — Long Sault Rapids, St Lawrence River : An
Inquiry into . . . Project to Develop Power therefrom. (Committee on
Forests) — Forest Protection in Canada, 1912. 4to. Toronto and Ottawa,
1913. (Presented by the High Commissioner for Canada.)

Commission Polaire Internationale. Proces-verbal de la Session tenue a Rome en

1913. 8vo. Bruxelles, 1913. (Presented.)

Fergusson (John C.). Fergusson’s “Percentage Unit” of Angular Measurement,
with Logarithms. 4to. London, 1912. (Presented by the Author.)

Geikie (James). The Antiquity of Man in Europe. (Munro Lectures, Edin-
burgh University, 1913.) 8vo. Edinburgh, 1914. (Presented by the
Author.)

.Mountains: their Origin, Growth, and Decay. 8vo. Edinburgh, 1913.

(Presented by the Author.)

Glaisher (James). Factor Tables for the Fourth, Fifth, and Sixth Millions. 4to.
London, 1879, 1880, 1883. {Purchased.)

Groningen, Academia Groningana MDCXIY-MCMXIY. 4to. Groningen, 1914.
(Presented, by Sir Edward Schafer.)

India, Census of, 1911. Yol. I. Part I. — Report. Part II. — Tables. Fol.

Calcutta, 1913. (Presented by the Government of India.)

Katanga, Rapport sur les Travaux de la Mission Scientifique du (1910-1912).
8vo. Bruxelles, 1913. (Presented by the “ Ministere des Colonies ,”
Bruxelles.)

Kristiania, Det. Kgl. Frederiks Universitets 100-aarsjubilseum, 1911. 4to.

Kristiania, 1913. (Presented by the University.)

Laurie (A. P.). The Pigments and Mediums of the Old Masters. 8vo. London,

1914. (Presented, by the Author.)

Louvain, Memories de Plnstitut Geologique de l’Universite de Louvain. Tome I.

4to. Louvain, 1913. (Presented by the University.)

M‘Gowan (J. P.). Investigation into the Disease of Sheep called “Scrapie.”
(Edinburgh and East of Scotland College of Agriculture.) 8vo. Edinburgh,
1914. ( Presented by the A uthor. )

369

1913-14.] Additions to Library by Gift or Purchase.

Millar (W. J.). Comparisons of some Chance Groupings with Mendel’s Laws.
(Buteshire Natural History Society.) 8vo. .Rothesay, 1914. ( Presented by

the Author.)

Moss (C. E.). Cambridge British Flora. Yol. II. — Salicaceae to Chenopodiaceae.
Fol, Cambridge, 1914. ( Purchased .)

Naperi De Arte Logistica. 4to. Edinburgh, 1839. ( Presented by the Misses

Sang ; originally presented to Dr Sang by the Editor , Mark Napier.)

Napier (Mark). Memoirs of John Napier. 4to. Edinburgh, 1834. (Presented by
the Misses Sang ; originally presented to Dr Sang by the Author.)

Philip (Alexander). The Reform of the Calendar. 8vo. London, 1914. ( Pre-

sented by the Author.)

Rayleigh (Lord). Scientific Papers. Vols. I-Y. 8vo. Cambridge, 1899-1912.
(. Presented by the Author.)

Sang (Edward). Elementary Arithmetic. 8vo. Edinburgh, 1856. ( Presented by

the Misses Sang.)

Higher Arithmetic. 8vo. Edinburgh, 1857. ( Presented by the Misses

Sang.)

Solution of Algebraic Equations of all Orders. 8vo. Edinburgh, 1829.

(Presented by the Misses Sang.)

Letters to, from Lieut. Shortrede, in connection with the preparation of

Shortrede’s Logarithmic Tables. Parinclia, India, 1836. (Presented by the
Misses Sang.)

Notice of Dioptric Light at Kirkcaldy. 8vo. Edinburgh, 1838. (Pre-
sented by the Misses Sang.)

Fifty Years’ Papers to the Royal Scottish Society of Arts. Jubilee

Presentation from the Fellows (1882). (Presented by the Misses Sang.)
Smith (J. G.). Strathendrick and its Inhabitants from Early Times. 4to.

Glasgow, 1896. (Presented by Sir William Bilsland.)

Solomon (J. I.). A Memorandum on the Pearl Fisheries of Ceylon. (Burma Shell
Co. Ltd.) Fol. Rangoon, 1909. (Presented by the Author.)

Stuckney, (J. J.). Table of Compound Interest at 1/8 per cent, and of Anti-
logarithms to Base 1 ‘00125. 4to. London, 1914. (Presented by the Author.)
Uppsala, Zoologiska Bidrag fran (med understbd af R. Biinsows Zoologiska Fond.).

Utgifna af A. Wiren. Bd. 1, 2. 8vo. Uppsala, 1911-13. (Presented.)
Yersluys (J.). Contribution a la Theorie de l’Ecoulement de l’Eau Souterraine.

8vo. Amsterdam, 1914. (Presented by the Author.)

Zeiller (C. R.). Palaeontological Pamphlets. 8vo. 4 to. Paris, 1905-1912. (Pre-
sented by the Author.)

VOL. XXXIV.

24

INDEX.

Abnormalities in Echinoids, by James Ritchie
and James A. Todd, 241-252.

Additions to Library, 368.

Address, Opening, from James Geikie, President,
4-9.

Analytical Study of the Mechanism of Writing,
by James Drever, 230-240.

Anderson (E. M.). The Path of a Ray of Light
in a Rotating Homogenous and Isotropic
Solid. See also Larmor., Sir Joseph, 69-76.

Antarctica, Notes on the Evolution of, by
T. W. Edgeworth David ( Title only), 296.

Atmosphere, Circulation of the, by W. N. Shaw.,
77-112.

Atmospheric Electrical Potential Gradient in
Industrial Districts, by Steuart and Jorgensen,
202-207.

Motion, Laws of, by W. N. Shaw, 79.

Persistence of, by W. N. Shaw, 88.

Structure, Computation from Soundings

with a Pilot Balloon, by W. N. Shaw, 97.

Auditory Organ in the Cetacea, by Sir Wm.
Turner, 10-22.

Australian Aboriginal. His relation to the
Tasmanian Aboriginal as deduced from a
S'tudy of the Calvaria. Part II. , by R. J. A.
Berry and A. W. D. Robertson, 144-189.

Berry (R. J. A.) and A. W. D. Robertson. The
place in Nature of the Tasmanian Aboriginal
as deduced from a Study of his Calvaria.
Part II. — His relation to the Australian
Aboriginal, 144-189.

Bigradients, Theory of, from 1859-1880, by
Thomas Muir, 32-59.

Buchner (L. W. G. ). A Study of the Curva-
tures of the Tasmanian Aboriginal Cranium,
128-143.

Bust of Lord Kelvin, Presentation of ( Frontis-
piece), 1-3.

Cetacea, Auditory Organ in, by Sir Wm.
Turner, 10-22.

Circulation of the Atmosphere, Study of, by
W. N. Shaw, 77-112.

Clague (T. M.). See Oliver, Sir Thomas.

Continuants, Some Factorable, by W. H.
Metzler, 223-229.

Convection of Air in the General Circulation of
the Atmosphere, by W. N. Shaw, 81, 107.

Court (Dorothy). Enzymatic Peptolysis in
Germinating Seeds, 113-127.

Cranium, Curvatures of the Tasmanian Abo-
riginal, by L. W. G. Buchner, 128-143.

Curvatures of the Tasmanian Aboriginal
Cranium, by L. W. G. Buchner, 128-143.

Darbishire (A. D.) and M. W. Gray. On the
Inheritance of Certain Characters of the Wool
of Sheep {Title only), 297.

David (T. W. Edgeworth). Notes on the
Evolution of Antarctica {Title only), 296.

Determinant, Some Factorable Minors of a
Compound, by W. H. Metzler, 27-31.

Drever (James). The Analytical Study of the
Mechanism of Writing, 230-240.

Echinoids, Abnormal, in the Collection of the
Royal Scottish Museum, James Ritchie and
James A. Todd, 241-252.

Enzymatic Peptolysis in Germinating Seeds, by
Dorothy Court, 113-127.

Exchanges, Library, List of, 340.

Fellows, Honorary, at January 1, 1915, 337-338.

Ordinary, Elected during Session 1913—

1914, 339.

List of Ordinary at January 1, 1915,

320-337.

Deceased and Resigned during Session

1913-1914, 339.

Four- dimensional Figure, Projection-Model of,
by D. M. Y. Sommerville, 253-258.

Geikie (Janies). Opening Address, 4-9.

Gibson (A. H. ). The Kinetic Energy of Viscous
Flow through a Circular Tube, 60-63.

Gibson (John), Obituary Notice of, 285-288.

Gray (M. W. ). See Darbishire, A. D.

Gunther (A. C. L. G. ), Obituary Notice of,
269-277.

Gunning Victoria Jubilee Prize, Regulations,
etc., for Award of, 305-311.

Hall, and Transverse Thermomagnetic Effects
and their Temperature Coefficients, by F.
Unwin, 208-222.

Eexadinellida, Siliceous Sponge of the Order,
from S. Shetland, by Sir Wm. Turner, 23-26.

Inheritance of Certain Characters of the Wool
of Sheep, by A. D. Darbishire and M. W.
Gray {Title only), 297.

Ionisation by Combustion, and Atmospheric Elec-
tricity, by Steuart and Jorgensen, 202-207.

Jorgensen (Invar). See Steuart, Dan. W.

Keith Prize, Award of, to James Russell, period
1911-1913, 298.

Regulations, etc., for Award,

305-311.

Kelvin (Lord), Presentation of Bust of {Frontis-
piece), 1-3.

370

Index.

371

Kinetic Energy of Viscous Flow through a
Circular Tube, by A. H. Gibson, 60-63.

Knott (C. G.). Changes of Electrical Resist-
ance accompanying Longitudinal and Trans-
verse Magnetizations in Iron and Steel, 259-
268.

Larmor (Sir Joseph). Note on Mr Anderson’s
Paper, ‘ ‘ Path of a Ray of Light in a Rotating
Solid,” 69-76.

Laurie (A. P. ). Obituary Notice of John
Gibson, 285-288.

Lead-poisoning, Electrolytic Treatment of. See
Thomas Oliver and T. M. Claque ( Title only),
296.

Library, Additions to, 368.

Library Exchanges, List of, 340.

Light, Path of a Ray of, in a Rotating Solid,
by E. M. Anderson, 69-76.

Mackay (John Sturgeon), Obituary Notice of,
278-284.

MTntosh (W. C.). Obituary Notice of

A. C. L. G. Gunther, 269-277.

M'Whan (J.). The Axial Inclination of Curves
of Thermoelectric Force : a Case from the
Thermoelectrics of Strained Wires, 64-68.

Magnetization, Longitudinal and Transverse,
Effect on Resistance of Iron, by C. G. Knott,
259-268.

Makdougall-Brisbane Prize, Regulations, etc.,
for Award of, 305-311.

Metzler (W. H.). Some Factorable Con-
tinuants, 223-229.

Some Factorable Minors of a Compound

Determinant, 27-31.

Minors of a Compound Determinant,

Some Factorable, 27-31.

Model of the 600-Cell in Space of Four Dimen-
sions, by D. M. Y. Sommerville, 253-
258.

Muir (Thomas). The Theory of Bigradients
from 1859-1880, 32-59.

Museum, Royal Scottish, Abnormal Echinoids
in the Collection of, by Janies Ritchie and
James A. Todd, 241-252.

Neill Prize, Award of, to W. S. Bruce, period

1911- 13, 298.

Regulations, etc., for Award, 305-311.

Obituary Notices of Fellows deceased in Session

1912- 1913. See President’s Opening Address,
4-9.

A. C. L. G. Gunther, 269-277 ;

John Sturgeon Mackay, 278-284 ; John
Gibson, 285-288.

Oliver (Sir Thomas) and T. M. Claque. The
Electrolytic Treatment of Lead-poisoning
( Title only), 296.

Oil-shales, Organic Matter in, by John B.
Robertson, 190-201.

Peptolysis, Enzymatic, in Germinating Seeds,
by Dorothy Court, 113-127.

Periodicals, etc., List of, 364.

Philip (George). Obituary Notice of J. S.
Mackay, 278-284.

Poisoning, Electrolytic Treatment of Lead-, by
Sir Thomas Oliver and T. M. Claque ( Title
only), 296.

President’s Opening Address, 4-9.

Prizes. See Keith, Makdougall-Brisbane, Neill,
and Gunning Victoria Jubilee Prizes, 305-11.

Resistance of Iron in Crossed Magnetic Fields,
Change of, by C. G. Knott, 259-268.

Ritchie (James) and James A. Todd. Abnormal
Echinoids in the Collection of the Royal
Scottish Museum, 241-252.

Robertson (A. W. D.). See Berry, R. J. A.

Robertson ( J ohn B. ). A Chemical Examination
of the Organic Matter in Oil- Shales, 190-201.

Rotating Solid, Path of a Ray of Light in, by
E. M. Anderson, 69-76.

Seeds, Enzymatic Peptolysis in, by Dorothy
Court, 113-127.

Shaw (W. N.). Principia Atmosph erica, a
Study of the Circulation of the Atmosphere,
77-112.

Sheep, Inheritance of Certain Characters of the
Wool of, by A. D. Darbishire and M. W.
Gray ( Title only), 297.

Siliceous Sponge of the Order Hexactinellida
from South Shetland, by Sir Wm. Turner,
23-26.

Smoke, and Atmospheric Electricity, by Steuart
and Jorgensen, 202-207.

Sommerville (D. L. Y.). Description of a
Projection-model of the 600-Cell in Space of
Four Dimensions, 253-258.

Sponge, Siliceous, of the Order Hexactinellida
from South Shetland, by Sir Wm. Turner,
23-26.

Steuart (Dan. W. ) and Ingvar Jorgensen.
N otes on the Atmospheric Electrical Potential
Gradient in the Industrial Districts around
Leeds, 202-207.

Tasmanian Aboriginal Cranium, A Study of the
Curvatures of, by L. W. G. Buchner, 128-143.

Tasmanian Aboriginal, His Relation to the
Australian Aboriginal as deduced from a
Study of his Calvaria. Part II. By R. J. A.
Berry and A. W. D. Robertson, 144-189.

Thermomagnetic Effects, Transverse, and Hall
Effect, Temperature Coefficients of, by F.
Unwin, 208-222.

Thermoelectric Force, Axial Inclination of
Curves of, by J. M‘Whan, 64-68.

Todd (James A.). See Ritchie, James.

Turner, Sir Wm. Note on a Siliceous Sponge
of the Order Hexactinellida from South Shet-
land, 23-26.

Observations on the Auditory Organ in

the Cetacea, 10-22.

Unwin, F. On the Hall and the Transverse
Thermomagnetic Effects and their Tempera-
ture Coefficients, 208-222.

Viscous Flow, The Kinetic Energy of, by A. H.
Gibson, 60-63.

Writing, The Analytical Study of the Mechanism
of, by James Drever, 230-240.

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MODEL INDEX.

Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly
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, 1902, pp.
, 1902, pp

IV

CONTENTS.

PAGE

Obituary Notices —

Dr A. C. L. G. Gunther, M.A., Ph.D., M.D., LL.D., F.R.S., etc.

By William C. MTntosh, . . . . .269

John Sturgeon Mackay, M.A., LL.D. By George Philip,

M.A., D.Sc., . . . . . 278

Professor John Gibson. By Principal A. P. Laurie, D.Sc., . 285

Appendix —

Laws of the Society, . . . . . . 293

The Keith, Makdougall-Brisbane, Neill, and Gunning Victoria

Jubilee Prizes, . . . . . . 298

Awards of the Keith, Makdougal] -Brisbane, Neill, and Gunning

Victoria Jubilee Prizes, ..... 300

Proceedings of the Statutory General Meeting, October 1913, . 305

Proceedings of the Ordinary Meetings, Session 1913-1914, . 306

Proceedings of the Statutory General Meeting, October 1914, . 312

Accounts of the Society, Session 1913-1914, . . . 313

The Council of the Society at October 1914, . . . 319

Alphabetical List of the Ordinary Fellows of the Society at

January 1915, ...... 320

List of Honorary Fellows of the Society, January 1915, . 337

List of Ordinary Fellows of the Society elected during Session

1913-1914, ....... 339

Honorary Fellows and Ordinary Fellows Deceased and Resigned

during Session 1913-1914, ..... 339

List of Library Exchanges, ..... 3A)

List of Periodicals Purchased by the Society, . . .364

Additions to Library during 1914, by Gift or Purchase, . . 368

Index, ......... 370

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