PROCEEDINGS

OF

THE EOYAL SOCIETY

EDINBURGH.

YOL. XIV.

NOVEMBER 1886 to JULY 1887.

EDINBURGH:

PRINTED BY NEILL AND COMPANY.

MDCCCLXXXVIII.

CONTENTS.

PAGE

Election of Office-Bearers, . . . . . 1

Chairman’s Opening Address, . . . . .2

Astronomical Tables for facilitating the Computation of Differential
Refraction, for Latitudes 56° and 57°-30. By the Hon. Lord
McLaren, . . . . . . . .21

On the Foundations of the Kinetic Theory of Gases. Part II. By
Professor Tait, . . . . . . .21

Fog Bow observed on Ben Nevis, 22nd October 1886. By R T.

Omond, Esq., Supt. B.N.O., . . . . . 24

Temperatures at Different Heights above Ground at Ben Nevis
Observatory. By R T. Omond, Esq., Supt. B.N.O., . . 24

Motion of Compound Bodies through Liquid. By the Rev. H. J.

Sharpe, M.A. Communicated by the President, . . .29

Note on Knots on Endless Cords. By A. B. Kempe, Esq. Com-
municated by Professor Tait. (Plate I.), . . . .36

On the Ring-Waves produced by throwing a Stone into Water. By
Sir W. Thomson, . . . . . . .37

On the Waves produced by a Ship advancing uniformly into Smooth
Water. By Sir W. Thomson, . . . . .37

Expansion of Functions in terms of Linear, Cylindric, Spherical, &c.,
Functions. By P. Alexander, Esq., M.A. Communicated by Dr
T. Muir, . . . . . . .37

On Even Distribution of Points in Space. By Professor Tait, . 37

Address on Processes of Refrigeration. By J. J. Coleman, Esq., . 38

On the Front and Rear of a Free Procession of Waves in Deep
Water. By Sir W. Thomson, . . . . .38

Numerical and other Additions to his Paper, read on 6th December
1886, on the Foundations of the Kinetic Theory of Gases. By
Professor Tait, . . . . . . .46

Intimation of an Improvement in Rankine’s Formula for Retaining
Walls. Given by Professor Armstrong on behalf of A. C. Elliott,

Esq., . . . . . . . .48

The Total Rainfall on the Land of the Globe, and its Relation to
the Discharge of Rivers. By J. Murray, Esq., Ph.D., V.P., . 48

Contents.

iy

PAGE

Chemical Affinity and Solution. By W. Durham, Esq., . . 48

Thermometer Screens. Part IY. By John Aitken, Esq. (Plates

II., III., IV.), . 53

On the General Effects of Molecular Attraction of Small Bange on
the Behaviour of a Group of Smooth Impinging Spheres. By
Professor Tait, . . . . . . .85

On a New Formula for the Pressure of Earth against a Retaining
Wall. By A. C. Elliott, Esq., B.Sc., C.E. Communicated by
Professor Armstrong, . . . . . .85

The Conducting Paths between the Cortex of the Cerebrum and the
Lower Centres, in relation to their Function. By Professor D. J.
Hamilton, . . . . . . . .97

Researches on Micro-Organisms, including ideas of a New Method
for their Destruction in Certain Cases of Contagious Disease. By
Dr A. B. Griffiths, F.R.S. (Edin.), . . . .97

On Cases of Instability in Open Structures. By E. Sang, Esq.,
LL.D., . . . . . . . .106

On the Increase of Electrolytic Polarization with Time. By W.

Peddie, Esq. Communicated by Professor Tait, . . . 107

Astronomical Notes. By Ralph Copeland, Esq., Ph.D. Communi-
cated by Lord McLaren, . . . . . .110

Further Determinations of the Effect of Pressure on the Maximum
Density Point of Water. By Professor Tait, . . .110

On the Height of the Land of the Globe above Sea-Level. By Dr J.
Murray, ........ 110

Note on the Effects of Explosives. By Professor Tait, . .110

Report on Fossil Fishes collected in Eskclale and Liddesdale. Part

I. Ganoidei — Supplement. By Dr Traquair, . . .111

On the Equilibrium of a Gas under its own Gravitation only. By

Sir W. Thomson, ....... Ill

On the Equilibrium of a Gas under its own Gravitation only. Part

II. By Sir W. Thomson, . . . . . .118

History of the Theory of Determinants. Part I. Determinants in

General : Hindenburg (1784) to Reiss (1829). By Dr Muir, . 118
Note on Solar Radiation. By John Aitken, Esq., . . .118

On Laplace’s Nebular Theory, considered in relation to Thermo-
dynamics. By Sir W. Thomson, . . . . .121

On a Class of Alternating Functions. By Dr Muir, . . .121

Note on Hoar-Frost. By John Aitken, Esq., . . .121

On the Quotient of a Simple Alternant by the Difference-Product
of the Variables. By Dr Muir, . . . . .125

Investigations on the Influence of certain Rays of the Solar Spectrum
on Root- Absorption and on the Growth of Plants. By Dr A. B.
Griffiths, F.R.S.E., F.C.S. (Lond. & Paris), and Mrs A. B.
Griffiths, . . . . . . . .125

Contents.

v

PAGE

Variations in the Value of the Monetary Standard. By Professor
Nicholson, . . . . . . .129

On Ice and Brines. By J. Y. Buchanan, Esq., . . .129

On the Distribution of Temperature in the Antarctic Ocean. By J.

Y. Buchanan, Esq., ....... 147

Note on a Formula for AM0*/ nl when n, i are very large Numbers.

By Professor Cayley, . . . . . .149

On the Fossil Flora of the Radstock Series of the Somerset and
Bristol Coal Fields. (Upper Coal Measures.) Part I. By R.
Kidston, Esq., F.G.S., ... ... 153

On the Achromatism of the Four-Lens Eye-Piece : New Arrangement
of the Lenses. By Edward Sang, Esq., LL.D., . . .153

An Effective Arrangement for Observing the Passage of the Sun’s
Image across the Wires of a Telescope. By Edward Sang, Esq.,
LL.D., . . . . . . .155

Observations on the Structural Characters of certain new or little-
known Earthworms. By Frank E. Beddard, Esq., M.A., Prosector
to the Zoological Society of London, and Lecturer on Biology at
Guy’s Hospital. (Plate V.), . . . . .156

On the Geology and Petrology of St Abb’s Head. By Professor
Geikie. (Plate VI.), ...... 177

Professor Rowland’s Photographs of the Solar Spectrum. Exhibited
by the Astronomer-Royal for Scotland, . . . .194

On Ship- Waves. By Sir W. Thomson, . . . .194

On the Instability in Fluid Motion. By Sir W. Thomson, . . 194

Experimental Research in Magnetism. By D. S. Sinclair, Esq.
Communicated by Principal Jamieson, .... 194

On the Summation of certain Series of Alternants. By A. H.

Anglin, Esq., M.A., LL.B., &c., .

Note on Cobaltic Alums. By Hugh Marshall, B.Sc.,

On the Effect produced on the Polarisation of Nerve by Stimulation.
By G. N. Stewart, Esq., ......

The Objective Cause of Sensation. Part III. — The Sense of Smell.

By Professor John Berry Hay craft, . . . .

On the Physics of Noise. By Professor Crum Brown,

On the Physical Properties of Methyl- Alcohol. By Professor Ditt-
mar and C. A. Fawsitt, Esq., .

On the Instability of the Double Sulphates

M"S04.R'2S04 + 6H20

of the Magnesium Series. By W. Dittmar, Esq.,

A Diatomaceous Deposit from North Tolsta, Lewis. By John
Rattray, Esq., .......

On the Increase of Electrolytic Polarization with Time. By W.
Peddie, Esq., B.Sc., ......

194

203

205

207

219

219

219

220

221

VL

Contents.

PAGE

On the BIoocl of Myxine. By Professor D’Arcy W. Thompson, . 221
On the Larynx and Stomach in Cetacea. By Professor D’Arcy W.
Thompson, ........ 221

On Transition Resistance at the Surface of Platinum Electrodes,
and the Action of Condensed Gaseous Films. By W. Peddie, Esq.,

B. Sc. (Plate VII.), 221

Researches on the Problematical Organs of the Invertebrata —

especially those of the Cephalopoda, Gasteropoda, Lamelli-
branchiata, Crustacea, Insecta, and Oligochseta. By Dr A. B.
Griffiths, E.R.S. (Edin.), F.C.S. (Bond. & Paris), Principal, and
Lecturer on Chemistry and Biology, School of Science, Lincoln;
late Lecturer on Chemistry, Technical School, Manchester, &c., . 230

The Nephridia of Lanice conchileqa , Malmgren. By J. T. Cunning-
ham, Esq., 238

On a Furnace capable of melting Nickel and Cobalt. By J. B.
Readman, Esq., ....... 240

On the Fossil Flora of the Radstock Series of the Somerset and
Bristol Coal Fields. Concluding Part. By R. Kidston, Esq., . 240
On the Discharge of Albumen from the Kidneys of Healthy People.

By Professor Grainger Stewart, M.D., .... 240

The Salinity and Temperature of the Moray Firth, and the Firths of
Inverness, Cromarty, and Dornoch. By Hugh Robert Mill, D.Sc.,
Scottish Marine Station. (Plate VIII.), .... 250

On the Presence of Bacteria in the Lymph, &c., of Living Fish and
other Vertebrates. By J. C. Ewart, M.D., Regius Professor of
Natural History, University of Edinburgh, . . . 262

On the Origin of the Great Alpine Lakes. By Professor Sacco,
University of Turin, ...... 271

On the Minute Oscillations of a Uniform Flexible Chain hung by
one End ; and on the Functions arising in the course of the In-
quiry. By E. Sang, Esq., LL.D. (Plate IX.), . . . 283

Note on the Biological Tests employed in determining the Purity of
Water. By A. W. Hare, Esq., M.B. Edin. (Plates X., XI.), . 306

Alternants which are Constant Multiples of the Difference-Product
of the Variables. By A. H. Anglin, Esq., M.A., . . .313

Glories, Halos, and Coronae seen from Ben Nevis Observatory.
Extracts from Log Book. By R. T. Omond, Esq. Communicated
by Professor Tait. (Plate XII.), ..... 314

Thermal Conductivity of Iron, Copper, and German Silver. By A.

C. Mitchell, Esq. Communicated by Professor Tait, . . 327

On the Probability that a Marriage entered into by a Man of any

Age, will be Fruitful. By T. B. Sprague, Esq., M.A., . . 327

On the Nephridia of Hirudo medicinalis. By Dr A. B. Griffiths,
F.R.S.E., F.C.S. (London & Paris), Principal, and Lecturer on
Chemistry and Biology, School of Science, Lincoln, . . 346

Contents.

VlL

PAGE

On Degenerated Specimens of Tulipa sylvestris. By Mrs A. B.

Griffiths. Communicated by Dr A. B. Griffiths, F.R.S.E., &c., . 349

The Luminous Organs of Nyctiphanes ‘ norvegica , Sars. By J. T.

Cunningham, B.A., and Rupert Yallentin, Esq., . . . 351

On a Constant Daniell Cell, for use as a Standard of Electromotive
Force. By Cosmo I. Burton, B.Sc., F.C.S., . . . 356

On Glories. By Professor Tait, ..... 358

Report on the Pennatulida dredged by H.M.S. u Porcupine.” By
A. Millies Marshall, M.D., D.Sc., M.A., F.R.S., Beyer Professor
of Zoology in the Owens College, and by G. H. Fowler, B.A.,
Ph.D., Berkeley Fellow of the Owens College, Manchester. Com-
municated by John Murray, Esq., Ph.D., .... 359

Stability of Fluid Motion. — Rectilineal Motion of Viscous Fluid be-
tween two Parallel Planes. By Sir W. Thomson, LL.D.,
F.R.S., . . . . . . . .359

Note on the Epiblastic Origin of the Segmental Duct in Teleostean
Fishes and in Birds. By George Brook, Esq., F.L.S., Lecturer on
Comparative Embryology in the University of Edinburgh. Com-
municated by Professor Sir Wm. Turner, F.R.S., . . . 368

Preliminary Note on the Chemistry of Strophantliin. By Thomas
R. Fraser, M.D., F.R.S., Professor of Materia Medica in the Uni-
versity of Edinburgh, ...... 370

On a New Diffusiometer and other Apparatus for Liquid Diffusion.

By J. J. Coleman, Esq., F.I.C., F.C.S., .... 374

On the Minute Structure of the Eye in certain Cymothoidse. By
Frank E. Beddard, Esq., M.A., F.Z.S., . . . .381

On the Mean Height of the Land of the Globe. By John Murray,

Esq., Ph.D., ........ 381

The Ghcetopoda Sedentaria of the Firth of Forth. By J. T. Cunning-
ham, Esq., B.A., ....... 381

Laws of Solution. Part II. By W. Durham, Esq., . . . 381

On the Partition of Energy between the Translatory and Rotational
Motions of a set of non-homogeneous Elastic Spheres. By Professor
W. Burnside. Communicated by Professor Tait, . . . 387

On the Salinity, Temperature, &c., of the Firth of Forth. By H. R.

Mill, Esq., D.Sc., ....... 387

The Direct Measurement of the Peltier Effect. By Albert Camp-
bell, Esq. Communicated by Professor Tait. (Plate XIII.), . 387
On some Vapour Densities at High Temperatures. By Alexander
Scott, Esq., M.A., D.Sc., ...... 410

On the Determination of the Plane Curve which forms the Outer
Limit of the Positions of a certain Point. By Dr C. Plarr. Com-
municated by Professor Tait, . . . . .415

The Thermal Windrose at the Ben Nevis Observatory. By A.
Rankine, Esq., ....... 416

vm

Contents .

page

On Ferric Ferricyanide as a Reagent for Detecting Traces of Reducing
Gases. By Professor Crum Brown, . . . .419

On the Compressibility of Water, of Mercury, and of Glass. By
Professor Tait, . . . . . . .419

An Account of some Experiments which show that Fibrin-Ferment
is absent from circulating Blood-Plasma, and which support the
view, first advanced by Sir Joseph Lister, that the Blood has no
spontaneous tendency to Coagulate. By Professor John Berry
Haycraft, ........ 419

On the Chemical Composition of the Water composing the Clyde
Sea Area. By Adam Dickie, Esq., .... 422

An Experimental Critique of the Chloroplatinate Methods for the
Determination of Potassium, including a redetermination of the
Constant Pt. By Professor Dittmar and Mr John M ‘Arthur, . 428

Addition to Thermometer Screens. Part IY. By John Aitken,

Esq., ........ 428

On the Quotient of a Simple Alternant by the Difference-Product of
the Variables. By Dr T. Muir, ..... 433

Chairman’s Closing Address, ...... 446

Minute of Meeting of Special Committee on the Victoria Jubilee
Prize, 27th June 1887, ...... 449

The Theory of Determinants in the Historical Order of its Develop-
ment. By Dr T. Muir, M.A., ..... 452

On the Conducting Paths between the Cortex of the Brain and the
Lower Centres in relation to Physiology and Pathology. By D. J.
Hamilton, M.B., F.R.C.S. Edin., F.R.S.E. , Professor of Pathology,
University of Aberdeen. (Plates XIV., XV.), . . .519

Donations to the Library, ...... 535

Index, ......... 555

Obituary Notices (see separate Index), . . . .561

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

vol. xiv. 1886-87. No. 123.

The 104th Session.

GENERAL STATUTORY MEETING.
Monday, 22 nd November 1886.

The following Council were elected : —

A. Forbes Irvine, Esq. of Drum.
David Milne Home, Esq. of Milne
Graden.

John Murray, Esq., Ph.D,

President.

Sir WILLIAM THOMSON, F.R.S.

Vice-Presidents.

Professor Sir Douglas Maclagan.
The Hon. Lord Maclaken.

Rev. Professor Flint, D.D.

General Secretary — Professor Tait.

Secretaries to Ordinary Meetings.

Professor Sir W. Turner, F.R.S.

Professor Crum Brown, F.R.S.

Treasurer — Adam Gillies Smith, Esq., C.A.

Curator of Library and Museum — Alexander Buchan, Esq., M.A.

Ordinary Members of Council.

Professor Chrystal.

Professor Dickson.

Professor Shield Nicholson.
T. B. Sprague, Esq.

Professor Butcher.

Professor M ‘Kendrick, F.R.S.

Thomas Muir, Esq., LL.D.
Professor MTntosh, F.R.S.
Robert Gray, Esq.

Dr Arthur Mitchell, C.B.
Stair Agnew, Esq., C.B.

R. M. Ferguson, Esq., Ph.D.

By a Resolution of the Society (19th January 1880), the following Hon.
Vice-Presidents, having filled the office of President, are also Members of the
Council : —

His Grace the DUKE of ARGYLL, K.T., D.C.L.

The Right Hon. LORD MONCREIFF of Tulliebole, LL.D.
THOMAS STEVENSON, Esq., M. Inst. C.E.

VOL. XIV, 15/7/87

A

2

Proceedings of Royal Society of Edinburgh. [eec. 6,

Monday, 6th December 1886.

♦

JOHN MURRAY, Esq., PhJD., Vice-President, in

the Chair.

1. Chairman’s Opening Address.

It is my privilege to welcome you at the commencement of this
new Session, which, from many indications, promises to be one of
great activity among the Fellows of the Society.

Since the close of last Session our esteemed President, Mr Thomas
Stevenson, has placed his resignation in the hands of the Council,
and, although asked to reconsider his decision, he urged, after con-
sultation with his physician, that, on account of his failing health,
he could not continue to hold a post, the duties connected with
which he was quite unable efficiently to discharge. I feel sure the
Fellows will join with me in hoping that Mr Stevenson may soon he
blessed with a return of good health, and that he may long continue
to he a contributor to the work of the Society.

Our new President, Sir William Thomson, is not a stranger to the
office ; when he last occupied the Presidential chair he conferred
many lasting benefits on the Society, and his re-election augurs well
for the future.

The vote recently taken among the Fellows, with reference to
the proposal to change the hour of the ordinary meetings of the
Society, has resulted in a majority for the usual hour of meeting
being retained. Still, as there was a large minority in favour of
some change, the Council will most probably arrange to hold some
meetings at four o’clock in the afternoon during the present Session.

Whether we look at the membership of the Society, the extent
and value of its publications, or the general activity of the members
with reference to scientific investigations, we have every reason to
congratulate ourselves on its prosperous condition, and to cherish
the notion that the Society has entered on the second century of its
existence with a vigour and prospect of usefulness unknown even at
any previous period of its career. This very prosperity, however,
brings with it new duties and responsibilities. Some new matters

1886.]

Chairman's Address.

3

of vital importance to the welfare of the Society are now forced on
the consideration of the Council and Fellows : it is to some of these
that I propose to refer this evening.

The membership of the Society, including Foreign and Honorary
Fellows, numbers at present 507, which is just about the strength
of the Royal Society of London. The number of ordinary Fellows
is, however, increasing at a somewhat rapid rate, and it is freely dis_
cussed, both among the Fellows and in the Council, whether the
time has not arrived when only a limited number of Fellows should
be elected each year ; — after the manner of the election to the
fellowship of the Royal Society of London and some foreign
societies.

At present, when a candidate is proposed by four or more Fellows,
the application remains for several weeks under the consideration of
the Council, and thereafter, if the Council be of opinion that the
candidate is likely to be a useful member of the Society, he is re-
commended to the Fellows for election. It would be a mistake to
suppose that all the names submitted to the Council are, as a matter
of course, recommended for election ; it not unfrequently happens
that names are withdrawn while under the consideration of the
Council, and some never pass the Council.

I have no hesitation in saying that I believe it would be a great
mistake to depart from this method of election, which has worked
so well in the past, and has secured as Fellows of the Society repre-
sentative men of all social positions, and from every department of
human activity and effort.

Why should we seek to limit the membership ? Every energetic
scientific man, and every man who is able and willing to assist in
any way in the discovery of new facts, new principles, new pro-
cesses, new knowledge, is a new strength to the Society, and should
be welcomed. If thirty or forty such men become candidates in
each year, let us have them all as Fellows ; the day has passed when
it is possible to number the elect either in science or literature !

If we were to adopt the system of selecting a definite number from
the candidates of each year — this means the placing of these can-
didates in a sort of competition with each other for the vacancies,
a most objectionable thing among grown-up men — we place a very
disagreeable duty on the Council; — canvassing would arise; dis-

4 Proceedings of Royal Society of Edinburgh. [dec. 6,

satisfaction would follow,, however carefully the selection be made ;
some men who would he most desirable Fellows would he prevented
from ever becoming candidates, and offence would he given to the
unsuccessful, whose names would ever afterwards be pilloried in
the Proceedings of our Society. A less objectionable plan would
be for the Council to invite a certain number of representative men
to become Fellows each year, hut it is doubtful if this would work
well so long as fellowship involves the payment of fees. There
seems to me nothing to fear from an increase in the number of
Fellows from year to year. The larger the membership, the more
are we likely to be in sympathy with the rapidly increasing number
of the general public who interest themselves in the acquisition
of new knowledge. We will be all the more powerful when we
approach the Government on matters of public interest, and none
the less able to give advice in Scottish scientific affairs. In his
anniversary address, a few days ago, to the Koyal Society of London,
the President suggests that that Society should be strengthened
by the election of a number of distinguished literary men. This
appears to be an admission that the election of fifteen from among
candidates each year does not secure that diversity which it is
desirable to have in a representative Society, and furnishes an
additional argument against the adoption of such a method of
election in our Society.

One of the best evidences of the prosperity of the Society is to
be found in the great increase in the size and value of the Society’s
publications. If we include the extra volumes on the Ben Nevis
observations and on the Botany of Socotra, which will shortly be
issued to the Fellows, then the Proceedings and Transactions of the
Society during the past three years probably surpass in bulk and
importance those of any other Society in the United Kingdom for
the same period. This must be gratifying to the Fellows, for the
money value of the publications in these years is greater than the
sums paid in annual fees. The illustrations for these papers have,
it is true, been a great drain on the funds of the Society, but the
money has been well spent. Just as it is the function of a Society
like this to publish in great detail new observations and discoveries,
which it would not pay an ordinary publisher to undertake, so
should the illustrations of these papers be kept up to a high standard

5

1886.] Chairmans Address.

of artistic merit. It is too often the case that the funds of Scientific
Societies demand that the cheapest and not the best shall be under-
taken in the matter of illustrations.

I commend it to some of the richer Fellows, if they might not
see their way to giving or bequeathing to the Society a fund from
which the Council might draw to assist in the careful and artistic
execution of such illustrations as may be inserted in the Society’s
publications.

The magnificent and valuable library of the Society, which Mr
Gordon informs me now approaches to twenty thousand volumes,
has been acquired chiefly by obtaining the Transactions and Pro-
ceedings of the other learned societies in exchange for our own.
Foreign societies have always paid us the compliment of placing
a high value on the work done by our Fellows, and published by
us. As a consequence we have not only the publications of the
great academies which have been long established in the great
capitals and other cities of Europe and America, but contributions
have flowed into the library from the remotest parts of the world :
from Shanghai, Hong-Kong, Japan, and Java in the far east, as
well as from our great dependencies and colonies of India, Australia,
and New Zealand. Again, we get Transactions and Proceedings
from the far west : from Rio de Janeiro, Buenos Ayres, Bolivia,
and Mexico, as well as from many rising cities and towns in the
United States and Canada.

At every meeting of the Library Committee fresh proposals of
exchange from Societies and Universities, not in scientific communi-
cation with us, have to be considered. As education and enlighten-
ment penetrate the various countries of the world, and extend their
vital influences to new centres of population, new societies are
formed, and, with the same desire for exchange on the part of the
new societies daily springing into life and activity, the acquisitions
of our library must go on increasing at a rapid rate, not only from
old but from new sources. In addition there are the donations
from Fellows and others, and the purchases which are made
annually. Unfortunately, the space at our disposal is now so
limited and inadequate that a considerable part of the library
cannot be referred to or consulted. This fact cannot be too widely
known, in order that active steps may be taken to provide a remedy.

6 Proceedings of Royal Society of Edinburgh. [dec. 6r

That remedy is not far to seek; in the new arrangements which
must follow the removal of the Antiquarian Museum, the Society’s
library should he spread over the greater part of this noble building,
which could not he devoted to a higher or better purpose than
accommodating, for the behoof of the leading scientific society of
Scotland, the literature of the learned Societies of all nations, — the
accumulated records of the scientific researches of the world.

The Council has considered it expedient to lay these facts regard-
ing the library before the Board of Manufactures, and has re-
quested the favourable consideration of the claims of the Society
for more space in this building.

For the prosecution of scientific investigations the Transactions
and Proceedings of learned societies are not only invaluable, but
indispensable. They fulfil the twofold purpose of showing what
has been accomplished in each department of science, and of serving
as starting points, on our part, of new advances into the unknown.

Mere scientific compilations, as distinguished from monographs,
however useful to the student, are comparatively of little service
to the investigator who is striving to extend the boundaries of his
science ; and it may be affirmed that many original researches, which
have conferred much honour on this Society, could not have been
successfully prosecuted without the aid derived from the literature
received from similar institutions showing what had most recently
been done in the same departments by workers in other parts of
the world.

It could be wished that the funds at the disposal of the Society
would permit of the acquisition of the records of scientific voyages,
which embody valuable original observations and investigations, as
well as numerous special monographs. Meanwhile, it is gratifying
to know that among the large and varied collection of memoirs
existing in this library, there are some which were searched for in
vain in the greatest of the metropolitan libraries, although that is
annually supported by large Government grants.

Let me give an illustration of the value of this Society and] its
library to the community.

When some six years ago I succeeded to the direction of the
work connected with the publication of the scientific results of the
“ Challenger ” Expedition, there was then no reason why the work

1886.]

Chairmans Address.

7

should be continued in Edinburgh, and I Avas on the point of re-
commending the Government to transfer the office to London,
chiefly on account of the difficulty connected with the access to a
fully equipped scientific library. Had the recommendation been
made it would, without much doubt, have been adopted. It was
not made, because I Avas assured by the Council of this Society that
every facility Avould be given to me, my assistants, and strangers
who might be engaged on “ Challenger ” work, for consultation of
books in the Royal Society library, and at the same time the Univer-
sity conferred certain privileges of a somewhat similar kind.

I suppose it is not altogether a matter of indifference to Scots-
men to know that the work connected with the largest scientific
publication ever issued by any country or age, has been chiefly
carried out in Edinburgh, or that Edinburgh would have liked it to
be said that, having once been commenced here, it Avas impossible
to carry it on in this city. But over and above the mere sentimental
aspect of the matter, the retention of the “Challenger” Office in Edin-
burgh has been a distinct material advantage to the country, for
the work which has been given to printers, binders, lithographers,
artists, wood engravers, and others, represents the expenditure of
many thousands of pounds annually. Then, there is the indirect
advantage of having many scientific men from abroad coming and
carrying on work here for short periods of time, and I am bound to
say some of them Avould have remained much longer had the library
facilities been better. Again, some special industries, such as litho-
graphy, have in consequence been greatly developed in our midst.
When the “ Challenger ” Avork was first commenced, it was believed
to be impossible to have the finest kind of lithographic and engrav-
ing work done in the United Kingdom; some authors even stipulated
that their illustrations should be done abroad. But noAv this litho-
graphic work can be done as well here as anywhere in the world, if
not better ; and I frequently receive from abroad requests to have
this kind of Avork undertaken by Edinburgh firms. It seems to me,
then, that anything that can be done to increase the completeness
or accessibility of the Royal Society library is to be regarded, not as
a favour conferred upon a small body of savants, but as a direct
boon to the city and the country of which it is the metropolis.

A Society like ours has a very special interest in seeing a truly

8 Proceedings of Royal Society of Edinburgh. [dec. 6,

complete national library established in Scotland, for to scientific
and literary investigators such a library is the most important
instrument of research. We must all of us rejoice that there is to
be a Free Library in Edinburgh, and it is to be hoped that it will
be established so as to give the public the freest possible access
to all the ordinary standard works and current literature. It may
even be hoped that the directors of the institution will be able to
specialise to some extent in the reference library, so as to embrace
works not now to be had in Edinburgh.

It must be remembered, however, that this Free Library will
mainly be a duplication of books already in Edinburgh libraries.
It in no way solves the question of a National Scottish Library,
which is the great desideratum for all engaged in the study of science
and literature.

There is a great wealth of libraries in Edinburgh, but they are to
a large extent inaccessible from want of room or from the antiquated
machinery connected with their proper consultation. There is a
popular belief that the Advocates’ Library contains every English
book. As a matter of fact, it is very defective in the literature of
some periods ; it lacks many important provincial publications, and
is of course very deficient in Indian, Colonial, and American works,
which are every year becoming more important. There are rela-
tively few foreign works in the Advocates’ Library, and were it not
for the excellent series of foreign treatises in the University Library,
Edinburgh would be very poorly supplied in this respect.

If I wish to consult all the authorities who have described the
ice of the Antarctic regions, I can find only some of the books in
Edinburgh. If I wish to consult the original authorities who have
described the desert of Sahara, I can. find only one or two of them
in the Edinburgh libraries. Gaps like these are not confined to
scientific or geographical works. Socialism is a subject not in the
background at present, yet one will seek in vain among our libraries
for some of the works of the best-known continental exponents of
the theory.

Every true Scotsman has an interest in seeing these defects speedily
remedied.

It is much to be regretted that there is no organisation by which
reference to the various libraries in Edinburgh could be facilitated

1886.]

Chairmans Address.

9

to those engaged in scientific and literary work. I have never
received a hook from the Advocates’, Physicians’, and some other
libraries without being indebted to the courtesy of some member of
these bodies; and although this be always willingly given, it becomes
irksome to all parties when repeated week after week. In connec"
tion with our “Challenger” work, we often find it more convenient
and expeditious to get books from London than from certain of the
Edinburgh libraries. It is not for the credit of the city that this
should be the case. I cannot but think that it would be a great
advantage to form a central board, composed of representatives of
the different library-owning societies and corporations of the city.
Such a board would do good service by preventing the duplication
of purchases among the various libraries where unnecessary. It
might have the power of granting the privilege to investigators of
consulting all the libraries to a limited extent ; but, more important
still, it might draw up a scheme for a National Library — a scheme
which, while allowing existing libraries to develop on their present
lines, would yet erect one of them, say the Advocates’, into a
National Library, whose function it would be to supplement or fill
up in those departments not embraced by the other libraries. It
seems to me that some such scheme would command support.

When we remember the large sums of public money that are
annually spent on national libraries in London, and that in addition
to the cost of buildings and maintenance, about ,£18,000 has been
spent during the past ten years on salaries and purchase of books
for the National Library in Dublin, then surely the claims of Scot-
land deserve some consideration. Were a good workable scheme
drawn up by some of our leading men, and supported by the public
generally, then even Scottish Parliamentary representatives might
awake to the fact that there are some Scottish questions worthy of
their attention and combined action.

Some time ago the Council of the Society drew the attention of
the Government to the fact, that no bathymetrical survey of the
Scottish freshwater lochs existed, except those of Loch Lomond and
Loch Awe; and urged the importance, in many branches of scientific
inquiry, of knowing the depth and form of such basins as Lochs
Morar, Maree, Lochy, Assynt, Linn, Tay, Ericht, with many others,

10 Pi ' oceedings of Poyal Society of Edinburgh . [dec. 6,

and expressed the hope that these surveys would be undertaken
at an early date, and, at all events, before the completion of the
Ordnance Survey of the country. The reply from the Treasury
was that these surveys could not be sanctioned, because they did
not come within the function of the Board of Admiralty or of the
survey department of the Office of Works. This matter was subse-
quently brought up in Parliament by Lord Balfour of Burleigh, but
no steps seem to have been taken to carry out the survey. It may
be hoped that this matter will not be allowed to drop. Quite
recently soundings of 175 and 180 fathoms have been obtained in
Loch Morar. This is the greatest depth that has hitherto been
found on the plateau on which the British Islands are situated ; to
get depths equal to this we must go towards the deep gut off the
coasts of Norway, or beyond the 100-fathom line off the coasts of
Ireland. There are also geological and biological problems of great
interest connected with the depths of these lochs.

Should these surveys not be undertaken a very important part of
the survey of the United Kingdom will be left untouched ; for it
cannot be denied that it is at least as important — sometimes much
more important — to know the depth of a lake than to know the height
of an adjoining mountain. It would be a matter for great regret if
the admirable surveys, which are now drawing to a close, and which
reflect so much credit on the officers who conducted them, and
honour on the scientific reputation of the country generally, should
be lowered in value by the great omission here pointed out.

The Council has recently had before it the subject of Antarctic
exploration, and has drawn up and printed a number of suggestions
as to the investigations which should be undertaken or attempted
in the event of such an expedition being fitted out. There can be
little doubt that a thorough exploration of these unknown regions
would enrich almost every branch of science with valuable observa-
tions ; the Antarctic appears to exert a controlling influence on the
atmospheric and oceanic circulation and magnetism of the globe, and
presents many interesting physical, geological, and zoological problems.
No steam vessel, protected for ice, has ever penetrated these seas,
and there are good reasons for believing that such vessels would be
able to find a place for wintering close to the land of the Antarctic

1886.]

Chairman’ s Address.

11

continent. We have at present no knowledge of the condition of
the Antarctic regions except during the summer months of January.
February, and March, and, although the first endeavour to pass a
winter in these regions would doubtless he accompanied with con-
siderable risk, still it must be attempted, and the duty of attempt-
ing it lies heavier on Great Britain than any other nation. If Great
Britain is to hold her proper position among the family of nations
she must explore the Antarctic, and it is to be hoped that the
numerous learned Societies of the United Kingdom will before long
press the matter on the attention of the Government.

During the past few years there has been great activity in the
examination of the biological conditions of the coasts, lochs, and
estuaries of Scotland, and some of the more important results have
appeared, or are about to appear, in the Transactions and Proceedings
of the Society.

In connection with the Scottish Marine Station, carried on under
the auspices of the Scottish Meteorological Society, there has been
conducted during the past three years a very valuable series of in-
vestigations into the physical and chemical conditions of the Firths
of Forth and Clyde, and various rivers and estuaries, which are of
great importance to a right understanding of the general meteor-
ology of the country.

The little steamer of the Station, fitted with the most approved
apparatus, has been constantly at work at all times of the year.
Three years’ observations on the Forth have given the general
conditions with regard to temperature and salinity for all seasons,
with the laws of their changes.

About the time of the vernal equinox all the water of the Firth
is of a uniform temperature ; there is a gradient of temperature
from river to sea and from surface to bottom in summer, the
warmest water being on the surface and towards the land. In
winter this state of matters is entirely reversed, at the autumnal
equinox there being again a uniform distribution of temperature.

Nearly a year’s observations have been completed on the much
more complicated and varied region of the Clyde. Here a vast
amount of heat is stored up in the waters of the deep lochs during
summer, and slowly given out again to the air during the winter
months, thus greatly modifying the climate of the West Coast of

12 Proceedings of Royal Society of Edinburgh. [dec. 6,

Scotland — a condition of things to which there is apparently
nothing analogous on the East Coast.

This influence is due to the great depth of the lochs and their
exposure to summer heat, and does not appear to he entirely inde-
pendent of the effects produced by the warm Atlantic water, which
flows over the shallow ridge stretching from Can tyre to the Ayr-
shire coast. Some of the preliminary results of these researches
have been presented to the Society by Dr Mill, hut all the observa-
tions are now in course of preparation for publication, and will
furnish physicists and meteorologists with many much-needed data.

I have already referred to the extra volume of the Society’s
Transactions , containing the Ben Nevis Observatory observations,
which will shortly be in the hands of the Fellows. Among meteor-
ologists in all parts of the world there has long been a desire
expressed to be furnished with copies of the Ben Nevis observa-
tions, and as the Directors have no funds for the purpose, the
Council have in the circumstances considered it a duty to under-
take their publication.

The Fellows are reminded that the Observatory buildings and
the road thereto are the property of the Royal Society of Edin-
burgh, that several donations from the Society’s funds were made
towards covering the expenses of the preliminary observations
before the erection of the permanent Observatory, and that the
direction of the Observatory is largely in the hands of the repre-
sentatives and Fellows of this Society. The Society has, therefore,
a deep interest in all that concerns the welfare of this unique high-
class Observatory.

As you are aware, the Observatory was erected in the summer of
1883, and formally opened by Mrs Cameron Campbell of Monzie,
the proprietrix of the land, on 17th October ; immediately thereafter
Mr Omond and two assistants went into residence, and the regular
work of hourly observations began in the end of November; the
Observatory was equipped with the best instruments that could be
obtained, several of these being of a novel character, suited to the
peculiar climate of the Observatory and to the new lines of observa-
tion it was proposed to carry out.

Ben Nevis was selected not merely as the highest mountain in

1886.]

Chairman s Address.

13

Great Britain, and situated in the very track of the south-westerly
winds from the Atlantic, which exercise so preponderating an
influence on the weather of Europe, hut because it rises to a height
of 4406 feet so close to the sea that a sea-level station may be
placed at about 4 miles from the summit — a consideration which
gives a value altogether unique to the observations.

The low-level station was established at Fort William, under the
charge of Mr Livingstone, of the Public Schools, at which observa-
tions are made five times each day, and with these are conjoined a
barograph and thermograph for the continuous record of these im-
portant elements of climate — atmospheric pressure and temperature.
Three years’ observations at this pair of stations have already been
made, and it is these which are now in the hands of the printer, and
will shortly appear as a volume of the Society’s Transactions.

The climatic difficulties were great, but they were successfully
surmounted (1) by the skill of the architect, Mr Sydney Mitchell,
who constructed the buildings, (2) by the heroic endurance and
fertility and readiness of resource displayed by Mr Omond and his
staff of assistants in meeting emergencies as they arose.

At most, if not all, other observatories only a comparatively few
of the observations are made by the observers personally, the usual
course being to use continuously recording instruments from which
the omitted hours are interpolated. But on Ben Nevis every re-
corded observation is actually noted by the observers. Further, it
usually happens that the observations of the temperature, humidity,
and movements of the air, and the rainfall are automatically recorded.
But on Ben Nevis, during the larger portion of the year, owing to
the snow-drifts and ice-incrustations formed on the instruments as
well as on everything outside the Observatory exposed to the wind,
these observations cannot, and, it may be confidently predicted,
never can, be made by self-recording instruments. Hence, if meteor-
ology and weather prediction are to make advances in those funda-
mental inquiries, which can be successfully prosecuted only by the
help of high-level observatories, the time will never come when such
heroic services as are now rendered to science by Mr Omond can be
dispensed with. Even barometric observations could not be utilised
in these inquiries, unless there be conjoined with them observations
of the temperature and the movements of the atmosphere.

14 Proceedings of Royal Society of Edinburgh. [dec. 6,

The high expectations formed of the great importance of this
Observatory have already been more than realised. The following
are among the more prominent of the results obtained from this
pair of high and low level stations : —

1. The rate of decrease of temperature with height has been
more correctly ascertained.

2. The rate of decrease of atmospheric pressure with height for
the different sea-level pressures and air-temperatures has been ascer-
tained with a high degree of accuracy.

3. The relations of the readings of the dry and wet bulb hygro-
meter to the vapour of the atmosphere have been worked out, under
the extraordinarily dry states of the air which are of such frequent
occurrence on the top of the mountain, from observational data to
a degree of accuracy not hitherto attained.

These results will, doubtless, in future be incorporated in all
books on meteorology and general physics.

As regards weather forecasting, the Ben Nevis observations con-
tribute information of such a value as no low-level observatory,
however efficiently equipped and superintended, can for a moment
lay claim to ; and it is to be enforced here, that when the Directors
are placed in a position to raise the five daily observations at Fort
William to twenty-four, the value of the Ben Nevis observing
system will be immensely enhanced. In other words, the Directors
of the Observatory attach the greatest importance to the establish-
ment of a low-level observatory at Fort William, at which observa-
tions could be made with the same fulness as at the Observatory on
the top of the mountain.

The great value attached to the observations of high-level observa-
tories is attested by the continued additions made to these stations
in different parts of the world, and by the observations made at
these stations many of the more important questions of meteorology
may doubtless be investigated. But there is no other high-level
observatory, and its conjoined low-level station, so happily situated
as Ben Nevis Observatory and the station at Fort William for sup-
plying physicists with observational data. This is due to the fact
that the former is on a peak and the latter close to the sea, the
ground sloping down to it, hy which the effects of solar and terres.
trial radiation are minimise'!.

1886.]

Chairmans Address .

15

It is only a few months ago that an inquiry, conducted on
scientific principles, into the hearing of the observations at the
Observatory and at the base of the mountain could he entered upon,
and its completion will necessarily occupy some time, owing to the
complex character of the problems to he dealt with.

The erection and maintenance of the Observatory during the past
three years have cost over <£7000, the funds having been obtained
solely from private subscriptions and learned Societies. During
this time the Directors have had to pay to the post office depart-
ment a rental of <£133 per annum for the use of the telegraph
wire from Fort William to the top of the mountain. In addition
to' this, the post office have received considerably over £100 for
tourist messages forwarded from the Observatory by Mr Omond and
his assistants. The daily despatch of the observations to the press
throughout the country is also a source of considerable income to
the post offi ;e department. It appears then that this Observatory,
established solely for the purposes of scientific investigation, instead
of being assisted by the Government, is actually a source of revenue
to a Government department.

You are aware that a sum of £15,000 is voted annually by
Parliament for general meteorological purposes, but more particu-
larly the meteorology of the British Islands. This grant is admini-
stered by a committee nominated by the Royal Society of London,
called the Meteorological Council. Although Ben Nevis Observatory
is certainly the best and most important meteorological observatory
in the United Kingdom, yet it has received no support from this
grant, if we except the annual sum of £100 which is paid on
condition of being supplied with a complete set of all the observa-
tions,— a bare equivalent for the mere clerk work required. In
1884 an application for £300, from the £15,000 grant, towards
the expenses of the Observatory was refused.

The Meteorological Council also intimated to the Directors that
they did not propose to have the observations at Ben Nevis wired
to London for use in making up the weather forecasts, until the
result of Mr Buchan’s discussion of the observations was completed;
but they offered no assistance towards carrying out that discussion,
although £1000 of the £15,300 is expressly stated to be for the
purposes of original investigation

16 Proceedings of Royal Society of Edinburgh. [dec. 6,

An application to the Government Grant Committee of the
Boyal Society of London for aid towards the expenses of the
Observatory has likewise been unsuccessful.

The refusal of assistance by the London Committees may be
partly due to the fact that there are many claims on the funds
which they administer, but it appears also to be very largely due
to a want of proper knowledge of what has been done, and what
may be reasonably expected to be done by the Observatory, there
being no observatory in these islands that can compete with the
Ben Nevis Observatory for the accuracy and intrinsic value of the
hourly observations ; and absolutely no pair of stations anywhere
in the world that can be named alongside the Observatory and the
station at Fort William, as contributing data in furtherance of our
knowledge of storms and the science of weather generally.

The Directors have given much time and thought to the affairs
of the Observatory during the past four years, and to many of them
it has been a cause of considerable personal expenditure, for the
expenses connected with frequent visits made to Ben Nevis for the
selection of the site, during the building and equipment of the
Observatory, and its subsequent inspections, have in no case been
charged against the Observatory funds, but have been borne by the
individual Directors. Not only so, but it has happened more than
once that some one of the Directors has placed considerable sums
to the credit of the Observatory in the bank, to enable the work to
go on without an hiatus.

The time has now arrived when it is necessary to place the
Observatory on some permanent footing, but before another appeal
is made to the public, the Council of this Society has resolved to
urge the claims of the Observatory on the consideration of the
Government, and to ask for a substantial donation towards the
annual expenses. In this, I feel sure, the Council will have the
support, not only of the Fellows of the learned Societies of Scotland,
but of the general public.

In the infancy of science it was possible, with simple and inex-
pensive appliances, to discover important facts which were lying as
it were on the surface, but no discoveries can now be expected
except by rising high above the surface, as in the case of Ben Nevis,
or descending far below it, as in the case of the exploration of our

1886.]

Chairman's Address.

17

deep lochs by means of a steam vessel and the most recent apparatus
for sounding, dredging, and taking temperatures ; the consequence
is that such scientific investigations cannot he undertaken even by
scientific men with private fortunes, and hence follows the necessity
for Government assistance.

From the estimates it appears —

1. That the Royal Society of London and five or six other learned
societies are accommodated in Burlington House free of rent.

2. That the Royal Geographical Society receives a grant of <£500
annually.

3. That there is an annual grant of £15,000 for meteorological
purposes, administered by a committee of the Royal Society of
London, £1000 of which is to be devoted to original investigations.

4. That a sum of £4000 is administered by the Government
Grant Committee of the Royal Society of London for scientific
research, and although that society is, in a sense, the representative
society of the United Kingdom, still its Council and Committees are
of necessity composed of Fellows resident in, or within accessible
distance of, London, the Fellows resident in Scotland being practi-
cally excluded from active participation in the management of the
Society.

5. That the Marine Biological Association has recently received
£5000 from the Government, and the promise of an annual grant
of £500 for five years, towards the establishment of a laboratory of
research in England.

6. That in Ireland the Royal Irish Academy receives a grant in
aid of £2000 annually, in addition to free accommodation and
about £400 annually for allowances and maintenances ; the Royal
Zoological Society of Ireland receives a grant in aid of £500
annually ; and the Royal Dublin Society appears, during the past
ten years, to have received considerable sums of money from public
funds; in addition there is a large sum granted annually for a
national library in Dublin.

7. That, with respect to Scotland, the only grant for scientific
purposes in aid of learned societies is £300 annually to the
Royal Society of Edinburgh, which is repaid to a department of
the Government in the form of rent.

One might well ask what Scotland had done that her learned

VOL. XIV. 15/7/87 B

18 Proceedings of Royal Society of Edinburgh. [dec. 6,

Societies and scientific men should be treated so niggardly as com-
pared with those in England and Ireland. It cannot be because
she does no scientific work. It is sometimes said, indeed, that in
literary matters Scotland, and especially Edinburgh, is a mere
shadow of her former self ; but in science this is not the case, and
it is towards scientific matters that the great ploughshare of human
thought and activity is, in this age, directed. I question if any
country in the world, taking into consideration its size, can show a
better record of scientific work, or a more excellent volume of scien-
tific literature, than Scotland, during the past ten or twenty years.

There can be no doubt that Scotland has a great grievance in the
fact that her learned Societies do not receive the same consideration
from Government as do similar societies in other parts of the United
Kingdom, and in the fact that the administration of all the grants,
in which she may be supposed to have a right to participate, is cen-
tralised in London and controlled by London Committees. Scotland
was refused a representative on the Meteorological Council, where
the expenses of the members are paid. Two representatives of this
Society are allowed on the committee of sixty members, which dis-
tributes the grant of <£4000 for research; but when two members of
the Council are sent twice a year to London it costs this Society
£50 annually, — a considerable charge against its funds. But there
is a unanimous opinion among Scottish scientific men that there
should be a grant in aid of the learned societies of Scotland, for the
purposes of scientific research, analogous to the Government grant
of £4000 to the Royal Society of London, which is distributed by
a committee in London. Several of the best qualified men in Scot-
land hesitate to apply for aid from the London committee, and,
especially as many of the younger men have been frequently dis-
appointed, there has sprung up a firm belief that the only satisfac-
tory arrangement for the scientific men resident in the northern
part of Great Britain is that there should be a grant for scientific
research to be distributed by a committee in Scotland, which would
be fully conversant with the nature of the investigations to be
undertaken, and personally acquainted with the applicants. There
can be little doubt that such a grant distributed locally would have
the effect of removing many of the barriers which at present impede
the progress of science in Scotland.

1886.]

Chairman's Address.

19

It is the primary object of our Society to promote the interests
of science and literature in Scotland, more especially in all that
relates to the extension of the boundaries of knowledge by the dis-
covery of new truths, as distinguished from the making known of
old truths. It claims, therefore, the right to memorialise the Govern-
ment on scientific affairs which it considers of national importance,
and in purely Scottish matters it holds that its President and
Council, and not the President and Council of the Royal Society
of London, should he the advisers of the Government.

The Council has, at various times in the past, called the attention
of the Government to the disadvantages under which Scotland
laboured in respect of aid to research, but the result has never been
satisfactory. In the attempt which the Council is now about to
make I would bespeak the co-operation and support of all Scotsmen
who believe it to be for the honour and well-being of the country
that our scientific institutions should not languish, or our scientific
men be discouraged, but that both should be urged to new advances
and greater conquests.

Hume Manuscripts.

Before the reading of the papers the Chairman made the follow-
ing statement : —

Some reference should, I think, be made to the concluding para-
graph of a review of the life of Hume, which recently appeared in
the Scotsman. It is as follows : —

“ Dr Knight has spared no pains to add by his own independent
research to the information given in J. Hill Burton’s work. He
mentions, however, that ‘ he has not been able to obtain access to
the volume of Hume MSS. in the custody of the Koval Society, the
Secretary being of opinion that Mr Hill Burton had sufficiently
examined these.’ Has the Secretary of the Royal Society any such
right to bar the way to further genuine research? How does he
know that nothing has been omitted and nothing has to be verified ?
This volume was not given as a present to the Royal Society to keep
as a curiosity in a glass case for its peculiar benefit, but given to
them as custodiers for the public. The decision of Professor Tait
amounts to asserting that this volume is never more to be seen by
mortal eye. It is well known that Plume entrusted to the Society

20 Proceedings of Royal Society of Edinburgh. [dec. 6,

his correspondence with Rousseau (after offering it to the British
Museum), not merely in order that it might he preserved, hut that
the world might he able to learn from it the true story of a famous
feud. If MSS. of purely literary or philosophical interest are to
he locked up jealously in the archives of a Society which is not
literary at all, hut scientific, the purpose of the depositors is defeated,
and the insistance on the private right of the Society becomes a
public wrong.”

As this article, if unanswered, might give rise to serious mis-
apprehension as to the action of the Society and of our General
Secretary, it is advisable to state —

1. The Royal Society of Edinburgh is, by its constitution, quite
as much a literary as a scientific society.

2. The General Secretary is not responsible for the decisions of
the Council of the Society, except in so far as he is, ex officio , one
of the twenty-seven members of Council.

3. The Hume MSS. were bequeathed to the Society by Baron
Hume in 1838, and they apparently contain papers which Hume in
his last will left particular instructions should be destroyed.

4. The Council of the Society has on several occasions since 1838
appointed committees to report as to the access that should be given
to these MSS.

5. The Council, recognising the duty of making public the
contents of the Hume MSS., and at the same time being anxious to
prevent the dissemination of mere hearsay scandal, affecting the
characters of men whose descendants are still among us, requested
the late Dr Hill Burton — whose competence no one will question —
to examine the MSS. and publish them so far as should seem at
once necessary and prudent.

6. More recently a committee of experts appointed by the Council
(on which are some of the most distinguished literary men in Edin-
burgh) has for a considerable time been engaged in the laborious
work of reperusal of these MSS., with the view of deciding how far
further publication of their contents may now be possible.

7. Pending the final decision of this committee, the Rousseau
portions of the MSS. have been for some time open to the inspection
of, and have been consulted by, investigators.

1886.] Professor Tait on the Kinetic Theory of Gases.

21

The following Communications were read : —

2. Astronomical Tables for facilitating the computation of
Differential Refraction, for Latitudes 56° and 57° ‘30.
By the Hon. Lord M‘Laren,

3. On the Foundations of the Kinetic Theory of Gases.

By Professor Tait.

In a former paper, printed in Trans. Roy. Soc. Edin ., 1886, I
showed that the recovery of the “ special ” state by a gas supposed
to consist of equal hard spheres takes place, at ordinary pressures
and temperatures, in a period of the order of 10" 9 seconds, at
highest.

This forms the indispensable preliminary to the present investiga-
tion. For it warrants us in assuming that, except in extreme cases
in which the causes tending to disturb the “ special ” state are at
least nearly as rapid and persistent in their action as is the tendency
to recovery, a local “ special ” state is maintained in every region of
the space occupied by a gas or gaseous mixture. This may be, and
in the cases now to be treated is, accompanied by a common
translatory motion of the particles (or, of each separate class of
particles) in the region — a motion which at each instant may vary
continuously from region to region, and may in any region vary
continuously with time.

A troublesome part of the investigation is the dealing -with a
number of complicated integrals which occur in it, and which (so far
as I know) can be treated only by quadratures. All are of the form

/'c° vyV
J 0 T ’

where v is that fraction of the whole number of particles of one
kind per cubic unit whose speeds (relatively to those of the same
kind, in the same region, as a whole ) lie between v and v + dv,
and 1/e is the mean free path of a particle whose speed is v.
Throughout the paper regard has been had to the fact that e must

22 Proceedings of Royal Society of Edinburgh. [dec. 6,

be treated as a function of v. So long as the particles are of
the same kind, or at least of equal mass if of different diameters,
such integrals are easy to evaluate ; but it is very different when
the masses differ in two mixed gases. In what follows, the merely
numerical factor of the expression above will be denoted by Cr, so
that the value of the expression is, when the masses and diameters
are equal, Cr/^7r«s2Ar/2, and the introduction of different diameters
merely introduces another factor. Here 3/2 h is the mean square
speed, n the number of particles per cubic unit, and s their common
diameter.

When the masses are unequal there will, in general, be different
mean free paths for particles of two different kinds, and the
integrals cannot be simplified in the above way. In this case the
integrals will be expressed as 1(^r, 9(£r.

(1) In my former paper I showed that the Yirial equation is, for
equal hard spheres exerting no molecular action other than the
impacts,

nPv2l 2 = | p(V — 2mrss/3) ,

where n is the number of particles, P the mass of one, s its diameter,
v‘ 2 the mean-square speed, p the pressure, and V the volume. The
quantity subtracted from the volume is four times the sum of the
volumes of the spheres ; and I pointed out that this expression
exactly agrees in form with Amagat’s experimental results for
hydrogen, which were conducted through wide ranges of pressure
and between 18° C. and 100° C.

In a mixture of equal numbers of two kinds of particles, of
diameters s15 s2, I find that for s 3 in the above formula we must put

iW + sw+tf),

where s = (s1 + s2)/2. Thus the “ultimate volume” is increased if
the sizes of the particles differ, though the mean diameter is
unaltered.

(2) Por the coefficient of viscosity in a single gas the value found
is

jyCi =pA.0,412
37 ms2 Jh fit

1886.] Professor Tait on the Kinetic Theory of Gases.

23

where p is the density, and A. the mean free path. The product pX.
is the same at all temperatures, so that the viscosity is as the square
root of the absolute temperature.

(3) The steady linear motion of heat in a gas is next considered,
temperature being supposed to be higher as we ascend, so as to
prevent complication by convection. It is assumed, as the basis of
the inquiry, that : —

Each horizontal layer of the gas is in the “ special ” state, com-
pounded with a vertical translation which is the same for all
particles in the layer.

The following are the chief results : —

(a) Since the pressure is constant throughout, we have

P n
2h '

so that njh is constant.

( b ) Since the motion is steady, no matter passes (on the whole)
across any horizontal plane. This gives for the speed of translation
of the layer at x,

(c) Equal amounts of energy are (on the whole) transferred across
unit area of each horizontal plane, per unit of time. The value is

E= - If nvvi(Xln+rJv)le-5a/v) ■

By the above value of p, and its consequence as to the ratio n/h ,
these expressions become

P /5

a~ elx 6^2 \2 ]

.5 p\

V

0*06,

(Ill , — s P l 25 r , r \ (Th 7 — &
V--Uh W(T °i-5C3 + Ca) = ^ VAO-45.

Since E is constant, by the conditions, we see that a also must
be constant. Hence as hr (where r is absolute temperature) is

constant, we have

i (It

t8- t constant, or
dx

t% = A + Bx* ,

24 Proceedings of Royal Society of Edinburgh. [dec. 6,

which, when the terminal conditions are assigned, gives the steady
distribution of temperature. The motion of the gas is analogous to
that of liquid mud when a scavenger tries to sweep it into a heap.
The broom produces a general translation which is counteracted by
the gravitation due to the slope, just as the translation of the gas is
balanced by the greater number of particles escaping from the colder
and denser layers than from the warmer and less dense.

In thermal foot-minute-centigrade measure, the conductivity of
air, at one atmosphere and ordinary temperatures, appears from the
above expressions to be about

Jin?' !

or about 1/28,000 of that of iron. Ho account, of course, is taken
of rotation or vibration of individual particles.

4. Fog Bow observed on Ben Nevis, 22nd October 1886.
By K. T. Omond, Supt. B.N.O.

(See Proceedings for June 20, below.)

5. Temperatures at Different Heights above Ground at Ben
Nevis Observatory. By R T. Omond, Supt. B.N.O.

During part of the recent summer (1886), in addition to the
ordinary temperature observations here, a set of readings were
taken in a Stevenson screen, at a height of 112 inches above
ground — that is, at about two and a half times the standard eleva-
tion of 48 inches. The high level screen was mounted at the top
of a stand used to carry the thermometers in winter, and consisting
of two stout upright posts or battens, with cross bars between them
at every 2 feet or so ; the screen is placed with the lower edge of
the back resting on one bar, and is tied to the one above it or to
the side posts. The screen used on this stand is smaller than the
standard Stevenson screen, but it is constructed in exactly the same
manner, with double louvred sides and the bottom open. It
measures inside 10 inches broad by 6 inches deep and 15 inches
high. The low level screen, which is mounted on four legs in the

1886.] Mr R. T. Omond on Temperatures at Ben Nevis. 25

usual manner, is about the ordinary size; it measures 15 by 10
by 15 inches. Readings of both sets of thermometers (high and
low) were taken hourly during part of July and the whole of
August. During the month of August, as well as these shade
temperatures, readings were taken of a black bulb in vacuo ,
belonging to Mr H. N. Dickson, and kindly lent by him for the
purpose. In this instrument the thermometer inside the glass
globe, instead of being a maximum, is a common thermometer,
with the bulb blackened in the usual way. The hourly readings
of this instrument indicate the solar radiation at the time of
observation, instead of, as in the usual maximum black bulb, giving-
only the greatest intensity since being last set. In the first column
of the table, at the end, the mean hourly values of this black bulb
for the month of August are given. It is noteworthy that the
maximum is almost exactly at twelve noon ; but, as Greenwich
time is used, it must be borne in mind that the mean time of the
sun’s meridian passage is about 12 hours 20 minutes, the longitude
being some 5° west. In the second and third columns respectively
of the table are the high and low level shade temperatures, and in
the fourth the difference between them, for the month of August
also. The values of the fourth column are shown graphically in
the highest line of the diagram. The average temperature for the
whole day is the same in both cases, but the upper thermometer
has a slightly less daily range, reading about one-tenth of a degree
F. higher at night, and from one to two tenths lower in the after-
noon. The result is exactly what would be expected, the upper
thermometer being further removed from the ground and less
exposed to its radiation, while the smallness of the differences
between the two can be accounted for by the exceedingly bad
weather of last August : during the whole month there were only
two fine days. A comparison of the readings on these two days
(the 19th and 22nd), shows a much greater difference. In the fifth
column of the table, the mean differences of the high and low level
thermometers on the two days is given, and these numbers are also
shown in the lower part of the diagram by the line which has the
greatest range. Two days is of course far too short a period to
give a satisfactory average and a smooth curve, but the general
aspect of the line shows that, from about sunrise till noon, the

26 Proceedings of Royal Society of Edinburgh. [dec. 6,

upper thermometer reads distinctly above the lower, from noon to
sunset distinctly below it, and during the night slightly above it
again. An examination of the black bulb temperatures for these
two days shows nothing calling for special note. The range is greater
than in the monthly average, but the curve is substantially the
same, except for a slight lagging of the maximum point, but the

Hours.

Black Bulb in
vacuo.

Temp. 48 inches
above ground.

Temp. 112 inches
above ground.

Diff. of high from
low temp.

Mean diff. of 2
fine days.

Mean diff'. of 9
foggy days.

Mclnt.

38*8

39-2

39 '4

+ 0-2

+ 0-2

+ 01

1

387

39T

39-2

+ 0T

+ 0-2

+ 07

2

38-4

38-8

38-8

o-o

+ o-i

o-o

3

38-4

38-7

38-8

+ 0 T

o-o

o-o

4

38-1

38-5

38-6

+ 0*1

+ 07

+ 07

5

38-8

38*4

38*5

+ 0T

+ 0-7

o-o

6

43-6

38-4

38-6

+ 0-2

+ 2*1

o-o

7

47-4

38-9

39-0

+ o-i

+ 1-0

o-o

8

53 '6

39-2

39-2

o-o

+ 0-6

o-o

9

57*9

39-6

39-5

-01

+ 0-4

o-o

10

60-7

39-8

39-8

o-o

+ 0-6

-07

11

64-5

40-3

40-2

-0T

+ 01

-0-2

12

67-0

40-9

407

-0-2

o-o

-01

13

64*3

41-3

41 T

-0-2

-0-3

-07

14

62*3

417

41-5

-0-2

-07

- 0'2

15

62-2

41-8

41*7

-0T

-0-6

o-o

16

58-1

42-0

41-8

-0-2

-1-0

-o-i

17

52*5

417

41-6

-0T

-0*4

0-0

18

46-8

41-2

41-2

o-o

+ 07

o-o

19

43*1

407

407

o-o

+ 0-2

o-o

20

407

40-6

40-6

o-o

0-0

+ 0-1

21

39-9

40-4

40-5

+ 0-1

+ 0-4

+ 0*1

22

39-8

40-3

40*4

+ 0T

i-0‘3

o-o

23

39-5

39-9

40-0

+ 0T

+ 0*2

+ 07

Mdnt.

39 '2

39-6

39*7

+ 0T

o-o

+ 01

Mean.

49*0

40 T

40T

o-o

period is too short to say anything definite about this. As a
contrast to these fine days, I have computed the mean differences
on nine days of continuous fog or mist. These differences are
given in column six of the table, and are shown by the line in the
lower part of the diagram with the least range. Here, though
there is still a tendency of the upper thermometer to read higher
at night and lower in the afternoon, the differences are very small ;

1886.] Mr R. T. Omond on Temperatures at Ben Nevis. 27

at only two hours do they exceed one-tenth of a degree. This
small difference on the foggy days fully bears out what I have
formerly observed on Ben Nevis, that in a saturated atmosphere —
with mist or fog present, it makes no practical difference how the
thermometers are placed, so long as the air can reach them at all
and they are shaded from the direct rays of the sun.

Differences of High from Loiv Thermometers.

As the surface of the hill top consists entirely of broken rock
without soil or vegetation, it seems probable that a large amount
of the difference between the two thermometers is directly due to
ground radiation. On a calm day with bright sunshine the stones
get so heated as to be disagreeable to handle, but there were un-
fortunately no such days last August ; still, the radiation of heat
during the day and of cold at night during ordinary clear weather
must be considerable, and the lower thermometer was much nearer
this source of heat and cold than the upper. It should, however,
be borne in mind that, as the screens are only open below and the
bulbs of the thermometers raised about four inches above the lower

28 Proceedings of Royal Society of Edinburqh. [dec. 6,

edge of the sides, they can only receive and transmit radiation from
and to that part of the ground that would he visible to an eye
placed where the bulbs are ; and that in theory the greater distance
of the upper thermometer from the ground would be exactly
counterbalanced by the larger area capable of acting on it, and the
radiation effects would be the same in both cases. The thermome-
ters were so mounted that the difference in the size of the screens
made little difference in the exposure to ground radiation. If the
screens themselves get heated and cooled by ground radiation, they
would correspondingly heat and cool the air as it passed through
the louvres, and thus affect the thermometers. In this latter case
the heating and cooling ought to be inversely as the square of their
distances from the ground — that is, the lower screen should be
affected nearly six times as much as the upper.

The afternoon difference may also be due to convection currents
arising from the heated ground; these would affect the lower
thermometer more than the upper, but it is difficult to see how
any such cause could give the morning difference, in which the
upper thermometer reads above the lower. It is possible, however,
that in fine weather the layer of air next the ground is so much
cooled by contact with the ground that there is a continuous
gradient of temperature rising with height above ground, at least
as high as the level of the upper screen. I hope to repeat the
experiment under more favourable conditions of weather, and also,
if possible, when the ground is covered with snow.

PRIVATE BUSINESS.

Messrs Asutosli Mukhopadhyay, M.A., <fcc., Joseph James Cole-
man, and John James Burnet were balloted for, and declared duly
elected Fellows of the Society.

1886.] Rev. H. J. Sharpe on Motion of Compound Bodies. 29

Monday , 20 th December 1886.

Sir WILLIAM THOMSON, President, in the Chair.

The following Communications were read : —

1. Motion of Compound Bodies through Liquid. By the
Rev. H. J. Sharpe, M.A. Communicated by the
President.

It is well known that the solution of the mathematical problem
of the motion of liquid arising from the motion through it of
solids has been effected in comparatively few instances, and in
these, such as the sphere and the ellipsoid, the surface is defined by
a single equation. In the following investigation, however, we
seem naturally to come across cases where the solid might be
described as “a compound body,” consisting as it does of parts
defined by different equations. It is possible that the method
employed might lead to the solution of analogous problems in
Sound, Heat, or Electricity.

DBAB'D' is the trace on the plane of the paper of a material
cylindrical surface, which is supposed to move through an infinite
mass of water in direction OA with a velocity which at the instant

30 Proceedings of Royal Society of Edinburgh. [dec. 20,

considered is c. BAB' is a semicircle with centre O, and the other
parts of the curve are symmetrical with respect to OA. If 0 A = ay
the polar equation of BD, referred to OA as prime radius, is
supposed to he

A tt r . 2a2.-.. 2 a*...

6 ~ 2 a Sm 6 + C23 ,^sm 26 " 3X5 ^Sm 4 6

+ 6jjr6si'l6e~&C,=0 ' 0)

Then the resulting irrotational motion of the liquid, supposed to
he in two dimensions only, can be completely determined. It may
he remarked that the series in (1), as well as all the like series in
this paper, can he presented in a finite form, hut, as the results are
rather complicated, perhaps it will he better to leave them as they
are. It does not matter whether we suppose the solid moving with
velocity c through the liquid at rest at infinity, or whether we
suppose the solid at rest, and the liquid moving past it with a
velocity which at infinity is - c. For simplicity, we shall suppose
the latter case. First, considering the reflection of the liquid
motion only from the semicircle BAB', let u and v be the velocities
of the fluid at any point P(a?, y) or (r, 0) of the fluid in the plane
of the paper. Let us assume

U = 2 ^2 cos mO - c , V = 2^5 sin »

where am, &c., are arbitrary constants. It is well known that these
expressions satisfy the hydrodynamical equations.

Then the velocity in the directions OP is u cos 6 + v sin 0, and

Cl

u cos 6 + v sin # = 2 ^ cos (m - 1)0 - c cos 0 .

Brow expand cos 6 by Fourier’s theorem in a series of cosines of
even multiples of 0 between the limits 0 and \tz of 0, which expan-
sion we observe will be true even at both limits. Then

a 2c 4c n~w

u cos 6 + v sin 0 = cos (m - l) 6 1 % cos 2 nO .

* X 7 7T 7T n=1

cos mr
4 n2 - 1

Now determine am, &c., by the condition that u cos 0 + v sin 0

1886.] Rev. H. J. Sharpe on Motion of Compound Bodies. 31

shall vanish when r = a ; we thus get m = 2n + 1 and the following
series of equations : —

a 7 r

a , 4c 1

<r

+

7 r

3.5

= 0,

4c 1 A
I T^ = °.

aJ

7T

1.3

4c 1

a7

y ~ — 0 , &c.

7 7T 5.7 ’

We thus get u + c

2c j a 2

— i - cos 0 + 7-7

7T I r l.£

2 a5

9

a'

O 0 COS 30 — “T COS 50 + “7 COS 70 - &c.

o r3 0.5 5.7 r'

v ■

2 c

7T

a .

— sm 0 ■
r

2 a3. 2 a5.

'0,1™ 30~a5?^sln50

It is well known that if we transform from polar to rectangular
co-ordinates, the above equations can he expressed in the form

u=f(x + iy) +f (x — iy),

v = i{f(x + iy) - f\x - iy) } ,

and when presented in this form we know that the equation of the
stream lines is

f{oc + iy) — fix - iy) = constant.

Determining in the particular case considered the form of the
function/, and then transferring back again to polar co-ordinates,
we find for the equation of the stream lines

A 7r r . A 2 a2r . nA

0-k- ~sm 0 + T sm
2 a 1.2.0 r *

2 a4 2 a5

- . . ■ — sin 4 0 + -Trsin 60 - &c. = constant..
3.4.5 r4 5.6.7?*

Dor the particular stream line which passes through the point B,
the above must he satisfied by r = a, 6 =* r, and in this case the
constant = 0, and we get equation (1), which is strictly a stream
line, hut which may evidently be considered as a material curve
joined to AB at B. It is evident that CE is an asymptote to this

32

Proceedings of Royal Society of Edinburgh . [dec. 20’

curve, where OC = 2a, touching the curve at the point r — 00 , 0 = -k.
We are concerned with values of 0 only from 0 to tt. We can
readily show that the curve BD touches the circle at B. For in

(1) putting a + Sr for r, and J7 r + 80 for 0, we get

s*-£sr-w( iL+^ + ^+&c.) = °!

or Sr = 0. If we retained terms involving SO2, we could readily
prove that a is the radius of curvature at B, and that C is the
centre of curvature, so that there must he a point of contrary flexure
between B and D. As before remarked, DBA# is a stream line.
Thus, as we pass along DB, (1) is its equation. When we get on
to the circle BA, we shoidd get, putting r — a,

2 2 2

0 - 1 7r sin 0 + s*n ^ ~ 3 4~5 s^n ^ + "5^6" 7 s*n ~ &c. = 0 >

and this shoidd be true from 0 = 0 to 0 = |7r. But if we were to
expand 0 - sin 0 by Fourier’s theorem in a series of sines of even
multiples of 0 between the limits 0 and Jvr of 0, we should get
exactly the above series, which verifies the work, and we may
observe that the expansion would be true even at the limits, for
0 - sin 0 vanishes when 0 = 0 and 0 = J7r.

It will be found on examination that if AB, instead of being a
quadrant, were any part of the semi-circumference, a similar pro-
position would hold good.

It can also be shown that if AB, instead of being a quadrant of a
circle, were a quadrant of an ellipse, a like proposition could be
established. I will give a slight sketch of the proof. Suppose AB
to be part of an ellipse, and suppose it to be moving parallel to OA
with a velocity V. Let u, v be the resulting absolute velocities of
the fluid at any point (x, y). Then we may take

dd> dch d2(b d2d>

W = dx’ ‘' = dy’ + • <2)

Now put x = c cosh /3 cos a, y — c sinh /3 sin a,
where c is a constant, sinh and cosh are the hyperbolic sine and
cosine, and a, /3 are new so-called curvilinear co-ordinates. Then

(2) becomes

d2<f> d2(f>

1886.] Rev. H. J. Sharpe on Motion of Compound Bodies. 33
Assume for a solution of this equation

dd> — mp .

f— = 2iCime sm ma ,
da

d(f) ^ -mi 3

-irt = 2iCime cos ma -l- G ,

dp

where C is a constant, and am, &c. are constants to be determined.
We may observe that the velocity at infinity normal to the ellipse
/3 = const, is dxfijVdp where P2 = |c2(cosh2/3 - cos 2a), so that whether
C is zero or finite, with the above assumption, the whole velocity at
infinity is zero. Now suppose /3 = /31 gives the solid cylinder, then
it will be found that the condition for reflection of the fluid motion
at /3 = /31 is

^ame "^cos ma + C = Yc sinh J31 cos a (3)

If the ellipse is complete, (3) must hold for all values of a from
0 to 7 r, and then we shall find that we must have C = 0 and m = 0.
This leads to the solution given in Art. 88 ( d ) of Lamb’s Motion of
Fluids. But if the reflection takes place at only a quadrant of the
ellipse, (3) admits of another solution. Expand in (3) cos a by
Fourier’s Theorem in a series of cosines of even multiples of a from
a = 0 to a = Jtt, and we get

2 cos 7 m

Now let

^ 2 f od z cos 7 m )

cosma4-G = - Vcsmh/jj < 1 - cos 2^a _ \ ( •

m = 2 n,

and

C = — Vcsinh R,

7T ' L

a2n e 2nl3l= - — Ycsinh/3

cos mr
'Hn2 - 1 ’

and we have a solution exactly analogous to the case of the circle.
It will be found also that instead of taking a quadrant of an ellipse,
we might take AB to be any arc and still get a similar proposition.

We will next take a case of motion in three dimensions. We
will suppose a solid hemisphere BAB' of radius a moving through
an infinite mass of liquid in direction OA, with a velocity which at
the instant considered is V, the velocity of the liquid at infinity
being zero. The motion of the liquid is supposed to be in planes
through OA, and to be symmetrical round it. We will suppose a

VOL. XIV. 20/8/87 c

34 Proceedings of Royal Society of Edinburgh. [dec. 20,

velocity - Y in direction Ox to be impressed upon the solid and
fluid, so as to bring the former to rest, and let <£ be the velocity
potential of the fluid motion relative to the solid at any point P
whose polar coordinates are r, 0. Then <£ satisfies Laplace’s
equation a2<£ = which changed to polar coordinates becomes

1P4, 2 <20 1 d f . \ _ „

dr* rdr + r* sin 6 d6\ d& ) ~

We may take for a solution of this equation

<£= - Vr cos <9 + a0 — + a2P2 -§ + a4P4 + &c.,

where P2, P4, & c., are Legendre’s coefficients of even order, and a0, a2,
<fcc., are constants to be determined. The first term is introduced
because the velocity at infinity parallel to OA must be - Y. We
can determine a0, a2, &c., by the condition that d<j)/dr must vanish,
when r = a.

This gives us

V cos 6 = - - (aQ + 3«2P2 + 5a4P4 + &c. ) . (4)

CL

This must be true from 0 = 0 to 0 — ^ r.

ISTow cos 6 can be expanded in a series of Legendre’s coefficients
of even orders between the above limits. Putting cos 0 = x,

^ rrP m,dx — q. \ ^ nPndx — 0 ,

which last is true if both m and n are even. We then get

and generally

a0 = “ 2 * a2 = “ »

r + 1 2.4. . .(r + 2)

It will be found that the differential equation to the stream

a

lines can be expressed in the form (putting — = p for shortness) ,

(1 x?) | Y^3 a2p d* + a4p3 + &c. | dp

| ^2 Vo£c + a0 + 3a2P2p2 + 5<x4P4p4 + &c. j<i«£ = 0. . (5)

1886.] Rev. H. J. Sharpe on Motion of Compound Bodies . 35

Remembering the known relation

if1-*2

) vf} +»(»+!) p«=°.

and examining the general term of (5), we see that (5) is an exact
differential. Therefore integrating we shall get for the equation of
the stream lines

(1 - x 2)

aV

>2 ^P

a,

2 P

2 + a

4

2pj 2 2 dx 4 4

-f &c • l - = C

For the particular stream line, which passes through the point
B, the above must he satisfied by p= 1, or £c = 0, and

aV

therefore C = — > so that its equation is

(1 - x2)

pf_

a* 2 dx + * 4

dP*

c/.r

f &c.

aV

— cIqX 2

(6)

For distant points p is small, therefore for such points neglecting
all the positive powers of p in the above, we can readily prove that
y — J(f)a is an asymptote, and that the curve lies below it. It is
interesting to see whether at B the curve goes up or down. To this
end, in (6) put a + 8r for r and Jtt + SO for 0, expand and retain not
beyond the first power of Sr and the second power of SO. It will
he found that we shall get

2 Sr - aSO2 + a
1 4w + 1

ft 2ft. + 1

~ i + f + + &c.

3.5. . .(2ft - 3) 3.5. ..(2ft + 1)

2.4.. .(2ft + 2) 2.4. ..(2ft- 2)

+ &c.

S0= 0

(7)

In order to get the terms after the 3rd in this series, we must
take ft from 3 to infinity. There seems to he no doubt that the
value of the series in the square brackets is zero, although it is
rather difficult to prove it algebraically, for the expansion (4) is
true even at the limits. Moreover the expansion (4) is never
differentiated, therefore def)/ dr is zero for r = a even at the point B,
therefore, as in the case of the circular cylinder, the stream line
through B must touch the circle at B ; assuming therefore that the
series in (7) is zero, the remaining terms show us that the curvature
at B is upwards, and the radius of curvature equal to a. The same
figure therefore as was employed for the circular cylinder will do for
this case, provided that we make OC = J(2)a instead of 2a.

36 Proceedings of Royal Society of Edinburgh. [dec. 20,

2. Note on Knots on Endless Cords. By A. B. Kempe, Esq.
Communicated by Prof. Tait. (Plate I.)

1. Each crossing divides the cord into two loops.

2. Any other crossing either lies on both these loops, say is
linked to the former crossing, or on one loop only, say is not linked
to the former crossing.

3. It can be shown without difficulty that if crossing a is linked
to crossing b, then crossing b is linked to crossing a ; and therefore,
also, if crossing a is not linked to crossing b, crossing b is not linked
to crossing a.

4. Hence pairs of crossings are of two sorts, viz., linked and
unlinked.

5. We have the two following fundamental laws : —

(a) The number of crossings linked to each crossing is even.

( b ) If two crossings are not linked to each other, the number
of crossings linked to both is even.

6. We may represent a knot diagrammatically thus : —

Represent the crossings by small circles or nuclei.

Join pairs of nuclei which represent pairs of linked crossings by
lines or links.

No lines are to be drawn in the case of unlinked pairs of crossings.

7. In these diagrams, in conformity with sec. 5, the number of
links proceeding from a nucleus must be even, and if two nuclei are
not joined by a link, the number of nuclei joined by links to both
must be even.

8. This mode of representing knots has the advantage of indicating
the degree of complexity of the various knots. Thus, the diagram
representing two distinct knots on the same string will consist of
two entirely detached portions, and nugatory crossings will be re-
presented by nuclei having no links proceeding from them.

9. In the plate the various knots of three , four , Jive, six , and
seven crossings are indicated in outline on this plan.

10. It will occasionally be convenient to represent pairs of cross-
ings which are unlinked by pairs of nuclei joined by a dotted line
or link, pairs of crossings which are linked not being joined at all.

Sec oud Me tli o d

Archibalds Peck Engravers -E<linr

1886*.] A. B. Kempe on Knots on Endless Cords. 37

The advantage of this mode of representation is that it involves a
smaller number of lines than the former mode, and thus the dia-
grams are simpler and clearer.

11. In the lower half of the plate the same knots are indicated
again, but on this new plan. [By an oversight the last, and the last
but two, of the seven-folds have been interchanged in this part of
the diagram.]

3. On the Bing- Waves produced by throwing a Stone into

Water. By Sir W. Thomson.

(Printed in full in the Philosophical Magazine , Jan. 1887.)

4. On the Waves produced by a Ship advancing uniformly"

into Smooth Water. By the Same.

(Phil. Mag., Jan. 1887.)

5. Expansion of Functions in terms of Linear, Cylindric,

Spherical, &c., Functions. By P. Alexander, M.A.
Communicated by Dr T. Muir.

(This paper is printed in the Transactions. )

6. On Even Distribution of Points in Space. By Prof. Tait.

[Abstract.)

The question raised is very closely connected with § 6 of my
paper on the Kinetic Theory of Gases [Trans. R.S.E. xxxiii. 71).
The result arrived at is that, when (in the thin layer) some particles
prevent others from doing their full duty, the formula should be

g - n^Sx ? instead of 1 - 711tts28x

as given in the text.

38

Proceedings of Royal Society of Edinburgh. [jan. 7,

Friday, 7th January 1887.

Sin DOUGLAS MACLAGAX, Vice-President, in the Chair.

At the request of the Council, Mr J. J. Coleman gave an
Address on Processes of Refrigeration.

The following Papers were laid on the Table : —

1. On the Front and Rear of a Free Procession of Waves in
Deep Water. By Sir William Thomson, F.R.S.

Preliminary.

General Problem of Deep-Sea Wave-Motion in two dimensions ,

(. Infinitesimal Motion.)

Taking x horizontal, and y vertically downwards; let ( x + £, y + f)
he, at time t , the position of the particle whose position at time 0 is
(x, y) ; let $ denote the velocity-potential at (x, y, t) ; and let P

denote its time-integral^^ dt&.

We have

J o dx

dP

dx

; and

V

=f\uf

Jo dy

dP

dy

(1).

Let p he the pressure at (a + £, y + rj). (The motion being infinite-
simal,) we have .

or, in virtue of (1),

P = G + g(y + rj)-

dt

n , . dP

p = C+ffy + g-

d2P
dt 2

The kinematical conditions are, the equation of continuity,

dffP dfP
dx1 + dy 2

and the boundary equation, in two parts — one relating to the upper

1887.] Sir W. Thomson on Procession of Waves. 39

surface, the other to the bottom. The latter, for our present case
of infinitely deep water, is simply

P •= 0 when y = oo (5).

To find the former, or upper-surface kinematical equation, at time
i, let it be y = 0 at time 0, and let j) be the height at time t above
the level y = 0, of the upper-surface particle whose coordinates at
time 0 are (x, 0). Remembering that f y positive was taken as
dowmvards, we have by (1),

The most general upper-surface dynamical condition which can
be imposed is

P(y = 0)==f(X’ t)

where / denotes an arbitrary function of the two independent
variables.

Suppose now the water to be at rest at time 0. It is clear from
dynamical considerations that the solution of (4), subject to the
conditions (5), (7), (3), is fully determinate : and when it is found,
(1) gives the position at time t of the fluid-particle which at time 0
was in any position ( x , y) ; and so completes the solution of the
problem.

The particular solution which we are now going to work out to
represent a uniform procession of waves commencing at time 0, and
produced and maintained by the application of changing pressure to
the surface in the neighbourhood of the zero of x, must, as its
appropriate form of (7), fulfil the condition

i?(y=o)== $(x) sin tot + F(a?) cos oit .... (8),

where g ( x ) and F ( x ) denote functions which vanish for all large
positive or negative values of x.

If we wish to make only a single procession, in the direction of
x positive for example, we may take

g(*) = I (9)-

A perfectly general formula is easily (by the Fourier-Poisson-
Oauchy method) written down to express the value of P ; and so,

40

Proceedings of Royal Society of Edinburgh. [jan. 7,

by (1) and (6), the complete solution of the problem : for g and F
any given arbitrary functions.

It is obvious that, so far as is concerned, the general solution
for x any considerable multiple of ± l , and exceeding ± l by not
less than two or three times the wave-length, 27ry/co2, must, for
values of t great enough to have let the front of the procession pass
the place x, be

sin

+ A cos r o)t - — ( - f)"l

L 9 J

L 9 J

and

for x positive,

= sin |^a)£ - ( - x +/) - A cos j^c ot - - x + f)J

for x negative,

H10);

where 51 and/ denote quantities calculable from the form of § ;
and A and f similarly from F. Further, it is obvious that the
front of each procession will, for any value of t not less than
several times the period and not less than several times the time one
of the wave-crests takes to travel through a space equal to l, be
independent of the particular forms of § and F. From the theory
of Stokes, Osborne Reynolds, and Rayleigh, we know that it
advances at half the speed of a wave-crest; but their theory, so
far as hitherto developed, does not teach us the law according to
which the front, as it advances, becomes longer and longer in pro-
portion to J t , nor even the fact that it does become longer and
longer. All the details of this interesting question are exquisitely
given in what follows : having been found with great ease for the
particular case,

IX*) = 0, and g(a) = j } * . . . (11),

where b denotes a length of any magnitude, which we shall take to
be very small in comparison with 27 ry/w2, the wave-length, We
shall in fact find that

iVo)-C +

{

{xZ+b^ + b } *

xi

+ 62

1

sin mi

(12),

in the particular processional case of the general equations
(1) . . . (6), which we now go on to work out.

1887.] Sir W. Thomson on Procession of Waves.

41

Remembering Cauchy and Poisson’s discovery that every surface
of particles which are in a horizontal plane when undisturbed
fulfils the condition of a free upper-surface (so that if all the water
above it were annulled the motion of the water remaining below it
would be undisturbed), in the case of free waves of infinitely deep
water; we see that when P(y=o) = const., we have also, in our
notation, p = const., for every constant value of y. Hence, looking
to (3) above, we must find, in the case of free waves.

9f P

dy

d* P
dt 2

(13);

for every value of y, and not only at the upper surface y = 0.
Thanking Cauchy and Poisson for this as a suggestion, hut not
assuming it without the proof of it which we immediately find ;
and borrowing now from Fourier* his celebrated “ instantaneous

dv d^v

plane-source ” f solution of his equation ^ f°r thermal con-

duction, assume, as an imaginary type-solution of (4) and (13) for
free waves,

(U),

(b + y + ixf

Mb+y+ix)

where t denotes J — 1. Whence, as a real solution by adding the

values of (14) for i and - 1, and dividing by J 2,

gte 1

4r2 f H15)-

1 f

gt2x

<£(*) = - | (r + y + bf eos'-^- + (r-y-bf sin

where

r — Y(y + b )2 4- a;2]-

Curves representing calculated results of this solution for free
waves were shown at the meeting of the British Association (Section
A) at Birmingham in September, and at the last meeting (December
20) of the Royal Society of Edinburgh. To build up of it a solu-
tion for a uniformly maintained procession of waves (a double
procession it shall be, of equal and similar waves travelling in the
two directions from x = 0) take

P(0= /dtcf>(t) (16);

J o

* TMorie Analytique de la Chaleur.
t Sir W. Thomson’s Collected Papers, vol. ii. p. 46.

42

Proceedings of Royal Society of Edinburgh. [jan. 7,

and

P= - / dt sin - t') = - f dt sin <*(t - $')P(£') . (17).

J o Jo

Since (/> ( t ), as we have seen, satisfies (13), P ( t ) must satisfy it
also. Hence

dP(t) _ d2P(t)

^ dy dt 2

. (18),

for all values oi x, y , and t. How by differentiation of (17) we
find, because P(0) = 0, and by (16),

dP

dt

- f dt' sin u>t' -^P (t - t') = - / dt' sin - 1') . (19);

J o dt J o

and differentiating this, we find, because <£(0) = (r + y + S)*?*"1

d2P (r + y + 6)» . /°* . ,d,u ^

— v u y sin wt - I dt sin co£ -=■ <£(2 - t )

Jo dt

dt 2

- - si„ * - Pdf sin «(< - t'ffP . (20).

r J n dt L

From this and the second form of (17) we find

9

dV d2 P (r + y + by .
= -sm J

dy dt 2 r

t

whence, by (18)

dV d2 P (r + y 4- by .

q — ‘ 2 -sm a it

u dy dt 2 r

(21);

(22);

and therefore finally, by (3) above, we have, for the surface
pressure,

p j (x2 + b2y + b \ * . /0QX

P»=0) = C+ \ + 62 1 sm“< • (23)>

as promised in (12) above.

To work out our solution, remember that dV/dt is the
velocity-potential of the motion ; and calling • this d>, we find,
by (19),

<E> = - j dt' sin (o{t — t')g>(t ) .... (24);

J o

1887.] Sir W. Thomson on Procession of Waves .

43

and by (22), (3), and (2) we find

1 [ (r + y + b)1 .

9

, , sin ait } . . . . (25).

dt r j v 7

What we chiefly want to know is the surface-value of rj , which
we have denoted hy - f) ; and we shall work this out for the case
5 = 0. But it is to he remarked that the assumption of 6 = 0 does
not diminish the generality of our problem, because the motion at
at any depth, e, below the upper surface with 6 = 0, is the same as
the motion at the surface, with b = c.

Put now 6 = 0 and y = 0 in (15) : we find

gt 2 . gt 2N

= * *(C08 E + sin e) - sin ('E + %

Using this in (24), and putting a2 — gf2/ix, we find

(26).

= -2 J- f

V gjo

■2 nVL

gj o.

da- 1 COS

cos

dcr sin g wt - 2

Vr)si

Sill I o~ +

7T

(27),

[("VD"-

d?\2 x t r

— or h co£ + -r

S' 4-

7 r

or- co£ + =

.</ 4_

(28).

Using now the following notation.

say 6 = j dO sin 02j cay 6= f dO cos 02 . (29),

J 0 J 0

for two integrals which have been tabulated by Airy * through

/ (£)

the range from 0 to 5*5^ ^ we reduce (28) to

+

cos( — — <o£ — —
\* 4.

. / (id TV

Sin g — X — C)t— T
\<7 4.

lor , (a
cost X + 0 it - —

\g 4,

or (ii 1

— a? 4- (at — 7-
^ 4>

Tracts” (Undulatory Theory of Optics, last page).

44

Proceedings of Eoyal Society of Edinburgh. [jan. 7,

The interpretation of this is eased by putting it into the form

<£ =

V 9

where

/t>

OJ 2 \ /w2

cos | — x - cot — ej - ix cos [ — x + 1 d-j

9

9

)}. (31).

Q = { \jay (if £ _ o,y?) + caff £)J

faff S" Vf)+*°,,(Vf)J}’ (32);

e = tan

.“KVfc-ys-KV:-)

4

“*(%/: i - Vi) + “K'V; J)

E = J ffft + Vy) - eayW f)l

+ [saff r,+Mf }) - saff ff } ’

(33);

(34);

and

/= tan

cay{t f + wff)~ sav(o \f)

(35).

my (* fh + “ f 'f) ~ Cay (mf

Now, remembering that cay (oo ) = say (so ) = \ / g , we see that if
^ \/X- is large, and tsj ^ w f *s ^aroe positive, we have

9

and therefore

R=0, Q= fn, e=0 . .

/2tt /a fix \

(b^sj — cos I <ot J . . ,

v * V 9 V 9 J

whence, and by (25) with b = 0,

. 1 • [w2x \ 1 / g .

; ‘ 9 V 9 L \ 9 / «> V 2wa J

or, since o> J (x/g) is very large,

f . io /'2tt . /m^x \

^-yv73,n(vwV • • •

(36) ;

(37)

(38) ;

(39).

1887.] Sir W. Thomson on Procession of Waves.

45

This represents a uniform procession of free waves, of which the
wave-length, A, and the wave-velocity, U, are as follows : —

A = 27ry/a)2, U = ^/co (40).

To explain the meaning of “ very large ” as we have just now
used it, let

x

= n\, which makes = ij^n, and— l/4?r Jn (41) .

Hence the term of (38) omitted in (39) is 1/47T Jn of that retained.
And the value of the R, omitted by (36) in (37), is of the order
1/2 J2 n of the Q which is retained, because

cay(co ) — cay( J2i m)=

sin (27m)
2

and say{o o ) — say( J2 7m=

cos (27 m)

(42),

2 J 27m

when n is very large.

In (36) and its consequence (31), we supposed if so large
that M is large positive ; let us next suppose t so

small that it is large negative; that is to say, let

t = 2o>x/g-m ^ — (43),

where m is a large positive numeric. Thus, remarking that cay
( - 6 )= - cay ((9), and say ( - 0) = - say ( 0 ), we have, by (43) and
(41) in (32),

Q= P^{[cavim)

if

- cay( rn)f + [say (m) - say( J27ni)ff (44);

and therefore, when m and n are each very large, Q=0. Because
n is large we still, as in (36), have R=0; and therefore the motion
is approximately zero, at any considerable number, n , of wave-
lengths from the origin, so long as m in (43) remains large. As
time advances, m decreases to 0, and on to — oo : and, watching
at the plac ex = n\, we see wave-motion gradually increasing from
nothing, till it becomes the regular procession of waves represented
by (39); and continues so unchanged for ever after. When m = 0,
that is to say, at the time

t = 2c or/g .

• • (45),

46

Proceedings of Royal Society of Edinburgh. [jan. 7,

Q has attained half its final value. The point x where this con-
dition is fulfilled at time t may he called the mid-front of the

procession. It travels at the velocity or half the wave-

velocity ; which agrees with the result of Stokes.

We may arbitrarily define “the front” as the succession of
augmenting waves which pass between the times corresponding to
m = +10 and ??i= -10 (or any other considerable number instead
of 10). Thus the time taken by the front, in passing the place
x = n\, is 40w_1 The space travelled by the mid-front in

this time is 20 yw-1 which may, arbitrarily, be defined as the

length of the front. It increases in proportion to Jn ; and there-
fore in proportion to Jt, as said above. The effect upon phase of
the changing waves in the front ; due to the fluctuations of e, and
to the law of augmentation of Q from zero to its final va lue ; is to
be illustrated by calculations and graphic representations, which I
hope will be given on a future occasion.

The rear of a wholly free procession of waves may be quite readily
studied after the constitution of the front has been fully investi-
gate, by superimposing an annulling surface-pressure upon the
originating pressure represented by (12) above, after the originating
pressure has been continued so long as to produce a procession of
any desired number of waves.

2. Numerical and other Additions to his Paper, read on
6th December 1886, on the Foundations of the Kinetic
Theory of Gases. By Professor Tait.

In the case of diffusion, in a long tube of unit section, suppose
that we have, at section x of the tube, w^s and n2 P2s per cubic
unit, with translational speeds cq and a2, respectively. If Gj be
the whole mass of the first gas on the negative side of the section,
it is shown that the rate of flow of that gas is

Obviously

47

1887.] .Professor Tait on Kinetic Theory of Gases.

The motion of the layer of Pxs at x is (if approximately steady)
given by the equation

d /IVh \ _ 8 2 + M PiP2 / _ \

A, *1 / 3 1 2 V .*1*1 Pj + Pj^1 2'>

where the right-hand side depends on the collisions between the
two kinds of gas in the layer, s being the semi- sum of the diameters.
Prom these we obtain

3 Pi + P2

1 1 / f~ \\ cZ2Gri

-+^0216i+»i2S1)j-^1.

dt \16s2 Jh1hfhl + A2) p

In the special case, when the masses and diameters are equal in

d2G

the two gases, the diffusion-coefficient (the multiplier of -^-21 above)
has the value

+3Cl)o-(

=-4a-8.

•677 Jh Jh

It is therefore inversely as the density, and directly as the square
root of the absolute temperature. And the case of two infinite
vessels, connected by a tube of length l and section S, and contain-
ing two gases whose particles have equal masses and diameters, the

SpA.

rate of flow of either is P8 in mass per unit of time.

Other cases are treated ; and among these it is shown that with
equal masses, and constant semi-sum of diameters, difference of
diameters favours diffusion. The remainder of the paper is devoted
to the interdiffusion of two gases whose particles have masses in the
special ratio 16:1, the case of oxygen and hydrogen. The rate of
diffusion (in a tube of unit section and of length l, connecting two
infinite vessels filled with the gases (the semi-sum s of the diameters
being constant) is given by the expression,

A . P
rrls 2 Jh '>

where A depends, as follows, on the ratio of the diameters : —

Ratio of Diameters. A.

0

1

1

3

1

1

3

1

1

0

3*48

3-31

3-46

3*79

4*26

48

Proceedings of Royal Society of Edinburgh. [jan. 17,

When the masses are unequal it is shown that the temperature
must he kept constant to insure a steady state of diffusion.

3. Intimation of an Improvement in Rankine’s Formula for
Retaining Walls. Given by Professor Armstrong on
behalf of Mr Elliott.

Monday, Vlth January 1887.

SHERIFF IRVINE, Vice-President, in the Chair.

The following Communications were read : —

1. The Total Rainfall on the Land of the Globe, and its
Relation to the Discharge of Rivers. By J. Murray,
Esq., Ph.D., V.P.

2. Chemical Affinity and Solution. By W. Durham, Esq.

In continuation of my inquiry into the evidence which thermo-
chemistry gives of the truth of my theory of chemical affinity and
solution, I would direct attention to the sulphates.

In the first instance, consider the well-known definite compound
sulphuric acid H2S04. The heat which is evolved on building up
this acid from its elements is 192920 units. When it is dissolved
in a large quantity of water the mixture evolves 17850 units,
making in all 210770 units. Now, consider how this is made up.
First, we have H20 with a combination heat of 68360 units, then
S03 with 103240 units. Further, we know that S combines with
H2, evolving 4740 units of heat, and let us assume, according to
my theory, that all the affinity of the S for O is not exhausted on
the combination S03, but that part remains in a less intense form
which can act on the O of the water, and in conjunction with H2 can
evolve 34413 units more, this being its average action on the
three atoms of O already combined. Add these numbers together,

1887.]

Mr W. Durham on Chemical Affinity.

49

and we have almost exactly the heat of formation and solution of
H2S04. Thus—

[H20] = 68360 [H2, S, O4] =192920

[S, O3] =103240 [H2S04,Aq] = 17850

[S, H2] = 4740
[SO3, 0]= 34413

210753 210770

Now, of course, I have assumed that S will develop 34413 units in
addition after combining with three atoms of O. Let us see, how-
ever, how this way of looking at the combination helps us as we go
on. Take next a very different sulphate, viz., BaS04. In building
this salt up from its elements, 338070 units of heat are evolved.
Analysing this in the same manner as in the case of H2S04 we have
[Ba, O] = 124240 units of heat, [S, 03] = 103240 units, together
equal to 227480 units, leaving 110590 units to he evolved on com-
bination of BaO with S03. Whence do these 110590 units come?
We have the answer at once when we know that [Ba, S] = about
109600. It is evident the S acts upon the Ba with as much
energy as if BaS were actually formed, and this is the cause of the
combination. In accordance with my theory, the S cannot act to
any extent on the O of the BaO owing to the energy with which
the Ba holds the O, being represented by 124240 units instead of
68360 as in the case of H20. Thus we have —

[Ba, O] 124240 [Ba, S, O4] 338070

[S, O3] 103240

227480

Difference 110590 = [Ba, S] 109600

338070 338070

Further, consider how the heat of neutralisation is accounted for.
BaO, on being dissolved in water, evolves 34520 units of heat, S03
evolves 39153, and the difference between the sum of these and
110590 is the heat of neutralisation. Thus —

[BaO, Aq] = 34520
[SO3, Aq] =39153
Neutralisation = 36896

VOL. XIV. 23/8/87

110569

D

50

Proceedings of Boy al Society of Edinburgh, [jan. 1 7,

Again, take SrS04, and proceeding exactly in the same way, we
have the following result: —

[Sr, O] = 128440 [Sr, S, O4] = 330900

[S, O3] =103240

231680

Difference 99220 = [Sr, S] 99200

330900 330900

[SrO, Aq] = 29340
[SO3, Aq] = 39153

Neutralisation = 30710
99203

Now, both these salts are insoluble in water for the same reason,
viz., that the full affinity of the S for the metal is exercised, and
nothing is left for the H2 or O of the water.

Let us take next CaS04, and we shall find some still more
remarkable results. In building this compound up 318370 units of
heat are evolved. Tabulated in the same way as in the other cases
we have —

[Ca, 0] = 130930 [Ca, S, O4] 318370

[S, O3] =103240

234170
Difference 84200

318370 318370

Now in this case the difference 84200 is not equal to the heat of
[Ca, S], which is 92000. The S therefore is not held with the
full strength of its affinity for Ca. There are 7800 units to spare.
What becomes of them ] Consider the following : —

[CaO, Aq] = 18330
[SO3, Aq] =39153
Neutralisation = 31440

88623

1887.]

Mr W. Durham on Chemical Affinity.

51

Now this exceeds 84200 by 4423, which is the heat of solution,
viz., 4440, and accounts for so much of the difference ; hut the
remarkable thing now comes in, CaS04 combines with 2H20, and
in doing so evolves 300 units of heat more than the heat of solu-
tion, viz., 4740, which is exactly the heat of combination of SH2.
We see, therefore, that owing to the whole affinity of the S for Ca
not being exercised in the compound CaS04, the S can exercise its
normal affinity towards H2 of the water, and as a consequence we
have CaS04 slightly soluble, while the other two analogous salts are
insoluble. Further, when this compound CaS042H20 is dissolved
in water, the excess of its heat above that of solution appears as
a negative quantity, therefore its heat of solution is - 300. Now
this admirably illustrates the meaning of these negative heats of
solution, and also two points to which I drew attention : — First,
the lowering of intensity of affinity. We have in this case affinity
represented by 300 units of so low a tension that its presence can
only he detected when acting on two molecules of water. On a
larger quantity it has no effect so far as temperature is concerned.
The second point is that every molecule of water exercises affinity
on every other molecule, but as the work done and undone must be
equal everywhere, there is no change of temperature ; but it is
entirely different if one or two molecules be bound to another
foreign body; the balance is then upset, and the result will be a
change of temperature in one direction or the other. There are
still about 3000 units of heat to account for. Now, I am not pre-
pared to say exactly where these will be found. According to my
theory the affinity of the S is now so reduced in intensity that it
cannot make its presence known by evolution of heat in the ordi-
nary way. It may be, however, that here we have the explanation
of the facts pointed out in my former papers regarding the precipi-
tation of clay suspended in water, by the addition of a very small
quantity of a soluble salt.

Take one more example as extremely interesting for the fresh
light it throws on the subject — consider Na2S04. In building this

compound up from its elements 328590 units of heat are evolved,
and in addition the compound combines with ten molecules of
water with an additional evolution of 19220 units. Proceeding as
in the other cases we have —

52

Proceedings of Royal Society of Edinburgh, [jan. 17,

[Na2,0] = 99760 [Na2, S, O4] =328590

[S, O3] =103240 [Na2 SO4, 10H2O] = 19220

203000
Difference 144810

347810 347810

Now, how is this difference of 144810 units accounted for? We
have first [Na2S] = 88200, and then we know that Na20 on being
dissolved in water evolves 55500 units of heat, which on my
principles are due to its unexhausted affinity for the O of the water ;
this affinity acts upon the O of the S03. Thus we have —

Na2S] = 88200
Na20, O] = 55500

143700

We have also heats of neutralisation and solution as follows : —

[Na20, Aq] = 55500 [Na2, O] = 99760 [Na2, S, O4] = 328590

[SO3, Aq] =39170 [S, O3] =103240 203000

N eutralisation = 31378

125590

Difference 458

126048 126048

Heat of solution = 460

The balance of 18760 units of heat in the formation of the crystal-
line salt appears as a negative quantity on solution as in the
analogous lime salt.

I have made a few determinations of the quantities of some
compounds dissolved in water to see how far these conclusions
derived from thermo-chemistry are borne out by actual quantities
dissolved.

In my last paper I stated that the heats of solution of chlorides
varied directhj as the affinity of the metal for O, and inversely as its
affinity for Cl. Consider the following table : —

MC12 - MO, Aq.
Ca = 20560
Sr = 26770
Ba = 35980

Quantity of MC13 dissolved in
100 parts of Water.

63 grains.

46

35

3)

33

1887.]

Mr W. Durham on Chemical Affinity.

53

Now, it is apparent at once that the quantity dissolved is almost
exactly inversely as the difference of heats, which is in complete
accordance with the laws laid down in my former paper. With the
nitrates the same relationship cannot be made so clear, as the
metals are in combination with O, and the data obtainable are
insufficient to trace the various affinities. The results, however, are
quite in accordance with the above, although the range is much
greater. Thus we have—

Quantity of M(N03)2 dissolved.

Ca = 1 1 1 grains.

Sr = 50 „

Ba = 7 „

The differences are in the same proportion as in the chlorides. The
sulphates I have already noticed.

The salts of those metals which form insoluble oxides or hydrates
I leave for future treatment, as the data obtainable are defective for
my purpose. So far as they go, however, they are in complete
accordance with those laws I have stated.

These facts seem to me to prove, without doubt, that solution is
entirely due to chemical affinity, and that chemical affinity does not
act, as has hitherto been supposed, in units, but in all proportions
according to the circumstances, and that in chemical combinations
of all degrees every atom acts upon every other atom according to
its affinity and the position in which it is placed. This way of
regarding chemical affinity reduces a perfect chaos of empirical
results into an orderly and systematic arrangement.

3. Thermometer Screens. Part IV. By John Aitken, Esq.

(Plates II., Ill, IV.)

The object of this paper is to describe a new thermometer screen,
and to give the results of some trials made this autumn and winter
with a Stevenson screen as generally used, and one modified in the
way described in a previous part of this investigation.* Also to
give comparative readings taken with those screens and with the
new one.

*“ Thermometer Screens,” Proc. Roy . Soc. Edin. , Part 117, p. 661.

54

Proceedings of Boy al Society of Edinburgh, [jan. 17,

Before entering on the subject of the paper, I wish to make a few
preliminary remarks on the cause of the difference in the readings
given by different screens and by other ways of protecting the
thermometers ; also to call attention to the interpretation we are
entitled to put on curves of temperature drawn from readings taken
at longer or shorter intervals of time.

All the methods in use for taking the temperature of the air
give different results. One cause of this difference is the more or
less perfect way in which the thermometer is protected from the
effects of radiation ; so that, while all tend to read too high during
the day, some read higher than others. But in addition to this,
there is another reason why the different arrangements give different
results. This second disturbing element we will, for want of a
special name, call the inertia of the apparatus. By the inertia of
the apparatus is simply meant the resistance offered by the ther-
mometer and its surroundings to change of temperature. The
inertia may, therefore, be measured by the time taken by the ther-
mometer to acquire the temperature of the air for a given amount
of change of temperature. Bor example, suppose the temperature
of the passing air to rise one degree, it would almost instantly
heat up any small body, such as a cobweb, to its own temperature,
but it would take a much longer time to heat up a larger body,
though similarly exposed. The time required will depend on the
mass and specific heat of the body, and on the shape and amount of
surface it presents to the passing air. We see from this, that if the
arrangement of apparatus we use to take the temperature of the air
has a small inertia, it may, if the temperature is rising, indicate
at first a higher temperature than an arrangement having a greater
inertia ; and, if the temperature does not remain long enough
at its highest point, the apparatus with small inertia will
indicate a higher maximum temperature than the other. To
illustrate this point, let us first consider a purely imaginary case.
We know that the temperature of the air during the forenoon
of a summer’s day is constantly changing. It does not rise regu-
larly, but rises to a certain extent, then falls, then rises and falls
again ; and though the general tendency may be upwards, there are
many breaks in the curve representing the rise of temperature
for the day. This results, as we shall see later on, from the manner

1887.] Mr John Aitken on Thermometer Screens.

55

in which the air is heated. In PI. II. fig. 1, the cufve A is
supposed to represent the changes in temperature of the air, drawn
to a scale on which the vertical lines represent half minutes,
while the horizontal lines represent half degrees. During one
minute the temperature often rises or falls more than one degree.
For convenience of illustration, this curve, representing the
temperature of the air, is shown as a smooth curve. In reality
it is not likely to he so, but in all probability is a very irregular
one. Suppose then the curve A represents the temperature of the
passing air, then the curve representing the temperature of any very
small body, such as a cobweb, will follow this one very closely.
But if the body is of any size, then the curve of its temperature will
be something like the curve B. Its temperature will rise and fall
with that of the passing air, but the two curves will not rise and fall
together, because the temperature of the body will go on rising after
that of the air has begun to fall, and it will continue to rise so long
as the air is the hotter of the two. In the curves, the temperature
of B is shown to be rising for more than half a minute after A has
attained its maximum, and it is not till A has fallen more than half
a degreee, and has the same temperature as B, that the latter ceases
to rise, and the curve of its temperature becomes horizontal. After
this A and B both fall, hut A more quickly than B, and B does not
attain its lowest point till after A has passed its lowest, and risen
to a certain amount, and acquired the temperature of B, after which
both curves rise, but A more quickly than B.

The points to he noted here are : First, that if the top of the
curve A had been the maximum for the day, then the inertia of B
would have prevented it acquiring the maximum temperature, so
that any arrangement of screen having a large inertia will tend to
give a lower reading than one with a small inertia.

The second point is, the effect of the inertia in retarding the time
of maximum temperature. The curve B does not arrive at its
maximum till some time later than the curve A. These considera-
tions help to explain why the daily maximum temperature does
not occur about mid-day, when the sun is at its highest, but at a
later hour. If we suppose the curve AA', continued as shown by
the dotted lines in the figure, to represent the intensity of solar
radiation, then the curve BE' will represent its heating effect on

56 Proceedings of Royal Society of Edinburgh, [jan. 17,

the air. When the sun is at its highest the air is receiving its
maximum heating effect, but owing to its inertia it does not acquire
its maximum temperature till a later hour, till near two o’clock, at
which hour the amount of heat received is balanced by that lost.
After that the temperature of the air falls, but the curve represent-
ing its fall is later than A, owing to the inertia of the air, which
affects a falling as well as a rising temperature. The same ex-
planation applies to the yearly maximum, and shows why it does
not occur in J une, when the sun is highest and the greatest number
of hours daily above the horizon, but at a later date, when its heat-
ing power has considerably diminished.

The curve C in the figure represents the effect which a still
greater inertia has on the rise of temperature in a body heated
by the air. As the temperature of A never falls quite to that of
C, the curve C never falls, but only varies in the rate at which it
rises. It will be as well to note here, that all these effects of
inertia in checking and retarding the heating of large bodies are
quite apart from the question of radiation and its effects on large
and small bodies, which, as has been shown in a previous paper,
acts in exactly the opposite way, and tends to heat large bodies
to a higher temperature than small ones.

Let us now turn to the practical consideration of the subject, and
see what the effect of inertia really is on the readings given by
different arrangements of apparatus. On PI. II. fig. 2, are shown
curves of temperatures drawn from readings given by different
arrangements, each having a different inertia. The curve FB shows
the readings of a very fine bulbed thermometer. This thermometer,
as was explained in a previous part of this investigation, was con-
structed to be used as a standard of air temperatures, with which
to compare the readings given by the different screens. The bulb of
this instrument is 25 mm. long, but it has a diameter of only about
1*5 mm. When in use, it is exposed under a horizontal sunshade
in the manner described in Part II., and the bulb is protected from
radiation by means of a sheath of pure silver, which fits it closely,
but does not press upon it.

The readings given by this instrument were considered to be
nearer the true temperature of the air than those given by any
other arrangement, as they always kept lowest while there was any

57

1887.] Mr John Aitken on Thermometer Screens.

radiation. It will, however, he evident that its inertia is very-
small, and wrhen exposed either without its silver sheath or when
covered with chemically deposited silver, its sensitiveness is very
remarkable, its indications showing constant fluctuations in the
temperature of the air, as the mercury is in a continual state of
pulsation whenever there is any radiation effect. These changes
amount often to more than a degree in less than a minute, even in
an October day, and are much greater in bright summer weather.
The fluctuations do not seem to he due to variations in the radia-
tion, as they are observed even when radiation appears to he con-
stant, either under a clear sun or after it has been under a dense
cloud for a time. These changes of temperature would seem to be
due to the air that is heated on the ground and on other radiation
heated bodies not being perfectly mixed with the colder air, one
part of the eddy formed by the passing air having more heated air
in it than another.*

The curve FB, fig. 2, is drawn from temperature given by this
fine-bulbed thermometer without any silver covering. The curve
LB shows the readings of another thermometer with a larger bulb,
exposed bare, alongside the fine-bulbed one. Its bulb is 22 mm.

* This conclusion seems to be confirmed by observations made by Mr Dickson
with this instrument at the top of Ben Nevis. He informs me that he never
observed any of these rapid fluctuations at that station. The air heated on
the slopes of the mountain will be carried away sideways by the wind, and the
small amount of heating effected by the limited area of ground at the top does
not seem to be sufficient to give rise to these changes.

Professor Langley, in his celebrated researches with the bolometer, has
observed certain fluctuations in the intensity of the solar radiation from
minute to minute. As these fluctuations were ten times the instrumental
errors, he is satisfied they have a real existence. He says the solar radiation
would have been constant, but that the amount transmitted varied from minute
to minute even in what appeared a cloudless sky. It is evident that the
fluctuations observed by Professor Langley and those indicated by the fine-
bulbed thermometer are not of the same order, although they take place at
about the same intervals. The variations given by the thermometer are much
too great to be due to variations in the amount of transmitted heat. As we have
a satisfactory explanation of the fluctuations indicated by the thermometer, it
seems possible that Professor Langley’s fluctuations may be due to the same
cause. It is very difficult to suppose a want of uniformity in the upper air so
great as to cause these fluctuations in such short intervals of time. It seems
more probable that the variations observed with the bolometer are due to the
imperfectly mixed hot and cold, moist and dry air near the surface of the
earth, which will affect the readings of that instrument by absorption and
by radiation.

58 Proceedings of Royal Society of Edinburgh, [jan. 17,

long and 7 mm. in diameter. It has therefore a greater inertia than
the other. A and B are the curves of temperature for two Steven-
son screens, one with the bottom open and the other with it closed;
while C is the curve of temperature given by the new screen
presently to be described. The temperatures shown in fig. 2 were
taken on the 18th October. There were a few passing clouds at
the time, and a strongish north-east wind was blowing. The readings
were taken simultaneously by two observers, at intervals of one
minute from 11 ’59 to 12 ’20, when they were stopped on account
of the radiation effect falling to zero, and all the different ther-
mometers reading nearly alike.

It will be seen from an examination of the curves that the fine-
bulbed thermometer moved much more rapidly than any of the
others. This is not shown so well in the curves as it might be,
as the interval of one minute is much too large to show the fluctu-
ation of this instrument, for in the interval between two observations
it often indicated temperature much above or below the recorded
readings. In the first rise of the curves from 12 to 12.2, there
is no very great difference in their steepness. This is probably
due to no observations being taken at 12.1; but take the rise
beginning at 12.4, and here the effect of the inertia of the
different arrangements is very marked. From 12.4 to 12.5 the
fine-bulbed thermometer rose 0°‘8, and the large bulb 0°*3, while
the screens only rose about 0°T. During the next minute the rate
of increase of temperature of the fine bulb greatly diminished, as it
was near the temperature of the air, while the rate of the others
increased. It will be noticed that the two exposed bulbs FB and
LB arrived at their maximum and began to fall before the screens
A and B got to their maxima, and so long as the fall continued
they kept falling in advance of the others, In the rapid fall which
began at 12.11, in one minute the fine bulb fell 0°'9, the large one
0o,7 ; while the screens A and B fell only about 0o,3, and they took
four minutes to fall the 0o,9 lost by the fine bulb in one minute.
One effect of this is that while the fine bulb, if read at very short
intervals, would give a curve like the edge of a saw, with irregular
teeth set at intervals of less than one minute, the inertia of the
screens causes them to smooth over these irregularities, and to give
a curve with fewer and less abrupt changes.

1887.] Mr John Aitken on Thermometer Screens.

59

It will he observed that while these curves show fairly well the
effect of inertia on the rate of the heating and cooling of the
thermometers, yet they do not show that the arrangement with
smallest inertia gives the highest readings, as we concluded from a
consideration of the curves in fig. 1. The reason for this is that
the curves in fig. 2 are complicated by radiation effects. The large
bulb and one Stevenson screen read higher than the fine-bulbed
thermometer. This was caused by those arrangements being
more affected by radiation than the fine bulb. If we take readings
given by the screen C and the fine bulb — the two which are least
affected by radiation — it will be observed that the fine bulb rises
above and falls below C, somewhat in the manner indicated in the
imaginary curves fig. 1, only it rises too high, owing to its being
more heated than C by radiation.

It may be as well to note here that the two thermometers exposed
under the sunshade did not give more correct temperatures than
the screens, hut it must he remembered that they were not coated
with silver when these readings were taken. It may be interesting
to note that the fine bulb gave lower readings than the large
bulb, though similarly exposed ; this will be seen from an examina-
tion of the curves FB and LB. All the curves in this figure
follow each other more closely than they would under many con-
ditions. The reason for their comparative closeness on this occasion
was doubtless the amount of wind that wras blowing at the time
the readings were taken. It is evident that a quick circulation of
air will have great influence in reducing the time necessary to heat
or cool the screens, and will have very much less effect on the
exposed bulbs. I much regret I was unable to return to this
investigation till late in the season, by which time the radiation
effects were greatly reduced, and, owing to the amount of had
weather, very few observations were made. The curves shown in
%• 2 are the result of the only one-minute observations I have
been able to make. If these readings had been taken in spring
or summer, and when there was sunshine and little wind, the
fluctuations would have been much more marked, and the relative
steepness of the different curves better brought out.

Turning now to the consideration of the question as to what
interpretation we are entitled to put on curves of temperature made

60 Proceedings of Royal Society of Edinburgh, [jan. 17,

from observations taken at longer or shorter intervals of time, a
very little consideration will show us that these curves, as generally
constructed, are in no sense curves of temperature.

An examination of the one-minute observations given in fig. 2
shows us that the curve of daily temperature is much too complicated
to be capable of being represented in the manner it generally is. A
few detached observations at hourly intervals tell us really very
little about the matter, and to attempt to draw a curve from these
can lead to no good, as the curve appears to give definiteness where
in fact almost all is unknown ; this is particularly the case when
there is any radiation. Observations taken at intervals so wide
apart as one hour really tell us nothing about the state of
matters in the intervals, and yet by connecting these hourly read-
ings by means of curves we not only indicate the temperatures in
the interval, but we may even represent the temperature at the hour
of observation to be rising or falling when in reality it may be
doing quite the opposite.

To illustrate the small value we are entitled to put on curves
drawn from hourly observations of temperature, the curves in PI. II.
fig. 3, are drawn from one of the few sets of observations taken
recently at regular intervals. The curve A is drawn from obser-
vations taken at five-minute intervals, and it will be seen that
during the two hours while the observations were made, there
were great fluctuations in the temperature. An examination of
fig. 2 will, however, show us that even during five-minute intervals
considerable changes may have taken place. The curve A, fig. 3, is
therefore not so variable as the actual state of the air was when
these five-minute readings were taken. Suppose now that, in-
stead of taking the temperature every five minutes, we had done it
at hourly intervals. If, for instance, we had selected, not the
hour but five minutes to the hour, for the time for taking our
readings, then we should have got the curve B. If, however,
we had selected five minutes past the hour for our observations,
we should have got the curve C, while if the readings had been
taken five minutes later the curve would have been I). This latter
curve would have shown a higher maximum for the day of 2° '75
above that given by curve B. This difference might have been
brought about, as stated, by the hour at which the observa-

61

1887.] Mr John Aitken on Thermometer Screens.

tions were made, or it might have resulted from the hour at which
the high maximum happened to be reached, or it might even have
been produced by an error in our time-keeper, either advancing or
retarding the time of observations, while keeping them at hourly
intervals. It is evident, therefore, that curves of temperature drawn
from readings taken at intervals, unless very short, have hut little
value, and may be most misleading. It would he better therefore,
instead of curving the results, simply to connect them with straight
lines, so as to enable the eye easily to catch the successive readings,
it being understood that these lines give no information as to the
state of matters between the observations.

New Screen.

In Part III. of this communication ( Proc . Roy. Soc. Eclin .,
Ho. 121) reference was made to some attempts made to check the
entrance of radiant heat through the air passages into the draught
tube screen. The most successful results were got by introducing
small screens between the bulb of the thermometer and the source
of radiation, and so arranging the air circulation that all air that
had touched the radiation-heated surfaces was drawn away through
side passages, and only the central core of unheated air allowed
to pass on to the centre of the screen, and come into contact with
the bulb and its surroundings. The plan, however, which was
found to work well in a room, in still air, was found to be quite
unsuitable for observations in the open air, owing to the wind
causing eddies inside the screen which interfered with the proper
circulation of the air, and mixed the air heated on the screens with
that entering the centre chamber ; an attempt was therefore made
to see if the principle could not be modified to enable it to be
applied in a form suitable for open-air observations.

A number of complicated forms suggested themselves, but as all
of them seemed likely to give rise to eddies inside the screen, they
were abandoned without trial. At last the simple form shown in
fig. 1 was designed, and a screen of this form was constructed
at the beginning of October. The figure shows a vertical sec-
tion through the centre. As will be seen, it is of extremely
simple construction. The circulation of air through this screen is
entirely affected by the natural movements of the air. Ho modifi-

62 Proceedings of Royal Society of Edinburgh, [jan. 17,

cation of it with draught tube has yet been attempted. The
screen consists of two distinct parts, — the lower, or screen proper,
surrounding the bulb of the thermometer, is constructed to protect the

thermometer from all radiation from below, while the upper part pro-
tects the lower screen from the direct rays of the sun. The upper
part consists of a square sunshade AA made of wood, and supported
in a horizontal position at the proper height from the ground by
means of four wooden supports LL attached to the corners, and fixed
firmly in the ground. If the direct rays of the sun fell on AA it
would get highly heated, and would heat the air on the under side
of it, which might affect the readings of the thermometer. To pre-
vent this, another piece of wood MM is placed over AA parallel to
it, but with an air space between the two, to check the passage of
heat downwards. The lower part of the screen consists of the three
plates C, D, and E, fixed parallel to each other and to the lower
side of the sunshade AA in the position shown. The plates are
held in their places by long screw nails passing through the four
corners. These plates may be made of any substance that is a non-
conductor of heat ; wood is the only material yet tried. The bulb
of the thermometer t is placed in the space between the two plates
C and D, where it is protected from all radiation both from above
and below, and to protect it from the horizontal radiation, it is
surrounded by the annular piece E shaped in the manner shown.
The stem of the thermometer t passes upwards through the sun-
shade, and is protected by means of the louvred box

When the screen was first used, the sunshade part consisted only
of the two pieces AA and MM, but when the sun got very low in
winter it wTas found to affect the correctness of the readings, and

63

1887.] Mr John Aitken on Thermometer Screens.

the small vertical sunshades 00 were added to the screen. These
pieces of wood are fixed in a sloping position, to prevent any air
heated on them from passing downwards towards the thermometer.
As these pieces will slightly interfere with the air circulation, it
is possible the screen will act better without them, if observations
do not require to be made when the sun is very low. They are
not, of course, required on the north side of the screen, or where
houses or trees shut out a low sun. The best size for the sunshade
has yet to he determined. If made larger than shown, say 3 feet
square, then only a very low sun could have any effect on the read-
ings. This screen for future reference is called screen C.

Let us look at the action of this screen when placed in the open
air. It will he seen that the air has a very free circulation through
it ; the plates being horizontal and placed at a distance from each
other, the air has a perfectly free passage through it from whatever
direction it may blow. It will he further noticed that the bulb is
perfectly protected from radiation from all bodies outside. Turning
now to the manner in which the heat absorbed by the screening
surfaces is prevented from affecting the readings of the thermometer :
First, the large sunshade AA prevents any part of the screen proper
from being heated by the direct rays of the sun, and it has thus only
the diffused radiation to contend with. The under side of AA will
be a good deal heated, hut the hot air in contact with it will pass
between AA and C, and not come into contact with the bulb.
The plate E, with the air space between it and D, prevents the heat
radiated from the ground passing upwards to the upper surface of
D. If D was a perfect non-conductor, E would be unnecessary.
The only hot air that really gets into the screen surrounding the
bulb is the air heated on the under surface of C and upper surface
of D, and also that heated on the upper and under surfaces of F.
As will be seen from the construction of the screen, very little heat
falls on the surfaces of C and D, so they will be but little heated ;
but the air that gets heated on these surfaces does not come into
contact with the bulb, but tends to flow straight through and out at
the other side of the screen, keeping to the surfaces of the plates.
This will not be the case when the wind is strong, but when the
conditions are trying, that is, with little wind, it seems probable
that the heated air will pass through without mixing much with the

64

Proceedings of Royal Society of Edinburgh, [jan. 17,

cold. It will be seen from this that the radiant heat which will
affect the thermometer will be that absorbed by the two horizontal
surfaces of F, and the heat absorbed at the outer surfaces of F, and
conducted through the wood into the inner chamber surrounding
the thermometer bulb. The amount of heat received from the first
of these sources will be very small, as the horizontal surfaces of F
receive most of their heat at second hand, that is, after being
radiated and reflected from C and D. The amount received by
direct radiation from without is very small, and is represented
by the angle KIH in the figure ; from which it will be seen that
these surfaces have a verv limited exposure to outside objects, and
the amount conducted through F is probably very small. It will be
seen from the sketch that the annular piece F has its outer surface
groove-shaped. The object of this groove is to prevent the air heated
on it from flowing into the inner chamber, the groove conducting it
round the outside. How far this groove is, necessary, or to what
extent it improves the readings, I cannot say, nor can I say
whether the double bottom is necessary, or whether the passage
between F and D might not be abolished, and the screen and
sunshade thus made smaller. It was thought advisable to take all
these precautions, as there was not time this season to work
upwards from the simpler to the more complicated ; these points
were therefore left for future consideration.

It may be mentioned that this screen has been tried without the
annular piece F, and it was found to work very well, but did not
give quite such low readings as with it in, and its inertia was also
much less without the ring. When the piece F is out, the bulb is
freely exposed to radiation from all surrounding objects ; but as the
space between C and D can then be reduced, the bulb does not get
a very wide view of the outside. Its readings without the annular
piece were very much more correct than the Stevenson screen. This
at first may seem strange, as the bulb of the thermometer in it is
much mere freely exposed to radiation than the one in the Steven-
son screen. The reason for its lower readings would appear to be
that it is exposed to the radiation from trees and other objects
high up, freely exposed to the wind, and therefore cooler ; whereas
the bulb in the Stevenson screen is exposed to the highly heated
grass. This new screen without the ring has not been tried in a

1887.] Mr John Aitken on Thermometer Screens.

65

situation exposed to walls and other large surfaces that get highly-
heated in the sunshine.

Owing to the lateness of the season, no trials with this screen
have been made under severe test conditions. In the beginning of
October it was fitted up on the lawn, and near it was placed a
horizontal sunshade under which was placed the fine-bulbed ther-
mometer with its silver sheath, and a considerable number of com-
parative readings were taken. This was done on a number of days
and in different conditions of weather, and the screen has proved itself
to be considerably in advance of all the others. Its readings being
quite as good as those given by the fine silvered bulb, I shall not
attempt to say which gives the lowest readings, as the conditions
of the trials have not been sufficiently severe or varied enough to
bring out any decided difference ; but under all conditions yet tried
the screen was quite as low as the silvered bulb. It is unnecessary
here to give any detailed account of these trials by themselves, but
I shall presently give some comparative readings taken with this
screen, with the Stevenson screen with the bottom open, and with
it closed, also with the silvered bulb, showing that the new screen
gives much lower and more correct readings than either of the
other screens, and, as the circulation through it is very free, these
lower temperatures cannot be due to the high inertia of the new
screen.

Trial of Screens.

In the first and second parts of this communication the results
were given of some trials of different methods of protecting the
thermometer against the effects of radiation. The conclusions
arrived at were, that the most correct readings were given by the
thermometer placed in a strong current of air produced by a suction
fan, or by a fine-bulbed thermometer exposed under a sunshade
with its bulb protected by a silver sheath. Readings taken by
these two methods agreed very well with each other, and either of
them was taken as a standard of temperature with which to com-
pare the readings given by the different screens. Compared with
these standards, the ordinary Stevenson screen was found to give
readings of from 10,3 to 2° ‘8 too high, when there was much radia-
tion and little wind. Further, it was found that when the Steven-
VOL. XIV. 24/8/87 E

66 Proceedings of Boy al Society of Edinburgh, [jan. 17,

son screen was closed with either a louvred or solid bottom the
error was greatly reduced.

After these tests were made, the Scottish Meteorological Society
took up the matter, and made a number of comparative trials with
the apparatus. The first of these tests were made at Granton in
the summer of 1885 by Mr H. N. Dickson. After the Granton
work was concluded, Mr Dickson took some of the screens to the
top of Ben Nevis, continued the investigation there, and produced a
most careful and elaborate set of observations under the conditions
existing at the top of the mountain. The Ben Nevis work has not
yet been published, hut Mr Dickson communicated some of the
results of his work at Granton to the Royal Society of Edinburgh.*
In this communication he gives curves of the temperatures for two
days. These temperatures were taken by the fan apparatus, the
silvered bulb, and one Stevenson screen with bottom open and
another with it closed. On examining these curves I was much
astonished to find that they confirmed none of the conclusions
arrived at from trials made here. At Granton the fan and silvered
bulb did not give the best results ; the silvered bulb read
highest throughout the whole of the second day, and further there
was little to choose between, in the readings of the Stevenson
sereens with open or closed bottoms.

These results obtained by Mr Dickson at Granton are so different
from mine, that I thought it necessary to reconsider the matter,
and again go over my work, under the conditions existing here. In
my first trials I had only one Stevenson screen ; its readings were
compared with those given by the fan apparatus and the thermo-
meter with silvered bulb ; and, comparing the readings with the
standards when the bottom was out and when it was in, the
result was greatly in favour of the observations made with the
bottom closed. Mr Dickson made his trials with two screens, — one
sent by me with louvred bottom and double top, and another of
the ordinary pattern, that is, with bottom open.

In the autumn, my old screen with its louvred bottom was
returned from the trials at Granton and Ben Nevis, and I obtained
a new one of the standard pattern and exactly similar, only with
open bottom and single top ; the latter of these screens in the

* Proc. Pioy. Soc. Pdin., No. 120, p. 199.

1887.] Mr John Aitken on Thermometer Screens.

67

following is called screen A, and the old one B. The screens were
fitted upon the lawn at a distance of about 15 feet apart, in as nearly
as possible similar exposures to sun and wind. This was done on
the 14th September, and in order to make sure that both screens
gave the same temperature, comparative trials were made with
them, the bottams of both being open. Though the day was not a
very suitable one for the test, as there was not much radiation, still
the old screen was found to give higher readings than the other
by about half a degree. This was owing to the paint being dirty,
and the surface of its louvres being better absorbers of beat than
the louvres of the new and clean one. The screens were now painted
white, after which they looked nearly alike in whiteness, and on trial
with both bottoms open were found to give readings nearly alike.

As it would be almost impossible to set up the two screens in posi-
tions exactly alike with regard to exposure to wind, radiation, &c.,
both screens were provided with movable bottoms, so that either
could be worked with the bottom closed while the other was open.
When testing the screens, sometimes the same screen was kept closed
throughout the whole day, at other times first the one then the
other would be closed, while the external conditions remained con-
stant, so as to check any difference in temperature due to position
or condition of screen, direction of wind, &c.

In these trials the ordinary thermometer used for taking wet and dry
bulb observations was employed. The wet bulb with its apparatus
was removed, and the thermometer in each screen was placed where
the wet one usually is, the index of the instrument being turned
slightly round, so that it could be read by opening the door to only
a very small extent. The object of this was to prevent radiant beat
entering and altering the readings while they were being taken; also
to prevent radiation beating the inside of the screen. The thermo-
meters with which most of the observations were made bad round
bulbs about 8 mm. diameter, but others with smaller bulbs were
occasionally used. All the thermometers were graduated on the
stems, had wide scales, and were easily read. In addition to the
Kew corrections, they were all carefully compared with each other
in water at intervals of 5 degrees or less. The room where these
comparisons were made was heated to the temperature of the
water, so that the temperature of the large volume of water surround-

68

Proceedings of Royal Society of Edinburgh, [jan. 17,

ing tlie thermometers might he kept constant, and the errors due
to imperfect mixing he as small as possible. It may he also
mentioned that the same thermometers were not kept in the same
screens, but they were changed from time to time, to check any error
that might arise from any unknown difference in the thermometers,
and every precaution that could be thought of was taken to
check the results.

The maximum thermometers used were all graduated on the stems
and placed vertically in the screens with their bulbs in the usual
position. They were held in their places by spring clips, to prevent
the position of the index being altered by shaking, a source of error
to which the metal-framed instruments loosely hung are very liable.
The instruments were carefully tested with their stems vertical.
The common maximum thermometers with metal frames and
placed horizontally were discarded, as they were found to give most
uncertain results, and never agreed with the others in the same screen,
owing to the index in these instruments moving too easily, and
more or less easily at different parts of the bore, thus forming a
longer or shorter air space at different parts of the scale. Further,
under certain conditions they gave different readings from the ordi-
nary thermometers with freely exposed bulbs. They read too low
if the high temperature remained only a short time, owing to their
greater inertia; and in the open Stevenson screen they read too high
when radiation remained strong for any length of time, owing to
their larger surface causing them to he much more heated than the
thermometers with freely exposed bulbs, as the frame and thermo-
meter really act as one surface. The maximum thermometers were
changed from screen to screen, generally every day or second day,
as an extra check on possible errors.

A great number of observations were made, extending from the
15th of September to the end of November. On many days
when there was much radiation, a great number of readings were
taken at short intervals, and on as many other days as possible the
temperature was taken by maximum thermometers. The result has
been entirely to confirm my first conclusions. The closed screen
always gave lower readings than the open one.

The fan apparatus was not put on trial, as there were too many
readings to he taken without it. In a trial like this the readings of

1887.] Mr John Aitken on Thermometer Screens. 69

all the instruments ought to he taken at the same moment, owing
to the constant changes of temperature in the air. In practice it is
therefore desirable to make the number of thermometers to be read as
few as possible. The silvered bulb was, however, again put on trial,
and as before, it gave readings much below the Stevenson screen;
considering the season, its readings were as much below the screen
as was observed in the first trials already mentioned.

On 21st September a number of readings were taken from time
to time during most of the day with the two Stevenson screens, the
bottom of A being closed, while B was open. These readings are
marked off at the top of PI. III., and the different readings connected
by straight lines. The day was fine, with passing clouds, a little
wind, and radiation fairly strong for the time of the year. It will
he observed, that till after mid-day there was but little difference in
the readings of the two screens ; this was owing to there being but
little radiation before that hour. At a little before 12 o’clock the
open screen was only 0o,3 above the closed one. A little before 1
o’clock the bottom was taken out of A, and by 1 o’clock both
screens read nearly alike.

The bottom was again put in A, and when the next reading was
taken at 1.15 the open screen read 0o,5 higher than the closed one,
and during the whole day the open one gave the highest readings,
the amount varying according to the radiation at the time. The black
parts at the top of the diagram represent sunshine; they cannot, how-
ever, be very correct, as they are drawn from the notes taken at the
hour the readings were made, and thus only represent the condition
of matters at that time, no intermediate record being taken. A
sunshine recorder would have enabled me to put in these curves
more correctly. The general result is, however, very easily seen from
the record given. It will be noticed, that whenever there was sun-
shine the open screen read much higher than the closed one, and that
during the absence of sunshine they tended to read alike, but it was
not till after radiation had entirely ceased that they read quite alike.
At the 2 o’clock and the 2.5 readings the open screen was 0o-9 higher
than the other, while a little before 3 o’clock the difference was as
much as 1°*1.

While this trial was in progress, in addition to the thermometer
placed where the wet bulb usually is, and which gave the readings

70

Proceedings of Royal Society of Edinburgh, [jan. 17,

shown on PL III., another thermometer was hung up at the hack of
each screen, with its bulb in the place where the bulb of the maximum
thermometer is usually situated, and readings of these thermometers
were taken at the same time as the others. These readings showed
that the thermometers placed at the back of the screens indicated on
this occasion a greater difference than those placed at the sides. The
one placed at the back of the screen with open bottom was as much
as 1°*4 higher than the one at the back of the closed screen.

The readings given in the middle of PI. TIL, taken on the 25th
September, show that the open bottom affects the readings not only
on fine sunshiny days, but also on dull ones. On the 25th, the
sky was uniformly covered all over with a dense mass of clouds,
through which the sun was never visible. But though clouded,
there was a good deal of heat reflected and radiated from the sky,
the surfaces of all exposed bodies were hotter than the air, and the
temperature of the grass rose as much as twelve degrees above the
temperature of the atmosphere. At the beginning of this trial screen
A was open, while B was closed. At 11 o’clock, when the first read-
ings were taken, there was but little difference in the temperatures
given by the two screens, but at 11.35 the open screen read 0°*5
higher than the closed one. After the 11.35 reading, the bottom
was taken out of B, and put into A. After which it will be seen
that the lines connecting the temperatures cross each other, and B,
which at first was closed and read lowest, now that it is open reads
higher than the closed one by 0o,6. These readings show that even
on a dull day there may be a considerable difference in the readings
given by the two screens.

The third set of observations at the foot of PL III. show a series
made on the 7th October with the two screens A and B and with
the new screen C. In these curves, as well as in those taken on the
25th September, there is a curve marked G. This curve represents
the temperature of the grass, and was taken by means of a thermo-
meter placed with its bulb on the grass underneath the open screen.
This curve is not drawn to the same scale as the others, as there
would not be room for it ; the temperature rises so high it could
not be represented within the limits of the plate. For this curve
each space between the lines represents 1 degree, instead of 0o,2 of a
degree, and as the disturbance produced by the hot grass will be in

1887.] Mr John Aitken on Thermometer Screens.

71

proportion to the excess of its temperature above that of the air, the
lowest curve — namely C, in the 7th October observations — is taken
as the base line, and the excess of the temperature of the grass above
C is marked off. For instance, at 11.30, the temperature of the air
as given by C was 57°, while the grass was 70°, or 13 degrees above
C. Read in this way, the G observations show us that at 12.10 the
grass was 18 ‘5 degrees above the temperature of the air.

No curve is given of the silvered-bulb observations, though they
were taken at the same time. The reason for this is that they would
only confuse the figure, as they were practically the same as those of
the screen C, only they were sometimes a little higher and at other
times a little lower than C, owing to the smaller inertia of the
silvered bulb.

The day on which this trial was made was fine, with some wind
from the south-west till near mid-day, when it fell, the air was clear,
and there were a few passing clouds. It wTas not thought advisable
to take readings till near 11 o’clock, as the Stevenson screens were
quite wet in the morning, and tended to read low, owing to the
evaporation. At 10.45, when the readings were begun, the bottom
of screen A was open, and B closed. Readings were taken with the
screens in this condition till 11.45. After which screen A was closed,
and B opened. At 12.30 the condition of the screens was again
reversed, B being closed and A open.

It will be noticed that from 10.45 to 11.45 there was not much
difference between the open screen A and the closed one B, even
though the radiation effect was strong, as will be seen from the
amount of sunshine indicated by the black area below the curves
and by the curve G. The maximum difference between A and B
amounted to only 0o,5 ; this was probably due to the strongish
wind blowing at the time. After 11.45, when the bottom of A was
closed, and B opened, the lines connecting the temperatures cross
each other, and B now, instead of being the lower, becomes much
the higher, the open screen showing a maximum difference of 1°‘5
at 12.10. This great error in the readings of the open screen was
doubtless due to the wind dying away at this hour. After the
bottoms were again reversed, the lines again cross each other ; but as
the sun did not again come out, and the radiation curve G fell very
low, there was not much difference in the two screens ; but it will

72

Proceedings of Royal Society of Edinburgh, [jan. 17,

be observed, that as long as the readings were taken, the open one
always read a little higher than the closed one.

The curve C shows the temperatures given by the new screen,
fig. 1. It will be observed that its readings are very much
below those of either of the Stevenson screens. This difference
varied from time to time, according to the amount of radiation, but
it always remained during the whole time of the observations a good
deal lower than the others. At 12.10 it attained its maximum
difference, being at that hour 2° *3 lower than the ordinary Stevenson,
and 0o,8 lower than the closed Stevenson.

In addition to the observation shown on PI. III. a number of
others have also been taken, but the particulars need not be given
here. The general result has always been the same. The Stevenson
screen with closed bottom always read lower than the open one, and
the C screen lower than either, the amount depending on the radia-
tion, wind, &c., at the time. The observations on PI. II. fig. 2,
show the readings of the three screens on the 18th October. On this
occasion the difference in the screens was not great. It will be seen
that the open Stevenson only went 0°'5 higher than the C screen,
while the closed one was only 0o,2 higher. This small difference
was due to the lateness of the season, the small amount of radia-
tion at the time, together with the strength and direction of the
wind. The wind was fresh, and from the north-east ; it therefore
entered by the cold side of the Stevenson screens, and tended to
keep the side of the screen on which the sun was shining colder
than if it had come from the opposite direction.

Further, in addition to these observations, made at short in-
tervals of time with the ordinary thermometers, the temperature
has been taken almost every day in the three screens by maximum
thermometers, and the result is always the same. On very few days
do they all read alike ; only when there is stormy weather and dense
masses of clouds ; at all other times there are differences, but the
three screens always keep the same relative position, C being lowest,
and the closed screen lower than the open. It may be mentioned,
that in these trials with the maximum thermometers, the same
instruments were not always kept in the same screens, but were
generally changed every morning, to equalize any instrumental errors,
and screens A and B were worked alternately open and closed.

1887.] Mr John Aitken on Thermometer Screens.

73

Even so late as the beginning of November, I was astonished to find
that the three screens gave very different readings, as will he seen
from the following maximum temperatures observed on 31st October
and 1st and 2nd November: —

Date.

Stevenson

Closed.

Stevenson

Open.

Screen

C.

October 31

55*4

561

55-0

November 1

51-5

51-8

50-6

„ 2

52'8

53-0

52-0

On these three days the weather was very fine, with sunshine
and little wind, and on all of these the ordinary Stevenson gave
readings of from 1° to 1°*2 higher than the C screen.

These differences in the readings astonished me greatly at the
time; and when on the 16th of November a difference of more than
a degree was again recorded in the readings of the Stevenson and
the C screen, I began to have some doubts as to the correctness
of the results, as I thought that long before November arrived
radiation would he so weak that it would not interfere seriously
with the correctness of the readings given by the Stevenson screen;
and yet the observations showed that on some days in this month
the error was very considerable. It was, therefore, thought advisable
to make some more trials of the screens by means of ordinary ther-
mometers, and taking readings at short intervals. The morning
of the 17th November being fine, with little wind and a cloudless
sky, readings were taken at five-minute intervals. On this occasion
it was not found possible to make a comparison between the
ordinary Stevenson screen and the modified form, because, owing
to the lowness of the sun, the shadows of the tops of one or two
distant trees passed across the screens, sometimes one and some-
times the other being in the shadow ; and as the screen in the
shade always read lowest, it was impossible to compare the open
with the closed one. They were therefore both worked open, and
the readings taken of the one in sunshine. These readings, with
those given by screen C, are shown in the middle series of observa-
tions in PI. IY. The readings were begun at 11.15 a.m., but the
Stevenson screens not being dry, no readings were taken with them

74 Proceedings of Royal Society of Edinburgh, [jan. 17,

till 11.45, at which hour there was a difference of 0°‘9 between
screen C and the Stevenson. At 12.5 the difference was as much
as 1°'2, after which it fell to about lo,0 at 12.30; after this hour the
weather changed, the sky clouded all over, the radiation effect gradually
fell, and the readings having no further interest were stopped.

The following day, the 18th, being a most perfect day, the trials
were continued. On this occasion the sun rose in a cloudless sky, and
shone brightly till it set. The sun was warmer, and the wind less
than on the previous day. All the conditions were thus favourable
for a trial of this kind, as they tended to bring out in a marked
manner any differences due to radiation. As on the previous day,
the readings were taken at five-minute intervals, with two short
breaks. They were begun at 10.15 a.m., and continued till
3.15 p.m.; the temperatures are all shown in the lowest series of
curves in PI. IV. It will be seen that on this occasion the
dilference was often more than lo,0, and attained a maximum
of 1 ° *85 at 2.20 p.m. The wide separation of the curves at
this hour was due to the wind dying quite away, so that, though
the louvres were not exposed to so strong a radiation at that hour
as they had been at an earlier part of the day, yet they got more
highly heated, as there was no wind to cool them.

It may be mentioned that the fine silvered bulb was also on trial
on these two days. It is, however, impossible to enter its readings
on PL IV., as they were almost exactly the same as screen C, scarcely
ever varying from it more than 0°*1 ; only once it was observed to
vary 0o,2, but generally the two readings were the same. We may,
therefore look on the readings given by the C screen as nearly
correct on those days, and those given by the Stevenson as too high.

We now come to the consideration of the cause of this very great
error in the Stevenson screen, so late in the year, when radiation is
so much reduced. As the error is principally due to the heating of
the louvres by solar radiation, and as the temperature to which
they are raised depends on the amount of heat received by them,
and the rate at which this heat is carried away by the air, we shall
consider these two points separately. First, as to the radiation.
On the two days on which these trials were made, two different
kinds of radiation thermometers were exposed to the sunshine.
One of them was an ordinary vacuum black-bulb thermometer,

1887.] Mr John Aitken on Thermometer Screens.

75

and the other was one of my radiation thermometers having a plate
14 inches square. The following are the maximum readings re-
corded : —

Date.

Vacuum Thermometer.

14" Black Plate.

November 17

81°'5

96°-5

„ 18

91°

113° '5

These radiation temperatures seem high for so low an elevation
as the sun attained at that date, for we must remember that the
temperature of the air was low at the time. Suppose it had been
a warm summer day, and the temperature of the air 75°, then the
same solar radiation as that of the 18th would have raised the
temperature of the vacuum thermometer to 121°, and the other one
to 143°'5. Still stronger radiation effects were observed on the 2nd
December; the air on this day was 32°, vac. 81°, and black surface
111°. This seems to point to a wonderful diathermancy of the
air in winter compared to summer. I write without sufficient
observations, but I imagine an equally low sun in summer would
not have anything like this heating effect.* Then again, the louvres
of the Stevenson screen are exposed almost perpendicularly to the
rays of a low sun ; they therefore receive more heat than from an
equally hot but higher sun in summer.

As stated, owing to shadows passing over the screen, it was not
found possible to make a comparison during the winter months
between the ordinary Stevenson and the modified form. This,
however, does not seem to be a matter of much importance, as we
can scarcely expect to find much difference in their readings at this
season. The daily maximum readings up to the 16th November
do indicate an advantage in favour of the closed form ; but this

* The greater diathermancy of the air in winter than in summer has been
observed by M. Soret at Geneva, and Professor Langley has carefully measured
it. He finds the greater transparency in winter to be chiefly for rays of short
wave lengths, and he finds a close relation between the diathermancy and the
amount of vapour in the air. I much regret I have no low-sun summer observa-
tions with which to compare my winter ones, but the difference in this climate
seems to be very much greater than that observed by M. Soret or Professor
Langley. This difference will probably be due to the position of my observa-
tions being much further north than Geneva or Mount Whitney, and subject
to greater extremes of dryness and moisture.

76

Proceedings of Royal Society of Edinburgh, [jan. 17,

may possibly be the result of accident, and due to the open screen
being more frequently in sunshine than the other, at the time the
maximum temperature was attained. The sun at this season being
very low, its rays strike so nearly horizontally they scarcely heat the
ground, all their heat being received by trees and other vertical
surfaces. There will therefore be but little heat radiated into the
screen from the ground, and there will not be much reflected. While
the observations were being made on the 17th and 18th November,
no thermometer was placed on the grass, as its indications would
have been valueless, owing to its showing a great difference in
temperature according to the situation of the bulb. It would have
read high and above the temperature of the air if it happened to be
in sunshine, but if shaded by the grass it would have read much
below the temperature of the air, as it was observed that the small
hollows in the grass which had got frozen during the night remained
frozen all day. It is evident from this that a thermometer placed on
the grass would not enable us to say whether an excess or deficiency
of heat was radiated in through the open bottom of the screen ; but
of course some heat would be reflected inwards, however cold the grass.

We may here refer to a point of some interest observed when
making these trials in November. In the previous parts of this
communication frequent mention has been made of the quick
fluctuations in the temperature of the passing air, as revealed
by the constant pulsations of the fine-bulbed thermometer. It was
observed in these last trials that these quick changes were almost
entirely absent. The mercury in the fine-bulbed thermometer rose
and fell nearly as steadily as the one in the C screen, seldom
varying from it more than 0°T. The apparent dulness in the
movements of this instrument would seem to be caused by the
entire change in the manner in which the air is heated by solar
radiation in winter compared to summer. When the sun is low the
ground is but little heated by its rays, and there is no layer of hot
air near its surface swept along by the wind, and imperfectly mixed
with the colder air above, to give rise to a succession of warm
and cold parts ; and the heating received by vertical surfaces is
distributed through a much greater depth of atmosphere, and is more
easily and perfectly mixed with the passing air. The air passing
the thermometer has therefore a much more uniform temperature

1887.] Mr John Aitken on Thermometer Screens. 77

with a low than with a high snn. If this is the correct explanation,
then it confirms our conclusion that the fluctuations observed in this
thermometer in summer were due to imperfectly mixed hot and
cold air, and not to variations in the radiation.

We now come to the consideration of the second point, namely,
the power of the passing air to check the effects of radiation. It is
very evident that this will depend on the rate at which the air
passes over the radiation-heated surfaces. Now, in summer, we
have— ^-apart altogether from what we call wind — an unstable con-
dition of the atmosphere which acts quite locally. Owing to the
heating of the ground, the air over it is rarefied and tends to rise ; its
stability is thus constantly disturbed by slight movements. But in
winter we have a totally different condition of matters. Radiation
from the earth being now in excess of that towards it, the surface
of the ground gets cooled, and the air on it tends to become denser,
and so keep closer to the ground, and if the country is flat, there is
no tendency as in summer to local movements, but on the contrary,
the tendency is towards stability. We thus see that the solar radia-
tion effect in summer is to cause — in addition to winds proper — slight
local airs, which prevent the surface of the louvres in the screen from
being highly heated ; whereas in winter the tendency owing to the
lowness of the sun is the other way, and we have degrees of calmness
in winter, quite unknown and impossible in summer. With these
two things, namely, the high heating power of even a low winter sun,
and the great calmness of air possible and frequent at this season,
we seem to have the explanation of the somewhat unexpectedly
great error of the Stevenson screen observed during the winter season.
The error at this season is due principally to the heating of
the louvres, and but little to heat radiated in through the open
bottom.

In connection with the more perfect calms which take place in
winter than in summer, and as showing their effects on the com-
parative cooling produced by them at the different seasons, we may
here refer to the readings given by the two forms of radiation ther-
mometers used in this investigation, namely, the ordinary black-
bulb thermometer in vacuo, and the flat black surface thermometer
having an area of 14 inches square. The ordinary black bulb gives
a very complicated result, indeed it is extremely difficult to interpret

78 Proceedings of Royal Society of Edinburgh, [jan. 17,

its readings. It measures, however, chiefly the intensity of the solar
radiation that is received at the surface of the earth, as modified by
the surroundings of the bulb. The flat black surface, on the other
hand, gives the intensity of the solar radiation as modified by air
currents ; the stronger the wind the lower the temperature recorded
for a given intensity of radiation ; whereas the black bulb in vacuo
is not much affected by wind, though it is affected by other and
rather obscure influences * the flat black surface therefore gives a
better indication of the climate than the black bulb. In fine
summer weather it was found that the flat black surface generally
read about 12 per cent, above the black bulb; but in winter this
difference has been found to be very much greater, on account of the
more perfect calms at that season permitting the exposed surface to
be more highly heated.

But further, it is found that there is a close relation between the
difference in the readings of the two radiation thermometers and the
errors of the Stevenson screen. An examination of the readings
taken in December show that as the ratio of the temperature of the
black surface to that of the black bulb increased, the error in the
screen increased along with it. When the ratio of the black surface
to the vacuum black bulb was under 1 -5, the error of the Stevenson
screen was about 1 degree, and as the ratio increased, the error in-
creased along with it. This error attained its maximum, as far as was
observed, about mid-day on the 13th of the month; at that hour
the temperature of the air was 34°, the vacuum black bulb 64°, and
the flat black surface 93°. The black bulb was thus 30° above the
temperature of the air, while the black surface was 59°, or in the
ratio of nearly two. At that hour the Stevenson screen reached its
maximum error for the day, being 2° '9 above the standard. It may
be noted that when the error of the screen was at its maximum the
vacuum thermometer did not register the maximum temperature for
the month ; indeed it was one of the lowest on the bright days, but
owing to the entire absence of wind at the time, the difference in the
heating effect of the sun’s rays on the two forms of radiation thermo-
meters, and the error of the Stevenson screen attained their maximum.

While on this subject, it may be as well to consider an effect of
these two tendencies of air when heated and when cooled, — the one
to instability and currents, the other to stability and calmness. Given

1887.] Mr John Aitken on Thermometer Screens.

79

a condition of weather in which there is no wind, then in summer
the effect of heating the air on the ground is to cause ascending
currents of hot air. There is thus an influence at work in summer
tending to keep the air near the ground at nearly the same tempera-
ture at all places within a considerable distance ; while the effect of
cooling the air in winter is precisely the opposite, as the cooled air
tends to sink down into hollows and remain there, where its
temperature is further reduced hy contact with radiating surfaces.
The cooling of the air in winter, therefore, in the absence of winds,
will tend to give rise to differences of temperature, which may
amount to some degrees within a limited area.

From the above we can see that on a day on which there is no
wind, the temperature of the air in an exposed situation, and where
the sun is shining, may he some degrees warmer than the air in a
cup-shaped hollow, into which the sun’s rays do not penetrate,
provided always that the sky overhead is clear and radiation into
space strong. Take the case of the 18th November : on that day
the temperature of the air was 45°, while the grass that was not
exposed to the sunshine was under 32°. We can easily imagine
conditions in which the air resting on grass at 32° in a hollow into
which the sun does not shine might easily be cooled some degrees
below the temperature of the air above. These observations are
suggested by the peculiar condition of matters reported from
different parts of London on the 24th November. In one part
of London the maximum temperature was 40°, wdiile at another
it did not rise above 32°, a difference of 8°, which might be
accounted for in the way above stated, as there was no wind at the
time.

A record having been kept for some time of the maximum
temperatures recorded by the three screens, the readings taken
from the 23rd September to the 25th November are marked off at
the top of PI. IY. The temperatures were not - taken every day,
but every observation taken is marked. Most of these are from
the readings of the maximum thermometers, but on those days on
which the screens were under trial, the readings taken at short
intervals were used, and the maximum recorded readings selected.
As it was impossible within the limits of the plate to record the
actual temperatures, only the differences between the readings are

80 Proceedings of Royal Society of Edinburgh, [jan. 17,

shown. The readings of the open Stevenson screen are used as a
base line, and the difference between its readings and those of the
closed Stevenson and the screen C are marked off, each series being
connected by straight lines. It will be seen that on only two
occasions did the screen C give the highest readings, and on these
exceptional occasions it was only 0°T higher. As the days on which
these occurred were dull and windy, the differences were probably
errors of observation, such as are quite to be expected. It will
be observed that the close screen generally held an intermediate
position between the open one and screen C, its readings being
better than the former, but not so good as the latter.

Accepting screen C as our standard, which we may do for the
present, its readings being the same as the fine silvered bulb, an
examination of the maximum temperature curves shows us that in
autumn and winter the Stevenson screen is frequently more than 1°
too high. In the first half of October it was more than 2o,0 too
high on two occasions, and in November it was a degree or more
wrong eight times — in addition to the seven times shown on plate
there was an error of 1°T on the last day of the month — and on
one occasion in that month it was as much as 1°*75 too high. The
differences shown in PI. IV. are the differences in the maximum
readings, but these are not necessarily the greatest differences for the
day. Of course, the differences in the maximum readings are what
are practically required, yet it may be interesting to note that this
may not be the greatest difference for the day. For instance, on the
21st November the maximum readings for the day were 39° ‘6 for
screen C, and 410,2 for the open Stevenson, thus giving a difference
in the maximum for the day of l°-6 as shown. The day being
very trying, a reading was taken at 1 o’clock, when the index of the
maximum thermometer in screen C was at 38° and in the Stevenson
at 40o,6, or a difference of 20,6. This great difference was due to
there being a dead calm a short time before.

The weather on the different days is not entered on the plate, as
it is quite unnecessary ; the curves speak for themselves. Whenever
the reading of the screen C was much below the others, the weather
was fine, and it was only during cloudy and stormy weather
that all three agreed.

The observations for December show that the maximum given

1887.] Mr John Aitken on Thermometer Screens.

81

by the Stevenson screen on eight days was one degree or more above
the maximum given by screen C. The maximum difference for the
month was 1 ° *75. The screens gave the same maximum on eleven
days, while the mean maximum temperature for the month wras 36° ‘78
by the Stevenson, and 36° ‘25 by the C screen ; that is, the C screen
gave an average maximum temperature of fully half a degree below
the Stevenson. Of course, the average error is determined very much
by the number of bright days in the month. Taking the average
error for the fine days of the month, it was about 1°*4, and that would
have been the error if the month had been bright throughout. The
difference for January 1887 promises to be very small. Owing to
the dull and clouded weather, the screens have read exactly alike on
almost every day of this month. The observations for December
and January are not entered in the plates.

Returning now to the consideration of why the result got by the
different screens at Granton differ so much from those obtained here,
I think I have taken every precaution to ensure the correctness of
my results; and yet we find, even so late as the middle of November,
that the Stevenson screen with open bottom gave higher readings
than the closed one ; also that the thermometer with its bulb
sheathed in silver gave, as in the previous trials, readings much
lower than either of them, and yet the observations made at Granton
show no such differences ; how then are we to account for the
difference in the results obtained at the two places ?

The first thing that suggests itself as a possible cause of the
differences is the condition of the louvres in the two screens. Was
the one dirtier than the other, or were the absorbing powers of
the paints on the two screens different? We have seen that, on a
not very trying day, in September, the absorbing powers of the
two screens used in my last trials caused a difference of about 0o-5.
On a bright day, such as those on which the Granton trials were
made, this difference would be greater ; and if the closed screen w^as
in the Granton trials the better absorber of the two, this might
have neutralised any advantage arising from its being closed.
With regard to the explanation of the high readings given by
the silvered bulb at Granton, I have great difficulty. No doubt,
any imperfection in the cleanness of the silver would increase its
absorbing powers and so raise the temperature, but doubtless care
vol. xiv. 7/9/87

F

82 Proceedings of Eoyal Society of Edinburgh, [jan. 17,

would be taken to keep the polish in as perfect a condition as
possible.

In addition, however, to these possible sources of error, there is
in the situation of the two places where the observations were made
an essential difference which would affect the results. The site of
the screens at Granton was very freely exposed to every breath of
wind, being on a knoll in the middle of a field near the sea shore,
perfectly open to the west, north, and east, while the land rose a
little to the south, and the screens were at a great distance from
trees or anything that could obstruct the free circulation of the air.
The site on which the screens are placed here is very different, and
not so good in many respects, though I think it will compare favour-
ably with the site of many screens in daily use. Here the screens
are on a lawn, and surrounded at no very great distance by trees.
As the surroundings of the screens seem to be a matter of greater
importance than might at first be thought, it will be as well that
I state more fully the conditions surrounding the screens here.
Standing at the screens, the view in the different directions is closed
in principally by trees. The view to the south and round by west
to north-west is closed in by a narrow line of trees running north
and south, at a distance of 26 yards at the point where it comes
nearest to the screens. From the north-west to the north-east, at a
distance of about 24 yards, there is a holly hedge 8 feet high, and
also a few trees. From north-east to east are trees at a distance.
From east to south-east a holly hedge running north and south, and
coming at its north end to within 12 yards of the screens. From
south-east to south are stables and kennels at a distance of 35 yards.
The ground slopes slightly down to the north. The screens are
placed east and west of each other, and all the ground in view is
under grass. It will be seen that, while the position is somewhat
sheltered from winds blowing from east to south-east, it is fairly
open to winds from south to south-west, as well as from north-west
and north-east. But, on the whole, it is evident the site is much,
more confined than the Granton one.

An evident result of the opener exposure of the Granton site is,
that the Stevenson screens would be kept cooler there, on account of
the freer circulation of the air through the louvres, the screens
would thus be both more nearly correct, and therefore nearly agree

1887.] Mr John Aitken on Thermometer Screens . 83

with each other and with the silvered bulb, at the more exposed
Granton site than at the more confined one here. Further, on both
days on which the Granton trials were made, the wind entered
the screens from the cold side. This of itself is a most important
point, especially if the sky is clear, as the cold sides of the screens
may be below the temperature of the air, and the passage of the
air in that direction prevents the advance inwards of the heat from
the sun-lieated louvres. I have noticed in the trials here that on
all occasions on which the wind was north of east or west the errors
were comparatively small. It therefore seems possible that the more
open exposure of the Granton site, together with the direction of
the wind at the time the two sets of the Granton observations were
made, are the principal causes of the difference in our results.

Since this paper was given in, Mr Dickson, who has continued
his trials with the Stevenson screens at the top of Ben Nevis, has
very kindly furnished me with an abstract of the result obtained in
that situation. He says the readings for thirty-four days gave the
following mean maxima : —

Stevenson, Open bottom, 41°-45.

„ Closed „ 41c,00.

Thus showing a difference in favour of the closed bottom of nearly
half a degree, a result confirming the conclusion arrived at in this
and a preceding paper.

The site here being surrounded by trees in almost every direction,
may in part explain the reason why screen C, even when the
annular piece F was removed, gave such correct readings. We have
seen that on the 7th October the temperature of the grass rose 18°
above the temperature of the air. Now that is the temperature to
which the thermometers in the Stevenson screen with open bottom
are exposed, while screen C, by its construction, cuts off all this
radiation and exposes the bulb to the radiation from the trees, which
will never be so highly heated as the grass, as they have a freer
circulation of air through them. This, combined with the very
free circulation of air through the screen, and the method adopted
for preventing the heated air touching the thermometer, would seem
to account for the low readings given by this screen even when the
piece F is removed.

84 Proceedings of Royal Society of Edinburgh, [jan. 17,

There would appear to be an advantage in favour of the C screen,
which may be referred to here. We have seen that when the louvres
of the Stevenson screen get dirty, they absorb more radiant heat, and
so increase the error of the readings. Many screens in daily use
must, from this cause, give too high readings. The screen C is,
however, not much affected from this cause; indeed, I am not quite
certain but that the screen will act quite as well if certain parts
are black. Tor instance, the sides of the plates C and D which
are exposed to the bulb of the thermometer might perhaps with
advantage be blackened. I have not yet been able experimentally
to determine this point, but many of my observations have been
taken with a large black patch in the centre of each plate. My
reason for testing this was, that if these surfaces are white, they
will reflect to the bulb some of the heat which falls on them ; but
if they are black, they will absorb this heat; and it seemed possible
that the increased amount of heat radiated by the blackened sur-
faces, together with the greater amount to which the air in contact
with them is heated, might affect the thermometer less than the heat
reflected by the white. It was not found possible to settle this point
by readings taken with the screen under the two conditions and com-
paring them with the silvered bulb, as the inertia of the two arrange-
ments is so different, and the effect sought for very small. This, with
many other matters connected with this screen, will be best settled
by means of two screens similar in all points save the one we wish
to test. For these trials, however, we must wait another warm
season. Although this new screen has acted very satisfactorily
up to the present time, giving readings almost exactly the same
as the fine silvered bulb standard, and much below those of the
Stevenson screen, yet it would be rash to conclude that it will be
superior under all conditions of climate. The various influences
to which thermometer screens are exposed are so numerous that
the unexpected has many opportunities of happening and upsetting
our hopes and expectations.

[A Postscript to this Paper will be found immediately after the
Proceedings of July 1887.]

Proc. Roy. Soc. Edin.

Vol. XIV PI. I!

A. RITCHIE or SON. COIN

I

Proc. Roy. Soc. Edin. Vol.XlV PI. Ill

A . BITCHIE t.

Proc. Roy. Soc. Edin. Vol. XIV PI. IV

ftlTCUlt & SON. ED<n'

.

1 f

,

> *

1887.] Professor Tait on Smooth Impinging Spheres.

85

4. On the General Effects of Molecular Attraction of Small
Range on the Behaviour of a Group of Smooth
Impinging Spheres. By Professor Tait.

(Abstract.)

The present instalment traces some of the consequences of
assuming the hard spherical particles of a gas to exert intense
molecular forces when at distances comparable with their diameters.
The effect of the new term in the virial in counteracting and at
last obliterating that due to the impacts, is traced as the gas is
gradually compressed.

Next, the spheres (still supposed to attract one another) are
regarded as capable of absorbing energy in a vibratory form, and
of losing it directly by radiation. In such a case the relative
translatory energy may be so reduced that pairs of spheres may
remain within molecular distance from one another. The bearing
of these results upon condensation, dissociation, &c., is given.

PRIVATE BUSINESS.

Mr Nanabhay A. F. Moos, L.C.E., B.Sc., Assistant Professor of
Engineering, College of Science, Bombay, was balloted for, and
declared duly elected a Fellow of the Society.

Monday , 31 st January 1887.

JOHN MURRAY, Ph.D., Vice-President, in the Chair.

The following Communications were read : —

1. On a New Formula for the Pressure of Earth against a
Retaining Wall. By A. C. Elliott, B.Sc., C.E. Com-
municated by Professor Armstrong.

There are two main distinct methods of attacking the problem
of the retaining wall. The first in chronological order is due to
Coulomb, and is variously named, perhaps most commonly as the
method of the Wedge of Least Resistance. Briefly characterised, it

86

Proceedings of Boy al Society of Edinburgh. [jan. 31,

might be said to depend upon the mathematical artifice of finding
the resultant force due to the mutual action of the earth mass, and
the wall a maximum, the earth being supposed to yield incipient^
under the action of its weight, and in opposition to friction and the
reaction in question, along an inclined plane determined so as to
fulfil that imposed condition. Coulomb’s method has been de-
veloped by various writers, and may be regarded as complete.

The second method is due to Rankine. It is based upon two
general dynamical principles, both of which are really involved in
Coulomb’s treatment, but which are there drawn upon as it were
incidentally rather than appealed to as fundamental principles.
Rankine’s first principle is merely a statement that the well-known
propositions in regard to the laws of static friction apply in the
interior of a granular mass of earth ; and, in particular, that there
is a coefficient of friction for earth upon earth of any given kind.
That some sort of physical datum of this nature with respect to any
given kind of earth may be properly assumed does not admit of
question ; but how far it answers to an ordinary physical constant,
or even an ordinary coefficient of friction, is by no means certain.
However, objections of this kind apply to Coulomb’s method with
even greater force, and the author proposes to attempt to push
Rankine’s theory farther on its present bases, rather than to discuss
preliminary difficulties. If, therefore, he shall be fortunate enough
to arrive by a path not altogether mistaken at certain results, he
would merely say that such are the consequences of adopting these
fundamental principles.

The first of the principles just referred to enabled Rankine to
formulate the conditions of equilibrium in the interior of an earth
mass generally, and in terms of certain data for particular cases
occurring in practice.

When he comes to deal with the action of the earth on a wall,
Rankine refers to his second principle, which was first distinctly
laid down by the late Canon Moseley. Briefly it is merely this : —
When a system is in equilibrium under a set of forces, those which
are called into existence by the action of the others are the least
possible consistent with the given conditions ; or, among a set of
forces, active and passive, in equilibrium, the passive forces are the
least possible.

1887.] Mr A. C. Elliott on Formula for Retaining Wall. 87

Rankine uses the term granular mass to indicate that the earth
is assumed to have no tenacity or cohesion. Some kinds of material
might fairly claim to he so described, but in ordinary practice it is
quite common to meet with earth which will stand with a vertical
face for a considerable time ; but since the action of time and
weather will inevitably result in the material ultimately assuming
a slope more or less constant for that particular kind, it is not only
prudent but necessary to allow for the almost total failure of tenacity
or cohesive strength with lapse of time. In the retaining wall
problem the effect of assuming any degree of tenacity being clearly
operative in reducing the resultant force representing the mutual
action of the earth mass and the wall, Rankine makes no scruple
to discarding tenacity altogether.

It may be remarked that Coulomb’s method implicitly takes
account of some degree of tenacity. Nearly all direct experiments
have shown considerable divergence between the actual overturning
moment of the earth pressure on the wall, and that calculated by
Coulomb’s or Rankine’s method (employing the accepted methods
for determining the principal constant), the divergence very com-
monly amounting to upwards of 50 per cent, in excess of the
observed value. The discrepancy is, in the' author’s opinion, in
great part clearly due to the ignoring in the mathematical investi-
gation of the effect of tenacity. On the ground that no satisfactory
allowance could be made on account of a quantity which is at once
a function of time and weather, Rankine, as has been already re-
marked, expressly rejects the tenacity from consideration, so that, in
the case of Rankine’s formula at least, one ought not to be surprised
if the calculated should exceed the actual overturning moment of
the earth pressure to a considerable extent.

But granting this, or at any rate taking leave of it, there still
remains the experimental evidence that Coulomb’s method in its
complete form, though much more unsatisfactory from a physical
point of view, gives better results than Rankine’s. Attention has
consequently been redirected to Rankine’s method with the object
if possible of removing this anomaly ; and, accordingly, it has been
pointed out that Rankine simply applies the conditions of equi-
librium, obtaining at a point in the interior of the earth mass, to a
point situated in the surface of separation, between the wall and

88

Proceedings of Boy al Society of Edinburgh, [jan. 31,

the earth mass, thus tacitly neglecting the boundary conditions.
Rankine, in short, neglects the friction between the earth mass and
the wall, or supposes the wall to he perfectly smooth. Dr Maurice
Levy and Professor Boussinesq have worked at the problem thus
presented, but the author is only partially acquainted with Prof.
Boussinesq’s results, and not at all with Dr Levy’s. In 1881
Mr Benjamin Baker read a paper before the Institution of Civil
Engineers, “ On the Actual Pressure of Earthwork ” — a valuable
contribution to the literature of the subject, to which reference will
afterwards be made. An interesting communication from Professor
Boussinesq is printed with the correspondence appended to the
paper, which will be found in vol. lxv. of the Proceedings.

The author will confine himself to the case where the surface of
the earth to be retained is level. Rankine’s hypothesis of a
granular material and the fundamental principles before mentioned
are assumed.

Fig. 1. — Vertical Section of a Right Prism of Earth.

Let ABC be a vertical section of a right prism of earth, whose
length-axis is parallel to the inner face of the wall, which will
here be assumed to be vertical. Let BC be in contact with the
wall, and AC horizontal ; also, let the prism be of unit length, and
let the transverse dimensions be very small.

1887.] Mr A. C. Elliott on Formula for Retaining Wall. 89

Consider the forces acting on the prism : —

(1) Its weight : this may he neglected in comparison with the

other impressed forces, which are small quantities of the
second order, while the weight is a small quantity of
the third order.

(2) The forces acting on the end faces of the right prism : — these

are independently balanced as regards the wall, and may
henceforth be left out of consideration.

(3) The remaining impressed forces acting parallel to the plane of

the section : of these let pv be the vertical pressure in the
neighbourhood of the prism, due to the column of earth ;
p0 the inclined pressure exerted by the wall.

/3 the angle between the direction of p0 and the normal to the
inner face of the wall, drawn outwards. This angle /?, in
the case where motion is just about to take place along the
interface BC, will be equal to the angle of friction for the
earth on the wall.

r the pressure of the contiguous earth on the face AB of the prism;
a the obliquity of r ; or the angle which the direction of the stress
r makes with the normal to AB ;

0 the angle BAC.

Considering first the equation of moments, it will appear that the
tangential stress on AC must be equal to the tangential stress on
BC ; but the tangential stress on BC is p0 sin j3 , which is therefore
the value of the tangential stress on AC.

Besolving vertically and horizontally

pvb+Posin/3. a~r cos (6 -a) . c = 0 . . . . (1)

p0 cos /3 . a+p0 sin /3 . b - r sin (6 - a) . c — 0 ... (2)

Dividing out by c and substituting in terms of 0,

pv cos 6 +p0 sin sin 0 = r cos (0 - a) .... (3)
p0 cos J3 sin 0 +p0 sin (3 cos 6 = r sin (0 - a) .... (4)

Eliminating r, and writing s for the ratio p0!pv

1 sin /3 tan 6 1 + tan a tan 0

s (cos j3 + sin j3 cot 6) 1 - tan a cot 0

O)

If now 6 be regarded as the independent, and a as the dependent
variable, to find the condition for a a maximum (5) must be

90

Proceedings of Roy cd Society of Edinburgh, [jan. 31,

differentiated with respect to 0 and

da

db

put equal to zero in the result

— i.e. (5) must he differentiated partially with respect to 0 . There
then results the condition

_ s sin /3
an a s cos {3 sin1 2 0 — cos2 0

• (6)

In strictness, this step ought to he immediately justified by an
examination of the sign of , under the condition (6). This will

he found to involve a considerable amount of labour ; and, since the
operation is essentially of the nature of a verification, the author
proposes to accept, for the present, (6) as the condition for a a
maximum, and afterwards to justify whatever assumption this may
involve, by a process of verification. The mere fact, however, of
obtaining a result which does not necessarily imply that a must be
zero, indicates the existence of a maximum or minimum condition
different from a = 0 ; which is, of course, the condition which a
fulfils when it is a minimum as regards mere numerical magni-
tude. Farther, from the theory of stress, it is known that, corre-
sponding to the maximum value of a, there is a maximum value
of equal numerical amount hut of opposite sign,

How the maximum value of a is to he <f>, the angle of repose ; the
angle, that is, whose tangent is the coefficient of friction of earth
upon earth, for earth of the given kind.

Let 01 be the value of 6, when a = cj>. Then 0 = 0X and a = cf> must
satisfy (5) and (6) simultaneously. Therefore —

1 + s sin /? tan #x 1 + tan tan 0l ^

s (cos/5 + sin/? cot 0X) 1 — tan </> cot 0i

and

tan (j)

ssin /3

scos/3 sin2 — cos2#!

(8)

(8) may be written

, 1 + s sin R cot <f) /qx

tan2 #! = — t 7> n 7-Tx ..... (9)

s (cos fj — sin p cot <p)

Eliminating 6i between (7) and (8) there is obtained finally, after
solving for s,

1887.] Mr A. C. Elliott on Formula for Retaining Wall. 91

cos (3(\+2 tan2 <f>) ± 2 sec <j> J cos2 /? tan2 </> - sin2 (3 . /jq\
4 sin2 j3 sec2 </> + cos2 (3

giving the relation between s, /3 , and </>, desired.

(10) may be written in a form more convenient for calculation
thus —

cos /3{2 — cos2 </>] ± 2 */cos2 /? — cos2 </> on

4 - cos2/?{4 - cos2 </>}

Again, when (3- 0 (11) may be written

s=l±sin^, ....... (12)

1 + sin </>

And it will also be observed that, when (3 = </>, the quantity under
the radical sign becomes zero, and when /?></>, negative,- rendering
the whole expression imaginary from a physical point of view.

These equations give two values of s consistent with the condi-
tions. Since, however, the reaction of the wall is a 'passive force,
corresponding to the active pressure of the earth, it appears at once
from Moseley’s principle that the smaller value of s must be taken.
Therefore, finally,

_ cos (3 [2 — cos2 </>} - 2 Jcos2 (3 — cos2 </>
4 — cos2/? {4 - cos 2</>}

and

1 - sin </>

s=- r — v when B

1 + Sill <f> 1

0

(13)

(14)

Given therefore the angle of repose of the earth, and the correspond-
ing friction angle for the earth on the wall, the direction and amount
of the mutual action becomes determinate if we assume that failure
cannot take place until (3 has attained its limiting value, which may
be denoted by (39 . It may be at once remarked that, however
closely (3 may approach to </>, it can never exceed that value ; since,
when /? = </>, the surface of separation, between the wall and the
earth, becomes a plane of rupture. When, on the other hand,
it is supposed with greater generality that at the time of fracture
/?2 >/?<</>, equilibrium must be destroyed without any relative
motion between the wall and the earth in the immediate neighbour-
hood of the inner face having, in the first instance, taken place. In
other words, the inclination denoted by j3 has not reached its

92

Proceedings of Royal Society of Edinburgh, [jan. 31,

limiting amount when failure occurs along one or both of the two
possible planes of rupture which may be shown to exist.

The author ventures to advance the view that the condition of
things may be rendered intelligible by a second application of
Moseley’s principle. Tor, consider the stability of the wall, and
suppose the critical condition to have been attained, and that so
before /3 had reached the value /i2. To the actual value of J3
looked upon for the moment as a limiting angle, there corresponds a
certain roughness of the wall ; and suppose that by some external
agency (such as a change of temperature or the like) the degree of
roughness of the actual wall to be, in effect, reduced to this value.
It is impossible to conceive that by a process such as this the
critical state can have been disturbed. On the other hand, there
can be no difficulty in perceiving that, if it is a fact that friction
between the earth and the wall adds to its stability, failure may
be brought about by simply allowing the degree of roughness to fall
ever so little below the critical value — the value, that is, which
corresponds to the actual value of /3 when the wall is in the critical
state. Hence /3 has a value such that the stability of the wall in
the critical state is a maximum ; or, in other words, the overturning
moment of the earth pressure for any given wall is a minimum with
respect to /?.

In most cases which occur in practice, /3 may range through all
values up to </> ; for not only are the inner faces of retaining walls
usually left rough, but they are frequently stepped in a manner
which makes a cross section somewhat resemble a flight of steps.

The author has calculated some numerical values for s, corre-
sponding to certain values of <£ and j3, which will be found in an
annexed table. He has also tabulated the corresponding values of
the ratio of breadth to depth of a wall whose density is equal to the
density of the earth, and whose moment of stability is just equal to
the overturning moment of the earth pressure. A polar curve
showing the values of these ratios for <j> = 40° corresponding to the
successive values of /3 is also annexed.

Equation (14) resulting from (13) by putting /3 = 0, is identical
with the corresponding formula of Rankine. The author has, how-
ever, farther verified the formula (13) and by consequence (6), for
the case where <£ = 60° and /3 = 30°. Inserting these values in (13),

1887.] Mr A. C. Elliott on Formula for Retaining Wall. 93

s= ’0853 — = 11-723

s

To find the principal axes for this stress system, put a = 0 in (5),
and let 0a he the corresponding value of 0. This gives, on solution
of the resulting quadratic,

]{fzl .

2 sin J3 si 4 sm2 ft
where / is written for 1 js.

■ (15)

Hence,

tan 0a = *046 or -21 ‘760
6a = 2° 38' or -87° 22'

Assigning to pv for simplicity the value 10, and making use of
(3) or (4),

/ = 10-02 r"= '718

where r' and r" denote respectively the greatest and least principal
stresses.

Now from Eankine’s ellipse of stress it is seen at once that the
obliquity has a maximum value on two sections symmetrically
situated with respect to the axes of amount

sin-1

t rr

ty* ^ ry*

r' + r7’

which for the case in point becomes —

sin~Ho-738 = sin_l 866 = 60° ;

and this agrees with the original assumption. The relative positions
of the two planes for which the obliquity is maximum, the principal
axes, and the vertical and horizontal directions are shown in the
diagram, upon which, also, the ellipse of stress for the system in
question has been represented.

Suppose, for simplicity, that the cross section of the wall is
rectangular. The oblique pressure y?0, inclined to the normal to
the inner face of the wall at the angle f3, is found, for any point,
simply by multiplying the ratio s by the pressure due to the column
of earth at that point. Let the earth have the uniform density pe.
Then the oblique pressure on the face at the depth h from the
surface is

Po — sJlpe.

94 Proceedings of Royal Society of Edinburgh. [jan. 31,

The force on an element of area 1 foot long horizontally, and of
depth dh is therefore

dV = shpedh.

Hence the whole action of the earth on the wall per foot-run is
represented by a force

P=2 fyisP •••••••• (16)

where b1 is the effective depth of the earth. P will act at the
centre of pressure, and be inclined at the angle /3 to the horizontal.
Let b be the breadth, h the height, and pm the density of the wall.
Then, equating the overturning moment to the moment of stability,
and solving a quadratic

b Pe $ ssm/3 f is sin /?\2 pm cos/? )

ftVsa ~ ^"+ vnr-j +h$~s~r • • (1,)

A good example of the divergence of the results obtained by
Rankine’s formula from actual facts, even where the earth mass
approximates to the hypothetical granular material of the mathe-
matical investigation, is adduced by Mr Baker in his paper, “ On
the Actual Pressure of Earthwork,” already referred to. The
example in question is not only interesting in itself, but has the
additional advantage of having been selected by Mr Elamant for an
application of Professor Boussinesq’s formulae.

Mr Baker says — “When the wood paving was recently laid in
Regent Street, the space being limited, the stacked wooden blocks
in many cases had to do duty as retaining walls to hold up the
broken stone ballast required for the concrete substructure. In one
instance (Example I.) the author noted that a wall of pitch pine
blocks, 4 feet high and 1 foot thick, sustained the vertical face of a
bank of old macadam materials which had been broken up, screened,
and tossed against this wall, until the bank had attained a height
of 3 feet 9 inches, a width at the top of about 5 feet, and slopes
on the farther sides, deviating little from P2 to 1” (Proc. Inst.
C.JE., vol. Ixv. p. 145). [P2 to 1 corresponds to an angle of

repose, 39° 48'].

ISTow, Rankine’s hypothesis amounts to putting /? = 0 in the
notation of the present paper. Putting therefore in (17)

1887.] Mr A. C. Elliott on Formula for Retaining Wall. 95

(3 = 0.
hY = 3-75.

fje= 101 lbs. per cub. foot. [Mr Baker.]

4

pm — 46 x = 49 lbs. per cub. foot. [Mr Baker.]

O' i o

there is found

*=•386 6 = 1-448 ft.

lu

But actually the wall was only 1 foot thick; whereas, as has just
appeared, according to Rankine’s formula it would just have been
on the point of overturning had it been 1*448 feet thick.

Fig. 2.

According to the view adopted in this paper (3 will assume a
value such that the overturning couple will be a minimum. Taking
39° 48', as within the errors of observation 40°, an examination of

96

Proceedings of Boy al Society of Edinburgh. [jan. 31,

o

hh

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1887.] Mr A. C. Elliott on Formula for Retaining Wall. 97

the appended table shows that for pe = pm this occurs when (3 is
about 35°. No great error will be introduced by assuming that (3
has this value for the case in point. Taking the corresponding
value of s from the table, and substituting in (17),

y= -2799 or 6 = 1-05 ft.
h

Professor Boussinesq’s expressions gave b from 10 to 11 J inches.

Fig. 3.

2. The Conducting Paths between the Cortex of the Cere-

brum and the Lower Centres, in relation to their Func-
tion. By Professor D. J. Hamilton.

3. Researches on Micro-Organisms, including ideas of a

New Method for their Destruction in Certain Cases
of Contagious Disease. By Dr A. B. Griffiths, E.RS.
(Edin.), E.C.S. (Lond. & Paris), Principal, and Lecturer
on Chemistry and Biology, School of Science, Lincoln;
late Lecturer on Chemistry, Technical School, Man-
chester, &c.

The opinion of the most profound workers in the so-called
“ germ diseases ” is, that these diseases are really due to the patho-
logical effects of chemical substances (ptomaines) elaborated and

secreted by certain micro-organisms. That is, a given contagious
VOL. XIV. 6/9/87 g

98

Proceedings of Boyal Society of Edinburgh. [jan, 31 ,

disease is rather the result of one or more compounds formed by
the life-history of a micro-organism, than the mere presence of that
micro-organism itself. By looking at certain cases in the above
light, we can well understand why persons suffering with cholera
die so rapidly. The alkaloid or ptomaine (discovered by Pouchet
in 1885) which the Comma bacillus secretes or forms is rapidly
absorbed into the blood, long before the bacillus itself is capable
of being absorbed by the mucous membrane of the intestine, and
then into the blood. It is a well-known fact that most micro-
organisms multiply with great rapidity in the media in which they
live, and if particular organisms can be destroyed, the harmful
effects of the products produced by their life-histories will not
increase, and the disease will soon be at an end.

Of course, I am fully aware that it must not be supposed that
because we find in the blood and tissues of man and animals
(suffering from a contagious disease) certain micro-organisms, that
these micro-organisms are necessarily the cause, or even indirectly
the cause, of that disease. Hot until we have obtained by pure
cultivations, in an artificial sterilised medium, the organisms in a
perfectly pure state, and then, by an injection into the blood of
man or an animal of the purified organisms, the disease is repro-
duced, can we say that a particular disease is the result of the
life-history of any particular micro-organism.

It is not my object here to describe the methods adopted by
physiological chemists to obtain pure cultivations of any given micro-
organism, although no interpretations can be given of any experi-
ments unless the experimenter has worked with purified organisms
obtained by artificial cultivation with all its precautions.

I wish to detail what appears to my mind the most reasonable
method for the treatment of those contagious diseases whose “ seat
of war ” is in the blood itself. I have already had the honour
of presenting to the Royal Society of Edinburgh a paper “ On
the Action of Salicylic Acid on Ferments ” (Proc. Roy. Soc.
Edin ., Ho. 121, pp. 527-530). It was shown in that paper
that an aqueous solution of salicylic acid (0‘2 grm. of the acid
in 1000 c.c. of water) was capable of destroying such micro-
organisms as Mycoderma aceti , Bacterium lactis , and Bacillus
butyricus ( B . amylobacter). It was found, on a close microscopical

1887.]

Dr A. B. Griffiths on Micro-Organisms.

99

examination with high powers, that the salicylic acid solution had
acted upon the form of cellulose forming the external wall of these
lowly organisms, perforating it, and ultimately destroying the life
of the organisms.

During the last nine months I have turned my attention to the
action of this salicylic acid solution upon other living micro-organisms.

First of all, I may state that when the above quantity of sali-
cylic acid was added to 1000 c.c. of sterilised wort, and then pure
cultivations of Mycoderma aceti were introduced into the wort
contained in an ordinary two-necked Pasteur’s flask (fig. 1), no
change took place in it, not even after a month had elapsed, and
the vessel kept all the time at the most suitable temperature

Fig. 1. — Pasteur’s Two-Necked Flask.

(32° to 38° C.) for the life-history of the organism. After a month
had passed, a small quantity of this wort was transferred (with all
physiological caution) into a second Pasteur’s flask containing
sterilised wort minus the salicylic acid. No change was observed
in the least, not after the elapse of a month. I experimented in
a like manner with Bacillus butyricus , Bacterium lactis , and
obtained similar results. From these experiments, and my previous
microscopical studies, I draw the conclusion that the salicylic acid
solution is an antiseptic agent destroying these low micro-organisms.
In the case of Bacillus butyricus , I found that the said salicylic
acid solution not only destroyed the organism, but its spores as
well. My friend, Mr W. L. Gadd, F.C.S. (Principal Chemical
Assistant to Dr W. Thomson, F.R.S.E., of the Royal Institution,
Manchester), writes me that recently he has examined “ a sample of

100 Proceedings of Royal Society of Edinburgh. [jan. 31,

damaged ginger beer which was quite thick and jelly-like This
injury was caused “ by a minute ferment which can easily be de-
stroyed by salicylic acid ” (Gadd).

1. Micrococcus prodigiosus.

The spherical micro-organism ( Micrococcus prodigiosus) which

has been found upon cooked and raw meat kept in the dark, was
found on transplanting into 1000 c.c. of sterilised beef-broth
(neutral) to grow well in the dark, and formed a thick pellicle on
the surface of the liquid. On the addition of 0*2 grm. of salicylic
acid to the broth, the growth ceased; and on transferring a portion
of this broth into another flask containing sterilised broth, no

Protoplasmic

mass.

M. prodigiosus.

Ked oil globules
in interstitial
substances

Fig. 2. — M. prodigiosus (zoogloea state) (much enlarged).

development took place, not after remaining in this fluid at a
temperature of about 34 C. for two weeks. I may say in passing
that I have found that the red pigment produced by this “ chromo-
genic micrococcus ” contains some compound of iron. On treating
these organisms upon a slide under the microscope, with a weak
solution of potassium sulphocyanate, a deeper red colour was pro-
duced, no doubt due to the formation of ferric sulphocyanate.
Again, when a solution of potassium ferrocyanide was run between
the slide and cover-slip containing Micrococcus prodigiosus , a blue
coloration was obtained of “ Prussian blue.” It appears from the
above that the colour produced by this micro-organism is some
iron compound.

2. Micrococcus aurantiacus and Bacterium aeruginosum.

I have also found that the salicylic acid solution proved fatal to
Micrococcus aurantiacus and Bacterium aeruginosum , the micro-
organisms found upon badly -made bread, that has been kept in a

1887.]

Dr A. B. Griffiths on Micro-Organisms .

101

damp place for three weeks. The first micro-organism produces
an orange colour, and the second a green colour upon bread. These
micro-organisms grow well in flour-paste at a temperature of about
34° C., forming a coloured skin upon the surface of the paste. If
the paste is treated, first of all, with salicylic acid, and then
M. aurantiacus and B. aeruginosum transplanted to the paste, they
do not produce any growth, and ultimately die. The salicylic acid
solution destroys the spores of these two micro-organisms, although
their spores are said to withstand a temperature of 125° C.

3. Micrococci found in Diarrhoea.

The micrococci found largely in secretions from the bowels of
persons suffering with diarrhoea were transplanted into sterilised
beef-hroth contained in a Pasteur flask (No. 1), and kept at 40° C.
They multiplied rapidly during two days. Another flask (No. 2),
containing sterilised beef-broth and salicylic acid (in the proportion
of 0’2 grm. of the acid in 1000 c.c. of the broth), was taken and
inoculated with these actively growing micrococci, but their growth
was stopped. On inoculating another flask (No. 3) with some of
the contents of flask (No. 2), and keeping it about 40° C. for three
weeks, no further growth took place. This proves that the salicylic
acid had killed the micrococci in question. I am fully aware that
it has not been thoroughly ascertained whether this micrococcus
is the cause of diarrhoea, yet, for my purpose, the above is to show
that the said salicylic acid destroys this micrococcus.

4. Leptothrix buccalis and Bacillus subtilis.

These non-pathogenic forms found in the healthy human mouth
are also destroyed by salicylic acid. When examined under the
microscope, there was the appearance of the solution of salicylic
acid perforating the cellulose wall of Bacillus subtilis , and so
destroying the organism (fig. 3, B). At first we notice the cell-
wall becomes thinner on the side that the salicylic acid solution is
being run in between the slide and cover-slip, and is then per-
forated.

5. Penicilium glaucum.

Penicilium glaucum (the mould of preserved fruits, old leather,
&c.). When mounted in a drop of water on the slide under the

102

Proceedings of Roycd Society of Edinburgh. [jan. 31,

microscope, it was observed that on running in between the slide
and cover-slip the solution of salicylic acid, the cellulose walls of
hyphse, conidia, conidiophores were all perforated, and ultimately
dissolved by the acid.

Fig. 3. — A, Bacillus subtilis (much enlarged). B, <—€ = Direction of
flow of salicylic acid solution.

N.B. — In fig. 3 B tlie cell-walls should be thinner (than in woodcut) and
perforated, especially on the observer’s right.

6. Vaccine Lymph.]

The micrococcus vaccinise, which is the active principle of the
vaccine virus (as shown by Pasteur, and not the fluid medium in
which these micrococci live their life-histories), is also acted upon
by salicylic acid, for the lymph so treated loses its power of
inoculation.

7. Micrococcus urece (Von Tieghem).

Micrococcus urece , or the zymogenic ferment of urine which
splits up urea into ammonium carbonate, is found in dumb-bells,
chains, and in the zoogloea state. If urine is allowed to stand
until it begins to smell of ammonia, and then a drop of this urine
examined microscopically, the Micrococcus urece will be found to
be present. If now fresh urine (sterilised) is treated with salicylic
acid, and then inoculated with Micrococcus urece (from the putrid
urine), no change at all occurs in the urine, not after the elapse of

1887.] Dr A. B. Griffiths on Micro-Organisms. 103

sixteen days. Therefore, I conclude that the said acid has acted
upon this organism in a similar manner to those already mentioned.

8. Protococcus vulgaris and Protococcus pluvialis (fig. 4).

These two species of Protococcus are 7iot acted upon by the solu-
tion of salicylic acid, and a much stronger solution of the acid has
no effect upon them. It appears that there is a difference in the

Protococcus

vulgaris.

Fig. 4.

atomic structure of the cellulose forming the cell-walls of these two
species of Protococcus and the various micro-organisms alluded to
in this paper; that is, the cellulose of Protococcus is more like
the cellulose of the higher forms of plant life, which is not acted
upon by the acid in question.

So far, we have seen that salicylic is an antiseptic agent, capable
of attacking or acting upon their cellulose walls.

This acid, and acids generally, appear adverse to the life-histories
of certain micro-organisms. It will he remembered that M. Boche-
fontaine swallowed secretions from choleraic patients containing
Comma bacilli , made up in the form of pills, without any serious
consequences. There is no doubt the acid properties of the gastric
juice in the stomach had acted upon these micro-organisms in some
way or other, and so prevented them living their life-histories in
the intestine.

The practical outcome of this piece of research (although far from

104 Proceedings of Royal Society of Edinburgh. [jan. 31,

completed) may prove a remedy (placed upon a scientific basis) for
certain contagious diseases whose organisms reside in the blood.

I may allude, in passing, that there is no science on such an
unsatisfactory basis as medicine, and the present method of
administering medicines (in such diseases as above) is first of all
into the stomach by means of the mouth. The medicine has to
pass through a good portion of the alimentary canal before it is
absorbed into the blood. The medicine may become changed
(before it is absorbed) by the various secretions pouring into the
alimentary canal. Hence, for those contagious diseases whose seat
of action is in the blood (the blood being their soil), we ought to
apply our remedy directly to the blood itself by injections.

With this idea in view (and from analogy of the action of
salicylic acid upon a large number of micro-organisms), it is
most probable that the above salicylic acid solution will destroy
Micrococcus erysijpelatosus, Micrococcus scarlatince, Bacillus malarias.
Bacillus tuberculosis, &c. These micro-organisms have been proved
to be the cause of the diseases in which they are found in great
numbers in the blood. Swine fever, cattle plague, pleuro-pneumonia
have also been proved to be the results of different species of micro-
coccus. All these organisms reside in the blood of man and
animals suffering with these diseases.

In the case of Bacillus tuberculosis , according to Dr E. Ereund
{Nature, vol. xxxiv. p. 581, Oct. 14, 1886), of Vienna, this micro-
organism appears to form cellulose within the blood of tuberculous
persons. This cellulose is a product of its ( B . tuberculosis ) life-
history, and we have seen in numerous cases that the salicylic acid
attacks micro-parasitic cellulose, if I can so use the expression.
Therefore the hint may be given, that salicylic acid may prove a
successful remedy in tuberculosis, when injected directly into the
blood of diseased patients.

It may be asked — If the salicylic acid solution is injected into the
blood, will it not destroy the red and white corpuscles ? On April
28, 1886, I opened a vein in my left arm, and injected into the
blood the solution of salicylic acid, and with the exception of a
headache or so there were no abnormal results.

A microscopical examination of the blood (two hours after
injection) revealed that the blood corpuscles were in a perfectly

1887.] Dr A. B. Griffiths on Micro-Organisms.

105

healthy state. The salicylic acid solution had no action upon the
corpuscles of blood of a poor quality. Hence, I have reason to
conclude that it may he, with a more extended study of the action
of this solution of salicylic acid upon disease “ germs ” and their
organisms, we have the most rational mode of treating those con-
tagious diseases whose seat of energy is in the blood.

Note to above Pager.

The oven for sterilising tubes, cotton- wool, &c., I use in my
experiments, was devised by my wife, and is seen in fig. 5. A
good point of this oven is, that the shelf contains a series of holes

Fig. 5. — Mrs Griffiths’ Form of Sterilising Oven, a , The ordinary chemical
thermometers passing into oven ; B, Copper shelf, with holes for tubes,
cotton- wool, &c. ; D, Iron support for oven over flame ; E, Paraffin oil lamp ;
F, Screw to raise the wick, &c. The temperature of oven heated with paraffin
oil can go as high as 155° C., and with gas, above 300° C.

106 Proceedings of Boy al Society of Edinburgh. [jan. 31,

of various sizes for test-tubes. By placing the test-tubes in
inverted positions (as in fig.), the heated air rises in the tubes, and
a current of air in each tube is formed, and thus destroys all
organisms and their spores, for they are detached by these currents
(of heated air rising), and exposed on all sides to the full heat of
the oven.

Monday, *7th February 1887.

The Hon. Lord M‘LABEN, Vice-President, in the Chair.

1. On Cases of Instability in Open Structures. By E.

Sang, LL.D.

{Abstract.)

In the course of some remarks on the design proposed for the
Forth Bridge, the author of this paper had enunciated the remark-
able theorem, that any symmetric structure built on a rectangular
base, and depending on linear resistance alone, is necessarily unstable.
The proof of it, given in the eleventh volume of the Transactions of
the Royal Scottish Society of Arts , is derived from considerations
affecting the special case ; but this theorem is only one of an ex-
tensive class, and therefore the subject of instability among linear
structures in general is here taken up.

In the case of regular or semi-regular arrangements, having the
corners of an upper supported from the corners of an under polygon,
it is shown that when the figures are of odd numbers the structures
are stable, while those with even numbers are unstable ; unless in-
deed the polygons be placed conformably, in which case the stability
extends to both classes.

The paper ends with the following admonition : — These cases
of instability in open structures have been elicited by means of the
simplest considerations in geometry and statics they lie indeed
on the very surface of mechanical inquiry. They do not occur as
isolated examples, but are arranged in extensive groups ; and, being
found in those classes of structures which may be called shapely,
they stand out as warning beacons to those engaged in engineering
pursuits.

1887.] Mr W. Peddie on Electrolytic Polarization.

107

2. On the Increase of Electrolytic Polarization with Time.
By W. Peddie, Esq. Communicated by Professor Tait.

In a paper communicated to this Society last Session I described
some preliminary experiments on this subject, which led to the
approximate empirical formula connecting current-strength and time

. 7 -ct-hde~et

i = a + oe

where a, b, c, d, and e are constants of positive sign. The electrodes

used were of platinum, and had a surface area of about 5 sq. cm.
Subsequently I have used platinum electrodes having an area of

108

Proceedings of Royal Society of Edinburgh. [feb. 7.

rather more than 60 sq. cm. The curves I obtained evidently pos-
sess, to a considerable extent, symmetry about an axis. They roughly
resemble hyperbolas, but have rather more curvature near the vertex.
A few of them are represented in fig. 2. Time is measured hori-
zontally, each scale-division representing 6J minutes. The numbers
on the vertical scale, when multiplied by 0*267, give the current-
strength in amperes. I used in each experiment a battery of 3 tray-
Daniell cells, the electromotive force of which remained constant
during the experiment. The battery was coupled in circuit with a
Helmholtz tangent galvanometer and the electrolytic cell. The
reduction factor of the galvanometer is 0*267. The needle of the
galvanometer ceased vibrating in about half a minute after com-
pleting the circuit, at which time the first reading was taken. The
following tables give the details of one experiment : —

Deflection in Degrees at intervals of One Quarter-Minute.

64*8, 64*4, 63*5, 62*7, 61*8, 60*9, 59*7, 58*8, 58*2, 58, 57*8, 57*4,
57, 56*7, 56*2, 55*7, 55*2, 54*6, 54, 53*6, 53*1, 52*7, 52*4, 51*9,
51*7, 51*4, 51*1, 50*9, 50*5, 50*3, 50, 49*8, 49*6, 49*4, 49*2, 48*9,
48*8, 48*6, 48*4, 48*3.

At intervals of One Half-Minute.

47*9, 47*6, 47*3, 47*1, 46*8, 46*6, 46*4, 46*2, 45*9, 45*8, 45*7,
45*6, 45*5, 45*3, 45*2, 45*1, 44*9, 44*8, 44*7, 44*5, 44*4, 44*3.

At intervals of One Minute.

44T, 43*9, 43*7, 43*6, 43*4, 43*2, 43 1, 42*8, 42*7, 42*6, 42*5,
42*3, 42*2, 42*1.

At intervals of Three Minutes.

41*6, 41*1, 40*8, 40*3, 39*9.

At intervals of Five Minutes.

39*4, 38*7, 38*4, 37*8, 37*4, 36*9, 36*6, 36*4, 36, 35*7, 35*4,
35T, 34*8, 34*5.

These results are shown graphically in the curve in fig. 1. In
each experiment the total resistance in the circuit was slightly
different. A special feature of the group of curves in fig. 2 is the
close parallelism of the axes.

1887.] Mr W. Peddie on Electrolytic Polarization.

109

I have adopted, as a better approximation to the law connecting
current-strength and time, the equation

. 7 ci - kt

i = a + be ^

The curve represented by this equation does not differ much from
that represented by the equation formerly given. It possesses to a
certain extent symmetry about an axis. In fig. 3 I have represented
a group of curves having this equation, passing through a given
point on the axis of i, and having a common asymptote. The curves
which pass to tbe left of the axis of i cannot, of course, represent
the physical phenomena, but they show the axial symmetry well.
If another group is drawn, the axis of i being a tangent, and each
member having a different horizontal asymptote, a close resemblance
between it and the group in fig. 2 is evident.

If equation (1) holds, we have

log (i ~-a) — ci = log b — kt . . . . (2).

Hence the quantity on the left-hand side of this equation plotted
against time should give a straight line. The group of points in
fig. 1 is obtained in this way from the curve in that figure. The
near coincidence of all the points with a straight line shows that
the curve is closely represented by an equation of the form (1).

I have also made an experiment with only one tray-Daniell cell
in the circuit. There was, consequently, no decomposition of the
electrolyte (an aqueous solution of sulphuric acid). In this case the
constant a must be zero. The equation

• n a mo l‘092t -0-40154
^ = 0•4168e

represents the results of observation almost exactly, the difference
being well within the limit of possible errors in drawing the curve
free-hand through the observed points. For small values of t there
is considerable discrepancy between the results of observation and
calculation in both experiments, so that the formula (1) must not
be applied when t is below a certain limit, which, for the results
tabulated above, is about 5 minutes.

110 Proceedings of Eoycd Society of Edinburgh. [fee. 7,

3. Astronomical Notes. By Balph Copeland, Esq., Ph.D.
Communicated by Lord M'Laren.

PRIVATE BUSINESS.

Dr J. B. Buist, Mr A. B. Brown, C.E., Mr Ferdinand Faithful
Begg, Mr J. Arthur Thomson, Dr Andrew Thomson, Dundee ; Mr
William Caldwell Crawford, Mr J. G. Bartholomew, Dr William
Hunter, Mr Thomas Goodall Nasmyth, Sir John Fowler, M. Inst.
C.E., Mr W. H. Barlow, M. Inst. C.E., and Mr John Muter were
balloted for, and declared duly elected Fellows of the Society.

Monday , 21 st February 1887.

Bev. Professor FLINT, D.D., Vice-President, in the Chair.

1. Further Determinations of the Effect of Pressure on the
Maximum Density Point of Water. By Professor Tait.

i

2. On the Height of the Land of the Globe above Sea-Level.

By Dr J. Murray.

3. Note on the Effects of Explosives. By Professor Tait.

[Abstract.)

Many of the victims of the dynamite explosion, a year or two
ago, in the London Underground Eailway, are said to have lost the
drum of one ear only, that nearest to the source. This seems to
point to a projectile, not an undulatory, motion of the air and of
the gases produced by the explosion. So long, in fact, as the dis-
turbance travels faster than sound, it must necessarily be of this
character, and would be capable of producing such effects.

Another curious fact apparently connected with the above is the
(considerable) finite diameter of a flash of forked lightning. Such

1887.] Professor Tait on the Effects of Explosives.

Ill

a flash is always photographed as a line of finite breadth, even
when the focal length is short and the focal adjustment perfect.
This cannot he ascribed to irradiation. The air seems, in fact, to
be driven outwards from the track of the discharge with such
speed as to render the immediately surrounding air instantaneously
self-luminous by compression.

Such considerations show at once how to explain the difference
between the effects of dynamite and those of gunpowder. The
latter is prepared expressly for the purpose of developing its energy
gradually. Thus while the flash of gunpowder fired in the open
is due mainly to combustion of scattered particles, — that produced
by dynamite is mainly due to impulsive compression of the sur-
rounding air, energy being conveyed to it much faster than it
can escape in the form of sound.

4. Report on Possil Pishes collected in Eskdale and Lid-
desdale. Part I. Ganoidei — Supplement. By Dr

Traquair.

5. On the Equilibrium of a Gas under its own Gravitation

only. By Sir W. Thomson.*

This problem, for the case of uniform temperature, was first, I
believe, proposed by Tait in the following highly interesting
question, set in the Ferguson Scholarship Examination (Glasgow,
October 2, 1885): — “Assuming Boyle’s Law for all pressures,
form the equation for the equilibrium-density at any distance from

* Note of February 22, 1887. — Having yesterday sent a finally revised
proof of this paper for press, I have to-day received a letter from Prof.
Newcomb, calling my attention to a most important paper by Mr J. Homer
Lane, “On the Theoretical Temperature of the Sun,” published in the
American Journal of Science for July 1870, p. 57, in which precisely the
same problem as that of my article is very powerfully dealt with, mathemati-
cally and practically. It is impossible now, before going to press, for me to
do more than refer to Mr Lane’s paper ; but I hope to profit by it very much
in the continuation of my present work which I intended, and still intend,
to make. — W. T.

112

Proceedings of Royal Society of Edinburgh. [feb. 21,

the centre of a spherical attracting mass, placed in an infinite space
filled originally with air; Find the special integral which depends
on a power of the distance from the centre of the sphere alone.”

The answer (in examinational style !) is : — Choose units properly ;
we have

dp

dr

• • a),

where p is the density at distance r from the centre. Assume

p = ArK (2).

We find A = 2, k = - 2 ; and therefore

P = (^)

satisfies the equation in the required form.

Tait informs me that this question occurred to him while writing
for Nature a review of Stokes’ Lecture * on Inferences from the
Spectrum Analysis of the Lights of Sun, Stars, Nebulae, and
Comets ; and in the Proceedings of the Edinburgh Mathematical
Society he has given some Transformations of the equation of
Equilibrium. The same statical problem has recently been forced
on myself by considerations which I could not avoid in connection
with a lecture which I recently gave in the Koyal Institution of
London, on “The Probable Origin, the Total Amount, and the
Possible Duration of the Sun’s Heat.”

Helmholtz’s explanation, attributing the Sun’s heat to condensa-
tion under mutual gravitation of all parts of the Sun’s mass,
becomes not a hypothesis but a statement of fact, when it is
admitted that no considerable part of the heat emitted from the
Sun is produced by present in-fall of meteoric matter from without.
The present communication is an instalment towards the gaseous
dynamics of the Sun, Stars, and Nebulae.

To facilitate calculation of practical results, let a kilometre be
the unit of length ; and the terrestrial-surface heaviness of a cubic
kilometre of water at unit density taken as the maximum density,
under ordinary pressure, be the unit of force (or approximately, a
thousand million tons heaviness at the earth’s surface). If jp be the

* Lecture III. of Second Course of “ Burnet Lectures,” Aberdeen, Dec.
1884 ; published, London, 1885 (Macmillan).

1887.] Sir W. Thomson on the Equilibrium of Gas.

113

pressure, p the density, and t the temperature from absolute zero,
we have, by Boyle and Charles’s laws,

p = Hpt (4);

where t denotes absolute (thermodynamic*) temperature, with 0°
C. taken as unit ; and H denotes what is commonly, in technical
language, called “ the height of the homogeneous atmosphere ” at
0° C. For dry common air, according to Regnault’s determination
of density,

H = 7 ‘985 kilometres (4').

Let /3 be the gravitational coefficient proper to the units chosen ;
so that fimm /D2 is the force between m, m' at distance D. The
earth’s mean density being 5 ’6, and radius 6370 kilometres, we
have

g-. 6370. 5*6/2 = 1; and therefore 4tt/?= 1/11890 .... (5).

Let now they), p, t of (4) be the pressure, density, and tempera-
ture at distance r from the centre of a spherical shell containing gas
in gross-dynamic f equilibrium. We have, by elementary hydro-
statics

whence

dr

• • (6)>

• • (7),

where M denotes the whole quantity of matter within raidius a from
the centre ; which may be a nucleus and gas, or may be all gas.

If the gas is enclosed in a rigid spherical shell, impermeable to
heat, and left to itself for a sufficiently long time, it settles into the
condition of gross-thermal equilibrium, by “ conduction of heat,” till
the temperature becomes uniform throughout. But if it were stirred

* The notation of the text is related to temperature Centigrade on the
thermodynamic principle (which is approximately temperature Centigrade by
the air-thermometer), as follows : —

1

273

(temperature Centigrade + 273) ;

see my Collected Mathematical and Physical Papers, vol. i. arts, xxxix. and
xlviii. part vi. §§ 99, 100; and article “Heat,” §§ 35-38 and 47-67, Encyc.
Brit., and vol. iii. (soon to be published) of Collected Papers.

t Not in molecular equilibrium of course ; and not in gross-thermal equi-
librium, except in the case of t uniform throughout the gas.

VOL. XIV. 16/9/87

H

114

Proceedings of Royal Society of Edinburgh, [feb. 21,

artificially all through its volume, currents not considerably dis-
turbing the static distribution of pressure and density will bring it
approximately to what I have called convective equilibrium * of
temperature, that is to say, the condition in which the temperature
in any part P is the same as that which any other part of the gas
would acquire if enclosed in an impermeable cylinder with piston,
and dilated or expanded to the same density as P. The natural
stirring produced in a great free fluid mass like the Sun’s, by the
cooling at the surface, must, I believe, maintain a somewhat close
approximation to convective equilibrium throughout the whole mass.
The known relations between temperature, pressure, and density for
the ideal “ perfect gas,” when condensed or allowed to expand in a
cylinder and piston of material impermeable to heat, are f

(8),

(9);

where k denotes the ratio of the thermal capacity of the gas,
pressure constant, to its thermal capacity, volume constant, which
is approximately equal to U41 or 1*40 (we shall take it 1’4) for all
gases, and all temperatures, densities, and pressures • and T denotes
the temperature corresponding to unit density in the particular
gaseous mass under consideration.

Using (8) to eliminate p from (7) we find

</r|_ dr J HT/c ' *

which, if we put pl~' = u .

1/(*-1) = k . . .

(10),

(11),

(12),

and / HT&

(13),

takes the remarkably simple form

d2u uK

dx 2 ic4

(14).

* See “On the Convective Equilibrium of Temperature in the Atmo-
sphere,” Manchester Phil. Soc., vol. ii. , 3rd series, 1861 ; and vol. iii. of
Collected Papers.

t See my Collected Mathematical and Physical Papers, vol. i. art. xlviif.
note 3.

1887.] Sir W. Thomson on the Equilibrium of Gas.

115

Let / (x) he a particular solution of this equation ; so that

/"(*)= -[/wr®-4 )

and therefore V. . . . (15y.

f'(inx)— - \_f(mx)\Km~ Ax~ ^ )

From this we derive a general solution with one disposable

constant, by assuming

u — Cf(mx ) (16);

which, substituted in (14), yields in virtue of (15),

m2 = c-*+i (17) ;

so that we have, as a general solution,

^ = C/^C-^->] (18).

Now the class of solutions of (14) which will interest us most is
that for which the density and temperature are finite and con-
tinuous from the centre outwards to a certain distance, finite as w
shall see presently, at which both vanish. In this class of cases u
increases from 0 to some infinite value, as x increases from some
finite value to oo . Hence if u = f(x) belongs to this class, u = Cf(mx)
also belongs to it; and (18) is the general solution for the class.
We have therefore, immediately, the following conclusions : —

(1) The diameters of different globular* gaseous stars of the
same kind of gas are inversely as the J(»<-l)th powers (or f
powers) of their central temperatures, at the times when, in the
process of gradual cooling, their temperatures at places of the same
densities are equal (or “ T ” the same for the different masses).
Thus, for example, one sixteenth central temperature corresponds to
eight-fold diameter; one eighty-first central temperature corresponds
to twenty-seven fold diameter.

(2) Under the same conditions as (1) (that is, H and T the same
for the different masses), the central densities are as the Kth powers

* This adjective excludes stars or nebul;e rotadmg steadily with so great
angular velocities as to be much flattened, or to be annular ; also nebulae
revolving circularly with different angular velocities at different distances
from the centre, as may be approximately the case with spiral nebulae.
It would approximately enough include the sun, with his small angular
velocity of once round in 25 days, were the fluid not too dense through a large
part of the interior to approximately obey gaseous law. It no doubt applies
very accurately to earlier times of the sun’s history, when he was much less
dense than he is now.

116 Proceedings of Royal Society of Edinburgh, [feb. 21,

(or |- powers) of the central temperatures; and therefore inversely

as the --‘jK - , or , or powers of the diameters.

k - I 2 — k 6

(3) Under still the same conditions as (1) and (2), the quantities

of matter in the two masses are inversely as the

powers (inversely as the cube roots) of their diameters.

(4) The diameters of different globular gaseous stars, of the same
kind of gas, and of the same central densities, are as the square roots
of their central temperatures.

(5) The diameters of different globular gaseous stars of different
kinds of gas, but of the same central densities and temperatures, are
inversely as the square roots of the specific densities of the gases.

(6) A single curve [^=/(^-1)] with scale of ordinate (r) and
scale of abscissa (y) properly assigned according to (18), (17), and
(11) shows for a globe of any kind of gas in molecular equilibrium,
of given mass and given diameter, the absolute temperature at any
distance from the centre. Another curve {[y with scales
correspondingly assigned, shows the distribution of density from
surface to centre.

It is easy to find, with any desired degree of accuracy, the
particular solution of (13), for which

u = A,

and ^ = A', where x = a
ax

. . (19),

a denoting any chosen value of x, and A and A' any two arbitrary
numerics, by successive applications of the formula

u

»+i

A- f dxi A' - f*dx-)

J a \ J a PJ

(20);

the quadratures being performed with labour moderately propor-
tional to tbe accuracy required, by tracing curves on “ section ’’-paper
(paper ruled with small squares) and counting the squares and parts
of squares in their areas. To begin, u0 may be taken arbitrarily ;
but it may conveniently be taken from a hasty graphic construction
by drawing, step by step, successive arcs * of a curve with radii of

* This method of graphically integrating a differential equation of the
second order, which first occurred to me many years ago as suitable for find-
ing the shapes of. particular cases of the capillary surface of revolution, was
successfully carried out for me by Prof. John Perry, when a student in my

1887.] Sir W. Thomson on the Equilibrium of Gas.

117

curvature calculated from (13) with the value of du]dx found from
the step-by-step process. If this preliminary construction is done
with care, by aid of good drawing-instruments, ux calculated from
uo by quadratures will be found to agree so closely with uQ, that v0
itself will be seen to be a good solution. If any difference is found
between the two, uY is the better : u2 is a closer approximation than
«q ; and so on, with no limit to the accuracy attainable.

Mr Magnus Maclean, my official assistant in the University of
Glasgow, has made a successful beginning of working out this pro-
cess for the case u = 1 6 where x = oo ; and has already obtained a
somewhat approximate solution, of which the produce useful for our
problem is expressed in the following table

dlu

Numerical Solution of 4

H- X U

0.

Distance from
centre
= r= l/x.

Keciprocal of
distance from
centre
= cc=l jr.

Temperature
- u.

Density

= w'2'5 .

Mass within dis-
tance r from the
centre
= du/dx

dxu2'5x--i

0

8

16-00

1024

■oo

•100

10

14-46

795-2

•28

•111

9

14-14

751-6

•38;

•125

8

13-71

695-8

•52

•143

7

13-10

621-2

•731

•167

6

12*20

520-0

1-056

•200

5

10-92

394-1

1-566

•250

4

9-00

243-0

2-336

•333

3

6-15

93-81

3-436

•500

2

2-25

7-595

4-366

•667

]-5

0

0

4-49

The deduction from these numbers, of results expressing in terms
of convenient units the temperature and density at any point of a
given mass of a known kind of gas, occupying a sphere of given
radius, must be reserved for a subsequent communication.

laboratory in 1874, in a series of skilfully executed drawings representing a
large variety of cases of the capillary surface of revolution, which have been
regularly shown in my Lectures to the Natural Philosophy Class of the Uni-
versity of Glasgow. These curves were recently published in the Proc. Roy.
Instit. (Lecture of Jan. 29, 1886), and Nature, July 22 and 29, and Aug. 19,
1886 ; also to appear in a volume of Lectures now in the press, to be published
in the Nature series.

118 Proceedings of Royal Society of Edinburgh, [fee. 21,

One interesting result which I can give at present, derived from
the first and last numbers of the several columns of the preceding
table, is, that the central density of a globular gaseous star is 22 J
times its average density.

Monday , 7th March 1887.

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

1. On the Equilibrium of a Gas under its own Gravitation

only. Part III. By Sir W. Thomson.

2. History of the Theory of Determinants. Part I. Deter-

minants in General: Hindenburg (1784) to Eeiss
(1829). By Dr Muir.

[This Paper is printed at the end of the Proceedings of the Session.]

3. Note on Solar Radiation. By Mr John Aitken.

In the many theories that have been advanced to explain the
comparative constancy of solar radiation in long past ages as evi-
denced by geological history, it has been generally assumed that the
temperature of the sun has not varied much, and to account for
its not falling in temperature a number of theories have been
advanced, all suggesting different sources from which it may have
received the energy which it radiates as heat. Since the chemical
theory was shown to be insufficient to account for the vast amount
of heat radiated, other theories, such as the meteoric theory and
the conservation of energy theory, have been advanced.

In all these theories it is generally assumed that in order that the
radiation from the sun may be constant its temperature must also he
constant, that, in fact, radiation from the sun is in proportion to its
temperature ; and that if the temperature of the sun falls, its radia-
tion effect at the earth’s surface will fall in direct proportion to

1887.]

Mr John Aitken on Solar Radiation.

119

its loss of heat. Now there are certain physical facts which have
induced me to think that this is not necessarily so. Nay, it seems
even possible that the amount of heat radiated by the sun might
go on increasing while its temperature was decreasing.

The facts which seem to point to this conclusion are — -

First , We know that different forms of matter vary greatly in
their power of radiating heat. For instance, a non-luminous gas
flame radiates far less heat than a luminous one, though actually at
a higher temperature, and a red-hot surface of platinum radiates far
less heat than an oxidised surface of iron of the same area and
temperature.

Second , We know that elementary bodies generally radiate far
less heat than compound ones. It has been shown that the radiating
powers of substances go on increasing with the increased com-
plexity of their constitution.

Third , We know that at high temperatures compound bodies are
decomposed or broken up into simpler forms. Or, to put it in another
way, and as a solar inhabitant would put it, bodies which have an
affinity for each other do not combine unless their temperature is
below a certain fixed point for the substances.

Combining these statements we see that in the sun, owing to its
high temperature, matter must he in much simpler forms than it is
on the earth, and all recent investigation points markedly in this
direction. It seems therefore in the highest degree probable that
the average radiating power of the matter in the sun is much less
than that of the matter of the earth. Again, the hotter the sun the
simpler its constitution will he, and the weaker its radiating power.
From this we see that there is no necessary proportion between the
temperature of the sun and the amount of heat it radiates, as change
of temperature is accompanied by change of constitution, and in-
crease of radiating power.

These considerations lead us on, and suggest that the store of
energy from which the sun has drawn in long past ages may possibly
he its own internal supply ; that the sun in its earlier ages was at
a much higher temperature than it is at present, hut, owing to
its simpler constitution, it radiated only about as much heat as it
does now, and that as its temperature fell its matter became more
compound, and its radiating power increased, which enables it now

120 Proceedings of Royal Society of Edinburgh. [mar. 7,

to keep up about the same radiation effect, though its temperature
may have fallen greatly.

It is evident that much of this is purely theoretical and formed
on rather a weak basis; we have so few measurements to go by.
Though it is a law that compound bodies radiate more than simple
ones, yet we do not know enough of the constitution of the sun to
say how much the increased radiating power, due to increased com-
plexity, would compensate for the fall of temperature. I have said
it might actually more than counteract the fall of temperature and
cause an increased radiation effect. It may, however, only balance
it, or it may even only reduce the rate of decrease of radiation,
and make it only a little less than proportional to the fall in tem-
perature.

The whole of these remarks are almost pure speculation. The
principal cause for their being written is to point out that the radiat-
ing power of the sun may have varied in quantity and quality from
age to age ; that its amount may not be directly proportional to its
absolute temperature ; and further, that it is extremely doubtful
whether we can apply to solar matter the radiation measurements
which have been obtained of earth matter, so that any estimates we
may make of the temperature of the sun from measurements of
solar radiation must be received with considerable hesitation.

Added 9 tli July 1887.

Sir William Thomson has shown that the sun has within itself
an enormous store of energy due to its high temperature. This
energy is altogether apart from what we on the earth are accustomed
to consider as the energy stored up in a hot body. He has
shown that the shrinkage or falling in of the great mass of the
sun due to cooling is capable of developing a very great amount of
energy. His calculations show, that if the shrinkage was so great
that the surface of the sun was to descend at the rate of 35 metres
per year, or 70 kilometres per 2000 years, there would be developed
about the same amount of energy that is radiated by the sun accord-
ing to the measurements taken by Pouillet.

Forbes has shown Pouillet’s measurements to be much too small,
and that the amount radiated by the sun is 1*6 greater than

1887.] Mr John Aitken on Solar 'Radiation. 121

Pouillet supposed. Professor Langley, by more perfect methods,
has shown that Forbes’s figure is also too small, and there are
evident reasons for supposing that even Langley’s measurements are
too low. The sun will therefore require to shrink a good deal
more than 35 metres per year to develop from gravitational sources
alone the energy radiated by it.

Apart, however, from the energy developed by shrinkage, there will
evidently he energy developed within the sun in another way while
it is cooling. The falling temperature will be accompanied by com-
bustion, though not in the manner supposed in the old combustion
theory of solar energy. There will, however, evidently he a de-
velopment of energy due to the combination or falling together of the
molecules which will ensue on the decrease of temperature. Here
we have a field for the chemist to come in and do for the chemical
part of the subject what Sir W. Thomson has done for the gravita-
tional. It must, however, be confessed that his task is a far more
difficult one, at least at present, as we know very little about the
condition of matter in the sun, and almost nothing about the
amount of energy developed when the simpler forms of matter
combine.

Now, though the sun may receive an enormous amount of energy
from those two sources, yet it is evident they can never keep the
temperature of the sun constant, because, before energy can be
developed in either of those ways, the temperature of the sun must
fall, and the energy developed will he in proportion to the amount
of the fall.

4. On Laplace’s Nebular Theory, considered in relation to
Thermodynamics. By Sir W. Thomson.

5. On a Class of Alternating Functions. By Dr Muir.

6. Note on Hoar-Frost. By Mr John Aitken.

Hoar-frost is generally described as frozen dew, and is supposed
to be deposited in the same manner and under the same conditions
as dew ; the only difference being in the temperature at which it is

122 Proceedings of Royal Society of Edinburgh. [mar. 7ri

deposited. Though in a general way this may be so, yet there are
certain differences in the conditions, and the manner in which the
vapour is condensed at the different temperatures, which seem worth
referring to.

If we examine a surface, such as a sheet of glass, exposed hori-
zontally near the ground on a dewy night, we shall generally find
that the windward edges are dry. This indicates that the air itself
is not cooled to the dew-point, though the surfaces of bodies exposed
to radiation are, and the air has to travel some distance over the
cold surface before its temperature is reduced to the dew-point. If,
however, we examine this same surface when the temperature is low
enough to cause the deposited moisture to form hoar-frost, we shall
frequently find a marked difference. The sheet of glass is generally
not only covered with the deposited vapour up to the windward
edges, but the deposit is heaviest along these edges, the ice
crystals growing furthest out in that direction. This peculiarity in
the deposition of the hoar-frost may also be observed on almost all
objects — such as branches of trees, iron fences, &c. The heaviest
deposit will often he found on the windward side and not on the
top, where we might expect to find it, owing to the stronger radia-
tion from that surface.

The question then is, What is the cause of this difference ? Why
should no vapour be deposited along the windward edges of surfaces
when the temperature is above 32°, while the heaviest deposit is
formed on these edges when the temperature is below the freezing-
point ? The dryness of that part of the dewed surface where the
air first touches it is caused by the air not being saturated, and
requiring to travel some distance over the cold surface before it is
cooled below its dew-point. When, however, hoar-frost is forming,
the air seems generally to act as if it were supersaturated : the
crystals growing most towards the wind seems to indicate that the
air does not require to be cooled before it deposits its moisture.
But is it possible for the air to he supersaturated 1 Under ordinary
conditions we know this is impossible. Owing to the vast amount
of dust in the air there is always plenty of free-surface present to
prevent this happening so long as the temperature is above the
freezing-point. When, however, the temperature falls below this
point, we have a much more complicated condition of matters.

1887.]

Mr John Aitken on Hoar-Frost.

123

A considerable time ago it was suggested by Professor James
Thomson and by Kirchhoff that the vapour pressure of ice might
be less than that of water at the same temperature ; Professor
Ramsay and Dr Young have shown that this is the case,* and they
have experimentally measured the comparative temperatures of ice
and water under the same vapour pressure. This they have done to
a temperature of 9 degrees below the freezing-point ; lower they
could not go, as the water always froze when its temperature was
reduced to that point. They found that the ice and the water had
the same temperature at 32°, and under a pressure of 4*6 mm. But
when the pressure was still further reduced, the water became colder
than the ice ; and when the pressure was about 3*20 mm. the water
was at a temperature of about 23°, while the ice was about 24°.
The water was thus about a degree colder than the ice.

It is evident, therefore, that if by any means the ice had been
cooled to the same temperature as the water, its vapour-pressure
would have been less than that of the water. So that if we have a
water-surface and an ice one at the same temperature and near each
other, vapour will tend to pass from the water to the ice, because,
the vapour pressure of the water being higher than that of ice,
the air which is saturated to a water surface is supersaturated to
an ice one.

Something like this seems to take place when hoar-frost is form-
ing. When the air is cooled, condensation takes place on the dust
nuclei, resulting in a foggy condensation. This moisture condensed
in the air seems always to keep the liquid form ; at least we do not
see during frosty weather any indications of the particles being
frozen. In the fogs formed low down in our atmosphere there are
no optical or other phenomena such as we might expect to find if
they were frozen. That the temperature of the air is far below the
freezing-point is no evidence that the fog particles will be solid, as it
is well known that water, even when in contact with solid surfaces,
and with what seem favourable nuclei for forming freezing centres,
may yet remain liquid at a temperature far below the freezing-
point. Thin films and small drops seem difficult to freeze ; I have
frequently seen my night-radiation thermometer cooled many degrees
below the freezing-point, and yet the film condensed on its surface

* Phil. Trans. Roy. Soc., part ii. , 1884.

124 Proceedings of Royal Society of Edinburgh. [mar. 7,

was in a liquid state. It seems, therefore, quite in keeping with our
knowledge that these fog particles in frosty weather may he liquid.

Such being the case, we have water particles floating in the
atmosphere during frosty and foggy weather, and the pressure of
the vapour in the air will correspond to that of a liquid surface ;
it will therefore be greater than that of an ice one at the same
temperature. Under these conditions the air will rapidly unburden
itself of part of its vapour when it comes into contact with an ice
surface. This seems to be the reason why hoar-frost grows in the
direction from which the air is moving, because the air, being super-
saturated, unburdens itself on the first ice surface with which it
comes into contact, and does not, as when dew is forming, require
to be brought into a condition to cause it to give up its vapour.

In the foregoing I have taken extreme conditions under which
dew and hoar-frost are formed, as they are better suited to illustrate
the point. There are, however, many intermediate conditions in
which both dew and hoar-frost appear to be deposited in nearly the
same way. On some nights the sheet of glass is dewed all over and
up to all the edges, and there are some nights on which no hoar-frost
is deposited on the windward edges of the plate, the air having to
pass some distance over the cold surface before its temperature is
low enough for it to deposit its moisture. The conditions under
which the plate is dewed to its edges are when there is no wind
and the air nearly saturated; and the conditions under which no
hoar-frost is deposited along the windward edges are when there is
some wind, a clear sky, and the air not saturated.

So far as my memory and recorded observations go, we never
have a heavy deposit of hoar-frost when the sky is clear, or in those
conditions in which we have our heaviest deposits of dew. On all
those occasions on which trees and every exposed surface become
clothed in crystal garments, and all nature in a single night be-
comes changed to a wondrously pure and fairy-like scene, the trans-
formation seems always to be accomplished in a thick and foggy
atmosphere, which requires the morning’s sun to dissolve the veil
and disclose its beauties. The thick and foggy state seems to be
the general condition of our atmosphere during the growth of these
heavy deposits of hoar-frost, and it is a necessary one, if the ex-
planation we have given is correct.

1887.]

Mr John Aitken on Hoar-Frost.

125

It will be observed that these thick and foggy nights, when heavy
deposits of hoar-frost are formed, are the very nights on which little
or no dew would he deposited, because the radiation would he checked
by the fog. These, however, are the very nights most favourable
for the deposit of hoar-frost, because the air has a large amount of
vapour in it, — is in fact saturated. And further, while dew re-
quires that the surface on which it is deposited be cooled by radia-
tion, this is not so necessary, and indeed may he absent, in the
formation of hoar-frost ; because the fog particles radiate and cool
the air to the saturated temperature of vapour at a water surface,
and the passing air discharges part of its vapour on all ice crystals
or other nuclei with which it comes in contact ; the passing air at
the same time absorbs the heat of crystallisation, while the heat of
condensation is balanced by the heat absorbed by the evaporation
from the water particles.

But, further, it will he observed that not only are those nights
on which hoar-frost is most abundant not similar to the nights on
which heavy dews are formed, but they are generally nights on
which there would be no dew at all if the temperature was above
the freezing-point ; these hoar-frosty nights do not therefore corre-
spond to dewy nights, when the temperature is higher, but rather
to those nights when every object is wet and dripping, not with
dew, but wet with deposited fog particles.

7. On the Quotient of a Simple Alternant by the Difference-

Product of the Variables. By Dr Muir.

8. Investigations on the Influence of certain Bays of the

Solar Spectrum on Root-Absorption and on the Growth
of Plants. By Dr A. B. Griffiths, F.R.S.E., F.C.S.
(Bond. & Paris), and Mrs A. B. Griffiths.

This paper details an investigation undertaken to see the influence
of certain rays of white light on root-absorption and assimilation
in the vegetable kingdom. One of us has been for some years in-
vestigating a problem as to the use of ferrous sulphate as a plant
food (see Dr Griffiths’ memoirs in Journal of Chemical Society

126

Proceedings of Royal Society of Edinburgh. [mar. 7,

[Trans.'], 1883, 1884, 1885, 1886, 1887). In the experiments to
be detailed here, we have used ferrous sulphate as an indicator of
root-absorption.

In seven small flower-pots, each filled with the same kind of soil,
and treated with a known weight of ferrous sulphate, were sown
some mustard seeds. When the little plants had made their appear-
ance above the soil, they were exposed for some hours each day to
the coloured lights of the spectrum.

No. 1 was exposed to the red part of the spectrum ; No. 2 to
the orange, and so on ; after so many hours’ exposure they were
removed to a dark place. This operation was performed for several
weeks, each pot being exposed to its own part of the spectrum daily
until the plants had grown to a considerable size. The plants in
each pot were then reduced to ashes, and submitted to analysis, the
following percentage of ferric oxide being found : —

Mustard Plants.

Pot No. 1 exposed to red part of spectrum, gave
,, 2 ,, orange

,, 3 ,, yellow

„ 4 ,, green

,, 5 ,, blue ,,

„ 6 ,, indigo

., 7 ,, violet „

Percentage of Fe203
in Ash.

. 0-92

. 1-43

. 2-51

. 1-90

. 071

. 0-20
. 075

The same number of seeds were placed in each pot, and each pot
received the same quantity of iron sulphate during the investigation.
The plants, as they grew, were watered from time to time with a

weak solution of ferrous sulphate, always of the same strength (see
figure).

We have also tried the same experiments upon bean seeds (work-
ing exactly under similar conditions as those detailed above), with
the following results : —

Bean Plants.

Percentage of Fe203
in Ash.

Pot No.

] exposed to red part of spectrum, gave

. 1-40

9 9

2

99

orange

99 *

. 275

n

3

9 9

yellow

9 9

. 4-52

9 9

4

9 9

green

9 9

. 3-34

9 >

5

9 »

blue

99 *

. 172

9 9

6

9 9

indigo

9 9

. 0 84

9 9

7

99

violet

9 9

. 0-53

1887.] Dr A. B. Griffiths on Rays of Solar Spectrum.

127

The soil used in the fourteen experiments

was a calcareous soil of the

following composition : —

Lime, ......

53-00

Organic matter, ....

1-50

Oxides of iron and alumina,

... 1 -62

Magnesia, ......

0-32

Potash and soda, ....

o-oi

Phosphoric acid, ....

0-04

Silica, ......

0-26

Chlorine, .....

o-oi

Sulphuric acid, ....

None.

Carbonic acid, ....

43-24

100-00

Graphic Representation of the Amount of Ferric Oxide in the Ashes

of Plants after growing in an Iron

Manure, and exposed to

various Rays of the Spectrum, illustrating Root- Absorption.

These experiments therefore show that the most active rays for root-
absorption coincide with those of assimilation. From the researches
of Drs Draper and Pfeifer, and those of Cloez and Gratiolet, it is
evident that the most favourable rays of white light are those lying
between the yellow and green. In their experiments the greatest
amount of oxygen was evolved in this part of the spectrum, there-
fore the largest amount of carbon is retained by the process of
assimilation. From our experiments we obtain the largest per-
centage of ferric oxide in the ashes of those plants exposed to the
yellow or yellow-green part of the spectrum, or between Fraunhofer’s

128 Proceedings of Royal Society of Edinburgh. [mar. 7,

lines D and E; therefore conclude that the most energetic rays of
white light for root-absorption coincide with those for assimilation.

In the presence of light, or the different rays of white light, the
two processes go on side by side.

Albuminoid Formation.

The mode of formation of albuminoids in the vegetable kingdom
is said to be unknown. We know, according to Lieberkiihn, that
the albumens have an empirical formula of C72H112N18S022. As this
molecule contains sulphur , the increase of protoplasmic (albuminoids)
matter in the living plants, as far as the sulphur is concerned, would
only have come from the sulphur of the ferrous sulphate, as there were
no other sulphates present in the soil. Moreover, we find the largest
percentage of albuminoids in the plants when they have been grown
in the yellow part of white light, as the following table shows : —

Percentage of Albuminoids.

Mustard

Plants.

Bean

Plants.

Pot No. 1 exposed to red part of spectrum, gave .
„ 2 „ orange

,, 3 ,, yellow ,,

,, 4 ,, green

j, 5 ,, blue ,, •

,, 6 „ indigo

,, 7 „ violet

23-3%

25- 5
27*6

26- 2
21*1
18-4
13-0

2- 4%
4 '2
6*5
5-3

3- 6
2-2
1*8

Also, the percentage of sulphur (estimated directly) was the largest
in each case when grown in the yellow part of the spectrum.

Dr W. J. Kussell, F.E.S. (of St Bartholomew’s Hospital, London),
found that in those plants grown by the aid of iron sulphate the rela-
tive amount of chlorophyll (in equal areas, and also in equal weights
of the leaves) is increased over those not grown with the iron manure.
The following table gives —

Dr Russell’s Estimation of Relative Amount of Chlorophyll in
the Leaves of Dr Griffiths’ Crops of 1884.

Chlorophyll in
equal areas of
the leaves.

Chlorophyll
in equal weights
of the leaves.

f (1) Beans grown with iron sulphate,

100

100

\ (2) ,, without ,,

79

76

f (1) Turnips grown with ,,

59

61

\ (2) ,, without ,,

40

39

1887.] Dr A. B. Griffiths on Rays of Solar Spectrum.

129

(For further details, see Journal Chemical Society, Trans., 1885,
page 54). This proves that a soluble iron salt nourishes the chloro-
phyll granules; and recently Prof. J. v. Sachs, in describing the
symptoms of vegetable chlorosis, recommends the salts of iron as a
remedy (Biedermann’s Centralblatt fur Agrikultur Chemie, vol xv.
part 9). It has been shown by one of us that crystals of iron sul-
phate have been found near to the chlorophyll granules when
sections of plants are examined under the highest powers of the
microscope (Journal Chemical Society, Trans., 1883, page 195).

Hence it appears that albuminoids, or, in other words, the proto-
plasm of the living cell, is formed by the combined action of assimi-
lation and root-absorption in the vicinity of the chlorophyll granules.
The sulphur required to complete the albumen molecule comes from
the decomposition of sulphates, and the nitrogen from the nitrates
or ammonia salts (added to the soil or derived from organic matter)
taken into the plant by root-absorption.

PRIVATE BUSINESS.

Mr Arthur Silva White, Mr W. Peddie, Mr H. M. Cadell, Mr G.
B. Wieland, and Mr A. H. Sexton were balloted for, and declared
duly elected Fellows of the Society.

Monday , 21 st March 1887.

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

1. Variations in the Value of the Monetary Standard.

By Professor Nicholson.

2. On Ice and Brines. By J. Y. Buchanan.

{Abstract.)

The composition of the ice produced in saline solutions, and more
particularly in sea-water, has frequently been the object of investi-
gation and of dispute. It might be thought that to a question of
VOL. XIV. 23/9/87 l

130 Proceedings of Royal Society of Edinburgh. [mar. 21,

whether ice so formed does or does not contain salt, experiment
would at once give a decisive answer. Yet, relying on experiment
alone, competent authorities have given contradictory answers. All
agree that ice, whether formed artificially in the laboratory by
freezing sea-water, or found in nature as one of the varieties of sea-
water ice, retains, in one form or another, and with great tenacity,
some of the salt existing in solution in the water. The question at
issue is whether this salt is to be attributed to the solid matter of
the ice or to the liquor mechanically adhering to it, from "which it
is impossible to free it. Most bodies, and especially those which
take a crystalline form, are easily purified and freed from all
suspected foreign matter, with a view to analysis, by the simple
operation of washing and drying. It is impossible to wash the
crystals, formed by freezing a saline solution, with distilled water,
because they melt at a temperature below that at which distilled
water freezes. The effect of the addition of a small quantity of
distilled water to a quantity of saline ice is at first the anomalous
one, that what was a wet sludge is transformed into a dry crystal-
line powder. It is, of course, impossible to dry the ice by heat,
and to do so by more intense freezing would be begging the question.
The experimental difficulties therefore account for some of the
divergence of opinion on the subject. The mixed character of the
substances examined has also much to do with it. As a rule, it may
be said that those investigators who have confined their observations
to the laboratory have concluded that the ice forming when saline
solutions of moderate concentration, including sea-water, are frozen,
is pure ice, and the salt from which it is impossible to free it entirely
belongs to the mother-liquor, while those who have collected and
examined sea-water ice in high latitudes have come to the opposite
conclusion.

During the Antarctic cruise of the “Challenger” I made a number
of observation on the sea- water ice found in those regions, and, re-
lying principally on the fact that the melting temperature of the ice
was markedly lower than that of fresh-water ice, and that it wTas
impossible by any of the ordinary means familiar to chemists for
freeing crystals from adhering mother-liquor to materially reduce its
salinity, I came to the conclusion that the ice forming in freezing
sea- water is not a mixture of pure ice and brine, but that it contains

1887.]

Mr J. Y. Buchanan on Ice and Brines.

131

the salt found in it in the solid state either as a crystalline hydrate
or as the anhydrous salt, hut most probably as a hydrate. In
dealing with the subject, Dr Otto Pettersson ( Water and lee ,
p. 302) quotes my observations, and also rejects the view that
“ sea-ice is in itself wholly destitute of salts, and only mechanically
incloses a certain quantity of unfrozen and concentrated sea- water.”
He founds his belief on the fact that numerous analyses of speci-
mens of sea-water ice have shown that the constitution of the saline
contents of different specimens of ice differs for each specimen, and
is always different from that of the saline contents of sea-water.
Were the salinity due to inclosed unfrozen and concentrated sea-
water, we “ ought to find by chemical analysis exactly the same
proportion between Cl, MgO, CaO, S03, &c., in the ice and in the
brine as in the sea- water itself.” He quotes numerous analyses
of specimens of sea-water ice from the Baltic and from the Arctic
Seas to show that this is not the case. Calling the percentage of
chlorine in each case 100, he found in various sea- waters the per-
centage of S03 to vary from 11 ’49 to 11*89. In specimens of sea-
water ice it varied from 12*8 to 76*6, and in brines separating from
the ice and remaining liquid at — 30° C. it varied from 1*14 to 1*16.

This argument appears conclusive. In order to explain all the
phenomena observed in connection with sea-water ice he cites
Guthrie’s investigations, which went to show that, in freezing
saline solutions, under a certain concentration, pure ice is formed at
a temperature which falls from 0° C., when the amount of salt
dissolved is infinitely small, to a certain definite temperature when
the solution contains a certain definite percentage of salt. Further
abstraction of heat then produces solidification of the solution as a
whole, in the form of a crystalline hydrate, of constant freezing-
and melting-point. To such hydrates, Guthrie gave the name of
cryohydrates. Pettersson quotes the following as being particularly
applicable to the case of sea-water : —

The cryohydrate

Contains per cent.

Solidifies at

of

of water.

°C.

NaCl .

76-39

-22

KC1

80-00

-114

CaCl2 .

72-00

-37-0

MgS04 .

78-14

- 5-0

Na2SG4 .

95*45

- 0-7

132 Proceedings of Boy al Society of Edinburgh. [mar. 21,

And he refers more particularly to the cryoliydrate of Na2S04
forming and melting at - 0o,7.

Now the bearing of Guthrie’s experiments is to show that, while
at sufficiently low temperatures, and with suitable concentration,
the water will solidify along with one or other of the salts in solu-
tion, until this low temperature and high concentration are attained,
pure ice must be the result of freezing.

The abnormal phenomena attending the formation and the melt-
ing of ice in saline solutions and sea-water find a natural explana-
tion in an observation which I have frequently quoted, and which
Dr Pettersson mentions in a footnote at p. 318, namely, that “ a
thermometer immersed in a mixture of snow and sea-water which is
constantly stirred indicates - 1°'8 C.” If this is true, it is clear that
my melting-point observations proved nothing. On repeating the ex-
periment I found it confirmed, and took the opportunity this winter
of investigating the matter more closely. The paper now communi-
cated to the Royal Society of Edinburgh contains the first portion of
the results. It deals with the subject under two heads, namely, (a)
the temperature at which sea-water and some other saline solutions
freeze, and the chemical constitution of the solid and the liquid
into which they are split by freezing ; and ( b ) the temperature at
which pure ice melts in sea-water and in a number of saline solu-
tions of different strengths.

(a) The freezing experiments were limited to sea- water and solu-
tions of NaCl comparable with sea-water.

Chloride of Sodium. — Four solutions were used, and they were
intended to contain 3, 2*5, 2, and 1’5 per cent. NaCl respectively.
Forty grammes of this solution, in a suitable beaker, were immersed
in a freezing mixture of such composition as to give a temperature
from 2° to 2° ’5 C. below the freezing temperature expected. The
temperature at which ice began to form (if necessary after adding a
minute splinter of ice) was noted, and the freezing was allowed to
continue with constant stirring till the temperature had fallen 0o,2
C. A specimen of the mother-liquor was removed, and the chlorine
in it determined ; the chlorine in the original solution had been
determined before. The beaker was then removed from the freezing
bath and allowed to melt. The temperature in all cases rose during
melting exactly as it had fallen during freezing. In the following

1887.] Mr J. Y. Buchanan on Ice and Brines. 133

table are given the means of the temperature at which ice began to
form in the original solution, and that of the liquid when the sample
of brine was taken, and the means of the chlorine found in the
original solution and in the brine sample : —

Mean freezing temperature, . -1°*875 C. - 1°*63 - 1°*30 — 0°*975j ;

Mean per cent. Cl., . . 3 *87 1*60 1*30 0*98

It will he seen that, in the dilute solutions experimented with,
the percentage of chlorine expresses, in terms of the Centigrade
scale, the lowering of the freezing-point of the solution.

Sea- Water. — Similar experiments were made with sea- water of
different degrees of concentration. In sea-water from the Birth of
Clyde containing 1*84 per cent, of chlorine, ice forms at - 1°*9 C.
The following results are from means of close-agreeing results : —

o o o o

Freezing temperature, . - 2*0 - 1 *5 - 1 '0 - 0 ‘5

Per cent, chlorine, . 1*94 1*445 0*963 0*475

Difference, . . . 0*06 0*055 0*037 0 025

Sea-water resembles a chloride of sodium solution containing
the same percentage of chlorine, and the resemblance is closer the
greater the dilution. When the beaker was removed from the
freezing-hath, the temperature rose during melting as it had fallen
during freezing. In these experiments, which had for their object
the determination of the temperature at which the crystals melted,
as well as that at which they began to form in the water, it was
impossible to remove a sample for analysis large enough to enable
the sulphuric acid to he determined in it.

For this purpose a series of observations were made, using
quantities of 300 grammes of sea-water. Freezing was continued
usually until the temperature had fallen 0°*3 C. below that at which
crystals began to form. The mother-liquor was then separated from
the crystals by means of a large pipette with fine orifice, before
removing the beaker from the freezing hath. The magma of
crystals was then brought rapidly on a filter and drained by means
of the jet pump. The ice, thus drained, was then melted, and the
three fractions were analysed. In the following table (I.) the
results of four experiments are given. In the one column (W) will
be found the weight of the original water taken and of the fractions
into which it was split on freezing ; in the other (R) will be found

134 Proceedings of Royal Society of Edinburgh. [mar. 21 ,

the ratio of S03 to Cl found by analysis, the chlorine being set
down as 100 ; thus, in I. the percentage of chlorine found in the
crystals, melting at the lowest temperature, was 1*497, and that of
the S03, 0*174 ; the ratio (R) is therefore 11*62.

Table I. — Freezing Sea-Water — Analyses of Fractions.

No. of Experiment,

I.

II.

III.

IV.

Nature of Water,

Forth 100 %.

Mother-liquor.

Clyde 100 %.

Clyde 50 %.

w.

R.

w.

R.

w.

R.

W.

R.

Original water,

300

11*83

90

11*67

300

11*58

300

11*21

Mother-liquor, .

J 170*6

11*67 j

• • •

11*83

102

11*57

78

11*67

Drainings,

• • •

• • •

94

11*56

109

• . .

Crystals, .

106

11*62

23

11*22

97

11*67

106

11*4

jj

22*5

11*11

...

...

...

...

...

...

It will be seen that the ratios (R) found for mother-liquor,
drainings, and ice agree with one another quite as closely as those
found in samples of pure sea-water from different localities. It is
to be remembered that in these experiments the water was frozen
gently — that is, the rate of abstraction of heat was low, the tem-
perature of the freezing bath being regulated so as to be about 2° C.
below the freezing temperature of the solution. Much of the error
and uncertainty about the freezing of saline solutions arises from
the violence of the methods employed. Judging then by the con-
stancy of the relation of the percentage of Cl to S03, we see that in
sea- water, frozen at moderate temperatures, the composition of the
saline contents of the original water, the mother-liquor, and the ice
is identical; and we are justified in concluding that it is probable
that the saltness of the ice is due to unfrozen and concentrated sea-
water adhering to it. Ice forming in even very weak saline solutions
closely resembles snow (which is ice forming in air), and has the
same remarkable power of retaining mechanically several times its
weight of water or brine.

If we assume that the ice formed in freezing sea-water is pure ice,
and that the saline ingredients are retained by the portion remaining
liquid, we can calculate the amount of ice which has been formed if
we know the salinity of the original water and that of the residual
brine. In the case of sea-water the salinity varies directly with the

1887.]

Mr J. Y. Buchanan on Ice and Brines.

135

jDercentage of chlorine. The weight of the brine remaining after
any freezing operation is found by multiplying the weight of the
original water used by the ratio of the chlorine percentage found
in the original water to that found in the brine. The difference
between the weight so found and that of the original water is the
weight of the ice formed. In Table II. the results of this calcu-
lation are given for Experiment III. on pure sea-water from the
Clyde, and for Experiment IY. on the same water diluted with an
equal weight of distilled water.

Table II.' — Calculation of Ice formed , on the basis of the Salinity
of the Original Water and of the Residual Brine.

No. of Experiment, .

III.

IY.

Weight of original water (grammes), .

W

300

300

Per cent. Cl in ditto, .....

c

1-836

0-923

Per cent. Cl in mother-liquor,

K

2-212

1-153

£

Weight of mother-liquor, . . W-^- =

L

249*0

293-3

Weight of ice, .... W-L =

I

51-0

60-7

Sea-water, like other saline solutions, is easily cooled several de-
grees below its freezing-point before crystals begin to form. While
cooling down to and below what was known to be its freezing-point,
simultaneous observations of the temperature of the sea-water and
the freezing-bath were made from half minute to half minute. From
these observations, the rate of abstraction of heat for different differ-
ences of temperature of sea-water and bath was found. At a given
moment a minute splinter of ice (weighing much less than a drop of
water) was introduced. Crystals immediately began to form, and
the temperature rose in from ten to fifteen seconds to the freezing-
point. During the freezing the temperatures of bath and sea- water
were observed at regular intervals. The heat removed is thus made
up of that eliminated during the few seconds when freezing began
and the temperature rose to the freezing-point, which is found by
multiplying the rise of temperature by the weight of liquid, and
that removed during the subsequent cooling, which is found
from the duration of the operation and the rate of loss of heat,
deduced from observations made during the cooling. The specific
heat of the solution is taken as that of the water which it contains,

136 Proceedings of Royal Society of Edinburgh. [mar. 21,

namely 09 6 5 for III., and 0*9825 for IV. The mean freezing
temperature was - 2° '05 for III. and - 1°*05 for IV. The latent heat
of water freezing at 0° is 79*25. The specific heat of ice being 0*5,
the latent heat of water freezing at -2o,05 is 78*22, and that of
water freezing at - 1°*05 is 78*73. In Experiment III. the total
heat extracted during the freezing was 4230x0*965 = 4082 heat
units (gramme-degrees), and dividing this by 78*22 we find 52*2
grammes as the weight of pure ice formed at — 2° *05 C., equivalent
to this abstraction of heat. In Experiment IV. the heat abstracted
was found to he 5193 x0*9825 = 5102. Dividing this by 78*73
we find 64*8 grammes as the equivalent weight of ice formed.

We have calculated the weight of ice which would he found, first
on the basis of the salinity of the solution ; and second, 011 the
basis of the observed thermal exchange, assuming in both cases
that, in the act of freezing pure ice is formed. Thus —

Table III.

No. of Experiment, .

III.

IY.

Calculated from thermal exchange,

,, ,, salinity,

Difference, .......

grammes.

52*2

51*0

1*2

grammes.

64-8

607

4*1

The agreement between the two quantities of ice formed as
calculated by the different methods is as close as could be expected,
and renders probable the truth of the common assumption that the
solid body formed is pure ice.

It has, moreover, been proved by Guthrie, Riidorff, and others
that, in solutions of the salts occurring in sea-water, ice does
separate out at first, and continues to separate out until the con-
centration has become many times greater than that of sea-water.
Assuming that in sea-water all the chlorine is united to sodium, 85
per cent, of the water would have to be removed as ice before a
cryohydrate would form, and if it contained nothing but sulphate
of soda in the proportion corresponding to the sulphuric acid found
in it, over 90 per cent, of the water would have to go as ice, before
the cryohydrate would be formed.

In my experiments about 15 per cent, of the weight of the water
was frozen out as ice, causing a lowering of freezing-point by0°*3 C.

1887.]

Mr J. Y. Buchanan on Ice and Brines.

137

In nature it is probable that the ice forming at the actual freezing
surface does so at an almost uniform temperature, the local concen-
tration produced by the formation of a crystal of ice being imme-
diately eliminated by the mass of water below. In the interstices
of the crystals there will be retained a weight of slightly concen-
trated sea-water at least as great as that of the ice crystals. These
retain the brine in a meshwork of cells, and, as the thickness of the
ice covering increases, and the freezing surface becomes more re-
mote, the ice and the brine become more and more exposed to the
atmospheric rigours of the Arctic winter. The brine will continue
to deposit ice until its concentration is such that, for example, the
cryohydrate of NaCl is ready to separate out. It probably will
separate out until it comes in conflict with, for instance, the chloride
of calcium or the chloride of magnesium, which will retain some
of the water, without solidifying, even at the lowest temperatures.
At the winter quarters of the “Vega” brine was observed oozing
out of sea- Water ice and liquid at a temperature of - 30° C. It
was very rich in calcium and especially magnesium chlorides. In
fact, it is probably quite impossible by any cold occurring in
nature to solidify sea-water.

b. Melting of pure ice in sea-water and other saline solutions. — A
large number of experiments were made with solutions of concen-
tration comparable with that of sea-water, and in one or two cases
the experiments were extended to low temperatures and strong
solutions. As a rule, from 50 to 100 grammes of solution, cooled
to 0° C., were mixed with an equal weight of pounded ice, also at
0° C. The thermometer used for all these determinations was one of
Geissler’s normal ones, divided into tenths of a degree Centigrade ;
and its zero-point was verified almost daily. Along with the
thermometer, a pipette of suitable capacity was immersed in the
beaker, and used with the thermometer for keeping the mass well
mixed. Its upper aperture was closed with a small cork, which
was removed from time to time to permit of some of the brine being
sucked up and allowed to run back again. The inside of the
pipette was thus kept constantly moistened with the slowly altering
solution in the beaker. The temperature was read after very
thorough mixing, and the sample thereupon immediately removed
and preserved for analysis.

138 Proceedings of Royal Society of Edinburgh. [mar. 21,

As a rule, samples were taken for analysis at intervals of 0°*4 C.
Tlie results for three classes of salt in dilute solutions are arranged in
Tables IV., V., and VI.

Table IV. — Giving the percentage of Chlorine in Solutions of various
Chlorides in which Ice melts at given Temperatures.

o a5

Chloride in Solution.

£ s
2* *3

HC1

pSTaCl

KC1

(Sea-Water.)

MgCl2

CaCl2

BaCl2

1 a

E-"g

Per cent. Chlorine in Solution.

° c.

-3.5

3*06

3-30

• 0 •

• • •

4-12

• • •

-3-0

2-68

3-02

3-00

• • «

3-62

3-70

-2*5

2-28

2-53

2-50

• • •

3-12

3*20

-2-0

1-85

2-02

2-00

• • •

2'62

2-70

2-72

-1-5

• . 0

1-50

1*50

1-500

1-19

2-15

2*10

-1-0

• • •

1-02

1-02

1 *034

1-51

1*50

1-47

-0-5

...

0-50

0-52

0-588

0-87

...

...

Table V. — Giving percentage of Potassium in Solutions of various
Potassium Salts in which Ice melts at given Temperatures.

Temperature

of

melting Ice.

Salt in Solution.

KC1

KI

rCI’M

2

KOH.

Per cent. K In Solution.

°c.

-3-0

3-29

3-02

3-15

e • •

-2*5

2-79

2-59

2-68

2-60

-2-0

2-28

2-13

2-17

2-08

-1*5

1-74

1-63

1-66

1-57

-1-0

1-18

1*13

1-12

• • •

-0-5

0-59

0-60

0-57

...

Table VI. — Giving percentage of Hydrogen in Solutions of various
Hydrogen Salts in which Ice melts at given Temperatures.

Temperature

of

melting Ice.

Salt in Solution.

h2so4

|HC1

hno3

HKO

Per cent. H in Solution.

;°c.

-3-0

0-144

0-076

0*077

, , ,

-2*5

0-119

0*065

0-065

0*066

-2-0

0-097

0-052

0-052

0-053

-1-5

0-073

,,

0-042

0-041

-1-0

0-048

...

0*032

...

1887.]

Mr J. Y. Buchanan on Ice and Brines.

139

On considering them, it was at once evident that the lowering of
the melting-point of ice followed the concentration of the solution,
hut the law deviated in all cases from that of strict proportionality
to the amount of salt dissolved, in some cases to a greater extent
than in others. In comparing the effects of different salts in solu-
tion on the melting-point of ice, no simple connection could he
traced between their absolute weights and the effects produced ; but
on comparing chemically equivalent weights, a very close connection
was discovered. This will he evident from the inspection of the
tables. In each the first column contains the temperatures at which
pure ice melts ; and in the parallel columns the percentages of
chlorine, potassium, or hydrogen in the solutions of the salts
indicated at the head of each column, when ice melts in them at
the temperature indicated. The figures thus give numbers pro-
portional in each table to the chemically equivalent weights of the
different salts. They show at first that, whereas the presence of
equal absolute weights in solution produces very different effects,
the presence of chemically equivalent weights produces very similar
effects. On closer inspection, it is seen that the effects are almost
identical where the elements to which the common constituent is
united belongs to the same group of the periodic series, and differ
sharply where these elements belong to different groups. In the
case of the chlorides of sodium and potassium the number expressing
the percentage * of chlorine in the solution expresses equally the
depression of the melting-point of ice in terms of the Centigrade
scale. The same depression of melting temperature is produced by
10 per cent, less of chlorine united to hydrogen, and by 30 to 35
per cent, more of chlorine when united to magnesium, calcium, or
barium.

The results obtained with sea-water are also given, for comparison.
It will be seen that it behaves very approximately as a solution of
chloride of sodium containing the same amount of chlorine.

It is perhaps not very astonishing that unit weight of potassium
in saline solution should produce the same effect in lowering the
melting-point of ice, whether it is united to Cl or I ; but it shows
clearly how independent this action is of the general character of
the body in solution when we find the effect produced by unit

* All percentages are by weight.

140 Proceedings of Royal Society of Edinburgh. [mar. 21,

weight of hydrogen identical, whether it is united to such opposite
radicles as Cl or OIL Table VL shows further the effect of valence.
While a given weight of hydrogen produces the same effect in
solution, whether it he united to the very different but both univalent
radicles Cl and OK, its effect is reduced by one-half when united to
the bivalent S04. That valence is not the only factor is shown by
comparing the effects of hydrogen and potassium when united to
the common element, chlorine. Hydrochloric acid in solution
produces a markedly more powerful lowering effect on the melting-
point of ice than the equivalent amount of chloride of potassium.
Of all the substances that I have experimented on5 hydrochloric
acid is the most energetic in reducing the melting-point of ice, and
with ordinary strong acid and pounded ice there is no difficulty in
producing temperatures as low as the freezing-point of mercury. In
the case of hydrochloric acid, sulphuric acid, chloride of sodium, and
chloride of calcium, I have carried my experiments tolow temperatures
and great concentration. But before passing to them it is well to
consider the more dilute solutions with regard to their density.

That the mere density of the solution in which the ice is melting
has no direct connection with the lowering of its melting-point is
shown by the following table, in which the specific gravities
(at 15° C.) are given of the solutions of different salts which gave
the same depressions of melting-point : —

Temperature of
ineltirig.

Specific Gravity of Solutions of

NaCl

KCl

MgCl2

CaCl2

BaCl2

dc.

-2-86

-1*8

1-03370

1-02174

1-03850

1-02535

1-03893

1-02715

1-04756

1-03262

1-06633

There are many similarities in the effects produced by greatly in-
creasing the pressure upon pure water and by dissolving salts in it.
First, there is an absolute diminution in the volume of the solution
as compared with the sum of the volumes of its components ;
second, in virtue of this compression by molecular forces it has be-
come less compressible by mechanical means ; third, the tempera-
ture of maximum density and the freezing temperature are lowered ;
and fourth, the former of these two temperatures is lowered
more rapidly than the latter. All these effects are produced in kind

1887.]

Mr J. Y. Buchanan on Ice and Brines.

141

by increasing the pressure on pure water. Whether, or in how far,
they agree in degree must he decided by future experiments.

Table YII.

Temperature

of

melting Ice.

Salt dissolved.

HC1

NaCl

CaCl2

Per cent. Cl in Solution.

°c.

-35

15*26

-30

13-98

• • a

15-97

-25

12-60

• • •

14-47

-20

11-00

a • a

12-65

-15

9-17

11-10

11-29

-10

7-02

8*40

8-93

- 5

4-15

4-72

5-65

Experiments ivitli Concentrated Solutions. — Several series of
experiments have been made with hydrochloric acid, chloride of
sodium, and chloride of calcium, and also with sulphuric acid.
Table YII. gives the results, in the same form as preceding tables,
for the chlorides.

It will he seen that, in proportion as the solution becomes more
concentrated, further additions of salt produce a greater effect in
lowering the melting-point of ice, and at a temperature of — 15° C.
equivalent weights of JSTaCl and CaCl2 produce identical results. In
Table YIII. the results for hydrochloric acid and sulphuric acid
are given in terms of the percentage of hydrogen in the solution.

Table YIII.

Temperature of
melting Ice.

Acid dissolved.

nci

H2S04

Per cent. H in Solution.

- 25° C.

0-355

0-538

-20

0-310

0-487

-15

0-258

0-418

-10

0*198

0-332

- 5

0-117

0-205

The temperatures given in these tables are all in terms of the same
thermometer, which has not been verified for this part of its scale
by comparison with a standard or with the air thermometer.

We have thus seen that, owing to its peculiar physical properties,
it is impossible to prepare the crystalline solid which separates from

142 Proceedings of Boy al Society of Edinburgh. [mar. 21,

sea-water and analogous saline solutions in a condition to enable the
question, whether the salt does or does not form part of the solid
matter of the crystals, to be solved directly by chemical analysis.

So far as chemical analysis is applicable, it is in favour of the
salt belonging exclusively to the adhering brine. When sea-water
is carefully frozen artificially, the ratio between the chlorine and the
sulphuric acid is the same for the solid contents of the original
water, the crystals, and the mother-liquor. It is exceedingly un-
likely, if part of the salt went into the crystals, leaving the re-
mainder in the brine, that there would be no selective separation of
its constituents.

It has been shown that snow or pure lake ice, which, when
melting by itself or immersed in pure water at atmospheric pressure,
melts at the constant temperature called 0° C. or 32° Fahr., changes
its melting temperature when immersed in a saline solution. The
altered melting temperature, however, is the same for solutions of
the same composition (no doubt with some allowance for pressure)
and different for solutions of different composition.

The temperature at which pure ice melts in a solution is identical
with that at which ice separates from the same solution on being
sufficiently cooled.

"When sea-water is frozen to the extent of 15 per cent, of its
mass, and the crystals so formed are allowed to melt in the liquid
in which they have been produced, they melt exactly as they have
been formed. If snow or pure ice be immersed in the brine formed
by partially freezing sea-water, it melts at the same temperature as
the ice which had been formed by freezing the sea-water, so long as
the chemical composition remains the same in each case.

The heat removed in freezing sea-water to the extent of 15 per
cent, of its mass accounted for the production of the same amount
of ice as was given by calculation on the basis of the chlorine found
in the mother-liquor.

When some saline solutions are cooled for a sufficient length of
time at a sufficiently low temperature, there arrives a certain con-
centration at a certain temperature, when further removal of heat
causes solidification of the brine as a whole (cryohydrate).

The concentration necessary for the solidification of even the
cryohydrate of highest melting temperature is such that in the

1887.] Mr J. Y. Buchanan on Ice and Brines. 143

primary freezing of the water of the sea no such body can he
formed. It would follow from this consideration alone that the
first ice formed on the sea in Arctic regions consists of pure ice,
and it is also certain that it would retain a large quantity of the
residual sea-water in its interstices. During the winter this in-
closed liquor would solidify in the interstices of the crystals to ice
and cryohydrates, in so far as the temperature and the nature of
the salts in solution would permit. From my experiments with
chloride of calcium, and the existence of hrines observed to remain
liquid at - 30° C. at the winter quarters of the “ Vega,” it is unlikely
that sea-water, as a whole, can ever he completely solidified in
nature. The presence of unfreezable or difficultly freezable brine
in freshly-formed sea-water ice, explains its eminently plastic char-
acter even at very low temperatures.

The fact that cryohydrates of different salts solidify and melt at
different temperatures, sufficiently explains the various composition
of different specimens of old sea ice.

The apparent expansion, near the melting-point, of ice formed by
freezing water which contains any salt at all is perfectly explained
on the hypothesis that in the act of freezing the water rigidly
excludes all saline matter from participation in its solidification.

The residual and unfreezable brine which remains in consider-
able quantity liquid when sea-water is frozen, must also remain in
greater or less quantity when fresh water is frozen. All natural
waters, including rain-water, contain some foreign and usually saline
ingredients. If we take chloride of sodium as the type of such
ingredients, and suppose a water to contain a quantity of this salt
equivalent to one part by weight of chlorine in a million parts of
water, then we should have a solution containing O'OOOl per cent,
of chlorine, and it would begin to freeze and to deposit pure ice at
a temperature of - 0o,0001 C.; and it would continue to do so
until, say, 999,000 parts of water had been deposited as ice. There
would then remain 1000 parts of residual water, which would
retain the salt, and would contain, therefore, 0T per cent, of
chlorine, and would not freeze until the temperature had fallen to
- 0°T C. This water would then deposit ice at temperatures
becoming progressively lower, until, when 900 more parts of ice
had been deposited, we should have 100 parts residual water, or

144 Proceedings of Royal Society of Edinburgh. [mar. 21,

brine as it might now be called, containing 1 per cent, of chlorine,
and remaining liquid at temperatures above - 1°*0 C. When 90
more parts of ice had been deposited, we should have 10 parts of
concentrated brine containing 10 per cent, chlorine and remaining
liquid as low as - 13° C. In the case imagined, we assume the saline
contents to consist of NaCI only, and with further concentration the
cryohydrate would no doubt separate out and the mass become
really solid. On reversing the operations, that is, warming the ice just
formed, we should, when the temperature has risen to about — 13° C.,
have 999,990 parts ice and 10 brine containing 10 per cent, chlorine.
Now, owing to the remarkable fact that pure ice, in contact with a
saline solution, melts at a temperature which depends on the nature
and the amount of the salt in the solution, and is identical with the
temperature at which ice separates from a solution of the same
composition on cooling, the brine liquefies more and more ice at
progressively rising temperatures, until, as before, when the temper-
ature of the mass has risen to -0°T C., it consists of 999,000
parts of ice and 1000 parts of liquid water, containing 1 part of
chlorine. The remainder of the ice will melt at a temperature
gradually rising from - 0o,l to 0° C.

The consideration of this example furnishes an easy explanation
of the anomalous behaviour of ice formed from anything but the
very purest distilled water, in the neighbourhood of its melting-
point. This subject has been studied with great care and thorough-
ness by Pettersson. The apparent expansion of all but the very
purest ice, when cooled below 0° C., is ascribed by him in part to
solid saline contents of the ice which exercise a disturbing and
unexplained influence on its physical properties. Viewed in the
light of the fact that the presence of even the smallest quantity of
saline matter in solution prevents the formation of ice at 0° C., and
promotes its liquefaction at temperatures below 0° C., we see that
this apparent expansion of the ice on cooling is probably due to
the fact that we are dealing, not with homogeneous solid ice, but
with a mixture of ice and saline solution. As the temperature
falls this solution deposits more and more ice, and its volume
increases. But the increase of volume is due to the formation of
ice out of water, and not to the expansion of a crystalline solid
already formed.

1887.]

Mr J. Y. Buchanan on Ice and Brines.

145

In Table IX. are given the volumes occupied by the ice (with
inclosed brine) formed by freezing 100,000 c.c. (at 0° C.) of a
water containing chloride of sodium equivalent to 7 grammes
chlorine in 1,000,000 cubic centimetres (at 0° C.).

Table IX. — Water containing 7 parts Cl in 1,000,000.

Temp.
0 C.

Water

frozen.

c.c.

Ice

formed.

c.c.

Brine

remain-

ing.

c.c.

Ice and
Brine,
c.c.

Pettersson

III.

Vol. of Ice
at T°.
c.c.

Diff.

T

Vj

®i

v2

Vn

P

P-v2

-0*07

99000

107979

1000

108979

108980

1

-0*10

99300

108306

700

109006

109007

1

-0*15

99533

108561

467

] 09028

109038

10

-0*20

99650

108687

350

109037

109048

11

-0*40

99825

108879

175

109054

109057

3

The volume (v2) of the ice and brine formed on freezing this
water is compared with that (P) observed by Pettersson in freezing
a sample of the distilled water in ordinary use in the laboratory.

It will be seen that the volumes observed by Pettersson agree
very closely with those calculated for a water containing 7 parts of
chlorine in a million, on the assumption that the saline matter is
contained entirely in adhering liquid brine.

The irregularities in the melting-points of bodies like acetic acid?
to which Pettersson refers, are without doubt due to a perfectly
similar cause.

Also the very low latent heat observed by Pettersson for sea-
water is to be explained by the fact that the salt retains a con-
siderable proportion of the water in the liquid state even at tem-
peratures many degrees below the freezing-point of distilled water.

Thus, he made two determinations of the latent heat of sea-water
containing P927 per cent. Cl and 3*53 per cent. salt. The freezing
took place in the one case between the temperatures - 9°*0 and
— 7°*47 C., and in the other between -8°*35 and -6°*94 C., and
the results he found were 52*7 and 51*5. The mean initial tem-
perature in these two experiments is -8° *7 C., and the mean final
temperature - 7°*2 C. At - 7° *2 C. ice would form on cooling, and
would melt on warming a solution of chloride of sodium containing
6*48 per cent. Cl, which represents 11*87 per cent, of the sea salt.
In order to concentrate a brine containing 3*53 per cent, salt to one

VOL. XIV. 23/9/87

K

146 Proceedings of Royal Society of Edinburgh. [mar. 21,

containing 11*87 per cent., 70 per cent, of the water in it must be
removed. Hence in sea-water freezing at a final temperature of

- 7° *2 C. there is formed 70 per cent, of ice, and there remains
liquid 30 per cent, of brine. Freezing began at the mean temperature

— 8°*7 C., and the latent heat of pure ice at this temperature is 75.
Calculating the latent heat of this mixture from the heat liberated
in the calorimeter during freezing, and assuming that the whole
mass had solidified, Pettersson’s results give the mean latent heat
of this sea- water as 52*1. Calculating the apparent latent heat on
the assumption that 70 per cent, of the mass solidifies into pure
ice and that 30 per cent, remains liquid, we get the number 51*5.
On all grounds therefore we must conclude that pure ice is the
primary product in freezing sea- water and saline solutions of mode-
rate concentration.

The plasticity of ice and the motion of glaciers receive a simple
and natural explanation when we see, as in Table IX., that, if the
water from which this ice is produced contains no more than 7
parts of chlorine per millon, it will, in the process of thawing,
when the temperature has risen to - 0°*07 C., consist to the extent
of 1 per cent, of its mass of liquid brine or water. The water
considered in Table IX. is certainly not less free from foreign
ingredients than rain or snow. It follows, therefore, that a glacier,
in a climate where the temperature is for the greater part of the
year above 0’° C., must have a tendency to flow , owing to the power
of saline solutions to deposit ice and to dissolve it at temperatures
below 0° C.

The verification of thermometers by comparison with the air
thermometer is always troublesome. It results from the above
investigations that, if the temperature at which ice melts in solu-
tions of a salt, such as chloride of calcium of different degrees of
concentration, were once and for all carefully determined by means
of a standard air thermometer, a thermometer could be indirectly
hut satisfactorily compared with the air thermometer at temperatures
below 0° C. by immersing it in a mixture of ice and chloride of
calcium solution, and taking a series of readings of the thermometer
and samples of the brine simultaneously. By determining the
chlorine in the samples the concentration of the brine is ascertained,
and the comparison with the standard effected.

1887.] Mr J. Y. Buchanan on Ice and Brines. 147

Freezing Mixtures. — The results obtained in examining the
melting-point of ice in saline solutions affords data for mixing
freezing baths of any degree of cooling power. With chloride of
sodium, for instance, a rough rule is to have such an amount of
salt dissolved in the brine that the percentage of chlorine shall
give the desired temperature in Centigrade degrees below the
freezing-point. In my experiments in freezing sea-water in quanti-
ties of 300 grammes, I usually made up the bath of 500 grammes
pounded ice, 400 grammes water, and 45 grammes common salt.
When mixed, the liquid contained about 4 per cent. Cl, and gave
a temperature a little below - 4° C. In the course of an hour the
liquid would contain 3 per cent, to 3*25 per cent. Cl, and the
temperature have risen to - 3° C. By using such baths freezing
operations can always be kept completely in hand.

3. On the Distribution of Temperature in the Antarctic Ocean.

By J. Y. Buchanan.

(Abstract.)

In the regions of the Antarctic Ocean where icebergs are numer-
ous, and where in winter the sea- water freezes, the distribution of
temperature in the deeper layers of water is peculiar. The facts are
detailed in the Challenger Narrative (vol. i.). The general result
of her observations went to show that, from the edge of the ice-
pack, a wedge of cold water stretches northwards for more than
12° of latitude, underlying and overlying strata at a higher tempera-
ture than itself (p. 418).

Although the conditions and facts likely to throw light upon the
cause of this phenomenon are discussed, no satisfactory explanation of
it is given. One important fact is noticed at p. 421 — “ The fact that
the cold wedge above referred to extended north just as far as the
icebergs did in March 1874 points to there being some connection
between the temperature and the presence of melting icebergs.” It
is well known that icebergs consist of land- ice, which is nearly
pure frozen water, and melts in the air at 32° F. It was
thought that the effect of immersion of such a substance in a
medium having a temperature 3° F. lower than its melting-point
would be to indefinitely preserve it — that, in fact, only the lower

148 Proceedings of Royal Society of Edinburgh. [mar. 21,

surfaces of the icebergs large enough to reach to the depth of 300
fathoms would suffer any melting at all. The existence of the cold
stratum was ascribed wholly to the cold brine, separated from the
ice on the freezing of the sea-water, sinking downwards with an
initial temperature of from 280,5 to 29° F. This cause, though
existing and in operation, is quite inadequate to produce the effect
observed. The facts related in the preceding paper furnish a com-
plete explanation of the cold wedge of water in the Antarctic Ocean
and the dependence of its thickness and temperature on the range
of icebergs. These enormous islands of ice, a very large proportion
of which rise in tabular form to a height of 200 to 300 feet above
the sea, float in many cases with their lower surfaces at a depth of
from 250 to 300 fathoms. The warmer and denser water coming
from lower latitudes (see Challenger Narr ., vol. i. p. 428) bathes
these lower surfaces, the temperature of the mixture at the surface
of contact falls, the heat abstracted from the sea-water melts a cor-
responding amount of the ice of the iceberg, and a saline solution is
produced, less salt, and therefore lighter than the water away from
contact with the iceberg, and having a temperature which depends
immediately on the strength of the resulting solution. Being lighter
than the surrounding water, this resulting solution necessarily flows
up along the sides of the berg to the surface, and its place is taken
by fresh undiluted sea-water, which in its turn is cooled, diluted, and
transferred to the surface. The result is the production of a means
of circulating and of cooling and equalising the temperature of
the water within the reach of icebergs. As there is continual
renewal of the ocean water brought into contact with the ice, and
as its composition is constant, the temperature produced is practi-
cally constant, namely, 28°*8 to 29o,0 F., or - l°-7 to - 1°*8 C.
The layer of lighter water from 50 to 80 fathoms thick at the
surface is due principally to this melting of land-ice, though it is
also due in small proportion to the melting of sea-ice.

Table giving the Temperature at which Ice melts in Sea-Water
containing different percentages of Chlorine.

Temp. C.,

. i°-o

1°T

l°-2

l°-3

l°-4

Per cent. Cl,

. 1-040

1-131

1-222

1-313

1-404

Temp. C,,

. l°-5

l°-6

l°-7

l°-8

l°-9

Per cent. Cl,

. 1-495

1-586

1-678

1-769

1-880

1887.] Mr J. Y. Buchanan on Distribution of Temperature. 149

The density (at 15°*56 C.) of the sea-water which comes in contact
with the lower surfaces of the icebergs is 1 *0255, which represents
a chlorine percentage of 1*90. Ice actually melting in this water
would produce a temperature of - 10,92 C. When ice is immersed
in this water it lowers its temperature, and a portion of the ice is
melted, producing dilution. The concentration, therefore, or chlorine
percentage, which will determine the melting temperature of the
ice, will be a little lower than that of the original sea- water. From the
“ Challenger ” observations we see that, on the confines of the pack
ice, the cold stratum of water has a uniform temperature of 29° F.

( — 1°*67 C.). Ice melts at this temperature in sea-water containing
1 *65 per cent, of chlorine. In this process ice is melted, so that
100 grammes pure warm sea- water become 119 grammes of diluted
cold sea-water. It will he observed that the ice which has been
formed in the atmosphere at a temperature of 32° F. comes in this
way to he melted at a temperature of 29° F. ; and the pressure
exerted by the 300 fathoms of sea-water, though it may assist in
the lowering of the melting temperature, is insufficient to account
for the amount.

Monday , Min April 1887.

Dr J. MUBBAY, Yice-President, in the Chair.
The following Communications were read : —

1. Note on a Formula for Aw0 ljnl when n, i are very large
Numbers. By Professor A. Cayley.

The following formula

q = e~(i+1)ln

is given by Laplace ( Theorie Analytique des Probcibilites, 2 ed.
Paris, 1814, p. 195) as an approximate value of An0i/n\ when n and
i are very large numbers, and is applied immediately afterwards to
the case where i is of the order n log n. As remarked by Professor

150 Proceedings of Royal Society of Edinburgh. [apeil 4,

Tait, it is certainly not applicable to fclie case wliere i is of the order
n, for taking i — A n, A a given number however large, then q is in-
definitely near to the very small value e~A, but nevertheless the last
term - \(n + i+ 2)q2, by taking n sufficiently large may be made as
large as we please, and the value would thus come out negative. It
is thus necessary that i should be at least of the order n log n ; but
it may be of any higher order..

Writing for greater convenience r = ne~i,n (where r is not very
large) then nq = re~1,n — r( 1 -X) if X = l-e~1/w, and the formula
becomes

A«o<

n

e-r(l-X) j~ J

i+1 —%n yar n -f i + 2

»-2/«

:n

n

n

1 11 11

Here X = if + \ 2~3 if an(^ exPonenlial

= l+rX+

n
r2X2

1.2

.. . is thus also expansible in negative powers

of n} and the formula becomes

A?QS" / r2X2

e~r 1 +rX +

nl

1.2

'l . e-Vn_

r 7i + i+2__2lnr2

n

n-

viz„, putting for X its value.

= e (l

, % 4- 1 — 2 7i .

+ r . ( — — e~lfn + 1 - e~lln

+ r

2n2

- n - % — 2

,-2/w

2 n2

i + 1 - 2%
2?^2

1 _ e-Vn^e-Vn+ _ g-1 fn'J'j

+ &C.}

or finally expanding the and taking the whole result as far as
1

— : coefficient of r is
nl

V 7i 2 n“ )\ n ) n 2n2 ’ n2 7

coefficient of r2 is

i+Ji\i+J_ I , -i-h.

n 2 n2 ) n 2 v? ’ ~ n 7i 2

1887.] Professor A. Cayley on a Formula for Aw0 i/n\ 151

whence the formula becomes

1 - 1 - i'

A”0*’ r f , 1 + At r

-~r J 1 + r — /- 1

n2

= e

x

n c

1.2

n

+ . .

It seems to me that the correct result up to this order of approxi-
mation is

Aw0*

n~

= e

1 + r

w-

1.2

1

+

n nc

My investigation is as follows : we have

A"0*’

= 1 -

n

n

1-

1

n

+

n. 7i — 1

T72~

1 -

n

+ . . .

the series being a finite one, but the number of terms is very large.
But observe that, however large n is, we can take i so large that the

second term n(\ — — ^ may be as small as we please ; taking this term

to be of moderate amount, say = r1, the subsequent terms will be not

ry* 2 ry* 3

very different from -A— , — i — , . . . and the approximate value

1 . 2 1.2.3

is 1 - - &c., which is a convergent series having its sum

= e~r\ To work this properly out, I represent the successive terms by

v r,2 ? 3 go that the series is

19 1.2’ 1.2.3’ “ *

= 1 - r-L +

To

~x + • •

1.2 1.2.3

Taking r a value at pleasure not very different from r1} and multi-
plying by

(l = )e~r. er = e-r.(l+r + ^

the sum is

= e"r. | 1 + (r - jq) + -t- r2)

+ T^r^^’3 “ 3?‘2ri + 3?t2 ~ rs) + • • •

1.2.3

Assume nowr = ne~'ln, we have

^1_J_^ =neX°s^ «) = r(l+X1); X1 = e 2 »s 3 «s

i\ = n

152 Proceedings of Royal Society of Edinburgh. [april 4,

and similarly

r2 = n.n-l . (l - = ti2^1 - . e log(1-^

(1 \ 1 4£ 1 8?

1 _ JL V2(l + X2) ; X2 - e 2 »* 3 »»-

•3 = n. n - 1 . ^1 - = 7i2(l - . etlog(1-^)

_ -L ?i _ L 7li
X3 = e 2 m2- • 3

— M •

It is now easy to calculate the successive terms r- r2 - 2 rrx + r2 ,

&c., and it is to be observed that, in the parts independent of the
X’s, we have only terms divided by n} n2, or higher powers of n :
thus in r4 - 4 r2rx + 6r2r2 — 4r3r3 + r4 we have r4 into

1-

44X-4

We thus obtain the formula

1 _ _3\ _ _3_ _ 6

n

n2 n 3

n' v

1

+

+

+

r

r2 / 1

172 \ n

ty"

1.2.3

n

<r>

ri1

-1X0

-2Xx+ (l--

1 \ n

X

- 3Xj + 3( 1 - — ]X2 - ( 1 -

n

1-- X

n

oti( - i i - 4X* + K1 - ih - 4(x - 7X1

— )x3

n ) 6

+ 1-

71

1 -

71

l-l

n

IX

where r = ne~iln as above, and X1? X2, • • • have the above-men-
tioned values, the exponentials being expanded in negative powers
of 71.

1887.] Professor A. Cayley on a Formula for ijni. 153

-h

Writing Xx = — f- , X

-2 i

we have

nc

AwO'

hi r1

o- = c-M l+r^o + TT -- +

?)!■

which is the foregoing approximate value.

2. On the Fossil Flora of the Eadstock Series of the Somer-
set and Bristol Coal Fields. (Upper Coal Measures.)
Part I. By E. Kidston, Esq., F.Gr.S.

3. On the Achromatism of the Four-Lens Eye-Piece: New
Arrangement of the Lenses. By Edward Sang, LL.D.

In designing a telescope for a particular class of observations, it
was found desirable to have a field-bar in the focus of the object-
glass, and, at the same time, to have an image of that object-glass
exterior to the eye-lens. These desiderata cannot both be got by
the achromatic arrangement of two lenses made of one material ; they
are combined in the ordinary four-lens eye-piece.

While investigating the action of the four lenses with a view to
a third condition, found, however, to be unattainable, I was led to
notice a porism altogether new to me, and which guides us to a
new arrangement of the lenses. Believing that this porism has
hitherto escaped notice, I venture to submit it to the Society.

Let B, C, D, E represent four thin lenses, all of one material,
arranged along the axis of a telescope, whose object-glass A is at a
distance beyond the limits of the page, and let us denote their
focal lengths by /13 f2, /3, /4 ,

f/ f2

B

C

D

E

bl

b2

b2>

while their distances are 61} U, &3; then the condition of achromatism
is contained in the equation

- 4 \\\

(A).

With this one condition of achromatism among the seven quantities,
we are at liberty to conjoin other conditions, subject of course to
their possibility. The most obvious collateral condition is that the
combination DE be achromatic in itself, so that it may be used
separately as an inverting eye-piece, This achromatism is expressed
by the equation

achromatic at the same time with the pair D, E, because this would
imply the condition fi+f2~ 2&x = 0, and would necessitate an
infinite value for b2. The equation (C) may be written in the form

in which the second member is altogether independent of f3 and /4.

Now, in arranging a Huygenian eye-piece, we may assume any
ratio between /3 and /4. If we wish to use a field-bar, as in sur-
veying instruments, we make /4 the greater, otherwise we prefer to
make /4 the lesser, because then, the image of the object-glass is out-
side of and close to the lens E, and so a large field of view is had.
In this case it is important that the Eheita’s lens D be well out of
the focus of E, in order that any minute imperfections or dust-
particles on its surface may be out of view. One maker may prefer
the ratio two to one; another maker may adopt that of three to one.

If then we have fixed upon some ratio n , and resolved to make in
all our Huygenian eye-pieces

fs=nf4

P),

1887.] Dr Edward Sang on Four-Lens Eye-Piece 155

the above equation takes the new form

(3rc- 1)&i-2w(/1+/2)_£i

and/3 becomes indeterminate when both the conditions

and

(3 n - 1)6, - 2»(/1 +/2) = 0 ,
Va + Wi+Za- Ji) = 0

are satisfied at the same time.
If, therefore, we make

hl 3 n - 1

and

• • (F)

we may use, along with these, any eye-piece C, D, provided that it
have

An eye-piece constructed in this way has the several advantages
belonging to all four-lens ones. It shows the objects in their natural
position ; it allows of a field-bar across which cobwebs and micro-
metric scales may be placed ; a stop between the lenses B and C,
having its aperture equal to the linage of the object-glass, cuts oft’
all extraneous light ; we may introduce there a sun-screen, which
shall not be heated so intensely as that usually placed outside of the
eye-lens E. But this particular arrangement superadds another.
Our inverting Huygenian eye-pieces having been all constructed to the
same ratio n , we screw on the portion B, C, D, or uprighter as it
may be called, and are then at liberty to use any one of our
battery, the magnifying powers being at the same time considerably
augmented.

4. An Effective Arrangement for Observing the Passage of
the Sun’s Image across the Wires of a Telescope. By
Edward Sang, LL.D.

At night the cobwebs of the telescope are invisible for want of
light ; we have to illuminate either the field or the wires, so as to
make them visible bv contrast. At noon the astronomer meets

156 Proceedings of Royal Society of Edinburgh. [april 4,

with the same kind of difficulty from an opposite cause ; the intense
sun’s light has to he obscured by a dark glass, which, at the same
time, completely obliterates the spider-lines ; these are only seen on
the sun’s face. In consequence, the advent of the sun’s edge to a
wire cannot he observed ; the line must be fairly on the sun’s face
before we can see it, and thus the noted instant is necessarily too
late, — too late by a quantity depending on the power of the telescope
and on the skill of the observer. Hence the estimate of the sun’s
apparent diameter from observations of the meridian passage may
he expected to err slightly in defect, while the thence-deduced
right ascension must be too great.

But, if a thin cloud pass before us, we use a paler screen and see
the wires over the whole field while the sun’s edge remains distinctly
defined ; the observations are then satisfactorily made. It occurred
to me that, at all times, we may make an artificial cloud, and, to-
day just four weeks ago, I laid a thin muslin over the object-glass
of my alt-azimuth, and got all that is needed.

5. Observations on the Structural Characters of certain new
or little-known Earthworms. By Frank E. Beddard,
M.A., Prosector to the Zoological Society of London, and
Lecturer on Biology at Guy’s Hospital. (Plate Y.)

The present paper contains a description of five apparently new
species of Lumbricidse from Australia and New Zealand, one of
these species being perhaps the type of a new genus, which I have
named Neodrilus ; the remaining species are Acanthodrilus neglectus,
from New Zealand, Perichoeta newcombei , Urochceta, sp. ?, from
Australia, and P. upoluensis, from one of the Pacific islands. I have
endeavoured to make these descriptions as full as the material,
in many cases in an excellent state of preservation, has enabled me
to do. I have also incorporated into this paper some few notes
on Pericliceta antarctica} Baird, a species which has not yet been
sufficiently discriminated.

Acanthodrilus neglectus , n. sp.

In my paper on New Zealand Lumbricidse, recently published in
the “ Proceedings of the Zoological Society ” (P. Z. S., 1885, pt. iv.),

Proc.Roj: Soc. Edinr, Vol.XlV, Plate V.

1'' ' -

McFarla<ne £c Erskine, Litkr^ EdinT

XI 11

c" ,:3i

jT" ■ 5 \

•

a. ::M

/T"^ — * , 7 /

(7 \5Vt

- , - 1®! /

/ u & r
/0q/L‘

1887.] Mr Frank E. Beddard on Earthworms. 157

I described two species of Acantliodrilus — A. novce-zelandice and
A. dissimilis — very closely allied in structure, and agreeing in a
number of points to differ from the third species, A. multiporus. A.
dissimilis is distinguished from A. novce-zelandice mainly by the
character of the sperm athecae ; these organs are present in both
species to the number of two pairs. In A. novce-zelandioe each
spermatheca, which is somewhat pear-shaped, is provided with a
number of small diverticula arranged round its external orifice ; in
A. dissimilis , the spermatheca has but a single pair of diverticula,
which are of very considerable size. The former species is also fre-
quently provided with a double dorsal blood-vessel ; this character
is, however, not absolutely distinctive of A. novce-zelandice ; some
individuals agree with A. dissimilis in possessing a single dorsal
vessel. I may state that the condition of the dorsal vessel is no
criterion of the age of the individual. In the largest specimens of
A. novce-zelandice dissected by me the dorsal vessel was double,
while those specimens in which it was represented by a single tube
happened to be very small.

On again looking through the collection of New Zealand earth-
worms which Prof. T. J. Parker kindly sent me, I find that I
have confounded two apparently distinct species under the name
of Acantliodrilus dissimilis.

As there are a large number of individuals of A. dissimilis which
fall into two series, I think that I am justified in making a specific,
or at least a subspecific distinction, although the point wherein the
two series of individuals differ is after all rather a small one ; but
it seems to me that a differential character, if it be constant for
a large number of specimens, is of importance, however small.

The accompanying drawings illustrate the difference to which I
refer.

In fig. 1, which represents the anterior segments of the body seen
ventrally, there are a pair of genital papillae situated on segment 10.
For this variety I shall retain the name A. dissimilis . In fig. 2
the genital papillae occupy a different position ; they are situated on
the 8th segment. For this variety I propose the name of A. neglectus.

Neodrilus monocystis, nov. gen. et sp.

On looking over a collection of earthworms which I have received

158 Proceedings of Royal Society of Edinburgh. [april 4,

from New Zealand by the kindness of Prof. T. J. Parker, I found
a single individual which differs from the rest in a number of
characters. The remaining specimens belong to three distinct new
species which I have lately described,* referring them to the genus
Acanthodrilus . The specimen which forms the subject of the

present communication appeared at first sight to belong to the
species Acanthodrilus dissimilis , F. E. B. , though considerably more
slender than any of the individuals of that species which the
collection contained.

The setse are disposed in four series of pairs, and the nephridial
pores alternate in position precisely as in Acanthodrilus dissimilis.
The elitellum occupies a similar position, and extends over an equal
number of segments, viz., 5 (13-17),, Instead of there being two
pairs of spermathecal apertures, there is only a single one situated
between the 7fch and 8th segments, on a line with the inferior pair
of setse. The male generative pore is placed upon the 17th segment,
and each pore is continuous with a groove upon the integument,
which extends over the following segment, and ends upon the
middle of the 19th segment. I could not, however, detect a second
pair of male generative pores upon this segment. In Acanthodrilus
dissimilis — at least in many individuals — there is a similar groove
connecting the genital pores of the 17th with those of the 19 th
segment entirely similar to that of Neodrilus. It is possible that
this supposed new genus Neodrilus is really an Acanthodrilus , in
which the posterior pair of male generative pores, together with
their glands, have not yet been developed. I am not aware, how-
ever, of any similar instance in the genus Acanthodrilus , and the
present species is fully mature. In favour of this supposition, how-
ever, is the condition of certain other peculiar accessory generative
structures which I have lately described t in a species of Acantho-
drilus from New Caledonia ; these are sometimes present and some-
times absent in mature individuals. Another possibility is that the
present individual is abnormal, and it is principally for these reasons
that I have hesitated in making a new genus ; though there can be
no doubt of the specific distinctness of the worm.

The male generative pore is continuous with a long, coiled,
tubular prostatic gland, the proximal region of which is a slender

* Proc. Zool. Soc., 1885, pt. iv. t Proc. Zool. Soc., 1886.

1887.]

Mr Frank E. Beddard on Earthworms.

159

muscular (fig. 3 m) tube, while the distal region is thick and glandular
(fig. 3 gl) ; with the aperture is also connected a thin-walled sac con-
taining a bundle of long penial setae.

Spermathecoe. — In the 8th segment are a pair of oval spcrma-
tliecee, which open on to the exterior in the groove which separates
this segment from the one in front. As is so generally the case,
they are provided with a diverticulum. The diverticulum of each
spermatheca lies in the segment in front of that which contains the
spermatheca itself, and is remarkable in being actually larger than
the spermatheca. In most, if not in all, the genera of earthworms
which are included in Perrier’s two groups, Intraclitellians and Post-
clitellians, the spermathecae open close to the anterior boundary of
the segment which contains them. In certain species of Lumbricus
and other Anteclitellian genera, the position is sometimes different,
the spermatliecal apertures being situated near to the posterior
boundary of their segment. In one instance, at any rate, the
spermathecae actually perforate the mesentery bounding the segment
which contains them on their way to the exterior. In a species of
earthworm lately described by myself in a note communicated to
the Eoyal Society of Edinburgh,* this is the case with one or more
of the seven pairs of spermathecae which are present in that species.
It might be imagined, therefore, that in Neodrilm the anterior
larger portion of the spermatheca really corresponds to the sper-
matheca, while the posterior smaller portion is the homologue
of the diverticulum so constantly found in Perichceta, Acanthodrilus ,
and in other genera. Without an examination of the minute
structure of the two regions of the spermatheca, it would be
difficult to say which was spermatheca and which diverticulum.
In three species of Acanthodrilus I have described, I believe for
the first time, a very marked difference in minute structure between
the spermatheca and the diverticulum, which is correlated with the
fact that the spermatozoa always appear to be stored up in the
diverticula. In the present species I find an identical difference
in the structure of the spermatheca and its appendage, which leads
to the inference that the anterior sac is the diverticulum. Seeing
that in many cases, especially in Perichceta , the diverticula of the
spermathecae extend into the segment anterior to that which con-
* Proc. Pioy. Soc. Edin., 1885-6, p. 451.

160 Proceedings of Royal Society of Edinburgh. [april 4,

tains the spermatheca itself, the disposition of these structures in
Neodrilus is perfectly normal.

The Nephridia have exactly the same structure as in Acanthodrilus
dissimilis, and, as already mentioned, alternate in position from
segment to segment in the same fashion. This fact cannot, how-
ever, he regarded as a proof that the two worms belong to the same
genus. I shall have occasion to point out in a future paper that an
Australian earthworm, Cryptodrilusfletcheri, n. sp., possesses nephridia
which are in every respect similar to those of Acanthodrilus and
Neodrilus in structure and in position, and other instances are there
mentioned.

Urochceta, sp.

The present description is the outcome of an investigation into
the structure of an Australian species of the genus Urochceta. The
specimens were kindly given to me by Mr S. Prout Newcombe, and
come from Queensland. I have been able to examine a large
number, all of which were in a very fair state of preservation for
microscopical examination.

The genus is at present known to inhabit Brazil, the West
Indies, Java, Sumatra, and Australia, and comprises only three
species at most. The first of these was originally described by Fritz
Miiller,* who met with it in Brazil, under the name of Lumbricus
corethrurus. The specific name “ brush-tail ” was given to the worm
on account of the irregular disposition of the setae at the posterior
end of the body ; the segments are in this region of the body very
close together, and the setae being usually (at least in the contracted
state of the body) much protracted and directed backwards, the
aptness of the name will be very evident to any one acquainted
with these worms. Fritz Muller did not thoroughly investigate the
structure of the worm, and was therefore unable to see any reason
for removing it from the genus Lumbricus.

A somewhat fuller account of the same species was given by
Perrier in his “ Recherches pour servir k l’histoire des lombriciens
serrestres.” f Perrier rightly created a new genus for the reception

* Arch. f. Naturg xxiii. ; Ann. and Mag. Nat. Hist., ser. 2, vol. xx. ;
Abh. d. naturf. Gesellsch. in Halle, v., vi., 1857 ; in Landplanarien, von
Max Schultze.

t Nouv. Arch. d. Museum, t. viii. (1872).

Mr Frank E. Beddard on Earthworms.

161

1 887.]

of this species, which he termed Urochceta, but he altered the
specific name of Muller into “ hystrix .” Two years later M. Perrier
published * a much more detailed and beautifully illustrated memoir
upon the same species, which he referred to more correctly under
the name of Urockceta corethrura. The specimens investigated by
Perrier were obtained, not only from Brazil, but also from the West
Indies (Martinique), and, which is more remarkable, from the
island of Java. Perrier is inclined to think that the occurrence
of the same species in the New World and in Java is rather to
be explained by its accidental importation into the latter country,
than to be regarded as of importance as a fact in geographical
disposition. The occurrence, however, of a very closely allied
species in the neighbouring island of Sumatra is somewhat against
the supposition, and I am not at all certain that the species to be
described in the present paper — a native of Australia — is really
different from Urochceta dubia.

A second species of the genus has been quite lately described by
Dr Horst, f under the name of Urochceta dubia , from Sumatra.
Dr Horst’s description is necessarily — owing to the poor condition
of his material — brief, and only refers to the more important
points.

The differences between Urochceta dubia and U. corethrurus are
chiefly in the position of the spermathecae (situated in segments
6, 7, 8, instead of 8, 9, 10) and in the fact that there are four
pairs of modified clitellar setae, a pair upon each of the segments
18, 19, 20, 21, instead of the single pair (on segment 20) of
U. corethrurus. It appears also that in Horst’s species all the
segments anterior to the clitellum are furnished with setae, while in
U. corethrura the first three segments are devoid of these structures;
furthermore, the irregularity in the arrangement of the setae begins
to be evident in segment 10 in U. dubia , and not until segment 14
in U. corethrurus.

The clitellum is very readily to be made out with specimens
of the Australian Urochceta , and occupies about eight segments,
commencing with the 14th and ending with the 22nd. Very
often the first and last of these segments were only partially

* Arch, de Zool. Exp., t. iii. (1874).
t Midden Sumatra, Vermes door Dr R. Horst, p. 7.

VOL. xiv. 30/9/87

L

162 Proceedings of Boy al Society of Edinburgh, [april 4>

invaded by glandular substance. In fully mature individuals the
clitellum was perfectly developed on the ventral as well as on the
dorsal side of the segments pertaining to it. A remarkable fact
about the clitellum of this species is that the glandular substance
is entirely undeveloped between the segments, so that this region
of the body is just as plainly segmented as any other region;
indeed, the contrast between the thick glandular appearance of
the segments themselves, and the deep furrows which separate
them, renders the segmentation if anything rather more conspicuous
than elsewhere.

It is to be noted that the number of segments occupied by the
clitellum and their position is the same as in the other two species
of Urochceta.

The disposition of the setce is remarkable ; in the anterior
segments of the body, comprising the first eight segments, the setae
are arranged, as in Lumbricus , in four series of pairs ; the two setae
of each pair are closely approximated to each other, and the
intervals between the pairs are not widely different.

In the 9th segment there is already some little difference in
the setae ; the two setae of each of the ventral pairs are at a little
greater distance from each other than in the preceding segments ;
the dorsal pair of setae of the right side is completely similar to
the same pair of setae in the foregoing segments ; on the left side,
however, the two setae have become widely separate, the distance
between them being much greater than that which separates the
individual setae of the ventral pairs.

In the next segment the two setae of each of the ventral pairs are
somewhat more widely separated from each other, but the two setae
of each of the dorsal pairs are again quite close together, as in the
earlier segments.

In the next few segments the two ventral pairs of setae remain
exactly as in the segments just described; the innermost setae of
the dorsal pairs correspond exactly in position to the innermost of
the same pair of setae in the earlier segments. The outermost setae,
however, vary very much in position, being sometimes nearer to,
and sometimes further away from the innermost setae ; moreover,
the two halves of the body are not symmetrical in this respect.

Throughout the greater part of the body, commencing shortly

1887.]

Mr Frank E. Beddard on Earthworms.

163

after the clitellar segments, if not earlier, the setse have a partly
regular, partly irregular arrangement. The ventral setse of eacli
pair have a fixed position, and correspond for a large number of
consecutive segments ; the dorsal setse of each pair are, on the
contrary, quite irregular in their disposition. There appears to be
no regular alternation in their arrangement ; it sometimes happens
that the seta of two consecutive segments will correspond in
position, sometimes the setse of one segment, and the next but
one or next but two, &c., that it is impossible to lay down any
general statements. The two halves of the body are not symmetrical
in respect of their setse. In the hinder part of the body there is
a perfectly regular alternation of the setse from segment to segment;
each seta of one segment is exactly between two setse of the
preceding and consecutive segments ; and this statement applies to
all the setse in that region of the body, hence there are exactly
sixteen rows in this region of the body, while there are a great
many more anteriorly.

In U. corethrurus the setse of the anterior segments are disposed
regularly and in pairs ; but the two setse of each pair do not appear
from Perrier’s description to be so closely applied as in my species.
They agree in the fact that in the posterior part of the body the
setse regularly alternate, each seta being placed between two setse of
the preceding and succeeding segments. Perrier, however, says
nothing about the disposition of the setse in the middle portion of
the body. I must assume, therefore, for the present that the
remarkable arrangement of the setse of my Urocliceta in this, by far
the greater portion of the body, is peculiar to that species, and dis-
tinguishes it from Urocliceta corethrurus. Dr Horst’s description
of Urocliceta d-ubia seems to show that this species differs but little
in this particular respect from U. corethrurus.

With regard to the shape of the setse, I have to record an
important difference from U. corethrurus. Perrier describes and
figures the setse in the latter species as being bifid at their free
extremity, and dwells upon the similarity in this respect to the
Naidea. Horst says nothing about the structure of the setse in
U. dubia. In my species I did not succeed in observing any
bifurcation of the distal extremity of the setse ; these structures are,
in fact, precisely similar to those of other earthworms. This differ-

164 Proceedings of Royal Society of Edinburgh, [april 4,

ence might be regarded as of generic value, were it not for the
correspondence in all other essentials of structure.

Another point of difference from U. corethrurus concerns the
genital setse ; not, however, in their general shape, for I find no
difference in this respect between the genital setae of my TJrochceta
and those figured by Perrier. But while in U. corethrurus the
genital setae are confined to segment 20, where they replace the
ventralmost setae on either side, my species has four pairs of these
peculiarly modified setae ; they have precisely the distribution
mentioned by Horst in U. duhia, being found upon segments 1 8-2 1 ,
and occupying the position of the ventralmost setae.

Inter segmental Septa. — As in so many other species and genera
of earthworms, the present species exhibits a thickening of certain
of the anterior mesenteries. There are four of these specially
thickened mesenteries, the first of which immediately follows the
gizzard; the last forms the posterior boundary of segment 10.
It is in the segments bounded by these thick mesenteries that the
spermatbecae lie.

The hindermost of these thickened mesenteries, as already stated,
marks off the 10th from the succeeding segment ; the arrangement
of the mesenteries in front of this does not correspond exactly with
the external segmentation. The posterior spermatheca lies in a
segment which is bounded anteriorly by the last but one of the
thickened mesenteries, and posteriorly by the last of these ; exter-
nally, however, this segment is distinctly separated by a cross furrow
into two segments; and, moreover, the difference between the
external and internal segmentation is not only marked by a cross
furrow, but also by what is more important, namely, a distinctly
double row of setae.

In the median ventral region of the body there are traces left
of the mesentery which should divide the 9th from the 10th
segment on either side of the nerve cord; and symmetrically dis-
posed in relation to the nerve cord and to each other is a muscular
band, which is attached above to the posterior stout mesentery, and
below to the furrow which marks the division between the 9 th
and 10th segments. The stout mesenteries are everywhere at their
insertion on to the body wall divided into separate muscular bands,
two of them only being left between segments 8 and 9.

1887.] Mr Frank E. Beddard on Earthworms. 165

A comparison of the above description with that of Perrier (loc.
cit. , p. 390) will show that there is some little difference in these
points from U. corethrurus. Perrier, in fact, states that in his
species the specially thickened mesenteries are inserted on to the
posterior margin of segments 5, 7, 8, 9, and 1 1 ; two segments, viz.,
6 and 10, appear therefore to have lost the posterior mesentery,
instead of only one segment, as in my species.

There is some difficulty in making an exact comparison between
the two species, because Perrier’s figure (pi. xv. fig. 28) does not
agree with his description. In the figure referred to there are but
four thickened mesenteries, which seem to correspond exactly in
their arrangement to the mesenteries of the Australian species.
There seems, however, to be a slight difference in position ; the
last thick mesentery in my species forms the posterior margin of
segment 10, if the commencement of the clitellum has been rightly
referred by me to the 12th segment. It is, however, not an easy
matter to differentiate the two or three anterior segments of the
body ; and, as Perrier had living specimens at his disposal, it is
probable that his enumeration of the segments is more correct than
mine. In this case the clitellum in my species begins a segment
later than in his.

Integument. — Perrier’s memoir contains a detailed account of the
structure of the integument (pp. 382-400), illustrated by numerous
figures. I cannot, however, altogether reconcile his description and
figures, in so far as they refer to the structure of the epidermis,
with the appearances presented by my own sections.

In fig. 1 Perrier gives a general view of the epidermis or surface
view, in which it is seen to be marked out into polygonal areas,
separated by a certain amount of interstitial matter ; some of these
contain granular bodies (lettered a in his figure), while others are
without them. Between the setae are certain very peculiar struc-
tures ( g ), which appear in section to be contained in sac-like diver-
ticula (fig. 3) of the chitinous cuticle. The bodies themselves are
highly refractive ; these evidently correspond to similar structures
described by Yejdovsky in Anachceta *

In transverse sections through the integument of my specimens of

* Monograph, d. Enchytr widen, p. 21 ; see also a paper by myself in Proc.
P<,oy. Soc. Lond., 1885, p. 464.

166 Proceedings of Boyal Society of Edinburgh, [april 4,

ZJrochceta, I have met with, these peculiar structures in abund-
ance. They stain very deeply in borax carmine, hut have the
appearance of being formed of some resistant substance, being fre-
quently indented; they lie at the base of the epidermic cells, just in
the position in which Perrier has figured them ( loc . cit ., pi. xii.
fig. 2 g). There is, however, this difference, that whereas in U.
corethrurus they almost invariably form a regular line between the
several setae of a segment, being but rarely disposed irregularly,
in my species the contrary is the case; they are very frequently
irregular in size as well as position, though they form always a
continuous row between the setae, and are not, as far as my ex-
perience goes, found elsewhere. Perrier is quite right in stating
that the polygonal areas in his figure correspond to cells, but has
overlooked the fact (which was not known at the time when he
wrote) that the u interstitial ” substance is also cellular, and consists
of elongated narrow cells, the polygonal spaces being occupied by
large glandular cells with granular contents which do not stain,
[n fig. 2, pi. xii. of Perrier’s memoir, a transverse section through
the epidermis is figured, which does not at all represent the appear-
ances presented by my sections. In Perrier’s figure are represented
a series of columnar granular cells, among which are a few peculiar
rod-like bodies; these latter I am unable to identify in my prepara-
tions, unless, indeed, they correspond to the columnar hypodermic
cells. The columnar granular cells appear to be a very inaccurate
representation of the large glandular cells, which appear to be
much more numerous in Urochceta than in Lumbricus. Judging
by other earthworms, it does not appear to be at all likely that M.
Perrier’s fig. 2 illustrates a real difference in the structure of the
epidermis from my species.

I have frequently noticed, on a superficial view of the epidermic,
irregularly shaped refractive bodies, like those figured by Perrier
and lettered a in his figure (pi. xii. fig. 1), within the glandular
cells.

Excretory Organs. — My species of TJrochceta possesses, like U.
corethrurus , a pair of large glands in the anterior segments
of the body, which have been termed by Perrier “glandes k
mucosite.” These glands open on to the exterior of the body
through a long duct with muscular walls. With regard to

1887.] Mr Frank E. Beddard on Earthworms. 167

the external orifice, Perrier remarks {hoc. cit., p. 460) : — “ En
faisant des coupes dans la region anterieure du corps, nous avous
constamment rencontre dans l’epaisseur meme des teguments un
canal circulaire entoure d’une sorte de sphincter et presentant des
cils vibratiles tres-reconaissables meme sur des individus desseches.
Nous avions d’abord pense que nous avions sous les yeux la coupe
de la portion du canal excreteur des glandes a mucosite qui est logee
dans les teguments ; mais nous n’avons pu nous convaincre de l’in-
exactitude [exactitude?] de cette appreciation. Dans nos coupes ce
canal s’est toujours montre unique, et les glandes a mucosite ont
des orificies excreteurs distincts ; de plus, le canal en question nous a
paru occuper la partie la plus anterieure du corps ; et ces faits sont
contraires a la supposition qui nous etait d’abord venue k l’esprit.”
If M. Perrier means to state in the above-quoted words that the
excretory duct of tlie “ glande a mucosite ” is furnished at its
termination with a “sphincter” like that which surrounds the
aperture of the nephridia, I am in a position to confirm the correct-
ness of his statement. By a series of transverse sections, I have
been able to trace on both sides of the body the duct of this gland
to its external opening, and I find that the latter is surrounded by
one of these peculiar bodies which Perrier was the first to record
in the case of the nephridia. On the other hand, the duct never
traversed the body walls except, of course, at the point where it
perforates it on its way to the exterior, and the two ducts were both
perfectly distinct. M. Perrier does not mention whether the single
duct which he found in the transverse section was situated laterally
or in the median line. I cannot detect any trace of cilia in these
canals, which, indeed seem to be hardly needed, as they are physio-
logically replaced by the muscular walls. The presence of the
“ sphincter ” is evidently an important additional resemblance
between the glandes a mucosite and the nephridia.

With regard to the nephridia , I am unable to find in my
species what Perrier states to be the relations of the internal
funnel in U. corethrurus. He says ( loc . cit., p. 438) — “ Les pavilions
vibratiles . . . (sont) tres-rapproches de la ligne mediane et appliques
contre la cloison. II y a la quelque chose de different de ce qu’on
observe chez les naidiens, ou les pavilions vibratiles traversent en
general la cloison anterieure de chaque anneau, fait que l’on retrouve

168 Proceedings of Royal Society of Edinburgh, [april 4,

aussi chez les Pontodrilus. Les Lombrics au contraire semblent
d’apr&s les auteurs, se comporter comme les Urochceta.”

M. Perrier figures ( loc . cit., pi. xvi. figs. 38, 39) the isolated
nepbridia, which obviously could not be detached entire if the funnel
were not situated in the same segment as that which bears the
external pore. Nevertheless, in my species I observed in numerous
cases that the internal funnel of the nephridium is situated in the
segment anterior to that which bears the external pore. I was able
to prove this point conclusively by a series of longitudinal sections.
It may be that Perrier’s specimens and mine differ in this respect,
which is certainly rather remarkable. Perrier’s assertion about
Lumbricus is evidently a slip. The funnel (figs. 6, 7, 8) of the
nephridium recalls that of Dendrobcena rubida (Yejdovsky, System
u. Morph, d. Oligochceten , pi. xiv. figs. 15, 16) in the extraordinary
development of cells, doubtfully regarded by Yejdovsky as peritoneal
cells, at the apex of the funnel.

A series of remarkable structures, termed by Perrier “ glandes
posterieures,” and described by him as a portion of the excretory
system, now remains for consideration.

These bodies are found as in V. corethrurus in the hinder region
of the body, but appear to be more numerous than in that species,
which has about forty pairs occupying as many segments.

M. Perrier gives a figure of one of theseglands (loc. cit., p. xvii. fig,
47), which only partially indicates their structure, as seen in my own
preparations. They are somewhat pear-shaped, and terminate in a
long slender peduncle, which disappears among the coils of the
nephridial tubules. Perrier supposes that they open in common
with the latter on to the exterior, but was unable to detect the
orifice. Mr Benham* has detected these peculiar glands — “ pyri-
form bodies ” — in his genus Urobenus , and his description of their
minute structure agrees pretty closely with my own observations ;
these glands open in Urobenus ventrally of the lower pair of setse,
while the nephridia open by the dorsal setse.

Pig. 4 represents one of those glands in Urochceta in longitudinal
section, reconstructed from a series of sections. It will be seen
that its structure is closely similar to that of the same glands in
Urobenus. The lumen of the gland is lined by a single row of

* Quart. Jour. Mic. Sci., 1886, p. 87, pi. viii. figs. 10, 21.

1887.]

Mr Frank E. Beddard on Earthworms.

169

peculiar cells, rounded and of large size, and each furnished with a
distinct nucleus. These cells are evidently larger in proportion, and
not so columnar as the corresponding cells in the pyriform vesicle
of Urobenus ; the rest of the gland lying to the outside of these
cells is occupied (fig. 5) by a granular substance, with minute darkly
staining bodies scattered throughout it (nuclei '?). The lumen
ceases some little way in front of the apex of the gland, which is
here entirely made up of the granular nucleated substance. It is
permeated by blood capillaries derived from the vessels which
supply the nephridia. The pear-shaped glandular region of the
pyriform vesicle has the structure just described ; distally it com-
municates with a slender muscular duct, which passes gradually
into the substance of the gland. The latter is bent upon itself,
as indicated in Perrier’s figure, so that the duct runs parallel with
the gland. But while in U. corethrurus and in Urobenus the duct
is directed towards the nerve cord, the flexure in my Urochoeta is
exactly in the opposite direction. The rounded cells lining the
lumen gradually decrease in importance, and the granular substance,
with its interspersed nuclei lying to the outside of these cells,
eventually disappears ; coinciclently with these charges the duct of
the gland acquires a delicate muscular coat, and the lining epithelium
finally becomes a flattened layer of cells. I have traced this
muscular sac to its opening on to the exterior in common with the
nephridium. Fig. 4 shows the termination of the duct in the
rosette-like organ which here as elsewhere guards the orifice of
the nephridium. The pyriform vesicle, therefore, is anatomically
a diverticulum of the nephridial duct in this species.

Spermathecoe. — These organs are present to the number of
three pairs ; they are situated in segments 7, 8, and 9, and
the aperture is in each case placed quite close to the anterior
margin of the segment. The sperm athecse of this species

are excessively delicate organs, and are often for this reason
difficult to distinguish ; they are also of very small size, as
compared with the spermatheca of many other worms. The
smallness of size is manifest rather in their breadth than in
their length ; when stretched out they reach rather further than
across the segment which contains them. These organs are some-
what club-shaped ; the distal region is extremely narrow, but widens

170 Proceedings of Royal Society of Edinburgh, [april 4,

out gradually passing backwards, and finally becomes dilated into an
oval sac. The spermathecse sometimes lie straight, and are some-
times coiled into a circle. The walls of the spermathecse are
very thin, owing to the slight development of muscles and the
character of the lining epithelium, consisting as it does of flattened
cells ; these structural features, together with the superficial covering
of rounded, vesicular, peritoneal cells, and the general shape of the
organs, gives the spermathecse a very strong resemblance to the
diverticula of the nephridia figured by myself in Acanthodrilus
novce-zelandice .* * * § In view of a possible homology between the
spermathecse and such diverticula, it is worth while to record the
points of similarity between the two series of organs. Further-
more, I may remark that in a large number of individuals, all fully
mature, there was no increased development visible in the sperma-
thecse, which undoubtedly have a certain appearance of immaturity.

The general shape of the spermathecse is very like that of the
spermathecse of Diachceta , f but they appear to be considerably
smaller in the present species, and also differ in that their aper-
tures on to the exterior are at the anterior, instead of at the
posterior, boundary of their respective segments.

In Urochceta corethrurus $ there are also three pairs of sperma-
thecc© not unlike those at present under discussion in shape, and
opening like them at the anterior margin of their segment ; they
are situated, however, rather further back (in segments 8, 9, 10) ;
further, in both Urochceta and Diacliceta the spermathecal segments
contain nephridia.

Perichceta neiucombei,§ n. sp.

This species is represented by eight individuals, of which four are
sexually mature, with a fully developed clitellum.

The colour of the species is a dark purple upon the dorsal surface,
gradually passing into a yellowish-brown upon the ventral surface ;
the intersegmental furrows dorsally, as well as ventrally, are of the

* Proc. Zool. Soc., 1885, pi. lii. fig, 5.

+ Benham, loc. cit., pi. ix. fig. 29.

+ Perrier, Arch. d. Zool. Exp., t. iii. (1874), p. 518, pi. xiii. fig. 12 pc;
pi. xvii. fig. 49.

§ Named after Mr S. Prout Newcombe.

1887.]

Mr Frank E. Beddard on Earthworms.

171

same colour as the ventral surface ; the clitellum also is distinguish-
able on the dorsal surface by its yellowish tinge.

It is interesting to note that the colour of this species is exactly
that of a species of Perionyx , from the Philippine Islands, the
characters of which I have recently described in a paper communi-
cated to the Zoological Society of London. *

The preoral lobe does not divide the circumoral segment.
Dorsal pores are present between all the posterior segments of
the body; in the four mature individuals the first pore is situated
between the 5th and 6th segments ; the clitellum is marked
anteriorly and posteriorly by a conspicuous pore.

The setce, as in other species of the genus, are disposed in a
continuous series, occupying the middle line of each segment ; they
are present on the clitellar segments.

The clitellum occupies three segments, Nos. 14, 15, 16 ; as in all
species of Pericliceta it is developed round the whole circumference
of the body.

The male and female generative pores are placed in exactly the
same situation as in other species. The female pore is placed upon
the 14th segment, within the row of setae in the middle line; the
male pores are upon the 18th segment, at some little distance from
each other, also within the row of setae.

The apertures of the spermathecoe are between 7-8 and 8-9.

A very striking external character of this worm is caused by the
great development of genital papillm.

These are developed on the preclitellar segments (fig. 10), as well
as on the segments which immediately precede, and on those
which follow the 18th segment.

The arrangement of the preclitellar papillae presents some indi-
vidual variation, which is probably due to the fact that some of the
specimens are more fully mature than others.

In one example the papillae were more numerous than in any of
the others. The 13th segment is furnished with a single papilla in
the ventral median line; the 11th and 12th segment have each
three papillae close together, one being median, and the other two
disposed symmetrically, one on either side; the 10th segment has
four papillae, of which the middle ones correspond in position to

* Proc. Zool. Soc., 1886, p. 298.

172 Proceedings of Royal Society of Edinburgh, [april 4,

the median papillae of the two succeeding segments ; the 9th
segment has a single papilla, corresponding in position to the outer-
most right-hand one of the 10th segment, the others being indistinct ;
the 7th and 8th segments have each a single median papilla. In
another example the 12th and 13th segments have a single median
papilla; the 10th and 11th segments have each three papillae; the
7th, 8th, and 9th a single median papilla.

Two other examples present an arrangement of the genital
papillae nearly identical with that last described, the only difference
being that the papillae on segments 7 and 8 are wanting.

In every case the papillae present the appearance of a circular
disc similar in colour to the clitellum, and surrounded by a whitish
line ; the greater part of the disc is placed in front of the row of
setae.

The postclitellar papillae are not so distinct as the preclitellar.
The whole of the ventral integument on the 17th, 18th, and 19th
segments lying between the male aperture is whiter in colour than
the rest, which renders it very difficult to map out the position of
the papillae. The 17th segment appeared to have a row of these
papillae; in the 18th and 19th segments I could only distinguish
two pairs of papillae, one placed outside of the male pore on the
18th, and in a corresponding position on the 19th segment, and the
other placed below, and both inside of the male pore. The 20th
segment has a median row of papillae (3 or 4), the 21st segment
has three median papillae. The postclitellar papillae are considerably
smaller than the preclitellar. I am inclined to think that the
whitish appearance of the integument between the male generative
pores is due to the crowding together of a row of papillae, which
become distinct and separate on the 20tb, and especially on the 21st
segment.

The large pharynx extends back to about segment 3 ; the gizzard
occupies segments 4, 5, and 6 ; it is important to notice that in every
case the segments in which the gizzard lies are separated from each
other by distinct, though rather delicate, mesenteries ; this fact is
worth recording, because in many species of Perichceta (and other
genera) the gizzard occupies two segments, and the median
mesentery has disappeared ; there seems to be, however, some con-
nection between this condition and the position of the gizzard.

1887.]

Mr Frank E. Beddard on Earthworms .

173

In the present species the gizzard lies anteriorly to the spermathecae ;
in those species where a mesentery has disappeared the gizzard lies
further back, and in the same segments with some or ail of the sper-
mathecae.

Calciferous glands are present in segments 10, 11, 12 ; they are,
however, rather dilatations of the lumen of the oesophagus than
distinct and separate glands.

The testes are situated in the 10th and 11th segments, close
to the nerve cord and on either side of it. Dr Bergh is perfectly
right in his statement * that the testes and vesiculae seminales of
Pericliceta are in all essentials similar to those of Lumbricus.
The testes in the present species are small digitate glands, and are
enclosed by the vesiculae, as is also the nerve cord. The vas deferens
passes along the body just below the testis ; the funnels of the
vasa deferentia open into the vesiculae seminales, which organs
extend from the 9th to the 12th segment.

The ovaries are very large, and are situated in the 13th segment.

The prostates occupy the usual position.

The spermathecae are present to the number of two pairs,
situated in segments 8 and 9 ; the large somewhat pear-shaped
pouch is provided with a small diverticulum on the dorsal side.

The only species of Pericliceta recorded from Australia are two
species, P. australis and P. coxii , described recently by Mr Fletcher. f
It is evident that my species agrees with these two in a great many
points ; in the first place, there appear to be no intestinal caeca ;
secondly, the shape and location of the spermathecae appears to be
identical in all three species. The first point of agreement is, how-
ever, of more importance than the latter. In a good number of
species of Pericliceta there are two pairs of spermathecse situated in
segments 8 and 9, and each furnished with a slender cylindrical
diverticulum ; it will be interesting to know if the absence of
intestinal caeca is characteristic of other Australian species of the
genus.

The present species, however, differs from both its Australian
congeners in the presence of vesiculae seminales in all of the segments
from 9-12 inclusive. Fletcher states that these structures are

* Zcitschr. f. wiss. Zool., 1886.
t Proc. Linn. Soc. JSf.S. W., June 1886, p. 561.

174 Proceedings of Royal Society of Edinburgh, [april 4,

absent in segments 10 and 11 in his species ; if this difference is
not really due to difference of age, it is clearly of great importance
as a distinctive character.

The arrangement of the nephridia is apparently very like what
has been described in P. australis and P. coxii , particularly in
the latter species, Fletcher’s description is as follows : — “ The seg-
mental organs consist of tufted glandular masses, which are large,
stalked, and dendriform in some of the most anterior segments, but
smaller and inconspicuous elsewhere.” I found these structures very
conspicuous indeed, and in the 14th and a few succeeding seg-
ments they have a very strong superficial resemblance to the ovaries,
with which organs their position almost exactly corresponds.

The most characteristic point of difference between my species
and the other two is the number and position of the genital papillae ;
a comparison of my description with that given by Mr Fletcher of
P. australis and P. coxii will show that the species differ greatly
in this respect. Mr Fletcher like myself appears to have examined
a considerable number of specimens.

Pericliceta upoluensis, n. sp.

This species of Pericliceta , like the last, is mainly characterised by
the number and arrangement of the genital papillae. It is a native
of the island of Upolu, in the South Pacific ; I am indebted to Mr
R. Damon, of Weymouth, for the opportunity of examining three
specimens.

It is an average-sized species, measuring 5 or 6 inches in length.

The apertures of the spermathecae are between 7-8 and 8-9.

The single aperture of the oviduct is upon segment 14.

The pores of the vasa deferentia are upon segment 18. Each
pore is surrounded by a circular area of integument which is marked
off from the rest.

The clitellum consists of only two segments, JSfos. 14 and 15.

The genital papillae are very small, compared, for example, with
those of the last species ; they occur in the neighbourhood of the
spermathecae as well as of the male generative apertures.

There is a single papillae on segment 9, situated in the median
ventral line and anteriorly to the row of setae. The rest of the
genital papillae (so far as my specimens enable me to speak positively)

1887.] Mr Frank E. Beddard on Earthworms. 175

are situated after the clitellum, i.e., in the neighbourhood of the
male generative openings. Each of the segments 16-20 (inclusive)
is furnished with a single median papilla, which occupies a precisely
similar position to that occupied by the median papilla of segment
9, that is to say, it lies near to the anterior border of the segment
(see fig. 11). The 18th segment possesses, in addition, a pair of
papillae, situated just within and close to the male generative orifices ;
these papillae are almost on the border line between this and the
following segment. The next segment (No. 19) has also an addi-
tional pair of genital papillae ; these are placed below and a little
to the outside of the generative pores ; hence they are placed very
close to the anterior border of their segment.

In its internal structure this species does not present any remark-
able features.

The gizzard is in segments 8 and 9, and as usual these segments
are not separated by a mesentery.

In the same two segments are situated the spermathecm (fig. 12),
which (see p. 173) are not very different in shape to those of the
last species.

The vesiculce seminales are in segments 11 and 12.

The ovaries are in segment 13.

The termination of the vas deferens is furnished with a prostate
gland, which has the usual lobulated structure.

The hearts are in segments 12 and 13, as is generally the case in
Perichceta.

Perichceta antarctica , Baird.

Megascolex [Perichceta) antarctica , Baird, Proc. Linn. Soc ., vol. xi.

(1873) p. 96.

This species has been described by Baird from a specimen in the
British Museum in the following terms: — “Body consisting of
about 180 rings. Setae, surrounding the body, short, black, rather
distant. Bings not keeled ; larger and more distinct at the anterior
extremity, closer at the posterior end, and all smooth. Length 7
inches.” Capt. F. W. Hutton, in his “ Catalogue of the hitherto
described Worms of New Zealand,”* mentions this species, which is
a native of New Zealand, and simply quotes Baird’s description.

* Trans. New Zealand Instit vol. xi. (1878) p. 317.

176 Proceedings of Boy al Society of Edinburgh, [april 4,

It is perfectly clear that the above-quoted specific diagnosis is
entirely insufficient to discriminate the species from many other
Perichcetce ; hut an examination of the specimen itself leads me to
believe that it is a distinct species. I am unable to give any
anatomical description, hut the worm exhibits an external character,
overlooked by Baird, which is of some value as an aid to dis-
criminating the species. The male genital pores are as usual
situated upon the 18th segment of the body, and at some distance
from each other; the 17th and 19th segments are each furnished
with a single median genital papilla placed exactly in the centre
of the segment, and therefore interrupting the line of setae. The
number and arrangement of the genital papillae seem to he, so far
as our knowledge goes, good characters for discriminating the dif-
ferent species of Perichceta ; although the number is apt to vary
somewhat (see p. 171) at different stages of maturity; the number
of papillae in the present species would have to he very largely
increased to come up to the number which are characteristic of
Perichceta newcombei (p. 171), the only other species of Perichceta
which has genital papillae in the median ventral line on the 17th
and 19th segments.

Explanation of Plate V.

Fig. 1. Acanthodrilus dissimilis.

Fig. 2. Acanthodrilus neglcdus.

Fig. 3. Neodrilus monocystis, section through prostate; m, muscular duct;
gl, glandular region.

Figs. 4-9. Urochceta, sp.

Fig. 4. Median longitudinal section through glandular appendix of nephri-
dium; d, glandular cul-de-sac; c, epithelial lining; b, muscular region;
a , “sphincter” surrounding aperture; m, mesentery.

Fig. 5. Transverse section through glandular appendix and a portion of
nephridium ; n, nephridial tubule ; c, d, regions similarly lettered in
fig. 4.

Figs. 6, 7, 8. Sections in various planes through nephridial funnel; p, peri-
toneal cells; p g, peculiar agglomeration of peritoneal cells in the
funnel.

Fig. 9. Transverse section of a nephridial tubule from hinder end of body;
c, peritoneal cells; b, blood corpuscles; n, nephridial tubule.

Fig. 10. Perichceta newcombei, ventral aspect.

Fig. 11. Perichceta upoluensis, ventral aspect.

Fig. 12. Spermatheca of last species.

'

f

/

Proc.Eoy.SoG.

Geological Map of SlAEbs UeaE, etc,

B as e oL oil ~dka£ or like Geologic al S urvey.

YoimPl.E

Scale of Miles.

4 5

1887.] Professor Geikie on Geology of St AWs Head. 177

6. Geology and Petrology of St Abb’s Head. By
Professor J. Geikie. (Plate VI.)

I. Introduction.

The observations recorded in this paper have reference chiefly to
the coast-sections at St Abb’s Head and Coldingham Shore. The
district was geologically surveyed some twenty-five years ago by
my brother, Dr A. Geikie, and subsequently described by him in
the Memoirs of the Geological Survey.* Since the publication of
that memoir, no further examination of the ground in question
appears to have been made. During the past summer I visited the
neighbourhood, principally for the purpose of studying the igneous
rocks which are so well exposed in sea-coast sections. At the date
of the Government Survey of Eastern Berwickshire the aid of the
microscope had not yet been invoked by field-geologists for the
purpose of determining rock-species, and I was therefore curious to
compare the igneous rocks of that region with those of similar age
which I had studied elsewhere in Scotland, and more especially
with the bedded and intrusive porphyrites and tuffs of the Gheviot
Hills and the Sidlaws.

The rocks of the district under review belong, as my brother has
shown, to two great systems — the Silurian and the Old Ked Sand-
stone. From Pettico Wick Harbour in the north, to Coldingham
Bay in the south, the coast cliffs are composed almost exclusively
of rocks of Old Red Sandstone age — Silurian strata appearing only
for a short interval, a little to the north of Coldingham Shore. The
latter reappear on the south side of Coldingham Bay, and continue
along the shore to Callercove Point, in the neighbourhood of Eye-
mouth. Inland from St Abb’s Head and Coldingham Shore they
extend for many miles. (See Map, Plate VI.)

II. The Silurian Rocks.

To the description of the Silurian strata given in the Geological
Survey’s Memoir, I have very little to add. They consist chiefly
of greywackes and shales, generally inclined at high angles, and
arranged in a series of more or less sharp anticlinal and synclinal
folds, which have an average N.E. and S.W. trend. In their least

* Geological Survey Memoirs : The Geology of East Berwickshire.

VOL. xiv. 7/10/87 M

178 Proceedings of Royal Society of Edinburgh, [april 4>

altered condition, they are well seen in the magnificent cliffs that
extend westward from Pettico Wick Harbour. Between Colding-
ham Bay and Callercove Point they are often much crushed,
crumpled, twisted, shattered, shifted, and confused — the irregular
puckerings and convolutions forming an interesting study. They
are minutely cracked and fissured in all directions, the fine cracks
and fissures being most frequently filled with white quartz, or with
haematite and limonite. Where the strata are most highly con-
torted, they frequently become seamed with a close, irregular net-
work of small veins and mere threads of quartz, the meshes between
which are often less than the 16th part of an inch in diameter.

Intrusive Felsite in the Silurian. — Through these excessively
contorted rocks ramify here and there tortuous dykes and veins of
felsite. The junction between those dykes and the rocks traversed
by them is generally well marked. But here and there it is much
confused — the fine-grained greywackes being baked and altered, and
having the same pale-grey colour as the felsite, so that the line of
parting between the two can hardly he distinguished by the un-
assisted eye. Under the microscope, however, the crystalline and
fragmental rocks are readily discriminated. These felsites are con-
fined to the Silurian areas. Nowhere, so far as I saw (and I tra-
versed a considerable area round Coldingham and Eyemouth), do any
of the felsitic intrusions penetrate rocks of Old Bed Sandstone age.

The rock of these dykes is grey or pale pinkish-grey in colour,
compact, sparingly porphyritic, with microscopic crystals of quartz
and felspar, — having, in short, the appearance of typical felsite.
Here and there veins of white quartz seam the dykes. Viewed
under the microscope the rock exhibits a microfelsitic base,
scattered through which are abundant small crystals of orthoclase,
and a few larger ones of the same mineral. Oligoclase also appears
in well-developed crystals, and to the same species some of the
smaller crystals of felspar seem to be referable. Both felspars show
alteration into saussurite, but this is most frequently the case with
the orthoclase. Crystals of quartz, often much corroded, but not
unfrequently showing well-defined pyramidal forms, are common ;
and they generally contain fluid cavities, sometimes in very great
abundance. One or two thin spicules of a dichroic mineral,
probably mica, were seen, but only in one section. The most

1887.] Professor Geikie on Geology of St Abb's Head. 179

remarkable feature presented by these felsites is the appearance of
minute veins which traverse the felsite irregularly, not infrequently
crossing and anastomosing with each other at all angles. They
vary in width from a mere line up to tL- or i of an inch in dia-
meter, and consist chiefly of quartz and felspar, apparently ortho-
clase. The quartz undoubtedly predominates, but here and there
felspar, or saussurite which replaces the felspar, forms the chief
ingredient. The quartz occurs in irregular crystalline aggregates
and granules, often crowded with fluid cavities, and frequently
containing enclosures of saussurite, and occasionally epidote. The
felspar also forms irregular crystalline aggregates, but is most
usually replaced by saussurite. Not infrequently it forms inter-
growths with the quartz, so as to give the veins a micropegmatitic
structure. Sometimes the walls of the veins are smooth and even ;
at other times the quartz and felspar (saussurite) seem to indent
the walls, as in the so-called “ segregation veins ” of granite. The
veins now described appear to be confined, as a rule, to the felsite,
but occasionally they pass outwards from the latter into the
adjacent greywacke.

III. The Old Red Sandstone Series.

The rocks assigned to the Old Red Sandstone are principally of
igneous or aqueo-igneous origin. There is one small patch of
conglomerate, however, which forms the upper portion of Bell Hill,
near the village of Coldingham Shore. This is indicated on the
Geological Survey’s map as of Upper Old Red Sandstone age. I
think it really belongs to the lower division of the series ; at all
events it is older than the bedded igneous rocks to be described
presently. It rests directly upon the Lower Silurian, and is in fact
composed exclusively of rounded fragments of greywacke, &c.,
derived from that formation. It nowhere overlies the igneous
rocks referred to, nor does it contain any admixture of fragments of
these. Its junction with them is, in short, a dislocation or fault,
which has a downthrow to the N.E. (see fig. 1).

The bold headland of St Abb’s is composed entirely of crystalline
and fragmental igneous rocks, some of these being bedded and
contemporaneous, and others amorphous and intrusive, while the
igneous rocks at Coldingham Shore and Coldingham Bay appear to

180 Proceedings of Royal Society of Edinburgh, [april 4,

be exclusively intrusive in character. I shall describe the rocks of
those two areas separately, although they probably all belong to the
same period of volcanic activity.

5W Bell Hill NE

Fig. 1. — Section across Bell Hill, showing relation of Basement Conglomerate
(c) to Igneous Rocks of St Abb’s Head (t, ip).

(a) Rocks of St Abb's Head.

The headland of St Abb’s Head extends from Pettico Wick south-
east to the Wrhite Heugh — a picturesque cliff and favourite resort of
sea-birds — about J of a mile north-west of Coldingham Shore. The
headland presents to the sea a bulwark of wild rugged precipices, in-
dented with numerous little bays and coves, only a few of which are
accessible from the land. It is separated from the rolling Silurian
uplands behind by a well-marked hollow that extends south-east from
Pettico Wick in the direction of the White Heugh. The headland,
as thus defined, is described by the Geological Survey as consisting
in the south-east partly of fragmental igneous rocks, and partly of
intrusive “felstone”; while between Horsecastle Pay and Pettico
Wick the area is coloured as intrusive felstone alone. Various sections
laid bare since the time the ground was examined by the Geological
Survey show that the northern part of the headland is made up
chiefly of bedded porpliyrite with some intercalated layers of tuff.
Of the latter the only good exposures seen are at Pettico Wick
Harbour and on the side of the road leading thence to the light-
house. The dip of these rocks is clearly towards the south-east,
the whole forming an ascending series, from Pettico Wick to the
Wuddy Eocks, with an approximate thickness of 1200 feet (see
fig. 2). Towards the south-east the beds are invaded by larger and
smaller masses and dykes of intrusive crystalline rock. As the dip
of the igneous series does not exceed 18° on an average, it is obvious
that the junction between these rocks and the vertical Silurian

1887.] Professor Geikie on Geology of St Abb's Head.

181

strata can only be a fault, having its downthrow to the north-east.
This is the dislocation already referred to as bringing down the

nw SE

S' Abbs Head

PctticoWic/Z Lighthouse Ki rich ill White Heugh

Fig. 2. — General Section across St Abb’s Head to Shore of Coldingham Bay
(scale 3 in. to 1 mile ; horizontal and vertical scale the same).

a, a, Probable position of Silurian strata under rocks of St Abb’s Head.
b, Conjectural position of basement conglomerate of Old Bed Sandstone
series, c, Inferred base of Volcanic series, p, p, p, Bedded porphyrites =
andesitic lavas, t , t, t, Bedded porphyrite-tuff ; at ts largely composed of
small scoriae. /3, (3, 13, Agglomerate and tuff in volcanic neck, ip, ip, ip,
Intrusive porphyrite. f, f, Fault at Halterem’s Loup, a1, Silurian strata
somewhat altered ; a2, Silurian strata much contorted and altered.

bedded igneous rocks of the Old Red Sandstone series against the
basement conglomerate of Bell Hill. It is well seen at Rutherford
Brae. Another fault, running at right angles to that just described,
forms the boundary between the Old Red and the Silurian on the
south side of Bell Hill. It is seen in section in the sea-cliffs at
Halterem’s Loup, where the Old Red Conglomerate is turned up at
a high angle against the Silurian greywackes and shales (see
fig. 3).

Fig. 3.— Section across Bell Hill, showing relation of Basement Conglomerate

to the Silurian strata.

182 Proceedings of Royal Society of Edinburgh, [april 4,

(1) The Basement Conglomerate. — The conglomerate of Bell
Hill would thus appear to be the oldest member of the Old Red
Sandstone series. It consists principally of water-worn shingle and
gravel, set in a matrix of arenaceous and argillaceous matter. The
stones, as mentioned already, have all been derived from the con-
tiguous Silurian strata. The lower appear to he upon the whole
coarser than the upper beds, stones 6 inches and more in diameter
being common in the former, while the latter are rather conglomer-
atic and pebbly grit and sandstone than conglomerate. The beds
dip towards the south-east, hut are turned up against the N.E. and
S.W. fault, while they trend steeply down towards the N.W. and
S.E. fault. The series is probably about 100 feet in thickness.

(2) The Igneous Series. — The lowest beds seen on the north
side of the N.W. and S.E. fault is a bedded porphyrite which is
overlaid by a thick layer of agglomeratic tuff. Above this comes a
succession of bedded porphyrites, about 250 feet or so in thickness,
and these beds are succeeded by 40 to 50 feet of various tuffs,
which dip in their turn under a second group of porphyrites.
These last do not appear to exceed 250 or 300 feet in thickness,
and are overlaid by some 400 feet of bedded tuffs.

Bedded Porphyrites. — These rocks having all the same character,
one general description will suffice. They are for the most part
fine-grained, purplish-blue or greyish-blue in colour, but frequently
stained brown or red with much diffused ferric and hydrous
ferric oxide. The joint-faces especially are often coated with hae-
matite and limonite, while thin veins and threads of the same
minerals are common. The rocks do not differ in general appear-
ance from the porphyrites of Old Red Sandstone and Lower
Carboniferous age which occur elsewhere in Scotland. They are,
upon the whole, not so markedly porphyritic with plagioclase as the
porphyrites of other districts, but closely resemble such fine-grained
rocks as that of Blackford Hill, and similar rocks met with in the
Braids and Pentlands. They are often highly scoriaceous and
amygdaloiclal above and below, and not infrequently contain, both
in their upper and under portions, irregular areas of fine-grained
tuff, consisting of amorphous, dust-like material, and comminuted
debris and small lapilli of highly porous porphyrite (see fig. 4).
In the upper parts of some of the old lava-flows this tuff appears

1887.] Professor Geikie on Geology of St Abb’s Head. 183

to fill up irregular clefts and vein-like cavites in tke porphyrite,
while in other places it appears involved in the porphyrite in such
a way as to suggest that it may probably consist of portions of the
shattered scoriaceous crust of the porphyrite, broken up and incor-
porated in the underlying mass while that was still in a fluid or
pasty condition. Occasionally so much of this tuff-like matter is
enclosed in the porphyrite that one is sometimes in doubt as to
whether the whole rock is not fragmental. Microscopic examina-
tion, however, clearly shows that this is not the case — the angular
and sub-angular lapilli and cinder-like fragments being completely
surrounded by or embedded in finely crystalline rock. The por-

Fig. 4. — Red Tuff (t, t, t), enclosed in Porphyrite («, a, a). Enclosures vary
from an inch or less up to a foot or more in diameter.

phvrites are all more or less weathered and earthy to some depth,
and it is thus difficult to obtain very fresh fractures. They form a
series of low broken escarpments facing the north-west, each
escarpment marking the outcrop of a bed. The beds appear to be
of variable thickness, some measuring about 15 feet, while others
mav reach as much as 50 feet or more.

Examined under the microscope, these rocks show a ground-mass
of colourless microliths and minute lath-like crystals of plagioclase,
diffused through which there is usually more or less non-differenti-
ated red ferritic matter. In some cases the ground-mass seems to
be composed chiefly of this unindividualised matter, with micro-
liths and small rods of plagioclase scattered less abundantly through
it. This is more especially the case with the amygdaloidal parts of
the rock, where occasionally the ground-mass consists almost ex-
clusively of non-differentiated matter, only a few recognisable
microliths making their appearance. There can be little doubt
that this unindividualised substance is simply the result of devitri-

184 Proceedings of Royal Society of Edinburgh, [april 4,

fication, and that originally these rocks contained no inconsiderable
proportion of glassy matter, especially in their upper and under
portions. In a number of the sections examined, however, no
trace of devitrified matter was observed, the ground-mass in such
cases consisting of an aggregate of microliths and minute crystals
of plagioclase, closely felted together, hut containing interstitially
abundant granules of ferrite, or magnetite passing into ferrite, along
with minute granules of pale greenish-yellow, and yellow serpentin-
ous matter and limonite, which are doubtless alteration products
replacing hornblende or pyroxene, or both. The porphyritic in-
gredients of these rocks are seldom prominent. Small and large
lath-like crystals of plagioclase are not uncommon, the larger
crystals seldom exceeding 1 mm. in length, and they are mostly
broken. They sometimes show fine zonal structure. The larger
crystals seem to he most common when the ground-mass is com-
posed chiefly of devitrified matter, with very minute microliths.
Pseudomorphs after hornblende and augite appear more or less
plentifully. These consist partly of yellow or greenish-yellow
serpeutine, sometimes veined with chrysolite, and partly of limonite.
Not infrequently the pseudomorph is composed internally of ser-
pentine, the outlines of the crystalline form being defined by
limonite, or magnetite and limonite. Very often the limonite forms
a meshwork of veins running through the serpentine, and occasion-
ally these veins approximate in direction to the cleavage-planes of
the original mineral. In many cases the shape of the pseudomorph
gives one no hint as to whether the replaced mineral was augite or
hornblende. Very often, however, the form is that of hornblende.
This is specially the case with such pseudomorphs as have well-
marked ferritic borders. In these one sees that the original
mineral must have been broken, and more or less corroded, the
ground-mass having often eaten into the heart of the crystal. A
few pseudomorphs show very distinctly the form of augite, and
some of these also contain inclusions of the ground-mass. Many of
the pseudomorphs are quite amorphous, some composed almost
entirely of serpentine, others almost exclusively of limonite : what
proportion of these may represent hornblende, and what proportion
augite, it is impossible to say. Of pseudomorphs having more or
less definite forms, those after hornblende appear to be the most

185

1887.] Professor Geikie on Geology of St Alb’s Head.

numerous, and this is probably the case with the amorphous ones
also. Fluidal structure is occasionally marked, the microliths and
lath-like crystals of plagioclase being grouped round the larger
porphyritic ingredients. In some of the rocks minute amygdal-
oidal cavities abound, and this even at a distance from the upper
and under surfaces of the flows. The cavities are filled generally
with calcite, or with calcite and quartz, or chalcedony. More rarely
zeolites are present. The larger amygdules in the more scoriaceous
portions of the rocks consist of the same minerals, calcite pre-
dominating. Most of the rocks are more or less deeply stained
with red ferritic matter.

The tuffaceous areas in the porphyrites afford an interesting
study. Occasionally they consist of broken or crushed scoriae of
one and the same kind of rock completely embedded in porphyrite.
These small lapilli or scoriae are generally finely and abundantly
porous, and show a dark devitrified ground-mass in which minute
microliths are more or less plentiful. They might quite well
represent fragments of the more scoriacous and glassy portions of
the same rock as that in which they are enclosed. In some places
the tuffaceous matter consists of finely comminuted debris of the same
or some closely similar rock, together with finer grit, and rounded
pseudomorphs of serpentine and limonite after hornblende or
pyroxene. The larger scorim and lapilli rarely exceed a hazel-nut
in size. They are enclosed in the porphyrite in such a way as to
show that this rock was in a fluid or pasty condition at the time
they became embedded, for the crystalline and microlithic ground-
mass lies between and among them. The tuffaceous areas now
described appear to be confined to the upper and lower parts of the
lava-flows, hut they occasionally occur nearer the middle. They
are generally distinguished from the rock in which they are
enclosed by their deeper red colour, a character which they have
in common with the beautiful red tuffs of Horsecastle Bay.

Bedded Tuffs. — These rocks present themselves amongst the por-
phyrites at three horizons, hut it is quite possible that thin layers
of similar fragmental materials, concealed by turf and superficial
debris, may occur at other levels. A continuous section across the
outcrops of the igneous series would probably show that each bed
of porphyrite was underlaid by tuff or tuffaceous deposits. The

186 Proceedings of Royal Society of Edinburgh, [april 4,

lowest bed of tuff is seen at Pettico Wick Harbour. ‘ This is a coarse
tuff or agglomerate of fragments of porphyrites, which are generally
dark purplish blue and red in colour, and more or less highly
amygdaloidal. The stones are angular and subangular in form, and
show no regular arrangement. They vary in size from small lapilli
up to blocks of more than 1 foot across — some measuring 2 feet in
diameter. Examined under the microscope, these porphyrites show
the same structure and composition as those already described. The
tuff rests upon a very irregular surface of porphyrite, and is overlaid,
in a like irregular manner, by a bedded porphyrite, which is very
vesicular and amygdaloidal at the line of junction. The junction is
somewhat confused in places by minor slips and faults.

On the side of the road leading from Pettico Wick to the light-
house various porphyrites are exposed, — some of which show the
curious vein-like and irregular inclusions of fine tuff already de-
scribed. These beds are overlaid by a considerable thickness of
well-bedded shaley tuffs, generally red in colour — the tuff being fine-
grained, and composed of comminuted debris of porphyrites. Some
of the beds contain many lapilli of larger size scattered through their
mass. They rest upon a dark purplish-blue amygdaloidal porphyrite,
and are traversed intrusively by a thin sheet of fine-grained porphyrite.
The junction is slightly confused, as at Pettico Wick, by faulting.

But by far the most extensive succession of tuffaceous strata is
that which occurs at the south-east end of the headland of St Abb’s.
These rocks are generally well bedded, and have a prevalent red
colour. They vary in texture from tuffaceous mudstones, in which
only grit and small lapilli occur, up to coarse-grained tuffs, in
which the included fragments may reach 1 foot or more in diameter.
The most common rock is a tuff composed of comminuted debris
and small lapilli, often not larger than a hazel-nut in size, but some-
times measuring 2 or 3 inches across. The grit and lapilli are of all
shades of red, purple, yellow, and blue — the red strongly predomi-
nating— so that the resulting tuff is finely mottled. In many cases
decomposition products, particularly calcite, permeate the rock in
all directions — giving rise to irregular white splatches, veinings, and
tangled thread-like areas — which show well on the warm red ground
of the tuff. Other parts of the tuff might be described as a breccia
of subangular and angular fragments, chiefly of amygdaloidal

1887.] Professor Geikie on Geology of St Abb’s Head. 187

porphyrites — the stones being set in a meagre matrix of comminuted
debris. These rocks dip S.E. at 18° to 20°. They are abundantly
pierced and traversed by dykes and irregular sheets and masses
of porphyrite, which will be described later on. In some places,
especially in the area extending from Raven’s Brae to Horse Castle,
the tuffs have been considerably baked and altered, so that it is
sometimes difficult in hand-specimens to distinguish between what
is tuff and what intrusive porphyrite. The fragmental character of
the altered tuff, however, is quite apparent under the microscope.

The fragments in these tuffs appear to consist exclusively of
varieties of porphyrite ; at all events I could find no other rock.
Most of the lapilli are vesicular and amygdaloidal — very many are
highly so, and have all the appearance of scoriae. The amygdules
being usually white are generally very conspicuous. A microscopic
examination of many of these included fragments shows that?, they
consist exclusively of porphyrite— the ground-mass being generally
vitreous, stony, or devitrified, but occasionally microlithic. The
description given above of the small lapilli, which occur in the
tuffaceous areas of the bedded porphyrites, holds equally true of the
lapilli of these bedded tuffs. A great number of the small stones
are evidently fragments of a vitreous scoriaceous porphyrite, and from
their highly vesicular character they might well have floated in
water at the time of their ejection — they are, in short, mere cinders.
The fragments which show a microlithic ground-mass often contain
also pseudomorphs after hornblende or pyroxene, and are evidently
true porphyrites. Red ferritic matter saturates most of the stones ;
but not a few of these are dark grey or blue, and it is such
fragments which show best the original vitreous character of the
ground-mass. Here and there amongst the fine comminuted matter,
or dust and grit, of the tuffs, small patches of serpentine and
limonite occur, and these, in some cases at least, alniost certainly
represent hornblende or pyroxene.

The tuffs are thus composed essentially of volcanic detritus. In
none of the specimens examined by me did I meet with any trace of
ordinary terrigenous sediment. Even the finest-grained portions
appear under the microscope to consist of minute fragments of
porous scoriaceous vitreous rock. There is no admixture of quartz-
grains and argillaceous matter, such as might have been derived from

188 Proceedings of Royal Society of Edinburgh, [april 4,

the adjacent Silurian rocks. If such derivative matter occur at all
it cannot he common, or I should hardly have missed it.

Intrusive Rocks. — Intrusive rocks, as already remarked, are well
developed in the headland of St Abb’s. These consist principally
of a compact fine-grained blue porphyrite, which is often reddened
with ferritic matter. It is a hard, tough rock, very irregularly
jointed. Here and there it is sparingly porphyritic with “ferrite”
— evidently pseudomorphous after pyroxene. The rock is a good
deal weathered, and fresh specimens are not readily obtained. Under
the microscope it shows a crypto-crystalline ground-mass — apparently
composed entirely of small crystals of plagioclase, hut owing to
weathering the characteristic form and striation of the crystals are
not well seen. There is no trace of non-individualised basis —
nothing resembling the vitreous and devitrified basis of the bedded
porphyrites. Scattered through this ground-mass occur occasional
large crystals of plagioclase, and here and there more or less abundant
pseudomorphs of limonite and serpentine after hornblende or
pyroxene — the latter apparently being most common. Diallage,
partially altered into limonite and serpentine, appears now and
again ; and probably many of the pseudomorphs just referred to
may represent this mineral. Other decomposition-products diffused
through the base in some sections are secondary quartz and
chalcedony, and, in thin veins, calcite and haematite or limonite.*

(b) Rocks of Coldingham Shore and Coldingham Bay.

The igneous rocks of this area are separated from those of the
region just described by a narrow belt of vertical Silurian strata
which occupy the cliffs and foreshore between Halterem’s Loup and
the Long Carr. At Halterem’s Loup the junction between the Old
Ked Sandstone and the Silurian is a well-marked fault. The grey-
wackes are considerably hardened and shattered, more especially as
they approach the igneous rocks of Coldingham Shore. At one or

* At Bell Hill the conglomerate is traversed by a dyke of mica-trap or
minette. This rock shows under the microscope a micro-crystalline ground-mass
full of felspar microliths and black magnetite dust. Scattered abundantly
through this ground-mass are small scales and larger crystals of biotite, many
of which are broken and twisted, and contain inclusions of the ground-mass.
Orthoclase appears sparingly, and a few irregular crystalline granules of quartz
are present. Magnetite is very plentiful.

1887.] Professor Geikie on Geology of St Abb's Head. 189

two places, near their junction with the latter, patches of tuff and
agglomerate occur upon the foreshore, as if resting directly upon the
Silurian ; but these patches are evidently of an intrusive character,
and appear to occupy vertical fisures in the surrounding greywackes,
which are extremely hardened and altered and very much reddened.
The actual junction of these greywackes with the main mass of the
igneous rocks presently to be described is likewise strongly suggestive
of the intrusive character of the latter. Similar appearances mark
the junction between these rocks and the Silurian greywackes on
the shores of Coldingham Bay. At that place the greywackes are
much jumbled, broken, and hardened, and saturated with red ferritic
matter. The Old Red igneous rocks do not overlie, but are intrusive
in the Silurian strata.

These igneous rocks consist partly of tuffs and agglomerates and
partly of porphyrite. The fragmental rocks are, for the most part,
quite unstratified, although here and there some trace of rude bedding
may be noted. They are of a dull red colour, and are made up of
angular and subangular fragments of all shapes and sizes up to
blocks measuring over a yard in diameter. These are set in a matrix
of smaller stones and comminuted debris. The whole appearance
of this coarse tuff, which in many places is quite an agglomerate —
that is to say, a coarse breccia of large stones and blocks — is similar to
that of those tuff's and agglomerates which elsewhere in Scotland are
found occupying the necks or throats of old volcanic orifices. All
the fragments consist of varieties of porphyrite — a great many of
which are precisely similar to the bedded porphyrites of St Abb’s
Head; others, however, are more markedly crystalline and porphyritic,
especially with plagioclase felspar. A number of these fragments
were examined under the microscope, but no new features of
importance were disclosed. Highly amygdaloidal and scoriaceous
fragments are common enough, but are not so strikingly prevalent
as in the well-bedded tuffs of Horsecastle Bay, &c. One may say
that, while in these latter scoriae predominate and fragments of less
porous rock do not abound, in the agglomerates of Coldingham Shore
it is just the reverse. From the lapilli and blocks of this agglomerate,
however, I did not succeed in getting any fresh specimens. Most of
the rocks are much altered, so much so indeed that all one can deter-
mine is the fact that clouded crystals of plagioclase occur more or less

190 Proceedings of Royal Society of Edinburgh, [afril 4,

numerously in a dull ferritic base. Patches and irregular aggregates
of ferric oxide are common enough also, and probably represent horn-
blende or pyroxene. The less altered specimens often show a devitri-
fied base, crowded with microliths and small crystals of plagioclase.
Scattered through this ground-mass are many larger crystals of
plagioclase. Upon the whole, highly porphyritic rocks appear to
be of more frequent occurrence in this agglomerate than they are in
the bedded series of porphyrites and tuffs at St Abb’s Head.

The unstratified agglomerate is irregularly traversed by masses
of close-grained porphyrite, which has the same general character
as the intrusive porphyrite near St Abb’s Head. This porphyrite
is, for the most part, much reddened with iron oxides, and con-
siderably weathered, so that fresh fractures are not readily obtained.
Where least weathered, it is a somewhat compact blue or purplish
rock. Here and there plagioclase felspar is conspicuous as a por-
phyritic ingredient, and now and again pyroxene (augite or diallage)
or pseudomorphs after pyroxene are visible. Thin veins and threads
of limonite and haematite are common.*

IY. General Conclusions as to the Old Red Sandstone Series.

The basement beds of this series, consisting of the conglomerate
of Bell Hill, are a mere fragment, and we cannot say much about
the conditions under which they were accumulated. They show us,
what indeed may be learned in many other parts of Scotland, that
the Lower Silurian strata had already been folded, crumpled, and
contorted, and excessively denuded before Old Red Sandstone
times. As the conglomerates contain not a single fragment of
igneous rock, it is most probable that their formation preceded
the outbreak of volcanic action in this neighbourhood.

The coarse tuff and agglomerate of Coldingham Shore fill up an
old volcanic orifice, from which the porphyrites and porphyrite-
tuffs of St Abb’s had previously been ejected. The great intrusions
of porphyrite which penetrate, not only the agglomerate of the
“ neck,” but the bedded tuffs and porphyrites, evidently belong to

* A dyke of basalt-rock crosses the intrusive porphyrites at the harbour,
Coldingham Shore. Unfortunately, I neglected to bring away a specimen of
the rock for closer examination. But I hope soon to revisit the district
for further study, and to supply the omission in a subsequent paper to the
Society.

1887.] Professor Geikie on Geology of St Abb’s Head. 191

a closing stage in the same period of volcanic activity. The dykes
of Bell Hill and the harbour are certainly of much more recent
date, and need not be considered in the present paper.

The south-east dip of the bedded igneous rocks of St Abb’s I
take to be due to the two large faults which form their boundary
lines. The original inclination of the strata, which need not have
been great, would necessarily be away from the neck of Coldingham
Shore. It is quite impossible to say what the extent of these faults
may be, but it is probably considerable, as the following considerations
will show. Neither the top nor the bottom of the bedded rocks is
seen, but the actual thickness displayed is not less than 1200 feet.
At present the beds dip towards S.E. at about 15°. If, therefore,
we take the beds at Pettico Wick to represent the basement beds of
the igneous series, which they certainly are not, then, to restore the
beds to horizontality, it is evident that the tuffs at the south-east end
of the headland of St Abb’s would require to be lifted up for some
1200 feet. But, on the supposition that all these bedded rocks have
been derived from the volcanic neck at Coldingham Shore, and would
at first, therefore, have a dip towards the north, it is obvious that the
subsequent downthrow produced by the N.W. and S.E. fault must
considerably exceed 1200 feet — say, 1300 or 1400 feet. A glance
at the section seen at Pettico Wick, however, shows us that the beds
there are not the basement beds of the series, for they are faulted
down against the Silurian. The actual base of the series is submerged.
If, therefore, the present S.E. dip of the porphyrites and tuffs be due
mainly, as I believe, to the fault at present referred to, the down-
throw of that dislocation must increase from N.W. to S.E., until it
reaches not less than 1300 feet. To the effect produced by this fault
we have to add that of the fault at Halterem’s Loup, which has a
downthrow to N.W., and has therefore had its share in bringing
about the S.E. dip of the bedded porphyrites and tuffs. It is im-
possible, however, to form even an approximate estimate of the
amount of downthrow produced by this latter fault. Erom the fact
that it seems to cut off the other, no trace of which occurs in the
rocks to the south, we may infer that its downthrow is considerable.
Be that as it may, it is quite certain that the tuffs of Horsecastle
Bay occupy a much higher horizon than the agglomerates exposed
upon the beach at Coldingham Shore.

192

Proceedings of Boyal Society of Edinburgh, [april 4,

While the geological structure of St Abb’s Head thus leads to
the conclusion that the bedded tuffs and porphyrites formerly
dipped in a northerly direction, and may thus have been ejected
from the volcanic focus in their neighbourhood, the petrological
evidence lends additional support to this conclusion. Fragments
of precisely the same porphyrites as those of St Abb’s Head occur
abundantly in the rock at Coldingham Shore. A few blocks and
fragments of greywacke were observed in the agglomerate, and
may, perhaps, be more plentiful than they seem to be, for, of
course, the agglomerate is only partially exposed ; but with these
exceptions all the stones I saw were porphyrites. Sections of the
finer-grained portions of the tuff examined under the microscope
showed in like manner that these are composed of the comminuted
debris of porphyrites.

From the fact that the bedded porphyrite-tuffs of St Abb’s Head
have evidently been arranged by and accumulated under water, we
may infer that the whole series, so far as that is exposed, is of
subaqueous origin — that, in the rocks now described, we have the
relics of an old subaqueous volcano of Old Red Sandstone times. The
bedded porphyrites offer many analogies with those of the Cheviot
Hills, the Sidlaws, and other regions of Old Red Sandstone volcanic
rocks. They are, in fact, only altered andesites, which, in their micro-
scopic structure, reproduce exactly what one sees in the andesites of
the Western Territories of North America. The intrusive porphy-
rites, however, which intersect the agglomerate and the bedded rocks
hardly resemble the intrusive masses of the Sidlaws, the Cheviots,
&c., those of the Sidlaws being mainly diabase (altered basalt-rock),
while those of the Cheviots are chiefly granite and felsite. Again,
the bedded scoriee-tuffs of St Abb’s Head are hardly paralleled by
any tuffs met with either in the Cheviots, the Sidlaws, or any other
region of Old Red Sandstone volcanic rocks known to me. Of
course, lapilli of highly porous and amygdaloidal porphyrites occur
commonly enough in many of those districts, but nowhere, so far
as I have seen, have we such a depth of fragmental materials con-
sisting almost exclusively of scoriae or cinders. These form the
highest beds of the series, and possibly represent the latest ejections
from the adjoining volcanic orifice. But they have suffered great de-
nudation, and certainly attained a greater thickness, and overspread

Professor Geikie on Geology of St Abb’s Read. 193

a muck wider area than they now occupy. This is evident from the
appearance at the surface of the intrusive porphyrites near St Abb’s
Head. These, there can be little doubt, cooled and consolidated
under the surface — the tuff which formerly covered them has been
washed away. The intrusion of these porphyrites marks the closing
stage in the volcanic activity of Old Red Sandstone times. It was
not until after lavas and fragmental materials had ceased to be
erupted, and the throat of the old volcano had become plugged with
angular debris and blocks, that the rocks in question were injected.
They evidently cooled under some pressure, but were probably not
of very deep-seated origin. Whether they ever rose to the actual
surface of the old volcano and overflowed, we cannot tell, for the
whole of that surface has of course disappeared. It is obvious,
however, that the molten masses from which they came must have
been of essentially the same composition as that from which the
bedded porphyrites were derived.

V. Glacial Phenomena.

The district described in this paper has been entirely overflowed
by ice. This is proved by the generally glaciated contour of the
rocks, which are smoothed from IST.W. to S.E. The escarpments
of porphyrites that faced the ice-flow have been bevelled off, and,
notwithstanding the weathered character of the rocks, well-marked
striae are met with here and there, the trend of which is E. 35 S.
Glaciated stones and clay occur in patches in the hollows of the
headland, and a considerable mass of till occupies the hollow that
separates the headland from the Silurian uplands. This is wrell
exposed in section at Pettico Wick. It presents no features that
require to be noted here, but is made up of the debris of rocks
which have come from the west or north-west.

PRIVATE BUSINESS.

A ballot was taken, and the following gentlemen were duly
elected Fellows of the Society : — Mr Alexander Goodman More,
Alexander M. M‘Aldowie, M.D., Mr James Hunter, Mr William
Gilmour, Mr Herbert H. Ashdown, M.B., and Mr J. Mackay
Bernard.

VOL. XIV. 7/10/87 N

194 Proceedings of Royal Society of Edinburgh, [april IS,

Monday, 18 th April 1887.

Sir WILLIAM THOMSON-, President, in the Chair.

Professor Rowland’s Photographs of the Solar Spectrum
were exhibited by the Astronomer-Royal for Scotland.

The following Communications were read: —

1. On Ship -Waves. By Sir W. Thomson.

2. On the Instability in Pluid Motion. By the Same.

3. Experimental Research in Magnetism. By Mr D. S.
Sinclair. Communicated by Principal Jamieson.

4. On the Summation of certain Series of Alternants.
By A. H. Anglin, M.A., LL.B., &c.

1. The summations referred to in the title depend on two
theorems — one already known, the other not hitherto published.
The first of these is to the effect that the quotient of any simple
Alternant by the difference-product of the variables is expressible as a
determinant whose elements are sums of homogeneous products of the
variables. For example,

1 ap aq ar

1 IP bq br
1 cp cq cr

= if (abed)

1 dp dq dr

0-1) 0-2) 0-3)
0-1) 0-2) 0-3)

0-1) (r- 2) (r-3)

where, generally, ( n ) denotes the sum of the homogeneous products
of a, b, c, d of n dimensions.

The other theorem may he enunciated, in a particular instance, as
follows : —

If three rows of four quantities each be taken, as

a n

Clc,

a3

h

a .

cl c2 C3 C4 J

1887.] Mr A. H. Anglin on Summation of Alternants. 195

and every possible determinant of the third degree be formed from
this matrix by deleting the last column of a row and the first element
of the other rows, the sum of these determinants is equal to the deter-
minant got from the matrix by deleting the second column : thus

cq

a2

«3

a2

CH

a 4

a2

a2

^4

ai

co

e

^4

h

h

+

h

+

b2

h

K

=

\

h

h

C2

C3

C4

C2

c?>

C4

Cl

C2

C3

C1

C3

0

and a like series equal to the determinant got by deleting the third
column, namely

a1

a2

a3

cq

a2

«3

a2

CO

«4

a1

a2

ai

\

h

h

+

h

h

+

\

h

h

=

h

h

h

C2

C3

ci

ci

C2

C3

ci

C2

C3

ci

0-2

C4

2. The proof of any case of this latter theorem depends on the
case before it. Thus, taking the matrix

the identity for the case of determinants of the second order is

ai a2

h h

+

a2 «3
&i b2

a.

a.

ai ^3

• (1),

the truth of it being self-evident.

Turning to the case for determinants of the third order, and
expanding each determinant in the left-hand side in terms of the
elements of the first column, we see that the coefficient of a1 is
| b3 c4 | , while the coefficient of a2 consists of the sum of two deter-
minants which by (1) is equal to | b2 c4 | ; and likewise for the
coefficients of the elements involving b’s and c’s. Hence we get

4

H

«4

a2

a2

a4

\

^4

+

h

h

ci

C3

C4

C2

C2

C4

and thus

“1

a2

a3

cq

a4

2

h

h

=

\

h

\

=

cq

0 2

C3

C4

A

C4

• • (2);

196 Proceedings of Royal Society of Edinburgh, [april 18
and in like manner,

a1

a2

CO

&

ax

«2

a4

h

b2

h

=

\

\

C3

ei

C2

C4

ai h2 C4I • ‘ (3)«

3. Taking the next case, arising out of tlie matrix

Cl C2 C3 C4 C5

cl4 d.2 do dA ,

consisting of four rows of five quantities each : we have to find the
value of

5

c

2

Cb

d2 d?) d4 db

or

where the suffix-order (1 2 3 4) occurs once in each determinant and
consequently consists of four terms. Expanding the determinants
as before, we see that the coefficient of aY is \ b3 c4 db | , while the
coefficient of a2 consists of three determinants whose sum by (2) is
equal to | b2 c4 d5 | ; and similarly for the coefficients of the elements
involving b, c , cl. Hence we get

and thus

aY

as

«4

aB

a2

<H

«4

«5

h

h

^4

h

+

h

h

h

h

ci

C3

C4

C5

C2

C4

C5

C?1

d3

d4

d5

<h

d2

d4

ch

= !

«i

lj3 C4

•

the value of

ai

a2

%

ci4

K

b.

K

b.

2

l

z

3

4

or

V

C2

CS

C4

C5

hj2

d3

d4

• w

consisting of six terms, in each of which the suffix-order (1 2 3 4)
occurs twice. Expanding in the same manner as before, it will be

1887.] Mr A. H. Anglin on Summation of Alternants. 197

seen that the coefficient of aY consists of the sum of three deter-
minants which by (2) is equal to \b2 cA db\, while the coefficient
of a2 likewise involves three determinants whose sum by (3) is
equal to \b2 c3 d5 | . Similar expressions holding for the coefficients
of the other elements in the first columns, we get

I a\ ^2 C4 ^5 I "b I a2 ^2 C3 ^5 I >

and thus

%2 = \ai b2 cA df (5).

Lastly, it may be shown in like manner that, in the case of

2

a.

dn

a2 a?> aA

b2 b3 b A

ds rf4 a ?b

or S3,

consisting of four terms, in each of which Ahe suffix-order (1 2 3 4)
occurs three times,

^3 = i ai ^2 C3 ^5 I (^)*

The results (4), (5), and (6) constitute the theorem in the case of
determinants of the fourth order, and are formed by deleting suc-
cessively the second, third, and fourth columns from the matrix out
of which they arise.

4. Thus, assuming the truth of the identities for the case of deter-
minants of the (n— l)th order, we can establish the corresponding
results for the case of determinants of the ?dh order ; that is to say,
taking the matrix

aA

a2

«3 ' '

. an _|

h

h

h ■

■ •

ci

C2

c3 .

• * ^ n- (-1

h

h

h ■

• • l'n+ 1 :

consisting of n rows of n+ 1 quantities each, we can obtain the
following n - 1 results involving determinants of the wth order,
and which are formed by deleting successively the second, third,
fourth, . . . , ni\\ columns from the matrix, viz. : —

198

Proceedings of Royal Society of Edinburgh, [aprtl 18,

al

a2 • • •

a

b2

h •••

bn+i

C2

Co . . .

o

Cn+ 1

or

~ i ai

b‘2 C4 • • • ln+ i 1

h

l3 ...

ln+1

ai

a2 . . .

««

h

b.2 ...

bn

C2

•

c3 . . .
•

^n+1

or X2

= K

c4 • • • ^w+1 I

l2

h •••

ln-f- 1

a!

a2 * * *

O'n

h

b2 . . .

K

ci

C2 ' . '

C n

d2

rl

• • •

d’n+1

or S3

= | ax

b-2 ^3 dfr . . . ln+1

h

X ■ ■ •

l’n+ 1

•

• • •

«i

• • •

«»

b2 . . .

bn

•

*

*

or Xn.

-i = 1

b% Cg . . . ll n _ 2 l'n -|-

/( 1 lie, ...

L l

3

ln-\ 1

where, generally, ^ consists of determinants in each of which
the suffix-order (1 2 3... n) occurs /x times, — „CV denoting the
number of combinations of n things taken g together.

We now propose, with the help of these identities, to effect the
summation of certain series of Alternants, obtaining results which
may be called Extensions of the known theorem referred to at the
outset.

1887.] Mr A. H. Anglin on Summation of Alternants. 199

1. Employing n letters a, b, c, .. . h, k, l — starting with, the case
of two general indices y and z, we have

| a°Zdc2 . . . hn~3kylz | = £}(abc . . . I) | (y - n + 2), (z - n + 1) | ,

which, for shortness, may he written in the form

[y, z] = I 2, 1 | £- (A).

Then

[y+1, z] + [y, z+l] =

3 2
2 1

t' +

2 1

3 2

=

3 1
3 1

3, 1

which result is the only Extension of equation (A).

Again, in the case of three general indices x, y, z, writing the
equation

| a%1 r2. . . gn~Ahxkylz | = tf(abc ... T) | (x - n + 3), (y - n + 2), (z - n + 1) |

in the form

we have
where

0, V, s] H 3, 2, 1 | £ (b)5

[x+l, y, z ] + [x, y+l,z] + [x, y,z+ 1] =

4 3 2

3 2 1

3 2 1

3 2 1

+

4 3 2

+

3 2 1

3 2 1

3 2 1

4 3 2

Expanding each determinant in terms of the elements of the first
column, the coefficient of x - n + 4 is | 2, 1 | , while that of x - n + 3
consists of the sum of two determinants which by (1) is equal to
1 3, 1 | ; and similarly for the coefficients of the elements involving
the other indices.

Hence

4 2 1
4 2 1
4 2 1

+

3 3 1
3 3 1
3 3 1,

and thus

2[> + i, y, «] = |4, 2, i \ch .... (2).

Further, we have

0+i, v + 1’ z1 + \.x + 1> y> z + 1] + 0> y + 1> s + 1] = s2£ >

where

4 3 2

4 3 2

3 2 1

4 3 2

+

3 2 1

+

4 3 2

3 2 1

4 3 2

4 3 2

j

200 Proceedings of Royal Society of Edinburgh. [april 18,
which, in the same manner as before, may he shown to he equal to

4 3 1

3 3 2

4 3 1

+

3 3 2

4 3 1

3 3 2

and thus

S[3+l, y+1, z] = \4r, 3, 1|{* . . . (3).

These two results are the Extensions of equation (B), and are
formed by deleting successively the second and third figures from
the series 4, 3, 2, 1 ; that is to say, the second and third columns
from the matrix

x — ?H- 4 , x-n + 3 , x — + 2 , x-n- (- 1
y -n + 4 , y — n + 3 , y - n + 2 , ?/ - % + 1

z-^ + 4, z — w + 3 , 2 - w + 2 , z - % + 1 .

2. Again, in the case of four general indices u, x, y, z, writing the
equation

| cdblc 2. . . fn~5guhxkHz | = | (u — n + 4), (x — n + 3), y - n + 2), (z — n 4- 1 ) | if
in the form

[u,x,y,z\ = |4, 3, 2, lj£-, .... (C),

we have

%[u + 1, x, y , =

2 consisting of four terms in each of which there is one index of
the form X+ 1, and where

5 4 3 2

4 3 2 1

4 3 2 1

4 3 2 1

4 3 2 1

+

5 4 3 2

+

4 3 2 1

+

4 3 2 1

4 3 2 1

4 3 2 1

5 4 3 2

4 3 2 1

4 3 2 1

4 3 2 1

4 3 2 1

5 4 3 2

Expanding these determinants as before, it may be shown by the
application of equation (2) that

S, = | 5, 3, 2, 1I + |4, 4, 2, 1 | ;

and we thus have

S|> + 1, x, y, z\ = | 5, 3, 2, 1 | £* . . . (4).

Farther, we have

%\_u + 1, x + 1, y, z\ — S2£* suppose,
where % consists of six terms in each of which there are two indices

1887.] Mr A. H. Anglin on Summation of Alternants. 201

of the form A+l, and where by equations (2) and (3) it will be
found that

S2 = | 5, 4, 2, 1 | + |4, 4, 3, 1 |;

and consequently

'$[u+ 1, x+ 1, y, z] = | 5, 4, 2, 1 p . . . (5).

Lastly, it may be shown in like manner that

S|> + 1, x+1, y + 1, s] = (|5, 4, 3, 1I + |4, 4, 3, 2|)P

= 15,4,3, 1|P (6).

The results (4), (5), and (6) are the Extensions of equation (C), and
their right-hand members are formed by deleting successively the
second, third, and fourth figures from the series 5, 4, 3, 2, 1 ; that
is, by deleting these columns successively from the corresponding
matrix. We may further observe that if we increase by unity one
index in the left-hand side of (C), the sum of the resulting alter-
nants is obtained by increasing by unity the elements of one column
in the right-hand side, thus giving the identity (4) ; while an in-
crease in two and three indices produces respectively a corresponding
increase in the elements of two and three columns, thus furnishing
equations (5) and (6).

3. To obtain the Extensions involving any number (v) of indices
we should thus assume the corresponding results for v — 1 indices,
and then deduce those for v.

Now, in the case of n— 3 general indices r, s, t, . . . z, we have
| a°b1c2dres . . . V | = | (r - 3), (s - 4), . . . , (z - n + 1 ) | p ,

which may be written in the form

t, ... z\ =

i 3, 4,

5,...

71=1

ip,

the Extensions of v

diich are

M

+
h— ‘

• • z] = 1 2,

4, 5, .

. . n-

■IIP

.

• (O'

S[r+ 1, 8 + 1,

t, ... z\ =

1 2, 3,

5,...

71- 1 |

£! • •

• (2)'

2[r + 1, 8+1,

• • •

t + 1 , u , .

■■*] =

1 2, 3,

4, 6, .

•

. . n- 1 |

P (3)'

while generally

S* = |2

, 3, i, . . .

/x+1,

/x + 3,

... 71

- 1 IP

• w

and lastly,

%+l, s+l,..+

+ 1, z] = \

2, 3, 4,

. . . n

- 3, n ■

- 1 1 £! • . .

(n - 4)'

202 Proceedings of Royal Society of Edinburgh, [april 18,

where, in general, ^ consists of m_3Cm terms in each of which there
are ^ indices of the form X + 1.

To deduce the Extensions involving n - 2 general indices
q, r, s, ... z from these n - 4 results, — we have

! a°blcqdr . . . lz\ = \ (q- 2), (r-3), . . . , (z-n+ 1)|£,
that is, in the above notation,

b, r, «,...«] = I 2, 3, 4, ... w - 1 i ? . . (D).

Then, if

3 [g + 1, r, s, . . . z] or S]_ = S^- ,

on writing down the determinants in Sx and expanding them in
terms of the elements of the first column in each, it may he shown
by equation (1)' that

Sx = | 1, 3, 4, . . . n - 1 1 + j 2, 2, 4, 5, . , . n - 1 | ,

and thus
Again, if

*i = \l, 3, 4, . . . n-l\£ .... (1).

2[? + l, r+l, s, . . . z] or 22 = S2£s
we shall find in like manner by equations (1)' and (2)' that
S2 = | 1, 2, 4, 5, . . . n — 1 | + 1 2, 2, 3, 5, . . . n - 1 1 ,
and consequently

S2 = | 1, 2, 4, 5, ...»-]]£» . . . . (2),

while by the application of (2)' and (3)' it may further be shown
that

+ 1, r+ 1, s + l, t, . . . z] or S3 = 1 1, 2, 3, 5, . . . n - 1 1 £* . (3).

Generally, to find the corresponding value of having terms

in each of which there are /x indices of the form A.+ 1, — suppose

Now since in ^ there are terms with the index q+1, and

n-fd/x. terms with the index q, on writing down and expanding the
determinants in as before, it will be seen that the coefficients of
q-l consists of the sum of w_3C/a_1 determinants which by equation
(fx - 1)' is equal to | 2, 3, 4, . . . /x, /x + 2, . . . n - 1 1 , while the co-
efficient of q - 2 consists of the sum of W_3CV determinants which by
equation (/x)' is equal to | 2, 3, 4, . . . /x + 1, /x + 3, . . . n - 1 | ; and

1887.] Mr A. H. Anglin on Summation of Alternants. 203

likewise for the coefficients of the elements involving the indices
r, s, t, . . . z. Hence we have

Sju. -~ | 1, 2, 3, . . . fi) /a - 1-2, . . . n — 1 |

+ | 2, 2, 3, . . . /a -f- 1, [a -f- 3, . . ,7i — 1 | j

and thus

2/a = | 1? 2, 3, . . . [i, \a + 2, . . . n — 1 | . . (f)-

Lastly, the corresponding value of

:% + l, r+ 1, . . . y + 1, z] or ln_3

is deduced in like manner by the use of equation (n - 4)', when we
get

Sw_s=| 1, 2, 3, . . . n-3, n-1 \g . . (n- 3).

The results (1), (2), (3), . . . (n- 3) are the Extensions of equation
(D), and their right-hand members are formed by deleting suc-
cessively the second, third, fourth, . . . , (n - 2)th figures from the
series 1, 2, 3, . . . n — 2, n — 1 ; that is, by deleting these columns
successively from the corresponding matrix. And we may further
notice that the coefficients of ^ in these n - 3 identities (correspond-
ing respectively to an increase by unity in 1, 2, 3, ... n — 3 indices),
are also formed by increasing by unity the elements of 1, 2, 3, . . .
7i-3 columns respectively of the determinant | (q - 2), (r - 3),
(s-4), . . . , (z-n+l) | .

5. Note on Cobaltic Alums. By Mr Hugh Marshall, B.Sc.

Erom a peculiar change of colour observed in the electrolysis of a
solution of copper-cobalt potassium sulphate, the author was recentl}r
induced to make some experiments on the behaviour of cobalt sul-
phate solution when electrolysed in such a manner that the reducing
product of the decomposition could not act on the solution. For
this purpose a divided cell was used, so that the two electrodes
were practically in separate vessels. The apparatus will be fully
described in a future communication.

It was found that an acid solution of cobalt sulphate alone is
not changed when submitted to electrolysis in the apparatus. If,
however, ammonium or potassium sulphate be also present, the
solution passes through a series of changes of colour, ultimately
becoming greenish-blue, and this, it was found, is due to oxidation

204 Proceedings of Royal Society of Edinburgh, [april 18,

of the cobalt from the cobaltous to the cobaltic state. This seemed
to point to the probable formation of an alum. Experiments were
therefore made in order to obtain crystals. The action was allowed
to go on for several days, so as to concentrate the liquid * when, in
the solution with ammonium sulphate, dark blue crystals separated
out. These were octahedral, showing also faces of the cube and
rhombic dodecahedron. The analysis of these showed that they
were ammonium-cobalt alum.

C0203

17-87

Theory.

17-05

(NH4)20

5-18

5-36

GO

O

CO

32-81

33-02

H20 (By Difif.)

44-14

44-57

100-00

100-00

When thoroughly dried the crystals are not unstable, but when
dissolved in water are quickly reduced. The solution in sulphuric
acid is not so soon decomposed. When the acid has been com-
pletely removed from the crystals, water seems to resolve them first
into the constituent sulphates. The oxygen liberated during decom-
position is partially in the form of ozone.

No satisfactory result was at first obtained with the potassium
sulphate solution, chiefly owing to the slight solubility of that salt.
If sufficient be not added the alum is decomposed. If, on the
other hand, too much be added, it crystallises out. The happy
medium can only be obtained by the addition of one or other
salt. After several experiments, crystals were obtained similar to
those of the ammonium alum, but they could not be separated from
the potassium sulphate with which they were mixed. Afterwards
a finely crystalline deposit was obtained, which on analysis appeared
to be the alum mixed with potassic sulphate.

Under similar conditions, nickel sulphate undergoes no change
whatever.

Other salts of cobalt undergo oxidation in presence of correspond-
ing alkali salts, forming evidently double salts ; these are at present
undergoing examination.

1887.] Mr G. N. Stewart on the Polarisation of Nerve. 205

6. On the Effect produced on the Polarisation of Nerve by
Stimulation. By Mr G. N. Stewart.

In this short paper I wish merely to give a summary of the chief
results of experiments made by me in February and March last in
the Physiological Institute of Berlin. Du Bois Beymond has
recently made an elaborate investigation of the galvanic polarisation
of muscle. Many years ago he made similar observations on nerve.
The question which occurred to me was, How does tetanus affect the
amount of polarisation in nerve 1 Apparently there has been no
previous work at this subject. It is not necessary to describe here
the arrangements used, nor the manner of making the observations,
as a detailed account, with discussion of the facts brought out, will
appear in the Journal of Physiology. When a current is passed
through a living nerve, the polarisation produced may be either
negative or positive. When it is negative, the polarisation current
is, of course, in the opposite direction to the polarising current.
Positive polarisation gives a current in the same direction as the
polarising stream. It depends upon the “ density ” of the polarising
current, and upon the time of flow, whether the deflection due to
the polarisation is purely negative, purely positive, or of double
sign. When it is of double sign, there is first a negative kick,
which is followed by a more persistent positive deflection. As a
matter of fact, there is every ground for believing, that in general
the two polarisations exist side by side in the polarised nerve.

The influence of stimulation on the polarisation, so far as my
experiments go, may be stated thus : —

1. In every case the effect 'produced by stimulation is in the
direction of diminution of the positive polarisation. — One says “ in
the direction of,” because increase of negative polarisation would
equally well explain the result. It is probable, however, for reasons
which need not be given here that it is the positive polarisation
which is affected.

2. The effect is, ivithin limits, greater the longer the time of flow of
the polarising stream. — This has only been shown for weak currents,
because strong currents depress the vitality of the nerve when they
are allowed to flow for any length of time. If, in the case of a weak

206 Proceedings of Royal Society of Edinburgh, [april 18.

polarising stream, a curve be constructed whose ordinates correspond
to amount of change of the polarisation, the abscissae representing
time of flow, this curve is found to have a maximum ; i.e ., when
the current is kept constant, the effect first increases with the time,
and then diminishes. Here the stimulus is, of course, also kept
constant.

3. The effect increases, within limits , ivith the density of the
polarising stream. — The curve plotted with current density as
abscissa, and amount of stimulation effect as ordinate, also reaches a
maximum, when the time of flow is kept constant.

4. The effect is less, as might be expected , the longer the interval
between breaking the polarising current and closing the galvanometer
circuit. — The persistency of it is sometimes, however, astonishing.

5. The effect increases with the strength of the stimulus. — Result
No. 1 has an important bearing on Hermann’s explanation of the
apparent diminution of resistance in a tetanised nerve, which I
propose to discuss at another time.

I must add that, in the case of a strong current, result No. 4 does
not always hold, the nerve apparently requiring some time to regain
its maximum of excitability.

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

vol. xiv. 1886-87. No. 124.

Monday, 2nd May 1887.

Sir DOUGLAS MACLAGAN, Vice-President, in the Chair.

The following Communications were read : —

1. The Objective Cause of Sensation. Part III. — The Sense
of Smell. By Prof. John Berry Hay craft.

The end-organs of the special senses are all built up on the same
type. The history of their development from simple ectodermic
cells suggests that similar agencies have been at work to produce
them. Both sapid and odorous substances, and indeed all gaseous
and liquid molecules, are now known to be in constant vibration,
and this vibration is more or less characteristic of the substance
examined.

The above considerations have led me, for the last five years, to
teach that, in all probability, it will be possible to connect quality
of taste and smell with the kind of vibrating stimulus, and that it
will be possible to demonstrate, as has already been done in the case
of sight and hearing, the truth of this general statement — that
quality of sensation will depend (the sensorium being in a normal
condition) upon the kind or character of the vibrating stimulus.
There is nothing very new in this idea. Without seeking for its
germs at an earlier period, we find it clearly enunciated by both
Hobbes and Hartley ; and in more recent times Mr Herbert Spencer
has lent the weight of his great authority in the same direction.
But of experimental proof, without which we cannot rest content,

VOL. XIV. 18/10/87 O

208 Proceedings of Royal Society of Edinburgh, [may 2,

nothing has been advanced. Casual allusions to the probable or
possible relationship between the tastes or smells of bodies and their
chemical natures are sometimes though rarely found in the text-books
of physiologists, but nothing more. While so much important work
has been carried on during the last few years by Helmholtz, Preyer,
Maxwell, Rayleigh, and others, in connection with both sound and
sight, no one, until quite recently, has turned his attention to the
investigation of either taste or smell.

In a most interesting and suggestive article in Nature (June 22,
1882), Prof. Ramsay brought forward many facts tending to demon-
strate the dependence of smell upon the vibratory motion of odorous
particles. He drew attention to the fact that many gases and
vapours of low specific gravity — their molecules vibrating therefore
with great rapidity — are perfectly odourless, and he saw in this an
analogy to the rapid vibrations of the ultra-violet rays of the
spectrum, and the rapid vibrations of an insect’s wing, both incapable
of producing any impression on the eye and ear. He also described
classes of substances alike in chemical and physical properties, such
as the alcohols or fatty acids, as having generic smells ; the higher
members of the groups producing sensations more powerful and
characteristic than those of the lower ones. It will be my endeavour
in the present paper to extend more fully this inquiry, and to de-
monstrate by experimental methods the fact that smell, like sight
and hearing, depends for its production on the vibrations of the
stimulating medium, the quality of the sensation depending, in all
cases, upon the kind of vibration which produces it.

In a paper read before the British Association in 1885, and printed
subsequently in the Proceedings of the Royal Society of Edinburgh
(1886), I was able clearly to demonstrate these points for the sense
of taste. That paper and the present one will be found to run on
exactly parallel lines ; one is almost a recapitulation of the other, for
what is true of taste is also true of smell. In order to avoid un-
necessary recapitulation, I have touched lightly on many questions
more fully discussed in the other paper, which should therefore be
consulted.

An investigation into the odorous properties of substances is to a
certain extent limited, as many of them are without smell, especially
those found in the inorganic world. In a description of odours one

1887.] Prof. J. B. Hay craft on the Sense of Smell.

209

is met with, this difficulty, that there is no nomenclature familiar to
every one. Hundreds of terms expressing the well-known colours of
familiar objects, enable one to describe by a single term almost any
tint and shade. We have cardinal, rose, magenta, maroon, carmine,
crimson, scarlet, and a dozen other shades of red alone, and all of
these can be expressed by words. The smells, however, and espe-
cially those of the chemist’s museum, are so unfamiliar, and often so
peculiar, that we are forced to speak of them simply as the odours of
the substances which produce them, or to say that they are like,
though never identical, with that of some other and better known
substance.

USTo two observers quite agree in their descriptions of a given odour,
and the information readily at hand in the text-books, but culled
from a hundred sources, is therefore not reliable. I have, for this
reason, availed myself freely of the kindness of my colleague Prof.
Tilden and my friend Prof. Ramsay, who have placed at my disposal
their private collections of chemical compounds. In almost every
case the description of a smell given in this paper is derived from
personal observation.

In the first place, let us study those few substances found among
inorganic compounds which have distinct smells. It is well known
that many substances, like arsenic, chlorine, sulphur, bromine, and
their compounds, have characteristic odours. Can we associate the
odours of these substances with any chemical or physical properties
they may possess, and show that when similar odours are produced
by two or more substances, then we have some similar chemical or
physical property present at the same time ?

In recent years a remarkable discovery of Hewlands has opened
up a fresh point of departure in the science of chemico-physics.
His observations led him to formulate a law which he termed the
law of octaves. Lothar Meyer, Mendel ejeff, and Carnelley, extending
his work, have shown that the “periodic-law,” as it is now called, is
one of vast application and importance. The nature of this periodic-
law is now so well known, thanks to the many recent publications
of Professor Carnelley, that it would be superfluous to attempt more
than roughly to sketch out its main features. If we arrange the
elements in the order of their atomic weights, beginning with that
which has the lowest, and passing to that which has the highest, we

210 Proceedings of Royal Society of Edinburgh. [may 2,

shall find a periodic recurrence of property or function in the series.
The first element is a monad, the second a dyad, the third a triad,
and the fourth a tetrad. Then we find the fifth a triad, the sixth a
dyad, and the seventh once more a monad. Then follows a second
series of seven elements, showing the same variation in atomicity ;
this repeats itself right through the list of elements. This periodic
recurrence of function is seen not only in the case of atomicity, hut
it may he also observed in the atomic volumes, the fusibility and the
electrical and other properties of the elements. There is then a
general resemblance in physical properties between the first, eighth,
fifteenth, &c., and between the second, ninth, and sixteenth
elements. Mendelejeff has arranged the elements in the convenient
tabular form given on the opposite page, which indicates these and
some other important facts.

Those elements which resemble one another, and which we can
pick out by taking every eighth one from that one from which we elect
to start, form what he calls a “ group,” and are arranged vertically.
The sets of seven elements each, arranged horizontally, form twelve
“ series.”

There is yet another point of importance. The elements of a
“ group,” which are in an even “ series,” are especially related to
one another ; so in like manner elements in an odd series of the
same group are similarly allied. Thus Li, Na, K, Cu, Rb, A g, Cs,
Au, have all these properties in common ; but in this group Na,
Cu, Ag, Au are most alike, and Li, K, Rb, and Cs, in like manner,
are most closely related.

In the paper to which I have already alluded I was able to
demonstrate the fact that elements in the same group are capable
of producing similar or related tastes. The power of producing a
given taste is then a property which, like the ordinary physical
qualities of the elements, follows the periodic law. As will now be
shown, the same obtains for smell.

In studying the facts of the case, let us start with Group VI.
We find here, in odd series, three well-known substances whose
compounds have strong and characteristic odours. Sulphuretted,
selenietted, and teluretted hydrogen have all a disagreeable odour
like that of rotten eggs. The compounds of the elements of this
group with methyl and ethyl are disagreeable and alliaceous. In

Table of Natural Classification of Elements — After Mendelejeff.

1887.] Prof. J. B. Haycraft on the Sense of Smell. 211

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Proceedings of Royal Society of Edinburgh. [may 2,

Group VII. chlorine, bromine, and iodine have very similar smells,
and so have the acids they form with hydrogen, and their com-
pounds with methyl, ethyl, ethylene, &c. Although similar in all
cases, yet they are not the same. One can distinguish the odour of
iodine from that of bromine or chlorine. It may be described as
having more flavour, and not so chlorous. Bromine is like them both,
having an odour intermediate between the two in quality. From a
study of the above substances, this is seen to hold good in all cases,
the odour uniformly changing, often to a slight degree, as we pass
from the lowest to the highest member of a group. A very marked
change is seen in the formyle compounds of Group VII. Chloro-
form has a fragrant and characteristic smell. So has bromoform,
but it has something else in addition, which is recognised as being
the odour of iodoform. Bromoform thus connects chloroform and
iodoform, these latter substances being very unlike one another.

There may then be so little difference in the odours of com-
pounds of the same group of elements that they may with difficulty
be distinguished. On the other hand, the differences may be great,
there being intermediate sensations produced by intermediate mem-
bers of the group. One is forcibly reminded of the changes in
sensation experienced in allowing the eye to traverse the spectrum
from one end towards the other. In a drawn-out spectrum, only a
part of which is visible, one passes, say, from orange into yellow,
and these colours are recognised as being different, and at the same
time alike. In a shorter spectrum the eye may pass from the
yellow into the red. The two sensations are quite different, but
the orange is seen to connect them. The importance of the
above statements — and they may be verified in the case of the
few odorous compounds in Group V. — will become apparent when
they are placed in juxtaposition with identical facts mentioned in
the previous paper on taste, and some recent observations of Pro-
fessor Carnelley.

In those groups of elements whose compounds are sapid, we find
that the same change in taste sensation is apparent as we pass from
lower to higher members of the group. Let us take as an example
Group VII., which furnishes us both with sapid and odorous
bodies

1887.] Prof. J. B. Haycraft on the Sense of Smell.

213

Group YII.

Element.

Potassium Compound.

Formyle Compound.

F

Salt and saline.

Cl

Salt, saline, bitter.

Characteristic odour of chloroform.

Mn

Br

Salt, saline, and bitter.

Intermediate odour.

I

Saline, bitter.

Characteristic odour of iodoform.

Potassium fluoride is salt — like common salt in taste. In addi-
tion it is slightly saline — like nitre. Chloride of potassium has a
suspicion of a bitter taste as well, and so has potassium bromide.
Potassium iodide has lost the taste of common salt, being a saline,
and bitter.

So far, then, we have seen that the power of producing taste
is a property or function of elements. Our knowledge of matter
is derived from its power of producing sensation within us.
In the case of sight and hearing we have associated quality in
sensation with the kind or character of the vibrating stimulus. If
it can be shown that elements belonging to the same “ group ” are
capable of vibrating in a way which is similar or related to one
another, then we have grounds upon which to draw an analogy
between smell, taste, sight, and hearing.

On account of our incomplete knowledge of the ultra-red and
ultra-violet regions of the spectrum, a final answer to this question
cannot perhaps be given. Only rough indications are to hand, but
these point in the same direction.

The chlorides of the alkaline earths have spectra which are nearly
related. The spectra of Group I. are not dissimilar, especially
potassium and rubidium, with the five groups of lines. Then, again,
the chlorides, bromides, and iodides of calcium and barium are
similar, the lines shifting towards the red end of the spectrum in a
way which is nearly proportional to the increase of atomic weight.

The colour of a substance is an index to the pitch of the vibra-
tions of its molecules. In a paper on the colour of chemical
compounds recently published in the Philosophical Magazine
(July 1874), Professor Carnelley demonstrated the existence of a
relationship between the salts of the same group of elements
in respect to colour. The salts, say the chlorides, of a group of

214 Proceedings of Royal Society of Edinburgh. [may 2,

metals may not be of the same colour, but we find that, in passing
to higher members of the group from the lower ones, a uniform
change in colour is to be observed. This change is produced by a
gradual shifting of the absorption towards the red end of the
spectrum, the molecules vibrating more and more slowly with in-
crease of atomic weight. This can be illustrated by the following
diagram taken from his paper : —

Metal.

Cl

I

Metal.

Cr04

As04

Na

White

White

Mg

Lemon yellow

White

Cu

White

Cream

Zn

Yellow

White

Ag

White

Light yellow

Cd

Orange yellow

White

Au

Yellow white

Golden yellow

Hg

Eed

Yellow

It is probable, then, that metals of the same group vibrate in a
similar way. This vibration we know is complex, consisting of
many wave-lengths of different pitch. When a metal vibrates, and
one of its vibrations falls within the scale of the visible spectrum,
we shall find the corresponding wave of another member of the
same group in the neighbourhood. If a higher member of the
group, it will absorb the light nearer the red end ; if a lower,
nearer the blue end of the spectrum. Together with this alteration
of pitch, we have corresponding alterations in the sensations pro-
duced, whether they be of sight, taste, or smell. Whatever reason
we have for associating quality of colour with the pitch of vibration,
we shall likewise have for associating quality of smell and taste
with the same physical cause.*

Amongst organic substances many are so closely allied that they
fall into distinct classes or groups. Thus we have the fatty acids,
alcohols, &c. If these be arranged in homologous series, commencing
with that which has the lowest, and passing to that which has the
highest molecular weight, a uniform change will be observed in many
physical properties on ascending the series. Thus the lower ones
may be gaseous, the middle ones liquid, and the higher ones solid.

* If a curve be constructed in which the ordinates represent the atomic
weights of the positive elements, and the abscissae a chromatic scale arising
from blue, green, &c., to black, we shall obtain a curve indicating that the
colours of the compounds are a periodic function of the elements arranged in
atomic series. This is well seen in the case of the normal iodides (Carnelley).

1887.] Prof. J. B. Haycraft on the Sense of Smell .

215

Professor Ramsay examined several of these groups, and came to
the following conclusions : — In the first case, that the smell of a
group was generic ; and, in the second case, that the smell became
more distinct, and gained in flavour in ascending from the lower to
the higher members. My observations are not quite in accordance
with the first statement, for I do not believe any uninitiated person
would find any resemblance, say, 1 between the odours of ethyl
alcohol and octyl alcohol, or of acetic and valeric acids, which
would prompt him in any way to class them together. I find that
in ascending the organic series, as in ascending one of Mendelejeffs
groups, the odour changes. This change may be slight, so that it
may be said with truth that there is a generic smell belonging to
the series ; or, more frequently, the change is so great that it is only
by a study of intermediate members that any continuity of sensation
can be made out.

These statements may be verified by a study of the following
tables. They are not as complete as I could have wished, owing to
my inability to obtain some of the rarer acids and alcohols.

Monatomic Alcohols.

CH3.OH Methyl alcohol =
C2H5.OH Ethyl „ =

C3H7.OH Propyl „ =

C4H9.OH Isobutyl ,, =

C5Hu.OH Amyl
CsHl7.OH Octyl „ =

Faint alcoholic odour.
Alcoholic odour.

Alcoholic odour with flavour.

[Flavour becomes more marked, and
the alcoholic odour less and less.

The term “ flavour ” expresses very badly what is meant. It is
only possible by experiment to become acquainted with the nature
of a smell.

Among the fatty acids another flavour equally characteristic
gradually supersedes the acetic odour of the first two members
of the group.

CHO.OH Formic acid
C2H2O.OH Acetic ,,
C3H5O.OH Propionic ,,

Fatty Acids.

= Acetic odour.

= Acetic odour.

= Acetic, together with a flavour.

216

Proceedings of Royal Society of Edinburgh. [may 2 ,

C4H7O.OH Butyric acid
C5H9O.OH Valeric ,,

( Slightly acetic, with a well-marked
l flavour.

| No longer acetic, the flavour alone
( is present.

In this case the smell has altogether changed in character. The
same holds good with the following series.

Acetates.

C.2H5.C2H302 Ethyl acetate =
C3H7.C2H302 Propyl „

C4H9,C2H302 Butyl „ =

C5H4.C2H302 Amyl „

Acetic and ethereal smell.

Acetic ethereal, with a flavour,
j Slightly acetic, with a pine-apple
1 flavour.

Pine-apple flavour, and not acetic.

If we pass to quite another group, the hydrocarbons, and starting
with benzene, replace first one, then two, and finally three atoms,
with methyl, the ethereal aromatic odour will be found progressively
to change in a manner which it is impossible to describe, but which
can readily be demonstrated.

Hydrocarbons.

C6H6 Benzene \

CH3.C6TI5 Methyl benzene ! Have a progressing and aromatic

2(CH3).C6H4 Dimethyl benzene f and ethereal odour.

3(CH3).CgH3 Trimethyl benzene j

The way in which the sensation changes, analogous to that ob-
served in studying Mendelejeff’s groups, can in a similar way be
explained on the vibration hypothesis.

I am not aware of any odorous organic series possessing at the
same time colour, although some of them have very weak absorption
bands. From a study of these latter, and from inferences drawn
from a study of other coloured series, it is possible to obtain an
insight into the state of vibrational activity of the substances in the
tables above. Dr W. J. Russell has investigated the absorption
bands of ammonia, alcohol, &c. These substances absorb light,
but to so slight an extent that long columns of the liquids have to
be examined before the bands are distinctly seen. Under these
conditions, ammonia gives several distinct and characteristic bands.

1887.] Prof. J. B. Hay craft on the Sense of Smell

217

If now an atom of hydrogen of the ammonia be replaced by methyl,
the ammonia hands are still visible, but they are shifted somewhat
towards the red end of the spectrum. Replacing the hydrogen by
the larger molecule of ethyl, the hands are seen to pass still nearer
to the end of the spectrum.

hTH3 Ammonia
CH3.NH2 Methylamine
C2H5.NH2 Ethylamine

Produce hands which shift to red end of
spectrum in ascending the series.

In the same way we find that common alcohol possesses absorp-
tion bands, seen also in the higher members of the group, but shift-
ing towards the red end of the spectrum in ascending the group.

C2H5.OH Alcohol \ Produce hands which shift to the red

C3Hf.OH Propyl alcohol > end of the spectrum in ascending the
C4H9.OH Butyl alcohol I series.

In the case of coloured acids, such as chromic and picric acids,
the salts too are coloured. If the hands of these acids he examined,
and if they he then converted into salts, the absorption will shift
towards the red end of the spectrum. It seems that the molecule,
having a certain vibrational character depending upon its structure,
is weighted by the added metal, the vibrations of which do not
probably appear at all in the visible spectrum, and, in consequence,
its pitch is lowered. If an odorous substance like acetic acid be
combined with another odorous substance, it is generally possible
to detect the two intermingled sensations in the compound. Ethyl
acetate is ethereal and acetous at the same time. Allyl sulphide is
like allyl alcohol, and has the odour of a sulphur compound as well.
In this case it is probable that those vibrations in each substance
which produce smell are not so much lowered in pitch by the new
substance with which they are combined as to change the character
of the sensations they are each capable of producing. The am-
monia vibrations are shifted towards the red end of the spectrum in
methylamine, but not enough to produce another sensation. In
other compounds of two odorous substances it may not be possible
to distinguish the original odours, and for the reason that the pitch
has shifted, as we have seen it often does, so as to produce quite a
different sensation.

218 Proceedings of Royal Society of Edinburgh. [may 2,

It may be urged as an objection to some of these conclusions, that
the same odours are often produced by substances, chemically speak-
ing, quite unlike each other. Thus benzoic aldehyde smells very
much like nitrobenzene. In the case of taste, too, there are many
examples of totally dissimilar bodies having indistinguishable acid
or sweet tastes. In answer to this objection one has only to re-
member that there are instances, equally numerous, of very different
substances which produce the same colour sensations. One may
produce exactly the same tint with either a chromate, a picrate, or
an aniline dye. It would be strange, indeed, if among the com-
plex vibrations of a compound, or even of an element, some tones
were not of the same pitch, as some of the vibrations of substances
quite dissimilar in general properties. When these tones fall within
the scale of the visible spectrum, the scale of taste, or smell sensa-
tions, we have, according to the vibration theory, a similar sensation
produced.

In this paper I have endeavoured to avoid all questions which
are matters of speculation. I have dealt only with already ascer-
tained facts, or those which can readily be verified. I do not
attempt to offer any hypothesis to account for the action of vibrating
matter on the olfactory end-organs. It may or may not be a
mechanical or a chemical action. This question is not raised. We
know next to nothing as to how it is that ether vibrations stimulate
the cones of the retina, still less can we guess at the action of
vibrating atoms and molecules of ordinary matter on the sensitive
end-organs of the nose. My aim has been to establish the fact that,
just as we have reason to connect differences in colour sensations
with differences in the vibration of the ether, so, in like manner we
have reason to connect differences in smells with differences in the
vibrations which call them into existence. This analogy is estab-
lished upon the following grounds: —

(1) In passing from the lower to the higher members of one of
Mendelejeff’s groups, such molecular vibrations as have been investi-
gated tend to become lower in pitch. At the same time the colour,
taste, and smell sensations alter in character when present.

(2) In passing from the lower to the higher members of an
organic series, such as the alcohols, such molecular vibrations as
have been investigated tend to become lower in pitch. When pre-

219

1887.] Prof. J. B. Hay craft on the Sense of Smell.

sent, the colour, taste, and smell sensations alter in character in the
manner that I have described.

2. On the Physics of Noise. By Professor Crum Brown.

[Abstract.)

The noises considered in this paper are uniform, continuous noises,
such as the fricatives of articulate speech : f, 0, s, y, &c. These
sounds are considered by the author to stand in a similar relation to
musical tones as lights with continuous spectra do to lights with
bright-line spectra. Methods were proposed for analysing these
uniform continuous noises, and also for imitating them by synthetic
means.

3. On the Physical Properties of Methyl-Alcohol. By
Professor Dittmar and C. A. Fawsitt, Esq.

4. On the Instability of the Double Sulphates
M"S04,B'2S04 4- 6H20
of the Magnesium Series. By W. Dittmar.

By a number of observations made incidentally in the preparation
of two of the double salts referred to in the heading, namely, the
compounds of sulphate of potash with sulphate of magnesia and
sulphate of ferrous oxide respectively, I had long come to suspect
that these two salts at any rate are not perfectly stable in opposition
to water. To settle the question, I have caused Mr James Pobson and
Mr Andrew Hodge, two young chemists working in my laboratory,
to inquire into the matter by systematic experiments. These were,
in general at least, conducted according to the following scheme : —
Starting from a known weight of sulphate of potash, this was dis-
solved in a proportion of hot water,* less than sufficient to hold the
intended double salt in solution after cooling ; there was then added
a known weight of the di-valent sulphate amounting to exactly 1 or

* In the case of FeS04 the water was acidified with a few drops of sulphuric
acid to prevent precipitation of ferric compounds.

220 Proceedings of Poyal Society of Edinburgh. [may 2,

1*1 or 1*2 ... 1*5 times MgO or FeO per 1K20 used, the solution
filtered hot into a basin, allowed to crystallise, and the crop of
crystals produced examined.

The results were similar in both cases, but I prefer to state them
in reference to the magnesia salt, because our experiments in regard
to it were more exhaustive than those with the iron salt.

The crystals deposited from a solution containing one or even
a little more than one MgO per 1K20 may look perfectly normal
en masse , but when examined more closely are invariably found
to be contaminated with a powdery coating which looks like,
and indeed substantially consists of, sulphate of potash. As the
proportion of magnesia increases, the relative quantity of free
sulphate of potash produced gets less and less, and at last vanishes
altogether. With 1*3, sometimes even with D2 times MgO per
1K20, we generally obtained normal-looking crystals, which con-
tained the correct percentage of water, and consequently consisted,
substantially at least, of the pure, unmixed double salt.

Similar results were obtained in the case of the ferrous double
salt ; in its case we determined the percentage of iron (by perman-
ganate) as a test for the degree of purity.

In neither case, however, have I been able as yet to determine
the exact conditions under which a given solution is sure to de-
posit perfectly normal crystals. Whether or not depends not merely
on the ratio between the weights of the two bases, but also on the
proportion of water, the temperature at which the crystals separate
out, and other independent variables.

I refrain from giving any further details, intending to complete
the investigation, to extend it to other double salts of the magnesium
series, and also to the alums, and then to present a complete and
detailed memoir.

5. A Diatomaceons Deposit from North Tolsta, Lewis.

By John Battray, Esq.

PRIVATE BUSINESS.

Mr H. A. Webster, Mr John S. Yeo, Mr John Cockburn, Dr A.
S. Cumming, and Mr J. W. Capstick were balloted for and declared
duly elected Fellows of the Society.

1887.] Mr W. Peddie on Electrolytic Polarization.

221

Monday , 16/A May 1887.

Lord MDABEN, Vice-President, in the Chair.

The following Communications were read : — •

1. On the Increase of Electrolytic Polarization with Time.

By W. Peddie, B.Sc.

(A bstract.)

This paper dealt only with cases in which the electromotive
force used is insufficient to produce decomposition. In such cases
the electrodes act as condensers. P>ut the observed law of variation
of current-strength with time is not exactly that which holds in
the charging of ordinary condensers. The author showed that the
deviation could be largely accounted for by the continual increase
of transition resistance, the existence of which he proves in a
separate paper on that subject.

2. On the Blood of Myxine. By Professor D’Arcy W.

Thompson.

3. On the Larynx and Stomach in Cetacea. By Professor

D’Arcy W. Thompson.

4. On Transition Resistance at the Surface of Platinum

Electrodes, and the Action of Condensed Gaseous Films.
By W. Peddie, B.Sc. (Plate VII.)

The question of the existence of true transition resistance at the
surface of certain electrodes in given liquids has been in debate
for many years, but has never yet been conclusively settled. It is
admitted universally that in certain cases such resistance does
occur, as, e.g., when a non-conducting oxide is formed on the surface
of the metal ; but the point in dispute is whether or not it occurs

222 Proceedings of Royal Society of Edinburgh. [may 16,

when no direct chemical action takes place between the metal and
the products of electrolysis, or between it and substances dissolved
in the liquid. The great difficulty in all experimental inquiry re-
garding the resistance of electrolytes is the difficulty of distinguish-
ing between the effects of true resistance and the effects of true
reverse electromotive force of polarization. For, if E he the direct
electromotive force producing a current x in a conducting circuit
which includes an electrolyte and has resistance R, while e is the
type of the polarization electromotive force, so that 5(e) is the total
reverse electromotive force, we have

E - 5 (e) = Raj .

But, if e contains a term proportional to aj, we can write this equa-
tion in the form

E-5(e') = (R + 5(p))^,

where p is the constant of proportionality. This shows that the
value of the resistance in the circuit, as determined by any of the
ordinary methods, may include a term which does not correspond to
a true resistance actually existing. Hence, usually, in measuring
the resistance, polarization is prevented by the use of alternating
currents — as in Kohlrausch’s method ; or an attempt is made to
eliminate its effects by keeping it constant while the resistance is
varied — as in Horsford’s method. And, in addition to this, resist-
ance at the surfaces of the electrodes must be distinguished from
other resistance in the circuit. Attempts have been made to do this
by means of measurements of the heat developed at the surfaces;
but this method is unsatisfactor}r, as there may be development of
heat at the surfaces from other causes than the presence of resistance.

Method of Observation.

In making experiments on the law connecting current-strength
and time, when one Daniell cell was placed, along with a galvano-
meter, in circuit with an electrolytic cell having platinum electrodes
and containing a solution of sulphuric acid, I noticed that the result
was very different according as the platinum plates had been newly
heated to redness or had been left for some hours in the liquid. In
the latter case the strength of current at a given time was, cceteris
paribus , much weaker than in the former (see first series of experi-

1887.]

Mr W. Peddie on Transition Resistance.

223

xnents, and Plate VII.). This was most probably due to alteration
of resistance or to alteration of capacity of the electrodes regarded as
condensers. To settle the point, I used a Helmholtz galvanometer
capable of indicating a current of the one ten-millionth part of an
ampere. It was necessary to use an instrument of such sensibility ;
for the current, although it started with a comparatively large value,
very rapidly fell to an exceedingly small fraction of its original
strength because of polarization. Evidently the initial value of the
current-strength is independent of polarization; and this constitutes
the great advantage of the present method. In order to bring the
first deflection of the index on the scale, it was necessary to shunt
the galvanometer. Of course, the deflection could not be read with
accuracy for some time after joining the battery in the circuit
because of oscillations of the galvanometer needle; but, by proper
shunting, the interval could be made as small as 10 seconds when
required. Readings of the deflection (to which the current-strength
is proportional) were taken at short intervals, and the results exhibited
graphically. The curve drawn through the points so obtained could
easily be continued backwards to cut the axis parallel to which
current was measured, thus giving the initial value. From this the
amount of resistance in the circuit could be obtained. I did not,
however, actually determine the resistance in this way. I obtained
the curve for the case when the electrodes had been left unheated for
some time ; then I washed the plates and heated them to redness, and
repeated the experiment under such conditions as to obtain a curve
coinciding practically with the former. The results showed that
in all cases a considerable additional resistance had to be placed
in the circuit to produce coincidence. This shows conclusively that
a transition resistance exists; and also gives an estimate of its
amount, for the transition resistance must be equal to the resist-
ance added in the second case. It is necessary to remark that the
resistance of the electrolyte was the same in both cases; and,
further, its total amount was very small in comparison with the
resistance of the rest of the circuit. Since only one Daniell cell
was used, the liquid was not decomposed, and the current-strength
after two or three seconds was only of the order of thousandths or
ten-thousandths of an ampere. Hence, although the temperature
coefficient of the resistance of the liquid is large, it was quite im-
VOL. XIV. 19/10/87

p

224 Proceedings of Royal Society of Edinburgh, [may 16,

possible that any appreciable rise of temperature could occur, the
mass of liquid being very large.

Experiments.

In the first series of experiments no additional resistance was
placed in the circuit when the plates had been heated. The results
obtained are shown graphically in Plate VII. The series of points
marked a give the results when the plates were newly heated.
Those marked b give the results when the plates had been left in
the liquid for half an hour after heating and performing the experi-
ments corresponding to a. Those marked c were obtained after the
plates were left in the liquid for a number of hours — about twenty,
more or less. A Tray-Daniell cell was used so as to give constant
electromotive force. Half a minute was allowed to elapse before
taking the first reading.

Experiment la. — Plates heated.

Deflection at intervals of 10 secs. — 92, 82, 75, 69, 66, 64, 59, 56,
53, 50, 49, 47, 46, 44, 43, 42, 40, 39, 38, 37, 36, 35, 35,
34, 34, 33.

At intervals of J min. — 32, 32, 32, 31, 30, 29, 29, 28, 28, 28.

At intervals of J min. — 27, 27, 26, 25, 24, 24, 23.

At intervals of 1 min. — 22, 21, 20, 19, 19, 18.

Experiment lb. — Plates connected by a copper wire for 30 min.

10 secs, interval. — 83, 70, 65, 60, 56, 53, 50, 48, 46, 45, 43,
42, 41, 40, 39, 38, 37, 37, 36.

J min. interval. — 35, 35, 34, 33, 32, 31, 30, 30, 29, 29.

J min. interval. — 28, 27, 26, 25.

1 min. interval.' — 24, 23, 21, 20, 20, 19.

Experiment 2 a. — Plates heated.

At intervals of 10 secs. — 93, 85, 76, 65, 63, 60, 57, 55, 52, 50,
48, 47, 46, 45, 44, 43.

J min. interval. — 40, 38, 37, 36, 35, 34, 33, 33, 32, 32.

J min. interval. — 28, 27, 26, 25, 25, 24, 24, 24.

1 min. interval.- — 22, 21, 21, 20, 20, 20.

1887.]

Mr W. Peddie on Transition Resistance .

225

Experiment 2 b. — Plates connected for 30 min.

10 secs.— 83, 76, 67, 64, 61, 57, 55, 53, 51, 49, 47, 46, 44,

43, 42, 41, 40.

1 min.— 38, 36, 35, 34, 34, 33, 33, 32, 31, 31, 30, 30.

I min.— 27, 26, 25, 24, 23, 23, 22, 22.

1 min.— 22, 21, 20, 19, 19, 19, 19.

Experiment 2c. — Plates connected for about 20 hours.

10 secs.— 24, 21, 18, 17, 15, 15, 14, 14, 13, 13.

£ min.— 11, 9, 8, 8, 8, 8, 7, 7.

J min. — 6, 5, 5, 5, 5, 5.

1 min. — 4, 3, 3.

Experiment 3 a. — Plates heated.

10 secs.— 91, 86, 78, 72, 67, 62, 60, 58, 55, 53, 51, 49, 48, 47,
46, 44, 43, 42, 41, 40, 39, 39, 38, 38, 37.

I min.— 36, 36, 35, 35, 34, 33, 33, 32.

\ min. — 31, 31, 31, 30.

1 min.— 28, 26, 24, 24, 23, 22, 21, 20, 20.

Experiment 35. — Plates connected for 30 min.

10 secs.— 86, 75, 68, 63, 60, 56, 53, 51, 49, 48, 47, 45, 45,

44, 43, 42.

I min.— 40, 40, 39, 38, 37, 36, 35, 34.

1 min.— 32, 32, 31, 30.

1 min.— 27, 26, 25, 24, 23, 22.

Experiment 3c. — Plates connected for about 20 hours.

10 secs.— 26, 21, 19, 15, 13, 13, 12, 12, 11, 11, 10, 10, 10, 10.
\ min. — 9, 8, 8, 7, 6, 6, 5, 5.

^ min. — 5, 5.

1 min. — 4, 4, 4.

Experiment 4 a. — Plates heated.

10 secs.— 96, 85, 76, 70, 66, 62, 59, 56, 53, 51, 50, 48, 47,

45, 44, 43, 42, 41, 41.

226

Proceedings of Boy al Society of Edinburgh, [may 16,

\ min. — 40, 39, 38, 37, 36, 35, 34, 33, 32, 32.

1 min.— 31, 31, 30, 29, 28, 27, 26.

1 min.— 25, 23, 22, 22, 21, 21, 21, 20, 20, 19, 19.

Experiment 4 b. — Plates connected for 30 min.

10 secs.— 84, 76, 67, 62, 58, 55, 52, 50, 49, 48, 46, 44, 42,
41, 40, 39.

1 min.— 38, 37, 36, 35, 34, 33, 32, 31, 30, 30.

J min. — 29, 28, 27, 27.

1 min. — 26, 25, 24, 23, 22.

Experiment 4 c. — Plates unconnected for about 20 hours.

10 secs.— 34, 27, 23, 21, 18, 16, 14, 13, 12, 11, 11, 10, 10, 10.

\ min. — 10, 10, 9, 9.

J miu.— 9, 9, 9, 9.

1 min. — 8, 8, 7, 6, 6.

These experiments show that when the plates are left in the
liquid for a considerable time, some cause produces a great diminu-
tion of current-strength. This may be either due to increase of
resistance or to decrease of capacity at the surface layers where
“ condenser-action” occurs. The above series of experiment does not
determine to which cause the diminution is due, since half a minute
elapsed between starting the current and taking readings ; but the
following series shows that, whether or not there be alteration of
capacity, there is great alteration of resistance. The galvanometer
was shunted, and readings were taken every 10 secs, after joining
the battery into the circuit.

Experiment 1. — Plates connected for about 40 hours.

Deflection. — 19, 13, 10, 9, 8, 7, 7, 6.

Experiment 1 a. — Plates heated, and 48 ohms added.

Deflection.— 18, 14, 13, 12, 12, 11, 10, 9.

Experiment lb. — Plates heated, and no additional resistance.

Deflection.— 25, 20, 15, 14, 13, 13, 12.

1887.] Mr W. Peddie on Transition Resistance. 227

Other experiments of the same kind were made, and gave nearly
the same result. So that evidently in the course of 40 hours a re-
sistance of about 40 or 50 ohms appeared in the circuit. The next
point to be determined was whether or not this resistance followed
the law of inverse proportionality to tbe surface. One or two pre-
liminary experiments were made, which showed that if the plates
were connected by a short copper wire for 15 minutes, all previous
polarization was discharged, — at least so far as the galvanometer
could detect it. In what follows the plates were raised roughly
about one-half out of the liquid, so that the transition-resistance
should be approximately doubled if it follows the above-mentioned
law. The numbers in this series of experiments cannot be compared
direetly with those in the first, as the arrangement of resistance in
the circuit was different.

Experiment 1. — Plates connected for about 40 hours.

Deflection. — 5, 4, 3, 3, 2.

Experiment la. — Plates heated, and 96 ohms added.
Deflection. — 5, 3, 2, 2, P5.

Experiment IK — Plates connected for half an hour, 110 ohms added.
Deflection. — 5, 4, 4, 3, 3, 3, 2.

Experiment 1 c. — Plates connected for half an hour, 110 ohms added.

Deflection. — 5, 4, 4, 3, 3.

Experiment Id. — Plates connected for one quarter of an hour;

no resistance added.

Deflection. — 18, 17, 16, 15, 14.

Other similar experiments giving much the same results were
made, but need not be quoted. Evidently the resistance is inversely
proportional to the area of the plates.

Time during which the Resistance Increases.

Experiments were made in which the plates were left half out of
the liquid for 20 hours. In this case a resistance of from 80 to 90
ohms, roughly, was found. (The numbers must be given roughly,

228

Proceedings of Royal Society of Edinburgh. [may 16,

for the apparatus did not admit of great accuracy, the galvanometer
being shunted by a wire of very small resistance.) In two or three
days the resistance was about 200 ohms. Once the plates were left
for eleven days, when a resistance of about 250 ohms was observed.
The process, therefore, goes on slowly for a long time.

Origin of the Resistance.

Most probably the resistance is due to the condensation, on
the surface of the electrodes, of gases dissolved in the liquid. To
test this, I left the plates in air instead of placing them in the liquid.
The resistance in this case was of the same magnitude as before,
and was evidently due to the condensation of atmospheric gases.
To obtain a stronger proof, however, I placed the plates, after being
heated, in an atmosphere of oxygen for about two hours. A resist-
ance was found in this case about equal to that which was caused
by leaving the plates in air for twenty hours. Leaving the plates
in air for two hours made no appreciable change in resistance.
Next, I connected the plates to the positive pole of a battery of
two Bunsen cells for two minutes, and decomposed water with
them, so that oxygen was developed on them. They were then
connected together for a quarter of an hour to get rid of polarization,
and then a resistance was observed equal to that got by leaving them
in oxygen for two hours. Nearly, but not quite, the same resistance
occurred if the plates were joined to the negative pole of the
Bunsens, so as to develop hydrogen on them. There can be no
doubt, then, but that the resistance is due to condensed films of gas.

Firmness of the Gaseous Deposit

That the deposit clings with excessive firmness to the surface of
the metal, is evident from the fact that nothing but heating to a red
heat destroyed the resistance. No amount of rubbing of the plates,
however hard, made any observable diminution.

Specific Resistance of the Films of Gas.

In order to determine the specific resistance of the deposit, a
knowledge of its thickness is necessary. Or, if one can assume
that the thickness is the same in different specimens of platinum,
it might be obtained from the above experiments (which can give

1887.] Mr W. Peddie on Transition Resistance. 229

the value of the product of the specific resistance and the thickness)
combined with experiments made on the resistance of a very fine
platinum wire, first, when newly heated, and, secondly, when left
unheated for some time. The latter experiments would give the
value of the ratio of the two quantities mentioned.

Meanwhile, if it may be assumed that the thickness of the con-
densed gases is of the same order as the thickness of condensed
moisture and gases on the surface of glass (given by Quincke as
5(10)~5 c.m. — Pogg. Ann.} 1859, and Wied. Ann., 1877), the above
experiments show that the order of the specific resistance is the
same as that of ordinary dielectrics.

Remarks.

If the film of gas had acted as a perfect dielectric no alteration of
resistance would have been perceptible. The fact that the resist-
ance appeared shows that to a great extent, if not entirely, the gas
assumes the potential of the metal on which it is condensed. Given
that the gases do assume the potential of the electrodes, it is
rendered highly probable that the resistance of the film will alter
with the potential; for the particles of the gas become mutually
repellent because of their similar electric charge, and so tend to alter
their relative positions against the attraction of the metal. That
such change of resistance with potential did occur was evident in the
experiments I made; for if the initial deflection was obtained after
the plates were leftunbeated for some hours, and was again obtained
after they had been connected for a short time to discharge polariza-
tion, it was smaller in the latter case than in the former, showing
that the gas had not yet assumed its previous physical condition.
Again, if the deflections be got as before, and the plates be
heated and an equal resistance put in circuit (so as to obtain the
same initial current), and the deflections again be taken, the rate
of decrease of current with time is always somewhat greater in the
former case than in the latter. This might be due to alteration
of resistance with potential, for the potential of the plates increases
with time after the battery is joined in. On the other hand, it
might be due to alteration of capacity.

Note. — In the Plate the point marked 1 corresponds to the first reading of
the galvanometer for the curves a and c. The point o' is related to the curves
b in the same way as o is to a and c.

230

Proceedings of Royal Society of Edinburgh. [may 16,

5. Researches on the Problematical Organs of the Inverte-
brata — especially those of the Cephalopoda, Gastero-
poda, Lamellibranchiata, Crustacea, Insecta, and
Oligochaeta. By Dr A. B. Griffiths, F.B.S. (Edin.),
F.C.S. (Lond. & Paris), Principal, and Lecturer on
Chemistry and Biology, School of Science, Lincoln ;
late Lecturer on Chemistry, Technical School,
Manchester, &c.

Being convinced that a thorough examination (both from a
chemical and physiological point of view) of the various problem-
atical organs of the Invertebrata will throw much light on their
physiology and their relationship to the Yertebrata, these investiga-
tions have been undertaken with that object in view.

I have already shown that the so-called " liver ” of Sepia
officinalis is a true pancreas , and not a liver ( Proc . Roy. Soc.
Edin., vol. xiii. No. 119, p. 120).

A. (I.) Nephridium of Cephalopoda.

Taking a fresh Sepia oficinalis as a type of the Cephalopoda, it
was found that its nephridia are true kidneys, or renal organs.
The venous blood, as it passes from the vena cava, is distributed by
a number of afferent branchial vessels which communicate with the
sacculated and glandular chambers (the nephridia). The blood
passes to the gills and then back to the heart.

After dissecting the nephridia from the bodies of several fresh
cuttle-fishes, the secretion of these glands was found to be acid to
litmus paper, the liquid deposits, upon standing a short time,
earthy matters. These earthy deposits were submitted to chemical
analysis. They are insoluble in distilled water, but readily soluble
in acetic acid. On neutralising a portion of the acetic acid solution
with ammonium hydrate, and then adding ammonium oxalate, a
white precipitate was obtained, indicating the presence of calcium.
Another portion of the acetic acid solution was neutralised, and to
the neutral solution silver nitrate added : a yellowish precipitate
was obtained. To another portion of the solution, ammonium
hydrate was added until alkaline, and to this alkaline solution a

1887.] Dr A, B. Griffiths on Organs of the Invertebmta. 231

small quantity of an aqueous solution of magnesium sulphate, with
the production of a white precipitate of ammonio-magnesium
phosphate. The presence of phosphoric acid in the earthy deposits
was confirmed by using the ammonium molybdate and the uranium
nitrate tests. Therefore, it must be concluded that these earthy
deposits consist of calcium phosphate. No calcium carbonate,
magnesium carbonate, nor any other compound was found in the
deposit.

Antr. vena
cava.

Nephridium

(kidney).

Ventricle.

Vein.

Capillaries.

\ntr. aorta.

* efferent bran-
chial vessels.

> Gill.

> Afferent bran-
chial vessels.

Auricle.

Post, vena cava.

Post, aorta.

Fig. 1. — Nephridium of Sepia officinalis.

The liquid portion of the secretion of the nephridia was ex-
amined by two separate methods : —

(a) The clear liquid from the nephridia (after the separation of
the calcium phosphate) was treated with a hot dilute solution of
sodium hydrate, then on adding hydrochloric acid, a slight flaky
precipitate is obtained ; and on examining these flakes under the
microscope, they were seen to consist of small crystals in rhombic
plates, prismatic needles, and stellar-shaped crystals. On treating
the secretion with alcohol, the rhombic crystals are deposited ;
these crystals are soluble in water. When these crystals are treated
with nitric acid, and heated gently with ammonia, the reddish
purple murexide [CsH4(NH4)N6Oc] is obtained, which was found
crystallised in prisms.

232 Proceedings of Poyal Society of Edinburgh, [may 16,

(b) Another method was applied to the clear liquid secreted by
the nephridia. The liquid was boiled in distilled water, and
evaporated carefully to dryness. The residue so obtained was
treated with absolute alcohol, and filtered. Boiling water wras
poured upon the residue on the filter paper, and to the aqueous
filtrate an excess of acetic acid was added. After standing 6 f
hours, crystals of uric acid were deposited, and recognised by the
chemico-microscopical tests already mentioned above. Further, it
was found that there was a small quantity of uric acid in the blood
of the vena cava, before it entered the nephridia ; but the blood
after passing into the branchiae contains no uric acid. From these
reactions, the secretions of the nephridia contain uric acid and
calcium phosphate, and prove that the nephridia of the Cephalo-
poda are true renal organs getting rid of the nitrogenous waste
matters, in the form of uric acid, contained in the pure blood as it
is brought to these organs (nephridia) by the vena cava.

(ii.) On the Renal Organs of Astacus fluviatilis, Anodonta cygnea,
Limax flavus, Helix aspersa, and Periplaneta orientalis.

It will be remembered that in a paper ( Proc . Roy. Soc., vol.
xxxviii. Ho. 236, p. 187) before the Boyal Society of London, I
have shown that the secretions of the so-called “ green glands ” of
Astacus fluviatiliis (crayfish) can be made to yield uric acid
(C5H4H403) and guanin (C5H5H50), showing these glands are
analogous in physiological function to the kidney of the higher
forms of animal life.

Mr Harold Follows, F.C.S., and myself (Chemical Pews, vol. li.
p. 211, and Jour. Cliem. Soc. [Abstracts], 1885, p. 921) have
established the renal functions of the organs of Bojanus in Ano-
donta cygnea (fresh-water mussel), by the isolation of uric acid
and urea from the secretions of those organs.

The isolation of uric acid crystals from the problematical renal
organs of the Invertebrata, commenced by myself (in my Boyal
Society’s paper on the green gland of Astacus) led Dr C. A.
MacMunn, M.A., F.C.S. (Journal of Physiology , vol. vii. Ho. 2,
p. 128) to prove the renal function of the Malpighian tubes of
Periplaneta orientalis , and in the nephridia of Helix aspersa and
Limax flavus.

1887.] Dr A. B. Griffiths on Organs of the Invertebrata. 233

(III.) Renal Organs of the Lamellibranchiata and Crustacea.

The organ of Bojanus or nephridium of My a arenaria (as well as
Anodonta cygnea ) contain uric acid and urea in their secretions,
and there is also a small quantity of calcium phosphate present in
the secretion of the organ of Bojanus. Mr Follows and myself
( Chemical Neivs, vol. li. p. 241, and Jour. Cliem. Soc. [Abstracts],
1885, p. 921) found “ a salt of calcium in minute quantities f hut
we could not make out the acid in combination ; subsequently it
was found to he phosphoric acid. The “ green glands ” of Homarus
vulgaris (lobster) easily yield uric acid crystals and small quanti-
ties of the base guanin.

Cuticle. ^

Epidermis. ^

Circular muscu- 4
lar layer.

Longitudinal 4
muscular layer.

Outer loop of A
nephridium.

External open-
ing of nephri-
dium.

Pig, 2. — Diagram of Nephridium of Lumbricus terrestris. A, the secretion
of the outer loop of the nephridium (segmental organ) contains the hugest
quantity of uric acid.

(IV.) Renal Organs of the Oligochceta.

After treating the segmental organs (nephridia) of freshly killed
Lumbricus terrestris (earthworm) in a similar manner to the

Dorsal vessel.

Middle loop of
nephridium.

Typhosole.

^ Hepatic cells, so-
called “ liver.”

» Inner loop of
nephridium,

.> Epithelium of
intestine.

Ventral v.

^ Coelom.

Internal opening
of nephridium.
> Vent, nerve cord.

Subneural vessel.

234 Proceedings of Royal Society of Edinburgh, [may 16,

nephridia of the Cephalopod, yields uric acid, but no guanin, urea,
or calcium phosphate. Therefore the “ segmental organs ” of
Lumbricus are renal in function, getting rid of the nitrogenous
waste matters contained in the blood, in the perivisceral cavity.

The largest amount of uric acid was found in the secretion con-
tained in the muscular part of the “ segmental organ ” (fig. 2,
outer looj) of nephridium).

The next table is a summary of the constituents of the nephridia
of certain divisions of the Invertebrata.

(Y.) Renal Organs and their Constituents.

Cephalopoda.

Gasteropoda.

Lamellibranchiata.

Crustacea.

Insecta.

Oligochseta.

Uric acid,

present.

present.

present.

present.

present.

present.

Urea,

absent.

...

present.

absent.

absent.

Guanin,

absent.

absent.

present.

absent.

Calcium phosphate,

present.

present.

absent.

absent.

B. (I.) Salivary Glands of Gasteropoda and Insecta.

The secretions of the “ salivary glands ” of the Insecta (Orthop-
tera) were investigated by taking as an example the Periplaneta
orientalis (cockroach).

The salivary glands of Periplaneta are situated on each side of
the oesophagus and crop, and extend posteriorly as far as the
abdomen. They are about u of an inch in length, and composed
of acini (fig. 3, b). Accompanying the glands are two salivary
receptacles, one on either side of the crop. A quantity of the
secretion was extracted by crushing about sixty glands of freshly
killed cockroaches. It was alkaline to test-papers. A portion of
the secretion was added to a small quantity of starch, the starch
being converted into glucose sugar in 12 minutes. The presence of
sugar was proved by the formation of red cuprous oxide by the
action of Fehling’s solution.

Another portion of the secretion was distilled (with the utmost
care) with dilute sulphuric acid ; and to the distillate ferric chloride
added, which gave a red colour indicating the presence of sulplio-

1887.] Dr A. B. Griffiths on Organs of the Invertehrata. 235

cyanates. The inorganic constituent, as far as I could make out,
consists only of calcium phosphate.

Turning once more to the soluble zymase (ferment) contained in
the secretion, it can he isolated by precipitating the secretion with
dilute phosphoric acid, adding lime-water, and filtering. The pre-
cipitate was dissolved in distilled water, and then reprecipitated by
alcohol. This precipitate converts starch into glucose sugar.

Fig. 3. — a and b, Salivary gland of Periplaneta orientalis (much enlarged).

I have already mentioned that the secretion of the salivary
glands of Periplaneta are alkaline. Out of 80 animals, I found 4
with the secretion decidedly acid. This acid property is most
probably due to pathological changes in the secretion of the said
four animals.

The largest quantity of diastatic or “ soluble ” ferment was to he
found in the secretion obtained from the glandular portion of the
organ and not from the salivary receptacles (fig. 3, a).

The salivary glands of Helix aspersa (snail) yielded a soluble
ferment, capable of converting starch into glucose sugar. The
ferric-chloride test failed to show the presence of sulpho-cyanates.
The mineral ingredients found were calcium and chlorine ; but I

236 Proceedings of Boy al Society of Edinburgh. [may 16,

could not detect the presence of phosphates or carbonates in the
salivary glands of Helix.

Therefore, from, these investigations, the salivary glands of the
Insecta and Gasteropoda are similar in physiological function to
the salivary glands of the higher animals.

The following table gives the constituents found in these two
divisions of the Invertebrata : —

(II.) Salivary Glands and tlieir Constituents.

Insecta (Orthoptera).

Gasteropoda.

Soluble diastatic ferment,

present, .

present.

Sulphocyanates,

present, .

?

Calcium phosphate,

present, .

?

Calcium,

present, .

present.

Chlorine,

absent, .

present.

C. (I.) On the “Liver” of the Gasteropoda , LamellibvancMata ,

Crustacea , and Insecta.

I have already proved the so-called “ liver ” of the Cephalopoda
is a true pancreas ( Proc . Roy. Soc. Edin., vol, xiii. No. 119,

p. 120).

The secretion of the “ liver ” of Astacus fluviatilus when fresh
gives an acid reaction.

(a) The secretion of the organ acts upon starch paste. The
starch granules disappear with the exception of their celluloid
covering ; and on treating with water, and then adding Fehling’s
solution, sugar in the dextrose form was obtained.

( b ) The secretion forms an emulsion with oils and fats yielding
subsequently fatty acids and glycerol.

(c) The action of the secretion upon milk was to render it trans-
parent.

(d) When a few drops of the secretion of the organ were ex-
amined with chemical reagents under the microscope, the following

1887.] Dr A. B. Griffiths on Organs of the Invertebrata. 237

reactions were observed : — On running in between the side and
cover-slip a solution of iodine in potassium iodide, a brown deposit
was obtained, and on running in concentrated nitric acid on another
slide containing a drop or two of the secretion, a yellow coloration
was formed, due to the formation of xanthoproteic acid. These
two reactions show the presence of albumen in the secretion of the
organ in question.

(e) The soluble ferment was extracted according to the Kistia-
kowsky method (Pfl tiger’s Archiv fur Physiologie , vol. ix. pp.
438-459). The ferment converts fibrin into leucin (a-amido-
caproic acid, C6H13N02) and tyrosin (oxyphenylamidopropionic acid,
C9HnN03).

(/) No glycocholic and taurocholic acids could he detected by
the Pettenkofer and other tests. No glycogen was found in the
organ or its secretion.

(g) The secretion contains about 5 per cent, of solids.

( h ) The secretion contains leucin and tyrosin.

Similar reactions were obtained with the secretion of the pyloric
coeca ( “ liver ” ) of Periplaneta orient alls, which substantiate and
further extend the investigations of Krukenberg, Plateau [Bull, de
V Acad. Roy. de Belgique , xli. 1874), Hoppe-Seyler, and others.

The secretion of the so-called “ livers ” of Helix aspersa, Umax
maximus , Limax flavus , My a arenaria , Anodonta cygnea , and
Lumbricus terrestris all yield similar reactions to those of the
secretions of the “ liver ” of Astacus fluviatilis.

From these investigations the conclusions to he drawn are, that
the so-called “ livers ” of the Gasteropoda, Lamellibranchiata,
Crustacea, Insec ta, and Oligoehmta are pancreatic in function, i.e.,
their secretions are more like the secretions of the pancreas of the
Yertebrata than the secretions of a liver.

In conclusion, I may say that the present work will be continued
on other problematical organs of the Invertebrata, and their analogy
or otherwise with organs whose functions are well established in
the Vertebrate division of animal life; for one cannot forget
Pope’s words —

“All are but parts of one stupendous whole.”

238 Proceedings of Royal Society of Edinburgh, [may 16,

Appendix.

List of Dr Griffiths’s published Papers on the Physiology of the

Invertebrata.

I. “ On the Extraction of Uric Acid Crystals from the Green
Gland of Astacus fluviatilis,” Proc. Roy. Soc., vol. xxxviii. p. 187 ;
Jour. Chem. Soc., 1885, p. 680; Science Gossip , No. 255, p. 57.

II. “ A Peculiar Excretory Product found in the ‘ Liver ’ of
Sepia officinalis ,” Chem. News , vol. xlviii. p. 37 ; Jour. Chem. Soc.
[Abstracts], 1884, p. 94.

III. “ Chemico-Physiological Investigations on the Cephalopod
Liver, and its identity as a true Pancreas,” Proc. Roy. Soc. Edin .,
No. 119, vol. xiii. p. 120; Chem. News , vol. li. p. 160; Chem.
Soc. Jour., 1885, p. 829.

IV. “ Chemico-Biological Examination of the Organs of Bojanus
in Anodontaf Chem. News, vol. li. p. 241 ; Jour. Chem. Soc., 1885,
p. 921 ; Manchester Guardian , May 30, 1885.

V. “ On some Points in the Physiology of Certain Organs of the
Alimentary Canal of Blatta periplaneta ,” Chem. News, vol. lii.
p. 195.

Also, since the present paper.

VI. “On the Nephridia and ‘ Liver ’ of Patella vulgataf Proc.
Roy. Soc., vol. xlii. p. 392.

VII. “ On the Nephridia of Hirudo medicinalisf read before
Royal Society of Edinburgh, July 4, 1887.

6. The Nephridia of Lanice conchilega, Malmgren. By

J. T. Cunningham.

{Abstract.)

The excretory system in this species has never been adequately
described; it presents an extremely interesting condition from a
morphological point of view. There are four well-developed
nephridia in somites 6-9, inclusive. Each of these commences by
an internal aperture or nephrostome, and consists of a bent tube
or loop, the inner side (the side nearer the median plane) of the

1887.] Mr Cunningham on Nephridia of Lanice conchilega. 239

loop being connected with the nephrostome, while the outer passes
downwards and opens into a longitudinal tube common to all the
four nepliridia of a side. Four openings, corresponding to the four
nephridia, place the longitudinal tube in communication with the
exterior ; these openings are close behind the upper ends of the
2nd to the 5th uncinigerous tori respectively ; the 1st uncinigerous
torus being in the 5th somite. The longitudinal tube is continued
backwards on each side through somites 10-13, representing four
more coalesced nephridia ; but in this region there are neither
internal nor external openings, nor any loops similar to those in
the more interior region ; the longitudinal tube is simple, almost
cylindrical, showing slight indentations between the successive
somites, which mark where the successive nephridia have coalesced.
The outer side of the whole longitudinal tube is in contact with
the ventral longitudinal muscles, while the upper and inner side is
beneath the oblique muscles. The internal openings already men-
tioned are situated immediately behind the notopodial fascicles
of setse of somites 5-8 inclusive. The longitudinal tube extends
into the 5th somite, but I could not find there an external opening.
Behind the 1st to the 4th somites are traces of incomplete septa,
of which that behind the 4th is the most complete. Attached to
the front of the latter septum is a nephrostome, but I could not
trace any connection between this and the part of the tube in the
5th somite. There are two other well-marked nephrostomata
attached to the septa behind somites 2 and 3, and these openings
lead into tubes seen in somites 3 and 4. I could not find external
openings in the two latter somites. There are thus eleven nephridia
represented altogether, — three rudimentary, in somites 3, 4, 5 ; four
perfect, in somites 6-9 ; and four imperfect, in somites 10-13 ; the
eight posterior being all in communication, their distal parts
having fused to form a longitudinal tube. This is the first case
in wdiich such a longitudinal coalescence of nephridia has been
discovered, and its morphological similarity to the condition in
Vertebrates is obvious.

The Astronomer-Royal for Scotland exhibited specimens illus-
trating Ives’s process of Isochromatic Photography.

By permission of the Meeting, Professor Tait stated to the Society
• vol. xiv. 3/11/87 Q

240 Proceedings of Royal Soeiety of Edinburgh. [june 6,

that he had just received a letter from Professor Amagat of Lyons,
containing an account of the solidification of tetrachloride of
carbon 6 p. 79° C., C2C14[CC14] by pressure only at ordinary tempera-
tures.

Monday , Qth June 1887.

J01IX MU EE AY, Ph.D., Vice-President, in the Chair.

The following Communications were read: —

1. On a Furnace capable of melting Nickel and Cobalt. By

J. B. Eeadman, Esq.

2. On the Fossil Flora of the Eadstock Series of the Somer-

set and Bristol Coal Fields. Concluding Part. By

E. Kidston, Esq.

3. On the Discharge of Albumen from the Kidneys of

Healthy People. By Prof. Grainger Stewart, M.D.

Great diversity of opinion exists as to the frequency of the oc-
currence of albuminuria in healthy people, and elaborate inquiries
have led different observers to conspicuously contradictory con-
clusions. Posner has said that his observations satisfy him that
traces of albumen exist in every normal urine, and may be demon-
strated if sufficiently delicate methods are employed. One of the
most distinguished authorities on the subject, Dr Senator of Berlin,
says that his observations supply good reason why he should con-
sider it not improbable that, if we were to examine the urine for
long periods at different hours of the day, and with great care, we
should sooner or later find it to contain albumen in the case of every
healthy man. Dr Kleudgen, in the course of a special study of
albuminuria in relation to epilepsy, came to the conclusion that
traces of albumen could be demonstrated in any urine above a
certain degree of concentration. Dr de la Celle de Chateaubourg
found albumen in the urine of 592 out of 701 healthy people whom

1887.] Prof. G. Stewart on Albumen from Kidneys. 241

he examined, that is in 84 per cent. Dr Capitan found that among
98 Drench soldiers 44 or 44 ’9 percent, had albuminuria. Professor
Lenbe, oil the other hand, found among 119 German soldiers whom
he examined that only 4 per cent, showed albumen on rising in
the morning, and 16 per cent, in the forenoon after a march of
several hours’ duration. Dr Van Noorden states that he found it
vary under different conditions among healthy German soldiers from
3 to 35 per cent. Dr Munro found albuminuria in 24 out of 220,
that is in lOd per cent., presumably healthy people examined for
life insurance in the United States of America. And Dr Leroux
found it only 19 times among 330 children, or in 5 ’76 per
cent.

Such contrariety of results made me think it desirable to make
a fresh series of observations upon this point, with the view of
determining (first) whether Posner is right in saying that albumen
is present in every urine ; (second) what proportion of presumably
healthy people have albumen in the urine in quantity sufficient for
demonstration by the tests ordinarily in use; and (third) what effects
various physiological conditions, such as diet, exercise, severe exertion,
and cold bathing, produced upon the discharge.

I have, with the aid of Dr Stevens, made some experiments with
the view of determining the first of these questions, and have tried
to repeat Posner’s observations. I do not feel sure that our results
were absolutely satisfactory, but the conclusion to which I am led in
the meantime is that albumen, if present at all in normal urine, is in
such extremely minute amount as to be barely discernible, or not
discoverable at all, with the most delicate tests, even after consider-
able concentration. The minute trace which appears sometimes to be
present is probably accounted for by the epithelial and other cellular
elements from the urinary passages which are present in greater or
less amount in every urine.

With the view of obtaining evidence as to the second question,
that is the proportion of presumably healthy people who have
albumen in their urine in quantity sufficient for demonstration by
the tests ordinarily in use, I have examined, with the assistance of
Dr Stevens and Mr Boddie, several series of presumably healthy
individuals. By the kindness of Dr Mills and Mr Fayrer, medical
officers of Edinburgh Castle, and of the Colonel and Adjutant of

242 Proceedings of Royal Society of Edinburgh. [june 6,

the Seaforth Highlanders, I was enabled to examine a series of 205
soldiers and applicants for admission to the army.

I also got specimens of urine from 74 healthy male adults engaged
in civil employments. By the kindness of Dr Sinclair and his resi-
dent assistant Dr Helme, I examined 80 healthy inmates of Craig-
lockhart Poorhouse ; and by the kindness of Dr Halliday Douglas
and Mr Munro, I had opportunity of examining the urine of a large
number of the inmates of the Orphan Hospital. We had thus in
all 407 presumably healthy individuals, with regard to whose urine
we made the most careful examination, sometimes on one, some-
times on several occasions.

The plan of testing adopted was in all cases the same. Urines
which were cloudy from any cause were carefully filtered. Those
which were clear were tested as passed. Each specimen was tested,
first with nitric acid by the contact method, by which, as previous
experiment had shown, we could discover albumen in the pro-
portion of 0‘003 per cent., or 0*0131 1 of a grain per ounce ; and by
picric acid, using the contact method, by which we could discover
albumen in the proportion of 0U0015 per cent., or 0U006555 of a
grain per ounce. Each specimen was also carefully tested for
peptones, using Eehling’s solution by the contact method, a plan
which certainly shows the presence of peptones very distinctly when
they are added to urine, and probably is a reliable test in cases of
peptonuria.

Taking specimens of urine passed by 407 presumably healthy
individuals, during the forenoon or about midday, we found that
albumen was present in 129, or a little over 31 '7 per cent. Of these
it was in quantity sufficient to be discovered by the cold nitric acid
test in 66, in lesser quantity in 63. In Table I. the greatest results
are shown —

Table I. — Showing incidence of Albuminuria in 407 presumably healthy
individuals ( forenoon or noon specimens).

Urines

Examined.

Albumen shown
by HN03.

Albumen shown
by Picric Acid.

Total.

Per cent.

407

66

63

129

31-7

But it was evident that a marked difference existed between

1887.] Prof. G. Stewart on Albumen from Kidneys. 243

various groups of individuals examined, as between soldiers and
men of corresponding life following civil occupations, and between
children and men about or above sixty. It is therefore necessary to
consider these groups separately. Among the soldiers and recruits
examined, 205 in number, 77, or 37'56 per cent., had albuminuria;
while of 74 adults in civil employments, 8, ox between 10 and 1 1 per
cent., showed the symptom. Of the former group it was shown by
nitric acid in 47, or 22-92 per cent.; by the picric acid only in 30, err
14*63 per cent. Of the latter group it was shown by nitric acid in
5, or 6*75 per cent. ; by picric acid only in 3, or 4 -05 per cent.
Table II. shows these results.

Table II. — Showing the incidence of Albuminuria in Soldiers and Civil

Population.

With HN03.

With Picric
Acid only.

Total.

Per cent.

Soldiers, . .

205

47

30

77

37-56

Civil Popula- 1
tion, . . J

- 74

5

3

8

10-8

In seeking to compare the facts in the case of children and old
people, I thought it desirable to get access to individuals in similar
position in life, and living under somewhat similar conditions, and I
was glad to avail myself of the opportunity afforded of examining
the inmates of Craiglockhart Poorhouse. We got specimens of the
urine of 40 men, about or above sixty years of age, resident in the
poorhouse, but not on the sick list. I found that albumen was pre-
sent in 27 of them, that is in 67*5 per cent. We also examined a
series of 40 children under puberty, and found that it was present
in 7, or in 17 ’5 percent. Nitric acid showed it in 9, that is in 22*5
per cent, of the old men. Picric acid in other 18, or 45 per cent. ;
while in the children nitric acid showed it in 2, or 5 per cent., and
picric acid in other 5, or 1 2 *5 per cent.

When these results are shown in a tabular form, we see at a glance
how striking is the contrast between the two groups.

It thus appears that of the four groups the old men in the poor-
house showed albuminuria most frequently, the soldiers next, the
children in the poorhouse next, and the least frequently apparent
were the young men engaged in civil occupations.

244 Proceedings of Royal Society of Edinburgh. [june 6,

Table III. — Showing incidence of Albuminuria in If) Children and 40 Old
People {presumably healthy ), inmates of CraiglocTchart Poorhouse.

With HN03.

With Picric
Acid.

Total.

Per cent.

Children under \
puberty, . . f

2

5

7

17-5

People about or \
above sixty, . J

9

18

27

67-5

It was not in my power to determine the cause of the albumin-
uria in the persons examined, but I took care to exclude cases of
the accidental accumulation of mucus or pus in the urinary tract,
and have included only four, viz., two soldiers and two of the old
men. In none of the cases was the albuminuria due to cardiac or
pulmonary diseases, and in very few was there occasion to suspect
the existence of Bright’s disease. On the other hand, there were
few cases whose clinical history corresponded to Pavy’s cyclical
albuminuria or Moxon’s albuminuria of adolescents.

Being anxious to supplement these observations, I asked two of
my former assistants, who are well known to me as careful and
accurate observers, Dr James Ritchie and Dr Graham Brown, to
give me the results as to albuminuria met with in the last 200 cases
which had been proposed for insurance in the two companies for
which they are medical referees. The tests employed had been heat
or cold nitric acid, and it was found that in one series of 200, 5 per
cent, showed albumen, and in the other series only 1 per cent, did
so. The former result corresponds pretty closely to what nitric acid
revealed in my own series of young men following civil employments,
but is considerably below the results brought out by Dr Munro in
his American statistics. The second series gives a much lower
percentage.

It is interesting to compare the results obtained in my other cate-
gories with those given by other observers. Leube found, among
German soldiers examined during the forenoon and after marching,
16 per cent, albuminuric. Van FToorden, at the same time of day,
found it in 35 per cent. Capitan found it among French soldiers
44*9 per cent., and I have found it among the Highlanders (includ-
ing recruits) in 37 ‘55 per cent.

1887.] Prof. G. Stewart on Albumen from Kidneys. 245

The Craiglockhart children gave a result less favourable than that
obtained by Leroux, for while he found albuminuria in only 5*76
per cent., I found it in 17 *5.

I am not aware of the publication of any series of observations
on old men corresponding to my Craiglockhart series.

In answer, then, to our second question, it appears that a trace of
albumen may be discovered by delicate tests in the urine of nearly
1 in 3 of the male population, if it be examined during the active
period of the forenoon, an hour or two after breakfast, although
before breakfast the proportion would be considerably smaller.

The third question is as to the effects produced by diet, exercise,
severe exertion, and cold bathing upon the discharge of albumen.

In order to determine the effects of diet, I obtained specimens of
the urine of 32 soldiers before and after breakfast, and found that
of these 15, or 5°625 per cent., had albuminuria on rising in the
morning; while 13, or 40 *52 5 per cent., showed it after the morning
meal. Thus, 8 who had not had albuminuria in the morning
acquired it after breakfast.

Among the 40 old men examined in Craiglockhart Poorhouse we
find that 15, or 37*5 per cent., showed albuminuria before break-
fast ; while after that meal 27, or 67°5 per cent., showed it. Thus
12 who had not had albuminuria on rising in the morning acquired
it after breakfast.

Among the 40 children we find that 5, or 12*5 per cent., showed
it before breakfast, and 17, or 17*5 per cent., showed it after break-
fast. Thus 2 who had not albuminuria on rising in the morning
acquired it after breakfast. Among 48 boys, inmates of the Orphan
Hospital, we found that before breakfast albumen was present in 7,
or 14*6 per cent. ; after breakfast, in 10, or 20*83 per cent.
Taking the four groups together, we have a series of 160 cases
examined before and after breakfast, and we find that of these, 32,
or 20 per cent., discharged albumen before breakfast; while 57,
or 30*5 per cent., showed it afterwards.

I have put these various results in a tabular form, which shows
very clearly that at all ages, and in the various conditions investi-
gated, the taking of breakfast is followed by an increased frequency
of albuminuria, but that the increase is greatest among the old men
and soldiers.

246 Proceedings of Royal Society of Edinburgh. [june 6,

Table IV. — Showing the Influence of Breakfast on the Discharge of
Albumen from the Kidneys.

No.

Before Breakfast.

After Breakfast.

No.

Per cent.

No.

Per cent.

Soldiers,

32

5

15-625

13

40-625

Old Men,

40

15

37-5

27

67-5

Children

40

5

12-5

7

17-5

(Craiglockhart),

Children

43

7

14-6

10

20-83

(Orphan Hospital)

Total,

160

32

20

57

35-6

In connection with this it is worthy of notice that in most of the
cases of after-breakfast albuminuria the quantity of albumen was
too minute to be shown by the cold nitric acid test, and also that
when it was present before, it was generally increased in amount
after the meal. But, on the other hand, there were two cases
among the children in which breakfast was followed by the disap-
pearance of albuminuria which had been present on rising. I have
met with facts corresponding to this in some of my albuminuric
patients. A gentleman who is at present under my care shows
copious albumen in the morning urine, and a comparatively small
quantity after breakfast.

Contrary to what one might expect, considering what is usually
taken for breakfast, as compared with what is taken for the other meals,
it appears that breakfast more frequently induces albuminuria, or an
increase of albumen, than the other meals. As to the explanation
of the influence of food in this respect, it is difficult to speak posi-
tively. I shall not at present seek to determine whether an altera-
tion of the blood, or the blood pressure, or of the vascular walls, or
epithelial structures, is at fault. It may also be remarked that the
mucin in the urine also increases after food, although not to the
same extent.

The next point investigated was the effect of muscular exercise
on albuminuria. It appeared desirable to distinguish between the
effects of moderate exercise and of severe and prolonged exertion.
Observations were therefore made upon soldiers before and after
their weekly march of seven to ten miles, and before and after the
fatigue duty of coal-carrying.

1887.] Prof. G. Stewart on Albumen from Kidneys. 247

Of 63 soldiers about to start for their weekly march of from seven
to ten miles in heavy marching order, 18, or 29 per cent., were found
to have albumen in their urine. After their march the urines of
58 of these men were examined, and 11, or 19 per cent., showed
albumen. The march out, therefore, distinctly diminished the
albuminuria. But as the march is taken in the forenoon, it occurred
to me that some of those who got rid of their tendency during the
march might have had a temporary albuminuria induced by break-
fast. I therefore examined the urine of 32 soldiers before breakfast,
after breakfast, and on their return from the march. It was found
that before breakfast albumen was present in 5, or 15 ‘6 23 per
cent.; after breakfast in 13, or 40625 per cent.; and after the
march in 9, or 28425 per cent. It was noticed also that in several
cases the amount of albumen diminished, although it did not wholly
disappear. It was thus shown that in a considerable proportion of
cases the march removed the dietetic albuminuria, and other obser-
vations which I have made justify the conclusion that the march
out exerts a favourable influence. It must, however, be observed
that in some cases the march induced albuminuria. In one of the
nine cases it occurred only after the march, the urine having been
quite free from albumen on rising and after breakfast, and in at least
one other case the amount of albumen was distinctly less after
breakfast than it was after the march. It is thus clear that the
effort of marching is sufficient to induce the symptom in some
people.

But while marching proved on the whole beneficial, the fatigue
duty of coal-carrying brought out a very different result. This work,
as carried on in Edinburgh Castle, obliges two men to carry a bucket
containing 80 lbs. of coal for several hundred feet up a rather steep
incline, and then up barrack stairs to the different floors. Each pair
of soldiers makes six or seven such journeys during the forenoon in
which they are told off to this duty. Of 36 soldiers engaged in
this work we found that 16, or 44 per cent., had albuminuria before
the labour commenced ; while 23, or 64 per cent., had albumen at the
end of it. On another day, when we were able to get the urine of
17 men engaged in this coal-carrying, 7 had albuminuria, equal to
a little over 41 per cent., although the observations were made, not
at the end, but in the course of their work.

248 Proceedings of Royal Society of Edinburgh. [june 6,

I have put in tabular form the facts elicited in this connection.

Table V. — Showing effects of Exercise and of severe Exertion , also of Breakfast

and Exercise.

No. Examined.

Before.

After.

Before.

After.

No.

P.cent.

No.

P.cent

March of 8 miles,

63

58

18

29

11

19

Fatigue duty —

coaling,

36

36

16

44

23

64

Breakfast and

Before]

Ir’kfast

After ’

3r’kfast

\

After !

March.

march,

32

32

5

15-6

13

40-6

9

28-1

From the facts thus given it is shown that violent exertion may
produce albuminuria, while moderate exercise tends rather in many
cases to diminish it. Statements have been made as to the urine of
the performers of pedestrian feats which confirm this experience.
Weston’s urine is said to have contained both albumen and tubecasts
at the end of one of his prolonged walks.

A very interesting observation has been made by Dr W. A.
Stirling, in a thesis sent in for the M.D. degree this year, and
he has permitted me to make use of it on this occasion. He
found in the course of an investigation as to the incidence of albu-
minuria in 369 boys, who are being educated in the training-ship at
Grays, Essex, that the boys who played wind instruments in the
band exhibited albuminuria in a much larger proportion than the
others. Thus, while, out of 64 boys so employed, 38, or 59 *4 per
cent., had albuminuria, out of 305 boys, otherwise under like con-
ditions, but not in the band, only 39, or 12 '8 per cent., showed the
symptoms.

These results may, as he remarks, be very naturally referred to
altered blood pressure due to habitual use of musical instruments.

With the view of testing this, I examined 24 boys who play
wind instruments in the band of the Orphan Hospital, and 24
boys in that Institution who are otherwise similarly placed, except
in not being members of the band. It appears, so far as their
numbers serve us for the purpose, that albuminuria is more fre-
quent among the band boys than among the others, but that there
is a diminution rather than increase at the end of an hour’s practice

1887.] Prof. G. Stewart on Albumen from Kidneys.

249

with the instruments. I have put the facts in tabular form, and
it is clear that no such discrepancy exists as in the training-ship
boys ; but still the statistics lend a certain measure of support to
Dr Stirling’s observations.

Table VI. — Showing incidence of Albuminuria in 2 If. Wind-Instrument
Band Boys and 24 other Boys ( Orphan Hospital).

No.

Before Breakfast.

After Breakfast.

After Playing.

hno3

Pic. A.

Total.

P.C.

HNOg

Pic. A.

Total.

P.C.

hno3

Pic. A.

Total.

P.C.

Band Boys,

24

2

3

5

20-8

2

4

6

25-0

1

2

3

12-5

Other Boys,

24

0

2

2

8-3

1

3

4

16-6

Some years ago Dr George Johnson of London drew attention to
the fact that albuminuria is sometimes induced by cold bathing. In
order to get some information upon this question, I got the urine of
21 boys passed on rising at 6 a.m., and that passed at 8 after a cold
plunge bath. It was found that when, before bathing, 4, or 19 ‘05
per cent., showed albumen, after it 5, or 23 -8 per cent., showed it. •
Among the boys so examined only a small number showed
albuminuria, and the amount of albumen was slight, for nitric acid
failed to detect it, but there was an increase both in the number
of cases affected and in the intensity of the condition, although
the effect was not very pronounced.

In Table VII. I have stated the results of these observations.
Table VII. — Showing effect of Cold Bathing on 21 Boys ( Orphan Hospital).

Before Bath (6 a.m.).

After Bath (8 a.m.).

With

HNOg.

Only
with
Pic. A.

Total.

Per cent.

With

HNOg.

Only
with
Pic. A.

Total.

Per cent.

0

4

4

19-05

0

5

5

23”08

I have not been able as yet to test the effects of mental excitement
or emotion upon any considerable number of healthy individuals, but
no doubt an investigation in suitable quarters might elicit interest-
ing results. This is indicated by the occurrence of such cases as
those recorded by Furbringer, of a medical man who never showed

250 Proceedings of Royal Society of Edinburgh. [june 6,

albuminuria as the result of long and fatiguing work, nor from the
use of a diet rich in albumen, nor from the free use of alcohol,
but constantly showed it in large amount when exposed to mental
excitement with depression.

The remarks which I have made apply only to the ordinary forms
of albumen and serum-albumen. With regard to the occurrence of
peptones, we discovered them in only 3 out of the whole series
of 771 specimens which were carefully examined in the course of
the investigations.

From the facts recorded, we seem entitled to conclude —

1. That albuminuria is much more common among presumably
healthy people than was formerly supposed, being demonstrable by
delicate tests in nearly one-third of those examined.

2. That there is no sufficient proof that albumen is normally
discharged from the human kidneys.

3. That the frequency of albuminuria increases as life advances,
being rare in children and young adults, and common in men at or
above sixty years of age.

4. That it is more common among those whose occupations in-
volve arduous bodily exercise than among those who have easy work.

5. That albuminuria frequently follows the taking of food,
especially of breakfast.

6. That moderate muscular effort rather diminishes than increases
albuminuria, except in rare cases.

7. That violent or prolonged exertion often induces albuminuria.

8. That cold bathing produces or increases it in some individuals.

9. That the existence of albuminuria is not of itself a sufficient
ground for the rejection of a proposal for life insurance.

10. That the discharge of peptones from the kidneys is exceed-
ingly rare in the presumably healthy.

4. The Salinity and Temperature of the Moray Firth, and
the Firths of Inverness, Cromarty, and Dornoch. By
Hugh Bobert Mill, D.Sc., Scottish Marine Station.
(Plate VIII.)

The recently published results obtained by the German gun-boat
“Drache” in the North Sea enabled a very good chart to be compiled

1887.] Dr H. R. Mill on Salinity and Temperature of Firths. 251

of the distribution of salinity* in the central, southern, and eastern
parts of that sea. JSTo observations had been made in the great bight
known as the Moray Rirtli, and this part of the map was accordingly
left blank. The general distribution of salinity is as follows : —
Water with more than 3-55 per cent, of salts in solution comes in
from the Atlantic between the Orkney and Shetland Islands * the
centre of the North Sea is filled with water with over 3 ‘50 per cent,
of dissolved salts ; while to the south and all round the coasts fresher
water is found. The line of 3 ‘50 salinity was found to approach
the Scottish coast at Berwick and again at Peterhead, but between
these it swept out in a wide curve to the north-east. There were
no available data by which the German Hydrographic Office could
determine whether the Moray Firth was in the area of water over
or under 3 '50 per cent, salinity.

Dr Macadam in 1866 made some observations in the Moray Firth ;
Dr J. Gibson in 1883 made a number on behalf of the Fishery
Board for Scotland;! and in 1885 Mr Ritchie and I examined that
part of the region about the mouth of the Spey. J In the discussion
which follows these results are considered, but most of the data used
are derived from the cruise of the “ Garland” in August 1886.

Dr Gibson and I proposed to the Fishery Board, in June 1886,
that they should extend and repeat the physical observations which
had been already made in the Moray Firth and the smaller sea-inlets
in connection with it. To this the Board acceded, and we drew up
a plan for carrying on the work. The steam-tender “ Garland” was
only available for three weeks from August 1st ; Dr Gibson was
unable to take part in the expedition, but I was ably assisted by Mr
F. Maitland Gibson, and, for part of the time, by Mr T. Morton
Ritchie, B.Sc.

The methods of working were similar to those which I have pre-
viously employed and frequently described to the Society. Negretti
and Zambra thermometers were used, fitted in the Scottish frame,
and the water-bottle described to the Royal Society in January 1886 §

* Ergebnisse der Untersiiclmngsfahrten S.M. Knbt. “ I)r ache ” in der Nor dsee
in deii Sommern 1881, 1882, und 1884. Berlin, 1886. Abstract in Scottish
Geographical Magazine , August 1887, iii. pp. 385-398.

t Fourth Annual Report, Fishery Board for Scotland, App. F, No. 12.

+ Proc. Roy. Soc. Edin ., 1885, xiii. pp. 460-485.

§ Proc. Roy. Soc. Edin., 1886, xiii. p. 545.

252 Proceedings of Royal Society of Edinburgh. [june 6,

was at first employed. This was afterwards modified and greatly im-
proved in one particular. The three locking springs clasping the
base-plate in the original instrument were removed, and their place
taken by two similar springs, emerging through windows in an outer
tube and clamping the bottle by pressing on the top of the collar of
the slip-cylinder after it had closed.

An exact copy of all the individual observations made during th
trip of August 1886 is given in the Eeport to the Fishery Board
presented by Dr Gibson and me. The present paper is merely in-
tended to summarise the results, and point out some of the more
general bearings of these observations.

The Moray Firth. — This great bay possesses a very interesting
configuration. The northern shore (Caithness) is rocky and steep ;
depth increases rapidly to over 20 fathoms, and then remains as a
broad submarine plateau, extending southward and eastward at an
average distance of 25 fathoms beneath the surface. The western
shore is shallow, the slope for some miles from land being slight ;
and the same remark applies to the western half of the south coast
(Morayshire) ; the eastern half of this coast (Aberdeenshire) is again
rocky, with deeper water close to. A tongue-shaped depression runs
in from the north-east along the southern portion of the firth, forming
a deep furrow in the plateau-like sea-bottom. This has a maximum
depth of 100 fathoms in a hole 10 miles north of Troup Head, and
brings water over 30 fathoms deep as a very narrow trough a con-
siderable distance west of Burghead, and close to the south shore.

Isolated observations at various times had shown that the salinity
of the great mass of water in the Moray Firth approached 3 '50 per
cent, very nearly. The density (at 15° *5 6 C.) corresponding to this
proportion of dissolved salts is 1*0260, and the density usually
found for both bottom and surface water by Dr Gibson in 1883, and
by me in 1886, was from 1*0257 to 1*0259. The agreement of all
the observations taken at intervals during three years is remarkable,
and indicates that beyond the distance of a few miles from land the
influence of the variations of weather (rainfall particularly), from one
season to another, on the salinity is very insignificant. Temperature
observations naturally do not agree so closely, for one season may
easily be a few weeks in advance of another, or behind it ; and the
fact that the temperature is a few degrees higher or lower at any

1887.] Dr H. R. Mill on Salinity and Temperature of Firths. 253

given date than it was at the same date in some other year is of
trifling importance. What must be compared, with regard to varia-
tions of temperature at one place, is not the absolute degree of
warmth at a particular depth, but the vertical distribution of warmth
and the annual changes of this in form and amount.

The following statement of the conditions of a section, from the
Ord of Caithness to Burghead on August 19th, will illustrate the
distribution of salinity in the open firth at that date. Station I.
was about 1 J miles south-east of the needle of Ord, the others each
10 miles farther south, the last being close to Burghead.

Table I.

Station.

I.

II.

III.

IY.

Density of surface water at 15°‘56 C., 1 ’02588

1-02581

1-02585

1-02510

,, bottom ,,

,, 1-02585

1-02587

1-02585

1-02573

Depth in fathoms,

19

26

26

10

State of tide,

. . 4| hrs. fid.

\ hr. eh.

2f hrs. eb.

4 hrs. eb.

This shows a very slight freshening towards the southern shore.
The increase of salinity seaward was shown, by many isolated ob-
servations, to be gradual but steady, although no regular east-and-
west section was made. The temperature from north to south, on
August 19, was as follows, the figures given being corrected to read-
ings of the Kew standard : —

Table II.

I.

II.

III.

IY.

Hour,

• e

13. 45

15.10

17.15

18.30

Air temp., .

.

55-2

57-0

55-5

58-0

Temp, of sea,

0 fthm.,

55-0

55-3

54-3

56-3

9 9

1 „

—

55-2

—

56-2

9 9

2 „

54-7

—

54-2

56-2

9 9

3 „

54-3

54-2

—

—

99

5 ? 5

53-5

53-8

53-5

54-7

9 9

6 „

—

53-8

— -

—

9 9

7 „

51-9

53-2

—

—

9 9

8 „

—

53-1

—

—

9 9

9 „

—

51-4

—

53-2

9 9

10 „

—

—

52-3

9 9

12 „

—

51-2

—

9 9

15 „

—

51 T

—

9 9

18 „

51*2

—

—

9 9

25 „

. . .

51-0

50-5

254 Proceedings of Royal Society of Edinburgh. [june 6,

An observation made off Dunbeath Castle (further north than -the
Orel), in 10 fathoms, gave temperature of 52° ’5 at the surface, and
52o,0 at bottom. Excepting this sounding, the observations of
temperature showed a warm layer falling from 55° or more at the
surface to 52° at 6 fathoms on the Caithness coast, and at 12 fathoms
on the Morayshire side. The minimum bottom temperature was
50° '5 just on the verge of the deep trough off Burghead. Plate
VIII., fig. 4, shows graphically the distribution in this section of sur-
face and bottom density, and of temperature at surface, 5 fathoms, 10
fathoms, and bottom. In the depression off Troup Head, at a depth
of 50 fathoms, an observation on August 23rd gave a temperature
of 54°'8 on the surface and 50° '4 on the bottom. The lowest tem-
perature of the trip was found on August 10, at the bottom of the
depression off Covesea Skerries, in 33 fathoms, the thermometer
reading being 49°’5. A section made from Fort George to this point
(30 miles) showed a perfectly horizontal and parallel arrangement of
the isotherms of 50°*5, 51°, 51° ‘5, 52° and 52°‘5, contrasting with the
dip to southward in the north-and-south section.

During the month of August the sea temperature on the west
coast of Scotland was 52° *5, from surface to bottom, off the Mull of
Cantyre, and in the Arran Basin, 53° or 54° on the surface, falling
to 47° *5 or 48° at 30 fathoms. The Moray Firth thus appears to
have been warmer than the western waters during this period.

The observations made in 1883, although not very numerous,
are sufficient to show that the bottom water was practically of the
same salinity then as in 1886; while the surface water near the
entrance of the Inverness Firth was much fresher at the earlier
date. This is quite as might be expected, since the summer of
1886 was exceptionally dry in the north-east of Scotland, and the
rivers and streams were unusually low.

Taking into consideration the facts that have been ascertained,
we conclude that the water of the Moray Firth is the saltest which
can be found near land in the North Sea, except on the bottom of
the Norwegian Gully, and possibly in the neighbourhood of the
Strait of Dover, where no observations have been made. The
influence of estuaries and rivers entering the Moray Firth appears
to effect a local and very superficial freshening.

The data available for the three tributary firths — of Inverness,

1887.] Dr H. R. Mill on Salinity and Temperature of Firths. 255

Cromarty, and Dornoch — are practically only those obtained in
1886, and the time over which their collection extended was much
too short to make them of more than comparative value. Import-
ant series of hourly observations, extending over the greater part of
a tide, were made in each firth, and to these more particular atten
tion may he paid, as they confirm and extend the results obtained
on the Spey in 1885, and on the estuary of the Forth at Kincardine
in May 1886.*

Inverness Firth. — This inlet is narrow and full of sand-hanks,
which divide it up into tortuous channels of very slight depth.
Near Fort George the water is a little over 10 fathoms deep, hut
further up 5 fathoms is about the average ; and the Beauly Basin
in which the firth terminates is much shallower. During the days
on which observations were made, the temperature of water in the
Inverness Firth was about 56° on the surface. The bottom tem-
perature was nearly the same in the shallower part of the firth, but
it fell in a very marked manner towards the sea, being 52°*7 at the
bottom off Fort George, and 51°*5 off Nairn. The average density
of the water at stations about 5 miles apart was as follows, but
the individual readings varied greatly with the tidal phase : —

Table III.

Place. Kessock.

Surface density at 1 5° *56 C., 1*01870
Bottom ,, ,, 1*01950

Number of cases, . . 16

Avocli.

1*02161

1*02281

6

Fort George. Off Nairn.
1*02269 1*02465

1*02397 1*02547

4 2

This shows a progressive increase of salinity seawards, and a
distinctly greater salinity for bottom water at all points. The
diagram, PI. VIII. fig. 5, represents graphically the distribution of
wmter density and temperature at surface and bottom, from Kessock,
past Fort George, out into the Moray Firth, to a position off Covesea
Skerries. Compared with the Firth of Forth, the rate of increase
of salinity is very rapid, and the difference between surface and
bottom more marked in the seaward reaches of the firth.

Numerous observations were made in the anchorage at Kessock
Roads, at various depths. The data for surface and bottom only
need be given here, but these are of considerable importance. The

* Proc. Roy. Soc. Edin., 1886, xiii. pp. 790-799.

VOL. XIV. 3/11/87

R

256 Proceedings of Royal Society of Edinburgh. [june 6,

relations will be made more apparent by the graphic treatment
adopted in PI. VIII. fig. 2. The density given is that by a small
hydrometer, and is not corrected for temperature, except in the
case of the observation on the 6th, at 15h45. The force of the
wind is expressed in degrees of Beaufort’s scale. The weather
throughout this set of observations was clear and dry.

Table IV. — Observations in Kessock Roads , off Clachnaharry.

Date.

Hour.

Wind.

Tide.

Depth.

Temperature.

Density.

Air.

Surface.

Bottom.

Surface.

Bottom.

Aug. 6

15.45

WSW.,5

q h. fid.

fm.

6*

o

56-0

55-9

1-02028

1-02041

5’

17.10

W., 4

H. W.

6*

67-0

57-3

55-9

1-0202

1-0200

55

18.5

...

1 h. eb.

62-5

57 T

56 T

1 -0198

1-0210

55

19.10

W., 2

2 „

60-4

57-0

56-7

1-0190

1-0195

55

20.10

W., 2

3 „

6

58-0

57-3

56-4

1-0190

1-0195

55

21.10

W., 1

4 „

°2

...

57-0

56-8

1-0190

1-0195

55

22.0

0

5 „

5

58-0

57-4

56-3

1-0177

1 -0185

55

23.0

...

6 „

4§

57-5

561

1-0178

1-0190

Aug. 7

0.0

...

| h. fid.

5

58 T

57-3

56-4

1-0180

1-0190

5 5

1.0

...

2 „

...

57-2

56-2

1-0180

1-0200

55

5.30

...

H. W.

64

...

...

1-0215

1-0210

This corresponds with results previously obtained at Kincardine,
and shows most of the features more prominently brought out by
observations in the firths of Cromarty and Dornoch.

Cromarty Firth. — The straight coast line running south-west-
ward from Tarbat Kess, and bordered by a band of water under
10 fathoms in depth, is broken by the abrupt hills which define
the entrance to the Cromarty Firth. Between them there is a
depth of over 25 fathoms; and a clearly “cut channel, with steeply
sloping sides, and more than 10 fathoms deep, runs straight west
through the wide shallows on either side to Alness Point, 10 miles
from the Sutors. The depth diminishes rapidly above Alness, and
the channel is much choked by sandbanks. Strong tidal streams

1887.] Dr H. R. Mill on Salinity and Temperature of Firths. 257

run in this firth, and considerable variations were observed in the
salinity of the water at high and at low tide. Temperature was
found to fall uniformly towards the sea, the average being 550,5
at Alness, and 5 4° *5 at the Sutors, on the surface ; while on the
bottom it was 54°*5 and 53°-8 respectively.

Table V, — Average Density of Water in Cromarty Firtli.

Position. Alness. Invergordon. Bet. Sut’rs. 2 m.out.Sut’rs.

Surface density at 15° *56 C., 1 ‘02308 1 ‘02331 1 ‘02465 1 ‘02515

Bottom „ ,, 1-02405 1 ‘02445 1 ‘02530 1 ‘02546

Number of cases, 12 7 5 4

This shows a variation of density almost exactly the same for
the 15 miles seaward from Alness as for the 15 miles seaward from
Queensferry in the Firth of Forth. The identity extends to
bottom as well as to surface water; but it must be remembered
that the data compared are not really comparable, since they are
on one side, the salinity of the Cromarty Firth in the middle of
August 1886, and on the other the mean salinity of the Firth of
Forth determined by numerous observations in 1884, 1885, and
1886. Also, it must be pointed out that the salinity two miles off
the Sutors of Cromarty is about equal to that at the Isle of May ;
while five miles out in the Moray Firth, a salinity is found which,
according to the German charts, is not to be met with nearer
than 30 or 40 miles east of the Isle of May.

The serial tidal observations at Alness are of considerable in-
terest. There were two sets of these. The first on 5th August,
for six hours, during the last three hours of flood-tide and the first
three of ebb, brought out the exact equivalence of the curves of
temperature and salinity, so that, substituting “ diminution of
salinity ” for “ increase of temperature,” any statement with regard
to tidal influence on temperature would be true of salinity also.
This series was taken rather near the mouth of the Alness river,
and sudden rushes of warm fresh water produced variations on the
surface which were not found at any depth beneath it. The
second series was taken from llb0 to 20h0 on August 12th,
and as low water was at 16h0 it comprised five hours of ebb and
four of flood. The resulting figures are given in Table VI., and
represented graphically in PI. VIII. fig. 3. The densities of the

258 Proceedings of Royal Society of Edinburgh. [june 6,

Table were all determined by the delicate hydrometer, and are
reduced to their value at 1 5°*56 C. Weather was dull, with some
showers, until 13h0, thereafter bright and dry.

Table YI. — Observations off Alness Point , Cromarty Firth.

Date.

Hour.

Wind.

Tide.

Depth.

Temperature.

Density.

Air.

Surface.

Bottom.

Surface.

Bottom.

fm.

O

O

O

Aug. 12

llh0

WSW.,2

1^ h. eb.

9

54-4

53-8

1-02431

1-02480

> 5

12.0

WSW.,2

Ol

■“2 55

9

56-2

55-3

53-8

1-02357

1-02482

??

13.0

0

°2 55

r-W

OO

57-8

55-3

54-0

1-02373

1-02470

14.0

0

41

*2 55

8

...

55*3

54-3

1-02370

1-02422

5?

15.0

0

51

55

6

58-0

55-4

(

55-2

1-02319

1-02369

16.0

0

L. W.

64

58 7

56T

55-8

1-02224

1-02344

? )

17.0

E., 2

1 h.fld.

64

58-3

56-4

55-2

1-02162

1-02336

> 5

18.0

E.,2

2 „

6|

56-0

561

55-2

1-02290

1-02391

? J

19.0

0

3 „

7

56-3

55*7

55-0

1-02317

1-02411

> 5

20.0

0

4 „

7

53-9

54-9

54*0

1-02396

1-02472

Note. — The position was changed a few yards nearer the north shore between
the 14h0 and 15h0 observations.

This series also shows the temperature and salinity to be in
close association. Hence, considering either the one quantity or
the other, the relative movements and gradual mixture or separa-
tion of the warmer and fresher upland water and the colder and
salter sea water may be traced out. The salinity at the bottom
remained constant for about three hours after high water, then
gradually diminished until low water, and again gradually in-
creased. Surface salinity remained practically unchanged, and
very near that of the bottom water, until two hours before low
tide, when it began to diminish, and came to a minimum (the
surface temperature coming to a maximum) one hour after low
tide. This marked the period of greatest difference between
surface and bottom salinity; that at the surface proceeded to
increase, presumably until high water. These observations show
that flood-tide sets in first at the bottom ; that the salt water first

1887.] Dr H. R. Mill on Salinity and Temperature of Firths. 259

appears there, and does not influence the surface for a considerable
time.

Dornoch Firth. — This firth is shallower than that of Inverness,
and in addition to its being shut off, like the Firth of Tay, by a
bar at its mouth, the channels inside are narrow, tortuous, ex-
tremely shallow, and constantly changing on account of the sand-
banks. The “ Garland ” navigated this firth under the charge of a
pilot, and only two days were spent in it. It is impossible to say
much regarding the variation of salinity with position, but this
appeared to be more rapid than in the other inlets examined. At
the Dune of Creich the density of the surface water was 1*01750,
and that of bottom wTater 1*01919 at high tide; off Dornoch,
inside the bar, the surface had a density of 1*02395, and the
bottom 1*02517 at \\ hours ebb, the distance from the Dune
being 9 miles. A few miles beyond the bar a density of
1*02588 reigns from surface to bottom. Temperature was high
in the Dornoch Firth (over 57°), but rapidly fell as the sea was
approached.

A very complete set of observations was made off Ardjachie
Point during the last 4J hours of ebb tide and the whole suc-
ceeding flood, hourly readings being made for twelve consecutive
hours. The data are given in Table VII., and the corresponding
curves in PI. VIII. fig. 1.

This is the most interesting record we obtained of the tidal move-
ments of salt and brackish water past a given point. From 4J to
1J hours before low tide both surface and bottom water grew
gradually fresher, while maintaining nearly the same difference in
salinity, i.e., the whole mass of water was moving seawards as a
uniform current. At \\ hours before low water the rate of
decrease of salinity in the bottom water diminished, that in the
surface water increased, and the difference between the two grew
greater. The second observation after low water showed a marked
increase in the bottom salinity, while the surface was at its mini-
mum ; this shows that the current on the bottom was slowed and
reversed before the outward surface current was affected. During
the next hour the surface water grew salter more rapidly, and then
for two hours gained on the bottom water ; so that 4|- hours after
low tide the water in the channel was nearly homogeneous, as far

260 Proceedings of Royal Society of Edinburgh. [june 6,

Table YII. — Observations in Ardjachie Roads , Dornoch Firth.

Date.

Hour.

Wind.

Tide.

Depth.

Temperature.

Density.

Air.

Surface.

Bottom.

Surface.

Bottom.

Aug. 17

15h 0

N.W., 4

2h. ebb.

fm.

5S

56-5

56°8

55 ‘9

1-02271

1-02339

55

16.0

N.W., 3

3 „

5

...

56-9

56-0

1-02116

1-02152

55

17.0

N.W., 2

4 „

5

...

56-8

56-9

1-02100

1-02137

55

18.0

N.W., 2

5 „

5

57-0

56*8

1-02039

1-02070

55

19.0

0

6 „

H

57-2

56-9

1-01867

1-02025

55

20.0

0

i h. fid.

3f

...

56-9

57-0

1-01817

1-01965

55

21.0

0

11 »

4

54-7

57 T

57-2

1-01815

1-02011

55

22.0

0

2i „

H

56-6

56-7

1-02054

1-02118

55

23.0

0

H „

5

53-0

56-4

56-3

1-02118

1-02184

Aug. 18

0.0

0

4| „

H

53-0

56-4

56-3

1-02207

1-02227

55

1.0

0

P)1

55

5S

52-5

56-3

55-7

1-02207

1-02408

55

2.0

0

H. W.

6

50*3

56-2

55-3

1-02189

1-02472

as regards vertical distribution of salinity. The following reading
showed a new condition altogether’; the bottom had increased in
salinity very greatly, and continued to do so until high water ; the
surface, on the other hand, remained constant, and even showed a
slight decrease. This means that after the water had been
thoroughly mixed, sea- water of greater density began to push its
way along the bottom, and the surface current of brackish water
being no longer driven up stream by a wall of uniform salinity,
resumed its downward course very slowly, and passed over the
salter water without mixing with it : in fact, ebb had begun on
the surface, while flood-tide continued down below. It thus
appears that, so far as the tidal movement of water is concerned,
the bottom of the channel in an estuary is before the surface in
phase.

The question of tidal currents in estuaries is a very important
one ; but for its thorough investigation it requires the simultaneous
■work of several assistants, and a large enough staff to carry on
uninterrupted observations for several successive tides. This I

1887.] Dr H. R. Mill on Salinity and Temperature of Firths. 261

have not been able to obtain hitherto ; but in my work on the
Spey with Mr Ritchie, on the Forth with Mr Morrison, and on the
Dornoch Firth with Mr F. M. Gibson, I have fully tested the
methods of studying the problem by means of observations of
salinity and temperature. Salinity determinations by means of a
very delicate hydrometer are certainly best in all cases ; but in
many, especially at certain periods of the year, the thermometer
gives an equally exact picture of the state of things, with far less
trouble and the cost of much less time. The collection of one
sample of water from a given depth, the bottling of it, determining
the density, calculating and reducing the result, occupies by my
method nearly 25 minutes, and cannot be finished on the spot
where observations are being made. No less-exact determination
of density is of permanent value, and it is obvious that the results
obtained cannot be ascertained in time to be of service in directing
the course of the observations. But the temperature can be found
simultaneously at three or more different depths, and the correct
result arrived at in rather less than five minutes ; hence, any sudden
change or apparent anomaly may be detected and investigated at
once. The combination of both methods is certainly best, but
wherever the river water is a few degrees warmer or colder than
that of the sea, I should emphatically recommend the use of the
thermometer as the chief instrument for investigating the flow of
the tidal currents.

No reference has been made in the foregoing to Dr Gibson’s
analysis of water samples collected in the region under consideration
in 1883, and discussed in his Fishery Board Report. Our joint plan
of work for 1886 comprised the collection of samples for chemical
analysis and gravimetric determination of density. About 50
specimens of water were collected, and the analysis is now pro-
ceeding, under Dr Gibson’s supervision.

I have to thank Dr Gibson for many suggestions in carrying out
the part of the joint work in which I am more immediately con-
cerned, and for his permission to publish separately the resume of
the observational results obtained.

262

Proceedings of Eoyal Society of Edinburgh. [june 6,

5. On the Presence of Bacteria in the Lymph, &c., of Living
Pish and other Vertebrates. By J. C. Ewart, M.D.,
Begins Professor of Natural History, University of
Edinburgh.

Baring the last ten years numerous investigations have been
made to ascertain whether ordinary ( i.e ., non-specific) bacteria exist
in the tissues of apparently healthy, living animals. As a result of
these inquiries, it has been clearly shown that while there is no
evidence of the existence of bacteria, under ordinary circumstances,
in the blood of the higher Vertebrata, there is abundance of evidence
of their presence in the blood of some fishes.

The existence of bacteria in fish has been specially studied by
MM. Olivier and Bichet. In a communication on the Microbes
of Marine Pish,* Olivier and Bichet point out that bacteria exist
(sometimes in great numbers) during life in the peritoneal fluid,
lymph, and blood of the whiting, red mullet, sand-eel, wrasse, dab,
and several other fish. Of the fish examined, the authors state that
(with the exception of the conger and the dog-fish) all the tissues
contained numerous bacteria, — long and short bacilli being espe-
cially abundant. By cultivations it was shown that bacteria also
existed in the tissues of both the conger and dog-fish. From the
observations made, Olivier and Bichet conclude that bacteria occur
so constantly in fish that they must be almost considered as
normal, and, further, that they are not putrefactive bacteria, because
when they rapidly multiply after the death of their host there is no
evidence of putrefaction.

In two subsequent papers (one dated 9th July and the other 17th
September 1883) the original observations are confirmed, and it is
further pointed out that bacteria are especially numerous in the
peritoneal cavity, and less numerous in the pericardial sinus, the
cerebro-spinal canal, and the blood of the heart, and that under
certain conditions the bacilli are mobile, and capable of being cul-
tivated.

I have recently had the opportunity of examining the blood, &c.,
of a number of both marine and fresh-water fishes, and I am able

* Compte Rendu , tome xcvi., Fevrier, 1883.

1887.] Prof. C. Ewart on Bacteria in Lymph, &c., of Fish. 263

to confirm to a certain extent Olivier and Richet’s observations.
Although I had often examined microscopically the blood and
tissues of fish, it was not until recently, when at work in the Oxford
Physiological Laboratory, that I was convinced that bacteria are
often present in immense numbers in the peritoneal fluid, and in
smaller numbers in the blood of apparently healthy fish.

I first noticed bacteria in the blood of a roach ( Leuciscus rutilus).
This roach, for some hours before it was taken from the water, had
been occasionally swimming on its side at the surface, — an indica-
tion that it was in an exhausted condition. Immediately after
the fish was killed, a drop of blood taken from the heart by a
sterilised pipette (with all the necessary precautions) was found to
contain a considerable number of slender motionless bacilli
measuring from ’003 to *008 mm. in length. On an average four
bacilli were visible in the field at a time with Zeiss’s P objective
and No. 1 eyepiece. The peritoneal fluid, which was next examined,
contained so many bacilli that it was impossible to count them ;
the bacilli were usually lying amongst large granular lymph cells,
and they were longer and more slender than those in the blood.
Similar bacilli were found in the lymphatics, spleen, liver, and
kidney, and they were abundant in the muscles in contact with
the peritoneum ; while very few were found in the muscles under
the skin of the trunk, and still fewer in the muscles of the tail.
The intestine was crowded with similar bacilli to those found in the
body-cavity, and in addition there were a number of large and small
bacteria and micrococci. Bacilli were also found in the walls of the
intestine and in the bile duct.

Believing that there was some relation between the diminished
vitality of the above roach and the numerous bacilli in the tissues,
I examined a considerable number of healthy roach and also other
fresh-water fish, e.g ., trout ( Salmo levenensis), perch ( Perea Jiuvia-
tilis ), carp ( Cyprinus auratus), and eels ( Anguilla vulgaris). In all
the healthy specimens examined, with the exception of the trout,
bacilli were found in the body-cavity. Bacilli were also present in
the blood of the carp, and on one occasion four bacilli were detected
in a drop of blood from what appeared to be a healthy roach. In
some the peritoneal fluid contained numerous bacilli, while in others
only a few wTere visible • generally there was some relation between

264 Proceedings of Royal Society of Edinburgh. [june g,

the number in the body-cavity and the number in the intestine,
and they were most abundant in fish which had lived for some
time in aquaria without food ; but in trout which had been fasting
for at least ten days no bacilli could be observed in the peritoneal
fluid. The carp which had bacilli in their blood had been living
for some months in a small glass aquarium.

The difference between the roach first examined and those
examined subsequently led me to endeavour to ascertain whether a
sudden change of temperature would produce any influence in the
number and distribution of the bacilli. As I anticipated, a rapid
change from a spring to a summer temperature (from 48° to 65° F.)
greatly diminished the vitality of all the fish experimented with,
except the carp. As the fish became more and more exhausted, the
bacilli gradually increased, and when the temperature was raised from
48° F. to 65° F. in two hours, the bacilli of the peritoneal fluid not
only increased in the roach, perch, carp, and eel, but they made
their appearance in considerable numbers in the body-cavity of the
trout, and on one occasion, a number of small bacilli were found in
the blood of a trout. Although the carp seemed to enjoy the rise
of temperature, they were not exempt from the increase of the
bacteria in the blood as well as in the peritoneal fluid. In some
specimens of blood as many as eight short slender bacilli were
visible in the field of the microscope at one time, and the peritoneal
fluid, in some instances, swarmed with long and short bacilli, some
of which were mobile.

In some of the roach, in which no organisms could be detected in
the blood, bacilli were found in the muscles immediately external
to the peritoneal cavity. Further, bacilli were always abundant in
the muscles of roach which had suffered from a sudden rise of
temperature. The above observations were confirmed by cultiva-
tions in gelatine, agar-agar, and infusions of fish muscles. In healthy
active specimens of the roach and perch cultivations were easily
obtained of the peritoneal bacilli, and generally also from the mus-
cular fibres lying near the peritoneum, but in no instance did I
succeed in obtaining cultivations when the blood, or the muscles
from immediately under the skin, were used for infecting the culture-
media.

Of the sea fish examined, I have found bacilli, sometimes long and

1887.] Prof. C. Ewart on Bacteria in Lymph , &c.} of Fish. 265

slender, sometimes short and thick, in the peritoneal fluid and blood
of the whiting ( Gadus merlangus), haddock ( Gadus ceglefnus ), cod
( Gadus morrhua), and herring ( Clupea harengus), and in the peri-
toneal fluid only of the flounder ( Platessa flesus), plaice ( Platessa vul-
garis), and lumpsucker ( Cyclopterus lump us). I have not hitherto
succeeded in demonstrating the existence of bacteria in either the
peritoneal fluid or blood of the skate ( Raia balls), dog-fish ( Acan -
thias vulgaris ), or fishing-frog ( Lopliius piscatorius).

Perhaps the difference in the number and distribution of bacteria
in the sea fish examined by Olivier and Eichet and those I have
recently studied may be accounted for, either by a difference in the
temperature of water from which the fish were taken, or by the fish
having been longer under less favourable conditions in the one case
than in the other.

It is extremely desirable that a continuous series of observations
should be carried on throughout the year, in order to ascertain
whether bacteria are more abundant in summer than they are in
winter, whether they increase or diminish before and during the
spawning period, and whether the bacteria indirectly influence the
migration and distribution of fish — the fish which readily suffer
from an increase of the bacteria in the peritoneal cavity either
remaining in comparatively cold seas or selecting cold currents when
they migrate in search of food, or in obedience to their spawning
instinct.

There can he no doubt that the bacteria enter the body-cavity by
penetrating the walls of the intestine, neither can there he any
doubt that having once established themselves in the peritoneal
fluid they do their utmost to find their way into the blood and
tissues. It may he taken for granted that ordinary bacteria flourish
in the intestinal canal of all vertebrates, and that they assist in
digestion by helping to disintegrate the food particles. Notwith-
standing the presence of active bacteria in the intestinal canal and
the bile and pancreatic ducts, I have failed to discover either
bacilli or micrococci in the body-cavity of either amphibia, reptiles,
birds, or mammals when in a healthy condition. Hence it may be
taken for granted — (1) that in the higher vertebrates under ordinary
circumstances the walls of the intestine form an effective filter or
screen which prevents the passage of the bacteria into the body-

266 Proceedings of Royal Society of Edinburgh. [june 6,

cavity, or (2) that the living cells of the mucous and other layers
so act on the bacteria that they are destroyed before they reach the
body-cavity, or (3) that the cells of the peritoneal fluid effectively
sterilise the bacteria which succeed in entering, or (4) that the
bacteria are destroyed as they pass along the lymphatics towards
the general circulation. The results which follow the injection of
septic and other solutions into the body-cavity of rabbits are con-
sidered at length in the Lumleian Lecture given by Dr Burden
Sanderson in March 1882. From the experiments referred to, it
was made clear that whenever the solution could not be at once ab-
sorbed without any irritation being set up, bacteria rapidly appeared
in the body-cavity, and caused death by producing poisonous bye-
products. In many fish, on the other hand, bacteria not only reach
uninjured the body-cavity, but continue to live there in considerable
numbers without disturbing seriously, if at all, the vital processes
of their host, — in other words, most fish seem capable of tolerating
the presence of one or more kinds of bacteria in the peritoneal fluid,
whilst others can even tolerate considerable numbers in their blood.
It seems, however, that there is a limit to this toleration, for when
the equilibrium is disturbed, when by a change of the surroundings
the vitality of the tissues is diminished, the bacteria rapidly in-
crease, and unless the tissues recover the position they have lost,
the bacteria may directly or indirectly cause death. It has been
suggested by Metsclinikoff and others, that bacteria are kept in
subjection chiefly through the influence of the colourless blood
corpuscles. This may be so in some cases, but it may be taken
for granted that the living tissues as a whole repel the advance of
the destructive organisms, and that some bacteria are arrested and
destroyed by one tissue, while other bacteria are sterilised by another.
A very small swing of the balance may determine whether a given
bacterium will develop or not. This may be inferred from the
behaviour of culture-media, e.g ., whether gelatine will act as a
suitable medium for a given bacterium may depend on its reaction
or on the amount of moisture it contains. In the same way, whether
a given bacterium is able to disintegrate a piece of muscle may
depend on the reaction or rigidity of the muscle.

The distribution of bacilli in the tissues of fish, in which the
conditions were favourable for their growth, is somewhat remark-

1887.] Prof. C. Ewart on Bacteria in Lymph , &c., of Fish. 267

able. The fact that even when the bacteria have extended into
numerous lymphatics, and even into the substance of the muscles
surrounding the body-cavity before they are found in appreciable
numbers in the blood, seem to indicate that the blood is most
active in destroying bacteria. Again, seeing that although, when
bacteria exist in considerable numbers in the inner layers of the
myotomes of the trunk, they are often entirely absent (as proved by
cultivations) from the outer layers of the same myotomes, it may
be inferred that the muscles also have considerable power in pre-
venting the spread of bacteria. Prom the observations made it
appears that bacteria travel easiest along the lymphatic canals and
spaces — the lymph cells being apparently less able to arrest their
progress than the blood corpuscles.

As to the nature of the bacilli found in fish nothing has hitherto
been determined. Olivier and Richet seemed to think they are
neither specific nor putrefactive. At first I thought they were
putrefactive, but not specific. Having made some further experi-
ments, I am now inclined to consider them specific, and not putre-
factive. I was led to believe they were putrefactive, because I
found the characteristic long delicate bacilli of the body-cavity in
immense numbers between the mascular fasciculi of fish in which
putrefaction had already set in. A perch, e.g ., which died having
the body-cavity and the blood well charged with bacilli, was placed
in a chamber with the temperature at 38° C. Fifteen hours afterwards
the mascular bundles, even near the root of the tail, were almost
completely enveloped with bacilli identical to those in the body-
cavity, the bacilli filling up the inter-muscular spaces, and forming
large irregular patches around the bundles. In this fish, twenty-four
hours after death, micrococci and bacteria were extremely few in
number, but before the fish had been forty-eight hours in the warm
chamber the bacilli had largely disappeared, and, in their place,
busily engaged breaking up the mascular fibres, first into fdaments
and then into small short segments, were numerous small
bacteria and micrococci. A trout, which contained bacilli in
nearly all the tissues during life, was placed in a solution of
phenol (5 per cent.) sufficiently long to destroy the organisms in
and around the fish (the intestine having previously been removed)
without reaching those in the muscles, and then transferred into

268 Proceedings of Royal Society of Edinburgh. [june 6,

sterilised water, and kept at a temperature which varied between 50°
and 65° F. Ten days afterwards the muscles had undergone no
marked change ; they were certainly not putrefying, and yet
living bacilli were sufficiently abundant in and around the fibres
composing them. The importance of the bacilli so often found in
fish being non-put ref active and being apparently non-morbific, i.e.,
not being associated with any special disease, will be readily
understood. Were they putrefactive, the preservation of fish as food
would be extremely difficult, and the danger of suffering from the
presence of noxious bye-products in the flesh of fish still greater
than it is at present. There is scarcely any escape from the
conclusion that the bacilli, as long as they survive after the death
of their host, must tend to the formation of bye-products of some
kind. Whether these bye-products have any influence in producing
the characteristic flavour of somewhat high fish it is impossible to
say, but it is extremely probable. In game in a high condition I
have always found bacteria, but even in grouse which had been
kept for three months during winter, very few putrefactive bacteria
were found in the large pectoral muscles.

Further observations will probably show there is a relation
between the facility with which bacteria penetrate into and
survive in the muscles, and what might be called their innate
vitality. In fish, in which relatively the percentage of water in
the muscles is low, and the fatty constituents high, the bacteria
may be less able to flourish than in fish in which the opposite
conditions obtain. Again, there seems to be a relation between
the number of bacteria present in any given fish and the time
at which putrefaction takes place. This, as observed above, is
apparently not necessarily a relation of cause and effect. The
presence of numerous bacteria seems to be an indication of dimin-
ished vitality, an indication that the muscles will fall a ready
prey to putrefactive bacteria as soon as they make their appear-
ance.

Olivier and Richet conclude their second paper as follows : —

“ En resume, nous croyons pouvoir conclure qu’il y a toujours ou
presque toujours des microbes dans les liquides lymphatiques des
poissons, et per consequent dans l’intimate de leurs tissus.”

This conclusion was apparently arrived at chiefly because, by

1887.] Prof. C. Ewart on Bacteria in Lymph, &c., of Fish. 269

means of cultivations, they convinced themselves that bacteria were
always present in the living tissues.

It will be instructive to quote one of their culture experiments.
The second experiment mentioned in the paper of the 9th July is
as follows : —

“Le 19 Juin, on econche avec des ciseaux rougis la queue d’un
gros Squale venant de lam er. On la trempe pendant soixante-dix
secondes dans un bain de paraffine a 218, puis on Texpose quelque
instants a la flamme d’une lampe de maniere a brhler la peripherie.
Le fragment ainsi sterilize quant h sa surface est plonge rapidment
dans un flacon rempli de paraffine liquide. Flacon et paraffine
ont 6te sterilizes au prealable par une temperature de 160° prolongee
pendent deux heures et demie, et Tuair n’a pu y rentrer pendant
le refroidissement qu’a travers un tampon d’ouate. Le flacon
n’est reste librement a l’air que pendant le temps strictement
necessaire pour introduire le poisson.

“ Le 29 Juin la chair musculaire n’a ancune odeur. Elle pre-
sente l’aspect et l’odeur du poisson frais. Elle contient des Bacilles
extremement nombreux, peu mobiles.”

From analogous experiments I have obtained somewhat different
results. For example, trout, roach, and eels which were gutted
immediately after death and introduced for a short time into a 5 per
cent, solution of phenol, and then transferred into sterilised water,
remained unchanged for weeks. When examined, dead bacteria
were found on the surface of the skin and in the peritoneal lining
of the body-cavity, but no living bacteria could be detected in the
muscles, nor did they appear in cultivations into which fragments
of muscle had been introduced. As was anticipated, when the fish
were placed in ordinary water, putrefaction at once set in. The
same results were gained by varying the experiment. A trout was
killed, and a strip of muscle 5 inches in length was removed under
antiseptic precautions from one side, and introduced into a flask of
sterilised water. The flask was kept for five days at a temperature
of 65° F. without any change taking place in the muscular fibres,
or any bacteria making their appearance either in the fibres or
in the water.

Hence in the meantime it may be taken for granted that while
bacteria exist in the tissues of some fish even at a comparatively

270 Proceedings of Boy al Society of Edinburgh. [june 6,

low temperature, tliey are not always, if ever, present in the tissues
of others.

This inquiry was carried on partly in Oxford and partly in
Edinburgh. I am much indebted to Dr Burdon Sanderson,
Waynflete Professor of Physiology in the University of Oxford,
for affording every facility his well-equipped laboratory could offer,
and for valuable advice, during the investigation.

Literature. — The memoirs which bear directly on this investiga-
tion have been already referred to. A list of papers dealing with
the existence of bacteria in living tissues will be found in the
Handbucli der Hygiene der Gewerbekrankheiten, 1 Theil, 2 Abtheil,
1 Heft. The following papers may be specially mentioned : —

(1) Meissner, Deutsche Zeitschrift filr Chirurgie , Bd. xiii., 1880,
p. 3446.

(2) Bosenbach, Deutsche Zeitschrift filr Chirurgie , Bd. xvii.,
1882, p. 342.

(3) Bonnet, Ichthyogathologischer Jahresbericht der Munchener
Thierarznei Schule , 1882-83.

PRIVATE BUSINESS.

Mr J. R. Dunstan, Mr Cosmo Innes Burton, and Mr Adolf P.
Schulze were balloted for, and declared duly elected Bellows of the
Society.

Professor Duns read a letter from Dr R. H. Gunning, intimating
his wish to found a prize, or prizes, to be known as the Victoria
Jubilee Prizes, to be awarded every three years. The Society
agreed to accept the trust, and to record their cordial thanks to Dr
Gunning, and remitted to the Council, along with Professor Duns,
to arrange details in accordance with Dr Gunning’s wishes.

1887.] Professor Sacco on Origin of Great Alpine Lakes. 271

Monday , 20 th June 1887.

Sheriff FORBES-IPtVINE, Vice-President, in the Chair.
The following Communications were read : —

Among the many and various controversies to which the geo-
logical study of the great chain of the Alps has given rise, not the
least interesting is that which has reference to the origin of the
beautiful lakes which occur most numerously in the lower reaches

seems to me to explain the origin of these remarkable basins, and
in place of these I now venture to adduce one of my own, which
has been suggested by some years’ observations on the Tertiary and
Quaternary accumulations of the valley of the Po. Of course, it
will be understood that I am far from denying that lacustrine
basins may owe their origin to many various causes ; and for lakes
in general I am inclined to adopt some such classification as the
following : —

It is not, however, with lakes in general that I am now about to
deal, but with our Alpine lakes in particular. In commencing the

1. On the Origin of the Great Alpine Lakes. By Professor
Federico Sacco, University of Turin.

of the mountain valleys. None of the theories hitherto set forth

Flexures of strata.
Fractures.

Superficial inequalities of deposits.
^Crateral hollows.

f Morainic accumulations.
Ice.

Alluvial deposits.

Dunes.

Lake-basins formed by dams I Littoral banks of sand, &c.
or barriers, as by . . . ' Landslips and rock-falls.

Drift-wood.

Lava.

Coral reefs.

. Beaver dams.

Lake-basinsformedby erosion,
as by

f Water, both as a subaerial and subterranean
| agent, causing local subsidences by removal
■{ of materials in solution, &c.

| Ice.

I Wind.

VOL. XIV.

3/11/87

s

272 Proceedings of Royal Society of Edinburgh. [june 20,

study of those lakes, we must, in the first place, transport ourselves
in imagination to that epoch of powerful earth-movement which,
according to most geologists, closed the Miocene period in the
Alpine lands, and gave to that mountain-region its last general up-
heaval. It was during this epoch of powerful movement that,
according to common belief, the Alps received their present oro-
graphic features, while many geologists were of opinion that the
formation of the great Alpine lake-basins ought to be assigned to
the same epoch of disturbance. With this latter opinion I cannot
agree. On the contrary, I have been led to conclude that the
movement of upheaval which brought the succeeding Pliocene
period to a close was of much greater extent than that which took
place after Miocene times ; and therefore, so far as regards the
question at present under review, viz., the origin of the Alpine
lake-basins, the Post-pliocenic movement is much the most im-
portant.

Be this as it may, it is quite certain that with the close of
Miocene times marine conditions entirely disappeared on the
northern side of the Alps. After that date the only deposits laid
down in that region are of fluvio-lacustrine, fluviatile, and glacial
origin ; and as none of these contains fossils, they do not furnish us
with a sufficiently exact basis for the study of the phenomena
which have taken place at the foot of the mountain-region since
Miocene times. By various geologists these unfossiliferous deposits,
which are in general gravelly in character, have been assigned to the
Messinian, to the Piacentian, and even to the Astian stage, and in
large measure also to the Quaternary. It is probable that during
each of these epochs some of the deposits in question were formed,
but as the classification of the latter is still far from being estab-
lished, it is better for our present purpose that we should confine
our attention to the post-miocenic accumulations which occur on
the south side of the Alps. These, unlike those of Switzerland, are
mostly marine and fossiliferous, and therefore afford us a more
secure basis for the study of the question at issue.

In the valley of the Po the Messinian is well marked, especially
at the foot of the Apennines, where it contains gypsum and marls
(with Dreissena , Melania, Melanopsis, Neritina, Paludina , Ceri-
thium ), arenaceous, and calcareous beds ; in other words, the Mes-

1887.] Professor Sacco on Origin of Great Alpine Lakes . 273

sinian consists principally of marshy and lagoon formations, in
strong contrast to the underlying Tortonian, which is chiefly of
deep-sea origin.

Along the foot of the Alps the Messinian is very poorly de-
veloped, and has been little studied. In the Eastern Alps, how-
ever, there occurs a certain old alluvial deposit, cemented into hard
rock, and containing terrestrial and lacustrine fossils. It has been
elevated and much disturbed, but here and there is seen to overlie
the Tortonian, while elsewhere it lies abruptly against much older
formations. This alluvium M. Taramelli is inclined to include in
the Messinian ; while M. Kossi * has assigned to the same geological
horizon the extensive marshy deposits of the province of Treviso.

But if in Northern Italy so strong a contrast exists between the
deposits of the Tortonian and Messinian epochs, while on the
northern side of the Alps the Upper Miocene strata are poorly de-
veloped, surely we must infer from this that a powerful movement
of elevation affected the region of the Alps and Apennines in post-
Tortonian times. Is it not evident that this upheaval finally
banished the sea from the northern side of the Alps, where it had
so long prevailed, while on the south side of the Alps it changed the
large and deep Tortonian gulf of the valley of the Po into a region
of lagoons, low lands, and marshes ? Is it not to this period that
the existing orography of the Alps, at all events in its general out-
lines, ought to be assigned ?

To this movement of powerful and wide-spread elevation suc-
ceeded another movement, also of great intensity, but in the
opposite direction. Thus in the valley of the Po the marshy
accumulations of the Messinian are overlaid directly by the deep-
sea deposits of the Piacentian. No marine deposits of Pliocene age
occur on the north side of the Alps, and Swiss geologists therefore
do not admit that the subsidence referred to affected their country.
For my part, I think it highly probable that the movement in
question did affect the whole mountain-region, but with varying in-
tensity. The absence of marine Pliocene on the north side of the
Alps I would attribute to the relatively higher position of that
region above the sea-level. In consequence of the upheaval of late

* “Note illustrative alia carta geologica della Provincia di Treviso,’’ Boll.
Soc. Geol. llal ., vol. iii. 1884.

274 Proceedings of Royal Society of Edinburgh. [june 20,

Miocene times, the sea retreated from Switzerland, and hence the
succeeding deposits consist, not of marine, hut terrestrial and lacus-
trine beds. These I take to he representative of the Tortonian and
Messinian of Italy. During the following Piacentian epoch the sea
invaded the valley of the Rhone, and reached as far as Lyons, hut
did not approach nearer to Switzerland.

It is to be noted in this connection that the invasion of the
Piacentian Sea was not general, even for the south side of the
Alps, for deposits of that age are wanting in Yenetia, east of Lake
Garda. It woidd appear, therefore, that the post-Messinian sub-
sidence was not nearly so well marked in this particular region as in
that which lay further to the west. Thus the Venetian districts,
with their continental deposits of Pliocene age, show phenomena
analogous to those met with on the northern side of the Alps.

Towards the middle of the Pliocene period, a movement of eleva-
vation was again initiated. This appears to have been somewhat
rapid in certain regions, for we find in places blue marls, with a
deep-sea fauna, overlaid directly by yellow sands charged with fossils
of littoral habitats. In other places the same deep-sea strata are
covered by continental accumulations, pointing in like manner to a
more or less rapid upheaval. In yet other places, however, we find
evidence of a gradual change from deep-sea to shallow-water con-
ditions, showing that the elevation may, after all, have been rather
protracted than rapid.

The distribution of the arenaceous marine deposits of the Astian
along the base of the Apennines (where they are widely and
almost continuously spread), and here and there also at the foot of
the Alps (such, for example, as the marly beds of the Piacentian),
leaves one in no doubt as to their stratigraphical position. At the
foot of the Alps, however, or at a little distance from these moun-
tains, we encounter certain gravelly deposits, generally quite un-
fossiliferous, and having a prevalent fluviatile character. These
gravels, according to some geologists, correspond in age to the yellow
marine sands of the Astian ; by others they are regarded as Quater-
nary accumulations. And so in Italy, as in Switzerland, there is
the same difficulty as to the precise stratigraphical position of these
deposits. But while in Switzerland their horizon has been variously
assigned to any stage — from the Messinian to the Quaternary — in

1887.] Professor Sacco on Origin of Great Alpine Lakes. 275

Italy they can only be of Astian or Quaternary age. Indeed, it
seems to me probable that just as in Switzerland, those unfossili-
ferous accumulations may truly belong in part to each of the stages
referred to — namely, to the Messinian, the Piacentian, the Astian,
and the Quaternary — so the unfossiliferous conglomerates in the
valley of the Po may belong in part to the Upper Pliocene, and in
part also to the Quaternary. I shall not attempt at present, how-
ever, to make this distinction, because it is still matter of doubt,
and would lead me into too long a discussion of what, after all, are
local details. Nevertheless, I should like to point out some of the
more important results obtained from a geological examination of
the upper valley of the Po. These may be summarised as follows : —

1. In certain parts of Piedmont, at a distance of more than 50
kilometres from the Maritime Alps, with their important valleys and
rivers (as, for example, between Villanuova and Villafranca, Asti),
there occur fluviatile and lacustrine deposits, consisting of marls,
sand, gravel, and conglomerate, which sometimes attain a thickness
of 100 metres, and which from their fossils, studied by me for some
years, I judge to be of Pliocene age (Villafranchian of Pareto).
These alluvial deposits rest upon the yellow sands of the Astian,
which in that district are of inconsiderable thickness.

2. In the valley of the Stura (Cuneo),* and in certain other dis-
tricts of Piedmont, one may see the yellow marine sands of Astian
age thinning off towards the mountains, taking on by degrees the
character of true littoral deposits, and then of marshy or lagoon-like
accumulations. Followed nearer the mountains, these accumula-
tions are covered and replaced by gravelly, sandy, and argillaceous
alluvia, which at first are probably marine, but seem to pass later-
ally into true continental deposits. The numerous fossils found by
me in these beds prove the latter to be of Upper Pliocene age.

3. In other regions of Piedmont, but nearer the mountains, as,
for example, between Morozzo and Yillanuora, Mondovi, the alluvia
in question repose conformably upon the marine blue marls of the
Piacentian, presenting in this manner a well-marked parallelism
with the yellow marly sands, which at a distance of only two kilo-
metres represent the marine Astian, and overlie the same horizon of

* F. Sacco, “La valle della Stura di Cuneo dal ponte del! Olla/' &c.,
Atti Soc. It. Sc. Nat., xxix. 1886.

276 Proceedings of Royal Society of Edinburgh. [june 20,

the Piacentian marls. These facts seem to me to demonstrate the
synchronism of the alluvial continental deposits nearer the moun-
tains with the marine beds of the Astian.

Now since we find that the yellow marine sands of the Astian
are represented along the foot-slopes of the Apennines by more or
less extensive gravelly, conglomeratic, torrential accumulations, and
since in the higher parts of Piedmont we encounter continental de-
posits of undoubted Pliocenic age (which attain a thickness of even
100 metres at a distance of more than 50 kilometres from the Mari-
time Alps, and rest directly upon the marine Astian), it seems only
reasonable to expect that similar continental accumulations ought to
be met with occupying a like geological position at the foot of the
Central Alps. Indeed, when we consider the more extensive drain-
age area of this latter region, its larger valleys and more imposing
water-flow, we can hardly doubt that more or less extensive alluvia,
synchronous with the Villafranchian of Piedmont, must have been
deposited during the second half of the Pliocene by the great rivers
then descending to the Pliocene sea. And these alluvia would
form irregular deltas, now and again anastomosing and dovetailing,
and spreading out from the Alps towards the Apennines. That
great alluvial accumulations do occur along the foot of the Central
Alps is of course well known, and the only question therefore that
remains for discussion is the classification and correlation of those
deposits. Unfortunately, owing to the fact that the cuttings made
by the river-courses in the plains of the Po are generally of incon-
siderable depth, the whole thickness of the alluvia is not seen, and
the determination of the deposits therefore is not an easy matter.
As a rule, it is only the superficial Quaternary conglomerates that
are exposed in sections. Por the same reasons which induce me to
believe that along the base of the Alps in Italy very extensive
Pliocenic alluvia exist, I am of opinion that a large proportion of
the alluvial accumulations, more especially the conglomerates, which
occupy a similar position at the northern foot of the Alps, ought to
be assigned to the Pliocene rather than the Quaternary.

But the second stage of the Pliocene period was characterised
not only by the commencement of the elevation of the Alpine and
Apennine regions, and by the accumulation of the marine and con-
tinental deposits already referred to, but by the initiation of those

1887.] Professor Sacco on Origin of Great Alpine Lakes. 277

glacial conditions which subsequently attained so great a develop-
ment. Even at an earlier stage than this, namely, in the Astian
epoch, the Alpine snow-fields and glaciers probably reached a not-
able development, especially in the northern part of the chain,
where the geographical and orographical conditions, together with
distance from the sea, would necessarily exert an influence favour-
able to glaciation. For these reasons, I incline to think that the
first glacial epoch of Swiss geologists coincided generally with the
closing stage of the Pliocene. If, as I believe, the first notable ex-
tension of glaciers began in Astian times, then we should expect to
encounter on the south side of the Alps very considerable alluvia of
Pliocene age, extending outwards from the mountains far into the
plains. And this is just what I do find.

The actual cause of this former great extension of the Alpine
glaciers I would assign to evaporation from a much wider water
area than presently exists. Much of what is now dry land in
Northern Italy was then submerged — the water being partly that
of the sea, partly lacustrine. The vapour rising from these sub-
merged areas, passing north over the Alps (which at that time were
being powerfully upheaved), would be precipitated as snow, and so
would eventually give rise to glaciers. It must be remembered that
the extraordinary glacier-development in question has, in all proba-
bility, not been the first to have taken place in the Alps. At
various horizons in the Tertiary strata great erratic blocks have been
met with. More especially is this the case with the Miocene of the
hills near Turin, where, scattered through sandy, marly strata of
marine origin, occur enormous blocks, angular in shape, which could
only have been carried by ice. It seems most likely that the ice-
bergs or ice-rafts by which they travelled were detached from the
front of the glaciers descending from the Alps into the sea of
Miocene times.

But if the movement of elevation began to be manifested more
or less pronouncedly during the Astian epoch, it was yet gradual
enough to allow of the continued accumulation of the deltas, which,
step by step, were compelled to recede from the foot of the Alps.
At the end of the Pliocene period, however, the movement assumed
extraordinary intensit}7-. Thus, the lower Pliocene (Piacentian) of
deep-sea origin were uplifted 350 or 400 metres, and even more

278 Proceedings of Royal Society of Edinburgh. [june 20,

than 500 metres in some sub-Alpine regions, whilst the upper
yellow sands (Astian) in the vicinity of the Alps were at certain
points raised more than 560 metres. In the sub-Apennines,
facing the Alps, the same deposits were uplifted 700 metres,
and in Southern Italy over 1000 metres. This movement, as I
believe (and not that which closed the Miocene period), was
the last great elevation of the Alps. It is to this Pliocenic
movement that I attribute the general orographic settlement of
the Alps. And it is to this last great elevation of the Alps
that I chiefly assign the formation of the existing lake-basins of
the sub-Alpine regions. These I believe to be due partly to
faults — often bifurcating as they pass down the valleys, — and
partly to the accentuation or formation of synclinal folds, and to
local uplifts and subsidences.

After this period of great elevation the Alpine glaciers, which
had already in the second stage of the Pliocene become strongly
developed, were now, owing to the changed orographic conditions,
compelled to form in cirques differing in shape from those of
Pliocene times, and to seek new paths in their descent to the low
grounds; but, erelong, making their way through deep valleys
newly opened, and preceded by the deposition of diluvial deposits
from the waters escaping from them, they reached the plain, and
piled up their great end moraines, forming the well-known morainic
amphitheatres opposite the mouths of the great Alpine valleys.
Underlying these terminal moraines, therefore, we always find a
more or less thick accumulation of diluvial conglomerate — the in-
duration of the deposits being due sometimes to infiltrated calcareous
matter, and sometimes apparently to the pressure exerted by the
glacier-ice which overflowed the gravels.

During the somewhat rapid descent of the glaciers to the low
grounds it seems obvious that the terrestrial waters which escaped
from them would accumulate in the lake-basins, the bottoms of
which would thus tend to be raised ; while the glaciers themselves,
when they reached those basins, would take some time to fill them
up. Before the glaciers could escape from the lacustrine troughs,
very considerable masses of gravel and shingle would be swept out
by the rivers and torrents, and spread over the low grounds that
extend outwards from the mountains. When at last the glaciers

1887.] Professor Sacco on Origin of Great Alpine Lakes. 279

debouched upon the plains, their path therefore lay over a region
more or less thickly covered with gravelly deposits, and we need
not wonder therefore at the great thickness attained by the con-
glomerates which we now meet with underneath the great terminal
moraines of Piedmont, &c. The occurrence of these conglomerates
has long been well known, ever indeed since attention was first
directed to them by Martins and Studer some forty years ago.

The “ morainic amphitheatres ” and the underlying and associated
diluvial gravel, &c., are the characteristic accumulations of the
glacial period, and correspond, in my opinion, to the similar accumu-
lations which, according to Swiss geplogists, belong to what they
term the ‘‘second glacial epoch.” From all the Alpine valleys at
this period powerful streams and torrents descended, and their pro-
ducts occur not only opposite the mouths of the greater Alpine
valleys which contained large glaciers, but spread out also into the
plains, and low grounds opposite mountain-v alleys in which no
glaciers appear to have existed. To these deposits various names
have been assigned, such as “Quaternary alluvia;” “ fluvio-lacus-
trine alluvia,” “diluvium,” “cones de dejection,” “Areneano” =
(gravelly sands with remains of Elephas primigenius , Megaceros ,
Cervus euryceros , (fee.); “Ferretto,” <fec.

It is unnecessary, however, to pause longer over this period, the
general conditions of which, so far as they relate to the Alps, are
sufficiently well known. The eventual decadence of the great
glaciers was, in my opinion, brought about by the gradual and
general elevation of the continent, and the consequent disappear-
ance of many wide marine and lacustrine areas. By the gradual
disappearance of those water areas evaporation was progressively
diminished, until the atmospheric precipitation on the Alps was
reduced by one-tenth, consequently the glaciers, for lack of aliment,
gradually retreated, and the great troughs in the mountain valleys
became lacustrine basins. (Probably, also, the gradual lowering of
the temperature of the globe may have had something to do with
diminished evaporation and precipitation.) Now, the lakes are
being gradually filled up by the sediment washed into them by
streams and rivers, so that the geologist can foresee a time when they
will become in this way entirely silted up. In Post-glacial times the
streams were not of such importance as those of the Glacial period,

280 Proceedings of Royal Society of Edinburgh. [june 20,

which in many respects may be looked upon as a period of torrents
and flooded rivers. Since the close of that period the rivers and
streams have been engaged in cutting down through the glacial and
fiuvio-glacial accumulations, so that in some places they have suc-
ceeded in reaching the Pliocene, and even the Miocene deposits.
This is especially the case in localities where a movement of up-
heaval had been longest continued, or where it had been most
pronounced. The erosive action of Post-glacial times having resulted
in the formation of alluvial terraces in the valleys over many wide
regions, we term this period the “ Terracian.”

Having now sketched in outline the phenomena connected with
the structure and origin of the great lake-basins of the Alps, I may
sum up in a few words my general conclusions. I am of opinion,
then, that these basins came into existence during that powerful
upheaval which closed the Pliocene — that, in short, they are the
direct result of that great movement. They owe their origin partly
to fractures and foldings of the strata, partly to subsidences and
elevation. They were preserved during the glacial period by the
glaciers which occupied them, and were only modified to a slight
degree by morainic obstructions, and by fluviatile and glacial erosion.

The form and distribution of the Alpine lakes seem readily
explained according to my views as follows : —

1. Along the south-east margin of Lake Garda the strata present
distinct folds, the axes of which run generally from west to east.
In other words, the undulations and folds of the strata along the
eastern side of the lake are approximately parallel to the plain of
the Po. Further to the east their direction is mostly from north-
west to south-east. The absence of great lake-basins in the Y enetian
Alps is noteworthy, and may be accounted for in various ways. It
is not unlikely, in the first place, that fractures and faults would
tend to take place more in the direction of the folds than perpendi-
cular to them ; again, during the last great upheaval, when new
foldings took place, these would probably be formed parallel to the
pre-existing ones, and only rarely perpendicular to them. Finally,
the Venetian Alps, according to Taramelli, experienced a less degree
of elevation in Post-pliocene times than the regions lying to the
west. Such considerations should lessen our surprise, that no great
lake-basins occur in the mountain-valleys east of Lake Garda.

1887.] Professor Sacco on Origin of Great Alpine Lakes. 281

2. Upon the south-west margin of that lake the foldings of the
strata run usually from south-west to north-east— a direction which
coincides generally with that maintained by the anticlinal and
synclinal axes of the Western Alps, and explains why the Central
Alps advance so much further into the plain of the Po than the
Eastern Alps. By this arrangement of the axes in the region under
review, it is obvious that the folds of the strata are directed
approximately perpendicular to the plain of the Po. Now, since
the faults and foldings which followed the trend of the original
undulations must have been both numerous and important ; and as
the Post-pliocene elevatory movement which took place in the
Alpine region to the west of Lake Garda was very powerful, it is
only natural that great sub-Alpine basins should have been formed
in that region, the general trend of these basins being perpendicular
to the plain of the Po.

3. In that region where the discordancy between the undulations
of the Central Alps and those of the Venetian Alps is most marked,
we ought to encounter the largest faults and most pronounced fold-
ings of the strata. Now, it is just in that particular region where
Lake Garda occurs — a lake which advances further than any of the
other Alpine lakes into the plain of the Po, and which in places
exceeds the great depth of 800 metres — so that its bottom is nearly
800 metres below the level of the sea.

4. The larger foldings which occur along the southern area of the
Eastern Alps are directed, as I have said, parallel to the plain of
the Po, thus differing notably from the Post-miocene and Post-
pliocene undulations of the Central Alps. This direction of the
folds of the Eastern Alps, taken in connection with the disposition
of the Alpine chain in a strong curved line, seems sufficient to
account for the absence of deep lacustrine basins at the foot of the
Venetian Alps.

5. The northern region of the central area of the chain (including
a large portion of the German Alps and the eastern part of Switzer-
land) having experienced conditions very similar to those which
have affected the Alps of Lombardy — for, doubtless the powerful
elevation that closed the Pliocene epoch influenced the whole area
in question, — we there meet with deep lacustrine basins similar to
those of Northern Italy. These basins we see extend in a direction

282 Proceedings of Royal Society of Edinburgh. [june 20.

perpendicular to the axes of the Alpine chain, and are sometimes,
as in the case of Lake Constance, bifurcated downwards, like not
a few Italian lakes.

6. In the more eastern part of Switzerland the phenomena referred
to in the preceding paragraph were complicated by the proximity of
the Jura Mountains, a chain which runs parallel to that of the
Alps. Hence the deep lake-basins were formed rather parallel than
normal to the axes of those chains.

7. It is -worthy of note that the orographic axes of the syn-
cline of the valley of the Po lies near the base of the Alps.
This explains why the lacustrine troughs, lying for the greater
part in solid rocks, shelve olf and end near the plain. We
must remember also that the Post-pliocene elevation of the Apen-
nines, where the Pliocene strata often reach an elevation of more
than 700 metres, must have been more intense than the contem-
poraneous movement of the Alps, where the Pliocene marine beds
do not rise more than 400 metres above the sea. It is highly
probable that a similar relation obtained between the Jura and the
Swiss Alps. Nor can I doubt that if the Apennines had approached
the Alps as closely as the Jura, we should have found the typical
direction of the Italian lacustrine basins modified in some cases.
Instead of being all perpendicular to the axis of the Alps, some of
them would have resembled the Lake of Geneva, the upper reaches
of which are normal, while the lower are parallel to tire main axis
of the mountains.

8. I admit the existence of a relation between the great Alpine
basins and the glaciers of Quaternary times ; but in my opinion this
relation is due neither to excavation by ice nor obstruction by
morainic debris, but simply to the conserving action of the glaciers.
The troughs, I believe, were occupied by the glaciers, and thus their
filling up by the fluvio-glacial detritus of the first half of the
Quaternary age was prevented.

In the following table I bring into one view the general conclu-
sions arrived at in the paper : —

1887.] Professor Sacco on Origin of Great Alpine Lakes. 283

>>

P

-M

r

'

Terracian,*

Retreat of the glaciers. Con-
version of the great troughs
into lakes. Powerful river
erosion, accompanied by the
formation of terraces.

Alluvia, Peat.

<y

b

Saharian—
(2nd Glacial
Epoch).

Great development of glaciers :
filling of the great troughs
by ice. Enormous streams.

Morainic amphi-
theatres. Drift.
Diluvium.

General excessive elevation of the Alps and Apennines, and settlement of
the existing Alpine orography. Formation or enlargement of many valleys,
and of almost all the lake-basins by faults, folds, elevations, and subsi-
dences.

Astian —

(1st Glacial
Epoch. )

Commencement of the general
elevation of the Alps and
Apennines. Initiation of the
great glacial development in
the Alps.

Continental fluviatile
or lacustrine, or
flu vio -glacial de-
posits. Yellow

and grey marine
sands.

Tertiary

PlACENTIAN.

General subsidence of the Alps
and Apennines.

Continental fluviatile
deposits. Blue

marine marls.

Messinian.

General powerful elevation of
the Alps and Apennines.
Outlining of the existing
Alpine orography.

Continental fluviatile
deposits. Marshy
deposits.

2. On the Minute Oscillations of a Uniform Flexible
Chain hung by one End ; and on the Functions
arising in the course of the Inquiry. By E. Sang, LL.D.
(Plate IX.)

Twenty-seven years ago the writer submitted to the Royal
Society of Edinburgh a paper on the minute oscillations of flexible
pendulums, in which some new general laws were expounded. He
proposes now to consider one case of the phenomenon more in
detail.

The investigation of extensive oscillations of a flexible system is
far beyond the present powers of the calculus, and we are restricted
to the consideration of disturbances not far from the mean position
of the system.

In the case of a thread having weights arranged on it at intervals,

* The Terracian embraces the epoch that intervened between the Glacial
and the Present, and corresponds to the Post-glacial of other geologists.

284

Proceedings of Royal Society of Edinburgh. [june 20,

tlie system is capable of as many simple oscillations as there are
attached bodies, and all the movements of which it is susceptible are
compounds of these simple ones. An imaginary flexible heavy line
may be regarded as composed of an infinite number of parts, and
thus for it there is an endless series of simple oscillations, each
having its own periodic time. The essential feature of our inquiry
is as to the manner of one of these.

The character of a simple oscillation may be illustrated thus: —
Let HO, fig. 1, represent the direction of the plummet, while the
waved line LIHFECBA (supposed, however, to be almost straight)
is the form of the chain at some particular instant ; then the motions
must be such that all the parts of the chain come simultaneously
into the position LtH/EcBO.

For this it is requisite that the tendency to redress the position
of any element, as P p, of the chain must be proportional to the
distance PQ and to the mass of the element. How the tension of
the chain at P is (in our restricted case) measured by the weight of
the part below, — that is by the length PA, which we hold as equal
to QO ; and that tension decomposed in the direction QP is pro-
portional to the sine of the inclination at P ; so that if we denote
OQ by 2, QP by x , and use Leibnitz’ notation, the tendency of the

dx

strain on PA to draw the element outwards is proportional to z -7- •

Similarly, the tension of the chain PE, which is proportional to 0 q,

dx'

causes a pull inwardly, indicated by and thus the ultimate

determination of the element P p towards the central line is pro-
portional to the difference —

and thus the general condition of a simple oscillation is expressed
by the differential equation of the second order

in which a is a coefficient constant all along the chain, but chang-
ing from one simple oscillation to another.

1887.] E. Sang on Oscillations of Uniform Flexible Chain. 285

The resolution of our physical problem is now converted into the
management of a case in the doctrine of functions, and thus it
acquires an importance far beyond any that the original question
can be supposed to possess. In this equation z stands as the

dx dix

primary variable, x as its function, as the first, as the second

derivative. Translated into geometry, we have the abscissa z, the

doc d2x

ordinate x , the inclination of the curve , and the curvature j

di

dx

or into mechanics, the time t (for z), the position x, the velocity jj >

d2oc

and the acceleration all combined in one formula; and the

resolution of it may imply that of whole classes of physical pro-
blems. It is in this light that the matter is again brought under
the notice of the Society.

The problem does not belong to the differential calculus, for in
that case we should need to have the relation of the primary z to
one of the derivatives explicitly declared; not to the integral
calculus, for then the connection between the primary and the
derivative would need to be given ; nor yet to the third co-ordinate
branch, for the relation of the primitive and derivative functions is
not prescribed.

For convenience in treating the matter, it is expedient to discard
Leibnitz’ notation for differentials of higher orders than the first,
and altogether to dispense with his notation of integrals.

dix

Such an expression as -j-g, is intended to represent the result of

five successive differentiations in which z is the primary or inde-
pendent variable and x the function. Here the sign of differentiation
is twice, and that of the order also twice, written. How, the
essentials to be indicated are, the idea of differentiation, the
primary, the function, and the order. The idea may conveniently
be indicated by the position of the marks ; Lagrange placed these
as accents over the function, thus : — x\ x11, xul, xlv, xv . This scheme
has two drawbacks; the position of the accents had long been
appropriated to the indices of powers, and there is no notice of the
primary ; Leibnitz’ notation clearly shows the distinction between

286 Proceedings of Roy cd Society of Edinburgh. [june 20,

g5x dPx

and — , whereas the mark xv can show none. The writer, in

dz5 dip

his “ Solution of Equations of all Orders,” Edinburgh, 1829, has
placed Lagrange’s accents as ante-subponents, and has written along
with them the primary, so that the symbol S2x is used to denote the
fifth derivative of x regarded as a function of z , while 5jc means the
corresponding differential coefficient when y is the independent
variable. In this way all the essentials are exhibited without
redundancy.

The symbols x , lzx, 2zx, 3zx., thus indicate a series of functions
deduced by the repeated operation called differentiation ; each one is,
as Lagrange says, the derivative of the preceding, and each one is
the primitive (integral) of the succeeding. So we may carry the
notation backwards by using the sign of reversion and write _lzx for
the function of which x is the derivative, — that is the fxdz of'
Leibnitz, and thus get the progression extending both ways

-32'^-' ? -22«, -12^ > } 1 2*U 22*^ 5 32*b &C.

Using this notation, the condition of a simple oscillation of the
chainTs expressed by

- ax = l2a? -f 2 . 2zx .

From this equation we have the second derivative in terms of x ,
of the first derivative lzx, and of the primary z ; and from it also we
easily obtain the subsequent derivatives, for on differentiating we find

— a . lzx = 2 . 2zx

+

z .

32^ 5

CL • =~ 3 • QzpC

+

z .

42^ 5

55

II

55

CO

1

+

z .

5 zX >

and in general - a . nzx = (?i+ + z . (n+2)zx ; we may also pro-

ceed backwards by integration, thus : —

and in general

a .

1

II

0

X

+

z .

a.

- 22^ — 1 •

-la®

+

z .

X

a .

-32^= - 2 . .

-22^

+

z .

-1 ZX

— a .

- nz^

= - in- 1)

• -(«-

-DzPO + Z.

55

N

cT

1

3

1

cf>x

to

represent some

one

of

these :

equation relating to it will take the general form

- a. <f>z = n. lz4>z +- 2: . 2 Zcf>z

1887.] E. Sang on Oscillations of Uniform Flexible Chain. 287

in which n may he any integer number, positive or negative ; and
thus the solution of our problem will virtually contain that of a
whole series of allied ones. The particular case, when n = 0, merits
notice, it becomes

- a . <f>z — z . 2z<f)Z

, a
or 2 tcf>z =

and therefore represents the movements of a body actuated by a

a

spring whose stiffness — becomes lessened in inverse proportion to

z

the elapsed time.

The coefficient a in these formulae regulates the scale on which
the abscissas 2 are measured, and if it be taken as unit, the periodic
time of the chain’s oscillation will be that of a simple pendulum
having the linear unit for its length ; so the generality of the results
will not be impaired by the assumption a= 1. Let us then seek to
determine the relation of x to the primary 2 from the equation

ry> I a; /y»

lAJ 1 gAs & • QyX' •

Naturally we try whether it be possible to represent a; by a series
of terms involving the powers of the variable 2. We shall suppose,
then,

x = A + Bz + C z2 + Ds3 + . . . Msn_1 + Ns” + &c.,

which gives, on being differentiated,

1?a; = B + 2Cz + 3Ds2 + 4E23 4- nNzn~1 + ,&c.,

z.2zx = 1. 2Cz + 2. 3D22 + 3.4Ez3 + 1)^N2W_1 + , &c.,

wherefore, equating the terms containing the like powers of z,

- A = B, -B — 4C, - C = 9D, -D = 16E, and

in general - M = n2N , so that
A A

B = -

Whence

x — A

2 >

C= +

l2. 22

1 +

Z2

D= -

23

12.22. 32

and so on.

z*

&c. |

12 (1 . 2)2 (1.2. 3)2 (1.2.3.4)2
where the multiplier A depends on the extent of the oscillation and
on the particular instant of time. For the present we may assume
A also to be unit and confine our attention to the equation

1 2

X A l2

22

22 . . . . 32

n1-

, &c.

VOL. XIV.

11/11/87

288 Proceedings of Royal Society of Edinburgh, [june *jo,

Each succeeding term of this progression is formed from its

z z z

antecedent by means of a factor of the form 7r„ , ^ 5 ••••—», so
J 22 32 nl

that, however large 2 may be taken, the denominator n 2 must

eventually come to exceed it ; and thus, although the terms may

increase at the beginning, they must ultimately come to decrease ;

and therefore the computation of x to within any prescribed degree

of precision is always possible.

The curve lies on the one or on the other side of the plumb-line,
according as the sum of the even terms of the progression exceeds
or falls short of the sum of the odd terms, and we can discover
which way only by the actual calculation. The intersections of
the curve with the middle line represent the points of suspension
of the oscillating chain, and therefore our attention is first called
to the discovery of those values of 2 which correspond to a? = 0.
From the mere aspect of the progression we could not even predict
that any such values are possible, or form any idea of the order of
the roots of this transcendental equation. The consideration of the
physical problem with which it is connected does indeed throw
light on the matter, and leads us to anticipate an endless succession
of roots more and more separated as we proceed upwards.

The accurate determination of these roots can only be reached by
trial; the computations are very operose, and we look for some
means for lessening the labour ; this is found in the law of succes-
sion of the derivatives. Let us suppose that, corresponding to some
value of 2, the ordinate x and its derivative lzx have been computed,
we are then able easily, particularly if 2 be represented by an integer
number, to deduce the subsequent derivatives. Thus —

2*®=

w

r-H

1

l

2

3z^ =

— lzx — 2 . 2 zx

Z

~~ 2 — ^ * 3^

izx —

*7. '■

and so on ;

and these enable us to deduce the values of x corresponding to
proximate values of 2 by the process described in the work above
referred to. When 2 is large these values evidently decrease at the
beginning, but as the order advances the multiplier of the last found

1887.] E. Sang on Oscillations of Uniform Flexible Chain. 289

derivative must come to exceed 0, and it may be that the progression
eventually becomes divergent ; into this matter we shall inquire
hereafter.

The first derivative ^ is expressed by the series

1 Z £1 2 23

~ I + l2 2 ~ l2. 22. 3 + 12.22. 32. 4 “ ’ ^c‘

whose terms stand between those of the preceding in such a manner
that, with scarcely augmented labour, one computation may be made

£2

to give both. Thus if we take a term of the series for x, say

2 2

and divide it by the next exponent 3, we get p 92 ^ a term of the

z z3

series for lzx ; and this again multiplied by ^ gives -2-f2 ^2 , the

succeeding term of the series for x.

To make a beginning, let us compute the values for z = 1 ;
these are

x= +. 22389, lza;= -. 57672.

On examining the relations of these numbers to unit and to each
other by the method of continued fractions, we get a remarkable
result for the ratio of the ordinate to its derivative. Proceeding in
the usual way of taking the greater from the less, the remainder
from the preceding, and so on, we get the quotients

2, 1 ; 1? 2 ; 1,3; 1,4; 1,5; &c.,

whence the successive approximations alternately in defect and in
excess.

2

1

1

2

1

3

1

0

1

2

3

5

13

18

67

85

33 &c'

1

0

1

1

2

5

~7

26

and if we follow the method of excesses, the quotients come out
1, 2, 3, 4, 5, &c., giving the chain of fractions

1 2 3 4 5 6

— 1_ 0 ! 2 5 18 85 492

0" T T T 2 7 33 191 &C‘5

290 Proceedings of Royal Society of Edinburgh. [june 20,

which lie all on one side of the absolute ratio, being indeed the
alternates of the preceding.

Now, in forming a list of the successive derivatives of x for 2=1,
according to the law above explained, and writing for clearness’
sake, A for *22389, B for *57672, we get the progression

X

X

+

A

B.

,x

rr

—

A

+

B.

X

=

+

2 A

—

B.

,x

=

—

5 A

+

2 B.

,x

=

+

18 A

—

7 B.

,x

=

—

85 A

+

33 B.

,x

&c.,

+ 492 A

&c.

191 B.

But these coefficients of A and B are developed exactly as are
the members of the approximating fractions, so that since A : B is
nearly as 191 : 492, the difference 492 A-191 B must be small, and
must continue to decrease as we proceed farther. Hence, if we can
show that the above progression of quotients 1, 2, 3, 4, &c., neces-
sarily holds good, we shall have demonstrated that the progression
of derivatives never becomes divergent.

If we treat the progressions A = x, B = — lzx by the method for
continued fractions, taking the excesses, and dividing each excess
by z, we get at once the following results : —

A = 1 -

B = 1 -

-A+ B = zC ; 0 = ^-

-B + 2C = zD; D = r^-g -
-C + 3D = £E; E = 1 g ^4"

z z2 z3

T2 + 1X22 ~ l2. 22.32 +

z ' z2 z3

JA2 + l2. 22.3 "... ii2.4 +

Z Z2 z3

l2. 2. 3 + . . 22. 3.4 . . 32.4.5 +

Z Zz2

H.2.3.4 + .. 22.3.4.5

z z2

l2.2.3.4.5 + ..22.3.4.5.6

- &c.,

- &c.,

and so on ; wherefore, in general, the formation of the fractions

1887.] E. Sang on Oscillations of Uniform Flexible Chain. 291

approximating to the ratio of A to B, is identical with that of the
coefficients of A and B in the expressions for the successive deriva-
tives ; in fact, the excesses above found are the very derivatives
themselves, with the alternate signs changed ; and thus it appears
that in no case can the progression of derivatives become divergent.

Proceeding now one step forward, the computations for z = 2 are
found to give x— -*19655 ; lzx= -*28928, so that the curve
must cross the axis between z = 1 and z = 2. The exact place of
crossing may conveniently be reached from either side ; it is at
z1 = 1*4-4580. Thus it appears that a chain having the length
1*44580 will perform a simple oscillation in the same time as will
a pendulum whose length is 1*00000. Or, conversely, that a
chain of the length unit will perform its slowest simple oscillation
along with a pendulum having *69166 for its length. These pro-
portions are shown in the figure, OB being the length of the chain,
OQ that of the pendulum oscillating along with it.

Proceeding onwards in search of the second crossing, we find it
to lie between z — 7 and 2 = 8, from either of which an easy
approximation gives us 22 = 7*61782, rather more than five times
the preceding ; this is the OE of the figure, the curved line
EDCBA representing in a most exaggerated way the character of
the oscillation. The second simple oscillation of the chain is thus
isochronous with that of a pendulum *13127 long, the length of
the chain being unit.

In continuing the search for the remote crossings, the labour of
the trial calculations increases greatly, and we seek to lessen the
toil by watching the progress of the distances ; and, to our consider-
able relief, find that the second differences are almost, though not
quite, constant, as is seen in the subjoined table for six crossings.

24 = 1*44579 64903

6*17201 90958

z2= 7*61781 55861

4*93191 70158

11*10393 61116

^3 = 18*72175 16977

4*93438 33025

16*03831 94141

2;4 = 34*76007 11118

4*93468 53785

20*97300 47926

£5 = 55*73307 59044

4*93475 75309

25*90776 23235

z6 = 81 *64083 82279

292 Proceedings of Boy cd Society of Edinburgh, [june 20,

Hence, after having computed the fourth crossing it was easy for
us to see that the fifth must he between 55 and 56 ; and now that
the sixth crossing has been accurately determined we readily infer
that the seventh must he at 112*48, the eighth at 148*26, and the
ninth at 188*97 nearly.

It is also worthy of remark that the second difference approaches
closely to the value of |-7r2, namely to 4*93480, and we are tempted
to conclude that this well-known number is the asymptote to which
the second difference tends. The mere arithmetical coincidence is
a weak argument in favour of this notion ; yet it is all that the
algebraic formula seems capable of supplying: we shall find a much
stronger argument in the character of the physical phenomenon
under review.

Lemma.

The vibration of the portion LH, comprised between two cross-
ings, is that of a musical string fixed at L and H, and stretched as
by a weight HO at its lower end ; and the preceding investigation
takes into account the change of strain due to the weight of the
cord. In the case of the musical string the tension is many times
greater than the weight of the cord, which weight, therefore, may
be neglected even when the string is upright.

Using as the linear unit the length of a pendulum oscillating in
the same time as the string, and as the unit of tension the weight
of one unit’s length of the string, and writing w for the tension
so measured, the differential equation of the curve is

— x = w . 2zx

of which the solution in its most general form is

. z z

x =p . sin — — + q. COS——T
SJW sjw

where p and q are coefficients depending on the initial motion and
on the elapsed time. In our present example q is zero, and the
equation of the curve at some particular instant becomes

Z

x=p . sm — =-,

V to

which applies strictly to the case when the two ends are on one
level.

1887.] E. Sang on Oscillations of Uniform Flexible Chain. 293

From this we see that x is zero when the arc represented

by — 'j- is zero, or is any multiple of the half circumference 7r ; that

is, when 2 = 0, z = tt Jw, z = 2tt Jw, &c., so that the curve must
cross its axis at points separated by the uniform distance i r Jw.

If now we imagine a second string having its tension greater than
that of the former by the weight of this length, or altogether
■tv + tt Jw ; the distance between its cusps, so as to keep the same
time of oscillation, must be

7T J(W + 7 T Jw) ,

and the increase, analogous to our second difference, becomes

TT JW

V { J(w + 7 r Jw) - Jw} = 7 T-

= 7T‘

Jw + J(w + TT Jw)

l

i+v(i+-^V

V Jw/

How when w increases, the fraction —j— decreases, and the

Jw

denominator of this fraction becomes more and more nearly equal
to 2, so this analogue of our second difference approaches to J7 r2 .

Having thus determined the points of crossing, we proceed to
consider the extreme distances to which the curve reaches on either
side, as at the points c, F, I of the figure. Thereat the curve is
parallel to the axis and the derivative lzx is zero ; we have no other
way of discovering these points than by the solution of the trans-
cendental equation

Z Z2 Z 3

I " R2 + 12.2'2.3

&C.

which we manage exactly as before — that is by calculations arranged
according to the fundamental law known as Taylor’s theorem. The
results, with the corresponding values of x, are

294 Proceedings of Boyal Society of Edinburgh, [june 20,

z

X

3-67049

8-63412

- *40276

12-30461

13-57025

4-93613

+ -30012

25-87486

18-50533

4-93508

- -24700

44-38019

23-44022

4-93489

+ -21836

67-82041

- -19647

Here the second differences of z are seen to he in excess of J7J-2,
and to tend towards it. These maximum points are below the
middles of their respective arcs by the distances

•86131

•86517

•86605

•86638

•86654

which evidently approximate to some definite limit. The exact
determination of this asymptote would he a matter of great diffi-
culty.

In passing from side to side of its axis the chain must change the
direction of its curvature, the concavity being in general toward the
axis ; hut the points of reflexure are not necessarily at the crossings.
At these points the second derivative must he zero ; now the very
genesis of the curve is contained in the equation

— x = lzx -f z2zx or 2 zx — - lz ,

wherefore for the points of reflexure D, G, K, the ordinate x and its
derivative lzx must he equal to each other with opposite signs. The

x dx

suhtangent of the curve is given by the formula or ~ x—-

CtX

in Leibnitz’ notation; wherefore the tangents applied at these points
must meet the axis at the distance of unit (that is the length of the
corresponding pendulum) above the points d , g , h, h of the figure,
as also is the case for the tangent applied at the lowest point A.

1887.] E. Sang on Oscillations of Uniform Flexible Chain. 295

Thus it seems that the portions AB, DE, GH, KL are convex
toward the axis.

The values of z corresponding to these points of reflexure are the
roots of the transcendental equation 2zx = 0, and are obtained in the
manner already described ; they, along with the corresponding
values of x, are

z

X

6-59365

- -13228

17-71250

+ -06448

33-75518

- -04001

54-73005

+ -02792

80-63878

- -02090

while the distances of the points of reflexure below the respective
crossings are

1*02416

1-00925

1-00489

1-00303

1-00206

The details connected with these singular points, namely, the
crossings, the maxima, and the reflexures are contained in the sub-
joined table : —

Singular Points

in

the Curve.

z

X

lzX

2 gX

0-00000

00000

+

1-00000

ooooo

1-00000

ooooo

+ -50000

ooooo

1-44579

64903

•ooooo

ooooo

—

•43175

48070

+ •29862

83407

3-67049

26605

—

•40275

93957

•ooooo

ooooo

+ -10972

89745

6-59365

41007

-

•13227

94874

+

•13227

94874

•ooooo

ooooo

7-61781

55861

•ooooo

ooooo

+

•12328

26057

- -01618

34589

12-30461

40804

+

•30011

57525

•ooooo

ooooo

- -02439

05051

17-71249

97297

+

•06448

25277

—

•06448

25277

•ooooo

ooooo

18-72175

16977

•ooooo

ooooo

—

•06273

64998

+ -00335

09952

25-87486

34727

-

•24700

48771

•ooooo

ooooo

+ -00965

04810

3375517

72165

—

•04000

79701

+

•04000

79701

•ooooo

ooooo

34-76007

11118

•ooooo

ooooo

+

•03942

82580

- -00113

42974

44-38019

17035

+

•21835

94072

•ooooo

ooooo

- -00492

01997

54-73004

72864

4-

•02791

85486

—

•02791

85486

•ooooo

ooooo

55-73307

59044

•ooooo

ooooo

—

•02767

63754

+ -00049

65880

67-82041

35683

—

•19646

53715

•ooooo

ooooo

+ -00289

68471

80-63877

90738

—

•02090

51560

+

•02090

51561

•ooooo

ooooo

81-64083

82279

•ooooo

ooooo

+

•02077

67294

- -00025

44894

296

Proceedings of Royal Society of Edinburgh, [june 20,

We have seen that the area of the curve represented by Jxdz or
by - lzoc, is the product of the abscissa 2 by l2x, the derivative of
the ordinate ; hence the area of the portion AOB is

1-44580 x -43175 = -62423.

But the derivative at C is zero, wherefore the area BcC on the sub-
tractive side must balance AOB on the additive side ; its value must
also be -62423. The derivative again becomes zero at F, and con-
sequently the areas CcE, E/F balance each other, each of them being-
given by the product of the abscissa OE into the derivative at E,
—that is by 7-61782 x -12328 or -93914.

The same law continues all along, the areas increasing, but more
and more slowly as we proceed upwards, as is seen from the sub-
joined list —

•62423

•31491

•93914

•23540

1-17454

*19599

1-37053

•17196

1-54249

•15374

1-69623

-•07951

- -03941

- -02403

- -01822

— from which, however, we can form no idea as to whether the
increase be or be not confined to within some definite limit.

Hitherto we have been considering the form of an indefinitely
long chain, whose oscillations are performed in a fixed time, namely,
that of a pendulum whose length is unit. We shall now proceed to
investigate the forms and times of oscillation of a chain having a
determinate length.

The simple oscillations of any chain, PO, are easily got from the
preceding investigations : thus the slowest oscillation, that in which
the whole chain swings from one side of its mean position to the
other side, is represented by the part BO of the first figure, the
ordinates of the curve being, in imagination, reduced so as to be

scarcely perceptible. If L be the total length of the chain, ^ ^

= Lx *69166 is the length of the pendulum oscillating synchron-
ously with it, and its oscillations are more frequent than that of a

1887.] E. Sang on Oscillations of Uniform Flexible Chain. 297

pendulum having the whole length L in the ratio of Jl *44580 :1 ,
that is, as 1 *20241 : 1. The chain makes almost exactly 101 oscil-
lations, while the simple pendulum makes 44.

The second oscillation, that in which the chain has one node, is
represented by the part EBO of the first figure ; and on dividing
PO of the second figure in the ratio of EB to BO, we get B', the
node of the actual chain ; on making OQ' also in proportion, we
have the length of the pendulum swinging in the same time as the

chain. This length is ^ -- or L x *13127 ; and consequently

these second oscillations are more frequent than those of a pen-
dulum whose length is L in the ratio of v/7’61782 to 1, that is, of
2-76004 to 1.

When two oscillations, represented by the (A) and the (B) of
figure 2, are coexistent, the character of the compound motion
results from the ratio of their periodic times, that is, of 1 -20241 to
2-76004. On examining this ratio by the method of continued
fractions, we find the successive quotients, 2, 3, 2, 1, 1, 2, 13, 2, 7,
&c., which give the approximating fractions —

1_ 3 7 10 17 44 o

2 ’ 7 5 16 ’ 23 ’ 39 ’ ToT ’

Taking the second of these for the sake of illustration, while (A)
has made three complete oscillations, (B) has made seven, and the
chain is (nearly) in the same position as at first, so that the same
phases would be repeated. But the periodic times are incom-
mensurate, and so the same phase can never be accurately repro-
duced.

The two sets of oscillations may or may not be in one plane ;
when they are in planes inclined to each other, the path of a point
in the chain is analogous to the curve produced by the vibration of
a straight wire whose periodic times are in the same ratio; only in
the present case the figure is not necessarily circumscribed by a
rectangle.

In order to form some idea of the compound movements, let us
draw AB, figure 3, to represent the extent of the oscillation (A),
and BC, inclined to it, to show that of the simple oscillation (B).
Then, having described a semicircle on each of these, we divide the

298 Proceedings of Royal Society of Edinburgh. [june 20,

one into some multiple of 7, the other into the corresponding multiple
of 3 equal parts (actually into 21 and 9). Perpendiculars drawn
from the points of section divide the diameters into graduated parts,
representing the distances passed over by the end of the chain in
equal portions of time during each of the separate simple oscilla-
tions. Having completed the rhomboid ABCD, and divided it
into a multitude of small rhomboids by parallels drawn through the
divisions of its sides, we begin at the corner of any one of these,
draw a line to the opposite corner, thence into the next, and so on,
passing from side to side of the entire rhomboid, until we return to
the first point. In this way we get an approximate representation
of the path of the lower end of the chain when a plane oscillation
(B) is imposed on a plane oscillation (A).

But the chain may perform two simple oscillations (A) in different
planes, the result being an elliptic movement ; and so also of the
oscillation (B) ; and then the compound of the two (or rather four)
must be got by carrying the centre of the one ellipse along the
circumference of the other, in the manner used for the epicycloid.

These curves present an endless diversity of form, according to
the dimensions and relative positions of the ellipses. Adopting the
ratio 7 : 3 for that of the periodic times, some of these are depicted
in figure 4, a, b, e, d , e. In a and b the ellipses have been placed
conformably and the curves are symmetric ; for a the motions were
made both in one direction, and, as in the analogous case of the
epicycloid, there are four , that is 7-3, lobes ; for b one of the
motions has been reversed, and we find ten , that is 7 + 3, lobes ;
c and d are corresponding examples with the axes of the ellipses set
obliquely; while fur e the ellipse (B) is compressed into a straight
line. These examples may give some faint idea of diversity of char-
acter among the curves.

While the lower end of the chain is describing some one of
these curves, the points higher up are performing each its own peculiar
evolution. As we ascend, the dimensions of the ellipse (B) decrease
more rapidly than do those of (A), and consequently, along with
its extent, the curve changes also its configuration ; and when we
arrive at the height of the node B', the quicker ellipse has collapsed
into a point, and the chain there describes simply the ellipse due
to the oscillation (A). Above this height the ellipse (B) reappears,

Pr o cmoy S o c. E dinT

lag % .

Fig 4 l.

Vol _XIY. a IX

Tig 4 a /.

Fig 4 Z.

Fig 4 & •

1887.] E. Sang on Oscillations of Uniform Flexible Chain. 299

with its radii opposed to their former directions, and thus we have a
new series of configurations ; at the same time, owing to the incom-
mensurability of the motions, the whole of these configurations
undergo a gradual change.

When the chain divides in three, its simple oscillations take the
form shown in (C) of figure 4 ; while ( D ) and (. E ) show the forms
when the chain is divided into four and five oscillating parts. The
respective lengths of the corresponding pendulum, the periodic
times, and the frequencies of oscillation are given in the following
table, in which the whole length of the chain is taken as the linear
unit, and the periodic time of a pendulum of that length as the unit
of time.

No.

Pendulum.

Periodic Time.

1

•691 6603

•831 6512

2

•131 2712

•362 3137

3

•053 4138

•231 1143

4

•028 7686

•169 6132

5

•017 9427

•133 9102

6

•012 2488

•110 6742

Frequency.

1- 202 4128

2- 760 0391

4- 326 8640

5- 895 7672
7-465 4589
9-035 5320

1-557 6263
1-566 8249
1-568 9032
1-569 6917
1-570 0731

Here the almost uniform increase of the frequencies is remark-
able, the difference approximates to J7 r, and this is in accordance
with what has been said of the successive roots of the equation
x — 0. On comparing the frequencies themselves with tt, we find

for 1, J 7r x 3*0619 ;
for 2, -g- 7r x 7*0234 ;
for 3, Jttx 11-0183;
for 4, tv x 15-0136 ;
for 5, -Jttx 19-0106;
for 6, |tt x 23-0088 ;

and we are tempted to conclude that, when the chain vibrates in a
great number (N) of parts, the frequency of its oscillation may be
denoted by ^7 r x (4IST - 1).

The closeness of these results to a simple arithmetical progression

300 Proceedings of Royal Society of Edinburgh, [june 20,

is a warning to ns against too hasty conclusions from experimental
data. Let us suppose for a moment that the periodic oscillations
of a chain had been of great importance ; while as yet we had
only observation to guide us, means had been found for counting
the numbers per minute, and it had been found that, within all the
attainable accuracy these are as the alternate odd numbers, 3, 7, 11,
15, 19, — this with the greater precision the farther we prosecute our
trials. Here then we have discovered a periodic law ! Nature has
a partiality for small numbers, — vibrating bodies divide inharmonic
ratio, substances combine in easy proportions. So, in seeking for
the law of light’s refraction, the constancy of the ratio of the sines
was accepted as absolute, while, as yet, the inaccuracy of the observa-
tions was so great as to cover the whole range of dispersion. Nay,
while we firmly hold to the simple laws of pressure and motion as
revealed to us by our experiments, may it not be that these only
exhibit close coincidences, resulting from more deeply-seated prin-
ciples? We know of the law of velocity only from experiment, but
the velocities observed by us are only relative variations, mere zerre's
in comparison with the speed with which we and our apparatus are
hurried along.

The function which has been under review, and its derivatives
and primitives, are all deducible from the generic property

- a.g>z = n.lzg>z + 0. tefe

in which, however, n is restricted to be an integer positive number.
It may be interesting to inquire into the phases when this restriction
is removed.

On making the same supposition as before, namely,

<£z = A + Bz + C z2 + D^3 + , &c.,

we find

- a A = 1 .

-aB = 2.(n + 1)C

- aC = 3 . (n + 2)D, &c.,

whence

f a Z a2 Z2 a 3 Z3 «

(f)Z==A\ 1 _^T + ^ + l)L2“^+l)(w + 2)l7273 + ’

which formula is applicable to all cases except those in which n is a
negative integer, for then the denominator of an would come to be zero.

1887.] E. Sang on Oscillations of Uniform Flexible Chain. 301
Let us first consider the case when n is We get

f 2 a Z 4 a2 z 2 8a3 Z3 16a4 z 4 „ }

^2 = A) 1_TT + IT3 172” 1.3.5 lT273 + 1.3.5.7 1.2.3.4 + ’ &C' J '

Since the powers of a accompany those of 2, its value serves
merely to fix the scale on which the z’s are to he measured, and
does not at all affect the generality of the formula. Let us then
assume the generic condition

~ife = biz<f>z + z‘2z&’

and we at once get

<j>z = A

z z 2

1 . 2 + 1 . 2. 3. 4

z3

O

+

If, having only this formula to guide us, we inquire as to the
shape of the curve represented by it, our course is to compute the
values of the ordinate corresponding to various values of the
abscissa. The series converges much more rapidly than that for
the oscillating chain, and the points of crossing are much more
remote; thus the first would be found at 2 = 2-46740, the second
at 2 = 22*20661, and the third at 2 = 61-68503. These numbers
are exactly in the ratios of 1, 9, and 25, and the first of them is
just \tt2. Moreover, in the course of this arithmetical quest, we
should find that the ordinate varies within the limits + 1 and - 1,
unlike the preceding, where the limits decrease.

In the present instance, however, we readily perceive that on
writing v2 for 2, our series becomes

V2 V4 V6

1_rT2 + TT7i-l7^6+ &c‘

the well-known representative of cos v ; and that thus our function
may be written

4>z = A . cos Jz .

But this formula defines only one part of the curve, namely, that
on one side of the origin of co-ordinates ; for the other part we
must have recourse to catenarian functions, and write

c/>2 = A . rod J - z.

302

Proceedings of Boyal Society of Edinburgh. [june 20

This convenience, however, is a rare one ; for the case when
n = - J, that is when the generating condition is

\0z — — ^.iz6z z. %z0z

the expression becomes

„ A f I Z

0z — A. I 1 + vr ~

3z2

f

5z 3

7z4

1. 2.3.4 1....6 1

3 + &C. }

for which no such facility presents itself.

For the purposes of calculation this may he written

i+l-(>Th+()A-oA+&°-

z

0

z

376

z

5T8

where the mark ( ) stands for the precedin
term.

z

6z

+

8

—

•080

0038

+

7

+

•379

2051

+

6

+

•773

2548

4-

5

+

1-141

9518

+

4

+

1-402

4478

+

3

+

1-549

0238

+

2

+

1-552

8556

+

1

+

1-381

7733

0

+

1-000

0000

—

1

+

•367

8795

—

2

—

•558

4152

—

3

—

1-827

1822

The first or lowest intersection is between z— -2 and z= - 1,
the second between z = + 7 and z — + 8 ; but the position of the
third has not been examined.

r 1

When n is a rational fraction such as - , if we make a = -j, the

s s

function takes the form

, 1 Z 11

<t>Z— 1 h

1 1

Z‘

r

r r + s Is. 2s r r + s r + 2s Is. 2s. 3s

&c.

Z

=i_()l —+o —

r s r + s 2s

-()

1

z

r+2s 3 s

+ &c.

1887.] E. Sang on Oscillations of Uniform Flexible Chain , 303

in which the denominators are the continued products of the terms
of two arithmetical progressions whose common difference is s.

The cases of n being zero, or being a negative integer, demand
special consideration. When n is zero the above general formula
would give cf>z = A (1 — oo ) ; but this infinity does not exist in the
nature of the problem — it has been introduced by our mode of pro-
cedure. The original condition - acfjz = z.2z(fiz may belong to a

cc

variety of physical problems, as to this one 2tx = a-^, in which the

incitement to motion is proportional to the distance directly and to
the time inversely. In this case we get

<f>Z = B |

z

- a A = 1 . 0 . B ,
- aB = 2 . 1 . C

- aC = 3 . 2 . D

- aD = 4 . 3 . E

a 22 a2 £3

A = 0, B = B ,
- a

C

D =
E =

1.2

- a
273

- a

3~4

w

B ,

C ,

D , &c.
z4

1 1 1.2T 1.2 1.2.3 1.2.3 1.2.3. 4 + &c* }

When n = 1 we have

- a A = 1 , ( - 1 ) . B

- aB = 2 . 0 . C

- aC = 3 . 1 .D

-aD = 4. 2 . E

A = 0

B = 0 , C = C
- a

r) = L3 C’

E =

- a

2.4 D, &c.

, nrtf z 2 a 23 a2 Zi ft3 ( s n )

1 1.2.3 + 1.2 1.2. 3.4 ~ 17273 1.2. 3.4.5H eSC'/

And similarly for n= - 2

T O , T, f ZS « 24 , g2 t < l

'"•3 1.2.3 1 1...4 + 1.2 1....5 &C’ }

where we at once observe that each series is the primitive (integral)
of the preceding.

VOL. xiv. 14/11/87 u

304 Proceedings of Royal Society of Edinburgh, [june 20,

In our original inquiry the tension at any point was measured by
the length of the chain below it, but if we suppose a load w to be
appended, that tension will be represented by w + 2, and the condi-
tion necessary for a simple oscillation will be expressed by

-ax = lz{(w + z)lzx } = lzx + (w + z) ,

and then the investigation becomes much more complex. On using
the same method as before we find

- ah = l2.B + 1.2w.C; C= _aA + 12-B;

1 .ziv

- aB = 22.C 4- 2.3w. D; D = ;

Z.ow

4- V- D

-«C = 32.D + 3 Aw. E ; E= - 0+- i

6 Aw

in which each new coefficient is deduced from the two preceding
ones. In this case the computation of the coefficients is very tedious,
while that of the function and of its derivative is more so ; but
these being found for any given 2, the successive derivatives are
found as before, for

— a.x — lzx

— (w + z)2zx ,

ct • 12,0c ~~ 2 0 2 zpc

= (w + z)3xx,

& • 2 ^ • 3

= (w + z)^x ,

and thus it is easy to compute the value for any proximate value
of 2.

The complexity in the preceding case arises from the circumstance
that the terms of the series for w.2zx are displaced from those of
z.2x; and that, therefore, each new coefficient involves the two pre-
ceding ones. Now the terms of lzx} z.x, z2.2zx, &c., are all coinci-
dent, and thus we are tempted to go one step farther and to propose
for inquiry the condition

ax — n. lzx +PZ.&.X + z2. 2; x .

Proceeding in the same way as before, we have

x = A

+ Bz

+

Cz2

+

D Z3 +

Ez4 +

la? = B

+ 2Cz

+

3Dz2

+

4Ez3 +

5Fz4 +

2 . <izX =

1 . 2Cz

+

2,3Dz2

+

3.4Ez3 +

4.5Fz4 +

2 ™ _
. zJj

1.

2. 3D z2

+ 2,

.3.4Ez3 + 3.4.5Fz4 +

1887.] E. Sang on Oscillations of Uniform Flexible Chain. 305

and thence the equations of condition,
a A = %B

aB = (2w+1.2/>)C
aC = (3 n + 2 . 3p + 1 . 2 . 3)D
aD = (4 n + 3 . ip 4- 2 . 3 . 4)E
aE = (5^ + 4.5p + 3.4.5)F , &c.,

which may be written

aA = n. IB
aB = (n+ \p)2Q>
aC = (n + 2p + 1 . 2)3D
eiD = (n + 3p + 2. 3)4D ,

and in general

aQ = + (r - 1 )p + (r - 2)(r - l)}rP ,

and thus the denominator in the term containing ar zr is the con-
tinued product of the natural numbers 1.2.3. up to r, multiplied
by the continued product of all the terms of the progression

(n-p + 2) + r(p — 3) + r2

for all values of r up to the same limit.

The terms of this progression can be resolved into products when-
ever n and p are such that (p - \)2 - in is a square number, and
then the denominators are the continued products of the terms of
three arithmetical progressions.

Thus when p — 3 and n = 1 , that is when the condition ax = lzx +
3z . ^ + z2 . 3zx is proposed, the solution becomes

x — A

- az a2z2

1 + 1

l3 13.23

+

a323

13.23.33

+ &c

■ }

in which the three progressions coincide.

On introducing fractional coefficients we get arithmetical pro-
gressions with differences other than unit ; thus, on making a — ^,
2

n = g p — 2 the three progressions become

1, 4, 7, 10, &c. ; 2, 5, 8, 11, &c., and 3, 6, 9, 12, &c.,

whose terms just fill up the progression of natural numbers, so that
for the condition

306 Proceedings of Royal Society of Edinburgh, [june 20,

we have

2

9

lzx+ Zz.^x + z2. 3zx

x — A

{

Z Z2 Z3 (J>

1 .2 .3 ~r I.2.3.4.5. 6 ~ 1 9 + t C

J

which is related to recurring functions of the third order.

There is thus opened up a wide field for research, rendered,
however, unprofitable by the absence of application to physical
phenomena.

3. Note on the Biological Tests employed in determining
the Purity of Water. By A. W. Hare, M.B. Edin.
(Plates X., XI.)

(From the Public Health Laboratories, Edinburgh University.)

Part I.

There are two experimental paths by which the facts relating to
organic impurity in water may be approached, the chemical and the
biological ; and there are two aspects in which these facts may be
regarded, the catalytic and the fermentative. The series of observa-
tions made in following the one path is the necessary complement
of that met with in the other. The path of chemical investigation
has been well cleared, and is easily traversed ; that of biological
inquiry is still beset by many impediments, and is as yet by no
means a safe one. It is the object of many recent researches, and
of this paper, to lessen these difficulties. The pollution of water
with organic substances is inevitably associated with the presence
of those organisms whose function it is in the economy of nature to
disintegrate such materials. These organisms in their turn are
dependent upon organic matter for their continued existence ; the
Bacteriacem to which they belong being distinguished from allied
forms by an entire absence of chlorophyll, which obliges them to
feed only on organic substances. The relation of these two factors
of pollution, each to each, is therefore a necessary one ; and due
regard must in all cases be paid to each in determining the degree
of pollution that their coexistence implies. It is further of

1887.] Mr A. W. Hare on the Purity of Water .

307

importance to inquire if their relation to one another can he more
closely analysed, and whether specific features of the one factor
are necessarily related to a certain constitution of the other. A
well-established case of such a relationship may be here cited in
illustration, and as indicating the direction in which the present
inquiry is to proceed. The Beggiatoa alba , a well-known fila-
mentous organism, is an inhabitant of warm sulphur springs, in
which it carries on a definite analytical function, decomposing
sulphur compounds in solution in the water, and giving off sul-
phuretted hydrogen. That such facts are of frequent occurrence
is shown by the work of Pasteur in the case of the Torula group ;
while the elaborate researches of Duclaux exhibit functional
specialism in this respect carried to an astonishing degree of com-
plexity. It is not then beside the mark to press the analysis of
aquatic microbes one stage further, and to inquire whether, in
addition to the fact of organic contamination predicable from their
presence, there is not a possibility of recognising definite species,
associated with special forms of organic material, particularly such
as are derived from sewage matter. In making this attempt an
initial difficulty is met with in the fact that a complete classification
of Bacteria according to their function is not yet made; their
provisional division into zymogenic, pathogenic, and chromogenic
forms, though of great dialectic convenience, is of no value in practical
questions, for each division is in part overlapped by portions of the
other two. A new classification must therefore be attempted to suit
the conditions of this inquiry ; and that which specially commends
itself as at once practical and well adapted to our purpose is based on
observing the nature of the pabulum on which various species subsist;
thus dividing them into groups according to the complexity of their
assimilative processes, as higher groups of organisms may be classi-
fied according to their carnivorous or herbivorous habits of life. In
the case of the Bacteria this classification can rest on no such
obvious diversity of function, for they are distinctly omnivorous ;
but there are important differences in the composition of the organic
matter in water, corresponding to the different sources from which
it is derived, and it is not unreasonable to expect that analogous
differences will be found to obtain amongst the species of microbes
associated with it. Two chief sources of organic material in rivers

308 Proceedings of Royal Society of Edinburgh. [june 20,

are to be recognised : the natural processes of vegetable growth and
decay contribute a large amount of soluble material which is carried
down by land drainage ; the other source, which supplies both
soluble and insoluble organic matter, is the drainage of towns where
a flushing system of sewage disposal obtains, and where its products
are poured into rivers. There is an important difference between
the organic material derived from these two sources. This differ-
ence does not depend on an original diversity of character between
animal and vegetable waste products ; for though such a diversity is
doubtless recognisable by delicate tests, it is too fine a point to found
a generalisation upon for any practical purpose. But the difference
that does obtain is due to the disparate stage of waste product
decomposition in which organic matter from the two sources reaches
a river. In both cases the disintegration is carried on by the
analytical action of micro-organisms, and finally results in the pro-
duction of such simpler substances as binary compounds of C, H,
N, and 0. In the vegetable waste products from land drainage
this process is far advanced, and the resulting materials are in a
soluble and much simplified form by the time they reach the river
water ; whereas in the animal and vegetable waste products present
in sewage the process is only commencing, and in places where the
drains are flushed into a river, additional insoluble matter may be
introduced, and may pass far down the stream before even the first
stage of its disintegration takes place, rendering it soluble, and thus
in a position for the completion of the process. It remains then to
inquire, in regard to the disintegration of organic matter, whether
the same microbes are present throughout the whole process, or one
group of ferments is replaced by another in correspondence with the
constantly changing chemical equations that express the several
stages by which it advances. That the latter is the case, analogy
strongly suggests, and experimental results go far to prove. As an
analogous case, that of the fermentation of sugar offers a good
example, where the first stage of the process is due to the action of
the Torula cerevisece , and concludes with the formation of alcohol ;
the further stage of acetous fermentation being produced by a
distinct species, the Mycoderma aceti. A similar case is that of the
lactic fermentation of milk, where Bacterium lactis initiates the
process, changing lactose into lactic acid, at which point the

309

1887.] Mr A. W. Hare on the Purity of Water.

Bacillus butyris makes its appearance, and from the lactic produces
butyric acid. It is difficult to prove distinctly that the same law
holds true in the disintegration of so complex a compound as
sewage matter ; but the direct evidence obtained from the investi-
gation of decomposing animal solutions points to that conclusion.
In such a substance Bacterium termo and its congeners appear, and
carry on their special functions of decomposition in a definite
sequence, one group commencing it labours where another has
completed its special share in the process. In the sequel, it will
appear, from a series of observations recently made, that different
species of microbes preponderate in the different areas of a sewage-
laden river, and it will be attempted to show how these distinctions
probably depend on the advance of successive fermentative processes
from stage to sta go, pari passu with the flow of the river from point
to point, from its initial area of sewage contamination till it is
restored to a state of relative purity. In the meantime, however,
the status of microbes in water of different qualities requires
attention. For the purpose of description it is convenient to
differentiate four qualities of water, viz., distilled water, spring
water, river water, and dilute sewage.

1. Distilled Water. — The absence of organic matter prevents any
great development of microbes in this medium. Yet marked
diversities are found in the behaviour of different species in this
respect. Whilst it has been shown by Crookes, Tidy, and Odling
that Bacillus anthracis does not long survive its introduction into
distilled water, and by P. Frankland that the same is true of Koch’s
Comma bacillus and of Finkler’s and Prior’s bacillus , yet it has been
shown that the hardy Bacillus pyocyaneus is capable of surviving
for a considerable time in such conditions, and that, in the first
place, it even increases in numbers (P. Frankland). Many of the
ordinary species present in atmospheric dust are also capable of living
in distilled water ; hence the necessity known to all bacteriologists of
keeping distilled water used for microscopic purposes rigidly free from
direct contact with the air, and of frequently obtaining supplies
freshly prepared. But these contaminations, though very serious
where exactitude of microscopic observation is at stake, have no
immediate hygienic importance, and we may consider distilled water
at least as an absolutely safe substance for human consumption.

310

Proceedings of Royal Society of Edinburgh . [june 2Q;

2. Spring Water . — Water from deep wells is always, in the first
instance, nearly free from the presence of microbes; that from shallow
wells may be seriously contaminated with sewage matter, and may
be loaded with organisms. Deep wells in the chalk at times supply
water rich in organic matter, but which only yields evidence of
microbic activity after it has stood for a time in contact with the
air. In such cases it is not unfrequently more crowded with
organisms even than river water, — a condition probably due to the
smaller number of species present in such cases ; for thus the struggle
of opposing vital requirements is avoided, and the total sum of pos-
sible individual life thereby increased.

3. River Water. — Glacier water is free from microbes, but in all
other cases river water contains a larger or smaller number of micro-
organisms, depending on the relative amount of organic matter that
it holds in solution. The nature of the land drained by a river, the
presence or absence of direct sewage infection, and the speed of
its flow, are the chief conditions affecting the purity of its water.
As will be shown in the second part of this paper, the popular sen-
timent in favour of rapid and tumultuous rivers as a source of
domestic supply is probably based on a misconception, and is com-
pletely at variance with sound deductions from the facts of the case.

4. Sewage. — The rich supplies of organic matter here present permit
of an enormous development of microbes, but the fermentative activity
thus established is of a duration inversely proportional to its inten-
sity. After a maximum development occurring on the third or
fourth day, a rapid decrease is observed in the number of microbes,
so that in the course of a week to ten days there may be a smaller
number in a sample of sewage than in a stored specimen of river
water (Bischof). In this case the large amount of food material is
rapidly exhausted by the disproportionate production of microbe
life ; and when the supply comes to an end, the death-rate amongst
the microbes is for a time excessive.

We must now turn to the tests employed in determining the
number and varieties of microbes present in water, and inquire into
their accuracy and reliability. Various methods have been suggested,
some giving quantitative, others qualitative results. It is obvious
that a method giving reliable information on both points is desirable,
since the total number of microbes present in a specimen of water

311

1887.] Mr A. W. Hare on the Purity of Water.

gives an indication of the quantity of. organic matter necessarily pre-
sent for the support of so much life ; and the special forms present
and their proportion to one another, is no less important, from the
indication thus given, as the sequel will show, of the state of decom-
position at which such organic material has arrived.

(a) Of the purely quantitative biological tests that by l( dilution ”
may be mentioned, employed by Fol and Dunant. It consists in
enormously diluting the sample to be tested with germless water in
a known proportion, and in inoculating a large number of culture
glasses with equal quantities of this mixture. The proportion of the
culture glasses remaining sterile to those showing microbe life affords
a basis for calculating the number of germs in the original specimen.
This method is inexact ; it labours under the twofold disadvantage
of depending on perfect mechanical mixing under great difficulties,
and of the certainty that the culture fluid used could not suit the re-
quirements of every microbe present; some, therefore, would not grow
in it, and would be omitted from the calculation. When the number
thus obtained is multiplied by the number of dilutions previously
carried out, the omissions thus made will be multiplied, and the re-
sulting error in the calculated total most serious.

(b) Of the purely qualitative methods may be mentioned that by
“ fractional cultivation,” successfully employed by Lister in separat-
ing species from one another. It is, however, so laborious as to be
inapplicable for practical purposes, although it was primarily instru-
mental in establishing the important scientific principle of specificity
amongst microbes.

(c) Another method is that proposed by Dupre, in which the
nature of organic impurities present is determined by observing
changes in the aeration of water, the gases absorbed and given off
giving an index of the amount of vital action occurring in the speci-
men investigated. It must be seriously doubted whether this can
ever be developed into an accurate method of observation : the
factors of sewage contamination are so variable under varied condi-
tions, that a uniformity of results is scarcely to be hoped for ; while
there is room for so many fallacies in this method, that it would
require confirmation from others before its results could be accepted.

(d) By far the best method of determining the number and
varieties of microbes in water is that introduced by Koch. It con-

312 Proceedings of Royal Society of Edinburgh. [june 20,

sists in mixing a sample of water of definite bulk with a quantity of
liquefied nutrient jelly previously sterilised. This mixture is poured
on a sterile glass plate with aseptic precautions. When it solidifies,
the microbes in it are fixed and develop, each becoming the centre of
a colony growing in the jelly, and each colony representing a “ pure
cultivation ” of its parent germ. The number of such colonies
bears a definite relation to the total number of microbes present in
the original sample of water, and their varied appearances show with
what diversity of species the sample was inhabited. Species which
cannot be recognised in this way at once may be identified by re-
moving a portion of one such colony to a separate quantity of
culture material, in which its characteristic growth may be separately
observed. A convenient form of apparatus is shown in Plate X.
It consists of a deep glass bell of 8 inches inside diameter, standing
in a glass dish that closely fits its mouth. Within are alternate
square glass plates and india-rubber washers, fitting closely to the
inside of the bell-jar. When the apparatus is closed it will travel
safely without any movement of the plate, and can thus be conveyed
to the near vicinity of the water which it is desired to test. The
plates are sterilised by heating at 170° C for one hour, and
the rings by steeping them in 1 per cent, aqueous solution of
per chloride of mercury for twenty-four hours. A piece of thick
filter paper soaked in the same solution is placed in the floor of the
apparatus. A series of ten or twelve plates is contained in the
apparatus. In making observations the upper two or three of these
should be used as “ control ” plates, since they run the greatest risk of
aerial contamination from their longer exposure to the air in manipu-
lating the apparatus. They are charged with a layer of the
nutrient jelly alone without the addition of the water to be tested.
If they give negative results, i.e. if the layer of nutrient jelly
upon them shows no foci of microbic growth, the manipulative
procedure in the experiment may be considered reliable. In
examining a river for microbes at different parts of its course,
one such set of twelve plates may advantageously be used at each
point, a measured quantity of the water being used in each case,
so that the experiments may have uniformity of scale throughout.
Two such experimental plates are shown in Plate XI., in which
the results of the test are shown in the case of a river examined

Proc. Roy. Soc.

Vol. XIV PLATE X.i

Plate Cultivation made with five drops of River Water Plate Cultivation made with five drops of River Water

above the point where the Sewage enters. below the point where the Sewage enters.

P roc.

Roy S

oc.

~n

o

*u

>

H

n

H

>

tn

r

n

Vol.XIV PLATE. XI.

1887.] Mr A. W. Hare on the Purity of Water.

313

immediately above, and again immediately below a source of sewage
contamination. The results obtained by this method in the case of
a rapid river with gross sewage contamination will be detailed in
the second part of this paper, where special attention will be drawn
to the way in which this test is of value in associating special forms
of microbes with special conditions of organic decomposition, thus
acting as a qualitative test of some degree of definite value in deter-
mining the purity of water.

(e) Another biological method is an extension of the preceding.
Having found by the preceding method what organisms are usual
inhabitants of a river, the introduction of a foreign organism at a
certain point, and its recovery from the stream at another by plate
cultivations, may give valuable evidence as to the condition of the
river-water between these points. The organism so employed must
be perfectly distinctive in its mode of growth, and its relation to
other organisms well known, as also its powers of survival and mul-
tiplication in a variety of conditions. Given these data, much may
be learned from its behaviour in various areas of the river examined.
In the second part of the paper such an experiment will be described.

In the present state of our knowledge of water testing, it would
be unwise to discard the methods of chemical examination for any
one, or a combination, of the above biological tests. But some of
them, and particularly that of Koch, are capable of affording strong
corroboration of the results obtained by chemical tests; and since
it is its vital rather than its purely chemical contaminations that
render water a source of danger to the health of the human subject,
it may safely be predicted that, when extended and rendered yet
more exact, these biological tests will become an essential element
in the experimental determination of the purity of water.

4. Alternants which are Constant Multiples of the
Difference-Product of the Variables, By A. H.
Anglin, Esq., M.A.

314

Proceedings of Boyal Society of Edinburgh . [june 20,

5. Glories, Halos, and Coronse seen from Ben Nevis Obser-
vatory. Extracts from Log Book. By R. T. Omond.
Communicated by Professor Tait. (Plate XII.)

Bed 2
Bed and
Blue
Bed1

D

May 23, 1886. — Solar corona seen at 12h. Colours
as in margin. Inner and outer reds distinct, but space
between very mixed in colours.

Radius of inner red, . 3° 25' 3° 25' 3° 18' 3° 25'

„ outer red, . 6° 41' 6° 35' 6° 41' 6° 41'

May 27, 1886. — At 13h bright solar halo seen; red inside, then
yellow, and blue outside.

Radius

of Red.

Yellow.

Blue.

I.

21°

24'

23° 44'

24° 43'

II.

22°

0'

22° 49'

24° 43'< — >

III.

22°

12'

23° 30'

24° 13' |

IV.

22°

0'

23° 3'

24° 43' f

The double-headed arrows show the diameters along which the
measurements (I., II., III., and IV.) were taken.

June 4, 1886. — At 5h 10m halo and mock suns seen. Halo red
inside and blue outside. Mock suns at each side, so bright as to
be dazzling ; right hand the brightest. Radius from centre of sun to
centre of mock suns = 23° 17'. Vertical white beam below sun, and
horizontal segment passing through mock sun ; this horizontal arc
was 12° 32' above the level-topped haze that hid the horizon. The
mock sun on the right was white and outside the red of the halo ;
the mock sun on the left side was coloured red, yellow, and blue
in same order as the halo. The following measurements of the
halo were made

Radius of red, . 22° 36' 22° 36'

„ yellow, . 23° 3' 23° 30'

„ blue, . 23° 44' 23° 44'

At 8h the halo was seen again ; rather faint.

Radius of inside of red, 22° 0'
,, outside of red, 23° 17'

,, outside of blue, 24° 43'

Measured on lower
segment of halo.

1887.] Mr R. T. Omond on Glories, Halos , and Corona ?.

315

August 14, 1886. — At 13h solar halo observed; no colours
visible. Radius = 23° 30, 23° 3', and 22° 36'.

October 7, 1886. — At 12h a solar fog-bow was observed. No
colours, only a broad white band.

Radius to inside of bow, . . 36° 20'

„ outside of bow, . . 43 36'

October 22, 1886. — Fog-bow seen at ID 25m. Colours as in
fig. 1 ; the order of colours in the glory was not determined. No
measurements were got. The pink was a badly-defined space, not
a true band.

October 25, 1886. — At 16h glory seen on fog to N.E. ; rather
misty and badly defined. Four rings, inmost a mere blotch;
second — the brightest of the four — yellow and red ; third, green and
red ; fourth, only red seen clearly. The third and fourth were only
seen occasionally.

Radius of first red,

„ second red, .
third red,
fourth red, .
yellow in second ring,
green in third ring,

November 5, 1886. — At 18h lunar corona seen; Blue
colours as on margin (outer blue probably a margin).

Radius of red = 2° 17' and of blue = 4° 43'. D

Well-defined halo seen all evening. Two measurements gave
as radius 22° 36' and 22° O'.

November 12, 1886. — Double fog-bow seen at 13h; outer bow
white, inner bow red and blue, red being inside.

Triple corona seen at 19h (lunar), colours as in margin.

Radius of inside red, . 1° 2J'

middle red, . 2° 29'

middle green, . 2° 3'

))

)>

1° 10' (bad observation)
3° 46'

6° 18'

7° 22'

2° 55'

4° 31'

j?

S5

Size apparently varying. Measurements were stopped
by the ice crystals deposited by passing mist clogging
the stephanome.

Portion of halo seen at 21h. Radius = 21° 13'.

Bed

Green

Blue

Bed

Yellow

Green

Blue

Eed

White

D

Proceedings of Royal Society of Edinburgh. [june 20,

November 14, 1886. — Triple lunar corona seen at 5h.
Colours as noted on margin.

Eadius of inner red, . 1° 23J'

,, middle red, . 2° 52'

,, outer red, . 3° 36'

,, inner blue, . 1° 34 J'

November 16, 1886. — Fog-bow seen at llh; red outside and
white inside. A fainter bow was seen inside this one at times.

December 16, 1886.— Glory and fog-bow seen at 15h, too fleeting
to measure. The glory was double, with reds outside ; the fog-bow
a broad whitish band, with occasionally another bow inside it
more sharply defined and coloured, but the order of its colours was
not observed.

December 20, 1886. — At 12h upper half of halo seen ; red inside,
white outside.

Eadius of middle of red, . . 21° 54'

,, junction of red and white, 22° 12'

,, middle of white, . . 23° 58'

December 26, 1886. — At 12h 30m misty glory and double fog-
bow seen ; outer bow had red outside, and inner bow red inside.
No measurements got.

December 30, 1886. — Double fog-bow seen at llh. Eed outside
outer bow and inside inner bow. The following rough measure-

ments were got : —

Eadius of outside of outer bow, . .41° 22'

„ middle „ . . 39° 20'

,, inside ,, . . 36° 36'

,, outside of inner bow, . .34° 44'

,, inside ,, . . 32° 20'

The first and last measurements give the radii of the outer and
inner red respectively.

Misty glory seen at 1 5h, colours as in fig. 2 ; the central spot a
confused mass of colour.

316

Eed 3
Green
Blue

Eed 2
Green
Blue
Eed 1
White

D

Eadius of red, .

. 1° 53'.

1887.] Mr R. T. Omond on Glories , Halos, and Coronce. 317

January 2, 1887. — At 18h triple corona seen, red outside in all
three rings ; outermost ring faint and evanescent. At times a
fourth ring was seen inside these, surrounding white space near
moon, but it was too small to measure (less than 50'). This corona
was formed on scud, size varied.

Radius of innermost red, . . 1° 22'.

,, middle red, . . 2° 5'

,, outermost red, . . 4° 23'.

When no scud was passing a (faint) blue corona was seen on the
clear sky. Radius = 3° 2'. Lunar fog-bow was also seen at 18h.
Radius about 38° 40'.

January 3, 1887. — Triple corona (lunar) seen at 19h; red
outside in all three rings.

Radius of first red, . . 0° 54' 0° 56' 1° 0'

,, second red, . .1° 48'

,, third red, . . 3° 36' 3° 15'

January 5, 1887. — Solar corona seen at 13h;
margin.

Radius of red1, . . . . 3° 7'

„ red2, . . . . 6° 12'

„ extreme outside of red1, . 4° 13'

colours as on

Red2
Green
Red 1
White

o

Lunar corona seen at 22h, colours as on margin ; yellow bands
narrow, but green broad and badly defined.

Radius of inner red, . . .3° 20'

outer red, . . .6° 29'

inner yellow, . . .2° 36'

outer yellow, . . .5° 22'

J5

}?

Red2

Yellow

Green

Red 1

Yellow

White

1

January 8, 1887. — Lunar halo seen at lh. Three measurements
of radius to inside edge of halo gave 21° 36', 22° O', 20° 5L,
Double solar corona seen at llh.

Radius of inner red, . . . 3° 31'

„ outer red, . . . 6° 7'

At same hour glory seen with four rings ; larger than usual, and
the colours broad and soft-looking. The innermost red was only
seen occasionally.

318

Proceedings of Royal Society of Edinburgh, [june 20,

Radius of second red, . . . . 4° 46'

„ third red, . . . 8° 43'

,, fourth red, . . . . 12° 6'

While measuring this glory, a cloud passed to southward of Ben
Nevis, and its shadow blotted out part of these three rings, hut did
not fall on the observer.

At 12h portion of glory seen on clouds to northward, though at
the time the shadow of the observer fell inside the edge of the
cliff (see fig. 3).

February 6, 1887. — Lunar fog bow seen at 2h.

Inside radius,
Outside „

33 56 ) , bow 6° 24' broad),
. 40° 20' J

February 8, 1887. — Double lunar corona at 23h and midnight.
Rather indistinct, apparently formed on cirrus clouds.

Radius of inner red,
outer red,

>)

2° V
4° 40'

February 9, 1887. — At 6h double lunar corona seen; colours as

Red2

Green

Blue

Violet

Red1

White

D

on margin.

>>

5)

1° 45' l
2° 19'

2° 50'

3° 15'

4° 0'

Radius of inner red,
violet, .
blue,
green, .
outer red,

February 12, 1887. — Double lunar corona seen at 7h; colours
as on margin. ;

Radius of inner red, . . 1° 14'

purple, . . 1° 34'

Red2

Yellow

Green

Purple

Red1

White

D

t?

jj

9 ?

green,
outer red,

1° 49'
2° 28'

February 13, 1887. — Double fog-bow seen at 12h, Trace
of red outside outer and inside inner bow. No measurements

gob

February 15, 1887. — A few passing glories seen at 14h 10m.
Solar corona observed on scud at 12h, always double, sometimes

1887.] Mr R. T. Omond on Glories, Halos, and Coronce. 319

triple; best seen when the send was uniform in thickness — not

filmy — and thin enough to see the blue sky through. The follow-
ing measurements were got ; those bracketed together were taken
at as nearly as possible the same time.

Radius of inner red, 3° 35' 3° 31' t 3° 52' j 4° 13' 3° 21'

„ outer red, 4° 28' 5° 43' 1 6° 55' i 7° 38

March 1, 1887. — Solar corona seen at 13h 10m on passing scud.
Three rings, red outside in each. The following measurements
were got : —

Radius of first red,

I.

1° 46'

II.

III.

IY.
1° 41'

„ second red,

29 26'

2° 34'

2° 39'

LO

o

t—1

„ third red, .

o

°q

...

...

...

At the same hour a faint red corona was seen on cirrus clouds
when the scud cleared off. Radius about 0° 56'.

At 17h misty red colour under sun, and solar corona formed on
scud. Three rings, red outside in each.

I.

11.

Radius of first red,

1° 41'

1° 25'

,, second red,

2° 23'

2° 26'

„ third red, .

3° 54'

. . .

III.

1° 19'
2° 30'

March 4, 1887. — Glories seen on passing fog all day. At llh
15m one seen from roof of Observatory, the shadow of the observer
falling on the snow about 10 yards away. Colours in following
order : — Shadow, white, red1, blue, green, red2, blue, reds.

Radius of inside edge of red1, . . 2° 15'

,, outside edge of red1, . . 3° 12'

Another glory seen from edge of cliff at llh 30m; no fog-bow
with it. It had four rings of colours arranged in the following
order : —

(The radii are given with the colours ; measurements taken to
outside of colour in each case.)

Vol. xiv. 15/11/87

x

320 Proceedings of Eoyal Society of Edinburgh, [june 20

Colours.
Faint red4, .
Faint green,
red3, .
yellow,

green,

Radii.

9° 28'

6° 12' and 6° 18'
5° 14'

40'

4°

4°

3° 25' and 3° 35

5JL'

°2

Dark bine, ....
red2, ....
yellow,
white,

Bad blue,

Yellowish red1, .

Centre of shadow.

The radii appeared to vary slightly as the surface of the fog on
which the glory was formed rose and fell.

Another glory seen at 14h 5m from edge of cliff. Four rings
with red outside in each.

1° 1 J' and 1° 4J'

Badius of second red,

.

3° 46'

,, seond yellow,

.

2° 40'

,, second blue,

.

1° 43'

,, third red,

.

10° 27'

„ third yellow,

.

6° 12'

„ third green, .

•

4° 25'

Bright glories, too fleeting to

measure,

were seen

the loose fog drifting across the hill top.

Solar corona seen at ll11 10m.

Colours and radii

n n Rad. to Centre

Colours. Qf Colour_

To Outer Edge
of Colour.

O

White,

Bed1,

Dark blue,

Green,

Bed2,

Dark blue,

Green,

Bed3,

Dark blue,

Green,

Bed4,

2C

2°

9'

30'

3° 54'

6° 48'

7° 591'

2° 27' and 2° 30'

4° 43' and 4° 37'

To Inner Edge.

1° 40'

3° 31'

1887.] Mr R. T. Omond on Glories, Halos, and Cor once. 321

Another solar corona seen at
12h 10m. Colours and radii
(outer edge of colour in each case)
as on margin.

o

Radii.

White

Yellow

• o •

Red1

. 2° 39' and 2' 39'

Dark blue

• • • •

Green

• e • •

Yellow .

.

Red2

. 4° 46'

Dark blue

.

Green

Red3

’. 7° 55'

Blue

Red1

. 9° 41'

Solar halo seen between 9 and 10 hours, as sketched in fig. 4;
colours as marked. The mock suns were red inside and blue outside;
they lay distinctly on the outer edge of the halo (A). The follow-
ing measurements of them were got : —

Radius of red,

,, white,

,, blue,

Left Moek Sun.

22° 49' and 23° 17'
23° 44' and 24° 13'
24° 28'

Right Mock Sun.
23° 3'

24° 13'

24° 58'

Faint traces of green and yellow were seen in the mock suns at
10h 10m. The mock suns and horizontal white bar were about 24°
above the horizon at 9h. As the sun rose higher the bar curved
upwards, and at noon was as sketched in fig. 5. The bar then
extended inside the halo A almost to the sun, which it had not
done in the morning.

The following measurements were got at various times during the
forenoon of the different parts by Mr Rankin : —

Sun to western mock sun, 23° 46'

,, eastern „ 23° 42'

,, white circle E, 79° 56' and 81° 23'

,, green at junction of C and I), 50° 26'

Red of C to red of A, 25° 28' and 24° 48'

Blue of C to blue of A, 25° 13' and 24° 32'

Green of C to green of A, 24° 20'

The arc B distinctly overlapped the halo A, the reds coinciding
above the sun ; but the arc D only touched the halo C, its red
combining apparently with the blue of C.

At 12h 20m measurements were made of the wings between halo

322

Proceedings of Royal Society of Edinburgh, [june 20,

A and arc B. Two points, P and Q (see fig. 6), were taken, and
tlieir distances measured from the sun (S) and the mock sun (Z).

S to Z
P to Q
S to Q
S to P
Z to Q
Z to P

23° 42'
13° 22'
24° 8'
29° 52'
28° 56'
19° 34'

The wings were not arcs of one circle; judging by the use of ring
of stephanome, their centres of curvature lay about midway between
the sun and the mock suns on either side.

One mock sun was seen again at 17h.

Radius of red, 22° 0' ; of yellow, 22° 36' ; of blue, 23° 17'.

March 16, 1887. — At ll11 two mock suns, with faint trace of white,
horizontal circle outside of them, seen on apparently perfectly clear
sky. No trace of 22° halo. Radius of eastern mock sun = 25° 13'.

April 5, 1887. — At 3h, double lunar
corona seen; colours and radii as on

Colour. Radii.

Red2 . . . 4° 13'

Yellow2 . . 3° 58'

Blue

mar§m* Red* .

Fog-bow (faint) seen at the same Yellow1 .

& x 7 Bluish White

time. ])

May 13, 1887. — At llh pink-coloured cloud seen with upper

part under sun, coloured blue, green, and red. Length of cloud

10'

38'

= 103°. Breadth = 6° 30'.

Radius of green (only distinct line of colour) = 12° 36'.

This cloud vanished suddenly, showing a halo on cirrus much
higher up. Shortly afterwards the halo got more distinct ; it had
inside it another ring, as in fig. 7. The outer ring was a distinct
halo, with red inside and blue outside; radius of red = 22° 12'.
The inner ring had only a faint tinge of red inside ; radius of this
red = 17° 54'. By llh 15m all had disappeared.

Coloured clouds were seen again several times during the day,
and at 1 7h a solar halo was again observed. The folloAving measure-
ments were got : —

Radius of red,

yellowish green, .
blue, .

. 21° 54' and 22° 12'

. 23° 17' „ 23° 17'

. 24° 28' „ 24° 13'.

y>

1887.] Mr R. T. Omond on Glories, Halos, and Coronce, 323

No trace of an inner ring was visible.

June 3, 1887. — Solar halo seen at llh and 12h.

At llh radius of red, .... 22° 18'

„ „ blue, .... 22° 43'

At 12h the halo had a segment projecting from its S.E. side (as
shown in fig. 8) that appeared to cut into the halo, but was not
visible inside it. The halo was brightly coloured — red inside and
blue inside ; the segment was tinged with red inside.

Radius of red of halo, . . . 22° 18' and 22° 0'

„ red of segment at farthest

point from sun, . . 25° 28'.

June 10, 1887. — Faint glory seen at 4h; no measurements got.

June 20, 1887. — Solar halo seen at 4h and 6h ; no measurements
got.

June 28, 1887. — Fog lying over the hills round all day, and
occasionally covering Ben Nevis also. At 20h glory seen on this
fog; three rings, badly defined, and too fleeting to measure, but
the middle ring was distinctly the brightest. Red outside in all
the rings.

June 29, 1887. — Fog-bow, occasionally double, observed at 5h
and 6h.

July 2, 1887. — Solar halo, seen at 7h, red inside; rather broad
and faint. Seen again at 9h and at 13h.

July 21, 1887. — At 10h 50m, a double glory was observed from
edge of cliff. The following measurements were taken : —

Radius of inner red, . 1° 57' 36" : 2° 1' 12" : 1° 59' 14"

,, outer red, . 3° 18' 0" : 3° 19' 30".

A double fog-bow was also seen at times. Red inside inner bow
and outside outer bow ; the rest of the bows were white.

A solar halo was seen at 8h ; no measurements got,

July 31, 1887. — Double rainbow7 seen at 18h 45m, primary bow
the brightest. Red outside primary, and inside secondary. The
following measurements were made from the centre of shadow of
observer’s head : —

Radius of red of primary, . . 42° 48' : 44° 17'

,, secondary, . . 53° 8'

324

Proceedings of Royal Society of Edinburgh, [june 20,

August 17, 1887. — Glory seen at 5h 7m. Single ring, badly
defined, with occasional traces of second outer ring. Radius of red
of first ring (two measurements), 3° 42' and 3° 52'.

August 19, 1887. — Glories seen about 9h 40m. Two rings distinct,
and two others outside these indistinct. Red outside in all. The
colour next the shadow was yellow; between its red (i.e., red1) and red2
was violet, and between red2 and red3 green. No measurements got.

A fog-bow was seen at 9h 45m, with glory inside it round shadow.

At 10h 22m another glory seen at cliff ; red outside, radius = 2° 36'.
The violet was a broad band reaching nearly, if not quite, to the
shadow.

Two other measurements of different glories about the same time
gave for radius of red, 3° 4' and 3° 13'.

Misty glories were seen at various times during the day.

A rainbow was seen at 19h.

August 21, 1887. — Triple glory seen at about 9h 30m ; colours as
in fig. 9.

Yellow* and red1 faint.

Yellow2 and red2 very distinct.

In 2 there was no green, and in 3 no blue [or only faint traces in
both cases].

In 3 the green and red were the most distinct colours ; yellow
barely visible.

When clouds or fog blew up the corrie where the glory was seen
the colours got blurred and indistinct.

The following measurements were taken by Mr Herbertson : —

Radius of yellow2 (inside edge of colour), . 2° 36' and 2° 32'

„ junction of yellow2 and red2, . 3° 15' „ 3° 29'

,, red2 (outside edge of colour), . 4° 25' „ 4° 18'

„ red3, „ . 7° 30'

„ green3, „ . 6° 48'

August 23, 1887. — At 5h 20m glory seen from window in tower
door. Two and three rings seen; red outside in each. No measure-
ments got.

August 28, 1887. — At 14h a rainbow was seen.

September 1, 1887. — At 22h an ill-defined white lunar halo was
observed.

1887.] Mr R. T. Omond on Glories , Halos , and Coronae. 325

September 4, 1887. — At 4h a lunar corona
observed; order of colours as shown on margin,
fleeting to measure.

was

Too

Pinkish red
Blue
Yellow
White

D

September 18, 1887. — Glories seen from edge of cliff in afternoon.
At 13h 30m measurements were made as under : —

Radius.

Outside of red2,

Middle of red2,

Inside of red2,

Green,

Blue,

Outside of red1,

Middle of red1,

Inside of red1,

Red glow round shadow, .
Shadow of observer,

6° 24' and 6° 29'
5° 34'

4° 56' and 5° 3'
4° 43'

4° 23'

4° 51' and 3° 46'
3° 44' „ 3° 35'

2° 56'

1° 121'

A fog-bow was observed at the same time, measuring 35° 16',
[To inside of bow ?]

September 21, 1887. — Tog lying over and hiding all the lower
hills most of the day. On this glories were seen frequently ; the
following measurements were got at 7h 10m. Order of colours as
on margin, with occasional traces of third red : —

Radius of red2,

00
T— 1

P

3° 15'

o

H-l

QO

3° 54'

Red2

Yellow2

„ yellow2,

2° 59'

3° 2'

3° 4'

2° 39'

Blue3

Red1

„ blue2, .

2° 17'

2° 21'

2° 24'

2° 12'

Yellow1

Shadow

After 8h the following measurements were got — some from top of
tower, and some from edge of cliff. The glory seemed to vary in
size as different parts of the fog drifted past : —

Tower.

Radius of red2, . 3° 15' 3° 44' 3° 50'

„ yellow2 2° 37' 2° 47' 2° 58'

„ blue2, . 2° 2' 2° 0' 2° 13'

„ red3,

Cliff.

4° 6' 3° 54'
3° 2' 2° 47'
2° 19' 1° 58'
6° 55' ...

October 4, 1887. — When fog was clearing off in early morning, a
double lunar corona was observed. The following were the order
of colours and radii measured at 5h : —

326

Proceedings of Royal Society of Edinburgh. [june 20,
2* White, yellow, orange, red,

2° 12'

Yiolet, bine, green, yellow, orange, red,

4° 34'.

Glories were also seen during the day on the fog in the valley to
northward.

The following measurements of one with five rings were taken
between llh and 12h : —

Radius of red5,
red4,
red3,
red2,
red1.

33

35

33

Too faint to measure.
6° 18'

4° 37'

2° 40'

0° 52 (about).

A lunar fog-bow was seen at 23h. Radius to inner edge (about)
38° 5'.

October 5, 1887.— At 2h fog was beginning to blow across the
hill top, and on it a distinct lunar fog-bow was seen, with traces of
faint second bow outside it. The following measurements of the
inner bow were got : —

Radius to inside edge, . . . 35° 4'

„ outside edge, . . . 41° 0'

A similar lunar fog-bow was seen at 3h ; there appeared to be a
faint trace of red about the outer edge of the inner bow. On both
these occasions a faint white patch of light was seen round the
shadow of the observer’s head, which was probably a lunar glory.

The fog-bow was seen again at 4h and 5h, but without any glory.
The following measurements were made at 4h : —

Radius to inside of inner bowr, . . .36° 3'

,, outside of inner bow, . . .41° 0'

October 15, 1887. — At 14h double fog-bow and glories observed;
no measurements got. At 14h 10m, and again at 16h 10m, a solar
corona was seen, triple each time. The following measurements
were got : —

Xoc.R.oy S.oc.Edm?

Vol XIV. PI. XII

ArcMT) aid & Peck Pin?

1887.] Mr R. T. Omond on Glories, Halos, and Coronm. 327

At 14h 10m.

At 16h 10m.
2° 6'

3° 35'

Radius of red1,

red2,

red3,

Note. — Fig. 10 is a sketcli of rainbow seen at Fort -William on
16th August 1887, at about 17h, by A. Rankin, J. Miller, W.
Stewart, and D. M£Kenzie.

Dr JOHN MURRAY, Yice-President, in the Chair.

The following Communications were read : —

1. Thermal Conductivity of Iron, Copper, and German

Silver. By A. C. Mitchell, Esq. Communicated by
Professor Tait.

2. On the Probability that a Marriage entered into by a
Man of any Age, will be Fruitful. By T. B. Sprague, M.A.

In a paper which I read before the Society in 1879, I gave the
results of an investigation I had made with the object of deter-
mining the probability, that a man marrying at any age over 40,
will, or will not, have children ; and I have now extended the
same enquiry to men of all ages. The statistics upon which my
former conclusions rested, related to 339 marriages entered into by
peers and their near relations, above the age of 40, and were ex-
tracted from Lodge’s Peerage for the year 1871. For all statistical
enquiries this work is, in my opinion, greatly preferable to any of
the other works that give records of the British Peerage. The
principal ground for this opinion is, that Lodge usually gives the
dates of birth of the daughters of each family, as well as those of
the sons ; whereas other Peerages generally omit those dates, and
place the names of the daughters (without any dates) after the
names of the sons, so that it is impossible to tell whether

Monday, 4 th July 1887.

328 Proceedings of Royal Society of Edinburgh. [july 4,

they are older or younger than their brothers. In the case of a
few families this practice is also adopted in Lodge, presumably
by special desire of the head of the family ; and it is a matter
of regret that this, together with other circumstances to be
presently mentioned, diminishes the value of the book for statistical
purposes.

I could have greatly increast the above mentioned number of
facts, if I had not thought it desirable altogether to exclude the
marriages of the persons given under the heading, “ Collateral
Branches”. But a very slight examination of the book, was suffi-
cient to satisfy me that the information as to the collateral branches
of each family, was very much less trustworthy than that relating
to the immediate family. There appears to be no very precise rule
according to which persons are transferred from the portion of the
work relating to the immediate family, which is printed in larger
type, to the “ Collateral Branches”, printed in smaller type. When
the title has descended to the present holder from his father and
grandfather, the name of the peer is given in the first instance,
with his date of birth, his date of succession to the title, and full
particulars of his marriages. Then follow the names and dates of
birth of his children, the dates of their marriages, if any, and the
dates of death of any who have died. In the case of the married
sons, similar information is given as to their children ; but this is
very rarely done in the case of the married daughters. After all the
usual information has thus been given as to the peer and his descend-
ants, we have the name of the peer’s father, with similar inform-
ation as to himself, his marriages, his children (other than the peer),
and their marriages. As in the case of the peer, no information is
given as to the children of the married daughters, the sisters of the
peer; but full information is given as to the children of the
married sons, the brothers of the peer ; in other words, we have
information as to the nephews and nieces of the peer who trace their
descent through the male line.

In some cases we next have the peer’s grandfather, with inform-
ation as to his children, who are the uncles and aunts of the peer ;
and, as in former cases, we have information as to the children of the
uncles, but not as to the children of the aunts ; and we thus get
particulars as to the first cousins of the peer who trace their descent

329

1887.] Mr T. B. Sprague on a Fruitful Marriage.

through the male line. In other cases, the name of the grandfather
is not given, hut under the Collateral Branches we have the names
of the uncles and aunts of the peer, with particulars as to their
children and grandchildren through the male line. In still other
cases, when all the uncles and aunts of the peer are dead, the
particulars as to them are no longer given ; but the children of
the uncles (who are cousins of the peer) are placed among the
Collateral Branches, and information is given as to the marriages of
the males and their children, and as to the marriages and children
of more distant male relatives, whose number is sometimes very
great.

An examination of a single copy of Lodge’s Peerage was sufficient
to show that the information as to the collateral branches, lacks
the completeness that is necessary for the purposes I had in view.
We constantly find it stated there that a particular man is dead,
but no date of death is given ; or that he is married and has issue,
but the date of marriage and the names of his children are not
given. The book claims to be corrected by the nobility; and,
although this may tend to secure accuracy as regards the immediate
family, the information as to the collateral branches is, in many
cases, just such as might be given by the head of the family, in
correcting the proofs from memory. He has not kept up intimate
relations with the numerous younger branches of the family ; but,
on looking through the proofs, and coming upon the name of a
cousin or other more remote relative, he remembers having heard
that he is dead, or that he is married and has children ; and
having no record at hand that will give him the exact date of
marriage or death, he contents himself with stating the mere fact
of marriage or death, without the date. A comparison of the
editions of Lodge for different years, subsequently proved that the in-
formation as to the collateral branches is in other respects deficient,
and that the marriages and births of children among them are not
regularly recorded in the work, from year to year, as they take place;
in fact, sometimes a marriage is not recorded for many years after
it has taken place ; and when it is first mentioned, a long list of
children of the marriage is given in addition. The fact, therefore,
that a man whose name appears among the collateral branches in
Lodge’s Peerage for any year, is not stated to have been married,

330

Proceedings of Royal Society of Edinburgh. [july 4,

cannot be accepted as evidence that he is not at that time married ;
and the fact that a married man is not mentioned as having children,
cannot be accepted as evidence that he has none. Another circum-
stance, which diminishes the value of Lodge’s Peerage for statistical
investigation, is the practice adopted in some families of giving,
among the collateral branches, the names, &c., only of the “ last
surviving” uncles, aunts, &c., omitting all mention of those who
are dead. It is clear that we may fall into very serious errors if we
draw conclusions from incomplete information of this kind, and
that very careful consideration is necessary to determine what use
may safely be made of it.

Such were the reasons which led me, on the former occasion,
to reject all the facts relating to the collateral branches ; but
further consideration showed me that, although the information
as to the collateral branches is, on the whole, much less trust-
worthy than that as to the immediate family, yet we cannot
safely lay down the rule, to take the latter and reject the
former; for, as wre have seen, no strict line can be drawn between
the two; the uncles and aunts and cousins being sometimes in-
cluded in the immediate family, and sometimes among the collateral
branches. In fact, we find, on comparing the editions for different
years, that uncles and aunts and cousins, who are given in one year’s
Peerage as members of the immediate family, will, after the lapse of
some years, when the peer has died, be transferred to the collateral
branches in the new volume. The distinction, therefore, between
the collateral branches and the immediate family, is one that cannot
be acted upon in practice; and we must seek for some other distinc-
tion.

Even among the immediate family, the information given is not
always full and trustworthy ; and the facts given in Lodge’s
Peerage for one year, sometimes differ from those given in the
edition for another year, or in Foster’s work to be presently men-
tioned. Careful examination soon showed me that the cases where
the information is most defective and least trustworthy, are those
of recent titles. When a man is created a peer who has been
married many years, the information as to his children is often less
full, and apparently less accurate, than in the case of peers who
inherited their titles ; and I therefore came to the conclusion that?

331

1887.] Mr T. B. Sprague on a Fruitful Marriage .

in the present enquiry, it would "be desirable to reject every marriage
entered into by a commoner who was subsequently created a peer.
For the same reason, if a son was married before his father was
created a peer, I rejected the son’s marriage. Similar considerations
apply to the cases where a peer did not succeed to the title in the
ordinary way, but establisht his claim to a title that had been
dormant for some time, or succeeded a distant relative ; and to the
cases where a peer was placed upon the roll of peers in consequence
of the reversal of an attainder against an ancestor. When a man’s
name has stood for a long series of years upon the roll of peers,
each fact as to his marriage, and as to the births and deaths or
marriages of his children, is usually recorded as it takes place, and
there is little risk of error or omission ; but when a man is created
a peer, or succeeds under the exceptional circumstances above
mentioned, the facts as to his family are not on record in the same
way, and have to be supplied by himself. No doubt in some cases
the new peer will give this information with all the desired accuracy,
but in a good many cases he will not ; and, as it is not possible
to say with certainty in which cases the information is complete
and exact, and in which it is defective or incorrect, the only
safe course is to reject the whole of the cases as clearly liable to
error.

In the present investigation I have, as before, taken Lodge’s
Peerage for 1871 as my starting point; but I have made extensive
use also of the new Peerage by Foster, publisht for the first time
in 1880, and I think it right to mention that this has supplied a
good many dates and other facts which are not given in Lodge.
Not only are a great number of additional dates of birth, marriage,
and death given — principally among the collateral branches — but in
many cases the names and dates of birth of children which are not
mentioned at all in Lodge. Foster seems not to have relied on the
somewhat questionable assistance of the peers themselves in re-
vising the proof sheets, but to have obtained in many cases docu-
mentary evidence in addition to that which the editor of Lodge
has used. Foster’s Peerage also gives information, omitted by
Lodge, as to the children of the married daughters of the peers
and of their relatives. It cannot, however, be safely used by itself
for ordinary statistical purposes ; for it not only omits the dates

332 Proceedings of Royal Society of Edinburgh. [july 4,

of birtli of the females of the family, and places the names of
the sisters in a family after the names of all the brothers, but it
also systematically omits all mention of children who died young ;
and when children have grown up to maturity and died unmarried,
they also are often omitted.

A careful examination of various Peerages has left upon my
mind the general impression that too much reliance should not
be placed upon individual facts contained in them. There are
many sources of error, which are in practice not sufficiently guarded
against. Sometimes an obvious misprint is made in the edition
for one year, and is repeated without correction in the editions
for several successive years. In a few cases there seems good
ground for believing Foster’s statement, that the information
furnisht by members of the peerage, has been intentionally
incorrect. Occasionally, though very rarely, the marriage of a peer
or his son is mentioned in one Peerage and not in another ; and the
same is the case with regard to the issue of some marriages. These
inaccuracies, however, are not sufficiently numerous to produce any
appreciable effect upon the general results of an enquiry of the
present kind ; and I think that, if proper precautions are adopted,
the vital statistics furnisht by the records of the British Peerage,
are more complete and trustworthy than we can hope to get in
almost any other way. Perhaps better statistics might be got
from the records of some of the Widows’ Funds which grant
benefits to the children, as well as to the widows, of members ; but,
in the absence of these, I think the Peerage statistics the best we
have.

Taking now a general survey of the facts supplied by the Peerage,
we see that they relate to different classes of persons, and that all
the facts so supplied are not equally trustworthy. We may, I
think, assume that, in general, the facts relating to each peer will be
the most complete and trustworthy ; that those relating to his
children during his life will be almost (or quite) as trustworthy; and
that the information will become less trustworthy in proportion as
the relationship to the peer of the day, is more distant. We have,
in the case of every peer included in our list, the necessary informa-
tion as to his sons, and their sons (if any), also as to his father,
his brothers, and their sons (who are the peer’s nephews). In

333

1887.] Mr T. B. Sprague on a Fruitful Marriage.

some cases we have also particulars as*to the grandfather (being the
father’s father), the father’s brothers, and their sons, who are
respectively uncles and cousins to the peer. The existing peer at any
time may thus he regarded as the central figure of a group, around
whom are arranged his different relations, at a greater or less dis-
tance, according as their degree of relationship is more or less remote.

Assuming now that the precautions we have taken have secured
that all the facts we extract from the Peerages are equally trust-
worthy, we have next to consider whether they are all equally suit-
able for our purpose. Our object is to obtain particulars of a large
number of marriages, which may be considered as a fair sample of
the whole; and then to ascertain how many of these resulted in the
birth of issue, and how many were childless. If, then, we extract all
the marriages of the peer and of his above-mentioned relations, will
these give us a fair average of cases suitable for the solution of our
problem1? Or is there anything in the principle on which our
selection of facts is made, that renders the marriages we select
unsuitable representatives <sf the general body *? One such circum-
stance becomes obvious at first sight. The peer may be single, or
married; and if the latter, he may either have children, or have
none. The same is the case with regard to his sons, his grandsons,
his brothers, his nephews, his uncles, and his cousins ; but we see
that his father and his grandfather had at least one son each ; each
of them, in fact, being included in our list for the very reason that
he had a son. It follows that, if we include in our enquiry the
information regarding the fathers and the grandfathers of the peers,
we shall not obtain trustworthy results ; for we shall have an undue
proportion of fruitful marriages. If we include in our list the
marriages of the peers’ fathers, we must, in order to get the proper
proportion of childless marriages, include also the marriages of all
their contemporaries who were married and had no children ; but to
attempt this would, I believe, be an impracticable task. If we took
only those fathers of peers who were themselves peers, we might
perhaps obtain a suitable body of statistics, by taking the marriages
of all contemporary peers who married but had no children. In
some cases these were succeeded by their brothers, or nephews, or
other relatives ; and all cases of this kind could probably be
traced without any great difficulty ; but, in a number of other cases,

334 Proceedings of Royal Society of Edinburgh. [july 4,

such peers have had no male relations to inherit the title, which
has therefore become extinct. In order to trace out cases of this
kind, it would he necessary to have a complete set of old volumes
of the Peerage, and ascertain by an examination of them which
titles became extinct each year, in consequence of the peer having
died without issue, although he was married. From several points
of view this would be a very interesting enquiry, but it was one
which I was not in a position to undertake : and if I had desired
to do so, I cannot see how it would have been possible to decide
how far back the enquiry should extend, so as to include the
proper number of holders of extinct titles, but not too many of
them. In a certain number of cases, moreover, the peers’ fathers
were not themselves peers, but were untitled men belonging to a
younger branch of the family ; and I imagine it would be quite im-
possible to lay down any principle upon which to determine all the
persons who may fairly, for the present purpose, be considered their
contemporaries. The difficulty, however, is completely got over by
excluding from consideration the marriages of the fathers and grand-
fathers of our peers, or, speaking more correctly, the marriages from
which our peers were descended. I have, therefore, if a peer’s father
or grandfather was married twice, or three, or four times, excluded
from consideration the marriage from which the peer was descended,
but have made use of the remaining marriages, — subject to a
correction that will be hereafter explained. I have also, in a few
cases, rejected all the facts relating to certain peers, when, from very
exceptional circumstances, such as residence in a foreign country,
the information was obviously incomplete.

Another circumstance may be noted : — The peers themselves are
all alive at the time at which our observations begin, and their
fathers and grandfathers are all dead ; but their sons, their brothers,
and their uncles, may be either living or dead. There seems, how-
ever, no reason for thinking that the fact that all the peers are
living, will affect to any appreciable extent, if at all, the probability
of their marriages being fruitful.

As already mentioned, my investigation commenced with Lodge’s
Peerage for 1871. The principal object was to ascertain what pro-
portion of marriages were fruitful : and as many marriages which
are not fruitful at once, become so in later years, it would be com-

1887.] Mr T. B. Sprague on a Fruitful Marriage.

335

paratively useless to include in the observations any existing
marriages that had subsisted for less than, say, ten years. I have
therefore taken no account of any marriage entered into after the
year 1870, these being the latest recorded in the Peerage for 1871 ;
and by examination of Lodge’s and Burke’s Peerages for 1884, I
ascertained in regard to each marriage whether it had been fruitful
up to the year 1883 inclusive. Thus every marriage included in my
observations, has either been dissolved by death (or divorce), or has
subsisted for at least thirteen years.

Proceeding, then, on the principles explained, I obtained informa-
tion as to the marriages of the peers of 1870 and certain of their
male relations ; and although, as far as I could see, the facts stated
in the Peerage with regard to all of these, were equally trustworthy
and suitable for my purpose, I decided, as a matter of precaution, to
extract and tabulate separately, the facts relating to the following
classes of men: — (1) the peers whose names are given in the
Peerage for 1871; (2) their fathers; (3) their grandfathers; (4)
their sons ; (5) their brothers ; (6) their uncles, being the fathers’
brothers ; and I did not consider it desirable to extend the enquiry
to the peers’ nephews, or cousins, or more remote relations.

To each marriage was assigned a distinctive number, and the
particulars were then written in a book in the following form : —

No.

Born

Title

Married . Age

Name

Widower

Wife horn A.o-e

Died

1

Children, j

Died. Married.

8. or D. No. Born.

1

2

3

VOL. XIV.

15/11/87

Y

336

Proceedings of Payed Society of Edinburgh. [july 4,

2nd Wife born

Age

2nd Married Age

2nd Widower

Died

Children.

S. or D.

No.

1

2

3

Born.

Died.

Married.

It is clear that from materials of this kind we can obtain much
information, not only as to the probability of a marriage being
fruitful, but as to the number of children to a marriage, the pro-
bability that they will be sons or daughters, the length of time
that elapses between marriage and the birth of the first child, and
the intervals between the births of successive children, &c. If the
age of the wife could also have been ascertained in every case,
much interesting information could have been obtained as to the
probability of a wife of any age having issue ; but it is only in
exceptional cases that the age of the wife can be determined — in
fact, only when she is a daughter belonging to one of the peerage
families. On the present occasion I confine myself to the considera-
tion of the one point as to the probability of the marriage being
fruitful. If any child has been born of a marriage, I have considered
it as a fruitful marriage, although all the children may have died
young in the lifetime of the father.

The number of marriages which are included in my observations
are, of peers 427; of their sons, 199; of their brothers, 511; of
their uncles, 384. On grouping these according to age at marriage,
I obtained the figures shown in the following table (A) : —

A comparison of these figures shows us that the percentages for
the brothers and uncles agree very well together, and that the pro-
portion of childless marriages is very much greater among these
two classes taken together, than among the peers and their sons.
This appears more clearly when the figures are combined as
shown in table (B) : —

1887.] Mr T. B. Sprague on a Fruitful Marriage . 337

Table A.- — Marriages of the Peers of 1870, and of their Sons ,

Brothers , and Uncles .

Age at
Marriage.

Peers of 1870.

Sous.

Brothers.

Uncles.

Marriages.

Of which
were
Childless.

Marriages.

Of which
were
Childless.

Marriages.

Of which
were

Child] ess.

Marriages.

Of which
were
Childless.

Number.

7.

Number.

%

Number.

%

Number.

%

16 to 29

248

30

12-1

134

23

17-2

278

64

23-0

193

44

22-8

30 ,, 39

108

16

14-8

63

11

17-5

170

47

27 -6

121

29

24-0

40 ,, 49

39

10

25*6

2

1

50-0

43

17

39-5

47

13

27-7

50 ,, 59

19

10

52-6

15

11

73-3

17

9

52-9

60 and upwards

13

9

69-2

...

...

...

5

4

80-0

6

6

100-0

Total

427

75

17-6

199

35

17*6

511

143

28*0

384

101

26-3

Table B, containing the facts of Table A, arranged in two classes.

Age at
Marriage.

!

Peers and Sons.

Brothers and Uncles.

m

a>

hJD

.2

Sh

£

Of which were
Childless.

02

CD

bC

.2

rH

5

£

Of which were
Childless.

Number.

Per-

centage.

Number.

Per-

centage.

16 to 29

382

53

13-9

471

108

22-9

30 „ 39

171

27

15-8

291

76

26-1

40 „ 49

41

11

26-8

90

30

33-3

50 ,, 59

19

10

52-6

32

20

62-5

60 and upwards

13

9

69-2

11

10

90-9

Total

626

110

17-6

895

244

27-3

The percentages here run so regularly, and the differences
between those relating to the two sets of observations are so great,
that we are forced to the conclusion that the differences cannot be
accidental, but that there must be something in the manner of
compiling our statistics, that necessarily causes the percentage of
childless marriages to be greater at all ages among the brothers and
uncles, than among the peers and their sons. It was not long
before I discovered a cause that accounted for a great deal of the
difference ; — in fact, I found that my class of peers’ brothers, in-

338 Proceedings of Roycd Society of Edinburgh. [july 4,

eluded a certain number of their elder brothers who had died without
male issue. In some cases, these were themselves peers, and were
succeeded by their younger brothers. In other cases, they wTere the
eldest sons or nephews of peers, and would have succeeded to the
title if they had lived ; but they died before the succession to the
title opened to them, so that the next brother succeeded. If these
men had left sons who succeeded to the title, they would have
appeared in my classification as peers’ fathers ; but in consequence
of their having no sons, they are placed in my class of peers’
brothers : and this circumstance causes that class to include an
undue proportion of men who died without issue. The same
remark applies to the class of peers’ uncles, which includes a
number of elder brothers of the peers’ fathers, who died without
leaving issue. The obvious way of eliminating this source of
error is to exclude from observation all such elder brothers of the
peers, and all uncles who were elder brothers of the fathers ; and to
consider only the younger brothers of the peers, and the younger
brothers of the fathers, who, for brevity, may be called “ younger
uncles”. When this was done, I got the figures shown in the
following table : —

Table C. — Marriages of the Younger Brothers of the Peers , and
of their Fathers’ Younger Brothers.

Age at
Marriage.

Y’nger Brothers.

Younger Uncles.

Total.

Marriages.

Of which
were
Childless.

Marriages.

Of which
were
Childless.

Marriages.

Of which
were
Childless.

Number.

%

CD

rO

5

6

7.

Number.

7c

16 to 29

253

47

18-6

168

28

16-7

421

75

17-8

30 „ 39

161

40

24-8

115

26

22-6

276

66

23-9

40 „ 49

43

17

39-5

46

13

28-3

89

30

33-7

50 „ 59

14

10

714

11

5

45-5

25

15

60-0

60 and upwards

5

4

80-0

5

5

100-0

10

9

90-0

Total

476

118

24*8

345

77

22-3

821

195

23-8

Comparing the figures for the younger brothers and the younger
uncles, we see that, excluding the very few marriages at 60 and

1887.] Mr T. B. Sprague on a Fruitful Marriage.

339

upwards, the proportion of childless marriages is at all ages greater
among the brothers than among the uncles. Similarly, referring
back to Table A, we see that the proportion of childless marriages
among the sons of peers, is at all ages greater than among the
peers themselves. In both cases, therefore, the proportion of
childless marriages is greater in the younger generation. This is
quite consistent with the proposition laid down by many writers,
that there is a constant tendency in the families of the peerage,
and of ruling classes generally, to die out ; and it suggests a tempt-
ing field of enquiry. No doubt many interesting and valuable
results would be obtained, if the experience of several successive
generations of the peerage families, were investigated with regard
to both their mortality and their fecundity ; but, although the
figures above given, as far as they go, certainly support the idea
that a gradual deterioration is taking place in the peerage families,
the figures involved are too small to be accepted as giving any
conclusive evidence on the point.

It is now time to compare the results thus far obtained, with
those given in my former paper, which related only to men over 40 at
marriage. For this purpose, my former figures are entered in the
following table, alongside of those now obtained for (1) peers and their
sons, (2) their younger brothers and their fathers’ younger brothers.

Table D.

Age at
Marriage.

Peers and their
Sons.

Y’nger Brothers
and

Younger Uncles.

Total.

Former

Observations.

Marriages.

Of which
were
Childless.

Marriages.

Of which
were
Childless.

Marriages.

Of which
were
Childless.

Marriages.

Of which
were
Childless.

Number.

o /

/ o

Number.

%

Number.

%

Number.

1

7.

16 to 29

382

53

13-9

421

75

17-8

803

128

15-9

...

30 „ 39

171

27

15-8

276

66

23-9

447

93

20-8

o

CD

41

11

26-8

89

30

33-7

130

41

31-5

196

56

28-6

50 „ 59

19

10

52-6

25

15

60-0

44

25

56-8

92

42

45-7

60 and upwards

13

9

69-2

10

9

90-0

23

18

78-3

51

39

76-5

All Ages

626

110

17-6

821

195

23-8

1447

305

21T

40 and upwards

73

30

41-1

124

54

43-5 i

197

84

42-6

339

137

40-4

340 Proceedings of Royal Society of Edinburgh. [july 4,

Tlie statistics I formerly made use of, differed from the present
ones in two respects : —

1. They included a number of fathers of peers, all of whom, of
course (as pointed out in the early part of this paper), left sons to
inherit the title. The exclusion of these fathers from the present
observations, has a tendency to increase the proportion of childless
marriages.

2. They included a number of elder brothers of the peers and
elder brothers of their fathers, these being men whose male issue
failed, that is to say, men who had either no children at all, or
only daughters, or if they had a son or sons, their male issue had
all died, and the title had therefore descended to a younger branch
of the family. The exclusion of these men has a tendency to
reduce the proportion of childless marriages.

These two tendencies are therefore in opposite directions ; and,
as it happens, they to a great extent neutralize each other, the
aggregate result being that my present observations show 197
marriages of men over 40, of which 84, or 42*6 per cent, were
childless; against 339 marriages formerly considered, of which 137,
or 40*4 per cent, were childless.*

Comparing now the figures shown in Table D with those in Table B,
we see that the exclusion of the elder brothers, and of the fathers’
elder brothers, has had the effect of reducing the proportion of
childless marriages at all ages, with a trifling exception at the ages
40-49 ; the reduction being particularly noticeable at the ages under
30, at which more than half the total marriages took place. The
new percentages given in Table D for the younger brothers and
the younger uncles, are much nearer to those for the peers and
their sons, than are our original figures in Table B, which related
to all the brothers and all the uncles ; but we see that at all ages,
the percentages for the younger brothers and the younger uncles,
are still greater than the corresponding ones for the peers and their
sons ; — in other words, that at all ages there is a less proportion of
childless marriages among the peers and their sons, than there is
among the younger brothers of the peers, and their fathers’ younger

* Including, as hereafter explained, certain marriages of the fathers and
grandfathers of peers, the total number of marriages of men over 40 included
in the present observations, is 259, of which 118, or 45 *5 per cent, were childless.

341

1887.] Mr T. B. Sprague on a Fruitful Marriage .

brothers. An explanation of this fact soon suggests itself. Com-
paring the position of an unmarried peer with that of his brothers,
it seems likely that the former, being in possession of the estates
which go along with the title, will feel more free to follow his
personal inclinations in the selection of a wife, than will be the case
with his younger brothers; and the same remark applies to the
peer’s eldest son, and to the eldest son of this eldest son, as com-
pared with their younger brothers. In other words, they may be
expected as a rule to marry wives who are personally attractive,
being young and of healthy constitutions ; while the younger
brothers may more frequently marry for money, the wife being in
many cases an heiress who, from her age, or from being herself an
only child, is less likely to have children. For the purpose of
testing this supposition, I next examined all the 626 marriages of
peers and their sons, and noted which of them were entered into
by a man who was at the time either a peer, or the heir-apparent
of a peer, or the eldest son of an heir-apparent ; and the results are
shown in the following table : —

Table E. — Marriages of Peers and of their Sons , distinguishing
those which were entered into by a Man who was either a Peer
or an Heir-Apparent.

Age at
Marriage.

Peers.

Sons of Peers.

Married as Peer
or Heir -Apparent.

Remainder.

Married as Heir-
Apparent.

Remainder.

Marriages.

Of which
were
Childless.

Marriages.

Of which
were
Childless.

W

(D

SI

ci

c5

S

Of which
were
Childless.

CC

<V

SD

.2

s

%

Of which
were
Childless.

Number.

Vo

Number.

7,

Number.

%

Number.

%

19 to 29

202

25

12-4

46

5

10-9

70

10

14-3

64

13

20-3

30 „ 39

89

13

14-6'

19

3

15-8

30

4

13-3

33

7

21-2

40 „ 49

32

8

25-0

7

2

28-6

1

1

100-0

1

0

o-o

50 ,, 59

17

9

52-9

2

1

50-0

60 and upwards

12

8

66-7

1

1

100-0

-■

Total

352

63

17-9

75

12

16-0

101

15

14-9

98

20

20-4

342 Proceedings of Payed Society of Edinburgh. [july 4,

As the numbers we are now dealing with are smaller than before,
the results do not proceed with so much regularity as those we
formerly obtained. The figures relating to the sons of peers, how-
ever, strongly support the above views ; as a much larger proportion
of the younger sons are childless, than is the case with those sons
who married as heir-apparent. The same is not the case, with the
peers ; in fact, if we take those peers who married under 40, the

figures in the two classes are : —

Marriages.

Of which were Childless.

Percentage.

Married as Heir-apparent,

291

38

13*1

Did not so marry,

65

8

12-3

the results being thus practically identical. One reason at once
suggests itself why the difference between the two classes should
be much less among the peers than among the sons ; namely, that
among the peers who did not marry as peer or heir-apparent, a
large proportion may at the time of their marriage have had, from
special circumstances, a practical certainty of succeeding to the title ;
for instance, through being heir-presumptive to an elderly unmarried
peer ; but I have not at present attempted to follow up this idea.

Combining the peers and sons of peers, we get the following-
figures : —

Table F. — Marriages of Peers and tlieir Sons ( Combined ), distin-
guishing those which were entered into by a Man who ivas Peer
or Heir-Apparent.

Age at Marriage.

Peers and Sons of Peers.

Married as Peer or
Heir-Apparent.

Did not so marry.

02

O

bo

.2

5

§

Of which were
Childless.

02

<D

bO

03

5

3

Of which were
Childless.

Number.

Per-

centage.

Number.

Per-

centage.

19 to 29

272

35

12-9

no

18

16-4

30 „ 39

119

17

14-3

52

10

19-2

40 „ 49

33

9

27 3

8

2

25-0

50 ,, 59

17

9

52-9

2

1

50-0

60 and upwards

12

8

66 ‘7

1

1

100-0

Total

453

78

17-2

173

32

18-5

1

1887.] Mr T. B. Sprague on a Fruitful Marriage.

343

A study of the results thus far obtained, satisfied me that
the most satisfactory course would he to arrange my facts
into two classes, the first relating to those men who married as
peer or heir-apparent, and the second to those who did not.
For business purposes, we of course prefer to err, if at all, on the
side of safety ; for instance, in calculating the risk attaching to
an insurance against the birth of issue, to take the probability of
issue rather above than below the truth, and thus to make use of
that body of facts which gives the smallest probability of failure
of issue.

In order to increase the number of the facts, especially at the
higher ages, I have thought it desirable to take into account, as
far as practicable, those marriages of the fathers and grandfathers
of peers, from which the peers were not descended. There were, in
all, 110 fathers and grandfathers who were more than once married.
In the case of 61, the peer was descended from the first marriage,
and in the remaining 49 from the second marriage. As already
mentioned, these 61 first marriages, of course, have to be excluded.
We must also exclude the 49 first marriages, corresponding to the
49 second marriages from which the peers were descended ; for it
is obvious that these 49 marriages will include an unduly large
number of cases where there was either no issue or no male issue.
We have thus to reject all the first marriages; and, of the second
marriages, we can only make use of the 61 that correspond to the

61 first marriages from which the peers were descended. We have
also 13 third marriages, and one fourth marriage, making in all 75
marriages of fathers and grandfathers, to be taken account of. In

62 of these, the man married when he was peer or heir-apparent ;
and in 13, he did not so marry.

Collecting our results, we now obtain the figures in the following
tables G and H, where it will be observed that, at each decennial
group of ages, the percentage of childless marriages is considerably
greater among those who did not marry as peer or heir-apparent,
than among those who did.

In order that our results may be practically useful for professional
purposes, as, for instance, in the calculation of the values of the
interests of the various heirs in disentail proceedings, it is necessary
to graduate the probabilities. This I have done by the graphic

344

Proceedings of Royal Society of Edinburgh.

[july 4,

Table G. — Marriages of Men ivho married as Peer or

Heir-Apparent.

Age at Marriage.

Peers.

Sons.

Fathers and
Grandfathers.

Total.

Marriages.

Of which
were

Childless.

Marriages.

Of which
were
Childless.

Marriages.

Of which
were

Childless.

Marriages.

Of wh
Chil

5

6
a

£

ich were
dless.

%

19 to 29

202

25

70

10

2

0

274

35

12-8

30 „ 39

89

13

30

4

8

1

127

18

142

40 „ 49

32

8

1

1

15

6

48

15

31-3

50 ,, 59

17

9

17

5

34

14

41-2

60 and upwards

12

8

20

18

32

26

81-3

Total

352

63

101

15

62

30

515

108

21-0

Table H. — Marriages of Men ivho did not marry as Peer or

Heir- Apparent.

Age at
Marriage.

Peers.

Younger

Sons.

Younger

Brothers.

Uncles,

(Fathers’

Younger

Brothers).

Fathers

and

Grand-

fathers.

Total.

CO

<V

b£

£

03

to

m

2

5

CO

<V

u

c3

o3

CO

CO

o

S

c_>

CO

QJ

bJD

c3

2

c5

CO

CO

<u

2

o

CO

Qj

tD

03

2

03

s

CO

CO

O

5

CO*

V

03

c

03

CO

CO

2

2

5

CO

0)

to

03

2

03

3

Of w
we
Child

O

rO

s

£

hich

re

Hess.

°/o

16 to 29

46

5

64

13

253

47

168

28

1

0

532

93

17-5

30 ,, 39

19

3

33

7

161

40

115

26

2

0

330

76

23-0

40 „ 49

7

2

1

0

43

17

46

13

6

3

103

35

34-0

50 „ 59

2

1

14

10

11

5

4

2

31

18

58 T

60 &e.

1

1

5

4

5

5

11

10

90-9

Total

75

12

98

20

476

118

345

77

13

5

1007

232

23-0

method, and the following tables show, for each of the two classes
of men mentioned above — (1) the number of marriages at each age,
contained in our observations, and the number of them which were
childless; and (2) the graduated probability that a marriage entered
into at any age, will be childless.

345

1887.] Mr T. B. Sprague on a Fruitful Marriage .

Table I. — Men married as Peer or Heir- Apparent. Adjusted
probability that the Marriage will be childless.

Age at
Marriage.

Number of
Marriages.

Of which
were Childless

Probability
that the
marriage
will be
Childless.

Age at
Marriage.

Number of
Marriages.

Of which
were Childless

Probability
that the
marriage
will be
Childless.

Age at
Marriage.

Number of
Marriages.

Of which
were Childless.

Probability
that the
marriage
will be
Childless.

19

1

•121

41

3

1

•230

63

1

...1

•725

20

9

2

•122

42

6

1

•245

64

1

4

*761

21

39

2

•123

43

5

2

•260

65

5

2

•794

22

31

4

*124

44

1

...

•275

66

2

1

•822

23

35

6

*125

45

4

1

•291

67

1

•846

24

25

4

•126

46

4

•307

68

...

•866

25

41

4

•127

47

3

2

•323

69

1

1

•883

26

31

4

•128

48

5

1

•339

70

1

1

•898

27

20

3

•129

49

4

2

•355

71

1

1

•912

28

26

4

•130

50

2

•372

72

1

1

•925

29

16

2

•131

51

4

1

•389

73

1

1

•937

30

24

3

•133

52

3

•407

74

1

1

•948

31

14

. . •

•135

53

3

1

•426

75

...

•958

32

15

2

•138

54

4

2

*447

76

1

i

•967

33

12

•142

55

1

1

•470

77

...

•975

34

17

3

•148

56

6

3

•495

78

1

i

•982

35

9

1

•156

57

5

2

•522

79

1

i

•988

36

10

2

•166

58

6

4

•551

80

...

•993

37

12

3

•177

59

...

. , .

•582

81

...

•997

38

7

2

•189

60

9

6

•615

82

...

1-000

39

7

2

•202

61

1

...

•650

40

13

5

•216

62

3

3

•687

515

108

Table J. — Men who did not marry as Peer or Heir -Apparent.
Adjusted probability that the Marriage will be childless.

Age at
Marriage.

Number of
Marriages.

Of which
were Childless.

Probability
that the
marri'i ge
will be
Childless.

Age at
Marriage.

Number of
Marriages.

Of which
were Childless

Probability
that the
marriage
will be
Childless.

Age at
Marriage.

Number of
Marriages.

j Of which

were Childless

Probability
that the
marriage
will be
Childless.

16

1

•138

38

16

3

•279

60

5

4

•852

17

• . .

•139

39

10

4

•288

61

1

1

•874

18

3

1

•140

40

11

4

•297

62

•892

19

3

, , .

•142

41

15

1

•307

63

1

1

•907

20

4

*144

42

13

7

•317

64

1

1

•920

21

39

6

•147

43

11

2

•327

65

1

1

•931

22

36

4

•151

44

12

6

•337

66

1

1

•941

23

45

4

•156

45

9

3

•347

67

1

1

*950

24

68

11

•162

46

9

3

•358

68

•958

25

59

11

‘•169

47

10

5

•370

69

•965

26

64

11

•177

48

9

2

•383

70

•971

27

82

19

’185

49

4

2

•398

71

•976

28

75

13

•193

50

5

2

•415

72

•980

29

53

13

•201

51

2

1

•433

73

•984

30

52

8

•209

52

4

1

•466

74

•987

31

46

12

•217

53

3

3

•514

75

*990

32

50

7

•225

54

5

1

•574

76

•993

33

42

12

•234

55

5

3

•644

77

•995

34

28

6

•243

56

3

3

•703

78

•997

35

28

6

•252

57

1

1

•752

79

•999

36

30

13

•261

58

2

2

•792

80

1-000

37

28

5

•270

59

1

1

•825

1

1

11007

1

232

346

Proceedings of Royal Society of Edinburgh. [july 4,

Simple inspection of the graduated probabilities shows that they
proceed with sufficient regularity. They will also satisfy the other
criterion of a good graduation, if the number of childless marriages,
as calculated from them, does not differ much from the actual
number. A comparison of this kind is made in the following
table : —

Table K. — Comparison of the actual and the calculated Numbers
of Childless Marriages in Quinquennial Groups of Ages.

Men who married as Peer or
Heir-Apparent..

Men who did not so marry.

Ages at

Marriage.

N umber

Childless Marriages.

Number

Childless Marriages.

of

Ol

Marriages.

Actual.

Calculated.

Marriages.

Actual.

Calculated.

16-24

140

18

17 "5

199

26

30-6

25-29

134

17

17T

333

67

61-7

30-34

82

8

11*4

218

45

48-8

35-39

45

10

7’9

112

31

29-9

40-44

28

9

6-6

62

20

19-6

45-49

20

6

6*5

41

15

15-0

50-54

16

4

6°5

19

8

9-3

55-59

18

10

9*4

12

10

8-5

60-64

15

10

10-5

8

7

7-0

65-69

9

8

7-3

3

3

2‘8

70-74

5

5

4-5

75-79

3

3

3-0

...

...

515

108

108-2

1007

232

233-2

In conclusion it may be useful to remind my readers that I have
considered a marriage to be fruitful, if any child has been born, even
although all the children born of the marriage may have died
young.

3. On the ISTephridia of Hirudo medicinalis. By Dr A. B.
Griffiths, F.R.S.E., F.C.S. (London and Paris) ; Prin-
cipal, and Lecturer on Chemistry and Biology, School
of Science, Lincoln.

The nephridia of Hirudo medicinalis , as is well known to bio-
logists, are in pairs extending from the second to the eighteenth
segments (somites). Each nephridium consists of a much convo-
luted cellular tube. The cells of the tube are perforated by small

347

1887.] Dr A. B. Griffiths on Hirudo medicinalis.

ducts. The nephridia (“ segmental organs ”) open externally on the
ventral side of the body.

In Lumbricus the nephridium communicates internally by a wide
funnel-shaped aperture (which is ciliated) with the perivisceral cavity,
but in Hirudo it opens internally by a “ cauliflower-headed ” portion
(the analogue of the funnel-shaped aperture of Lumbricus) into the
perinephrostomial sinus. Each nephridium consists of five principal
parts — (1) posterior lobe, (2) anterior lobe, (3) apical lobe, (4) the
testis lobe, (5) the vesicle, with its duct, which opens externally.

The nephridia of Hirudo are covered by a pigmented connective
tissue. These pigments are no doubt the histohsematin of Dr C. A.
MacMunn,* for he says in another paper — “ I have found that
throughout the whole animal kingdom, in each tissue and organ,
there are present colouring matters ” ( Proc . Birmingham Philosophi-
cal Soc., vol. v. part 1, p. 211). I have shown in my paper f the
presence of uric acid in the nephridia of the Oligochseta.

In the present paper details are given of the extraction of uric
acid from the nephridia or “ segment organs ” of the Hirudinea.
The species taken for investigation was Hirudo medicinalis. The
secretions of the nephridia were obtained from a considerable num-
ber of freshly killed leeches, and examined by similar chemical and
microscopical reactions as I have employed in my paper already
cited, and in one “ On the Nephridia and Liver of Patella vulgata”%
read before the Royal Society of London, June 16, 1887. It may
he useful to give the details of the processes. The secretions were
examined by two separate methods — -

(a) The clear liquid from the nephridia was treated with a hot
dilute solution of sodium hydrate, and then, on the addition of
hydrochloric acid, a slight flaky precipitate is obtained, after some
hours’ standing. These flakes were seen, under the microscope, to
consist of various crystalline forms. On treating these crystals with
nitric acid, and then gently heating with ammonia, the reddish-
purple murexide is produced, which crystallises in four-sided prisms.
The secretion alone, when treated with alcohol, deposits rhombic

* Proc. Roy. Soc., No. 240, 1886, and Philos. Trans., 1886.

+ “ Researches on the Problematical Organs of the Invertebrata, especially
those of the Cephalopoda, Gasteropoda, Lamellibranchiata, Crustacea, Insecta,
and Oligochseta,” read before the Royal Society, Edinburgh, May 16, 1887.

% Proc. Roy. Soc., vol. xlii. (1887), p. 392.

348 Proceedings of Royal Society of Edinburgh. [july 4,

crystals. According to tlie test of Dr Schiff {Ann. Chem. Pliarm .,
vol. cix. p. G7) for uric acid, these crystals were dissolved in a drop
or two of sodium carbonate solution, and then poured upon a piece
of filter-paper moistened with a solution of silver nitrate : a dark
brown stain of metallic silver was obtained.

(b) Another process was used as follows : — To the liquid secreted
by the nephridia of Hirudo boiling water (distilled) was added, and
then evaporated carefully to dryness. The residue so obtained was
treated with absolute alcohol, and filtered. Boiling water was
poured upon the residue, and an excess of acetic acid added to the
filtrate (aqueous). After standing several hours, crystals of uric
acid made their appearance, and were easily recognised by the
chemical and microscopical tests mentioned above.

Further than this, the presence of sodium was found in the secre-
tions of the nephridia of Hirudo. It may be that the uric acid is
in combination with sodium as a sodium urate.

From this investigation the nephridium of the Hirudinea func-
tions as a true kidney.

Renal Organs of the Hirudinea aud Oligochceta and their

Constituents.

Hirudinea.

Oligocliafia.

Uric acid, .....

Sodium, .... . .

Urea, ......

Guanin, ......

Calcium phosphate,

present.

99

absent.

99
9 9

present.

absent.

9 9
9 y
99

The minute structure of the excretory organs in general of the
Oligochseta, especially those of Lumbricus terrestris, have been
worked out by Dr E. Claparede, and detailed in his “ Histologische
Untersuchungen fiber den Regenwurm ” {Zeitsclirift fur Wissen-
schaftliche Zoologie , vol. xix.), and also by Professor Gegenbaur,
“ Ueber die sogenannten ftespirationsorgane des Regen wurms ”
{Zeitsch. W. Zool ., vol. iv.).

1887.] Mrs Griffiths on Specimens of Tulipa sylvestris. 349

4. On Degenerated Specimens of Tulipa sylvestris. By
Mrs A. B. Griffiths. Communicated by Dr A. B.
Griffiths, F.B.S.E., &c.

This note describes a peculiar yet interesting form of degenerated
Tulipa sylvestris. Last June (1886) the tulip bulbs were removed
(after growing and flowering in very rich soil), and set in the
December of the same year in a soil of poor quality. The plants
did not flower until the present June.

These degenerated forms have the usual erect scapes found in
the genus Tulipa ; but the inflorescence has the form of well-
marked umbels. The flowers were small (fig. 1), and consisted of
the usual parts of Tulipa sylvestris , namely, a
yellow polyphyllous and inferior perianth (with
six perianth leaves). The stamens were hex-
androus and hypogynous ; the pistil syncarpous
and superior; the placentation was axile, and
the ovary divided into three cells. The unusual
inflorescence and the peculiar shape of the petaloid
segments of the perianth were so unlike Tulipa
that the present investigation was undertaken as
a point of some interest to botanists.

The bulbs, leaves, and peduncle had developed

. . Fig. 1.— Flower of

the strong odour of the oil of onions or garlic, degenerated Tulip

The essential oil was extracted by distilling the (natural size)*

peduncle, leaves, and bulbs separately with water. The essential

oil was then obtained from this, distillated by repeated fractionation

and rectification over potassium.

This purified essential oil had a boiling point of 141° C., and
yielded upon analysis a percentage composition similar to that of
allyl sulphide , as is shown by the following figures : —

Theory. Found.

I. IL

C6 = 72 = 63T5% 63-24 % 63-17%

H10= 10 = 8-77 „ 8-69 „ 872 „

III.

63-21 %
873 „
28-06 „

S = 32 = 28-07
114

350 Proceedings of Royal Society of Edinburgh. [july 4,

(I wish, here, to thank my husband [Dr Griffiths] for the above
determinations.)

Then, again, on the addition of an alcoholic solution of silver
nitrate to the purified oil, a white precipitate is thrown down.
This precipitate, when allowed to crystallise from hot alcohol,
separates in white needle-shaped crystals (fig. 2), as observed by

low power under the micro-
scope. This crystalline pre-
cipitate is no doubt the
silver nitrate compound of
allyl sulphide,

(C3B 5) 3 S ( AgNOs) j

gj The bulbs, peduncles, and
leaves of this degenerated
form of Tulip a sylvestris all
yielded the same essential
oil as above. No oil of
mustard was detected in the
above distillate as is usual
(according to Dr Pless, Ann.
Cliem. Pharm ., vol. lviii.
p. 36) during the distillation of some plants containing either of
the two isomeric oils of garlic and onion.

Fig. 2.

-Needle-shaped crystals of
(C3H5)2S(AgN03)2”

It is well known that many species of Allium yield, on distilla-
tion, allyl sulphide ; also several genera of the Cruciferae yield the
same chemical compound under similar treatment. Amongst these,
Iberis amain, Alliaria officinalis, Tldaspi arvense (Wertlieim, Ann.
Chem. Pliarm., vol. li. p. 289, and vol. liv. p. 297). But the
essential oil, which is capable of yielding allyl sulphide, has not
been found in the genus Tulipa, although it, like Allium, belongs to
the Liliaceae.

It has been shown by Professor Alphonse de Candolle ( Origin of
Cultivated, Plants, p. 66) that the onion ( Allium cepa) is a very old
form of the vegetable kingdom. He says : — “ Its [onion] cultiva-
tion in Southern Asia and eastern region of the Mediterranean dates

from a very early epoch.” Therefore, if the cultivated onion is a
very ancient variety, what must be the age of its wild ancestor ?
From the facts detailed in this paper, is it not likely that the wild

1887.] Mrs Griffiths on Specimens q/Tulipa sylvestris. 351

tulip ( Tulip a sylvestris ) is a descendent from the genus Allium , and
that by a change in the surroundings and other causes these par-
ticular plants have retrograded in certain points (namely, the pro-
duction of an oil identical with oil of onions, and the inflorescence
similar to the onion family) to the original ancestral type. To con-
clude, in the words of Darwin, “ As we have no written pedigrees,
we are forced to trace community of descent by resemblances of any
kind ” ( Origin of Species).

5. The Luminous Organs of Nyctiphanes norvegica , Sars. By
J. T. Cunningham, B.A., and Rupert Yallentin.

The fact that light was emitted in the dark by a Schizopodous
shrimp was first noticed by J. Vaughan Thomson, who, in his
Zoological Researches , published about 1820, describes a species
which he observed to be luminous under the name Noctiluca. He
mentions the presence of scattered spots of red pigment in the
animal, hut was quite unaware that the production of light was
confined to certain definite organs enveloped by this pigment — was
indeed unaware of the existence of the organs which form the
subject of this paper. Later on, when the family of the Euphausiidse
was defined, various accounts were given of certain complicated
organs of spherical shape in the animals belonging to the family.
These organs were generally considered to he organs of vision, and
were called accessory eyes. The most detailed account of the structure
of these supposed eyes was given by Claus,* in 1863. The fact that
the Euphausiidse were luminous, was however known to the naturalists
on hoard the “Challenger,” and a paragraph is devoted to the subject
in the Narrative of the Cruise of that ship (vol. i. p. 713). It is
there stated that the phosphorescent light emitted by the species
of the Euphausiidse was frequently under observation during the
voyage. It was found that when one of the animals newly caught
was taken up by a pair of forceps, a pair of bright phosphorescent
spots was observed immediately behind the eyes, other two pairs on
the trunk, and four other spots along the median ventral line of the

* “Ueber einige Schizopoden und niedere Malakostraken Messina’s,” Zeits.
f. Wiss. Zool ., Bd. xiii.

VOL. XIV. 17/11/87

z

352 Proceedings of Royal Society of Edinburgh. [july 4,

tail : that these could all be seen, easily by the unaided eye : that
the pair close to the eyes was first and most brilliantly illuminated,
and then the light, which was bluish white, spread to the other
organs in the trunk and tail : that after a brilliant flash had been
emitted, the organs glowed for some time with a dull light : that
the light was given out at will by the animal, and usually but not
always on irritation : that subsequent flashes became less and less
bright till the animal appeared to lose the power of emitting light :
that if the organs were removed by the forceps, the points of the
latter glowed brightly for some time, and when the animal was
dying the whole body was frequently illuminated by a diffused light:
that the phosphorescent organs appeared under the microscope as
pale red spots with a central clear lenticular body, and the light
came from the red pigment. It is further mentioned that in August
1880 Mr John Murray observed at night, on the surface of the sea
in the Faeroe Channel, large patches and long streaks of apparently
milky- white water, and the tow-nets caught in these places immense
numbers of Nyctiphanes norvegica , M. Sars, about half the size of
the adult, and the peculiar appearance of the water seemed to be due
to the diffused light emitted from the phosphorescent organs of this
species.

That the organs, erroneously called accessory eyes, were in reality
luminous or “ phosphorescent ” organs was definitely asserted by Prof.
G. C. Sars, in his Keport on the Schizopoda of the “Challenger.” He
gives an account of their structure, but does not discuss very fully the
questions concerning the method and mechanism of the production of
light. Mr W. Patten* only last year has again attempted to maintain
that these organs are eyes and not luminous organs ; but in view of
the evidence of Sars and others and of our own experiments, Mr
Patten’s arguments need no special refutation; they are indeed con-
tradicted sufficiently by the postscript which is added to his paper
by Drs Giesbreclit and Paul Meyer, who personally observed the
luminosity of Euphausia.

We have studied these organs and their function in Nyctiphanes
norvegica, Sars, which is abundant in certain deep places in the
Clyde sea-area. We obtained it in 95 fathoms off Brodick Bay, by

* “Eyes of Molluscs and Arthropods,” Mitt, aus der Zool. Stat. zn Neapcl ,

1886.

1887.] Mr J. T. Cunningham on Nyctiphanes norvegica. 353

means of the shrimp trawl worked a little above the bottom. We
kept the animals alive in the “ Ark ” at Millport, and there made
observations and experiments on the luminous organs in the fresh
state. Their structure was investigated by Mr Yallentin, by means
of the preserved material, at the Granton Laboratory of the Scottish
Marine Station.

The distribution of the organs in the body has been completely
described by Sars. There are three pairs and four median single.
The first pair are in the eye peduncles immediately behind and
dorsal to the eyes. The 2nd pair are in the basal joints of
the 2nd pair of thoracic appendages, and each of these is on the
internal side looking towards the median line of the body. The
3rd pair are in the basal joints of the 7th pair of thoracic appen-
dages; each is on the external side, and looks backwards and
outwards. Of the four unpaired organs, one is in the middle of the
ventral surface of each of the first four abdominal somites.

All the organs except the pair in the eye peduncles are perfectly
similar in structure. The organ forms a spherical body lying
immediately beneath the epidermis, and almost entirely independent
of the surrounding tissues. The envelope of the posterior half of
the organ is formed by a hemispherical cup of considerable thick-
ness, of laminated or stratified structure, appearing fibrous in section,
and non-cellular. Internal to this is a cellular layer, consisting of
large cubical cells to the exterior, and smaller cells at the internal
surface. The hollow of the hemisphere within this layer is entirely
filled with a non-nucleated fibrous mass, the fibres or rods being
externally perpendicular to the surface of the cellular layer, but in
the centre crossing one another at right angles. In front of this
fibrous mass is a lens of perfectly homogeneous and highly refract-
ing substance. This is surrounded and clasped by a ring of a
structure similar to that of the stratified layer. Outside the fibrous
ring and the lens is a cellular layer, whose nucleated cells are smaller
in size than those of the posterior cellular layer. Outside the
posterior half of the organ, forming a thin mosaic-like epithelium
over the stratified layer, is a coating of flat polygonal red pigment
cells, which are a specialised set of the red mesoblastic cliromato-
phores which occur beneath the epidermis in various parts of the
body. Cellular strands may be occasionally detected passing from

354

Proceedings of Royal Society of Edinburgh. [july 4,

the surrounding tissues in between the anterior and posterior halves
of the organ, but we have not satisfied ourselves that these strands
are either muscular or nervous. The relations of the various layers
are for the most part correctly described by Claus and Sars ; but the
former described a cuticle enveloping the whole organ, which does
not exist, and the latter did not correctly describe the relation of the
external pigmented epithelium to the stratified layer.

With regard to the emission of light, our experiments confirm
the evidence of previous observations, that the luminosity is inter-
mittent, and, as far as can be judged, closely dependent on stimula-
tion. The following experiments were made : —

1. Mechanical Stimulation. — In total darkness the hand was
inserted into a vessel containing sea-water in which some of the
animals were swimming, and moved about. When an animal was
touched it instantly emitted light. When an animal was taken
between the fingers and removed from the water, all the organs
shone brilliantly for 5 to 10 secs., while the animal was flapping
its abdomen and trying to escape; then followed a series of separate
flashes, and after 10 secs, more the emission of light ceased
altogether, until fresh stimulation was applied by means of a squeeze
between the finger and thumb, when all the organs immediately
flashed.

When a fresh animal was crushed between the two hands, certain
particles of the tissue became luminous, and remained so till they
were dried up.

When one of the organs was crushed on the stage of the micro,
scope, the field became immediately illuminated, and remained so
for some time.

2. Chemical Stimulation. — When a living animal was placed into
saturated solution of bichloride of mercury, all the organs shone
most brilliantly during the energetic struggles preceding death : the
luminosity lasted usually 5 to 7 secs., but in one case for 30 secs.

When a specimen was placed in nitric acid per cent., the same
result occurred.

In both cases the posterior organs ceased to shine first, and the pair
in the eye peduncles were the last to cease shining. One of us spent a
whole morning at Millport in examination of the organs in the fresh
state, by means of the microscope, with the object of ascertaining

1887.] Mr J. T. Cunningham on Nyctiphanes norvegica. 355

from which particular portion of the organ the light proceeded.
The results of this examination were afterwards verified by both of
us together. In this investigation, no evidence was obtained in
support of Sars’ opinion that the light principally emanated from
the central mass of fibres behind the lens. When the organ was
crushed beneath a cover glass, and examined in daylight, it was not
difficult to separate the different layers from one another. The
exterior pigment cells were in this process dispersed, and every
other part of the organ, with a single exception, was found to be
perfectly colourless and transparent. The exception was the inner
superficial portion of the stratified layer, which may for the time be
named the argentea. This portion, when viewed by transmitted light,
was seen to have a beautiful luminous purple colour, like a sunset
tint. The purple was reddish at first, but gradually became more
blue as time went on, till after about half an hour the colour was a
deep blue or violet. When the transmitted light was shut off, and
the preparation was viewed by reflected light without a condenser,
the colour of the same region was the complementary tint of that seen
by transmitted light. The peculiarity of this colour was, that it
appeared to be luminous ; that is, no part of the preparation could
be seen at all in the field but this colour, which shone with a greenish-
yellow light. When the light was entirely excluded, the whole
preparation was invisible. It follows from this, that the inner
surface of the argentea possesses in a marked degree the property of
fluorescence. It was afterwards found that such a preparation, when
viewed in the dark with the naked eye, contained a luminous spot,
and this spot was always found to be the inner portion of the
argentea. The phosphorescence was not visible through the micro-
scope, simply because the light was absorbed by the lenses ; but
when light fell on the preparation, although it was not sufficient to
render visible other parts of the organs, the inner surface of the
argentea, by its fluorescent action on the most refrangible rays of the
spectrum, became visible, just as in the case of uranium glass.
Another fact is of great interest. When a living specimen of
the animal is crushed between the hands and rubbed with the
fingers, certain pieces of the mangled tissue are seen to be luminous
in the dark. Such pieces can be picked off with the forceps and
examined with the microscope, and are always found to be morsels

356 Proceedings of Royal Society of Edinburgh. [july 4,

of the argentea. One of us was tempted to conclude from these
facts that the luminosity of the organs in the living animal was entirely
and exclusively due to the purely physical property of fluorescence
in the internal portion of the argentea. But this conclusion is quite
inconsistent with the intermittent emission of the light and its
dependence on stimulation. Moreover, in other luminous organs,
e.g., Lamypris splendidula , the light has been shown to come from
a thick mass of cells, and no layer resembling the argentea of
Nydiphanes is present. At present we conclude that probably the
posterior cell layer in Nydiphanes is the active agent in producing
light when acted on by a nervous impulse, and that the light is
much intensified by the fluorescent property of the surface of the
argentea. Of the function of the central mass of rod or fibres we
have ascertained nothing at all. The lens is obviously there in
order to concentrate the light, while the anterior cellular cap is
merely a transparent cornea. The fibrous iris-like ring round the
lens perhaps acts as a diaphragm, though it undoubtedly is not
pigmented and is transparent. We hope shortly to make renewed
attempts to elucidate the mechanism of the organs.

6. On a Constant Daniell Cell, for nse as a Standard of
Electromotive Force. By Cosmo I. Burton, B.Sc., F.C.S.

This cell consists of two tubes about three inches long and half
an inch in diameter, sealed at one end, and connected together near
the closed end by a glass tube about four inches long, having a
glass tap in the middle.

The hole through the plug of the tap is filled with plaster of
Paris, made as nearly as possible flush with the glass surfaces. This
plaster plug serves as a porous septum between the two tubes, which
represent respectively the two compartments of a Daniell cell — the
one tube containing a copper rod immersed in a saturated solution
of copper sulphate, the other a zinc rod in a solution of zinc sul-
phate, of as nearly as may be the same density as the copper
solution. The cell is designed for use only with the quadrant
electrometer, and must never be short-circuited.

When the cell is used the tap is turned “on,” i.e ., so that the

1887.] Mr C. I. Burton on a Constant Daniell Cell. 357

ends of the plaster plug are opposite the two tubes containing
solutions. Immediately that the observations are completed, the
tap is turned off, and so diffusion of the solutions completely pre-
vented. The tap is made of the peculiar shape shown in the

diagram, in order that it may only he turned in one direction, and
so the possible transfer of a minute quantity of the one solution into
the opposite tube is avoided.

Several years ago Mr A. P. Laurie and I used this cell con-
stantly for four months, and during that time it showed no change
of E.M.F., as compared with a standard Latimer Clark, readings
being made to three figures only. More recently Professor Ayrton,
of the City and Guilds Technical Schools, London, very kindly
undertook to compare this cell with a standard Latimer Clark of
his own construction, and also with Fleming’s standard Daniell.
The results of the comparison are given in the following table.
E.M.F. of standard Latimer Clark is taken as unity.

Date.

Standard Flem-
ing, E.M.F.

Experimental
Cell, E.M.F.

Temperature of

Room.

Standard
Latimer Clark.

1886.

f 07466

0-7476

18° -2 C.

16°-9 C.

May 13.

t 0-7462

0-7476

9 9

9 9

on

J 0-7505

0-7485

18 °*6

16°-1

,, AO.

\0 -7500

07489

19° *6

18° -1

„ 31.

0-7509

17°-9

16°-8

Oct. 7.

0-7456

0-7468

...

16°-8

358

Proceedings of Royal Society of Edinburgh. [july 4,

On looking at the cell again, about eight months later, the copper
wire was found corroded through, and contact broken. In order to
avoid this accident, it is well to use copper rod not less than one-
eighth of an inch thick, as copper is somewhat soluble in solution of
sulphate of copper (see Gray, Phil. Mag., 1886, p. 389).

The corks used to support the copper and zinc rods should he
carefully paraffined, and every precaution taken to prevent evapora-
tion of the solutions.

The observation in the above table, dated May 31, was taken
rather hurriedly, and Professor Ayrton considers it untrustworthy.
Omitting this result, it is seen that the experimental cell has a very
constant E.M.F., and that the change, after about five months, was
very small.

7. On Glories. By Professor Tait.

(Abstract.)

When Mr Omond was appointed to the Ben-Hevis Observatory
I requested him to take every opportunity of observing what are
called Glories — specially noting, when possible, their angular
diameters and the order of their colours, so that it might he
possible to decide upon the exact mode in which they are produced.

Young, while attributing to their true cause the spurious (or
supernumerary) rainbows, proceeds to say: — “ The circles, some-
times seen encompassing the observer’s shadow in a mist, are
perhaps more nearly related to the common colours of thin plates
as seen by reflection.” — \_Lectures, II. p. 645].

How from Mr Omond’s observations it appears that the mists to
which the glories are due produce coronse of, say, 2° or 3° radius ; —
from which it follows that the diameter of the particles is some-
where of the order yqW incb. It is thence shown that, were
Young’s explanation correct, the radii of the rings would vary with
great rapidity in passing from one kind of homogeneous light to
another. This is altogether irreconcilable with Mr Omond’s obser-
vations.

That the glories are not of the nature of spurious rainbows is
shown very simply by the fact that they are more intense as their
radii are smaller.

1887.]

Professor Tait on Glories.

359

Hence, the only possible explanation is diffraction depending
on the form of the vertex of the reflected wave. The form of
an originally plane wave, once reflected inside a drop of water is,
roughly, when the central ray has just emerged, a portion of an
hyperboloid of revolution, doubled back cusp-wise round its border.
An approximate calculation is given, based on this assumption.

A simple first approximation to the theory of glories is given
by the behaviour of a plane wave incident normally on a screen
pierced with a great number of very small circular apertures of
nearly equal size. They are thus, to a certain extent, analogous to
coronse.

8. Report on the Pennatulida, dredged by H.M.S. “ Porcu-
pine.” By A. Milnes Marshall, M.D., D.Sc., M.A.,
P.R.S., Beyer Professor of Zoology in the Owens
College, and by G. H. Fowler, B.A., Ph.D., Berkeley
Fellow of the Owens College, Manchester. Communi-
cated by John Murray, Esq., Ph.D.

Friday , 15 th July 1887.

JOHN MURRAY, Ph.D., Vice-President, in the Chair.
The following Communications were read : —

1. Stability of Fluid Motion. — Rectilineal Motion of Viscous
Fluid between two Parallel Planes. By Sir W. Thomson,
LL.D., F.R.S.

27. Since the communication of the first of this series of articles
to the Royal Society of Edinburgh in April, and its publication in
the Philosophical Magazine in May and June, the stability or in-
stability of the steady motion of a viscous fluid has been proposed
as subject for the Adams Prize of the University of Cambridge for
1888.* The present communication (§§ 27-40) solves the simpler

* See Phil. Mag., July 1887.

360 Proceedings of Boy al Society of Edinburgh, [july 15,

of the two cases’ specially referred to by the examiners in their
announcement, and prepares the way for the investigation of the
less simple by a preliminary laying down, in §§ 27-29, and equations
(7) to (12) below, of the fundamental equations of motion of a
viscous fluid kept moving by gravity between two infinite plane
boundaries inclined to the horizon at any angle I, and given with
any motion deviating infinitely little from the determinate steady
motion which would be the unique and essentially stable solution
if the viscosity were sufficiently large. It seems probable, almost
certain, indeed, that analysis similar to that of §§ 38 and 39 will
demonstrate that the steady motion is stable for any viscosity, how-
ever small ; and that the practical unsteadiness pointed out by
Stokes forty years ago, and so admirably investigated experimentally
five or six years ago by Osborne Keynolds, is to be explained by
limits of stability becoming narrower and narrower the smaller is
the viscosity.

Let OX be chosen in one of the bounding planes, parallel to the
direction of the rectilineal motion ; and 0 Y perpendicular to the
two planes. Let the x y-, z- component velocities, and the pressure
at ( x , y , 0, t ) be denoted by U + u, v, and p respectively ; U denot-
ing a function of (y, t ). Then, calling the density of the fluid
unity, and the viscosity /a, we have, as the equations of motion,*

du dv dw n .

dx + dy+ dz ' ' ’

s(U + «) + (U + «)s + t^(U + «) + ws = ^v*(U + «) — s + y8ml,

dv ,,, . dv dv

Tt + ^ + u^ + v +

c ^

^ 1

II

/xV2v

dp T

- -p - q cos I ,
dy J

dw /TT . die die

m+^+u^+% +

dw

w— =
dz

pV2W

dp
dz ’

pi U2

where V2 denotes the “Laplacian” — . + — + — — •

uxr dyA dz2.

28. If we have u — 0, v — 0, iv = 0 ; j? = C — g cos I y + gx sin I ;
these four equations are satisfied identically; except the first of (2),
which becomes

* Stokes’s Collected Payers, vol. i. p. 93.

1887.] Sir W. Thomson on Stability of Fluid Motion. 361

This is reduced to

if we put

dF d?F . _
dv d2v

' ' '

U = v + \g sin I//x. ( b 2 - y 2)

(»)•

(4) ,

(5) .

For terminal conditions (the hounding planes supposed to be ?/ = 0
and y = b, we may have

v = F(t) when y = 0 )

» V=*I

where F and g denote arbitrary functions. These equations (4)
and (6) show (what was found forty-two years ago by Stokes) that
the diffusion of velocity in parallel layers, provided it is exactly in
parallel layers , through a viscous fluid, follows Fourier’s law of the
“linear” diffusion of heat through a homogeneous solid. Now,
towards answering the highly important and interesting question
which Stokes raised, — Is this laminar motion unstable in some
cases'? — go hack to (1) and (2), and in them suppose u, v, w to he
each infinitely small: (1) is unchanged ; (2) with U eliminated by
(5), become

where

dw

dt

dv

dt

dw

dt

+ [„ + ic(b2-P)]^ + c(f?-f

• (7),

+ [v+lc(V- P)}%

9 dp

= U 2v--f
dy

• (8).

+ [v + ic(b*-f)]d£

1

§

[>

3.

II

• (9),

c = g sinl/fjL .

• (io),

and, for brevity, p now denotes, instead of as before the pressure,
the pressure + g cos I y.

We will suppose v to he a function of y and t determined by (4)
and (6). Thus (1) and (7), (8), (9) are four equations which, with
proper initial and boundary conditions, determine the four unknown
quantities u, v , w, p ; in terms of x, y, z, t.

29. It is convenient to eliminate u and w ; by taking ^

of (7), (8), (9), and adding. Thus we find, in virtue of (1),

362

Proceedings of Royal Society of Edinburgh, [july 15,

This and (8) are two equations for tire determination of vainly.
Eliminating between them, we find

a single equation which, with proper initial and boundary condi-
tions, determines the one unknown, v. When v is thus found, (8),
(7), (9) determine p, u, and w.

30. An interesting and practically important case is presented by
supposing one or both of the bounding planes to be kept oscillating
in its own plane ; that is, E and § of (6) to be periodic functions of
t. For example, take

F = a cos wt , § = 0 .
The corresponding periodic solution of (4) is

(13).

(b-y)+/£.

to

2;u

v — a-

b ./ - b . /

E v 2ja - e v

to

2^

COS

• • (14)

In connection with this case there is no particular interest in sup-
posing a current to be maintained by gravity ; and we shall there-
fore take c — 0, which reduces (7), (8), (9), (11), (12) to

du

du

dv

dp

dt

+

vdx +

dyV

= fX\/2U-

dx

dv

+

dv

0

dp

dt

Vdx

= p v v -

dy

dw

dw

dy

dt

+

Vdx

II

1=

<1

bs

§

dz

~dv dv 0

d\]2v d2v dv d\? 2v
dt + dig2 dx V dx

fA\7*V

• (15),
■ (16),
. (17),

• (18),

. (19);

in all of which v is the function of (y, t ) expressed by (14).

These equations (15) . . . (19) are of course satisfied byw = 0,
v = 0, w - 0, p = 0. The question of stability is, Does every possible
solution of them come to this in time ? It seems to me probable
that it does ; but I cannot, at present at all events, enter on the

1887.] Sir W. Thomson on Stability of Fluid Motion. 363

investigation. The case of b = oo is specially important and in-
teresting.

31. The present communication is confined to the much simpler
case in which the two hounding planes are kept moving relatively
with constant velocity ; including as sub-case the two planes held at
rest, and the fluid caused by gravity to move between them. But we
shall first take the much simpler sub- case, in which there is relative
motion of the two planes, and no gravity. This is the very simplest
of all cases of the general question of the Stability or Instability of
the Motion of a Viscous Fluid. It is the second of the two cases
prescribed by the Examiners for the Adams Prize of 1888. I have
ascertained, and I now proceed to give the proof, that in this sub-
case the steady motion is wholly stable, however small or however
great be the viscosity ; and this without limitation to two-dimen-
sional motion of the admissible disturbances.

32. In our present sub-case, let /3b be the relative velocity of the
two planes ; so that in (6) we may take F = 0, $ = (3b ; and the
corresponding steady solution of (4) is

v = (3y .

Thus equation (19) becomes reduced to

where

dt+PyTx=^ *{>

C= v2« j

and (18), (15), (16), (17) become

2/3 dx= - V p

du n du n o dp

m + py-+ji^liVH-Tx

dv n dv

dt+/Sydi

dw r. dw

dt+^dx

9 dp

= ^V-dy

9 wyv

= y. y AW - -A

dp

dz

(20).

(21);

• • (22),

• • (23),

• • (24),

. . (25).

It may be remarked that equations (22) . . . (25) imply (1), and
that any four of the five determines the four quantities u, v, w, p.

364

Proceedings of Royal Society of Edinburgh, [july 15,

It will still be convenient occasionally to use (1). We proceed to
find the complete solution of the problem before us, consisting of
expressions for u, v, iv, p satisfying (22) . . . (25) for all values of
x, y, z, t ; and the following initial and boundary conditions : —

when t = 0: u, v, w, to be arbitrary functions )
of x, y, z, subject only to (1) j

u = 0, v = 0, w — 0, for y = 0 and all values of x, z, t (
u = 0, v = 0, w— 0, for y = b „ „ j

■ (26);
• (27)-

33. First let us find a particular solution u, v, w, p, which shall
satisfy the initial conditions (26), irrespectively of the boundary
conditions (27), except as follows : —

V = 0, when t — 0 and y = 0

V = 0, when t = 0 and y = b

(28).

Next, find another particular solution, u, it), p, satisfying the
following initial and boundary equations : — ■

it = 0, = 0, tt) = 0, when t — 0 . . . . (29),

it -Ml = 0, t> + V = 0, tt) + w = 0, when y = 0 )

and when y = b)

(30).

The required complete solution will then be

m = U + u, v = + z^ = U) + w. . . . (31).

34. To find u, V, W, remark that, if y. were zero, the complete
integral of (21) would be

l = arb. func. ( x - /3yt) ;

and take therefore as a trial for a type-solution with ju not zero,

£

»p i \mx + {n -mpt)y+ qz\

(32);

where T is a function of t, and t denotes Substituting

accordingly in (21), we find

rTV

— = — y[m2 + {n- m/St)2 + g2]T .... (33);

whence, by integration,

-pt[m2+n2+q2-nnipt+^ pw]

By the second of (21) and (32) we find

(34).

1887.] Sir W. Thomson on Stability of Fluid Motion. 365

i[mx+ (n - mpt)y+qz ]

v= -T-i 7

m2 + (n — m/3t) 2 + q 2

whence, by (22),

i[m.r+(n - mpi)y+qz\

v = - 2/3miTr - e- .

[m2 + (w - m/3t)2 + g'2]2

Using this in (25), and putting

w = }yeL[mx+(n-mpt)y+qz]

we find

dW

dt

- fx[m 2 + (/? - m/3t)2 + q2~\ W

2/3mqT

\m2 + (n- mj3t)2 + g2]

which, integrated, gives W.

Having thus found v and w , we find u by (i), as follows

(35) ;

(36) .

(37) ,

(38) ,

W =

(n - 7nfit)v + qiv

m

(39).

35. Realising by adding type-solutions for ± i and ± n, with
proper values of C, we arrive at a complete real type-solution with,
for v, the following — in which K denotes an arbitrary constant : —

■ |ui[m2+rc2+g2 _ nmpt+^rrfipW CQg

m2 + (n + 7n(3t )2 + q2 sin

\mx + (n + 7n/3t)y + qz\

- y.t[m'2+n2+q‘2+nmpt+im2pW]

. \mx + (n + mpt)y + qz] J- (40).

m 2 + (n + 7n(3t)2 + q2 sm

This gives, when t — 0,

v —

+ K

m2 + n2 + q2
which fulfils (28) if we make

n = iiry/b (42);

sin ny ^0s(mx + F) ■ • • (41)>

and allows us, by proper summation for all values of i from 1 to oo ,
and summation or integration with reference to ra and q, with
properly determined values of K, after the manner of Fourier, to
give any arbitrarily assigned value to vt=0 for every value of a?, y, z,

from x = — co

„ y = °

to X = + 00 ,

„ y=b,

„ z = + co .

. . (43).

366 Proceedings of Royal Society of Edinburgh, [july 15,

The same summation and integration applied to (40) gives v for
all values of t , x, y, z; and then by (38), (37), (39) we find corre-
sponding determinant values of w and u.

36. To give now an arbitrary initial value, w0, to the 2-component
of velocity, for every value of x , y, z, add to the solution ( u , v, w ),
which we have now found, a particular solution (u\ v', w') fulfilling
the following conditions : —

v = 0 for all values of t , x, y, z ;
id — W0 - iv0 for t = 0, and all values of x, y, z

and to he found from (25) and (1), by remarking that v =0 makes,
by (22), y/ = 0, and therefore (23) and (25) become

du'

dt

did

dt

du' o ,

+/3^=mvV

• • (45),

• - (46),

Solving (46); just as we solved (21) by (32), (33), (34); and then
realising and summing to satisfy the arbitrary initial condition, as
we did for v in (40), (41), (42), we achieve the determination of
id ; and by (1) we determine the corresponding u\ ipso facto satisfy-
ing (45). Lastly, putting together our two solutions, we find

u = u + u\ v = v, w = w + id , . . . (47),

as a solution of (26) without (27), in answer to the first requisition
of § 33. It remains to find u, t), It), in answer to the second
requisition of § 33.

37. This we shall do by first finding a real (simple harmonic)
periodic solution of (21), (22), (23), (25), fulfilling the condition

u = A cos wt + B sin wt
v — C cos wt -j- 1) sin wt
w = E cos wt + F sin wt
u — Q l cos + sin wt

v = (S, cos wt + 2) sin wt
w = (£ cos wt + § sin wt

when y = b

■ (48),

where A, B, C, D, E, F, 33, (£, 2), (S, § are twelve arbitrary

functions of ( x , z).

Then by taking

of each of these after

1887.] Sir W. Thomson on Stability of Fluid Motion . 367

the manner of Fourier, we solve the problem of determining the
motion produced throughout the fluid, by giving to every point of
each of its approximately plane boundaries an infinitesimal displace-
ment of which each of the three components is an arbitrary function
of x, z, t. Lastly, by taking these functions each = 0 from t — - oo
to t — 0, and each equal to minus the value of u, v, w for every point
of each boundary, we find the U, ty, U) of § 33. The solution of
our problem of;§ 32 is then completed by equations (31). To do
all this is a mere routine after an imaginary type solution is pro-
vided as follows : —

38. To satisfy (21) assume

v _ i {(ot-\-mx+qz^

= ^M+^+2^{H€^(^3+22) + K€-^(m2+?2) + L/(y) + MF(y)} . (49),

where H, K, L, M are arbitrary constants and /, F any two par-
ticular solutions of

+ </*)£

. (50).

This equation, if we put

mplfji = y, and ra2 -}- cf + tw/'/x = A .... (51),

becomes

y^ = (\ + iy y)£ (52);

which, integrated in ascending powers of (A + tyy), gives two par-
ticular solutions, which we may conveniently take for our / and F,
as follows : —

/(s/)=i- —

F (y) = A + tyy

(A + iy y)\ y~4(A + tyy)6 y -g(A + ty//)9 , ^
T2 — 6.5. 3.2 9. 8. 6. 5. 3. 2^ '

y-2(A + ty yY y-4(A + ty yf y “6(A + tyy)10

O 7. 6. 4. 3 10.9.7.6.4.3

+ &c.

(53).

39. These series are essentially convergent for all values of y. Hence

in (49) we have a solution continuous from y = 0 to y = b ; and by

its four arbitrary constants we can give any prescribed values to V,

and — for y = 0 and y = b. This done, find p determinately by
dy

(24) ; and then integrate (25) for w in an essentially convergent
series of ascending powers of A + iyy, which is easily worked out,
VOL. xiv. 31/12/87 2 A

368 Proceedings of Royal Society of Edinburgh, [july 15,

but need not be written down at present, except in abstract as
follows : —

w = (54);

where

SB = Hg1(A + t72/) + Kg2(X + i7|/) + Lg3(X + i7)/) i

+ MJ4(X + <w) + p£^(»i+fl + >■

Here P and Q are the two fresh constants, due to the integration
for iv. By these we can give to W any prescribed values for y = 0
and y = b. Lastly, by (1), with (49), we have

where

u

= Ue i(wi ^mx+qz)

U = -(— — +^-2b)

\nii y m /

Our six arbitrary constants H, K, L, M, P, Q clearly allow us to
give any prescribed values to each of U, 93, 933, for y = 0 and for
y = b. Thus the completion of the realised problem with real data
of arbitrary functions, as described in § 37, becomes a mere affair of
routine.

40. Now remark that the (u, v, w) solution of § 34 comes essen-
tially to nothing, asymptotically as time advances, as we see by (33),
(34), and (38). Hence the (it, t), it)) of § 37, which rise gradually
from zero at t — 0, come asymptotically to zero again as t increases
to oo . We conclude that the steady motion is stable.

2. Note on the Epiblastic Origin of the Segmental Duct in
Teleostean Fishes and in Birds. By George Brook,
F.L.S., Lecturer on Comparative Embryology in the
University of Edinburgh. Communicated by Prof. Sir
Wm. Turner, F.B.S.

Our knowledge of the development of the excretory system in both
vertebrates and invertebrates is as yet very incomplete, perhaps
more so than of any other system. Until quite recently the whole
of the urogenital system of the vertebrates was supposed to be
derived from the mesoblast. This view received a sudden check

1887.] Mr G. Brook on Epiblastic Origin of Duct. 369

when, on the publication of Graf Spee’s researches on the guinea
pig in 1884, the segmental (pronephric) duct was shown to have
an epiblastic origin. Hensen, indeed, had noted the fact some
years previously, but no notice had been taken of his discovery
until Graf Spee called attention to it. Hensen has recently taken
up the subject again, and Flemming has published a confirmatory
account for the rabbit. Thus there appears no further room for
doubting the epiblastic origin of the segmental duct in mammals.
It does not necessarily follow that the whole excretory system has
an epiblastic origin, but further information is required on the sub-
ject. Towards the end of 1886 Van Wijhe demonstrated the
epiblastic origin of the segmental duct in Elasmobranchs, and
during the present year Yon Perenyi has announced that the
epiblast plays a similar part in Rana and Lacerta. During the past
few months I have been enabled to confirm Yon Perenyi’s researches
so far as Rana is concerned, and have also found that, in regard to
the formation of the segmental duct, Teleostean fishes, and probably
also birds, are in agreement with other types. The epiblastic origin
of the segmental duct is probably a feature common to the Yerte-
brata generally.

In the trout the segmental duct arises almost precisely in the
manner described and figured by Flemming for the rabbit. In a
twenty-seven days’ embryo the duct is well marked in the middle
trank region, and thins out both anteriorly and posteriorly. An-
teriorly the duct appears as a thickening of that portion of the
surface epiblast overlying the intermediate cell mass ; that is to
say, the segmental duct arises from that part of the epiblast dorsal
to the portion of the mesoblast from which it was formerly supposed
to be derived. Passing posteriorly the epiblastic thickening be-
comes more and more important, and in the middle trunk region
forms a large rounded mass of cells still partly attached to the
epiblast, and situated between the vertebral plate and the lateral
mesoblast. The lumen of the duct appears first as an irregular
cavity, and later the whole mass loses its connection with the
epiblast, and becomes pressed in amongst the “ intermediate cell
mass ” during the formation of the lateral body folds.

The origin of the segmental duct in birds does not appear to be
quite as clear. Anteriorly, the epiblast covering the central nervous

370 Proceedings of Boy cil Society of Edinburgh, [july 15,

system and the vertebral plates in chick embryos of forty to forty-
eight hours forms a thin membrane. On nearing the ventral portion
of the vertebral plates the epiblast becomes slightly thickened, while
immediately beyond the vertebral plates there is a slight involu-
tion and a considerable thickening in the outer layer. On passing
to the lateral mesoblast the epiblast again thins out. Here, evi-
dently, is an epiblastic thickening corresponding precisely in position
with that forming the segmental duct in other vertebrates. In the
chick, however, the “ intermediate cell mass ” is comparatively large,
and the epiblastic thickening soon becomes fused with the meso-
blast. In a forty-eight hour chick embryo I have noticed a curved
line more distinctly shown in some sections than in others, which
I take to define the limit of the epiblast. In the posterior portion
of the embryo the epiblast and “ intermediate cell mass ” are quite
separate, and I was unable to trace any thickening in the epiblast
of that region. Probably, therefore, the duct is pushed backwards
from the anterior portion without coming into contact with the
epiblast. This, at any rate, is the mode of development previously
described in Elasmobranchs and birds, when the segmental duct was
supposed to have a mesoblastic origin.

The whole of these recent researches must necessarily lead to a
modification in our views of the morphology of the vertebrate
excretory apparatus. Haddon has recently suggested that primi-
tively the nephridia (derived from the mesoblast) opened on each
side into a lateral groove, that later this groove deepened and
formed a closed canal, which subsequently acquired a secondary
opening to the exterior through the cloaca.

I propose to discuss this subject more fully in a future paper.

3. Preliminary Note on the Chemistry of Strophanthin.
By Thomas It. Fraser, M.D., F.P.S., Professor of Materia
Medica in the University of Edinburgh.

Since my former communications, in which several facts relating
to the chemistry of Strophanthus hispidus have been stated, I have
completed a systematic examination of various parts of this plant,
and more particularly of the seeds. Eeserving a detailed descrip-

1887.] Professor Fraser on Chemistry of Strophanthin. 371

tion of the results of this examination, I propose now to mention
only a few of these results in a brief form.

The active principle, to which I have given the name Strophan-
thin, occurs most abundantly in the seeds. By a very simple
process, consisting essentially of the separation of oil by means of
ether from the alcoholic extract, I obtained some years ago a crys-
talline body having great pharmacological activity, and possessing
the characteristics of a glucoside. In subsequent experiments,
however, although the same process was followed, a well-marked
crystalline product was not always obtained, and it soon became
evident that this difference was due to some difference in the con-
dition of the seeds which had been operated with. Thus, from seeds
collected by the late Bishop Mackenzie more than twenty years ago,
and also from seeds sent to me by Mr Buchanan of Blantyre, East
Africa, in 1881, I had no difficulty in separating an active principle
in the form of well-marked minute crystals ; but from seeds ob-
tained from Mr Buchanan in 1885, and also from seeds liberally
placed at my disposal by Mr Moir and by Messrs Burroughs, Well-
come & Co. last year, I failed to obtain an equally definite crystalline
body. I also found that the body obtained by the process formerly
described, whether in well-defined crystals or not, was resolvable
by acetate of lead into at least two bodies, one of which is an
extremely active glucoside, and the other an acid, for which I would
suggest the name kombic acid. It having become apparent, there-
fore, that the strophanthin first described is not a simple substance,
attempts were made to improve the process so as to separate
strophanthin in a more pure form than I had originally succeeded
in doing. The result of these attempts has been the adoption of a
process whose essential steps are the following : —

Starting with the product obtained by the earlier process, it is
dissolved in water, tannic acid is added to the solution, the tannate
is digested with recently precipitated oxide of lead, and then
extracted with rectified and proof spirit. This extract is dissolved
in a small quantity of rectified spirit, and the solution is pre-
cipitated by ether. The precipitate is finally dissolved in weak
alcohol, and through this solution carbonic acid is passed for several
hours, by which means lead is completely got rid of. After filtra-
tion the solution is evaporated at a low temperature, and the

372 Proceedings of Royal Society of Edinburgh. [july 15,

product is dried in vacuo over sulphuric acid. In the process of
drying, it first assumes a translucent, gummy appearance, and then
becomes opaque and white.

Strophanthin thus obtained is imperfectly crystalline, neutral or
faintly acid in reaction, intensely hitter, freely soluble in water, less
so in rectified spirit, and practically insoluble in ether and chloro-
form. It hums without residue, and it does not contain nitrogen.
When subjected to ultimate analysis its percentage composition,
taking, for the sake of brevity, the average of several closely
agreeing combustions, was found to he —

Carbon, 55 ’976.

Hydrogen, 7 ‘75 4.

Oxygen, 36 ‘283.

This percentage composition fairly corresponds with the formula,

The effects of a number of reagents upon it have been deter-
mined. In the meantime the following may be stated : — Strong
sulphuric acid produces a bright green colour, which soon becomes
greenish yellow and brown ; sulphuric acid and bichromate of
potash, in addition to the changes produced by sulphuric acid, a
blue colour ; phospho-molybdic acid, after contact for a few hours,
a bluish green, which, on the addition of a few drops of water,
becomes pure blue ; * nitric or hydrochloric acid, a yellowish brown ;
and caustic potash, ammonia, and other alkalies a faint yellow.
With a 1 per cent, solution in water, phospho-molybdic acid causes,
somewhat slowly, a bright green colour, which after prolonged con-
tact becomes greenish blue ; * nitrate of silver, a reddish brown
colour, and a slight dark precipitate ; caustic potash and other
alkalies, a very faint yellow ; dilute sulphuric acid, a faint white
opalescence ; and tannic acid, an abundant white precipitate, soluble
in excess both _ of strophanthin and of tannic acid. The solution,
tested at the ordinary temperature, is not changed in appearance by
acetate or subacetate of lead, perchloride of platinum, chloride of
gold, perchloride of iron, perchloride of iron and sulphuric acid,
perchloride of mercury, sulphate of copper, bichromate of potassium,

* Since this paper was communicated, I have found that the blue colour
may he almost instantaneously produced by adding an alkali, such as solution
of potash, after the addition of the phospho-molybdic acid.

1887.] Professor Fraser on Chemistry of Strophanthin. 373

iodide of potassium, nor by many other reagents ; except that nearly
all acid reagents cause the solution to become slightly hazy, and it
is then found that the solution contains glucose. This decom-
position is also produced by sulphuretted hydrogen, and for this
reason it is not advisable to use sulphuretted hydrogen in any pro-
cess for preparing strophanthin.

Indeed, all the mineral acids, excepting carbonic acid and many
of the organic acids, resolve strophanthin, even in the cold, into
glucose and a substance which I have named strophanthidin. A
very pretty crystallisation of the latter is spontaneously produced,
in a few hours, in a solution of strophanthin in 1*5 per cent,
sulphuric acid. Contact at the ordinary temperature for even
three days with dilute sulphuric acid does not apparently entirely
decompose the strophanthin, as an additional quantity of glucose
seems to be afterwards produced when the solution, filtered from
strophanthidin, is heated at 212° F. for a few hours. Thus, when
strophanthin was decomposed at the ordinary temperature by contact
for about three days with 1 *5 per cent, sulphuric acid, there was
obtained 3 7 ’5 per cent, of crystalline strophanthidin, and about 20
per cent, of glucose.* The crystals of strophanthidin having been
removed by filtration, and the almost colourless, bitter, and acid
fluid having been boiled for four hours, it was now found that the
glucose had increased to 26*64 per cent., and that about 4*3 per
cent, of an amorphous brownish substance had been formed.

This action of acids renders it apparent that an acid, and especially
a mineral acid, should not be used in the preparation of strophanthin.
Thus, in 1877, seven years after the publication of my first com-
munications on this subject, Hardy and Gallois described a process
in which, by using for the extraction of the seeds rectified spirit
acidulated with hydrocholic acid, they obtained a crystalline pro-
duct which they believed to be strophanthin. There can be little
doubt, however, that their crystalline product was strophanthidin,
not only because the process they employed would decompose the
strophanthin into strophanthidin and glucose, but also because

* In the solution obtained by this decomposition, the exact estimation of
glucose by Fehling’s solution is rendered difficult and uncertain by a green
colour being produced, which persists after the blue colour of Fehling’s solu-
tion has disappeared.

374 Proceedings of Royal Society of Edinburgh, [july 15,

their crystalline product was found by them not to yield glucose when
it was heated with dilute sulphuric acid. Hence they concluded
that strophanthin is not a glucoside (Comptes Rendus de VAcademie
des Sciences, Ixxxiv., 1877, p. 261 ; and Journal de Pharmacie
et de Chemie, xxv., 1877, p. 177). The glucosidal character
of strophanthin, however, has now been amply demonstrated by a
large number of experiments which I have made, and by the ex-
periments of subsequent observers, and especially by those of A.
W. Gerrard, described in an interesting paper published this year
( The Pharmaceutical Journal and Transactions, 14th May 1887,
p. 923). Further, the solution obtained when strophanthin is
decomposed by sulphuric acid has been fermented with yeast, and
carbonic acid, representing 23*64 per cent, of glucose, has been ob-
tained.

4. On a New Diffusiometer and other Apparatus for Liquid
Diffusion. By J. J. Coleman, F.I.C., F.C.S.

Supposing a tall glass tube open at both ends be cemented into a
reservoir packed full of common salt, and the tube then carefully
filled up with water, and the whole apparatus immersed overhead
in a jar of water, in a few days or weeks (depending upon the
length of the tube) particles of salt will arrive at the top of the tube
and diffuse into the water atmosphere.

When this condition arrives, which Fick calls “ dynamic equi-
librium,5’ diffusion takes place at a uniform rate, the mathematical
expression of the process being stated as follows : —

Let K denote the quantity of salt which in a normal state of
diffusion passes in a unit of time through a unit of horizontal
section of a cylindrical tube whose height is equal to the unit of
length, this being called the diffusion coefficient ; also let Q be the
quantity of salt which in the time t flows from the mouth of the
tube ; S its horizontal section ; d the density of the liquid at the
bottom ; and h the height of the tube ; then

Q = Kc&
h

Experiments subsequent to those of Fick have caused some doubt
as to whether the “ coefficient of diffusion” is the same for all

1887.] Mr J. J. Coleman on a New Diffusiometer.

375

densities, but the conclusion lie came to, that under the conditions
of his experiments the quantities diffused are directly as the times of
diffusion , is easily and elegantly shown by using concentrated acids
or alkalies instead of common salt.

Thus taking a tube 9 millimetres in diameter and 20 ’5 centimetres
long, and cementing it into a reservoir, which in shape may con-
veniently be that of the reservoir of a glass spirit-lamp, holding 350
grammes of hydrochloric acid of 1 T7 sp. gr., and immersing the whole
in a jar 25 centimetres high and 12 cm. diameter, kept at a uniform
temperature of 16° C., containing 2000 c.c. of water, and changing
the water every two or three days, and commencing after the 21st
day to estimate the acid diffused, it was found to be very uniform,
viz. : —

Milligrams.

9 9 '9 from 21st to 24th day,
98*4 ,, 24th to 27th ,,

103-2 „ 27th to 30th „

98*4 ,, 30th to 33rd ,,

Milligrams.

33- 3 per day.
32-8

34- 4
32-8

55

55

55

Average, 33 -3 per day.

The use of such modern indicators as phenolphthalein and
methyl orange has rendered the end reaction of a volumetric pro-
cess so delicate, that no difficulty is experienced in measuring such
small quantities as one part of acid in 20,000 of water, which were
about the conditions of these experiments.

Turning attention now to what happens in a diffusion tube before
“ dynamic equilibrium ” is established, which indeed is typical of all
eases in which the diffused column is constantly being elongated by
ascent of fresh particles from the bottom of a tube of constant
diameter, I have devised a piece of apparatus which renders this
motion visible to the eye, and which mathematical considerations
developed by physicists indicate, should he as the square root of the
times of diffusion.

The principle upon which the apparatus is constructed is as
follows : —

If a glass jar is nearly filled with very dilute acid coloured red
with methyl orange (sodium methyl-amido-azo-benzene-sulphonate),
and a solution of caustic soda or potash is run by a fine pipette to the
bottom of the jar underneath the acid, the alkali diffuses and changes

376 Proceedings of Royal Society of Edinburgh. [july 15,

the colour of the methyl red to bright yellow, the line of demarcation
being as strongly defined as that of oil floating upon water, and this
even if the diffusion is carried on for thirty -five or forty days.

The caustic alkali solution is most advantageously placed in an
open-mouthed vessel of such capacity that a barometer tube, 1 2 mm.
to 15 mm. inside diameter, containing the reddened acid can be
overturned therein with its mouth downwards, the acid being kept
in the tube by means of an india-rubber disc, attached by three
platinum wires to a cork sliding on the tube, which thus acts as a
valve to be thrust down when the time for starting diffusion arrives.
The tubes I prefer are about 12 "5 mm. diameter and 600 mm. long,
accurately graduated in millimetres.

The drawing herewith illustrates the construction of this instru-
ment or “liquid diffusiometer,” surrounded byja glass bell’, jar to
prevent its being affected in temperature by air currents.

1887.] Mr J. J. Coleman on a New Diffusiometer. 377

The following experiments were made by diffusing caustic potash
of three different densities into reddened dilute hydrochloric acid,
which latter in every case required T45 milligramme of potash
(KHO) per c.c. to turn the colour from red to yellow. The reservoirs
of each were about 60 millimetres diameter, and contained about
200 c.c. of alkali solution, so that its strength was approximately
constant during the diffusions.

The diffusions were made in a chest of wood, of 2 cubic metre
capacity, with hollow walls filled with dry sawdust, this being again
placed in a room of nearly constant temperature. Similar precautions
were also adopted with the experiments verifying Ficks’ law, already
detailed in this paper.

It will be seen from this table that the result of the experiments
demonstrate to the eye a fundamental law of diffusion, common not
only to material particles, but to the imponderable agents, heat
and electricity. Sir W. Thomson has also pointed out to me that,
according to theory, and supposing the coefficient of diffusion is
not variable, the heights of the columns in Table I. should have
been identical, provided the acid had been regulated of varying
densities to correspond with the alkali.

Further experiments detailed in Table II. were then made which
confirm this anticipation,* or rather, which show that if there is
any variation in the coefficient it must be small.

Experiments were also made with caustic soda (hfaHO), which
are recorded in Table III., and I have found that the apparatus can
also be made available for measuring the diffusibility of acids by
diffusing them into slightly ammoniacal water coloured yellow with
methyl orange, f We are thus supplied with a new method of
ascertaining the diffusibility of a large number of chemical com-
pounds, and also a method of checking the accuracy of the burette
method of determining diffusibility, which I described in the Phil.
Mag. in January last. The instrument may be also constructed on
a larger scale for lecture demonstrations.

* The difference between the heights was reduced to 6 millimetres instead
of 31. See also confirmatory experiments detailed in Table IV., added
September 1887.

t See Table IY. for details.

378 Proceedings of Royal Society of Edinburgh. [july 15,

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Table II. — Diffusion of Caustic Potash of Different Densities into very Dilute Hydrochloric Acid of

Densities to correspond at a Temperature of 16° C.

1887.] Mr J. J. Coleman on a New Diffusiometer

379

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1887.]

Mr W. Durham on Laws of Solution.

381

5. On the Minute Structure of the Eye in certain Cymo-
thoiche. By Frank E. Beddard, Esq., M.A., E.Z.S.

8. On the Mean Height of the Land of the Globe. By

John Murray, Esq.

7. The Ohsetopoda Sedentaria of the Firth of Forth. By
J. T. Cunningham, Esq., B.A.

Monday, 1 8th Jidy 1887.

Sheriff EOBBES IEVINE, Vice-President, in the Chair.

The Chairman intimated the foundation by Dr Gunning of the
Victoria Jubilee Prize , and the conditions of award which have
been approved by the Donor, and added that the Prize of One
Hundred Guineas from this source had been this year awarded by
the Council to Sir William Thomson, for a remarkable series of
papers on Hydrokinetics, especially of Waves and Vortices, forming
some of the most valuable that have been communicated to the
Society.

The following Communications were read : —

1. Laws of Solution. Part II. By V . Durham, Esq.

From the note in my former paper on the above subject it is
easy to deduce the following formula, which expresses the relations
between the heats of chemical combination and the heats of solu-
tion : —

Heat of Combination. Heat of Combination.

f [M,X2] l ,

: [M,0,Aq]|

l - [H2 X2, Aq] / 1

l - [H20] /

Heat of Neutrality. Heat of Solution.

[MOAq,H2X2Aq] ± {MX2,Aq + }.

This formula is perfectly general for chlorides, bromides, iodides,
sulphates, and nitrates, and whether the oxides and salts are soluble
nr insoluble. It shows that the heats of solution pass from negative

382 Proceedings of Royal Society of Edinburgh, [july 15,

to positive values through, zero when the salts are insoluble. As in
soluble salts the heat of neutralisation is practically constant, it
follows that the heats of solution vary with the relative variations of
[M,X2] and [M,0,Aq] involving definite chemical actions. We
should expect, therefore, that the heats of solution would vary in
a periodic manner with the nature of the elements, as with other
chemical phenomena. The following diagram, representing the heat
of solution of the chlorides, although defective in many places from
want of data, seems distinctly to show that this is so, and that solu-
tion is a periodic function of the weights of the elements.

1887.] Mr W. Durham on Laws of Solution. 383

In this diagram there are several points worthy of particular
notice.

1. Although given to illustrate solution it would equally well

illustrate the relations between [M,X2] and [M,0,Aq], which
are relations of chemical affinity.

2. The rapid rise of heat of solution after Na and K. I have not

data for Rb and Cs, but have no doubt they would exhibit
analogous relations, and have connected them by dotted lines
to Sr and Ba.

3. After each rapid rise there are several chlorides which are more

or less decomposed by solution. These chlorides occur
between Li and FI, A1 and Cl, Ca and Mn, Zn and Br, Sr
and Rh, and Sn and I, perfectly regular recurring pheno-
mena.

4. The peculiar nature of the curve between Mn and Zn noticed

in many other phenomena, and especially the sudden rise
from Cu to Zn, this latter relation is repeated between Ag
and Cd. Now, it is remarkable that the atomic weights of
Cu and Zn are almost exactly as much lower than the atomic
weight of Br as those of Ag and Cd are than that of I, the
next negative element.

5. The first maximum point is at Al, whose atomic weight is

almost exactly midway between the atomic weights of FI and
Cl. The next maximum is Ni, with atomic weight between
Cl and Br. The third maximum should be at Rh, but data
are wanting.

6. The curve between Hg, Tl, and Pb suggests a repetition of the

curve between Ni, Cu, and Zn,

7. The remarkably regular relations between Ca, Sr, and Ba,

whose chemical similarity is well known.

If we pass from chlorides to bromides or iodides the change in
the heat of solution can be represented by a very simple formula.
For instance, the change from chlorides to bromides is as follows : — -

Heat of Combination.

< [M,C12] ) r M,Br2]

1 — [H2,Cl2Aq]j - t - [H2,Br2,Aq]

VOL. XIV. 19/1/88

Heat of Solution.

= [MBr2,Aq] - [MCl2,Aq] ,
2 b

384 Proceedings of Royal Society of Edinburgh. [july 18,

That is to say, the heats of solution of any metallic chloride and
bromide vary inversely as the difference between the excess of the
heat of combination of the metallic chloride over the heat of com-
bination of hydrogen chloride in water, and the excess of the heat
of combination of the metallic bromide over the heat of combination

of the hydrogen bromide in water,
make this plain : —

The following examples will

Heat of Combination.

Heat of Solution.

[Ca,Cl2] =169820

17410

- [H2,Cl2,Aq] = 78630

91190

[Ca,Br2] = 140850

24510

- [H2, Br2Aq] 56760

84090

Difference + 7100

Difference - 7100

[Sr, Cl2] = 184550

11140

- rii2,Cl2,Aq] 78630

105920

[Sr,Br2] 157700

16110

- [H2,Br2, Aq] 56760

100940

Difference + 4980

- 4970

[Ba,Cl2] 194740

2070

- [H2,Cl2Aq] 78630

116110

[BaBr2] 169960

4980

- [H2,Br2,Aq] 56760

113200

Difference + 2910

Difference - 2910

We again see from these results how intimately heat of solution
is related to heat of chemical combination. Whenever an element
develops less energy in combination with bromine than with
chlorine relatively to the hydrogen compounds of these same nega-
tive elements, the energy is not lost ; it immediately appears in the
heat of solution. It is worthy of note also how regularly the differ-
ence increases by about 2000 units as we pass from the barium to
the strontium and calcium salts.

1887.] Mr W. Durham on Laws of Solution. 385

Perfectly analogous results are obtained on changing the positive
element of the salt instead of the negative. In every case we find
the heat of solution regulated by the chemical affinities (as measured
by heat) of the elements. Another instructive instance of the rela-
tions of chemical affinity and solution is found in the double salts
of the form MS04, R"S04, 6H20, where M forms crystals of the
composition MS047H20. In the double salts E/'S04 takes the
place of one molecule of H20, and develops more or less heat in so
doing. How the thermal results of solution of the double salt seems
to indicate that decomposition is brought about.

Consider the following : —

Heats of Combination.

[ZnS04,K2S0,6H20] = 23950

[ZnS04,7H20] = 22690

Difference = + 1260

Heats of Solution.

[ZnS04K2S046H20 Aq] =-11900

[ZnS047H20,Aq] = - 4260

[K2S04,Aq] - 6380

- 10640

Difference - 1260

In fact, putting the double crystalline salt into solution brings the
mixture to exactly the same thermal state as if the constituent
sulphates were separately dissolved in water.

{Added July 16, 1887.)

It has been said that no argument as to residual affinity can be
based on thermal results because we do not know the fundamental
units, but it appears to me there is no force whatever in this objec-
tion, as we are not dealing with absolute affinity but only with
differences, and thermal chemistry is particularly fitted to show these
differences. Thus, for instance, Cl in combining with Sr develops
10190 units less heat than it does when combining with Ba. How
the question is, What becomes of these 10190 units'? Are they lost
entirely, or is there residual affinity left in SrCl2 to that amount %

386 Proceedings of Royal Society of Edinburgh, [july 18,

The heat of solution appears to me to answer this question at once
when we take into account that Sr acts upon 0 with less energy
than Ba does. Thus —

[Ba,Cl2] — [Sr, Cl2] =10190 [BaCl2,Aq] 2070

[Ba,0,Aq] - [Sr,0,Aq] 980 [SrCl2Aq] 11140

Difference + 9210

9070

or, in other words, the heat deficient in the combination [Sr, Cl2] as
compared with [Ba,Cl2] appears in the extra heat of solution of
SrCl2 as compared with BaCl2. This is not an isolated case, but
appears in every chloride, so that if the heat of combination with O
of the various metals was constant, the heat of solution would vary
inversely in every case as the heat of combination. The slight
difference of 140 units in above case appears as a difference in the
heats of neutrality of the two salts.

We can, however, get rid of all consideration of the heats of com-
bination with oxygen by the help of the formula already given,

( M"C12 \ _ ( M"Br2 |

t - H2,Cl2,Aqj ” { - H2,Br2,Aq j

{M"Br2,Aq} - {M"Cl2,Aq} ,

for we can take the metals in pairs and have on the one side of the
equation only the differences of the heats of combination, and on
the other the differences of the heats of solution, and we shall see
they are exactly complementary ; as the one increases the other
decreases. That is to say, the more energy that is run down to the
form of heat in the formation of any salt the less energy is there
left to run down to the same form in solution, and vice versa. In
fact, the one is entirely dependent on the other, and it seems to me
absolutely certain that if the one phenomenon is due to chemical
affinity, so is the other. The following list, taken at random, of
bromides, chlorides, sulphates, and nitrates will show this : —

Heat of Combination. Difference

Heat of Solution.

Difference.

[Ba,Cl2]

- [Ba,Br2] = 24780

- 2910

[Sr, Cl2]

- [Sr,Br2] = 26850

- 4970

2070

• +

2060

[Sr, Cl2]

— [Sr,Br2] = 26850

- 4970

[Ca,Cl2]

- [Ca,Br2] = 28970

- 7100

2120

+

2120

1887.]

Mr W. Durham on Laws of Solution.

387

Heat of Combination.

[Zn,S04] - [Zn,Cl2]

[Cd,S04] - [Cd,Cl2]

[Ca,S04j - [Ca,Br2]
[Zn,S04] - [Zn,Br2]

[Li2,N2,0«] - [Li2, Cl2]
[Ca,N2,0<J] - [Ca,Cl2]

[Sr,N2,06] -[Sr, Cl2]
[Na2N2,06] - [Na2,Cl2]

Difference.

= 132860

= 128310

+ 4550

= 177520

= 154140

+23380

39620

36820

+ 2800

39280

31120

• + 8160

Heat of Solution. Difference.
+ 2800

+ 7700
■ 4900

- 20070

- 3400

23470

- 16280

- 13460
2820

- 15760

- 7700

8060

The only exceptions to above rule occur when the heat of neutralisa-
tion differs very greatly from the average, but this difference exactly
accounts for the discrepancy. Thus in the case of BaS04, the heat
of neutralisation is abnormal to the extent in which it differs from
above law.

2. On the Partition of Energy between the Translatory and
Rotational Motions of a set of non-homogeneous Elastic
Spheres. By Professor W. Burnside. Communicated
by Professor Tait.

3. On the Salinity, Temperature, &c. of the Firth of Forth.

By H. R. Mill, D.Sc.

4. The Direct Measurement of the Peltier Effect. By Albert
Campbell, B.A. Communicated by Professor Tait.
(Plate XIII.)

The researches described in this paper had for their object the
direct measurement of the Peltier effect, with a view to verify the
hypotheses regarding it and the laws deduced from these. Hither-
to it has been a pure assumption that the Peltier effect vanishes at
the neutral point. As this important assumption forms part of the
basis of the received theory of thermoelectricity, to prove it was
one of the main objects of these experiments.

Very recently, Signor Batelli (Atti della Societd Reale de Torino ,

388 Proceedings of Royal Society of Edinburgh, [july 18,

May 1887) lias attempted to prove experimentally the vanishing of
the Peltier effect at the neutral point in the case of certain alloys,
whose neutral points with lead are at temperatures not much above
the ordinary temperature of the air. In his method the Peltier
effects produced by a current at the junctions of a thermopile (of
the alloys A and B) are measured by the thermopile itself. Now
at the neutral point of A and B, the thermoelectric power of the
thermopile becomes zero, and hence the pile becomes, at that tem-
perature, a wholly inefficient means of measuring any heating or
cooling effect. Therefore Signor Batelli’s experiments by no means
establish the vanishing of the Peltier effect at the neutral point.

In the following experiments, measurements were made of the
Peltier effect both above and below the neutral point, and these
were compared with the values calculated from the directly ob-
served neutral point, taking Professor Tait’s supposition a — Id.
Thus if to be the absolute temperature of the neutral point of any
two metals (whose lines are straight), then, according to the theory
of the thermoelectric diagram, their Peltier effect at absolute
temperature t is proportional to tit - to ). The neutral points of
the specimens used were accordingly found in the ordinary way
by heating up a junction in oil, and these were the only data
necessary in finding the calculated values with which the observed
values were compared.

The apparatus used was a modification of that described by the
writer in a paper read before this Society in 1882 ; it was con-
structed in the following manner : —

The ends of two strips of sheet iron (say) were soldered (or
in the case of some metals, brazed) to the lower ends of an arch of
sheet cadmium (say). The other ends of the iron strips had
several copper wires soldered to them, leading to a rocking commu-
tator connected with four cells of a Thomson’s “ tray-Daniell ”
battery. In this circuit was also included a Helmholtz tangent
galvanometer, which served to measure the battery current. The
differences of temperatures of the iron-cadmium junctions were
measured by means of an iron-German-silver thermopile (of 16 or
20 junctions), bent into the shape of an arch, whose ends were
inserted in the trenches between the iron and cadmium, being
insulated from them by thin asbestos paper. The whole was packed

1887.] Mr A. Campbell on Measurement of Peltier Effect. 383

tightly in asbestos wool in the middle of a series of copper boxes
or tubes, separated from one another by asbestos packing. A
thermometer was inserted with its bulb as near to the junctions as
possible. By properly arranging Bunsen burners underneath, it
was possible to maintain the junctions at a constant and uniform
temperature. Throughout the whole series of experiments, the
mercury thermometers employed were regularly compared (at the
ordinary temperature) with a standard one which was never heated
up, and which had been compared with a Kew standard. All the
temperature readings were thus corrected.

The following was the usual mode of observation: — When the
temperature had become sufficiently uniform (which was often not
until several hours after the heating was begun), the current was
sent in the positive direction for 30 seconds, then broken for 30
seconds, put on in the negative direction for 30 more, broken for
30 more, and so on, for about 10 minutes. The deflections of the
mirror galvanometer (connected with the measuring thermopile)
and of the Helmholtz galvanometer were observed simultaneously
at the end of each period of 30 seconds. If the scale-readings of

the mirror galvanometer be aly a2) as , a4, a5, (ax being

the original zero-point), then the average of — a2y a4 — a3, - a6 — «5,

....... is taken as the measure of the temperature difference

caused by the given current (in 30 seconds).

Since the specific heats of most metals increase considerably as
the temperature rises, it is necessary, in comparing the Peltier
effects at two temperatures, to make a correction for the change in
specific heats. In the absence of definite measurements, this in-
crease in specific heat was taken as approximately =y^o per degree
centigrade for iron and nickel, and =yoVo Per degree for cadmium,
zinc, and German silver. This correction was reckoned from 20° C.

The correctness of the method was tested by applying it to prove
that the Peltier effect is proportional to the strength of the current.
As was to be expected, the temperature nearly always rose slowly
during the ten minutes’ observations (owing to the Joule effect);
a small correction was applied for this. Table I. gives some of the
measurements of the Peltier effect for different current-strengths.
The first three sets are for iron-cadmium, and the fourth for iron-

zmc.

390 Proceedings of Royal Society of Edinburgh. [july 18,

Table I.

Temperature C.

Mean

Thermopile

Deflection.

Mean Current
Deflection.

Observed
Ratio of
Peltier
Effects.

Ratio of
Currents.

18° 7 to 1 8°*9
19°-1 to 19°'3

265-9

129-7

798

398

2-044

2-005

95° -5 to 95° *9

121-6

877-9

2-143

2-106

95° -9 to 96° *2

52-25

415*9

95° 7 to 96°'2

72-17

718-1

1-899

1-910

96°-2 to 96°-7

36-13

375-9

20° -7 to 21° -3

174-0

206-7

1-796

1 -772

21°*3 to 21°'3

97-9

116-7

The following are some of the measurements at different tempera-
tures

Iron and Cadmium.

Iron and cadmium were selected as having a comparatively low
neutral point. The specimens used were ordinary sheet iron and
tolerably pure cadmium. The neutral point found by heating up
a junction in oil was 144° ’0 C. At 144° C. the direct measurement
showed absolutely no Peltier effect , a small irreversible effect alone
being visible ; while the same current gave a mean deflection of
308 scale divisions at 21° C, and -240 divisions at 199°T C.
Also at 139°’0 the Peltier effect was small, but still of the same
sign as that at 21° C. Table II. gives some measurements at other
temperatures, the last column being the ratio of the Peltier effects

Table II.

No.

Low Tempera-
ture.

High Temperature.

Observed Ratio.

Calculated Ratio.

1

0°

o

2

66° -9

1-475

1-447

2

O

o

!>>

rH

72° -6

1-782

1-878

3

f— 1

OO

0

OO

95°-7

2-073

2-050

4

19°-2

95°-l

2 051

2-024

5

17° "8

199°-1

-1-271

-1-410

1887.] Mr A. Campbell on Measurement of Peltier Effect. 391

(low temperature to high) calculated from neutral point 144° C.
In Nos. 3 and 4 the temperature was kept uniform by means of a
double steam-jacket surrounding a small copper box in which the
junctions and thermopile were packed. By this means the tempera-
ture could be kept very steady and uniform.

Zinc and Iron.

The metals here used were ordinary sheet zinc and thin tinplate.
In order that the junctions might stand a temperature above 200° C. ,
they were soldered with a suitable alloy of zinc and tin. Thin
strips were cut from the same specimens, and the neutral point was
found (by heating their junction in oil) to be 1 96°*7 C. The
directly observed Peltier effect wTas found to vanish about 204° C.
The temperature, however, was falling slowly at the time, which
would account for this disagreement. Table III. gives a measure-
ment taken just before the temperature had fallen to 204°. The
last column gives the ratio calculated from 204° as neutral point : —

Table III.

Low Temperature.

High Temperature.

Ratio Observed.

Ratio Calculated
from 204° C.

22°'5

215°

-9738

-9-80

Nickel and German Silver .

The peculiar form of the nickel line between 150° and 300° (X
made it interesting to find whether the Peltier effect between nickel
and any other metal (or alloy) agrees with the theory between these
temperatures. German silver was chosen as being an alloy whose
Peltier effect with nickel ought to vary in a striking manner.
According to the thermoelectric diagram, their Peltier effect divided
by the absolute temperature should remain constant till at least
150° C., and then decrease uniformly till it vanishes at the neutral
point ; beyond this it should change sign and increase till about
300° C. (above which it should probably remain constant for some
distance).

The usual form of apparatus was used, but in this case the

392 Proceedings of Royal Society of Edinburgh. [july 18,

German silver strips had to be brazed to the nickel, that the
junctions might stand the high temperatures. The neutral point
of the pair was found as usual by long strips cut from the same
sheets. Since, in the brazing, the metals had to be brought to a
high temperature, these long strips, as well as the pieces that were
to be brazed, were all annealed by heating to bright redness and
slowly cooling.

In order to measure the thermoelectric power of nickel German
silver at the various temperatures, the following method was
used : — The current, instead of being sent through Ni-Arg junc-
tions, was sent through the measuring (FeArg) thermopile, and the
Peltier effects caused in the thermopile junctions measured by
connecting the nickel and German silver strip to the galvanometer.
The deflection here in the galvanometer would be proportional to
the product of the Peltier effect of FeArg, and the thermoelectric
power of NiArg. Now, it has been shown by former experiments
by the writer* that the Peltier effect of FeArg varies as the
absolute temperature. Hence we can at once find the thermo-
electric power of the NiArg at any temperature.

The junctions in this case were packed in four thick copper
tubes, one inside the other, with asbestos wool between. As this
arrangement gave a very uniform temperature at the junctions, most
of the readings were taken with the temperature rising slowly,
except those at 17°*8, 19o,0, 23o,0, and 2540,3 C., when the tempera-
ture was fairly steady. The temperatures above 285° C. are not
very certain. For convenience in heating, the tubes had to be
almost horizontal. This, unfortunately, caused the mercury in the
thermometer to boil at a temperature much below its boiling point
at atmospheric pressure. The readings 340° and 330°, therefore,
are only estimated.

In Table IV. are given some of the measurements of the Peltier
effect in NiArg. The second column gives D/Ctf, where D is the
FeArg thermopile deflection, C the battery current through NiArg,
and t the absolute temperature. In Table V. are the measurements
of the thermoelectric power of NiArg (by sending the current
through the FeArg thermopile). The second column gives the

* Proc. Roy. Soc. Edin ., 1882. If we introduce the specific-heat correction
(12 % per ° C.) we get a much nearer agreement than that shown there.

1887.] Mr A. Campbell on Measurement of Peltier Effect. 393

values of DJCf where Dj = deflection in HiArg circuit, C1 =
battery current, and t = absolute temperature. In both tables the
correction for increase in specific heat was introduced.

Table IV.

Table V.

(Battery Current through NiArg.)

Temp. C.

D

C t

Temp. C.

D

C t

1 — i

o

OO

*0683

220°-0

•0321

19°‘0

•0691

222° -0

*0304

64°T

•0637

223° -8

•0308

69°-0

•0689

225° -3

•0293

70°-0

•0686

226°-9

•0314

75° *7

•0657

228° -5

•0310

81°-8

•0657

230°-l

•0267

98°-0

•0649

2310,9

•0258

101°-0

•0659

233° -2

•0253

1 1 8° *8

•0632

234° *5

•0234

121°-0

•0657

235° -8

•0235

124°-9

•0652

237° -2

•0223

206° -2

•0471

237° -9

*0190

208° -8

•0439

254°-3

- -0006

210° 7

•0431

283°

- -0153

212°-9

•0435

284°

- -0208

21 4° ‘8

•0390

285 °"4

- -0228

216°-4

•0369

300°i

- -0640

218°-4

•0335

(Battery Current through
FeArg pile.)

Temp. C.

Di

C yt

23°’0

•134

114°-5

•143

153° -3

•134

157° 3

•123

166°-3

•0982

169° *9

•1023

173°-8

•0975

1 77° *4

•0915

181°-0

•0925

210° -8

•0740

254° -3

- '0012

O

o

CO I
N !

- -0204

275° -6

- -0392

278° -0

- '0527

290°?

- -0614

302°

- *0879

330° ?

- -16

The neutral point of the NiArg, found by heating up a junction
in oil, was 2500,6 C. The curve drawn from Table IV. shows a
vanishing of the Peltier effect at 2 5 3° *7, while from Table V. the
thermoelectric 'power vanishes at 2 5 3° ’4. Ho measurement was

made exactly at the directly observed neutral point, but the small-

394 Proceedings of Royal Society of Edinburgh. [july 18,

ness of the effect at 254° -3 is pretty strong evidence that it vanishes
at most a degree or two from the directly found neutral point.

The numbers in Tables IV. and V. agree fairly well with the
fact that the nickel and German silver lines are parallel up to at
least 150° C., and that between its two bends the nickel line is
straight. Above 250° C. the deflections of the FeArg thermopile
cannot be taken as accurately measuring the small temperature
differences, for the Arg line is no longer parallel to the iron line.
The numbers have not been corrected for this. The very small
correction due to the resistance of the measuring thermopile in-
creasing with the temperature has been neglected.

In conclusion, I must express my thanks to Professor Tait, in
whose laboratory these investigations were carried out, for kindly
placing at my disposal much of the necessary apparatus, as well as
for his ever-ready advice. I also desire to express my thanks to
Messrs J. T. Morrison and A. H. Mackenzie for their most valuable
aid, and to Messrs Shand and Buchan for their kind help in the
determination of the neutral points.

{Added December 1887.)

§ 1. Description of Apparatus.

The above investigations were continued by the writer and Mr
J. T. Morrison, at the laboratory of the former, near Londonderry.
As the galvanometers were arranged so as to give much more delicate
measurements than those in the preceding experiments, a few words
of description are here necessary. The galvanometer connected with
the measuring thermopile had a lens of about 10 feet focal length.
Of the galvanometers used for measuring the battery current, the
Helmholtz had a lens of 1 2 feet focal length, and the other mirror
galvanometer one of 6 feet. The scales, each 1 metre in length,
were of translucent paper, stretched between two boards whose
edges were circular arcs of the proper radius. The divisions were 2
millimetres each, and could be read to y^-ths. In order that the
battery current might be more steady, the commutator was so
arranged that the moment the current was broken it was immediately
short-circuited through a similar resistance. For greater accuracy

1887.] Mr A. Campbell on Measurement of Peltier Effect. 395

and convenience, the high temperature thermometer was always read
with a telescope.

At first it was thought desirable, instead of employing the Helm-
holtz galvanometer, to measure the battery current in all cases by
the Peltier effect in a standard set of iron-German-silver junctions,
which would, it was hoped, integrate the current during the period
of time for which it was run. Although this arrangement was sub-
sequently discarded as a current-measurer, some interesting results
were obtained from it. It consisted of 23 squares of sheet iron and
German silver (each 3 cms. square), soldered, three by three, into
seven strips, which were then soldered to one another in zigzag form.
Along the middle junctions were placed the ends (100 in all) of 7
iron German silver thermopiles, insulated from the junctions by
thin paper. The whole was wrapped tightly in wadding, and placed
in a tin box surrounded by cold water. A thermometer was inserted
with its bulb touching the metals. The current was sent through
the iron-German-silver zigzag, and the Peltier effects measured by
the thermopiles.

§ 2. Time Curves of Peltier Effect.

In order to investigate the rate at which the growing Peltier
effect temperature-difference showed itself by the thermopile de-
flection, the following simple chronographic method was adopted.
In this a number of observers were made use of. Observer A held
a watch to his ear, and counted half seconds aloud in exact time
with its beats, also making and breaking the battery circuit at
exactly the proper times. Observer B, watching the galvanometer
scale, said sharply the syllables, “ Tic, tac, to, tee, tic, tac, to, tee,”
and so on, as the light-spot passed over certain prearranged divisions
of the scale. Eight other observers noted down the numbers after
which they heard the tic, tac, to, or tee, one of these words being
allotted to each pair of observers. This method p roved wonderfully
accurate. The pairs of observers very seldom disagreed by half a
second, although the numbers had to be noted very rapidly. The
results of some of the measurements are given in Tables VI., VII., and
VIII., which are for three different current-strengths. In these the
current was put on for 100 half-seconds, broken for 100, put on in

396

Proceedings of Royal Society of Edinburgh. [july 18,

the opposite direction for 100, and broken again for 100 more.
These periods were chosen so that the deflection might become
nearly constant before the current was broken. The current, which
was from 2 or 3 Bunsen cells, was very nearly constant throughout
the 200 seconds. The curves (1), (2), and (3) in the diagram are
drawn from these tables, the abscissa being the time (in half-seconds)
and the ordinate the galvanometer deflection.

Table VI. Curve (1).

Time,

A Seconds.

Deflection.

Time,

A Seconds.

Deflection.

Time,

\ Seconds.

Deflection.

Time,
s Seconds.

[Deflection.

0

0

92

1660

1

Reverse

283

-1590

3

100

94

1680

200 )

current

287

-1600

4

200

99

1690

(

made.

293

-1610

5-5

300

100 |

Current

201

100

298 -5

-1620

7

400

broken.

204

0

300 |

Current

8

500

104

1600

205

- 100

broken.

10

600

106

1400

207

- 200

302

-1600

11

700

111-5

1000

210

- 400

304

-1500

13

800

113

900

210

- 500

307

-1300

15

900

116

800

213

- 600

309'5

- 1100

18

1000

117

700

215

- 700

311

-1000

21

1100

121

600

217

- 800

313

- 900

25

1200

123

550

223

-1000

315

- 800

29

1300

125

500

227

-1100

317

- 700

33

1350

128

450

229

-1200

319

- 600

36

1400

130

400

234

-1300

323

- 500

40

1450

133

350

239

- 1350

325

- 450

45

1500

137

300

244

-1400

327

- 400

52

1550

143

250

246

-1450

329

- 350

53

1560

149

200

248

-1470

336

- 300

59

1580

162

150

257

-1510

340

- 250

61

1590

165

140

261

-1520

347

- 200

65

1600

167

130

263

-1530

355

- 150

67

1620

174

120

265

- 1540

376

- 100

72

1630

179

110

268

-1550

381

- 50

75

1640

187

100

274

-1570

390

- 40

78

1650

278

-1580

§ 3. Thermoelectric Power of Iron German Silver.

As in all the above experiments the measurements were made by
means of iron-German-silver thermopiles, it was highly important
that the thermoelectric power of the iron and German silver used
should be carefully measured throughout the range of tempera-
tures at which the piles were used. Bor this purpose, the FeArg
junction, instead of being heated in oil, was packed in asbestos

0002

2000

1887.] Mr A. Campbell on Measurement of Peltier Effect. 397

Table VII. Curve (2).

Time,

£ Seconds

Deflection.

Time,

| Seconds

Deflection.

Time,

J Seconds.

Deflection.

Time,

\ Seconds.

Deflection.

0 {

Current

112

709

210-7

-291

300 |

Current

made.

115

609

212-5

-391

broken.

1-5

9

118

509

218

-491

302-5

-891

4

109

120

459

221-4

-541

306

-791

7

209

122-5

409

222

-591

309

- 691

10

309

125-5

359

226

-641

312

-591

13

409

129

309

229-5

-691

315

-491

16-5

509

134-5

209

235

-741

318

-441

20-5

609

135

199

236

-751

320-2

-391

25

709

137

189

237

-761

323

-341

28

759

139-5

179

239

-771

326

-291

32

809

141

169

240

-781

330

-241

38-5

859

144

159

241

-791

335-5

-191

475

909

144

149

243

- 801

337-5

-181

497

929

148

139

244

.-811

339

-171

51-5

939

151-5

119

246

-821

340

-161

54-5

949

154

109

248

-831

342

-151

57-5

959

158-5

89

250

-841

344

-141

61

969

161

79

251-5

- 851

345

-131

64-5

979

168

69

256

-861

347-5

-121

76-5

999

174

59

258

-871

350-5

-111

83-4

1009

184

49

261

-881

352-5

-101

90

1019

194-5

39

263

-891

355-5

- 91

98

1029

l

Reverse

4 268

-901

360

- 81

100 |

Current

200 ]

current

[ 2727

- 911

364-5

- 71

broken.

(

made.

J 277

-921

371-2

- 61

103

1009

2025

9

284-5

-931

377-5

- 51

106

909

205

- 91

290

-941

392

- 41

108-7

809

208

-191

299-7

-951

Table VIII. Curve (3).

Time,

Seconds.

Deflection.

0 {

Current

made.

3-5

23

5-5

73

9

123

13

173

• 17-7

223

22-5

273

32

323

47

373

53

383

59

393

68

403

82

413

98-5

423

Current

broken.

Time,
i Seconds.

Deflection.

107

323

112

273

116

223

121

173

128

123

143

73

147-7

63

153-2

53

159

43

177

33

f

Reverse

200 ]

current

1

made.

201

23

201*2

3

2C8

-127

212

-177

Time,
r Seconds.

Deflection.

215-2

-227

219

-277

227

-327

236

-337

241

-347

243

-357

248

-367

255

-377

260-7

-387

270

-397

282

-407

300 |

Current

broken.

303-2

-377

306-7

-327

309-5

-277

Time,

J Seconds.

Deflection.

314

- 227

319

-177

3207

- 167

322

-157

325

-137

326-7

-127

328

-117

332

- 97

335

- 87

337-5

- 77

339

- 67

344-5

- 57

349-2

- 47

357-5

- 37

370

- 27

394

- 17

398

Proceedings of Roy cd Society of Edinburgh. [july 18,

inside two small copper cylinders, and brought to an almost steady
temperature by the well-screened flame of a spirit-lamp beneath. A
thermometer was inserted with its bulb touching the junction. The
cold junction (well varnished) was kept in a large can of water ; the
temperature of this seldom varied by more than *3 of a degree C.
Several hours usually elapsed between each reading. The reading
at each temperature was the mean of four deflections, two to each
side of the scale. Table IX. gives a set of the measurements : tx is
the cold temperature, t2 the hot, and D the mean deflection. The
third column shows how nearly constant the thermoelectric power
remains up to about 250° C.

Table IX.

| w

k

D

k

k

D

k ~ k

k~k

9°-4 C.

63° -5 C.

8-627

9°-5 C.

167°-1 C.

8-739

9°-4

65° ’3

8-658

9°-7

192° -3

8-727

9°-3

85°-5

8-734

9°-6

205°-l

8-719

9°*3

127°'l

8-761

9°-7

214°-6

8-715

9°*6

152°-1

8-704

9°-8

233°-6

8-688

9°*5

153°-5

8-675

9°-8

245°-7

8'668

Similar measurements with the sheet iron and German silver
used in the experiments described below showed the lines of the
specimens to be very nearly parallel. The neutral point of the
nickel and German silver used in the experiments tabulated in
Tables IY. and V. was carefully redetermined by this method, and
found to be 252° '3 C., which agrees with Tables IV. and V. even
more closely than the former determination did.

§ 4. Comparison of Peltier Effect ivith Thermoelectric Power.

Further experiments were also made in order to compare the
measurements of the Peltier effect with those of the thermoelectric
power in the same specimens. The apparatus here used consisted
essentially of two thermopiles (one of FeZn and the other of
FeArg) of the same size and shape, and having the same number
of junctions each. These were arranged, junction to junction, in as
symmetrical a manner as possible.

1887.] Mr A. Campbell on Measurement of Peltier Effect. 399

Two forms of this arrangement were used. In the first (a) the
thermopiles were two broad strips (formed of alternate squares of
the metals), bent into zigzags which fitted one within the other.
The one zigzag was of iron and zinc, and the other of iron and
German silver. The iron used here was thin tinplate, and none of
the metals were annealed. This arrangement was not perfectly sym-
metrical j the second modification (6) was , however. It consisted of
four zigzag thermopiles of 18 junctions each, almost identical in
size and form, made of strips of thin sheet metal, 3 cms. long and
about 5 mms. broad. Two of them were of FeArg and the other two
of FeZn. These were arranged in the form of a square, with their
junctions interlaced, the similar piles being at opposite sides of the
square. Insulation was ensured by strips of asbestos paper separat-
ing the junctions from one another. (The insulation was tested both
at high and low temperatures, and was found to be practically perfect.)
Clearly this arrangement was perfectly symmetrical. In this case
the iron used was thin tinplate which had had the tin almost com-
pletely burnt off it at a red heat ; the zinc and German silver were
also well annealed. In both cases, the copper boxes or tubes in
which the piles were heated up were surrounded by asbestos wool
and fireclay bricks, and the heating was done by a spirit-lamp care-
fully shut in from air currents. Nearly all the measurements were
made when the temperatures had become almost 'perfectly steady.

The battery current, which was from two Tray-Danaells, was kept
as constant as possible by gradually diminishing the resistance of
the circuit as the current showed signs of falling. It was measured
by a mirror galvanometer doubly shunted by copper shunts. In
using both (a) and (&), the intervals for current, no-current, &c., were
chosen of such a length that a permanent state of temperature dis-
tribution had been almost reached before the end of each interval.
For ( a ) the periods were 60 secs, each, and for ( b ) 90 secs. each.
The thermopile measurements were made in much the same manner
as in the case of nickel German silver described above p.e., Peltier
effect in pile (1) measured by pile (2), and then Peltier effect in pile
(2) measured by pile (1)].

In arrangement (b) the resistance of the galvanometer + FeArg
thermopiles was 2-053 ohms, while that of galvanometer + FeZn
piles was P963 ohms. This difference of resistance also diminished

VOL. XIV. 27/1/88 2 o

400 Proceedings of Royal Society of Edinburgh. [july 18,

as the temperature rose. As it was the E.M.F.s that were to be
compared, the indications of the FeZn piles had to be corrected for
this difference of resistance (and also for the change in this differ-
ence). In (a), as the piles had both such small resistance, this
correction was not required.

The specific heat correction was deduced from the measurements
described below. Unfortunately no measurement was made in the
case of zinc ; so the change in specific heat for it was assumed as
TO % per degree C. If , s2 , s3 be the specific heats of Fe, Arg, and
Zn ; u\, iv 2, w3 the relative weights of the thermopile strips of these
metals; a1, a2i a3 the respective percentage increments of the
specific heats (per degree C.) ; then the complete correction (% per
deg. C.) has been taken as

2a1w1s1 + a2w2s2 -f a3w3s3
2w1s1 + w2s2 + w3s3.

This gives

T04 % per degree C. at 110° C.,

T08 % . „ at 120° C.,

and so on up to

T36 % per degree C. at 180° C.

From the values within this range of temperature those at lower
temperatures were found by extrapolation. The effect of the small
amount of brass and solder in the junctions was neglected. The
specific heat of German silver was taken as TO.

In Table X. are the results obtained with arrangement (a), and in
Table XI. those with arrangement ( b ). In the measurements

marked X the current was sent through the FeZn, and the Peltier
effect measured by the FeArg ; in those marked Y the current was
sent through the FeArg and the Peltier effect measured by the

FeZn. The third column gives the observed values of ~ (corrected

Ct

as above), where D is the mean thermopile deflection (mean of 6),
C the mean current, and t the absolute temperature.

From the following tables it is clear that (within the limits of
experimental error) — has the same value in the X as in the Y

D

measurements ; but the values of — — found do not lie on the curve

\jt

1887.] Mr A. Campbell on Measurement of Peltier Effect. 401

D

Ct

= A + B£.

Now by careful measurements (heating a junc-

tion, &c.) the thermoelectric power of the FeArg was found to be
cpiite constant throughout the range of temperatures used. The
FeZn line also was found to be straight. Therefore some other cor-
rection (possibly for conduction) would have to be introduced if
these measurements are to agree, in this respect, with the received
theory.

Table X.

Tempera-

ture.

D

Ct

Observed.

D

Ct

Calculated.

Tempera-

ture.

D

Ct

Observed.

D

Ct

Calculated.

X

11°'4 C.

1613

1599

X

74° -3

1304

1322

Y

1 1° *6

1599

1599

X

81°-0

1275

1279

X

38° T

1461

1515

Y

106°-8

1079

1080

Y

38° -8

1474

1510

X

109o,0

1053

1061

X

39°-7

1455

1508

Y

116°*6

1039

993

X

72°-9

1332

1332

Y

143° -7

739-8

722

Y

73° *1

1333

1330

X

144°-0

722-6

718-4

Table XI.

Tempera-

ture.

D

Ct

Observed.

D

Ct

Calculated.

Tempera-

ture.

D

Ct

Observed.

D

Ct

Calculated.

X

8° -9 C.

1533

1533

Y

129°-1 C.

699-3

665-9

X

11°T

1523

1525

X

163°-7

254-9

250-0

X

59° -0

1269

1280

Y

161°-3

251-3

281-2

Y

60° -0

1283

1274

Y

172° -8

147-9

128-3

X

61°-1

1280

1267

X

l74°-2

96-9

99-1

X

95°-3

1009

1001

X

180° -6

11-4

19-8

Y

96° -0

988-6

995-0

Y

183°'2

0

- 17 T

X

96°-4

978-6

990-5

X

l83°-2

- 28*4

- 17-1

X

129° -5

703-9

661-5

X

191°-5

- 123-7

-163-2

The values of in Table X. agree approximately with the

formula

D

Ct

= 1622 - 1-590(9- -O32302,

where 6 = temperature centigrade.

The fourth column in Table X. gives the values calculated from

this formula.

This would make

D

Ct

vanish at 200° *8 C. and

at - 250o,0 C. Now, the directly measured neutral point of the
FeZn used is 196°*9 C.

402

Proceedings of Royal Society of Edinburgh. [july is.

Similarly, the values in Table XI. are (as is shown by the fourth
column) in fair agreement with the formula

-5 = (182 - #)(8'58 + -03150),

Kjt

D

so that - — vanishes at 182° C. (and would also vanish at - 208 *8° C.).
Q^t

The directly observed neutral point (by heating up junction) was
190°-0 C.

Let us consider now the interpretation of the first clearly proved

result, viz., that -5_ (corrected) has the same value for a given
C t

temperature whether the battery current goes through the FeZn
pile or the FeArg pile. (Let it be noted that all the corrections
and all the conditions were the same in the corresponding X and Y
measurements, so that this result is definitely proved.)

Let the absolute temperature = t;
the Peltier effect of FeZn = tf(t) ;
the Peltier effect of FeAr g = t<f>(t) ;
the thermoelectric power of FeZn = F(£) ;
and that of FeArg, which by measurement is known
to be constant, = a.

The above experimental result becomes

«/(0 = ■#>(«)• F(/) •

■ • (i).

And this is found to be still true (at least to within about 1° C.)
when <h(t) = 0, i.e ., the Peltier effect, tf(t), vanishes at the neutral
point.*

The interpretation of equation (1) is that the Peltier effect in
FeZn is equal to the product of the absolute temperature , the
thermoelectric power, and some function of the absolute temperature
which is the same for all pairs of metals, f That is —

m

m

If it be taken as proved (and it has been to a certain extent) that

* 183° C. (and not 190° C.) is clearly the true neutral point of the FeZn
piles, since at 183° their thermoelectric power vanishes.

t Similar measurements with two thermopiles of FeArg and NiArg also
warrant this conclusion.

1887.] Mr A. Campbell on Measurement of Peltier Effect. 403

the Peltier effect in FeArg varies as the absolute temperature, the
result in equation (1) at once establishes the usual theory. In any
case, equation (1) perfectly agrees with the received theory.

Experiments were also made with the four thermopiles inter
laced in the order FeArg, FeArg, FeZn, FeZn, the alternate
ones being connected. With this difference, everything was done
just as in the last described experiments. In Table XII. are the re-
sults. The current was passed sometimes through the one pair of
piles (FeArg and FeZn) and sometimes through the other pair.
These two ways are marked P and Q in the table. The last column

gives the values of the square root of 5- corrected for change in

\jt

specific heat, by T2 % per degree C. [Assumption (1st).] This is
not strictly accurate.

Table XII.

Temperature.

e.

Thermopiles

Deflection.

D.

D
C t

/-

V c t

(corrected).

p

7°'l C.

3191

1635

1283

Q

7° -3

3204

1606

1272

P

70.7

2504

1568

1259

Q

7° *8

2447

1568

1257

Q

91° -7

3811

1585

1326

P

93° -8

3972

1571

1322

Q

94°-8

3788

1564

1320

P

98°T

4846

1555

1318

Q

100°-5

6098

1573

1327

P

151°*3

4932

1601

1377

Q

153° -0

5063

1581

1369

P

153° -9

5120

1603

1378

It will be found that the values of ^/5L(Corrected) lie very nearly

on a straight line ; we may take the coincidence as exact (assump-
tion 2nd), i.e ., that

= (a + Ptf (3)"

Xow, supposing (assumption 3rd) that the four sets of thermopile
junctions have, all of them, the same heat capacity (which is true
to within about 1 %), we have, following the notation used above —

404 Proceedings of Boy at Society of Edinburgh . [july 18,

•= a<f>(t) - aft) - + V(t).f(t) *

= [>-F(£)]

by the experimental result in equation (2),

^ = [a-F(f)][a-F(«)fy(<) (0-

Also, since F(tf), the thermoelectric power of FeZn, is known to be
of the form p + qt, the experimental result in equation (3) may
be written

where n and b are independent of t, . \ we have proved (by experi-
ment) that

[a - F (£)] [a - F(ty\\f/(t) = n[b ± F(^)]2 ;

i {/(t) must be independent of t.

And thus equation (2) becomes

m

Thus we have established by experiment (and the three assumptions
noted above) that the Peltier effect is proportional to the product of
the thermoelectric power and the absolute temperature.

§ 5. Measurement of Change in Specific Heat.

As the correction for increase of specific heat due to rise of tem-
perature becomes very large at the higher temperatures, it wras
necessary to measure it for the metals used in the above experiments,
A new method of doing this occurred to the writer, and, although
he believes that much more accurate results might be got by this
method, the results already obtained seem worth publication. The
method consists in measuring, at different temperatures, the Joule
effect in a strip or strips of the given metal. For this purpose two
narrow strips (of iron, say) were doubled along the two sets of
junctions of an FeArg thermopile (wrapped in thin asbestos paper),

* These four terms correspond to the four sets of thermopile junctions.

= xj/(t) - constant.

1887.] Mr A. Campbell on Measurement of Peltier Effect. 405

and the whole tied between asbestos boards and copper plates.
The whole was packed, in the usual manner, in asbestos within
a copper box. The current was passed through the strips alter-
nately (and for such periods as gave almost steady conditions of
temperature), and the Joule effect found from the deflections in
exactly the same manner as the Peltier effect in the foregoing ex-
periments. Now the rise of temperature thus measured is directly
proportional to the resistance of the strips, and inversely proportional
to the heat capacity of the strips, asbestos, and thermopile ends.
Thus, by observing also the change in resistance, we can at once
calculate the change in heat capacity. By this method the correction
is measured under almost exactly the same conditions as those under
which it is to be applied. The influence of the asbestos paper
(which was of very small mass) may be neglected. The widely
different values of the correction found for the various metals seem to
show that the capacity of the thermopile ends (which were of much
smaller mass than the strips) may also be neglected. Thus the
results may be considered as tolerably accurate measurements of the
changes of specific heat in the various strips used.

The resistance measurements were made with a Wheatstone’s
bridge of the ordinary form. A thin strip of the given metal,
soldered or brazed to two thick copper wires, was packed in asbestos
in copper boxes. The measurements were all made at nearly steady *
temperatures, as it was found that when this was not the case, in-
consistent results were obtained.

As the thermopile resistance formed a considerable fraction of the
resistance of the galvanometer circuit, it had to be measured at
different temperatures, and a correction introduced for this. In
measuring this resistance, the battery contacts had to be short, other-
wise the Peltier effects began soon to show themselves. Table XIII.
gives some of these measurements. In this, as in all the other
resistance and Joule effect measurements, the whole percentage in-
crease from the value at the lowest temperature was calculated, and
from this the mean percentage increase per degree C. from the lowest
temperature. The resistance of the galvanometer and its connections
was I '667 ohms.

In order to test how far the thermopile deflections were a proper
* I.e., not varying much more than 2° C. in half-an-hour.

406 Proceedings of Royal Society of Edinburgh. [july 18,

measure of the Joule effect, a comparison of the deflections (D)
with the square of the current (C2) was made for several strengths

Table XIII.

Temperature.

Resistance
of Pile

+ Galvanometer.

Whole per cent.
Increase.

Mean Increase
per cent,
per 1° C.

8° -8 C.

2158

0

0

87°'3

2-186

1-30

•0169

92° -6

2-187

1-34

•0159

120° T

2-200

1-95

•0175

131°-8

2-205

2-18

•0178

155° *7

2-215

2-64

■0180

222°‘l

2-248

4-17

•0195

2270,1

2-249

4-22

•0193

247°'4

2-261

4-77

.0200

257° -2

2-267

5-05

•0203

265°-6

2-271

5-24

•0204

278° 1

2-278

5-56

*0206

of current. Table XIY. gives the results for iron strips. The
periods were 3 minutes each. As the temperature varied slightly,

the last column gives ^ corrected for the small changes in re-

C2

sistance and specific heat. That the proportionality of D to C2
holds pretty nearly will be seen.

Table XIY. — Joule Effect compared with (Current)2.

Temperature.

D.

C.

D

C2Xl°3-

D

coXio3
(Corrected to
15°-8 C.)

15° -8C.

1284

1439

•6203

•6203

16°-3C.

761

1113

•6146

•6134

15° -8C.

113

425

•6256

•6256

15° -30.

282

668

•6319

•6331

Time curves were also drawn for the Joule effect heating, by the
same method as in the case of the Peltier effect. In Table XY. is
given a set of the readings for the Joule effect in a narrow copper
strip. The periods here were 150 half-seconds (instead of 100).
The curve is number 4 in the diagram. Por convenience of com-
parison with the Peltier effect curves, the 150-periods have been
reduced in scale, so as to coincide with the 100-periods of (1), (2),

1887.] Mr A. Campbell on Measurement of Peltier Effect. 407

and (3) ; the deflections, however, are represented on a scale
one-third larger than they actually were.

Table XV. — Joule Effect in Copper Strip.

Time,

| Seconds.

Deflection.

Time,

J Seconds.

Deflection.

Time,

| Seconds.

Deflection.

Time,

£ Seconds.

Deflection.

3-6

19

154

1119

310-5

219

462

1119

6-5

69

160-6

1069

313

269

465-2

1069

9

119

162-6

1019

315-3

319

467-5

1019

13-5

169

165

969

317-6

369

470

969

16

219

168-2

919

320-5

419

473-2

919

18

269

170-6

869

323-5

469

475-5

869

22-5

319

173

819

325-3

519

478

819

24-3

369

176-5

769

329

569

480-7

769

27

419

179-2

719

331-6

619

483-7

719

30-3

469

182

669

334-3

669

487-5

669

32-6

519

185-3

619

338

719

491

619

35-5

569

189

569

341-3

769

495

569

39-3

619

193

519

345-6

819

499

519

43

669

197-5

469

350

869

505

469

47

719

201-6

419

355-6

919

510-5

419

51-2

769

208

369

361

969

518

369

57-6

819

214-6

319

367-5

1019

526 *2

319

62-5

869

221-6

269

375-7

1069

536-5

269

69-2

919

230-5

219

385-6

1119

551-5

219

76-6

969

245-3

169

401

1169

581

169

87

1019

265-6

119

426

1219

• • •

101-5

1069

300

74

450

1249

• • •

...

125-5

1119

305

119

457-3

1219

...

• . •

150

1199

308

169

460

1169

...

...

In the tables which follow are given the measurements of the
resistance and Joule effect, and the changes in specific heat deduced
from them. In the case of the iron and cadmium the Joule effects
were measured at the same time, iron being at one end of the
thermopile and cadmium at the other. Also in this case the battery
current was measured by the Joule effect in iron strips round the ends
of another thermopile. With regard to the results for German

Table XVI. — Change of Resistance of Cadmium.

Temperature.

Whole per cent,
increase.

Mean increase per cent,
per 1° C.

12° -8 C.

0

0

78° -2

12-53

•3863

81°-1

12-65

•3880

97°'8

13-22

•3788

104° -2

13-55

•3885

130°-0

14-07

•3472

137°-8

14-96

•3968

152° -2

15-56

•3988

154°-4

15-52

•4000

!75°-5

16 48

•4052

408 Proceedings of Royal Society of Edinburgh. [july 18,

silver, much confidence cannot be placed upon the resistance
measurements (in Table XXIII.) ; the changes were so small that,
with the ordinary form of Wheatstone’s bridge used, sufficient accu-
racy could not be obtained.

Table XVII. — Change of Joule Effect in Cadmium.

Temperature 18° C. to

Whole per cent,
increase.

Mean increase per cent,
per 1° C.

110° -8

32-9

•354

122° -2

32-53

•315

143°*8

38-25

•304

173° -0

3776

•218

Table XVIII. — Change of Resistance of Iron.

Temperature.

Whole per cent. Increase.

Mean Increase per cent,
per 1° C.

14° -4 C.

0

0

97° -2

45-4

•548

122°-0

59-9

•556

150° "4

77 7

•5714

l78°-9

95-1

•5781

. 197°-8

109-9

•5994

215°-5

123-7

•6151

27 7° -8

178-9

•6790

Table XIX. — Joule Effect in Iron.

Temperature 18° C. to

Whole per cent.
Increase.

Mean Increase per
cent, per 1° C.

Same corrected.*

110° ’8

3612

•389

•391

122° -2

38-4

*369

•386

143°-8

45-53

•362

•380

l73°-0

89-13

•347

•365

Table XX. — Change of Resistance of Nickel.

Temperature.

Whole per cent.
Increase.

Mean Increase
per cent, per 1°C.

Temperature.

Whole per
cent, in-
crease.

Mean In-
crease per
cent, per 1° C.

13°‘0 C.

0

0

239° -3

115-0

•5084

86°T

29-39

•4021

236°-8

112-4

•5023

98°-3

34-03

•3990

271° '7

139-1

•5376

1 49° *7

57-15

•4180

285° -8

149T

•5466

154°-3

62-84

•4448

289°T

151-6

•5491

154°-6

63T6

•4454

290°-9

152-4

•5483

199° T

88-39

•4750

297° T

159-2

•5604

200° -4

89-78

•4792

307°-2

168-0

•5711

210°-4

94-23

•4823

308° -5

169-4

•5735

* For change in resistance of thermopile.

1887.] Mr A. Campbell on Measurement of Peltier Effect. 409
Table XXI. — Joule Effect in Nickel.

Temperature.

Pile Deflection
D.

D

C2.

Whole per
cent In-

Mean In-
crease per

Same

Corrected.

crease.

cent, per 1° C.

14° -2 C.

996-3

924-7

151°*9

928-3

1396-5

50-7

•3681

•386

16°*4

1037-5

989-7

...

...

« • •

97°'0

987-25

1268-6

27-14

•3367

•343

169°-4

933-8

1519-2

53-5

•3497

•369

223° -6

882-9

1747

76-5

•3681

•388

280° -8

990-7

1918

93-8

•3646

•385

Table XXII.

— Joule Effect in German Silver.

Temperature.

Pile Deflection
D.

D

C2.

Whole per
cent. In-
crease.

Mean In-
crease per
cent.perl°C.

Same

corrected.

14°-6*

1046

2357

0

13°'8

1303-4

2295

0

. 0 0

0 O 0

80° -0

1022-4

2291

-0-2

- -003

•0139

127°‘4

1054

2289

-0-26

- -0023

•0155

142° -0*

1253-9

2322

-1-1

- -008

•0098

181°-6

977-5

2155

-6-09

- -0303

-•0118

262° -3

919-75

2079

-9-43

- -0380

- -0184

Table XXIII. — Change of Resistance of German Silver.

Temperature.

Whole per cent. Increase.

Mean Increase per cent,
per 1° C.

17°T C.

0

95°-3

1-93

•025

122° -6

3-00

•0280

158°-6

3-78

•0267

193°-4

5-07

•0288

197°-6

5-64

•0311

328° -2

10-0

•0321

r281°-0

9-71

•0368

275° *0

9-54

•0370

Table XXIY. — Changes of Specific Heat.

Cadmium.

Mean Increase per
cent, per 1° C. from
18° C. to

Iron.

Mean Increase per
cent, per 1° C. from
18° C. to

Nickel.

Mean Increase per
cent, per 1° C. from
18° C. to

German Silver.

Mean Increase per
cent, per 1° C. from
14° C. to

1 10° *8

•02

110°

•161

97°

•056

80°

•009

122°-2

•072

122°

T70

152°

•05

127°

•0115

143° -8

•076

144°

T88

170°

•091

142°

•0182

173° -0

•168

173"

•215

224°

•106

181°

•0297

...

...

...

280°

•175

262°

•0505

* These two belong to a separate set, and therefore the percentages for
142o,0 C. given are taken from 14° '6 C.

410 Proceedings of Royal Society of Edinburgh. [july 18,

5. Od some Vapour Densities at High Temperatures. By
Alexander Scott, M.A., D.Sc.

The apparatus used in the following determinations is that of
Victor Meyer, modified as described in a paper published in 1879,
“ On the Vapour Densities of Potassium and Sodium,”* by Professor
Dewar and the author. In the experiments here described, the
platinum vessel was further protected by a casing of iron, and the
intervening space filled with magnesia, the iron casing being em-
bedded in sand enclosed between two crucibles. In Series I.
hydrogen was the gas used to fill the apparatus, hut in all the
others nitrogen prepared from the atmosphere by mixing it with
ammonia and drawing the mixture over red-hot copper, then through
dilute sulphuric acid into large glass gasholders, from which it
was expelled after drying into the vapour-density apparatus. The
nitrogen thus prepared almost invariably contains a small quantity
of hydrogen, and this is a decided advantage for most of the sub-
stances used. The temperature of the furnace (which was an
ordinary wind furnace, with 35-feet draught, and fed with coke)
was considerably above the melting-point of cast iron, but was
barely hot enough to volatilise rapidly potassium iodide and silver
chloride, and this gives their results rather high. The best way of
weighing the potassium and sodium was found to be to cut rapidly
a piece of the required weight as nearly as possible, and instantly
wrap it up in a tared piece of thin platinum foil and weigh again.
The sodium kept remarkably well thus, but the potassium was not
so satisfactory. To check the weights, pieces were similarly weighed
and thrown into water, when it was found to require 23'8 to 24-3
milligrams of sodium to give 11T6 c.c. of hydrogen, according as
an ordinary Becker’s balance, turning with a milligram was used,
or a finer one turning with T milligram, the more rapid though
coarser one giving thus the best results ; of potassium similarly
46 ‘3 milligrams were required.

The weight in milligrams of the substance which would be required
to give 22 '33 cubic centimetres of vapour is taken as the molecular
weight.

* Proc. Roy. Soc. Lond., vol. xxxii., 1879.

ir

A. Platinum vessel.

B. Iron casing.

C. Fireclay crucibles.

D. Tube to nitrogen

gas-holders.

E. Platinum tube for

expelling va-
pours.

Between A and B
calcined mag-
nesium.

Between B and C
sand.

This illustration belongs to paper by Dr Alexander Scott, p. 410.

1887.]

Mr A. Scott on some Vapour Densities.

411

Series I. — Apparatus filled with hydrogefi, which tended to escape
when the substance was introduced, and so give too high a
number for the molecular weight ; coarser balance used.

Molecular

•030 sodium

gave 23‘3 c.c., at 0° C. and 760 mm. pressure,

giving 28*7

•035

9 5

,, 23'6 ,, ,,

9 9

„ 331

•037

5 5

,, 30 ‘4 ,, ,,

9 9

„ 27-1

•033

9 5

„ 27-9 ,,

99

„ 26*4

Mean for sodium, 28 '8

Series

II.-

-Same arrangement, but

the apparatus

filled with

nitrogen.

Gram.

Molecular

weight.

029

sodium

gave

26 -8 c.c.,

at 0°

C. and 760 mm. pressure,

giving

241

032

9 9

> ?

29-7 „

99

9 9

9 9

24-0

034

99

39

31*2 „

9 9

9 9

9 9

24-3

030

9 9

9 9

27-6 „

9 3

99

99

24-3

032

9 9

9 9

30-5 ,,

9 9

9 9

9 9

23*4

029

9 9

93

25-6 ,,

99

9 9

99

25-3

024

99

9 9

22-6 ,,

9 9

9 9

99

237

026 potassium

9 9

13-9 „

9 9

9 9

9 9

41-8

045

99

9 9

251 „

9 9

3 9

9 9

40-0

042

9 9

9 9

21-9 ,,

9 9

9 9

9 9

42-9

052

9 9

9 9

28-4 „

9 9

9 9

9 9

40-9

Mean for sodium,

24-2

Mean for potassium,

411

Series III. -—Same arrangement as Series II.

Molecular

Gram. weight.

•042 sodium gave

36 ‘9 c.c. at

d

o

O

and 760 mm. pressure, giving 251

•026 „

21-0 „

99

„ „ 277

•028

231 „

9 9

„ „ 26-7

•036 potassium ,,

18-2 „

9 9

„ 44-2

Mean for sodium, 26 ’6

Series IV. — Same arrangement as above, but the finer balance was

used in the weighings.

Molecular

Gram. weight.

•046 potassium gave 23 ‘2 c.c. at 0° C. and 760 mm. pressure, giving 44 '2
'056 ,, „ 27-4 ,, ,, ,, „ 457

412

Proceedings of Royal Society of Edinburgh. [july 18,

Series IY. — continued.

r

Molecular

Gram

Weight.

•059

potassium

gave

25 '0 e.c. at 0° C. and 760 mm. pressure, giving 52 *8

•052

9 9

22*8 „

9 9 9 9

51-0

•071

99

9 9

35-2 „

9 9 9 9

45-1

•060

9 9

9 9

30-6 ,, ,,

9 9 9 9

43 8

•023

sodium

9 9

W-2 „

9 9 9 9

267

•032

9 9

9 9

25-9 ,, ,,

9 9 9 9

27 -6

•035

9 9

9 9

28-5

9 9 9 9

27*4

•029

9 9

9 9

22-0 „

9 9 9 9

29*4

•033

9 9

9 9

24-6 „

9 9 9 9

30-0

'119 pot. iodide

9 9

14’3 ,, ,,

9 9 9 9

185-6

Mean for sodium,

28-2

Mean for potassium,

47-1

Series Y. — Same arrangement of apparatus; fine balance.

Molecular

Gram.

weight.

‘267 mercury gave

29*3

c.Co at

0° C.,

and 760 mm.

giving

203-3

•249 ,, ,,

27-4

9 9

9 9

9 9

99

202-8

•305 lead chloride ,,

25-6

99

9 9

99

9 9

265-4

•293

25-2

V

99

9 9

9 9

260-0

•319 cadmium bromide ,,

29 7

9 9

9 9

9 9

9 9

240-0

•340 „ „{

311

35-3

h

9 9

9 9

” {

244-4

214-8

'340 cadmium iodide ,,

31*2

9 9

9 9

9 9

9 9

243 -3

•411

35-4

9)

9 9

9 9

9 9

259-0

•162 silver chloride ,,

22-4

9 9

99

99

9 9

161-5

°191 potassium iodide ,,

22-4

99

99

9 9

9 9

190-5

"203 ,, ,,

24-3

9 9

9 9

99

9 9

186-7

•277 mercuric sulphide ,,

37-2

9 9

9 9

99

99

166-6

The mercury was used to test the apparatus, and indicates that
the results obtained are a little too high.

The cadmium bromide seemed to cease giving off gas like the other
substances, but if the measuring tube be left in position, an additional
quantity of gas is obtained, most probably from further dissociation
of the vapour into its elements. The cadmium iodide dissociated
very largely as indicated by its low vapour density and by expelling
the vapours, when large quantities of free iodine were observed.
Silver chloride and potassium iodide volatilised very slowly; the
vapour of the latter seemed to be free from every trace of free
iodine.

1887.] Mr A. Scott on some Vapour Densities. 413

Series YI. — Same arrangement of apparatus.

Molecular

Gram.

•227 chromic chloride gave

29 "8 c.e.

at 0° C. and 760 mm.,

giving

weight,

170-0

•100

9 9

14*7 „

5 9 5 5

5 5

152-2

•120

59

18-8 „

9 9 9 5

5 9

142-5

•149 manganous chloride

5 5

25-0 „

5 9 9 5

5 )

133-0

•142

55

241 „

5 9 5 5

9 9

131-6

■164 mercuric chloride

99

25-8 „

5 5 5 9

5 9

142-0

•167

95

22-0 ,,

9 5 5 9

5 9

169-3

*180 mercuric sulphide

55

25-3 ,,

9 5 5 9

9 9

1587

•145

5 5

20-2 „

5 5 5 9

5 5

1601

*250 mercurous chloride

95

28-9 „

5 9 5 5

5 9

193-4

•223

55

25-6 „

5 9 9 5

5 5

194-1

■068 sulphur

55

23-2 „

9 9 5 9

5 5

65-3

The results of the chromium chloride are not very concordant,
and may he due to traces of water. The sample used was sublimed
and raised to a red heat before using ; green oxide was observed on
the tube for expelling the vapours. Mercuric chloride seems to
dissociate largely into its elements, as do the sulphide and mer-
curous chloride. Sulphur was used to check the apparatus.

Series YII. — Same arrangement of apparatus.

Molecular

Gram. weight.

288 caesium iodide gave

24'0 c.c.,

at 0° C.

and 760 mm.,

giving

268-0

305

5 9

25-7 „

5 5

5 5

99

265-0

270

59

22-5 „

5 9

9 5

5 5

267-9

203 rubidium iodide

5 9

19-3 „

99

5 9

5 5

234-6

199

5 5

201 „

5 5

5 9

5 5

221-5

202

59

20-3 „

5 9

9 5

5 9

221-8

185 potassium iodide

5 9

22 "5 , ,

9 5

5 9

5 5

183-5

176

9 9

21-9 „

5 5

5 5

5 5

179-0

143

99

17-8 „

5 5

5 9

5 9

179-3

196 caesium chloride

5 9

23-4 ,,

5 9

5 5

59

187-2

157

5 9

19-5 „

5 5

9 9

9 5

179-5

175

5 9

21-8 „

59

55

9 9

178-9

114 rubidium chloride

5 5

18-6 „

95

5 5

99

136-9

121

9 5

19-2 „

5 5

9 5

5 9

140-4

130

9 9

20-6 ,,

5 5

5 5

5 9

141-0

147 silver chloride

99

20-5 „

95

5 9

5 9

160-2

The substances in this series were fused before use, so as to be
perfectly dry. They were also very pure, their equivalents being
determined by titration with silver nitrate.

414

Proceedings of Royal Society of Edinburgh, [july 18,

Series VIII. — Same arrangement of apparatus.

Molecular

Gram. weight.

•173 ferric chloride gave

28 ‘5 c.c., at

0° 0.

and 760 mm.,

giving

135-7

•093

16-0 „

3 3

3 3

3 3

129-6

•120

19-3 „

3 3

3 3

3 3

138-6

•076 ,, „

12-0 „

3 3

3 3

3 3

140-7

•145 iodine ,,

18-7 „

3 3

3 3

» 3

1731

•171 „

20-6 „

3 3

3 3

3 3

185-5

•070 sulphur ,,

22-8 „

3 3

3 3

3 3

68-5

'055 ,, ,,

18-0 „

3 3

33

3 3

68-0

The ferric chloride was sublimed immediately before use, but its
extremely hygroscopic nature renders it highly probable that the
vapour would contain hydrochloric acid.

The iodine indicates the dissociation of its diatomic molecules, as
has already been shown by V. Meyer.

Sulphur again used as a check.

The values obtained for the molecular weights from the above
experiments may be thus tabulated : —

Values. Molecular formula

Experimental.

Theoretical.

indicated.

Sodium,

. 25-5

23

Na

Potassium,

. 37-7

39

K

Mercury,

. 203

200

Hg

Sulphur,

. 67-3

64

s2

Iodine,

. 179-3

169

(I2 + 2I)

Caesium iodide,

. 267

260

Csl

Caesium chloride, .

. 179-2

168-5

CsCl

Rubidium iodide, .

. 221-6

212*3

Rbl

Rubidium chloride,

. 139-4

120-8

RbCl

Potassium iodide, .

. 184-1

164

KI

Silver chloride,

. 160-8

143-5

AgCl

Lead chloride,

. 262-7

278

PbCl2

Manganous chloride,

. 132-3

126

MnCl2

Ferric chloride,

. 136-1

162-5

FeCl3"

Chromic chloride,

. 154-9

159

CrCl3

Cadmium bromide,

. 242-2

272

CdBr2

Cadmium iodide, .

. 251-1

366

(Cdl2 + Cd + I + I)

Mercuric sulphide,

. 161-8

155

(2Hg + S2)

Mercurous chloride,

. 193 7

2Hg + Cl2 = 157 1

Mixtures of Hg + Cl2

Mercuric chloride,

. 155-6

Hg + Cl2 = 135-5 J

with some HgCl2

The platinum vessel after the first experiment seemed to have
no action whatever on the vapours of potassium and sodium, and
the tables above given contain the results of every experiment made

1887.] Mr A. Scott on some Vapour Densities.

415

with the exception of one with sodium, which was the first done
in a new platinum vessel. It may be taken then as conclusively
proved that the molecules of potassium and sodium are monatomic
at high temperatures.

Mercury, sulphur, and iodine were used to test the apparatus
and the degree of accuracy to be expected, and gave results quite in
accordance with those of other experimenters, as did also mercuric
sulphide. Both chlorides of mercury seem to undergo a very large
amount of dissociation into their elements, though not to the same
extent as the sulphide.

The results for the chlorides and iodides of caesium, rubidium,
and potassium point to the ordinarily received formulae as the
correct ones, as is the case with the chlorides of manganese, silver,
and lead, which last seems to dissociate to a certain extent.

The bromide and iodide of cadmium also seem to dissociate largely
at the temperature employed. Ferric and chromic chlorides give
results which seem to point conclusively to the formulae FeCl3 and
CrCl3 as the true ones, the chromic chloride giving results very
closely corresponding to this, and the ferric chloride considerably
lower, which may be due to water absorbed during weighing (which
was done as above described for potassium), and this giving a larger
volume of hydrochloric acid than the ferric chloride from which it
would be produced, gives too low a number for the molecular
weight.

Potassium fluoride was tried, but gave no vapour whatever, and
phosphorus at once destroyed the vessel.

One experiment with arsenic trioxide gave results pointing to
As406 as its formula, but further experiments are in progress with
it and several other bodies, the results of which I hope to be able
to communicate shortly.

6. On the Determination of the Plane Curve which forms
the Outer Limit of the Positions of a certain Point.
By Dr G. Plarr, Communicated by Professor Tait.

2 D

VOL. XIV.

28/1/88

416 Proceedings of Royal Society of Edinburgh. [july 18,

7. The Thermal Windrose at the Ben Nevis Observatory.

By A. Bankine.

The Table, showing the Thermal Windrose, accompanying this
paper, was computed from the observations made at the Ben Nevis
Observatory during the three years ending May 1887. It shows
the mean temperatures, on the mean of the three years, of the
different winds for each month, for the year, and for the seasons.
The direction of the wind is observed to the thirty -two points of the
compass, but in this table the temperatures are only shown for eight
points, the intermediate points having all been added on to these
eight points in the same way as that described by Mr Omond inh is
paper on “Winds and Rainfall” in the Journal of the Scottish
Meteorological Society , namely, the by winds were added to their
adjacent octants, and the points half-way between the octants were
on the odd day of each month added to the octant to their right,
looking out from the centre of the compass card, i.e., they were veered
two points, and on the even days to that on their left, i.e., they were
backed two points. The mean temperature of each direction of wind
for each month was found by tabulating the hourly observations of
temperature under the direction of wind observed at the same time,
or under its octant as above, and then taking the arithmetical mean.
When the wind was variable, or its direction doubtful, the tempera-
ture was entered in the column for calms and variables. These
variable winds belong chiefly to the northern half of the compass,
their existence being principally due to the abrupt and precipitous
character of the north side of the Ben. The temperatures given in
the table are those indicated by thermometers which in summer
and autumn are protected in the regulation Stevenson screen, and
in winter and spring in a smaller pattern of the same, which can
he shifted up or down a ladder-like stand, so as to be always at or
near the standard height of 4 feet above the surface of the snow.

There are two columns of monthly means in the table, one giving
the mean temperature for each month, deduced in the ordinary
manner from the daily means, and the other giving the mean of the
temperatures in the table under the eight wind directions. It will
be seen that there is a considerable difference between these mean

417

1887.] Mr A. Rankine on the Thermal Windrose.

temperatures in certain months, which difference is obviously due
to the inequality of the frequency of the different winds.

As the character and relative frequency of each wind have
already been discussed by Mr Omond, it only remains to add a few
words regarding wind-temperature, as far as the accompanying table
sheds any light on the subject.

The first point to be noticed is, that on the mean of the year the
south is the warmest wind, its temperature being 3 2° "6 ; and the
north-east is the coldest wind, its temperature being 26° '5 ; and
also that the winds in their order of highest temperature are — S.,
S.W., W. (N.W. = S.E.), E., 1ST., N.E., — the north-west and south-
east winds being equal in temperature, and the east and north winds
almost so. In each of the seasons the north-east wind is the coldest,
and, with one exception, the south is the warmest, the exception
being winter, when the warmest wind is the south-west. An
inspection of the results for the different months shows that the
above order of highest temperature of the directions varies consider-
ably from month to month, as does also the difference between the
temperatures of the warmest and coldest winds in each month, the
maximum difference being 10° *7 in March, and the minimum
40-2 in April ; while the mean of all the monthly differences is 6° *7.
This difference on the mean of the seasons is greater in winter
and spring than in summer and autumn, being least in summer.
Though the means for the year and for the seasons show that the
warmest and coldest points are almost constant, yet the monthly
results show that these points oscillate, the warmest point
markedly and the coldest rather less so. During the winter
months the warmest point is south-west, but, as the year advances,
it swings round through south to south-east, which is its direction
in July and September. The coldest point is north-east for nine
months ; and though in February it is south-east, in June east, and
in November north, it has not so well defined an oscillation as the
warmest point.

The differences between the annual ranges of temperature of the
different directions of wind seem to point to the cause of this
oscillation in the direction of the warmest wind, as being the degree
to which the yearly march of temperature affects the areas over
which these winds blow. The south-east wind has an annual range,

418

Proceedings of Boyal Society of Edinburgh. [july 18,

in mean monthly temperature, of 24° *3, its temperature in February,
for which month it is the coldest wind, being 19° *7 ; and in July,
when it is not only the warmest for that month, but also for the
whole year, its temperature is 44° -0. The wind having the least
annual range is the north-west, its temperature in January being
24° T, and in August 35° ‘8, thus giving it a range of 14°*4. The
mean annual range for the directions S.W., W., N.W., is 15° *6.,
and that for S.E., E., N.E., is 20°*7. The difference between these
ranges is apparently due to the fact that the easterly winds blow
over land, and the westerly winds over sea, — land areas being
subject to greater extremes of temperature than sea areas, and this
is apparently the cause of the oscillation above referred to. In the
tables given with Mr Omond’s paper on “ Winds and Rainfall ” in this
number of the Journal,* it is seen that the greater number of south-
east winds belong to anticyclonic systems, and this also may have
a good deal to do with the great annual range of temperature of the
south-east wind. A comparison of the temperatures of the same
direction of wind in cyclonic and anticyclonic systems has not as
yet been made ; but I could see, when working up this table, that
such a comparison would probably result in interesting and useful
knowledge. It may be noted that each of the directions, S., S.W.,

Thermal Windrose, Ben Nevis Observatory. ( Computed from the
Observations of the three Years, June 1884 to May 1887.)

N.

N.E.

E.

S.E.

S.

S.W.

W.

N.W.

Calm or
Vari-
able.

Mean of
Month.

Mean of
8 Winds

January

20-6

18-7

18-8

20-5

23-3

25-3

24-2

24-1

22-1

22-9

2D9

February

21-5

21-5

21-9

19-7

24-3

27-8

27-4

24-8

21-1

24-0

23-6

March

19-9

18-2

19-5

197

28-9

28-3

27-9

26-5

23-1

22-8

23-2

April

24-3

24-1

24-4

27-8

27-9

28-3

271

26-0

26-2

26-5

26-5

May

27-9

27-4

29-5

31-4

3D5

31-8

30-0

29-0

29-9

29-9

29-8

June

35-5

33-6

33-5

37-5

38-1

37-3

36-5

35-8

36-7

36-2

36-0

July

37-3

33-9

38 9

44-0

42-8

411

40-1

38-0

38-5

40-6

39-5

August

36-2

35-8

36 2

40-7

42-5

41-8

39-5

38-5

37-9

40-7

38-9

September

31-9

31-1

34'4

40-5

39-5

37-8

36-7

34-7

34-1

36-9

35-8

October

29-9

28-6

29-0

31-4

33-8

32-7

31-8

31-1

30-6

31-2

31-0

November

25-2

25-4

26-3

26-6

30-2

' 31-3

30-2

29-5

25-8

28-2

28-1

December

21-4

19-5

21-1

22-9

27-9

27-0

25-8

25-8

23-5

23-4

23-9

Year

27-6

26-5

27-8

30-2

32-6

32-5

31-4

30-2

291

30-3

29-8

Spring

23-7

23-2

24-5

26-3

30-0

29-5

28-3

27-2

26-4

26-4

26-5

Summer

36-3

34-4

36-2

40-7

41-1

40-1

38-7

37-4

37-7

39-2

38-1

Autumn

29-0

28-4

29-9

32-8

34-5

33-9

32-9

31-8

30-2

32-1

31-6

Winter

21-2

19-9

20-6

21-0

25-2

26-7

25-6

24-9

22-2

23-4

23-1

* See Journal of Scottish Meteorological Society , vol. vii. p. 275, and vol.
viii. p. 18.

1887.] Mr A. Rankine on the Thermal Windrose.

419

W., and N.W., attains its minimum temperature in January, and
each of the directions, N., N.E., E., and S.E., in March; while all
the directions except N.E. and N.W. have their maxima in July,
the two exceptions occurring a month later.

8. On Ferric Ferricyanide as a Reagent for Detecting Traces
of Reducing Gases. By Professor Crum Brown.

The brown solution obtained when solutions of ferric chloride
and potassium ferricyanide are mixed, which may be regarded as
containing ferric ferricyanide, is, as is well known, very readily
turned blue by reducing agents, Prussian blue or Turnbull’s blue
being formed. The author uses strips of filter paper dipped in the
freshly prepared solution to test for traces of reducing gases, such
as sulphuretted hydrogen, sulphurous acid, &c. As nitrous fumes
also blue the brown solution, reducing it, traces of them can be
detected by using together a piece of paper prepared as above and a
piece of iodised starch paper.

9. On the Compressibility of Water, of Mercury, and of
Glass. By Professor Tait.

19. An Account of some Experiments which show that
Fibrin-Ferment is absent from circulating Blood-
Plasma, and which support the view, first advanced by
Sir Joseph Lister, that the Blood has no spontaneous
tendency to Coagulate. By Professor John Berry
Hay craft.

(Abstract.)

Sir Astley Cooper and Turner Thackrah taught that blood was a
fluid tending to coagulate, but inhibited from doing so by the living
vascular walls. This view is erroneously ascribed to Briicke, who
himself only professes to support it.

Sir Joseph Lister considers that blood of itself does not tend to

420

Proceedings of Boycd Society of Edinburgh. [july 18,

coagulate. When shed from the body this condition is actively
induced by its contact with foreign matter. It is unnecessary, there-
fore, to assume that the vascular wall has any inhibitory power.

In order conclusively to determine which view is the correct one,
it is necessary to obtain blood which is neither in contact with the
vascular wall nor with a solid foreign body This I have succeeded
in doing by immersing drops of blood in fluids differing from it
in surface tension, such as oil, paraffin, &c.

Many experiments were made, notably the receiving of blood
upon the greased surface of a mica plate immersed in a vessel full
of paraffin oil. The drops remained fluid sometimes for two or three
hours. The most successful experiments wTere, however, performed
by injecting a viscous mixture of vaseline and paraffin oil into the
vein of a sheep. It was mixed with the blood so as to isolate
drops of blood in the midst of the viscous mass. These remained
fluid on more than one occasion for twelve hours afterwards.

The conclusion I drew from these experiments was that blood
required the influence of solid matter to bring about coagulation,
and that the view of Sir Joseph Lister — which he had himself
supported by the strongest arguments — was correct.

Shortly after the completion of these experiments, the important
results of Dr Freund’s were published. He had been traversing
almost exactly the same ground that I had, and at the same
time.

There is a general belief that white blood corpuscles are con-
stantly breaking down in the blood-vessels, setting free fibrin-
ferment. This view we owe mainly to Alexander Schmidt and his
school. Moreover, ferment when artificially injected into the blood-
vessels soon disappears.

I had been led by my experiments to the fact that the smallest
quantity of fibrous ferment will in time coagulate a considerable
mass of blood, and inasmuch as blood remains fluid in a ligatured
vein for twelve or twenty-four hours, it is improbable that blood
corpuscles are constantly breaking down and setting free ferment,
unless we suppose that its action is prevented by the vascular wall.
This latter supposition both Freund’s and my own experiments
have shown to be highly improbable.

In order by a direct experiment to determine whether the vascular

1887.] Professor Hay craft’s Abstract of Experiments. 421

walls destroy the ferment in any way, I performed the following
experiment : —

Dilute blood ferment was injected and reinjected several times
into the blood-vessels of a dog, previously freed from blood. The
injected solution was as powerful in causing the coagulation of
hydrocele fluid as a similar solution which had not been passed
through the vessels.

It is probable, therefore, that any injected ferment is destroyed
within special organs or eliminated from the system. This would
of course be a priori most probable. One is driven to conclude,
therefore, that in the course of the ordinary circulation (whatever
may take place in glandular structures) corpuscles do not break
down, nor is free ferment present in the plasma.

It is stated, however, by many to be present.

Believing that this assumption is due to want of care in mani-
pulation, I repeated well-known experiments, adopting special pre-
cautions.

Previous experimenters had obtained blood either from a cut
vessel or from one fitted with a glass cannula. The blood must,
therefore, have come in contact for a moment — a sufficient time
to produce ferment — with the cut surface of the vessel or with the
cannula. The blood was then received into a vessel containing a
saturated solution of sulphate of magnesia. After filtration, the
plasma was found to possess the power of clotting, on dilution.

I repeated this experiment, mixing the magnesium sulphate
solution with the blood while the latter teas still within a blood-
vessel (an excised vein). After filtration, the diluted and dialysed
plasma did not coagulate.

I am inclined then to believe that blood corpuscles do not break
down in the blood-vessels, or that if they do they do not set free
any ferment. This latter is not present in circulating blood, which
only fends to coagulate when it is brought in contact with solid
matter.

The exact way in which this solid matter acts, I hope to discuss
in a subsequent paper.

422

Proceedings of Boyal Society of Edinburgh. [july 18,

11. On the Chemical Composition of the Water composing
the Clyde Sea Area. By Adam Dickie.

About the beginning of this year I was requested by a sub-com-
mittee of the Government Grant Committee* to determine some of
the components of a series of samples of sea water, which were to
he collected during the year at various parts and at different times in
the Clyde sea area by the observers of the Scottish Marine Station.
The collections were chiefly made under the immediate direction of
Dr H. R. Mill. Since January, accordingly, I have been working
at this, and have completed in all eighty-nine analyses, the results of
which I now take the liberty of placing before this Society. There
are various reasons why this paper should consist of little more than
tables of results, one of which is that, having little or no experience
in the science of oceanography, it would be presumptuous in me to
draw conclusions from my results which would no doubt strike any
one acquainted with that science at once. Another reason is that,
though acquainted with some of the physical conditions under
which the samples were taken, such as depth, temperature, place of
collection, and date, I am quite ignorant of other conditions quite
as important, if not more so, in my estimation, as, for instance, pre-
sence or absence of some freshwater stream near place of collection,
state of tide, rainfall, &c., — all conditions which would no doubt in-
fluence more or less materially the salinity of the water.

It is needless for me even to describe the methods of analysis I
adopted, as, with one exception, I have adhered strictly to the
methods so fully described by Dr Dittmar in his memoir on the
“ Challenger ” waters. The exception was in the case of the chlorine,
in the analysis of which, though using the modification of Volhard’s
method described in the memoir for my final titration, I employed
Mohr’s method, in which chromate of potash is used as an indicator
for the preliminary.

It was intended at first to determine the chlorine, the sulphuric
acid, the alkalinity, and the suspended matter, but the latter I only
completed in some of the first batch of samples. In estimating this

* The sub-committee consisted of Professor Dittmar, Professor Crum Brown ,
and Mr John Murray.

1887.] Mr A. Dickie on Chemical Analyses of Sea Water. 423

I proceeded as follows : — After determining the other components,
I weighed the bottle and all that remained of the sea water, filtered
the water through a tared filter paper (which was then dried at
100° C. and weighed), and then weighed bottle again, the difference
of course being weight of water filtered. I found that, whilst there
was generally about a kilogramme of water filtered, the weight of
suspended matter never amounted to more than 8 mgrms., and was
sometimes not more than 1J mgrms., and, as the probable error in
weighing would amount to a not inconsiderable portion of this small
weight, I considered that the importance of the result obtained was
not worth the time and labour employed in the getting of it, which
was sometimes considerable.

Appended is a table of results.

The first six columns of this table explain themselves. Column
A gives the chlorine in grms. per kilo. ; column B gives the sul-
phuric acid (S03) in grms. per kilo.; C and D are the alkalinity
columns ; C gives the amount of C02 present as normal carbonate
in mgrms. per litre; and D the amount in mgrms. per 100 mgrms.
of total salts. In this latter, as I did not estimate the total salts, I
have calculated from the chlorine, using the number 55*43 as equi-
valent to 100 parts total salts, that being the number which Dr
Dittmar establishes in his “ Challenger ” memoir. Column E gives
the ratios existing in the different samples between the chlorine and
the sulphuric acid ; i.e., the weight of S03 per unit of chlorine.

On glancing over the chlorines ascertained in the “ Challenger ”
work, we find that in no sample was the chlorine less than 18 grms.
per kilo., that the largest number of samples gives quantities between
19 and 20 grms. per kilo., and that the sample having greatest
amount contained 20*64 grms. per kilo. In above table we find
that the largest amount of chlorine is contained in Ho. 2619 =
18*946 grms. per kilo., a sample taken’ in the channel south of
Sanda ; and the least in Ho. 1423 = 1*1692 grms. per kilo., a
Lochfyne sample. But though the difference between these two
figures is considerable, the general variation in the quantity of chlo-
rine is not so great, for we find that out of the eighty -nine samples
only eight (all of them surface samples) contain less than 16 grms.
per kilo., and only five less than 14 grms. per kilo.

The difference in salinity between surface and bottom water is

Table of Results.

424

Proceedings of Royal Society of Edinburgh, [july 18,

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1887.] Mr A. Dickie on Chemical Analyses of Sea Water. 425

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426 Proceedings of Royal Society of Edinburgh. [jux,y 18,

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1887.] Mr A. Dickie on Chemical Analyses of Sea Water. 427

very marked. In every instance the amount of chlorine is greater
in bottom than in surface samples taken at the same spot. It is
also curious to note that, where three samples have been taken (a
surface, a bottom, and one from some intermediate depth), the
chlorine in the latter is always greater than in the surface, and less
than in the bottom samples, leaving one to infer that the chlorine
in estuary water, at least, increases steadily from surface to bottom.
I may here state that in five cases were surface, intermediate, and
bottom samples collected, and in every one of these the above rule
holds good.

The alkalinity was determined in 250 c.c. of the water, by means
of titration with ~ normal acid and alkali. The mean over all the

i _

samples for alkalinity, in terms of 100 parts total salts, or, in other
words, the weight of C02 present as normal carbonates, expressed
in terms of 100 parts total salts, or of 55 ‘43 parts chlorines, is as
T482 is to 100. The mean alkalinity of the forty-one surface
samples is T5, and of the thirty-nine bottom samples T470.
In the “Challenger” water the mean over all was *1520, that of
fifteen surface waters T492, and that of sixty-three bottom waters
•1540.

The sulphuric acid was determined in about 50 grms., strictly in
accordance with the method described by Dr Dittmar in his “ Chal-
lenger ” memoir. These results are shown in columns B and E of
the table, B giving the sulphuric acid (S03) per kilo., which, of
course, varied with the quantity of chlorine ; and E the quantity
expressed in mgrms. per mgrm. of chlorine. In the latter column
the results, except in three cases, are fairly constant. In the three
exceptional cases, which are enclosed in brackets, it is noticeable
that the amount of chlorine is remarkably small, and, of course, in
the analysis the amount of BaS04 to be weighed would he corre-
spondingly small, so I suppose the lowness of the results arises from
the probable error in weighing, which, of course, in a calculation
of this kind is multiplied up enormously. The average quantity of
sulphuric acid (S03), in terms of the grammes of chlorine, is T175 ;
whilst in the “Challenger” water it was T1576, a somewhat lower
figure.

428 Proceedings of Royal Society of Edinburgh, [july 18,

12. An Experimental Critique of the Chloroplatinate
Methods for the Determination of Potassium, including
a redetermination of the Constant Pt. By Professor
Dittmar and Mr John M‘ Arthur.

13. Addition to Thermometer Screens. Part IV. By

J. Aitken, Esq.

{Added August 1887.)

I much regret it has not been possible for me, during this
summer, experimentally to determine the best forms and sizes of
the details in the construction of the C screen ; nor have I been
able to keep a continuous record of its readings. Only a few
observations have been made at intervals with it, as originally
constructed, and shown in fig. 1 of this paper, and with the
Stevenson screens. The result of all these trials is to confirm the
conclusions already arrived at. The C screen always gave the lowest
readings when there was any radiation. The Stevenson screen,
when worked under the ordinary conditions, that is with bottom
open, generally gave on fine days readings of about two degrees too
high; while the readings given with the Stevenson screen with
bottom closed were higher than those of the C screen, but con-

Date.

Temp, by
C Screen.

Error of
Stevenson
Screen.

Radiation
by Large
Ball.

Radiation

by

Vacuum

Thermo-

meter.

Temp, of
Ball.

Ratio x
Temp, of
Black Ball.

Force of
Wind.

Temp, in
Vacuum.

July 23

63°-9

0°-6

20°

45°

•44

9

3

24

65°

l°-0

28°

69°

•40

11

4

25

63°

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26°

60°

•43

11

4

26

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25°

53°

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12

3

27

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22°

41°

•53

12

5

28

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23°

49°

•47

11

5

29

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48° -5

•43

9

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30

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29°

62°

•47

14

2

31

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2° -3

38°

57° -5

•66

25

1

Aug. 1

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14

2

16

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44°

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18

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22

1

1887.]

Mr J. Aitken on Thermometer Screens.

429

siderably lower than those got with the bottom open. On dull and
windy days the differences in the readings were not so great.

To illustrate the influence of the weather on the readings of the
Stevenson screen with open bottom, I shall use all the readings
taken with the screens between the 23rd July and the 19th August
of this year; these are arranged in the table (p. 428).

In the first column of the table are the dates of the observa-
tions ; in the second column the temperatures of the air as given
by the C screen ; in the third column is the excess error of the
Stevenson screen with bottom open; and in the last column is the
estimated force of the wind, on a scale of from 0* to 10. It will
be seen from the last column, that from the 23rd to the 29th July
the weather was stormy, and that on the following days there was but
little wind. The effect of these two conditions on the comparative
readings of the screens is very evident. While the wind was strong
it will be noticed that the difference between them was often less
than one degree, but when the wind fell it was frequently more than
two degrees.

One object of meteorological observatories is to tell us something
about the climate of the place — that is, something about its effects
on animal and vegetable life. Now it is admitted by every one that
the indications of the instruments in general use in our observatories
do not by any means agree with the indications given by our
bodies. The thermometer often says one thing, while our feelings
indicate something quite different. No doubt, part of this disagree-
ment is the result of the more or less healthy condition of our
bodies at the time ; they are, so to speak, instruments with shifting
scale. But apart from this, there is frequently a wide difference
between the indications of the meteorological instruments and the
average feeling of a great number of people. This results from the
meteorological instruments not being affected by the same causes as
our bodies. The thermometer may indicate that the air is warm,
while we may feel it to be cold. This may be the result of the air
being dry, and causing a cooling effect by a rapid evaporation from
our bodies. We have therefore to check the readings of the dry bulb
thermometer by a reference to the wet one ; we thus get a greater
similarity between the indications of the meteorological instruments
and those of our bodies.

430 Proceedings of Royal Society of Edinburgh, [july 18,

On our solar radiation measurements, we however have no such
check. The thermometer with blackened bulb in vacuo may indicate
a very strong solar radiation, and yet we may feel it chilly ; or it
may indicate a comparatively low radiation effect, and we may feel
warm. This difference in the indications may be due to different
causes, but no doubt wind is one of the most important. The wind
has but little effect on the solar radiation thermometer, while it has
a most powerful influence in checking the heating effect of the sun
on our bodies. It seems therefore desirable that some other
instrument be designed for the purpose of showing the radiation
effect, as tempered by the wind, in order that our observatories may
tell us something more definite about the climate of the place.

The radiation thermometer described in a previous part of this
communication is affected by the wind, and might be used for this
purpose ; but owing to the absorbing surface being flat, it is neces-
sary that it be kept always turned towards the sun ; it is not,
therefore, suitable for ordinary work. In place of it, I have for
some time used a large hollow sphere made of thin metal, and
having a thermometer fitted to it, with its bulb in the centre.
What size this ball ought to be has not yet been determined,
but if observations are to be taken with an instrument of this
kind, all that seems necessary is, that a uniform size of ball be
adopted for all observatories, and that it be made of the same
kind and thickness of metal. The size of the ball, if not too small,
does not seem to affect the readings much. Readings have been
taken here with two balls — one 15 cm. in diameter, and the other
40 cm. Readings given by the 40 cm. ball will be given later on ;
those given by the smaller ball were only 2° or 3° lower than the
large one.

These hollow balls have also been used for night radiation
measurements. The readings obtained with them are not so valuable
as those got with flat-surfaced instruments, as they do not get cooled
so much. While the flat surface gets cooled 10° or 11° below the
temperature of the air on a clear night, the large ball falls only 5° or
6° and the small one not so much by 1° or 2°. When in use, the
balls are fixed to a post at the same height as the screen, and at no
great distance from it. This method of taking radiation tempera-
tures at night seems to be better than the one in general use. The

1887.]

Mr J. Aitken on Thermometer Screens.

431

plan generally adopted of taking the readings of a thermometer
placed on the grass is open to many objections. The temperature
indicated by a thermometer so placed is affected by the greater or
less amount of heat communicated upwards from the ground, by the
amount of air circulating just at the place where the bulb happens
to be, and other local influences, to many of which the ball at four
feet from the ground is not exposed. By changing very slightly the
position of the bulb of the thermometer placed on the grass, we
can greatly alter its readings, whereas this is not the case with the
ball at four feet from the ground. In the large ball used here there
are fixed two tubes in a horizontal position. One of these tubes
holds a maximum, the other a minimum thermometer.

Returning to the table showing the difference in the readings of
the Stevenson and the C screens. In the fourth column will be
found the effect of solar radiation in heating the 40 cm, ball. The
figures given are not the temperatures given by the ball, but the ex-
cess of this temperature above that of the air, or, in other words, it is
the heating effect of the radiation. For instance, on the 23rd of July
the temperature of the ball was 84°, the air was 64°, and the heating
effect of the sun was thus 20° as entered. In the fifth column are
the solar radiation temperatures taken by the black bulb in vacuo.
These temperatures are treated in the same way as those given
by the black ball ; the figures show how much the thermometer was
heated above the temperature of the air.

It will be noticed that though the error of the Stevenson screen is
due to radiation, yet it follows the indications of neither of these radia-
tion thermometers. This is quite to be expected, because the error of
the screen is the effect of radiation as modified by wind. Though the
readings of the ball give the effect of radiation as modified by wind,
yet these readings alone do not tell us how much they are affected
by wind. For instance, the black ball might be heated to only a
small amount, either by a strong sun checked by a strong wind, or
by a feeble radiation unchecked by wind. If, however, we compare
the temperatures of the black ball with those of the black bulb in
vacuo , we at once see the effect of the wind. FTo two of these readings
for any day bear the same relation to each other. When there was
much wind, the black ball was heated only to about 04 times the
temperature of the black bulb ; whereas when there was little wind

VOL. XIV. 28/1/88 2 E

432 Proceedings of Boyal Society of Edinburgh, [july 18,

it was heated to 066 times. If then we divide the temperature of
the black hall by that of the black bulb, we get a series of numbers
inversely proportional to the cooling effect of the wind. These
numbers are given in the sixth column. If now we multiply the
numbers so obtained by the heating effect of the radiation on the
black ball, we get a series of numbers representing the combined
effects of solar radiation and wind. These numbers are given in the
seventh column.

It will be observed that the numbers so calculated vary with the
errors of the Stevenson screen given in the third column, and that
when they are divided by 10 the figures in the two columns agree
fairly well with each other. It will, however, be noticed that the
figures agree much better when the weather is calm and settled than
when it is stormy. This was probably due to the fact that during
the windy days it was also cloudy, with only short gleams of sun-
shine, sufficient to heat up the black ball and black bulb, but not
long enough continued to heat up the screens; or it may have been
due to the maximum radiation temperatures not having happened
at the same time as the maximum air temperature. The errors
during the cloudy weather were thus probably smaller than they
would have been if there had been continued sunshine.

It would thus appear that, by taking observations with a black
ball and a black bulb in vacuo, we can calculate pretty well what
will be the excess in the readings of the Stevenson screen over those
of the G screen. And further, a comparison of readings taken in
this way also tells us something about the climate of the place
which cannot be ascertained by an examination of the readings of
the black bulb in vacuo alone. On the 24th July, for instance, the
black bulb in vacuo was heated 69° above the temperature of the
air, while the black ball was only heated 28°, and the error of the
Stevenson screen was only 1°; whereas on the 18th August, when
the black bulb in vacuo was not heated quite so much, the black
ball had its temperature raised 42° ’5, and the error in the Stevenson
screen was 2° *6. As the thermometer in the Stevenson screen is
influenced very much in the same way as our bodies, by radiation
modified by wind, we may look on the figures given in the seventh
column of the table as representing more nearly the climatic con-
ditions than those given by any other method at present in use.

1887.]

Dr T. Muir on Simple Alternants.

433

14. On the Quotient of a Simple Alternant by the Difference-
Product of the Variables. By Thomas Muir, M.A., LL.D.

On 17th March 1879 I gave to the Royal Society of Edinburgh
an account of some researches on the subject of Alternants. A
short descriptive abstract of the communication was published in
the Proceedings , vol. x. pp. 102, 103, the concluding paragraph of
which is as follows : —

“ Vow it is well known that the alternant whose indices are
in order 0, 1, 2, 3, . . . . is equal to the difference-product
of its variables. In regard to every other alternant it is
evident that it must contain the said difference-product as a
factor, but what the co-factor should be is not so readily seen.
In particular cases, doubtless, it can be found without much
difficulty, but a general method of obtaining it has hitherto
been a desideratum. Such a general method the author has
discovered along with a number of less important results bear-
ing on the same special form of determinant.”

These results were never published, as, very shortly after the date
referred to, the volume of the Giornale di Matematica for 1878
arrived, and I found that what I had looked upon as my most
important theorem, was given and proved by Garbieri at the begin-
ning of the volume.

Vow, however, that fresh interest in the subject has been
awakened by the very able papers of Professor Woolsey Johnson,
which have recently appeared in the American Journal of Mathe-
matics (vii. pp. 345-352, 380-388) and Quarterly Journal of
Mathematics (xxi. pp. 217-224), I desire to resuscitate my method.
Happily there is no question of priority involved. The methods are
diverse, and the superiority lies entirely with Professor Johnson’s.
His reduction-theorem

<*(0, P cl) = H3-2,*>-i + <Ac . a( 0, p - 1, q - 2) ,

his discovery of the existence of the symmetric function Q which
is the difference of a{ 0, p, q, r) and a( 1, p, q , r— 1), and his mode
of determining the said function, are things of which I had not
dreamed, and which I consider the most notable results added to
the theory of alternants for a great many years.

434 Proceedings of Royal Society of Edinburgh, [july 18,
The quotient

1

a 3

a 6

1

a

a2

1

b 3

b 6

1

b

b2

1

c3

c6

1

c

c 2

i.e. | «°53c6 1 4- 1 a%lc2 j ,

or, say, A(0, 3, 6) A(0, 1, 2) ,

or, still more shortly, <z(0, 3, 6) ,

is evidently a homogeneous symmetric function of degree
3 + 6 -(1 + 2), i.e. 6, and when expressed as a sum of single
symmetric functions will be of the form

%cdb2 + x%odbc + y^,a3bs + z%a%2c + u%a2b2c2 .

The problem is to determine x, y, z, u.

Professor Johnson’s method is to use repeatedly his above-
mentioned reduction-theorem. Tims

a(0,3,6) = H42 + a5cH2>1 + a2b2c2 H00 ,

= Xa^b2 + %a^bc + % a3bs + ^ a%2c + %a2b2c2 \

+ abc(1a2b + %abc) >

+ a2b2c2. )

= Z2a452 + %a^bc + %a2b?’ + 2 %a%2c + 3 %a2b2c2 .

My method contrasts with this in that it determines the co-
efficients x} y, z, u separately. Besides, therefore, being of interest
as throwing a side-light on Professor Johnson’s method, it may be
found useful when only one or a very few coefficients are wanted,
and it has certainly been the means of arriving at several more or
less noteworthy results.

The basis of it is the expansion of the alternants in terms of
alternants of lower orders.

Alternants of Third Order.

First Example. — Required the coefficient of a%2c in the ex-
pansion of a( 0, 3, 6).

Solution. — Write the integers from 0 to 6, and separate them
into three groups A, B, C, by putting a bar before 0, 3 and 6 ; thus

o l i

3 4 5

A

B

6 .
C

1887.]

Dr T. Muir on Simple Alternants.

435

In the group A delete those which are greater than the index of c
in %a%2c. Find in how many ways a number from group A, with
a number from group B, will give the sum 4, 4 being 1 more than
the sum of the last two indices in %cidb2c. This number of times,
2, is the coefficient required.

The solution is here put at greater length than need be, in order
that when taken with the corresponding solution for the case of
alternants of the fourth order, the generality of the method may be
apparent. It may be enunciated quite shortly as a theorem, viz.: —

The coefficient of %axbvcz in the expansion of \ afhpcq \ -7- 1 a%lc2 1 is
the number of ways in 'winch by taking a number from

0, 1, 2, . . . , z-1, z

and a number from

P,P+ 1, • • • , -1

the sum y + z + 1 may be obtained.

Second Example. — Required the coefficient of %a%^c2 in the ex-
pansion of a( 0, 3, 8).

Solution. — The two groups here are 0, 1, 2 and 3, 4, 5, 6, 7;
and the sum 6 can be made up from them in three ways, viz.
0 + 6, 1 + 5, 2 + 4. The coefficient therefore is 3.

Alternants of Fourth Order.

First Example. — Required the coefficient of %a^b2c2d in the
expansion of a( 0, 2, 4, 9).

Solution. — Write the integers from 0 to 9, and separate them
into four groups A, B, C, D, by putting a bar before 0, 2, 4 and 9 ;
thus

0 1

2 3

4 5 6 7 8

A

B

C

In group A delete, if necessary, those which are greater than the
index of d in ^a*b2c2d. Take the integers from 0 to the index of
d inclusive, and unite each with such a number as will make the
sum 4, that is to say, 1 more than the sum of the last two indices
of '%aitb2c2d : this gives

0,4; 1,3.

Take three numbers, one from A, one from B, and one from C,

436

Proceedings of Royal Society of Edinburgh, [july 18,

whose sum is 8, that is, 1 + 2 more than the sum of the last three
indices of ^a462c2<i : this gives

0, 2, 6; 0, 3, 5; 1, 2, 5; 1, 3, 4.

Bring then each of the pairs to each of the triads, thus

h, k
l, mt n,

and inquire if they dovetail, that is to say, if k<n<fm, and
h<m<^l. It is seen that 0, 4 dovetails two times, and 1, 3 four
times; that is, altogether, six times. The coefficient required is (3.

I had never attempted to deal with expansions of so high a
degree as a(0, 5, 13, 17) which is Professor Johnson’s example.
But the following will show that the work necessary for obtaining
three consecutive coefficients of this expansion is not heavy.

Second Example. — Required the coefficients of ^a1059cbi3,
3a1069c6^4, 5«1069c5c75 in the expansion of cc(0, 5, 13, 17).

Solution. — The groups are —

0 1 2 3 4

5 6 7 8 9 10 11 12

13 14 15 16

A

B

C

Pairs with sum 11, i.e. 1 + (3 + 7), and lowest member ^>3.

0,11; 1,10; 2,9; 3,8.

Triads from A, B and C with sum 22, i.e. 1 + 2 + (3 + 7 + 9).

0,6,16; 0,7,15; 0,8,14; 0,9,13;

1,5,16; 1,6,15; 1,7,14; 1,8,13;

2,5,15; 2,6,14; 2,7,13;

3, 5, 14; 3, 6, 13.

Number of dovetailings in the case of 0, 11 4,

)> )•>

55 55 55

55 55 55

which is the first coefficient required.

In finding the coefficient of 5a1069c6<i4 the integer 4 would not
be deleted in group A, and there would therefore be another triad
4, 5, 13. There would also be another pair 4, 17, and consequently

1, 10

8,

2, 9

11,

3, 8

12:

Total,

35,

Dr T. Muir on Simple Alternants .

1887.]

437

the number of dovetailings would be increased by 2 + 3 + 3 + 2 + 1,
i.e. 11; so that the coefficient in this instance would be 46.

In finding the coefficient of 2,a10b9c5d5 the only new point of
difference would be an additional pair, 5, 6. This would cause
1 + 1 + 1 + 1 additional dovetailings, and would consequently make
the coefficient 46 + 4, i.e. 50.

The method may sometimes be used to obtain more general
results. Thus —

Third Example , — Required the coefficient of %as~7b2c2d2 in the
expansion of a( 0, 1, 4, s), where of course s- 7 >2, that is, s>9.

0

1 2 3

4 5 s- 1

A

B

c

Duads: 0,

5;

1, 4; 2, 3.

Triads: 0,

1, 8;

0, 2, 7;

0, 3, 6.

Humber of dovetailings; 3 + 2 + 1, i.e. 6, which is the coefficient
required, and which, be it observed, is independent of s.

In this way have been obtained several important theorems, to
which I shall now pass. The first is —

The expansion of | cd>blS‘d?J+s | + 1 a°blc2d 3 | or a( 0 1 3 3 + s) con-
sists of all the single symmetric functions ivhicli have no index
greater than s, and the sum of whose indices is s+ 1, the coefficient
of each function being less by 1 than the number of different letters
appearing in any of its terms. (i.)

Tor example, to find the expansion of | a°blc^d7 | -f- 1 a%lc2d 3 | or
a(0 13 7) we subtract each index of the divisor from the corre-
sponding index of the dividend, and thus are led to the first of the
symmetric functions in the quotient, viz. Then writing

downthe succeeding symmetric functions %a%2^a%c, %a2b2ci % a2bcd ,
and prefixing to each a coefficient less by 1 than the number of
letters appearing in any term of the function, we have

a( 0 13 7) = + %a%2 + 2 ta%c + T%a2b2c + 3 ta2bcd.

The proof is as follows: — The only functions which can occur in
the expansion must be of the form 'SaabP, %aalAcy, faab^cyd8; conse-
quently all that we have to do is to determine the coefficients of

438

Proceedings of Royal Society of Edinburgh, [july 18,

these forms. The groups into which the integers from 0 to 3 + s

must be divided are

| 0 | 1 2 | 3 4 | 3+*

and for the case of %aabPcyds
the duads are

0, y + 8 + 1 ; 1 , y + 8 ; ; 8, y + 1 :

the triads

0, 1, /3 + y + 8 + 2; 0, 2, /3 + y + 8 + 1 :

and therefore the number of dovetailings 3, which is the required
coefficient.

For the case of %aab&cy the only duad is

0, y + 1 ;

the triads are

0, 1) 0 + y + 2 ) 0, 2,/3 + y+ l,

and consequently the number of dovetailings is 2, as was required
to be shown.

For the case of %aab&, there is again only one duad

0,1;

and two triads

0, 1,0+2; 0,2, 0 + 1:

and therefore manifestly only 1 dovetailing.

Our first theorem is thus established.

The second is — The expansion of \ a%2c3d3+s | + 1 a°blc2d 3 | or
a(0, 2, 3, 3 + s) consists of the single symmetric function 2; a*bc and
all the like functions succeeding it, the coefficient of every term
involving three letters being 1, and the coefficient of every term

involving four letters being 3 (ii.)

For example,

a( 0 2 3 6) = %a%c + %a2b2c + 3 %a2bcd .

Here only two forms of terms require to be considered, viz.
%aab$cy and %aab$cydP. The groups into which the integers
0, 1, 2, . . . . , 3 + s must be separated are

| 0 1 | 2 | 3 4 5 | 3 + *.

For the case of %aab$cyd8, the duads are

0, y + 8 + 1 ; 1 , y + 8 ; ; 8, y + 1 :

1887.] Dr T. Muir on Simple Alternants. 439

the triads are

0, 2, /? + y + S + l; 1, 2, f3 + y + S :

and consequently the number of dovetailings 3, as has been
asserted.

For the case of ^aalTcy, there is only one duad

0, y + 1 ;

two triads

0, 2, (3 + y + 1 ; 1, 2, /? + y ,

and therefore, as is at once seen, only 1 dovetailing. And this
establishes the theorem.

These two theorems and one well known before this (v. Theory
of Determinants, § 123) constitute an interesting group.

Denoting by crn the sum of all the symmetric functions whose
terms involve n letters and are of the sth degree, we may write the
third theorem referred to in the form

<x(0, 1, 2, 3 + s) — oq + <t2+ cr3 + <x4 .

But by the two new theorems

cc(0, 1, 3, 2 + s) = cr o + 2 <r 3 + 3?r4 ,

a(0, 2, 3, 1 + s) = or3 + 3 <t4 .

And again by the third theorem

a( 1 , 2, 3, .?) == d £ .

We can thus express oq, o-2, cr3, or4, in terms of the four functions
on the left, the result evidently being

oq = a(0 1 2 3 + s) - a(0 1 3 2 + s) + a{0 2 3 1 + s) - a( 1 2 3 s) ,

o-2= a(0 1 3 2 + s) - 2 . a(0 2 3 1 +*) + 3 . a(l 2 3 *) ,

q- t = a(0 2 3 1 + s) - 3 . a( 1 2 3s),

c r4= a(l 2 3 «) .

Of course if these last could be established independently, we
should have a very simple additional method of obtaining the
identities from which they are here derived.

The third theorem is — The expansion of

a{ 0, 1, q, r) - a( 0, 2, q, r - 1) + a( 1, 2, q, r - 2)

440

Proceedings of Boy cd Society of .Edinburgh. [july 18,

consists of the symmetric function %ar~3bq~2 and the like functions

succeeding it , the coefficient in every case being 1 (hi.)

For example,

a( 0 1 3 7)-a(0 2 3 6)+a(l 2 3 5)

= %a^b + 'ZPb2 + %as>bc + %a2b2c + %a?bcd ,

or, as we may for shortness’ sake write,

= [3a4& + ] .

Seeking first for the coefficient of 2,aabP we find that it is deter-
mined for a(0 1 q r) by considering

fO, 1,0 + 2

JO, 2,0 + 1

the cluad 0, 1 along with the triads -<J 0, 3, (3

i

lo, q-1, fi-q+i;

that it is determined for a( 0, 2, g, r— 1) by considering

(0, 2,/J + l

i 0, 3, /3

the duad 0, 1 along with the triads -[

[0, q-l, (3- q + 4:

fl 2 0

. I 1 3 (3-1

and the triads

[12-1 Z^-2 + 3;

and that it is determined for a(l, 2, q, r- 2) by considering

fl 2/5

I 1 3 (3-1

the duad 0, 1 along with the triads -J

[ 1 q-1 (3-q + 3.

Flow if the number of dovetailings in the first case be x, and in
the last case y, it is clear that in the second case they must be
( x — Y) + y: hence the coefficient of every term of the form in

a(0, 1, q , r) - a(0, 2, q, r - 1) + a(l, 2, q, r - 2) is 1 .

Next, the coefficient of %aab^(^ is determined for a(0, 1, q, r) by

considering

1887.]

Dr T. Muir on Simple Alternants.

441

the duad 0, y + 1 along with the triads ]

f 0, l,/? + y + 2

0, 2, f3 + y + 1

03 9. ~ + +

for a(0, 2, g, r - 1) by considering

the duad 0, y + 1 along with the triads ]

(0, 2, /? + y + 1

and the triads ]

^0, 2-1, /3 + y- 2 + 4

f 1? 2, fi + y

1, 3, /3 + y- 1

[ 1, 2-1, /3 + y~2 + 3;

and for a(l, 2, y, r — 2) by considering
the duad 0, y + 1 along with the triads <

1, 2, (3 + y

1 > 3, /3 + y - 1

[ 1, 2 ~ 1> /? + y “2 + 3 .

Hence, as before, the number of dovetailings is x\ (x' ) + y\
y ; and, therefore, the coefficient required is

x' - {(«'- 1 ) + y'} + yf
i.e. 1.

Lastly, the coefficient of '2ta(tbPcyds is determined for a(0, 1, q, r) by
considering

f 0, y + 8 + 1

[0, 1, /3 + y + 8+2

. . . . ll,y + 8 along with each 0, 2, /? + y + 8+l

each of the duads <

.... ot the triads <

IS, y+1

for a(0, 2, y, r - 1) by considering
f 0, y + 8 + 1

[0, 2-1, £ + y + S-2 + 4;

i

each of the duads -<

1, y + 8

along with each
of the triads

0, 2, /3 + y + 8+ l

| 0, 2 - 1 » /3 + y + 8~2 + 4

8, y + 1 [

/ 1, 2, /? -h y + 8

and along with each )

of the triads ) . n , Q

l 1, 2-1, p + y + 8-2 + 3;

442 Proceedings of Eoyal Society of Edinburgh, [july 18,

and for a(l, 2, q , r - 2) by considering

f 0, y + S + 1 f 1, /? + y + S

„ _ , ! l,y + S along with each I

eacn of the duads < ' <

of the triads |

S, y + 1 1^1, ^ — 1, /3-hy/ + S — <y + 3.

There is more trouble here in comparing the number of dovetail-
ing^ in the case of a( 0, 1, q, r) with the first set in the case of

a( 0, 2, q, r- 1), but the result is the same as before, viz. x" and

x" — 1 ; so that the coefficient is again 1.

And thus the theorem is established.

The case where q = r — 1 is important, as it furnishes a result
similar to those of the first two theorems. Putting <? = 2 + s and
r = 3 + s we obtain

ct( 0, 1, 2 + s, 3 + s) = + [] + n(0, 2, 2 + s, 2 -f- s) — ct(l, 2, 2 + s, 1 + s)

— + ] -f- 0 + ct(l 5 2, 1 + s, 2 + s)

= [5as6s + ] + abed . a(0, 1, s, 1 + s) ;

and as the a( ) on the right is the same function of s, as the
a( ) on the left is of s + 2, we see that by repeated application
of the result, the full expansion of a(0, 1, 2 + s, 3 + 5) in terms of
symmetric functions is obtainable. We have, in fact,

a(0, 1, 2 + s, 3 + s)

- + ] + abcd{\%as~2bs~2 + ] + abed . a(0, l,s-2, s-1)}

= + ] + [^as_15s-1c^ + ] + \^as~2bs~2c2d2 + ] + .... (iv.)

For example,

a(0, 1, 6. 7 ) = \%a4b4 + ] + \_^a3bhd + ] + \^a2b2c2d2 + ],

= 2a4b4 + 'Zct4b3c + %a4b2c2 + 2a4b2cd + 2 a3b3c2 + 2,a3b3cd + ~2a3b2c2d + %a2b2c2d2 \

+ 2a3b3cd + ~Za3b2c2d + '2id?b2(?d 2
+ 3,a2b2c2d2, J

= 2a4b4 + 2a4b3c + 2 a4b2c 2 + 2 a4b2cd + %(t3b3c2 + 2 '2a3b3cd + 2'Xa3b2c2d + 3 2a2b2c2

The fifth theorem is, in symbols,

a(0, 2, 2+s, 3 + s) - a(l, 2, 1 + s, 3 + s) = \%asbsc + ] . . (v.)

The only point of the proof which requires care is where the
dovetailings of the

1887.]

Dr T. Muir on Simple Alternants.

443

duads

\ 0, y + 8 + 1

j 7 + S

< 2, y + 8 - 1

L ^ 7 + 1

with the triads

0, /5 + y + 8 — s f 1, 2+5

1, /l + y + 8 — S , 2 + 5

have to be shown to be 1 more than those of the same duads

with the triads j + y + ^ s + 1, 1+5
* 1, /? + y + 8 - 5, 2 + 5.

The second triad in the two cases being the same may be neglected ;
and then we have only to note that the middle elements of the
remaining triads are the same, and that the final elements 2+5
and 1+5 are, for the purpose in view, as good as if they were the
same, because the lesser of them is greater than y + 8.

Returning now to the third theorem, and putting q = 2 + 5, and
r 4 + 5 we have

0, 1,2 + 5, 4 + 5) = 1b' + ] + ct(0, 2, 2 + 5, 3 + 5) — ct(l, 2, 2 + 5, 2 + 5).

But by the preceding theorem (v.)

ct(0, 2, 2 + 5, 3 + 5) = \%asbsc + ] + abed . a(0, 1,5, s + 2) .

Hence

a(0, 1,2 + 5,4 + 5) = p&s-1&s+ ] + [3«s&sc + ] + aM.a(0, 1,5,5 + 2) (vi.)

— a theorem which enables us to write down the full expansion
of a(0, 1, 2 + 5, 4 + 5) in terms of symmetric functions, because
«(0, 1, 5, 5 + 2) is the same function of 5 that a(0, 1, 2 + 5, 4 + 5) is of
5+2.

Further, the fifth theorem, with the help of the expansion just
obtained, gives us the like expansion for a(0, 2, 2 + 5, 3 + 5) .

All the theorems assist materially in lightening the labour of
tabulating the expansions of the a functions. The following are
the tables for the functions of order 4 and degrees 1 to 9.

Degree 1.

a(0124) = %a.

cc(0125 ) = ta‘1 + tab.
(0134)= %ab.

Degree 2.

444

Proceedings of Eoyal Society of Edinburgh, [july 18,

Degree 3.

a(0126) = 4- 4- %abc.

a(0135) = %a?b + 2 %abc.
a(0234) = %abc.

Degree 4.

a(0127) — + %Pb + ^odb2 + 5 a2bc + %abcd .

a(0136) = %a% + ta2b2 + 2 %a2bc + Seabed.

a(Ol 45) = %a2b2 + S cdbc + 2 %abcd.

a( 0235)= %cpbc 4- Seabed.

« ( 1 234) = %abcd.

Degree 5.

a(01 28) = ^a5 4- Scdb 4- %a%2 + %cdbc + 1ta2b2c 4- garbed.
a(0137) = %Pb 4- %a?b2 4- 2 %a*bc + 2 %a2b2c 4- 3 %a2bcd.
a(0 1 46) = %a2b2 4- %a%c + 2 %a2b2c 4- 3 %a2bcd.

a(0236) = 2Pbc+ %a2b2e + ?>%a2bcd.

a(0245) = %a2b2c 4- 2 HaPbcd.

a(1235)= %a2bcd.

Degree 6.

2«6

2a56

'S.cdbc

2fts63

2orb-c

~%o?bcd

2aW

%1b~cd

a(0129)

1

1

1

1

1

1

1

1

1

a(0138)

1

1

2

1

2

3

2

3

o(0147)

1

1

1

2

3 .

3

4

a(0237)

1

0

1

3

1

3

a(0156)

1

1

1

1

2

a(0246)

1

2

2

4

a(1236)

1

0

1

a(0345)

1

1

a(1245)

1

1887.]

Dr T. Muir on Simple Alternants.

445

Degree 7.

7000

0100

5200

a(01210)

1

1

1

a(0139)

1

1

o(0148)

a(0238)

a(0157)

a(0247)

a(1237)

a(0256)

a(0346)

a(1246)

a(1345)

1

5110

4300

4210

4111

1

1

1

1

2

1

2

3

1

1

2

3

1

0

1

3

1

1

1

1

2

1

3310

3220

3211

2221

1

1

1

1

2

2

3

3

2

3

4

5

1

1

3

3

2

2

3

4

1

2

4

6

0

0

1

1

1

1

2

3

1

1

3

1

2

1

Degree 8.

8000

7100

6200 6110

5300

5210

5111

4400

4310

4220

4211

3320

3311

3221 2222

a(01211)

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

a(01310)

1

1

2

1

2

3

1

2

2

o

O

2

3

3

3

«(0149)

1

1

1

2

3

1

2

3

4

3

4

5

6

a(0239)

i

0

1

3

0

1

1

3

1

3

3

3

a(0158)

1

1

1

X

1

2

2

3

3

4

5

6

a(0248)

1

2

0

1

2

4

2

4

6

8

a(1238)

1

0

0

0

1

0

1

1

1

a(0167)

1

1

1

1

1

2

2

3

a(0257)

.

1

1

2

2

4

5

7

a(0347)

1

1

1

1

3

6

a(1247)

1

0

1

2

3

a(0356)

1

1

2

3

a(1256)

1

1

2

a(1346)

1

3

a(2345)

1

Degree 9.

9000

8100 7200

7110

6300

6210

6111

54005310

5220

5211

4410

4320

4311

42213330

3321

3222

a(01212)

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

a(01311)

1

1

2

1

2

3

1

2

2

3

2

2

3

3

2

3

3

a(01il0)

1

1

1

2

3

1

2

3

4

<r>

3

4

5

3

5

6

a(02310)

1

0

1

3

0

1

1

3

l

1

3

3

1

3

3

a(0159)

1

1

1

1

2

2

3

2

3

4

5

4

6

7

a(0249)

1

2

0

1

2

4

1

2

4

6

2

6

8

a(1289)

1

0

0

0

1

0

0

1

1

0

1

1

a(0168)

1

1

1

1

2

2

3

3

2

4

5

a(0258)

1

1

2

1

2

4

5

3

7

9

a(0348)

1

1

0

1

1

3

1

3

6

a(1248)

1

0

0

1

2

0

2

3

<x(0267)

1

1

2

2

1

3

4

a(0357)

1

1

2

2

4

6

a(1257)

1

1

0

2

3

a(1347)

1

0

1

3

a(0456)

1

1

1

a(1356)

1

2

a(2346)

1

446 Proceedings of Royal Society of Edinburgh, [july 18,

15. Eemarks by the Chairman on Closing the Session.

I am told by our Secretary, whose authority on such a subject I
dare not venture to dispute, that on this the last meeting of the
Session, the duty falls on the retiring Vice-President of making a
few remarks on the business of that Session, including some infor-
mation as to the number of new and of deceased Fellows, the papers
that have been read on each subject, and other similar information.

This duty I now proceed, to the best of my power, to discharge.

It will, I am sure, be gratifying to the members to be told that
the supply of papers during the present Session has been even
more ample than on former occasions, and I trust that we are not
guilty of undue vanity in believing that the contributions of this
year show the same deep and patient research, the same knowledge
of what has already been done, both in this country and abroad,
and the same mastery over the latest and best methods of mathe-
matical and physical investigation, which have hitherto distinguished
the Fellows of this Society, and have given value to its transactions
in the estimation of similar learned institutions elsewhere.

As matter of statistics, it may be noted that in Physics the
number of papers read has been 22, in Mathematics 8, in Astronomy
6, Meteorology 7, Engineering 2, Chemistry 6, Physical Geography
3, Anatomy and Physiology 10, Botany 2, Biology 6, Geology and
Palaeontology 4, Political Economy 1.

It is also satisfactory to know that of late numerous candidates
have sought admission to Fellowship. During the last Session 36
were admitted as Fellows ; in the present the number has been
35. Many of these are men of high promise, and not a few have
already given evidence of scientific ability by the papers they have
published in our Proceedings and Transactions.

On the other hand, death has, since the opening of the Session,
made serious inroads on our ranks. Since last November nine
Fellows of our Society have died.

When among these I mention the name of Thomas Stevenson, it
is impossible not to think with sadness how short a time has run
since, as the valued President of our Society, he occupied this chair,
and from it delivered addresses to which we listened with instruction

1887.]

The Chairmans Address.

447

and pleasure. Those who heard him on these occasions, and those
who were associated with him in the discharge of the Society’s
business, must all deeply regret that his tenure of office was so
short, and that the close of his life came so soon. Born of a
family to whom we owe the wonderful advance which has taken
place in the science of lighthouse-illumination, it was his fortune to
carry to still further perfection that branch of scientific knowledge
which had been so handed down to him, a branch of knowledge, it
need scarcely be added, among the most admirable in its practical
results, providing not for one nation alone but “in salutem omnium ”
for the mariners and the argosies of all nations, a series of star-like
guides over the otherwise trackless ocean. It has been said in an
able and affectionate filial tribute to his memory, which I cannot
resist quoting, that “ his lights were in every part of the world guid-
ing the mariner ; his firm were consulting engineers to the Indian,
the New Zealand, and the Japanese Lighthouse Boards; in Germany
he had been called the Nestor of lighthouse-illumination; even in
France, where his claims were long denied, he was at last, on the
occasion of the late Exposition, recognised and medalled.” Few
men, it has also been truly said, were more beloved in Edinburgh,
where he breathed an air that pleased him; and I am sure few
men have ever been more highly regarded by this Society than our
late President.

It is with feelings of deep and unfeigned regret that we recall
the loss which the Society has suffered in the death of Mr Robert
Gray. We all feel that in him we have lost a warm personal
friend. He was the highest authority on Scottish Ornithology, and
had a large and accurate acquaintance with other branches of natural
history. He was Secretary of the Royal Physical Society, and by
his able and energetic management may almost be said to have
given it a new lease of life. He rendered valuable service to our
own Association, which devolved on him some of its most delicate
and difficult business. His bright and genial presence will long
and regretfully be missed at the meetings of this Society and its
Council.

The brilliant early career of Adam Gifford, both at the bar and
on the bench, and the affecting circumstances under which that
career was ended, as it were in the noontide of life, are familiar to

VOL. XIV. 31/1/88 2 F

448

Proceedings of Royal Society of Edinburgh. [july 18,

many whose tastes lie altogether outside of the profession which he
adorned. But Lord Gifford was not a lawyer merely ; and during
those years when the shadow of death was upon him he had, along
with other and higher consolations, the ample stores of philosophy
and poetry, and the varied studies of earlier years.

By the death of Alexander Gibson, advocate, Secretary of the
Educational Endowments Commission, the public service, as well
as his many personal friends, have suffered a loss which will not
easily be repaired. Born at Kirkcaldy — the birth-place, as I need
not remind this learned audience, of Adam Smith, the founder of
Political Economy as a separate branch of human knowledge, — like
Smith, young Gibson received the first of his education at the
burgh school of that town. Graduating afterwards in Arts in the
University of Edinburgh, he took an active part in the Diagnostic
Society, and speedily gained the reputation of a student of great
acuteness and of wide reading, both in literature and in law. He
was also much interested in natural philosophy and science, and
in that department of his professional knowledge which Leibnitz, at
once a jurist and a mathematician, pronounced to rank next to
geometry in the soundness of its principles and the certainty of its
conclusions, the noble system of equity of the Roman law. I
quote his words — “ I have often said that after the writings of
geometricians there exists nothing which, in point of strength,
subtility, and depth, can be compared with the works of the Roman
lawyers” (Dugald Stewart’s Works, by Hamilton, vol. i. p. 186,
1854).*

But to return from this digression. “ Time and the hour ” forbid
my making more than passing mention of many names of which I
should willingly have said more in this place.

Mr William Denny of Dumbarton was a distinguished naval
constructor, and, as such, a large employer of labour. He took a
keen interest in the improvement of the working classes, and his
death caused a widely felt sorrow among a large circle of friends,
not in this country only but abroad.

* Dixi ssepius, post scripta geometrarum, nihil extare quod vi ac subtilitate
cum Romanorum jureconsultorum sci'iptis comparari potest tantum nervi
adest tantum profunditatis (Leibnitz’ Works, by Dutens, vol. iv. part 3,
pp. 267, 268).

1887.]

The Chairman’ s Address.

449

Mr James Pringle, who at the time of his death was Provost of
Leith, received his education at the High School of Edinburgh, and
was distinguished by his aptitude for classics. During his long
connection with Leith he took a prominent part in promoting all
its interests, and as chief magistrate rendered important services to
the town.

Dr William Brown, who died in January last, was, I believe, the
oldest member of this Society, having been admitted in 1835. He
had filled the office of President of the Eoyal College of Surgeons,
and enjoyed a high reputation as a consulting physician.

Dr Butherford Haldane, LL.D., was one of the most respected
members of the medical profession in Edinburgh. After leaving
our University he went abroad, for further study, to Vienna and
Paris, spending eighteen months in the French capital. He became
successively a lecturer on Pathology and on the Practice of Medicine
in the Extra-Mural School. By his professional brethren he was
regarded as an authority on all medical questions. He was a man
of great learning; and his early death cannot fail to be much
regretted by the Society.

The Eev. Francis Le Grix White, although, from residence at a
distance from Edinburgh, personally but little known to many of
us, kept up correspondence with the Society, was a man of varied
accomplishments, and took an active part in organising scientific
lectures in Cumberland and Westmoreland. He also promoted
everything which tended to elevate those classes over whom his
influence extended.

It only now remains for me to acknowledge the valuable help
which I have received in the preparation of these notes from our
friend Mr Gordon.

16. Minute of Meeting of Special Committee on the
Victoria Jubilee Prize, 27th June 1887.

Victoria Jubilee Prize, founded by Dr Gunning of Eio Janeiro

This Prize, founded in 1887, consisting of the interest of £1000,
is to be awarded triennially by the Council of the Eoyal Society of
Edinburgh.

450 Proceedings of Boy al Society of Edinburgh, [july 18,

The Prize is to be given in recognition of original work in Physics,
Chemistry, or Pure or Applied Mathematics.

Evidence of such work may be afforded either by a paper pre-
sented 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 is open to men of science resident in, or connected with
Scotland.

The first award shall be in the year 1887, and shall consist of a
sum of money. In accordance with the wish of the donor, the
Council of the Society may on fit occasion award the Prize for work
of a definite kind to be undertaken during the succeeding three
years by a scientific man of recognised ability.

Before entering on the last of the subjects of this evening’s
meeting, it will interest you to learn that, heartily joining as we
all do in the loyal and affectionate homage of the whole nation on
the completion by the Queen of the 50th year of her happy and
beneficent reign, the following Address has been forwarded to the
Secretary of State for presentation, the arrangements not permitting
its presentation by our President : —

“ Madam, may it please your Majesty, — We, the President and
Council of the Boyal Society of Edinburgh, humbly address your
Majesty on this, the 50th anniversary of your Majesty’s illustrious
reign, and desire to express, on behalf of the Society, their loyal
attachment to your Majesty, and to the institution of the Crown,
represented in the person of our present gracious and distinguished
Sovereign.

“ The Royal Society of Edinburgh was constituted in the year
1782, for the promotion of scientific and literary research, by a
Charter from King George the Third. In times past it has counted
amongst its members many statesmen, and men of letters and
science, who have discussed freely the public and political questions
of the times. But on one subject there has happily been entire
unanimity — the maintenance of the principle of constitutional
monarchy as established in the British Empire under the guidance
of your Majestv and your Royal predecessors.

1887.] Minute of Committee — Victoria Jubilee Prize .

451

“ We are deeply sensible of the advantages which, we have derived,
during the past fifty years of social and legislative progress, from
the presence, at the head of the affairs of this great Empire, of
a Sovereign who is dissociated from the contentions of political
parties, and is possessed of those high personal qualities which
enable the Crown to exert a moderating and controlling influence in
the public life of the country.

“ As a Scottish Society, we claim a share in the sentiments of pride
and loyal attachment which your Majesty’s personal relations with
Scotland have evoked in the hearts of our fellow-countrymen. We
trust that your Majesty may long continue to derive health and
solace from annual visits to your Majesty’s Highland home ; and
we at the same time regard your Majesty’s gracious presence amongst
us as a guarantee of that interest in, and knowledge of our distinc-
tively national affairs, which, as Scotsmen, we most highly value.

“ In addressing the Royal Successor of the ancient Scottish
Sovereigns, who in troubled times ruled this country with courage
and ability, we may conclude by offering to your Majesty our most
respectful and loyal congratulations on the good fortune, peace, and
prosperity which have hitherto accompanied your Majesty’s brilliant
and eventful reign ; and by expressing the hope that the interests
of science and learning, with which this Society is connected, and
whose marvellous development has been one of the characteristic
features of that reign, may continue to flourish, as heretofore, under
your Majesty’s gracious encouragement and protection.

Signed on behalf of the Council of the Royal Society of
Edinburgh.

June 1887.

William Thomson, President.

452

Proceedings of Royal Society of Edinburgh. [july is.

17. The Theory of Determinants in the Historical Order of
its Development. By Thomas Muir, M.A., LL.D.

Part I. (continued). Determinants in General (1779-1812).

Now it is at once manifest that the successive developments here
obtained of the determinant \xyzt\ are letter by letter identical with
the successive “ lignes ” obtained by Bdzout from the unreal product
xyzt ; but that instead of having one arbitrary step succeeding
another, as in the application of Bezout’s rule, there is here a fluent
reasonableness characterising the whole process.* As for the
peculiarities requiring elucidation in the series of special examples
above referred to, they are seen, when looked at in this light, to be
but matters of course.

Not only so, but it will be found that the translation of xy into
\xy\ &c., is an unfailing key to much that follows in Bdzout in con-
nection with the subject. Por example, let us take the wide exten-
sion of the rule which is expounded later on in the treatise, in a
section headed

* If the fact at the basis of the process were made use of nowadays, it would
be advantageous, of course, in the first instance to simplify the determinant as
much as possible. For example, the equations being (Bezout, p. 178)

2x + 4?/ + 5s = 22 \

3a? + 5y + 2s=30 (

5x + 6y + 4s=43 ) ,

we might proceed as follows: —

2

4

5

-22

0

2

n

-6

3

5

2

-30

=

1

1

— 3

-8

5

6

4

-43

0

-3

-3

9

X

y

z

t

X

y

z

t

0

0

9

0

0

0

1

0

1

0

-4

-5

= 27

1

0

0

-5

0

-1

-1

3

0

-1

0

3

X

V

z

t

X

y

z

t

27 { t + Oz 3 y — 5^| ;
whence x = 5, y=3, z= 0.

1887.] Dr T. Muir on the Theory of Determinants.

453

Considerations utiles pour abreger considerablement
le calcul des coefficients qui servent a V elimination.

There are in all fifteen pages (pp. 208-223, §§ 252-270) devoted to
the subject. The contents of three paragraphs will give a suffi-
ciently clear idea of the nature of the whole. The notation used is
identical with that of Laplace, e.g .,

(ah') = ad - a’b ,

(add') = {ad - a'd)c" - {ad' - a"b)c' + (a'b" - a"d)c ,

Two of the three selected paragraphs stand as follows : —

“ (264.) Cette maniere de proceder au calcul des inconnues,
en les grouppant, n’est pas applicable seulement a notre objet;
elle peut en general etre appliquee dans toutes les equations du
premier degre.

“ Si l’on avoit, par exemple, les quatre equations suivantes

ax + by +cz + dt +e =0,

ax -{-by -f- c z -{- d t -{- e — 0,

a!'x + b"y + cz + d"t + e" = 0,

a"'x + d"y + c"z + d"'t + e'" = 0.

En se rappellant que chaque inconnue a pour valeur le coeffi-
cient qu’elle se trouve avoir dans la derniere ligne , divise con-
stamment par celui que l’inconnue introduite aura dans cette
meme ligne , on verra bientot qu’on peut reduire le calcul a
chercher le coefficient de Tune quelconque des inconnues dans
la derniere ligne ; parce que de la meme mani&re qu’on en aura
calcuffi un, on calculera de meme tous les autres : ou meme,
lorsqu’on en aura calcuffi un, on pourra en deduire tous les
autres, lorsque les equations auront toute la generalite possible.
Or pour avoir la valeur du coefficient d’une des inconnues dans
la derniere ligne, la question se reduit a calculer la valeur du
produit des autres inconnues. Mais pour ne pas se tromper
sur les signes, il faudra toujours ne pas perdre de vue, la place
que cette inconnue est censee occuper dans le produit de toutes
les inconnues. Ainsi, dans le cas present, au lieu de calculer
generalement la derniere ligne pour avoir xyztu , je calcule

454

Proceedings of Royal Society of Edinburgh. [july 18,

settlement cette derniere ligne pour yztu : et pour 1’avoir de la
maniere la plus commode, je grouppe en cette maniere yz.tu , et
je procede comme il suit, au calcul des lignes, observant que y
est cense a la seconde place.

Premiere ligne. - bz.tu-yz. die,

Seconde ligne. + {bc').tu-bz.d'u + b'z.du + yz.{de'),

Troisieme ligne. - {bc').d"u + {bc").d’u - bz.{d'e") - { b'c").du + bfz.{de ") - b"z.(der),
Quatrieme ligne. + {be'). {d"e'") - {be"), {d'e'") + {be"’), {d'e") + {b'c"). {de’")

-{b>c,").{de") + {b"c"').{de')-,

e’est le coefficient de x dans la derniere ligne.

“Pour avoir celui de u, je calculerois de meme la valeur de
xyzt. en le grouppant ainsi, xy.zt, et je trouverois pour valeur
du coefficient de u dans la derniere ligne, la quantite

i

(aV) . (c'd'") - (ab") . (c'dm) + (ah'") . (c'cl") + (a'b") . (cd'")

- (a’b'") fed") + (a"b'”).(cd');

“ D’oii je conclus

+ {be') . (d"e'") - {be") . {d'e'") + {be"') . {d’e") + {b'c") . {de"’) - pc'") . {de") + (b"c'") . {de')
= {ab') . { c"d '") - {ab"). {c'd'") + {ab"') . {dd") + {a'b"). {cd!") - {a'b"') . {cd") + {a"V") . {cd')

et ainsi de suite.

“ (265.) Si j’avois les cinq equations suivantes —
ax + by + cz +dr +et +f =0,
a'x + b'y + d z +d'r +eft +/' =0,
a"x + bny + c"z + dnr + e"t + /" = 0,
a'"x + bmy + c"fz + dmr + e'”t + = 0,

aiyx + bivy + cwz + cPr + eu’t + f*r = 0.

Je calculerois, par exemple, le coefficient de x dans la derniere
ligne, en calculant yzr.tu , ou yz.rtu , on yz.rt.2i.

“ Si j’avois six equations dont les inconnues fussent x, y, z, r, s
et t , je calculerois, par exemple, le coefficient de x, en calcu-
lant ou yz.rs.tn , ou yzrs.tu, ou yzr.stu , et ainsi de suite,”

The next paragraph deals with an illustrative example. The
twelve equations —

1887.] Dr T. Muir on the Theory of Determinants.

455

Aa + A' a' + A" a" =0

Ab+A'b' + A"b" =0

Ac + A’c’ + A"c" + Ba + B'o' + B "a" = 0

+ B5+B'6' + B"5" =0

+ Bc+ B'e'+BV =0

+ B d + B 'd' + B"ci" + C a + C 'a + C "a" = 0

+ C6 + C'6' + C"b" =0

+ Cc + C V + C"c" = 0

+ C d + C 'cl' + C"d" + Da + D'a' + D "a" = 0

+ D6 + D'&' + D"i" = 0
+ Dc + DV + D"c" = 0

Ad + A'd' + A "d" + Da + D 'a + D"a" = 0

are given, and what is required is the result of the elimination
( equation de condition ) of the twelve quantities — -a,a',a",b,b',b‘',c,c',
c",d,d',d". This is found to he —

(ab'c").[(bc'd")s - ( ab'c"Y-{ab'd ")} = 0.

The two paragraphs quoted (§§ 264, 265) show that Bezout
could obtain with considerably increased ease and certitude any one
of Laplace’s expansions of numerator and denominator. What it
accomplished in the illustrative example is virtually, in modern
symbolism, the reduction of

a

t

a

a"

b

y

b"

•

•

•

•

•

•

c

c

Jt

c

a

a

a'

•

.

•

b

V

b"

•

•

•

c

c

n

c

•

«

.

d

d!

d"

a

a

a'

#

b

V

b"

•

c

c

ft

c

•

•

d

d!

d"

d

d'

d"

•

/ „ ff

a a a

b V b"

t n

c c c

a a a"

to the form

456 Proceedings of Royal Society of Edinburgh. [july 18,

Although this can he done nowadays with ease by means of
Laplace’s expansion-theorem in its modern garb, it may be safely
affirmed that Laplace himself, using his own process, would not have
succeeded in making the reduction. Considerable importance thus
attaches from more than one point of view to Bezout’s curious
“ rule.”

The only other section with which we are concerned bears the
heading

Methocle 'pour trouver des fonctions ddun nombre
quelconque de quantites, qui soient zero par elles-
memes.

In the second paragraph of the section the principle is explained as
follows : —

“(216) Concevons un nombre n d’equations du premier degre
renfermant un nombre n + 1 d’inconnues, et sans ancun terme
absolument connu.

“ Imaginons que 1’on augmente le nombre de ces equations, de
l’une d’entr’elles; alors il est clair que ce que nous appellons la
derniere ligne, sera non seulement 1’equation de condition
necessaire pour que ce nombre n+ 1 d’equations ait lieu ; mais
encore que cette equation de condition aura lieu; en sorte
qu’elle sera une fonction des coefficiens de ces equations, la-
quelle sera zero par elle-meme.

“ Voila done un moyen tres-simple pour trouver un nombre
?z+l* de fonctions d’un nombre n+ 1 de quantites, lesquelles
fonctions soient zero par elles-memes.”

For example, the pair of equations

ax+by +cz =0 )
a'x + b'y + cz = 0 J

is taken, the first equation is repeated, and for this set of three
equations the equation de condition is found to be

( at > - ab)c - {ad - a!d)b + {be - b'c)a = 0 .

“ Or il est clair que la troisieme equation n’exprimant rien
de different de la premiere, cette derniere quantite doit etre
zero par elle-meme : done si on a ces deux suites de quantites

* Should be n.

1887.] Dr T. Muir on the Theory of Determinants.

457

b, c

t -it t

a , u , c

on peut etre assure qu’on aura toujours

( ab' - ab)c - (ac — a'c)b + (be - b'c)a = 0 .

“ Et si au lieu de joindre la premiere equation, c’eftt ete la
seconde, nous aurions trouve de meme

(ab' - a'b)c - (ac - a'c)b' + (be' - b'c)a = 0.”

Similarly in regard to the quantities

a , b, c, cl

a\ b', c\ d'

„tl iff ft itt

a , o , cy a

the identity

\(ab' — ab) c" - (ac — ac) b" + (be' - b'c) anl\d

- [(ab' - a'b)d" - (ad' - a'd)b" + (bd' - b'd)a"]c
+ [(ac - a'c) d" — (ad' - a'd)c" + (cd' — cd) a"~\b

- [(be - b'c) d" - (bd' - b'd) c" + (cd' - c'd) b"]a = 0

and two others are established, the general theorem of course being
merely referred to as easily obtainable.

Thus far there is in substance nothing new. What we have
obtained is simply a different aspect of Vandermonde’s theorem,
that when two indices of either set are alike the function vanishes , or,
as we should now say, a determinant with two rows identical is
equal to zero. Indeed the identities are used by Vandermonde in
Bezout’s form when solving a set of simultaneous equations. But
what follows is important.

By taking two of these identities

(ab' - a'b)c - (ac' — ac)b + (be - b'c)a = 0
(ab' - ab)c - (ac - a'c)b' + (be' - b'c)a = 0 ,

multiplying both sides of the first by d\ both sides of the second
by d, and subtracting, there is obtained in regard to the quantities

a, b, c, d
a\ b\ c , d'

the identity

(ah' - a'b)(ed' - c'd) - (ac - a'c)(bd' - b'd) + (be - b'c)(ad' - a' cl) — 0 .

458 Proceedings of Royal Society of Edinburgh. [july is.

Similarly by taking the three next identities before obtained,

which for shortness we may write in modern notation,

«/ /

\ab'c"\d -

- \ab'd"\c

+ 1 ac d \b —

| bcd"\a —

0,

\ab'c"\d' -

- \ab'd!'\d

+ \acd"\b' -

\bc'd"\a' =

0,

| ab'c"\d" -

- \ab'd"\c"

+ \acd"\b" -

\bc'd"\a" =

0,

there is

deduced in regard to the quantities

a, b,

c, d, e

)

a ', If

c', d\ e

/

a", b\

cf d", e

the identities

\ab'e" |

. \dd |

- \ab'd!

j.|ce' | +

\ac'dn\ . | bef |

- \bc'd"\

. | ae |

= 0,

\ab'c"\

. \de" |

— | ab'd!

j.|ce"| +

\add"\.\be” \

- \bcd"\

. | ae" |

= 0,

\ab'c" |

. \d'e"

| - | ab'd

"|.|cV'| +

\ac’d"\.\b'e"\

\ - \bc'd"\

. \ae"\

= 0.

Finally these last three identities are taken, both sides of the first
multiplied by /", both sides of the second by-/', both sides of
the third by f and then by addition there is obtained in regard to
the quantities

a , b ,

a', b',

af bf

the identity

\ab'e'\.\def"\ - \ab'd''\.\ce'f"\ + \acd"\.\bef"\ - \bcd"\.\ae'f"\ = 0.

c, d, e, f

f it t /•/

^ 5 ^ 5 ^ 5 af

// iff ft aft

c , d , e , /

The subject of what may appropriately be called vanishing aggre-
gates of determinant-products is not pursued farther, the concluding
paragraph being

“ (223) En voila assez pour faire connoitre la route qu’on doit
tenir, pour trouver ces sortes des theoremes. On voit qu’il y
a une infinite d’autres combinaisons a faire, et qui donneront
chacune de nouvelles fonctions, qui seront zero par elles-memes :
mais cela est facile a trouver actuellement.”*

* It is very curious to observe, in passing, that although Bezout does not
obtain all his vanishing aggregates directly by means of the principle which
he so carefully states at the commencement, nevertheless every one of them
can be so obtained. He does not extend the principle beyond the case where
only one of the original equations is repeated. If, however, we take the
equations

ax + by +cz + die = 0 ,
a'x + b'y + c'z + d'tv = 0 ,

459

1887.] Dr T. Muir on the Theory of Determinants.

Our second list of Bezoub’s contributions thus is: —

(1) An unexplained artificial process for finding the numerators

and denominators of fractions "which express the values of the
unknowns in a set of linear equations, or for finding the resultant
of the elimination of n quantities from n 4- 1 linear equations, — a
process especially useful when the coefficients have particular
values. (n. 3 + hi. 4 + iv. 2.)

(2) An improved mode of finding Laplace’s expansions, especially

(but not exclusively) useful when the coefficients have particular
values. (xiv. 3.)

(3) A proof of Vandermonde’s theorem regarding the effect of

the equality of two indices belonging to the same set. (xii. 3.)

(4) A series of identities regarding vanishing aggregates of

products. (xxiii.)

HINDENBURG, C. F. (1784).

[/ Specimen analyticum de lineis curvis secundi ordinis , in delucida-
tionem Analyseos Finitorum Kaestneriance. Auctore Clvristiano
Friderico Riidigero. Cum praefatione Caroli Friderici
FLindenburgii, professor is Lipsiensis. (xlviii + 74 pp.) pp. xiv-
xlviii. Lipsiceff

One of the problems dealt with by Biidiger being the finding
of the equation of the conic passing through five given points
(“ coeffcientium determinate Traiectoriae secundi ordinis per data
quinque puncta ”), Hindenburg, in his preface, takes occasion to
show how the generalised problem for \n{in + 3) points has been
treated, pointing out that it is, of course, immediately dependent
on the solution of a set of simultaneous linear equations. He directs
attention to the labours of Cramer and B4zout, specially lauding
the method of the latter, given in the treatise of 1779. Then he

repeat both of them so as to have a set of four, and then proceed by the
methode pour abreger to find the equation de condition , we obtain

\ab'\.\cd'\ - \ac'\.\bd'\ + \ad'\.\bc’\+ \fict\.\ad'\ - \bd'\.\ac'\ + \cd'\.\ab'\ = 0,

i.e. <i[\ab,\.\cd'\ - \ac'\.\bd'\ + \ad'\.\bc'\} = 0.

This is the identity at foot of p. 457, and all the others are readily seen to be
obtainable in the same way.

* My best thanks are due the Committee of Management of University Col-
lege, London, for the loan of a copy of Hindenburg’s tract from the Graves
Library.

460 Proceedings of Royal Society of Edinburgh. [july is,

says — “ Hctec de Opere Bezoldino in universam, quod plurimis
adhuc Lectoribus nostris ignotum erit , dicta suffciant. Nunc
Regulam ipsam proponam .”. . . . The seventeen pages which
follow, contain a tolerably close Latin translation of the Regie
generate pour calcider . , and the Methode pour trouver . . . ,

pp. 172-187, §§ 198-223, which have been expounded above.
Cramer’s rule is next given, the second mode of putting it being-
in words, and the first as follows: —

“ Sint plures Incognitse z , y, x , w , &c. totidemque Aequa-
tiones simplices indeterminate

A1 = Zh + Y ly + XL: + W % + &c.

A2 = Z2z + Y 2y + X2x + W 2w + &c.

A3 = Z% + Y3y + X3x + W hv + &c.

A4 = ZH + Y 4y + X% + W% + &c.

Ac. Ac. Ac. Ac. Ac. &c.

Erit, , positis terminorum signis, ut praecipitur in

fine Tabulse, pag. seq.

AYXWVUT (vn. 3.)

_ Permut (1, 2, 3, 4, 5, 6, 7, )

Perrnut (1, 2, 3, 4. 5, 6, 7, ... . .)
ZYXWYUT ”

The similar expressions for y , x, w, v, u, t, are given, and then the
“ regula signorum .” After an illustrative example, the question of
the sequence of the signs is taken up.

“ Quod si itaque +%/(!, 2, 3, . . ., n) denotet signorum
vicissitudines, quibus hie afficiuntur Permutationum a numeris
1, 2, 3, . . . n singulse species, et-sp(l, 2, 3, . . . n) signa
contrarict vel opposita : appatet fore

sp(l,2) = +*fif(l) -^(0

s^(l, 2, 3) =+^(1,2) -^(1,2) +sg( 1,2)

sg( 1, 2, 3, 4)= + sp(l, 2, 3) - sp(l, 2, 3) + ^(l, 2,3)-sg(l, 2, 3)

unde, quia S£/(l) est +, facile eruitur

sp(l, 2) esse H —

sg(l, 2, 3) . ... -\ + 4 —

6^(1, 2, 3, 4). . . .+ + + + + +

+ -f + -t- + +

461

1887.] Dr T. Muir on the Theory of Determinants.

and it is pointed out that the first sign is always + , and the last
+ or - according as the number 1 + 2 + 3+ . . . + (?z - 1) is even
or odd.

Bearing in mind that Hindenburg wrote his permutations in a
definite order, this remark regarding the sequence of signs entitles
us to view him as the author of a combined rule of term-formation
and rule of signs, which may he formulated as follows: —

Write the permutations of 1, 2, 3, . . ., n in ascending order of
magnitude as if they were numbers; make the first sign + , the
second — , the next pair contrary in sign to the first pair , the th ird
pair contrary in sign to the second pair, the next six (1.2.3) contrary
in sign to the first six , the third six contrary in sign to the second six,
the fourth six contrary in sign to the third six, the next twenty -
four (1. 2.3.4) contrary in sign to the first twenty-four , and so
on. (n. 4 + hi. 5.)

ROTHE, H. A. (1800).

[Ueber Permutationen, in Beziehung auf die Stellen ihrer Elemente.
Anwendung der daraus abgeleiteten Satze auf das Eliminations-
problem. Sammlung combinatorisch-analytischer Abhand-
lungen, herausg. v. C. F. Hindenburg, ii. pp. 263-305.]

Rothe was a follower of Hindenburg, knew Hindenburg’s preface
to Rudiger’s Specimen Analyticum, and was familiar with what had
been done by Cramer and Bezout (see his words at p. 305). His
memoir is very explicit and formal, proposition following definition,
and corollary following proposition, in the most methodical manner.

The idea which is made the basis of it, that of place-index
(“ Stellenexponent ”), is an ill-advised and purposeless modification
of Cramer’s idea of a “ derangement.” The definition is as follows:
— In any permutation of the first n integers, the place-index of any
integer is got by counting the integer itself, and all the elements after
it which are less than it. For example, in the permutation

6, 4, 3, 9, 8, 10, 1, 7, 2, 5

of the first ten integers, the place-index of 9 is 6, and that of 7 is 3.
The counting of the integer itself makes the place-index always one
more than the number of “ derangements ” connected with the

462 Proceedings of Royal Society of Edinburgh. [july 18,

integer. This necessitates the introduction of a corresponding
modification of Cramer’s “rule of signs,” viz.

“ 3. Willkiihrlicher Satz. Jede Permutation der Elemente
1, 2, 3, . . . , r, werde mit dem Zeichen + versehen, wenn
entweder gar keine, oder eine gerade Menge gerader Zahlen,
unter ihren Stellenexponenten vorkommt ; mit dem Zeichen -
hingegen, wenn die Menge der geraden Zahlen, unter den
Stellenexponenten ungerade ist.” (hi. 6.)

It is difficult to suggest any justification for the changes here intro-
duced. The author himself refers to none. Indeed, in the very
next paragraph he points out that to ascertain whether there be an
even number of even integers among the place-indices is the same as
to diminish each of the place-indices by 1, and ascertain whether
there be an even number of odd integers, that is, whether the sum
of the odd integers be even. He then concludes —

“ Man kann also auch die Regel so ausdriicken: Jede Per-
mutation bekommt das Zeichen + wenn die Summe der um 1
verminderten Stellenexponenten gerade, — hingegen, wenn
sie ungerade ist.”

This is simply Cramer’s rule, and it is the only rule of signs
employed henceforward in the memoir, the expression “ die Summe
der um 1 verminderten Stellenexponenten,” occurring over and over
again as a periphrasis for “ the number of derangements.”

The next four pages are occupied with a very lengthy but
thorough investigation of the theorem that two permutations differ
in sign , if they be so related that either is got from the other by the
interchange of two of the elements of the latter. Strictly speaking,
however, the proposition proved is something more definite than
this, viz,—

If in a permutation of the integers 1.2, ... r there be d integers
intermediate in place and value between any two , A and B, of the
integers , the interchanging of the said two icould increase or dimmish
the number of inversions of order by 2J + 1. (hi. 7.)

The proof consists in finding the sum of the place-indices for the
given permutation in terms of d as just defined, c the number of
elements less than both A and B and situated between them, / the
number of such elements situated to the right of B, and e the

1887.] Dr T. Muir on the Theory of Determinants. 463

number of elements between A and B in value and situated to the
right of B; then finding in like manner the sum of the place-
indices for the new permutation; and finally comparing the two
sums. The concluding sentence is as follows : —

“ Denn da so ist die Summe der Stellenex-

ponenten der . zweyten Permutation um cl + e+1 -e + d oder
um 2^+1 grosser, als bey der ersten Permutation ; folglich
gilt das auch bey der Summe der um 1 verminderten Stellen-
exponenten, da bey beyden Permutationen r einerley ist.
Also ist die eine Summe gerade, die andere ungerade, folglich
haben nach (4) beyde Permutationen verschiedene Zeichen.”

As immediate deductions from this, it is pointed out that

The sign of any one permutation may be determined tchen the
sign of any other is known , by counting the number of interchanges
necessary to transform the one permutation into the other ; (iii. 8.)
and that

If one element of a permutation be made to take up a new place ,
by being , as it were, passed over m other elements, the sign of the
new permutation is the same as, or different from , that of the original
according as m is even or odd. (iii. 9.)

A third corollary is given, but it is, strictly speaking, a self-
evident corollary to the second corollary, and is quite unimportant.

Bothe’s next theorem is —

The permutations of 1, 2, 3, . . . . , n being arranged after the
manner in ivhich numbers are arranged in ascending order of magni-
tude, any tiro consecutive permutations will have the same sign, if the
first place in which they differ be the (4n + 3)th or (4n + 4)th from the
end, and will be of opposite sign if the said place be the (4n+ l)th
or (4n + 2)th from the end. (iii. 10.)

Thus if the permutations of 1, 2, 3, . . . . , 10 be taken, and
arranged as specified, two which will occur consecutively are

8, 4, 9, 3, 10, 7, 6, 5, 2, 1
8, 4, 9, 5, 1, 2, 3, 6, 7, 10;

and as the first place in which these differ is the 7th from the end,
it is affirmed that the signs preceding them must be alike. The

VOL. xiv. 31/1/88 2 G

464 Proceedings of Royal Society of Edinburgh. [july 18,

mode of proving the theorem will he readily understood by seeing
it applied to this illustrative example. Taking the permutation

8, 4, 9, 3, 10, 7, 6, 5, 2, 1 ,
and interchanging 3 and 5 we have the permutation

8, 4, 9, 5, 10, 7, 6, 3, 2, 1 ,
and thence by cyclical changes the permutation

8, 4, 9, 5, 1, 2, 3, 6, 7, 10,
the number of alterations of sign thus being

1 + (5 + 4 + 3 + 2 + 1)
i.e. 1 + J(5x6),

— an even number.

Annexed to the theorem is the following corollary, which is not
essentially sufficient from Hindenburg’s proposition regarding the
sequence of signs, —

If the permutations of 1, 2, 3, . . . , n - 1 be arranged after the
manner in which numbers are arranged in ascending order of
magnitude , and also in like manner the permutations of 1, 2, 3,

. . . . , n — 1, n, then those permutations of the latter arranged set
which begin with r, say , hare in order the same signs as the permu-
tations of the former arranged set, or different signs, according as r
is odd or even. (hi. 11.)

For example, arranging the permutations of 1, 2, 3, each with its
proper sign in front, we have

+ 1, 2, 3
-1, 3, 2
-2, 1, 3
+ 2, 3, 1
+ 3, 1, 2
-3, 2, 1;

then arranging those permutations of 1, 2, 3, 4 which begin with
3 say, each with its proper sign, we have

+ 3, 1, 2, 4

- 3, 1, 4, 2

- 3, 2, 1, 4

+ 3, 2, 4, 1

+ 3, 4, 1, 2

- 3, 4, 2, 1 ;

(B)

1887.] Dr T. Mair on the Theory of Determinants.

465

and the two series of signs are seen to be identical, 3 being an odd
number. Viewing this quite independently of the theorem to
which it is annexed, it is evident that a change of sign at any
point in the series (A) implies a change at the corresponding point
in the other series, and consequently attention need only be paid to
the first sign of (B) as compared with the first sign of (A). Now
the first sign of (A) must necessarily be always plus, there being no
inversions; and the first sign of (B) depends on the changes
necessary for the transformation of the natural order 1, 2, 3, 4,
into 3, 1, 2, 4. The truth of the corollary is thus apparent.

A second corollary is given, but it is of still less consequence, the
difference between it and the first being that in the arranged set (B)
the place whose occupant remains unchanged may be any one of the
n places. (hi. 12.)

The next few paragraphs concern the subject of “ conjugate
permutations” ( verwandte Permutationen ), — apparently a fresh
conception. The definition is —

Tivo permutations of the numbers 1, 2, 3, . . . , n are called
conjugate when each number and the number of the place which it
occupies in the one permutation are interchanged in the case of the
other per mutati on. (xxiv.)

For example, the permutations

3, 8, 5, 10, 9, 4, 6, 1, 7, 2 (A)

8, 10, 1, 6, 3, 7, 9, 2, 5, 4 (B)

are conjugate, because 3 is in the 1st place of (A) and 1 is in the
3rd place of (B), 8 is in the 2nd place of (A), and 2 is in the 8th place
of B, and so on in every case.

The first theorem obtained is —

Conjugate permutations have the same sign. (hi. 13.)

This is proved in a curious and interesting way, a special
conjugate pair being considered, viz., the pair just given as an
example. To commence with, a square divided into 10 x 10 equal
squares is drawn, the vertical rows of small squares being numbered
1, 2, 3, &c. from left to right, and the horizontal rows 1, 2, 3, &c.
from the top downwards. The permutation

3, 8, 5, 10, 9, 4, 6, 1, 7, 2

466 Proceedings of Royal Society of Edinburgh. [july 18,

is then represented by putting a dot in each of the horizontal rows,
in the first under 3, in the second under 8, and so on ; so that if
the rows he taken in order, and the number above each dot read,
the given permutation is obtained. For the representation of the
conjugate permutation nothing further is necessary: we obtain it
at once if we only turn the paper round clockwise until the
vertical rows are horizontal, and read off in order the numbers
above the dots. In the next place the number of “ derangements ”
belonging to the permutation 3, 8, 5, . . . .is indicated by insert-
ing a cross in every small square which is to the left of one dot
and above another ; thus the two crosses in the first horizontal row
correspond to the two “ derangements ” 32, 31; the six crosses in
the second horizontal row to the
six “derangements” 85, 84, 86,

81, 87, 82; and so on. Then it J

is observed that if we turn the ^

paper and try to indicate the 4
“ derangements ” of the conjugate 5
permutation by inserting a cross 6
in every small square which is to 7

the right of one dot and above ^

9

another, we obtain exactly the
same crosses as before. The signs
of the two permutations must thus be alike.

Immediately following this, the 24 permutations of 1, 2, 3, 4 are
given in a column, each one having opposite it, in a parallel column,
its conjugate permutation. The existence of self-conjugate permuta-
tions, e.p., the permutation 3, 4, 1, 2 is thus brought to notice, and
the substance of the following theorem in regard to them is given : —

If be the number of self-conjugate permutations of the first n
integers , then

U« = Uw-i + (w- l)Un_2 . .... (xxv.)

where Uj = 1 and U2 =* 2.

This, however, is the only one of his results which Rothe does not
attempt to prove.

In the second part of the memoir, which contains the application
of the theorems of the first part to the solution of a set of linear

1887.] Dr T. Muir on the Theory of Determinants. 467

equations, there is not so much that is noteworthy. Methods
previously known are followed, the new features being formality
and rigour of demonstration.

The coefficients of the equations being

11, 12, 13, .... , lr
21, 22, 23, .... , 2r

rl, r 2, r3, . . . . , rr

it is noted, as Vandermonde had remarked, that the common
denominator of the values of the unknown may be got in two ways,
viz., by permuting either all the second integers of the couples,
11, 22, 33, . . . . , rr, or all the first integers : but this is supple-
mented by a proof, that if any term be taken, e.g.,

16.24.33.47.51.68.79.82.95

with the couples so arranged that the first integers are in ascending
order, and the sign be determined from the number of inversions in
the series of second integers, then the sign obtained will be the same
as would be got by arranging the couples so as to have the second
integers in ascending order, and determining the sign from the
inversions in the series of first integers. The proof rests entirely on
the previous theorem, that conjugate permutations have the same
sign ; indeed the new proposition is little else than another form of
this theorem. (in. 14.)

The desirability of an appropriate notation for the cofactor, which
any one of the coefficients has in the common denominator is
recognised,* and the want supplied by prefixing f to the coefficient
in question ; for example, the cofactor of 32 is denoted by

f 32.

It is thus at once seen that the denominator itself is equal to

In. fl n + '2n.{2n +....+ rnSrn,
or n\ . TM + ?z2.fw2 +. . . .+ nrSnr. (vi. 2.)

Also by this means one of Bezout’s (or Vandermonde’s) general
theorems becomes easily expressible in symbols, viz.,

Iw.flm + 2n.f2m +.... + rn.frm = 0, (xil 4.)

* Lagrange’s use of a corresponding letter from a different alphabet must
not be forgotten.

468 Proceedings of Royal Society of Edinburgh. [july 18,

the proof of which is given as follows. In all the terms of f 1 m,
every one of the integers except one occurs as the first integer of a
couple, and every one of the integers except m occurs as the second
integer of a couple : consequently, in every term of \n . f lm, the
first places of the couples are occupied by the integers from 1 to r
inclusive, while in the second places, m is still the only integer
awanting, and n occurs twice. Suppose then all the terms of

lmflm + 2w.f2m + ....+ rn . frm

so written, that the first integers of the couples are in ascending
order of magnitude, and let us attend to a single term

..... -pm ...... • qn •

in which the two couples, having n for second integer, are the

y»th and qth. If we inquire from which of the expressions

In. f lm, 2mf2m, .... this term comes, we see that it is a

term of both pn. fpm and qn. fqm, and must, therefore, occur

twice. Further, we see that mpn.fqm it has the sign of the term

• pm • • qn •

of the common denominator, and that in qn . fpm, it has the sign of
the term

..... 'pn> ...... • qm • ......

of the common denominator. But these two terms of the common
denominator have different signs : consequently

ltt.fl m + 2mf2m + . . . . + rn.frm

consists of pairs of equal terms with unlike signs, and thus vanishes
identically. (xn. 4.)

These preparations having been attended to, the set of r equations
with r unknowns is solved by Laplace’s method ; and a verification
made after the manner of Vandermonde. It is also pointed out,
that if the solution of a set of equations, say the four

axA + bx2 + cx3 + dxA = s1 ]
ex1 + fx2 + gx 3 + hxA = s2 j
ixx + Jix.2 + lx 3 + mxA = s3 |
nx1 + ox2 +px 3 + qxA =sA J

1887.] Dr T. Muir on the Theory of Determinants.

469

be

x 2 = As± + Bs2 + Csg + Ds4 ]
x2 — Es4 + Es2 + Gs3 + Hs4 I
xB — Is4 + Iv6‘2 "1" Esg + Ms4 |

% 4 = NSj + 0^2 -r P^3 + Q$4 J ,

then the solution of the set

m + ^3 +ny± = vi'

fyi +fy2+^n + °y± = v2 >
cyi +yy2+lVs +py±=v3 \
dy1 + liy2 + myB + qy± = v4 j ,

which has the same coefficients differently disposed, will be

y1- A^ + Ewg +1% + Nv4'

y2 = Bv1 + Fv2 + K«?3 4- Ov4

yB — Oy4 + + D^3 + P^4 |

y4 = Dv1 + Ht72 + Mv3 + Q«J4 J ; . . . (xxvi.)

and hence, that the solution of a set having the special form

axx + bx2 + ex 3 + dxA = s4 ]

bx1 + ex2 +fx 3 + ya*4 = s2 I

CMJj +/o?2 + ^txs + ^4 = % |

<fe4 + gx2 + ixB +jx± — s4 J

will itself take the same form, viz.

A$4 + B§2 + C§3 + Ds4 — a?4 ]
Bs4 + Es2 + Es2 •+• Gs4 = x2 I
04 + Fs2 + Hs3 + Is4 = xB
Ds4 + G§2 P 1% + Js4 = x^

(xxvi. 2.)

GAUSS (1801).

\Disquisitiones Arithmetics. Auctore D. Carolo Friderico Gauss.

167 pp. Lips.]

The connection of Gauss with our theory was very similar to
that of Lagrange, and doubtless was due to the fact that Lagrange
had preceded him. The fifth chapter of his famous work, which is
the only chapter we are concerned with, bears the title “ De formis
squat ionihusque indeterminatis secundi gradusf and its subject may
be described in exactly the same words as Lagrange used in regard

470 Proceedings of Royal Society of Edinburgh. [july 18,

to his memoir Recherches d' Aritlimetique (1773: see above), viz.
“les nombres qui peuvent etre representees par la formule
B£2 + Ctu + D«/2.”

Gauss writes bis form of the second degree thus —

axx + 2b xy + cyy ;

and for shortness speaks of it as the form (a, b, c). The function
of the coefficients a, b , c, which was found by Lagrange to be
of notable importance in the discussion of the form, Gauss calls the
“ determinant of the form,” the exact words of his definition being

“ Numerum bb - ac , a cuius indole proprietates fornne
(i a , b, c ) imprimis pendere in sequentibus docebimus, deter -
minantem huius formse uocabimus.” (xv. 2.)

Here then we have the first use of the term which with an extended
signification has in our day come to be so familiar. It must be
carefully noted that the more general functions, to which the name
came afterwards to be given, also repeatedly occur in the course of
Gauss’ work, e.g. the function a§ - /3y in his statement of Lagrange’s
theorem (xxn.)

b'b' - ac = (bb - ac)(a 8 - /fy)2

But such functions are not spoken of as belonging to the same
category as bb - ac. In fact the new term introduced by Gauss
was not “ determinant ” but “ determinant of a form,” being thus
perfectly identical in meaning and usage with the modern term
“ discriminant.”

Notwithstanding the title of the chapter Gauss did not confine
himself to forms of two variables. A digression is made for the
purpose of considering the ternary quadratic form (“ formam
ternariam secundi gradus”),

axx + axx' + a"x"x" + 2 bx'x" + 2b' xx" + 2b" xx,
or as he shortly denotes it

(a, a\ a"\

b , b\ b'j .

In the matter of nomenclature the following paragraph of this
digression is interesting

“ Ponendo bb — a' a" — A, b'b' - aa" = A', b"b" — cia' = A”,
ab-b'b" = B, a'b'-bb"= B', a"b" -W = B",

1887.] Dr T. Muir on the Theory of Determinants. 471

oritur alia forma

/A A' A"\
\B B' B'7

quam forme

. . . . F

fa a

a \

U b'

v)

• . f

adjundam dicemus. Hinc rursus inuenitur, denotando breui-
tatis caussa numerum

abb + AAA + a"b"b" - ad a" - 2 bb'b" per D,

BB - A' A" = aT), B'B' - AA" - AD, B"B" - AA' = A'D,

AB - B'B'' = bD, A'B' - BB" = V D, A"B" - BB' - b" D,

unde patet, forme F adjunctam esse formam

/aD, AD, A'D\

\6D, AD, A'D/ .

Numerum D, a cuius indole proprietates forme ternarie / im-
primis pendent, determinantem hums forme uocabimus (xv. 2) ;
hoc modo determinans formae F sit = DD, sive aequalis quadrate
determinantis formae/, cui adjuncta est.”

In this there is no advance so far as the theory of modern deter
minants is concerned, the identities given being those numbered
(xx) and (xxi) under Lagrange. On the same page, however, an
extension is given of Lagrange’s theorem (xxii), regarding the
determinant of the new form obtained by effecting a linear substi-
tution on a given form. Gauss’ words in regard to this are —

“ Si forma aliqua ternaria / determinantis D, cuius indeter-
minate sunt tJC1 y *)(j y tD (puta prima = «, &c.) in formam ternariam
g determinantis E, cuius indeterminate sunt y , y\ y ", trans-
mutatur per substitutionem talem

a =a-y +y y’\

A =dy +(3y' + fy" ,
d' — d'y +/3Y + /V',

ubi nouern coefficientes a, /?, &c. omnes supponuntur esse
numeri integri, breuitatis caussa neglectis indeterminatis
simpliciter dicemus, / transire in g per substitutionem (S)

472 Proceedings of Royal Society of Edinburgh. [july 18,

a, ft y

d, ft, y

a , , 7

atque / implicare ipsam g, siue sub f contentam esse. Ex
tali itaque snppositione sponte sequuntur sex equationes pro
sex coefficientibus in g, quas apponere non erit necessarium :
hinc antem per calculum facilem sequentes conclusiones
eitoluuntur :

“ I. Designato breuitatis caussa numero

a /3'y" + ft/ a/' + yd — y fi'd' - a y ($" — fidy"

per k inuenitur post debitas reductiones

E = MD, ...... (xxii. 2.)

• ••••••••

When freed from its connection with ternary quadratic forms the
theorem in determinants here involved is

If A0 = a0a02 + axai + a2a22 + 2&0a1a2 + 251a0a2 +262a0a1,

Ai = UqPq" + + 2&0/3j/32 2G^o^2 + >

A2 = ao7o2 + ai7i + a-2l2 + 2&o7i7‘2 + 2&i7o72 + 2&27o7i >

B0 = a0£o7o + + %0272 + Wi7* + /327i) + ^i(^o72 + £27o) + ^(0o7i + #i7o)

Bj = a0a o7q + «i«i7i + «2«272 + &o(ai72 + «27i> + &i(«o72 + a27o) + &2(«o7i + «i7o)
Bo = ^oaO^O ®laI$l "t ttoC*o^2 + &o(al$2 "t °2^l) "t ^l(a0^2 "t" a2$o) ^2(a0$l "t aI@o) j

then

A0B02 + A1B12 + A2B22 - A0A1A2 - 2B0B1B2
= (a060- + 4 a.ff — agxyi^ — 260&1&2)j

X (a0ft y2 + ft)7la2 + 7oai/^2 ~ 7oAa2 — ao7ift — /Vite)2*

As thus viewed it is an instance of the multiplication-theorem, the
product of three determinants (in the modern sense) being ex-
pressed as a single determinant.

The multiplication-theorem is also not very distantly connected
with the following other statement of Gauss : —

“ Si forma ternaria / formam ternarium f implicat atque haec
formam f": implicabit etiani / ipsam /". Facillime enim per-
spicietur, si transeat

/ in /' per substitutionem

A 7

a,

f in f" per substitutionem

e, t

1887.] Dr T. Muir on the Theory of Determinants.

473

/ transmutatum iri per substitutionem

aS + f3&' + yS", ae + /3t + ye' at, + ftf + y£"
a 8 + /TS' + y'8" a'e + 0V + y'e" af + /3'£ + yf"
a '8 + p"8' + y"8" ae + /TV + y V ' a"£ + + y (xxn. 3. )

MORGE (1809).

[Essai duplication de l’analyse a quelques parties de la geometrie
elementaire. Journ. de VEc. Polyt., viii. pp. 107-109.]

Lagrange, as we have already seen, was led to certain identities
regarding the expression

xy'z" + yzx' + zx'y" — xtfy" - yxfz" — zyx"

in the course of investigations on the subject of triangular pyramids.
The position of Monge is that of Lagrange reversed. Erom the
theory of equations he derives identities connecting such expressions,
and translates them into geometrical theorems.

The simpler of these identities, as being already chronicled, we
pass over. At p. 107 he takes the three equations

ayx 4- bxx + cyy + d^z + e1 = 0
a 2u + b2x + e2y + d2z + e2 — 0
a3u + b3x + c3y + d3z + e3 = 0 ,

and eliminating every pair of the letters u, x, y, z, obtains the six
equations

pu 4- ax + P = 0

(1)

yx + Py + Q = 0

(2)

8y + yz + M = 0

(3)

az + 8u + N = 0

(4)

yu - ay + S = 0

(5)

Pz - Sx + R = 0

(6);

the ten letters

a, /?, y, 8, M, E", P, Q, R, S

being used to stand for the lengthy expressions which we nowa-
days denote by

I b-^e2d3 | , [ ayz^d 3 j , | afj,~)d3 ( , | af)c)C3 j ,

I ^1^2^3 I J i I 5 I h^2^3 I 5 — | ^1^2^3 I "> I ^1^2^3 I ’ i ^1^2% I '

Then, taking triads of these six equations, e.g ., the triads (1), (2),
(5), he derives the identities

474 Proceedings of Eoyal Society of Edinburgh.

[JULY 18,

aQ + /?S — yP = 0 ]

SP +aR = 0 I
-yN +SS + aM = 0 j

— /3M + yft + 8Q = 0 J ,
or

— \b-lc2d^[.\a1d2e^ + {a^dflbft^e^ — \afb2d^[.\cld2e^

\a\ ^2C3l • lci^2e3l l^lC2^sl • \aiC2G^[ ~ i^lC2^3l • l^ic2^3l

— . 1^1^363! + I^VsI-IVW “f" l^lC2^3l'ltt1^2e3i

— I^Cg^gl. + |tti^2^3l- laiC2e3l “ \ai^2e^

= 0
= 0
= 0
= 0

1

[- (xxm. 2.)
1

J

which in their turn, he says, by processes of elimination, may he
the source of many others. For example, each of the four being
linear and homogeneous in a, /3, y, 8, these letters may all he
eliminated with the result

PuS + QISr-PM = 0,
or

\aiC#A • l^l^2e3l “ l^lC2%l — l^l^3! • 1^1 ^2^1 “

Also, eliminating P from the first and second, S from the first and
third, Q from the first and fourth, and so on, we have

- j3yN + 8aQ + /3SS + ay ft = 0 ,
a/3M + y8P — /3yN — 8aQ = 0 ,
a/5M — ySP + /38S — ay It = 0 ,

&c. &c.

i.e.

J ct]Cft% |-| ei-J^d's |*1 b iC2e3 ]

1 tt1^2C3 1 • 1

VA 1’l

jH-

| a^cfL^ j.j af> 2C3 |.| bfl$% 1 "f

| b1c2d2> |.|

“iMsI-l

&c.

&c.

(xxvm.)

Monge does not pursue the subject further. His method, how-
ever, is seen to he quite general ; and we can readily believe that
he possessed numerous other identities of the same kind. This is
borne out by a statement in Binet’s important memoir of 1812.
Binet, who was familiar with what had been done by Vandermonde,
Laplace, and Gauss, says (p. 286) : — “M. Monge m’a communique,
depuis la lecture de ce memoir©, d’autres theoremes tres-remarquables
sus ces r6sultantes ; mais ils ne sont pas du genre de ceux que nous
nous proposons de donner ici.”

1887.] Dr T. Muir on the Theory of Determinants.

475

HIESCH (1809).

[Sammlung von Aufgaben aus cler Theorie der algebraischen Gleich-
ungen, von Meier Hirsch. pp. 103-107. Berlin, 1809.]

The 4th Chapter Von der Elimination u. s. w., contains five pages
on the subject of the solution of simultaneous linear equations.
These embrace nothing more noteworthy than a statement, without
proof, of Cramer’s rule, separated into three parts (iv., iii. 2, v.),
and carefully worded.

BINET (May 1811).

[Memoire sur la theorie des axes conjugues et des momens d’inertie
des corps. Journ. de VEcole Polytechnique , ix. (pp. 41-67),
pp. 45, 46.]*

In this well-known memoir, in which the conception of the
moment of inertia of a body with respect to a plane was first made
known, there repeatedly occur expressions, which at the present
day would appear in the notation of determinants. There is only
one paragraph, however, containing anything new in regard to these
functions. It stands as follows : —

“Le moment d’inertie minimum pris par rapport au plan
(C), a pour valeur

1,ink 2 =/2 x

ABC - AF2 - BE2 - CD2 + 2DEF

r’(BC - F2) + AC - E2) + i2(AB - D2) + 2gh(EF - CD) + 2gi(DF - BE) + 2hi(DE - AF) •
Si, dans le numerateur,

ABC - AF2 - BE2 - CD2 + 2 DEE

on remplace A, B, C, &c. par 2mx2, 21 my 2, &c. que ces lettres
represented, on a

^mx^my^mz2 - '$mx2(’%myz)2 - %my2{%nxz)2
- 2 mz2{%mxy )2 + T%mxy'%mxz%myz ,

et l’on peut s’assurer que cette expression est identique a

%mm'm"(xy'z” + yz'x" + zx'y" - xzy" - yx'z" - zy'x")2 ;

par une transformation analogue, on peut ramener la quantite

* An abstract of this is given in the Nouv. Bull, des Sciences par la Societe
Pkilomatique, ii. pp. 312-316.

476 Proceedings of Royal Society of Edinburgh. [july 18,

<72(BC-F2) +h 2 (AC-E2) + i 2 (AB-D2)

+ 2^(EF - CD) + 2 gi(m - BE) + 27w(DE - AF) ,

a celle-ci

%mm\g(yz - zy) + h (zx - xz') + iixy - yx')]2.”

■*

Now the numerator referred to would at the present day he written.

A D E
DBF
E F C ,

and since %mx2, &c. stand for mx 2 -J- mxxf + 7n2x22 + . . . , &c., the
first identity given may be put in the form

mx2 + mxx2 + m2x22 + . .
mxy + mlx1y1 + m2x2y2 + . .
mxz + m-jpcfa + m2x2z2 + . .

mxy + m1x1y1 + m2x2y2 + . .
my2 +m1y12 +m2y2 2 + ..
myz + myy-fo + m2y2z2 +. .

mxz + m^xxzx + m2x2z2 + .
myz + mxyxzx + m2y2z2 + .
mz2 + m-fi2 + m2z2 + .

X

Xx

x2

2

X

xx

x3

mmgn2

y

Vi

V2

+ mm1m3

y

Vi

y 3

z

%

*2

z

h

%

+ . . . (xvm. 2.)

where xv y2, . . . are for convenience written instead of x, y" , . . .
It will be seen that this is an important extension of a theorem of
Lagrange, the latter theorem being the very special case of the
present obtained by putting m = mY — m2 — 1, and m3 = m4 = . . . = 0,
— a fact which is brought still more clearly into evidence if,
instead of the left-hand member of the identity, we write the
modern contraction for it, viz.

mx m1x1 m2x2 m3x3 . . . .

my mly1 m2y2 m3y3 . . . .

mz m xzx m9z2 m3z3 . . . .

Again the denominator

X

xx

x2

x3 ....

X

y

yi

y 2

y% • • • •

z

*t

%

*3 ....

<72(BC - F2) + 7z2 (AC-E2) + i2 (AB-D2)
+ 2y7z(EF - CD) + 2gi(UF - BE) + 27w(DE - AF)

being in modern notation

g h i
g A D E

li D B F

i E F C ,

1887.] Dr T. Muir on the Theory of Determinants. 477

the second identity may be written

g h i

g mx2 + mxxf + . . . mxy 4- mlxly1 + . . . mxz + + . . .

h mxy 4- m1x-[yl-\- . . . my 2 + ??qy12 +. . . myz + mgjyz +. . .

i mxz 4- myx.yz^ 4 . . . myz 4 mxy^zx + . . . mz2 + mxz i2 +••• I

g

X

xx

2

9

X

x2

2

g

xx

x.2

mm1

h

y

Vi

4 mm2

h

y

V2

+

mxm„

h

yi

2/2

%

z

Z 1

i

z

Z2

i

Z 1

z2

This also is an important theorem, and is not so much an extension
of previous work as a breaking of fresh ground.

BINET (November 1811).

[Sur quelques formules d’algebre, et sur leur application a des
expressions qui ont rapport aux axes conjugues des corps.
Nouv. Bull, des Sciences par la Societe Philomatique , ii.
pp. 389-392.]

In this paper Binet returns to the consideration of the first of
the two identities which have just been referred to, writing it nowT
in the form

~%(xyz" — xzy" 4- yzx ' — yx'z" + zxy” — zy'x") 2
= %x2Hy2%z2 - %x?{%yz)2 — '%y2(%xz)2 - %z2(%xy)2 + T%xy%xz%yz .

He puts it in the same category as the identity

%{yz - zy)2 = '%y2'2z2 - ('Syz)2 ,

which he speaks of as being then known. Further, he says

“ Ces deux formules sont du meme genre que la suivante

f ux'y"z'" - ux'z"y'" 4 uy'z"x - uy'x"z'" + uz'x”y"'
] 4 xz'tfvJ" - xz'u"y"' 4 xu'z"y'" - xu'y"z’" 4 yz'u"x!"
[ +yx'z"ur" - yx'u"z'" + zu'y"x'" - zu'x"y'" + zx'y"u"'

- uz'y"x'" 4 xy'u"z - xy'z"v!" 'j

- yz'x"u 4 yu'x"z"' - yu'z"x"' j.

- zxtu"y'" 4 zy'x"u'" - zy'u"x'" j

2:

= ^u2^x2%y2%z2 — 'Hu2%x2f$yz)2 - %u2'%y2(f£;xz)2 - %u2%z2(2xy)2

— '%x2%y2(K%uz)2 — ^x2%z2C%uy)2 - %y2%z2{^ux2)

4- ^%u2^xy%xz%yz + 2 %x2^uy%uz%yz 4 2 %y2%ux%uz%xz
4 2 %z2%uxi%uy^xy 4 (%ux)2(%yz)2 4- (^uyfif^xz)2 + (%uz)2(f&xy)2

- TLux%xy%y?i%zu — 2 '%uy%yz%zx%xru ~ 2 '2iuy%yx%xz%zu ,

478

Proceedings of Royal Society of Edinburgh,. [july 18,

— a result which in modern notation would take the form

u

ux

u2

%

2

U

ux

u2

v4

X

xx

x2

X3

+

X

X1

x2

x4

y

Vi

y*

Vs

y

y\

y 2

y 4

z

*i

%

z,

o

z

%

Z2

id + uf + . . ux + u xxx + . . uy 4- ulyl + . . uz + uxzx + . .

ux 4- urx-i + . . x1 + x,2 + . . xy + x,y, + . . xz + xa. + . . ,

O O (XVIII. 3

uy + ulyl + . . xy+x1y1 + .. y2 + y2 +.. yz + yxzx + ..

uz + uxzx + . . xz + xxzx + . . yz + yxzx + . . z2 + z2 + . .

It is thus clear that, in November 1811, Binet was well on the way
towards a great generalisation. He even says that the three
identities may he looked upon

“ comme les trois premieres d’une suite de formules con-
struites d’apres une meme loi facile a saisir.”

He merely indicates, however, the mode of proof he would adopt
for the results obtained, and refers to possible applications of them
in investigations regarding the Method of Least Squares (Laplace,
Connaissance des Terns , 1813) and the Centre of Gravity (Lagrange,
Mem. de Berlin , 1783). The mode of proof need not he given
here, as it turns up again in the far more important memoir in
which the theorem in all its generality falls to be considered.

DE PRASSE (1811).

[Commentationes Mathematicse. Auctore Mauricio de Prasse. 120 pp.
Lips., 1804, 1812. Pp. 89-102 ; Commentatio vii.* : Demon-
stratio eliminations Cramerianse.]

Of previous writings the one which De Prasse’s most resembles is
Rothe’s. There is less of it, and it shows less freshness ; hut there
is the same stiff formality of arrangement, and the same effort at
rigour of demonstration.

* Separate copies of the Demonstratio eliminationis Crameriance are also to
be found, bearing the invitation title-page :

Ad memoriam Kregelio-Sternbachianam in auditorio philosophorum die
xviii Julii mdcccxi. h. ix celebrandam invitant ordinum Academics
Lips. Decani seniores cceterique adsessores .... Demonstratio elimi-
nationis Crameriance.

It is these copies which fix the date. See Nature , xxxvii. pp. 246, 247.

1887.] Dr T. Muir on the Theory of Determinants. 479

The definition of a permutation (variatio) being given, the first
problem (which, however, is called a theorem) is propounded, viz.,
to tabulate the permutations of a, /3, y, 8, . . . (“ Variationum ex
elementis a, A 7, • • . constructarum et in Classes combinatorias
digestarum Tabulam par are ”). The result is

a

0

7

8}

a0

ay

a5

j3a

I3y

08 [

ya

7/3

78 [

5a

80

87 J

a07

a05 '

ay 0

ay5

a50

a5y

13 ay

0a8

07a

078

05 a

087 !

7 “0

yad

70a

70S

78a

780

5 a 0

807

50a

807

5ya

870 >

ajSyS -

af35y

ay

ay5/3

adfiy

a5y/3

f3ay5

/3a5y

I3ya5

07 5a

1 35ay

j35ya

ya/35

7«5/3

70a5

y fi5a

y5a{3

y5 f3a

5a(3y

5 ay /3

5/3ay

5/3ya

5ya(3

5y /3 a ■

>•

2 H

VOL. XIV. 31/1/88

480 Proceedings of Royal Society of Edinburgh. [july 18,

The first row of the permutations involving two letters is got by
taking the first letter of the previous row and annexing each of the
others to it in succession and in the orde** of their occurrence ; the
second row is got in like manner from the second letter ; and so on.
Similarly the first row of permutations involving three letters is got
from afi the first obtained permutation of two letters, the second
row from ay the next obtained permutation of two letters, and
so on.*

The second problem (and on this occasion actually so designated)
is somewhat quaint in its indefiniteness, viz., to prefix to each per-
mutation the sign + or the sign -- , so that the sum of all the
permutations involving the same number of letters (>1) may
vanish (“ Singulis Variationibus, omissis repetitionibus, signa + et
— it a praefigere, ut summa secundoe et cujuslibet classis insequentis
evanescat”). There is no indefiniteness or multiplicity about the
solution, which in substance is : — Make the permutations in every
row of the preceding table alternately + and - , the first sign of
all being + , and the first permutation of every other row having
the same sign as the permutation from which it was derived. In
this way the table becomes

+ a, - /3, +7, - 5 }

+ a/3, — ay, + a5 ^

-/3a, + &y, - /35 1
* + ya, -7/3, +75 |

- 5a, 4- 5/8, - 57 J

4- a/87, — a/38 1

— 07/8, + a7^

4-a5/3, — a57

— /3a7, + j8a5
+ /87a, - /87s

— /85a, 4-/857
4"7a/8, — 7a5
~7/3a, 4-7/85
4- 75a, —75^3

— 5 a/3, 4- 5a7
4- 5 /8a, — 5/87

— 57a, 4- 57 IS ,

* It will be seen that the order in which the permutations come to hand in
this process of tabulation is the order in which they would be arranged accord-
ing to magnitude if each permutation were viewed as a number of which
a, /8, 7, 5 were the digits, a being < /3 < 7 < 5 (“ ordo lexicographicus,” “ lexi-

cographische Anordnung” of Ilindenburg).

1887.] Dr T. Muir on the, Theory of Determinants,

481

+ a/3 y8 ^

— a@$y j

— cry/SS !

-J- aydfi
-f ad/3y

— 0.57,8

|

J

— /3ay8
+ fia$y
+ /87a 8

— fiy$a

, — jSSay j

-f fitiya :|

y

-f 70/68 I

— 7 a8/8

— 7,808
-f 7/85 a
+ 780,8

— 78/50

— 00/87
4- 807/8
+ S/607

— 8,87a

— dyafi

+ §7 0a J «

A proof by tbe metliod of mathematical induction (so-called) is
given that with these signs the sum of all the permutations of any
group vanishes.

Up to this point the essence of what has been furnished is a
combined rule of term-formation and rule of signs. (11. 5 -f in, 15.)
In connection with it Bezout’s rule of the year 1764 may be
recalled.

The third problem is to determine the sign of any single per-
mutation from consideration of the permutation itself. The solution
is : — Under each letter of the given permutation put all the letters
which precede it in the natural arrangement and which are not
found to precede it in the given permutation ; and make the sum +
or - according as the total number of such letters is even or odd.

“ Exemp. Dafoe complexiones sint hse ;

€yS 8 , Saey , eSya , S/2ey •

Literse secundum I subjiciantur

482 Proceedings of Boy al Society of Edinburgh. [july 18,

a a a a

a. (3(3

a a a .

a a a a

P/3/3

Py

(3(3(3

P-y

y

y

yy

y

8

8

quarum numeri sunt

9

6

9

7

qui complexionibus datis prsefigi jubent signa

+

5)

The proof that this rule of signs, which is manifestly nothing else
than Cramer’s, leads to the same results as the previous rule, is
quite easily understood if a particular permutation he first con-
sidered. For example, let the sign of the particular permutation
8(3ay be wanted. Following the first rule, we should require to
note four different members, viz.,

(1) the no. of the column in which 8(3ay occurs in the 4th group,

(2) „ „ 8(3a „ 3rd „

(3) „ „ 3/3 „ 2nd „

(4) ,, ,, 8 ,, 1st ,,

The first of these numbers being 1, we should infer that in fixing
the sign of 8(3ay in the fourth group there had been no change from
the sign of 8(3a in the third group ; the second number being also 1,
we should make a like inference ; the third number being 2, we
should infer that in fixing the sign of 8/3 in the second group there
had been 1 change from the sign of 8 in the first group ; and
finally, the fourth number being 4, we should infer that in fixing
the sign of 8 in the first group there had been 3 changes from the
sign of a in that group. The total number of changes from the
sign of a in the first group being thus 3 + 1 + 0 + 0, i.e., 4, the sign
would be made +. Now the 3 in this aggregate is simply the
number of letters in the first group which precede 8, the 1 is simply
the number of letters taken along with 8 before /3 comes to be taken
along with it to form 8/3 in the second group, and the two zeros
correspond to the fact that 8(3a on the third group and 8/3ay on the
fourth group have no permutation standing to the left of them.
Consequently to count the number of changes (3 + 1 + 0 + 0) from the

1887.] Dr T. Muir on the Theory of Determinants. 483

sign of a in accordance with the first rule is the same as to count
the number of letters placed under the given permutation, thus,

b/Say

aa . .

P

7

in accordance with the second rule.

Another point of resemblance between Rothe and De Prasse is
thus made manifest, viz., that they both refused to accept Cramer’s
rule of signs as fundamental, preferring to base their work on a
rule equally arbitrary, and then to deduce Cramer’s from it.

In case it may have escaped the reader, attention may likewise be
drawn to the fact that De Prasse prefixes a sign not only to per-
mutations involving all the letters dealt with, but also to any
permutation whatever involving a less number ; so that in reckoning
the sign of aSj3 , say, the full number of letters from which a, 8, /3
are chosen must be known.

A theorem like Hindenburg’s is next given, viz., If the permuta-
tions of any group he separated into sub-groups, (1) those which begin
with a, (2) those which begin with /3, and so on, then the series of
signs of the 3rd, 5th, and other odd sub-groups is identical with the
series of signs of the sub-group, and the signs of any one of the
even sub-groups is got by changing each sign of the first sub-group
into the opposite sign. (iii. 16.)

It is more extensive than Hindenburg’s in that it is true of per-
mutations which involve less than all the letters, provided such per-
mutations have had their signs fixed in accordance with De Prasse’s
rule. The proof depends, of course, on the first rule of signs, and
consists in showing that if the theorem be true for any group it
must, by the said rule, be true for the next group. It will be
remembered that Hindenburg gave no proof.

Following this is Rothe’s theorem regarding the interchange of
two elements of a permutation, or rather an extension of the theorem
to signed permutations involving less than the whole number of
letters. The proof is as lengthy as Rothe’s, even more unnecessary
letters than Rothe’s c, f, e being introduced. (hi. 17.)

The last theorem is Vandermonde’s (xil); and this is followed by

484 Proceedings of Boy ctl Society of Edinburgh. [july 18,

two pages of application to the solution of simultaneous linear
equations.

No reference is made by De Prasse to Hindenburg, Rothe, or
Vandermonde.

WRONSKI (1812).

[Refutation de la Th4orie des Fonctions Analytiques de Lagrange,
Par Hbene Wronski, pp. 14, 15, . . . , 132, 133. Paris.]

In 1810 Wronski presented to the Institute of France a memoir
on the so-called Technie de T Algorithmic, which with his usual
sanguine enthusiasm he viewed as the essential part of a new
branch of Mathematics. It contained a very general theorem, now
known as “ Wronski’s theorem,” for the expansion of functions, — a
theorem requiring for its expression the use of a notation for what
Wronski styled combinatory sums. The memoir consisted merely
of a statement of results, and probably on this account, although
favourably reported on by Lagrange and Lacroix, was not printed.
The subject of it, however, turns up repeatedly in the Refutation
printed two years later; and from the indications there given we
can so far form an idea of the grasp which Wronski had of the
theory of the said sums.

At page 14 the following passage occurs: — -

“ Soient X1? X2, X3, &c. pleusieurs fonctions d’une quantite
variable. Nommons somme combinatoire , et designons par la
lettre hebraique sin , de la maniere que voici

^[AaXx . A6X2 . AcX3 . . . A*XJ , (xv. 3) (vn. 4)

la somme des produits des differences de ces fonctions, com-
poses de la maniere suivante : Forrnez, avec les exposans
a, b, c, . . . , p des differences dont il est question, toutes les
permutations possibles; donnez ces exposans, dans chaque
ordre de leurs permutations, aux differences consecutives qui
composent le produit

AX1 . AX2 . A3 . . . AX,- ;

donnez de plus, aux produits separes, formes de cette maniere,
le signe positif lorsque le nombre de variations des exposans
a, b} c, etc., considers dans leur ordre alphabetique, est nul on

1887.] Dr T. Muir on the Theory of Determinants. 485

pair, et le signe negatif lorsque ce nombre cle variations est
impair ; enfin, prenez la somme de tous ces produits separes. —
Yous anrez ainsi, par exemple,

^[A^XJ - A“Xj ,

«?[>*! . A6X2] = AaXr A&X2 - A6Xx . AaX2 ,

The new name, combinatory sum , and the new notation, did not
originate in ignorance of the work of previous investigators, for
memoirs of Vandermonde and Laplace are referred to. The only
fresh and real point of interest lies in the fact that the first index of
every pair of indices is not attached to the same letter as the second
index, but belongs to an operational symbol preceding this letter,
and is used for the purpose of denoting repetition of the operation.
This and the allied fact that the elements are not all independent
of each other, A:X3 and A2X15 for example, being connected by the
equation

A2Xx = A(A1X1),

indicate that Wronski’s combinatory sums form a special class with
properties peculiar to themselves.

BINET (November 1812).

[Memoire sur un systeme de formules analytiques, et leur applica-
tion a des considerations g^ometriques. Journ. cle VEc. Polyt .,
ix. cah. 16, pp. 280-302, . . .]

It would seem as if the above-noted frequent recurrence of
functions of the same kind had led Binet to a special study of them.
In the memoir we have now come to, his standpoint towards them
is changed. They are viewed as functions having a history : for
information regarding them, the writings of Vandermonde, Laplace,
Lagrange, and Gauss are referred to: they are spoken of by Laplace’s
name for them, resultantes d deux lettres , ci trois lettres , d quatre
lettres , &c. ; and the first twenty-three pages of the memoir are
devoted expressly to establishing new theorems regarding them.

Of these the fundamental, and by far the most notable, is the
afterwards well-known multiplication-theorem. It is enunciated at
the outset as follows : —

486

Proceedings of Boy cd Society of Edinburgh, [july 18,

“ Lorsqu’on a deux systemes de n lettres chacun, et nous
supposerons chaque systeme ecrit avec une seule lettre portant
divers accens, qui serviront a ranger dans le meme ordre les
deux systemes ; on peut former avec ces lettres un nombre

n-- de resultantes a deux lettres, en ne prenant dans le

second terme de chacune, que des lettres portant les memes
accens que celles du premier. Si, avec deux autres systemes
de lettres, on forme encore des resultantes a deux lettres, et
qu’on les multiplie cbacune par sa correspondante obtenue des
deux premiers systemes, e’est-a-dire, par celle dont les lettres
portent les memes accens; la somme des produits de toutes
ces resultantes correspondantes sera elle-meme une resultante
a deux lettres, dont les termes ou lettres seront des sommes
de produits des eldmens des deux systemes portant les
memes accens. Avec deux groupes de trois systemes de
lettres chacun, on peut former semblablement deux series de
resultantes a trois lettres ; faisant ensuite la somme des pro-
duits de celles qui se correspondent par les accens de leurs
lettres, on aura encore une resultante k trois lettres. Pareille
chose ayant lieu pour des resultantes a quatre lettres, &c., on
peut conclure ce theoreme: Le produit d’un nombre quel-
conque de sommes de produits * de deux resultantes correspon-
dantes de meme ordre, est encore une resultante de cet ordre.”

(xvn. 4 + xvin. 4.)

The mode of proof adopted is lengthy, laborious, and not very
satisfactory, except as affording a verification of the theorem for the
cases of “resultantes” of low orders. It rests too on certain
identities, the demonstration of which is open to similar criticism.
All that Binet says regarding these absolutely essential identities
is (p. 284) —

“ Je representerai par %a la somme a' + a" + a"' + &c., des
quantites a', a'\ a"\ &c. ; par %ab la somme des produits
ab + a'b' + a"b" + &c., dans chacun desquels les lettres a et b
ont le meme accent; par %ab' la somme a'b" + b'ct" + ab'" + &c.,

* There is an extension here which one is scarcely prepared for, viz., “ le
produit d'un nombre quelconque de sommes de produits instead of la somme
d un nombre de produits.

1887.] Dr T. Muir on the Theory of Determinants. 487

la tous les produits d’un des a par un des b, portent
un accent different de celui de a; par %ab'd' la sonime
a'b"c" + b'c'a" + c'a"b"' + <fcc., et ainsi de suite. Cela pos6, on
verifie aisement les formules suivantes :

%ab' = %a%b - %ab ,

%ab'c" = %a%b%c + 2 %abe - ^a^bc - %b%ca - %c^ab ,

%ab'c"d’" = tdtb^c%d - Qtabcd

- %a%b^ed - %a%c%bd - %a%d%bc

- %c%d%ab — %b%d%ac - %l)%c%ad
+ %ab%cd + %ac%bd + %ab*%bc
+ 2 %a%bcd -f 2 %b%cda + 2 %c%dab
+ 2%d^abe,

% ab'c"dme'v = %a%b%c%d%e + &c. ,

&c.

It is thus seen that not only is no general proof of the identities
given, but that even the law of formation of the right-hand members
of the identities themselves is left undivulged. The exact words
employed in the demonstration of the first case of the multiplication-
theorem are (p. 286)—

“Avec un nombre n de lettres y\y'\y"\ &c. et un meme

nombre de rz , z\ z", &c. on peut former rt1 — — resultantes a deux

A

lettres (y, z"), (y\ z "), &c. (y", z'") &c. ; ayant forme pareille-
ment avec les lettres, v, v", v"\ &c., &c., les resul-

tantes (v, £"), (v, &c., (v", &c., considerons la somme

%(y, z)(y , £') des produits des resultantes qui se correspondent
par les accens dans les deux systemes. On voit, en develop-
pant, par la multiplication, chacun des termes de cette somme,
qu’elle revient a

%yv.z'£ - %zv.y'% .

A ces deux dernieres integrates, on peut appliquer la transfor-
mation indiquee par la premiere des formules de Tart. 1 : on
parvient ainsi a

2(y, z')(v, £') = %yv%z^ - tzv%yt.

Ce dernier membre pouvant etre assimile a la forme (y, «'), il

* Meant for 'Zad.

483

Proceedings of Poyal Society of Edinburgh. [july 18,

en resulte que le produit d’un nombre quelconque de fonctions,
telles que %{y, z')(v, £'), est lui-meme de la forme (y, z) .”

The application here of the identity

%ab' — %a%b - % ab

requires a little attention. The result of multiplication and classi-
fication of the terms is

%yv.z'Z - tzv.yf ,
or, as it might preferably be written,

%{yv .z£) - {tzv .y(})
and this we know from the said identity

= \%yv . 24 - %(yv . z£j] - [22V . 2 \yl - 2(zv . ?/£)] ,
which, because of the equality of 2 (yv . 4) and 2 (zv . yt), becomes

2 yv . 2z£ - 2 zv . 2 yl .

The inherent weak points, however, of the mode of demonstration
stand out more clearly when the next case comes to be considered,
viz., the case for resultants of the third order. From the three sets
of n letters

t ft

X9 X, X 9 .....

?/> y\ v",

f n

2, 2,0, .....

all possible “ r4sultantes a trois lettres ” are formed, and each re-
sultant is multiplied by the corresponding resultant formed from
other three sets of n letters ,

t, c, r,

r n

V, V, V ,

z, t, r,

Each of these \n(n - l)(w— 2) products consists of 36 terms, there
being thus 6n(n - 1 )(n - 2) terms in all. But these Qn(n - 1 )(n - 2)
terms are found to be separable into six groups, viz.

+ 2 {xS.y'v'.JT}, +2{^.2V.^T}, ....

so that the result which we are able to register at this point is

2 {xgj X') = 2*£ • yv . z"£ " + 2 y( . 2V . *"£"

+ 2 zg.afv'.y'T -2 xPdv' .y'X'

-2 yi.dv’ .W-M.tfv'

1887.] Dr T. Muir on the Theory of Determinants.

489

To the right hand member of this the substitution

%abrc" = + 2 %dbc — 'ZaSbc - %b%ca - %c%ab

is now applied six times in succession ; that is to say, for

^ J- If If <>!!

Axt, . y v . z 4

and the five other term-aggregates which follow, we substitute
+ 2%(oc£ . yv . z£)

- . z£) - %yv$(zt . x£) - • yv)

and five other like expressions. By this means we arrive, “ toute
reduction faite,” at

%{x,y\z")(&'£') = %x&yvM + ty&zvtx^ + %s&xv$yZ

- %xgfav%y£ - %yi%xv%z'Q - %z£$yv%x£> ,
which is the result desired.

It is easy to imagine the troubles in store for any one who might
have the hardihood to attempt to establish the next case in the
same manner.

If Binet’s multiplication-theorem he described as expressing a
sum of products of resultants as a single resultant , his next theorem
may he said to give a sum of products of sums of resultants as a
sum of resultants. The paragraph in regard to it is a little too much
condensed to be perfectly clear, and must therefore he given
verbatim. It is (p. 288) — -

“ Designons par S (y'f) une somme de resultantes, telle que

(y/.0 + (y„W) + (y + &c- ;

e’est-a-dire,

y,z, ~z,v, +y„z„ ~z„y„ + y,„z,„

z„',y„" + ;

et continuous d’employer la caracteristique S pour les integrales
relatives aux accens superieurs des lettres. L’expression
^[S(y,^) . S(v,£')] devient par le developpement de chacun de
ses termes, et en vertu de la premiere formule de l’art. 1 ou de
celle du no. 4 ,

+%„ »>„£, - +&c.

+ 2z,c„ - 3z,v„5 y,i„ + %y - 2z„u„%X, + &o.

+ &C.

490 Proceedings of Royal Society of Edinburgh, [july 18,

En indiquant done par Sx des integrates qui supposent, dans
chaque terme, les rnernes accens inferieurs aux lettres du
meme alphabet, ces accens pouvant etre ou non les memes
pour celles des alphabets differens, on pourra ecrire la
precedente suite, en faisant usage de ce signe, ce qui donne

S[S(y, OS(v,f)] = s ,[ZyvM-$zvZyQ-

Cette nouvelle quantite est encore de la forme S(y', z"), en
sorte qu’on peut dire que le produit de fonctions, telles que

S{S(y, z') S(i>, 0} ,
sera lui-meme de la forme S (y, z").”

This, if I understand it correctly, may he paraphrased and ex-
panded as follows: —

Take the product of two sums of s resultants, viz.

toiVI + \v*W\ + feVI + •••• +
x {KW + WV\ + h^l + •••• + Wl}

or a \y}z?\ • 3 IV42I,

s=l s=l

where, it will he observed, all the resultants in the first factor
are obtained from the first resultant \yfzf\ by merely changing
the lower indices into 2, 3, . . . , s in succession, and that the
second factor is got from the first by writing v for y and £ for z.
Then form all the like products whose first factors are

I2/1VI, biVl> • • • ? \Vin~\n\‘,

these being along with \yfzf\ the \n{n- 1) resultants derivable
from the two sets of n quantities

Vi, Vi, Vi, • ■ • • , V*

1 2 3 r; W'

^1 > ^1 J # * 1 5 ^1 *

The sum of these \n{n- 1) products may be represented, if we
choose, by

m<n

Now if the multiplications be performed, there will be s 2 terms in
each product, and the theorem we are concerned with has its origin
in the fact that the sum of all 'the first terms of the products is

1887.] Dr T. Muir on the Theory of Determinants.

491

expressible as a resultant by applying the multiplication-theorem,
likewise the sum of all the second terms, and so on, the result
being an aggregate of s 2 resultants. For if we fix upon a particular
term of the first product, say the term

\yhW\Wtj\

which arises from the multiplication of the hth term of the first
factor by the 7dh term of the second factor, then take the corre-
sponding term of the other products, and write down their sum

\yfrh\-Wti?\ + \yh\

|V£*3|

+ + | y,r%

n— 1

it is manifest that this sum is by the multiplication-theorem

VhV1} + yhW + - • • • +Vhnvkn
Vhtk + V2tk + • • • • + VhVh

ZhW + ZhW + • • • .+zhnvtn
Zh'U1 + *k%2 + • • • • + zhnLn

Consequently since h may be any integer from 1 to s, and h like-
wise any integer from 1 to s, the theorem arrived at is accurately
expressed in modern notation as follows : —

n= 2
?n < n

r s—s

S|

L s=i

y,mz,n I • s’ | v,”L

s—1

1

h=s VhW + VhW + • • • + ukv* + ZhW + •

+ yft*2 + • • • + yhnLn + •

= 22

7c=l A=1

or

y,} yk2 . .

k= 1 h=l

Vh

V Vk2 .
& Ik2 .

Vk

S' v

4fc

4- 7 ni> 7
^ zh vk

4-7 nr 7
^Tzh 4 k

It is easily seen to be true of resultants of any order, as Binet
himself points out. (xxx.)

When s is put equal to 1, it degenerates into the multiplication-
theorem.

The theorem which follows upon this, but which is quite
unconnected with it, may be at once stated in modern notation.
It is —

If ^|aqy2z3| denote the sum of the resultants obtainable from
the three sets of n quantities

/y» /y» ry* /y»

cA/2 g • 9 • •

Vi y» Vs • • • • y»

h Z2 Z3 • • • • Zn,

492 Proceedings of Roy cd Society of Edinburgh. [july 18,

and 2 1 x1y2 \ denote the like sum obtainable from the first two
sets, then

2Ky2*3| = %x.%\yxz2\ + %y.%\zxx2\ + %z.%\xxy2\ (xxxi.)

This is arrived at by writing out the terms of 2>|?/1z2| , of S|2pr2| , and
of in parallel columns, thus

\Vi h\

\Z1 X2I

1*^1 y^\

\Vi h\

\h ^3 i

K Vz\

Vu-l«n |

| Zn-lXn 1

1 • 0
J— «

then deriving n results from the members of the first row by
multiplying by xv y^ zx respectively and adding, multiplying by
x.2, y2, z2, and adding, and so on ; then treating the second and
remaining rows in the same way ; and then finally adding all the
n . \n(n — 1) results together. Each of these results is a vanishing
or non-vanishing resultant of the 3rd order, and it will be found
that each non- vanishing resultant occurs twice with the sign + and
once with the sign — .

This process is readily seen to be simply the same as performing
the multiplications indicated in the right-hand member of (xxxl), i.e .,

(x1 + x2 + . . .+xn)(\yYz2\ + \y^\ +. . .+ \yn-<zn\)

+ 0/1 + 2/2 + * • .+2/»)( \*XX2\ + \Z±X3\ + . . .+

+ (zl+z2 + . . .+zn) i\x-g/2\ + |aqy3j +. . .+ |#»_iy„|) ,

summing every three corresponding terms in the products, and

writing the sum as a vanishing or non-vanishing resultant. There
would be n . \n{n- 1) resultants in all; but as each suffix occurs
n- 1 times in the second factors and once in the first factors, there
must be in each product n— 1 terms having the said suffix occurring
twice : consequently there must be n - 1 resultants vanishing on
account of this recurrence, and therefore altogether n(n - 1) vanish-
ing resultants. Of the non-vanishing resultants, — in number equal
to n . \n(ii - 1) - n(n ~ 1), or \n{n - 1)(% - 2), — each one of the
form

I xhVkzi I where h<Jc<l

493

1887.] Dr T. Muir on the Theory of Determinants.

must be accompanied by two others,

| xkyhzt | and | xpyhzk | ,
and the sum of these is

I W | - | XhV&i | + | xhV£i i ,

i.en

I xhVhzi | •

The final result is thus the sum of the resultants of the form

c i

I xkVi£i | where h<k<l, and 1 = 3, 4, . . . , n,

the number of them, as we may see from two different standpoints,
being

J n(n - 1 ){n - 2) .

Returning to the series of identities,

^3 1 ^1^2 1 "b y3|^2l d" % | ^1^/2 1 ~ \xlV2Zz\ ’

^4l2/i%l + y4l%l + = K V2h\’

(fee. (fee.

which by addition give the result

%xt\yxz2\ + %y%\zxx2\ + %z%\xYy2\ = %\xxy^\,

Binet next raises both sides of all of them to the second power, and
obtains

^\xiU^\2 = 2«2:%i22.|2 + %25|^2|2 + 3z22|aqy2|2 >

I

+ 2Sjz2(iz1*2|.|*iy2l) + 2Sz*5(|*1?/2|.|?/122|) i(xxxn.)

+ 2S*2/S(|2/1z2|.|z1a:2|)J

Substituting for . . . . , their equivalents as given

by the multiplication-theorem, he then deduces

S|W3l2 = ^2%2^2 d~ 2 %yz%zx%xy — ^2(^2*)2 |

-%y\%zxf - %z\%xyf,)

not failing to note that this is not a fresh result, but merely a case
of the multiplication-theorem in which the factors are equal.

By putting the right-hand member here into the form

%y^{%^%x^ - {^yzf} + ^2l^2%2-(^y)2}

- %x2{%y2%z2 - (^yz)2} + T%yz\%zx%xy - %yz%x2} ,

there is next arrived at the first identity of the set

494

Proceedings of Boyal Society of Edinburgh. [july 18,

2 | I2

= $y22\hx2 12 + Sz2S|*i2/2I2 - Sa^ly^l2 + ^y^\hx2\\xiV^ , )

= %z>% \xggff + lix2%\ylz2\2 - %y2%\zxx2^ + 2^2^|x]?/2|j^2| , Wxxxm.)

= |2 + Sy2^^ |2 - %z2%\xlyf‘ + 23^31^2 |bf£2l , J

and immediately from these the set

2K2/2%|2=^2%^2!2 + ^^fiVzfydf + 2^%iZ2M^2l>i

= ^2E|^2|2 +. txytly^fz^ + tyz^z^.fgg^ , l (xxxiv.)
= %z2%\x1y2\2 + %yz$\zjx2\.\x$2\ + 'Zzx%\x1y2\.\y1z2\ . )

We may note in passing that either of these sets leads at once to
the initial theorem

$%\x1y#$ = '2fr2%\y1z2f + %22 1%^2|2 + 2z22Ky2|2

+ 2%yz%\z1x2\.\x1y2\ + 2%zx%\x1y2\.\y1z2\

+ 2%xy%\y1z2\.\z1x2\ ,

and that with the multiplication-theorem already established this
reverse order would be the more natural.

The next step taken is the formation of resultants of the 2nd order
from elements which are themselves resultants of the 2nd order ;
viz., just as from the three rows of n quantities

ry» ry* ry> ry*

*^1 *^2 ^3 • 9 9 •

Vl V2 ds • • • • Vn

ci ^2 ^3 • • • • ^ n

there were formed the three other rows of fj n(n- 1) quantities

\VlZ2\ > 1^1% 1 » '

• • • 5 \vM ? (^2^3) ? • • *

i ^\X2 1 ) !%^SI ’ *

.... 1 z,xm\ , \z-xd\ . . . .

, . . . 2 t X A

5 1 1 W 1 5 | 2 3 15

K?/2l 5 | *^l2/3 i J *

• • • J 1 X\V n | ) |*^2^3 1 ’ * *

• • • , K-l^nl

so from the latter three other rows of quantities

bi a?2|

I^i^sl

| - 2^n|

| ^"n - lAil

l^y2l

l^l^i

K-2&J

!''-n - l^n | J

K2/2I

fci-SS&J

K-lJ/nl

te!

\Vih\

|2/«-2^w|

li/n-l^w) }

|yAl

|2/izs!

l2/n-2^nl

1 Vn 1^«|

1^1 ^2!

K ^3 1

k-2^1

bn - 1 ^nl 5

495

1887.] Dr T. Muir on the Theory of Determinants.
are formed, the number in each new row being clearly

i.e ., \n{n - 1) (n - 2) {n + 1) .

The new quantities are, of course, not written by Binet in the form

III!’

but the fact that they are resultants of the 2nd order is carefully
noted. Each of them is shown to be transformable, by a theorem
which may be viewed as an extension of a result given by Lagrange,
so as to have two of the elements resultants of the 3rd order, and
the others resultants of the 1st order. This is done by taking, for
example, the identities

xfyM + yh\Wj\ + ^ = fjjjiZjl ,

XklVif + yjc\wA + ZkfiVA = Wyif >

multiplying both sides of the first by xk) and both sides of the
second by xh , subtracting, and writing the result in the form

KVhW^A + \xkzh H^l = ocjc\xhyizj\ - xh\3ckyiZj\ ,

xk

fkyfzj\

WVi*A

where of course it has to be noted that in many cases one of the
resultants of the 3rd order will vanish. The quantities, therefore,
to be dealt with, are

• • • , xAxhVizA ~ xAx*VizA > • • •

ViWj^A > • • ■

• • • , the I y h^ixj | - yfy^A > • • •

Z1 \Xl V2ZA > • • ■

• > zAzhxiVA - zAziMjA > • • •

. . , % n\Xn-2y n-V^n\ •

By raising each of the elements of the first row to the second power,
taking the sum and simplifying, we could, we are told, show that
the result would be

3|a,1y2^3|‘j .

Very prudently, however, another process is chosen. It is recalled
that the quantities in the third triad of rows are related to those in
the second as those in the second are related to those in the first,
and that consequently the required sum of squares of resultants is,
by the multiplication-theorem itself, expressible as a resultant, viz.,
vol. xiv. 1/2/88 2 1

496

Proceedings of Boyal Society of Edinburgh. [july 18,

^\Wh\ > I x\y?> I }" ~ ^ I P • ^ I x\V% I2 (^i^i^l I ^1^/2 1 )2 ’

where the elements of the resultant on the right are sums of
products of quantities in the second triad of rows. Then the same
theorem is used to make a further step backwards, viz., to express
each of these three sums of products of resultants as a resultant
whose elements are sums of products of the quantities in the first
triad of rows, the effect of the substitution being

2||zi*2I > I ! |2 = — (Sz1*1)2}{S*12S2/12 — (Say/i)2}

- \$z1xl%x]yl - jS*!2}2 .

Simple multiplication transforms this into

2x 2 1 S^S^Szj2 - ty^{%z ft)2 - )

' 1 ( + 2’Sfljlz1'S,z1x{%xly1 - 2x12(Sj/1z1)2 > ’

which, by still another use of the multiplication-theorem, we know
is equal to

%\xxyfa 'j2.

The set of six results of which this is one, is

SXj2 =S*12S|a:1?/2z3|2,

SYj2 = S^2 2|Ws|2 ,
tZ? =Sz12S|cc12/2z3|2,

SYjZj = S^ZjSta^Zgl2 ,

SZjXj = 2zr«1S!x1:y2z3!2 »

SXjY1 =

if, for shortness, we denote the quantities of the third triad of
rows by

-^2>

Y1( Y2,

z2,

Following these, and deduced by means of them, is an equally
noteworthy theorem regarding the sums of squares of all the result-
ants of the third order, which can he formed from the quantities
of the second triad of rows, Denoting these quantities tempo-
rarily by

£i> &

Vi>

£u £2’

(xxxv.)

497

1887.] Dr T. Muir on the Theory of Determinants.
we know (xxxn.) that

32|&2f8|2 = SX^2 + SY,2^2 + SZ^2
+ ^ + 2^ZxXx . SfA

+ 22X1Y1 . ;

whence, by using the set of six results just obtained, we have
3S|f1%&|2

= SIa. .2 f I

1 1 2'3 1 + 22 v^v^ih + 2S^. 2%*! + 22^.2^ )

and therefore, again by (xxxn.)

SI4%&P = {S^AI2}2- (xxxvi.)

It is finally pointed out that from the third triad of rows there
might, in like manner, be formed a fourth triad, and analogous
identities obtained ; also that, instead of starting with three rows,
we might start with four ,

1 1»

^2>

^3» *

5 t,n

Xl>

«2»

x.3, .

. . . , Xn

Vi>

V2 3

Vs ’ •

• * * } Vn

zv

^2’

%3 •

• • * ) }

form from them other four

tWsI*

>

|^1 f 2*^3 1 j

V\x2y^ 3

thence in the same way a third four, and in connection therewith
establish the identity

+ = 0 (xxxi. 2)

and other analogues. (xxxn. 2 + xxxv. 2.)

The rest of the memoir, 52 pages, consists of geometrical appli-
cations of the series of theorems thus obtained.

CAUCHY (1812).

[Memoire sur les fonctions qui ne peuvent obtenir que deux
valeurs egales et de signes contraires par suite des transpositions

498

Proceedings of Royal Society of Edinburgh. [july 18,

operees entre les variables qu’elles renferment. Journ. de VEc.
Polyt ., x. Cali. 17, pp. 29-112.]

This masterly memoir of 84 pages was read to the Institute on
the same day (30th November) as Binet’s memoir, of which we
have just given an account. The coincidence of date has to be
carefully noted, because the memoirs have in part a common ground,
and because there is a presumption that the authors, knowing this
beforehand, had, in a friendly way, arranged for simultaneous
publicity. Binet’s words on the matter are —

“ Ayant en derni&rement occasion de parler a M. Cauchy,
ingenieur des ponts et chaussees, du theoreme generale que j’ai
enonce ci-dessus, il me dit etre parvenu, dans des recherches
analogues a celles de M. Gauss, a des theoremes d’analyse qui
devaient avoir rapport aux miens. Je m’en suis assure, en
jetant les yeux sur ces formules : mais j ’ignore si elles ont la
meme generality que les miennes : nous y sommes arrives, je
crois, par des voies tres-differentes.”

And Cauchy’s corroboration is (p. Ill) —

“ J’avais rencontre l’ete dernier, a Cherbourg, ou j’etais fixe
par les travaux de mon etat, ce theoreme et quelques autres du
meme genre, en cherchant a generaliser les formules de M.
Gauss. M. Binet, dont je me felicite d’etre 1’ami, avait ete
conduit aux memes resultats par des recherches differentes.
De retour a Paris, j’etais occupe de poursuivre mon travail,
lorsque j’allai le voir. II me monfcra son theoreme qui etait
semblable au mien. Seulement il designait sous le nom de
resultante ce que j’avais appele determinants

Cauchy prefaces his memoir by another, entitled

Sur le nombre des valeurs quune fonction pent
acquerir lorsquon y permute de toutes les manieres
possibles les quantites quelle renferme.

This latter must to a certain extent be taken into account, because
it serves to show the point of view which he considered most
natural for examining the subject, and also the exact position held
by the functions now called determinants, when functions in

1887.] Dr T. Muir on the Theory of Determinants.

499

general come to be classified according to the number of values they
are able to assume in certain circumstances.

At the outset of it the writings of Lagrange, Vandermonde,
and Kuffini are referred to ; tbe fact is recalled that the maxi-
mum number of values which a function can acquire by inter-
changes among its n variables is 1.2.3 .... n\ also that when
the maximum is not obtained, the actual number must be a factor
of the maximum; and then proof is given of the very notable
theorem that the number of values cannot be less than the greatest
prime contained in n without being equal to 2. It is pointed out
likewise that functions capable of having only two values are
known from Vandermonde to be constructive for any number of
variables. For example, the number of variables being three,
av a.2, aB, all that is needed is to form their difference-product

(<x3 — a2) (a3 — a x) (a2 — af)
or

afa2 + afaY + afa3 - (a32a1 + afa3 + afaf) ,
when it is found that either of the parts

afa2 + afaY + afa3 ,
or

afaY + afa3 + afa2 ,

is an instance of a function capable of only two values by permu-
tation of the variables ; the result indeed of any permutation being
merely that the one function passes into the other. Further, the
whole expression

afa2 + afax + afaB - («32cq + afaB + afa2)

is another example, the difference between the two values which it
can assume being however a difference of sign merely. As a refer-
ence to the title of the memoir of November 1812 will show, it is
functions of this latter class which Cauchy there considers.

At the commencement he contrasts them with functions which
suffer no change whatever by permutation of variables, that is to
say, sigmmetric functions : and, noting the fact, afterwards ascer-
tained, that the new functions consist of terms alternately + and - ,
and that were it not for this alternation of sign they would be
symmetric functions, he decides to extend the term “ symmetric ”
to them, and having done so, seeks to distinguish them from ordi-

500

Proceedings of Royal Society of Edinburgh, [july 18,

nary symmetric functions by calling them “fonctions symetriques
alternees,” and calling the other “ fonctions symetriques per-
manentes.” Cauchy’s view of determinants may therefore now
be described by saying that he considered them as a special class of
alternating symmetric functions.

To include them, however, either the adoption of a convention
is necessary, or an extension of the definition must be made. For
example, a1b2 ~ °f\ is not an alternating function, unless the
elements be so related that the interchange of ax and a2 necessitates
the interchange of bY and b2 at the same time; or unless the definition
be so worded that interchange shall refer to suffixes, not to letters.
Cauchy selects the former course, his words being (p. 30)

“ concevons les di verses suites de quantites

6^25 $2* • • • • j d'n

b\> b2, . ... , bn

Ci, c2, . ... , cn

tellement liees entre elles, que la transposition de deux indices
pris dans Tune des suites, necessite la merne transposition dans
toutes les autres ; alors, les quantites

bit ^i» • • • ) b2, c2 , . . . , b g, c3, ... .
pourront etre considerees comme des fonctions semblables de

® • e e y

et par suite, les fonctions de

av ci>

, a2, b2, c2, ° . • , an, bn , cn, ....

qui ne changeront pas de valeur, mais tout au plus de signe, en
vertu de transpositions operees entre les indices 1, 2, 3, .... n,
devront etre rangees parmi les fonctions symetriques de
«!, a2, . . . , an , ou, ce que revient au meme, des indices
1, 2, 3, . . . , n. Ainsi

a\ + + 4 axa2 ,

+ a2b2 + «3&3 + 2C!C2C3 ,
af2 + a^b 3 + affi-^ 4- a2b^ •{■ a3b2 + af3 ,
cos ( ax - a2) cos ( ax - a3) cos ( a2 - a3) ,

501

1887.] Dr. T. Muir on the Theory of Determinants.

seront des fonctions symetriques permanentes, la premiere du
second ordre et les autres du troisieme ; et au contraire,

cif>2 “H af) 3 -t- af>Y — af>^ — cq53 — af>2 >
sin (a1 — a2) sin (cq - af sin ( a2 — a3)
seront des fonctions symetriques alternees du troisieme ordre.”

The question of nomenclature being settled there next arises the
question of notation. This also is decided on the ground of the
resemblance of the functions to symmetric functions. It being
known that any symmetric function is representable by a typical
term preceded by a symbol indicating permutation of the variables,
e.g.

S(a1b2) or S*(aA) standing for a1b2-{-a2b1

and S 3(a1b9) standing for a1b2 + a2bs + afl + a2b1 + ajb2 + a1bB ;

also, that any non-symmetric function may be taken as the typical
term of a symmetric function, the question arises whether the like
may not be true of alternating functions. A lengthy examination
of the latter point leads to the conclusion that any non-symmetric
function K cannot be the originating or typical term of an alter-
nating function unless it satisfies a certain condition, viz., that it be
such that any value of it obtained by an even number of transposi-
tions of indices will be different from any other value obtained by
an odd number of transpositions. Should, however, this condition
be satisfied, and Ka, K^, Ky, .... be all the values of the former
kind, and Kx, K M, K^, .... all the values of the latter kind, then

(Ka + K^ + Ky + . . . . ) — (Ka + K^ + K„ + ....)
is an alternating function and is appropriately representable by

S(±K)

if the indices appearing in K alone are to be permuted, and by

Sw( ± K)

if the indices to be permuted be 1, 2, 3, . . . , n. For example,
taking the typical term axb2 we have

S ( ± cq52) = af)2 - a2b1 ,

and S3( ± of 2) = af 2 + a2bB + ajbY - - aBb0 - a1 bB ,

= S3( + afj = S3( + afz) = . . . .

502 Proceedings of Royal Society of Edinburgh. [july 18,

S4( ± a1b2) is an impossibility, as when there are four indices a1b2
does not satisfy the condition required of a typical term ; indeed,
Cauchy notes that the number of indices in any term must either be
the total number or 1 less.

The number of permutations being even, it is clear that the
number of + terms Ka, K^, . ... is the same as the number of
negative terms Ka, K^, (x. 2)

a generalisation of a remark of Vandermonde’s.

Further, since Ka, Kp, . . . are all the terms that arise from an
even number of transpositions, and Ka, Km, .... all those that
arise from an odd number of transpositions, it is plain that any
single transposition performed upon each of the terms of the
function

(Ka + K/3 + Ky + . . . . )-(Ka + Km + Kv + . . . . )
must change it into

(Ka + K^ + K„ + . . . . ) — (Ka + K|S + Ivy + . . . . )

— this is, in fact, the proof that it is an alternating function — con-
sequently each of the parts

Ka + K|3 + Ky + ....,

Ka + K^ + Kv + ....,

belongs to the class of functions which have only two different
values.

Also it is evident that if throughout the function any particular
index be changed into another and no further alteration made , the
resulting expression must be equal to zero , (xii. 5)

a theorem regarding alternating functions which is the generalisation
of a theorem of Vandermonde’s.

We have lastly to note, that the criterion which determines
whether a particular K belongs to the class Ka, K^, .... or to the
class Ka, K^, .... is incidentally shown to be reducible to a more
practical form. For example, if the term be K0, and it be derivable
from K , say, by the change of the suffixes 1, 2, 3, 4, 5, 6, 7 into
3, 2, 6, 5, 4, 1, 7, that is to say, in Cauchy’s language by means of
the substitution

1. 2. 3. 4. 5. 6. 7

1887.] Dr T. Muir on the Theory of Determinants.

503

we transform this substitution into a “ product ” of “ circular ”
substitutions, viz., into

and subtracting the number of “ factors,” 4, from the total number
of suffixes 7, make the sign + or - according as this difference is even
or odd.

Here the subject of general alternating functions may be left for
the present. What remains of the first part of the memoir, refers to
special cases, which naturally fall to be considered in another chapter
of our history. At the close of the part, Cauchy says (p. 51) —

“ Je vais maintenant examiner particulierement une certaine
espece de fonctions symetriques altern^es qui s’offfent d’elles-
memes dans un grand nombre de recherches analytiques. C’est
au moyen de ces fonctions qu’on exprime les valeurs generates
des inconnues que renferment plusieurs equations du premier
degre. Elies se representent toutes les fois qu’on a des
equations a former, ainsi que dans la theorie generale de
l’elimination.”

The writings of Laplace, Vandermonde, Bezout, and Gauss are
referred to, and from the latter the name “ determinant ” is adopted.

The second part bears the title —

Des fonctions symetriques alternees designees sous le
nom de deter minans.

and opens with the following explanatory definition (p. 51) — -

“ Soient av a2, .... , an plusieurs quantites differentes
en nombre egal a n. On a fait voir ci-dessus qu’en multi-
pliant le produit de ces quantites, ou

CL-^CLqfXiQ • • • •

par le produit de leurs differences respectives, ou par

(a2 - of) (a3 - af) . . . (an - af) (a3 - a2) . . . (an - a2) . . . (an - an_i)
on obtenait pour resultat la fonction symetrique alternee
S( ± aYafaf ann) ,

504

Proceedings of Royal Society of Edinburgh, [july 18,

qni par consequent se trouve toujours egale au produit

• • • • CLyi

x (a2 - a1)(a3 - a2) . . . ( an - a1)(a3 -a2) . . . (an - «2) . . . (an - an a) .

Supposons maintenant que Ton developpe ce dernier produit,
et que dans chaque terme du developpement on remplace
1’exposant de chaque lettre par un second indice egale a
l’exposant dont il s’agit, en ecrivant par exemple ars au lieu
de ars, et aSiT au lieu de asr, on obtiendra pour resultat une
nouvelle fonction symetrique alternee, qui, au lieu d’etre
representee par

S(± a11a.22af .... ann)
sera representee par

S(± ®l*1^2*2®3*3 * • • • n) )

le signe S etant relatif aux premiers indices de chaque lettre.
Telle est la forme la plus generale des fonctions que je
d^signerai dans la suite sous le nom de determinans. Si l’on
suppose successive ment *

n — 1, n = 2, &c

on trouvera

S( ^ ^l*i^2'2)

S( ± ^1*1^2* 2^3*3)

&C. ....

aV 1^2*2 ^2* 1^1’ 2 ’

Cty l^2'2^3'3 ""H ^9* 0^4 • 3 ^3* 1^1*2^°* 3

CL-^* 4^3* o^9* ^ ^3* 1^2* 9^1* 3 ^2*1^1*2^33

pour les determinans du second, du troisieme ordre, &c. . . . .

In regard to this it is important to notice that there are really
two definitions given us. The latter, viz., that involved in the
symbolism of alternating functions,

S( + t?2*1^2'2^3,3 * • • • n)

contains nothing more than Leibnitz’s rule of formation and an
improved rule of signs. The former is new and may be paraphrased
as follows : —

7/ the multiplications indicated in the expression
x (a2 - a1)(a3 - oq) . . . (an - a1)(a3 - a2) . . . ( an - a2) . . . ( an - an_2)

* n = 2, n = 3, &c. is meant.

1887.] Dr T. Muir on the Theory of Determinants.

505

be performed , and in the result every index of a power be changed
into a second suffix, e.g., ars into ar>s, the expression so obtained is
called a determinant (vm. 2),

and is denoted by

S (±a1.1a2.2a3.% .... an.n) (vii. 5).

In this definition the rule of signs and the rule of term-formation
are inseparable — a peculiarity already observed in the case of
Bezout’s rule of 1764.

After the definitions various technical terms are introduced. The
n 2 different quantities involved in

S ( + • • • • ®rvn)

are arranged thus

f ari 5

aV2 1

al‘3 ’ * *

. . a^.n

j a2‘l ’

a2'2 ">

a2- 3 ’ ‘ •

. . a2.n

] a3’l ’

&c. .

a3'2 J

CO

CO

e

. . a^.n

. an’l 5

an.2 ,

av.% , . .

• ° an. n

“ sur un nomhre egal a n de lignes horizontales et sur autant de
colonnes verticales,” and as thus arranged are said to form a
symmetric system of order n. The individual quantities avl, &c.
are called the terms of the system, and the letter a when free of
suffixes the characteristic . The u terms ” in a horizontal line are
said to form a suite horizontal, in a vertical column a suite verticale.
Conjugate terms are defined as those whose suffixes (“ indices ”)
differ in order, e.g., a2.3 and a3.2; and terms which are self-conjugate,
e.g., avl, a2.2, . . . are called principal terms. The determinant is
said to belong to the system, or to be the determinant of the system.
The parts of the expanded determinant which are connected by the
signs + and - are called symmetric products, and the product

avia2’2az'z • • • • an.n

of the principal “ terms ” is called the principal product. The
“ principal product,” however, is also called the terme indicatif of
the determinant, and thus an awkward double use of the word
“ terme ” is brought into prominence. The system

506

Proceedings of Royal Society of Edinburgh. [july 18,

f av\

a2'l

a2,'\ • • • •

j aV2

(^2* o

a3. 2 • • • •

i avz

CO

03

(X3.3 . . . .

j &C.

1 aVn

a2' n

a^.n . . . .

Cf*n%\

^k'3

C^n'n

derived from the previous system by interchanging the suffixes of
each “ terme ” is said to be conjugate to the previous system. A
symbol for each of these systems is got by taking the last “ terme ”
of its first “ suite horizontal, ” and enclosing the “ terme ” in
brackets : in this way we are enabled to say that {avj) and (an.j)
are conjugate systems.

In the course of these explanations a modification of the rule of
term-formation is incidentally noted, the form taken being specially
applicable when the quantities of the system have been disposed in
a square. Cauchy’s wording of this now familiar rule is (p. 55) —

. .... “ pour former chacun des termes dont il s’agit, il
suffira de multiplier entre elles n quantites differentes prises
respectivement dans les differentes colonnes verticales clu
systeme, et situees en merne temps dans les diverses lignes
horizontales de ce systffine.”

Here we may note in passing that the disposal of the “ termes ” in
a square might have enabled Cauchy to point out (which he did not
do) the difference between Gauss’ use of the word “ determinant ”
and his own, by saying that the “ determinant of a form ” had its
conjugate u termes ” equal.

The rule of signs applicable to alternating functions in general
is modified for the special case of determinants, and takes the
following form (p. 56) : —

“ l^tant donne un produit symetrique quelconque, pour ob-
tenir le signe dont il est affecte dans le determinant

S( i ^Tl ^2' 2^3*3 • • • • ^ n'n )

il suffira d’appliquer la regie qui sert a determiner le signe d’un
terme pris a volonte dans une fonction symetrique alternee.
Soit

a>a ci 1 3.0 a^.n

le produit symetrique dont il s’agit, et designons par g le

1887.] Dr T. Muir on the Theory of Determinants. 507

nombre des substitutions circulates 4quivalentes a la substi-
tution

A 2 3 n\

\« P y O'

Ce produit devra etre affecte du signe + , si n - g est un
nombre pair, et du signe — dans le cas contraire.” (in. 18).

Thus if the sign of the term

aQ'l a§'2 ^3-3 ai'4 a9’5 a2'Q ab'7 a4’S ^7*9

in the determinant

S( ± avl ct2'2 az’3 ' • • • ^9*9)5

be wanted, we write the series of first suffixes 6, 8, . . . under the
corresponding suffixes of the “ principal product,” that is to say,
under the series 1, 2, 3 . . .9, obtaining the interchange

/I 2345678 9\

\6 8 3 1 9 2 5 4 7/;

this we separate into circular interchanges, finding them three in
number, viz.,

/3\ /5 7 9\ /I 2 4 6 8\

\3/» *9 5 7/’l6 8 1 2 4/;

and the determinant being of the 9th order, we thence conclude that
the desired sign is ( - )9"3, i.e., + . In connection with this subject
a modification of Cramer’s rule is given, no reference being made to
“ derangements ” at all. Put into the fewest possible words it is —
The sign of the term aa.x ap.2 . . . . a$.n is the same as the sign of
the difference-product of the first suffixes , that is, the sign of

(ft ~ a) (y “ a)

For example, the sign of

(111. 19).

a6'l a8'2 a3'3 al*4 aXb a2'6 ab'7 a4‘8 a7‘9 >

above sought, is the sign of the difference-product of

6, 8, 3, 1, 9, 2, 5, 4, 7

i.e., the sign of

(7 - 4) (7 - 5) (7 - 2) (7 - 9) (7 - 1) (7 - 3) (7 - 8) (7 - 6)

x (4 - 5) (4 - 2) (4-6)

x (5-2) (5-6)

x (8-6)

508 Proceedings of Royal Society of Edinburgh, [july 18,

The object which Cauchy had in view in stating the rule in this un-
necessarily complex form was doubtless to show its essential identity
with the rule implied in his new definition. He says (p. 58) —

“ On demontre facilement cette regie par ce qui precede,
attendu qu’une transposition operee entre deux indices change
toujours, comme on l’a fait voir, le signe du produit

(h/3 ^a) (^y ^a) • • • • ^a) (hy ^js) • • • • >

et par consequent celui du produit

((3-a) (y- a) . . . (£-a) (y-fi) . . . . ”

The way having thus been prepared, the propositions of deter-
minants are entered on. Those known to his predecessors we may
dispose of rapidly, giving little, if anything, more than the enuncia-
tion of them, in order that the new garb in which they appear may
be seen.

. . . . “ le determinant du systeme (< an .x) est egal a celui du
systeme (arn) En consequence, dans Texpression

S( =*= • • ' • an'n)

on peut supposer indifieremment, ou que le signe S se rapporte
aux premiers indices, ou qu’il se rapporte aux seconds : (ix. 2).

Si Ton echange entre elles deux suites horizontales ou deux
suites verticales du systeme (arw) de maniere a faire passer
dans une des suites tons les termes de 1’autre et reciproque-
ment on obtiendra un nouveau systeme symetrique, dont le
determinant sera evidemment egal mais de signe contraire a
celui du systeme ( aVn ). Si Ton repete la meme operation
plusieurs fois de suite, on obtiendra divers syst&mes syme-
triques dont les determinans seront egaux entre eux, mais
alternativement positifs et negatifs. On peut faire la meme
remarque a 1’egard du systeme (an.-^) (xi. 3).

si Ton developpe la fonction symetrique alternee

dl it Cl ^2‘2 • • • • ^w-l*w-l)J

tous les termes du developpement seront des produits syme-
triques de 1’ordre n, qui auront l’unite pour coefficient. Ces

1887.] Dr T. Muir on the Theory of Determinants.

509

termes seront done respectivement egaux a ceux qu’on obtient
en developpant le determinant

Dw 8>( db ^2- 2 • • • • an. ri) )

et comme le produit principal avla2.2 . . . an.n est positif de
part et d’autre, on aura necessairement

Dw = S[ =•= an.nS( =*= dyi a2.2 .... an_l.n_1 )] (vi. 3)

d'n’ifn’n d“ ^■n-\“nhn-\'n d" • « • • d“ «

En general, si Ton designe par /x Tun des indices 1, 2, 3, . . . , n
on trouvera de la meme maniere

Dw = S[ =*= ^ ^1*1 ^2’2 • • • • ^fJL- l^/u.+1'M+l ' ' '

(VI. 4).

..... Cette derniere equation

0 = ai'J>i > d- d- . . . d- awvbn> (XII. 6)

sera satisfacte toutes les fois que v et /x seront deux nombres
differens l’un de l’autre.

.... on aura done aussi

D „ = a/t.16jx.1 d- aM.2&M.2 + . . . . d- (vi. 4)

0 = av.jb^ + av.2bfJi.2 + . . . . -i- av.nbfJL.n (xii. 6)

les indices [x et v etant censes inegaux.”

The expressions here denoted by bvl, bv2 , . . . . are spoken of

as adjugate (“ adjointes”) to avv av2 , .

. . ; and the system

f ^1*1 \'2

J ^2-1 ^2-2

j &C

. b2.n

5n. j bn. 2

• i*n'n

as adjugate to the system ( aVn ). Similarly the system {bn.j) is said
to be adjugate to the system (an.j) ; and, on the other hand, it is
said to be adjugate and conjugate to the system (aVn).

Up to this point no new property has been brought forward.
The following paragraph (p. 68), however, opens new ground, the
formula given in it being of some considerable importance in the
after development of the theory.

“ Si dans le systeme de quantites (a^j) on supprime la derniere

510

Proceedings of Royal Society of Edinburgh. [july is,

suite horizontale et la derniere suite verticale, on aura le
systeme suivant,

avl ,

a2.x ... .

«2"1 3

a-2'2

®2*» - 1 ’

&c. . .

• •

an- 1*2

®n- \‘n- 1 3

que je designerai a Fordinaire par (< aVn_ 1).

“ Soit maintenant (eVn-^) le systeme adjoint au precedent. Si
dans Fequation (13) on change b en e et n en n — 1, ou aura
en general

D^i = bn.n — + ...+ afJL.n_^efJ_.n_^ .

Pour deduire de cette derniere equation la valeur de b .n1 il
suffira en vertu des regies etablies, de changer en an.v dans
Fexpression precedente de bn.n, et de changer en outre le signe
du second membre : ou aura done generalement

bfx-n — K-lVl "h ^w*2^ju,*2 b b *

Si dans cette equation on donne successivement a /x toutes les
valeurs entieres depuis 1 jusqu’a n- 1, et que l’on substitue
les valeurs qui en resulteront pour bVn , b
Fequation

/25W

i"-bn_ yn dans

10 w vP\'n b Cley.fc^n "b * * * * "b an.nbn.n ,

on obtiendra la formule suivante,

= a,

n’nun’n

[ <h

vf^n' ;

Lei’l

+

^2‘n^n‘ 2^2"

2 b • •

. 4- an

- \'vf ^n

31 - 1^31 “ 1* 31 - 1

+

an.2^Y2

+

an' 3ei*3

+ . .

. + an

n- 1)

+

<^2,n(

an' Ie2*l

+

an‘Se2’3

+ . .

. + an.

»- Ie2*

>3 — 1 )

+

&C.

. +

1

1*1 +

(^n‘2en-l‘2

+ . . .

"b anm n _ 2671 -

l*3*-2)*

Cette equation peut etre mise sous la forme

Dn = an.n D*n.]. - XS n~1(av.nan.fllcv.fl), (xxxvii.)

les deux signes S etant relatifs le premier a l’indice /x et le
second a Findice v.”

This is the well-known formula nowadays described as giving
* Misprint in original, for

1887.] Dr T. Muir on the Theory of Determinants.

511

the development of a determinant according to binary products of
a row and column. The special row here used is the wth and the
special column the nth likewise.

The four pages regarding the application of determinants to the
solution of a set of simultaneous equations may be passed over with
the remark that they give evidence of the importance attached by
Cauchy to his new definition of determinants, the solution in the
case of the example

+ blx1 = mY
a2x1 + b2x2 = m2

being first put in the form

mb(b - m) am(m - a)

X ~ ab(b - a ) » ^ ~ ab{b - a) 1

and similarly in the case of the example

arxx + brx 2 + crx3 = mr (r = 1 , 2, 3) .

The determinant solution of a set of simultaneous equations is
put to good use by Cauchy to obtain new properties of the functions.
Taking the set of equations

f + «i-2^2 *t" d" aynXn = 771^

a + a2.2x2 + + a2.nxn = m2

&c

an. -yX\ "I- a n. 2x2 “l- ..... *1“ ctn.nxn

and solving for xv x2, . . . he obtains of course the set

mlbvl + m2b2.1 + + mnbn. x = Dnxl: j

mfv2 -f mjb2.2 + + mnbn.2 = Dvx2 , j

&c

mfjyn + m2b2.n + + mnbn.n — X)nxn , J

where bri, b2.l, have the signification above indicated,

and Dn stands for S( ± avla2.2 . . . an.n). This second set may
be treated in the same way as the first set, the quantities
mv m2, . . . , mn being viewed as the unknowns. To express the
result the system of quantities adjugate to (brn) is denoted by
(c1<n), and the determinant of the system (bVn) is denoted by BM, the
new set thus being

vol. xiv, 13/2/88 2 R

512

Proceedings of Royal Society of Edinburgh. [july 18,

'criD^i

+

^l‘2^nX2

4- . .

- . +

Cy nPnXn

Bn???!

^ C2’ll)nXl

+

C2'2^nX2

+ . . .

^2 ‘nPnXn

B nm2

&C. . .

+

Cn. gx2

+ . .

. . ■+•

Cn'nP iftn

B nmn

Cauchy then proceeds (p. 77)—

“ Bes equations (27) peuvent encore etre niises sous la forme
suivante,

Dn

cn^i

DM

+ CV2jTX2

+ . . .

, . DW/i

’ ( l'n I , Xn ?

K

B)w

c2iip h

^ n

, I)n

^ °2*2p“^2

+ * 6 .

. B)w

• + c2rn-^xn = m2 ,

<fec. . .

• e • • e .

J)n

Cn- 1

, Dw.t

+ Cn'2^p~X2
£>n

+ . . . .

B )n

Cn>n~rrXn “ Uln ,

Bw

et commes celles-ci doivent avoir lieu en merne temps que les
equations (20), sans que l’on suppose d’ailleurs entre les termes
de la suite xv x2, . . . . , xn et ceux du systeme (n1>n) aucune
relation particuliere, il faudra necessairement que Ton ait quels
que soient g et v,

D.

^V‘rT)" ~~ 9

ou

B*

(XXXVIII.)

Cette equation etablit un rapport constant entre les termes du
syst&me (avj) et les termes du systeme adjoint du second
ordre (cr„).”

More definitely, and in more modern nomenclature, the theorem is
The ratio of any element of a determinant to the corresponding
element of the second adjugate determinant is equal to the ratio of
the determinant itself to its first adjugate . (xxxviil)

Attention is next directed to the group of equations—

1887.]

Dr T. Muir on the Theory of Determinants,

513

rH

03

1!

II

II

rH

03

3*

r»

?f

cf

cf

+

+ ■

+

•

•

•

+

+

+

03

03

03

rH

03

k

3

03

03

03

3

cf

3S

+

+

+

rH

rH

rH

r— (

03

<3

rH

rH

rH

s

£

k

3

3

3

*

*

03

03

O!

rH

3

03

3S

II

II .

II

8

s

5

3^

03

<M

3

03

d

3

+

+

+

+

+

+

03

03

rH

03

e

3'

03

03

(N

03

03

C^l

C$

S

3

+

+ '

+

rH

rH

rH

rH

3

03

e

Jp

rH

rH *

rH

03

03

03

d

3

3

rH

r-l

rH

rH>

■Vj

3

II

II .

i

03

3

rH

^ *

3

d

+

+

+

+

+

+

03

03

03

03

5*

e

e

03

03

03

rH

rH

3

3

d

+

+

+

r-H

rH

rH

03

£

3_ .

^5

*-<

rH.

1h

r— <

3

d

514 Proceedings of Royal Society of Edinburgh. [july 18,
Here there are three symmetric systems of quantities

(«!•») ? (^1‘m) 5 (mVn) )

the first appearing in every column of equations, the second in
every row, and the third only once. The determinants of these
systems are denoted by

Dm , Sn , M„ ,
respectively : that is to say

T)M = S(:h ^1*1 ^2*2 • • • ®»'n)

&n = S( ± aria2.2 . . . an.n)

Mn = S(±m1.1w2.2 . . . m.n.n) .

If now in

+ * * • ®n*»)

there he substituted for mrl, m1>2 their values as given by

the group of equations, there will be obtained a function of all the
a’s and as, which must be an alternating function with respect to
the first indices of the cC s and also with respect to the first indices
of the a’s. Further, since each of the m's is of the first degree in
the a* 8 and of the first degree also in the a’s, each term of the
development of S(±m1.1m2.2 .... mn.n) must evidently be of
the form

— ®'1’M®'2"I/ • • • • • . . • Cln.n .

But the development by reason of its double alternating character
cannot contain such a term without containing all the terms of the
product

ih d~ oq*ju, a-2,v • ' * • • • a n‘Tt 5) •

Consequently it must equal one or more products of this kind. But
again the indices fi, v, . . ., ir are either all different or not. If
they be different, we have

S(±arjtAa2.v . . . an.ff) = ± S(± arla2.2 . . . a„.n)=±8„;
and if any two of them be equal

it ai’M- a2’V * * * 7r) = ^ *

The like is true in regard to S ± (arix,a2.v, . . . an.n,). This enables
us to conclude that the development of Mn is equal to one or more
products of the form

± T>n8n :

Mn = cDJn ,

in other words, that

1887.] Dr T. Muir on the Theory of Determinants. 515

where c is a constant. But if we take the very special case where

= 1 5 = 1 j — 0, a^.v 0,

and where consequently

“1? wv„ — ^ )

M„=l, Dn=l, SB=1,

c = l .

we see that
and that therefore
Hence the final result is

Mn = DA .

(xvn. 5).

This, the now well-known multiplication-theorem of determinants,
Cauchy puts in words as follows (p. 82) : —

Lorsqu’un systeme de quant it es est determine symetriquement
au moyen de deux autres systemes, le determinant du systeme
resultant est toujours eg at au produit des determinans des deux
systemes composans. (xvn. 5).

It is quite clear, from what has been said above, that it was dis-
covered independently, and about the same time, bv Binet and
Cauchy, and ought to bear the names of both. Binet has the
further merit of having reached a theorem of which Cauchy’s is a
special case, and then made an additional generalisation in a dif-
ferent direction ; and Cauchy has the advantage over Binet of
having produced, along with his special case, a satisfactory proof
of it.

From the theorem Cauchy goes on to deduce several results
equally important. Substituting for the system (aVn) the system
(brn) adjugate to ( aVn ) so that

SW=S( + ’ ‘ * ^n'v) ~ B„ J

we know that then

WW = Dn and m(L.v = 0;

that consequently Mw consists of but a single term, viz.

mrim2. 2 . . . mn.n, i.e. Dnn :
and that therefore by the theorem

d;=bj>m,
b^d;;1.

whence

(xxi. 2).

516

Proceedings of Royal Society of Edinburgh. [july 18,

This result, afterwards so well known, Cauchy translates into words
as follows (p. 82)

. ... le determinant du systeme (bVn) adjoint au systeme (aVn)
est egal d la, (n— 1 )me puissance du determinant de ce dernier
systeme . (xxi. 2).

Again, by returning to the identity,

n

and substituting the value of Bn just obtained, there is deduced the
result

= ( xxxix.)

or, in words,

. . . etant donne un ter me quelconque aY.v du systeme (ar«),
pour obtenir le ter me correspondant du systhne adjoint du
second ordre (cVv) il sujjira de multiplier le terme donne par la
in — 2)me puissance du determinant du premier systeme. (xxxix.)

A considerable amount of space (pp. 82-92) is devoted to the
consideration of the adjugate systems of

(«!■») 3 (®1*«) J (mrn) 3

and the adjugates of these adjugates ; but nothing new is elicited.
The section closes with the manifest identity

(arl 4- a2ll 4- . .

• + an-i) 4- a2<i 4 - •

. 4 -an.j)

+ (cip2 "h a2'2 •

• • Ta„.2) (a1.2 + a2.2 + . .

. + an.2)

4-&C. .......

4- (a1.n 4- a.2.n + . ,

• T ®-n.ii) (U].w 4" a2.n 4- . •

. + ct . )

niy i 4* m2.^ • ■

. 4- mn. T

4* my2 4“ m2. 2 4- . .

, + mv.2

4-

d"mi •« + %«+ • ■ • + mn' n 3

which, using later technical terms, we may express as follows : —

If there be two determinants, and the sum of the elements of one
first column be midtiplied by the sum of the elements of the other
first column, the sum of the elements of one second column by the sum
of the elements of the other second column, and so on, then the sum
of these products is equal to the sum of the elements of the product
of the two determinants. (xl.)

1837.] Dr T. Muir on the Theory of Determinants. 517
The third section breaks entirely fresh ground, its heading being

Des Systemes de Quantites derivees et de
leurs Determinans.

Of the integers 1, 2, 3, . . n all the possible sets of p integers
are supposed to he taken, and arranged in order on the principle
that any one has precedence of any other if the product of the
members of the former he less than the product of the members of
the latter. The number n{n - 1) . . . . (n — p + 1) / 1. 2. 3 . . . . p
of the said sets being denoted by P, the Pth and last set would
thus be

n — p + 1, n —p 4- 2, . . . . ., n— 1, n.

Now, any two of the sets being fixed upon, say the /Ph and Ph, the
system of quantities (aVn) is returned to, and from it are deleted
(1) all the “ ternies ” whose first index is not found in the set,
and (2) all the “ termes ” whose second index is not found in the
Ph set. What is left after this action is clearly “ un systeme de
quantites symetriques de l’ordre pf the determinant of which may

be denoted by a For example, if fx = v= 1, all the a’s would be

deleted whose first or second index was not included in the set
1, 2, 3, . . p} and there would be left the system

K-l al’2 * * ’ * aVP

S $2* 1 2 «•*«>« ^9 • p

| &c. ......

g .... dp.p

of which the determinant would be denoted by

c py.

aVl •

As any one of the P sets could be taken along with any other, pre»
paratory to forming such a determinant, there would necessarily be
in all P x P possible determinants. Arranged in a square as
follows : — -

( p )

C p)

( V )

avl

aV2 ....

avp

( p )

(p)

( p )

a2'l

flf-22 ....

a2 F

&c.

......

( p )

(P)

( P )

Op J

2 ....

a tv

518 Proceedings of Royal Society of Edinburgh. [july 18.

they manifestly form “ un systeme symetrique de Tordre P,” the
determinant of which, in strict accordance with previous convention,
is denoted by

p

«rp

Cauchy then proceeds (p. 96) —

Si Ton donne successivement k p toutes les valeurs
1, 2, 3, . . . ., n - 3, n - 2, n — 1

P prendra les valeurs suivantes,
n(n - 1) n(n - 1 )(n - 2)

n

1 . 2

1.2.3

n(n - 1)
1 . 2

et Ton obtiendra par suite un nomhre egal a n - 1 de systkmes
symetriques differens les uns des autres, dont le premier sera
le systeme donne (aVr) . Ces differens systemes seront designds
respectivement par

(«i-)> [«i- ’%f\ > [«?; n(n-\(n; 2)]

[fe]- [^•%)]> (C);

je les appellerai systemes derives de (aVn) . Parmi ces systkmes,
ceux qui correspondent a des valeurs de p dont la somme est
egale a n sont toujours de merne ordre ; je les appellerai
systemes derives complementaires. Ainsi en general

l pt ( ( n~P)\

sont deux systemes derives complementaires Tun de l’nutre,
dont Tordre est egal a

n(n- 1) . . . . (n-p+ 1)

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

yol. xiv. 1886-87. No. 125.

On the Conducting Paths between the Cortex of the
Brain and the Lower Centres in relation to Physiology
and Pathology. By D. J. Hamilton, M.B., F.R.C.S.Edin.,
F.R.S.E., Professor of Pathology, University of Aberdeen.
(Plates XIV., XV.)

(Read 31st January 1887.)

Methods. — The great difficulties heretofore encountered in investi-
gating the course of nerve fibres in the brain have been, firstly, the
want of a method of preparation by which their gross anatomy
could he thoroughly exposed, and, secondly, the failure of any
previously known process of staining to satisfactorily indicate their
direction on microscopic examination. In endeavouring to collect
reliable data from the records of lesions of the human brain, it
becomes only too evident that until more efficient methods of
localising lesions he adopted than those generally dn use at the
present day, little can possibly be added to the knowledge we already
possess.

The methods of preparation I now employ for demonstrating the
connections of the brain are chiefly the gelatine-potash process I
formerly described in the Journal of Anatomy and Physiology
(vol. xix., 1885, p. 385), along with a modification of Weigert’s
heematoxylene - copper stain for medullated nerve fibres lately
published by me in the same periodical (vol. xxi., 1887, p. 444).

VOL. XIV. 15/5/88 2 L

520

Proceedings of Royal Society of Edinburgh. [jan. 31 ,

The former method is suited solely for naked eye observation.
The main objection to Weigert’s stain is, as mentioned by its
author, that it cannot be adapted to cutting the tissue in the freezing
microtome. The modification above referred to has been introduced
with the view of overcoming this. The reaction of the nerve-
medulla is quite as intense if not more so than that obtainable
by the original procedure.

Could one unite the aniline-black stain of Sankey and Lewis for
nerve cells with this modification of Weigert’s stain for nerve fibres,
little would remain to be desired for microscopic demonstration.
The difficulty, however, is that the aniline-black dye will give its
proper reaction only when the brain is perfectly fresh, whereas the
hsematoxylene will act upon the nerve-medulla only when it has
been hardened in a chrome salt. I have, however, already managed
to partially combine the two, and see no insuperable barrier to
complete success.

The Callosal Fibres. — It is, I think, almost universally believed
at the present day that the corpus callosum is a commissure ; that
anatomically it unites equivalent areas in the two cerebral hemi-
spheres, and that physiologically it serves to bring these into
functional harmony. Some years ago, when working at the pathol-
ogy of the brain, I came upon certain appearances which tended to
shake my belief in the commissural theory, and which led to an
inquiry, part of the results of which is embodied in this paper.
The appearances alluded to are to be seen in the brain of any
mammal when it has been hardened in Muller’s fluid, but best
in those in which the organ is of large size, as in Man. It
was in Man that I first noticed the appearance, but I have since
then found that it exists in all the mammalian brains I have
examined. The Muller’s fluid, in the case of a large brain such
as that of Man, must be injected from the main vessels at the
base in order to insure that it will penetrate deeply and in sufficient
quantity.

If such a brain, when completely hardened, be simply cut into a
series of perpendicular transverse segments, each of about half an
inch in thickness, the following can be readily seen with the naked
eye or with a simple lens : —

Coming out of the corpus callosum at each side is a large arched

1887.] Prof. D. J. Hamilton on the Cortex of the Brain. 521

mass of fibres (see PI. XIY. fig. 1), which leaving this body and con-
tinuous with it turns upwards, outwards, and downwards in the
centrum ovale. The arcuate mass varies somewhat in shape at
different parts of the brain. Thus, anteriorly it represents an almost
complete semicircle, while posteriorly it becomes more pointed. The
fibres entering into the composition of the arched mass subse-
quently pass into the inner and outer capsules. The greater hulk
of them, however, enters the inner capsule, and in its anterior limb
the capsule is almost entirely composed of them ; while a consider-
able portion also seems to run into the outer capsule, constituting
the inner of the two kyers of which it consists. Their further
course and attachments to underlying parts will be subsequently
considered.

In a former paper [Journal of Anatomy and Physiology , vol. xix.,
1885, p. 385) 1 have named this mass of fibres the “crossed
callosal tract”; and as all my work since then has tended to fully
bear out the view I at that time entertained of its significance, I
propose still to adhere to this nomenclature.

In order to get at once to the gist of the arguments I intend
using to explain the nature of this crossed callosal tract, I shall
start with the postulate that it is mainly composed of callosal fibres
which have arisen from the cortex, which have crossed in the corpus
callosum, and which, instead of turning upwards to become attached
to points in the opposite cortex corresponding with those from
which they sprang, are now turning downwards into the two capsules
to become subsequently united to the basal or other ganglia presently
to be enumerated.

If it be true that the crossed callosal tract represents the fibres
derived from the opposite cortex, which have passed over in the
corpus callosum, and which are now turning down to the two
capsules, the following data ought to admit of verification : —

1. The crossed callosal tract ought to be capable of being dis-

sected out ;

2. It ought to be co-extensive with the corpus callosum ; and

3. It should be possible to trace the fibres microscopically as

they turn downwards.

I shall consider each of these in order.

522

Proceedings of Boy cd Society of Edinburgh. [jan. 31,

1. Foville long ago (“ Traite complet de l’Anatomie, de la Physio-
logic, et de la Pathologie du Systeme Nerveux Cerebro-spinal,” Atlas)
showed that an arched ridge of fibres could be exposed by simple
dissection turning downwards at each side of the corpus callosum,
and figured appearances which, allowing for a certain amount
of artistic embellishment, substantially represent what actually
exists. (The author here exhibited a brain, previously hardened
in Muller’s fluid, in which this dissection had been made, and in
which the arcuate mass of fibres was distinctly displayed. He
further showed this arcuate mass in horizontal sections prepared by
his gelatine-potash method, in which it was quite clearly mapped out.
Its fibres had a more or less transverse direction, so that they con-
trasted with those coming from the cortex, and the outer border of
the mass where they turn downwards was quite sharply differentiated.
The fact that the arcuate mass is seen on horizontal section com-
pletely does away with the notion that Foville’s dissection was
artificial. In a series of horizontal sections the crest of the ridge
was found to correspond in position with that in the dissection, the
site of it being at a point considerably below the level of the cortex
at the vertex.)

2. That the crossed callosal tract is co-extensive with the corpus
callosum can be proved by dissecting it out, or by examining it in a
horizontal gelatine-potash preparation.

3. To trace microscopically the fibres curving downwards from
the corpus callosum is not such an easy matter as might be supposed,
owing in great part to the fibres running in different planes between
their points of origin and insertion.

Meynert has alleged that he could trace single fibres from the
cortex of one side through the corpus callosum into the cortex of
the opposite. For my own part I can hardly credit this statement,
for, after having spent an immense deal of labour upon the subject,
and working with methods far more refined than those employed by
Meynert, it has never been my good fortune to follow a single axis
cylinder from the one side to the other even in the smallest
mammals. The fibres diverge and run so obliquely after crossing
that I question if a section made in any one plane would suffice to
expose their entire course.

If the brain be cut perpendicularly in an oblique antero-posterior

1887.] Prof. D. J. Hamilton on the Cortex of the Brain. 523

direction , however, the bundles of callosal nerve fibres can be traced
from about the middle line continuously down to the outer and inner
capsules , instead of upwards to the cortex as generally asserted .
In PI. XV. fig. 2 I have given an accurate drawing of a section
of the human brain ( x 10 diams.), stained and prepared by my
modification of Weigert’s method, and taken from a region corre-
sponding to the front of the basal ganglia. The parts of the
preparation included in the drawing are the tectorial part of the
corpus callosum (c.c.), the crossed callosal tract ( c.c.t .), the plexiform
nucleus ( p.n.)f the head of the caudate nucleus ( c.n .), and the inner
capsule (i.c.). The section from which the drawing was taken was
made perpendicularly in the oblique antero-posterior direction just
indicated. By so doing the continuity of a certain number of
callosal fibres, as will be noticed, can be followed in a direction
downwards, although it will be remarked that even here some of
them (as at s.c.f.) have been obliquely divided.

Prom the drawing it is evident that the bulk of the fibres issuing
from the side of the tectorial part ( c.c .) of the corpus callosum
sweep distinctly upwards, outwards, and downwards towards the
inner capsule (i.c.). They are united in coarse bundles, and thus
can be readily distinguished from those entering it (v.c.f. and p>.n.f.),
which, although in bundles, are less condensed, and which, more-
over, spread out in a radiate or fan-shaped manner. When the brain
is cut in a perpendicular transverse direction the continuity of these
fibres cannot be seen, because they have been severed by lying at
an angle to the plane of section. Hence it is, I believe, that they
have remained so long unnoticed. In no case have I been able to
see a single bundle of fibres run upwards after emerging. After
having crossed, the whole mass seems to turn downwards to the
capsules, and to form the greater part of their bulk.

In two late numbers of Brain (vols. viii. and ix.), Dr Beevor
has taken exception to this view as originally enunciated by me
in a communication to the Boyal Society ( Proceedings , No. 230,
1884), and in papers which I subsequently published in the
Journal of Anatomy and Physiology ( loc . cit.), in Brain (vol. viii.,
1886, p. 145), and elsewhere. He says that in the marmoset he has
been unable to see the fibres turning downwards in the manner I
* For description of this body see the sequel.

524 Proceedings of Royal Society of Edinburgh. [jan. 31,

have described, and gives a drawing which he considers demonstrates
that my view is wrong, and that the old idea of the fibres passing
from cortex to cortex is correct* He asserts that this drawing
is not a diagrammatic scheme, but an actual representation of a
preparation in his possession. He further states that he has made
oblique sections as I had directed, but still has been unable to see
what I described.

When I read this criticism, I felt certain of two things: first,
that Dr Beevor had not examined preparations cut in the oblique
direction I have recommended; and, secondly, that the drawing above
referred to was not an actual representation of the preparation from
which it was said to have been taken. I was convinced that what he
had endeavoured to depict consisted in reality of the fibres passing
into the corpus callosum, and that he had entirely failed to see, as
had happened to others, those which were issuing from it , owing to
his having cut the brain transversely instead of obliquely. In
justice to Dr Beevor’s statement, however, I resolved to see his
preparations for myself, and to hear his explanation of them by
word of mouth. I am constantly being reminded by so-called
critics that they are still sceptical of my statements, and the most
ardent are those who have never taken the trouble to examine my
work, nor really to work at the subject for themselves. The matter
is not one which can be settled in an offhand manner, but requires
the most careful scrutiny. If it had been easy to demonstrate what
I have recorded, it would long ago have been done.

My anticipations in regard to the basis on which Dr Beevor’s
criticism was founded were more than realised. I emphatically state
that the drawing of the corpus callosum given in his critique in
Brain (vol. ix.) is very far from being an actual representation of
the preparation from which it was taken. The continuity of the
fibres is not such as he depicts, for immediately at the outer margin
of the corpus callosum there is a break in the preparation caused
by a large number of fibres having been cut off abruptly, which
is not represented in the drawing. The fibres so cut across consti-
tute those I have described as turning downwards. They have
been severed, because they do not lie in the same plane as those

* Ferrier, I find, has somewhat hastily reiterated this statement in the
latest edition of his work on the Functions of the Brain.

1887.] Prof. D. J. Hamilton on the Cortex of the Brain. 525

entering the body. I further found that the oblique preparations
he employed had been cut in an entirely wrong direction, in a
direction which was calculated to divide the crossed callosal fibres,
instead of rendering them more apparent. As I have elsewhere
stated, he has not followed the directions I have so explicitly
given in various of my published papers, and hence it is useless to
argue the point. If he will harden the human brain, or, say, that
of a sheep, by the method I have recommended, and cut this per-
pendicularly in an oblique antero-posterior direction, he will see
what I have described. It is impossible, as I have already indicated,
to trace individual axis-cylinders throughout their entire course,
but the continuity of individual bundles between the corpus callosum
and the capsules can be demonstrated with facility. The difficulty
of tracing the course of the crossed callosal fibres rests in this, that
those which lie anteriorly after crossing run obliquely backwards ,
ivhile those which lie posteriorly run obliquely forwards , the point
to which they all tend to converge being the knee of the inner
capsule.

It consequently happens that in whatever plane the organ may
be cut, the fibres wTill be divided at some point. In a completely
transverse perpendicular section the crossed callosal fibres are
usually divided, and being represented only by small fragments, are
very apt to be overlooked in the dense mass of nerve-medulla lying
in their neighbourhood.

The Cortical Plexuses. — Of late years a good deal has been
written of the most interesting plexus of medullated fibres which
exists in the cortex of the cerebellum and cerebrum, by Exner
(Sitzungsb. d. k. Akademie d. Wissensch., vol. Ixxxiii. Ab. iii.,
Eeb. 1881), Butzke (Arch. f. Psychiatrie, vol. iii., 1872), Gerlach
(Centralb. f. d. med. Wissensch ., 1872, p. 273), Boll (Arch. f.
Psychiatrie , vol. iv., 1874, p. 1), Bindfleisch (M. Schultze's Arch. f.
mik. Anat., vol. viii. p. 453), and others. It seems likely, as Hill
suggests, that since the discovery of these fine cortical plexuses our
whole notions of what are known as nerve centres , and of the communi-
cation that exists between nerve cells and fibres, will shortly be revolu-
tionised. The plexuses to which I refer can be seen only when
certain methods of staining are employed. Exner, who is generally
regarded as having discovered the plexus in the cerebral cortex,

526 Proceedings of Boyal Society of Edinburgh. [jan. 31,

employed perosmic acid and ammonia, but since then the reagent
used for the purpose of demonstrating it has almost exclusively been
Weigert’s hsematoxylene dye previously referred to.* In the cortex
of the cerebellum the plexus is probably densest, but it is present
in all parts of the cerebral cortex as well.

Continuity of Cortical Plexus with that in White Matter. — What
I would specially wish to direct attention to at present, however,
is that this plexus not only prevails in the cortical grey matter,
but that it appears to intertwine itself round the nerve fibres
throughout a great part of the white. The large medullated nerve
fibres from the cortex run into the white matter, but almost
immediately become surrounded by a dense padding or casing of
this nerve network. At first it might be supposed to be simply
connective tissue, and it has in bygone times been always regarded,
when indistinctly seen by less favourable means of demonstration,
simply as the branching neuroglia. The plexus I refer to, however,
as pervading the white matter of the brain is a true nerve structure,
and that which is found in the cortex of the cerebrum and cerebellum
is an extension or outcrop of this. The appearance presented by
it a short way within the cortical grey matter, of the motor region,
towards the vertex is shown in PI. XV. fig. 3. The large medullated
trunks (a., a.) are seen coming down from the grey cortex, but shortly
after penetrating into the white matter of the centrum ovale they
become encased, as it were, in a dense and complex mass of medullated
fibres (d.). Between its fibres is the granular neuroglia (c.), which
seems to fill all the meshes formed by it.

The Plexiform Nucleus. — A similar medullated plexus also exists
in certain of the ganglia, such as the thalamus and lenticular
nucleus. In the former it is in a high state of development, but
there is one part of the brain in which it reaches even a higher
grade of complexity. I refer to a little comma-shaped body (fig. 2,
j o.n.) which lies in the angle constituted by the under aspect of the
tectorial part of the corpus callosum and the upper surface of the
caudate nucleus. This body, whose presence I do not remember
having seen referred to, is one mass of a dense and complicated nerve
plexus, and, so far as I am able to discover, is without nerve cells. It

* Since this paper was read various modifications of Exner’s method have
been introduced by Pal of Vienna and others.

1887.] Prof. D. J. Hamilton on the Cortex of the Brain. 527

is contiguous to the caudate nucleus below, but the tissue of the
one is separated from that of the other by a sharp line of demar-
cation. It passes for a short way underneath the corpus callosum,
and at its lower extremity posteriorly, seems to he united with
the taenia semicircularis. Its fibres are directly continuous with
the fibres of the plexus in the white matter just referred to. It is
most developed anteriorly in the region of the head of the caudate
nucleus.

In PL XIY. fig. 4 I have given a drawing of the plexus constituting
this body as it appears when magnified about 350 diameters. The
part from which the drawing was taken was immediately adjacent to
the inner capsule at the point x. in fig. 2. The plexiform nucleus
(j).n., p.n.,p.n.,) is seen to the right ; a few of the fibres of the inner
capsule (i.c.) to the left. It will be noticed that the main bulk
of the body is made up of an intertwining felt-work of nerve fibres.
They stain deeply with Weigert’s copper-hsematoxylene dye, and
between them, as in other regions of the brain, a quantity of
granular neuroglia is interposed. It is only lately that I have made
out the true nature of this body, and on account of its structure I
propose to name it the plexiform nucleus.

Points of Origin of the Callosal Fibres. — The most of the callosal
fibres which come down from the vertex appear to run directly
into the corpus callosum. Their usual appearance and direction
are represented in fig. 2 ( v.c.f. , v.e.f). In passing downwards
they interlace with those leaving the corpus callosum, and which
are turning downwards to the two capsules.

Those, however, which are derived from the lower third or half
of the cortex between the Sylvian fossa and the great longitudinal
fissure (fig. 2, p.nf p.n.f.) do not appear to run directly into the
corpus callosum, but pass first of all into the plexiform nucleus just
described. Shortly after issuing from the grey matter they become
united into loose bundles which penetrate through the fibres of the
crossed callosal tract, and which seem to lose themselves within the
plexiform nucleus by breaking up into its reticular network. From
this reticular network fresh fibres appear to arise, and to enter
the corpus callosum. In all probability, these turn downwards
on the opposite side into the two capsules as fibres of the crossed
callosal tract. This plexiform nucleus would thus possibly represent

528 Proceedings of Royal Society of Edinburgh. [jan. 31,

a meeting-point for many of the callosal fibres before they proceed
to cross, the individual fibres losing their identity within it by
splitting into an anastomising common network, from which again
fresh fibres appear to arise and travel across the corpus callosum
to the opposite side.

The fibres which enter this body are chiefly derived from the
motor centres which in Man have been found to preside over the
muscles of the tongue and face, that is to say, the lower parts
of the ascending frontal and parietal convolutions, and it is
conceivable that the function of the plexus contained in it is to
correlate and associate their action.

Destinations of the Callosal Fibres. — After passing into the inner
and outer capsules, the arched callosal fibres just described become
united into dense bundles. A very large proportion of them lose
themselves in the thalamus opticus. The excessively fibrous appear-
ance which the thalamus presents is due to these fibres passing
into it. They probably break up into a network, in the meshes
of which the nerve cells are intercalated.

Are these nerve cells directly connected with the nerve fibres
entering the ganglion, or is the network referred to intermediate ?
It seems more likely that the union is not direct, but that a plexus
intervenes between the two, and that this plexus simply surrounds
the nerve cells. I am even not at all convinced that the processes
of the nerve cells are in all cases directly connected with the plexus.
May not nerve energy generated in cells exert its influence upon
nerve fibres in ways other than by direct continuity ? Is it not
possible that it may be transferred to the coils of a dense plexus
through the liquid and neuroglia which fill up the intervals in the
tissue, and that, conversely, peripheral stimuli may thus be eonveyed
to a nerve cell ? I think this is at least conceivable, and the idea
has of late been entertained by several physiologists, both in this
country and abroad.

Few, if any, callosal fibres end in the caudate nucleus , and,
curiously, as if supporting this observation, the plexus in this gan-
glion seems to be very scanty. .The lenticidar nucleus may receive
through the striae medullares a considerable number, and probably
some of the fibres connected with the red nucleus may be also
callosal. A large number appear to end in the pons and medulla

1887.] Prof. D. J. Hamilton on the Cortex of the Brain. 529

oblongata , while there is a probability of certain of them even ex-
tending down to the spinal cord.

The Direct Fibres. — This paper, however, is concerned with the
connections between the cerebral cortex and the centres lower down,
and as yet I have referred to only one set, namely, those which are
callosal and which cross from the opposite side. There are others,
of course, which run down directly, and of these the motor fibres
are among the most important. These direct motor fibres lie to
the outside of the crossed callosal tract (fig. 2, d.f.), and, like it,
bend somewhat outwards in circumventing the ventricle. Those
derived from the marginal gyrus seem, at least in the sheep, to lie
in very close apposition with the fibres of the crossed callosal tract.
In Man I calculate that about one-third of the fibres entering the
anterior two-thirds of the posterior limb of the inner capsule are
direct, while the remainder are crossed callosal.

Prom experiments made upon the cortex, it is evident that these
direct fibres are derived from a wide area, one, indeed, so wide that
it comes to be a question how it is that they are so few in number
when they decussate in the medulla and become connected directly,
or through the intermediation of the spinal cord, with the peri-
pheral nerves. The notion at present held by most physiologists is
that from the motor cells of the cortex fibres issue which are con-
tinuously prolonged downwards to the spinal cord. But if we con-
sider the matter for a moment, it is evident that they must have
been much reduced in hulk by the time they have reached the
medulla, and that the pyramidal fibres of the medulla or cord
cannot represent the whole of the motor fibres derived from the
motor area. How, then, is this sudden falling off to be accounted
for My present conviction is that the direct continuity of the
process of a ganglion motor cell in the cortex with the pyramidal
tracts of the spinal cord is a myth. I am strongly inclined to
believe that, just as in the case of many of the callosal fibres, the
motor fibres break up into a plexus, from which again fresh fibres,
those which enter the pyramidal tracts, take their origin. When
the pyramidal tracts in the cord are affected by secondary degenera-
tion, they are mapped out with the utmost precision, and the
degeneration never overlaps them. Can the same be said of the
degeneration further up in the centrum ovale ? I do not think that

530

Proceedings of Boyal Society of Edinburgh. [jan. 31,

it can. There is always more or less diffusion of the tract imme-
diately and for some distance below the point of lesion, if that be
cortical, and the explanation I think is to be found in the inter-
position of this plexus. The plexus is a means of reduction and
association, a means by which the action of the many fibres coming
from a particular cortical area may be combined and correlated in
the few.

But the direct fibres entering the inner capsule are not all motor
in their function. There are many other bands which enter it and
whose function varies. Thus there is a large contingent of fibres
which passes into its posterior limb from the parieto-occipital region,
and whose function, there cannot be much doubt, is sensory. It
has been shown, over and over again, that when it is destroyed
hemianassthesia results. Then there is a large band of fibres
which comes from the prefrontal region, and which enters the
anterior limb on its way back to the anterior nucleus of the
thalamus, to which it becomes attached. The geniculate bodies and
the pulvinar finally are connected by direct bands with the occipital
region.

Plexus most abundant in Man . — One of the main differences which
exist between the brain of Man and that of the lower mammalian
types consists in the disproportional size of the white and grey
matters. In Man the white matter is relatively more abundant than
in the brain of any other mammal I have examined, and the lower
we go in the scale the greater the disproportion appears to be.

Now, the cause of this seems mainly to reside in the fact that
this intertwining plexus which ramifies through the whole centrum
ovale is vastly more abundant in Man than in the lower animals,
and hence, probably, the superiority of the human brain as an
instrument of association may be accounted for.

Connections of Thalamus Opticus. — I have said that a large
number of callosal fibres pass into the thalamus opticus. They lose
themselves in it, apparently by becoming connected with a dense
plexus. In conclusion, let me ask the question whether there are
any fibres which leave the thalamus, and, if so, where they go to ?
Do fibres descend from the thalamus into the cerebral peduncle,
ultimately to enter the spinal cord? I am becoming daily more
and more convinced that, if such do exist, they must be small in

1887.] Prof. D. J. Hamilton on the Cortex of the Brain. 531

number. Certain bands of fibres which are not callosal, no doubt
enter the thalamus, but these seem to connect it with parts of the
cortex which experiment has shown are associated with definite and
well-located functions. Thus there are the three so-called 'peduncles
of the thalamus, uniting it respectively with the prefrontal region,
with the nucleus amygdalaris in the temporo-sphenoidal lobe,
and with the hippocampus major. But these differ entirely in their
nature from the fibres which are supposed to leave the thalamus
and to pass downwards with the other descending cerebral tracts, and
it seems to me that the latter, if they do exist, must be in small
quantity.

How, then, is the thalamus connected peripherally, and what is it3
use ? As yet any statement on this subject must necessarily be
largely conjectural, but, all things considered, there is reason for at
least supposing that this ganglion is largely concerned with the
education of the brain through the optic nerves and corpus callosum .
Of all the nerves in the body the optics are those by which the
brain is mainly educated. They are in constant use, imperceptibly
opening up the cortical grey matter to impressions made upon the
periphery by light vibrations. What is the connecting link between
the peripheral retina and the central cortex 1 The visual centre
is said to be located in the occipital lobe, but the optic must
subserve a far wider function in educating other parts of the cortex
as well as this small area % How is it that the motor centres, for
instance, are educated to a particular complicated act, purely through
the sense of sight ? What is the mechanism by which a sudden
visual impression, accompanied by a sense of danger, will serve to
throw the body instantaneously into a complicated attitude of
defence1? This introduces far too wide a subject of discussion
to take up at present ; but it seems to me likely that the callosal
fibres entering the thalamus constitute the substratum by which
these acts are accomplished ; that they are, in fact, the means
by which the opposite side of the brain is educated through
vision.

Where the corpus callosum has been destroyed in infancy, im-
becility seems to have been the invariable result. There are certain
records of congenital deficiencies of this body which have been
unaccompanied by any symptoms of note, more especially one

532 Proceedings of Royal Society of Edinburgh. [jan. 31,

described by Eicbler [Arch, f Psycliiat., vol. viii. p. 355). It seems,
however, that in these cases we have to do not with a deficiency
in the actual callosal fibres, but with a malformation by which
they have failed to decussate in the middle line, just as so frequently
happens in the anterior pyramids.

On the supposition that the thalamus subserves the purpose of
concentrating the fibres which educate the higher centres through
the optic, it can readily be understood how, if it were destroyed in
adult life, no very evident symptoms might follow. It has already
to a great extent subserved its purpose. The higher centres have
been educated, and are capable of discharging their functions apart
from the channels through which that education has been imparted.
It has played its part, so to speak, in infancy and youtb, and may
now in a manner be considered as functionally inert. The im-
pressions made upon the cerebral cortex through it are quite pos-
sibly recalled by a perfectly different set of channels ; for I do not
see why in the internal economy of the brain there may not be
paths for educating the higher centres through vision, hearing,
touch, and so on, and a whole set of other paths by which the
results of this education may be brought into action. If such be
the case — and I advance this with all due caution — the callosal
system of fibres might be regarded as the great educating
system ; while the direct bundles to which I have adverted would
constitute the means of adapting this education to a utilitarian
purpose.

In the case of those born blind, the education of the cortex would
of course be carried on through other channels, namely, through
those of the remaining special senses. The nuclei of the nerves
connected with these are situated in great part in the pons, medulla
oblongata, and spinal cord, and these again, as already mentioned,
appear to be extensively united to crossed callosal fibres which have
descended in the inner capsule. By the agency of these callosal
fibres they are placed in communication with the cerebral cortex on
the opposite side of the body. The same mechanism for educating
the cortex in fact prevails here as in the case of the optic ; that is
to say, there is, firstly, the peripheral nerve to receive the impres-
sion ; secondly, an intermediate nucleus to which the nerve is
bound ; and, thirdly, a system of fibres (callosal) by means of

1887.] Prof. D. J. Hamilton on the Cortex of the Brain. 533

which this nucleus is placed in continuity with the opposite cerebral
cortex.

The arrangement seems a probable one ; all the most important
motor and sensory channels seem to cross the middle line at some
point. We see this exemplified in its most simple form in the
ordinary ascending and descending paths in the spinal cord ; and
there seems good reason for believing that the same type of con-
struction prevails higher up. The callosal fibres would thus
represent the decussation of the multiform tracts which do not cross
in any of the commissures or decussations lower down. The greater
number of them are probably not motor nor purely sensory in their
function, but in great part educational. They are, in fact, the
means of impressing the opposite cortical centres with the stimuli
that have been made upon the intermediate centres lower down.

Explanation of Plates XIV., XV.

Fig. 1. Perpendicular opaque transverse section through the region of
the infundibulum of human brain hardened by injecting Midler’s fluid.

"Natural size. In the centre is the corpus callosum, and at each side of
it, turning upwards, outwards, and downwards in the centrum ovale to the
two capsules, is the arched mass of fibres which I have named the crossed
callosal tract. The fibres coming in to the corpus callosum from the cortex
of the vertex and elsewhere are seen interlacing with the fibres of this
arched mass. The drawing was made with the greatest care, and may be
taken as being as nearly as possible a facsimile of the preparation from
which it was copied. The brain, after being thoroughly hardened, was
simply cut into segments about half an inch thick, whose surfaces were
polished in the freezing microtome. Nothing further was done to it.
The drawing represents the surface of one of these segments.

Fig. 2. Perpendicular oblique antero-posterior section of human brain
through the corpus callosum and crossed callosal tract, x 10-20 diams.
Stained by the author’s modification of Weigert’s copper-heematoxylene
process, c.c., corpus callosum ; c.c.t.: crossed callosal tract ; v.c.f., v.c.f,
callosal fibres from the vertex ; p.n.f. , p.n.f, same, from cortex lower down,
running towards the plexiform nucleus (p.n.) ; d.f, direct cortical fibres
lying outside the crossed callosal tract, and running down to the inner
capsule ( i.c .); s.c.f., severed callosal fibres of the crossed callosal tract;
c.n., caudate nucleus ; x ., part of preparation from which figure 3 was
drawn.

Fig. 3. Portion of white matter immediately under the grey mantle of
the cortex at the vertex in the motor region. Stained as in figure 2.
x 300 diams. a., a., bundles of large medullated fibres passing downwards
from the grey matter ; b., a clot in a blood-vessel ; c., the granular neur-
oglia ; d., the felt-like plexus of nerve fibres surrounding the straight
bundles coming from the cortex.

534

Proceedings of Eoyal Society of Edinburgh.

Fig. 4. Part of plexiform nucleus and adjacent inner capsule, taken
from the preparation depicted in figure 2 at point x. x 350 diams.
p.n., p.n ., p.n., outer border of plexiform nucleus ; i.c.f, i.c.f descending
fibres of inner capsule ; u.c.f., u.c.f., cortical fibres derived from the grey
matter shortly above the Sylvian fossa, and which apparently end in the
nerve network of the plexiform nucleus.

\

.

Pxoc. Roy. Soc. Edmr

F. Ruth, Lift1 Edinr

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Proc.Roy. So'c.EdinT

Yol. XIV, Pl. XV

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Proc.Roy. Soc.Edm1 , Vol.XFV, PI. XT.

Donations to the Library of the Royal Society from

1885 to 1887.

I. Transactions and Proceedings from Learned Societies,

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vol. xiv. 16/5/88 2 M

536

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Fortschritte der Physik im Jahre 1881. Dargestellt von der
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Magnetical and Meteorological Observations made at the Govern-
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of Edinburgh , Session 1886-87. 537

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538

Proceedings of the Royal Society

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539

of Edinburgh , Session 1886—87.

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University of Cincinnati. — Publications of the Observatory. Zone
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540

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The Scientific Transactions of the Royal Dublin Society. Vol. III.
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Dunecht Observatory. — Determinations of Longitude and Latitude, 1885.
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Berichte fiber die Senckenbergische Naturforschencle Gesellschaft.
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541

of Edinburgh , Session 1886-87.

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Gottingen. — Abhandlungen der Konigl. Gesellschaft der Wissenschaften.
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Nachrichten von der K. Gesellschaft der Wissenschaften und der
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Hongkong Observatory. — Magnetic and Meteorological Observations during
1886. Fol.

542

Proceedings of the Royal Society

Indian Government , Calcutta. — Records of the Geological Survey of India.
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The Flora of British India. By Sir J. D. Hooker, M.D. Part
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Operations of the Great Trigonometrical Survey. Yol. IVa.

1886. 4to.

Jay an. — Transactions of the Seismological Society. Yols. X., XI.

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Preisschriften gekront u. herausgegeben von der Ffirstlich Jab-
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8vo.

543

of Edinburgh , Session 1886—87.

Leyden. — University. — Inaugural Dissertations.

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Academia Real. Memorias. Tom. V., YI. 1882-86.

Cartas de Alfonso de Albuquerque, seguidas de documentos que
as elucidan. Tomo I. 1884.

Jornal. Nros XXX.-XLIY. 1881-87.

Conferenci'as : — Acerca dos Infinitamente Pequenos. 1884.

Circulacao da Materia. 1886.

Historia dos Estabelecimentos. Tom. X.-XIY. 1882-85.

As Provincias Ultramarinas. Tom. I.— III. 1883-85.

Curso de Silvicultura, por A. X. P. Coutinho. Tomo I. 1886.

0 Mercader de Veneza. Traduccao, por Buliao Pato. 1881.
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Journal of the Anthropological Institute of Great Britain and
Ireland. Yols. XYI., XYII. 1886-87. 8vo.

Journal of the Society of Arts. 1886-87. 8vo.

J ournal of the Royal Asiatic Society of Great Britain and Ireland.
Yol. XIX. 1887. 8vo.

Nautical Almanac and Astronomical Ephemeris for the Year
1891. {From the Lords of the Admiralty.)

Monthly Notices of the Royal Astronomical Society. Yols.
XLYII., XLVIII. 1886-87. 8vo. — Memoirs of the Royal

Astronomical Society, Vol. XLVIII. 2. 1885. 4to.

Reports of the Scientific Results of the Exploring Voyage of
H.M.S. “Challenger.” Yols. XX.-XXII. (Zoology.) 1887. 4to.
{From the Lords of the Treasury.)

Journal and Abstracts of Proceedings of the Chemical Society.
1886-87. 8vo.

Transactions of the Clinical Society of London. Yol. XX. 1 887.
Minutes of Proceedings of the Institution of Civil Engineers,
Yols. LXXXVIII.-XC. 1886-87. 8vo.

Institution of Mechanical Engineers, Proceedings. 1887. 8vo.
Proceedings of the Royal Geographical Society. New Series.
Yol. IX. 1887. 8vo.

Quarterly Journal of the Geological Society. Vol. XLIII. 1887 ;
Abstracts, 1886-87.

Proceedings of the Geologists’ Association. Yol. X. 1887.
Journal of the East Indian Association. Vol. XIX. 1887. 8vo.
Colonial and Indian Exhibition Report. 1886. 8vo.

Journal of the Linnean Society. Zoology. 1886-87. — Botany.
1886-87.

544

Proceedings of the Royal Society

London. — The Transactions of the Linnean Society. Second Series.

Botany. Yol. II. 1886-87. Zoology. Yol. IY. 1887. 4to.

Proceedings of the London Mathematical Society. 1886-87. 8vo.

Medical and Chirurgical Transactions published by the Royal
Medical and Chirurgical Society. Yol. LXX. 1887. 8vo. —
Proceedings of the Royal Medical and Chirurgical Society.
New Series. Yol. I. 1887. 8vo.

Quarterly Journal of the Meteorological Society. 1886-87.
8vo.

Meteorological Society. — The Meteorological Record : Monthly
Returns of Observations made at the Stations of the
Meteorological Society. Nos. 23-27. 1886-87.

Meteorological Council. — Report of the Meteorological Council to
the Royal Society. Report for Year ending 31st March
1887.

Quarterly Weather Report of the Meteorological Office.
New Series. For 1878-79. 4to.

Meteorological Observations at Stations of Second Orders,
for 1883. 4to.

Hourly Readings. 1884-85.

Monthly Weather Report. 1886-87.

Weekly Weather Report. 1886-87.

Atlantic Weather Charts. Part III. February-May
1883.

Journal of the Royal Microscopical Society, containing its Trans-
actions and Proceedings. New Series. 1886-87. 8vo.

Statistical Report of the Health of the Navy for 1885. {From the
Lords Commissioners of the Admiralty.)

The Mineralogical Magazine and Journal of the Mineralogical
Society of Great Britain and Ireland. Nos. 34, 35. 1886-87.

8vo.

British Museum. — Catalogue of the Lizards. Yol. III. By
G. A. Boulenger. 1887.

A Guide to the Exhibition Galleries in the Departments of
Geology and Palaeontology. 1886.

Guide to the Galleries of Reptiles and Fishes. 1887.

Guide to the Shell and Starfish Galleries. 1887.

Guide to the Sculptures of the Parthenon in the Depart-
ment of Greek and Roman Antiquities. 1886.

Guide to the Mausoleum Room in the Department of
Greek and Roman Antiquities. 1886.

Guide to the Nimrod Central Saloon. 1886.

Catalogue of English Coins. Anglo-Saxon Series. Yol. I.
1887.

Catalogue of the Greek Coins of Peloponnesus in the
British Museum. 1886. 8vo.

Transactions of the Pathological Society of London. Vols.
XXXYI., XXXVII. 1885-86. — Proceedings, 1885-86. 8vo.

545

of Edinburgh, Session 1886-87.

London. — Pharmaceutical Society, Journal of, 1886, 1887.

Philosophical Transactions of the Royal Society. Yols. CLXXVI.-
CLXXVIII. 1885-87. — Proceedings of the Royal Society. Yols.
XLII., XLIII. 1886-87.

Proceedings of the Royal Institution of Great Britain. 1887.
Journal of the Statistical Society. Yol. L. 1887. 8vo. And
Catalogue of Library, 1886.

Transactions of the Zoological Society of London. Yol. XII.
1886-87. 4to. — Proceedings for the year 1887. 8vo.

Louvain. — Annuaires de l’Universite cle Louvain. 1887. 12mo.

Liber Memorialis, 1887.

Lund. — Acta Universitatis Lunclensis. Mathematik och Naturvetenskap.

Tom. XXII., XXIII. 1885-86. — Philosophi, &c. Tom.

XXII., XXIII. 1885-86. — Ratts och Staatsvetenskap. Tom.

XXIII. 1885-86.

Luxemburg. — L’Institut Royal Grand-Ducal. Tome XX. 1886.

Observations Meteorologiques. Moyennes de la Peri ode 1854-
1883.

Lyons. — Memoires de PA.cademie des Sciences, Belles-Lettres et Arts.

Classe des Sciences, Tome XXYII. 1885. — Classe des Lettres,
Tome XXIII. 1886.

Musee Guiinet. Annales, Tomes X., XI., XII. 1886-1887. 8vo.
— Revue de l’Histoire des Religions. Tomes XI Y., XY., XVI.
1886-87.

Madras. — Journal of Literature and Science. 1886-87.

Madrid. — Memorias de la Comision Geologica de Espana. Provincia de
Alava. 1885.

Boletin de la Commission del Mapa Geologico de Espana. Tomo
XIII. 2. 1886.

Academia de Ciencias. — Memorias, Tom. XI., XII., XIII.
1887. — Revista de los Progresos de las Ciencias. Tomo XXII.
1887. 8vo.

Manchester. — Transactions of the Manchester Geological Society. Yol.
XIX. 1886-87.

Literary and Philosophical Society. Memoirs, 3rd Series, Yol.
X. 1887. — Proceedings. Yols. XXV., XX YI. 1886-87. 8vo.
Marseilles. — Bulletin de la Societe Scientifique Industrielle. 1885.
Mexico. — Sociedad Scientifica “ Antonio Alzate.” Tomo I. 1887.
Milan. — Reale Istituto di Science e Lettere. Memorie : Classe di Lettere
e Scienze Morali e Politiche. Yol. XVII. 1885.

Atti della Societa Italiana di Scienze Naturali. Yol. XXYII I.
1886. 8vo.

Publicazioni del Reale Osservatorio di Brera in Milano. XXY.
4to. Osservazioni Meteorologiclie Orarie — Simplificazioni nel
Calcolo delle Perturbazioni dei piccoli Pianeti da A. Venturi.
Stelle cadenti (1871), &c. 1886-87. 8vo.

Atti della Societa Crittogamologica Italiana. Congresso nazion-
ale Botanica Crittogamica. 1887. 8vo.

546

Proceedings of the Poyal Society

Milan. — Societa d’Industriali Italiana. Yol. I. 1887. 8vo.

Modena. — Memorie della Regia Accademia di Scienze Lettere ed Arti.
Ser. II. Tom. IY. 1886. 4to.

Atti della Societa dei Naturalisti. Ser. III. Yol. Y. 1886.

Montpellier. — Academie des Sciences et Lettres cle Montpellier : Memoires
de la Section des Sciences. Tome XI. 1885-86. — Section des
Lettres. Tome VIII. Fasc. 1, 2, 3, 1886-87. Tom. VI., 1,
1886.

Montreal. — Natural History Society, Proceedings of. 1887. 8vo.

Moscow. — Annales de PObservatoire de Moscou. 2e Ser. Yol I. 1884.
4to.

Beilage zum Bulletin de la Societe Imperiale des Naturalistes de
Moscou. Meteorologische Beobachtungen, 1886. 8vo.

Nouveaux Memoires de la Societe Imperiale des Naturalistes de
Moscou. Tome XV. 1885.

Munich. — Abhandlungen der k.Bayerischen Akademie der Wissenschaften
der Mathematiscb-Physikalischen Classe, Bd. XV., XYI. 1886,
1887. — Pliilosophisch-Philologische Classe, Bd. XYI. 1885. —
Historische Classe, Bd. XVII. 1885. — Sitzungsberichte der

Mathematisch-Physikalischen Classe der k. B. Akademie der
Wissenschaften. 1886, 1887.— Sitzungsberichte der Philoso-
phisch-Philol. und der Historischen Classe, 1886, 1887. 8vo.

Miinchene Sternwarte. Astronomische Bestimmung der Pol-
holien, 1885. 4to.

Gedachtnissreden auf Leopold von Ranke und Joseph von
Frauenhofer. 1887. 4to.

Naples. — Memorie della R. Accademia delle Scienze Fisiche e Mate-
matiche. Ser. III. Tom. Y. 1885.

Rendiconti della R. Accademia. 1886. 4to.

Mittheilungen aus der Zoologischen Station zu Neapel. Bde. VI.,
VII. 1887. 8vo.

Neuchatel. — Bulletin de la Societe des Sciences Naturelles de Neuchatel.
Tome XY. 1886.

New York. — Bulletin of the American Museum of Natural History.
1886. 8vo.

Natural History of York. Palseontology. Vol. V. Pt. 1 — Mono-
myaria, by James Hall. Albany, 1879. 4to.

American Geographical Society. Yol. XIX. 1887. 8vo.

Nice . — Annales de PObservatoire. Tom. II. 1887.

Nijmegen. — Nederlandsch Kruidkundig Archief. — Yerslagen en Mede-
deelingen der Nederlandsche Botanische Yereeniging. 2e Serie.
4e Heel, 5e Stuk. 1887.

Oberpfalz und Regensburg. — Verhandlungen des historischen Vereines.
Bde. XL.-XLI. 1886-87. 8vo.

Odessa. — Zapiski Novorossiskago Obshestva Estestvoispuitatelei. Tom.
XI. 1887. 8vo.

Offenbach. — Yerein fur Naturkunde ; Jahresbericht, 1885-87. 8vo.

Ohio. — Mechanics Institute. Yol. II. 1883.

of Edinburgh , Session 1886-87. 547

Oxford. — Results of Astronomical Observations at the Radcliffe Observa-
tory. XLI.-XLII. 1884-85. 8vo.

Palermo. — Hortus Botanicus Palermitanus. 1886.

Paris. — Comptes Rendus des Seances de l’Academie des Sciences. Dec.
1886 to Dec. 1887. 4to.

Oeuvres completes de Laplace. Tome VII. 1887. 4to.

Oeuvres completes d’ Augustin Cauchy, publiees sous la Direction
de l’Academie. 2e Serie, Tome VI. 1887.

Comptes Rendus de l’Academie des Inscriptions et Belles-Lettres.
1886-87. 8vo.

Bulletins de la Societe d’Anthropologie. 1887. 8vo.

Annales de l’Ecole Xormale Superieure. Tome XL No. 4.
1882.

Annales des Mines, 1885-86.

Bulletins des Seances de la Societe Nationale d’Agriculture de
France. 1887. 8vo. — Memoires. Tome CXXXI. 1887.
Bulletins de la Societe de Geographic. 1886, 1887. — Comptes
Rendus. 1886-87.

Societe Geologique de France. — Bulletins. 3e Serie. Tomes X.,
XV. 1886-87. 8vo. — Memoires, 3e Serie. Tome IV. (3).
Formation des Couches de Houille. 1887. 4to.

Annales Hydrographiques. 1887. 8vo.

Mission Scientifique du Cap Horn. 1882-83. Tome IV. Geologie.

Tome VI. Zoologie. 4to. {From Minister of Marine.)
Publications du Depot de la Marine, 1886-87.

Annales de l’Observatoire de Paris. Memoires. Tome XVIII.
1881-82.

Rapport Annuel sur l’Etat de l’Observatoire de Paris par M. le
Confcre-amiral Mouchez, pour l’Annee, 1886.

Journal de Ecole Polytechnique. 54, 55 Cahiers. 1886, 1887.
Bulletins de la Societe Mathematique de France. Tome XV.
1887. 8vo.

Ministere de lTnstruction Publique. Dictionnaire de l’Ancienne
Langue Frangaise et de tous ses Dialectes du IXe au XVe Siecle.
Par Frederic Godefroy. Fasc. 46-49. Paris. 4to. — Cartulaire
Lyonnais. Par M. C. Guigue. Tome I. 1885.

Museum d’Histoire Naturelle. Rapports Annuels de MM. les
Professeurs et Chefs de Service. — Nouvelles Archives du
Museum cl’Histoire Naturelle. 2me Serie. Tome IX. 1886.
Societe Fran§aise de Physique. Seances, 1886-87. Collection de
Memoires relatifs a la Physique. Tomes II. et III. 8vo. —
Memoires sur l’Electrodynamique. 1885-87.

Societe Philomathique. Bulletin XI. 1887.

Catalogue des Etoiles. 0h-6h. Tome I. 1887. 4to. — Positions
observees des Etoiles. 1837-81. 4to.

Societe Zoologique. Bulletin 1887.

Pennsylvania. — Annual Report for 1886. — Geological Relations of the
Nanticoke Disaster. By C. A. Ashburner. 1887. — Geologic

548

Proceedings of the Royal Society

Distribution of Natural Gas in the United States. By C. A.
Ashburner. 1887.

Perthshire. — Society of Natural History. Yol. I. 1886.

Philadelphia. — Proceedings of the American Philosophical Society for
Promoting Useful Knowledge. Nos. 124-126. 1886-87. 8vo.

Proceedings of the Academy of Natural Sciences for 1886-87.
Poulkova. — Nicolai-Hauptsternwarte. Jahresbericht fur 1884-85. 8vo.

— Zeitstern-ephemeriden auf das Jahr 1886. — Tabulae Quanti-
tatum Besselianarum. 1885-1889.

Die Beschlusse der Washingtoner Meridian-Conferenz. Von 0.
Struve.

Prague. — Astronomische und Magnetische Beobachtungen an der K. K.
Stern warte zu Prag., in 1886.

Queensland. — Its Resources and Institutions. Vol. I. 1886. 8vo.

Queensland Branch of the Royal Geographical Society of Aus-
tralasia. Yol. II. 1887.

Weather Charts. By C. L. Wragge, Brisbane. 1887.

Rhineland and Westphalia. — Yerhandlungen des Naturhistorischen
Yereines der preussischen Rheinlande u. Westfalens. See Bonn.
Rome. — Atti della R. Accademia dei Lincei. Rendiconti. 1886-87. —
Memorie. Classe di Scienze Mor. Storiche et Filol.
Serie IY.

Memorie della Societa degli Spettroscopisti Italiani. 1886-87. 8vo.
Atti dell’ Accademia Ponteficia dei Lincei, 1886-87. 8vo.

Rousdon Observatory. — Meteorological Observations for 1887.

St Petersburgh. — Bulletins cle l’Academie Imperiale des Sciences de St
Petersbourg. Tomes XXXI. 1886-87. Memoires de l’Academie.
Imperiale des Sciences. Tomes XXXIY.-XXXY. 1886-87.
4to.

Journal Russkago Phisico-Chimicheskago Obtschestva. Tom.
XYIII. 1886. 8 vo.

Otcliet Imperatorskago Russkago Geographicheskago Obtschestva.
1887. 8vo.

Beobachtungen der Russischen Polarstation an der Lenamiindung.

Theil II. Meteorologische Beobachtungen.

Annalen des Physicalischen Central -Observatoriums. Jahrg.
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Repertorium fur Meteorologie, herausgegeben von der Kaiser-
lichen Akademie der Wissenschaften. Bd. YIII. 1883. 8vo.
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Yol. IV. 1887. 4to.

Salem. — Essex Institute. Bulletin of the Essex Institute. Vol. XVIIJ.
1886.

Peabody Academy of Science. Vol. II. 1886.

Shanghai. — Journal of the China Branch of the Royal Asiatic Society.

N. S. Yols. XXI.-XXIII. 1886-87. 8vo.

Steiermarh — Mittheilungen des Naturwissenschaftlichen Yereines.

1886. 8vo.

of Edinburgh , Session 1886-87.

549

Strasbourg — Inaugural Dissertations. 1887.

Stuttgart. — Jahresliefte des Yereins fur vaterlandische Naturkunde in
Wiirttemberg, Jahrg. 1886. 8vo.

Switzerland — Nouveaux Memoires de la Societe Helvetique des Sciences
Naturelles. Band XXIX. 1885.

Comptes Bendus et Actes de la Societe Helvetique des Sciences
Naturelles, reunie & Geneve, 1886, a Frauenfeld, 1887. 8vo.
Societe Geologique Suisse. Revue XVI. 1886.

Sydney — The Proceedings of the Linnean Society of New South Wales.
Second Series. Yols. I.— III. 1886-87. 8vo.

Journal and Proceedings of the Royal Society of New South
Wales. Yol. XX. 1886. 8vo.

Australian Museum. Catalogue of the Fossils, 1883. 8vo. —
Notes for Collectors of Specimens of Natural History and
Geological Specimens. 1887. 8vo. — Descriptive Catalogue of
the Medusae of the Australian Seas. 1887. 8vo. — Catalogue,
with Notes of Minerals, by A. F. Ratte. 1885. Geology of
the Vegetable Creek Tin Mining Field. 1887. 4to.

Tacubaya. — Observatorio Astronomico. Annuario 1887.

Tasmania. — Proceedings of the Royal Society of Tasmania for 1886-87.
8vo.

Tijtis. — Magnetische Beobachtungen. 1884-85. 8vo.

Meteorologische Beobachtungen. 1885. 8vo.

Toronto. — The Canadian Journal and Proceedings of the Canadian
Institute. New Series. Vol. IY. 1887. 8vo.

Toulouse. — Annales de la Faculte des Sciences. Tomes I.— II. 1887-88.
Trenton. — Journal of the Natural History Society. 1887.

Trieste. — Bolletino della Societa Adriatica di Scienze Naturali. Yol.
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Tromsd. — Tromso Museum Aarshefter. No. X. 1887.

Turin. — Memorie della Reale Accademia delle Scienze di Torino. Serie
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delle Scienze di Torino. Vol. XXII. 1887.

Bolletino dell’ Osservatorio della Regia Universita di Torino.
Anno 1886.

Bolletino di Zoologia ed Anatomia Comparata della Universita di
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Upsala. — Bulletin Meteorologique Mensuel de TObservatoire de l’Univer-
site d’Upsal. Yols. XVII.-XVIII. 1885-86. 4to.

Nova Acta Regice Societatis Scientiarum Upsaliensis. Ser. 3a.
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Utrecht. — Verslag van het Verhandelde in de Provinciaal Utrechtsch
Genootschap van Kunsten en Wetenschappen, 1885. —
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Venice. — Atti del Reale Istituto Yeneto di Scienze, Lettere ed Arti.
Ser. YI. Tomi IY., Y. 1886-87.

Victoria. — Transactions and Proceedings of the Royal Society of Victoria.
Yols. XXII., XXIII. 1886-87.

550

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Victoria. — Statistical Register and Australian Statistics for tire years
1886-87, with a Report by the Government Statist.

Natural History of Victoria. Prodromus of the Zoology of
Victoria. Decade I. 1888.

Victorian Year-book for 1885-86.

Vienna . — Denkschriften der K.-K. Akademie der Wissenschaften. Math.

Naturwissenschaftliche Classe. Bd. LI., LII. 1886-87. — Philo-
sophisch-historische Classe. Bd. XXXV. 1886.
Sitzungsberichte der Math. -Natur wissenschaften Classe. Bde.
XCIII.-XCIV. 1886. — Philosoph.-Historisch e Classe. Bde.

CXII.-CXIV. 1883-85.

Archiv fiir Oesterreichische Geschichte. Bde. LXVIIL-LXX.
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Almanach der K.-K. Akademie der Wissenschaften fur 1886.
8vo.

Jahrbiicher der K. K. Central Anstalt fiir Meteorologie und
Erdmagnetismus, Jahrg. Neue Folge; fiir 1884-87. 4to.
Verhandlungen der K. K. Geologischen Reichsanstalt. 1886-87.
Abhandlungen der K. K. Geologischen Reichsanstalt. Bd. XI.
1886-87. 4to.

Jahrbiicher der K. Iv. Geologischen Anstalt. Bde. XXXVI.,
XXXVII. 1887.

Verhandlungen der K. K. Zoologisch-Botanischen Gesellschaft.

Bde. XXXVI., XXXVII. 1886-87.

Annalen der K. K. Naturhistorischen-Hofmuseums. Bd. II.
1887.

Arbeiten aus clem Zoologischen Institute. Tom. VII. 1887.
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Washington. — National Academy of Sciences. — Memoirs. Vol. III.
1886.

United States Naval Observatory. Astronomical and Meteorolo-
gical Observations made during the year 1883. 4to. — Report,
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Astronomical Papers of the American Ephemeris and Nautical
Almanac. Vols. II., III. 1884-85.

Signal Service Office — War Department. — Report of the Chief
Signal Officer, General W. B. Hazen, for 1885-86. 8vo. —

Professional Papers of the Signal Service. No. 18. 1885.

Fourth Annual Report of the Bureau of Ethnology to the Secre-
tary of the Smithsonian Institution. 1882-83. 8vo.

American Geographical Society. Nos. 1-7. 1886.

Fifth and Sixth Annual Reports of the United States Geological
Survey. 1883-84, 1884-85. 8vo.

United States Geological Survey. Monographs. Vol. X. (Dino-
cerata). 1882-83. 4to. — Vol. XI., Geological History of Lake
Lahonton. 1885-86.

of Edinburgh, Session 1886—87.

551

Washington. — Bulletins. Nos. 30-39. 1886. 8vo. — Mineral Resources of
United States. 1886.

Reports of the Superintendent of the United States Coast and
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Philosophical Society. Bulletins. Vol. IX. 1887.

Smithsonian Miscellaneous Collections. Yols. XXVIII -XXXI.
1882-88. 8vo.

Smithsonian Contributions to Knowledge. Vol. XXV, 1885.
Smithsonian Reports for 1885. 8vo.

Bulletin of the Philosophical Society of Washington. Vols.
VII.-IX. 1885-87. 8vo.

Wellington. — Transactions and Proceedings of the New Zealand Institute.
Vol. XIX. 1887.

Reports of Geological Explorations (New Zealand) during 1885-
87, with Maps and Sections. 8vo. {From the New Zealand
Institute.)

Colonial Museum and Geological Survey. Twentieth, Twenty-
First, and Twenty-Second Annual Reports. 1884-87.

Studies in Zoology for New Zealand Students. 1887.

Census of New Zealand, taken in 1886.

Wisconsin. — University Observatory. Observations. Vol. V. 1887.
Wurzburg Universitdt. — Uber Sehnerven Degeneration und Sehnerven
Kreuzung. Von Dr J. Michel. 1887.

Yorkshire. — Geological and Polytechnic Society. Vol. IX. Pt. 2. 1887.

Zurich. — Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich.
31er Jahrg. 1886. 8vo.

II. From Authors, &c., 1885-87.

Academy of Science Minutes. Minutes of the Academy of Physics
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Claude Er shine, Esq., London , through Sheriff JEneas Mackay.)

Albrecht. Verlauft der Nervenstrom in nicht geschlossener, oder
geschlossener Strombahn. Erlangen, 1887. 8vo.

Balbin (Valentin). Elementos de Calculo de los Cuaterniones y sus
Aplicaciones Principales a la Geometria, al Analisis, y a la Mecanica.
Buenos Ayres, 1887. 8vo.

Bischoffsheim (M.). L’Observatoire de Nice (a Series of Photographs
of the Buildings, Instruments, &c.) Folio. 1888.

Bowman (F. H.), F.R.S.E. Report on Wools (Colonial and Exhibition
Papers). 1886.

Buist (John B.), M.D., F.R.S.E. Vaccinia and Variola: a Study of their
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Burns (Edward), F.S.A. Scot. The Coinage of Scotland. Illustrated
from the Cabinet of Thomas Coats, Esq. of Ferguslie, and other
Collections. Vols. I., II. Text; Vol. III. Plates. Edinburgh, 1887.
4to. ( Presented by James Coats, Esq., junior of Ferguslie.)

VOL. XIV. 16/5/88 2 N

552

Proceedings of the Royal Society

Deuchar (David). The Progress of Life Assurance Business in the
United Kingdom. Edinburgh, 1888. 4to.

Eccles (A. Symons). The Physiological Effects of Massage, &c. — Sciatica
— Sleeplessness. London, 1887. 8vo.

Fairley (T.), F.B.S.E. On the various Forms of Filter Pumps or Water-
Jet Aspirators. Manchester, 1887. 8vo.

Fievez (Oh.). Recherches sur le Spectre du Carbone dans PArc Electrique,
en rapport avec le Spectre des Cometes et le Spectre Solaire. Brux.
1885. 4to.

Grewingk (Professor C.). Lebensbild des Prof. C. Grewingk. 1887. 8vo.
Hann (Dr Julius). Bericht fiber die Fortschritte der Geographischen
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Hincle (Dr George Jennings). On the Organic Origin of Chert in
the Carboniferous Limestone Serie s of Ireland. London, 1887. 8vo.

The Microscopic Structure of the Malm or Firestone Rock of

Merstham and Godstone, Surrey. 1886. 8vo.

Kolliker (Professor A. von). Ueber die Entwicklung der Nagel
Wurzburg, 1888. 8vc.

Ueber die Entstehung des Pigmentes in den Oberhautgebilden.

Leipzig, 1887. 8vo.

Laurie (A. P.). Experiments on the Heats of Combinations of the
Metals with the Halogens, as determined by Measurements of their
Electromotive Forces in specially constructed Voltaic Cells. 1886.
8vo.

Lediard (Henry A.). A Test for the Presence of Iodine in the Body.
1882. 8vo.

Dislocation of the Elbow Backwards, with Fracture of the

Coronoid Process. 1884. 8vo.

Fibro-Cystic Myoma of Uterus Septicaemia. 1884. 8vo.

Salmon Disease. 1884. 8vo.

Lieblein (J.). Handel und Schiffart auf deni Rothen Meere in alten
Zeiten: nach Aegyptischen Quellen. Kristiania, 1886. 8vo.
Lockwood (Professor Samuel). Raising Diatoms in the Laboratory.
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M‘Gregor (James Gordon). An Elementary Treatise on Kinematics and
Dynamics. London, 1887. 8vo.

Mallet (F. R.). A Manual of the Geography of India. Part IV.
Mineralogy. Calcutta, 1887. 8vo.

Marilaun (A. Kerner v.). Studien fiber die Flora der Diluvialzeit in
den Oestlichen Alpen.

Monaco (Le Prince Albert de). Deuxieme Campagne Scientifique de
“ l’Hirondelle ” dans PAtlantique Nord, 1885. Paris, 1887. 8vo.
Les Recherches Zoologiques poursnivies durant la seconde Cam-
pagne Scientifique de PHirondelle. 1886. 4to.

— Sur une Experience entreprise pour determiner la Direction des

Courants de PAtlantique, 2e Campagne de lTIirondelle. Paris, 1887.
4to.

- Sur la troisieme Campagne Scientifique de lTIirondelle.

of Edinburgh , Session 1886-87.

553

Monaco (Le Prince Albert cle). Sur des Courbes Barometriques enregis-
trees pendant la Troisieme Campagne Scientifique de l’Hirondelle.
Paris, 188V. 4to.

Nicholson (J. Shield). The Measurement of Variations in the V alue of
the Monetary Standard. London, 1887. 8vo.

Nipher (F. E.). The Volt, the Ohm, and the Ampere. St Louis, 1888.
8vo.

Saint Lager (Dr). Histoire des Herbiers. Paris, 1885. 8vo.

Stevenson (Charles A.). On the Dredging of the Lower Estuary of the
Clyde. London, 1887. 8vo.

Description of the Electric Light on the Isle of May. London,

1887. 8vo.

Velschow (Franz A.). The Natural Law of relation between Rainfall
and Vegetable Life, and its application to Australia. London, 1888.
8vo.

INDEX.

Acctnthodrilus neglectus , 156.

dissimilis, distinguished from,

157.

novce-zelandice , 157.

Addresses : —

Introductory Address, by John
Murray, on Opening Session
1886-87, 2.

Address on Processes of Refri-
geration, by J. J. Coleman, 38.
Closing Address of Session
1886-87, by Chairman (Sheriff
Forbes Irvine), 446.

Address to the Queen on the
completion of the 50th year of
her reign, 451.

Affinity, Chemical, by W. Durham, 48.
Aitken (John), Thermometer Screens,
Pt. IV., 53, 428.

Note on Solar Radiation, 118.

Note on Hoar-Frost, 121.

Albumen : its Discharge from the
Kidneys of Healthy People, by
Professor Grainger Stewart, 240.
Alexander (P.), Expansion of Func-
tions in terms of Linear, Cylindric,
Spherical, &c. , Functions, 37.
Alpine Lakes, their Origin, by Pro-
fessor Federico Sacco, 271.
Alternants. — On the Quotient of a
Simple Alternant by the Difference-
Product of the Variables, by Dr
Thomas Muir, 125, 433.

Alternating Functions, by Dr

Thomas Muir, 121.

On the Summation of certain

Series in Alternants, by A. H.
Anglin, 194.

Alternants which are Constant

Multiples of the Difference-Products
of the Variables, by A. H. Anglin,
313.

VOL. XIV. 16/5/88

Alums (Cobaltic), by Hugh Marshall,
203.

Anglin (A. H. ) on the Summation of
certain Series in Alternants, 194.

— Alternants which are Constant

Multiples of the Difference-Product
of the Variables, 313.

Anguilla vulgaris, Bacilli found in
Body- Cavity of, 263.

Anodonta cygnea , Renal Organs of,
232, 237.

Antarctic Ocean, the Distribution of
Temperature in, by J. Y. Buchanan,
147.

Astacus fluviatilis, Renal Organs of,
232, 236, 237.

Astronomical Tables for facilitating
the Computation of Differential Re-
fraction for Latitudes 56° and 57°‘30,
by the Hon. Lord M‘Laren, 21.

Astronomical Notes, by Dr Ralph
Copeland, 110.

Bacillus subtilis , 101.

tuberculosis , 104.

Bacteria, their presence in the Lymph,
&c., of Living Fish and other
Vertebrates, by Professor J. C.
Ewart, 252.

Bacterium aeruginosum , 100.

Beddard (Frank E.), Observations on
the Structural Characters of certain
new or little-known Earthworms,
156.

on the Minute Structure of

the Eye in certain Cymothoidse, 381.

Ben Nevis Observatory. — Tempera-
tures at Different Heights above
Ground at Ben Nevis Observatory,
by R. T. Omond, 24.

Blood. — Some Experiments which
show that Fibrin-Ferment is absent

2 o

556

Index.

from circulating Blood- Plasma, and
supporting Sir Joseph Lister’s view
that the Blood has no spontaneous
tendency to Coagulate, 419.

Brines and Ice, by J. Y. Buchanan,
129.

Brook (George), Note on the Epi-
blastic. Origin of the Segmental
Duct in Teleostean Fishes and in
Birds, 368.

Brown (Professor Crum) on the
Physics of Noise, 219.

on Ferric Ferricyanide as a

Reagent for Detecting Traces of
Reducing Gases, 419.

Buchanan (J. Y.) on Ice and Brines,
129.

on the Distribution of Tem-
perature in the Antarctic Ocean,
147.

Burnside (Professor W.) on the Par-
tition of Energy between the Trans-
latory and Rotational Motions of
a set of non-homogeneous Elastic
Spheres, 387.

Burton (Cosmo I.) on a Constant
Daniell Cell, for use as a Standard
of Electromotive Force, 356.

Campbell (Albert), the Direct Mea-
surement of the Peltier Effect, 387.

Cayley (Professor), Note on a For-
mula for A "O'/A'’ when n, i are very
large Numbers, 149.

Cephalopoda, their Problematical Or-
gans, by Dr A. B. Griffiths, 230.

Cetacea, on the Larynx and Stomach
in, by Professor D’Arcy Thompson,
221.

Chcetopoda seclentaria of the Firth of
Forth, by J. T. Cunningham, 381.

Chain. — The Minute Oscillations of a
Uniform Flexible Chain hung by
one End, 283.

Chemical Affinity and Solution, by W.
Durham, 48.

Clupea harengus , 265.

Clyde Sea Area, the Chemical Com-
position of the Water of, by Adam
Dickie, 422.

Cobaltic Alums, by Hugh Marshall,
203.

Coldingham Bay, Rocks of, 183.

Coleman (J. J.), Address on Pro-
cesses of Refrigeration, 38.

on a New Diffusiometer and

other Apparatus for Liquid Diffu-
sion, 374.

Compound Bodies, their Motion
through Liquid, by the Rev. Id. J.
Sharpe, 29.

Compressibility of Water, of Mercury,
and of Glass, by Professor Tait,
419.

Copeland (Dr Ralph), Astronomical
Notes, 110.

Coronae seen from Ben Nevis Observa-
tory, by R. T. Omond, 314.

Cortex, of the Cerebrum. — The Con-
ducting Paths between the Cortex
of the Cerebrum and the Lower
Centres, in relation to their Func-
tion, 97.

Cromarty Firth, its Temperature and
Salinity, 250.

Crustacea, their Problematical Organs,
by Dr A. B. Griffiths, 230.

Cunningham (J. T. ), the Nephridia
of Lanice conchilega, 238.

— the Chcetopoda sedentaria

of the Firth of Forth, 381.

and Rupert Vallentin, the

Luminous Organs of Nyctiphanes
norvegica (Sars), 351.

Curve. — On the Plane Curve which
forms the Outer Limit of the Posi-
tions of a Certain Point, by Dr G.
Plarr, 415.

Cyclopterus lumpus , Bacilli found in,
265.

Cy.mothoidae. — The Minute Structure
in certain Cymothoidae, by Frank
E. Beddard, 381.

Cyprinus auratus, Bacilli found in
the Body-Cavity of, 263.

Daniell Cell. — The Use of a Constant
Daniell Cell as a Standard of Elec-
tromotive Force, by Cosmo I. Bur-
ton, 356.

Anty/W when n, i are very large Num-
bers, by Professor Cayley, 149.

Determinants. — History of the Theory
of Determinants, Pt. I. 118, 452.

Diatomaceous Deposit from North
Tolsta, by John Rattray, 220.

Dickie (Adam) on the Chemical Com-
position of the Water composing the
Clyde Sea Area, 422.

Diffusiometer (a New), and other Ap-
paratus for Liquid Diffusion, 374.

Dittmar (Professor W.) and Fawsitt
(C. A.) on the Physical Properties
of Methyl- Alcohol, 219.

Dittmar (Professor) on the Instabi-
lity of the Double Sulphates
M"S04.R'2S04 + 6H20 of the Mag-
nesium Series, 219.

and M ‘Arthur (John), Expe-
rimental Critique on the Chloro-
platinate Methods for the Deter-
mination of Potassium, 428.

Index.

557

Donations to the Library, 535.

Dornoch Firth, its Temperature and
Salinity, by Dr Hugh Robert Mill,
250.

Durham (William), Chemical Affinity
and Solution, 48.

Laws of Solution, Part II., 381.

Earthworms. —Structural Characters
of certain new or little-known Earth-
worms, by F. E. Beddard, 156.

Election of Office-Bearers for Session
1886-87, 1.

Electrolytic Polarization, its Increase
with Time, by W. Peddie, 107, 221.

Electromotive Force, Standard of, by
Cosmo I. Burton, 356.

Elliott (A. C.), Improvement in Ran-
kine’s Formula for Retaining Walls,
48, 85.

Energy, its Partition between the
Translatory and Rotational Motions
of a set of non-homogeneous
Elastic Spheres, 387.

Epiblastic Origin of the Segmental
Duct in Teleostean Fishes and
Birds, by George Brook, 368.

Ewart (Professor J. C.) on the Pre-
sence of Bacteria in the Lymph,
&c. , of Living Fish and other Ver-
tebrates, 252.

Explosives, on the Effects of, by
Professor Tait, 110.

Eye, its Structure in certain Cymo-
thoidse, by Frank E. Beddard, 381.

Eye-Piece. — On the Achromatism of a
Four-Lens Eye-Piece : New Ar-
rangement of the Lenses, by Dr E.
Sang, 153.

Fawsitt (C. A.) and Dittmar (Prof. W.)
on Methyl -Alcohol, 219.

Ferric Ferricyanide as a Reagent for
Detecting Traces of Reducing Gases,

419.

Fibrin-Ferment absent from Blood-
Plasma, 419.

Fluid Motion, on the Instability of,
by Sir W. Thomson, 194.

Stability of Fluid Motion.

Rectilineal Motion of Viscous Fluid
between two Parallel Planes, by Sir
William Thomson, 359.

Forth (Firth of), its Salinity, Tem-
perature, &c., by Dr H. R. Mill, 387.

Fossil Fishes collected in Eskdale
and Liddesdale. I. Ganoidei, by Dr
Traquair, 111.

Fossil Flora of the Somerset and
Bristol Coal Fields, by R. Kidston,
153, 240.

Fowler (G. H.), and Professor A.
Milnes Marshall, Report on the
Pennatulida dredged by H.M.S.
“ Porcupine,” 359.

Fraser (Professor Thomas R.), Note
on the Chemistry of Strophanthin,
370.

Functions. — Expansion of Functions
in terms of Linear, Cylindric,
Spherical, &c., Functions, by P.
Alexander, 37.

Furnace capable of melting Nickel
and Cobalt, by J. B. Readman, 240.

Gadus ceglefinus, Bacilli found in,
265.

Gadus merlangus, Bacilli found in,
265.

Gadus morrhua , Bacilli found in,
265.

Gas. — Equilibrium of Gas under its
own Gravitation only, 111, 118.

Gases, Kinetic Theory of, by Professor
Tait, 24.

Gaseous Films, Action of, by W.
Peddie, 221.

Gasteropoda, their Problematical
Organs, by Dr A. B. Griffiths, 230.

Geikie (Professor James) on the Geo-
logy and Petrology of St Abb’s
Head, 177.

Glories seen from Ben Nevis Observa-
tory, by R. T. Omond, 314.

— by Professor Tait, 358.

Griffiths (Dr A. B.), Researches on
Micro-Organisms, including a New
Method for their Destruction in cer-
tain Cases of Contagious Disease, 97.

and Griffiths (Mrs A. B.),

Investigations on the Influence of
certain Rays of the Solar Spectrum
on Root-Absorption and the Growth
of Plants, 125.

Researches on the Problemati-
cal Organs of the Invertebrata
(Cephalopoda, Gasteropoda, Lamelli-
branchiata, Crustacea, Insecta, and
Oligochseta), 230.

— — — on the Nephridia of Hirudo
medicinalis, 346.

Griffiths (Mrs A. B. ) on Degenerated
Specimens of Tulip a sylvestris , 349.

Halos and Coronse seen from Ben
Nevis Observatory, by R. T. Omond,
314.

Hamilton (Professor D. J.), the
Conducting Paths between the
Cortex of the Cerebrum and the
Lower Centres in relation to their
Function, 97, 519.

558

Index.

Hare (A. W., M.B.) on the Biologi-
cal Tests in Determining the Purity
of W ater, 306.

Haycraft (Professor J. Berry), the
Objective Cause of Sensation. Pt.
III. The Sense of Smell, 207.

Some Experiments which show

that Fibrin-Ferment is absent from
circulating Blood-Plasma, and sup-
porting Sir Joseph Lister’s view that
the Blood has no spontaneous ten-
dency to Coagulate, 419.

Height of the Land of the Globe
above Sea-Level, 110.

Height (Mean) of the Land of the
Globe, by John Murray, 381.

Helix aspersa, Renal Organs of, 232,
237.

Hirudo medicinalis, its Nephridia,
by Dr A. B. Griffiths, 346.

Hoar-Frost, by John Aitken, 121.

Ice andBrines,by J. Y. Buchanan, 129.

Insecta, their Problematical Organs,
by Dr A. B. Griffiths, 230.

Instability in Open Structures, by Dr
E. Sang, 106.

in Fluid Motion, by Sir Wra,

Thomson, 194.

Inverness Firth, its Temperature and
Salinity, 250.

Irvine (Sheriff Forbes), delivers
Closing Address of Session 1886-87,
446.

Kernpe (A. B.), Note on Knots on
Endless Cords, 36.

Kidston (Robert), Fossil Flora of the
Radstock Series of the Somerset
and Bristol Coal Fields, 153, 240.

Kinetic Theory of Gases, Part II., by
Professor Tait, 21.

Additions to Paper on Founda-
tions of the Kinetic Theory of Gases,
by Professor Tait, 46.

On the General Effects of

Molecular Attraction of Small
Range on the Behaviour of a Group
of Smooth Impinging Spheres, 85.

Knots on Endless Cords, by A. B.
Kernpe, 36.

Lamellibranchiata, their Problemati-
cal Organs, by Dr A. B. Griffiths,
230.

Lanice conchilega , the Nephridia of,
by J. T. Cunningham, 238.

Laplace’s Nebular Theory, in relation
to Thermodynamics, by Sir William
Thomson, 121.

Leptothrix bucccdis, 101.

Leuciscus rutilus, Bacteria in the
Blood of, 263.

Library, Donations to, 535.

Limax flavus, 232, 237.

maximus, 237.

Liquid. — Motion of Compound Bodies
through Liquid, 29.

Lister (Sir Joseph), his View that the
Blood has no spontaneous Ten-
dency to Coagulate, 419.

Lophius piscatorius , 265.

Lumbricus terrestris, Renal Organs
of, 233, 237, 348.

M ‘Arthur (John) on Chloroplatinate
Methods for Determination of Potas-
sium, 428.

Magnetism, Experimental Research
in, by D. S. Sinclair, 194.

Marriage. — The Probability that a
Marriage entered into by a Man of
any Age, will be Fruitful, by T. B.
Sprague, 327.

Marshall (Professor A. Milnes), and
G. H. Fowler, on the Penna-
tulida Dredged by H.M.S. “Por-
cupine,” 359.

Marshall (Hugh) on the Cobaltic
Alums, 203.

M ‘ Laren (The Hon. Lord), Astrono-
mical Tables for Facilitating the
Computation of Diffential Refrac-
tion for Latitudes 56° and 57° ‘30, 21.

Megciscolex ( Perichscta ) (Antarctica,
175.

Methyl- Alcohol, on the Physical Pro-
perties of, by Professor W. Dittmar
and C. A. Fawsitt, 219.

Micrococcus prodigiosus , 100.

aurantiacus , 100.

ureas, 102.

Micro-Organisms, Researches on, in-
cluding a new Method for their
Destruction in Contagions Disease,
by Dr A. B. Griffiths, 97.

Mill (Dr Hugh Robert), the Salinity
and Temperature of the Moray
Firth, and the Firths of Inverness,
Cromarty, and Dornoch, 250.

on the Salinity, Temperature,

&c., of the Firth of Forth, 387.

Mitchell (Mr A. C.), Thermal Con-
ductivity of Iron, Copper, and
German Silver, 327.

Molecular Attraction of Small Range
on the Behaviour of a Group of
Smooth Impinging Spheres, by Pro-
fessor Tait, 85.

Monetary Standard, Variations in the
Value of, by Professor Shield Nichol-
son, 129.

Index.

559

Moray Firth, its Temperature and
Salinity, by Dr H. R. Mill, 250.

Muir (Dr Thomas), Determinants.
Part I. Determinants in General,
Hindenburg (1784) to Reiss (1829),
118, 452.

on a Class of Alternating

Functions, 121.

on the Quotient of a Simple

Alternant by the Difference-Product
of the Variables, 125, 433.

Murray (John, Ph.D.), Opening Ad-
dress, Session 1886-87, 2.

the Total Rainfall of the

Land of the Globe, and its Rela-
tion to the Discharge of Rivers, 48.

on the Height of the Land of

the Globe above Sea- Level, by John
Murray, Ph.D., 110.

on the Mean Height of the

Land of the Globe, by John
Murray, 381.

Mya arenaria, Renal Organs of, 233,
237.

Myxine , the Blood of, by Professor
D’Arcy W. Thompson, 221.

Neodrilus monocystis, 158.

Nerve- Polarization, Effect of Stimula-
tion on, by G. N. Stewart, 205.

Nicholson (Professor Shield), Varia-
tions in the Value of the Monetary
Standard, 129.

Noise, the Physics of, by Professor
Crum Brown, 219.

Nyctiphanes norvegica, the Lumi-
nous Organs of, by J. T. Cun-
ningham and Rupert Vallentin, 351.

Oligochseta, their Problematical Or-
gans, by Dr A. B. Griffiths, 230.

Omond (R. T.), Temperatures at dif-
ferent Heights above ground at Ben
Nevis Observatory, 24.

Glories, Halos, and Coronae

seen from Ben Nevis Observatory,
314.

Open Structures, Cases of Instability
in, by Dr E. Sang, 106.

Oscillations of a Uniform Flexible
Chain hung by one End, by Dr
Edward Sang, 283.

Oven (Sterilising), Mrs Griffith’s Form
of, 105.

Peddie (William) on Increase of
Electrolytic Polarization with Time,
107, 221.

Transition Resistance at Sur-
face of Platinum Electrodes, and the
Action of Condensed Gaseous Films,

221.

Peltier Effect, its Direct Measurement,
by Mr Albert Campbell, 387.

Penicilium glaucum, 101.

Pennatulida dredged by H.M.S.
“ Porcupine,” 359.

Perea fiuviatilis, Bacilli found in
Body- Cavity of, 263.

Pericheeta antarctica, 175.

australis, 173.

coxii, 173.

newcombei , 170.

upoluensis, 174.

Periplaneta orientalis, 232, 234, 235,
237.

Plants. — The Influence of certain
Rays of the Solar Spectrum on Root-
Absorption and the Growth of
Plants, by Dr A. B. Griffiths and
Mrs A. B. Griffiths, 125.

Plarr (Dr G.) on the Determination
of the Plane Curve which forms the
Outer Limit of the Positions of a
certain Point, 415.

Platessa Jlesus, Bacilli found in, 265.

vulgaris, Bacilli found in, 265.

Platinum Electrodes, Resistance at
Surface of, by W. Peddie, 221.

Points in Space. — On Even Distribu-
tion of Points in Space, by Profes-
sor Tait, 37.

Polarization.— See Electrolytic Polar-
ization.

Polarization of Nerve by Stimulation,
by G. N. Stewart, 205.

(Electrolytic) ; its Increase

with Time, by W. Peddie, 221.

Potassium, Chloroplatinate Methods
for the Determination of, by Pro-
fessor Dittmar and John M ‘Arthur,
428.

Prize. —Minute of Meeting of Special
Committee on the Victoria Jubilee
Prize, 27th June 1887, 449.

Protococcus pluvialis, 103.

— — - — vulgaris, 103.

Paia batis, 265.

Rainfall of the Land of the Globe,
and its Relation to Discharge of
Rivers, by John Murray, Ph.D. ; 48.

Rankine (A.), the Thermal Wind-
rose at the Ben Nevis Observatory,
416.

Rankine’s Formula for Retaining
Walls, Improvement in, by A. C.
Elliott, 48, 85.

Rattray (John), a Diatomaceous De-
posit from North Tolsta, 220.

Readman (J. B.) on a Furnace cap-
able of Melting Nickel and Cobalt,
240.

560

Index.

Refraction Tables (Differential) for
Latitudes 56° and 57°' 30, by the
Hon. Lord M'Laren, 21.

Refrigeration, Processes of, by J. J.
Coleman, 38.

Ring- Waves produced by throwing a
Stone into Water, by Sir William
Thomson, 37.

Rowland (Professor), Photographs of
the Solar Spectrum, 194.

Sacco (Professor Federico) on the
Origin of the Great Alpine Lakes,
271.

Salicylic Acid as an Agent for De-
stroying Micro-Organisms, 99.

Salmo levenensis , 263.

Sang (Edward, LL.D.) on Cases of
Instability in Open Structures, 106.

on the Achromatism of a Four-

Lens Eye-Piece : New Arrangement
of the Lenses, 153.

Effective Arrangement for ob-
serving the Passage of the Sun’s
Image across the Wires of a Tele-
scope, 155.

on the Minute Oscillations

of a Uniform Flexible Chain hung
by one End ; and on the Functions
arising in the course of the In-
quiry, 283.

Scott (Alexander), on some Vapour
Densities at High Temperatures, 410.

Segmental Duct. — Note on the Epi-
blastic Origin of the Segmental
Duct in Teleostean Fishes and in
Birds, by George Brook, 368.

Sensation, Objective Cause of. Part
III. Sense of Smell, by Professor J.
Berry Haycraft, 207.

Sepia officinalis, 230.

Sharpe (Rev. H. J.), Motion of Com-
pound Bodies through Liquid, 29.

Sinclair (D. S.), Experimental Re-
search in Magnetism, 194.

Smell, Sense of, by Professor John
Berry Haycraft, 207.

Solar Radiation, by John Aitken,
118.

Solar Spectrum. — The Influence of
certain Rays of the Solar Spectrum
on Root- Absorption and the Growth
of Plants, by Dr A. B. Griffiths
and Mrs A. B. Griffiths, 125.

Professor Rowland’s Photo-
graphs of the Solar Spectrum, 194.

Solution, Laws of, by W. Durham,
381.

Space. — On Even Distribution of
Points in Space, by Professor Tait,

Spheres (Non elastic). See Burnside,
Professor W.

Sprague (T. B.) on the Probability
that a Marriage entered into by a
Man of any Age, will be Fruitful,
327.

St Abb’s Head, Geology and Petro-
logy of, by Professor Geikie, 177.

Sterilising Oven, Mrs Griffith’s Form
of, 105.

Stewart (G. N.) on the Effect

produced on the Polarization of
Nerve by Stimulation 205.

Stewart (Professor Grainger) on the
Discharge of Albumen from the
Kidneys of Healthy People, 240.

Strophanthin, the Chemistry of, by
Professor Thomas R. Fraser, 370.

Sulphates (Double), Instability of, by
Professor W. Dittmar, 219.

Sun’s Image. — Effective Arrangement
for observing the Passage of the
Sun’s Image across the Wires of a
Telescope, by Dr Edward Sang,
155.

Tait (Professor) on the Foundations
of the Kinetic Theory of Gases.
Part II., 21, 46.

on Even Distribution of Points

in Space, 37.

on the General Effects of

Molecular Attraction of Small
Range on the Behaviour of a
Group of Smooth Impinging
Spheres, 85.

on the Effects of Explosives,

110.

on Glories, 358.

Further Determinations of the

Effect of Pressure on the Maximum
Density Point of Water, 110.

on the Compressibility of

Water, of Mercury, and of Glass,
419.

Teleostean Fishes, Epiblastic Origin
of, by George Brook, 368.

Tests in Determining the Purity of
Water, by A. W. Hare, M.B.,
306.

Thermal Conductivity of Iron, Copper,
and German Silver, by A. C.
Mitchell, 327.

Thermal Windrose at Ben Nevis Ob-
servatory, by A. Rankine, 416.

Thermodynamics.— Laplace’s Nebular
Theory, considered in relation to
Thermodynamics, by Sir William
Thomson, 121.

Thermometer Screens, Part IV., by
John Aitken, 53, 428.

Index.

561

Thompson (Professor D’Arcy W.) on
the Blood of Myxine, 221.

on the Larynx and Stomach in

Cetacea, 221.

Thomson (Sir William, P.R.S.E.)
on the Ring- Waves produced by
throwing a Stone into Water, 37.

on the Waves produced by a

Ship advancing uniformly into
Smooth Water, 37.

on the Front and Rear of a

Free Procession of Waves in Deep
Water, 38.

on the Equilibrium of a Gas

under its own Gravitation only, 111,
118.

on Laplace’s Nebular Theory

considered in relation to Thermo-
dynamics, 121.

on Ship-Waves, 194.

on the Instability in Fluid

Motion, 194.

Stability of Fluid Motion. —

Rectilineal Motion of Viscous Fluid
between two Parallel Planes, 359.

Tolsta, Diatomaceous Deposit from,
by John Rattray, 220.

Traquair (DrR. H.), Report on Fossil
Fishes collected in Eskdale and
Liddesdale. Part I. Ganoidei,
111.

Tulipa sylvestris, Degenerated Speci-
mens of, by Mrs A. B. Griffiths,
349.

Urobenus, 168.

Urocheeta, 160.

corethrura, 161.

dubia, 161.

Vallentin (Rupert), and J. T. Cun-
ningham, the Luminous Organs of
Nyctiphanes norvegica, 351.

Vapour Densities at High Tempera-
tures, by Alexander Scott, 410.

Victoria jubilee Prize. — Minute of
Meeting of Special Committee on
Victoria Jubilee Prize, 27th June
1887, 449.

Viscous Fluid, Rectilineal Motion of,
between two Parallel Planes, by Sir
William Thomson, 359.

Water, Effect of Pressure on the
Maximum Density Point of, by
Prof. Tait, 110.

Biological Tests for Determin-
ing its Purity, by A. W. Hare, 306.

Waves. — Waves produced by a Ship
advancing uniformly into Smooth
Water, by Sir William Thomson, 37.

Ring- Waves produced by

throwing a Stone into Water, by
Sir William Thomson, 37.

Front and Rear of a Free

Procession of Waves in Deep Water,
by Sir William Thomson, 38.

On Ship- Waves, by Sir Wm.

Thomson, 194.

W indrose. — The Thermal W indrose
at Ben Nevis Observatoiy, by A.
Rankine, 416.

OBITUARY NOTICES OF FELLOWS DECEASED.

(Separate paging at end of Volume. )

PAGE

Alexander (General Sir James Edward). By Lady Alexander, . 170
Alexander (Dr William Lindsay). By the Rev. Professor Flint, D.D., 138
Anderson (David of Moredun). By A. Campbell Swinton, Esq.

of Kimmerghame, . . . . . .28

Archer (Professor Thomas Croxen). By J. D. Marwick, LL.D,, . 110
Bell (Charles Davidson). By the Astronomer-Royal for Scotland, . 14

Cameron (Augustus John Darling). By Thomas Stevenson, Esq.,

P.R.S.E., . . . . . .137

Chambers (Dr William). By David Patrick, Esq., M.A., . . 143

Cormack (Sir John). By Professor Maclagan, . . .53

Cotterill (Bishop). By Dr Cazenove, . . . .151

Darwin (Charles). By Professor Cossar Ewart, . . .1

Denny (William). By John Henderson, jun., Esq., F.R.S.E., . 162

562

Index to Obituary Notices.

PAGE

Douglas (Francis Brown). By Professor Duns, D.D., . . 123

Grant (Sir Alexander). By Professor Sellar, , . . .99

Haldane (Dr Daniel Rutherford). By Dr John Smith and Dr Heron

Watson, ........ 163

Hallard (Frederick). By Thomas M‘Kie, Esq., Advocate, . . 32

Jenkin (Prof. Henry Charles Fleeming). By W. H. P., . .117

Laidlay (John Watson). By the Representatives of Deceased, . 120
Liouville (Joseph). By Professor Chrystal, . . . .83

M‘Culloch (John). By Francis Brown Douglas, Esq., . . 28

Maclagan (David). By Professor Duns, D.D., . . .124

M‘Nair (John). By Thomas Stevenson, Esq., P.R.S.E., . . 138

Macnee (Sir Daniel). By the Rev. Walter C. Smith, D.D., . . 24

M‘Neill (Sir John). By Professor Duns, D.D., . . . 129

Miller (John). By George Miller Cunningham, Esq., C.E., . . 96

Milroy (John), Assoc. Inst. C.E. By the Representatives of Deceased, 167
Mitchell (Joseph). By the Representatives of Deceased, . .115

Morehead (Dr Charles). By James Sanderson, F.R.C.S.E., . . 41

Muir (Dr John). By Professor Eggeling, . . . .34

Napier (James). By Robert R. Tatlock, Esq., F.R.S.E., . . 105

Plantamour (Emile). By the Astronomer-Royal for Scotland, . 6

Pringle (James), Provost of Leith. By Representatives of Deceased, 166
Raleigh (Samuel). By David Maclagan, Esq., . . .29

Redford (Rev. Francis). By Henry Barnes, M.D., . . . 133

Robertson (General A. C.). By Thomas Stevenson, Esq., P.R.S.E., 136
Robertson (Dr William). By George Seton, Esq., . . .22

Rumble (Thomas William). By William Connor Steel Rumble,

Esq., . . . . . . . .80

Russell (Alexander James, C.S.). By the Representatives of Deceased, 174
Smith (Dr John Alexander). By Professor Duns, D.D., . .126

Spence (Professor James). By Professor Chiene, M.D., . . 31

Stevenson (David). By David Alan Stevenson, Esq., C.E., . 145

Thomson (Sir Charles Wyville). By Peter Redfern, M.D., . . 58

Watson (Dr Morrison). By Professor Alfred H. Young, . .131

Williamson (Dr Thomas). By the Representatives of Deceased, . 167
Wilson (Robert). By Professor Fleeming Jenkin, . . .91

Wohler (Friedrich). By Professor Dittmar, . . .43

Wurtz (Charles Adolph). By Professor Crum Brown, . . 97

Young (Dr James, of Kelly). By Dr Angus Smith, . . .94

[Obituary Notices.

OBITUARY NOTICES.

OBITUARY NOTICES.

Charles Darwin. By Professor Cossar Ewart.

Charles Robert Darwin, who was the son of Dr. R. W. Darwin,
and grandson of the distinguished Dr. Erasmus Darwin, was
born at Shrewsbury on February 12, 1809. His mother was a
daughter of Josiah Wedgwood. Of his early life little is at present
known. For a time he attended the school at Shrewsbury, of
which Dr. Butler, afterwards Bishop of Lichfield, was master. It
having been decided that he should study medicine, he was at the
age of sixteen (1825) sent to the University of Edinburgh. After
two sessions at Edinburgh, he gave up the study of medicine, and
entered Christ’s College, Cambridge, to study for the Church.
While in Edinburgh Mr. Darwin seems to have directed his atten-
tion chiefly to botany and natural history. During his second
session (1826-27) he became a member of the University Plinean
Society, and, as the MS. records testify, took part in its discus-
sions, and read before it at least two papers. One of these papers
referred to the ova of Flustra , the other pointed out that the small
black globular body hitherto mistaken for the Fucus lor was in
reality the ovum of the Pontobdella muricata. These papers pro-
bably contained the results of Mr. Darwin’s earliest scientific obser-
vations. At a subsequent meeting of the Society he presented
“ specimens of Pontobdella muricata ova and young.”

After the usual course at Cambridge, Mr. Darwin obtained the
B.A. degree in 1831, and in 1837 he was promoted to the degree
of M.A. Already an entomologist, on entering Cambridge he soon
became acquainted with the distinguished naturalist Professor

Henslow. Judging from letters published, Professor Henslow seems

a

2

more than any other to have been instrumental in leading Mr.
Darwin to take a deep interest in natural science ; and not only
to have ably assisted and advised him in his pursuits, hut to have
gained his life-long admiration and esteem. Further, we are in-
debted to Professor Henslow for urging Mr. Darwin (notwithstand-
ing the objections offered that it might unsettle him for the Church)
to accompany Captain Fitzroy in the “Beagle,” — a voyage in which
we cannot but feel great interest, not only because of the enormous
work Mr. Darwin accomplished single-handed, but more especially
because it was during this voyage that the great generalisations oc-
curred to him which will ever be associated with his name, and which
mark a new epoch in biology, and have had a more profound influ-
ence on science than any other doctrines ever published.

Three years after returning from his voyage round the world,
Mr. Darwin married, and in 1842 settled at Down, in Kent, where
he remained living the quiet life of a country gentleman until his
death on the 19 th of April last,

Mr. Darwin was elected an Honorary Fellow of the Society in
1865.

Of Mr. Darwin’s work, the influence it has already had, and the
influence it is likely to have in time to come, it is almost impossible
to form any estimate, and still more difficult is it for us to realise
his personal character, and the loss we have sustained in his
death ; for however great he was as a worker, he was still greater
as a man. We have only to be reminded of the wonderful mani-
festations of reverence and regard which followed the announcement
of his death, to understand how universal has been his influence,
and how keenly his work has been everywhere appreciated. As
has been well said, in the “ memorial notices,” his wholly irreparable
loss is “ not merely because of his wonderfully genial, simple, and
generous nature, his cheerful and animated conversation, and the
infinite variety and accuracy of his information, but because the
more one knew of him, the more he seemed the incorporated ideal
of a man of science ; ” and that it was not his great reasoning
powers, vast knowledge, and tenacious industry “which impressed
those who were admitted to his intimacy with involuntary venera-
tion, but a certain intense almost passionate honesty by which
all his thoughts and actions were irradiated as by a central fire

3

and 'again, that his “ character was chiefly marked by a certain
grand and cheerful simplicity, strangely and beautifully united with
a deep and thoughtful wisdom, which, together with his illimitable
kindness to others, and complete forgetfulness of himself, made a
combination as loveable as it was venerable.”

When we consider Mr. Darwin’s work, we are led to regard him
as one of the most fortunate and successful observers of natural
phenomena, and as the greatest generaliser in the whole history of
biology ; and further, we are impressed with the' great influence
his generalisations have had on all other sciences.

What, in a few words, may be said to be Mr. Darwin’s great
work ] It is not that he first propounded the theory of evolution ,
nor so much that, taking into consideration heredity, the struggle
for existence, and the survival of the fittest, he hit upon the idea
of natural selection , as that by undertaking elaborate investigations,
by collecting facts from every possible source, and by pondering
over and testing his conclusions again and again, he was able, after
many years of patient industry, to publish an all but complete proof
of evolution. He has thus not only increased our knowledge, but,
by establishing a new principle, has completely revolutionised
biology, introduced order where there was confusion, and laid new
foundations on which naturalists are raising a fair and comely
edifice, which will form the best and most lasting monument of
the great philosopher of the nineteenth century.

So familiar are we all with Mr. Darwin’s writings, that it is
scarcely necessary to do more than mention some of the more im-
portant ones. First of all, one naturally thinks of that mine of
wealth to the naturalist, the Origin of Species, in which we have
condensed into an exceedingly small compass facts, enough for
a dozen volumes ; yet notwithstanding the great condensa-
tion manifested throughout this book, the reasoning is evident
from beginning to end, and the conclusions stand unassail-
able. It reads as if it were the epitome of a whole series of
works which the author had intended to write, and for which
material had been collected, rather than as an introduction; an
epitome, however, so complete and suggestive in itself that, like a
picked army, it was able to fight its way so effectively, that it was
found to be practically unnecessary to fall back upon the vast

4

reserves which had been accumulated in order to support by detailed
evidence the new doctrines. Hence, after publishing The Variations
of Plants and Animals under Domestication , Mr. Darwin was again
able to turn to Nature, not so much now for evidence of his theory,
as by applying the principle of natural selection to point out how
hitherto obscure problems might be explained.

In the Variation of Animals and Plants , and in the Expression
of the Emotions in Man and Animals, we have further evidence
of Mr. Darwin’s enormous power of work, his faculty for collecting
and arranging facts, and of the remarkable ability he possessed of draw-
ing from them conclusions which indicated a wonderful insight into
the secrets of nature. Further, in all of these works, as also in the
Origin of Species, we have numerous observations of great impor-
tance and interest, which mark out Mr. Darwin at once as an able
and careful investigator ; but his fitness for pure zoological work is
still more evident when we turn to the Naturalist’s Voyage Round
the World, and to the Monographs on the Cirripedia. Those
familiar with the elaborate memoirs on the Cirripedia, must feel
that Mr. Darwin was as capable of prosecuting purely morpho-
logical work as he was in performing physiological experiments, or
of working out philosophical problems, and that although his
zoological investigations are thrown into the background by his
profound generalisations, they are of themselves of sufficient
importance to entitle him to rank with the greatest biologists of any
age.

"What has been said of Mr. Darwin as a zoologist, may almost
with equal propriety be said of him as a botanist and geologist. To
quote again from the “ memorial notices — “ It is not too much to
say that each of his botanical investigations, taken on its own
merits, would alone have made the reputation of any ordinary
botanist.” Most of his investigations on plants were communicated
to the Linnean Society, and then published in a collected form.
A volume on The Effects of Cross and Self-Fertilisation in the Vege-
table Kingdom, was published in 1876, and in the following year
appeared the results of his work On the Different Forms of Flowers
on Plants of the same Species ; and in addition to these we have
the memoirs On the Various Contrivances by which Orchids are
Fertilised by Insects ; The Movements and Habits of Climbing

5

Plants ; and also the well-known treatise on Insectivorous Plants .
We perhaps learn best the influence of Mr. Darwin’s work
on botanical science when we compare the ideas held as to
the distribution of plants before and after the publication of
the Origin of Species. Previously, it was generally believed
that the different species and genera were special creations,
and that the regions in which the same forms occurred being similar,
had led to the creation of similar plants. This theory entirely
failed to account for the appearance of similar plants in regions
which had nothing in common in their physical conditions, and
for their absence from places where the conditions were similar ;
whereas, as pointed out by Sir Joseph Hooker, by adopting Mr.
Darwin’s theory, “ The theory of the modification of species after
migration and isolation, their appearance in distant localities is
only a question of time and changed physical conditions.”

Mr. Darwin’s geological work was chiefly the outcome of his
voyage in the “ Beagle.” The most important of these is the masterly
treatise On the Structure and Distribution of Coral Reefs. As with
zoology and botany, however, his generalisations have had more
influence than his special investigations. About the time when
advanced geologists were beginning to feel that the old notions
about fossils utterly failed to account for the distribution of
organisms in the rocks, they were startled with the announce-
ment of the theory of natural selection, and soon deeply im-
pressed with the fact insisted on by Mr. Darwin, that the geo-
logical record was still very imperfect. Just as this theory has
hurried on by leaps and bounds the study of embryology, so it has
given a mighty impulse to palaeontology. Having no longer to
battle over what is, or what is not, a species, palaeontologists are
now vieing with embryologists in working out the ancestral history
of organisms. The work of Professor Marsh alone amply testifies
as to the success of these investigations. Hot the least important of
Mr. Darwin’s works, from a geological point of view, is his treatise on
Vegetable Mould and Earthworms. A paper “ On the Formation
of Mould” was read at the Geological Society in 1840. After
more than forty years, during which period he made numerous
additional observations and experiments, his book on Earthworms
made its appearance — this, with the exception of two papers, read

6

before the Linnean Society shortly before his death, being his last
work.

We might now indicate what"" influence Mr. Darwin has had on
mental and other sciences : how that, through his general nobility
of character, and his moral attributes rising pre-eminently above his
intellect, he has been able to effect the greatest revolution of
modern times without creating more than a passing show of strife
and bitterness : and how all his work was accomplished under
physical difficulties which an ordinary man would have considered
excuse enough to regard himself as a confirmed and helpless
invalid ; but feeling intensely how difficult it is to express in words
what one feels regarding Mr. Darwin, we shall refrain from saying
more. Those who knew the chaotic condition to which Biology
had been reduced before the appearance of the Origin of Species in
the memorable year of 1859, and who have had the opportunity of
observing order take the place of confusion, and light that of dark-
ness, can best testify to the mighty influence of Mr. Darwin and to
the loss the cause of science has sustained in his death. As we lament
our loss, let us however remember that, in one sense, the hero so
many of us worshipped is still with us, and that he lived to see his
great life-work completed and justly appreciated in all parts of the
civilised world. J. Cossar Ewart.

Emile Plantamour. By the Astronomer Boyal for Scotland.

On September 7th of the present year, at the age of 67, died our
Foreign Associate, Emile Plantamour, director of the Observatory
of Geneva, and professor of both astronomy and physical geo-
graphy in the university of the same city.

Victim at last to a sudden accession of consumptive disease, he
died in full possession of his admirable mental faculties, and as
universally regretted as he had lived generally respected, not only
in his own, but in every other country where science is known and
civilisation appreciated ; for well had he exhibited throughout his
whole career how much of kindly goodness, as well as intellectual
ability, does so often characterise those who are snatched out of this
world immaturely by that insatiable malady of the lungs.

Born on the 14th of May 1815 in Geneva — a year after his little
father-state had escaped from its temporary subjection to the first
Bonapartist empire of France, and had joined the Helvetic Con-
federacy— Emile Plantamour’s commencing epoch was that of young
Switzerland, and he ultimately became as excellent a representative
as could be found anywhere of that peculiar yet admirable microcosm
of a republic, whose strict observance of law and order the red
agitators of Paris can by no means understand ; and even the
United States of North America, republicans and democrats alike,
do not altogether comprehend how it can. continue to exist so
anomalously to them — “ a republic without a president ! ” And yet
it not only exists, but lasts and grows, produces wealthy families
too, capable, as with the Plantamours, of educating themselves up
to the highest pitch of usefulness to their State, without seeking
any help from others beyond the use of the self-supporting institu-
tions in that case already made and provided.

But just as the school, or “the old college,” wherein the young
Plantamour spent the earliest of his hard-working years of learning
as a boy, was of that staid and solid character that might be
expected in an institution founded by Calvin, soon after the
Beformation, so the comfortable private means of the older Planta-
mour’s, like that of so many other Genevan families, had been
attained in a manner worthily corresponding thereto. For not by
manufactures nor by commerce, still less by speculations or bubble
companies, were those tidy little Alpine accumulations obtained,
but by the magnificent moral control of the progenitors of the family
and their successors, one and all determining to live, though put to
any straits for a time, on half only of their yearly income, leaving
the other half to grow at compound interest.

Emile Plantamour himself was still too young to think much of
these things while at Calvin’s school; but by the time he had
passed through that institution, also through the higher academy of
Hofroyl, and then the classes of the Genevan University, he was
called on to choose his future walk in life as a working member
of the busy republican mountain hive. So he elected to be an
astronomer — a Helvetian astronomer of course. But what is there
peculiar in that prefix'? This mainly, that while the Helvetian
confederation forms so small a patch of country, surrounded by

8

great empires, it yet possesses more diversity of populations than
any of them ; so that hut for the mysterious cord of Helvetic unity,
its French cantons would he ever fighting against the German, and
the Italian against both. Wherefore, all the great and good citizens
of that up and down mountainous land seem ever to have a most
difficult problem of their own to work at, viz., how to keep up the
vigour and elasticity, the frictional polish and emulating fervour of
those several competing nationalities, while inducing them, never-
theless, to do all peacefully, and voluntarily to contribute each their
best characteristics, so as to raise the united name of a Swiss
republican for virtue and education, valour, prudence, and under-
standing, above that of all collections of men, if possible, ruled in
any other manner. Wherefore, thus did M. Plantamour proceed on
attaining to virile growth and privileges.

From the university of his native city he went to Paris, and
studied for two years under Arago, that grand specimen of the
Celtic Gaul ; a man of superb genius, of commanding presence, of
daring flights into the connection and bearings of hitherto untrod
branches of physical science ; and with whom occasional researches
into the curiosities of magnetism, or the uncultivated jungles of
meteorology, combined with public displays of fervid eloquence — took
the place of regular observatory work, and was thought everything
of, almost up to adoration, in the midst of a Latino-Celtic popu-
lation.

After highly approving himself and his mountain-born abilities
among that class of men, descendants of warriors and native chiefs
of long, long ago, — Emile Plantamour went north to Konigsberg,
and there, under the grandest soul in all Germany for philosophical
breadth, instrumental skill, and mathematical power in gravitational
astronomy — though originally only a grocer’s apprentice, the illus-
trious Bessel — he learned by what kind of steady work and calm
devotion in a quiet home the Teutonic mind obtains some of its
highest triumphs. While thus truly a student studying under
Bessel, young Plantamour produced, as a thesis, a most creditable
essay ‘‘On the Determination of the Orbit of a Comet according to
Gibers’ Method from three Observations.” Next he went into
Berlin, where, under the celebrated Encke, he learned the still more
rigid work of meridian astronomy, besides enjoying the improving

9

society of the great traveller Humboldt, the magnetieal mathe-
matician Gauss, and the astronomical analyst Hansen.

Returning to Geneva in 1839, the venerable Alfred Gautier retired,
and Plantamour, able now to look on astronomy from every side,
or as a Switzer of each and every diversely tongued canton, was
installed as director of the observatory, with powers to choose and
direct accordingly. Wherefore thus he proceeded. Hot with any
of the two or three great observatories of the three or four gigantic
countries, powerful governments, and populous nations around him,
would he contend in their ancient and still prescriptive work of
procuring new expressions for the oldest fundamentals of the grand
classic astronomy of sun, moon, and principal planets ; no fresh and
always minutely differing values would he attempt for the exact
quantities of precession and nutation, for the aberration of light, for
refraction, and sun-distance ; on each of which inquiries such
myriads of pounds sterling have been, and still are, being spent,
and libraries of books written in the great centres of civilisation ;
but, while fully appreciating both the grandeur and difficulty of
those problems as much as any of the savants working at them, he
chose more especially “ the orbits of Comets ” as the future distinc-
tive subject of his observatory labours.

Comets, however, will not always come just when they are
wanted ; and so, for a time, we find the disciple of the German
Bessel, remembering anew the Gallic Arago, and to such purpose,
that the very earliest of his published memoirs in his new director-
ship, was on “ Atmospheric Electricity.” Then came two years
observations of terrestrial magnetism. And next, duly considering
the wants of those of his countrymen engaged in the staple industry
of Geneva, watch-making, he organised a department in the obser-
vatory where watches and chronometers sent in by the local makers
are submitted to a variety of scientific tests, the results published,
and prizes awarded for the best time-keepers ; with the happiest
effects too in promoting improvements in that most delicate branch
of all the mechanical arts.

But in 1843, Plantamour’s own faithful waiting was at length
rewarded by the apparition of one of the most splendid, and in
every way remarkable, comets of modern times. Seen first in broad
daylight close to the sun, and afterwards hurrying away into the

10

depths of space with a longer train than any known comet since
Newton’s day, this chief of comets, in 1843, opened a new epoch of
activity among all the observatories ; while Plantamour was the
first of the computers to announce that in its perihelian passage this
comet must have almost grazed the very surface of the sun. That
it must have seen for two hours the sun’s incandescent disc under
an angle of practically 180°, and have been exposed for that length
of time to a radiation sufficient to vapourise iron, platinum, and every
known metal ; yet had it lived, preserved its movement, and gone
off at last apparently uninfluenced on its regular orbit. And what
kind of orbit was that 1

Ah ! That indeed is the question ; never more abundantly dis-
cussed too than at this moment in connection with a comet of the
present year. Plantamour had been strong enough in his first
theoretical university essay on the beauty of determining a comet’s
orbit from three observations ; but he soon learned in practice that
no three observations ever taken by man, much less the first three
that are usually secured of such a sudden and unexpected intruder
as the great comet of 1843, can give more than a very wide approxi-
mation to that one of all the orbital elements which the public most
cares for, viz., its period ; and thence the date when it will next be
seen, as well as that when it was last visible. He showed indeed
without controversy, that it was a closed orbit, and of no very great
duration; but whether of 165 years, or 22, or even less — and
why, in that case it had not been seen oftener, subsequent to its
supposed record in 1868, he left for the future to determine.

And now comets followed one another quickly ; the next with
which Plantamour occupied himself being the second of 1844,
called the Comet of Mauvais ; and a most opposite one it was to
that of 1843 in almost every particular. For this of 1844, though
little more at any time than barely visible to the naked eye,
remained within telescopic range for nearly nine months ; was well
and numerously observed during the whole of the time, and gave
to M. Plantamour’s calculations, perfected as they were in this in-
stance by his careful introduction of corrections for planetary pertur-
bations, a perihelion distance of so much as 78 millions of miles;
and a period, reaching the hitherto unheard of extent, of 102,000
years, subject to an uncertainty of not more than ^th of the -whole.

11

Again in 184G came the separation of Biela’s comet into two.
These were long followed up by Plantamour, both by observation
and calculation • until he at length proved them to be each pro-
ceeding on its own independent course through space, quite un-
influenced by the other. It was but a small telescopic comet at any
time, until that startling telegraphic announcement of Herr Klin-
kerfues to Mr. Pogson at the Madras Observatory, on December 2
(1872), thus concentrating the results of his long and difficult
orbital calculations “Biela touched earth on November 27, search
near 0 centauri.” Pogson accordingly turned his telescope in that
southern direction, and found a retreating, and already far-off patch
of cometary matter in that quarter. But what had the inhabitants
of the northern side of the earth witnessed on the 27th of Novem-
ber1? A brilliant display of shooting stars so-called, or isolated
meteoric stones, darting through the upper rarefied air at the rate of
more than 1000 miles a minute, and taking the regular meteoric
observers quite by surprise, as being an altogether abnormal and
unexpected vision to them.

Here, accordingly, was admirable authority for Plantamour adding
to the Besselian astronomy of cometary orbits, the physical studies
of the Aragonian school. But his observatory was ill supplied with
instruments of size and quality adapted to such researches, and
neither the University of Geneva, nor the politicians thereof, were
inclined to spend anything to improve them. So, by noble self-
denial, and out of the economies of his ancestors, Plantamour
supplied a fine equatorial, with objective of 10 inches aperture, with
tower and revolving dome, to the establishment ; and kept it
thenceforward at excellent work for the credit of the community
and the promotion of astronomy.

The situation, too, was deserving of being so powerfully instru-
mentalised. No less than 10 degrees of latitude further south than
Edinburgh, raised on a plateau 1200 feet above the sea-level, in a
drier and generally warmer air, and with far less of dreadful coal
smoke belching around from blackened and blackening chimneys ;
a telescope could there be used to its full advantage ; and the
climate itself would afford, especially in the land, and to a country-
man, of Saussure, a most deeply interesting study.

Prom his very first appointment to the observatory, Plantamour

12

had continued in the Bibliotheque Universelle Journal , the publica-
tion of the comparative meteorological observations begun to be
taken long before, both at Geneva and at the Hospice on Mount
St. Bernard ; the earliest example it is said of a systematic study of
the climate of elevated regions ; and the results, discussed as they
were by the hand of a master, were eventually published in his
work entitled The Climate of Geneva from 50 years of Observa-
tion. To these again he added his brilliant studies of the physical
geography of the region, chiefly from the astronomical and accurate
point of view ; conducting extensive levellings, both instrumental
and barometric, over the highest ridges, and through the deepest
valleys of Europe; determining also the force of gravity by pendulum
observations in numerous localities, and their longitudes both by
telegraphic signals and geodesic measures of the most exact kind.

In short, this admirable man, as our own learned and most
devoted librarian, Mr. James Gordon — to whom I owe much of
these materials, has kindly informed me — produced in his time no
less than 83 distinct memoirs, varying in size from pamphlet to
book, with a distribution of their subjects, something as follows, —

Cometary, observations and calculations .
Astronomy, general .....

Eclipses, Solar transits, new planets or planetoids
Magnetic .......

Atmospheric Electricity ....

Meteorologic ......

Hypsometric and Geodesic ....

27
6
8
2

1

28

11

besides several other memoirs in conjunction with M. Hirsch and
M. Birner, chiefly geodetic.

No wonder then that his local biographers have described, that
even in his later years, when though over-shadowed by the threaten-
ings of his eventually fatal disease, he yet worked a full eight hours
a day ; and at a kind of astronomical labour which does not exactly
repose the mind. Yet through it all, they record that he was ever
the gentleman, the man useful to the community, and always ready
to give his services wherever they were asked. Oh ! what abne-
gation of self, for who amongst us, living happily under an ancient,
long consolidated, and much loved constitutional monarchy, can

13

presume to know the many republican calls that were made on
Citizen Plantamour’s time and attention.

" All the scions of our richer families,” said a fine old specimen
of a New York State country gentleman to me not long ago, “ find
it expedient to enter into politics, in order to understand the mind
of the people, and endeavour to lead public opinion.” So too did
Plantamour, and with success. Por he was listened to with
deference whenever he spoke, even in the most radical assemblies.
And if not personally present, the mere statement by any orator
there that “ Plantamour thinks so,” would often suffice to carry
the day.

And in Emile Plantamour there was something more and beyond
mere political wisdom to admire. Eor when I had, on one occasion,
the honour of receiving a letter from him ; and which, beginning
with a discussion of the Meteorology of the xiiith vol. of the Edin-
burgh Astronomical Observations , went on to speak of various little
local institutions he was interested in, as his Bible Society, his
Scripture reading Society among the poor, and other similar insti-
tutions, a lady listening to my reading started to her feet and
demanded “ What French savant was capable of such ideas.”

So then I had to explain, that although the letter might be
written in the French language, the man himself was a Switzer ;
horn in Geneva ; and educated in a school founded by Calvin, and
approved of by John Knox. Whence immediately she understood
the possibility, or even recognised the origin, of that wide philan-
throphy joined to the highest science. And this meeting will
doubtless similarly appreciate how much our Society has lost in
every way by Emile Plantamour’s recent demise ; so very soon too,
or within 18 months, after the Council had selected his name to
occupy that honoured place amongst our Foreign Associates which
the Eoyal Society of Edinburgh has always desired to see filled by
some representative of that noble, though circumscribed, community
dwelling amongst the higher Alps.

C. P. S.

14

Charles Davidson Bell. By the Astronomer-Boy al for

Scotland.

Late and for long the Surveyor-General of our vast colony of the
Cape of Good Hope, elected an Ordinary Bellow of this Society on
March 4, 1878. Died here on the 7th of April 1882, aged 69.

Born at Newhall, in the parish of Crail, in the East Neuk of
Bife, in 1813, in a family of three, and of so long lived a race that
his mother lived to 85, his father attained to 90, his father’s elder
brother, General Sir John Bell, a leading officer of the Staff Corps
in the Peninsular War, and highly approved of by the Duke of
Wellington, reached the still nobler age of 95, and a grand-aunt
lived to be 101, while his own brother and sister are still living,
hale and hearty ; — it might therefore have been hoped, that when
Charles D. Bell retired from southern official life to this country, in
1874, there were yet many years before him, wherein to exercise at
leisure the many fine talents wherewith he was gifted, and in a
manner to show forth something of the fervid love and even
ecstatic devotion he always bore to his native land, notwithstanding
his long separation from it.

But that was not to be. The trials and the stresses he had gone
through in the South African climate and country were too many
and too severe, however successfully they seemed to be overcome at
the time. Success, indeed, usually crowned almost everything he
undertook ; and he would have had a far more notable name among
us had his career been confined to Old Scotland, instead of being
spent so entirely as it was from his sixteenth to his sixty-first year
in that new and greater Scotland which stretches now all across the
ffiobe, from Canada in the north-west to Australia and New Zealand

O '

in the south-east, with the Cape as a very central stronghold.
Originally, no doubt, the Cape was a Dutch colony, but one wherein
it was long ago remarked to me, that among the many British
residents that had come flocking in, every one who got on best,
whether in the higher or lower walks of life, was always a Scotch-
man. And one of the most noteworthy of those, because mainly by
such original efforts and innate qualities of his own, was the subject
of this notice.

Though leaving his country at so early an age (in 1829), Charles

15

D. Bell’s preparations and prospects were good ; for lie had attended
classes at St. Andrews University, in fellow-studentship with John
Goodsir (afterwards Professor of Anatomy in Edinburgh) and his
brother Joseph, the minister. While at the Cape, his uncle, then
Colonel Bell, private secretary to the Governor, and afterwards and
for many years the sage and steady Colonial Secretary, was greatly
interested in him.

After a period of service in the Secretary’s office, C. D. Bell was
transferred to that of the Master of the Supreme Court, and then to
the Audit Office of the Colonial Government, becoming a favourite
everywhere ; until it seemed as if his friends intended the young
man for a future of nothing but quiet, resident, jog-trot official life
in Cape Town itself, and no further. But in 1833, Sir (then plain
Dr.) Andrew Smith (of the Army Medical Service) succeeded in
organising an exploring expedition for penetrating into the interior
of South Africa on a grander scale than anything hitherto attempted.
Whereupon the internal fires of C. D. Bell’s own spirit broke forth ;
and, against the advice and even strenuous opposition of his legal
guardians (for he was still under • age), he would give up all his
other prospects in order to seize this opportunity of penetrating into
the great unknown. And though he was allowed to join the party
at the last moment, it was only on condition of taking the lowest
place in it.

An old friend, who well remembered meeting him just after he
received his leave, has some years since described in print the wild
enthusiasm with which C. D. Bell galloped through the streets of
Cape Town to dash off preparations for the immediate start. He
was a hand some-looking young fellow too ; not very tall, but broad-
built and muscular, with a rather brown complexion, but regular
features of refined and sculpturesque character, piercing black eyes,
and dark lank hair.

The expedition, in spite of its numbers, was generally looked on
as one of imminent danger. The latest previous expedition had
been cut off to a man ; and no previous parties had ever returned
without having undergone more or less perils of thirst, of hunger,
of wild beasts, of lurking Bushmen with poisoned arrows, and whole
tribes of more openly slaughtering foes. But away went this new
expedition, striking straight across those stony tablelands of blinding

16

sunshine, roasting heat, and terrestrial drought, which fence in the
Cape Colony along its northern and north-western frontiers almost as
imperviously to all ordinary travellers as though they were walls of
iron rising up to skies of brass, and intended to prevent inquirers
from entering into the mysterious interior beyond, stretching away,
as it was then supposed, uninterruptedly to the Equator itself.

A Kaffir war breaking out soon afterwards on the north-east
frontier of the colony, the expedition was lost for a time to sight
and hearing ; but after three years it returned safe, successfully too,
on the whole, and with C. D. Bell raised by shere merit and proved
capacity to be its second in command. But he had done far more
than merely rule over others, and order their services ; for when
the Association which had defrayed the expenses of the expedition
held a public meeting in 1836 to exhibit its results (a meeting at
which Sir John Herschel, then in the colony on astronomical
research, presided, and gave a splendid address), every one was
astonished, delighted, and instructed at finding the walls of the
room decorated by nearly three hundred of C. D. Bell’s drawings.
He had been the artist of the expedition, and such an artist as
showed him to possess a soul of true genius, if there be any one in
the world of whom that can be properly said.

There, in those matchless drawings, was the peculiar country the
expedition had passed through, in its minuter as well as larger
features ; unadulterated, moreover, artistically by any methods of
drawing taught at home on English trees and hedges and shady
lanes; for C. D. Bell had taught himself in South Africa on exactly
what nature presented to him there. Hence was the great interior’s
physical geography, geology, and vegetation, too, where there was any,
depicted again and again, either in brilliant colour, or chiaroscuro
force of black and white, and almost perfect truth of outline ; with
the very atmosphere also before one to look into, as it shimmered
and boiled in the vividness of solar light, and over stony surfaces
heated up to 140° or 150° Eahr. ; but yet garnished with episodes
of the wild animals of the region — generally gigantic mammals, of
South Africa to-day, but of other parts of the earth only in some
past geological age ; and with lifelike examples of the natives of
every tribe whose lands the expedition had traversed, depicted in
their most characteristic avocations. From little Bushmen securing

17

once in a way a mountain of meat, in a desert without water, by
taking a two-horned rhinoceros in a pit-fall, to the Zulu regiments
of King Moselikatse going forth with cow-hide shield and stabbing
assegai to exterminate some neighbouring tribe ; or the poor of his
kingdom, with famine girdles braced tightly round their loins,
following in the track of lions, in hopes of partaking of some of
their leavings : they were all on those faithful sheets of paper.
While, so keen was C. D. Bell’s appreciation of the ridiculous, that
if there was any young fop among the nearly naked Bechuana or
Malokolo, who wore his dress of a few jackals’ tails and some glass
beads with a particular twist of his own invention, and thought he
looked so handsome in it that all the women must be falling in love
with him, this native-born dandy was sure to figure in some one or
other of Mr. Bell’s drawings ; for he drew as much, or more, from
memory in the silent watches of the night, as by sketching direct
from nature through the day.

That that brilliant collection of pieces of graphical information
never saw the light again until, after twenty years, a few of them
straggled out to illustrate later travellers’ books, — was no fault of
Mr. Bell’s. For he had necessarily to give them up to his chief ;
and he, a very learned naturalist, and taken up far more with curio-
sities in the way of undescribed snakes, — was allowed by the
Association to carry out. a scheme of his own for obtaining renewed
funds for more expeditions, by exhibiting all his natural history
treasures in that focus of wealth and Government patronage, Lon-
don ; but with a result which totally failed to pay its own expenses.

Meanwhile Mr. Bell quietly re-entered the Audit Office of the
Colonial Government, where he was raised from his former junior
position to be chief clerk ; and not long after that received the
acting clerkship to the Legislative Council, holding that honourable
position during a two years’ absence of the proper officer.

But mere pen-work within four walls was not enough to satisfy
C. I). Bell’s aspirations, or assure his conscience that he was thereby
turning to the utmost account all the varied talents committed to
him by his Creator. In 1838, therefore, he began to turn his
attention to surveying, and became soon after, one of the sworn land
surveyors of the colony; — a colony twice the size of Great Britain,
but with a population of half the city of Edinburgh. A colony of

b

18

immense, craggy, rocky, mountain ranges (Le Vaillant termed ono
of them “ the backbone of the earth ”), and extensive desert plains,
with a nice variation in the quality of their barrenness accordingly
as they were of deep sand or ferruginous clay, mixed or unmixed
with salt and gypsum. A colony, too, where the British element of
population was still in utmost minority ; and where the surveying
system hitherto in vogue in the back, or over-berg, country had
been — to let any Dutch boer, wanting land, choose some possible
central water-hole in Government or unoccupied ground, and
then ride round it on horseback for three hours, or drive round it
on an ox-waggon for three days, according to its degree of want
of vegetation ; such interested boer undertaking to remember
against all future comers what particular isolated bushes, or great
rocks in the weary land, he had seen during such circumferential
ride or drive, and had then and there chosen to be his baakens, or
landmarks for ever afterwards.

As population increased, such a system was of course most fruitful
in land disputes, and the then Surveyor-General, Colonel Mitchell,
formerly of the Portuguese Legion in the Peninsular War, found his
attempts to introduce accurate surveying into town lots grievously
swamped by having presently the legal business of certain Land-
drosts, Heem-raden, and up-country Dutch Civil Commissioners,
further thrust upon him, and his then sole assistant, Mr. Hertzog. He
applied, therefore, in 1840, and obtained Mr. Bell's appointment as
Second Assistant Surveyor-General ; when he (C. D. Bell) was
immediately sent off on a long and solitary travel, occupying several
months (quite a geographical exploration in itself, in his little ox-
cart, and attended only by a Malay driver and a Hottentot leader of
the oxen), to the north-western corner of the colony, to settle dis-
puted claims there ; some of them on the cool Khamiesberg granite
mountains 5000 and " 6000 feet high, others in the hot and arid
plains below, or the sandstone ranges and steppe formations further
eastward and northward, even as ' far as to the Orange River below
its falls. And he settled them so satisfactorily, and with so much
calmness and wisdom, that the Dutch boers ever after that always
addressed him, though still only twenty-seven years of age, by their
title of highest honour, viz., “ Old Mynheer Bell.”

He was next appointed to organise a survey office in the eastern

19

district of the colony, where so many Scotch settlers were established
under Pringle and others many years before, in what the Dutch
had stigmatised as the “ Zuureveld,” or field where the grass was
sour, and in their eyes, and to their means and resources, good for
nothing, except to stick Englishmen in, to serve as buffer between
them and the Kaffirs. From thence he was taken for a time by the
new Governor of the colony, Sir Peregrine Maitland, to inspect the
Kaffir frontier and interior districts. And again, in 1845, across the
. upper Orange Fiver to Zwartkopjies, “ where,” says a local print,
“the information he had acquired in the expedition of 1833 was
found extremely useful.” No doubt it was, too, and yet not suffi-
ciently utilised by the Government at home; for had it been,
several calamitous disasters of recent years, and excitations of inter-
national hatred in the north-east of that country, would have been
avoided. The distribution, too, of the British settlers would have
been arranged in a manner to profit far more by the physical geo-
graphy of South Africa ; which offers a Brazilian climate on one side
against an Arabia Deserta on the other, if you only go far enough
in either direction from the intermediate point of Table Mountain
and Table Bay, where the Dutch first landed, and for so long looked
upon it as their only and commanding centre for their agriculture,
commerce, and government in all the southern hemisphere.

In 1848 Mr. Bell became, on the demise of Colonel Mitchell (a
demise much lamented, and hastened in no small degree by the extra
anxieties of his office), full Surveyor-General of the Cape of Good
Hope. Thenceforward, for twenty-six years, he ruled in that
department with a suavity, firmness, and knowledge that obtained
the best possible results for Government, out of an otherwise almost
hopeless, tangled collection of conflicting interests, old legislations,
and changed ideas. His thorough knowledge of the colony in which
he had grown up to man’s estate, his mature development of a
judicial breadth of view, combined with his scientific skill and
mechanical abilities, were evidently becoming more and more appre-
ciated ; for, spite of the over-work of his own office, he was so
frequently requested to join divers Government committees, and
prepare special reports, such as that on the establishment for con-
victs, lepers, and lunatics on Robben Island, the newly-found copper
fields of Little Nam aqua land : and various lines of road to open up

20

hitherto untrodden districts : until at last, such extra demands of
the upper colonial officials culminated in this, — that whereas they
had quarrelled with and dismissed their recently imported English
engineer-in-chief for a proposed line of Metropolitan Railway,
extending from Cape Town to the Berg River Yalley, and some
one must he found to take his place, they unanimously agreed that
C. D. Bell was that man ; because he was the only one amongst
them who could lay out railway curves, build bridges, raise em-
bankments, bore tunnels, inspect locomotives, and, in a word, save
them, the great officials of the new “ responsible Government,” so
called, in the eyes of the people, and before public opinion.

And he did help them through that great difficulty by extra-
ordinary exertions of his own, and which he could hardly have
accomplished at his then advanced age, but that he had never spared
himself. He had lived a triple life all along ; first, his official life,
whose duties were always paramount with him ; second, his private
social life, where he was always a favourite; and lastly, his artistic
life, which occupied almost every Other moment of his existence.

In 1846, while still in Cape Town, by shere dint of his know*
ledge of the eastern country and people, he produced a long series
of drawings in black and white, representing events in the Kaffir
war then raging under Sir Peregrine Maitland, — drawings which
astonished and delighted the soldiers who had been engaged in the
operations, — and, being' sent home, were taken on one occasion by
the Duke of Wellington into his private study, to con over alone,
before giving his opinion on the conduct of that war to the House
of Lords.

In 1847, having come home on a short leave of absence, Mr.
Bell procured from Messrs. Schenck & Co. of this city, a litho-
graphic press and stones, learned to work it himself, threw off at
once a number of South African subjects, varying from the Rev.
Mr. Moffat preaching to Bechuanas, down to Amakosa Kaffirs
torturing a wounded prisoner ; and took the whole plant out with
him to Cape Town, a novel and important accession at that time to
its means of graphic multiplication.

There he further worked at oil painting ; and when the com-
munity at last began to awake to the importance of art culture, and
opened an exhibition of pictures, he carried off their gold medal for

21

a spirited historical painting, representing Van Biebeck founding
the Cape Colony in 1650.

Wood carving next came in for attention during some of C. D.
Bell’s spare hours ; also modelling in clay ; such models, after
baking in an oven, being then painted in natural colours. Bor the
object of most of these artistic works “ in the round” was to pre-
serve the physiognomy, manners, customs, tastes, and traditions of
the native races of South Africa. He had enjoyed the opportunity of
seeing those races on his first arrival in their country, still numerous,
distinctive, and true in their stationary savagedom to a long past
antiquity ; but before he left, they were rapidly losing, under new
conditions, those characteristic features, as well as their ancient,
imperfect mother tongues.

Such then was the man, Charles D. Bell, who, leaving most of
those precious works behind him, or having given them away right
and left too generously as soon as completed, returned to this country
in 1874, with his second wife (a Cape lady), two sons, and a
daughter. Giving vent immediately to his long pent-up passionate
admiration for his native land, he soon joined the Antiquaries and
the Meteorological Societies, as well as our own ; wrote on the
ancient harps of Scotland, and began to illustrate in painting some
of the touching ballads of the country’s former days. But his
existence was saddened by the quickly following deaths of mother,
father, and uncle. Then he suddenly lost the use of one eye.
Without external change, or internal feel, the sight power was gone.
He had always been very short of sight, however keen ; and it was
that eye, whose surrounding muscular contractions had enabled him
to keep a strong concave lens always in place through fifty years of
excellent work, which had now suddenly broken down.

But most of all was he affected by the sudden and totally unex-
pected demise at Crail, during a summer residence there last year,
in his father’s old house, of his beloved Wife. His faithful spirit
never recovered that blow, and he but lingered on for some six
months further, until he followed her himself.

I cannot expect that, with my imperfect knowledge of his most
multifarious life, I have in any way succeeded in representing it as
it so fully deserves to be represented, in all its noble character and
just proportions. Hor is there, perhaps, the most pressing of all

22

necessities that X should do so before the present audience ; for it is
not we, but the Cape people who should erect a statue to him : to
him, Charles D. Bell, who did, and accomplished, and suffered so
much for them and amongst them, through all the best years of
his long period of a most hard-working life and publicly useful
career. C. P. S.

William Robertson, lVI.JD. By George Seton, Esq.,

Advocate.

Dr. William Robertson was born in Edinburgh on the 8th of
January 1818. He was the eldest son of Mr. George Robertson,
Keeper of the Records in H.M. General Register House, by Eliza
Brown, his wife, sister to General Sir George Brown, of Crimean
fame, and Mr. Peter Brown, well known as an agriculturist and
land valuator in the north of Scotland. He obtained his early
education at the Edinburgh Academy, from which he passed to the
University ; and, after completing the medical curriculum, he con-
tinued his studies at Paris, Berlin, and Vienna. In 1839 he
graduated M.D. of Edinburgh, his Thesis being on Enlargement of
the Heart,- which proved to be the disease from which he suffered
prior to his death. Eour years afterwards he was admitted a
Eellow of the Royal College of Physicians. He acted for some time
as a physician in the Royal Infirmary, the Eever and Cholera
Hospitals, and the Hew Town Dispensary; and, holding the
appointment of Inspector-Physician of the British Civil Hospital
at Renkioi, in virtue of the recommendation of Sir Robert Chris-
tison, he served as a physician during the Crimean war. He was at
one time editor of the Edinburgh Monthly Journal of Medical Science ,
to which he contributed several papers. On the resignation of Dr.
Stark, in 1874, he was appointed to the post of Superintendent of
the Statistical Department in the General Registry Office of Births,
Deaths, and Marriages, having previously acted as Medical Registrar
for Scotland. One of his latest official works was the preparation
of the Report prefixed to the first volume relative to the Scottish
Census of 1881. In 1876, on the death of Dr. Warburton Begbie,
he became medical officer to the Scottish Widows’ Fund, having by
that time gained large experience in matters connected with Life

Insurance, in the capacity of medical referee to the Guardian and
Scottish Equitable Societies.

Distinguished by his diagnostic skill and his thorough knowledge
of therapeutics, but for his modest and retiring disposition Dr.
Robertson might, in the opinion of competent judges, have taken a
very distinguished place as a consulting physician ; and, owing to his
high reputation as a mathematician and a statist, he was eminently
fitted for the two appointments which he held at the time of his
death. His capacity for figures was of a very high order. He did not
hesitate, however, to facilitate his elaborate calculations by the use
of the arithmometer, which he was able to turn to the best account,
owing to his remarkable memory and his powers of numerical
combination.

Hor were his acquirements confined to physical and mathematical
science. While well versed in classical as well as modern literature,
he was an excellent linguist, being familiar with French, German,
Italian, and Turkish, and possessing a fair acquaintance with Spanish
and Dutch.

In social life he was a universal favourite, in consequence of his
kindly .and genial disposition, his fund of anecdote, and his well-
stored mind. One of the original members of the Edinburgh
Evening Club, he seldom failed to appear at its bi-weekly meetings,
where the blank which his lamented death has caused will not
easily be supplied. His cordial sympathy with the young was an
interesting feature in his character. He was a devoted member
of the Church of Scotland, and his political tendencies were Con-
servative.

In connection with his official appointment in the Registrar-
General’s Department, it may be mentioned that the office of Joint
Deputy Keepers of the Records was held, in the first instance, by
Dr. Robertson’s grandfather and granduncle, in succession to whom
it was held, also jointly, by his father and uncle, and singly, at a
later period, by his brother George Brown Robertson, Writer to the
Signet, who died in 1873. Accordingly, the official connection of
the family with the General Register House extended over a period
of upwards of a hundred years.

Dr. Robertson became a Fellow of the Royal Society in 1860.

His death occurred at his residence in Albany Street on the 25th of

24

August 1882, at the comparatively early age of sixty -four. He had
been in failing health *for about two years, but it was only a week
before he died that he became seriously ill. His funeral took place
in Warriston Cemetery on the 29th of August, and was attended by
a large concourse of attached relatives and friends.

Hr. Robertson is survived by two sisters, with one of whom he
resided, while the other is the wife of Mr. John Gillespie, Writer
to the Signet, and Secretary to the Royal Company of Archers.
His youngest brother, Alexander, a promising artillery officer, was
one of the many victims of the Indian Mutiny of 1857.

Since the above was prepared, the writer has received a letter
from one of Hr. Robertson’s medical compeers (Hr. George Bell) in
reply to an application on the subject of his chess-playing, in which
he says : — “ Hr. Robertson was no ordinary chess-player ; he
understood the game, and practised it with judgment and skill. I
know this, for the ‘ chequered field’ was our favourite meeting-place
during many years. Always pleasant there as elsewhere, Edinburgh
does not know what a rare son she has lost. Though undemon-
strative, the Royal Society had few such members as William
Robertson.”

Sir Haniel Macnee. By the Rev. Walter C. Smith, H.H.

Haniel Macnee’s life, like that of most hard workers, was not a
very eventful one. Its chief incidents were its productions, and
these were nowise startling, but rather such as might have been
looked for — fruits of patient labour, and proofs of quiet growth.
Born at Eintry in 1806, he lost his father while yet a mere child;
but he was happy in having a mother who could understand and
guide his youth. Very likely that youth puzzled her a little at first,
for she would fain have trained him for merchandise and money-
making, and his gifts did not lie at all in that line. The sleepy
valley of the Endrick, among the green Campsie hills, had to pro-
duce its genius like other Scottish glens ; and probably his mother
had her anxiety, as well as her pride, when it began to dawn upon
her that she had given birth to one of that wayward race. I suppose

25

he did his school tasks fairly well for her sake ; hut after school
hours, if he was not fishing the water, he was sketching his com-
panions, or telling the drollest stories of things he had seen or heard,
which were truly pictures of the vividest kind. So she concluded
that he was horn to be an artist ; and that, no doubt, was his own
opinion also. Yet, with all his well -merited success, it may be
doubted Avhether they were not both of them mistaken. That he
had genius w.as clear enough, and that he was fond of drawing
pictures was plain to every one who knew him. But whether his
genius would best find its true field in painting the outward or the
inward man — faces or characters — that the gossips of Fintry could
hardly be expected to determine. It showed some courage then, at that
early stage of Scottish art, to devote a boy of thirteen to so precari-
ous a means of living ; but it would, no doubt, have looked like
very madness to bring him up for the career of a man of letters.
Yet, excellent as his portraits are — and some of them caught not the
features only, but the very spirit of the sitter — those who knew
him, and can remember the delicate shades and dramatic play of
character in the stories with which he was wont to brighten our
social intercourse, will hardly doubt that his real power lay rather
in word-painting than in material pigments. The patient industry
which he devoted to art would have made him a subtle dramatist —
a writer of such comedies as Scotland has never yet produced, or a
novelist to rival her very best. I am not sure, then, that in making
an excellent painter of him, we did not lose something greater still,
for which nature had specially endowed him.

There was a Glasgow artist, at this time, who bore the honourable
name of John Knox, to w^iich, however, he has not added any fresh
lustre, for he will probably be known hereafter chiefly as the
teacher of Daniel Macnee and Horatio Macculloch. Yet there
must have been something in him to have trained two such men.
These two formed their life-long friendship in Knox’s studio ; and
many a trip, doubtless, the two lads had together to the lochs of
Argyle and Dumbarton, and many a Highland story they picked up,
and learned to interpret well the character both of its scenery and
its people. Afterwards Macnee came to Edinburgh, and studied
at the Academy there, along with Thomas Duncan, Scott Lauder,
and David Scott, who all became his warm friends. For there was

26

no mean jealousy in his nature, but he gladly recognised the genius
of his compeers, even when their views of art differed wholly from
his own. In the end, having been admitted an Academician with-
out passing through the humbler grade of Associate, he settled in
Glasgow, till he was elected to the Presidency of the Eoyal Scottish
Academy, on the death of Sir George Harvey in 1876.

It was in Glasgow, then, that his life-work was really done, and

probably the necessities of “ pot-boiling ” dictated the path it

*

was to follow. How and then, for a season, indeed, he sent for
exhibition some simple rural study— “ A Peat Sledge,” or “ A Burn-
side,” or. “ A Pretty Picture of Children ” — which had a touch of
pure poetic fancy. Put these were short flights into a region which
he could not afford to cultivate ; and ere long he settled down to
the steady business of portrait painting. Pembrandt and Eeynolds,
Vandyke and Eaeburn, have shown that this may he a very noble
branch of art ; and Macnee’s portraits of the late Dr. Wardlaw
and Mr. Dalgleish prove that he had no mean idea of the work of
his profession. But if painting was the right vehicle for his genius
to express itself in, we should have expected to find him rather
following in the wake of Wilkie than of Eaeburn, and showing on
his canvass that dramatic power, and insight into Scottish character,
and rarely delicate humour, which were the richest gifts, and most
real qualities of his mind. Nothing of this, however, can be found
in all his work. Even in painting portraits, though among so
many he must have come across some faces which had Scotch
character and humour like his own, yet I am not aware of any of
his pictures which suggest what a wealth of laughter lay in the
man. It would almost seem as if his art was not his natural utter-
ance, but a mere skill of hand, and that this successful painter,
after all, had not “ found his mission,” and has left no real record
of his brilliant genius, except in the short-lived memory of his
friends. For assuredly, however excellent his likenesses are, and
however ably some of them are painted, they give no adequate
conception of that singularly- rich and fertile and dramatic portrayer
of national character, who could so nicely hit off not local dialect
only, but local habits of thought, with strokes of finer insight that
pierced far into the deepest heart of man. Of all this, however,
nothing now remains. Ho other tongue could reproduce those tales5

27

which, had no plot to speak of, which were at times even a mere
thread of extravagance, hut in which the characters were so felici-
tously sketched with touches of such kindly humour, that they
themselves could only have joined heartily in the mirth which they
evoked. For this was a marked feature of his genius ; there was
not a drop of gall in it. If he saw all the oddities of a Glasgow
bailie, an Airdrie miner, a Paisley shopkeeper, a Highland gillie or

drover, or minister, “ he handled them as if he loved them,” and,

*

indeed, he did like them all the better for the flavour of individual
character they had.

I would not be understood as anywise undervaluing his artistic
powers, which were of no mean order, but they certainly would
have attained a still higher rank had his canvas been covered with
many figures representing the men who lived so vividly in his
stories, and reflecting the dramatic lights in which he could have
placed them. Most likely this was at first prevented by the res
angusta domi, and when easy times came his role was already
determined for him. So he went on painting portraits — many
of them ; and making warm friends — many of them, too. Art
naturally drew to him Macculloch, Sam Bough, Brodie, and
others ; and his rare social qualities as naturally associated him
with Outram, Glassford Bell, and Herman MacLeod. Brighter
evenings there were not in all Scotland than those which
brought together the authors of the Annuity and Billy Buttons
and Daniel Macnee — and the brightest of them all was Macnee.
He was the last of them, too, and perhaps this fact, that he had
been left alone by these, his dearest friends, made him more willing
at last to leave Glasgow, and take up the burden of the Presidency,
even when his own health began to be uncertain.

How he discharged those duties, and commended himself to all
bis brother artists by hearty kindness and frank recognition of their
several powers — how he also interested himself in the meetings and
business of our Boyal Society — how he soon became as valued a mem-
ber of general society in Edinburgh as he had been in Glasgow ;
— -all this is known to you all, and all the more is our sorrow that
bis stay among us was so brief.

28

David Anderson of Moredun. By A. Campbell Swinton

of Kimmerghame.

Mr. David Anderson of Moredun, who died in Edinburgh in his
ninetieth year, was the eldest son of Mr. Samuel Anderson of
Moredun, banker in this city, the head of a family many members
of which have been well known and highly respected. Mr.
Anderson was long a leading partner in the banking house of
Sir William Forbes & Company, and when that firm was, in 1838,
merged in the establishment now known as the Union Bank of
Scotland, he continued for many years an active director of the
new body. There was no citizen of Edinburgh, whose generous
aid was more readily given, to every object which commended itself
to his approval as likely to benefit his countrymen of any class or
condition ; and consequently there is no one whose loss will be
more seriously felt, when any measure of public utility is in con-
templation. He was elected a Fellow of the Society in 1849, but
never took an active part in its proceedings. He was, however, a
man of cultivated taste and varied information, whose warm heart
and genial disposition made him a universal favourite among a large
circle of friends. And as one of the Trustees of Fettes College,
he showed his interest in the higher education of the country by
endowing two scholarships of the annual value of <£100 each, with
a view of enabling distinguished pupils of that school to prosecute
their studies at one or other of the English universities.

John M‘Culloch. By Francis Brown Douglas.

Mr. John M‘Culloch was a native of Galloway, born in 1807.

He died at Edinburgh 13th July 1882, in the 76th year of his age.

After attending classes at the Glasgow University he came to this
*

city, when he entered the British Linen Company Bank, and
remained in connection with it for a period of fifty-five years, much
esteemed for his probity and business habits. Many a journey he
undertook to bring gold from London for the bank’s purposes, and
to take it back when no longer required.

He had a kindly feeling for the poor and helpless, and was

29

induced, shortly after coming to Edinburgh, to become a visitor of
the Society for Belief of the Destitute Sick. He was appointed
its treasurer, an office he filled for nearly forty years, ever seeking
to promote the usefulness of that institution in his own way, and
to increase its funds. He also latterly took an active part in the
management of St. Cuthbert’s Parochial Board, being the more
interested in this from his connection with the West Kirk session,
of which he was an elder for no less than fifty-five years.

Mr. M‘Culloch was admitted a Fellow of the Eoyal Society on
2nd January 1866, and was a very regular attender at its meetings
- — generally, indeed, present unless prevented by illness. In his
later years he was subject to sharp attacks of cold and rheumatism,
which much impaired his strength and health, and from one of
which, with other complications, arose his last illness and death.

Samuel Baleigh, C.A. By David Maclagan, F.R.S.E.

Mr. Samuel Ealeigh was a native of Galloway, having been
born on a farm near Castle Douglas held by his father. His early
education he obtained in the parish school and high school there ;
where his brother, afterwards a distinguished Nonconformist divine
in London, was being trained at the same time. After a brief
apprenticeship to a local solicitor, Samuel Ealeigh resolved to go to
Edinburgh, and seek there some opening which might afford him an
opportunity of securing a position of usefulness and success.

He entered the University as a student at the Law Classes, and
at once made his mark by carrying off Professor Macvey Napier’s
first Conveyancing Prize.

There, as always, he was a man of unwearied industry, and used
to say that his object in reading systematically the English Classics
was to acquire a good style of composition. Those who remember
his power of expression in writing, either on business or more
general subjects, will recognise how successfully he achieved his
purpose.

Very soon he became partner of Mr. William Campbell of Queens-
hill, Writer to the Signet, like himself a Galloway man.

It was very well known to Mr. Ealeigh’s friends that his tastes

30

lay in the direction of figures and finance more than of law alone,
and that he possessed a singular proficiency in dealing with them.
The offer therefore of a partnership with Mr. Archibald Borthwick
— one of the ablest accountants in Edinburgh — was readily accepted
by him ; and the partnership so constituted, of two men of great
powers, and in very many of their special qualities the complement
of each other, became one of the outstanding firms of Edinburgh,
recognised as such by all professions. The arrangement, however,
only lasted until 1857, when the crash of the Western Bank failure
led all interested in that calamity to cast about for suitable men to
extricate matters, and Baleigh was selected along with other three,
who are now each at the head of leading Scottish banks.

The changes in his professional life, which are not always a
favourable experience, proved remarkably so with him. He got an
insight in business of quite unwonted range and variety ; and he
was just the man to extract and utilise the best elements out of
such a career.

It was not therefore surprising that when in 1859 the office of
Manager of the Scottish Widows’ Fund Life Assurance Society
became vacant, the Directors sought to secure his services. The
offer somewhat perplexed him. His professional prospects were so
good that he felt it was a doubtful step to enter upon this new
life, and he asked and obtained time to consider the proposal. After
consultation with friends on whose judgment he relied, he closed
with the offer, and became Manager of a Society which, even at
that time, stood in the very highest rank among Scottish offices,
and which, under his management, was to acquire the position of
unapproached pre-eminence which it holds in Great Britain. It was
not only, however, the large increase of its business which gave
such universal public confidence, but the knowledge of his skill in
manipulating and investing large sums of money, and in devising
and working out the best ways of distributing the very large profits
which accumulated during each septennial period.

Although never taking a public part in political or ecclesiastical
affairs, for which, he had little leisure and no taste, he took a deep
interest in all such matters — held very decided views regarding
them — and was often consulted, and always ready with his counsel.

In the year 1880 the labours and responsibilities of his business

31

life began to tell upon him, and he resigned his appointment. Ilis
retirement was of short duration; and he died 26th July 1882.

Professor James Spence. By Professor Chiene,

M.D, F.K.C.S.E.

James Spence was born in Edinburgh on the 31st day of March
1812. His father sent him, in the first instance, to a boarding-
school at Galashiels, and afterwards to the Edinburgh High School.
He entered the University at the age of 13, attended the medical
classes in the University and Extra-mural School, and obtained the
diploma of the Eoyal College of Surgeons in 1832. His first ambi-
tion was to enter the army or navy, and for this purpose he studied
in Paris, and passed the examination for a surgeon in the navy.
After two voyages to India in troopships, he apparently abandoned
the idea of public service, and settled in Edinburgh. It may with
truth be said that he then (1835) commenced that career as a
teacher and surgeon which paved the way for his appointment as
Professor of Surgery in 1861. He first, for seven years, acted as
Demonstrator of Anatomy to Professor Monro ( tertius ). He then
taught Anatomy in the Extra-mural School until 1819, when, having
obtained the Fellowship of the Eoyal College of Surgeons, he
became a Lecturer on Surgery. He held this appointment until his
election as Professor of Surgery in 1861. In 1865 he was made
Surgeon in Ordinary to the Queen for Scotland. In 1866 he became
a Fellow of the Eoyal Society of Edinburgh.

For nearly half a century James Spence was intimately associated
with the teaching of Anatomy and Surgery in this city. From the
very first he adopted a course of self-education, and under many
difficulties he gradually but surely made his way to the front; and
at the time of his death (June 1882) he had attained a position in
which he was esteemed by all as the representative of Scottish
Surgery. He possessed most marked manipulative skill, and was.
a very successful practitioner.

He has left, as a result of his long practical experience, a most
valuable work on the Practice of Surgery. To tracheotomy, hernio-
tomy, the ligature of vessels, urinary diseases, and methods of

32

amputation, he paid special attention, and has done much to advance
our knowledge.

James Spence is an example of a man who slowly rose to eminence
by earnest, honest work. He will he remembered as a teacher who
had always something worth telling on every practical question, and
who told it in a way easily remembered. His systematic lectures
were essentially clinical.

Much loved by those who knew him best, his memory will long
remain in the Edinburgh school as. a faithful teacher, a good
operator, and a kind friend.

Frederick Hallard. By Thomas M‘Kie, Advocate.

Frederick Hallard, Advocate, senior Sheriff-Substitute of Mid-
Lothian, died in this city on 12th January 1882, aged sixty-one.
His father was a soldier in the French army, who, after the Bevolu-
tion of 1793, emigrated to this country, and, along with other
Boyalist refugees, took up his abode in Edinburgh as a teacher of
his native language. Here he married, lived, and died. His son
Frederick was born in this city in May 1821. At the age of four,
he was taken to Avranches, his paternal home in Normandy; and
there, and at Paris, he received a sound, and liberal education. At
sixteen he returned to Edinburgh. The strong affection he always
had for the city of his birth arose not more from admiration of its
material beauty, than out of regard for its intellectual renown, and
the friendly intercourse which existed between it and France in the
olden time. Being destined for the Scotch bar, young Hallard attended
the usual classes at the University of Edinburgh, and proved himself
a diligent and distinguished student. He was admitted to the bar
in 1844, joined the Speculative Society, and after acting for some
years as a reporter on the Jurist , he was, in 1855, appointed by the
late Sheriff Gordon junior Sheriff-Substitute for Mid-Lothian.
From that time until his death, he discharged the duties of his
office with a manly independence of spirit and judicial integrity of
purpose, rarely equalled. The year before his judicial appointment,
he married Mary Carr Bobertson, a daughter of the late Mr. James
Bobertson of this city. The marriage was one of affection, and for

33

many years was a source of uninterrupted happiness. But' of the
nine children horn of the marriage, death carried off three in as
many months ; shortly afterwards, the grave was again opened to
receive his beloved wife, and in 1873 he had yet again to follow to
the tomb his eldest son, Frederick, a youth of great brightness and
promise. Against this overwhelming affliction Mr. Hallard bore up
outwardly with manly fortitude ; but those who knew him best
knew too well how the sad ruin of his once happy home haunted
his memory, and bowed to the earth a spirit shrinkingly sensitive
and keenly affectionate. It was then that he truly felt the consola-
tions of philosophy ; for he had loved letters from his early youth
with a devotion which grew with his growth, strengthened with his
manhood, and continued with him to the end. His literary tastes
had adorned and brightened his life in the times of prosperity, and
when the sorrowful days came, these tastes weaned him from him-
self, and gave him comfort, if not consolation. One charm of his
society was, that along with a love for all things lovely and of good
report, he united in a singular manner, in his own person, two
separate nationalities. For his intimate acquaintance with French
literature, history, politics, and jurisprudence was happily com-
bined with a wide knowledge of, and a lively interest in, everything
pertaining to the literature and jurisprudence of our own country.
To his other accomplishments he added a keen relish for classical
studies, and particularly Greek.

Besides doing his judicial duties, Mr. Hallard for many years,
and until his death, acted as a Director of the Philosophical Institu-
tion, and took an active part in the management of its affairs. The
useful work he did there cannot be better summarised than in the
words of its Yice-President, Dr. William Smith, who at a meeting of
the Directors of that Institution thus spoke of Mr. Hallard : — “ We
can call to mind how much his fine tastes, his varied culture, and
his active helpfulness, his ready aid, always willing and gracefully
rendered, have contributed to our success. Associated with him as
I have been for nearly thirty years, no one knows better than I do
how much we have been indebted to him in these respects; and I
had looked forward to the time when you might permit me to retire
from this chair, which by your favour and indulgence I have occupied
so long, and called on him to fill it with new and fresh efficiency.”

c

34

Mr. Hallard became a Fellow of the Royal Society on twenty-first
January 1867. He was proud of its diploma, pretty constant
in liis attendance at its meetings, but never read a paper, nor took
part in the debates. This was partly owing to an inherent modesty
of nature, and partly because his knowledge and the bent of his
mind were much more literary and philosophical than scientific.
He published several able pamphlets on legal topics, one of them
being entitled “ The Inferior Judge,” and he took a prominent in-
terest in all questions affecting a reform of the law. Apart from

*

these he did not write much ; yet what he did write showed such
vivacity, grace, and culture, that, like the aroma of good wine, it
served but to whet the appetite and to make one wish he had
written more. But that was not to be ; and so he has passed away
from among us, still to be held in fond remembrance by a wide circle
of friends.

Du. J ohn Muir. By Professor Eggeling.

Dr. John Muir, who died on the 7th of March last, was born at
Glasgow on the 5th February 1810, being the eldest son of Mr.
William Muir, at one time a magistrate of that city. After receiving
his early education at the grammar school of Irvine and the
University of Glasgow, he passed to Haileybury College, then the
training institution for the civil servants of the East India Com-
pany. In 1828 he proceeded to India, and, having passed with
distinction through the College of Fort William, and served for
some years as assistant secretary to the Board of Revenue at Alla-
habad, and afterwards as a commissioner for investigating claims
to hold land rent free in the Meerut Division, he was appointed
magistrate and collector at Azimgurh. During his occupancy of
these posts (a period of some fifteen years) he always devoted a
large portion of his leisure to the study of Sanscrit literature ; and
so well did he succeed in mastering the language, that he himself
composed several treatises in Sanskrit metre and prose, vizi? a
description of England, a sketch of the history of India, and two
treatises setting forth the essentials of the Christian doctrines and
ethics ; and delivered to the students of Sanskrit at Benares lectures
in that language on mental philosophy, and kindred subjects (1843).

35

In 1844 the combination of the hitherto separate Sanskrit and
English colleges at Benares was resolved upon, and John Muir was
appointed first principal of the institution. In an address delivered
by the Hon. James Thomason, Lieut. -Governor of the H.W.P., at
the opening of the Benares Hew College, on 11th January 1853,
credit is given to Mr. Muir for having succeeded “ in introducing
into the college a stricter discipline and a better system of educa-
tion.” This post John Muir held for one year, when he was suc-
ceeded by Dr. Ballantyne, he himself reverting to the judicial
branch of the service, as civil and session judge at Euttehpore.
Erom his parting address to the students of the Benares College, on
the 10th Eebruary 1843, I extract the following passages as charac-
teristic of the man : — “ How, I am anxious that your reasonable
ambition should be satisfied • I desire to see you all rise to wealth
and honour ; but I am more solicitous that high principles should
now be implanted in your minds, which in after life may bear the
precious fruits of integrity, wisdom, and piety. I wish that you
should be devoted to study, not so much for the outward advantages
it brings, as because you love that truth to which it ought to lead ;
because you appreciate the most valuable results of education, I
mean intelligence, enlargement of mind, the cultivation of your
judgment and other faculties ; acquaintance with the wonderful
works of God, and the laws by which He rules the universe * — above
all, because you find that sound instruction is auxiliary to moral
improvement. These are the motives which best deserve to be
urged at length to stimulate you to the earnest pursuit of know-
ledge.” After a brief outline of some of the chief departments of
Sanskrit literature, he continues : — “ There is, however, one subject
which, more than any other, demands your earnest attention, both
during the course of your education and after its close ; I mean
your moral improvement. If the instruction you have received in
the college have not inspired you with the love of goodness, of truth,
integrity, justice, purity, and piety, as well as with a desire to prac-
tise all these virtues which in theory you admire, it will have
effected but little. Mere intellectual, unattended by moral improve-
ment, may render you only more accomplished in wickedness. True
wisdom cannot exist apart from goodness. However strengthened
by discipline your powers may be, they will always be directed to

36

tlie attainment of ignoble or comparatively insignificant objects,
if they are not guided and hallowed by virtuous principle. True
self respect, real happiness, the blessing of God, and your everlast-
ing welfare, all depend on you strictly regulating your lives accord-
ing to the dictates of conscience and the Divine will.”

In 1854, having completed his term of service, John Muir
returned to England, and, after a brief residence in London, he
settled permanently in Edinburgh. During his last few years in
India his earlier literary attempts at religious subjects were followed
up by a Life of the Apostle Paul , and an Examination of Religion,
both of them in Sanscrit verse, with English (the former treatise
also with Bengali and Hindi) translations. The deep interest which
he always took, not only in the moral improvement of the Hindus,
but in religious and theological matters generally, led him, in later
years, to offer to the University of Cambridge a prize of £500 for
the best exposition of the errors of Indian philosophy, and the
principles of Christianity in a form suitable for learned Hindus ;
and to the University of Glasgow a prize of £100 for proficiency in
Hebrew scholarship, open to all Scottish graduates in arts of not
more than six years’ standing. It also prompted him, some years
since, to endow, for a period of five years, a lectureship on the
Comparative Science of Eeligion in the University of Edinburgh.
Moreover, it induced him to take up the systematic study of the
religious literature of India, and the writings of modern European
theologians. The results of many years of unwearied research were
laid down in a number of papers, mostly contributed to the Journal
of the Royal Asiatic Society , and ultimately collected in four
volumes of Original Sanskrit Texts on the Origin and History
of the People of India , their Religion and Institutions. This
work, of which a revised and greatly enlarged edition, in five
volumes, was published in 1868-70, forms by far the most com-
plete and trustworthy digest of authentic texts bearing on the
growth of the Brahmanical doctrines and institutions. The amount
of patient, methodical research with which the various religious
conceptions of the ancient Hindus are traced by him from their
first germs through the various phases of development; and the
impartial spirit with which he reproduces and examines the often
conflicting views of European scholars on single points of Hindu

37

tradition, are beyond all praise. His English translation of the
frequently obscure texts, as a German scholar has justly said,
i( betrays throughout a master’s hand.” To insure accuracy in his
interpretation of difficult passages, Muir would save himself no
trouble, but would write letters upon letters to Sanskrit scholars
who he thought might be able to clear up his difficulties. I
have sometimes heard it remarked that, in dealing with important
questions, Muir too often contents himself with stating the conflict-
ing views of others, without giving any decided opinion of his own
one way or the other, when he was at least as competent as any
other scholar to pronounce on these points. To a certain extent
this is no doubt true ; but it is only what might be expected from
so cautious and conscientious an inquirer, whose sole aim was to get
at the truth ; and who, while ever anxious to allow every one a fair
hearing, shrank instinctively from committing himself to a definite
alternative where the available data appeared to him insufficient for
forming a conviction. His mind, indeed, was singularly open to
argument ; it was as free fiom preconceived ideas as it was disin-
clined to hasty conclusions. As in his literary inquiries regarding
the bygone ages of Indian belief, so in his own religious views,
which, it would seem, were somewhat modified, in his latter years,
by a close study of modern theological writings. Liberty of research
and teaching, in whatsoever department of human science, was to
him an article of faith, which neither his natural reserve, nor out-
side considerations of any kind, could keep him from vindicating. The
powerful impetus imparted to the study of the Vedic texts, some
thirty years ago, gave rise to an animated discussion as to the degree
of authority to be assigned to the traditionary interpretation of the
sacred lyrics, as handed down in the native commentaries. Into
this literary warfare Muir threw himself with the full weight of his
scholarship, in a manner showing how well he knew to fight for the
principle of free research, so dear to him. A distinguished Sanskrit
scholar had given his opinion to the effect that “ in the pre-
sent stage of- Yaidik studies in Europe, it seemed to him the
safer course to follow native tradition rather than to accept too
readily the arbitrary conjectures which Continental scholars so often
hazard.” This remark drew forth, after a few weeks, Muir’s excel-
lent paper “On the Interpretation of the Veda ” (Jour, of the Roy.

38

Asiatic Soc., 1866). Writing with more warmth than he usually
displayed in his writings, he therein proved conclusively that it is
a mistake to speak of an unbroken chain of Hindu tradition, the
meaning of the Yeda having already become largely obscure by the
time a school' of exegesis arose ; and that, therefore, the scholars
alluded to (viz., Roth and his school) were quite justified in emails
cipating themselves from the trammels of native tradition, and
calling into requisition all the other available resources of philo-
logy, thereby laying the foundation of a true interpretation of the
Yeda.

After the completion of the second edition of the Original San-
skrit Texts , Dr. Muir was by no means satisfied to rest on his
laurels. He continued his studies as assiduously as ever, though
perhaps with a less definite object in view; printing from time to
time, for private distribution, small collections of metrical transla-
tions of characteristic passages he met with in his reading, generally
of a moral or religious tendency. These were ultimately published, in
a collected form, in a volume of Trubner’s Oriental series, with parallel
passages from the Bible and classical authors. In his interesting in-
troduction, he discusses the difficult question as to whether an ac-
quaintance with the Christian Scriptures may have exercised some
influence on the religious ideas of the Hindus in the earlier cen-
turies of our era ; an influence which has been asserted to be
traceable more especially in the Bhagavad-glta, the famous philoso-
phical episode of the Mahabharata. Although Muir does not arrive
at any definite conclusion on this point, he seems, on the whole, to
incline to the assumption of an independent origin of the work in
question. The particular object he had in view in making this
collection may best be stated in his own words : — “ But however the
question of the obligations of the Bhagavad-glta, or of some other
parts of the Mahabharata, to Christianity may be decided, the
decision can scarcely affect the determination of the farther and very
different question of the originality or otherwise, as far as any
foreign influences are concerned, of the great bulk of the moral and
religious sentiments embraced in my collection. These sentiments
and observations are the natural expression of the feelings and
experiences of universal humanity ; and the higher and nobler por-
tion of them cannot be regarded as peculiar to Christianity. The

39

correctness of this view is placed beyond a doubt by the parallels
which I have adduced from classical writers. It is my impression,
however, that the sentiments of humanity, mercy, forgiveness, and
unselfishness are more natural to the Indian than to the Greek and
Roman authors, unless, perhaps, in the case of those of the latter
who were in fluen'ced by philosophical speculation. This tenderness
of Indian sentiment may possibly have been in part derived from
Buddhism, which, however, itself was of purely Indian growth.”
The publication of this volume seems to have left a void in his mind
which, deepened by the loss of his good and gentle sister, who had
been for many years the faithful companion of his solitary life, had
at times a depressing influence on his spirits. Still, however, he
pursued his course of reading, and only a few months before his
death he issued to his friends another small collection of metrical
translations from the Mahabharata, including the highly poetical
episode of Savitrl.

While the literary researches of John Muir have gained for him
a place in the’ foremost rank of Sanskritists, and have thus contri-
buted in a remarkable degree to the credit of Scottish scholarship
in an important branch of Oriental studies — as those of his dis-
tinguished brother, Sir William Muir, have done in another branch
—John Muir deserves to be not less gratefully remembered by his
countrymen for the eminent services he has rendered to the cause of
education in Scotland. The want of a recognised medium of instruc-
tion on his favourite subjects of study in any of the Scottish uni-
versities induced him, in 1862, to offer to the Senatus of the
Edinburgh University the sum of <£4000 for the foundation of a
chair of Sanskrit and Comparative Philology; on the condition
that the interest of this capital should be supplemented by an
annual grant from Government of the same amount. In 1876 this
munificent gift was increased by a further sum yielding an addition
to the emoluments of the chair of £50 a year. In one respect Dr.
Muir’s expectations in founding the chair were disappointed. It
appears that, in drawing up the deed of endowment, he had intended
to provide, beside the systematic courses of instruction, for annual
courses of lectures of a more popular kind to be open to any non-
matriculated persons that might wish to attend them. Unfortu-
nately, however, the terms of the deed were not sufficiently definite

40

to exclude an interpretation more in harmony with the existing
arrangements of university teaching ; and, though the question was
long and carefully considered by the Senatus — I myself deeming it
my duty to support Dr. Muir’s interpretation — they found it impos-
sible to consent to what might have proved a somewhat inconvenient
precedent. Nevertheless, Dr. Muir continued to the last to show
the warmest interest in the objects of the chair, by giving annual
prizes for distinguished attainment in the several classes. He also
offered a (still available) prize of <£100 to the first student that
should take the degree of Doctor of Science in the department of
Sanskrit and Comparative Philology. To his liberality the Uni-
versity Library owes a very considerable portion of its Oriental
and Philological books. The connection of his name with our
University, in this respect, has been further strengthened, since
his death, through the presentation, by Sir William Muir, of the
large collection of Oriental and Philological books left by his
brother. In accepting this splendid gift, the Library Committee
resolved that this collection, together with the books previously
presented by Dr. Muir, should be kept separate from the general
library, under the designation of the “ Muir Collection.” Dr. Muir
also took a prominent part in the founding, in 1868, of the Shaw
scholarship in mental philosophy (in honour of his uncle, Sir John
Shaw, at one time Lord Mayor of London, and a director of the
East India Company) ; and in originating and conducting the
Association for Promoting the Better Endowment of Edinburgh
University, having acted for ten years as honorary secretary of
that most useful society. Dr. Muir’s interest and liberality were not,
however, confined to the University of Edinburgh ; but the other
Scottish universities also, I believe, received from him numerous
donations of books ; and to the Berlin University he presented, a
few months before bis death, the sum of £50, to form the nucleus
for a scholarship in Sanskrit philology. In recognition of his ser-
vices to higher education, Dr. Muir was appointed a member of
the last Scottish Universities Commission. To the report of the
commissioners Dr. Muir, in accordance with his principles, added
a note urging the consideration of the advisability of the theological
chairs in the universities being thrown open to members of all the
churches.

41

John Muir’s eminence as a scholar obtained for him the honorary
degrees of D.C.L. from the Oxford University, of LL.D. from
the Edinburgh University, and of Doctor of Philosophy from the
University of Bonn ; as well as the title of a corresponding member
of the French Academy, the Royal Prussian Academy of Sciences,
and a foreign member of the Leyden Society for the Cultivation of
Dutch Literature. He joined the Royal Society of Edinburgh in
1861, and at their meeting on Eeb. 16, 1863, he read, by request
of the Council, a highly interesting paper “ On the Recent Progress
of Sanskrit Studies.” This and several other papers contributed by
him were published in the Society’s Transactions.

John Muir was loved by all who knew him for his extreme kind-
heartedness and truthfulness, his love of humanity, and the purity
of his life. His memory ought to be. dear to every Scotsman.

Dr. Charles Morehead. By James Sanderson, E.R.C.S.E.,
Deputy Inspector-General of Hospitals, Madras Army.

Dr. Charles Morehead, C.I.E., M.D. Edin., F.R.C.P. Lond.,
and Honorary Surgeon to Her Majesty, was born in Edinburgh
in 1807, and died suddenly at Wilton Castle, Redcar, Yorkshire,
on the 24th of August 1882, in the 75th year of his age. He was
the second son of the Rev. Robert Morehead, D.D., Dean of
Edinburgh, and afterwards rector of Easington, Yorkshire. His
mother was Margaret, daughter of the Rev. Charles Wilson, Pro-
fessor of Church History in the University of St. Andrews.

He was educated at the High School of Edinburgh, for which
through life he cherished a strong affection, and at the time of his
death was one of the very few remaining members of the Carson
Club. He entered the medical classes in the University of Edin-
burgh about 1825, where he distinguished himself as a student
more particularly in the science classes. In the early part of his
studies he manifested great ardour in the study of clinical medicine,
and soon attracted the attention of Professor Alison, whose clerk he
became at the end of his course.

Dr. Morehead graduated as M.D. in 1828, and thereafter prose-
cuted his medical studies for upwards of a year in Paris, under the

famous physician Louis, with whom he kept up an intimate corres-
pondence till his death.

At the age of 22, Dr. Morehead entered the Bombay Medical
Service, and was soon placed on the personal staff of Sir Robert
Grant, Governor of Bombay, and continued to serve in that capacity
till Sir Robert’s death in 1838. He was president of the Medical
and Physical Society of Bombay from 1837 to 1859, and during
that time contributed largely to the Transactions of the Society.
He acted also as secretary to the Board of H ative Education from its
establishment in 1840 to 1845. In connection with this last subject
he long ably advocated in various ways, and through various
channels, the opinion that the instruction and education of the
natives of India should be through the medium of the English
language; and at last, in 1845, had the satisfaction of seeing his
ideas carried into practical effect in the founding of the Grant
Medical College, one of the chief features of which was the
education of the natives by means of the English language. The
practice has now for long been universally adopted, with the best
results, both as regards the governors and governed of our Indian
Empire.

About this time, the large and well-equipped native hospital,
named after Sir Jamsetjee Jejeebhoy, was established at the joint
expense of the Government and Sir Jamsetjee, for practical instruc-
tion in clinical teaching. To Dr. Morehead belongs the merit of
introducing this branch of medical training, which at that time did
not form a regular part of the curriculum even in the medical
schools of the United Kingdom. It was but fitting that Dr.
Morehead was appointed first Principal and first Professor of Medi-
cine to the College, and first Physician to the Hospital.

A bust of Dr. Morehead has been placed in the hall of the
College as a memorial of its eminent Principal and Professor, by the
students and friends of the college.

During these years Dr. Morehead was patiently collecting in the
course of his practice as a physician, and from other available
sources, observations on the diseases of India, the results of which
lie published in his valuable work on Indian Diseases , a book
which still holds its place as a standard authority in the treatment
of the tropical diseases of Hindostan. His last service to the pro-

43

fession, before leaving India for England in 1859, was the
characteristic one of the formation of a society composed of the old
students of the Grant College, which has served not merely as a
bond of union, but been also productive of no inconsiderable practical
advantages to its members.

On his return from India he was offered the professorship of
medicine in Netley Hospital, then just founded, which, however, the
state of his health obliged him to decline.

In 1862, he retired from the service with the rank of Deputy
Inspector-General of Hospitals ; in 1857 he was appointed Honorary
Surgeon to the Queen, and in 1881 was made a Companion of the
Order of the Indian Empire.

Dr. Morehead will be long and best known by his important
researches into the diseases of India, based on a truly scientific
diagnosis, and so successfully set forth in his great work on the
subject ; and by the insight and strength of will by which he suc-
ceeded in making clinical medicine so prominent a feature of the
medical education of natives in Western India.

It only remains to add that in 1875 Dr. Morehead published the
• Memorials of the Life and Writings of his Father, the Eev. Dr.
Kobert Morehead. He was elected a Fellow of this Society on the
15th January 1860.

Friedrich Wohler. By Professor Dittmar. .

On the 23rd of September 1882, this great man closed his eyes to
cro to rest after a noble and glorious career in the service of chemical
science, extending over two generations. Some sixty years ago,
when the elementary nature of chlorine had just been established
and the isolation of cyanogen was still a novelty, young Wohler
already worked as an investigator, — the same Wohler who rejoiced
with us over the synthesis of indigo. Of the world of chemical
discoveries that lie between he magna pars fuit.

To desire to know something of the mould of external circum-
stances into which such a great life was cast is no vulgar curiosity.
The writer, accordingly, had no hesitation in availing himself of an
opportunity which presented itself some time ago for obtaining

44

authentic information from Mr. A. Wohler of Schonhof of Bocken-
heim, the great chemist’s only son. From Mr. Wohler’s letter we
extract the following biographical sketch : —

Friedrich Wohler was horn on the 31st July 1800, in Eschersheim,
a village near Frankfort-on- the-Main. He received his first instruct
tion from his father, a man well versed in economical and physical
science, as also in philosophy and pedagogics ; and, besides, attended
the village school in Rodelheim, where his father owned a small
landed estate. In 1812 the family removed to Frankfurt, where
he attended the gymnasium, and by the kindness of a scientific friend,
Dr. Buck, who, besides a thorough knowledge of the subjects, possessed
the necessary appliances, was introduced to the study of mineralogy,
more especially, hut also of chemistry and physics. [Conjointly
with this Dr. Buch, Wohler, as early as 1821, published an investi-
gation on “ Selenium in a Bohemian mineral,” — his debut as an
investigator.] After having completed his curriculum at the
gymnasium, Wohler went to the University of Marburg as a student
of medicine. In 1821 he left Marburg to continue his studies at
Heidelberg, where he took his degree as doctor of medicine but,
on the advice of Leopold Gmelin, decided upon devoting himself
henceforth to chemistry. He completed his chemical education at
Stockholm under Berzelius, in whose laboratory he worked for a
considerable time, and with whom, during his subsequent life, he
maintained the most friendly relations. While in Sweden he took
part in a scientific expedition through Norway, which made him
acquainted with the brothers Brogniart and Humphrey Davy.

After his return from Sweden, in 1825, he accepted a call to Berlin
as teacher of chemistry in the then newly-erected Gewerbschule, and
remained there until 1832, when family affairs caused him to take
up his abode in Cassel. In 1836 Wohler became Professor of
Chemistry in the Medical Faculty of the University of Gottingen,
which office, in his case, was combined with that of Insj>ector-General
of Pharmacy for Hanover. He held his chair to the day of his death
on the 23rd September 1882. After only three days illness he died,
deeply mourned by his widow, children, grand children, and great-
grand children, in the 83rd year of his life.

To pass now to what for us, as part of the republic of science, is
Wohler’s real biography.

45

The superabundance of experimental genius in the chemical camp
must account for the fact that the border-lands between chemistry
proper and the collateral sciences of physics, physiology, &c., have
been cultivated chiefly by men who called themselves chemists. It
is there that Bunsen, Graham, Kopp, Liebig, Begnault, gathered
part of their laurels. If it were possible to characterise Wohler by
one stroke of the pen, we should say that of such border-land work
he did very little — all his work lies in the very core of the science ;
but on this only relatively narrow field he simply ranks with Scheele,
no other name, except perhaps that of Berzelius, could fitly be
placed alongside of these two.

To begin with Wohler’s minor contributions, and at the same
time qualify what we have just said of him in a negative sense, let
us state that Wohler, while a student of medicine in Heidelberg,
published a thesis on the excretion of substances by the kidneys,
for which a prize was awarded to him by the Medical Faculty of that
University in 1823. Mauy years later he resumed this subject
conjointly with Frerichs; the memoir is in the Annalen dev Chemie
for 1848 (vol. lxv. p. 325). In this connection we may state that
we owe to Wohler the best method for the detection of arsenic and
other mineral poisons in complex organic mixtures. It is described
shortly in his Mineral Analyse in Beispielen. (The original memoir
is in the Annalen , for 1849, vol. lxix. p. 364.)

We have not been able to find out exactly what Wohler did
while in Berzelius’s laboratory, and presume that, as a sensible man,
he there mainly confined himself to learning the great master’s
methods. Nothing but a short notice on “Improvements in the
Preparation of Potassium,” dates from the Stockholm period. It
is significant, however, as forming the small beginning of. a brilliant
series of researches on the isolation of elementary substances and their
properties, a subject for which he evidently had a great love, as he
always comes back to it in the intervals of other work. In 1827 lie*
for the first time, succeeded in isolating aluminium, the metal of clay,
by means of a method which was soon found to be more generally ap-
plicable. Alumina, like many other metallic oxides, is not reducible
by electrolysis or by the action of charcoal at any temperature. But,
when heated with charcoal in chlorine gas, it passes into the state of a
volatile chloride. What Wohler found was that this chloride when

46

heated with potassium or sodium, readily gives up its chlorine and
assumes the elementary form. The aluminium which Wohler thus
obtained was a grey powder; but in 1845 he succeeded in producing
the metal in the shape of well-fused, fully metallic globules.
Wohler, on this second occasion, correctly ascertained all the pro-
perties which everybody now knows to be characteristic of this
metal, and it is as wfell to add that where Wohler’s aluminium
differed from what now occurs in Commerce under this name, it
differed to its own advantage. That Wohler should not have seen
the practical importance of his discovery, is what we refuse to
believe; if he never even suggested an attempt to manufacture the
metal industrially, this is the natural consequence of the circum-
stances in which he was placed. For these we now should feel
thankful ; if, instead of quiet little Gottingen, a place like Birming-
ham had been his abode, he would, perhaps, have been lost to
science for all the rest of his life.

The earlier aluminium research was followed, in 1828, by the
isolation of beryllium and yttrium. These earlier metal reductions
fall into the Berlin period. While in Cassel he worked out pro-
cesses for the manufacture of nickel free from arsenic, and this laid
the foundation for what is now a flourishing chemical industry in
Germany. The several methods for the analysis of nickel and
cobalt ores which he describes in his Mineral- Analyse are, wre pre-
sume, an incidental outcome of this work. This subject was one of
his favourite topics; as late as 1877 we see him coming back to it
in the publication of a short cut for the separation of nickel and
cobalt from arsenic and iron.

In 1849 metallic titanium arrested his attention. Since the
days of Wollaston those beautiful copper- like cubes which are
occasionally met with in blown-out blast furnaces, had been sup-
posed to be metallic titanium pure and simple. Wohler observed
that the reputed metal, when fused with caustic alkali, emitted
torrents of ammonia, and on further inquiry ascertained the crystals
to be a ternary compound, containing the elements of a nitride and
of a cyanide of the metal. In pursuance of this research Wohler
taught us how to prepare real titanium and really pure titanic acid.

In 1854 Deville’s energetic attempts to produce aluminium in-
dustrially, caused Wohler to turn his attention again to this early

47

and almost forgotten child of his genius. His first incentive, no
doubt, was the natural and just desire to claim his right as the real
discoverer of what Deville, in his ignorance of foreign scientific
work, quite honestly thought he had been the first to find
out. This priority dispute came to a very satisfactory issue.
Deville, after a little pardonable hesitation, bravely acknowledged
Wohlers priority, and the two henceforth were friends and worked
together.

The first fruit of this happy union was a memorable joint re-
search (published in 1856 and 1857), which led to their discovery
of an adamantine and of a graphitoidal — in addition to the long
known amorphous — modification of boron. This graphitoidal species
subsequently (in their own hands) proved a mistake ; but the
adamantine . modification lives to this day as a true analogue of
ordinary (carbon) diamond.

From boron to silicon is an easy transition, so we need not
wonder at finding Wohler, in 1857, engaged (conjointly with the
physicist Buff) in a research on new compounds of silicon. On
electrolysing a solution of common salt with silicon — containing
aluminium, as a positive electrode, they obtained a self-inflammable
gas which they recognised as hydrogen contaminated with the pre-
viously unknown hydride of silicon SiH4, which body Wohler
subsequently (with the co-operation of Martius) obtained in a state
of greater purity. Wohler and Buff also obtained, though in an
impure state, what were subsequently recognised by Friedel and
Ladenburg as silicon-chloroform and as silicon-formic anhydride.

Within the limits of this notice we could not reasonably attempt
anything like a complete account of Wohler’s numerous researches on
inorganic subjects ; but we must not omit to at least allude to his
researches on metallic or semi-metallic nitrides. What we know of
this as yet little understood class of bodies, with barely an exception,
came out of his laboratory, if it was not done by himself in the
strict sense of the word.

We also Can only refer to the numerous processes which Wohler i
in the course of his long laboratory practice, has worked out for the
preparation of pure chemicals, and for the execution of exact
analytical separations. Wohler had better things to do than to take
up analytical problems for their own sake ; but what he did in this

48

direction incidentally — with his left hand, so to say, while his right
was engaged in greater work — amounts to a great deal. With the
two exceptions of Heinrich Eose and Kohert Bunsen, no man has
done more than Wohler has for the perfection of analytical methods.
The analysis of meteorites was one of his favourite specialties, and
one of his results in regard to these must not be withheld from a
Scottish Society. We refer to his discovery of organic matter in a
meteorite which he examined in 1864.

If Wohler had done nothing more than what has been referred
to explicitly or implicitly in the above, his work, even for the fifty
years of unbroken health which Providence granted him for its
execution, wTould have to he admitted to he both mutta and mullum ;
hut far more important than even all that are his researches in
organic chemistry.

Wohler’s first organic research dates from 1821, when (as a
student in Heidelberg) he discovered persulphocyanic acid, a
compound of sulphur with the sulphocyanic acid which, the year
before, had been analysed by Berzelius. But fraught with greater
consequences was his discovery of cyanic acid in 1822. Organic
chemistry might be said to date from it in two senses. When, in
1828, Wohler prepared the amnionic salt of his acid, he was
astonished to find that the salt, although made by what appeared
to be a straight-forward double decomposition, did not exhibit the
character of an ammonia salt at all, but turned out to be identical
with urea, a substance which heretofore had been known only as
one of the organic components of urine. A momentous discovery
for that time I A wide and impassable gulf then, in the minds of
chemists, separated the mineral from the organic kingdom. In
organic bodies all appeared to be derivable from their elements by
a succession of acts of binary combination ; the full analysis of such
a body contained in itself the full instruction for its synthetical
production in the laboratory. Organic substances, on the other
hand, were supposed to be things of an entirely different order;
in them the few elements which they all consist of, were assumed
to be united with one another, each with each, in a mysterious
manner, which could be brought about only by the agency of vital
force. Vital force, it was now seen, had nothing to do with the
formation of urea at any rate. The gulf was bridged over, and a

49

great and new morning full of the highest promise dawned over
chemistry. If the promise was more than fulfilled, if organic
chemistry from a mere possibility developed into a reality, we owe
this chiefly to the great researches which were carried out conjointly
by Wohler and Liebig.

Two years after Wohler had discovered cyanic acid, Liebig and
Gay-Lussac inquired into the nature of that dangerously explosive
compound known as fulminate of mercury (which had been dis-
covered twenty-four years before by Howard), and proved it to be the
mercuric salt of an acid which, although clearly a thing of its own
kind, had precisely the same elementary composition as Wohler’s
cyanic acid, a result which, at that time, appeared hardly credible.
These doubts, however, were set to rest by a joint investigation on
the oxygenated acids of cyanogen, which Liebig and Wohler pub-
lished in 1830. In their research they proved, both analytically
and synthetically, that cyanic and cyanuric acid, although distinct
bodies, have the same elementary composition, and that the former,
when simply kept in a sealed-up tube, gradually passes ivholly into
a porcelain-like neutral solid, cy am elide, which is widely different
from either. By these discoveries, and by Wohler’s synthesis of
urea, the fact of isomerism was firmly established. Compared with
this great conquest their joint work on mellitic acid (1830), and on
sulphovinic acid (1831), appears small ; it sinks into insignificance
when viewed in the light of their immortal researches on bitter
almond oil and on uric acid.

In 1832 bitter-almond oil was supposed to be to bitter almonds
what a hundred and one other essential oils are to their vegetable
sources. Of its chemistry nothing was known except the fact that
it contains loosely combined prussic acid, and that, when kept for a
long time, it is liable to deposit a crystalline solid, as various other
essential oils do. Liebig and Wohler, being struck by the absence
from even powdered bitter almonds of the intense smell charac-
teristic of the oil, set about tracing the latter to its origin, and soon
solved the question. In 1830 Robiquet and Boutron-Charlard had
succeeded in extracting from bitter almonds a crystalline nitrogenous
solid, soluble without decomposition in alcohol and in water, which
they called amygdaline. What Liebig and Wohler found, was that
when bitter-almond meal is mashed up with water, this amygdaline,

d

50

by the action of the water and a ferment (common to both sweet
and hitter almonds), breaks up into sugar, prussic acid, and hitter-
almond oil. They also succeeded in separating the prussic acid
from the distilled oil, and found the thus purified oil to he a non-
poisonous liquid of the composition C71I60. This liquid, when
exposed to the air, readily takes up oxygen and assumes the form
of a solid which is identical, at the same time, with the quasi-
stearoptene of the oil and with Scheele’s benzoic acid C7H602.
When treated with chlorine the purified oil yields a chloride
C7H5Q . Cl; the chlorine of which, by treatment with the respective
potassium compounds, is displaced by its equivalent in bromine,
iodine, sulphur, cyanogen, and, on treatment with ammonia, by the
group 1STH2. Water converts it into hydrochloric and benzoic
acids. In all these reactions the group C7H50 holds together, it
moves forwards and backwards as if it were a compound element.
A common-place enough fact in the eyes of the chemical student of
1882, but a most wonderful revelation to the chemist of 1832.
Berzelius, who certainly was not much given to dealing in super-
latives, greeted the discovery in his Jahresbericht as opening up a
new era in organic chemistry, and, rejecting the prosaic name of
benzoyl which Wohler and Liebig had given to their radical, pro-
posed to name it proine or orthrine, from 77-pa/t the beginning of
the day, or orthrine, from opOpos the dawn of the morning.

It is part of the glory of the two men that, in regard to none of
their joint researches, the outer world ever had any hint given to it as
to what was the one’s and what was the other’s share in the work
although they rarely worked together in the same laboratory,
Wohler would work away in Gottingen and Liebig in Giessen;
they only compared notes and slumped the whole into one memoir.

Going by what we know of the genius of the two great men, we
should say that in the benzoyl research Liebig’s hand is more
distinctly visible, while the one on uric acid (published 1837)
impresses one as having more of the Wohler element in it.
Uric acid was discovered by Scheele in 1776. It is a constant
component of urine, but more readily prepared from the excre-
ment of birds and serpents. Its general properties and its rela-
tions to bases are all that was known of it when Liebig and
Wohler took it in hand. Apart from an isolated observation of

51

Brugnatelli’s, who as early as 1817 obtained from it, by oxidation,
a crystalline product, which he called “ erythric acid,” Wohler
and Liebig, by, in a sense following in Brugnatelli’s footsteps, but
looking with sharper chemical eyes, discovered, instead of one, a whole
host of derivatives, the disentanglement of which, even to them, must
have been a tough problem. But they did not rest before each and
every one of the bodies had given a clear account of itself.
Liebig, somewhere in his Chemical Letters, spricht ein grosses
wort gelassen aus, “ of any scientific investigation worthy of the
name, the main results can be summed up in a few words.” It
holds for his and Wohler’s case. Uric acid when oxidised behaves
as if it were potential urea plus potential mesoxalic acid C303. (OII)2.
Part of the urea comes out as such ; the rest unites with the
mesoxalic acid into a “ureide” with elimination of water, formed
from the two (HO)’s of the acid and two of the hydrogens in one
molecule of the urea. This is alloxan (Brugnatelli’s erythric
acid in a pure state). But alloxan itself, when further oxydised,
loses part of its carbon as carbonic acid and becomes para-
banic acid , the ureide of oxalic acid C202(0H)2. Either ureide,
when treated with caustic alkali, takes up first one and then a second
molecule of water to form, in the first instance, alloxanic and
oxaluric (hydro-parabanic) acid, in the second, urea plus mesoxalic
and oxalic acid respectively. Either ureide, when subjected to re-
ducing agents, takes up one atom of hydrogen per molecule and is
reduced, the one to alloxantine, the other to oxalantine. A more
limited oxidation of uric acid leads to the formation of allantoine
which, before Liebig and Wohler, had been known only as a com-
ponent of the allantois-liquid of the cow. These few notes do not pre-
tend to do justice to the great research; but they will suffice to give to
the general reader a notion of its importance. Liebig and Wohler’s
work — apart from a few isolated though not inglorious attempts —
was not continued until Baeyer took it up and rounded it off.
Baeyer has enabled us to see clearly certain relations which had
before been obscure ; but it is worthy of notice that, while over-
hauling the whole of Liebig and Wohler’s work, he found nothing
to rectify ; it all proved solid masonry on which he was able to
build without resetting a single stone.

After their uric acid research the ways of Wohler and Liebig

52

diverged. The latter continued to prosecute organic research ;
the former turned his attention more to inorganic subjects, not
exclusively though, as the well-known research on narcotine
(which was carried out in his laboratory, part by himself, part by
Blytli, and published in 1848) is alone sufficient to prove.

As a teacher Wohler ranks with Liebig and Berzelius. In a sense
he was the greatest of the three. Berzelius, we believe, never had
the facilities afforded to him for teaching large numbers of students
in his laboratory ; and as to Liebig, even he lacked the many-
sidedness which formed so characteristic a feature in the Gottingen
laboratory as long as it really was under Wohler’s personal direction.
One student might wish to work on organic chemistry, another on
minerals, a third on metallurgy, a fourth on rare elements ; let them
all go to Wohler and they all, like the fifth or sixth, would find
themselves in the right place.

That Wohler in these circumstances should have been able to do
much of literary work would appear incredible if we did not know
it to be so. His Grundriss der Gliemie , which he published anony-
mously at first, has passed through many editions and been trans-
lated into various foreign languages ; never, we are sorry to say, into
English. A more valuable teaching book still, and more unique in
its character, is his excellent Practische Uebungen in der cliemischen
A nalyse (entitled in the second edition Mineral- Analyse in Beisjpielen ),
which has been translated twice into English, once in this
country by Hofmann, and a second time (from the second
German edition) in America. To a man like him the compilation
of either book probably gave little trouble ; what must have taken
up a very large portion of his valuable time, are his translations of
Berzelius’s Lehrbuch der Chemie , and of all the many successive
volumes of Berzelius’s Jahresbericht , which works only thus became
really available to the scientific world at large. We must not omit
to state in this connection that since 1838 Wohler has been one of
the editors of Liebig’s Annalen.

Wohler’s last publication dates from 1880. It treats of a new
kind of galvanic element in which the one metal aluminium serves
for either pole. We mention this as showing that he continued
working to almost the edge of his grave.

53

Sir John Eose Cormack. By Professor Maclagan.

John Eose Cormack was bom on 1st March 1815, on the classic
banks of Gala Water, in the Manse of Stow, of which parish his
father, the Rev. John Cormack, D.D., was minister. His mother
belonged to the old northern clan of Rose, her brother, Sir John
Eose of Holm, being a distinguished Indian officer.

Cormack’s primary education, like that of so many Scotchmen
who have risen to distinction, was got in the parish school ; his
secondary education at the High School of Edinburgh ; and his
professional education at the University of Edinburgh, in which he
became a student of medicine. During his whole University
career he was a hard-working student, and took the degree of M.D.
on 1st August 1837, on which occasion he got a University gold
medal for his thesis on the subject of Death from the Entry of Air
into the Veins. On this subject subsequently, both in a surgical,
obstetrical, and medico-legal aspect, he made some further observa-
tions in the years 1838 and 1850, and he again made it the subject
of a thesis when he took the degree of M.D. of Paris in 1870.

This was not, however, his first attempt at authorship, for he had
the year before his graduation gained the prize of the Harveian
Society of Edinburgh for an essay on Creasote, which he subse-
quently published as a thin octavo. It is curious to note the
affection which Cormack retained for his first scientific love, for
Creasote figures not only in many of his prescriptions in future
years, but we find that creasote water (cresylic acid) was used by
him in his surgical experience during the siege of Paris in 1871,
instead of the closely allied carbolic acid now so familiar to
everybody.

Having taken his degree with gold medal honours in 1837, he
went to Paris, where he followed out his professional studies, chiefly
under Andral as regarded medicine, and Velpeau as regarded
surgery. He then returned to Scotland, and determined to settle in
practice in Edinburgh, and became a Fellow of the Eoyal College
of Physicians of Edinburgh 2nd February 1841. Practice came
scantily, but Cormack could not be idle. He became a lecturer on
Medical Jurisprudence in the Extra Academical School, and then

54

lie entered upon that course of medical journalism which was a
leading characteristic of a great part of his subsequent life. In
1842, under the name of the London and Edinburgh Medical
Journal , he started that monthly Journal of Medicine, which, under
some changes of designation and varieties of editorship, continues
to be an important vehicle of scientific and practical medicine ; its
334th number being that for April 1883.

In 1842 he was appointed physician to the Fever Hospital in
connection with the Royal Infirmary, and in this capacity he had
a large experience of the remarkable epidemic of Relapsing Fever,
which in 1843 occurred in Edinburgh and other towns in Scotland.
The labour which he bestowed on his hospital work, and the
accurate details which he preserved of his cases, are a striking
character of the hard-working nature of the man. His observations
were given to the profession in the form of a book on this epidemic,
which had, up to that time, not been so fully and accurately
described, and he subsequently published some additional remarks
on the subject in the London Medical Gazette for April 1849.

Cor mack’s journalistic venture, and his work as a hospital
physician, did not, however, bring him much in the way of practice,
and accordingly he migrated to London, where he remained but a
short while, settling in practice in its neighbourhood at Putney.

In the English metropolis his journalistic propensities again
manifested themselves. Besides writing leaders and other unsigned
articles in some of the London medical journals, he became editor
of the Association Medical Journal , the organ of the Provincial
Medical Association. But this he gave up in 1856. The journal
was much improved under his management, and still exists as the
British Medical Journal, the organ of that large and influential body
the British Medical Association.

Cormack did not, however, succeed in practice at Putney. His
journalism brought him much notoriety and some ill-will, but it
was perhaps itself adverse to his success as a practitioner, and it
was necessary for him to look to something which would add to the
means of maintaining a rising family.

An elderly lady who resided at Tours in France required a
British medical man to be always with her, and accordingly he went
to France, with the life and language of wdrich he was familiar.

55

This, however, was a source of income which could not he otherwise
than temporary, and in the course of time his patient died, and he
had once more to look for a field of practice. He went to Paris,
and to enable him to practise there he took the degree of M.D. of
Paris in 1870, using for the thesis which he was bound to present
to the Faculty the old subject of the Entrance of Air into the
Veins, with the addition of his further observations which have
been already mentioned. The sun seemed at last to be shining on
his side of the hedge. Sir Joseph Oliffe, then the leading English
physician in Paris, was old, and soon died, and Cormack got into
good practice among the English, and to some extent among the
French community. He was appointed physician to the British
Embassy, and all seemed to be getting on prosperously with him.
But soon the Franco-German war broke out, and with it came the
downfall of the Second Empire. Paris was besieged by the Germans,
and after this disaster the Commune followed. Cormack’s prospects
of an easy-going practice were thrown to the winds, and, like every
one in Paris, he felt how hard are the uses of adversity. But now it
was in this dark hour of disaster that Cormack really came forth
in great form and showed what was in the man. Amid the silent
horrors of a severe winter, and the loud-sounding horrors of foreign
invasion and civil war, he showed that he was a good man, by
bringing out of his professional treasure things new and old. It
was not now the work of a civil practitioner, but that of a military
medical officer, that he had to undertake. If anything be needed
to prove the propriety of every aspirant to the medical profession,
being ascertained, before he gets his degree, to be qualified, not
only in one, but in all the practical branches of his profession,
Cormack’s case would supply it. His whole work hitherto had
been essentially that of a physician, he now came out strongly as an
operating surgeon, bringing to the front the surgical lessons he had in
his youth received from Lister, Syme, and others in the surgical
wards in the Edinburgh Infirmary, and some of his cases were really
triumphant results of conservative surgery. It was in the Ambulance
Anglaise , established near his then residence, and maintained
entirely by Sir Richard Wallace, that he did his surgical work, and
the writer of this notice saw one of his triumphs in the person of
the Communist, Alphonse Brunet, whose arm he saved by resection

56

of the shoulder joint after it had been shattered by a rifle bullet
For his good and courageous work at this time he was rewarded both
by the British and French Governments, being knighted by our
Queen, and made a Chevalier of the Legion of Honour.

Peace being at length restored, Cormack returned to his more
usual- work of physician, but now just as the sun of prosperity had
begun to shine upon him, and when he had received honours of
which any man might be proud, the end drew near. He had never
fairly got over the effects of his exertions during the war. Although
still looking fairly well, and in his usual good temper and spirits, he
was a sufferer from bladder disease, and he died on 13tlr May 1882.

This was not the only bereavement which the Franco-German
and Commune wars brought upon the Cormack family. In 1842
Cormack had married Miss Hine, the daughter of a merchant at
Trelawney, Jamaica. She, too, was one of the victims of these times
of political trouble. She never recovered from the effects of the
privation and distress to which all Paris at that time had been more
or less subjected. The inclemency of a hard snowy winter, the
bursting of shells and the rattle of the fusillade, the crash of falling
houses, the want of due supplies of food, and the necessity of
waiting, sometimes for hours, in the queue of persons who had to
go, single file, to the bakers’ shops to get their loaf of bread, were
not likely to leave unshattered the health of a lady born in the
West Indies, and who had been the mother of eleven children, and
no one therefore need be surprised to learn that in three months
Lady Cormack followed her husband to the grave. She died on 19tli
July 1882.

Cormack had had eleven children, and among his trials of life
was the mortality which occurred among them. Two died in
childhood, of scarlet fever and typhoid respectively. One who was
grown up died in Brazil, of phthisis after yellow fever. In 1876
death dealt heavy blows on Cormack. His daughter, Mrs Lyon,
died in India soon after giving birth to a boy, who was a great
solace to his grandfather in his last years ; and within a week of this
event in India he lost in Paris his son Bailey Cormack, who was a
promising young member of the medical profession — his father’s
right hand man in his surgical work in the war time, and whose
excellent qualities cannot be better recorded than they are in the

57

following preface to Sir John’s account of his patient Brunet, whose
case has already been alluded to : —

“ For nearly a year I had not seen him (Brunet) till we met on
the 29tli April 1876, at the funeral of my dear son John Rose
Bailey Cormack. Weeping bitterly he grasped my hand, and said,

‘ I never liked any one so much as Dr Bailey : he did not know
what fear was, but he was to me and all the other wounded kind
as a brother and gentle as a woman.’ Injustice to Brunet, I cannot
refrain from here placing on record his tender appreciation and
beautiful tribute to my late son — my skilful assistant in most
trying circumstances — one who was the joy and hope of my life.
It is pleasant to record that even men of £ Communistic type ’ are
amenable to kindness, and can love as well as hate their fellow-
men.”

Shortly after Bailey Cormack’s death, his sister Margaret died of
pleurisy, induced, it was thought, by nursing her brother.

Five of the family survive, one married and three unmarried
daughters, and a son, Charles Edward, who, following his father’s
footsteps, is now a student of medicine.

Cormack was a voluminous writer, exclusive of what he did in
the way of journalism. In 1876, under the title of Clinical Studies ,
he republished his various detached writings in two volumes.
These embrace such a variety of subjects besides those already
noticed, as cholera, scarlatina, granular kidney, several gynaeco-
logical matters, infantile convulsions, diphtheria, syphilis, concussion
of the brain, and certain forms of insanity. It can by no means be
said that all these are of equal clinical importance, but all of them
manifest good observing power and determination to study the
subject fully.

It was a considerable shock to many of Cormack’s friends to
learn after his death that he had left his family in straitened
circumstances. It is revealing no secret to mention this, for it was
prominently brought forward by the British Medical Journal in
the very practical form of advocating a memorial subscription for
the benefit of Lady Cormack and her family. The way in which
this was responded to, showed that Cormack had had many friends
who esteemed him highly. It did not surprise those, however, who
knew, nor will it surprise any one who hears the narrative of his

58

chequered life, as stated in this notice. It is obvious that Cormack
never got into that steady sort of practice which fills the purse.
His journalistic work was an impediment rather than a help to
him. It is not easy to see why he did not succeed in practice,
especially at Putney, where he had a good opening. It was not
want of professional knowledge j his writings show that this was
full and extensive. It was nothing wrong with his morale or his
relations with religion, for although he did not carry a broad
phylactery, or enlarge the border of his garments, he was essentially
a quietly and unobtrusively Christian man. It is neither pleasing
nor profitable to pursue this theme, and one can only fall back upon
the trite expression of the country of his adoption, that he wanted
the “ Je ne sais quoi the absence of which has hindered the
success of many a man as full of erudition and observing power as
himself.

Cormack was a warm and steadfast friend, and the writer of
these lines desires to record that this was the constant relation to
himself of the subject of this obituary notice.

Sir Charles Wyville Thomson, F.It.SS. L. and E. By Peter

Eedfern, M.D. Bond.

Charles Wyville Thomson was born on the 5th of March 1830 at
Bonsyde, a small property in Linlithgowshire, which had long been
in his family. His father was the late Mr Andrew Thomson, who
spent most of his life abroad as a surgeon in the service of the
Honourable East India Company. His mother was Sarah Ann
Drummond, the only daughter of Dr Wyville Smith, Inspector of
Military Hospitals. His grandfather was a distinguished Edinburgh
clergyman, and his great-grandfather was “Principall Clerke of
Chancellary” at the time of the Bebellion of 1745. His father was
rather a strict disciplinarian, and expected to see successive distinc-
tions at school and college following in the wake of the admirable
education which he placed at the command of his son.

These were stirring times for Scotland. Unembarrassed by
troubles from without, her people were continually struggling for
intellectual advancement. They furnished and maintained schools

59

of the highest class in the larger towns, and such as offered classical
training to the youth, in the whole length and breadth of the
country, in preparation for the Universities. In Edinburgh, Glas-
gow, Aberdeen, and St Andrews, she gave university education to
twice as large a proportion of her population as Prussia did ; and it
is not to he wondered at that her sons have distinguished themselves
in every corner of the globe. In settling in the north of Ireland,
they introduced order and liberty, manufactures and prosperity, and
raised one of its towns at least to take its place amongst the most
enterprising and prosperous in the United Kingdom, whilst they
themselves neither required soldiers nor police for the maintenance
of order and securing the advantages of the administration of just
laws. These were the days of Thomson’s youth.

The mother’s fond affection for her son led her to anticipate his
wishes — to supply his wants — and to present him to his father as
almost faultless in every relation of his early life. The son’s de-
votion to his parents led him to make many an effort for their
gratification, no less than for his own success in life. His early
training was at Merchiston Castle School, when it was under the
management of Mr Charles Chalmers, brother of the famous divine.
Mr Thomas Chalmers, of Longcroft, near Linlithgow, and son of
the then proprietor of the school, stated at a meeting of the com-
missioners of supply for the county of Linlithgow, that “when
young Thomson entered the school he himself had passed from
being a scholar to the position of a master, and thus became Thom-
son’s first teacher in some of those branches of science in which he
afterwards became so eminent.” Mr Chalmers adds — “Ho doubt
the lessons he received were of a very elementary description, still I
may he allowed to recall with some satisfaction, if not pride, the
happy early days of our intercourse, when, with botanical boxes or
geological hammers in hand, we rambled on Saturday holidays, or in
the long summer evenings, among the woods of Braid and Colin -
ton, or over the uplands of the beautiful Pentland Hills, in search
of some of the interesting flora or geological and mineral speci-
mens in which the neiglibourood of Edinburgh so richly abounds,”
and then describes the exultation and satisfaction with which they
returned with any new or rare specimen after a long day’s excursion.
Mr Chalmers says that Thomson was a universal favourite with his

60

schoolfellows, and was highly esteemed by his teachers for his con-
scientious discharge of every duty.

Shortly after he had entered the University his desire to engage
in original work began to show itself in his devotion to the study of
botany and zoology. It was his original intention to graduate in
medicine, but the attractions of biological science were too great to
permit of his devoting any large amount of attention to the other
subjects of medical study, and at length he gave up all idea of
qualifying as a medical man or entering into medical practice. At
this early period his desire to be free from the trammels of customary
methods of study, and to trust to his own efforts, was well shown
by the reply which Professor Balfour, then Professor of Botany, made
to him on his soliciting a certificate of attendance on his class — “ I
will willingly testify to your knowledge of botany, but I cannot
certify that you attended my class.” This early formed spirit of
self-reliance and determination to investigate natural objects them-
selves, rather than trust merely to the results of the observations of
others, seems to have pervaded his life, and to have led to the
urgent requests he continually made for aid to establish collec-
tions in public institutions, and at length to the appeal to the
Government itself for the means of carrying out what became the
most important work of his life, that of determining the physical
and vital conditions which prevail at different depths of the ocean.

I first met Wyville Thomson at the house of my late dear friend,
Professor J. H. Bennett, at the time of the meeting of the British
Association in Edinburgh in 1850, when the friendship commenced
which remained unbroken for a single hour during the whole of his
life. I was greatly impressed with his knowledge of botany, and
with the energy and determination in the pursuit of science of one
who appeared to me to have the most tempting professional career
open before him.

Dr Dickie had been removed from the University and King’s
College, Aberdeen, to the chair of Natural History in Queen’s
College, Belfast. Finding that Thomson had no disinclination to
devote himself, for some time at least, to scientific work, I had the
pleasure of recommending him for the vacant lectureship, and
seeing him start on the career which ended so brilliantly but pre-
maturely. In 1851 he was prevailed on to leave King’s and to

61

lecture in Marisclial College, Aberdeen, where he continued to study
his favourite subjects and to teach botany until 1853, when he was
selected by the Crown as the successor to the Bev. Wm. Xlincks,
F.L.S., in the chair of Natural History in Queen’s College, Cork.

The charming flora and fauna of Aberdeen, which had been
laboriously worked for years by Dr Dickie, who had indicated the
spots where the most interesting specimens were to be met with, was
open and ready for further examination by the more daring and
speculative spirit of Thomson. It was not long before a visit to his
study possessed the greatest attractions and charms. Around the
room, on shelves, tables, and floor alike, there lay, in what would
have seemed to a casual observer the most grotesque confusion, the
treasures of description and illustration of the most eminent natur-
alists of the day and of former times. The shelves and mantelpiece
were, shortly, crowded with selected and neatly preserved specimens
of Polyzoa and sertularian zoophytes taken in the neighbourhood,
picked off the fishermen’s lines, or dredged up by Thomson him-
self ; here and there lay heaps of plants already in their places in
the herbarium, or in process of preparation for being preserved; and,
what was more charming than all, there were bowls and dishes and
aquaria of all kinds, containing the actual living specimens which
were being examined, and of which the characters were rendered
permanent by the naturalist-artist himself in the most beautifully
executed drawings. Amidst all these signs of true scientific work
there were indications of the enjoyment which the tenant of this
sanctum himself derived from indulging in his natural tastes. The
specimens of the most elegant forms were always in the foreground ;
there never failed to be seen two or three rare or beautiful flowers,
made ten times more beautiful than ordinary by the tasteful way in
which they were displayed, whilst the newest photographs or
sketches of the glens or other scenery in the neighbourhood found
a home on any unoccupied spots there chanced to be on the walls.
Those who had the privilege of witnessing the progress of this
happy life, of noticing how the varying forms of these elegant
sertularians gradually proclaimed their mode of development, how
their myriad medusoids were produced, at length set free, and then
settled in life, under the observation of the loving intruder into
Xheir inner life, could not but wonder how time was obtained for all

62

this varied work, attended as it was with the enjoyment of the
pleasures of social life, and with that of adding to those pleasures
the charms of wit, of elegance, and manner of one who was equally
at home, and even more happy, in the society of ladies and educated
men than in the company of his home family of zoophytes, or other
of the lower forms of living beings.

Thus two or three of the earlier years of the public life of Wyville
Thomson were spent. They produced many papers of great interest,
which were published in the Annals of Natural History and other
periodicals, and gave birth to very noticeable philosophical specula-
tions on the development of certain medusoid forms, startling many
older naturalists, and only partially accepted by others, such as
Johnston of Berwick-upon-Tweed, and Edward Forbes, who con-
sidered them too daring advances on what was then known of the
modes of life of those beings.

On leaving Aberdeen, Thomson had secured a large number of
sincere friends to whom his departure was a great loss. His kind-
ness of heart and his many estimable social qualities had made him
desired in every circle, whilst in both the colleges to which he
had been attached he was looked upon as a rising naturalist, des-
tined to attain great eminence as years advanced. The degree of
LL.D. was conferred upon him by Marischal College, Aberdeen.

In Cork, to the duties of teaching botany, those of teaching
zoology were added, and both were discharged with equal vigour
and success. But other changes were awaiting him. Early in
1854 he married Jane, the elder daughter of Adam Dawson, Esq.,
deputy lieutenant of the county of Linlithgow, and proprietor of
Bonnytown, the neighbouring estate to Bonsyde. As the friend
of the bridegroom, I had the pleasure of participating in the great
gathering of members of the county families, and of Thomson’s
numerous Edinburgh friends, to celebrate what was deemed a most
auspicious union of two families, both held in high estimation by
all who knew them. In the same year the chair of Mineralogy
and Geology in Queen’s College, Belfast, became vacant by the
resignation of Professor Frederick M‘Coy, who was elected to a
professorship in the new University of Melbourne, and Thomson
was then transferred from Cork to Belfast.

The studies incident on the occupation of the chair of

63

Mineralogy and Geology and tlie charge of the Natural History
Museum, following in succession on the study of Botany and
Zoology, the subjects of Thomson’s former chairs, now completed
his training as a Professor of Natural History. He devoted much
time and attention to Palaeontology, and thus, in comparing the
old world forms with those at present existing, obtained much
useful insight into the relations between them. Under his guidance
the Museum of the College was greatly enlarged, especially in the
departments of Zoology and Palaeontology, and his efforts in this
respect received the hearty co-operation of the president and vice-
president. Specimens for teaching and for the enrichment of the
museum were sought for everywhere, and properly arranged and
classified. Whatever new objects possessed unusual interest were
made the subjects of papers read before scientific societies, or pub-
lished in the journals of the day. It was at this time that a paper
appeared on a genus of Trilobites; this had been read before the
London Geological Society. Another, on a fossil Cirriped, was
published in the Annals of Natural History. One can well
imagine the growing consciousness of power in dealing with fossil
forms which Thomson’s previous knowledge of the existing living
forms gave him, and that, as the accumulation of specimens pro-
ceeded, the series would be seen to be in certain parts more or less
complete, whilst in others it would be found wanting, and thus the
necessity of further investigation would be pointed out. It was
natural that, when he came to the collection and investigation of
the numerous varieties of extinct forms of echinoderms, the eye
which was always open to the charms of beauty should have been
arrested, and that it should have occurred to him that what was
needed for a complete understanding of them was a correct know-
ledge of everything which their living forms could teach. From
this time he returned to his study of the development of the larval
forms of these low organisms, especially with reference to Comatula
and Pentacrinus, no doubt with the hope of arriving at some
general conclusions as to the relations of their peculiar mode of
development with that of the higher animals, and of showing their
connection with extinct forms.

Mr J. Y. Thomson had found his Pentacrinus Europams in the
Bay of Cork in 1823, and was thus the first to discover a recent

64

encrinite in the seas of Europe, as he was the first who ever had
the opportunity of examining one in its living state. As the result
he declared it to be the young of Comatula, and, comparing his
youngest Comatula with the oldest Pentacrinus he could find, he
demonstrated this relation to the satisfaction of Professor Edward
Forbes, Dr Ball of Dublin, and the late William Thompson of
Belfast. Yet much remained to be done to clear up the whole
history of this single form, and this occupied Wyville Thomson
for several years. A sketch of his “ On the Embryogeny of
Comatula rosacea ” appeared in the Proceedings of the Royal
Society for 1858, a paper “On the Embryology of Asteracanthion
violaceus ” was published in the Microscopical Society's Journal
for 1861-62, and his paper “ On the Pentacrinoid Stages of
Comatula” was sent to the Royal Society in December 1862, read
in February 1863, and published in the Philosophical Transactions
for 1865. This paper is a model of care and accuracy, illustrated
by many beautiful and highly artistic drawings of the various
stages, executed by the author, and itself attests his powers of
research and his accuracy of discrimination and delineation. Whilst
engaged in this work, Thomson accumulated a large amount of
material, with a view to give an account of the whole genus Penta-
crinus at some future time. Indeed, as far as these researches on
development are concerned, it is almost to be regretted that they
so soon led to the great work of deep sea research, which, when
once entered upon, took up so large an amount of time.

In a correspondence with Michael Sars, the celebrated Professor
of Zoology in the University of Christiania, Wyville Thomson
learned that the professor’s son, M. Oscar Sars, whilst engaged,
as one of the acting Commissioners of Fisheries, in a series of
investigations as to the fisheries off the Loffoten Islands, north-west
of the coast of Norway, had dredged up from about 300 fathoms a
number of living animal forms. In response to an invitation from
Professor Sars, Thomson visited Norway to examine these objects,
and he states that amongst them there was a small crinoid of sur-
passing interest, which they at once recognised as a degraded type
of the Apiocrinidse, an order which had up to that time been
regarded as entirely extinct. Some years previously M. Absjornsen,
dredging in 200 fathoms in the Hardangerfjord, procured several

65

examples of a starfish “ Brisinga,” which seems to find its nearest
ally in the fossil genus Protaster. In this way it had become
certain that animal life does not cease in the ocean at a depth of a
few hundred fathoms, as the late Edward Forbes had supposed.
Wyville Thomson tells us that, long previously to 1868, he “had
a profound conviction that the land of promise for the naturalist,
the only remaining region where there were endless novelties of
extraordinary interest ready to the hand which had the means of
gathering them, was the bottom of the deep sea.” And when, in
his visit to Norway, he became fully acquainted with the advant-
ages which Professor Sars and his son had enjoyed through the
means of their Government, he resolved to lose no opportunity of
pointing out how greatly the Government of the most powerful
maritime nation in the world might aid science by placing at the
disposal of naturalists one of their numerous unemployed vessels to
assist in the exploration of the ocean depths. A favourable oppor-
tunity presented itself when engaged with Dr W. B. Carpenter in
working out the structure and development of the Crinoicls in the
spring of 1868. Dr Carpenter was a vice-president of the Eoyal
Society, through which body alone it seemed that the Government
could be influenced. He considered the subject carefully, and hav-
ing arrived at a conclusion favourable to the project, it was resolved
that he should bring the subject under the notice of the Society,
introducing it by a letter which his colleague was to write to him
after his return to London. The Eoyal Society and the Govern-
ment entered heartily into the plan, and the dredging cruises of
H.M.S. “ Lightning” and “Porcupine” and the expedition of the
“ Challenger” were the result.

It has been already stated that Wyville Thomson was appointed
to the chair of Mineralogy and Geology in Queen’s College, Belfast,
in 1854. On the removal of Dr Dickie to Aberdeen in 1860, the
duties of the chair ofBota ny and Zoology were also entrusted to
him, and he became from that time Professor of Natural History in
these four branches. For the discharge of these duties he was very
peculiarly fitted from the happy way in which he had at different
times been called upon to teach the four subjects in succession.
He had now the entire responsibility of the department of Natural
History. In the year 1860 he Was admitted to the degree of LL.D.

e

66

in the Queen’s University ad eundem. As a resident in Belfast he
entered heartily into every plan for the spread of knowledge or the
improvement of his townsmen. He was an active member of the
^Natural History and Philosophical Society, and at its meetings he
contributed many valuable papers. As a lecturer he was fluent in
style, easy in manner, and lucid in thought and expression. He
conveyed to his hearers much of the interest he had in his subject,
and encouraged them to engage in original work. He was instru-
mental in placing the School of Science and Art in its present rela-
tion to South Kensington, and took a constant and lively interest
in its success.

He was an active member of the local committee in connection
with the meeting of the Social Science Congress in Belfast, under
the presidency of the Earl of Dufferin, in 1867.

Interested in education, and attached to the system on which the

Queen’s Colleges and Queen’s University were founded, he strenu-

\

ously opposed all attempts to interfere with their academic character
or their privileges. When a supplemental charter was issued, which
it was believed would lessen the necessity for thorough academic
training to obtain degrees in the Queen’s University, Wyville
Thomson came forward very prominently, and succeeded in col-
lecting large funds, and obtaining still further guarantees from an
influential committee, which enabled the validity of the charter to
be tested in the Court of Queen’s Bench. The result was that,
after long and protracted arguments, an injunction was granted in
1867 by the Master of the Bolls which rendered the supplemental
charter inoperative, and helped to prevent for many years the
substitution of a system of mere examinations for the most
complete academic training which prevailed in any university.

Begardless of the differences of religious and political opinion
which prevailed in Belfast, he was courteous to all, tolerant of
every opinion frankly formed, and never obtrusive of his own.
He was esteemed by all classes and parties, he had friends every-
where, and his house was always open to all of distinction in
science or art who might happen to visit Belfast. Engrossed in
his own proper studies, he never obtruded them upon others, hut
whenever assistance or advice in connection with them were
needed, he spared no pains to make both effective. His tact,

67

consideration, and good taste never failed him. His passion for
flowers seemed a part of his nature ; he cultivated them with the
greatest care, and, though delighting to display them to the
greatest advantage in his own house, he enjoyed equally his
regular practice of carrying any particularly choice specimen he
might have grown to present it to some of his many friends.

In 1867 he was made Vice-President of the Jury on Raw
Products at the Paris Exhibition.

On the 30th May 1868 he addressed the letter to Dr Carpenter
which was previously agreed upon, pointing out that Edward
Forbes’s conclusion, that a zero of animal life was reached at a
depth of a few hundred fathoms, was incorrect, as had been proved
by M. Absjornsen’s dredging starfishes at 200 fathoms, and by
M. Oscar Ears dredging living crinoids from 300 fathoms ; that the
effect of pressure has probably been greatly exaggerated, because an
equal pressure within and without by water would probably produce
no injurious effect on animal life, and might even contribute to
increase the aeration of the vrater ; and that, looking at the con-
dition of the cave fauna, it is probable that the diminution of
light at great depths may only affect the development of colour and
of the organs of sight. He suggested that, whilst dredging at 1000
fathoms was quite beyond the reach of private enterprise, it was
quite practicable if the Admiralty could be induced to grant the
use of a vessel for the purpose. He proposed to start from.
Aberdeen, to go first to the Rockall fishing banks, and thence
north-westward towards the coast of Greenland, rather to the north
of Cape Farewell.

Dr Carpenter wrote to General Sabine enclosing Professor
Wyville Thomson’s letter, pointing out the admirable results
obtained by M. Sars, with similar aid granted by the Swedish
Government ; and showing that he and Dr Thomson had restricted
their request within such conditions as could, without great expense
or inconvenience, he acceded to by the Admiralty. On the evening
of the day on which Dr Carpenter’s letter was written, General
Sabine brought the subject under the consideration of the council
of the Royal Society, who at once approved of the proposal, recom-
mended it to the favourable consideration of the authorities of the
Admiralty, and advanced a sum of £100 to meet expenses. The

68

Lords Commissioners of the Admiralty wrote on the 14th July that
they had given orders for Her Majesty’s steam vessel “ Lightning ”
to be prepared immediately at Pembroke to meet the wishes of the
Royal Society. The “ Lightning ” left Pembroke on the 4th
August 1868. Drs Carpenter and Thomson, and Dr Carpenter’s
son Herbert, joined the vessel at Oban, whence they sailed on the
8th August. They reached Stornoway on the 9th, and left it for
the north on the 11th. On the same afternoon they dredged in 60
to 100 fathoms ; on the 13th in 450 fathoms, finding no bottom,
but the high temperature of 9 ‘5° C.; afterwards in 600 to 700
fathoms in the same locality. Bad weather frequently impeded the
dredging operations. On the return of the vessel to Stornoway on
the 9th September, Dr Wyville Thomson was obliged to leave her
to attend to duties in Dublin, but Dr Carpenter remained with the
vessel, left Stornoway again on the 14th September and dredged in
650 fathoms, but on the 21st the weather was so bad that the work
had to be concluded. There were only ten days available for
dredging in the whole six weeks, and on only four of these was the
vessel in water over 500 fathoms deep. Yet a fair measure of
success had been achieved.

It was shown that varied and abundant animal life, represented
by all the invertebrate groups, occurs at depths in the ocean down to
650 fathoms at least ; and that, instead of deep sea water having an
invariable temperature of 4° C., great masses of water, at tempera-
tures varying from 2° C. to 6*5° C., maintain a remarkable system of
oceanic circulation, and yet keep so distinct from each other that
both may be found within the limit of an hour’s sail. It was also
ascertained that a large proportion of the forms living at great
depths of the sea are of unknown species, and identical with tertiary
fossils previously believed to be extinct.

The next year, 1869, saw Wyville Thomson again engaged in the
examination of the physical, chemical, and biological conditions of
the ocean depths, for the Lords Commissioners of the Admiralty
had acceded to the additional request of the council of the Royal
Society and had set apart the “ Porcupine,” a small vessel fitted up
for surveying purposes and admirably adapted for the continuance
of these researches, from the beginning of May to the middle of
September. As it was impossible for those connected with the

69

previous expeditions to be absent from their public duties for any
large portion of this time, it was resolved that there should be
three separate cruises, one on the west coast of Ireland, the Porcu-
pine Bank, and the channel between Rockall and the coast of
Scotland, under the scientific charge of Mr Gwyn defines, F.R.S. ;
a second to the north of Rockall, leading northwards to the point
where the expedition of 1868 left off, under the charge of Dr
Thomson ; and the third to work over the “ Lightning Channel ”
and check the former observations, under the direction of Dr
Carpenter.

Mr Gwyn Jeffries was favoured with remarkably fine weather,
and found it possible to dredge during seven days at depths greater
than 1200 fathoms, and on four days at less depths. His deepest
dredging was 1476 fathoms, and the whole of them yielded an
abundance of novel and interesting results in every invertebrate
sub-kingdom.

Captain Calver was accustomed to minute accuracy in surveying,
and thoroughly versed in the use of instruments and in the bear-
ings of scientific investigation. His crew were chiefly known and
tried men, Shetlanders who had spent many successive summers in
the “ Porcupine ” under his command. Aided by a staff of zealous
officers, Captain Calver soon obtained so entire a mastery over the
operation of dredging that he made it almost a certainty at depths
at which this kind of exploration would have been previously
deemed out of the question. Wyville Thomson at once recognised
these favourable conditions, and having found that the experiences
of the previous year, and all their anticipations for the present, had
been realised, at least for the depth of nearly 1500 fathoms, and
that even at that depth nearly all the types of living marine inver-
tebrata were represented, though the number of species seemed
reduced and the size of the animals dwarfed, he suggested that it
would be desirable that the second cruise should he made in deeper
water than had originally been intended, and pointed out the
position of the deepest water easily accessible, 250 miles west of
Ushant, as a fitting place for the next observations.

The Hydrographer cordially acquiesced in this proposed change
of plan, and it was arranged that the next dredging should be done
at this spotj in water 2500 fathoms deep. Professor Wyville

70

Thomson left Belfast in the “ Porcupine ” to take the scientific
direction of this cruise on the 17th. July 1869, taking with him
Mr Hunter, F.C.S., chemical assistant in Queen’s College, Belfast,
to examine and analyse the samples of sea water. At Queenstown
Mr P. Herbert Carpenter joined the ship to practise the gas
analysis which he was to undertake on the third cruise.

The vessel proceeded on her voyage at 7 p.m. on the 19 th July,
steaming in a south-westerly direction across the mouth of the
channel. At 4.30 a.m. on the 21st they were still only on the
plateau of the channel in 95 fathoms of water, hut from midday to
the afternoon they passed over the edge of the plateau and dredged
in 725 fathoms, the bathymetrical horizon of vitreous sponges in
the northern seas, bringing up several specimens of these beautiful
forms, and a slight admixture of globigerina ooze in sand. On the
22nd they were in water of about the greatest depth they had reason
to expect, 2435 fathoms, at a temperature of 2 ‘5° C. A successful
dredging yielded 1^ cwt. of grey chalk mud, containing examples of
each of the invertebrate sub-kingdoms, which, though dead, had
evidently been alive when they entered the dredge. Similar
results attended a dredging on the 23rd at the same depth, after
which the party returned to the coast of Ireland, dredging and
noting the results at intervals on the way. The vessel reached
Cork on the 2nd August, and Belfast on the 4th.

She left again on the third cruise for the year, on the 1 1th
August, under the direction of Dr Carpenter, Mr P. H. ' Car-
penter undertaking the analyses, and Wyville Thomson accompany-
ing them. He busied himself in drawing, naming, and describing
new species, and in noting the great general features of the
prevailing physical and vital conditions. It is scarcely possible for
anyone, however little imaginative, to read the graphic accounts of
the incidents of these voyages without having his enthusiasm
aroused, and almost wishing to have been present on many of the
occasions so forcibly depicted. It seems more like a dream than a
reality that at a single haul the dredge should have brought up
in its bag and on its tangles not less than 20,000 specimens
of the pretty little urchin, Echinus norvegicus1 and we have Dr
Thomson’s authority for such an event having happened. On
other occasions, one is irresistibly brought to watch, with bated

71

breath, the landing of the great prizes which the dredge had
collected. His account of the glimpses from time to time as the
dredge was coming in, of what seemed to be a large scarlet urchin,
the disappearance of it now and then as if lost altogether, then its
quiet settling down as a round red cake, and beginning to pant, —
that he had to summon up some resolution before taking the weird
little monster in his hand, — show the graphic power of the author
no less than the enthusiasm of the naturalist.

I cannot forbear giving another illuatration : — “ I do not believe
human dredger ever got such a hank The special inhabitants of
that particular region — vitreous sponges and echinodcrms — had
taken quite kindly to the tangles, warping themselves into them,
and sticking through them and over them, till the mass was such
that we could scarcely get it on hoard. Dozens of great Holtenise,
like

Wrinkled head and aged.

With silver beard and hair ; 1

a dozen of the best of them breaking off just at that critical point
where everything doubles its weight by being lifted out of the
water, and sinking slowly away hack again to our inexpressible
anguish ; glossy whisps of Hyalonema spicules ; a bushel of the
pretty little mushroom-like Tisiphonia ; a fiery constellation of the
scarlet Astropeden tenuispinus ; while a whole tangle was ensan-
guined by the 4 disjecta membra 7 of a splendid Brisinga.”

The effect of the brilliant phosphorescence of the contents of the
dredge are vividly pourtrayed ; and the argument in favour of the
urchins, which are only one-fourth of the size of others whose
characters are indistinguishable from theirs, being dwarfed speci-
mens of the same genus, is not easily forgotten “ The Shetland
variety of Equus cabcdlus is certainly not more than one-fourth the
size of an ordinary London dray-horse, and I do not know that
there is any good reason why there should not be a pony form of
an urchin as well as of a horse. ”

Wyville Thomson had arranged with his colleagues to take part
in an exploration of the deep sea to the south of Europe and the
Mediterranean in 1870, hut he was prevented from doing so by an
attack of fever. Yet he gave at second hand a brief account of the

first part of the work under the direction of Mr Gwyn Jeffries to
complete his sketch of the condition and fauna of the North
Atlantic ; and directed attention to the entirely exceptional con-
ditions of temperature and animal life observed by Dr Carpenter in
the Mediterranean as compared with the outer ocean.

In the whole life of Thomson, notwithstanding his vivid ap-
preciation and accurate descriptions of the most minute details of
structure necessary for the determination of new species, and for
allotting them their proper position in nature, he never allowed
himself to be dragged down to the level of a mere collector, accumu-
lating myriads of individual objects and cataloguing them. He
invariably rose superior to details, and, subordinating them as
merely means for arriving at just conclusions regarding the physical
and vital characters of the earth and its living freight in long past
ages or the present time, he devoted his best thoughts to the con-
sideration of the means by which great results might be achieved.
The idea that either individual or even imperial aid was necessary
neither occasioned him anxiety nor- discouraged him ; lie resolutely
set forth the conditions, showed how important results could be
arrived at, and the means never failed him.

His discussion of the effects of the Gulf Stream on the climate of
the coasts of Northern Europe, in comparison with the influence of
any possible general ocean circulation, is a good illustration of bis
wide and powerful grasp of natural phenomena bearing on any par-
ticular point. He had measured in the North Atlantic the extent
of the warm and cold areas of water, and recognised the fauna
which are proper to each ; he had determined the existence of the
vast layer of cold water, 1500 fathoms thick, at the bottom of the
Bay of Biscay, and that the temperature there at 1230 fathoms from
the surface is the same as that of the bottom off Rockall ; he saw
that, whilst the communication of the North Atlantic and the Arctic
Sea is restricted, the communication with the Antarctic basin is, as
he describes it “ open as the day,” — a continuous and wide valley,
upwards of 2000 fathoms in depth, stretching northwards along the
western coasts of Africa and Europe ; and then pointed out how
much less startling than it appears at first sight is the suggestion
that the cold water filling deep ocean valleys in the northern hemi-
sphere may be partly derived from the southern. He calls to mind

73

that the floor of the Atlantic is covered by a creamy, floccnlent
layer of microscopic animals ; whilst, wherever there is any known
current, this deposit is absent and replaced by gravel, and thus show's
that the movement of any cold indraught of water at the bottom
must be excessively slow. He dispels the chimerical idea that there
is a kind of equatorial diaphragm between the northern and southern
ocean basins, and explains that it is only on the surface of the sea
that a line is drawn between the two hemispheres by the equatorial
current. He then gives as evidence of the slow indraught of cold
water from the Southern Sea, that it is colder than the mean winter
temperature of the area which it occupies and that of the crust of
the earth, and that its temperature rises as it is traced northward ;
whilst, owing to Behring’s Straits being only 40 fathoms deep,
there is no adequate northern source of such a body of cold water.

In 1869 Wyville Thomson was elected a Fellow of the Royal
Society; and in the year following, on the resignation of Dr
Allman, he was appointed Professor of Natural History in the Uni-
versity of Edinburgh. His friends in Belfast recognised the dis-
tinction which had thus been conferred upon him, but felt the
loss which the college and the town had sustained by his re-
moval, and, on taking leave of him, presented him with a handsome
service of plate and an illuminated address at a public meeting pre-
sided over by the mayor. The honorary degree of D.Sc. was
conferred upon him by the Queen's University about the same time.

His duties now became more arduous than ever. His class-room
was crowded with students, whom he taught not merely by lectures
but by practical demonstrations. In 1871, the meeting of the
British Association in Edinburgh, the arrangement and plans of
the new University buildings, troubles in connection with the
admission of females to the college classes, and the transfer of the
Museum of which he was Regius Keeper, to the Museum of Science
and Art, added greatly to his necessary labours.

At this time the rapid extension of ocean telegraphy gave prac-
tical value to everything which concerned the depth of the ocean,
the character of its bottom, and the presence there of animals which
might injure the coverings of telegraphic cables, whilst great interest
was being manifested by the public in the remarkably novel experi-
ences of the cruises of the “Lightning” and the “Porcupine.”

74

From America and from Europe more or less effective expeditions
had been sent out, but it was evident that it rested very specially
with England to lay down the first broad outlines of the physical
and biological conditions of the bottom of the ocean.

The circumstances were very propitious ; and when Dr Carpenter
addressed a letter to the Eirst Lord of the Admiralty, urging the
despatch of a circumnavigating expedition for this purpose, their
lordships, after a favourable report of the Hydrographer to the
Navy, agreed to despatch such an expedition, if the Eoyal Society
recommended it and furnished them with a feasible scheme.

Mr Lowe, then Chancellor of the Exchequer, with great interest
and sagacity, saw that such an enterprise was entirely beyond the
reach of private means, and agreed to furnish the necessary funds.
The “ Challenger” was chosen for the purpose, with Captain Nfres,
a surveying officer of great experience and skill, to command her,
and Professor Wyville Thomson as director of the Civilian Scientific
Staff. He tells us that “ when the suggestion was made to him at
the commencement of the negotiations to join the expedition, the
sacrifice appeared in every way too great ; but as the various arrange-
ments progressed, so many friendly plans were proposed on all hands
to smooth away every difficulty, that he finally accepted a post
which, to a younger naturalist, without the ties of a family and a
responsible home, would be perhaps among the most delightful the
world could offer,”

The President and Council of the Poyal Society nominated the
members of the Civilian Scientific Staff, and a Circumnavigating
Committee, amongst whom were Dr Carpenter and Dr Wyville
Thomson, suggested a scheme whereby it was believed the best
results might be obtained. Sixteen of the eighteen large guns
which the “ Challenger ” carried were removed ; she was fitted with
a natural history workroom, a chemical laboratory, and furnished
with every scientific appliance to the satisfaction of the director,
and in a way entirely unprecedented for scientific purposes. With
a ship thus equipped, and the responsibility of directing the most
delicate and difficult scientific observations at sea for a period of
three or four years, Dr Wyville Thomson left Portsmouth on the
21st December 1872 with the good wishes and ardently expressed
hopes of every lover of science in Great Britain.

The first part of the voyage, that to the Canary Islands, was made
merely tentative, with a view of getting everything on board into
perfect order for correct observations, and dividing the labour of
research in the most convenient way amongst the members of the
staff.

On the 14th February 1873 the “ Challenger” sailed from Santa
Cruz to cross the Atlantic, and the real work of the expedition
commenced. She reached Sombrero on the 15tli March, the Ber-
mudas on the 4th April, and Halifax on the 9th of May. Leaving
Halifax again on the 15th, she went southwards and back to the
Bermudas, to make another section of the Gulf Stream. On both
occasions the most detailed and interesting observations were made.
Subsequently she crossed the Atlantic three times, visited Australia,
New Zealand, the Malay Archipelago, Hong Kong, and Valparaiso,
sailing altogether 68,930 miles, and returning to Sheerness on the
24th May 1876, after an absence of three years and a half.

Shortly after his return, Dr C. Wyville Thomson received the
honour of knighthood, and was appointed by the Lords Com-
missioners of Her Majesty’s Treasury “Director of the ‘ Challenger’
Expedition Commission.” In the same year he was awarded a
Royal Medal by the Royal Society for his successful direction of
the scientific investigations carried on by H.M.S. “Challenger.”

In July he and the other members of the scientific staff of the
“ Challenger” were entertained at a banquet in Edinburgh. On
going with Emeritus Professor Balfour to TJpsala, as the repre-
sentative of the Senatus of the University of Edinburgh on the
occasion of the tercentenary of that ancient University, the King
of Sweden created him a Knight of the Order of the Polar Star.
He was a Eellow of the Royal Societies of London and Edinburgh,
a Eellow of the Royal Irish Academy, Ph.D. Jena, Fellow of the
Linnean, Geological, Zoological, and Palaeontological Societies of
London, and of various foreign and colonial institutes. In 1877
he was appointed to deliver the Rede Lecture1 at Cambridge, and
in 1878 he presided over the Geographical Section of the British
Association at its meeting in Dublin, and was made LL.D. of the
University of Dublin.

Sir Charles discharged the duties of his chair with his customary
vigour on his return from the voyage of the “Challenger,” and

76

worked laboriously at the vast amount of material and observations
which had been accumulated. In 1877 he published two volumes
of a preliminary account of the results of the voyage, a work of
surpassing interest, not alone from the scientific value of the obser-
vations recorded in it, and the conclusions which the author draws
from them, but for the beautifully executed illustrations it contains,
and the graphic sketches which occur here and there of the general
as well as the scientific features of the places visited and examined.
In this work Sir Charles has recognised the valuable assistance of
his colleagues in the scientific staff; the aid which all the naval
officers, without exception, gave in the most friendly spirit to the
civilian staff; the wonderful temper with which the commander
and first lieutenant tolerated all the irregularities inseparable from
dredging and other scientific work; the friendly readiness with
which the chief of the naval scientific staff placed his valuable
observations at the disposal of the civilian staff ; the patience and
care displayed by the lieutenants who superintended the dredging
and trawling and the estimations of temperature ; and his debt of
gratitude to the sailors for the respect and consideration with which
they treated all the civilians on board.

These were, no doubt, remarkable results — this combination of
everyone on board to achieve success, this subordination of the
discipline, cleanliness, and order of a man-of-war to the prosecution
of the study of Natural Science in various departments ; and it
cannot be doubted that they were mainly due to the genial dis-
position, the many engaging social qualities, the gentlemanly
bearing, and the untiring energy of Sir Charles Wyville Thomson.

He admitted that the strain, both mental and physical, was long
and severe, and that it had told upon all of them. His friends
observed that, with the continuance of the labours necessary for
bringing out the full account of the whole results of the “ Chal-
lenger” Expedition, his vigour by no means kept pace, but until
1879 there was no real cause for anxiety. In June of that year,
however, he had a serious illness, from which he only partially
recovered. His place in the University of Edinburgh had to be
supplied, and at length arrangements were made for securing to
him a well-deserved retiring allowance. From time to time he
persevered in endeavouring to forward the publication of the com-

77

plete reports of the Expedition, and still attended meetings of the
Commissioners of Supply for his native county. He even sat as
magistrate sixteen days before his fatal illness. But from his first
seizure he was unable to discharge the duties of his chair, and
retired from them altogether in the October of 1881. Subsequently
he had also to relinquish his position as “ Director of the 4 Chal-
lenger’ Expedition Commission.” In the beginning of March 1882
his critical condition was manifested by his making a personal
application to be relieved from attending at the Fiars’ Court on the
10th of that month, the very day on which his last seizure proved
fatal. He died at the early age of fifty-two, having made many
lasting contributions to science, secured large numbers of sincere
admirers and friends, and received the applause and approval of
scientific men everywhere for the wisdom, energy, skill, and
courtesy which he had shown in the direction of the most extended
and successful of scientific expeditions.

Lady Wyville Thomson survives her husband. He left an only
child — Mr Frank Thomson, M.A. Ed., a student of medicine.

The Commissioners of Supply of the county of Linlithgow, with
a committee of scientific and other friends in Edinburgh, have
collected several hundred pounds for the purpose of erecting a
lasting memorial to commemorate the distinguished services of the
late Sir Charles Wyville Thomson, and it has been resolved to
place a bust by Hutchison in the University of Edinburgh, and a
memorial window in the beautiful collegiate church in his native
place.

The following is a list of Sir C. Wyville Thomson’s principal
publications : —

On the Application of Photography to the Compound Microscope.
Brit. Assoc. Rep., part 2, 1850.

Notes on some Scotch Zoophytes and Polyzoa. Annals Nat.
Hist., ix., 1852.

On the Character of the Sertularian Zoophytes. Brit, .dssoc.
Rep., part 2, 1852.

Notes on some British Zoophytes. Annals Nat. Hist., xi., 1853.

On Native Irish Zoophytes and their Allies. Nat. Hist. Rev.,
ii., 1855.

78

On the Embryogeny of Comatula rosacea , Luth. Roy . Soc.
Proc ., ix., 1857-59.

On some Species of Acidaspis from Silurian Beds of South of
Scotland. Geol. Jour., 1857.

Description of Loricula macadami, a new fossil Cirripede. Ann.
and Mag., 1858.

On New Genera and Species of Polyzoa from the collection of
Professor Harvey, Dublin. A7 at. Hist. Rev., July 1858.

On a New Palaeozoic Group of the Echinodermata. Edin. New
Phil. Jour., xiii., 1861.

On the Embryology of Aster acanthion violaceus, Lin. Mic. Soc.
Jour., i., 1861-62.

On the Development of Synajpta inliae.rens. Mic. Soc. Jour., ii.,
1862.

On Distorted Human Skulls. Nat. Hist. Rev.T 1862.

On the Embryology of Echinodermata. Nat. Hist. Rev., 1863,
1864.

On the Embryogeny of Antedon rosaceus, Linch ( Comatula
rosaceus of Lamarck). Phil. Trans., 1865.

On Professor Steenstrup’s “ Views on the Obliquity of Elounders.”
Ann. Mag. Nat. Hist., 1865.

Sea Lilies (Cenocrinus — Neocrinus — Comatula). Intellect. Ohs.,
vi., 1865.

7 v

On the Glass Pope (Hyalonema). Intellect. Ohs., xi., 1867.

On the Vitreous Sponges. Ann. Mag. Nat. Hist., 1868.

On Holtenia, a Genus of Vitreous Sponges. Phil. Trans., clix.,
1869.

Geological Dynamics. Glas. Geol. Soc., 1869.

On the Depths of the Sea. Roy. Dublin Soc. Jour., v., 1870.

Osteology of Polypterus. Jour. Anat., 1870.

On Deep-Sea Climates. Nature, ii. 1870.

Preliminary Report in connection with Drs W. B. Carpenter
and J. G. Jeffries of the Scientific Exploration of the Deep Sea in
H.M.S. “Porcupine.’7 Roy. Soc. Proc., xviii., 1870.

On the Distribution of Temperature in the North Atlantic.
Nature, iv., 1871.

On the Continuity of the Chalk. Nature, iii., 1871.

79

On the Structure of the Palaeozoic Crinoids. Edin. Roy. Soc.
Proc., vii., 1871.

Notice of a New Family (Echinothuridae) of the Echinodermata.
Edin. Roy. Soc. Proc., vii., 1872.

Deep Sea Echiuidea. Ann. May. Nat. Hist., 1872.

On the Crinoids of the “Porcupine” Deep-Sea Dredging Expedi-
tion. Edin. Roy. Soc. Proc., vii., 1872.

Opening Address on the Eipening and Decay of Fruit. Edin.
Bot. Soc. Trans., 1873.

On the Echinoidea of the “ Porcupine ” Deep-Sea Dredging
Expeditions. Pliil. Trans. 1874 ; Proc. Roy. Soc., 1872.

The Depths of the Sea. (1 vol.), 1873.

On Dredgings and Deep-Sea Soundings in the South Atlantic, in
a letter to Admiral Richards, C.B., F.R.S. Roy. Soc. Proc., 1874.

Preliminary Notes on the Nature of the Sea-bottom, procured by
the Soundings of H.M.S. “Challenger” during her Cruise in the
Southern Sea in 1874. Roy. Soc. Proc., 1874.

Report to the Admiralty on the Cruise of H.M.S. “ Challenger”
from July to November 1874. Roy. Soc. Proc., 1875.

Notice of New Living Crinoids belonging to the Apiocrinidae.
Linn. Soc. Jour., “Zoology,” vol. xiii.

Report to the Admiralty on the Cruise of H.M.S. “Challenger”
from June to August 1875. Roy. Soc. Proc., 1875.

Some Peculiarities in the Mode of Propagation of certain Echino-
dernis of the Southern Sea. Linn. Soc. Jour., “ Zoology,” vol.
xiii., 1878.

Preliminary Report to Admiralty on the Cruise of the “ Chal-
lenger” between Hawaii and Valparaiso. Proc. Roy. Soc., 1876.

Preliminary Report to Admiralty on the Cruise of the “ Chal-
lenger” from Falkland Island to Monte Video. Proc. Roy. Soc.,
1876.

On the Structure and Relations of the Genus Holopus. Edin.
Roy. Soc. Proc., 1877.

Voyage of the “ Challenger. The Atlantic. (2 vols.), 1877.

On the Conditions of the Antartic Regions. Glas. Science
Lectures' Assoc., 1877.

Presidential Address to the Geographical Section. Brit. Assoc.,
Dublin, 1878.

80

The General Introduction to the Zoological Series of the Eeports

of the Voyage of the ‘‘Challenger.” Vol. i., “Zool.,” 1880.

Note. — Sir Charles Wyville Thomson had also undertaken to
write the “ Eeport on the Crinoidea ” of the voyage of the
“ Challenger ” in conjunction with Dr P. H. Carpenter.

Mr Thomas William Eumble. By William Connor Steel

Mr Thomas William Eumble was born in London, 26th Decem-
ber 1832. He received part of his education at the Eeading
Grammar School, under the celebrated Dr Valpy. At an early age
he was transferred to the office of his father, an architect in good
practice, where he was taught the rudiments of his future profession.
Tiring of the dull routine of the drawing-office, he left home to try
his fortune across the Atlantic, where, after many adventures, he was
appointed in November 1850 assistant engineer on the Central
Eailroad of New Jersey, under J. Laurie, Esq., C.E., he being then
not quite 18 years of age. He remained in America till June 1852,
during which time he was actively engaged in laying out the Erie
and Forest Lawn Cemeteries, superintending the building of the
Berks County Baths, the Buffalo Public Wash-houses, &c., and
occasionally giving lectures on architectural and engineering subjects.
Dr Calvin Fairbanks, in a letter dated 1st October 1851, speaks thus
of his ability as a lecturer : — “ I must say I was gratified with the
clearness with which you presented the necessity of developing the
yet undeveloped facts in architecture, in your last evening’s lecture.
It would have been happy had there been a more general interest at
an earlier period. I hope, Sir, it may be convenient for you to
favour us again with a repetition of the same, followed by illustra-
tions and remarks.”

Almost immediately on his return to England, Mr Eumble
obtained work in Kensington, superintending the building of All
Saints’ Church and the laying out of the Kensington Park Estate.

In October 1853 he went out to Bombay, as assistant engineer
on the Bombay, Baroda, and Central India Eailway, then in course
of construction. An attack of fever obliged him to return on sick

Eumble.

leave to England, “where he arrived in February 1854. He next
obtained the post of engineering superintendent of the Arthington
Extension Waterworks under Mr Hawkesley, with whom he re-
mained till the completion of the work, when he received a flatter-
ing letter from Mr Alderman Hepper, chairman of the Leeds Water
Works Committee, expressing the great satisfaction of that body
with the manner in which he had conducted the works. Returning
to London, Mr Rumble experienced some difficulty in finding
employment to his taste, and was, for short periods, draughtsman
in the offices of Messrs Conybeare and Brikinshaw, the London and
South-Western Railway Company, the Admiralty, &c., till in 1857
he was appointed engineer to the Atlas Steel Works, then entirely
in the hands of Mr (now Sir) John Brown, in which capacity he was
entrusted with the conduct of many transactions requiring much
tact and diplomacy. In 1858 Mr Rumble was elected Fellow of
the Society of Engineers' in 1860 a member of the Institute of
Mechanical Engineers ; in 1861 a member of the Institute of Naval
Architects ; and in 1866 a Fellow of the Royal Microscopical Society,
in the proceedings of which body he was always deeply interested.

During these years Mr Rumble had opened an office in West-
minster, and was practising as a civil and mechanical engineer, and
was fortunate enough to secure much good work. In 1869 he paid
a second visit to the United States, and spent six months visiting
many engineering shops and acquiring a thorough knowledge of the
recent mechanical improvements. Shortly after his return to Eng-
land, Mr Rumble had the honour of two interviews with his late
Majesty the Emperor Napoleon, who was pleased to express his satis-
faction with the plans, drawings, &c., submitted for his approval.
On New Year’s Day, 1872, Mr Rumble was again in New York, and
visited the various Safe Deposit Companies in that and other cities,
with the view of obtaining information for the National Safe Deposit
Company, then about to be formed in London. He visited Phila-
delphia, Boston, Halifax, &c., and the ruins of Chicago, then scarcely
cold after the great fire, and examined the vaults and safes remain-
ing intact. He returned to London on the 28th January, and was
for the rest of the year employed in designing the safes, strong-rooms,
buildings, and other arrangements of the National Safe Deposit
Company, which were afterwards carried out under his superintend-

/

82

ence at the corner of Queen Victoria Street. The extravagance of
his partner at this time considerably involved Mr Rumble, and in
1875 he dissolved the partnership. In 1876 Mr Rumble obtained
the position of chief engineer of the Southwark and Vauxhall Water
Company. His unceasing energy and untiring industry gradually
brought this company, from the state of confusion in which he
found it, to such a state of order that the dividends rose from 2J
to 71 per cent. In 1877 he was admitted member of the Institution
of Civil Engineers. In 1878 he successfully laid a 30-inch main
under the Thames at Richmond without the aid of dams — the only
feat of the kind accomplished at that date in England. Under Mr
Rumble’s direction a trench was dredged across the bed of the river
a few feet below Richmond Bridge. The lengths of the pipe, made
on the ball and socket principle, were joined on the banks of the
river, and in the early morning of July 3rd were shipped on board
three barges strongly lashed together, carefully brought into position,
and safely lowered into the trench. When the necessary connections
at either end were made, the main was charged, and has ever since
been in full work. During the year 1879 the Directors of the
Southwark and Vauxhall Water Company determined to supplement
the supply of water derived from the Thames by sinking a well into
the chalk. In conjunction with Professors Prestwich and Ansted, Mr
Rumble selected a spot in the Manor Park, Streatham ; a trial bore-
hole was made, and in 1881 the sinking of the well begun. The
work is still in progress, but so far fully justifies the hopes formed
for its success. Struck by Mr Rumble’s manner of handling the
matter, and entirely without his knowledge, Professor Prestwich and
Professor Ansted proposed him as Eellow of the Geological Society,
into which he was admitted in December 1879. In February 1881
he was elected Eellow of the Royal Society of Edinburgh.

Towards the end of 1881 the excessive overwork and heavy
responsibilities of his position began to tell on his health, which
steadily though very gradually failed, and he developed symptoms
of pernicious anaemia which defied every effort to overcome it.
In December 1882 Sir William Jenner recommended immediate
and absolute rest of body and mind for six months. Leave of
absence being unanimously granted by the directors of the company,
various places were visited in search of health, until on the 5th

83

April 1883 lie returned to Bonchurch, Isle of Wight, where he
rapidly grew worse, and died on Saturday, 21st April, surrounded
by nearly all his family. He was buried in the Hew Churchyard,
Bonchurch, on 28th April.

Mr Rumble was twice married, and has left a large family to
mourn his loss. In business Mr Rumble was straightforward and
unerringly honest to his employers, often nervous about small
matters, but without fear in cases of grave import, when he was
always calm and self-possessed. The rapidity and clearness of his
perceptive faculties amounted almost to the gift of second sight, and
led him to form swift conclusions which rarely proved false. His
firmness in dealing with faults in those under his charge was
moderated by great kindness to his men when suffering under any
affliction, illness, or distress. He was considered by them always
more as a friend than master, and they showed their appreciation of
his goodness by presenting him with a testimonial on the celebration
of his 50th birthday, 26th December 1882. In private life Mr
Rumble’s genial spirits, shrewd observations, and witty remarks,
endeared him to a large circle of friends. Indeed, his critical con-
dition was almost to the last concealed by his courageous efforts
to appear better than he was, and thus relieve the anxiety of his
family. He possessed a most retentive memory, and had the faculty
of readily assimilating those portions of the books he read which
were likely to be useful to him in his professional work. His
travels over the greater part of Europe and America naturally en-
larged his ideas, and he drew full benefit from the varied experience
thus acquired. He had deeply studied the legal as well as the
technical points of his profession, and so was particularly well fitted
to fill the various appointments he held during his lifetime.

Joseph Liouyille. By Professor Chrystal.

Joseph Liouville was born at St Omer on the 24th March 1809.
He came of a family of Lorrainers, more than one of whom were
distinguished for talents beyond the common. Liouville’s father
held a public office under the Empire, and an elder brother, Felix
Silvestre Jean Baptiste, was a distinguished Parisian advocate.
Joseph gave early indications of mathematical ability, and entered

84

upon that stereotyped course of training which has been famous

for the nurture of so many Frenchmen of genius. At the age of

/

sixteen he entered the Ecole Polytechnique, and on leaving it in
1827 was classed as an engineer in the Department of Eoads and
Bridges. After two years he forsook engineering for the cultivation
of the higher mathematics. He speedily distinguished himself in
his chosen career; for as early as 1829 we find a paper of his
(“Demonstration d’un Theoreme d’^Dctricite Dynamique”) in the
Annales de Cliimie et de Physique; and in 1831 he became a
repetiteur, and seven years later a professor, in the Polytechnic
School. In the interval he had performed perhaps his greatest
service to his favourite science by starting in 1836 The Journal
de Mathematiques Pares et Appliquees. This journal came most
opportunely to fill the gap left by the discontinuance of the Annales
de Gergonne ; but it could scarcely have attained its brilliant success
had it not been for the many excellent qualities of its editor, whose
critical discernment, that enabled him to enter so readily into the
spirit of the works of other mathematicians, and to assist at the
dehut of so many men of distinction, — whose amiability, candour,
and freedom from national prejudice,1 — whose own inexhaustible
powers as a contributor of original memoirs, all combined to fit him
uniquely for the post which he filled so admirably for nearly forty
years.

In 1839 Liouville was elected a member of the Academy of
Sciences in succession to Lalande, and the year following he was
put upon the Board of Longitude, in whose proceedings he took a
lively interest to the end of his life. In 1852 he became a pro-
fessor in the College de France, and continued to lecture in that
capacity until about a year before his death.

If we except his continually recurring successes as a teacher and
as an investigator in the most recondite of all the sciences, and the
honours accorded to him by the scientific world in token of their
appreciation, Liouville’s public career was uneventful, as the career
of a devoted man of science usually is. On one occasion, however,
he departed from the “even tenor of his way.” In 1848, a year
of much tribulation for France, he received a flattering mark of
widely spread popular esteem by being elected a member of the
“ Constituent Assembly.” He promptly answered this call of

85

public duty, and served bis alloted time with efficiency if without
special distinction. When, however, his mandate expired, instead
of seeking re-election, he betook himself once more to the uninter-
rupted pursuit of the career for which his abilities best fitted him.

Liouville was as fortunate in his private life as he was successful
in his public career. He lived to a good old age in the happiest
domestic circumstances, until a cruel accident deprived him of his
wife. His son, a councillor in the Court of Haney, died soon after-
wards, and the aged mathematician never completely recovered from
the effects of this double bereavement. Although his health gave
way, his intellect remained unclouded ; and it was only in the
beginning of 1882 that he gave up his favourite work of lecturing
at the College de France. He still continued, however, to attend
the meetings of the Academy, but expressed to his friends his con-
sciousness that the end was near. He died on the 8th September
1882, as he himself said, “in his turn”; for, since the death of
Chasles, he had been the patriarch among European mathema-
ticians.

Some idea of the extent of Liouville’s mathematical writings may
be obtained by consulting The Catalogue of Scientific Memoirs
published by the Poyal Society of London. The entries under
Liouville’s name number 379, and cover some twelve pages. Many
of these are merely remarks made on contributions to his journal,
or notes appended to works by other mathematicians wdiich he
edited; yet, brief as they are, they frequently contain matter of
much importance. As specimens of this part of his work, we may
mention his “ Hotes on Two Letters of Mr Thomson relative to the
Employment of a Hew System of Orthogonal Coordinates in certain
Problems in the Theories of Heat and Electricity, and in the
Problem of the Distribution of Electricity on the Segment of a
Spherical Shell of Infinite Thinness” {Jour. cl. Math., xii. 1847),
in which he draws attention to the analytical and geometrical im-
portance of the method of Inversion, which had just been brought
under the notice of mathematicians by the brilliant use that
Thomson had made of it in his physical researches.

In another note {Jour. d. Math., xv. 1850) he enunciates the
important theorem that the equation

dx2 + dy2 + dz 2 = X(da2 -!- dj32 + dy2) ,

86

where x, y, z, X are functions of a, /3, y, has for its unique solution
the stereographic or inversion transformation.

The following rough analysis will give some idea of the territory
covered by his more elaborate memoirs : —

One of the earliest subjects that engaged his attention was
Generalised Differentiation (“Diffehentielles a Indices Quelconques”).
The subject is developed at considerable length in five memoirs
printed in the 13th and 15th volumes of the Journal de Vficole
Polytechnique (1832 --37).

Some of his most important work relates to the Integral Calculus,
more particularly that part of it which deals with the theory of
elliptic and other transcendental functions.

The earliest memoirs on the subject are two in the Journal de
Vfcole Polytechnique (xiv. Cah. 1833, see also Comptes Rendus,
1837), “On the Determination of Integrals whose value is
Algebraical.” He here follows up the researches of Abel on the
same subject ; and arrives, inter alia , at the following important
results : —

1. If x be any rational function of x, then fdx^-v, if algebraically
expressible at all, can be expressed in the form P ^/x, P being
rational. And, farther, that the integral fdx can always be
reduced to the form 0/ ?^/T, where T is a known rational integral
function, and 6 a rational integral function whose coefficients have

to be determined. This theorem enables us at once to find the value

*

of the integral, if it is algebraically expressible ; or else to show that
it has no finite algebraical value.

2. If y be an algebraical function of x, i.e., connected with x by
means of an equation F(a?, y) = 0, which is rational and integral in
both x and y , then, if the integral fydx is expressible explicitly
in finite terms by means of algebraic, exponential, or logarithmic
functions, it will be expressible in the form

fydx = DA log u + E log v +....+ C log w ;

where AB . . . . C are constants, and t, u, v, ... . w algebraic
functions of x.

Among the other memoirs on the present subject may be
mentioned the following : —

“ On the Elliptic Transcendents of the First and Second Species,

87

considered as Functions of their Amplitude.” Jour. Pc. Polytech.,
xiv., 1834, and Jour, de Math., v., 1840.

“On the Integration of a Class of Transcendent Functions.”
Jour, de Math., xiii., 1835.

“On a Flew Use of Elliptic Functions in Celestial Mechanics.”
Jour, de Math., i., 1836.

“ On the Classification of Transcendents, and on the Impossibility
of Expressing the Eoots of certain Equations as a Finite Function
of their Coefficients.” Jour, de Math., ii., 1837.

“ On a very Extensive Class of Quantities whose value is neither
Algebraic nor reducible to Algebraic Irrationals.” Jour, de Math.,
xvi., 1851.

Relating to the theory of differential equations, we have the
following : — -

“On the Equation of Riccati.” Jour, de VPc. Polytech ,, xiv.,
1833.

“ On a Question in the Calculus of Partial Differences.” Jour,
de Math., i., 1836.

“On the Development of Functions or Parts of Functions in
Series, whose various terms satisfy the same Differential Equation
of the Second Order containing a Variable Parameter.” Three
Memoirs. Jour, de Math., i. and ii., 1836-37.

“ On the Integration of the Equation ^ .” Jour, de VPc.

CLC CvJu

Polytech., xv., 1837.

“ On the Theory of Linear Differential Equations, and on the
Development of Functions in Series.” Jour, de Math., iii., 1838.

“ On the Integration of a Class of Differential Equations of the
Second Order explicitly Infinite Terms.” Jour, de Math., iv.,
1839.

Some of Liouville’s most important work was in the department
of applied mathematics. When, in 1834, Jacobi enunciated his
theorem that an ellipsoid with three unequal axes is a possible
figure of equilibrium for a mass of rotating fluid, and challenged the
French mathematicians to give a proof, Liouville at once published
one in the Journal de VPcole Polytechnique, xiv., 1834. He after-
wards returned to the problem, and, in continuation of the work of
Meyer on the same subject, showed that Jacobi’s form is not possible

88

unless the ratio of the angular momentum to the mass exceeds
a certain limit. — Comptes Rendas , xvi., 1843; Jour, de Math.,

1851.

In the Journal de Matliematigues for 1855 we have a farther
contribution to this branch of hydrodynamics in the memoir
entitled “ General Formulae relating to the question of the Stability
of the Equilibrium of a mass of Homogeneous Liquid rotating
uniformly about an Axis.’7 The memoir, “On a passage of the
Mecanique Celeste relating to the Theory of the Figure of the
Planets” {Jour, de Math., ii., 1837), in which he points out and
corrects an error of Laplace, should also be mentioned.

On dynamics we have three memoirs in vols. xi., xii., and xiv. of
the Journal de Mathematiques, dealing with certain cases in which
the equations of motion of a material point, or of a system of such,
can be integrated. The equations are transformed by the substitu-
tion of various systems of generalised coordinates (mostly elliptic
coordinates), and then the form of the Force Function (Potential) is
so specified that integration in finite terms shall be possible. The
third of these memoirs, which deals with a system of material
particles, is interesting mainly as regards the theory of Abelian
integrals. In addition to these there are memoirs, 11 On a particular
case of the Problem of Three Bodies,” Jour, de Math., i., 1856 ; and
“ On Developments of a chapter in Poisson’s Mecanique ,” Jour,
de Math., iii., 1858.

Liouville made several contributions to Planetary Theory, among
which which we may specially mention his memoir, “ On the Secular
Variations of the Angles between the straight lines that form the
Intersections of the Orbits of Jupiter, Saturn, and Uranus.” Jour,
de Math., iv., 1839.

In a variety of scattered notes are to be found some very important
additions to our knowledge of Theoretical Dynamics. Perhaps the
most striking of these is that “ On a Remarkable Expression of the
Quantity which in the Movement of a System of Material Particles
connected in any way is a minimum in virtue of the principle of
Least Action.” , Jour, de Math., 1856. If we take the case of a
single free particle, and use Cartesian coordinates, Liouville’s result
for the form of the integral which expresses the action is — ■

89

( .cie .d&\- , t m .doy ,

Vdz ~dy) +Vdx Xdz) +

02

where 0 is a function of xyz , which satisfies the equation

Liouville gives this theorem in terms of generalised coordinates
for any system of particles, and points out that it opens up a new
method of treatment leading readily to all the known results of
Theoretical Dynamics.

During the latter part of his life, Liouville’s researches were
almost entirely directed to the Theory of Numbers. From 1857 to
1873 we have a list of over 200 notes and memoirs on this subject,
all published in his own journal. A few occur with earlier dates,
for examples the following : —

“ On the equation Z2n — Y2n = 2XW.” Jour, do Math., v., 1840.

“ On a Theorem of the Indeterminate Analysis.” Comptes Rendus ,

x., 1840.

“ On the Two Forms x2 + y2 + z2 + t2, x2 + 2 y2 + 3 z2 -f- 6t2.” Jour,
de Math., x., 1845.

The most important of all the memoirs on this subject are the
series entitled “On some General Formuke which may be useful in
the Theory of Numbers.” Jour, de Math., vols. iii.-viii., New
Ser., 1858-1863.

Yery few of the longer memoirs are devoted to Pure Geometry ;
but many interesting and novel geometrical theorems occur in-
cidentally in Liouville’s mathematical writings. A full account of
these will be found in the third chapter of Chasles’ “ Eeport on the
Progress of Geometry in France.” — Recueil de Rapports sur VRtat
des Retires et les Pr ogres des Sciences en France, Paris, 1870.

We may mention here some of the results arrived at in two
memoirs, “ On certain general Geometrical Propositions, and on
the Theory of Elimination in Algebraical Equations (Jour. deMath.,
vi., 1841), and “Developments of a Geometrical Theorem” {Jour,
de Math., 1844). The following results among others are arrived
at : —

1. The points of contact of a geometrical surface with all the

90

tangent planes parallel to a given plane have a fixed centre of
mean position whose position is independent of the direction of the
given plane.

2. The centre of mean position of the meeting points of two
algebraical curves is also the centre of mean position of the meeting
points of the asymptotes of one of them with the other or with its
asymptotes.

3. If through the points of intersection of a curve and a circle
normals to the curve he drawn, these normals intercept on a trans-
versal through the centre of the circle segments measured from the
centre, which are such that the sum of their reciprocals is zero.

If the circle he drawn to touch the curve at P, and we take for
the transversal the normal at P, this proposition gives us a con-
struction for the centre of curvature at P.

4. Considering all the tangents to a curve parallel to a given line.
The centre of mean position of the points of contact is the centre
of mean position of the interventions of the asymptotes.

The centres of curvature corresponding to the points of contact
have the same centre of mean position as the points of contact
themselves ; the sum of all the corresponding radii of curvature is
zero, and the same is true of the sum of their inverses.

5. Considering all tangent planes to a surface parallel to a given
plane, the sum of the principal radii of curvature at the points of
contact is zero, and the same is true of the sums of their reciprocals.

The work of the scientific teacher is scarcely less important than
that of the scientific investigator, although the record of the former
is more perishable, being at best an oral tradition handed over by
the immediate disciples of the master. It would appear that in
this walk Liouville was worthy to rank with his illustrious prede-
cessor Monge, whose pupils shed such lustre on the French school
of mathematicians. M. Faye, in his funeral oration, says, “M.
Liouville was one of the most brilliant professors that ever lectured.
So lively was my youthful impression of his lectures that to this
day I have a vivid recollection of the captivating clearness that was
so peculiarly his own. Accordingly, when in later years I had the
good fortune to hear him speak at the Institute, I was the less sur-
prised at the effect which his words produced on my colleagues, who
marvelled at being able, for a moment, under his guidance, to pene-

91

trate the most difficult questions of the higher analysis. No one,
with the exception perhaps of Arago, ever produced this effect in
the same degree.”

His lectures at the College de France were attended by the elite
of French mathematicians, and doubtless did much to keep alive the
ardent spirit of pure mathematical research which still lives among
his countrymen. Among those who either were his pupils or were
indebted to his encouragement and patronage may he reckoned Le
Verrier, Hermite, Bertrand, Serret, Bour, Bonnet, Mannheim, all of
whom are or have been pillars of French science.

If we compare Liouville as an investigator with other great con-
temporaries whose rolls of achievement like his own are already
closed, we can scarcely put him in the highest rank of all, along
with Abel and Jacobi, whose fortune it was in the course of their
discoveries to open up new fields of research and create new branches
of the analytic art. Nevertheless, so profound are some of his
isolated contributions, and so elegant is all his mathematical writing,
that it will be long before the traces of his handiwork vanish from
the fabric of mathematical science ; and it seems certain that future
generations will accord him all but the highest rank in the temple
of mathematical fame.

Robert Wilson. By Professor Fleeming Jenkin, F.B.SS.

L. and E.

Mr Robert Wilson was born in 1803 at Dunbar. In 1810 he
lost his father, who was connected with the royal and mercantile
navies. This brave man, after having twice reached the wreck of
the “ Pallas ” frigate in the Dunbar life-boat, was drowned in the
third attempt to reach the ship and rescue the remainder.

Mr Robert Wilson was apprenticed to a joiner, and, like many
other distinguished Scotchmen of the same generation, he owed his
high standing as a mechanical engineer almost entirely to his natural
genius, since he does not appear to have received any special ad-
vantages in respect of education.

During his apprenticeship, and at a date considerably prior to the
successful introduction of the screw propeller into our navy, he

92

made models of boats with various forms of screw, which worked
successfully. He himself considered that the first idea of the screw
propeller had occurred to him as a mere child ; his first model was-
that of a ship 2J feet long, and a drawing which he published of
it in later life shows a very good four-bladed screw propeller ; he
attempted unsuccessfully to drive this by a windmill on the boat.
In 1821, after seeing the “Tourist” paddle steamer, he made some
further experiments, but having to leave the sea coast he dropped
the subject. In 1825 he returned to Dunbar, and again attacked
the problem, trying first four blades, then three, and then two, driven
by the main-spring of a clock. At first the screw was placed in
front of the rudder, and the sketches since published by Mr Wilson
show the exact arrangement now usually adopted. He abandoned
this plan, however, in consequence of leakage at the stern tube ; and
in order to get the opening above water line he used two single
blade right and left propellers immersed for less than half their
diameter and driven in opposite directions, being placed one behind
the other, and connected by bevel wheels.

In 1827 young Wilson was introduced to the Earl of Lauderdale,
whose son saw a small boat about 3 feet being driven in this way.
Lord Lauderdale appears to have brought the matter to the notice
of the Admiralty, but the young inventor met with no encourage-
ment in official quarters. He next exhibited his model before the
Dunbar Mechanics’ Institution. A record of the exhibition was
made in the minutes of the institution for October 18, 1827 ; and
the Edinburgh Mercury of the 29th December 1827 alludes to the
invention. The Highland Society of Scotland in 1828 appointed a
committee, which after seeing the small model made a grant of £10,
to enable Mr Wilson to have propellers made on a larger scale.
Consequently a boat 25 feet long was fitted with a pair of these
screw blades, to be driven by two men with winch handles ; the
committee, which included two captains in the Royal Navy, reported
very favourably on the performance of this boat, during a trip in
Leith Roads, lasting 17 \ minutes. The model became the property
of the Highland Society.

In 1832 a committee of the Society of Arts reported favourably
on the trial of another model 18 feet long, fitted with the same
arrangement of two blades revolving in opposite directions. The

93

prize committee of this Society awarded him a silver medal and a
prize of five sovereigns, pointing out in their report that the stern
paddles, as they call the propellers, “ can be kept altogether under
water and out of the reach of surf, and answer equally well in rough
as in smooth sea.”

Mr James Hunter of Thurston had introduced the invention suc-
cessively to the Dunbar Institute, the Highland Society, and the
Society of Arts. Notwithstanding the encouragement received from
those Societies and the support given by various influential men,
the Admiralty, to whom he again applied, declined to make any trial
of the plan, and Mr Wilson had the mortification of seeing the
simple screw introduced into the navy by Mr Smith of Hendon.

Mr Wilson was, however, by no means the first who had thought
of a screw as the propeller of a boat, and it must be admitted that
he pushed the right and left hand geared screws in preference to the
simple plan which was ultimately successful. He met with some
reward indirectly, becoming known to many influential persons as an
ingenious and able young mechanic; and ultimately in 1880 he had
the satisfaction of receiving a sum of £500 from the Admiralty for
the use of his double-action screw propeller as applied to the fish
torpedo.

In 1832 Mr Wilson was in business as an engineer in Edinburgh,
in the North Back of the Canongate. A few years afterwards he
went to Manchester, and in 1838 he was manager of the famous
Bridgewater Foundry at Patricroft. That he should, with no edu-
cational advantages, have attained this position at thirty-five years
of age, is perhaps as high a testimony to his ability as his connec-
tion with the screw propeller or even with his steam hammer itself.
It is universally admitted that the conception of the steam hammer
was due to Mr James Nasmyth, but Bobert Wilson was the
inventor of important details which he considered essential to
its success. On the one hand, we must remember that a steam
hammer at Creuzot, suggested by Mr Nasmyth’s sketch, worked suc-
cessfully with no assistance given by Mr Wilson ; but on the other
hand, there is no doubt that some details largely used in connection
with the hammer, as commonly made in England, were due wholly
or in great part to Mr Wilson. There was unfortunately some dis-
agreement between him and Mr Nasmyth on this point ; and indeed

94

it is nearly impossible, when men are working together at the im-
provement of a machine, to appraise with any exactness the precise
share of merit due to each.

The first steam hammer made in England was delivered to the
Lowmoor Iron Works in 1843. Mr Wilson left Patricroft, and
became engineer to the Lowmoor Works, where in 1853 he added
what is known as the circular-balanced valve to the original machine.
This invention was patented by Mr Wilson. In 185G, when Mr
James Nasmyth retired from business to follow the scientific pur-
suits by which he has greatly added to his reputation, Mr R Wilson
was recalled to Patricroft, where he became the managing partner of
Messrs Nasmyth, Wilson, & Co.

Mr Wilson did not take much part in local affairs, but was for
some years president of the Patricroft Mechanics’ Institution. In
1873 he was elected a Fellow of the Eoyal Society of Edinburgh.
He continued to apply himself to the management of his works
until his death, which occurred on the 28th July 1882.

A list of no less than thirty patents stand in his name, either
solely or jointly with others.

Mr Wilson will be remembered as worthy of mention among the
group of able Scotch mechanicians who, by their power of invention,
energy, and business capacity, have not only won distinction and
wealth for themselves, but have added to the resources and strength
of the empire

James Young, LL.D., F.RS. By Dr Angus Smith.

James Young was born in Glasgow, and on leaving school was
engaged for some time in a joiner’s shop. It is characteristic of
his energy that at this time he would, during his" holidays, make
long journeys on foot, having on one occasion walked as far as
Aberdeen, and on another having walked the greater part of the
way to London, visiting places of historic interest on his way. His
occupation in the joiner’s shop was the occasion of his becoming
a chemist. He attended the class of chemistry in Anderson’s
College, and his skill as a workman led to his being employed
by Professor Graham, who then taught the class, in constructing

95

pieces of apparatus for tlie experiments. By his usefulness and
intelligence he eventually became assistant to Professor Graham,
and lectured when the Professor was absent. He lield tbe assistant-
sliip for seven years, and accompanied Professor Graham to London
when the latter obtained a chair in University College. Among
liis friends at Glasgow were Dr Stenhouse, F.B.S., Dr Lyon
Playfair, and Charles Griffin, an eminent manufacturer of chemical
apparatus.

Young now engaged in the great enterprise from which he
became widely known as a public benefactor, and which was destined
to bring him both fame and profit. One Mr Oakes mentioned to Dr
Lyon Playfair that there was oil flowing from a pit at Alf reton in
Derbyshire. Dr Playfair then told this to Young, who at once
perceived what an improvement might be made in the system of
domestic lighting by the utilisation of this natural product. The
flow of petroleum, small though it was, from the source in question,
and the results obtained from it by Young, were the means of leading
the Americans to avail themselves of the vast supplies of this useful
substance that are to be found in their own continent.

The discovery, however, with which his name is most intimately
associated, was his mode of obtaining oils from coal and shale, by
which he succeeded in producing an ilium inant oil at a price which
enabled him to compete with the oil that was latterly obtained in
such quantities from the petroleum springs in America.

Young did not discover solid paraffin; two little bits had been
produced before his time ; but he saw that it could be profitably
made on a large scale, and, by the methods he introduced, hundreds
of tons of solid paraffin are now made annually, and by his
improved processes in the manufacture of this article he has
transformed the candle, as he had previously by the introduction of
petroleum transformed the lamp.

He founded a chair for the advancement of Technical or
Economic Chemistry in Anderson’s College, Glasgow, whilst he
liberally contributed to the endowment of professorships in other
branches of science in that institution.

When he worked in the laboratory of Professor Graham, solid
caustic soda, as now manufactured on a large scale, could only be
made in small quantities in silver vessels. Dr Young first made

96

it in iron vessels, and caused to be recalled an order for a silver
vessel to cost <£1500, by showing how that alkali could be prepared
in iron.

He had the degree of LL.D. conferred on him, and became a
Fellow of the Royal Society. He was elected a Fellow of this
Society on April 1st, 1861. He was Deputy-Lieutenant for Kin-
cardineshire. Though his successful enterprises had brought him
wealth, he was unostentatious in his habits, and of a kindly and
hospitable disposition. He died in May 1883.

John Miller, M.Inst.C.E.

Mr John Miller was born at Ayr on the 26th of July 1805.
He was educated at the Academy of his native town, and on
leaving it entered a solicitor’s office ; but feeling no liking for the
legal profession, he determined to abandon it for that of a Civil
Engineer. After making himself well acquainted with the theory
and practice of engineering, he became a partner of Mr Thomas
Grainger, M.Inst.C.E., whose office was in Edinburgh. Whilst
in partnership with that gentleman, he was engaged in constructing
roads in various counties in Scotland, and in the south of Ireland,
and was acting engineer for the Dundee and Arbroath Railway;
the Glasgow, Ayr, and Kilmarnock Railway ; the Edinburgh and
Glasgow ISTorth British Railway. He also designed and constructed
the North British Railway, Edinburgh to Berwick, and the Edin-
burgh and Hawick Railway ; the Dundee and Perth Railway ; the
Stirling and Dunfermline Railway. Mr Miller was also engineer
for many other lines, both in Scotland and England. In November
1845 he deposited in Parliament plans for upwards of 1500 miles
of railway.

On the above railways there are probably some of the finest
viaducts in Great Britain, notably the Almond Valley Viaduct,
consisting of 46 arches of 50-feet span ; the Dunglass Viaduct, the
centre arch of which has a span of 135 feet; whilst the centre arch
of the Ballochmyle Viaduct has a span of 180 feet. Mr Miller,
however, always considered the Lugar Viaduct, with nine arches of

97

50-feet span, and four of 30-feet span, as his greatest work. The
rails of that viaduct are 150 feet above the Eiver Lugar.

Mr Miller retired from the profession of Civil Engineer in 1850.
In 1868 he was returned to Parliament as one of the members for
the city of Edinburgh, but lost his seat at the General Election in
1874. He purchased the estates of Leithenhopes in Peeblesshire,
and Drumlithie in Kincardineshire, and devoted a great part of his
time to improving them. He died on the 8th May 1883.

Mr Miller at the time of his death was Senior Member of the
Institution of Civil Engineers, and was elected a Fellow of this
Society in 1841.

Charles Adolph Wurtz.

Charles Adolph Wurtz was born on November 26, 1817, at
Wolfheim, in Alsace. He studied at the University of Strasburg,
where he completed the medical curriculum by taking the Doctor’s
degree in 1843. From Strasburg he went to Paris, where he
occupied several positions successively, until he became in 1883
Professor at the Ecole de Medicine; and in 1866 he was made
Dean of the Faculty. In 1867 he was elected member de l’lnstitut,
in preference to Berthelot, who was his only serious opponent. He
died on the 12th May 1884, having only three weeks previously
pronounced a brilliant and affectionate eloge at the tomb of his
great master Dumas, whose successor as perpetual Secretary of the
Academy he was, on all sides, designated to be.

Few chemists have done more or more remarkable work than
Wurtz. His first publication is on the nature of hypophosphorous
acid, which he explained ; and in the course of his studies on the
compounds of phosphorus he discovered the oxychloride. In hydride
of copper he discovered the first definite combination of hydrogen
with a metallic body. In 1848 he made perhaps his most import-
ant discovery, namely, that of the compound ammonias, which did
so much to assist in establishing the type-theory of his countryman
and contemporary Gerhardt. It was extended by his discovery of
glycol and the consequent introduction of the idea of polyatomic
alcohols. The controversy on the constitution of lactic acid, in

9

9

98

which. Wurtz took an important part, had the effect of clearing up
the distinction between the atomicity and the basicity of an acid.
In 1855 he discovered the mixed alcoholic radicals by a method
which has since become a standard one for the synthesis of
hydrocarbons. His researches on aldol , a body uniting in itself
the properties of an alcohol and an aldehyde, bring us down to the
present date.

It would he impossible, in a notice of reasonable length, to give
any adequate idea of the importance of the work done by Wurtz
during the forty years of his active life of investigation, and it
would he equally impossible adequately to appreciate the far-
reaching effect which the school which he founded around him has
had in the development of modern chemistry. Many of his most
illustrious pupils remained to the last workers in his laboratory,
influenced by the spirit of enlightenment with which he inspired
all who came in contact with him. The personal charm which
Wurtz exercised on all who were associated with him cannot he
better expressed than in the words spoken at his grave by his
distinguished pupil and attached friend Friedel. After extolling
his rare powers as a lecturer, he says — “ We see him in his labora-
tory, receiving with unwearying kindness even the humblest of his
pupils, interesting himself in his work, and discussing his ideas as
with an equal, sowing his ideas broadcast, and as happy and proud
of a discovery made by one of his pupils as he was modest and
unassertive of his own. Singularly open to new ideas, and afraid
of no scientific speculation, however hold, provided it received the
sanction of experiment, he was peculiarly fitted to promote the
progress of science, and to lead it over firm and solid ground. It
wras owing to these rare qualities that he attracted so many chemists,
both French and foreign, to his laboratory. Of these many in
their turn have become masters, and all will unite in saying that
the time which they passed in daily association with Wurtz counts
amongst the happiest and most fruitful of their lives.”

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Sir A. Grant.

By the death of Sir A. Grant on the 30th November 1884 the
Royal Society of Edinburgh lost one of its Vice-Presidents, who
took a constant interest in its proceedings ; the University lost a
Principal who for sixteen years administered its affairs with remark-
able ability and success, and who has left a more enduring mark on
its history than any Principal during the present century; and the
cause of liberal education in Scotland lost one of its most enlightened
and consistent supporters. Although of Scottish extraction, he was,
unlike all previous Principals of the University, neither born nor
educated in Scotland; and when invited at the age of forty-two to
assume his position in Edinburgh, he had already gained distinction,
in two widely separate spheres of usefulness, as a scholar and writer
on philosophy, as a teacher and lecturer, and as an administrator
of education. Erom the time when his own University course wTas
finished, his whole life was devoted to the practical work or to the
organisation and administration of education : first, during ten years,
from 1849 to 1859, in the University of Oxford; next, for nine
years, from 1859 to 1868, in the Presidencies of Madras and
Bombay; and finally, for sixteen years, from 1868 to 1884, in the
University of Edinburgh. In Oxford and in India, as well as in
Edinburgh, his influence is still felt and his loss regretted by many
friends.

By birth he belonged, on the father’s side, to an old Scottish
family, the Grants of Dalvey on Spey side. His mother was of mixed
French and Scottish extraction, and was the daughter of a planter
in the Danish West Indian Island of Santa Cruz. The family
estate in Morayshire had been sold by his grandfather, and the
whole fortune, which had been invested in West India property,
had been lost before Sir Alexander succeeded his father as 8th
Baronet in 1858. He was born in New York on the 13th
September 1826, and passed two or three years of his childhood in
the West Indies. The principal part of his school education was
received at Harrow, which he entered in 1839, and left as head of
the school in 1845. In November 1844 he had been elected to a
Balliol scholarship, and he entered on residence at Oxford in the

100

Easter term of the following year. He came up to the University
an excellent classical scholar of the type produced by the great
English public schools, and with the social tastes and disposition
which are fostered in those schools. He was especially eminent in
Greek and Latin composition, and the faculty of lucid and graceful
statement developed by these accomplishments proved of invaluable
service to him in the various administrative duties which he was
called upon in after life to perform. He combined with his
scholarly attainments an appreciative taste for modern literature, and
especially for the great English poets, and his interest in the philo-
sophical, which are combined with the more strictly literary, studies
of the University, and in the speculative questions by which Oxford
life was powerfully stirred in the years succeeding the great religious
movement of which Dr Newman was the centre, was soon awakened.
He read widely and discriminatingly, but with no special eye for
examinations ; and thus it happened that his name is remembered
among those of a select few (including Clough, Mr M. Arnold, Mr
Eroude, Mr Freeman, M. Pattison, and others), who, by their
subsequent eminence, justified the opinion that the second class in
Litterce Humaniores often contained men of greater power and
promise, if of less minute knowledge, than the first. He graduated
in 1848, and in the following year he was elected, out of a large
number of candidates, to an Oriel Fellowship. As circumstances
had made it necessary for him to support himself from this time
forward by his own exertions, he immediately became one of the
private tutors, a class somewhat like that of the privat-docenten in
the German Universities, who performed a much more important
part in Oxford education in those days than they do at present.
The preparation of the best men for their final examination in philo-
sophy was almost entirely in their hands. Although most of them
were men of older standing, he very soon was recognised as the
most eminent of the body, and amongst his pupils were several men
who have since obtained distinction in various walks of life, who
acknowledged the benefit they derived from his instruction. He
lived with his pupils on the most easy and familiar footing, and
attached them to himself by his friendliness and social geniality.
At the same time, he taught his subject — the Nicomachean Ethics of
Aristotle — more thoroughly than it had been taught in England

101

before bis day. While fully realising the living interest which the
book, regarded as a treatise on human nature, has for all times, he
was one of the first to recognise the truth, now universally acted
upon, that it was to be interpreted, not vaguely and arbitrarily in
accordance with any theological bias or with the moral sentiment
of our own time, but historically in accordance with the evolution
of Greek thought and the conditions of Greek life, and with the
whole system of the Aristotelian philosophy. The mature result of
his study and teaching was his edition of the Ethics of Aristotle,
the first volume of which was first published in 1857. It is on
this work, of which a fourth edition appeared a few weeks before his
death, that his reputation as a scholar and a writer on philosophy
mainly rests. Though it is more than a quarter of a century since
it was given to the world, and though during all that time the
subject has been assiduously studied and taught at Oxford, his
edition still remains the standard one, and among English scholars
his name is as familiarly associated with the Ethics of Aristotle
as that of Conington with Virgil, and of Munro with Lucretius. In
proof of the estimate still formed of its merits by those who are
constantly using it, I may be allowed to quote the words of one of
the most competent among the younger tutors at Oxford. While
admitting that the work is exposed to some criticism in the
present day, he adds — “We are too apt not to realise how much
such a work has done directly and indirectly for the appreciation of
Greek philosophy in this country. It was the first and it still
remains the only attempt in any language to unite a scholarly study
of the very difficult text with a literary and philosophical apprecia-
tion of the treatise in its relation to the whole history of Greek
thought. Certainly no one of the German editions attempts any-
thing so extensive, and only one of them (in Latin) has a philo-
sophical value.” He goes on a few sentences later — “ In Edinburgh
his name will always be associated with a most brilliant period in
the history of the University. Throughout the world of English-
speaking scholars he will be remembered as one of those who have
set before themselves and others an ideal of scholarship which
excludes neither philosophical thinking nor a regard for literary
excellence. We are sometimes apt to boast that this is a specially
English or even a specially Oxonian ideal ; we are too often

102

reminded that few even endeavour to attain it, and any of these few
can ill be missed.” *

It is no paradox to say that even the defects of the work, such as
they are, as well as the great merits which make it the best intro-
duction to the study of Greek ethical philosophy, are connected
with what was his greatest quality — the largeness and breadth of his
nature. It was not possible for him to become a pure specialist —
a mere scholar, or abstract thinker, or man of letters. A complete
change in his circumstances, which took place shortly after the
publication of this work, made it clear that he was rather a man of
great general capacity, fitted to obtain success and eminence in any
important province of life, than one born with the special bent and
genius of a scholar or philosopher. During the last twenty-five
years of his life it was to the sphere of action more than to that of
thought and research that his energies were directed ; and, however
great may have been the loss to the University of Oxford, and to
classical learning, caused by this diversion of his powers, there is
little doubt that his own capacities were expanded by it, and that
he was enabled to do more useful work in the world than if he had
been appointed to the Professorship of Moral Philosophy in Oxford,
for which he was an unsuccessful candidate in the year 1859. His
marriage in that year with the daughter of Professor Perrier of St
Andrews, and the grand- daughter of “ Christopher North,” was the
immediate cause of his seeking a new career in India, and was
probably the remote cause of his final connection with the University
of Edinburgh. He accompanied Sir Charles Trevelyan to Madras,
and began his career in that Presidency as Inspector of Native
Schools. Prom Madras he was soon called to the Presidency of
Bombay, where in rapid succession he filled the posts of Professor
of History and Political Economy in the Elphinstone College, of
Principal of that College, of Vice-Chancellor of the University of
Bombay, of Director of Public Instruction, and of Member of the
Legislative Council in the Presidency. The best work of his life
was probably that which he gave to India, during the nine years of
his active employment there. His name was soon as familiarly
associated with Bombay as it had been, and still is, with the Ethics
of Aristotle. An important Government minute of the 3rd October

* Oxford Magazine, January 21, 1885.

103

1868, after his appointment as Principal of the University of Edin-
burgh, affirms that he had “ undoubtedly set his mark on the history
of education in India.” It adds — “ While supporting the complete
independence of the University, he used it as the crown of the
Government educational system.” In a despatch written about the
same time to the Governor of the Presidency, the Duke of Argyll,
then Secretary of State for India, speaks of “ the solidity and
reality of his administration,” and concludes with expressing “con-
currence in the just remarks recorded by your Excellency in Council,
relative to the very valuable services rendered by Sir A. Grant to
the cause of education in India.” A minute of the University of
Bombay, of the same time, speaks of “ his ability in administration,”
of “ his important suggestions and effective aid in the revision of
the bye-laws of the University, especially as bearing on the exten-
sion, arrangement, and balance of studies,” of “ his temper and tact
when discharging the duties of the chair,” and of “ his extensive
influence with the public in the matter of endowments and bene-
ficiaries.” Great as his intellectual gifts of organisation and adminis-
tration were, the power of his personality was still more remarkable.
Along with his general interest in Indian education he combined
a warm personal interest in individuals, and the aid which he
afforded to the advancement of able and deserving men among them
is still gratefully remembered by natives of India.

He entered on his duties in Edinburgh in the beginning of the winter
session of 1868-69, and continued during the remainder of his life to
perform them with ever-growing capacity and knowledge, and with
the most loyal attachment to the institution to which he came as a
complete stranger. With his sound practical sagacity he combined
a high imaginative faculty, and while minutely attending to and
mastering the details of business, he set constantly before himself the
ideal of what the University ought to be as a nursery of intellect and
character, and as an organ for the elevation of national life. He
gained the entire confidence of his colleagues in the Senatus,
whether they agreed or disagreed with him on particular questions,
by the impression he produced of absolute devotion to the good of
the University. He gained the regard and admiration of the students
by his frank, dignified, and cordial bearing in all his relations with
them, and by his genuine sympathy with them in their aspirations,

104

their work, and their amusements. He wished every one to feel as
he did, proud of his University, and determined to uphold its credit
by intellectual effort and by honourable conduct.

Although the pursuits of the last twenty-five years of his life
tended to force him into the groove of action, rather than of letters,
yet they were by no means barren in literary results. In India,
besides delivering several interesting addresses, which may still be
read with pleasure and instruction, he was a frequent contributor to
the English newspapers published in the Presidency. His recently
published History of the University of Edinburgh is the most im-
portant literary product of his later years. Inspired and pervaded by
his idealising love of his University, it is a work at once of learned
research and of strong human interest in its record of many of those
by whom the chairs in the University were filled at various times.
His Lives of Aristotle and of Xenophon, undertaken for Blackwood’s
series of Ancient Classics, are written with scholarly taste and
simplicity, and with that insight and vivacity of feeling which,
without vulgarising it, can invest an ancient theme with modern
meaning. His last address to the students, delivered only a few
weeks before his death, affords more than his more elaborate works a
true image of the man, in his intellectual power, his serious enthusiasm,
his large-heartedness, the dignity and simplicity of his bearing. It
produces an indefinable impression of greatness. His colleagues in
the University, certainly, will always think of him as their “ greatest,
yet with least pretence.”

Xo record of his career would be complete without some reference
to the services which he rendered when a member of the Scotch
Education Board. His most eminent colleague on that Board ascribes
to him the chief credit in preparing the First Scotch Code, which
was “ a great improvement on anything of the kind previously pre-
pared.” He adds — “ My own clear impression is, that no man ever
knew about educational organisation from top to bottom better than
Grant.” His eminence as a scholar and administrator was recog-
nised by the Universities of Oxford and Cambridge, of Edinburgh
and Glasgow, which conferred on him their honorary degrees of
D.C.L. and LL.D. The most enduring monument of his Principal-
ship will be the Xew University Buildings, which owe more to his
active services and his personal influence than to any other in-

105

strumentality. The great Tercentenary celebration of 1884 will,
through all the future history of the University, be associated with
his name. The conception of the celebration was altogether his,
and its successful realisation owed more to him than to any one else.
The shock of his unexpected death, on the 30th of November
1884, following so quickly on the memorable events of the pre-
ceding April, is still fresh in the memory of his colleagues in the
University and in this Society.

James Napier. By Bobert R. Tatlock, F.I.C., F.C.S., F.R.S.E.

James Napier was born in the village of Partick, one of the
suburbs of Glasgow, in 1810. His father was a hand-loom weaver
in humble circumstances, and his mother was a sempstress. At the
age of seven or thereby he was sent to a small day school in the
village, kept by Mr Neil, a medical student, where in less than
twelve months he learned to read with comparative fluency. On
account of the straitened means of his parents, however, he was
then sent to work, and found employment as a “tearer” in a calico
printing works, his remuneration being Is. 3d. per week. When
he was between twelve and thirteen years of age he was put to his
father’s trade, and, being conscious of the limited character of his
education, he endeavoured successfully to earn a little money, by
extraneous efforts of various kinds, to enable him to attend a night
school for two winters, by which his writing and knowledge of
arithmetic were greatly improved.

Owing to dulness in the weaving trade, he betook himself to that
of a dyer, and was employed by the Messrs Gilchrist at their works,
Meadowside, Partick, where, at the age of eighteen, he was promoted
to the post of foreman “piece dyer,” his wages being then 11s. per
week. When only twenty-one years of age he married, on the
slender income of 13s. per week. About the year 1833, on account
of the dull condition of the dyeing trade, a trades-union was formed
among the workmen, in which he joined, and would not be dissuaded,
even by offers of extra remuneration from his employers, in conse-
quence of which he was dismissed. He was next employed as a

106

dyer at Glasgow Field Bleach Works, where he remained for four
years, after which, his health failing, he endeavoured to earn a sub-
sistence by keeping a lending library, but without success, and
ultimately returned to the dye-works where he was first employed,
in the capacity of a clerk. Prior to this Mr Napier had written an
essay of great excellence on dyeing, which had attracted the notice
of the late Mr John Joseph Griffin, who combined the business of
a dealer in chemical and philosophical apparatus with that of a
publisher, in Glasgow, and afterwards in London. He accepted an
appointment in this establishment to prepare and bottle chemical
reagents, and to make up apparatus — an employment which he
found very congenial, as in some autobiographical notes which he
has left, he says : — £<r My position brought me into contact with all
sorts of inquirers ; people in different trades came, not only to buy
apparatus, but to question about difficulties. I had access to all
kinds of chemistry books, and gave willing search to help them, thus
gaining a knowledge of different trades ; but I wanted system, and
to improve myself in this respect, I invited the members of our
Mutual Instruction Society to my house, and went through a course
of chemistry, following Graham’s work. By these means, and by
nightly study, I obtained a pretty good knowledge of the principles
of the science.” It was, doubtless, while in this employment that
he made the acquaintance of the late Dr James Young, F.R.S., of
Kelly, at that time laboratory assistant to the late Professor Graham,
of Anderson’s College, Glasgow, who afterwards became Master of
the Mint, which resulted in a life-long and most friendly intimacy.
In the year 1839 the results obtained by Mr Thomas Spencer in the
new art of electrotyping and electro-metallurgy excited much interest,
and Mr Napier, on Mr Griffin’s account, carried out some laborious
and important work with the object of applying the art to useful
purposes, such as copying woodcuts and engraving plates, &c.; and
in 1842 he was appointed to take a leading position in the London
electroplating works of Messrs Elkington & Mason, where, it is
needless to say, he discharged his duties in a manner which reflected
the highest credit upon him, some of the work which he turned out
being truly very tine. The interest he took in the process of copper-
smelting led to the discovery of a great improvement in the refining
and granulation of copper, by the application of soda ash, in which

107

he encountered much opposition, notwithstanding which the process
was taken up and wrought by a private company in 1847, who
acquired the Spitty Works at Swansea for the purpose, the result
of which was that at the end of the first year the hooks showed a
net profit amounting to <£19,000, or upwards of 55 per cent., £900
of which fell to Mr Napier’s share. Tn 1844 he devised and
described a process for extracting silver from its ores by calcination
with common salt, which was, in principle, identical with the
“ wet process,” devised by Mr William Henderson many years later,
for the extraction of copper from poor ores. He also, some time there-
after, patented a method for the removal of tin, antimony, arsenic,
&c., from poor Cornish ores. In 1852 he revised and extended
some magazine papers which he had previously published, and they
were published and issued by Messrs Griffin & Co., under the title
of A Manual of the Art of Dyeing. This was succeeded by his
well-known hook entitled A Manual of Electro-Metallurgy , which
in 1860 reached a fourth edition.

Mr Napier returned to Glasgow in 1849, and to his native place — -
Partick — in 1852, where he engaged in literary work and interested
himself in its sanitary condition, analysing its potable waters, and
instigating the movement which led to Partick being made a Police
Burgh for its own local government. For several years he thus
occupied himself, but retained his laboratory, employing himself as
an investigating and consulting chemist. In 1860 he was requested
by the Marquis of Breadalbane to visit and inspect a copper mine
on his estate at Killin, on the south side of Loch Tay, which had
been worked for years without profit, the result of which was that the
works were started on the spot, under Mr Napier’s superintendence,
for preparation of copper regulus and the manufacture of sulphuric
acid and artificial manures, but owing to the failure in the quality
of the ore from the mine these were soon suspended. In 1861 he
returned to Glasgow, and commenced business as consulting chemist,
where he continued till 1864, when he erected sulphuric acid works
at Vinegar Hill, near Glasgow, the operations of which occupied his
time and attention for six or seven years. Being then relieved of
the active management by his son, he returned to his literary
pursuits, and soon produced his Notes and Reminiscences of
Partick (1873), Ancient Workers in Metals , Manufacturing

108

Arts of Ancient Times (1879), and Old Ballad Folk-Lore
(1879).

From the annexed list of his papers it will be seen that Mr
Napier has earned for himself a recognised position in general
science, and particularly in the special branches of technical
chemistry and metallurgical science which were so congenial to
him ; and that, with a more liberal education, his mental activity
and aptitude for scientific study would have won for him a great
name in the scientific world.

Mr Napier was elected a Fellow of this Society in 1874. He
was also a Fellow of the Chemical Society, and took much active
interest in the local scientific societies with which he was connected,
particularly the Philosophical, Natural History, and Archaeological
Societies of Glasgow. He was likewise a zealous worker in the
management of Anderson’s College, and of the “ Young” Technical
School, Glasgow, of which he was a trustee. The loss of his wife
in the year 1881 proved a heavy blow to him, from which he never
fully recovered; and on 1st December 1884 he terminated an
active and useful life at the age of seventy-four, esteemed and
respected by all who knew him.

Bibliography.

1. On the Solubility of the Metals in Persulphate and Perchloride of Iron.

Chem. Soc. Mem., ii., 1843-45, pp. 16-20; Phil. Mag., xxiv., 1884,
pp. 365-370.

2. Observations upon the Decomposition of the Double Cyanides by an

Electric Current. Chem. Soc. Mem., ii., 1843-45, pp. 158-161 ; Phil.
Mag., xxv., 1844, pp. 779-881.

3. Observations on the Decomposition of Metallic Salts by an Electric

Current. [1845.] Chem. Soc. Mem., ii., 1843-45, pp. 255-260 ;
Archives de VElectr., v., 1845, pp. 159-167 ; Phil. Mag., xxvi., 1845,
pp. 211-217.

4. Electricity Developed in Manufacturing Processes. Walker s Eledr. Mag.,

i., 1845, pp. 499-502.

5. On Electrical Endosmose. Chem. Soc. Mem., iii. , 1845-48, pp. 28-38 ;

Bibl. Univ. Archives, ii., 1846, pp. 245-354 ; Phil. Mag., xxix., 1846,

pp. 10-21.

6. On the Unequal Decomposition of Electrolytes, and the Theory of

Electrolysis. [1846.] Chem,. Soc. Mem., iii., 1846-48, pp. 47-53 ;
Phil. Mag., xxix. pp. 92-99.

7. On Copper Sheathing and the probable Cause of its Deterioration. Glas.

Phil. Soc. Proc., iii., 1848-53, pp. 161-173.

8. The Effects upon Health of inhaling the Fumes of Cyanide of Potassium

Solutions. Glas. Phil. Soc. Proc., iii., 1848-53, pp. 188-192.

109

9. Remarks upon Mineral Yeins and Water- Worn Stones. Glas. Phil. Soc.
Proc., iii., 1848-53, pp. 231-238.

10. Remarks upon Sandstones used for Buildings, &c. Glas. Phil. Soc. Proc.,

iii., 1848-53, pp. 313-322.

11. On Spurious Coins. Glas. Phil. Soc. Proc., iii., 1848-53, pp. 344-350.

12. On Copper-Smelting. Phil. Mag., iv., 1852, pp. 45-59, 262-271, 345-355,

453-465 ; v., 1853, pp. 30-39, 175-184, 345-354, 486-493.

13. Observations on the Trap Dykes in the Sea-Shore between the Bays of

Brodick and Lamlash, in Arran. Edin. New Phil. Jour., ii., 1855,
pp. 81-83.

14. On the Action of Heat on Gold, and its Alloy with Copper. Chem. Soc.

Jour., x., 1858, pp. 229-233.

15. On Metallic Deposits found in two Chimneys attached to Reverberatory

Furnaces, one being used for melting an Alloy of Silver and Copper
and the other an Alloy of Silver and Gold. Chem. Soc. Jour., xi.,

1859, pp. 168-173.

16. On Incrustations in Steam Boilers. 1858. Glas. Phil. Soc. Proc., iv.,

1860, pp. 191-198. •

17. Analysis of a small portion of Stone fused by Lightning. May 1854.

Glas. Phil. Soc. Proc., iv. , 1860, p. 206.

18. On Trap Dykes between Condon and the south end of Whiting Bay, Island

of Arran. Glas. Phil. Soc. Proc., iv., 1860, pp. 321-324.

19. Black and Clayband Ironstones ; their Composition and Yaluation.

Glas. Phil. Soc. Proc., v., 1864, pp. 210-217.

20. On the Cyanides of the Metals, and their Combination with Cyanide of

Potassium. Chem. Soc. Mem., ii., 1843-45, pp. 82-96 ; Phil. Mag.,
xxv., 1844, pp. 56-71. (This paper was prepared conjointly by Mr
papier and Mr C. J. O. Glassford.)

21. On the Dynamics of the Galvanic Battery. Phil. Mag., xxii., 1864,

pp. 52-54.

22. Notes upon Dyeing and Dyed Colours in Ancient Times. Glas. Phil. Soc.

Proc., v., 1864, pp. 175-197.

23. On Ancient Mortars and Cement. Glas. Phil. Soc. Proc., 1867, x. pp.

86-98.

24. Notes on Partick in Olden Times. Glas. Archoeol. Soc. Trans., i., 1886,

pp. 256-271.

25. On some Popular Superstitions common in Partick forty years ago. Glas.

Archoeol. Soc. Trans., i., 1868, pp. 391-398.

26. The Farmer and the Chemist. Glas. Phil. Soc. Proc.,ry ii., 1871, pp. 387—

398.

27. On the Results of some Experiments on the Leaves of various Trees and

Shrubs. Glas. Nat. His. Soc. Proc., iii., 1878, pp. 105, 106.

28. Miscellaneous Notes in Natural History. Glas. Nat. His. Soc. Proc., iii.,

1878, pp. 194, 195.

Communications to the “Sanitary Journal.”

1. On Damp Walls and Newly Built Houses. Nov. 1, 1876, i. p. 156.

2. The best Means of Drying the Walls of Newly Built Houses. Dec. 1,

1876, i. p. 162.

3. The Rivers Pollution Scheme. April 1, 1879, iii. p. 53.

4. Water Supply for Yillas. Oct. 1, 1880, iv. p. 255.

no

Professor Thomas Croxen Archer. By J. D. Marwick,

LL.D.

Thomas Croxen Archer, Director of the Edinburgh Museum of
Science and Art, was born in Northamptonshire in 1817, and was
educated in London as a surgeon. When about twenty-five years
of age, however, he received an appointment in the Import Depart-
ment of the Customs at Liverpool, and in that service he remained,
receiving successive promotions, till 1856. Having a natural taste
for botany, which he had zealously cultivated as a branch of his
medical studies, Mr Archer took a keen scientific interest in all the
vegetable imports of Liverpool, and when the authorities of that
city were invited by the promoters of the Great Exhibition of 1851
to contribute to its success, and were puzzled to know how best to
do so, Mr Archer proposed a scheme which met with universal
acceptance. His suggestion was that Liverpool should be repre-
sented by a complete and systematically arranged collection of
specimens of all the mineral, animal, and vegetable importations
into the Mersey, and this scheme was admirably carried into effect
under his own direction. He was subsequently invited to write one
of the official reports on the Exhibition. Th,e services rendered by
him in connection with this collection, and also as agent in Liver-
pool for the Exhibition, were recognised by a medal ; and in the
following year he was appointed agent in Liverpool for the Crystal
Palace Company, who marked their sense of the value of his work
for it during 1852-3 by conferring three medals upon him. In the
latter of these years Mr Archer contributed a volume on “ Economic
Botany” to a series of popular works on Natural History published
by Lowell, Reeve, & Co., of London. About this time Sir
William Hooker was forming the great museum of Economic Botany
at Kew, and had much correspondence on the subject with Mr
Archer, who afterwards set himself, with characteristic energy, to
make a somewhat similar, though smaller, collection for the Royal
Institution at Liverpool. His interest in botany also attracted him
to the Botanic Gardens of the city, in which he took an active
concern, and led to many excursions in the neighbouring counties,

Ill

in the pursuit of his favourite study. He was appointed Lecturer
on Botany in the Medical School at Liverpool, and afterwards
Professor of Botany in Queen’s College and in Blackburn College
of the same city.

On 10th May 1860, Mr Archer became Director of the Edin-
burgh Industrial Museum, a name which was subsequently, by
order of the Committee of Council on Education, changed into
that of the Edinburgh Museum of Science and Art. The office
had become vacant by the death of Professor George Wilson, who
had done much, by the charm of his persuasive advocacy, to com-
mend the objects of the museum to the public. But the state of his
health, and the want of any suitable building in which the necessary
collections could be exhibited, prevented much progress being made.
Shortly after Mr Archer’s appointment, however, the requisite steps
were taken by the Government to proceed with the erection of
a suitable museum, and in 1861 the foundation stone of the
present building was laid by the lamented Prince Consort. To
all the work connected with that ceremony — with the subsequent
completion of the structure — with the transference to it of the
collection made by Professor George Wilson, and also of his own
private collection of upwards of two hundred specimens, chiefly

of vegetable products used in the Arts — and with the supple-

*

menting and completing of these collections, Mr Archer devoted
himself with untiring energy. What written appeals did not
succeed in obtaining for the museum, personal solicitation at the
various centres of industry rarely failed to secure. The enthusiasm
of the director carried everything before it, and year after year he
went over various countries in Europe, visiting important seats of
manufacture and noteworthy art collections, and carrying back with
him, as purchases or free gifts, the results of his untiring labours to
enrich the museum at Edinburgh or South Kensington. When the
eastern wing of the present building was completed, everything that
Mr Archer could do to hasten on the extension of the central portion
was done, and when the central portion was completed, no effort on
his part was spared to induce the Government to complete the entire
structure by the erection of the west wing now in progress. This
he had the satisfaction of seeing commenced. In the arrangement
and classification of the museum, as it now exists, and in the

112

completeness with which every exhibit is made to tell its own
story to the student, there remains, and will, it is to be hoped long
remain, the evidence of Mr Archer’s loving care and devotion to his
work.

Mr Archer was appointed one of the jurors of the International
Exhibition of 1862, and, along with Mr Peterson of the office of
Crown Domains in St Petersburg, wrote an official report on the
vegetable substances used in manufactures shown at that Exhibition.
His services in relation to this work were acknowledged by a medal;
and in the following year he was appointed a Corresponding Mem-
ber of the Ministry of Crown Domains of Russia. He acted as
Associate Commissioner at the Paris Universal Exhibition of 1867,
and reported on the class of exhibits connected with forest products,
for which report he received three medals. In 1870 he reported on
the International Exhibition in London; and in 1871 he was com-
missioned by the British Government to attend the Exhibition at
Moscow and Copenhagen. He was appointed a member of the
Committee for Selection of the annual International Exhibition of
1872, for which Exhibition also he acted as Deputy Commissioner
for Scotland. In 1873 he was appointed a juror at the Vienna
Exhibition held in that year, and he prepared several reports for the
British Commission in connection with it. His services at this
Exhibition were acknowledged by the decoration of a Commander
of the Order of Franz- Joseph of Austria. In the same year he
was awarded the gold medal of the Russian Ministry of Crown
Domains; and, in recognition of literary and scientific merit, was
appointed Chevalier of the Order of St Hiago of Portugal. In
1876 Mr Archer was appointed Executive Commissioner for Great
Britain and Ireland, along with Colonel Sandford, at the Phila-
delphia Exhibition of 1876, and in recognition of this service he
was awarded a medal. In 1878 he acted as one of the jurors in
the Paris Universal Exhibition of that year.

Mr Archer was connected with many literary and scientific
societies. He was a director of the Royal Institution of Liverpool,
a life member of the Liverpool Literary and Philosophical Society,
an honorary member of the Liverpool Chemists’ Association, a
member of the Liverpool Microscopical Society (of which he was for
several years secretary), an honorary member of the Birkenhead

113

Philosophical Society, a president of the Botanical Society of Edin-
burgh, a member of Council of the Royal Society of Edinburgh,
and a member of the Royal Society Club, a president of the Royal
Scottish Society of Arts, a secretary of the Edinburgh Microscopical
Society, an honorary member of the Edinburgh Geological Society,
a fellow of the Society of Antiquaries of Scotland, an honorary presi-
dent of the Edinburgh Association of Science and Art, an honorary
member of the Pharmaceutical Society of Great Britain, and an
honorary member of the Pharmaceutical Society of Austria, the
Philosophical Society of America, Philadelphia, and the Eranklin
Institute of Pennsylvania.

He was a liberal contributor to the Transactions of the various
literary and philosophical societies with which he was connected, to
the Art Journal , and Journal of the Society of Arts , to the eighth
edition of the Encyclopaedia Britannica, to Chambers's Encyclopaedia ,
and to other works.

Called frequently to London on the business of his Department,
Mr Archer had occasion to be there in February 1885, and had
arranged to return to Edinburgh on the 19th of that month. Two
of his daughters had joined him in the Midland Grand Hotel, and
were proceeding to breakfast, intending afterwards to accompany
him to the railway station, when, without premonition of any kind,
he fell down in the hall and expired. He was predeceased in
1879 by his wife, and is survived by one son and four daughters.
His eldest son and a daughter predeceased him.

Mr Archer was a man of great energy of character, and of wide
and varied information. Throughout life he enjoyed exceptional
facilities for becoming acquainted with an infinite variety of men
and things in this country and abroad, and these facilities he utilised
to the fullest extent. His retentive memory supplied him with
inexhaustible sources of interesting conversation, and — underlying
occasional apparent sharpness of manner — there were unfailing
kindness, a high sense of honour, and, to those who knew him
best, a depth and tenderness of feeling which were irresistibly
attractive.

The writer of the present notice enjoyed Mr Archer’s friendship for
five-and-twenty years. He had the privilege of accompanying him
in travels abroad, and enjoying his close friendship at home, and

h

114

the result of that long and intimate knowledge entitles him to say
that no more faithful public servant, no truer or more reliable
friend, could be desired than Mr Archer was.

P.S. — Since this notice was prepared the writer has had placed
in his hands the following letter from Colonel Donnelly, the
secretary of the Science and Art Department, to Mr Archer’s
son : —

Science and Art Department.

3 rd March 1886.

Sir, — The Lords of Committee of Council on Education have
directed me to convey to you and the other members of his family
their sense of the loss which has been sustained by the Science
and Art Department by the death of Professor Archer.

My Lords deeply regret losing so valuable an officer; and, in
desiring me to express their condolence with those who are mourn-
xng for him, have instructed me to place on record their appreciation
of the exceptional zeal, energy, and ability with which he at all
times discharged the important duties intrusted to him at the Edin-
burgh Museum of Science and Art.

They consider that it was mainly owing to his exertions that this
Museum, which may almost be said to have been created by him,
attained such popularity and importance since it was opened to the
public under his direction in 1860. — I am, Sir, your obedient
servant,

(Signed) W. D. Donnelly.

Cecil Archer, Esq., 20 Greenhill
Place, Edinburgh.

115

Joseph Mitchell.

Joseph Mitchell, civil engineer, for long resident in Inverness,
and latterly in London, was born at Forres on the 3rd November
1803. His father, John Mitchell, was appointed, under Mr Telford,
as inspector of works, in connection with the extensive road works,
which, with the other great works then being carried out by Mr
Telford, were the first means of opening up the Highlands to full
access with the southern parts of Great Britain. Mr John Mitchell
held the general inspectorship of the extensive system of com-
munication known as the Highland Boads and Bridges. It is
worthy of remark that Mr John Mitchell attracted the attention
not only of Mr Telford, but also of the poet Southey, who wrote
in terms of high commendation, both of his talents and moral
qualities.

Joseph Mitchell seems in many respects to have inherited his
father’s energy and abilities. He was educated at the celebrated
Academy of Inverness, which for many years was under the charge
of the well-known Alexander Nimmo, C.E., who was long the per-
sonal friend of Telford and of Sir David Brewster, for whose Ency-
clopaedia, he wrote several articles.

Mr Mitchell became a Fellow of this Society in 1843. He be-
came a civil engineer under the immediate auspices of Mr Telford,
who caused him to engage in the practical masonry of the lockgates
of the Caledonian Canal at Fort Augustus, after which Mr Mitchell
not only became an apprentice in his office, but an inmate of his
house, a striking proof of the high opinion which that great
engineer had formed of his personal qualities. Here he made the
first survey of the St Catherine Docks, which were carried out under
Mr Telford’s superintendence.

In 1824, when only twenty-one years of age, the whole of the High-
land Boads and Bridges system was, on the death of his father, put
under Mr Joseph Mitchell’s charge, a fact which shows how great
a trust was reposed in him by Mr Telford. During the long period
of thirty-nine years he had these roads, extending over the rugged
and difficult counties of Inverness, Boss, Cromarty, Sutherland, and
Caithness, not only to inspect but to provide additional roads and

116

bridges over the most difficult ravines and passes and the most
formidable kind of rivers. There was in all this difficult country-
ample room for varied engineering practice, which was throughout
of a most successful type. Besides all this Government work, he
carried on an extensive private practice, involving the expenditure
of about £180,000. He was also employed by Government to
design and erect forty churches in outlying districts and lonely
islands.

In 1828 he was appointed engineer to the Scottish Fishery Board,
and designed and superintended the execution of very many useful
harbours, as for example at Burnmoutk, Coldingham, and Dunglass,
in Berwickshire, at Buckhaven and Cellardyke on the Fife coast, as
well as at various fishing stations on the coasts of Caithness and
among the Hebrides. The large fishing harbour at Dunbar, which
cost nearly £40,000, was also one of Mitchell’s, as well as Lybster,
on the Caithness coast, where, in order to avoid as much as possible
conflict with the open sea, he preferred to recess the basin land-
wards of high water, instead of carrying the works outwards. He
also designed improvements at Wick on the same principle. Mr
Mitchell is well known as having been the engineer of the extensive
work known as the Highland Bailway between Perth and Inver-
ness, as well as of most of the railways to the northward of Inver-
ness. Mr Mitchell, in conjunction with Messrs William and
Murdoch Paterson, was engineer for the Skye line.

Mr Mitchell has left behind him so many works of a varied, and
some of them of a difficult nature, as to prove his natural sagacity
and skill. He was always highly esteemed by his professional
brethren for his geniality and high professional honour as well as
his ability. True and genial as a friend, his death was felt by
many as a personal loss, both in Scotland and in London, where he
principally lived in later years. He died in London on 26th
November 1883, at the advanced age of eighty years.

117

Professor HENRY CHARLES FLEEMING JENKIN. By W. H. P.

Professor Henry Charles Fleeming Jenkin, only child of Captain
Charles Jenkin, R.U., of Stowling Court, Kent, and his wife (Cora
Jackson), a Scotchwoman and a novelist of some mark, was horn
in Kent on the 25th of March 1833. Fleeming Jenkin was at the
age of seven taken to Scotland, when he went to Dr Burnett's
school at Jedburgh. There he stayed for three years, and then for
other three years attended the Edinburgh Academy. In 1847 he
went to school in Paris, where he saw the Revolution of 1848, of
which he was wont to give vivid and interesting descriptions; and
after the June riots he left for Italy, where he attended the Univer-
sity of Genoa in the Arts Faculty, taking his degree as Master of
Arts in 1850. It was at Genoa also, in a locomotive shop, that he
began his distinguished career as an engineer, under Philip Taylor
of Marseilles. In 1851 he returned to England, and was apprenticed
to Fairbairn’s in Manchester for three years. His first practical
work was done under Mr Hemans, on a survey for the Lukmanier
Railway, in Switzerland ; then he went to Messrs Penn at Green-
wich ; and then to Messrs Liddell & Gordon, in railway work.
Thence he went to Messrs Kewall (Birkenhead), while they were
engaged on making the first Atlantic cable in 1857. He was very
soon entrusted with the chief management of the Messrs Ne wall's
engineering and electrical business. His work included superin-
tendence of machine construction in the factory, the designing of
picking-up and paying-out machinery, the fitting up of steamships
for submarine cables and the electrical testing. This work he
continued to do during the making of part of the first Atlantic
cable, of the Red Sea cable, of a cable from Singapore to Batavia,
and of several Mediterranean cables. In 1859, the year of his
marriage with Ann, daughter of the late Mr Alfred Austin, C.B.,
he was elected Associate I.C.E., and began to write on scientific
subjects, encouraged thereto by Professor (now Sir William)
Thomson, whom he had first known through Mr Gordon, of Liddell
& Gordon. In 1860 he took out a patent jointly with Sir
William Thomson for signalling apparatus through long submarine
cables, and in 1861 he entered into a partnership, which lasted

118

seven years, with. Mr H. C. Forde for general and telegraphic
engineering. In the same year he acted as second in command
nnder Sir William Thomson at the establishment of the British
Association Committee on electrical standards. Of this committee
he was appointed secretary, and he wrote their reports for several
years. He also carried out most of the committee’s important
experiments in conjunction with Clerk Maxwell and others. He
was juror for Physical Apparatus at the 1862 Exhibition, and was
named Reporter for Electrical Apparatus. In 1865 the late
C. F. Yarley joined Sir William Thomson and Fleeming Jenkin in
an agreement to work at the development of the signalling apparatus
through long submarine cables already referred to. The apparatus
devised by the three inventors was used by all the great companies,
and Jenkin displayed a remarkable business faculty in the commercial
management of the patent. In this same year Jenkin was elected
a Fellow of the Royal Society, and in 1866 he was appointed
Professor of Engineering at University College, London. In 1868
he dissolved partnership with Mr Forde, and resigned his post at
University College, in order to accept the Chair of Engineering in
Edinburgh University, which chair he filled until his death. After
accepting this post he entered into a new partnership with Sir
William Thomson, under the provisions of which Sir William and
he acted as joint engineers to various submarine cable companies.
Among the lines which were laid under their direction were those
of the Western and Brazilian Telegraph Company, the Platino-
Brazileien Telegraph Company, the West Indian and Panama
Telegraph Company, and the Mackay-Bennett or Commercial Cable
Company. In 1871 Fleeming Jenkin was President of the
Mechanical Section of the British Association, which met that year
at Edinburgh; and in 1873 he went to Brazil in the interests of the
Western and Brazilian Telegraph Company. In 1877, in a lecture
at Edinburgh given for the Edinburgh Philosophical Institution, he
took occasion to propose the establishment of a Sanitary Protection
Association. In consequence the Edinburgh Sanitary Protection
Association was started, and succeeded so well that its example has
since been followed in many parts both of Great Britain and of the
United States. To most of these associations in Great Britain
Fleeming Jenkin was consulting engineer. At the Paris Exhibi-

119

tion of 1878 he was juror in Engineering, and in 1884 was juror
in Electricity in the Health Exhibition in London. From 1879
onwards to the time of his death he was Vice-President of the
R.S.E., and from this Society he had the Keith Prize for the period
1877-79. This, the Society’s highest distinction, was awarded for
his paper on “ The Application of Graphic Methods to the Determina-
tion of the Efficiency of Machinery,” a continuation, full, however,
of originality, of the subject treated in Reuleaux’s Kinematics of
Mechanism. In 1882 he took out his first patent for “ Telpherage,”
a system of electrical carrying of burdens, or at need of passengers.
The Telpher line is a conductor, which may be either flexible or
rigid, of electricity supporting an electric motor and train of steps or
of travelling chairs, which hang below it, and itself supported by
strong posts. The line is in electrically distinct sections, and the
train, itself a continuous conductor, and larger than any section,
bridges over the interval between successive sections as it passes.
The power is derived from a fixed engine and dynamos placed at
convenient distance from the line. The “ Telpherage Company,”
whose first working line was opened at Glynde, four months after
Jenkin’s death, which took place on the 12th of June 1885, was
due to Jenkin’s joining forces with Messrs Ayrton & Perry, who
were, like him, turning their attention to the application of electricity
to locomotion. His death was due to the unfortunate result of a
surgical operation, slight in itself.

Apart from his own most special work, and from the sanitary
engineering work which has been referred to, and which has had
wide and good influence, Professor Jenkin took a deep and keen
interest in Technical Education (he was for many years a Director
of the Watt Institution) and in science generally. Witness among
other instances his reviews of the Origin of Species [North British
Review , June 1867) and of the Atomic Theory, an article supported
by Munro’s Lucretius ( North British Review , 1868). Both Darwin
and Munro, in subsequent editions of their works, acknowledged the
value of Professor Jenkin’s criticism. In the fine arts, and notably
in dramatic art in its widest sense, his interest was equally keen and
wide y but by the world at large, outside his own belongings and
friends, he will be remembered best for his special and admirable
work in electricity and engineering.

120

John Watson Laidlay.

John Watson Laidlay was horn at Glasgow on the 27th of March
1808. At an early age he went to London, and began his education
at a private school at Blackheath.

After passing through the ordinary curriculum there, he com-
menced a brief course of technical study, preparatory to going out
to India, and with this view entered the laboratory of Faraday, by
whom he was initiated in practical chemistry. At the same time
he studied Hindustani under Dr Gilchrist, and it was here that he
made the acquaintance of Bishop Heher.

This period was, however, very short ; when he reached only his
seventeenth year it was decided to send him out at once to India,
and at this point his normal education may be said to have ended,
his subsequent learning, the varied extent and scholarly accuracy of
which was known only to his intimate friends, being entirely the
result of self-imposed study.

In the end of 1825 he reached Calcutta, and joined his uncles,
Messrs John and Robert Watson, merchants and indigo planters,
Bengal, who subsequently purchased from the East India Company
many of their best silk filatures and indigo factories, such as
Berhampore, Rampore-Beauleah, Surdah, &ct

He was now constantly in charge of one or other of the filatures,
and succeeded in introducing several valuable improvements in the
machinery for winding silk.

His spare time he devoted to studying science and natural history,
but, above all, the Oriental languages, for which he had a very
decided talent ; and, in addition to the native dialects, soon made
himself familiar with Persian, Arabic, Sanskrit, and subsequently
Chinese.

He originated the Bibliotheca Indica , a serial publication of
native literature, which has proved a most valuable work, and is
still continued.

His love of deciphering inscriptions on ancient monuments was
great ; and, with a view to assisting the labours of those engaged
in this work in India, he translated The Pilgrimage of Fa Hian
from the French edition of the Foe Koue Ki , with additional
notes and illustrations of his own.

121

He made a valuable collection of coins, including many uniques ;
a portion of these were unfortunately stolen, but the remainder,
together with his collection of shells, he presented to the British
Museum.

His most numerous literary and scientific publications appeared
from time to time in the Journal of the Asiatic Society , to which he
acted as co-secretary, and afterwards vice-president and secretary to
the Natural History Department.

He also compiled a comparative dictionary of Chinese words, and
made translations of several Persian poems and other works, which
were never published.

In 1839 he visited the Straits of Malacca for his health, and
there he made the acquaintance of Rajah Sir James Brook. He
went home to England in 1843, where he married, and returned the
following year.

The remainder of his time in India, until his final return to
England in 1850, was spent at Calcutta, where he associated with
the leading scientific and literary men of the day, together with
many other notable people.

On leaving India he gave up active work, and shortly settled
down at Seacliff, Haddingtonshire, where he spent the remainder of
his life.

He was now elected a Fellow of the Royal Society of Edinburgh,
in whose proceedings he took a lively interest, although prevented
by uncertain health from taking an active part in their meetings.
He also became a member of various other societies in this country.

At all times of a retiring and unambitious disposition, he showed
little inclination to enter society afresh and without the companion-
ship of his former friends, but preferred rather to cherish and extend
those kindred studies which had been so much to him in the past.
In the quiet of his unostentatious life at Seacliff, he found a never-
failing source of pleasure in his library, his laboratory, and in the
wider field of nature. His was essentially a pure love of scientific
truth for its own sake, and, although furnished with introductions
which would have brought him in contact with many celebrated
literary and scientific men, his extreme humility and modesty of
self-assertion prevented him from availing himself of these oppor-
tunities of bringing his own learning into greater prominence.

122

Thoroughly versed in the classics, he delighted to read and re-read
the works of the principal authors, most of whom he could quote
at pleasure. Perhaps his favourite modern language was Italian,
and Dante his favourite poet. Schiller and Goethe, too, he held in
high esteem, while in our own literature he was intimately con-
versant with all the standard authors.

In the sciences, chemistry, archaeology, geology, meteorology, and
natural history, each afforded an inexhaustible field of research, his
varied reading enabling him to keep abreast of the latest discoveries.

In medicine his knowledge was extensive and accurate, and so
late as his seventieth year he attended, for his own pleasure, a
whole winter course of anatomy at the Edinburgh University, under
Professor Turner.

Some time before his death his eyesight began to fail, and thus
he was reluctantly forced to abandon, one by one, his favourite
studies; but his memory continued clear until his death, which took
place upon the 8th of March 1885.

In private life he was esteemed by all who knew him for the
gentleness of his disposition, his kindness and unvarying courtesy to
all, rich and poor alike ; but few, save his own family, knew his
completely unselfish nature, his infinite goodness of heart.

The following papers are recorded under his name : —

On Catadioptric Microscopes. Journal of the Asiatic Society ,
vol. iii., 1834.

Analysis of Raw Silk. Yol. iv., 1835.

On the Rate of Evaporation in the Open Sea. Yol. xiv., 1845.

On the Coins of the Independent Mohammedan Sovereigns of
Bengal. Yol. xv., 1846.

Sanskrit Inscription from Behar. Yol. xvii., 1848.

Daily Evaporation in Calcutta. Ibid.

Note on the Nido-Scythia Coins. Ibid.

Note on the Inscriptions found in Province Wellesley. Ibid.

Notice of a Chinese Geographical Work. Yol. xviii., 1849.

Note on an Inscription from Keddah. Ibid.

On Preparing Fac-similes of Coins, &c. Ibid.

On the Connection between Indo-Chinese and Indo-European
Languages. Journal of the Royal Asiatic Society , vol. xvi.
p. 59, 1856.

123

Francis Brown Douglas, Esq. By Professor Duns, D.D.

Francis Brown Douglas was born at Largs, Ayrshire, April 2,
1814. His father was Mr Archibald Douglas, advocate, Edin-
burgh, and his mother was a daughter of Dr Francis Brown of St
Vincent. He was educated at the Edinburgh High School, and for
a short time in England. In early youth he went to the West
Indies, where he was soon called to undertake the management of
family estates. On his return to Scotland he studied for the
Scottish Bar, and was admitted an advocate in 1837. He practised
at the Bar for a short time only. Having an ample private fortune,
he felt himself at full liberty to follow pursuits to him more con-
genial than the hard work of his profession, and accordingly he
devoted his time and energy earnestly to municipal, philanthropic,
and religious work. He was elected a Fellow of this Society in
1839. A man of general culture, he was intimately acquainted
with several branches of current literature, and took a warm interest
in public education. He was elected a member of the Edinburgh
School Board when it was formed in 1872, and continued to serve
in it till last election. Mr Brown Douglas entered the Edinburgh
Town Council in 1850, and, after having acted as a magistrate for
several years, he was chosen Lord Provost of the city in 1859.
Two events occurred in the course of his Lord Provostship which
may be mentioned, viz., the passing of the Annuity Tax Act, and
the laying of the foundation stones of the Hew Post Office and the
Hational Museum by the Prince Consort. Mr Brown Douglas was
a Liberal in politics. He stood for the representation of the city in
1856, but was defeated. Later, he became a candidate for the
St Andrews Burghs, but was again unsuccessful.

It was, however, chiefly in connection with religious and philan-
thropic work that he stood prominently out before his fellow-
citizens. For more than forty years his name was associated with
almost all movements of this kind. He threw himself with great
earnestness and zeal into the Scottish ecclesiastical controversies
that characterised the decade ending in 1843. He continued till the
time of his death in August 1885 to take the most active and cordial
interest in the work of the Free Church, both at home and abroad,

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and succeeded Mr David Maclagan in the convenership of its Con-
tinental Committee.

Mr Brown Douglas devoted a great deal of time and attention to
some aspects of philanthropy which do not bulk largely in the public
eye, but are full of good to many. He was for forty years president
of the District Sick Society. He took an active share in the
Society for Teaching the Blind in their own houses, in the Indigent
Old Men’s Society, and other kindred institutions — bringing, as
director or as member, to their affairs sound practical wisdom*
excellent business habits, wide views, keen sympathy, and helpful
liberality.

Mr Brown Douglas was twice married — first in 1845, to Mary,
second daughter of the late Charles Maitland Christie, Esq. of
Durie, and again, in 1852, to Marianne, second daughter of the
late Hon. Alexander Leslie Melville, who, -with four sons and six
daughters, survives him.

David Maclagan, F.B.S.E. By Professor Duns, D.D.

David Maclagan was born in Edinburgh on the 9th of October
1824. His father, Dr Maclagan, a distinguished physician, had
retired from the Army Medical Service after a noted career, and
had settled down to a highly successful civil practice in Edinburgh.
His mother was Miss Whiteside of Ayr. David was the fourth of
seven sons, six of whom survive — Professor Douglas Maclagan,
M.D., Dr Philip Whiteside Maclagan, Berwick-on-Tweed, General
Maclagan, R.E., William Dairy mple Maclagan, Lord Bishop of
Lichfield, John Thomson Maclagan, Secretary of the Church of
Scotland’s Widows’ Eund, and Dr J. M‘Grigor Maclagan, Biding
Mill-on-Tyne. Mr Maclagan was educated at the Edinburgh High
School. He began business life in the office of “ The Scottish
Union Insurance Company,” and was appointed manager of “The
Insurance Company of Scotland” in 1847. He was an original
member of the Society of Accountants, a body which was incorpor-
ated by charter in 1854. Mr Maclagan removed to London in
1862, on his appointment as secretary to “The Alliance Eire and
Life Insurance Company.” In this position, his business associations

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brought him into close relations with the Kothschilds, Mr Goschen,
Sir Moses Montefiore, and other well-known financiers. His
acquaintanceship with Sir Moses soon ripened into intimate and
lasting friendship. Mr Maclagan returned to Edinburgh in 1866,
and entered on the managership of the Edinburgh Life Assurance
Company, an office which he retained till his death on the 30th of
March 1883, at Mentone, whither, for health’s sake, he had gone to
spend the winter. In 1848 Mr Maclagan married Miss Jane Finlay,
who, with five sons, still survives.

On his return to his native city he threw himself with great
heartiness and zeal into religious and philanthropic work. He was
one of the most earnest promoters of the Apprentice School Associa-
tion, a society which at the time did much good, both by supplying
the means of education to a much neglected class, and also by leading
the way to better arrangements for the same purpose. Mr Maclagan
was elected a Fellow of this Society in 1872.

A man of academic tastes, fond of literature, the intimate friend
of many engaged in literary and scientific work, and himself earnestly
interested in the growth of knowledge, he yet found himself, in a
great measure, precluded from practical literary effort by the onerous
duties of his business position, and the devotion to work necessary
to success in his profession. He had, however, as a relaxation and a
delight, early cultivated the habit of the pen, and he has left good
evidence of his scholarly accomplishments, intellectual vigour, and
fine taste. From boyhood almost Mr Maclagan had taken great
interest in Scottish religious and ecclesiastical movements. The
stirring events which preceded and immediately followed the Scottish
Church crisis of 1843 greatly influenced him. He entered into them
with an earnestness and fervour in strong contrast with his wonted
quiet and placid habits of thought. And though some rough points
of his churchism may have afterwards been a good deal smoothed
down, there was not, through life, any abatement of his early
enthusiasm and zeal. Yet few men were freer from sectarian nar-
rowness. His toleration for the views of others was as characteristic
of him as the firmness with which he held his own. The writer, as
Secretary of the Free Church College Committee, was associated for
more than ten years with Mr Maclagan in work in which he had
good opportunity to observe the breadth and the balance of his well-

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stored mind, the singular wisdom of his counsel, his sound judgment,
and practical sagacity. Mr Maclagan was for many years a member of
this Committee, and the Convener of its Finance Sub-Committee by
which the Committee itself is guided in its administration of College
property and finance. Reference is made to this to indicate the great
business ability, tact, and shrewdness which Mr Maclagan brought to
bear on it. Mr Maclagan was also for several years Convener of the
Free Church’s Continental Committee — an office which had been
previously held by Sheriff Jameson, and, later, by Sheriff Cleghorn.
He was an effective public speaker, and never spoke on any question
of interest but when he had something to say, while his utterances
were always clear, pointed, earnest, and telling. JSTot withstanding
the engrossment of business life, he did a good deal of literary
work, mostly of a biographical kind. His last effort was a brief,
but hearty, appreciative notice of his friend the late Mr Samuel
Raleigh, written at the request of the Council of this Society. The
death of Mr Maclagan was the removal from a wide circle of friends,
and from the Fellows of this Society, of an accomplished Christian
gentleman. In his able and touching “ Memorial Sketch” of Thomas
Cleghorn, “ one of his dearest and truest friends,” Mr Maclagan
wrote of Sheriff Jameson in terms singularly applicable to himself :
— “A mind well cultivated, and always fresh in thought and feeling
— a decision in religious matters, thorough and uncompromising,
united with a large toleration of the views of others — characterised
him ; while he was a lover of all good men, and the blithest of
companions in hours of relaxation and social fellowship.”

Dr John Alexander Smith. By Professor Duns, D.D.

John Alexander Smith was born in Hope Street, Edinburgh, in
June 1818. His father was the late James Smith, a well-known
Edinburgh architect. Mr Smith was educated at the High School
and the University of Edinburgh. While still a student he became
a Fellow of the Royal Physical Society. He graduated in medicine
in 1840, was elected a Fellow of the Society of Antiquaries of
Scotland in 1847, a Fellow of this Society in 1863, a Fellow of the
Royal College of Physicians in 1865, and succeeded the late Dr

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Somerville in the Treasurership of the College in 1874. Dr Smith
began practice as a physician, and continued in it through life, hut
his practice was never large. Possessed of means sufficient to enable
him to follow his tastes for natural science and archaeology, inde-
pendently of professional income, these pursuits became the leading
work of his life. But his professional brethren were never slow to
acknowledge his skill in the diagnosis and treatment of disease.
Had circumstances made it necessary to devote himself earnestly to
his profession, it would hardly have been possible for him to have
done half the work he accomplished in the literature of his favourite
studies and in behalf of the Societies of which he was a Fellow.

When Dr Smith joined the Eoyal Physical Society it counted
among its working Fellows, Knox, Captain Thomas Brown, Car-
penter, Edward Forbes, Greville, Simpson, Goodsir, George Wilson,
John Coldstream, Sir J. G. Daly ell, Charles Maclaren, and, later,
Robert Chambers, John Fleming, Hugh Miller, and others who have
done good work in Scottish Zoology and Geology. Dr Smith suc-
ceeded the late Sir Wyville Thomson as its Secretary, an office which
he held for more than twenty years. In addition to his work as
Secretary, he contributed many papers to the Society, some of much
value. More than a hundred notices of birds, many of them new to
Scotland, and some new to Britain, were written by him. In these
he put on record all peculiarities as to time of visit, plumage, food,
&c. In the Proceedings of the same Society are between twenty and
thirty notices of fishes by him, including remarks on the divergence
of some of the specimens from typical varieties in hermaphroditism,
and other highly exceptional features. But he did not limit his
observation to birds and fishes. Insects, reptiles, and mammals were
described with equal interest and skill, while several mineralogical
notices indicate his familiarity with this branch. On resigning the
office of Secretary he was elected President, and in November 1876
delivered the address at the opening of the 106th Session of the
Society. This address contains a complete list of his friend Dr
Strethill Wright’s numerous original papers on Protozoa and Ccelen-
terata, and in a somewhat incisive way he states his opinion of
Darwinism, and frankly avows his belief in the doctrine of special
creation and in the Bible views of the natural history of man.

On the 16th of April 1866 Dr Smith read to this Society a

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paper entitled “ Description of Calamoichthys, a New Genus of
Ganoid Fish, from Old Calabar, Western Africa, forming an addition
to the Family Polypterini.” This paper, which is illustrated by two
plates, is published in the Transactions for Session 1865-66. It
affords an exceedingly good proof of Dr Smith’s ability as a natur-
alist. Several specimens of both sexes were examined. The char-
acteristics are precise, and embrace the minutiae of every part, while
much interesting information is given concerning the habits and
food of these forms.

Dr Smith also contributed papers to the Edinburgh New
Philosophical Journal, the Annals and Magazine of Natural
History, and the Journal of Anatomy.

Dr Smith was Secretary of the Society of Antiquaries from 1852
till the time of his death, with the exception of two triennial
periods, 1870-75 and 1875-78, when he held the office of Vice-
President. Between 1850 and 1882, he contributed forty-five
papers to its Proceedings. For many years he acted as joint-editor
of the Proceedings, first in association with his intimate friend
David Laing, and afterwards with Dr Arthur Mitchell. Dr
Smith’s archaeological contributions are all interesting, and many of
them valuable additions to the literature of Archaeology. They
illustrate the wide range of his knowledge. And all who were
acquainted with his conscientious habits of study, with his devotion
to true scientific method, and with the thoroughness of the investi-
gation brought to bear on the subjects in hand, will not think it
too much to affirm that he dealt with each of these subjects as if it
only had ever held the chief place in his thought. His papers
might be grouped thus, — Prehistoric Eemains, Eoman Eemains,
Mediaeval Eemains, Antiquarian Literature, Eock Sculpturings, and
Archaeo-Zoology. His contributions to the last group are very
able and important. They bear emphatic testimony to Dr Smith’s
great attainments in Comparative Zoology. With characteristic
precision he identifies the bones of mammal, bird, and fish, and
skilfully uses the articles found in cave, or grave, or gravel heap in
association with them, to serve for deductions touching the industrial
conditions of the time, or for supplying a key to the age of the
deposits themselves in which they occur. He did much, along with
others who survive, to apply the recognised principles of historical

129

criticism to antiquarian research, to free this branch of knowledge
from the reproach of mere “ curiosity hunting,” and to give to
Scotland a school of Archaeology as thoroughly in the lines of true
science as her school of Geology was held to he. This might he
very fully illustrated by a criticism of his special contributions to
this branch of study, such as the papers on “ Roman Remains found
near the Village of Newstead,” or his “ Notes on Melrose Abbey,”
or his “ Notices of the Ancient Cattle of Scotland,” or his “ Notice
of the Remains of the Reindeer found in Scotland.” The last
named is a peculiarly able and exhaustive paper. It is crowded
with facts, which supply abundant material for trustworthy general-
isations as to the climate and the inhabitants of the localities where
the remains occurred.

In January 1883, Dr Smith began to suffer from the growth of a
tumour in the upper jaw, which in a few weeks assumed a malignant
form. But, both in the intense pain of the early stages of the
disease, and in the rapid waste of the affected parts in the later ones,
it was great satisfaction to his friends to see how calmly and bravely
the Christian hope, which had long been his, enabled him to bear
his sore affliction. He died on the evening of the 17th of August
1883.

Sir John MNeill. By Professor Duns, D.D.

The Right Honourable Sir John M‘Neill, G.C.B., third son of
John M‘Neill, Esq. of Colonsay and Oronsay, was born at Oronsaj
House, Argyllshire, August 12, 1795. He studied at the Universities
of St Andrews and Edinburgh. Having graduated in medicine in
1815, he proceeded to India as an army surgeon. Four years later
he was attached to the H.E.I.C.’s mission to Persia, — first in a
medical and afterwards in a diplomatic capacity. His linguistic
attainments, apt business habits, natural shrewdness, literary
acquirements, and wide knowledge of Eastern affairs led to his
appointment as assistant Envoy at Teheran in 1831. In 1834 he
became secretary of the Embassy, and in 1836 he was appointed
Envoy Extraordinary and Minister Plenipotentiary at the Court

i

130

of the Shall — a position which he held for about six years. Soon
after he became Ambassador an anonymous work on the influence
of Russia in the East was published, and generally ascribed to Sir
John. The work attracted a good deal of attention in England at
the time. After his return home, he was appointed in 1845
chairman of the new Board of Supervision for Relief of the Poor in
Scotland, an office which he held till 1868. While head of the
Board of Supervision he made an extended tour of investigation,
by desire of Government, through the Western Highlands, during
the period of the famine. The Report which resulted from this
tour was published in 1861. Characterised by much ability and
great good sense, the Report is full of interest, both for the informa-
tion it contains and for the remedial measures recommended in it,
the chief of which, emigration, has recently been much canvassed
in connection with the present social and industrial condition of
the Highlands and Islands.

During the Crimean War, Sir John was requested by the Minister
of War, Lord Panmure, to proceed along with Colonel Tulloch to
the Crimea, and make careful inquiry into the disasters of that
campaign in connection with the defective commissariat. On
presenting the joint Report in 1855, Sir John received the thanks
of Parliament and the distinction of G.C.B. He was sworn a
member of the Privy Council in 1857. Though the accuracy of
some parts of this Report wTas called in question by the military
commission at home on the same subject, its value was generally
admitted. Sir John was a D.C.L. of the University of Oxford, and
LL.D. of Edinburgh. He was for some years one of the curators
of the University of Edinburgh, and at the time of his death was
honorary president of the Edinburgh Literary Institute. He
became a Eellow of this Society in 1840, and was a member of many
other learned societies, both British and foreign.

His latter years were spent partly at his residence, Burnhead, near
Edinburgh, and partly at his villa, Poralto, Cannes, where he died
on May 17, 1883.

Sir John was, by one of his marriages, brother-in-law of Professor
John Wilson (Christopher North), and by his marriage in 1870 he
became brother-in-law of the present Duke of Argyll.

131

Morrison Watson, M.D., F.R.C.P., F.R.SS. Edin. and Lond.
By Professor Alfred H. Young.

Among the Josses sustained by the Royal Society during the past
year, that occasioned by the sudden death of Dr Morrison Watson
was perhaps the saddest.

In the prime of life, and apparently in good health. Dr Watson,
when seized with the illness which soon afterwards proved fatal,
was engaged in the active duties of the chair of Anatomy in the
Owens College at Manchester, to which he had been elected — as
the first occupant — eleven years previously. Prior to this, Dr
Watson resided in Edinburgh, where he received— at the Queen
Street Institution — his early education, and where later he studied
medicine in the University, and in course of time took the degree
of Doctor of Medicine. For some years he worked in the anato-
mical rooms of the University as demonstrator with Professor
Goodsir, and thereafter with Professor Turner, by the latter of
whom he was appointed to the office of principal demonstrator of
anatomy. It was during this period that Dr Watson became a
Fellow of the Royal Society, whilst more recently he was also
elected a Fellow of the Royal Society of London.

By his friends, and he had many, he was regarded with feelings
of the highest respect and esteem, and the news of his sudden and
early death gave rise to widespread expressions of deep and sympa-
thetic regret. To those who knew him best he was a genial and
affectionate friend, and it was only those perhaps who could fully
realise his sturdy independence of character, his straightforward
nature, and the strength and depth of his friendship.

The loss which the Medical School of Manchester and the Owens
College sustains by Professor Watson’s death is great. He was
appointed to the newly instituted chair of Anatomy, at the period
when the amalgamation of the previously separate institutions, the
Medical School and the Owens College, was effected, and he at
once devoted himself with energy and vigour to the work of
creating a School of Anatomy in Manchester. Under his direction
the resources for teaching were greatly developed and materially
augmented, and the now fairly complete collection in the Anato-

132

mical Museum of the Owens College was formed under his direct
supervision. As a lecturer, Dr Watson was lucid and always
practical. Alike by his own work, and by the generous encourage-
ment he readily gave to others, he fostered a spirit for original
investigation in the Anatomical School of the Owens College with
such success, that it now occupies a prominent position amongst the
English schools as one of the few in which, not only is human
anatomy efficiently taught, but in which good work is also done in
the wider field of animal morphology. It is to he hoped that in
this respect the influence of Dr Watson’s work will continue to
exercise its power for good over the future of the anatomical depart-
ment of the Medical School at Manchester.

Of Dr Watson’s own additions to scientific anatomy, undoubtedly
the most complete is the able and comprehensive contribution to
the reports of H.M.S. “Challenger” (vol. vii., Zoology) — “On the
Anatomy of the Spheniscidse.” An important memoir, “ On the
Anatomy of the Northern Beluga ( Deljoliinapterus Leucas) com-
pared with that of other Whales,” of which he was joint author,
appeared in the Transactions of the Royal Society of Edinburgh
(vol. xxix.). A more recent paper by Dr Watson, “ On the Female
Organs and Placentation of the Raccoon,” was communicated to the
Royal Society of London (1881). The results of many of his
investigations were communicated to the Zoological Society of
London, — notably a series of interesting papers, “ On the Anatomy
of Hycena crocuta ” (1877-81); “On the Anatomy of Chlamydo-
phorous Truncatus ” (1879); “On the Muscular Anatomy of Pro-
teles ” (1882) ; and “On the Anatomy of the Indian Elephant”
(1881-83). To the Journal of Anatomy and Physiology Dr Watson
contributed articles, “ On the Mechanism of Perching in Birds ”
(1869), which constituted part of a graduation thesis for which a
gold medal was given ; on “ The Termination of the Thoracic Duct
on the Right Side” (1872); “Notes on a Remarkable Case of
Pharyngeal Diverticulum ” (1874); on “A Case of Double Aortic
Arch” (1877); on “The Homology of the Sexual Organs, illus-
trated by Comparative Anatomy and Pathology” (1879); on “The
Curvatores Coccygis Muscle in Man ” (1880) ; and a series of “ Con-
tributions to the Anatomy of the Indian Elephant” (1871-73). Dr
Watson’s remaining writings include papers on “The Anatomy of

133

the Elk” {Journal of the Linnean Society , vol. xiv.) ; “Notes on
. . . . two Species of Crustacea {Ann. and Mag. of Nat. History ,
1870), and “Notes on Congenital Absence of the Kidney” {Edin.
Med. Jour., 1874).

Rev. Francis Red ford, M.A. By Henry Barnes, M.D.

The Rev. Francis Bedford, M.A., who died on the 20th of last
September, was one of the oldest and most notable clergymen in the
diocese of Carlisle. He was horn at York in 1813, and at an early
period showed remarkable intelligence and aptitude for scientific
work. He received his early education in the public schools of the
city in which he was born, and afterwards, with the intention of
adopting the medical profession, he entered King’s College, London,
as a medical student. After obtaining some considerable amount
of medical training, which was very useful to him in after life,
circumstances arose which made it desirable that he should adopt
another career, and in 1837 he was sent out by the Church
Missionary Society to Trinidad as a catechist. He remained in
that country for four years, doing much good work, but owing to
failure in health he was compelled to return to this country in
1841.

He then set about studying for the ministry of the English
Church, and I am informed he was ordained deacon on June 11,
1843, by Charles James Blomfield, Bishop of London. He held
curacies both in Herefordshire and Nottinghamshire, but a love of
missionary work and travel induced him to again try the climate of
the West Indies, and in 1844 he went out to Jamaica. A break-
down in his health compelled him to return in 1847. Three years
later, in 1850, he was appointed to the living of St Paul’s, Silloth,
and here he continued to reside during the remainder of his life.
Here it was that he made those observations on meteorology by
which he will chiefly be remembered. At the time of his appoint-
ment, the now popular watering-place of Silloth was a desert of
sandhills ; there was not a single house there, and the part which he
took in developing the place and promoting its prosperity is generally
recognised. In the place of a sandy desert, there is now an

134

important seaport, with its docks, pier, regular railway and steam-
boat communication, and abundant accommodation for visitors.
By his meteorological observations, which were regularly published
in the Reports of the Registrar-General and in the Transactions of
the English and Scottish Meteorological Societies, of both of which
he was a Fellow, he demonstrated the remarkable fact, that as
regards the amount of ozone, signifying an absence of impurity, and
in the amount of sunshine, Silloth occupied a very conspicuous
position. This demonstration, proved by the careful record of many
years’ observations, has given Silloth a character which has undoubt-
edly contributed to its popularity as a health resort. He was the
honorary secretary of the Cumberland and Westmoreland Con-
valescent Institution, from its foundation in 1862 to within a few
weeks of his death, and by his energy and painstaking efforts in
this capacity, he contributed materially to the success and prosperity
of this valuable institution. His knowledge of botany was con-
siderable, and he was an intimate friend of the late Professor
Balfour. In the use of the microscope and telescope he was often
engaged, and for many years he was a Eellow of the Royal
Astronomical Society. The degree of M.A. was conferred upon
him in 1860 by the Archbishop of Canterbury, and he was elected
a Eellow of this Society in 1865.

Although he was in the daily habit of making scientific observa-
tions, I cannot find that he ever contributed any paper to our Pro-
ceedings. This is much to be regretted, as he had undoubtedly
accumulated much valuable material, and the record of his labours
in the department of meteorology fill many volumes. These have
now come into my possession, and as I do not think a more fitting-
home could be found for them than the Royal Society of Edinburgh,
I have much pleasure in handing them over for permanent preserva-
tion. In doing so it may be of service if I give a short account of
the contents.

No. 1 . A large volume of meteorological observations, taken daily
at 9 a.m. and 9 p.m. from March 1854 to December 1868, giving
the rainfall, wind, thermometer, hygrometer, and barometer. The
ozone observations commence in April 1868. There is an interval
of a few years, and the observations begin again in January 1874,
and continue to December 1875.

135

No. 2. A volume containing observations of a similar kind, taken
twice daily from January 1876 to January 1877.

No. 3. Twelve volumes containing detailed observations for the
following years, viz., 1871, 1872, 1873, 1876, 1877, 1878, 1879,
1880, 1881, 1882, 1883, and 1884. The sunshine observations
commence in 1881.

No. 4. A volume containing full observations from October 1876
to March 1877.

No. 5. A volume containing daily notes on thermometry and
rainfall for 1869 and 1870, and monthly averages for 1872 and
1873.

No. 6. A volume giving a comparative statement of the rainfall,
and readings of barometer and thermometer taken at Lewisham,
Kent ; Highfield House, Notts ; and St Paul’s Parsonage, Cumber-
land, from March 1854 to February 1855.

Together with these volumes there is another MSS. volume illus-
trative of the meteorological history of this district, which I desire
to present to the Society at the same time. It is a volume of
observations from January 1838 to May 1842, taken at Carlisle by
the late William Elliot, M.D. Edin., and was found among Mr
Ledford’s papers.

Before a Society like this, it would be out of place to refer to the
manner in which he discharged his parochial and ministerial duties.
Suffice it to say that he had many attached friends, that he found
his chief relaxation in scientific studies, and that in a widely scattered
agricultural community he could not find much companionship.
The development of Silloth did much to give him, in this latter
matter, much of what he formerly missed, and few of the scientific
visitors left without visiting his observatory.

His health of late years had not been robust, but latterly
symptoms of malignant disease of the abdomen set in. His last
illness, which was of a painful character, was borne with great
fortitude. No one knew better than himself there was only one
possible termination, but amid his sufferings he found relief by
turning to his scientific pursuits, and by the reflection that during
the course of a long and active life he had accumulated observations
that would be of value to his fellow-men.

136

General A. C. Eobertson. By T. Stevenson, P.R.S.A.

General A. G Robertson, the eldest son of Lieutenant David
Eobertson, of Eoyal Marines, was bom at Edinburgh, February 8,
1816, and was educated at the High School and University there.
I knew him from boyhood as a bom soldier, always ready to fight
his battles with other boys under every circumstance of disadvantage,
and when he found a difficulty in getting his commission he at once
joined other volunteers from this country who took part in fighting
against Dom Miguel in Portugal in 1834. Serving under Sir de
Lucy Evans, he saw much heavy service with the British Auxiliary
Legion in the north of Spain. He was present at the relief of
St Sebastian and at the other battles which followed in quick
succession during the years 1836 and 1837. At Ametza Eobertson
was severely wounded by a rock splinter from a round shot. He
received for his services in Spain two medals and the cross of the
first class of San Fernando. Eobertson had risen to be captain in
the Legion when, owing to some difference with his commanding
officer, he threw up his commission and enlisted in another regiment,
and rose again to be captain — a promotion which took place before
he was one-and-twenty. In 1837 he obtained a commission in the
34th Regiment, serving with it for three years in Canada, having
got his company in 1845.

In 1842-43 he had studied at the Senior Department, Sandhurst
— the germ of the present Staff College, — and obtained superior
certificates in mathematics and surveying. In April 1846 he ex-
changed into the 8th (the King’s), with which he continued for the
remaining twenty-nine years of his regimental service. A few days
after the arrival of his regiment at Delhi, Eobertson joined if there
along with Colonel Baird Smith of the Engineers, and served in the
siege till September 11, when the breakdown of his health com-
pelled his being sent to the hills. Colonel Greathead says in his
diary : — “ Robertson was under fire from seven in the morning until
six in the evening;” and again, regarding the mutiny, “The work
was very well done, and the King’s behaved very steadily under
Captain Robertson, who is one of the bravest and coolest men under
fire that can be seen.” For his services during the mutiny he was

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mentioned in despatches, received the brevets of major and
lieut.-colonel, a medal and two clasps; and after obtaining his lien-
tenant-colonelcy in 1865, he commanded the 2nd battalion of the
King’s — a post which he retained for nine years at Malta and in
various home quarters. In 1876 he was nominated to the command
of the 13th and 14th Brigade Depots, retiring finally in 1878. He
was gazetted C.B. on 2nd June 1877, and 24th March 1880 was
appointed honorary colonel of the 15th Lancashire Rifle Volun-
teers.

After his retirement he lived chiefly in Edinburgh, and subse-
quently died at Liverpool, on 2nd December 1884, of a disease of
an incurable and most painful nature, borne with singular patience
and cheerfulness. Robertson was a man of much thoughtfulness,
as well as a zealous soldier, and wrote with great independence on
the following subjects : — Infantry ; the tactics of the three arms ;
on the first three parts of the field exercises and evolutions of the
army, and on some of the resemblances and differences between
them and the corresponding part of the French ordnance, &c. ; on
the means of applying the principle of stimulating the voluntary
exertions of individuals to the improvement of the system of military
training; and a variety of other subjects connected with his
profession. Besides which, he devoted his leisure for some years
to a verse translation of “Jerusalem Delivered.” In later years he
re-edited the Historical Record of the King’s Regiment. Robertson
was therefore a man whom we may well be proud to reckon among
our Fellows.

Augustus John Darling Cameron. By T. Stevenson,

P.R.S.A.

Augustus John Darling Cameron, the only son of the late John
Cameron of Edinburgh, was born in October 1841, and was educated
at the High School and University there. In 1860 he began an
apprenticeship as a civil engineer with the late Mr John Paterson.
He was subsequently in the employment of Messrs Foreman and
M‘Call, Glasgow, and Messrs Wylie & Peddie, and was engaged on
railway and other works. He held an appointment of engineer in

138

the India Office for several years, after which he was engineer to
the South London Tramways Company, and under his superintend-
ence the various lines of that company were constructed. He died
on 27th November 1884. He was elected a member of the Institu-
tion of Civil Engineers in 1880, and a Eellow of this Society on 6th
June 1881.

John M‘Naik. By T. Stevenson, P.R.S.A.

John M‘Nair was for nearly twenty years a Eellow of the Royal
Society of Edinburgh. He took a lively interest in physical subjects,
but owing to his advanced age, and the latterly feeble state of his
health, was prevented from attending our meetings very regularly.
He was born at Belvidere, near Glasgow, in 1801, and died at
Edinburgh in his eighty-fifth year.

William Lindsay Alexander By Professor Flint.

William Lindsay Alexander was born at Leith on 24th August
1808. He was educated at the High School of his native town and
in the Universities of Edinburgh and St Andrews. He distin-
guished himself in all his classes, but especially in those of Latin,
Greek, Logic, and Moral Philosophy. While at St Andrews his
earlier religious impressions were much deepened by intercourse
with a pious fellow-student, and through the inspiring influence of
Dr Chalmers. Although he began preaching when still a student
of Arts, it was not until 1832, five years after he had left college,
that he made choice of the Christian ministry as his profession.
Teaching, literature, law, medicine, all presented themselves to him
with competing claims. During the greater portion of this period
of indecision and unsettlement he was occupied as classical tutor
in the Congregational Academy at Blackburn. Passing through
Liverpool in 1832, he was persuaded to occupy for a Sunday the
pulpit of Newington Street Independent Chapel, then vacant. The
result was that he remained in charge of the congregation for a

139

year and a half, putting his qualifications for the ministry to a
thorough test, and gradually coming to feel that he had found his
true vocation. He afterwards went to Germany, and studied
theology for a short time in Halle and Leipsic.

On 5th February 1835 he was ordained to the ministry, and
became the pastor of the congregation meeting in what was then
called “North College Street Chapel,” Edinburgh. The connection
then formed lasted somewhat over forty-two years. Mr Alexander
at once gained, and to the last retained, great popularity as a
preacher. In stimulating and guiding the Christian energies of his
congregation he was also eminently successful. Gradually he
attained in his own denomination an influence with which that of
no one else in Scotland could he compared, while his services to the
common Christian cause, his genuine catholicity of spirit, and his
candour and courtesy even as a controversialist, made his name
honoured in all denominations. His scholarship, literary talents,
and theological acquirements became attested by writings which
spread his reputation far beyond the limits of Britain. Notwith-
standing a certain shyness and reserve of manner, his amiability and
affectionateness of nature attracted to him numerous warmly attached
friends. Among the events and dates of his life during his
ministry in Edinburgh, these may he specified, — his marriage in
August 1837 ; his delivery of the Congregational Lecture at London
in 1840; his editorship of the Congregational Magazine from 1836
to 1840 ; his receiving of the degree of Doctor of Divinity from the
University of St Andrews in 1845 ; his candidature for the chair of
Moral Philosophy in the University of Edinburgh in 1852; his
appointment to the Professorship of Theology in the Congregational
College in 1854; his removal with his people from Argyle Square
to Queen Street Hall in 1855, and thence to the new church (St
Augustine Church) on George the Fourth Bridge in 1861 ; his
election as examiner in philosophy at St Andrews University in
1861 ; his visit to Palestine in 1869 ; his selection as a member of
the Old Testament Revision Company in 1870 ; his appointment
by the Council of Edinburgh University assessor to the University
Court in 1871, and reappointment in 1875 ; and “ the greatest sorrow
of his life,” the death of Mrs Alexander in the last-named year.
He published The Connection and Harmony of the Old and New

140

Testaments in 1841 ; Anglo -Catholicism not Apostolic in 1843 ;
Switzerland and the Swiss Churches in 1846 ; Christ and
Christianity in 1854 ; The Life and Correspondence of Ralph
Wardlaw, D.D., in 1856 ; Christian Thought and Work in 1862;
and St Paul at Athens in 1865. He contributed to the eighth
edition of the Encyclopaedia Britannica three elaborate treatises —
Moral Philosophy (vol. xv., 1858), Holy Scriptures (vol. xix., 1859),
and Theology (vol. xxi., 1860). From 1861 to 1869 he superin-
tended the publication of the third edition of Kitto’s Cyclopaedia
of Biblical Literature , and supplied a very large number of the
articles which appeared in it. He was also the author of at least
forty sermons, lectures, or pamphlets, published separately, and a
frequent contributor to Reviews and Magazines.

Dr Alexander resigned his ministerial charge on 6th June 1877,
and was in the same year appointed Principal of the Theological
Hall, while retaining his professorship. From a sense of growing
infirmity, these latter offices also he resigned in 1881. In 1884 he
received the degree of LL.D. from the University of Edinburgh, on
the occasion of its Tercentenary. Amidst deep and wide regret, on
the 20th December of that year, he died at Pinkieburn, leaving
behind him many a good work to perpetuate 'and endear his memory,
and the example of an unsullied and beneficent, faithful, and con-
sistent life.

Dr Alexander was elected a Fellow of the Royal Society on 29th
April 1867, one of the vice-presidents on 24th November 1873,
and was re-elected a vice-president on 22nd November 1880. He
wrote a number of obituary notices of eminent members, and
delivered the Opening Address of the Session 1876-77.

Having indicated the chief facts of his life, let us now glance at
the chief aspects of his character.

It was impossible to think of him otherwise than as a remark-
ably accomplished scholar. He was throughout his life an earnest
student. No one knew better that knowledge is not the supreme
object of human life, yet no one could realise more how precious
and pleasant it is, and how closely connected with what is best.
Hence a large portion of his daily life was given to its acquisition,
and not selfishly, but in the belief that through self-improvement he
would the more profit others. He had a keen interest in most

141

kinds of science and learning; had cultivated with special care
various departments of theology and philosophy ; was intimately
conversant with Biblical studies ; was widely read in classical and
modern literature ; and was an excellent Latinist, Hellenist, and
Hebraist. His mastery over the classical tongues as poetical media
is amply attested by the collection of Greek and Latin verses which
he printed privately and dedicated to his brethren of the Hellenic
Society. His attainments as a Hebraist he had many opportunities
of applying. He delighted in good English poetry, and was the
author of a considerable number of very meritorious English
hymns.

The amount of literary work which Dr Alexander performed
must be regarded as marvellous, when it is considered with what
diligence and success he discharged the many duties of his ministry
and professorship. Yet none of his writings bear the marks of
hasty and inadequate preparation. The briefest articles from his
pen in Kitto are carefully executed. That he achieved so much as
an author was doubtless due largely to strength and readiness of
memory, clearness and vigour of thought, and facility of accurate
and appropriate expression, but it was due as largely to his self-
denying and methodical employment of his time. In this respect
few can ever have surpassed him. At the commencement of his
ministry he formed the resolution never to have what people called
“ a spare hour,’5 but to lay out his work every day so as to know
each hour exactly what to do ; and to this resolution he steadily
adhered to the close of his life.

From the time that he listened to Chalmers in St Andrews, philo-
sophy, and especially moral philosophy, had strong attractions for him.
How high was his estimate of philosophy and his ideal of the
philosopher may be best learned from his eloquent and elaborate
address to the Philosophical Society of the University of Edinburgh
on his election as president in 1875. The most adequate measure
of his philosophical ability is, however, the treatise on Moral
Philosophy in the Encydopcedia Britannica. It presents us with a
clearly defined, well-arranged, skilfully rounded system of ethical
science. If not exhibiting much originality, it displays extensive
learning and careful and independent reflection. It fully entitles its
author to an honourable place among Scottish moral philosophers.

142

Dr Alexander devoted, of course, far more of his time and energy
to theology than to philosophy. And it may safely be said that
among his contemporaries in Scotland there was no more generally
accomplished a theologian, although he was doubtless surpassed by
several of them in particular qualities. He attained a high reach of
excellence alike in exegetical, historical, apologetic, systematic, and
practical theology. In all these departments he produced excellent
wTorks. On any special theological problem he could at once bring
to bear ample knowledge and a rich combination of strong and
disciplined mental powers. It cannot, indeed, be said that in
theology, any more than in philosophy, he opened up or even
followed out new paths of research. His mind rapidly reached
maturity, and the religious opinions which he formed in youth
remained almost unmodified to the close of his life. Within the
limits of so-called orthodoxy, however, his intellect acted with
admirable freedom and effectiveness. He held firmly to the
Calvinistic system of doctrine and to the Congregational scheme
of Church government, but with conspicuous independence of
judgment. On various theological and ecclesiastical questions he
differed decidedly even from those with whom he was in the main
most in agreement. This appears very clearly in his Memoirs of
Dr Wardlaw, in which criticism mingles so largely with admira-
tion.

Dr Alexander took a somewhat prominent part in most of the
religious controversies of his time. On the platform and through
the press he felt called to set forth his views on Episcopacy, Anglo-
Catholicism, Romanism, Church Establishments, and the like; he
was drawn into the Voluntary, Spiritual Independence, Morrisonian,
and some minor conflicts. It will be admitted by all, however,
that while he .always fought with vigour, he also always fought
without bitterness or unfairness, and obviously from no love of
strife itself or desire for personal or party victory, but from a sense
of what he felt due to truth and the public good. As was to Lave
been expected in the case of one whose mind wTas so justly balanced
and so catholic in its sympathies, the more experience he acquired
of religious controversy the more disappointed he became with its
results, and in his later life he kept aloof from it.

As a pulpit orator he was of remarkable merit. Never aiming at

143

popularity, making it a rule not to prepare so-called “great sermons,”
constantly dealing largely in the exposition of Scripture and the
setting forth of doctrine, habitually keeping feeling under restraint,
and very sparing of gesture and action, he was yet not only a most
instructive, but a most interesting and impressive preacher. His
tall stature and noble presence, his admirable delivery, his style
refined yet strong, somewhat elaborate but also singularly lucid, the
amount of knowledge which he communicated, and of light which
he cast on Scripture, his intellectual force, his vivid and deep realisa-
tion of spiritual things, and the judiciousness and pointedness of
his practical applications of truth, combined to make him a great
and beneficent power in the pulpit.

As a man his character commanded universal respect. None
doubted his piety and benevolence any more than his learning or
ability. He gained many friends, and alienated none. He was
especially at home in scholarly and intellectual society, and where
at home he was a charming companion, unaffected and genial, with
a keen sense of humour and hearty love of mirth, and with an
inexhaustible store of anecdotes, which he delighted to tell, and
which he told exceedingly well.

His private and domestic life has been gracefully delineated by
Miss E. T. McLaren, in reminiscences originally printed for private
circulation, but now incorporated in the Life of Dr Alexander by
the Rev. Mr Ross. Mr Ross himself, as an old student of Dr
Alexander, has given us an account of his character and work as
a professor, from which it is apparent that he was nowhere more
admirable and successful than in his class-room.

The memory of Dr William Lindsay Alexander will be long
affectionately cherished and highly honoured.

William Chambers, LL.D. By David Patrick, M.A.

William Chambers, one of the founders of the publishing firm
of William and Robert Chambers, and in his later years distinguished
for his public spirit as a citizen, was born at Peebles on the 16th
April 1800, his father being a cotton manufacturer there. William,

144

the eldest son, received a fair elementary education at Peebles *
but as, owing to the father’s misfortune, his school days terminated
with his thirteenth year, his education for life-work was mainly
due to the habit, very early acquired and long maintained, of
miscellaneous and extensive reading. The household migrated to
Edinburgh in 1813, and next year William was apprenticed to a
bookseller. Immediately after his five years’ apprenticeship was
out, he began business in a very humble way for himself, and soon
added to bookselling the occupation of a jobbing-printer. He by-
and-by ventured to print and publish small pamphlets written or
compiled by himself or his younger brother Eobert, also established
as a bookseller in Edinburgh. Through much industry, care, and
economy they each prospered, and by 1825 what they called their
“dark ages” had closed for ever. In 1825 William produced
The Booh of Scotland , and had a share with his brother in compil-
ing a gazetteer; but it was the Chambers's Edinburgh Journal ,
projected and started by "William in 1832, that brought great and
permanent success to both brothers. Erom the beginning, Eobert
was the most important contributor to the Journal ; and a month
or two after it was fairly afloat, the two brothers united their
resources and enterprise under the now so well known firm of
W. & E. Chambers. Other important publications of the firm were
the Information for the People (1833); the Educational Course ,
comprising an extensive series of text-books in history, science, and
literature ; the Miscellany ; the Encyclopaedia (10 vols., 1859-1868);
the Cyclopaedia of Literature , and numerous works by Eobert
Chambers. In 1859 the elder brother presented his native town
with a public library, reading room, and museum. In 1865 he
was chosen Lord Provost of the city of Edinburgh, and in this
capacity carried out a very important measure for the improvement
of the city, by substituting healthy houses and airy streets for lanes
and closes of pestiferous hovels. He was the chief promoter of a
partial restoration of the ancient Kirk of St Giles; and in 1878-83
he carried out a more complete and extensive restoration at his own
expense. He found time to write an admirable county history of
Peeblesshire (1864), a short history of France, sketches of tours in
Holland, America, Italy, and France, various other short works, and
a memoir (with autobiographical reminiscences) of his brother Eobert,

145

who was a member of this Society from 1840 till his death 1871, and
is known as the author of numerous works, including the Traditions
of Edinburgh, the History of the Rebellion , the Ancient Sea Margins ,
and the (anonymously published) Vestiges of Creation. William
became a fellow of the Royal Society of Edinburgh in 1860 ; and
he was made LL.D. by Edinburgh University in 1872. For his
services to the cause of public instruction, and his work as a civic
ruler, an offer of knighthood, which he declined, was made in
1881. But when, a fortnight before his death, a baronetcy was
offered him, he accepted it. It had not, however, been formally
conferred or gazetted, when on the 20th May 1883 he died, at the
advanced age of more than 83 years, and but a few days before the
ceremony that marked the completion of the last work of his life,
the reopening of the 'restored church of St Giles. He was buried
in the place of his birth, and many manifestations were made of
esteem and gratitude for his services to English-speaking men and
women, by providing works of instruction and entertainment ac-
cessible at small cost to all of whatever rank or condition. His
life of unremitting labour and his remarkable business abilities
brought to him wealth, honour, and influence, and these were by
him faithfully turned to account for the general good.

David Stevenson.

David Stevenson, the third son of the late Mr Robert Stevenson,
the well-known civil engineer, was born at Edinburgh on the 1 1th.
January 1815. Educated at the High School and University of
Edinburgh, he elected from the first to follow his father’s profession.
Before entering on his apprenticeship he was for some time in the
workshops of one of the best millwrights of the day, where he
acquired manipulative skill and the proper methods of working in
different materials, — a course he always advocated for those who
intended to follow the profession of civil engineering. After
serving a regular pupilage under his father, during which period he
had ample opportunities of attending various engineering works in
progress, he was for some time engaged with Mr Mackenzie on

k

146

railway works, particularly the Edgehill Tunnel and the Liverpool
and Manchester Railway. He gave a description of the “ Liverpool
and Manchester Railway ” to the Royal Scottish Society of Arts
in February 1835, and was awarded their medal for his exposition.
This paper was followed, in March 1836, by “Remarks on the
Dublin and Kingston Railway.” In 1835 Brunei asked Mr
Stevenson to join his staff at the Thames Tunnel works, — an offer
which he could not accept, as he had been appointed to superintend
the construction of other works.

During the summer of the year 1837, Mr Stevenson made a tour
in Canada and the United States, and the result of his inspection
of the engineering works of these countries was given in a volume,
published in 1838, entitled “Sketch of the Civil Engineering of
North America,” which was republished with additions in 1859,
as one of Weale’s series of engineering works. The engineering
practice therein described was peculiarly applicable to newly de-
veloped countries, where timber forms the chief material employed.
The views expressed and the drawings given in this book, with
reference to the fine lines and speed of American river and lake
steamers, were received in this country by shipbuilders with distrust,
if not ridicule; but the bluff bows of British sea-going and river
steamers, and short-stroke engines, all below deck, gave way to finer
lines and engines of high power and long stroke ; and soon there-
after steamships were plying on the Clyde at higher speed than in
America. He had models made in New York of two of the fastest
steamers, — a sea and river boat, — which were submitted to the
Admiralty after his book was published; but as the “lines” had
been there given, the authorities did not care for the models, and
they ultimately went to the Russian Government. In this book Mr
Stevenson also pointed out the true conditions under which waves
are formed, which his subsequent experience as a marine engineer
amply corroborated.

Mr Stevenson entered into partnership with his father and
brother Alan in 1838. As his father was then nearly 67 years of
age, and his brother was wholly engaged with the arduous works at
Skerryvore Lighthouse, the entire management of the business fell
upon Mr Stevenson, and very soon his advice was much sought in
reference to the improvement of rivers and harbours, and the con-

147

struction of docks and other marine works. There are, indeed,
very few rivers and harbours in Scotland with which he was not
in some way professionally connected. He was also called upon to
report or to execute works for the improvement of the rivers Dee,
Lune, Ribble, and Wear in England ; the Erne and Foyle in
Ireland ; and the Forth, Tay, Ness, Nith, and Clyde in Scotland.
He designed and executed the works of restoration and enlargement
of the Fossdyke in Lincolnshire, — the oldest artificial navigation in
Britain, — the widening and deepening being accomplished without
stopping the traffic. His advice was also taken on many important
questions relating to salmon fishings in rivers and estuaries, and in
his Report of August 1842 on the Dornoch Fishings, he defined
the different compartments of rivers, according to their physical
characteristics, as “sea proper,” “tidal,” and “river proper.” The
views expressed in this report were subsequently treated at
greater length in “ Remarks on the Improvement of Tidal Rivers,”
communicated to this Society on 17th March 1845, which paper
was afterwards published in a separate form by Mr Weale. In this
paper he stated his views with regard to the special works which
should be undertaken for the improvement of the different com-
partments, and he showed conclusively that, if tidal propagation
were accelerated, difference of level or height of head will be
lessened and the velocity of the tide currents decreased ; and
the notion that, by deepening a river and removing obstructions,
the water in it may be caused to rise higher and to endanger pro-
perty on its banks, was without foundation. All his subsequent
experience went to prove that the views expressed more than forty
years ago were sound. He was also the first to enunciate the true
theory of the origin of bars at the mouths of rivers, and to point out
the works necessary for removing them and preventing their re-
formation. The necessity of having accurate data before designing
works for the improvement of rivers, estuaries, and harbours led to
his writing a treatise on the “ Application of Marine Surveying and
Hydrometry to the Practice of Civil Engineering.” His known
standing as a marine engineer led his old friend, the late Mr Adam
Black, to invite him to write the article “ Inland Navigation ” for
the last edition of the Encyclopaedia Britannica. This article was
republished in 1858 as a separate treatise, entitled “Canal and

148

River Engineering,” and it is now in its third edition. In this
book he has given the results of his practice in the treatment of
rivers, and it will long remain the standard work in this difficult
branch of engineering. In 1877, at the request of the authorities,
he delivered a course of four lectures on “ Canal and River
Engineering ” to the students of the School of Military Engineer-
ing, Chatham.

During the height of the railway mania, when speculators were
overwhelming the Admiralty and Woods and Forests with schemes
too numerous to be dealt with by the officials, Mr Stevenson was
appointed to hold Courts of Inquiry, under the “Preliminary
Inquiries Act,” into the merits of a large number of railway and
harbour projects and water-supply schemes, and in all cases save
one his views were given effect to by the Authorities and Committees
of Parliament. This exception was the proposed crossing of the
Clyde by the Caledonian Railway. He reported that the railway
might be allowed to cross the Clyde above Stockwell Bridge, but
the Admiralty refused their sanction. A crossing, however, was
subsequently applied for, and has been made.

In 1853 Mr Stevenson succeeded his brother Alan as engineer to
the Northern Lighthouse Board, and, along with his brother Thomas,
who was at a subsequent date conjoined with him in the engineership,
he designed and executed no fewer than twenty-eight beacons and
thirty lighthouses, three of which — on North Unst, Dhu Heartach,
and the Chickens Rocks — were works of great difficulty, requiring
the exercise of great engineering skill. The advice of the firm
was also taken by the Governments of India, Newfoundland, New
Zealand, and Japan on lighthouse matters, and schemes for the
lighting of the whole coasts of the two last countries were matured,
and are now being carried out. In connection with the lighting of
the coasts of Japan, where earthquakes are of frequent occurrence,
Mr Stevenson devised the aseismatic arrangement, to mitigate
the effect of shocks on the somewhat delicate apparatus used in
lighthouses, and was awarded the Makdougall-Brisbane Medal of
the Royal Scottish Society of Arts for his invention. Mr Steven-
son took a great interest in the introduction of paraffin as an
illuminant for lighthouses, instead of the more expensive colza oil.
After experiments conducted at Edinburgh with the Doty burners,

149

and actual trial during a month at Girdleness Lighthouse, a report
was made to the Northern Lighthouse Board, embodying the follow-
ing results: — That paraffin, as now manufactured, with a high specific
gravity and flashing point, is safe ; that the flame is of great purity
and intensity, and easily maintained ; the lamp glasses and lamps
used for colza are equally suitable for paraffin ; and that the initial
power of the lights on the Scottish coasts would be exalted, and
this, too, at an annual saving of £3500. The relative merits of
colza oil and paraffin were thus settled, and most British and
many European, foreign, and colonial lighthouses now consume
paraffin, with an increased luminous intensity, and decreased cost
of maintenance.

Mr Stevenson frequently appeared before Parliamentary Com-
mittees, and also gave evidence before Special Committees and
Royal Commissions on Harbours, River Improvements, Harbours of
Refuge and Lighthouses. For these Committees and Commissions
he always prepared with scrupulous care ; and he was a most con-
scientious witness, never entering the box without being satisfied
as to the soundness of the cause he was supporting ; and in no case
did a Committee ever throw out a Bill, the Parliamentary plans
and estimates of which he had prepared. In his native city Mr
Stevenson was greatly respected, and his advice on many important
matters connected with city improvements was sought and highly
valued. His views on the city improvement scheme, as conveyed
to Lord Provost Chambers and the late Mr David Cousin, city
architect, along with his letters which appeared in the Scotsman at
the time, greatly facilitated the initiation of this great sanitary im-
provement, now nearing its completion. Among other local works,
his firm designed and carried out the Edinburgh and Leith and
North Leith sewerage schemes, and the widening of the North
Bridge.

Mr Stevenson was consulting engineer to the Convention of
Royal Burghs of Scotland and to the Highland and Agricultural
Society. In the affairs of the latter he took a lively interest,
especially in the trials of improved agricultural implements; and be
contributed several papers and reports to their Transactions , notably
one on the reclamation of land, and one on the relative merits of
different systems of steam ploughing. The paper on “Reclamation

150

and Protection of Agricultural Land ” was republished as a separate
treatise in 1874.

Mr Stevenson’s books have taken a permanent place in engineer-
ing literature. Amid the exacting calls of his profession he found
time to write many papers on engineering and cognate subjects, in
addition to the books already noticed. He also wrote several
articles for the last and the present editions of the Encyclopedia
Britannica , among which may be noticed “ Canal,” “ Cofferdam,”
“ Diving,” and {£ Dredging.” He was also the author of Our Light-
houses, being two articles written for his old friend, Dr Norman
Macleod, while editor of Good Words , subsequently republished by
Messrs Black, and of the Life of Robert Stevenson , published in
1878.

Mr Stevenson was twice elected President of the Royal Scottish
Society of Arts, and for his Presidential Address of 1869 he chose
as his subject “ Altered Relations of British and Foreign Industries
and Manufactures,” in which he strongly urged the propriety of
artisans improving their manipulative skill and their knowledge
and management of the materials with which they had to deal, if
they did not wish to be distanced in the race by foreign competition.
He was elected a Fellow of this Society in 1844, and subsequently
acted as a member of Council and one of its Vice-Presidents. In addi-
tion to the “ Remarks on the Improvement of Tidal Rivers ” already
noticed, and several obituary notices of professional brethren, he
contributed to our Proceedings “ Notices of the Works designed by
Sir C. A. Hartley for the Improvement of the Danube,” “ Notices
of the Ravages of the Limnoria Terebrans on Creosoted Timber, and
on Greenheart Timber.” “ Notice of Two Earthquakes on the West
Coast of Scotland,” and “ Notice of Striated Rock Surfaces on North
Berwick Law.” He was elected a Member of the Institution of
Civil Engineers in 1844, and acted as a member of its Council from
1877 till 1883, when he retired on account of ill-health; he was
also a member of the Soci6t6 des Ingenieurs Civils, Paris, and of
other learned Societies.

Mr Stevenson took a warm interest in the better endowment of
the Chairs of the University of Edinburgh, and was mainly instru-
mental in founding the Glover Divinity Fellowship. He was a
great lover of art in all its branches, and had formed a somewhat

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valuable collection of etchings and engravings, begun when a boy
at the High School, his school companion in print-hunting being a
life-long friend, Sir Theodore Martin. He was a man of sound
judgment, unswerving rectitude, utterly devoid of ostentation,
kind, open, and easily accessible. He was practically laid aside
from work for about two years, and he died at North Berwick, on
the 17th July 1886, in the seventy-second year of his age.

Bishop Cotterill. By Dr Cazenove.

Henry Cotterill was born in the year 1812, on the 6th day of
January, a day ecclesiastically known as the Feast of the Epiphany,
and in popular parlance as Twelfth Night. He was the son of the
Rev. Joseph Cotterill, rector of Blakeney, in the county of
Norfolk. Mr Cotterill had been educated at Cambridge, and had
taken a high degree, coming out as Seventh Wrangler. The
grandfather of the future Bishop had also been a Cantabrigian, and
was known in Sheffield as a man of culture. He was the author of
a book of family prayers. All three were successively members of
the same College. All three could say, with the poet Wordsworth,
“ The Evangelist St John my patron was,”
and all could, with him, avow a fondness for mathematical as well
as for classical studies.

In classics Henry Cotterill found a preceptress in his mother.
This lady, known before her marriage as Miss Anne Boak, was very
clever and clear-headed. She was a great friend of the celebrated
Hannah More, and to some extent assisted that lady in the
preparation of a tale, which was widely read at the time of its
publication, Ccelebs in Search of a Wife. Miss Boak contributed
some chapters which contained descriptions of scenery. She had
also a considerable acquaintance with mathematics, and was
generally a learned woman.

Not only did she superintend the education of her three daughters,
but she instructed her two sons, Henry and George Cotterill, in
Latin, until they were fifteen years of age.

Here, it will be said, is a clear case of heredity. I am far from

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wishing to dispute the point ; hut we must not, I think, neglect
another element of the case. A distinguished scholar and mathe-
matician, who had been well acquainted with a school which was
attended by boys from homes of very varied station and character,
told me that, as a rule, the difference was immense between the
progress of the pupils who went back daily, or at set periods, to
homes where they heard nothing connected with their studies, and
those who, when not at school, lived in the houses of relatives or
of friends, which were the abodes of educated people. Extra-
ordinary genius will no doubt triumph over these and many other
obstacles. But to the youthful student the lack of sympathy
at home is a formidable disadvantage. Oliver Wendell Holmes
implies, I think, that it has been found so in the United States
of America, as well as in Europe. And the inquirers into the
influence of heredity ought, it seems to me, to take some pains in
examining into this phase of the question, and ask whether this
and that man of mark did or did not in youth enjoy the benefit
of an atmosphere of culture.

Whatever be the decision, it is at least clear that Henry Cotterill
was in this respect exceptionally favoured. He began to receive
lessons in Latin when he was five years old; and at the age of
fifteen he and his brother George were, as a favour, accepted as
private pupils at Cambridge, by Mr Scholefield, subsequently so
celebrated as the Regius Professor of Greek in the University of
Cambridge. From this admirable teacher Henry Cotterill learnt
his first lessons in Greek, and to his latest day he always expressed
his deep gratitude to his tutor, and his keen sense of the good
fortune he had enjoyed in having had such a preceptor. Hor was
he less favoured in mathematics. A very eminent mathematician,
William Hopkins (father of a philanthropic lady, Miss Ellice
Hopkins, subsequently a great friend of the Bishop’s), took charge
of his studies in Mathesis.

At a later date, a brilliant Cambridge scholar described, in
beautiful Greek Iambics, how Jupiter, being angry with mortals,
commissioned Vulcan to invent a new plague, and how from this
command came forth the penal infliction of mathematical study.
Such was not, as has already been observed, the sentiment cherished
towards the science of lines and of numbers by this youthful

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classic. Contrariwise, his proficiency in this new field of learning
seems to have even surpassed that which he achieved in ancient
languages. And during vacations he was sure of living in an
atmosphere wThere his studies would receive abundance of encourage-
ment and sympathy. His sisters were ladies of cultivated taste,
the youngest especially being a good Latin scholar.

At Cambridge he found friends among contemporaries, and also
some among seniors, who, in different ways, influenced his career.
Among the seniors, besides the tutors already named, he was
acquainted with Professor Sedgwick, with Professor Airy (after-
wards the Astronomer Royal), and the aged Mr Simeon. Among
those of his own standing may be named Mr Dickinson, afterwards
representative in Parliament for Somersetshire ; and a member of a
highly gifted family, a Merivale, brother of a distinguished Oxonian,
W. Herman Merivale, and of equally eminent Cantabrigians, such as
the present Dean of Ely. But specially intimate was he with a son
of the Bight Hon. Henry Goulburn, sometime Chancellor of the
Exchequer. In both classics and mathematics these two, Goulburn
and Cotterill, were keen, but most friendly rivals. We cannot doubt
but that from such guides and friends, and from several more like
them, Henry Cotterill must have learned a great deal, though the
intercourse cannot possibly have been a merely one-sided bargain.
Some of them, as Merivale and Goulburn, were not permitted to
display all their powers, having died at a comparatively early age.

In 1832, a year known in British history as that of the passing of
the Reform Bill, Henry Cotterill was elected a scholar of St John’s
College, Cambridge. In that same year he won the University Bell
Scholarship, one of the blue ribands of undergraduate life, as an
evidence of proficiency in classics ; though its glories are perhaps
slightly limited by its being confined to the sons of clergymen.

In 1835 he took his Bachelor’s degree, his work at Cambridge
culminating in the extraordinary success of his being Senior
Wrangler, First Smith’s Prizeman, and ninth in the First Class of
the Classical Tripos, which was headed by the Second Wrangler, his
young friend Henry Goulburn. This achievement probably justifies
the remark of the late Principal of the University of Edinburgh,
Sir Alexander Grant, that Henry Cotterill left Cambridge bearing
a greater weight of honours than any other student had gained.

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Among the few rivals who have nearly approximated, may he
named Charles Webb Le Bas, afterwards Principal of Hailebury
College, and the Hon. William Cavendish, now Duke of Devon-
shire. Almost as a matter of course, Mr Cotterill was, soon after
taking his degree, elected a Fellow of St John’s.

The present imperfect sketch is mainly concerned with the career
of its subject in relation to those gifts which would be felt to con-
stitute his claim to become a Fellow of this Royal Society. But it
is impossible to pass by in silence certain elements of the case
which exercised a very real, though in part an indirect, influence
upon his mental development.

At this juncture he might have laid out for himself a course of
life which would necessitate his remaining a man of study rather
than of action ; or he might have chosen a profession, such as that
of the bar, in which it would be possible, while relegating to a
secondary position his Cambridge studies, to make use of the mental
training thus acquired. His University had abundant examples to
encourage him in either of these directions, — brilliant honour-men
who had become famous as scholars or men of science, and others
who had been conspicuous as barristers and as judges.

But the tone of another profession ruled in the home in which
he had been brought up, even more strongly than the love of
culture for its own sake, or for the prizes which might thereby be
won. Entirely by his own choice, — though no doubt it was a choice
greatly moulded by the influences around him, — Henry Cotterill
resolved to take Holy Orders. But this was not all. His father
had begun to cherish, in his maturer years, a keen sympathy with
missionary work. It came seemingly too late in life for him to
change his sphere of labour. But he had expressed a hope that
his sons, even if they did not feel called to devote their lives to
direct missionary work, might at least for a time occupy positions
in which they could support and assist missionary efforts. The
father’s wish was never forgotten by the son, who always regarded
it as a grave mistake to send out to our Colonies only clergy of
powers below the average.

Henry Cotterill was ordained deacon in 1835, and priest in the
year following. In this latter year a presentation to one of the
East India Company’s chaplaincies was placed in the gift of the

University of Cambridge. Much to the surprise of many friends
and of still more numerous bystanders, Mr Cotterill accepted the
nomination. That such a step was not calculated to lead to pre-
ferment at home was obvious enough ; but the father entirely
sanctioned the proceeding ; and the son never, I believe, for a
moment regretted it.

The appointment took him to the Madras Presidency. Before
leaving England he vacated his fellowship by marriage with Anna,
daughter of John Panther, Esq. of Bellevue, in Jamaica. By
this honoured and much-respected lady, who lives to mourn his
loss, he became the father of four sons and two daughters, of whom
all, but one daughter, have survived him.

At Madras he saw much of missionary work among the heathen,
and acquired an interest in it which never left him. But the
climate did not suit him, and at the end of eight years’ residence
his health was seriously affected. In 1847 he returned to England,
and accepted the position of Vice-Principal of Brighton College, a
newly founded institution. In 1851 he succeeded to the Principal-
ship, rendered vacant by the death of its previous occupant, Dr
Maclean.

Although this College prospered greatly under his care, there
were those among his friends who felt that it was not a sphere
that afforded full scope for his varied powers. One of these, a
layman, a member of a family deeply interested in missions, walk-
ing in London, is said to have noticed an advertising board headed
by the words “Wasted Steam.” The title suggested to this
gentleman’s mind instances of such loss among men whom he had
known, and it struck him that Henry Cotterill was at that moment
an example of such waste. “By the way,” so his thoughts ran
onward, “ Archbishop Sumner told me that the See of Grahams-
town had become vacant by the decease of Bishop Armstrong, and
that a successor was being sought for it. Mr Cotterill would be
the very man for the place.” Fired by this idea, he at once pro-
ceeded to Lambeth, and the result was that on November 23rd,
1856, Henry Cotterill was consecrated and then duly gazetted as
Lord Bishop of Grahamstown.

The Bishop of Capetown, Dr Gray, seems at first to have feared
that he and his new colleague might not work harmoniously. An

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unlooked-for event brought them into thorough concord with each
other. In the year 1836, that is to say the year after that of
Mr Cotterill’s Senior Wranglership, the place of Second Wrangler
had been won by a member of St John’s, who was thereupon
elected Fellow of that College. His name was Colenso; and after
having had experience, both in tuition as a mathematical master
at Harrow, and also in pastoral work as a country vicar, he had
been selected for the office of Bishop of Natal. Dr Colenso
published works certainly of a startling character ; and his former
brother-fellow, the Bishop of Grahamstown, in November 1863,
formed part of an Episcopal Court which condemned the teaching
of Bishop Colenso as heretical. This sentence was not confirmed
by the State, inasmuch as the Privy Council declined to recognise
the legal validity of the letters-patent granted to Bishop Gray, and
of his claims to act as Metropolitan. The opinion, however, de-
livered by Bishop Cotterill was allowed on all sides to be one of
remarkable clearness and ability.

In 1867 the Archbishop of Canterbury, Dr Longley, held a
gathering at Lambeth of the Bishops of the Anglican Communion ;
and a similar one took place in 1878, under the presidency of
Archbishop Tait. On both occasions Bishop Cotterill was chosen
to act, in company with an English prelate, as a general secretary ;
and also as sole secretary to a committee appointed to consider the
constitution of the Colonial daughters of the Anglican Church, and
their relations to the mother Church of England. In these
situations he enjoyed an opportunity of showing to those around
him his capacity for business, his judicial temper, and his largeness
of view. These qualities made a special impression upon some of
the Bishops who had come from Scotland and from America.

The acquaintance with his powers thus obtained greatly
influenced the clerical and lay electors of the Episcopal Church in
the diocese of Edinburgh, when in 1871 they were seeking for a
coadjutor to Bishop Terrot. Other candidates withdrew, and on
April 26th the Bishop of Grahamstown was elected by the vote of
both the clerical and lay chambers, nernine contradicente , to the
office of coadjutor Bishop. Bishop Terrot only survived this event
by about eleven months ; and as Dr Cotterill had been chosen cum
jure successions, he became full Bishop in April 1872.

157

With the details of his rule we are not here concerned : and it
must suffice to say, that he proved himself to be active, energetic,
tolerant, and accessible. If, as seems possible, these qualities were
more quickly recognised by the clergy than by the laity of his
communion, this may have arisen from the fact that the former,
being brought into more immediate contact, saw most of him, and
that his good gifts were of a character that required such intercourse
to bring them out in all their fulness.

He was greatly interested in the proceedings of this Royal Society
of Edinburgh, of which he was elected a Fellow soon after his
arrival in Scotland. He was chosen a member of the Council, and
subsequently one of the Vice-Presidents. If he did not contribute
any papers, such as the valuable ones supplied by his predecessor,
Bishop Terrot, it must be remembered that the clerical duties of the
occupant of his post had been largely increased. Most especially
during eight years (1871-1879) his mind was occupied with the
erection and organisation of the Cathedral, which sprung from the
munificent bequest of Barbara and Mary Walker. In this com-
plicated task he was held to have been eminently successful. It
is perhaps permissible to remark that, in his association with the
savans of this Society and of the University he expressed himself
as greatly gratified with the large amount of ability among the
votaries of physical science, which was ranged upon the side of
belief, in that great contest with unbelief, which Goethe in well-
known words has declared to be “ the proper, peculiar, and deepest
theme of universal and human history.”

It remains to say something concerning the indirect and the
direct influence of his academical studies upon his professional life.
Indirectly it taught him, as it has taught so many academical
students, not to be satisfied with mere surface work in any depart-
ment of study. Two illustrations, out of several that might be
adduced, will serve to illustrate my meaning.

At Madras, during the tenure of his East Indian chaplaincy, he
was brought into controversy with some of our Roman Catholic
fellow-Christians. Hot content to take the account of their tenets
from hearsay and popular estimate, he made a serious study of
the works of a famous champion of Roman theology, Cardinal
Bellarmine; and to the close of his life he was able to cite concessions

158

or ingenious replies, which he had met with in the pages of that
eminent controversialist. He had been brought up, and always
remained, a devoted son of the Reformation. But he was not averse
to the study of the schoolmen, especially Aquinas ; and he re-
cognised, not wholly without admiration, in the theology which he
so firmly opposed, a system which, in his own words, “ touched the
human mind at a great many points.”

Again, in South Africa he found a system of law very different
from that to which he had been accustomed in England. Dutch
law, like Scottish law, is largely based upon that of ancient Rome.
Straightway he became a student of Roman law. Whether the
study of that or of any other system will render a mind judicial, if
it is thoroughly imbued with the advocate-temper, may he doubted;
hut it can hardly he questioned that where its teaching falls on a
congenial soil, it has a tendency to strengthen the upgrowth of a
judicial harvest hy reason of its general essence of admirable clearness
and common sense. In 1878 some difficulties in the will of the
Misses Walker were brought before the First Division of the Court
of Session in Edinburgh. Bishop Cotterill’s interpretation of certain
clauses had been disputed by some of the Walker Trustees, includ-
ing at least one eminent lawyer. The Court entirely confirmed the
Bishop’s view, and rejected that of his chief opponent.

As a scholar and a divine he was naturally much interested in
the Revision of the New Testament. In the main he sympathised
with the Revisers, and in general preached from their version. In
the field of what may perhaps be called constructive theology his
most important production was probably the volume entitled The
Genesis of the Church, an original and thoughtful work, which
may, though in a quiet and comparatively unnoticed manner,
considerably influence the divinity of the future.

But as was to be expected from one who kept up his acquaintance
with physical science, Bishop Cotterill was especially drawn towards
the field of apologetic theology. Among contemporary writers none
fixed his attention more than the late Dr Mozley, whom Sir James
Paget — no mean judge — has called u perhaps the most philosophic
divine of our age.” The Unseen Universe at once arrested his notice,
and in 1876 he contributed to the third number of the Church
Quarterly Review a sympathetic and able criticism of this remark-

159

able work. This was, I believe, his only contribution of any length
to periodical literature. He was also, however, greatly struck by
Philosophic Doubts , the work of a gentleman since known as the
Right Hon. A. G. Balfour, successively Secretary of State for
Scotland and for Ireland ; all the more so in that he had prepared
for the Victoria Institute a paper based upon a somewhat similar
stratum of thought, entitled “The Relation between Science and
Religion, through the principles of Unity, Order, and Causation.”

This last-named paper was read in 1880. But it may be re-
garded as a continuation of a similar address delivered before the
same Institute in 1878, “On the true Relation between Scientific
Thought and Religious Belief ; ” which was followed by what
many consider his happiest effort in this direction, namely, the
small volume entitled Does Science aid Faith ? published in
1882.

His acquaintance with colonial life not only led to his being on
several occasions associated with English prelates in the choice of
Anglican bishops for distant sees, but also induced him to deliver
addresses bearing on the problems connected with modern civilisa-
tion. Among such papers may be named “Vital Christianity as
affected by the present State of Science and Civilisation,” read at
Leeds during a Church Congress held there in 1873, and three
lectures given at St Paul’s Church, in York Place, Edinburgh,
entitled “Progress.” In compositions of this nature he not un-
frequently avowed his obligations to several writers outside the
ordinary range of theological study ; such as, for instance, Eichte
and Mr Herbert Spencer.

Very friendly relations, dating from the Lambeth Conference,
existed between him and the Anglican prelates of the United
States. He paid a visit to America, which he greatly enjoyed, in
1880; and was subsequently appointed Bedell Lecturer. These
lectures, however, were read for him in 1884. Their subject was
“ Revealed Religion in Relation to the Moral Being of God.”

There have been men of science who have combined with their
gifts of knowledge that of a remarkable literary style. Such in
Prance was the famous naturalist Buffon; and no one, whether ally
or opponent, would deny this possession to Professor Huxley. It
may be doubted whether, in the case of Bishop Cotterill, the gift of

160

expression was quite on a par with the general level of his very
high and varied endowments. It was probably, as a rule, happier
in friendly conversational discussion than in set aud formal efforts,
whether spoken or written. With diffidence it may be suggested
that the little volume already named, and the article in the Church
Quarterly Review , are favourable examples of his style, when at its
best.

He met the announcement that a fatal disease had seized him
with singular calmness and Christian fortitude. His illness was
cheered not only by the devoted assiduity of the partner of his
life, and the other members of a most united family, but also by a
sympathy which extended far beyond the limits of his own com-
munion. He left the Church, over which he had presided, very
grateful to him for his work, which had not only won the affection
and respect of those worshipping in the Cathedral and other Epis-
copal churches, but had also tended to draw into closer communion
two congregations which had previously been disunited. He was
probably happier in a disestablished than he would have been in
an Established Church, inasmuch as the conflicts in England be-
tween Church and State were to him a source of perplexity and
regret.

He used to praise his contemporary, Archbishop Tait (in
company with whom he had been consecrated Bishop), for never
becoming too old to learn. It was an eulogy which might be
fairly applied to himself. The condition of Scotland was in many
respects very different from that of South Africa. He took pains
to learn those differences. Erom his visit to America, from events
of the day, from thinkers much younger than himself, if they were
adepts in any special lines of thought or study, he was most will-
ing to learn;* thus showing that he cherished in his inmost heart
a deep humility, which chastened what might have been the temp-
tation of his great acquirements and successes. Most prominently
did this and other graces shine forth during the period of his latest
illness in 1885.

* The Rev. David Greig, M.A. of Aberdeen University, now Rector of
Cottenham ; and Dr Dowden, who has succeeded him in his Episcopate, may
without invidiousness be named as illustrating this remark. The Bishop was
also very sensible of the value of recent works of learned Presbyterian divines,
such as those of Professors Flint and Milligan.

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[ Note added December 23, 1887.]

Since the above notice was written, Professor Tait has reminded
me of the name of Dr Perry, late Bishop of Melbourne, as that of
a Senior Wrangler, who, like Bishop Cotterill, had also taken a
high place in the Classical Tripos ; and my friend and relative, the
Rev. Dr Luard, Registrary of the University of Cambridge, has,
at my request, furnished me with a list of the most interesting
examples of double honours taken at Cambridge between the years
1753 and 1854. I pass over those who did not win the highest
place in one of the two departments (though it contains many
names of students who rose to celebrity or high station in after
life), and confine myself to a selection from the list of Senior
Medallists, Senior Classics, or Senior Wranglers.

Among the Senior Medallists, who were also very high
Wranglers, may he named Craven (afterwards Master of St
John’s), 1753 ; Halifax (Bishop of St Asaph), 1754; Law (Bishop
of Elphin), 1766 ; Law (Bishop of Bath and Wells), 1781 ; (Arch-
deacon) Wrangham, 1790; Maltby (Bishop of Durham), 1792;
Tindall (Chief Justice), 1799 ; Grant (Lord Glenelg), 1801 ; Parke
(Lord Wensleydale), 1803; Blomfield (Bishop of London), 1808;
Graham (Bishop of Chester), 1816; Hugh James Rose, 1817;
Ollivant (Bishop of Llandaff), 1821.

Among the Senior Classics (some being also Senior Medallists)
who were very high Wranglers, were (Professor) Selwyn, 1828;
(Professor) Westcott, 1848; J. B. Liglitfoot (Bishop of Durham),
1851.

Of the four Senior 'Wranglers, who have also been Senior
Medallists, only two became subsequently eminent — Kaye (Bishop
of Lincoln), 1804, and Alderson (Baron of the Exchequer), 1809. 1

The other Senior Wranglers who have been high in the Classical
Tripos (since its institution in 1825) have been comparatively few;
and Henry Cotterill appears to stand alone in combining 'with the
Senior Wranglership, and a high place in the Classical Tripos, the
position of First Smith’s Prizeman.

I

162

William Denny, C.E. By John Henderson, Jun., E.R.S.E.

William Denny was bom in Dumbarton on 25th May 1847.
His education was commenced in the Academy of his native town.
Shortly afterwards he was sent to Jersey, more particularly for the
sake of his health, and after a residence of four years he returned
to Scotland, and was placed in the Edinburgh High School, where
he remained until he was seventeen years of age.

He had resolved to become a shipbuilder, and on leaving the
High School in 1864 he entered his father’s ship-yard in Dumbarton
as an apprentice, and passed through the several departments, where
he laid the groundwork of his future ability as a naval architect.

In 1868 Mr Denny became a partner in the firm of William
Denny & Bros., and shortly after assumed the administrative
charge of the extensive business conducted by the firm. He con-
tinued to occupy this position until his death on 17th March 1887.

He early showed great promise of becoming an eminent naval
architect, and introduced a more scientific basis in all the practical
work of shipbuilding. He wrote many papers, and took a pro-
minent part in all discussions in connection with his profession.

Mr Denny had great force of character, and a wonderful gift of
inspiring his staff, and those with whom he came in contact, with
his own enthusiasm and earnest perseverance in carrying his in-
vestigations and experiments to a conclusion.

He was a fluent speaker, and his professional and other papers,
which he read from time to time, were noted for the finished
manner in which they were prepared and delivered.

He took a prominent part in the introduction of steel for shipbuild-
ing, and did much to bring it into the general use it now obtains.
He introduced an admirable system of conference between his firm
and delegates from all trades represented in the works, in order to
adjust and arrange all questions of wages, rules, &c., and these
conferences were under his presidency during the last year of his
life at home.

Such deep and active interest as he had in everything connected
with the scientific part of his business would have absorbed all the
energies of most men, but not so with William Denny. His nature
was many-sided, and his sympathies were broad and deep. He was

163

well read in many subjects, and proved himself a capable lecturer
on art, politics, and many other subjects, in which he took a deep
interest. Possessed of a warm and affectionate nature, he will be
long remembered for the interest he took in every one with whom
he came in contact, and the generous, but wise, assistance he was
ever ready to afford in advancing the well-being of all who had the
good fortune to know him.

Among the papers which he wrote were “ The Worth of Wages ” ;
“ Dimensions of Sea-going Ships ” ; “ On the Difficulties of Speed
Calculations,” for the latter paper he was awarded the Marine
Engineering Medal of the Institution of Engineers and Shipbuilders
in Scotland; “ The Speed and Carrying of Screw Steamers,” being
the Watt Lecture delivered before the Philosophical Society of
Greenock; “On the Question of Success”; “ Christianity in this
Life ” ; of the latter he was only spared to conclude the first part.

Mr Denny was appointed by the Government a member of the
Load Line Committee, and he took an active part in all its investi-
gations. He was a member of Council of the Institution of Naval
Architects, a member of the Institution of Engineers and Ship-
builders in Scotland, of which he was president at the time of his
death. He was also member of the Institution of Civil Engineers
and of the Iron and Steel Institute. He was elected a Eellow of
this Society on 3rd February 1879.

Dr Daniel Rutherford Haldane. — From materials
supplied by Dr John Smith, LL.D., and Dr
Heron Watson.

Dr D. Rutherford Haldane was the son of James Alexander
Haldane, who founded the Scottish Congregational body, and has
sometimes been called the Wliitefield of Scotland. He was of the
family of the Haldanes of Gleneagles.

Our deceased Fellow was educated at the High School of
Edinburgh, and during the six years of his attendance there his
usual place in class was about third, — the dux for the first three
years being “ blind Laurie,” and when that distinguished pupil left,

164

the next dux was one who afterwards has done good work in
another profession, the Rev. John M‘Laren, D.D., minister of
Larbert.

On leaving the High School, he studied at the University of this
city until he obtained his medical degree. When he graduated
as Doctor of Medicine, a gold medal was presented to him for his
thesis on Diseases of the Liver.

He subsequently went abroad for the purpose of further study
at the great medical schools of Vienna and Paris. He resided at
the latter capital for eighteen months, and whilst there acquired a
remarkable fluency in the French language, which he ever after-
wards retained. On his return to Edinburgh he was appointed
House Physician to the Infirmary, in which capacity he had acted
prior to going abroad, and not long after this he was elected
Physician to the Royal Public Dispensary and the New Town
Dispensary. He subsequently became a Lecturer on Medical
Jurisprudence, Pathologist to the Royal Infirmary, and Teacher
of Pathology and Morbid Anatomy in the Extra-Mural School at
Surgeons’ Hall. On Dr Alexander Wood retiring from his
Lectureship at the College of Surgeons, Dr Haldane began to
lecture on the Practice of Physic in that institution, and at the
same time he gave lectures on Clinical Medicine at the Infirmary.
His classes were very popular with the students, as he had the
reputation of being one of the best teachers in the Edinburgh
School of Medicine. In 1876, about three hundred of his former
pupils, among whom were many of our best known practitioners,
presented him with an address in which his powers of accurate
diagnosis, the clearness and grace of his style as a lecturer, and his
vivid powers of description, were adverted to in terms of grateful
appreciation.

In 1852 he was elected a Fellow of the Royal College of
Physicians, and he afterwards held successively the offices of
Secretary and President of that body. Whilst acting as Secretary
to the College of Physicians, he took an important part in promot-
ing the scheme under which the Royal Colleges of Physicians and
Surgeons in Edinburgh, with the Faculty of Physicians and
Surgeons of Glasgow, arranged to grant a conjoint examination
and diploma to their students, known as the Double Qualification.

165

Tor his services in instituting this diploma, a handsome service of
silver plate was presented to him. He was the representative of
the College of Physicians at the General Council of Medical
Education, and at the Infirmary Board. The General Council,
Edinburgh University, elected him their assessor at the University
Court.

He was also for several years medical officer of the Scottish
Equitable Life Assurance Society. In acknowledging his services
in this capacity, the Directors stated in their minutes — “ that his
perfect mastery of his profession, and the sound judgment which
characterised his opinions were so conspicuous, that the Board
placed the most perfect confidence in his advice, and are certain
that it has been of the utmost value to the Society.”

Dr Haldane chiefly devoted himself to the teaching and con-
sulting departments of his profession. His contributions to the
science of medicine were mainly of the nature of occasional practical
papers, read before various professional bodies and associations, and
constituted in not a few cases interesting additions to our know-
ledge of diseases of the heart, the nervous system, and alimentary
canal. Eor a number of years he edited the Edinburgh Medical
Journal with ability and success.

His life was destined to be cut short unexpectedly. On the
Christmas day of 1886, when leaving his house, his foot slipped,
and in falling he broke the lower part of his right leg. Com-
plications, leading to a complete collapse of his system, followed on
this injury, and he died on the 12th of April 1886.

The death of a physician so eminent and so widely known and
appreciated, was the occasion of much regret both to the profession
and the public of Edinburgh ; and the more so as in private life
he was distinguished by the gentleness and courtesy of his manners,
his straightforwardness and high sense of honour. His funeral was
attended by the Presidents and Fellows of the Royal Colleges of
Physicians and Surgeons, and by a large assemblage of the general
public. He was elected a Fellow of this Society in 1867.

166

James Pringle.

James Pringle was born in Edinburgh in 1822. He was the
son of Mr Murray Pringle, who for thirty years held the office of
Secretary in the Adjutant-General’s Office, and a similar position in
the Naval and Military Academy, which long existed in the city.
He received his education at the High School of Edinburgh, where
he made great proficiency in the study of the classics, and stood
third among his fellow-students in the list of honours during the
last year of his educational course.

On leaving the High School he became a clerk to the Edinburgh
Eoperie Company. His business abilities and capacity for hard
work led to his being promoted to the position of cashier in the
Company’s office, and on the occurrence of a vacancy in the man-
agement the entire responsibility of conducting the Company’s
business was devolved on him.

About six years ago, he began to take a prominent part in the
public business of Leith, when he was returned as representative
of the ratepayers to the Leith Dock Commission. Entering the
Town Council of Leith in 1881, he was elected Provost of
the burgh in November of that year, and continued to occupy the
position till the time of his death. Like his predecessor in the
civic chair, he was an ardent supporter of the Leith improvement
scheme, and he was particularly active in obtaining a Provisional
Order for the better preservation of Leith Links. He displayed
great tact and energy, as well as unfailing courtesy, in the discharge
of his onerous duties as chief Magistrate, and he took an active
interest in all associations and movements for the amelioration of
the condition of the poor, and the relief of suffering.

Mr Pringle also held the honourable office of Deputy-Lieutenant
of the county. He found time to take an intelligent interest in
the proceedings of the Geographical Society, and he was elected a
Fellow of this Society on the 6th of April 1885. He died on the
11th of December 1886. His funeral, which was a public one,
called forth an expression of general sympathy and regard, such as,
perhaps, had never before been witnessed in the town over which
he presided.

167

Dr Thomas Williamson.

Dr Williamson was born at Greenock in 1815, and claimed to
be the last surviving representative of tbe ancient family of the
Napiers of Kilmahew. When quite young, he was sent to study
medicine at the University of Edinburgh, where he took his degree
of M.D. at the age of twenty, in the same year becoming a licentiate
of the Royal College of Surgeons, an institution of which he was
elected a Eellow in 1857. He was one of the oldest members of
the Medico-Chirurgical Society, and of the Royal Society of
Edinburgh. In early life he held several public offices. He was
for fully thirty years surgeon in Leith Hospital, and during the
whole of his long residence in Leith took a warm interest in the
welfare of that institution. At the time of his death he held the
appointments of parochial medical officer and public vaccinator for
the parish of South Leith, and medical officer of health for the
entire burgh. The latter office obliged him to board vessels com-
ing from ports where any epidemic was prevalent, and to his
foresight is due the readiness in which Leith has been held, during
the late visitations of cholera on the Continent, to deal with any
emergency which might arise. His various public duties were
performed with untiring vigilance and care, and he enjoyed the un-
qualified respect of his fellow citizens, among whom his long resi-
dence rendered his figure one of the most familiar in the community.
Dr Williamson was an occasional contributor to medical journals
on topics chiefly relating to sanitation. He published various
pamphlets, and delivered several popular lectures on subjects relat-
ing to public health, and read a paper on the subject at one of the
meetings of the Social Science Congress at Edinburgh, which
was printed in their reports. On returning from Colinton, he was
seized with an attack of apoplexy which terminated fatally on the
30th of December 1885. He was elected a Fellow of this Society on
7th December 1857.

John Mileoy, Assoc. Inst. C.E.

The death has just been announced of Mr John Milroy, Assoc.
Inst. C.E., one of the remaining links between the present and the
great days of railway construction in which the late Mr Thomas

168

Brassey played a prominent part. Mr Milroy died at his residence,
Torsonce House, Stow, near Edinburgh. For the past two years he
had been in failing health, and ten days before his decease he was
seized with a shock of paralysis, from the effects of which he never
recovered. Mr Milroy was very early associated with Mr Brassey
in railway work, so far back, indeed, as the year 1840, in the
construction of the first line between Glasgow and Greenock, now
belonging to the Caledonian Bailway Company, and on which he
was a sub-contractor. The most serious portion of that contract
was the cutting of the well-known Bishopton Tunnel, which was
carried almost entirely through a dense tough whinstone. Mr
Milroy subsequently acted as agent for Mr Brassey and for Messrs.
Brassey & Mackenzie in the construction of lines of railway of
great extent on the Continent, the first of them being the Paris and
Bouen Bailway, with the late Mr J oseph Locke as the engineer-in-
chief. He was also engaged in the same capacity on the Bouen
and Havre, the Nantes and Caen, and the Caen and Cherbourg
railways. A few years later Mr Milroy likewise served Mr Brassey
as his agent in the construction of well-nigh eighty miles of the
Great Northern Bailway ; and there were various other railway
undertakings with which he was connected, not only in this
country, but also in France and Italy ; indeed, a considerable
portion of his life was spent on the Continent, where he became
exceedingly well known and greatly esteemed on account of his
personal character. About a quarter of a century ago, Mr Milroy
settled down in his native country, in order to take charge of some
large works in which he was interested, along with the eminent
firm with whom he had been already associated for about twenty
years. The chief of those works was the construction of the City
of Glasgow Union Bail way, from the plans of Mr (now Sir) John
Fowler. It included some difficult pieces of constructional work
to connect the Glasgow and South-Western Bail way on the south
of the Clyde with the North British system of railways on the
north side. There was also a very important iron girder bridge
across the Clyde, together with the Sighthill Bailway and the
Harbour Bailway running past Pollokshields and under a public
roadway, a canal, and two other lines of railway. While engaged
in sinking the cylinders for the viaduct over the Clyde, Mr Milroy

169

brought into use a new excavator of bis own invention, which
subsequently did much excellent service in the construction of
subaqueous works. While in and about Glasgow the deceased
was induced to take two important contracts on his own account,
two pieces of work involved in the extension of the harbour of
Glasgow, namely, Plantation and Mavisbank Quays. In the
former of these works, the superstructure was built on foundation
piers which were formed of successive rings of brick-work, according
to the plans of Mr James Deas, engineer to the Clyde Trust. In
the construction of Mavisbank Quay, a marked improvement was
made in the character of the subaqueous pier foundations, which
were formed of concrete, the piers being most securely bound to-
gether. The Milroy excavator was here used to excellent purpose,
enabling the piers to sink to depths of 50 ft. to 60 ft. or 70 ft.
In these harbour works Mr Milroy was closely associated with Mr
Deas, and he had as his right-hand man Mr George A. Waghorn,
who also saw much service under Mr Brassey’s firm. The various
works which he carried out in the Glasgow district, including those
for which he was the sole contractor, cost nearly 1J millions
sterling.

After having retired from active life, Mr Milroy passed his
remaining years on the estate of Torsonce, which he acquired in the
year 1879, and on which he occupied his time in making consider-
able improvements by building, roadmaking, &c. At his death he
was eighty years of age. He was of a most retiring disposition,
and when not occupied in superintending the improvements on his
estate, devoted the last years of his life to the study of those
branches of science wrhich were most closely connected with his
profession. He was elected a Fellow of this Society in 1875.

170

General Sir James Edward Alexander, Kt.,

C.B., K.C.L.S., &c.

General Sir James Edward Alexander, of Westerton, Stirling-
shire, who was born in Stirling on the 16th October 1803, and
whose decease took place at the Isle of Wight 2nd April 1885, was
a collateral descendant of the family of the first Baronet, William
Alexander of Menstrie, afterwards Earl of Stirling.*

After passing through the College of Edinburgh and Glasgow, he
proceeded at an early age to India to join his relative Sir Thomas
Munro, then governor of Madras. He there devoted himself to the
study of Oriental languages, passed the required examinations, and
was appointed to the Madras Light Cavalry, and adjutant of the
governor’s body guard. He was afterwards transferred to the 13th
Light Dragoons in January 1825, and volunteering for active service
proceeded to Burmah, was present in the field, and took part in the
first Burmah war.

After the peace his acquirements were recognised by his being
appointed attache to the Persian Mission, under Sir John Macdonald
Kinneir ; while acting with the Persian army on the field against
the Russians, he so distinguished himself that he received the Order
of the Lion and Sun.

In consequence of his proficiency in Eastern languages and
general attainments, he was offered, on return to England, a
professorship at the College of Heylebury, but, declining this
employment, he instead joined the senior department of the
Military Staff College, obtained a first-class certificate, and shortly
afterwards was promoted to a lieutenancy in the 16th Lancers.
He then obtained a year’s leave of absence, to enable him to
complete his military studies, and to join the Royal Engineers at
Chatham, under Sir Charles Paisley.

He next saw service with the Russian army of Field-Marshal
Diebitch, then engaged in operations against the Turks. At the
conclusion of this service, and while on his return to England, a
slightly untoward incident occurred to him. Proceeding in a
Russian frigate by way of Sebastopol, he was there placed in
quarantine, in consequence of some cases of the plague having

* He was buried in the old Logie kirkyard, near Menstrie.

171

appeared on board. The port chanced to be visited at the time
by H.M.S. “ Blonde,” commanded by [ Captain, afterwards Sir
Edmund and Lord Lyons (commander-in-chief of the fleet during
the Crimean war), then cruising in tbe Black Sea. Captain Lyons
alone was allowed to land at the quarantine station, when be
naturally communicated with bis fellow-countryman. On tbe
departure of tbe “ Blonde,” Sir James Alexander was immediately
arrested by tbe Russian authorities, on suspicion of being an
emissary of the British Government. He was arbitrarily confined
two months in Sebastopol with other prisoners, and finally, in tbe
depth of winter, sent under guard to St Petersburg, where, after
undergoing further confinement and hard treatment, he was at
length, by the intervention of the British ambassador, released, but
without compensation for the unjust usage he had received — only a
slight apology from the Emperor Nicholas in person.

He returned to England by Sweden and Denmark, and in
recognition of the valuable information, plans, and reports he was
enabled to furnish with regard to Russia and Turkey, he was
promoted to an unattached captaincy.

Sir James was now selected by the Colonial Office to undertake
an important commission of inquiry into the state of slavery in
North and South America, receiving from the Secretary of State
letters and credentials to the various governors of provinces, &c.
On the conclusion of this mission he was examined before a
committee of the House of Lords, by whom his able report was
highly appreciated.

He shortly afterwards returned to full pay, and joined as a
captain the 42nd Highlanders (Black Watch). While serving with
this regiment, he was invited by the Royal Geographical Society
to make explorations in Africa, and readily accepted a duty so
congenial to his active and enterprising character; but the British
expedition then being in the field against Don Miguel, he took the
opportunity it afforded him of seeing further active service and
acquiring further geographical knowledge by joining the expedi-
tionary force. His effective service was rewarded by receiving from
Don Pedro the rank of lieut. -colonel. He then proceeded on
his mission in H.M.S. “Thalia” round the west coast of Africa,
visiting the different settlements.

172

On arrival at the Cape, finding the war with the Caffres already
commenced, and the time accordingly unfavourable for explorations,
he joined the troops in the field under Sir Benjamin D’Urban, by
whom he was appointed aide-de-camp. At the conclusion of the
war, Sir James Alexander resumed his mission of exploration, and
proceeded into the interior, accompanied only by seven men —
encountering successfully the dangers, difficulties, and hardships to
which at that time travellers in South Africa were subjected. In
one year he accomplished 4000 miles, and completed a full re-
port of the countries of the great Hamaquas, Boshmans, and Hill
Damaras.

On returning to England, Sir James E. Alexander received the
honour of knighthood for his services in Africa, being the first
knight created by the Queen in person after Her Majesty’s
accession. His African duties had obliged him to go temporarily
on half pay; but he returned shortly to full pay as a captain in the
14th Regiment, then serving in Horth America. There he was
asked to undertake and accepted the arduous duty of exploring
and surveying in the construction of a military road through the
forests of Hew Brunswick and Canada from Quebec to Halifax,
acting as assistant royal engineer on this most trying service
during 1844-45. He received no promotion or reward, beyond a
slight addition to pay while so engaged, for this arduous service
which he had been invited to undertake.

On Sir Benjamin D’Urban being appointed commander of the
forces in Canada, he immediately reappointed Sir James as his
aide-de-camp, a post he retained until Sir Benjamin’s death in
Montreal. Sir William Rowen succeeding to the command, he was
again offered the aide-de-cam pship, and served on the staff of that
distinguished officer for 5J years. He rejoined his regiment as
major on the breaking out of the Crimean war, shortly became
lieut. -colonel, and succeeded to its command during the siege of
Sebastopol, at the fall of which stronghold he was present.

During this time of scarcity and hardship, his regiment wras
notorious for the beneficial arrangements for their supply and com-
fort that his previous experience on active service had enabled him
to make for the comfort and welfare of his men.

Sir James Alexander was next appointed to the command of a

173

depot battalion, but was shortly selected to raise the 2nd battalion
of bis old regiment, the 1 4th : this he so quickly did, and so rapidly
brought them into an effective state, that his battalion was the first
of the new 2nd battalions that proceeded on service in the field ; this
was to New Zealand, to engage in the Maori war. Here he com-
manded for some time in the province of Taranaki, and under Sir
Duncan Cameron the important outposts at Waikato.

He was then promoted to major-general in 1868, lieut. -general in
1877, and general in 1881. He received during his service seven
war medals, but the reception only of the C.B. (3rd Class of the
Order of the Bath) will be considered but an inadequate acknow-
ledgment of long and arduous service.

Sir James Alexander was the author of various works of travel
and of a biographical and military character, such as his Life of the
Duke of Wellington , Canada as it is, &c., Passages in the Life of
a Soldier, and others relating to the various countries with which he
was personally acquainted, as well as the contributor of numerous
articles in periodicals on the military, scientific, and social topics of
the day.

The deep interest he took in all questions relating to the interests
and improvements of the army, especially as regarded its equip-
ments, and his untiring exertions in promoting these objects to the
utmost of his power, are well known. He was among the foremost
and most strenuous supporters of those who called public attention
to the long-neglected justice of granting medals for the Peninsular
services of the army, hitherto unrecognised by distinctive decora-
tions. This movement was eventually carried to a successful result,
through the influence and advocacy of the Duke of Kichmoncl in
the House of Lords, and with the military authorities, was much
indebted to the indefatigable exertions of Sir James Alexander.

Mainly also to his exertions may be truly attributed the ultimate
erection of the Egyptian obelisk (called Cleopatra’s Needle) in its
present site on the Thames Embankment. This obelisk, presented
by Egypt to England in recognition of the services of the British
army in Egypt under Abercrombie, owing to untoward circumstances
which prevented its shipment to England, for which arrangements
had been made at the expense of the army, was allowed from that
up to the present to lie neglected on the shore of Alexandria

174

harbour, at the point intended as that of embarkation; and the
English Government having refused to incur the expense of its
removal, it would finally have been broken up in 1874, had not Sir
J ames Alexander, who had long endeavoured to call public attention
to the matter, personally interfered, and undertaken at his own
expense a voyage to Alexandria, and, with the aid of the British
consul-general, succeeded in rescuing it from destruction. On his
return he renewed his exertions, so many years unsuccessful, and
obtained the munificent pecuniary assistance of Sir Erasmus
Wilson, by which after great difficulties the obelisk was transported
to England and erected in its present site. The country must he
considered indebted to Sir James Alexander’s persevering energy
for its possession of this most valuable and interesting antiquity.

It would be difficult to enumerate the various other works of
public and private character, whether in England or abroad, in
which he was constantly engaged, and bore a leading and prominent
part ; these will long be gratefully remembered by those who bene-
fited by his exertions.

Of him may truly be said, that in all countries whatever good
work he found at his hand to do that he did with heart and soul ;
and in him those who had the privilege of his acquaintance recog-
nised that highest type of character, the single-hearted, high-
minded Christian gentleman, whose life was devoted to duty and to
the promotion of the interest and welfare of his fellow countrymen,
and the communities among whom his lot might be more imme-
diately cast.

Alexander James Russell, C.S.

Mr Alexander James Russell, Clerk to Her Majesty’s Signet,
Edinburgh, who died recently — 8th January 1887 — at the age of
seventy-two, was head of the firm known formerly as Russell &
Hicolson, C.S., and latterly as Russell & Dunlop, and the business
which he carried on was one of the oldest in Edinburgh, dating-
back to the end of the seventeenth century, and having descended
in the direct line from father to son.

His father, Mr John Russell, was principal Clerk of Session, and

175

Secretary of the Royal Society of Edinburgh, and his great-great
grandfather was solicitor for the sale of the forfeited estates in
Scotland after the Rebellion of 1715, and one of the original
shareholders of the Bank of Scotland. On his mother’s side, Mr
Russell was closely related to the ancient Scottish family of Murray
of Polmaise, his mother having been the daughter of the late Mr
Murray of Polmaise, and he was a great-grandson of Principal
Robertson, the Scottish historian. He was for many years a director
of the National Bank of Scotland and of the Standard Life Assurance
Company, and for some time latterly solicitor to that Company.
In politics he was a Conservative, but he did not take any active
part in political life. Mr Russell was married — first, to Miss
Magdalene Stein, daughter of the late Andrew Stein, Esq. of
Wester-Greenyards, Fifeshire, and secondly, to Miss Elizabeth Anne
Lancaster, daughter of the late Samuel Lancaster, Esq. of Hem-
borough, Devon, who now survives him. He left also an only son,
Colonel J. Cecil Russell, late of the 12th Lancers, and for some time
an equerry to the Prince of Wales.

PROCEEDINGS

OF TIIE

ROYAL SOCIETY OF EDINBURGH,

SESSION 1886-87.

iQ

CONTENTS.

(Mndral Statutory Meeting , Monday, 22ncl November 1886.
Election of Office-Bearers, .....

PAGE

1

Monday, 6th December 1886.

Chairman’s Opening Address, ....... 2

Astronomical Tables for facilitating the Computation of Differential Refraction,

for Latitudes 56° and 57o,30. By the Hon. Lord McLaren, . . 21

On the Foundations of the Kinetic Theory of Gases. Part II. By Professor

Tait, .......... 21

Fog Bow observed on Ben Nevis, 22nd October 1886. By R. T. Omond, Esq.,

Supt. B.N.O., 24

Temperatures at Different Heights above Ground at Ben Nevis Observatory.

By R. T. Omond, Esq., Supt. B.N.O., ..... 24

Monday , 20 tli December 1886.

Motion of Compound Bodies through Liquid. By the Rev. H. J. Sharpe,

M.A. Communicated by the President, . . . . .29

Note on Knots on Endless Cords. By A. B. Kempe, Esq. Communicated by

Professor Tait. (Plate I.), ....... 36

On the Ring-Waves produced bv throwing a Stone into Water. Bv Sir W.

Thomson, ......... 37

On the Waves produced by a Ship advancing uniformly into Smooth Water.

• By Sir W. Thomson, ........ 37

Expansion of Functions in terms of Linear, Cylindric, Spherical, &c., Functions.

By P. Alexander, Esq., M.A. Communicated by Dr T. Muir, . . 37

On Even Distribution of Points in Space. By Professor Tait, . . .37

Friday, 7th January 1887.

Address on Processes of Refrigeration. By J. J. Coleman, Esq., . . 38

On the Front and Rear of a Free Procession of Waves in Deep Water. By Sir

W. Thomson, ......... 38

Numerical and other Additions to his Paper, read on 6th December 1886, on the

Foundations of the Kinetic Theory of Gases. By Professor Tait, . . 46

Intimation of an Improvement in Rankine’s Formula for Retaining Walls.

Given by Professor Armstrong on behalf of A. C. Elliott, Esq., . . 48

Monday, 17th January 1887.

The Total Rainfall on the Land of the Globe, and its Relation to the Discharge

of Rivers. By J. Murray, Esq., Ph.D., V.P., . . . . .48

Chemical Affinity and Solution. By W. Durham, Esq., . .48

Thermometer Screens. Part IV. By John Aitken, Esq. (Plates II., III., IV.), 53

On the General Effects of Molecular Attraction of Small Range on the Behaviour

of a Group of Smooth Impinging Spheres. By Professor Tait, . , 85

Monday, 31s£ January 1887.

On a New Formula for the Pressure of Earth against a Retaining Wall. By A.

C. Elliott, Esq., B.Sc., C.E. Communicated by Professor Armstrong, . 85

The Conducting Paths between the Cortex of the Cerebrum and the Lower

Centres, in relation to their Function. By Professor D. J. Hamilton, . 97

Researches on Micro-Organisms, including ideas of a New Method for their
Destruction in Certain Cases of Contagious Disease. By Dr A. B.
Griffiths, F.R.S. (Edin.), ....... 97

On the Conducting Paths between the Cortex of the Brain and the Lower Centres
in relation to Physiology and Pathology. By D. J. Hamilton, M.B.,

F.R.C.S. Edin., F.R.S.E., Professor of Pathology, University of Aberdeen.

(Plates XIV., XV.), . . . . . . . 97,519

11

Monday , 7 th February 1887.

On Cases of Instability in Open Structures. By E. Sang, Esq., LL.D.,

On the Increase of Electrolytic Polarization with Time, By W. Peddie, Esq.
Communicated by Professor Tait, ......

Astronomical Notes. By Ralph Copeland, Esq., Ph.D. Communicated by
LordM‘LAREN,

Monday , 21 st February 1887.

Further Determinations of the Effect of Pressure on the Maximum Density
Point of Water. By Professor Tait, ......

On the Height of the Land of the Globe above Sea-Level. By Dr J. Murray,
Note on the Effects of Explosives. By Professor Tait, ....

Report on Fossil Fishes collected in Eskdale and Liddesdale. Part I. Ganoidei
— Supplement. By Dr Traquair, ......

On the Equilibrium of a Gas under its own Gravitation only. By Sir W.
Thomson, .........

Monday , 7th March 1887.

On the Equilibrium of a Gas under its own Gravitation only. Part II. By Sir
W. Thomson, .........

History of the Theory of Determinants. Part I. Determinants in General:
Hindenburg (1784) to Reiss (1829). By Dr Muir, ....

Note on Solar Radiation. By John Aitken, Esq., ....

On Laplace’s Nebular Theory, considered in relation to Thermodynamics. By
Sir W. Thomson, ........

On a Class of Alternating Functions. By Dr Muir, ....

Note on Hoar-Frost. By John Aitken, Esq., . . . . .

On the Quotient of a Simple Alternant by the Difference-Product of the
Variables. By Dr Muir, .......

Investigations on the Influence of certain Rays of the Solar Spectrum on Root
Absorption and on the Growth of Plants. By Dr A. B. Griffiths, F.R.S.E.,
F.C.S. (Lond. and Paris), and Mrs A. B. Griffiths,

Monday, 21 st March 1887.

Variations in the Value of the Monetary Standard. By Professor Nicholson, .
On Ice and Brines. By J. Y. Buchanan, Esq., .....
On the Distribution of Temperature in the Antarctic Ocean. By J. Y.
Buchanan, Esq., ........

Monday, 4th April 1887.

Note on a Formula for An0 i/ni when n, i are very large Numbers. By Professor
Cayley, .........

On the Fossil Flora of the Radstock Series of the Somerset and Bristol Coal
Fields. (Upper Coal Measures.) Part I. By R. Kidston, Esq., F.G.S., .
On the Achromatism of the Four-Lens Eye-Piece : New Arrangement of the
Lenses. By Edward Sang, Esq., LL.D., .....

An Effective Arrangement for Observing the Passage of the Sun’s Image across
the Wires of a Telescope. By Edward Sang, 'Esq., LL.D., . -

Observations on the Structural Characters of certain new or little-known Earth-
worms. By Frank E. Beddard, Esq., M.A., Prosector to the Zoological
Society of London, and Lecturer on Biology at Guy’s Hospital. (Plate V.),
On the Geology and Petrology of St Abb’s Head.- By Prof. Geikie. (Plate VI.),

Monday, 18 th April 1887.

Professor Rowland’s Photographs of the Solar Spectrum. Exhibited by the
Astronomer-Royal for Scotland, .....

On Ship-Waves. By Sir W. Thomson, ......

On the Instability in Fluid Motion. By Sir W. Thomson,

Experimental Research in Magnetism. By D. S. Sinclair, Esq., Communi-
cated by Principal Jamieson, . . . . .

On the Summation of certain Series of Alternants. By A. H. Anglin, Esq.,

M. A., LL.B., &c., ........

Note on Cobaltic Alums. By Hugh Marshall, B.Sc., ....

On the Effect produced on the Polarisation of Nerve by Stimulation. By G.

N. Stewart, Esq., . .....

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205

PAGE

Monday , 2nd Ma\y 1887.

The Objective Cause of Sensation. Part III. — The Sense of Smell. By

Professor John Berry Hay craft, ...... 207

On the Physics of Noise. By Professor Crum Brown, .... 219

On the Physical Properties of Methyl-Alcohol. By Professor Dittmar and C.

A. Fawsitt, Esq., ........ 219

On the Instability of the Double Sulphates

M"S04.R'2S04 + 6H20

of the Magnesium Series. By W. Dittmar, Esq., . . . .219

A Diatomaceous Deposit from North Tolsta, Lewis. By John Rattray, Esq., . 220

Monday, \6th May 1887.

On the Increase of Electrolytic Polarization with Time. By W. Peddie, Esci.,

B. Sc., .......... 221

On the Blood of Myxine. By Professor D’Arcy W. Thompson, . . .221

On the Larynx and Stomach in Cetacea. By Professor D’Arcy W. Thompson, 221

On Transition Resistance at the Surface of Platinum Electrodes, and the Action

of Condensed Gaseous Films. By W. Peddie, Esq., B.Sc. (Plate VII.), . 221

Researches on the Problematical Organs of- the Invertebrata — especially those of
the Cephalopoda, Gasteropoda, Lamellibranchiata, Crustacea, Insecta, and
Oligochseta. By Dr A. B. Griffiths, F.R.S. (Edin.), F.C.S. (Lond. &

Paris), Principal, and Lecturer on Chemistry and Biology, School of Science,
Lincoln ; late Lecturer on Chemistry, Technical School, Manchester, &c., . 230

The Nephridia of Lanice conchilega, Malmgren. By J. T. Cunningham, Esq., . 238

Monday, 6th June 1887.

On a Furnace capable of melting Nickel and Cobalt. By J. B. Readman, Esq., 240
On the Fossil Flora of the Radstock Series of the Somerset and Bristol Coal

Fields. Concluding Part. By R. Kidston, Esq., .... 240

On the Discharge of Albumen from the Kidneys of Healthy People. By Pro-
fessor Grainger Stewart, M.D., ...... 240

The Salinity and Temperature of the Moray Firth, and the Firths of Inverness,
Cromarty, and Dornoch. By Hugh Robert Mill, D.Sc., Scottish Marine
Station. (Plate VIII.), ....... 250

On the Presence of Bacteria in the Lymph, &c., of Living Fish and other Verte
brates. By J. C. Ewart, M.D., Regius Professor of Natural History, Uni-
versity of Edinburgh, ........ 262

Monday, 20th June 1887.

On the Origin of the Great Alpine Lakes. By Professor Sacco, University of

Turin, . . . . . . . . . 271

On the Minute Oscillations of a Uniform Flexible Chain hung by one End ; and
on the Functions arising in the course of the Inquiry. By E. Sang, Esq.,

LL.D. (Plate IX.), . . . ... . .283

Note on the Biological Tests employed in determining the Purity of Water. By

A. W. Hare, Esq., M.B. Edin. (Plates X., XI.), .... 306

Alternants which are Constant Multiples of the Difference-Product of the

Variables. By A. H. Anglin, Esq., M.A., ..... 313

Glories, Halos, and Coronse seen from Ben Nevis Observatory. Extracts from
Log Book. By R. T. Omond, Esq. Communicated by Professor Tait.

(Plate XII.), 314

Monday, 4th July 1887.

Thermal Conductivity of Iron, Copper, and German Silver. By A. C. Mitchell,

Esq. Communicated by Professor Tait, ..... 327

On the Probability that a Marriage entered into by a Man of any Age, will be

Fruitful. By T. B. Sprague, Esq., M. A., . 327

On the Nephridia of Hirudo medicinalis. By Dr A. B. Griffiths, F.R.S.E.,

F.C.S. (London & Paris), Principal, and Lecturer on Chemistry and
Biology, School of Science, Lincoln, ...... 346

On Degenerated Specimens of Tulipa sylvestris. By Mrs A. B. Griffiths.

Communicated by Dr A. B. Griffiths, F.R.S.E., &c., . . . 349

The Luminous Organs of Nyctiplianes norvegica , Sars. By J. T. Cunningham,

B. A., and Rupert Vallentin, Esq., . . . . . 351

On a Constant Daniell Cell, for use as a Standard of Electromotive Force. By

Cosmo I. Burton, B.Sc., F.C.S., . .... 356

IV

On Glories. By Professor Tait, .......

Report on the Pennatulida dredged by H.M.S. “ Porcupine.” By A. Milnes
Marshall, M.D., D.Sc., M.A., F.B.S., Beyer Professor of Zoology in the
Owens College, and by G. H. Fowler, B.A., Ph.D., Berkeley Fellow of the
Owens College, Manchester. Communicated by John Murray, Esq., Ph.D.,

Friday, 15 tli July 1887.

Stability of Fluid Motion. — Rectilineal Motion of Viscous Fluid between two
Parallel Planes. By Sir W. Thomson, LL.D., F.R.S.,

Note on the Epiblastic Origin of the Segmental Duct in Teleostean Fishes and in
Birds. By George Brook, Esq., F.L.S., Lecturer on Comparative Em-
bryology in the University of Edinburgh. Communicated by Professor
Sir William Turner, F.R.S., . . . .

Preliminary Note on the Chemistry of Strophanthin. By Thomas R. Fraser,
M.D., F.R.S., Professor of Materia Medica in the University of Edinburgh,
On a New Diffusiometer and other Apparatus for Liquid Diffusion. By J. J.
Coleman, Esq., F.I.C., F.C.S.,

On the Minute Structure of the Eye in certain Cymothoidse. By Frank E.
Beddard, Esq., M.A., F.Z.S.,

On the Mean Height of the Land of the Globe. By John Murray, Esq., Ph.D.,
The Chcetopoda Sedentaria of the Firth of Forth. By J. T. Cunningham,

Esq., B.A., . . • .

Monday, 18th July 1887.

Laws of Solution. Part II. By W. Durham, Esq., ....

On the Partition of Energy between the Translatory and Rotational Motions of
a set of non-homogeneous Elastic Spheres. By Professor W. Burnside.
Communicated by Professor Tait, ......

On the Salinity, Temperature, &c., of the Firth of Forth. By H. R. Mill, Esq.,
D.Sc., ..........

The Direct Measurement of the Peltier Effect. By Albert Campbell, Esq.
Communicated by Professor Tait. (Plate XIII.), ....

On some Vapour Densities at High Temperatures. By Alexander Scott,
Esq., M.A., D.Sc., . . .....

On tbe Determination of the Plane Curve which forms the Outer Limit of the
Positions of a certain Point. By Dr G. Plarr. Communicated by
Professor Tait, ........

The Thermal Windrose at the Ben Nevis Observatory. By A. Rankine, Esq.,

On Ferric Ferricyanide as a Reagent for Detecting Traces^of Reducing Gases.
By Professor Crum Brown, . . . . 1

On the Compressibility of Water, of Mercury, and of Glass, f By Professor Tait,

An Account of some Experiments which show that Fibrm-Ferment is absent
from circulating Blood-Plasma, and whicb support the wiew, first advanced
bjr Sir Joseph Lister, that the Blood has no spontaneous tendency to
Coagulate. By Professor John Berry Haycraft, . .

On the Chemical Composition of the Water composing the Clyde Sea Area. By
Adam Dickie, Esq., . . . . .

An Experimental Critique of the Chloroplatinate Methods for the Determina-
tion of Potassium, including a redetermination of the Constant Pt. By
Professor Dittmar and Mr John M ‘Arthur, ....

Addition to Thermometer Screens. Part IV. By John Aitken, Esq.,

On the Quotient of a Simple Alternant by the Difference-Product of the
Variables. By Dr T. Muir, .......

Chairman’s Closing Address, .......

Minute of Meeting of Special Committee on the Victoria Jubilee Prize, 27th
June 1887, .........

The Theory of Determinants in the Historical Order of its Development. By
Dr T. Muir, M.A., . . ....

Donations to the Library, . ...

Index, . ...

Obituary Notices, . . . (81-

31

37

38

38

381

381

387
38',
3£ ,
41

415

416

419

419

4L9

422

428

428

433

446

449

452

535

555

-mV

v ^ fcf

a f 4 Hr

i

H

f

l

4